Answer:
√43
Step-by-step explanation:
Implement the Pythagorean formula to solve for sides of a right triangle: a^2 + b^2 = c^2, where "a" and "b" are the legs and "c" is the hypotenuse.
a = √6 and c = 49
√6^2 + b^2 = 49
6 + b^2 = 49
b^2 = 43
b = √43
Answer:
The square root of 43
Step-by-step explanation:
I did this in class the other day
There are 1255 students in Sarah's high school. 40% of the students are taking Spanish. How many students are not taking spanish?
Enter the repeating digit:
2/3 = 0.?
Answer:
6
the recurring digit is 6
ANS: 0.6
Order these numbers from least to greatest.
2.8, 2.5081, 1.935, 2.58
2.8
<
2.5081
<
1.935
2.58
Answer:
Step-by-step explanation:
1.935<2.5081<2.58<2.8
∵1.9350<2.5081<2.5800<2.8000
What is the slope of the line that passes through the points (1, 6) and (1, 31)? Write
your answer in simplest form.
The slope of the line that passes through the points (1, 6) and (1, 31) is, ∞
What is slope?Slope is a ratio of change in y-coordinate w.r.t. change in x-coordinate. The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.
So formula for the slope is,
m = change in y coordinate/change in x coordinate = Δy/Δx = y₂-y₁/x₂-x₁
Given that,
the line passes through the points, (1,6) and (1,31)
So, we can calculate slope for the line by using formula when two are given,
m = y₂-y₁/x₂-x₁
x₁ = 1
y₁ = 6
x₂ = 1
y₂ = 31
m = 31-(6)/1-1
m ≈ ∞
Therefore, The line is parallel to y-axis
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Question
An advertising sales representative has sales totaling $4500. For these sales, the representative earns a commission of $360.
Which proportion could be used to find the commission amount for sales totaling $15,000?
The commission amount for sales totaling $15,000 is $600.
How to calculate the value?From the information, the advertising sales representative has sales totaling $4500 and for these sales, the representative earns a commission of $360.
Therefore, the commission fraction will be:
= Commission / Sales
= 360 / 4500
= 1/25
Therefore, the commission on $15000 will be:
= 1/25 × $15000
= $600
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Answer:
(1) where y = 18 when x = 2.
What is the value of x when y = 36?
= 4
(2) when x is 4, y is 11.
What is the constant of proportionality for this relationship?
= 2.75
(3) What is 34% of 650?
=4.875
(4) 28 7
16 4
12 3
=1/4x
(5) Last month 288 people attended the monthly bingo night. This month 243 people attended bingo night.
= 15.6
(6) Over 6.8 months, a tree grew 7.48 inches.
=1.1
(7) A party-size bag of chips contains 15 ounces. This is 750% of the amount in the snack-size bag.
=2
(8) An advertising sales representative has sales totaling $4500. For these sales, the representative earns a commission of $360.
Which proportion could be used to find the commission amount for sales totaling $15,000?
=360/4500=x/15,000
(9) Brad's dinner bill, including a 16% tip, is $10.44.
= 9
(10) Do the values in the table represent a proportional relationship?
x 2 4 6 8
y 3.2 6.4 9.6 12.8
Select from the drop-down menu to correctly complete the statement.
response - correct
All of the y-values are a constant multiple of the corresponding x-values, so the relationship is proportional.
(11) Molly estimated the width of a poster to be 21 inches. The actual width is 26 inches.
=19.2
(12) Solve for x.
x−9= −5/24
=1 7/8
(13) Each 1/2 inch on a scale model represents an actual length of 1/6 of a yard.
=3
(14) Landon is buying a shirt priced at $19.99. The sales tax is 8.5%.
= 21.69
(15) A sprinter ran 100 meters in 15 seconds.
=400
(16) Two gears are connected and rotating at the same time. The smaller gear completes 3 2/3 rotations every time the larger gear completes 1/3 of a rotation.
=11
(17) Jasmine dumped her box of spare change and found out that she had saved 128 coins. She separated them and counted 48 dimes.
What percent of Jasmine's coins are dimes?
= 37.5
(18) A pair of boots costing $299 is marked down 45%.
= 164.45
(19) Figure 1 is dilated to get Figure 2.
What is the scale factor?
Enter your answer in simplest form in the box.
=5/8
(20) y=5/x Not proportional
y=5(−2x) Proportional
y=x/4 Proportional
y=6x+4 Not proportional
Step-by-step explanation:
Hey here u go i so tired lol completely POOPED God bless u have a great test
if a 10800 cm^2 of material is available to make a box with a square base and an open top find the largest possible volume of the box
The largest possible volume of the box is 108000cm^3.
How can the largest possible volume of the box be found?The concept is the concept of
We can represent the length of the square box as x
we can also represent the surface of the box as S
we can represent the height of the square box as y
we can represent the volume as V= xy
Then since the top of the box is open and we can equate the material of the box is equal with surface area of box.
then S=[x^2 +2xy +2xy]
= x^2 +4xy
Then substitute the value of S we have
10800= x^2 +4xy
y= [10800-x^2/4x]
V=2700 * 1/4X^2
V=2700 * 1/4X^2
Then substitute the value of y into
V= xy
= x[10800-x^2/4x]
V= 2700x - 3/4X^2
Differentiate the volume to 0
=3x^2 = 2700
X^2 = 3600
X = 60 and Y = 30
V=2700 * 1/4X^2
V= 270(60) - 1/4* (60)^2 = 108000cm^3
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i need help please, :))))))
Answer:
AAS
Step-by-step explanation:
Two angles and two sides are marked as congruent. Vertical angles are congruent, so the answer is AAS
Bucket a and bucket b have the same shade of blue paint. If white paint is added to bucket b, which bucket would have the darker shade of blue paint
Answer:
Bucket a would be a darker shade because the white makes bucket b lighter.
2x + 2y = 18
x=3-y Solve for x and y
Answer: x=-y+9
y=-x+9
Step-by-step explanation:
Find the y-intercept of the following function. f(x)=21x2−31x−68
The y-intercept for the given function is (0, -68).
The given function is f(x)=21x²-31x-68.
What is a y-intercept?An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (31/42,−6673/84)
Focus: (31/42,−556/7)
Axis of Symmetry: x=31/42
Directrix: y=−3337/42
Plot (0, -68) and (31/42, -6673/84)
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
y-intercept is (0, -68).
Hence, the y-intercept for the given function is (0, -68).
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Determine which set of side measurements could be used to form a right triangle.
5, 10, 30
2, 3, 4
square root of 26, square root of 34, 60
square root of 11, 7, square root of 60
Answer:
the 4th one
Step-by-step explanation:
because we determined by Pythagorean theorem (the square root of 11)2 + 7 the power of 2 =
(the square root of 60)2 .....square root cancelled by power of 2
11 + 49 = 60
60 = 60
solve the system of linear inequalities by graphing
-2x+y greater than or equal to -3
y greater than 1/3x+ 2
The solution to the system of linear inequalities -2x + y ≥ -3 and y > 1/3x + 2 is (3, 3)
How to determine the solution to the system?In this case, the system of inequalities is given as
-2x + y ≥ -3
y > 1/3x + 2
Next, we plot the graph of the system of inequalities
In this case, the point of intersection of the inequalities represent the solution to the system
From the graph, the lines intersect at (3, -3)
Hence, the solution is (3, 3)
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The mean age of 12 women in an office is 22 years old. The mean age of 3 men in an office is 24 years old. What is the mean age (nearest year) of all the people in the office?
The mean age (nearest year) of all the people in the office is 22.4.
How to find the mean age?Using this formula to find the mean age
Mean age = Sum of men and women age / Number of men and women
Let plug in the formula
Mean age = ( 12 women × 22 years old) + (3 men × 24 years old) / 12 women + 3 men
Mean age = 264 + 72 / 12 +3
Mean age = 336 /15
Mean age = 22.4
Therefore the mean age is 22.4.
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m∠7 = 100° . Find the measure of ∠5
The measures of angles 5 and 3 is 100 degrees.
How to find the measure of angles in intersecting lines?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles, linear angles etc.
Therefore,
m∠7 = m∠5 (corresponding angles)
corresponding angles are congruent.
Therefore,
m∠5 = 100 degrees
m∠3 = m∠7(alternate angles)
m∠3 = 100 degrees.
Alternate angles are congruent.
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Humberto walks 3 miles due north then turns around and walks 5 miles due south how far is Humberto from his starting point
Humberto's displacement is 2 miles due south far from his starting point.
How is the displacement completed?We understand that displacement is a vector quantity with both magnitude and direction, while distance is a scalar quantity with only magnitude.
Displacement, unlike distance, shows the direction and position of an object from its original base. This means that displacement refers to how far an object has traveled out of its original position with the direction included.
In other words, displacement shows the object's overall change in position and the direction of the new position from the former.
Starting point = 0
Distance covered toward the north = 3 miles
Distance covered toward the south = 5 miles
Displacement = 2 (0 - 3 + 5) miles
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solve by using substitution 2x-3y=-12 and x+y=9
NO LINKS!! Please assist me with this problem Part 1m
Answer:
(x + 8)² + (y - 8)² = 64=======================
Given ConditionsTangent to x-axis,Tangent to y-axis,In the second quadrant,Radius is 8 units.SolutionEquation of circle:
(x - h)² + (y - k)² = r², where (h, k) is center and r - radiusThe center is the radius long distance from the x- axis to left and y-axis up same distance, this makes it in the second quadrant.
So the coordinates of the center are:
x = - 8, y = 8The equation is:
(x - (-8))² + (y - 8)² = 8²(x + 8)² + (y - 8)² = 64Answer:
[tex](x+8)^2+(y-8)^2=64[/tex]
Step-by-step explanation:
Required conditions:
Tangent to both axes.Center in the second quadrant.Radius = 8 units.If the circle is tangent to both axes, its center will be the same distance from both axes. That distance is its radius.
If the center of the circle is in quadrant II, the center will have a negative x-value and a positive y-value → (-x, y).
Therefore, the coordinates of the center will be (0-r, 0+r) where r is the radius.
If the radius is 8 units, then the center is (-8, 8).
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Substitute the found center and given radius into the formula to create an equation for the circle that satisfies the given conditions:
[tex]\implies (x-(-8))^2+(y-8)^2=8^2[/tex]
[tex]\implies (x+8)^2+(y-8)^2=64[/tex]
The black graph is the graph of y = f(x).
Choose the equation for the red graph.
A. y - 1 = f(x)
B. = f(x)
C. y = f(x - 1)
D. y = f()
1
Answer:
It's A.
Step-by-step explanation:
If you subtract from y, the graph moves to the right. If you add, it moves to the left.
In Chase's grade, 162 students are enrolled in health and 38 students are not. What
percentage of the students in the school are enrolled in health?
Write your answer using a percent sign (%).
2 percentage of the students in the school are enrolled in health .
How do percentages work?
10%, a comparative figure denoting one hundredth of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.students are enrolled in health = 162
students are enrolled not in health = 38
162 + 38 = 200 Add
Total of 100 Students
then ,
200/100
= 2%
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The revenue for a business, as a function of units produced, x, is shown below by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to break even.
R(x) = 24x
C(x) = 17x + 161
We could finish this question by applying the linar programming concept.
The profit function for the business is P(x) = 7x - 161
The number of units must be produced for the business to break even is
To find the formula of profit function, we have to understand first that profit is the remaining of revenue after being reduced by costs. Hence we could write this equation:
Profit = Revenue - Costs
Profit = R(x) - C(x)
If we create a new function P(x) that represent profit function, hence we could rewrite the profit function into:
P(x) = R(x) - C(x) ... (i)
Based on the question, we have both revenue and costs formulas as stated below:
R(x) = 24x ... (ii)
C(x) = 17x + 161 ...(iii)
We could subtitute equations (ii) and (iii) into equation (i) to get the profit formula:
P(x) = R(x) - C(x)
P(x) = 24x - (17x+161)
P(x) = 7x - 161 ... (iv)
To get the units must be produced, we have to understand that Break Even is a condition where the revenue is exactly the same of its costs, or when the profit is 0 (zero). Hence we could write the equation:
P(x) = 0 ...(v) --> Break Even
Then we would subtitute the equation (iv) into equation (v) to find the units must be produced (x) to achieve the break even.
P(x) = 0
7x - 161 = 0
7x = 161
x = 23 ... (vi)
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(-3y)^4 write the power as a product of powers
Answer: 81y^4
Step-by-step explanation:
expand then calculate, -3 to the power of 4+81 then 81 added to y ^4 81y^4 is your finally power.
A standard die is rolled. Find the probability that the number rolled is greater than 1. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Consider f(x) = 3x² 30x - 72.
Find the x-intercept(s) and y-intercept of f(x).
The x - intercept (s) is x = [tex]\sqrt[3]{\frac{4}{5} }[/tex] and y - intercept (s) is -72
Given,
In the question:
The function is given as :
Consider f(x) = 3x² 30x - 72.
To find the x-intercept(s) and y-intercept of f(x).
Now, According to the question:
f(x) = 3x²× 30x - 72.
f(x) = 90[tex]x^{3}[/tex] - 72
Solve the equation:
90[tex]x^{3}[/tex] = 72
Make the leading coefficient of the variable one
[tex]x^3 = 72/90\\[/tex]
Cross out the common factor
[tex]x^3[/tex] = 4/5
Take the n-th root on both sides:
x = [tex]\sqrt[3]{\frac{4}{5} }[/tex]
To find the y - intercept(s)
f(x) = 3x²× 30x - 72.
Set x = 0
f(0) = 3 × 0 × 30 × 0 - 72
f(0) = - 72
Hence, The x - intercept (s) is x = [tex]\sqrt[3]{\frac{4}{5} }[/tex] and y - intercept (s) is -72
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Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one
day. It is reasonable to assume that the population is approximately normal.
4.754 4.372 4.174 4.678 4.424 4.227
4.123 4.254 3.951 4.291 4.414
(a) Construct a 95% confidence interval for the mean rate. Round the answer to at least four decimal places.
A 95% confidence interval for the mean rate is < M
Using the confidence interval, a 95% confidence interval for the mean rate is (4.4206,4.2106).
In the given question, we have to construct a 95% confidence interval for the mean rate.
There is given interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day.
It is reasonable to assume that the population is approximately normal.
4.754, 4.375, 4.173, 4.678, 4.425, 4.227, 4.126, 4.250, 3.951, 4.197
We find the mean
Mean=4.754+4.375+4.173+4.678+4.425+4.227+4.126+4.250+3.951+4.197/10
Mean=43.156/10
Mean=4.3156
Standard Deviation(S)=√(x−mean)^2/n−1
S=√(4.754−4.3156)^2/10−1
S=√(0.4384)^2/9
S=√0.1922/9
S=√0.02136
S=0.1462
95%=0.95 confidence interval for z is
Z= [tex]z_{\alpha /2,dt}[/tex]
dt=n−1
dt=10−1
dt=9
[tex]\alpha[/tex] = 1−0.95=0.05
[tex]\alpha /2[/tex]=0.05/2=0.025
Z= [tex]z_{0.025,9}[/tex]
Z= 2.262
Confidence interval
CI=Mean±Z× s/√n
CI=4.3156±2.262× 0.1462/√10
CI=4.3156±2.262× 0.1462/3.1623
CI=4.3156±2.262×0.0462
CI=4.3156±0.105
CI=(4.3156+0.105),(4.3156−0.105)
CI=(4.4206,4.2106)
Hence, a 95% confidence interval for the mean rate is (4.4206,4.2106).
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The graph of a quadratic function with vertex (4, 2) is
Find the range and the domain.
Write the range and domain using interval notation.
For the given graph of quadratic function whose vertex is (4,2) , the domain and the range in the interval notation is given by :
Domain = ( -∞ , ∞ )
Range = ( 2 , ∞ )
As given in the question,
For the given graph of quadratic function ,
Given graph represents the parabola.
Standard equation of the parabola with vertex ( h, k) is given by,
y = a ( x - h )² + k
Substitute the value ( h ,k ) = ( 4, 2 )
y = a ( x - 4 )² + 2
As it is a parabola in the first quadrant and faces in the upward direction,
Value of x tends to -∞ to ∞
Domain = ( -∞ , ∞ )
Minimum value of y coordinate is 2 and increases to ∞.
Range = ( 2, ∞ )
Therefore, for the given graph of quadratic function whose vertex is (4,2) , the domain and the range in the interval notation is given by :
Domain = ( -∞ , ∞ )
Range = ( 2 , ∞ )
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what is the sum or difference of cos 61° + cos 45°?
The value of the trigonometric function Cos61° + Cos45° is 1.192
The given expression is Cos61° + Cos45°
Now, we have :
Cos61° = 0.4848
and Cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = 0.7072
Now, Cos61° + Cos45° = 0.4848 + 0.7072 = 1.192
Trigonometry is a branch of arithmetic that research relationships among side lengths and angles of triangles. the field emerged within the Hellenistic global at some stage in the third century BC from packages of geometry to astronomical research.
The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant , cosine , cotangent , secant , sine , and tangent .
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Count on from 6. Write the number
that shows 2 more.
Using the addition, the number that shows 2 more count from 6 is 8.
In the given question we have to write the number that shows 2 more.
We have to start counting from 6.
To write the number that shows 2 more we add 2 in 6, then again add 2 in the result of add of 2 and 6 and so on.
Hence the number that shows 2 more starting from 6 is
6+2=8
So the number that shows 2 more is 8.
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Which expression is equivalent to 8 ^ -3
The expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
First, let us understand the exponents or power:
A power, or index, is a little floating number that appears next to a number or letter.
It is denoted as a^m.
where a = base number
and m = power or index number.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe are given:
8^-3
We can solve as;
8^-3 = 8^(3 * -1) = (8^3) ^ -1 = 1 / 8^3 [since a⁻¹ = 1 / a]
So, 8^-3 = 1 / 8^3.
Thus, the expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 4 to 3. If there were 6706 total votes, how many yes votes were there?
We can see that there are 3,832 yes votes, we did that by using the given ratio.
How many yes votes were there?We know that the ratio of yes votes to no votes was 4 to 3, so from each 7 votes, 4 are yes and 3 are no.
Then if we take the total number of votes, and we multiply it by (4/7), we will get the total number of yes votes.
In this case we know that the total number of votes is 6706, then the number of yes votes is:
(4/7)*6706 = 3,832
There are 3,832 yes votes.
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Please Help 2
Find (f/g)(x) if f(x)=x2+x+1 and g(x)=-x2-x-1
Answer:
-1
Step-by-step explanation:
Take -1 as common form the denominator then cancel out the whole term i.e x²-x-1 and -1 remains.