Write a polynomial to represent the area of the shaded region. Then solve for x given that the area of the shaded region is 24 square units.
3x2 + x - 6; x = 3
3x2 + 7x - 6; x = 2
3x2 + 7x - 6; x = 5
WILL GIVE BRAINLIEST WITH EXPLANATION
Answers
Answer:
[tex]3x^{2}[/tex] +x -6 ; x = 3
Step-by-step explanation:
PART 1: The Polynomial
1. Set up the Equation: (x+3)(3x-2) - 6x
You want to find the area of the larger of the 2 rectangles that way you can subtract the area of the smaller one to get the shaded area (if that makes sense). You multiply length by width to get the area so you will multiply (x+3) by (3x - 2). The same applies to the smaller of the two rectangles, so that will be 6x.
2.FOIL: [tex]3x^{2}[/tex] - 2x + 9x -6 - 6x
You are going to want to foil (x+3) and (3x-2). If you are unfamiliar with the FOIL method I would recommend watching a Khan Academy video about it.
3. Simplify: [tex]3x^{2}[/tex] +x -6
Add and subtract like terms. This will be your polynomial.
PART 2: The Value of x
1. Set up the Equation: [tex]3x^{2}[/tex] +x -6 = 24
You will set the polynomial to equal 24 the polynomial and number both equal the size of the shaded area
2. Subtract: [tex]3x^{2}[/tex] +x -30 = 0
Subtract 24 from both sides.
3. Factor: (3x + 10)(x - 3) = 0
4. Set each group to equal zero.
a. 3x + 10 = 0
3x = -10
x = -10/3
----------------
b. x - 3 = 0
x = 3
5. Check both the answers in [tex]3x^{2}[/tex] +x -6 = 24 to see if your answers are correct. The answer would be x = 3.
Polynomial representing the area of the shaded region will be (3x² - x - 6) square units and the value of 'x' is 3.
Area of a rectangle:Area of a rectangle is given by the expression,Area of a rectangle = Length × Width
Given in the picture,
Larger rectangle with measures,Length = (x + 3) units
Width = (3x - 2) units
Small rectangle with measures,Length = x units
Width = 6 units
Area of the shaded region = Area of the larger rectangle - Area of the smaller rectangle.
Area of the larger rectangle = (3x - 2) × (x + 3) square units
Area of the smaller rectangle = 6x square units
Area of the shaded region = (3x - 2)(x + 3) - 6x
= 3x(x + 3) - 2(x + 3) - 6x
= 3x² + 9x - 2x - 6 - 6x
= (3x² + x - 6) square units
If the area of the shaded region is 24 square units.
3x² + x - 6 = 24 [Substitute the values]
3x² + x - 30 = 0
3x² + 10x - 9x - 30 = 0 [Factor the equation]
x(3x + 10) + 3(3x + 10) = 0
(x - 3)(3x + 10) = 0
[tex]x=3,-\frac{10}{3}[/tex]
Therefore, polynomial representing the area of the shaded region will be (3x² - x - 6) square units and the value of x is 3.
Learn more about the area of a rectangle here,
https://brainly.com/question/1256199?referrer=searchResults
Related Questions
Bus a and bus b leave the bus depot at 6pm bus A takes 20 minutes to do its route and bus B takes 45 minutes to complete its route at what time are they both back at the bus depot together
Give your answer as a 12-hour clock time
Answers
Answer:
9:00pm
Step-by-step explanation:
20 + 20 + 20 +20 + 20 + 20 + 20 + 20 +20 = 180
45 + 45 + 45 + 45 = 180
Bus A would've taken 9 routes and Bus B would've taken 4, to reach the bus depot together
180 mins - hours = 3 hours
6 + 3 = 9
Select the correct answer. Solve the equation by completing the square. 0 = x2 − 14x A. x = 0, 14 B. x = -56, 42 C. x = -42, 56 D. x = -14, 0
Answers
Answer:
A
Step-by-step explanation:
Given
x² - 14x = 0
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 7)x + 49 = 0 + 49
(x - 7)² = 49 ( take the square root of both sides )
x - 7 = ± [tex]\sqrt{49}[/tex] = ± 7 ( add 7 to both sides )
x = 7 ± 7 , thus
x = 7 + 7 = 14 or x = 7 - 7 = 0
PLEASEEE HELP
Which table represents a linear function
Answers
if f(x) = -x+5 and g(x) = x^2 , what is (g º f)(-1)
Answers
can you show me a picture then maybe i can help you
Which point is the centroid of the triangle?
Question 5 options:
A)
D
B)
G
C)
F
D)
C
Answers
Answer:
The answer is B) G
Step-by-step explanation:
G is at the center of the triangle. It is a centroid because it is where all the medians meet.
Solve the following system of equations.
x-2y = 10
y = -6x +34
I have 9 more questions so please answer all
I have 9 more please answer all
Answers
Answer:
x = 6, y = -2
Step-by-step explanation:
x-2y = 10
y = -6x +34
Substitute the second equation into the first for y
x - 2(-6x+34) = 10
Distribute
x +12x - 68 = 10
Combine like terms
13x -68 = 10
Add 68 to each side
13x - 68+68 = 10+68
13x = 78
Divide each side by 13
13x/13 = 78/13
x = 6
Now find y
y = -6x+34
y = -6(6)+34
y = -36+34
=-2
Answer:
x = 6 y = -2
Step-by-step explanation:
x-2y = 10
x = 10 + 2y
y = -6x +34
y = -6(10 + 2y) + 34
y = -60 - 12y + 34
13y = -26
y = -2
x = 10 + 2(-2)
x = 10 - 4
x = 6
Find f (8) when f (x)=-26/x+7
Answers
Answer:
Step-by-step explanation:
f(x) = 26/x + 7
[tex]f(8)=\frac{-26}{8}+7\\\\=-3.25+7\\\\=3.75[/tex]
The length of a rectangle is 5 cm longer than its width.
If the perimeter of the rectangle is 30 cm, find its area.
Answers
Equation To write :2 {x+ ( x+5) }=30
Let's solve your equation step-by-step.
2(x+x+5)=30
Step 1: Simplify both sides of the equation.
2(x+x+5)=30
(2)(x)+(2)(x)+(2)(5)=30(Distribute)
2x+2x+10=30
(2x+2x)+(10)=30(Combine Like Terms)
4x+10=30
4x+10=30
Step 2: Subtract 10 from both sides.
4x+10−10=30−10
4x=20
Step 3: Divide both sides by 4.
4x
4
=
20
4
x=5
So... x+5=10.
Area =5x10=50 cm squared.
Answer:
5
Step-by-step explanation:
Okay, so P = perimeter, and the problem says P = 30
Let's call x the width, and y is the length.
In the perimeter formula, 2X + 2Y = P
so 2X + 2Y = 30
The problem also tells us that that x = y+5, so now let's do some substituting and replace X with Y+5
2(y+5) + 2Y = 30
2y+10 +2Y = 30
4y+10=30
-10. -10
4y=20
Y=5
TRIED MY BEST PRETTY SURE ITS RIGHT
someone please help me haha
Answers
Step-by-step explanation:
6(2x^2 - x - 28)
6(2x + 7)(x - 4)
What is the area of the triangle shown below?
Answers
Answer:
65
Step-by-step explanation:
In order to find the area you have to complete a formula for triangles going Area = 1/2 bh ( bh means base time the height height is the 13 and the base is the 10 in the photo.)
This is urgent, please answer!
A cake has two layers as shown. Each layer is in the shape of a cube.
The bottom of the cake and the area where the two cakes meet are not frosted. How much of the cake is frosted?
Answers
Answer:
I believe it is 65 inches.
Step-by-step explanation:
If you add all the surfaces up besides the sides that are not frosted then it is 65 inches.
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 30 m
hl
What is the volume of the sphere?
10 m
20 m
30
Answers
Answer:
The volume of the sphere is 20 m
Step-by-step explanation:
Given
Solid Shapes: Cylinder and Sphere
Volume of the cylinder [tex]= 30m^3[/tex]
Required
Volume of the sphere
First, we need to calculate the radius of the cylinder
The formula goes thus
[tex]V = \pi r^2h[/tex]
By substituting 30 for V, we have
[tex]30 = \pi r^2h[/tex]
Divide through by h
[tex]\frac{30}{h} = \frac{\pi r^2h}{h}[/tex]
[tex]\frac{30}{h} = \pi r^2[/tex]
Calculating the volume of the sphere
The formula goes thus
[tex]V = \frac{4}{3}\pi r^3[/tex]
Expand Expression
[tex]V = \frac{4}{3} * \pi r^2 * r[/tex]
Substitute [tex]\frac{30}{h} = \pi r^2[/tex]
[tex]V = \frac{4}{3} * \frac{30}{h} * r[/tex]
Simplify Expression
[tex]V = \frac{4}{1} * \frac{10}{h} * r[/tex]
[tex]V = \frac{40}{h} * r[/tex]
Given that the height of the cylinder and the sphere are equal
This means that the height of the cylinder equals the diameter of the sphere.
Mathematically; This is represented by
h = D
Where D represents diameter of the sphere
Recall that D = 2r (2 * radius)
Substitute 2r for D
h = 2r
Substitute h = 2r in [tex]V = \frac{40}{h} * r[/tex]; This gives
[tex]V = \frac{40}{2r} * r[/tex]
[tex]V = \frac{40r}{2r}[/tex]
[tex]V = 20[/tex]
Hence, the volume of the sphere is 20 m
A friend bought 2 boxes of pencils and 8 notebooks for school, and it cost him $11. He went back to the store the same day to buy supplies for his younger brother. He spent $11.25 on 3 boxes of pencils and 5 notenooks. How much would 9 notebooks cost?
Answers
Answer:
9 notebooks would cost $6.75
Step-by-step explanation:
How I solved this problem was by taking the data and writing it out first.
During one trip, he got 2 boxes of pencils and 8 notebooks for $11.00
During the second trip, he got 3 boxes of pencils and 5 notebooks for $11.25
This led me to believe that the boxes were definitely more expensive than the notebooks, as there were many notebooks bought during the first trip, yet that trip was cheaper than the second. So, by the process of elimination, I started off the value of the notebooks to be $0.50, and the boxes of pencils to be $3.00, and I continued to experiment with values until I found two values that would work in both scenarios, the values being $2.50 for a box of pencils, and $0.75 for a notebook. (I know there's likely an easier way of doing this, but I haven't done a problem like this in a while, and this method works just fine. It's just a bit more time consuming.)
1st Case: 2(2.50) + 8(0.75) = 11
2 times 2.50 equals 5, and 8 times 0.75 equals 6. 5 added to 6 gives you a sum of 11.
2nd Case: 3(2.50) + 5(0.75) = 11.25
3 times 2.50 equals 7.50, and 5 times 0.75 equals 3.75. 7.50 added to 3.75 gives you a sum of 11.25
Now that it is known how much each notebook costs ($0.75), you would take that value and multiply it by 9, since you're wanting to know how many 9 would cost, and this gives you a product of $6.75.
I hope this helps :)
Answer:
it would cost £6.75
Step-by-step explanation:
Which statement about the credibility of this source is most accurate ? A.
Answers
Answer:
C. The source is credible because it contains facts and information that are accurate.
Step-by-step explanation:
The statistics(60%) used provide facts on the topic that make the source credibleBRAINLIEST AGAIN!! Hurry! <-w->
2.) What is the volume of the sculpture. Use 3.14 for π.
*Volume of the sculpture
= Volume of the cube - Volume of the cylinder
*Volume of the cube = s³ (side x side x side)
*Volume of the cylinder = πr²h (3.14 x radius x radius x height)
Answers
= 803.75
803.75 is the volume of the sculpture
Which of the following does NOT make you credit worthy?
a
Making payments on time
b
Having a savings account
c
Having too much of your income already obligated in credit
d
Having a well-paying job
Answers
Find the least common denominator (LCD) of
3
7
and
5
8
Answers
Answer:
56
Step-by-step explanation:
7 is a prime number
7*8 = 56
The least common denominator is 56
3/7 * 8/8 = 24/56
5/8*7/7 = 35/56
Answer:840
Step-by-step explanation:
Twenty people apply for an open position at an accountant's office. The distribution of ages of the applicants is shown in the box plot.
Distribution of Applicant's Ages
How many of
age in years
the applicants have ages that fall within the box of the box plot?
Please help!!!!
Answers
Answer:
The number of applicants that have ages that fall within the box of the boxplot = 10.
Step-by-step explanation:
box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value.
The boxplot usually consists of a box and a whisker plot.
The whiskers represent data that is less than the first quartile or 25th percentile and data that is more than the third quartile or 75th percentile.
The box of the boxplot is bounded by the first quartile or 25th percentile and the third quartile or 75th percentile.
Hence, the fraction of the distribution that is usually contained in the box of the boxplot is (75 - 25), 50% of the distribution.
The total number of applicants = 20
50% of 20 = 10.
Hence, the number of applicants that have ages that fall within the box of the boxplot = 10
Hope this Helps!!!
A recipe says that 3/4 cup of water is needed to make 1 loaf of bread which measurements represents the number of cups of water needed to make 8 loaves of bread
Answers
Answer:
i think six cups?
Step-by-step explanation:
i took 3/4 and multiplied it by 8 and got 6
Can you help me again pleaseee
Answers
Answer:
Take a picture of the graph too
Step-by-step explanation:
What is 10,000 written as a power with a base of 10? Enter your answer in the box
Answers
The exponent tells you how many times ten is to be multiplied by iteslf to equal the number you wish to write. For example, 100 can be written as 10x10 = 102. 10,000 = 10x10x10x10 = 104.
Answer: 10*10^3 or 10^4
Step-by-step explanation:
2/4 % × 70 = _____
stieliniarb kram lliw (read that backwards. may need to write it down
Answers
Answer:
3.5
Step-by-step explanation:
Select the correct answer.
Solve the equation by completing the square.
x^2 - 18x + ___ = 4 + ___
Answers
Answer:
A!!!!
Step-by-step explanation:
Can someone help me ASAP? I don’t understand some answers because don’t the trees take in carbon to photosynthesize but won’t the deers also release carbon by cellular respiration?
A herd of deers lives in a forest where they eat the leaves of trees. The number of energy storage molecules in the tress and in the deers has increased. What has happened to the amount of carbon in the trees and in the deer?
The amount of carbon in the trees and in the deer . . .
A) has increased.
B) has decreased.
C) has not changed.
D) is not related to the number of energy storage molecules.
Answers
Answer:
a
Step-by-step explanation:
it makes sence for the answer to be a because
Answer:
The amount of carbon in the trees and in the deer . . .
A) has increased.
Explanation:
Carbon is the basis for all living cells, it is responsible for the making and storing of energy. So if the number of energy storage molecules increases, the amount of carbon will increase because carbon is used to make those molecules.
Your question on carbon dioxide and photosynthesis having an effect is valid, but the loss of carbon wouldn't be much compared to the energy storage molecules, so we wouldn't consider that a factor in this case.
PLZ HELP ASAP: What is the Value of X? Photo below, I’ll give you brainlest
Answers
Answer:
5
Step-by-step explanation:
im pretty sure its 5
Answer:
6
Step-by-step explanation:
Use the pythagorean theroem,
h^2=p^2+b^2
p^2=h^2-b^2
p=sqrt (10)^2-(8)^2
p=sqrt 100-64
p=sqrt 36
p=6
Using the image below to answer the question. Using the segment addition postulate find the value of X
Answers
(7x+9)+(3x+4)=143
10x+13=143
10x=130
X=13
The value of x is 13. Therefore, option B is the correct answer.
Given that, EF=7x+9, FG=3x+4 and EG=143.
What is a line segment?A line segment is a part of a line that connects two points which are considered to be its endpoints. It is the distance between two points that can be measured.
Now, EG=EF+FG
⇒143=7x+9+3x+4
⇒10x+13=143
⇒10x=130
⇒x=13
The value of x is 13. Therefore, option B is the correct answer.
To learn more about the line segment visit:
https://brainly.com/question/25727583.
#SPJ2
The circle above has a radius of 12 cm. What is the area of the circle? Use = 3.14
Answers
Answer:
452.39
Step-by-step explanation:
C=[tex]\pi[/tex]r 2
C= 3.14 times 12(2)
Look at the attached picture
Hope it will be helpful to you...
please help me out! i have a few more of these questions, about 3
Answers
Step-by-step explanation:
The y-intercept will be (0, 1). From that point, go 4 units to the right and 1 unit down. That is your next point. Keep doing that and then connect the points to make a line. Hope this helps!
Mia made 5 pies. What fraction represents all of the pies?
5/10, 5/1, 5/5, 1/5
Answers
Answer:
5/5
Step-by-step explanation:
So imagine you have 1 pie, and its fresh out of the oven so its still hole, that makes it 1/1 or ! whole, the same with 5 because the pies are still whole and not eaten its 5/5
i need to know how to do this one!!!!!!!!!!!! its to raise my grade!!!!!!!!!!
Evaluate the radical.
27−−√3
Enter your answer in the box.
Answers
Answer:
27+square root to 3 is 28.73205081
Step-by-step explanation:
Hope I helped
