if there are 720 different classes in one quarter at time, each in its own room, different rooms will be required 720 rooms.
To answer this question, we need to understand that each class needs its own room. Therefore, the number of rooms required will be equal to the number of classes. In this case, there are 720 different classes in one quarter, so 720 different rooms will be required. Each room can accommodate one class at a time, so the total number of rooms needed is 720.
Number of Classes = 720
Number of Rooms Required = Number of Classes = 720
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to see the overall long-term tendency of the series, we should set large weight w in exponential smoothing. group of answer choices true false
to see the overall long-term tendency of the series, we should set large weight w in exponential smoothing is True statement.
Exponential smoothing is a technique used to smooth out data to uncover trends and make predictions. When setting the weight (w) for exponential smoothing, a large w will result in a longer-term trend being captured by the smoothing. This is because a larger w will give more weight to the older data points, and thus the overall long-term tendency of the series will be more visible. Therefore, it is true that setting a large weight w in exponential smoothing will help to see the overall long-term tendency of the series.
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Christian found two trees directly across from each other in a canyon. When he moved 100 feet from the tree on his side (parallel to the edge of the canyon), the angle formed by the tree on his side and the tree on the other side was 70°. Find the distance across the canyon.
Answer:
130 ft
Step-by-step explanation:
The distance across the canyon is 130 feet.
When Christian moved 100 feet from the tree on his side, the angle formed by the tree on his side and the tree on the other side was 70°. This means that the distance across the canyon is the length of the opposite side of the right triangle formed by Christian's position, the tree on his side, and the tree on the other side.
To find the length of the opposite side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the distance across the canyon, and the other two sides are 100 feet and the length of the opposite side of the triangle.
We can write this as an equation: (distance across the canyon)^2 = (100 feet)^2 + (opposite side of the triangle)^2.
To solve for the distance across the canyon, we can take the square root of both sides of the equation: distance across the canyon = √((100 feet)^2 + (opposite side of the triangle)^2).
Since the length of the opposite side of the triangle is equal to the length of the adjacent side (100 feet) divided by the tangent of the angle formed by the tree on his side and the tree on the other side, we can substitute this value into the equation above: distance across the canyon = √((100 feet)^2 + (100 feet / tan 70°)^2).
To calculate the value of tan 70°, we can use a calculator or look up the value in a table of trigonometric functions. The value of tan 70° is approximately 1.73. We can substitute this value into the equation above to get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2).
We can now use a calculator to evaluate this expression and find the distance across the canyon. When we do this, we get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2) ≈ 130 feet.
Therefore, the distance across the canyon is approximately 130 feet.
Lulu the Lucky puts chests of gems into her treasure vault. Each chest holds the same number of
gems. The table below shows the number of gems Lulu received from three different adventures
and the number of chests she needed to hold the gems.
Number of gems
Number of chests
Adventure A
600
2
Adventure B
1500
5
Adventure C
4800
16
Write an equation to describe the relationship between g, the number of gems, and c, the
number of chests.
Answer:
The relationship between the number of gems and the number of chests can be represented by an equation in the form of g = kc, where g is the number of gems, c is the number of chests, and k is a constant.
To find the value of the constant k, we can substitute the values from one of the adventures into the equation and solve for k. For example, using the values from Adventure A:
g = 600
c = 2
Substituting these values into the equation, we get:
600 = k * 2
Solving for k, we get:
k = 600 / 2 = 300
Therefore, the equation that describes the relationship between the number of gems and the number of chests is:
g = 300c
Using the information provided in the table, we know that for Adventure B, Lulu received 1500 gems and needed 5 chests to hold them. Substituting these values into the equation, we get:
g = 1500
c = 5
Substituting these values into the equation g = 300c, we get:
1500 = 300 * 5
This equation can be used to determine the number of chests needed to hold a given number of gems, or vice versa. For example, to find the number of chests needed to hold 1200 gems, we can substitute 1200 for g and solve for c:
g = 1200
c = 1200 / 300 = 4
Thus, 4 chests would be needed to hold 1200 gems.
Write a linear function f(x) = mx + b for the graph.
(-2,-6) (-1,-2.5) (0,1) (1,4.5)
Answer:
Step-by-step explanation:
To write a linear function for a given set of points, we can use the slope-intercept form of the equation, which has the form f(x) = mx + b. The coefficient m is the slope of the line and the constant b is the y-intercept, where the line crosses the y-axis.
To find the slope m of the line, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. For example, we can use the points (-2, -6) and (-1, -2.5) to find the slope:
m = (y2 - y1) / (x2 - x1) = (-2.5 - (-6)) / (-1 - (-2)) = 3.5 / 1 = 3.5
Now that we know the slope, we can use any of the given points to find the y-intercept b. For example, we can use the point (0, 1):
f(x) = mx + b
1 = 3.5 * 0 + b
b = 1
Therefore, the linear function that passes through the given points is:
f(x) = 3.5x + 1
Note that we could also have used any of the other points to find the y-intercept, and we would have arrived at the same result.
Gina ha 32 item to hip and 11 hipping boxe. The large hipping boxe can hold 4 item each. The mall hipping boxe can hold 2 item each. Gina ha exactly enough boxe for her item. How many of each type of box doe he have?
Gina uses 11 shipping boxes to pack 32 items. For this, she requires about 5 large boxes and 6 small boxes.
A box is a type of container used to store contents. The majority of boxes have rectangular sides that are flat, parallel, and straight. Boxes can be very small or very large, and they can be used for everything from functional to decorative purposes.
Given that Gina has 32 items and 11 shipping boxes to pack. The large box can hold 4 items and the small can hold 2 items. Then, the total number of large and small boxes required is calculated logically as follows.
The first five boxes are large and the next five boxes are small. Then we can pack about 20 (4×5) items in large boxes and about 10 (2×5) items in small boxes. The remaining 2 items are left and these will be packed in small boxes. So she requires about 5 large boxes and 6 small boxes.
The complete question is -
Gina has 32 items to ship and 11 shipping boxes. The large shipping box can hold 4 items each. The small shipping boxes can hold 2 items each. Gina has exactly enough boxes for her item. How many of each type of box does she have?
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Solve this system of equations using substitution algebraically.
1/2x+6y=12
y=x+15
The solution to the system of equation is x = -12 and y = 3.
How to solve system of equations?System of equation can be solved using different method such as elimination method, graphical method and substitution method,
Therefore, let's solve the system of equation by using substitution method.
1 / 2 x + 6y = 12
y = x + 15
substitute the value of y in equation(i)
1 / 2 x + 6(x + 15) = 12
1 / 2 x + 6x + 90 = 12
6 1 / 2 x = 12 - 90
13 / 2 x = - 78
cross multiply
13x = -78 × 2
13x = -156
divide both sides by 13
x = -156 / 13
x = - 12
Let's find the value of y.
y = -12 + 15
y = 3
Therefore,
x = -12
y = 3
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Which function is increasing on the interval (-∞, ∞)?
O A. g(x) = -4(2^x)
O B. f(x) = -3x + 7
O c. h(x) = 2^x - 1
O D. j(x) = x² + 8x + 1
Which function is growing on the (-, ) interval? O A. g(x) = "-4(2^x)" O B. f(x)= "-3x"+7 O C. h(x)= 2x—1 O D. j(x)= x2 + 8x+1
Try searching for Which function is rising on the range (-, ) instead. O A. g(x) = -4(2^x) O B. f(x) = -3x + 7, O c. h(x) = 2x - 1, and O D. j(x) = x2 + 8x + 1.
Which function is increasing on the interval (- ∞ ∞?
Image result for Which function is increasing on the interval (-∞, ∞)? O A. g(x) = -4(2^x) O B. f(x) = -3x + 7 O c. h(x) = 2^x - 1 O D. j(x) = x² + 8x + 1
Since, x and y are arbitrary values, therefore, f (x) < f (y) whenever x < y. Therefore, the interval (-∞, ∞) is a strictly increasing interval for f(x) = 3x + 5
The interval is increasing if the value of the function f(x) increases with an increase in the value of x and it is decreasing if f(x) decreases with a decrease in x.
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one segment measures 161 cm. Calculate its multiple according to the number 3 and its submultiple according to the number 7
By using multiplication and division, it can be calculated that-
The multiple according to the number 3 = 162
The submultiple according to the number 7 = 7
What is multiplication and division?
Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.
Division is the process in which a value of single unit can be calculated from the value of multiple unit.
The number to be divided is called dividend. The number by which dividend is divided is the divisor. The result obtained is called quotient and the remaining part is the remainder.
This is a problem of multiplication and division.
One segment measures 161 cm
So, to find the multiple according to the number 3, we have to divide 161 by 3
161 [tex]\div[/tex] 3 = 53.67
Nearest integer of 53.67 is 54
The multiple according to the number 3 = 54 [tex]\times[/tex] 3 = 162
To find the submultiple according to the number 7, we have to divide 161 by 7
161 [tex]\div[/tex] 7 = 23
Nearest integer of 23 is 23
The submultiple according to the number 7 = 161 [tex]\div[/tex] 23 = 7
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The area of a square is square units. What is the side length of one side of the square? units units units units.
The side length of the square is (b) 8n¹⁸ units
How to determine the side length of the squareSee below for the complete question
From the question, we have the following parameters that can be used in our computation:
Area = 64n36 square units
Express the exponents as superscripts
So, we have the following representation
Area = 64n³⁶ square units
Take the square roots of both sides
So, we have the following representation
√Area = √64n³⁶ square units
Evaluate the exponents
Length = √64n³⁶ units
So, we have
Length = 8n¹⁸ units
Hence, the side length is (b) 8n¹⁸ units
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Complete question
The area of a square is 64n36 square units. What is the side length of one side of the square?
8n6 units
8n18 units
64n6 units
64,18 units
Type the correct answer in the box. use numerals instead of words. enter the number of the topic sentence.Consider this expression. underroot x4-y2When r = 3 and y = -6, the value of the expression is____.
When the variables r = 3 and y = -6, the value of the expression is -27.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables, parameters, and numerical quantities (number).
Based on the information provided, the mathematical expression is given by;
Mathematical expression = √x⁴ - y²
Substituting the given parameters into the mathematical expression, we have;
Mathematical expression = √(3)⁴ - (-6)²
Mathematical expression = √81 - 36
Mathematical expression = 9 - 36
Mathematical expression = -27.
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Complete Question:
Type the correct answer in the box. use numerals instead of words. Enter the number of the topic sentence.
Consider this expression. √x⁴ - y². When r = 3 and y = -6, the value of the expression is____.
Isabel plans to watch 3 movies each month. Write an equation to represent the total number of movies
In that she will watch in m months
Answer:
3m
Step-by-step explanation:
hope this helps :D
A taxi firm charges a fixed amount of £f, for each journey and then p pence a mile. A 4-miles journey costs £5.40 A 7-miles journey costs £7.80 How much will a 9-miles journey cost?
Answer:
£9.40
Step-by-step explanation:
Given variables:
f = fixed amount for each journey (in pounds)p = pence per mileDefined variables:
Let x = number of miles.Let y = total cost (in pounds).1 pound = 100 pence ⇒ 1 pence = 0.01 pounds
Therefore, the equation that models the given scenario is:
[tex]y = 0.01px +f[/tex]
Given:
A 4-mile journey costs £5.40A 7-mile journey costs £7.80Substitute the given information into the equation to create two equations:
[tex]\implies f+0.01(4)p=5.40[/tex]
[tex]\implies f+0.01(7)p=7.80[/tex]
Therefore:
[tex]\implies f+0.04p=5.40[/tex]
[tex]\implies f+0.07p=7.80[/tex]
Subtract the first equation from the second to eliminate f:
[tex]\implies 0.03p=2.40[/tex]
Solve for p:
[tex]\implies \dfrac{0.03p}{0.03}=\dfrac{2.40}{0.03}[/tex]
[tex]\implies p=80[/tex]
Substitute the found value of p into one of the equations and solve for f:
[tex]\implies f+0.04(80)=5.40[/tex]
[tex]\implies f+3.20=5.40[/tex]
[tex]\implies f=2.20[/tex]
Substitute the found values of p and f into the equation to create an equation for the cost of x miles:
[tex]\implies y=0.8x+2.2[/tex]
To find the cost of a 9-mile journey, substitute x = 9 into the found equation:
[tex]\implies 0.8(9)+2.2=9.40[/tex]
Therefore, the cost of a 9-mile journey is £9.40.
Please help I’m giving brainlyest
Answer:
A. Eight-four percent of 6th grade girls surveyed prefer cereal A
Step-by-step explanation:
Out of 100 6th grade students, 50 were girls and 50 were boys.
42% of the 100 students i. e. 42 were girls who preferred cereal A
Percentage of girls who liked cereal A = (42/50)x100%
= 84%
Answer:
A
Step-by-step explanation:
42% of entire 6th grade girls were surveyed
it means that 84% of ONLY the 6th grade girls liked Cereal A
2 A bag contains three red counters, four green counters, two yellow counters and one white
counter. Two counters are drawn from the bag one after the other, without being replaced.
Calculate:
a P(two red counters)
b P(two green counters)
c P(two yellow counters)
d P(white and then red)
e P(white or yellow, in either order but not both)
f P(white or red, in either order but not both).
g What is the probability of drawing a white or yellow counter first and then any colour second?
Answer: P(WY)=1/10*2/9=1/45
P(YW)=2/10*1/9=1/45
P(WY or YW)=2/45
Also 2C1*1C1/10C2=2×1/45=2/45
2/5
Step-by-step explanation:
Hay people need some help on this can you do?.
Answer:
Erik's chips are a better buy by 10 cents per ounce
Step-by-step explanation:
Erik's chips cost by ounce: $0.32
Al's chips cost by ounce: $0.42
This means the Eriks chips are better to buy
Second one:
Answer: 1.26
Step-by-step explanation:
Since he bought a 18 gallon tank of gas with regular fuel for 55.08.
The station across the street sold regular fuel for 2.99 per gallon. A 18 gallon tank will cost:
= 18 × 2.99
= 53.82
The amount that could have been saved would be:
= 55.08 - 53.82
= 1.26
to obtain a smaller margin of error choose a larger confidence level. choose a smaller confidence level.om/input?i
To obtain a smaller margin of error, choose a smaller confidence level.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error
z = found by using a z-score table
SD = sample standard deviation
n = sample size
Based on the formula, to reduce the margin of error, the z-score, z, must be small. In order to have a smaller value of z, the probability, p, should also be small. And to obtain a small probability, choose a smaller confidence level.
Hence, to reduce the margin of error, use a lower confidence level.
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Jen Butler has been pricing Speed-Pass train fares for a group trip to New York Three adults and four children must pay $120. Two adults and three children must pay $85. Find the price of the adult's
ticket and the price of a child's ticket.
The adult's ticket will cost $20 while the children's ticket will cost $15.
To find the cost of the ticketsFrom the question, we have that;
Three adults and four children must pay $120
Representing this in an equation
Let adults = a
Let children = c
3a + 4c = 120 -----1
Also;
Two adults and three children must pay $85.
Representing this in an equation
2a + 3c = 85 -----2
From equation 1
a = [tex]\frac{120 - 4c}{3}[/tex] ----- 3
Substituting a in equation 2
[tex]2 (\frac{120 - 4c}{3} ) + 3c = 85[/tex]
[tex]\frac{240 - 8c}{3} + 3c = 85[/tex]
Multiplying through by 3
240 - 8c + 9c = 255
c = 15
To find a when c = 15
Substitute c = 15 in equation 3
[tex]a = \frac{120 - 4(15)}{3}[/tex]
[tex]a = \frac{120 - 60}{3}[/tex]
a = 20
Therefore, the Adult's ticket is $20 and the children's ticket is $15.
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use implicit differentiation to find ∂z/∂x and ∂z/∂y. e7z = xyz
The implicit differentiation of [tex]\dfrac {dz}{dx}[/tex] is [tex]\dfrac {yz}{7e^{7z}-xy}[/tex] and for [tex]\dfrac {dz}{dy}[/tex] it is [tex]\dfrac {xz}{7e^{7z}-xy}[/tex].
In implicit differentiation, we differentiate every aspect of an equation with variables (commonly x and y) through treating one of the variables as a feature of the other.
It is given that,
[tex]e^{7z}=xyz[/tex]
Differentiate both sides with respect to x,
Only treat y as constant and z and x as variables.
[tex]\frac{{e^{7z}}{dx} }{\frac{dz}{dx}} =\frac{yd(xz)}{dx}[/tex]
use chain rule in left hand side
[tex]\frac {e^{7z}}{dx} \times \frac{dz}{dx} =\frac{yd(xz)}{dx}[/tex]
use product rule in RHS
[tex]7e^{7z} \times\frac{dz}{dx}=yx \times\frac{dz}{dx+z} \\\\7e^{7z} \times\frac{dz}{dx}=xy \times\frac{dz}{dx} +yz\\\\\frac{dz}{dx}=\frac{yz}{7e^{7z-xy}}[/tex]
It is given that,
[tex]e^{7z}=xyz[/tex]
Differentiate both sides with respect to y,
Only treat x as constant and z and y as variables.
[tex]\dfrac {d (e^7z)}{dy}= \dfrac {d(xyz)}{dy}[/tex]
use chain rule in left hand side
[tex]\dfrac {d (e^7z)}{dy} \times \dfrac{dy}{dx}=\dfrac {yd(xz)}{dy}[/tex]
use product rule in RHS
[tex]7 (e^{7z}) \times \dfrac{dz}{dy}=xy \dfrac{dz}{dy+z}\\\\(7e^{7z})\times \dfrac{dz}{dy}=xz\\\\\dfrac{dz}{dy}=\dfrac {xz}{7e^{7z}-xy}[/tex]
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What is the value of K if the expression (- 5x3 + 4x2 – 3x + K) is divided by (x-1), and obtains a remainder of 10?
Answer:
14
Step-by-step explanation:
To find the value of K, we need to use the remainder theorem. The remainder theorem states that if a polynomial is divided by (x - a), where a is a number, the remainder of the division will be equal to the value of the polynomial when x is equal to a. In this case, the remainder of the division is 10, so we need to find the value of the polynomial when x is equal to 1.
To find this value, we need to plug 1 into the original polynomial and evaluate it. This gives us (- 5 * 1^3 + 4 * 1^2 – 3 * 1 + K) = (- 5 + 4 – 3 + K) = (- 4 + K). Since the remainder of the division is 10, we know that (- 4 + K) = 10. This means that K = 14.
Therefore, the value of K in the original polynomial is 14.
The value of K is 14.
What is Remainder Theorem?If a polynomial function f(x) is divided by (x - c), the remainder R is given by: R = f(c)
According to the remainder theorem, if a polynomial f(x) is divided by (x - c), where c is a constant, the remainder is equal to f(c).
In this case, we know that the remainder is 10 when the expression is divided by (x - 1). So, we can substitute x = 1 into the expression and set it equal to 10 to find the value of K.
Substituting x = 1 into the expression, we get:
(-5 (1)³ + 4(1)² - 3(1) + k)= 0
-5 + 4 -3 + k = 0
k -4 = 0
k = 4
Therefore, the value of K is 14.
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if mx, my, sx, and sy are known, what would be the most helpful additional number to know for calculating the regression line for x and y?
If MX, MY, sX, and sY are known, the additional number that would be the most helpful to know for calculating the regression line for X and Y is r.
What is r in line of regression?In the context of simple linear regression, r means the correlation between the predictor variable, x, and the response variable, y. And r² means the proportion of the variance in the response variable which can be explained by the predictor variable in the regression model.
It is also considered as denotation of the Pearson correlation coefficient, that is a measure of any linear trend between two variables. The value of r ranges between −1 and 1. When r = zero, it means that there is no linear association between the variables.
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please help me solve this algebraic expression
Answer: 0
Solution Steps:
m=25 n=5
25/5-5
a building 34.98 feet tall has a shadow that is 38.85 feet long. find the angle of elevation of the sun to the nearest hundredth of a degree.
The angle of elevation of the sun to the nearest hundredth of a degree is 66.83°.
Since we are giving with the height of the building which is 34.98 feet and the length of the shadow which is 38.85 feet long. , so we can use the trigonometric ratios, where we know that about tan, that is:
angle = arctan (length of the shadow/height of the building )
=>angle = arctan (38.85/34.98)
=> angle = arctan (1.1056)
=> angle = 66.83°
so,it is the angle of elevation of the sun.
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A relation is plotted as a linear function on the coordinate plane starting at point a (0, 3)and ending at point b (2, 7). What is the rate of change for the linear function and what is its initial value? select from the drop-down menus to correctly complete the statements. The rate of change is choose. And the initial value is choose. .
The rate of change of the plot is 2
The initial value the line joining points is 3
The rate of change between 2 points is defined as the change of y cordinate with respect to change of x cordinate
rate of change = slope of line = Δy/ Δx =[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
point a(0,3) is the initial point and point b(2,7) is the 2nd point
so [tex](x_1,y_1)[/tex] = (0,3) and [tex](x_2, y_2)[/tex] = (2,7)
rate of change = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> (7-3)/(2-0)
=>4/2
so rate of change = 2
Initial value is the y intercept of the line i.e is we write an equation of the line the value of y when x=0 is the inital value
so at point a (0,3) value of x=0 and at that time value of y=3
and hence initial value = 3
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30 points per question
The parameters for the exponential function are given as follows:
Initial value: 500.Growth rate of 18% annualy.Hence the exponential function that gives the value of the book in t years after 2010 is of:
V(t) = 500(1.18)^t.
2017 is 7 years after 2010, hence the value is calculated as follows:
V(7) = 500 x (1.18)^7 = $1,592.74.
What is the exponential function for the table?First we obtain the rate of change, dividing consecutive entries of the table, as follows:
b = 62.99/34.99 = 1.8.
Thus the function is defined as follows:
f(x) = a(1.8)^x.
When x = 3, f(x) = 34.99, hence the intercept a is calculated as follows:
34.99 = a(1.8)³
a = 34.99/(1.8)³
a = 6.
Then the function is:
f(x) = 6(1.8)^x.
What is the estimate for 2023?Taking 2016 as the reference year, the initial value is of:
a = 80.
Then the growth rate is of:
b = 132/80.
b = 1.65.
Then the function for the amount in x years after 2016 is of:
f(x) = 80(1.65)^x.
2023 is 7 years after 2016, hence the estimate is given as follows:
f(7) = 80 x (1.65)^7 = 2664 people.
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To solve 3÷1/5, Jordan thinks about giving monkeys 1/5 of a banana each and how many monkeys he could give a banana piece to if he had 3 whole bananas. What is the quotient of 3 and 1/5?
The quotient of 3 and 1/5 is 15.
How to find the quotient?A quotient is a quantity produced by the division of two numbers in arithmetic. The quotient is widely used in mathematics and is also known as the integer part of a division, a fraction, or a ratio.
The quotient is the result of performing division operations on two numbers. It is essentially the result of the division method. In arithmetic division, four main terms are used: divisor, dividend, quotient, and remainder
In this case, we want to divide 3 and 1/5. This will be:
= 3 ÷ 1/5
= 3 × 5
= 15.
The quotient is 15.
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Loda is writing an article about climate change. Her article will be about the issues of landfills and her suggestions on alternate ways to deal with household waste. Which type of text structure would best fit this article?.
This article would be best suited to a text structure of Problem and Solution.
Explain the pattern of the text structure?The hierarchical patterns used in longer or more complicated texts that are acceptable for the genre as well as purpose are known as text structures. A few examples of text structures are sequence/process, exposition, time order/chronology, provision, compare/contrast, issue, cause/effect, inductive/deductive, and research.Research on the development of literacy during the previous two decades has revealed:
a) Students' understanding as to what they read is improved when they are aware of the various text structures including their purposes.b) Before other, more intricate forms, some set of defined are simpler to understand and learn.A literary device that introduces a problem in the first paragraph and section before moving on to how to solve it in the following paragraph or section.
Example:
The opening paragraph raises the issue of local landfills being overfilled. The next sentence gives information about a recycling program created to address the problem.To know more about the text structure, here
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Corey i making a wall-mounted bookhelf. It ha 2 helve, with a third piece of wood interecting them. To upport the helve, Corey order ome L-bracket to put between the helve and the cropiece. He meaure angle 6. How many bracket hould he order to have one for every angle that i congruent to angle 6? Explain. Two parallel line interected by a tranveral. The angle formed along the top line, tarting at the top left and moving clockwie, are 1, 2, 4, and 3. The correponding angle formed along the bottom line, tarting at the top left and moving clockwie, are 5, 6, 8, and 7. A. 2; ∠7 i congruent to ∠6. B. 2; ∠3 i congruent to ∠6. C. 3; ∠7, ∠3 are both congruent to ∠6. D. 4; ∠7, ∠2, ∠3 are all congruent to ∠6
Corey would be needing six L-brackets to have one for every angle that is congruent to angle 6 in order to meet the requirement .
As we know that in order to support the shelves, Corey needs to buy six L-brackets. This is to be done in such a way that the two shelves, combined with the connecting piece, will form a shape with six congruent angles.
This is so because the connecting piece, the two shelves, and the form they make have six congruent angles. Corey will therefore require six brackets to hold up all the angles.
Corey will require one bracket for each angle in order to support it. To make sure he orders the proper size bracket for each angle, the length of the angle should be measured correctly.
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Solve for X
A. X = -8 degree
B. X = 8 degree
C. X = 4 degree
D. X = -4 degree
Please help!!
Answer:
B. X = 8 degree
Step-by-step explanation:
8x - 4 = 60 degree
8x = 64 degree
x = 8 degree
So, the answer is B
Answer:
x = 8°
Step-by-step explanation:
The angle that say 60° and the angle that says 8x -4 ARE BOTH EQUAL.
They are called Alternate Interior Angles
Let's write an equation to represent this relationship, then we solve it to find x
8x - 4 = 60
SOLVE
8x = 60 + 4
8x = 64
x = 64 / 8
x = 8 °
In the triangles below, Angle AOI is congruent to Angle IEA. Find each missing measure.
The values of the variables and the measures of the angles, found using the congruency of ΔAOI and ΔIEA are;
w = 2 [tex]{}[/tex] ∠EAI = 45°
x = 4 [tex]{}[/tex] ∠AOI = 128°
y = 7 [tex]{}[/tex] ∠OIA = 45°
z = 20 [tex]{}[/tex] ∠IEA = 128°
What are congruent triangles?Two triangles are congruent if two angles and a non included side of one triangle are congruent to two angles and a non included side of another triangle.
The relationship between the triangles ΔAOI and ΔIEA is ΔAOI ≅ ΔIEA
Therefore; ∠IEA is congruent to ∠AOI, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
∠IEA ≅ ∠AOI
Therefore; ∠IEA = ∠AOI by the definition of congruency
(6·z + 8)° = (7·z - 12)°
7·z - 6·z = (8 + 12)° = 20°
z = 20°
∠AOI = (7·z - 12)°
Therefore;
∠AOI = (7 × 20 - 12)° = 128°
∠IEA = 128°
Similarly; AO ≅ EI by CPCTC
AO = EI definition of congruency
5·w - 6 = 2·w
5·w - 2·w = 6
3·w = 6
w = 6 ÷ 3 = 2
w = 2
∠OIA ≅ ∠EAI by CPCTC
Therefore; ∠OIA = ∠EAI definition of congruency
(7·x + 17)° = 3·(4·x - 1)° substitution property
(7·x + 17)° = 3·(4·x - 1)° = (12·x - 3)°
12·x - 7·x = 17° + 3° = 20°
5·x = 20°
x = 20° ÷ 5 = 4°
x = 4°
∠EAI = 3·(4·x - 1)°
∠OIA = (7·x + 17)°
Therefore;
∠EAI = 3·(4×4 - 1)° = 45°
∠OIA = (7×4 + 17)° = 45°
y° + (7·z - 12)° + 3·(4·x - 1)° = 180° (angle sum property of a triangle)
∠AOI = (7·z - 12)° = 128°
∠EAI = 3·(4·x - 1)° = 45°
Therefore;
y° + 128° + 45° = 180°
y° = 180° - (128° + 45°) = 7°
y° = 7°
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3^4 + 18 ÷ 3 +2 pls what is the =
The value of the given expression, 3^4 + 18 ÷ 3 +2, is 89
Evaluating an expressionFrom the question, we are to determine the value of the given expression
The given expression is
3^4 + 18 ÷ 3 +2
First, we will write the expression properly
The given expression written properly is
3⁴ + 18 ÷ 3 +2
Using PEMDAS
P - Parentheses
E - Exponent
M - Multiplication
D - Division
A - Addition
S - Subtraction
Then,
3⁴ + 18 ÷ 3 +2
81 + 18 ÷ 3 + 2
81 + 6 + 2
= 89
Hence, the value is 89
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