The point at which this cable would pass through the road shown is at the y-intercept of (0, -17/2).
How to determine an equation and the point on this perpendicular line?Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
By critically observing the road shown in the graph above, the points on the line include the following:
Points (x, y) = (0, -2)
Points (x, y) = (-3, 0)
Substituting the given points into the formula, we have;
Slope, m = (0 + 2)/(-3 - 0)
Slope, m = 2/-3
Slope, m = -2/3.
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
-2/3 × m₂ = -1
-2m₂ = -3
m₂ = 3/2
At point (7, 2), a linear equation for the line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represent the points.c represents the y-intercept.Substituting the given points into the formula, we have;
y - 2 = 3/2(x - 7)
y - 2 = 3x/2 - 21/2
y = 3x/2 - 21/2 + 2
y = 3x/2 - 17/2
At the y-intercept of (0, -17/2), the cable pass through the road.
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I can’t solve this question can someone help me please? But please put step by step or not it’s fine!
2[6²(0.5 - 1.1)]
Answer:
-43.2
Step-by-step explanation:
2 x (6^2 (0.5-1.1))
2 x (6^2 (-0.6))
2 x (-36 x -0.6)
2 x (-21.6)
- 43.2
Answer:
Step-by-step explanation:2[6²(0.5-1.1)]
2[6²(-0.6)]
2[6×6(-0.6)]
2[36(-0.6)]
2[-21.6]
=> -43.2
the red figure is similar to the blue figure. Describe a sequence of transformations in which the blue figure is the image of the red figure
The sequence of transformations that produces the blue figure from the red figure are;
A dilation by a scale factor of 3 about the origin, [tex]D_{(3, \,O)}[/tex] followed by a translation of 11 units to the left and 11 units up, [tex]T_{(-11, \, 11)}[/tex]What is a transformation in geometry?A geometric transformation is the change to a geometric figure or shape by translating, reflecting, dilating, or rotating the figure.
The coordinates of the vertices of the red triangle are;
A(2, -2), B(2, -4), C(5, -4)
AB = -2 - (-4) = 2
BC = 5 - 2 = 3
AC = √((5 - 2)² + (-4 - (-2))²) = √(13)
The coordinates of the vertices of the blue triangle are;
D(-5, 5), E(-5, -1), and F(4, -1)
DE = 5 - (-1) = 6
EF = 4 - (-5) = 9
DF = √((4 - (-5))² + (-1 - 5)²) = 3·√(13)
The lengths of the sides of the blue triangle are DE/AB = 6/2 = 3 times the length of the sides of the red triangle
The points of the image of the red triangle following a dilation by a scale factor of 3 are;
A(2, -2) [tex]\underrightarrow{D_3}[/tex] A'(2 × 3, -2 × 3) = A'(6, -6)
B(2, -4) [tex]\underrightarrow{D_3}[/tex] B'(2 × 3, -4 × 3) = B'(6, -12)
C(5, -4) [tex]\underrightarrow{D_3}[/tex] C'(5 × 3, -4 × 3) = C'(15, -12)
The difference between the coordinates of the points A' and D are;
Horizontal translation = -5 - 6 = -11
Vertical translation = 5 - (-6) = 11
The triangle A'B'C' is translated 11 units to the 11 units to the left and 11 units upwards using the rule, [tex]T_{(-11,\, 11)}[/tex]
The sequence of transformation is a dilation by a scale factor of 3, centered at the origin, [tex]D_{3, \,O}[/tex] followed by a translation of 11 units to the left and 11 units to upwards.
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Laurie earns $7. 50 per hour at the fruit stand plus an extra $2. 00 per hour on sundays. One week in august, she worked on sunday, monday, and wednesday. She worked the same number of hours on monday and on wednesday. On sunday she worked 4 hours. If she earned a total of $83. 00 for the week, how many hours did laurie work on monday? enter and solve an equation.
If she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be 3.
Define equation.In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.
Given,
if she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be: 3.
$7.5= 1 hour various days
Sunday: $9.50 or ($7.50+$2.00) = 1 hour
Sunday = 4 + $9.50 = 38
Let Monday equal x $7.5 = 7.5x.
Let Wednesday equal x $7.5 equal x.
Let the total income be $83
Let x be the amount of hours.
Hence:
The first step is to create
Equation:
7.5x+7.5x+38=83
The next step is to determine the number of hours Laurie worked on Monday.
x =83-38÷ 7.5+7.5
x=83-38÷15
x=45÷15
3 hours = x
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The average annual rainfall for a town is 43.2 inches. What is the average monthly rainfall?
Answer: 3.6
Step-by-step explanation: Annual means yearly, therefore 43.2 divided by 12 is 3.6. So 3.6 inches monthly.
How does a qualitative graph describe the relationship between quantities? Explain your reasoning.
Qualitative graphs depict the relationship between two quantities without including numerical values.
The benefit is that it only shows the overall trend of the effect. When we experiment with these variables, we can immediately see how the graph will look. This could validate our findings.
A quantitative relationship emerges as one variable influencing another, which can be seen with a graph. Examine how each variable is represented on the graph, as well as how quantitative relationships are stated using equations.
Quantitative data refers to data that's represented by numbers.
This is the result of graphing all of the data points. Look at that, our data points have formed a straight line! We can draw the line in using a ruler to make it more visible. We'll notice that the line passes through all of the points in our data, indicating that there is a definite relationship in our quantitative data.
Thus, qualitative graphs depict the relationship between two quantities without including numerical values.
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i need help with this question i will give brainliest!!
Answer:
Question 1 is G.
Question 2 is B
Question 3 is D
Question 4 is A.
Step-by-step explanation:
Solve the system by using elimination:
3x + 6y = 10
2x + 3y = 5
Answer:
(0, [tex]\frac{5}{3}[/tex] )
Step-by-step explanation:
3x + 6y = 10 → (1)
2x + 3y = 5 → (2)
multiplying (2) by - 2 and adding to (1) will eliminate y
- 4x - 6y = - 10 → (3)
add (1) and (3) term by term to eliminate y
- x + 0 = 0
- x = 0
x = 0
substitute x = 0 into either of the 2 equations and solve for x
substituting into (2)
2(0) + 3y = 5
3y = 5 ( divide both sides by 3 )
y = [tex]\frac{5}{3}[/tex]
solution is (0, [tex]\frac{5}{3}[/tex] )
Tre typed 456 words in 8 minutes mary typed at the same rate as Tre how long would it take mary to type 945 words
Answer:
16.57894736842105
Step-by-step explanation:
456÷8=57so tre types 57 words per minuteA/Q=
945÷57=16.57894736842105so it'll take 16 mins to type 945 wordsFind the multiplier of 0.5%
The multiplier of 0.5% is 0.005
How determine the multiplier of 0.5%?
A percentage multiplier is a number that is used to calculate a percentage of an amount
In order to determine 0.5% of a number we can multiply the number by a multiplier:
0.5% = 0.5/100 = 0.005
Therefore, 0.005 is the multiplier
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The value in dollar of a $3,000 invetment after n year i given by f(n) = 3,000(1. 05)n. Find the value of the invetment (in dollar) after 4 year. (Round your anwer to the nearet cent. )
The value of investment after 4 years would be $12600
What is investment?
Spending money on an item with the intention of seeing its value rise over time is known as investing. Sacrificing any current item, whether time, money, or effort, is necessary for investment. In the world of finance, investing is done in order to profit from the asset that is being put up for investment.
Main body:
f(n) = 3000(1.05)n
where n= no. of years invested
here n= 4
so total investment = 3000*1.05*4
= $12600
Hence the value of investment is $12600.
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I have two turtles. Today, the older turtle's age is $11$ times that of the younger turtle. In $24$ years, the older turtle's age will only be $7$ times that of the younger turtle. If both turtles survive until then, how many years from today will the older turtle's age be $3$ times that of the younger turtle?
Answer: A number which is divided by 5, with the result as 50 less than if the number had been divided by 6 would be; -1500
How to solve Algebra Word Problems?
Let the number be x. We are asked that it is divided by 5, and the result is 50 less than if the number had been divided by 6;
(x/6) - (x/5) = 50
Multiply by 30 to get;
5x - 6x = 1500
-x = 1500
x = -1500
Let the older turtle be represented x and the younger one be y.
Todays age,
Older turtle = 11y years
Younger turtle = y years
Also the equation form as;
11y + 24 = 7(y + 24)
11y + 24 = 7y + 168
11y - 7y = 168 - 24
4y = 144
y = 144/4
y = 36
Thus;
Age of older turtle today = 396 years
Age of younger turtle today = 36 years
Therefore,
3(36 + t) = 396 + t
108 + 3t = 396 + t
2t = 292
t = 292/2
t = 146 years
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Step-by-step explanation:
You buy a basket of 24 strawberries. You eat them as you walk to the beach. It takes the same amount of time to walk each block. When you are halfway there, half of the berries are gone. After walking 3 more blocks, you still have 5 blocks to go. You reach the beach 28 minutes after you began. One-sixth of your strawberries are left.
You walked
blocks in 28 minutes. At this rate you walk 1 block in
minute(s)
second(s).
The graph of the function, f(x) = x2 - 5x - 7 opens
and has a
value.
The two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14).
What is a general equation of a quadratic equation?The general equation of a quadratic equation is -
y = ax² + bx + c
It has two possible roots. It has a degree of 2.
Given is the graph of the function, f(x) = x² - 5x - 7.
We have the following -
f(x) = x² - 5x - 7.
We will draw the graph of this function.
Now, the graph cuts the [x] axis at (-1.14) and (6.14).
Therefore, the two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14). The graph opens upwards.
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I need help please!!!
Answer:
-10/9
Step-by-step explanation:
Use the slope formula: s=(y2-y1)/(x2-x1)
It doesn't matter the order.
Let's say 0 is x2 and 5 is y2; 9 is x1 and -5 is y1
Plug in the equation: s=[(5)-(-5)]/[(0)-(9)]
Simplify and solve: s=[5+5]/[-9]
s = -10/9
Bumper car A (281 kg) moving
+2.82 m/s makes an elastic
collision with bumper car B
(209 kg) moving +1.72 m/s.
What is the velocity of car A after
the collision?
(Unit = m/s)
Remember: right is +, left is -
Enter
After collision, Car A moves with a velocity of 4.1 m/s
Elastic CollisionAn elastic collision is a collision in which there is no net loss in kinetic energy in the system due to the collision. Both momentum and kinetic energy are conserved in an elastic collision. It can be either one-dimensional or two-dimensional. In the real world, perfectly elastic collision is impossible because there is bound to be some energy conversion, however small. However, though there is no change in the linear momentum of the whole system, there is a change in the individual momenta of the involved components, which are equal and opposite in magnitude and cancel each other out and the initial energy is conserved.
The formula of elastic collision is given as
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Assuming after collision, car B has a velocity of 0m/s
281(2.82) + 209(1.72) = 281 * v + 0
792.42 + 359.48 = 281v
1151.9 = 281v
v = 1151.9 / 281
v = 4.1 m/s
The velocity of car A after collision is 4.1 m/s
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the function h(x) is a transformation of the square root parent function
f(x)=[tex]\sqrt{x}[/tex]. what function is h(x)
The function h(x) is a translation of 4 units to the left, so the correct options is B.
h(x) = √(x + 4)
What is the rule for function h(x)?We know that h(x) is a transformation on the parent square root function:
f(x) = √x
If we look at the graphs, we can see h(x) is translated 4 units to the left.
Now, for a function f(x), we define a horizontal translation of N units as:
h(x) = f(x + N)
if N < 0, the translation is to the right.
if N > 0, the translation is to the left.
In this case we have a translation of 4 units to the left, then N = 4, so we can write:
h(x)= f(x + 4)
Replacing the function f(x) we get:
h(x) = √(x + 4)
So the correct option is B.
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francine wants to join a health club and has narrowed it down to two choices. the sportshaus charges an initiation fee of $ 500 and $ 10 per month. fitness first has an initiation fee of $ 50 and charges $ 25 month.
The equation for the total cost for Sports Haus is 500 + 10x and the equation for Fitness First is 50 + 25x .
In the question ,
it is given that ,
Francie wants to join the health Club .
For the Sports Haus the initiation fees = $500
per month charge = $10
let the number of months be= "x" ,
so , the equation to represent the total cost for Sports Haus Club for x months is 500 + 10x .
For the Fitness First the initiation fees = $50
per month charge = $25
so , the equation to represent the total cost for Fitness First Club for x months is 50 + 25x .
Therefore , The equation for the total cost for Sports Haus is 500 + 10x and the equation for Fitness First is 50 + 25x .
The given question is incomplete , the complete question is
Francine wants to join a health club and has narrowed it down to two choices. The Sports Haus charges an initiation fee of $ 500 and $ 10 per month. Fitness First has an initiation fee of $ 50 and charges $ 25 month . write an equation for the total cost of each health club for x months .
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Construct a square with vertex A inscribed in the given circle
Answer:
see attached
Step-by-step explanation:
You want to construct an inscribed square in circle C with vertex A.
StepsReference the attached figure.
With the compass set to a radius greater than AC, draw arc BE centered at A.With the same compass setting, draw arc GH centered at F, which is the second intersection of line AC with circle C.Identify the points where the arcs intersect as I and J. Draw line IJ.Identify the points where line IJ intersects circle C as K and L.The desired inscribed square is AKFL.
A triangle has two sides of length 12 and 18. What is the smallest possible whole-number length for the third side?
Answer:
7
Step-by-step explanation:
You want the integer length of the shortest third side that will form a triangle with sides 12 and 18.
Triangle inequalityThe triangle inequality requires the sum of any two sides exceed the measure of the third side. If x is the short side, we want ...
x +12 > 18
x > 6 . . . . . . subtract 12
The smallest integer greater than 6 is 7.
The third side must be at least 7 units long.
__
Additional comment
Some authors write the triangle inequality as a+b≥c. If you use that version, then the shortest side can be 6 units. The resulting "triangle" will have zero area, and will look like a line segment 18 units long.
Write an equation of the line with the given slope and y-intercept
Slope : -3
y-intercept : 7
Answer:
y = - 3x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 3 and y- intercept c = 7 , then
y = - 3x + 7 ← equation of line
The temperature in a town increased 18°F in 4 hours. The temperature decreased 40°F in the next 6 hours. Write the total change in temperature as a rate in the form of a quotient of integers.
The total change in temperature is 58°F.
What is temperature?It should be noted that temperature simply means the degree of hotness and coldness in a body.
In this situation, the temperature in a town increased 18°F in 4 hours and the temperature decreased 40°F in the next 6 hours.
The change in temperature will be:
= Old temperature - New temperature
= 18°F - (-40°F)
= 18°F + 40°F
= 58°F
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What is a sampling proportion?
Answer:
it describes the proportion of individuals in a sample with a certain characteristic or trait
Step-by-step explanation:
to find sampling proportion, u have to divide the number of people or items who have the characteristic of interest by the total number of people/items in the sample.
It describes the percentage of people in a sample who possess a particular quality or attribute.
What is a sampling proportion?
The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.
Formula to calculate sampling proportion
p′ = x / n
where,
x: the number of successes
n: the sample size
p′: sample proportion
Hence, it describes the percentage of people in a sample who possess a particular quality or attribute.
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Graph the line with y-intercept 3 and slope -4/3
The line graphed with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
m=(y₂-y₁) / (x₂-x₁)
It is given that, the line is having the y-intercept 3 and slope -4/3.
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
The equation with the y-intercept 3 and slope -4/3 is,
y=mx+c
y= -4/3x+3
3y= -4x+9
Thus, the line graph with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.
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On a scale drawing, a building has length 12.4 cm and width 9.4 cm. The real length of the building is 62 metres. Work out, in metres, the real width of the building.
The real width of the building is given by 47 meters.
Given that the actual length of the building is 62 meters.
In a scale drawing, the length of the building is 12.4 cm.
So, 12.4 cm = 62 meters
1 cm = 62/12.4 = 620/124 = 5 meters.
Also given that the width of building on scale drawing = 9.4 cm
Hence the real width of the building = 9.4 * 5 = 47 meters.
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Which statement best reflects the solutions of the equation X over X minus one minus one over X -2 equals 2X -5 over X squared minus 3X +2
The statement which best reflects the solutions of the equation; as given in the task content is; x = 3 is a valid solution and x = 2 is an extraneous solution.
What is the solution of the equation?It follows from the task content that the statement which represents the solution of the given equation be determined.
Since the given equation can be written algebraically as follows;
x/(x - 1) - 1/(x - 2) = (2x - 5) / (x² - 3x + 2)
By observation; (x - 1) (x - 2) = x² - 3x + 2.
Therefore, by multiplying through the equation by; x² - 3x + 2; we have;
x (x - 2) - 1 (x - 1) = 2x - 5
x² - 2x - x + 1 = 2x - 5
x² - 5x + 6 = 0.
Hence, the equation above can be solved quadratically so that we have;
(x - 3) (x - 2) = 0.
Therefore, the solution to the given equation is; x = -3 Or x = 2.
However, the solution x = 2 renders the equation undefined, hence, it is not a valid solution but an extraneous solution.
Therefore, the statement which reflects the solutions to the given equation is; x = 3.
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Function g can be thought of as a translated (shifted) version of f(x) = x^2
The new function's equation is g(x) = (x - 2)² + 6
Given,
The parent function, f(x) = x²
We have to determine the equation for the new function g(x)
Vertical shift:
The parent function is clearly pushed 6 units upward from the graph.
The general formula to increase the c units on the graph is f(x) + c
As a result, by using the rule, the new function g(x)of vertical shift is provided by g(x) = x² + 6
Horizontal shift:
It is clear from the graph that the parent function has been moved 2 units to the right.
To move the graph's c units to the right, follow this basic formula: f(x - c)
Consequently, the new function g(xhorizontal )'s shift is given by g(x) = (x - 2)²
The new function g( x ) is as follows:
The equation results in the new function being shifted 2 units to the right and 6 units upward.
g(x) = (x - 2)² + 6
Therefore, the new function's equation is g(x) = (x - 2)² + 6
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HELP PLEASE!!!! I don't understand this.
Answer:
1 yes y does vary directly with x
2 to find slope apply the given formula,
y2-y1/m2-m1
2/3 is slope
then the equation should be
y=2/3x
good luck
The graph of the function f(x)=log5(x) is stretched vertically by a factor of 3, reflected over the x-axis, reflected over the y-axis, and shifted down by 4 units.
Find the equation of the function g(x) described above.
Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button.
The equation of the function g(x), considering the transformations, is given as follows:
[tex]g(x) = -3\log_5{(-x)} - 4[/tex]
How to obtain the equation of function g(x)?The equation of function g(x) is obtained applying the transformations to the parent function f(x).
The parent function f(x) is given as follows:
f(x) = log5(x).
The vertical stretch by a factor of 3 is represented by a multiplication of f(x) by 3, hence:
g(x) = 3log5(x).
The reflection over the x-axis is represented by a multiplication of the function by -1, hence:
g(x) = -3log5(x).
The reflection over the y-axis is represented by a multiplication by -1 inside the domain of the function, hence:
g(x) = -3log5(-x).
The shift down by four units is represented by a subtraction of the function by four, hence:
g(x) = -3log5(-x) - 4.
Using Latex for better visualization:
[tex]g(x) = -3\log_5{(-x)} - 4[/tex]
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Find the determinant of a n x n matrix A with 2’s on the diagonal, 1’s above
the diagonal, and 0’s below the diagonal.
The determinant of nxn matrix A 2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.
From the given information, the matrix will appear as follows
[tex]A= \left[\begin{array}{ccccc}2&1&......&1 &1\\0&2&......&1 &1\\0&0&2 ......&1 &1\\0&0&0 ......&2 &1\\0&0&0 ......&2 &1\\0&0&0 ......&0 &2\end{array}\right][/tex]
The matrix is nxn, there are n rows and n columns. As we can see, this matrix has an upper diagonal, and in terms of linear algebra, its determinant is the sum of all its principal diagonal members. As a result, the matrix's determinant is: 2^n
Therefore, the determinant of a n x n matrix A with 2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.
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In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x)=log(x), to achieve the graph of g(x)=log(-3x+9) + 4
The graph g(x)=log(-3x + 9)+4 is the outcome of a transformation on the function, f (x) = log (x), which can be visualized as a reflection across the y-axis. Then you contract by a factor of 3 horizontally, 3 to the right, and 4 to the up.
What is a function?The connection between an independent variable and a dependent variable is established by a mathematical expression, rule, or law (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given function:
Parent function: f(x) = log(x)
Transformation function: g(x) = log(-3x + 9) + 4
Step 1 - Shift 3 unit right, to achieve the function
y = log (x - 3) (x - 3)
Step 2 - Reduce the graph by thrice by multiplying x by three:
y = log 3(x - 3) (x - 3)
Step 3 - The formula y = log 3(x - 3) to line -3 = x is to be reflected to obtain: y = -3 (x - 3)
Step 4 - The function y = log 1 - 3(x - 3) should be translated by four units to reach
Therefore, the function can be transformed by reflection and translation.
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