Use the figure shown to the
right to write a polynomial
that represents the areatof
the shaded region. Express
the polynomial in standard
form, that is, in descending
powers of x.
The polynomial that represents the area of the shaded region is ]
(Simplify your answer. Type your answer in standard form.)
Answers
Answer:
4x + 16
Step-by-step explanation:
The area of the shaded region = area of the outer rectangle - area of the inner rectangle
Area of rectangle = l*w
Area of outer rectangle, where length (l) = (x + 5), and width (w) = (x + 4):
Area = (x + 5)(x + 4)
Expand
x(x + 4) +5(x + 4)
x² + 4x + 5x + 20
area of outer rectangle = x² + 9x + 20
Area of inner rectangle, where length (l) = (x + 4), and width (w) = (x + 1):
Area = (x + 4)(x + 1)
Expand
x(x + 1) +4(x + 1)
x² + x + 4x + 4
Area of inner rectangle = x² + 5x + 4
Area of shaded region = (x² + 9x + 20) - (x² + 5x + 4)
x² + 9x + 20 - x² - 5x - 4
Collect like terms together
x² - x² + 9x - 5x + 20 - 4
4x + 16
Area of the shaded region = 4x + 16
Related Questions
If 3x - 8= -2, find the value of x - 6.
Answers
Answer:
x-6 = -4
Step-by-step explanation:
3x - 8= -2
Add 8 to each side
3x - 8+8= -2+8
3x = 6
Divide by 3
3x/3 = 6/2
x =2
We want to find x-6
2-6 = -4
Answer: - 4
Step-by-step explanation:
3x - 8 = -2
3x = -2 + 8
3x = 6
x = 6/3
x = 2
so, therefore x - 6 => 2 - 6 = -4
Marie goes to the clothing store. Her purchases equal $89.25. The sales tax is 8%. How much tax does she pay?
A $7.14
B $7.86
C S71.40
D S78.60
Answers
Answer: A. $7.14
Step-by-step explanation:
price × percentage of sales tax=amount of tax
89.25 × 8%=$7.14
Hope this helps!! :)
Please let me know if you have any question
The area of a rectangular wall of a barn is 90 square feet. It’s length is 8 feet longer than twice it’s width. Find the length and width of the wall of the barn
Answers
Answer: The answer is that the length is square ft, and the width is .
Step-by-step explanation:
The length and width of the wall of the barn are 18, 9
What is the area of rectangle?The area of rectangle is product of length and width
Given area of rectangle is 90 ft²
given length = 8 ft + 2ₓ width
l = 8 +2 w
area = l × w
90 = (8 +2 w) × w
90= 8w +2w²
2w²+ 8w -90 =0 or w²+4w - 45 =0
On solving w= 9, -5
as width cannot be negative so w= 9
l= 8+2×9
l=26
Thus the length and width of the wall of the barn are 18, 9
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Can someone help me with these word problems?
Answers
500 *.25= 125
500-125= 375
2) (5/8)* 32= 20 girls in class
(3/8)* 32= 12 BOYS in class
4) 19+42+X=87
62+X= 87 (add 19 and 42 together )
X=25 ( subtract 87 from 62)
The following list details the numbers of tickets sold for a talent show grade 9:22; grade 10:32; grade 11: 41; and grade 12:30. What are the
domain and range of this relation?
A domain: (22, 32, 41, 30); range: {9, 10, 11, 12}
B. domain: {9, 22, 10, 32); range: {11, 41, 12, 30}
C. domain: {9, 10, 11, 12); range: (22, 32, 41, 30)
D
domain: {11, 41, 12, 30}; range: {9, 22, 10, 32)
Answers
Answer: C. domain: {9, 10, 11, 12); range: (22, 32, 41, 30)
Step-by-step explanation:
The data set is:
(9, 22)
(10,32)
(11, 41)
(12, 30).
In the usual notation, the number at the left is the input (belons to the domain) and the number in the right is the output (belongs to the range).
Then the domain would be:
{9, 10, 11, 12}
and the range:
{22, 32, 41, 30}
The correct option is C
Find the value of x in the triangle shown below.
Answers
Answer:
55
Step-by-step explanation:
98+27+x=180
Answer:
Step-by-step explanation:
x + 98° + 27° = 180
x + 125° = 180°
x = 55°
A city council consists of 8 members. Of the 3 men on the committee, 1 has a bachelor's degree and the other 2 have master's degrees. Of the 5 women on the committee, 4 have bachelor's degrees and 1 has a master's degree. A member is chosen at random to take notes at a meeting. What is the probability that the committee member has a bachelor's degree?
Answers
Answer:
5/8
Step-by-step explanation:
1 man, 4 women out of 8 people total
Old Mc Donald raises ducks and cows. The animals have a total of 100 heads and 354 feet. How many ducks and how many cows does Old Mc Donald have?
Answers
Answer:
The number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.
Step-by-step explanation:
We are given that Old Mc Donald raises ducks and cows. The animals have a total of 100 heads and 354 feet.
Let the number of ducks Old Mc Donald raises be 'x' and the number of cows Old Mc Donald raises be 'y'.
So, according to the question;
The first condition states that the animals have a total of 100 heads, that means;[tex]x+y=100[/tex]
[tex]x=100-y[/tex] -------------------- [equation 1]
{because one head of a duck and one head of cow}
The second condition states that the animals have a total of 354 feet, that means;[tex]2x+4y=354[/tex]
[tex]x+2y=177[/tex] --------------- [equation 2]
{because there are two feet of a duck and four feet of cow}
Now, putting the value of x in equation 2 we get;
[tex]100-y+2y=177[/tex]
[tex]y=177-100[/tex]
y = 77 cows
Putting this value of y in equation 1 we get;
x = 100 - y
x = 100 - 77 = 23 ducks
Hence, the number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.
The city of Atlanta plans to hold a parade after the Atlanta Falcons win the Super Bowl. They intend to allow fans to watch from the sidewalk on both sides of Peachtree Street. The parade route will be 1 mile long (5,280 feet are in a mile) and the sidewalks are 10 feet deep. If the average person takes up 3 square feet of space, what is the estimate for the number of people who can attend the parade?
Answers
Answer:
17600 people.
Step-by-step explanation:
Given that The parade route will be 1 mile long (5,280 feet are in a mile) and the sidewalks are 10 feet deep.
The area of the parade route will be
5280 × 10 = 52800 ft^2
If the average person takes up 3 square feet of space, then, divide the area by 3. That is,
52800 / 3 = 17600 people.
Therefore, the estimate for the number of people who can attend the parade will be 17600 people.
Help ASAP it’s either
68degrees
110 degrees
136 degrees
or 112 degrees
Answers
Answer:112
Step-by-step explanation: Line SW is 180 degrees since it is a straight line. Subtract angle TBU 18 and angle UBW 50 from line SW 180 to get angle SBU which is 112.
What are the 2-dimensional components of a cylinder
Answers
Answer: 2 circles and a rectangle
Step-by-step explanation:
Rita has 1 3/4 yards of red material, 3 1/3 yards of blue material, and 4 1/2 yards of striped material. Altogether, how much material does Rita have?
Answers
Answer:
9 7/12
Step-by-step explanation:
1 3/4 + 3 1/3 + 4 1/2
1 + 3 + 4 = 8
8 + 3/4 + 1/3 + 1/2
8 + 9/12 + 4/12 + 6/12
8 + 19/12
8+ 1 7/12
9 + 7/12
9 7/12
i need help , what’s the answer ?
Answers
Answer:
D,
Step-by-step explanation:
that's because you only factorise when you have a common factor, ax-3b cannot be factorised because they have nothing in common so it is wrong to use x to factorise it. If you want to be sure that it is not factorisable, try expanding it and you'll see that you will not get the same answer.
Given the formula C= 1/2t(c1-c2), solve for t.
Answers
Answer:
[tex]t=\frac{2C}{c1-c2}[/tex]
Step-by-step explanation:
[tex]C=\frac{1}{2}t(c1-c2)\\2(C)=2(\frac{1}{2}t(c1-c2))\\2C=t(c1-c2)\\\frac{2C}{c1-c2}=\frac{t(c1-c2)}{c1-c2}\\t=\frac{2C}{c1-c2}[/tex]
Answer:
[tex]t=\frac{2C}{c_{1}-c_{2}}[/tex]
Step-by-step explanation:
[tex]C=\frac{1}{2}*t(c_{1}-C_{2})\\\\[/tex]
Multiply both sides by 2,
[tex]2*C=2*\frac{1}{2}*t*(c_{1}-c_{2})\\\\2C=t*(c_{1}-c_{2})\\\\\frac{2C}{(c_{1}-c_{2})}=t\\\\\\t=\frac{2C}{c_{1}-c_{2}}[/tex]
find the angle made by the line joining 5,3 and -1,-3 with the positive direction of x-axis
Answers
Answer:
45°
Step-by-step explanation:
gradient of the line:
Let A (-1,-3) and B (5,3)
tan a = (yB - yA) / (xB - xA) = (3 - -3) / (5 - -1) = 6/6 = 1
--> the angle made by the line and positive direction of x-axis is:
[tex]a = { \tan}^{ - 1} (1) = 45[/tex]
1. Mr. Jones's class collected tissue boxes. The
class brought in a total of 30 boxes. If the tissue
box dimensions are listed below, then how much
space will Mr. Jones need?
4 in
С
3 in
7 in
Answers
Answer:
420 inches of space in all equal length width and height
Step-by-step explanation:
Because 4+3+7 = 14 x 30
it all equals up to 420
Mr. Jones will need 420 inches of space in all equal length, width, and height.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations.
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
We have been given that the tissue box dimensions are 4, 3, and 7
If the class brought in a total of 30 boxes.
So the required space would be : (4+3+7)×30 = 14 × 30
it all equals up to 420.
Hence, he will need 420 inches of space in all equal length, width, and height.
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Multiplying a number by which of the following would result in a smaller number?
O 100
O 101
O 102
10-1
Answers
Answer:
10^(-1)
Step-by-step explanation:
Recall that a value that is multiplied by a number that is between 0 and 1 will result in a number that is smaller than the original number.
the first 3 are all greater than 1, hence will result in a greater value if when multiplied with another number.
The last one is 10^(-1) = 0.1
Anything multiplied by 0.1 will result in a value that is 1/10th of the original value.
Hence this is the answer.
Answer:
10/\-1 is correct
Step-by-step explanation:
Help please functions problem
Answers
Answer:
f(3) = 24
Step-by-step explanation:
substitute X for 3.
F(3) = 3 * (2) ^3
= 24
1=2 to the power x
2 to the power 0=2to the power x
x=0
The line y= -x + 3 best models which of the following scatter plots?
Answers
Answer:
a
Step-by-step explanation:
Since we have a negative slope, that means the correlation for the scatter plot also has to be negative.
Since the only scatter plot that has a negative correlation is graph A, a is our answer.
Chicken eggs can be categorized as large if they weigh at least 2 ounces. Clare weighs 48 large eggs and finds that they have a mean weight of 2.1 ounces and a mean absolute deviation of 0.08 ounces. Interpret 0.08 ounces in this situation.
Answers
Answer: The average difference of weights of all 48 eggs from mean eight is 0.08.
Step-by-step explanation:
The mean absolute deviation of a data interprets the mean distance between each data point and the mean.
When this distance goes larger it means data has greater variability
Given, 48 large eggs have a mean weight of 2.1 ounces and a mean absolute deviation of 0.08 ounces.
It means that the average difference of weights of all 48 eggs from mean eight is 0.08.
S=(n-2).180
(Solve for n)
Answers
Answer:
[tex]n = \frac{S}{180} + 2[/tex]Step-by-step explanation:
S = 180 × ( n - 2)
To solve for n divide both sides by 180°
That's
[tex]n - 2 = \frac{S}{180} [/tex]Add 2 to both sides in order to isolate n
That's
[tex]n + 2 - 2 = \frac{S}{180} + 2[/tex]We have the final answer as
[tex]n = \frac{S}{180} + 2[/tex]Hope this helps you
The table below shows the birth weight and the weight for the first three weeks of a baby whale. Determine the slope and y-intercept of the linear equation that models this data, write the equation and predict the baby whale’s weight at 4 weeks.
Week
Weight (lbs)
0
5000
1
6400
2
7800
3
9200
Student’s Work
Student’s Answer
A. y= 9200x+1400; 10,600 lbs
B. y= 5000x+1400; 21,400 lbs
C. y= 1400x+ 5000; 10,600 lbs
D. y= 5000 +41400; 21,400 lbs
Answers
Answer:
C
Step-by-step explanation:
The slope is 1400. And the y intercept is 5000 because when x=0 y=5000. And if you multiply 1400 by 4 and then add 5000 you get 10,600 lbs for the weight at 4 weeks.
The slope is 1400 and the y-intercept is 5000 of the linear equation which is the correct answer would be option (C) y = 1400x + 5000; 10,600 lbs.
What is the slope of the line?The slope of the line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
We have to determine the slope and y-intercept of the linear equation that models this data,
Week Weight (lbs)
0 5000
1 6400
2 7800
3 9200
Slope = (7800 - 6400)/(2 - 1) = 1400
There is a 1400 slope.
And since y=5000 for x=0, the y-intercept is 5000.
So the equation of a baby whale’s weight at 4 weeks is y = 1400x + 5000
Hence, the correct answer would be option (C)
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Solve for b:
3(b - 4) = -3
Answers
Answer:
b=3
Step-by-step explanation:
it is in the picture
Answer:
b = 3Step-by-step explanation:
=> 3(b - 4) = -3
=> 3b - 12 = -3
=> 3b = -3 + 12
=> 3b = 9
=> b = 9/3
=> b = 3
1.) A boy has $12 saved. He decides to start saving on a regular basis. He figures out that he
can
save $1.50 per day. What is the total amount he will have saved after 1 day? 2 days? 3 days?
17days? X days?
Answers
Answer:
12 + (1.50 multiplied by x)
Step-by-step explanation:
You have 12 dollars as the base. For every x days (x is the amount of how many days) he'd save $1.50. For one day, he'd save 1.50 plus his 12 dollars. Two days, he'd save 12 + (1.50 x x). Three, it'll be 12 + (1.50 x x) and so on.
I hope this helped. :)
I dont understand what this mean or how to solve it.
-(8 - 2)
Answers
Answer:
-6
Step-by-step explanation:
1. Always do the parentheses first. solve 8-2 to get 6.
-(8-2) = -(6) = -6
1. simplify inside parentheses
a) 8 - 2 = 6
2. multiply by whatever is outside the parentheses
a) (-1)(6) = -6
Let me know if you need me to clarify on something!
How do I express 32 kilometeters in miles?
Answers
Answer:
19.84 Miles
give or take
Step-by-step explanation:
1 km is .62 miles
.62 x 32 = 19.84
Answer:
19.88 miles
Step-by-step explanation:
Given h(x) = -2x + 5, solve for a when h(x) = 3.
Answers
Answer:
Step-by-step explanation:
-2x + 5 = 3
-2x = -2
x = 1
Answer as a decimal with four decimal places.
Answers
Answer:
Answer as a fraction. Do not include spaces in your answer.
1st question
-31/15
2nd question
19/40
3rd = Answer as a decimal with four decimal places
0.8333…
4th = fraction
5th =rational
6th =rational
Step-by-step explanation:
edge 2021
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression can be reduced to 0.8333.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be written as shown below,
[tex]2.5 \times 0.\bar3[/tex]
= (25/10) × (1/3)
= 25/30
= 5/6
= 0.8333....
Hence, the given expression can be reduced to 0.8333.
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Perimeter of square = 12 1/2 in
Side length of square=
Answers
3 + root 3 *2 +root 2
Answers
Answer:
6 + 3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
(3 + [tex]\sqrt{3}[/tex] )(2 + [tex]\sqrt{2}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
3(2 + [tex]\sqrt{2}[/tex] ) + [tex]\sqrt{3}[/tex] (2 + [tex]\sqrt{2}[/tex] ) ← distribute both parenthesis
= 6 + 3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex]