In the figure shown at right, the area of the large rectangle is (5x)(8x+1) and the area of the small rectangle is (4x)(2x) which of the following expression represents the area of the shaded region?
Answers
Given:
Area of large rectangle = (8x + 1)(5x)
Area of small rectangle = (4x)(2x)
To find area of the shaded region, subtract the area of the small rectangle from the large rectangle.
We have:
Area of large rectangle =
[tex]\begin{gathered} (8x+1)(5x) \\ \\ =8x(5x)+1(5x) \\ \\ =40x^2+5x \end{gathered}[/tex]Area of small rectangle =
[tex]\begin{gathered} (4x)(2x) \\ \\ =8x^2 \end{gathered}[/tex]Area of shaded region =
[tex]\begin{gathered} (40x^2+5x)-(8x^2) \\ \\ 40x^2+5x-8x^2 \\ \\ \text{Combine like terms:} \\ 40x^2-8x^2+5x \\ \\ =32x^2+5x \end{gathered}[/tex]Therefore, the area of the shaded region is = 32x² + 5x
ANSWER:
[tex]32x^{2}+5x[/tex]Related Questions
You get paid
$10.75 an hour at your job and the newest video game costs
$60.00 Find the inequality that represents the number of hours you will need to work in order to afford the video game. Use x as a variable
Answers
The inequality that represents the number of hours you will need to work in order to afford the video game is x ≥ 5.58.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤
Let the number of hours be represented as x.
The person is paid $10.75 an hour at your job and the newest video game costs $60.00. This will be illustrated as:
10.75x ≥ 60
Divide
x ≥ 60 / 10.75
x ≥ 5.58
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A group of 40 children attended a baseball game on a field trip. Each child received either a hot dog or a bag of popcorn. Hot dogs were $2.25 and popcorn was $1.75. If the total bill was $83.50, how many hotdogs and bags of popcorn were purchased?
Write the equations for the situation above. (Use the variable x for hotdogs and y for popcorn)
Answers
Answer:
See Explanation
Step-by-step explanation:
[tex]x+y=40\\2.25x+1.75y=83.5\\[/tex]
from the first you have
[tex]h=40-p[/tex] substitute into the second:
[tex]2.25(40-p)+ 1.75x= 83.5\\90-2.25y+1.75x= 83.5[/tex]remaining
[tex]0.5y=6.5\\p= \frac{6.5}{0.5} =13\\[/tex]
substitute back into [tex]h= 40 - y\\h = 40 - 13 = 27[/tex]
Hope this helped :)
consider the dihedral point group constructed from two generators express a 3d matrix representation for the two generators of the group in the hexagonal basis
Answers
the groups generated by two elements of order 2 are K4 and dihedral group.
We are given that G be a finite group with x, y belong to G have two elements of order two.
We have to prove that <x,y> is either abelian or isomorphic to a dihedral group.
<x,y> means the group generated by two elements of order 2.
We know that Zn is a cyclic group and number of elements of order 2 is always odd in number and generated by one element .So , given group is not isomorphic to Zn
But we are given that two elements of order 2 in given group
Therefore, group G can be K4 or dihedral group
Because the groups generated by two elements of order 2 are K4 and dihedral group.
We know that is abelian group of order 4 and every element of K4 is of order 2 except identity element and generated by 2 elements of order 2 and dihedral group can be also generated by two elements of order 2
Hence, <x,y> is isomorphic to K4 or D2.
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Use the rational zeros theorem to list all possible rational zeros of the following.
Answers
The given function is:
[tex]g(x)=-25x^3-5x^2-2x-1[/tex]The theorem states that the factors are p/q where p is the factors of the last term (constant term) and q is the factors of the leading coefficient.
Here the leading coefficient is -25 and the constant term is -1.
The factors are listed below:
[tex]\begin{gathered} -25\Rightarrow\pm25,\pm5,\pm1\Rightarrow q \\ -1=\pm1\Rightarrow p \end{gathered}[/tex]So the value of p/q can be the values shown below:
[tex]\frac{p}{q}\Rightarrow\pm\frac{1}{25},\pm\frac{1}{5},\pm1[/tex]Hence the possible zeroes of the given function are:
[tex]\pm\frac{1}{25},\pm\frac{1}{5},\pm1[/tex]Use the distributive property to write an equivalent expression.
9(7r−3s+10)
Thanks!
Answers
Answer:
63r-27s+90
Step-by-step explanation:
9 times 7 is 63
9 times -3 is -27
9 times 10 is 90
Richey bought a 35-pound bag of dog food on Monday. His dog eats an
average of 3.5 pounds a day. How many pounds will remain in the bag after 8
days? 7 pounds
Answers
In 8 days, Richey’s dog will eat 28 pounds of dog food. 3.5 x 8 = 28. To find how much is left, subtract 28 from 35. 35-28=7 lbs
Answer:
Step-by-step explanation:
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Please help me out with questions 20.-24.
Answers
Answer:
answers are in the photo
Which relation represents a function?
Answers
Find the area of the triangle described below. Round to the nearest hundredth.b = 20, a = 29, c = 21
Answers
Solution
We want to find the area of the triangle given te sides
b = 20
a = 29
c = 21
Note: Hero formula for calculating the Area of a Triangle
We will first find S
[tex]\begin{gathered} S=\frac{a+b+c}{2} \\ S=\frac{29+20+21}{2} \\ S=35 \end{gathered}[/tex]To find the Area
[tex]\begin{gathered} Area=\sqrt[]{S(S-a)(S-b)(S-c)} \\ Area=\sqrt[]{35(35-29)(35-20)(35-21)} \\ Area=\sqrt[]{35\times6\times15\times14} \\ Area=\sqrt[]{44100} \\ Area=210 \end{gathered}[/tex]Therefore, the area is
[tex]Area=210[/tex]Erica prepared 13 flower
arrangements after working 2 hours. How many hours did Erica work if she prepared 26 flower arrangements?
Answers
Erica worked 4 hours to prepare 26 flower arrangements.
Erica prepared 13 flower arrangements after working 2 hours.
Time Erica took to prepare 1 flower arrangement = 2 / 13 hours.
Therefore time Erica took to prepare 26 flower arrangement = 2/13 x 26 hours.
=4 hours.
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PLS HELP 9th Grade MAth
Answers
The equation of the given linear function passing through two points is
y = 6 -2x.
What is equation of a linear function passing through given two points?Let (x₁, y₁) and (x₂, y₂) be two points on the given linear function whose equation in variables x and y is given by formula below.
(y - y₁) = {(y₂ -y₁)/(x₂-x₁)} (x -x₁)
Given that f is a linear function ,
f(-3) = 12
f(6) = -6
⇒(x₁, y₁) = ( -3,12)
(x₂, y₂) = ( 6,-6)
Thus the equation of the linear function is :
⇒ y - 12 = { ( -6-12)/(6-(-3))} ( x - (-3))
⇒ y - 12 = { -18/ 9} ( x +3)
⇒ y - 12 = -2 ( x+3)
⇒ y = 12 -2x - 6
⇒ y = 6 -2x
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Find the slope of the line that passes through (2, 12) and (4, 3). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
The slope of the line passing through the coordinates (2, 12) and (4, 3) is -9/2.
Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 2, 12 )
x₁ = 2y₁ = 12Point 2( 4,3 )
x₂ = 4y₂ = 3To determine the slope, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 3 - 12 )/( 4 - 2 )
Slope m = ( -9 )/( 2 )
Slope m = -9/2
Therefore, the slope of the line is -9/2.
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Select the correct answer from the drop-down menu.The answer choices are in the black box.....which one is it?
Answers
ANSWER
C and D
EXPLANATION
Step 1: Given that:
[tex]C\text{ = }\begin{bmatrix}{2} & 1{} & {} \\ {1} & {}2 & {} \\ {2} & {1} & \end{bmatrix}\text{ and D = }\begin{bmatrix}{\sqrt[]{4}} & 1{} & {} \\ {1} & {}\sqrt[]{4} & {} \\ {\sqrt[]{4}} & {1} & \end{bmatrix}[/tex]Step 2: Simplify matrix D
[tex]\begin{gathered} \text{D = }\begin{bmatrix}{\sqrt[]{4}} & 1{} & {} \\ {1} & {}\sqrt[]{4} & {} \\ {\sqrt[]{4}} & {1} & \end{bmatrix}\text{ = }\begin{bmatrix}{2} & 1{} & {} \\ {1} & {}2 & {} \\ {2} & {1} & \end{bmatrix}\text{ since }\sqrt[]{4}\text{ = 2.} \\ \end{gathered}[/tex]Hence, matrices C and D are equal.
The following figure shows the entire graph of a relationship.
Does the graph represent a function?
Yes or no
Answers
Answer:
No
Step-by-step explanation:
The graph fails the vertical line test. More than one y-value is on one x-value.
x/x+2 - 4/x-2 algeriac equation
Answers
The solution of the given equation in quadratic form will be; (x^{2} -6x - 8)/(x^{2} -4 )
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
WE have been given an algebric equation as;
x/x+2 - 4/x-2
Solving it;
[tex]\dfrac{x}{x+2 }- \dfrac{4}{x-2}\\\\\\\dfrac{x(x-2)}{x+2 }- \dfrac{4(x+2 )}{x-2}\\\\\\\dfrac{x(x-2)- 4(x+2 )}{(x+2 )(x-2)}\\\\\\\dfrac{x^{2} -2x- 4x - 8}{x^{2} -2^{2} }\\\\\\\dfrac{x^{2} -6x - 8}{x^{2} -4 }[/tex]
Hence, the solution of the given equation in quadratic form will be;
(x^{2} -6x - 8)/(x^{2} -4 )
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FRUIT Ronald buys fresh fruit from a fruit stand. Apples cost $5 per pound and peaches cost $6 per pound. He has $60 to spend. The table
shows the function relating the number of pounds of apples, x, and the number of pounds of peaches, y, Ronald could purchase.
Apples (lb) Peaches (lb)
X
y
0
1.2
3
6
7.2
12
The ?
y
10
9
7.5
5
4
0
Hintercept shows that if Ronald buys only apples, he can buy ?
intercept shows that if Ronald buys only peaches, he can buy ?
pounds. The
pounds
Answers
Answer:
a
Step-by-step explanation:
your a could be the same.
You have a $25 calling card. calls made using the card within the united states costs $10 per minute. while calls made from the us to france cost $25 per minute. write an inequality that relates the number of minutes x you can use for calls within the us and the number of minutes y you can use from de us and france
Answers
Answer:
10× + 25y ≤ 25
Answer:
0.1x + 0.25y ≤ 25
Step-by-step explanation:
A call within the US is $0.10, a call to France is $0.25, and you have $25.00. Your total amount of money spent depends on how many calls you make. Now, turn this information into an inequality.
10. (2, -4); slope = -3
Answers
The equation (-4 = -3x + 2) is formed and plotted on the graph (Refer to the graph attached below).
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph. Charts and graphs come in a variety of styles. Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types.So, the equation can be:
The slope is -3 and the coordinates are (2, -4):Formula: y = MX + bWhere m is the slope.From the equation:
y = MX + b-4 = -3x + 2Now, plot the equation on the graph as follows:
(Refer to the graph attached below)Therefore, the equation (-4 = -3x + 2) is formed and plotted on the graph (Refer to the graph attached below).
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The correct question is given below:
From the equation and plot it on a graph when, (2, -4) and slope = -3.
Rewrite 4^-3 x 4 using a single positive exponent.
Answers
The term 4^-3 x 4 can be rewritten using a single positive exponent as 1/4^2.
What is positive exponent?The positive exponent serves as the exponents that contain a positive number, it should be noted that the exponent is the degree at the top[ of the given number which is a negative exponents and the question expect us to turn it to a positive exponents after simplification of the given terms which will be simplified below to the simplest expression.
To rewrite the given term so that it can have a positive exponents then it can be expressed as :
=4^-3 x 4
= 4^-2
1/4^2
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←
For the given function, find (a) f(1) (b) f(-2).
(a) f(1) =
(b) f(-2) =
Answers
For the given functions , f(1) = -3 and f(-2) = -6 .
In the question
a graph is given
we have to find the value of the functions f(1) and f(-2)
the value of f(1) means the value of y, when x=1 .
we see that ,
on the graph when x = 1 , the value of y = -3 .
so the value of [tex]f(1)[/tex] = -3 .
the value of f(-2) means the value of y, when x = -2 .
we see that ,
on the graph when x = -2 , the value of y = -6 .
so the value of [tex]f(-2)[/tex] = -6 .
Therefore , For the given functions , f(1) = -3 and f(-2) = -6 .
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True or false
-5/-1 = 5?
(0/-4) = 0?
-3/1 = -3?
- 8/0 = 0?
Answers
Checking if the results of the following divisions are true or false.
a) -5/-1 = 5 ↔ True
The fraction, (remembering that it is a division), -5/-1 can be simplified to 5 by removing the negative sign from the numerator and denominator.
b) (0/-4) = 0 ↔ True
We know that any number divided by zero, the result will always be zero.
c) -3/1 = -3 ↔ True
Any number divided by one equals the same number.
d) -8/0 = 0 ↔ False
A normal number simply cannot be divided by 0.
The three previous divisions are true, that is, your answers are correct. While the last one can't, since it can't be divided by 0, this one is false.
Ayuda es para mañana son similar figures
Answers
Answer:
2. x = 2
3. x = 43.2
4. x = 3.6
Step-by-step explanation:
solve the equation for all values of x in simplest form (x+1)^2=15
Answers
Answer: [tex]x=-1 \pm \sqrt{15}[/tex]
Step-by-step explanation:
[tex](x+1)^2 =15\\\\x+1 =\pm \sqrt{15}\\\\x=-1 \pm \sqrt{15}[/tex]
Passes to the point( -5, 6) and has a slope equal to 3
Help due tomorrow !!
Answers
The equation of a line that passes through the point ( -5, 6) and has a slope equal to 3 is y = 3x + 21
How to find equation of a line using slope?The equation of the line passes through the point (-5, 6) and has a slope equal to 3.
Therefore, the equation of a line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = 3x + b
slope = 3
using (-5, 6), let's find the y-intercept
6 = 3(-5) + b
6 = - 15 + b
b = 6 + 15
b = 21
Therefore, the equation of the line is y = 3x + 21
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Which equation has a graph that is parallel to the graph 2x-y = -1
Answers
The equation whose graph is parallel to that of line 2x - y = - 1 is →
y = - 2x - 1
What is the general equation of straight line?
The general equation of straight line is -
y = mx + c
Given is an equation of line as → 2x - y = - 1
The equation of the line whose graph will be parallel to that of the graph of line 2x - y = -1, will have same slope as that of given line itself.
2x - y = - 1
y = -2x - 1
m = -2
The equation whose graph is parallel to that of 2x - y = -1 is -
y = - 2x - 1
Therefore, the equation whose graph is parallel to that of line 2x - y = - 1 is → y = - 2x - 1
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The figure to the right shows a square floor plan with a smaller square area that will accommodate a combination fountain and pool. The floor with the fountain-pool area removed has an area of 432 square meters and a perimeter of 90 meters. Find the dimensions of the floor and the dimensions of the square that will accommodate the fountain and pool
Answers
Considering the area and the perimeter of a square, it is found that:
Each length of the large square floor is of 21 meters, and each length of the small square floor is of 3 meters.
What are the area and the perimeter of a square?Supposing a square of side length s, the area and the perimeter are given as follows:
Area: A = s².Perimeter: P = 4s.The area of the figure is given by the subtraction of the area of the large square, of side length x, by the area of the small square, of side length y, hence:
A = x² - y²
x² - y² = 432.
The perimeter of the figure is the perimeter of the square of side length s added to two edges of the smaller square of side length s, hence:
P = 4x + 2y
4x + 2y = 90.
Then the system of equations to find the dimensions is given as follows:
x² - y² = 432.4x + 2y = 90.The solution of this system is given by:
x = 21 m (each length of the large square floor).y = 3 m (each length of the small square floor).Missing informationThe problem is completed by the image given at the end of the answer.
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HELP PLEASE!!!!!!!!!!!
What is the dimensions of a rectangle that is 32ft by 8ft after it is dilated by a scale factor of 7/8
Answers
Dimensions of rectangle after dilation of scale factor 7/8 will be
[tex] (\frac{7}{2},14), (\frac{-7}{2},14), (\frac{-7}{2},-14), (\frac{7}{2},-14) [/tex]
Dilation of rectangle :-Dilation means the area of any rectangle increases or decreases due to change in it's dimensions but the shape of that rectangle will remain same.
Now Consider the point of dilation as the center of rectangle and assume that the center of given rectangle is at the origin.
As given the length and width of rectangle is 32ft and 8ft respectively.
∴ The Dimensions of rectangle will be (4,16), (-4,16), (-4,-16) and (4,-16).
Now As the rectangle is diluted by the factor of 7/8.
So Now New Dimensions are Calculated by simply multiplying the available dimensions with the scale factor of dilation.
∴ new Dimension after dilation will be
[tex] (4(\frac{7}{8}),16(\frac{7}{8})), (-4(\frac{7}{8}),16(\frac{7}{8})), (-4(\frac{7}{8}),-16(\frac{7}{8})), (4(\frac{7}{8}),-16(\frac{7}{8})) [/tex]
∴ Dimension after dilution will be ;
[tex] (\frac{7}{2},14), (\frac{-7}{2},14), (\frac{-7}{2},-14), (\frac{7}{2},-14) [/tex]
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Please help immediately
What is the equation of the line that passes through Point (6, 0) and has a Slope of -1/2.
I know that it is f(x) = -1/2x + 3 but I need a step by step and clear explanation.
Answers
Answer:
[tex]y = - \frac{1}{2} x + 3[/tex]
Step-by-step explanation:
Please see the attached images for the full solution.
Note that when y is replaced with f(x), it is known as a function instead of an equation.
does anyone know how to solve and find out the answer? Thank you so much if you help!
Answers
Answer:
perpendicular
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 )
y = - [tex]\frac{2}{3}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
3x - 2y = 4 ( subtract 3x from both sides )
- 2y = - 3x + 4 ( divide through by - 2 )
y = [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form
with slope m = [tex]\frac{3}{2}[/tex]
• Parallel lines have equal slopes.
clearly the slopes are not equal, so not parallel.
• the product of the slopes of perpendicular lines = - 1
- [tex]\frac{2}{3}[/tex] × [tex]\frac{3}{2}[/tex] = - 1
then the lines are perpendicular to each other.
Answer:
The lines are perpendicular.
Step-by-step explanation:
[tex]3x -2y=4[/tex]
Step 1: Add -3x to both sides.
[tex]3x-2y+-3x=4+-3x[/tex]
[tex]-2y=-3x+4[/tex]
Step 2: Divide both sides by -2.
[tex]\frac{-2y}{-2} =\frac{-3x+4}{-2}[/tex]
[tex]y=\frac{3}{2} x-2[/tex]
Finally...
[tex]y=\frac{3}{2} x-2\neq y=-\frac{2}{3} x+5[/tex] so the lines are not parallel.
However, [tex]\frac{3}{2}[/tex] is the opposite reciprocal of [tex]-\frac{2}{3}[/tex], so, the lines are perpendicular.
(You can also try drawing the lines.)
In the designers proposal, they state that the paths EC and DB each measure 100 feet. They also state that the garden will require 140 feet of hedges. Are their numbers reasonable?
Answers
We are given a circle whose diamter is 100 feet. To find out if 140 feet of hedges will fit into it given all the oother dimensions, we will have to calculate the lengths of the chords that correspond to the hedges.
First, let us solve for AE.
[tex]\begin{gathered} chord=2r\sin\theta \\ \\ AE=100\sin50 \\ AE=76.6 \end{gathered}[/tex]We used θ = 50 degrees because we know that the measurement of the arc is equal to the measurement of the central angle.
Now, to solve for the length of ED, we need to find out the measurement of the central angle that subtend it.
Segments AD and EC intersect, thus the following equation must be true for the angles that they form and the arcs that they subtend:
[tex]\begin{gathered} m\angle EXA=\frac{1}{2}(m\hat{AE}+m\hat{DC}) \\ \\ 70=\frac{1}{2}(50+m\hat{DC}) \\ \\ 140=(50+m\hat{DC}) \\ \\ 90=m\hat{DC} \end{gathered}[/tex]Again, using the formula for finding the length of a chord, we can now solve for the length of ED.
[tex]\begin{gathered} chord=2r\sin(\theta) \\ \\ ED=100\sin90 \\ ED=100 \end{gathered}[/tex]Finally, we need to calculate the length of BC. But we know that BC = ED because the diameters meet at a 90-degree angle and so the chords that they subtend are all congruent. You may also think of ∠BYC as being vertical to ∠EYD. So BC should be equal to ED either way. BC = 100
So the total length of the hedges is:
[tex]\begin{gathered} AE+ED+BC \\ =76.6+100+100 \\ =276.6ft \end{gathered}[/tex]Therefore, the numbers given by the designers are not reasonable. 140 feet is too short for the hedges.