Answers
Area of bigger rectangle
A = (x+1)(x+1) = x^2 + 2x + 1
2)
Area of smaller rectangle
A = 5(x - 7) = 5x - 35
3)
The difference:
(x^2 + 2x + 1) - (5x - 35)
= x^2 + 2x + 1 - 5x +35
= x^2 - 3x + 36
area of the shaded region = x^2 - 3x + 36
You first have to find the area of the bigger rectangle
You find this by multiplying the sides
(x + 1)(x + 1) = x^2 + 2x + 1
Next you have to find the area of the smaller rectangle
(x - 7) * 5 = 5x - 35
Subtract the two polynomials
(x^2 + 2x + 1) - (5x - 35) = x^2 - 3x + 36
The answer is [tex] x^{2} -3x + 36[/tex]
Hope this helps!
Related Questions
Morgan uses 1/4 of her supply of raisins to make a trail mix and 3/8 of her supply of raisins to make cookies.If Morgan uses 5 pounds of raisins, how many pounds of raisins are in her supply.
Answers
3/8=37.5%
37.5%+25%=62.5%
62.5%=0.625
5/0.625=8
Morgan has 8 pounds of raisins in her supply.
Select the equations that are equivalent to the equation y – 2 = 3(x + 6). Select all that apply.
y = 3x + 20
y = 3x + 6
2x - y = -3
3x - y = -20
Answers
y = 3x + 20
3x - y = -20
The explanation is shown below:
1. You have the folllowing expression given in the problem above:
y-2=3(x+6)
2. If you solve it for y, you have:
y-2=3x+18
y=3x+18+2
y=3x+20
3. And if you move the variables to the left member, you have:
3x-y=-20
Therefore, as you can see, the correct answer are the options mentioned above.
Which of the following is not an example of like terms? A. 2 and –6 B. 2b and –6b C. 2b and 2 D. 2b^2 and 6b^2
Answers
This is because in order have like terms, they have to have the same properties. One of them (2b) has a variable next to it, while the other does not. This makes them not alike.
Hope this helps! :)
You are looking at two different houses. house #1 would have a daily 5-mile commute to work, while house #2 would have a daily 20-mile commute. how much more co2 would you produce annually if you buy house #2? (hint: driving 1 mile produces 1.1 lb of co2 and you work 240 days/year.)
Answers
5 (miles a day) x 240 (work days a year) = 1,200 miles
total co2 produced = 1.1 x 1200 = 1,320 lbs of CO2 a year
Annual Commute from house 2:
20 (miles a day) x 240 (work days a year) = 4,800 miles
Total CO2 produced = 1.1 x 4800 = 5,280 lbs of CO2 a year
Difference = 5,280 - 1,320 = 3,960 more if you buy house 2.
Answer:
B: 3960 lb
Step-by-step explanation:
vhslearning
Anyone know?
A. 99
B. 100
C. 121
D. Cannot be determined
Answers
Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.
By being congruent, the corresponding angles and sides are equal.
Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].
By using [tex]\angle A = \angle F[/tex]
So, [tex]100^\circ = \angle 1[/tex]
Therefore, the measure of angle 1 is 100 degrees.
So, Option B is the correct answer.
Phil is offered a 3-year contract with a law firm. His first year earnings would be $81,000 with an annual raise of 15%.
What would Phil's total earnings be over the term of the contract?
Enter your answer, rounded to two decimal places, in the box.
Answers
Second year: 1.15($81000) = $93150
Third year: 1.15($93150) = $107122.50
Add these three together to get Phil's total salary over the 3 years of his contract.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%. Phil's total earnings would be over the term of the contract is $281272.5.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%.
First year
= $81000
Second year
1.15 x ($81000)
= $93150
Third year
1.15 x ($93150)
= $107122.50
Phil's total earnings would be over the term of the contract
= $81000 + $93150 + $107122.50
= 281272.5
Learn more about addition here;
https://brainly.com/question/545875
#SPJ2
A circle has a radius of 7.2 feet and a central angle aob that measures 112°. what is the area of sector aob? use 3.14 for pi and round your answer to the nearest tenth.
Answers
A=θ/360πr²
but
θ=112°, r=7.2 ft, π=3.14
hence
A=112/360×3.14×7.2²
A=50.64192 ft²
A~50.6 ft²
Evaluate the expression
A. arctan ( - \sqrt{3} )
B. Arctan ( - \sqrt{3} )
Pls help i need this asap!
Answers
[tex]\tan x=-\sqrt3[/tex]
where [tex]x[/tex] lies in what you might call the "principal branch". That is, [tex]\arctan x[/tex] is bounded below by [tex]-\dfrac\pi2[/tex] and above by [tex]\dfrac\pi2[/tex], so it's only a valid inverse of [tex]\tan x[/tex] if we restrict the domain of [tex]\tan x[/tex] to [tex]-\dfrac\pi2<x<\dfrac\pi2[/tex].
In other words, [tex]x[/tex] is some angle whose terminus lies in either the first or fourth quadrant (I'm assuming you're at least a little familiar with the typical unit circle diagrams used in trig). The only value of [tex]x[/tex] in this domain that satisfies the equation above is [tex]x=-\dfrac\pi3[/tex].
On the other hand, [tex]\mathrm{Arctan}(-\sqrt 3)[/tex] captures all possible values of [tex]x[/tex] that satisfy
[tex]\tan x=-\sqrt3[/tex]
First, we know that [tex]\tan(x+\pi)=\tan x[/tex] (in other words, [tex]\tan[/tex] has a period of [tex]\pi[/tex]), so in fact [tex]\tan(x+2\pi)=\tan(x-2\pi)=\cdots=\tan x[/tex] as well. In general, then, we know that [tex]x+n\pi[/tex] will be a valid solution to the equation above, where [tex]n[/tex] is any integer.
Earlier we found that [tex]\arctan(-\sqrt3)=-\dfrac\pi3[/tex], so in this case, [tex]\mathrm{Arctan}(-\sqrt3)=-\dfrac\pi3+n\pi[/tex] for [tex]n\in\mathbb Z[/tex].
The requried both A and B refer to the same calculation, which is finding the inverse tangent of -√3. The result is -60 degrees or -π/3 radians.
A. The expression "arctan(-√3)" represents the inverse tangent function of the value -√3. The inverse tangent function returns an angle whose tangent is equal to the given value.
To evaluate arctan(-√3), we can use a calculator or reference table that provides trigonometric function values. In this case, the value is approximately -60 degrees or -π/3 radians.
B. The expression "Arctan(-√3)" is the same as "arctan(-√3)" and represents the inverse tangent function of -√3. The uppercase "Arctan" notation is commonly used in mathematical literature and calculators to represent the inverse tangent function.
Learn more about trigonometric functions here:
https://brainly.com/question/1542663
#SPJ6
what is the volume of the cylinder?
radius=7 height=18
A.126
B.252
C.2268
D.882
Answers
Answer:
Option D. [tex]882\pi\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
In this problem we have
[tex]r=7\ units[/tex]
[tex]h=18\ units[/tex]
substitute
[tex]V=\pi (7^{2})(18)=882\pi\ units^{3}[/tex] -----> exact value of the volume
How would I write #3
Answers
PLEASE HELP!!! ASAP!!!!!!!!!!!!!!! 10 POINTS
Expand the number 1800 into its corresponding exponential form.
2^3 · 3^2 · 5^2
9^2 · 100
8 · 9 · 25
2^2 · 3^3 · 5^2
Select expression equal to ^3√320
4
4^3√5
5^3√4
5^3√5
Answers
[tex]\sqrt[3]{320}\\\\320|2\\160|2\\.\ 80|2\\.\ 40|2\\.\ 20|2\\.\ 10|2\\.\ \ 5|5\\.\ \ 1|\\\\320=2\cdot2\cdot2\cdot2\cdot2\cdo2\cdot5=2^3\cdot2^3\cdot5=2^3\cdot2^3\cdot\\\\\sqrt[3]{320}=\sqrt[3]{2^3\cdot2^3\cdot5}=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}\cdot\sqrt[3]{5}=2\cdot2\sqrt[3]{5}=4\sqrt[3]5\\\\Answer:\ \boxed{\sqrt[3]{320}=4\sqrt[3]{5}}[/tex]
They all have factors that can be smaller so
8= 2^3
3=3^2
25= 5^2
So they answer is 2^3 x 3^2 x 5^5
The antarctic peninsula is less than 700 miles from what continent
Answers
Which path is a Hamiltonian circuit?
Answers
The range of y=1x−2+3 is y=0.
true
false
Answers
Find the equation of the line that passes through (-2,5) and is parallel toy= -1/3x+2
Answers
If lines are parallel, then their slopes are equal, so m=-1/3.
So we can write
y=(-1/3)x+b
To find be, we need substitute value's of x and y using point (-2,5).
5=(-1/3)*(-2)+b
5=2/3+b
b= 5-2/3=15/3-2/3=13/3
The equation of the line is
y=(-1/3)x+13/3
In how many ways can 4 blue flags 3 green flags and 2 flags be arranged
Answers
[tex]\text {Number of ways } = \dfrac{9!}{4!3!2!} = 1260[/tex]
--------------------------------
Answer: 1260 ways
--------------------------------
You can calculate the number of ways to arrange the flags using the formula for permutations of multi-sets. We substitute the quantities of each flag color into the formula, which yields our answer of 1260 ways to arrange the flags.
Explanation:The question is asking about permutations of different objects— in this case, flags of multiple colors. For such problem, you can use the formula for permutations of multiset:
P(n1, n2, ..., nk) = (n1 + n2 + ... + nk)! / (n1! * n2! * ... * nk!)
Where n1, n2, ..., nk represent the counts of each distinct item (in this case, flag colors).
For our flags, you would substitute n1=4 (blue flags), n2=3 (green flags), and n3=2 (red flags). Applying the formula gives us (4+3+2)! / (4!*3!*2!) = 9! / (4!*3!*2!) = 1260.
So, "there are 1260 ways to arrange 4 blue flags, 3 green flags and 2 red flags that the student has".
Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ12
The length of a rectangle is 5 yd less than three times the width, and the area of the rectangle is 28 yd2 . find the dimensions of the rectangle.
Answers
The formula for the area of a rectangle is A = lw. Substitute, so then it's 28 = (3x-5) * x, and you evaluate.
Hope this helps you! And rate so I can see if I did well!
The dimensions of the rectangle are width = 4 yds and length = 7 yds.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that the length of a rectangle is 5 yds less than three times the width,
The area of the rectangle is 28 yds square.
Let the width of the rectangle is x
So the length of the rectangle = 3x - 5
The area of a rectangle = x × (3x - 5)
28 = 3x² - 5x
3x² - 5x - 28 = 0
(3x + 7)(x - 4) = 0
3x + 7 = 0 and and x - 4 = 0
x = -7/3 and x = 4
Take x = 4 as the width
So the length of the rectangle = 3(4) - 5 = 12 - 5 = 7
Therefore, the dimensions of the rectangle are width = 4 yds and length = 7 yds.
Learn more about the Area of the rectangle here:
brainly.com/question/20693059
#SPJ5
Tracy can wallpaper 7 rooms in a new house in 21 hours. together with her trainee they can wallpaper the 7 rooms in 12 hours. how long would it take the trainee working by herself to do the job? round to the nearest tenth.
Answers
We have then:
x: time it takes the trainee to do the work alone.
For this case we have the following equation:
7/21 + 7 / x = 7/12
Solving for x we have:
x = 28 hours
Answer:
it would take the trainee working by herself about:
x = 28 hours
On a highway, Nick's car uses 12.5 gallons of gas to travel 240 miles. The gas tank in Nick's car holds 20 gallons of gas. How far can Nick's car travel on a highway using a full tank of gas?
Answers
20 : x
[tex]12.5x = 4800 \\ x = 384[/tex]
Answer : Nick's car can travel 384 miles using a full tank of gas.
Hope this helps. - M
Answer:
Nick's car can travel 384 miles using a full tank of gas.
Step-by-step explanation:
Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 3 + x - 3x2 = 9 A) (x - 1 6 )2 = 71 36 B) (x - 1 3 )2 = 71 36 C) (x - 1 6 )2 = - 71 36 Eliminate D) (x - 1 3 )2 = - 71 36
Answers
3+x-3x^2=9
putting like terms together we have:
-3x^2+x=6
dividing through by -3 we get:
x^2-x/3=-2
but
c=(b/2a)^2
c=(-1/6)^2=1/36
thus the expression will be:
x^2-x/3+1/36=-2+1/36
1/36(6x-1)²=-71/36
the answer is:
1/36(6x-1)²=-71/36
Solve for x in the image below
Answers
Answer : x = 8
Hope this helps. - M
The value of x in the equation given is 8
Using the equations given for our Calculation;
7/8 - 1/x = 3/4Take the L.C.M of 8 and x ; which is 8x
(7x - 8) / 8x = 3/4
Now we cross multiply;
4(7x - 8) = 3 * 8x
open the bracket
28x - 32 = 24x
28x - 24x = 32
4x = 32
x = 8
Hence, the value of x = 8
Learn more on equations: https://brainly.com/question/2972832
#SPJ2
A spherical ball of wax with a radius of 4 inches is melted and poured into a container shaped like a rectangular prism with a 6 inch x 6 inch base. What is the height of the melted wax in the new shape?
Answers
Volume of the spherical ball = 4/3 π (4)³ = 267.95 in³
Area of a rectangular prism = Length x Width x Height
267.95 = 6 x 6 x Height
Height = 267.95 ÷ 36 = 7.44 in
Answer: 7.44 inch
What is the probability that a randomly selected house with 2 bathrooms has 3 bedrooms?
0.2
0.4
0.6
0.8
Answers
there is a total of 30 houses with 2 bathrooms
the probability is 24 /30 = 0.8
[tex] |\Omega|=30\\
|A|=24\\\\
P(A)=\dfrac{24}{30}=\dfrac{4}{5}=0.8 [/tex]
ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)
Answers
Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2)
y - 3x = – 8-----> y=3x-8------> the slope m=3
we know that
if two lines are perpendicular
then
m1*m2=-1
m1=3
so
m2=-1/3
with m=-1/3 and point (3, 2) find the equation of the line
y=mx+b
2=(-1/3)*3+b------> 2=-1+b-----> b=3
the equation of the line is
y=(-1/3)x+3
the answer is
y=(-1/3)x+3
see the attached figure
PLEASE HELP: Question above ☝☝☝
Answers
I'm actually pretty sure it's B
Lines that are not in the same plane are called _____ lines. A.perpendicular B.transversal C.skew D.parallel
Answers
Skew is a line that does not have a same plane.
Hope it helped you.
-Charlie
Thanks!
Lines that are not in the same plane are called skew lines.
What is a line?"A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely."
Given, two lines are not in the same plane.
Here, perpendicular lines, transversal lines, and parallel lines should be in the same plane.
Two lines are called skew lines are two lines if they do not intersect and are not parallel.
Therefore, skew lines are not in the same plane.
Learn more about lines here: https://brainly.com/question/2506929
#SPJ2
Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura. How long would Tammy take to do the job alone?
3 hrs.
4 hrs.
6 hrs.
Answers
Time = x hr/job ; Rate = 1/x job/hr
Jeri DATA
Time = x+2 hr/job ; Rate = 1/(x+2) job/hr
Tammy DATA:
Time = (x+2)/2 hr/job ; Rate = 2/(x+2) job/hr.
Together DATA:
time = 4/3 hr/job ; Rate = 3/4 job/hr
EQUATION:
rate + rate + rate = together rate
1/x + 1/(x+2) + 2/(x+2) = 3/4
Multiply thru by 4x(x+2) to get:
4(x+2) + 4x + 8x = 3x(x+2)
16x + 8 = 3x^2+6x
3x^2-10x-8 = 0
3x^2-12x+2x-8 = 0
3x(x-4)+2(x-4) = 0
(x-4)(3x+2) = 0
Positive answer:
x = 4 hrs. time for Laura to do the job
x+2=6 hrs. time for Jeri to do the job
(x+2)/2 = 3 hrs. time for Tammy to do the job
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura.
The equations are given as,
T + J + L = 1 + 20/60
T + J + L = 1.333 ....1
J = 2T ....2
J = 2 + L ....3
The rate for Laura, Tammy, and Jeri will be given as,
Laura DATA:
Time = x hr/job ; Rate = 1/x job/hr
Jeri DATA:
Time = x+2 hr/job ; Rate = 1/(x+2) job/hr
Tammy DATA:
Time = (x+2)/2 hr/job ; Rate = 2/(x+2) job/hr.
Together DATA:
Time = 4/3 hr/job ; Rate = 3/4 job/hr
The equation is given as,
Rate + Rate + Rate = Together rate
1/x + 1/(x+2) + 2/(x+2) = 3/4
Multiply the equation by 4x(x+2) to get:
4(x+2) + 4x + 8x = 3x(x+2)
16x + 8 = 3x^2+6x
3x^2-10x-8 = 0
3x^2-12x+2x-8 = 0
3x(x-4)+2(x-4) = 0
(x-4)(3x+2) = 0
x = 4, - 2/3
The number of hours that Tammy takes to do the job alone will be 4 hours. Then the correct option is B.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. to avoid confusion between "o" and zero and between "i" and one, the letters "o" and "i" are not used. how many distinct license plates can be formed in this state?
Answers
He altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 89000 square centimeters?
Answers
A = (1/2) * (b) * (h)
Where,
b: base of the triangle
h: height of the triangle
Deriving the area we have:
A '= (1/2) * ((b') * (h) + (b) * (h '))
Clearing b' we have:
b '= (2A' - (b) * (h ')) / (h)
We must look for the value of the base:
A = (1/2) * (b) * (h)
Substituting values:
89000 = (1/2) * (b) * (10000)
b = (89000) / (5000)
b = 17.8 cm
Then, the speed at which the base changes is:
b '= (2 * (3500) - (17.8) * (3000)) / (10000)
b '= -4.64 cm / min
Answer:
The base of the triangle is decreasing at:
4.64 cm / min
The recursive rule for a sequence is shown. an=an−1+7 a1=17 what is the explicit rule for this sequence?
Answers
an=a(n-1)+7; a1=17
to get the explicit formula we proceed as follows:
common difference=7
a1=17
but the explicit formula for arithmetic sequence is:
an=a+(n-1)d
where:
a=fist term
n=number of terms
d=common difference
plugging the values in the formula we get:
an=17+(n-1)7
simplifying we get
an=17+7n-7
an=7n+10
Answer: an=7n+10
The explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
The recursive rule is given as:
[tex]a_n=a_{n-1}+7[/tex]
[tex]a_1 = 17[/tex]
The above shows that the sequence is an arithmetic sequence.
Start by calculating a2
We have:
[tex]a_n=a_{n-1}+7[/tex]
Substitute 2 for n
[tex]a_2=a_1+7[/tex]
This gives
[tex]a_2 = 17 + 7[/tex]
[tex]a_2 = 24[/tex]
So, we have:
a1=17
a2 = 24
The common difference (d) is:
d =a2 - a1
d = 24 - 17
d = 7
The explicit rule is then calculated as:
[tex]a_n = a_1 + (n - 1)d[/tex]
This gives
[tex]a_n = 17 + (n - 1) * 7[/tex]
Expand
[tex]a_n = 17 - 7 + 7n[/tex]
[tex]a_n = 10 + 7n[/tex]
Hence, the explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
Read more about arithmetic sequence at:
https://brainly.com/question/6561461