the equation of the line is,
y = 2x + 5
the slope of the line is m = 2
the slope of the line perpendicular to y = 2x + 5 is ,
m = -1/2
it is passing through (-2,8)
so the equation of the line is
[tex]y-8=(-\frac{1}{2})(x-(-2))[/tex][tex]\begin{gathered} y-8=-\frac{1}{2}x-1 \\ y=-\frac{1}{2}x+7 \end{gathered}[/tex]thus the equation of the line is,
y = -1/2 x + 7
19. Charlotte has a success rate of about 20%for making baskets in attempts duringbasketball games. She wants to determinethe probability that she will have to make atleast 5 attempts during a game in order tomake a basket. She designed a simulationwhere she spun a spinner that was dividedinto 5 equal sections, one of which wascolored red. She counted how many timesshe had to spin the spinner in each trialbefore it landed on red. The results of her20 trials are shown below.5, 2, 7, 2, 3, 4, 10, 6,4,6,3, 6, 6, 4, 8,5,7,7,1,5According to this simulation, what is theprobability that Charlotte will have tomake at least 5 attempts in order to makea basket?
We have the results of a simulation that consists of 20 trials, they are the following:
5, 2, 7, 2, 3, 4, 10, 6, 4, 6, 3, 6, 6, 4, 8, 5, 7, 7, 1, 5
Each number of the results represent the number of attempts needed to make a basket.
Q) We want to know the probability to have to make at least 5 attempts to make a basket.
A) According to the question, we must compute P(# attemps ≥ 5). We can comput
solve the polynomial in standard form1) y=(x-3)^2-3(x-4)
we reduce the equal terms and we obtain the answer is
[tex]y=x^2-9x+21[/tex]Select the correct answer.What is the value of the third quartile of the data set represented by this box plot?HHHH12 14 16 18 20 22 24 26 28 30 32 34 36OA19B.21C26OD.29
A box plot is a standardized way of displaying the distribution of data based on a five-number summary (“minimum”, first quartile (Q1), median, third quartile (Q3), and “maximum”).
The points at the beginning and end of the graph show the outliers (minimum and maximum values).
The outer lines on the left and right of the box show the first quartile and third quartile respectively, while the line inside the box is the median.
From the question, the third quartile (Q3) is the outer line to the right of the box, and its value is 29.
Therefore, OPTION D (29) is correct.
What is the range of the function?Type the range using interval notation example : (#,#]
The range of the function is the values of y
Then to find it, look for the smallest and the greatest value of y of the graph of the function
From the given figure
The lowest value of y is -1
The highest value of y is 3
Then the range of the function is [-1, 3]
Harry owns a car dealership during a sale one week he sold 8 small cars out of 11 cars he sold Harry sold a total of 33 cars doing the sale. How many cars did he sell during the sale?a. 8b. 9c. 24d. 33
Harry sold 8 smalls cars out of 11 cars.
At the end of the sale He sold 33 cars.
In order to determine how many small cars did Harry sell in the week, you take into account that the proportion of small cars for each sale is 8/11.
To find the total small cars sold in the week you multiply the proportion of small cars by the total cars sold in the week, just as follow:
(8/11)33 = 8(33/11) = 8(3) = 24
Hence, the small cars sold during the week were 24.
c. 24
lan's mom works two part time jobs, one in the morning and one in the afternoon, for a total of 35 hours each 5-daywork week. If her schedule is the same each day, and she works 4 hours each morning, how many hours does she workin the afternoon?
lan's mom work for total 35 hours in 5-days week, so each day she worked for,
[tex]\frac{35}{5}=7[/tex]So Ian's mom worked 7 hours each, in which she work 4 hours each morning.
Determine the number of hour's Ian's mom work in afternoon in one day.
[tex]7-4=3\text{ }[/tex]So each day Ian's mom work 3 hours in the afternoon.
Graph the system of inequalities {y > 3x+2 and y<-2x+1. Which two quadrants does the solution lie in?
Quadrants 2 and 3
Explanation
[tex]\begin{cases}y>3x+2 \\ y\leq-2x+1\end{cases}[/tex]
Step 1
graph inequality 1
[tex]y>3x+2[/tex]a)Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
so
[tex]\begin{gathered} y=3x+2 \\ i)\text{ for x= 0} \\ y=3(0)+2=0+2=2 \\ so \\ A(0,2) \\ i)\text{ for x= -1} \\ y=3(-1)+2=-3+2=-1 \\ B(-1,-1) \end{gathered}[/tex]draw a line that passes trough P1 ( 0,2) and P2( -1,-1) and
b)shade below the line for a "less than" (y< or y≤).
so
[tex]y>3x+2[/tex]Step 2
graph inequality 2
[tex]\begin{gathered} y\leq-2x+1 \\ \end{gathered}[/tex]a)Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
so
[tex]\begin{gathered} y=-2x+1 \\ i)\text{ for x= 0} \\ y=-2\cdot(0)+1=0+1=1 \\ so \\ C(0,1) \\ i)\text{ for x= -1} \\ y=-2(-1)+1=2+1=3 \\ D(-1,3) \end{gathered}[/tex]draw a line that passes trough C ( 0,1) and D( -1,3) and
b)shade below the line for a "less than" (y< or y≤).
so
[tex]\begin{gathered} y\leq-2x+1 \\ \end{gathered}[/tex]Step 3
finally, the solution is the intersection of the shaded areas,hence
therefores, the solution lies in
Quadrants 2 and 3
I hope this helps you
. Find the value of x when: 4/(x - 8) = 8/2 *
The value of x is 9
Explanation:Given the equation:
[tex]\frac{4}{x-8}=\frac{8}{2}[/tex]Multiply both sides by 2(x-8)
[tex]\begin{gathered} 4\times2=8(x-8) \\ 8=8(x-8) \end{gathered}[/tex]Divide both sides by 8
[tex]x-8=1[/tex]Finally, add 8 to both sides
[tex]x=1+8=9[/tex]The function g(x) is a transformation of the quadratic parent function, f(x) =2. What function is g(x)?5f(x)5g(x)O A. g() = {x?O B. g(x) = -122C. g(x) = 4x2O D. g(x) = -4x2
we have that
the aprent function
f(x)=x^2
g(x) is a reflection over x -axis of the parent function with a vertical dilation
so
g(x)=-ax^2
Find the value of the leading coefficient a
looking at the graph
For x=1
the value of g(x) is -4
therefore
the answer is the option g(x)=-4x^26.) find a formula for the area of a rhombus ( see figure 12.52) in terms of the good distances between opposite vertices. Explain why your formula is valid.
For the Rhombus you know that:
The opposite sides are parallel
All sides have equal length
Its diagonals bisect each other in right angles
You can calculate the area of the Rhombus by either mutiplying its whide by its length, and sice its 4 sides are of equal lenght, the area will be equal to the square of one of it's sides (s):
[tex]A=s^2[/tex]Or using its diagonals (d1 and d2) you can calculate its area as:
[tex]A=\frac{(d_1\cdot d_2)}{2}[/tex](a) Name the vertex (b) Which direction does the graph open? (c) Find the Axis of Symmetry (d) Graph (e) Maximum or Minimum (f) Name the domain and range. (9) Write the equation in standard form
The vertex of the parabolic equation y = (x+2) (x-2) is at (0,4) .
The given equation is of the form y = (x+2) (x-2).
This can be simplified using the properties of algebra:
y = x² - 4
the graph of the parabolic function y = x² - 4 is attached below.
a) The vertex of this graph is at (0,4) .
b) The graph opens upwards
c)The axis of symmetry of the graph is the y-axis or the line x = 0
e)For finding the maximum and minimum values we find the derivative of x.
y = x² - 4
dy/dx = 2x
at dy/dx = 0 , x = 0
at x=0 , y= - 4
hence the function has a minimum value at -4 and the maximum value of y is infinity.
f) Domain of the function (-∝ < x < ∝)
range of the function ( y ≥ 4 )
g) The equation in the standard form is given by y = x² - 4 .
Disclaimer: The missing equation is y = (x+2)(x-2).
to learn more about vertex visit:
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A house increase value by 32% since it was purchased. If the current value is $495,000, what is the value when it was purchased?
Answer:
$375,000.
Explanation:
Let the value of the house when it was purchased = x
If its value increases by 32%, then its current value will be:
[tex]x+(32\%\text{ of x)}[/tex]Since we are told that the current value is $495,000, then:
[tex]x+(32\%\text{ of x)=495,000}[/tex]We solve for x.
[tex]\begin{gathered} x+0.32x=495,000 \\ 1.32x=495,000 \\ x=\frac{495,000}{1.32} \\ x=\$375,000 \end{gathered}[/tex]The value of the house when it was purchased was $375,000.
Line DA bisects angle EAC, line AB is congruent to line BC, measure of angle B is 74 and measure of angle EAD =44 degrees. Find measure of angle EAB.
From the given information, since AB is congruent to BC then triangle ABC is issoceles,
therefore, the base angles measure the same and they are denoted by x. Since interior angles of any triangle add up to 180, we have
[tex]74+x+x=180[/tex]which gives
[tex]\begin{gathered} 74+2x=180 \\ 2x=180-74 \\ 2x=106 \\ x=\frac{106}{2} \\ x=53 \end{gathered}[/tex]Then, each base angle measure 53 degrees.
On the other hand, since DA bisects angleEAC then angle DAC measure the same as angle EAD, that is,
Therefore, angleEAB is equal to
[tex]m\angle EAB=x+44+44[/tex]By substituting our last result, we have
[tex]\begin{gathered} m\angle EAB=53+44+44 \\ m\angle EAB=53+88 \\ m\angle EAB=141 \end{gathered}[/tex]then, the answer is 141 degrees
Let g(x) = - 7x + 4. Find g(2)
The given expression : g(x) = -7x+4
to find the value of g(2)
Substitute x = 2 in the function of g(x)
g(x) = -7x + 4
g(2) = -7 (2) +4
g(2) = -14+4
g(2) = -10
Answer : -10
An accountant used to charge $72 perhour, but recently decided to charge 25%less. Now how much does she charge perhour?
ANSWER :
EXPLANATION :
It takes Mike’s 40 minutes to type and spell check six pages find how many pages he can type and spell check in one. Five hours round answer to the nearest 10th
Ok, so it takes Mike 40 minutes to work on 6 pages. Let's calculate how many he types in 1.5 hours.
In order to calculate that, we'll use a cross product. But first, let's see how many minutes 1.5 hours are correspondent to:
1 hours - 60 minutes
1.5 hours - x
x= 60*1.5 = 90 minutes.
So:
40 min - 6 pages
90 min - x
40x = 6*90
40x = 540
x= 13.5 pages
He will type and spell check 13.5 pages.
As part of an art installation, Larry wants to tie a piece of rope from the end of a 10m branch that is sticking out of the ground at 23.58 degrees angle to the end of a 1 m tall stake that is 4 m west of the end of the branch. The plans for the installation are shown below. Answer the questions below:1. How many meters above the ground is the end of the branch?2. What is the shortest possible rope length (in meters) that Larry can use to attach the end of the branch to the top of the stake?
Given data:
The length of branch is BC=10 m.
The given angle is β=23.58 degrees.
1)
The expression for the height of the branch above the ground is,
[tex]h=BC(\sin \beta)[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} h=(10m)(sin(23.58^{\circ})) \\ =4m\text{ } \end{gathered}[/tex]Thus, the height of the branch above the ground is 4 m.
IncorrectYour answer is incorrectA vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C()0.3x-66x + 13,267. What is the minimum unit cost?Do not round your answer.Unit cost: S1dxCheckSave For LaterSubmit AssignmentPrencyAceeshhy1125 PMWednesday1620212021 MMcGraw-H Education, All Riathts Resered.Torms of Use9Type here to search
Please check that the expression for the cost you typed reflects what you read in the problem.
Isn't there a "square" in one of the "x" values of the cost equation?
Great. I see now the actual equation for cost to be:
Cost = 0.3 x^2 - 66 x + 13267.
The minimum unit cost will be given by the minimum of this quadratic function (a parabola) which has a minimum at the parabola's vertex. Notice this is a parabola with branches pointing UP because the coefficient of the term in x^2 is POSITIVE.
Recall then the equation for the x position of the vertex of a pparabola with equation of the form:
y = a x^2 + b x + c
the x-position of the vertex is: x = - b / (2a)
which in our case gives:
x of the vertex = - (- 66) / (2 * 0.3) = 110
Then, since the x values represent the number of cars that are made , we now that that minimum occurs when the number of cars produced is 110.
We replace this value in the cost equation and get:
Cost = 0.3 (110)^2 - 66 (110) + 13267 = 9637
Then, the unit cost for making the 110 cars is $9637, which is in fact the minimum value we were looking for.
x+4/-2=-1how to solve this problem
Solve;
[tex]\begin{gathered} \frac{x+4}{-2}=-1 \\ \text{Cross multiply and you have;} \\ x+4=-2\times-1 \\ x+4=2 \\ \text{Subtract 4 from both sides of the equation} \\ x+4-4=2-4 \\ x=-2 \end{gathered}[/tex]Is (1, 2). (5,2), (5,4), (7,6). (11, 6) (11,8) a function, yes or no?!!!!
The group of points (1, 2). (5,2), (5,4), (7,6). (11, 6) (11,8) is not a function as it doesn't satisfy the condition that there is one and only one value in the image space for every element in the domain.
We have the points (5, 2) and (5, 4), which shows two values (y=2 and y=4) for the same point in the domain (x=5).
It also happens for (11, 6) and (11,8).
PLEASE HELP!!!
Match the number with the most specific number set to which it belongs.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
-45
100−−−√
89−−√
4.91919191.....
-2/5
0.12112111211112....
The translation rule that matches the transformation for congruent angles is given as follows:
(x,y) -> (x + 4, y - 5).
What are the translations?The translations are movements to the triangle in each of these directions:
Up.Down.Left.Right.There were two translations in this problem, listed as follows:
From triangle GHI to triangle G'H'I'.From triangle G'H'I' to triangle G''H''I''.For the first translation, the triangle was moved down five units, hence the rule is given as follows:
y -> y - 5.
For the second translation, the triangle was moved right four units, hence the rule is given as follows:
The complete translation, obtained by the combination of each translation, is given as follows:
(x,y) -> (x + 4, y - 5).
Meaning that the first option is the correct option.
More can be learned about translations at brainly.com/question/28174785
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Drag each label to the correct location on the flowchart.Given: Line l and line m intersectProve: Complete the proof. is supplementaryto is supplementaryto Line l and line mintersect
Solution:
The question asked to prove that
[tex]\angle1\cong\angle3[/tex]The given statement is
Line l and line m intersect
Linear pair theorem:
In math, the linear pair postulate or linear pair theorem, says the same in mathematical terms. If two angles form a linear pair, then the measures of the angles add up to 180
Also,
Two angles are called supplementary when their measures add up to 180 degrees.
That is,
[tex]\begin{gathered} \angle2\text{ is supplementary to }\angle3 \\ \angle2+\angle3=180^0 \\ \angle3\text{ is supplementary to }\angle4 \\ \angle3+\angle4=180^0 \\ \angle1\text{ is supplementary to }\angle4 \\ \angle1+\angle4=180^0 \\ \angle2\text{ is supplementary to }\angle3 \\ \angle2+\angle3=180^0 \\ \angle1\text{ is supplementary to }\angle2 \\ \angle1+\angle2=180^0 \end{gathered}[/tex]Hence,
Linear pair theorem :
∠1 is supplementary to ∠2
∠2 is supplementary to ∠3
Congruent Supplements Theorem:
If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.
Since angles 1 and 3 are supplements of the same angle 2
Therefore,
With the statement above we can conclude that
∠1 ≅ ∠3 (congruent supplements theorem)
Assume the given function is one-to-one. Find the indicated value:If f(3)=2 then f^{-1}(2)=AnswerIf f^{-1}(-2)=-1 then f(-1)=?Answer
The question asks us to perform the inverse of two functions.
To solve this question, we need to understand how the inverse of a function works.
The inverse of a function is defined thus:
[tex]\begin{gathered} \text{if }f(x)=y \\ x=f^{-1}(y) \end{gathered}[/tex]With this definition, we can solve the questions.
Question 1:
[tex]\begin{gathered} f(3)=2 \\ \therefore f^{-1}(2)=3_{} \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} f^{-1}(-2)=-1_{} \\ \\ \therefore f(-1)=-2 \end{gathered}[/tex]Thus, the answers are
[tex]\begin{gathered} \text{Question 1:} \\ f^{-1}(2)=3 \\ \\ \text{Question 2:} \\ f(-1)=-2 \end{gathered}[/tex]
The sum of two numbers is 12 ar their difference is 4.
This problem is sysyem of equations
Equation 1 x + y = 12
A grocery store is giving a reusable bag to every person who donates more than $5 to charity. Daniel donates $5. Will he get a bag? Explain how you know?The problem deals with the same thing if they get a reusable bag if they donate $5 dollars to charity but it says Courtney donates $1.25 dollars will she get a bag? Explain why?
Daniel will not going to get a bag
why?
lets read the statement, a part of it
person who donates more than $5 to charity
the key word here is more,
daniel donates exact 5 dollars,
so he will not get a bag
Courtney cant get a bag, because she donates even less,
to get a bag you need to donate, according to the statement , 5 dollars or more,
so for example, you need to donate 5.01 dollars to get a bag
What is the growth percentage of h(x) = .5(2)" ?A200%B2%100%D10%
We can compute the growth percentage, computing first, two consecutive values, as follows:
[tex]\begin{gathered} h(1)=0.5(2)^1=0.5(2)=1 \\ h(2)=0.5(2)^2=0.5(4)=2 \end{gathered}[/tex]Then, the growth percentage is:
[tex]\frac{h(2)-h(1)}{h(1)}\cdot100=\frac{2-1}{1}\cdot100=100\text{ \%}[/tex]eighty-two million, eighty thousand, eleven to standard notation
Given: eighty-two million, eighty thousand, eleven
To Determine: The standard notation of the given number
Solution
Let us first write the numbers in figure
[tex]\begin{gathered} 82,000,000+80,000+11 \\ =82,080,011 \end{gathered}[/tex]Please note Standard notation of a number is when a number is written with only number digits
Hence, the standard notation of the given is 82, 080, 011
What specific measure of a geometric figure is shown in the image?90100 110 12080 70 6013014049 15030 40 50 60 70 80140 130 120 110 10070 20 1010 170160 170 1800 i10294 5 632-N5LLLLLLLLگی۔LEO A. A 140 mm side lengthO B. A 40° angleO C. A 140° angleOO D. A 180 mm side length
ANSWER :
The answer is C. a 140-degree angle
EXPLANATION :
A protractor is used to measure the angle.
From the figure, the angle is 140 degrees.
Solve the right triangle with a=60.6 and C= 90 degrees. Round off the results according to the table below
SOLUTION
Given the question in the image, the following are the soluton steps to answer the question.
STEP 1: Draw the given triangle
STEP 2: Write the given parameters
[tex]\theta=90^{\circ},a=60.6[/tex]Since we do not know the measure of any of the two remaining angles, we cannot solve for the required sides and angles.
Hence, There is no enough information to solve the triangle
6. Which of the following statements must be true when 0 < a < 1 ?. sqrt a a >1II. 2a < 1III. a ^ 2 - a ^ 3 < 0A. I onlyB. III onlyC.I and III onlyD.II and III only
Given:
The following inequalities:
[tex]\frac{\sqrt[]{a}}{a}>1\rightrightarrows\frac{1}{\sqrt[]{a}}[/tex]When 0 < a < 1
So, the denominator will be always < 1
so, all the fraction will be greater than 1
So, the first inequality True
[tex]\begin{gathered} 2a<1 \\ a<\frac{1}{2} \end{gathered}[/tex]when 0 < a < 1
The inequality will be true as a < 1/2
The inequality will be wrong when a >1/2
So, the second inequality is wrong
[tex]\begin{gathered} a^2-a^3<0 \\ a^2(1-a)<0 \end{gathered}[/tex]The inequality true when a >1
so, for 0 < a < 1, the inequality is wrong
So, the answer will be option A. I only