Given: Ratio of students that voted for A compared to B is 7:4
A recieved 21 votes so let B recieve x votes.
So as the given ratios,
[tex]\frac{7}{4}=\frac{21}{x}[/tex][tex]x=\frac{21\times4}{7}=12[/tex]Hence, combined votes received by candidate A and B is 12+21=33
13. What transformations take place by graphing the function below in respect to its parents go
function? Check all that apply.
Up 7 units
Down 7 units
Left 7 units
Right 7 units
3
f(x)=(x+7)² +2
Up 2 units
Down 2 units
Left 2 units
Right 2 units
Theis)
Textes
Vertical Stretch
Vertical Compression
Reflection in x-axis
Reflection in y-axis
81
The graph is being transformed Right 7 units and Down 2 units.
The function is given as:
f (x) = (x + 7)² + 2
This can also be written as:
y = (x + 7)² + 2
y - 2 = (x + 7)²
Now, we can see the following transformations:
The graph is translated 7 units to the right.
Also, it is being translated 2 units to the down.
So, the option will be
Right 7 units and Down 2 units
Therefore, we get that, the graph is being transformed Right 7 units and Down 2 units.
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determine the length of the unknown side of the right angle
We are given the right-angle triangle with two known sides and one unknown side.
We can use the Pythagoras theorem to find the length of the unknown side.
Recall that Pythagoras theorem is given by
[tex]a^2+b^2=c^2[/tex]Where c is the side opposite to the 90° angle.
Let us substitute the given values into the above equation
[tex]a^2+(9)^2=(15)^2[/tex]Simplify the equation
[tex]\begin{gathered} a^2+81=225^{} \\ a^2=225-81 \\ a^2=144 \end{gathered}[/tex]Take the square root on both sides
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{144} \\ a=12 \end{gathered}[/tex]Therefore, the length of the third side of the right angle tri
You invested $9000 between two accounts paying 4% and 7% annual interest. If the total interest earned for the year was $510, how much was invested at each rate?
Let x represent the amount invested at 7%.
Then 9000-x is the amount invested at 4%
total interest earned is:
0.07x + 0.04(9000-x) = 510
0.07x + 360 - 0.04x = 510
0.03x = 150
x = 5000 the amount invested at 7%
9000 - 5000 = 4000 the amount invested at 4%
A quadrilateral is formed by the points A(1,-1), B(0,3), C(5,5), and D(6, 1). Plot the points and use the distance formula to find the lengths of all 4 sides. What type of quadrilateral is this?
If we have the given points on a cartesian point, the result would be:
It is not difficult to see that these points will form a rhombus. In this case, we do expect that the opposite sides have the same size. To verify it, we will use the following formula to calculate the distance among the given points:
[tex]d_{P1-P2}=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Substituting each pair, we have:
AB
[tex]\begin{gathered} d_{AB}=\sqrt[]{(1-0)^2+(-1-3)^2}=\sqrt[]{1^2+(-4)^2}=\sqrt[]{1+16}_{} \\ d_{AB}=\sqrt[]{17} \end{gathered}[/tex]BC
[tex]undefined[/tex]If D is the midpoint of AB and AD = 2x + 6 and AB = 32, then find AD. Draw thepicture.AD =
The diagram representing the line AB and midpoint D is shown bel;ow.
Therefore, 16=2x+6.
[tex]\begin{gathered} 2x=10 \\ x=5 \end{gathered}[/tex]Then, the magnitude of AD will be,
[tex]\begin{gathered} AD=(2\times5)+6 \\ AD=16 \end{gathered}[/tex]Therefore, the answer is 16.
Which of the following are possible sidelengths for a triangle?A. 16, 8, 10B. 4, 12,6C. 6, 9, 17
Step-by-step explanation:
Triangle rule
a + b > c
This implies that the summation of first and second leg must be greaterthan the third leg
For Option A
a = 16, b = 8, and c = 10
16 + 8 > 10
60 is what % of 150? Can you help?
Given:
There are given that the final number is 150.
Explanation:
According to the question:
We need to find the percentage number.
Then,
Suppose the percentage number is x.
Then,
The equation will be:
[tex]150\times x\%=60[/tex]Now,
We need to solve the above equation for the value of x.
Then,
Divide by 150 on both sides of the equation:
[tex]\frac{150}{150}\times x\operatorname{\%}=\frac{60}{150}[/tex]Then,
[tex]\begin{gathered} x\%=\frac{60}{150} \\ x\operatorname{\%}=\frac{6}{15} \\ x\operatorname{\%}=0.4 \\ x=0.4\times100 \\ x=40 \end{gathered}[/tex]Final answer:
Hence, the percentage is 40%.
1. Use the image below to find the midpoint of segments BD and AC B 5 С D -5 4 3 2 1 1 2 3 4 5 2. Classify triangle ABC as either equilateral, right, isosceles, or none. 5 C B 2 A -3 -2 -1 2 3 4 5 6 -2
1. We have that B (-2,4) and D (2,1), then the midpoint has coordinates
[tex]\begin{gathered} x=\frac{-2+2}{2}=0 \\ y=\frac{4+1}{2}=\frac{5}{2} \end{gathered}[/tex]and the midpoint is (0,5/2).
On the other hand A (-4,1) and C (4,4), so the midpoint has coordinates
[tex]\begin{gathered} x=\frac{-4+4}{2}=0 \\ y=\frac{1+4}{2}=\frac{5}{2} \end{gathered}[/tex]and the midpoint is (0, 5/2).
In conclusion, the midpoint of segments BD and AC is (0,5/2).
2. To classify the triangle we need to know the length of its sides
[tex]\begin{gathered} \bar{AB}=\sqrt[]{(3-(-2))^2+\mleft(0+2\mright)^2}=\sqrt[]{25+4}=\sqrt[]{29} \\ \bar{BC}=\sqrt[]{(2-(-2))^2+(4-2)^2}=\sqrt[]{16+4}=\sqrt[]{20} \\ \bar{AC}=\sqrt[]{(3-2)^2+(4-0)^2}=\sqrt[]{1+16}=\sqrt[]{17} \end{gathered}[/tex]Since neither of its sides has equal length, then it is not equilateral os isosceles. Besides,
[tex]17^2+20^2\ne29^2[/tex]Then it is not a right triangle.
In conclusion the answer is none of the options
The Hudson family is saving for a
family vacation to Disney World.
They determine that the trip will
cost $3,200. Mr. and Mrs.
Hudson have already set aside
$1,500 for the trip. If they leave
in 16 weeks, then how much
will they need to save
each week?
As per the unitary method, they need to save $106.25 each week.
Unitary method:
Basically, the unitary method is a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.
Given,
The Hudson family is saving for a family vacation to Disney World. They determine that the trip will cost $3,200. Mr. and Mrs. Hudson have already set aside $1,500 for the trip.
Here we need to find the amount they need to save for each week if they leave in 16 weeks.
While we looking into the given question,
Total amount of Saving = $3,200.
Amount in hand = $1,500
So, the amount need is calculated as,
=> 3200 - 1500
=> 1700
Here we have the 16 week time,
So, the saving for each week is calculated as,
=> 1700/16
=> 106.25
Therefore, the family have to save $106.25 for each week.
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y=1/2x what is the b, or y-intercept in this equation
The given equation is
[tex]y=\frac{1}{2}x[/tex]The slope-intercept form is
[tex]y=mx+b[/tex]The given equation can be written as follows.
[tex]y=\frac{1}{2}x+0[/tex]Comparing this equation with slope-intercept form, we get b=0.
Hence the value of b or y-intercept in the given equation is 0.
Jack has an old scooter. He wants to sell it for 60% off the current price. The
market price is $130. What should his asking price be? Explain your reasoning.
perimeter of a square must be greater than 118 inches but less than 156 inches .find the range of the possible side lengths that satisfy these conditions . formula p= 4sput answer in interval notation.
the perimeter of a square must be greater than 118 inches but less than 156 inches.
Perimeter = 4 side lenght
P = 4 s
118 < 4s < 156
Divide by 4
29.5 < s < 39
(29.5 , 39 )
3С21In the similaritytransformation of AABCto ADEF, AABC was dilated bya scale factor of [? ], reflectedacross the J, and movedthrough the translation [ ].BА-7-6-5-4m, 002-1 0.12.39ShoesDA. 2B. 1/2C. 3D. 1/3
Scale factor is the ratio of corresponding sides in two(2) similar geometric figures.
Taking one similar side of the two(2) figures, we have:
[tex]\begin{gathered} \frac{DF}{CA}=\frac{2}{1}=2 \\ \text{Thus, scale factor is 2} \end{gathered}[/tex]Hence, the correct option is option A
It is reflected across the x-axis and moved through the translation (3, 1)
I need help in math can you please help me please
Trigonometric Equations
Solve:
[tex]9\tan ^3x=3\tan x[/tex]In the interval [0,2pi)
We have to find all the values of x that make equality stand. First, divide by 3:
[tex]3\tan ^3x=\tan x[/tex]Subtract tan x
[tex]3\tan ^3x-\tan x=0[/tex]Factor tan x out:
[tex]\tan x(3\tan ^2x-1)=0[/tex]One solution comes immediately:
tan x = 0
There are two angles whose tangent is 0:
[tex]x=0\text{ , x=}\pi[/tex]The other solutions come when equating:
[tex]3\tan ^2x-1=0[/tex]Adding 1, and dividing by 3:
[tex]\tan ^2x=\frac{1}{3}[/tex]Taking the square root:
[tex]\tan x=\sqrt[\square]{\frac{1}{3}}=\pm\frac{\sqrt[]{3}}{3}[/tex]The positive answer gives us two solutions:
[tex]\tan x=\frac{\sqrt[]{3}}{3}[/tex]x=pi/6 and x=7pi/6
The negative answer also gives us two solutions:
[tex]\tan x=-\frac{\sqrt[]{3}}{3}[/tex]x=5pi/6, 11pi/6
Summarizing the solutions are:
{
Hello I just need the answer for “What is the inverse for the equation y=x^2+16”
Given:
The given equation is
[tex]y=x^2+16[/tex]Required:
We need to find the inverse for the equation.
Explanation:
[tex]\text{ Let y=f\lparen x\rparen and }x=f^{-1}(y)\text{ and substitute }x=f^{-1}(y)\text{ in the given equation.}[/tex][tex]y=(f^{-1}(y))^2+16[/tex]Substract 16 from both sides of the equation.
[tex]y-16=(f^{-1}(y))^2+16-16[/tex][tex]y-16=(f^{-1}(y))^2[/tex]Take square root on both sides of the equation.
[tex]\pm\sqrt{(y-16)}=f^{-1}(y)[/tex][tex]f^{-1}(y)=\pm\sqrt{(y-16)}[/tex]Replace y=x in the equation.
[tex]f^{-1}(x)=\pm\sqrt{x-16}[/tex]Final answer:
[tex]f^{-1}(x)=\pm\sqrt{x-16}[/tex]Jessica furniture store is trying to figure out if she bought a couch at wholesale price for $113 and she mark up by 45%. what price should she sell the couch
original price = $113
MArkup = 45% = 45/100 = 0.45 ( decimal form)
Sell price = 113 (1 + 0.45) = 113 * 1.45 = $163.85
6ft 3ft 8ft 16ft area of irregular figures
Solution.
From the figure given we will have to find the
(Area of A) + (The Area of B)
STEP 1 :
For figure B
b = 3
h = 6
[tex]\begin{gathered} \text{Area of A = }\frac{1}{2}\times b\times h \\ \text{ = }\frac{1}{2}\times3\times6 \\ \text{ = }\frac{18}{2}\text{ = 9} \end{gathered}[/tex]Step 2:
For Figure A
L = 16
b = 8ft
Area of B = L x B
= 16 x 8
= 128
STEP 3
Area of A + Area of B
128 + 9 = 137 square feet
Find the equation of the line in standard form that passes through the following points simplify your answer
Given: Two points
[tex]\begin{gathered} Point1:(10,11) \\ Point2:(10,7) \end{gathered}[/tex][tex]\begin{gathered} Point1:(10,11) \\ Point2:(10,7) \end{gathered}[/tex]To Determine: The equation of the line in standard form that passes through the given points
Solution
The equation of a line passing through two different points is given as
[tex]\begin{gathered} Point1:(x_1,y_1) \\ Point2:(x_2,y_2) \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Substitte the given coordinates of the points given into the formula
[tex]\begin{gathered} \frac{y-11}{x-10}=\frac{7-11}{10-10} \\ \frac{y-11}{x-10}=\frac{-4}{0} \\ cross-multiply \\ Since\text{ the slope is undefine} \\ The\text{ equation of the line is } \\ x=10 \end{gathered}[/tex]The standard form of a line is given as
[tex]Ax+By=C[/tex]But since the x-coordinates of the points are equal, then the formula for slope is not applicable (the denominator equals 0).
In this case, we say that the slope is undefined (the line is vertical).
This means that the equation of the line doesn't contain y.
Thus, the equation of the line is x=10.
Answer: the slope is undefined.
The equation of the line is x = 10.
F(x) = x^3 + x^2 + 9x + 9 Find all zeros including irrational and/ or complexFactor f completely into linear factors Part of it completed: The zeros are -1, 3i, and -3i
Given:
[tex]F\left(x\right)=x^3+x^2+9x+9[/tex]To find:
The zeros
Explanation:
Factorizing by grouping method,
[tex]\begin{gathered} F\left(x\right)=x^3+x^2+9x+9 \\ =x^2(x+1)+9(x+1) \\ =(x+1)(x^2+9) \end{gathered}[/tex]The zeros are found by equating the factors with zero.
[tex]\begin{gathered} x+1=0 \\ x=-1 \end{gathered}[/tex]And we have,
[tex]\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\pm\sqrt{-9} \\ x=\pm3i \end{gathered}[/tex]So, the zeros are,
[tex]-1,3i,-3i[/tex]Final answer:
The zeros are,
[tex]-1,3i,-3i[/tex]A real estate agent believes that most of the home prices are low with few homes have very high prices in a certain area in his county. If his description on home prices in this area is accurate, which of the following shape best describe the distribution of home prices in this area?SymmetricalNormalNegatively skewedPositively skewe
GIVEN:
We are told that a real estate agent believes that most of the home prices are low with very few homes having very high prices in a certain area.
Required;
If his description is accurate, which shape best describes the distribution of home prices in this area?
Explanation;
For data distribution, the graph can take on different shapes dpending on how the data is distributed. In this particular instance, most of the data is lying on the left side of the graph. In other words, the curve is more elevated on the left side while its very low towards the right side.
The following picture is an illustration of this scenario;
This is "Positively skewed data distribution."
ANSWER:
Positively skewed.
A mattress with a list price of $2300 will be discounted 30% at the time of purchase. What is the sale price before taxes?
So,
30% of $2300 is:
[tex]\frac{30\cdot2300}{100}=690[/tex]So that's the amount that will be discounted. Therefore, the sale price before taxes is $2300 - $690 = $1610
Solve this equation:-36q = 18
Given:
[tex]36q=18[/tex]Required:
To solve the given equation.
Explanation:
Consider
[tex]36q=18[/tex]Divide 36 on both side, we get
[tex]\begin{gathered} \frac{36q}{36}=\frac{18}{36} \\ \\ q=\frac{18}{36} \\ \\ q=\frac{1}{2} \end{gathered}[/tex]Final Answer:
[tex]q=\frac{1}{2}[/tex]Find the range of the function for the given domain. {-5, -1, 0, 2, 10}
[tex]g(x)=x^{2}+2[/tex]
A. 2
B. -23
C. 3
D. 1
E. 102
F. 27
G. 6
The range of the function g(x) = x² + 2 for the given domain is found to be {27,3,25,6,102}.
What is the difference between domain and range in function?The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value.
How do you find domain and range in the absence of numbers?To determine the domain of a function, f(x), determine which values of x cause f(x) to be undefined/not real. The usual procedure for determining range is to find x in terms of f(x) and then locate values of f(x) for which x is not defined.
Given:
g(x) = x² + 2
Domain of the function: {-5, -1, 0, 2, 10}
We need to find the range.
Let us substitute x = -5 in g(x)
g(-5) = (-5)² + 2
= 27
g(-1) = (-1)² + 2
= 3
g(0) = (0)² +(-5)²
= 25
g(2) = (2)² + 2
=6
g(10) = (10)² + 2
= 102
Therefore, the range of the given function g(x) = x² + 2 for a given domain is found to be {27,3,25,6,102}.
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For each value of v, determine whether it is a solution to v - 42 = 11
Given equation:
[tex]v\text{ - 42 = 11}[/tex]The first step is to solve the equation i.e. find the value of v
[tex]\begin{gathered} Collect\text{ like terms} \\ v\text{ = 11 + 42} \\ v\text{ = 53} \end{gathered}[/tex]The given options
At a certain hospital 39080 patients had their falls reported in the winter of 2004, thisrose to 42045 patients in the winter of 2014 (Lifespan, 2019). How would you calculatethe percentage rise in patients from 2004 to 2014?In a several sentences, how would you apply this to your life or job? If you had to teachsomeone who did not know how to this, what would be the steps from beginning to endthat you would use to teach them so that they would eventually do it accurately as youwould?Professor,I would calculate the percentage rise in patients from 2004 to 2014 by
Percentage rise in patients from 2004 to 2014 = 7.59%
Explanation:The number of patients in 2004 = 39080
The number of patients in 2014 = 42045
Increase in the number of patients = (The number of patients in 2014) - (The number of patients in 2004)
Rise in the number of patients = 42045 - 39080
Rise in the number of patients = 2965
[tex]\begin{gathered} \text{Percentage rise in patients = }\frac{\text{Rise in the number of patients}}{\text{Number of patients in 2004}}\times100 \\ Percentage\text{ rise in patients = }\frac{2965}{39080}\times100 \\ \text{Percentage rise in patients = }7.59\text{ \%} \end{gathered}[/tex]Percentage rise in patients from 2004 to 2014 = 7.59%
Convert the measurement as indicated 83 qt = Gal Qt
20 gallons 3 quarts
Explanation:Note that:
1 quart = 0.25 gallons
83 quarts can be written as
80 quarts + 3 quarts
80 quarts = 80 x 0.25 gallons
80 quarts = 20 gallons
Therefore:
83 quarts = 20 gallons 3 quarts
I really need help with number 6find the value of x that makes abcd a parallelogram.
Given:
The adjacent angles of the parallelogram are,
[tex]28,\text{ and }3x[/tex]To find:
The value of x.
Explanation:
We know that,
The sum of the two adjacent angles between the parallel lines is supplementary.
So, we write,
[tex]\begin{gathered} 28+3x=180 \\ 3x=180-28 \\ 3x=152 \\ x=50.66 \\ x\approx50.7 \end{gathered}[/tex]Thus, the value of x is 50.7.
Final answer:
The value of x is 50.7.
Hello can you assist me with number 11Find the midpoint
Answer:
(-3, 2.5)
Explanation:
The midpoint of two points of coordinates (x1, y1) and (x2, y2) has the following coordinates
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}_{})[/tex]Then, the midpoint can be calculated replacing (x1, y1) = (3, 3) and (x2, y2) = (-9, 2), so
[tex](\frac{3+(-9)}{2},\frac{3+2}{2})=(\frac{-6}{2},\frac{5}{2})=(-3,2.5)[/tex]Therefore, the midpoint is (-3, 2.5)
What is the slope of the line that passes through the points (10,8) and (7,14)?
Answer:
Step-by-step explanation:
-0.5
Consider the equation. y=1/4(x-5)^2-3Vertex (5,-3)The next step in graphing a parabola is to find points that will determine the shape of the curve. Find the point on the graph of this parabola that has the X-coordinates X=3.
We have the equation:
[tex]y=\frac{1}{4}(x-5)^2-3[/tex]This is a parabola expressed in vertex form, where the vertex is (h,k) = (5,-3).
We have to graph the parabola. To do that we need another point, as we already know the vertex and, therefore, the axis of symmetry (x = 5).
We can find another point by giving a value to x and calculating y.
For example, with x = 3 we get:
[tex]\begin{gathered} y(3)=\frac{1}{4}(3-5)^2-3 \\ y(3)=\frac{1}{4}(-2)^2-3 \\ y(3)=\frac{1}{4}\cdot4-3 \\ y(3)=1-3 \\ y(3)=-2 \end{gathered}[/tex]The point that belongs to the parabola when x = 3 is (3, -2).
Then, we can graph the two points and draw the parabola as:
Because of the symmetry at x = 5, we also know that two units to the right, at x = 7, we will have the same value of y that we have for x = 3.
With at least 3 points, we can graph a parabola.
The actual graph is:
If we want to add more precision to our graph, we can calculate more points that belong to the parabola.
For example, at the other side of the vertex, we can calculate the value of y for x = 6:
[tex]\begin{gathered} y(6)=\frac{1}{4}(6-5)^2-3 \\ y(6)=\frac{1}{4}(1)^2-3^{} \\ y(6)=\frac{1}{4}-3 \\ y(6)=\frac{1}{4}-\frac{12}{4}^{} \\ y(6)=-\frac{11}{4}=-2.75 \end{gathered}[/tex]We can add this to the plot as:
We have to aproximate the position of y as the grid only shows integers and y = -2.75.
Answer:
The points in the parabola are (5,-3), (3,-2) and (6,-2.75). We need at least 3 points to plot a parabola.