For each pair of numbers, tell: By what percent of the first number is the second number larger? By what percent of the second number is the first number smaller? 100 and 110

Answers

Answer 1

Final answer:

The second number, 110, is 10 percent larger than the first number, 100. Conversely, the first number, 100, is approximately 9.09 percent smaller than the second number, 110.

Explanation:

To find by what percent the second number is larger than the first, we calculate the difference between the two numbers and then divide by the first number, multiplying the result by 100. For the numbers 100 and 110:

Subtract the first number from the second: 110 - 100 = 10.

Divide the difference by the first number: 10 / 100 = 0.10.

Multiply by 100 to find the percentage: 0.10 * 100 = 10 percent.

Now, to find by what percent the first number is smaller than the second number:

Again, find the difference: 110 - 100 = 10.

But this time, divide by the second number: 10 / 110 = ~0.0909.

Multiply by 100 to find the percentage: ~0.0909 * 100 = approximately 9.09 percent.

Therefore, 110 is 10 percent larger than 100, while 100 is approximately 9.09 percent smaller than 110.

Related Questions

The length of a rectangle is 5 times the width. If the perimeter is to be greater than or equal to 108 meters. What are the possible values of the width?

Answers

length = 5(width)
perimeter is 2l + 2w
The perimeter must be ≥ 108 meters
5w + 5w + w + w ≥ 108
12w ≥108
divide both sides by 12
w ≥ 9

The width can be greater than or equal to 9 meters.

Hope this helps

The smallest possible value for the width of the rectangle is 9 meters, given that the perimeter must be greater than or equal to 108 meters and the length is 5 times the width.

The question asks for the possible values of the width of a rectangle where the length is 5 times the width and the perimeter is greater than or equal to 108 meters.

Step-by-step explanation:

Let's call the width of the rectangle w. The length is then 5w. The perimeter P of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.

In this case, P = 2(5w) + 2w = 10w + 2w = 12w. Now, we know that P >= 108, so 12w >= 108.

To find the smallest value for w, we divide both sides by 12: w >= 9. Thus, the width of the rectangle must be at least 9 meters.

Solve the equation using square roots. x2 -9=0

Answers

x^2 - 9 = 0
x^2 = 9
x = 3

3^2 - 9 = 0
9 - 9 = 0
0 = 0

The answer is x = 3

Hope this helps =)

Answer: x = 3, x= - 3

Step-by-step explanation:

x^2 - 9 = 0

=> x^2 = 9

=> x = 3, x= - 3

If it's 10 A.M. Eastern Standard Time in New York City, what time is it in Los Angeles? A. 1:00 P.M. B. 9:00 A.M. C. 7:00 A.M D. 12:00 P.M.

Answers

7:00 am C. Hope this helps!

HEY THERE!!

The answer is C. 7:00 A.M.

~ TRUE BOSS

If two chords are the same distance from the center of a circle, then they are _____________.
a. parallel
b. congruent
c. perpendicular

Answers

Answer: Congruent

Step-by-step explanation:

If two chords are the same distance from the center of a circle, then they are congruent, the correct option is B.

What are congruent triangles?

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes length of line segment AB, and so on for others).

We are given that;

The distance between the chords is same

Now,

According to 1 and 2, if two chords are the same distance from the center of a circle, then they are congruent. This means they have the same length and subtend equal angles at the center.

Therefore, the answer will be congruent.

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A square with one side length represented by an expression is shown below. 6(3x+8)+32+12x. Use the properties of operations to write three different equivalent expressions to represent the lengths of the other three sides of the square. One of your expressions should contain only two terms

Answers

expression 1) 18x+48+32+12x
expression 2) 30x+48+32
expression 3) 30x+80

The length of each side of the square can be represented by the equivalent expressions 30x + 80, 10(3x + 8), and 2(15x) + 2(40), with the first expression being in the simplest form and containing only two terms.

The student is provided with an expression for the side length of a square and is asked to write equivalent expressions representing the lengths of the other three sides. Since all four sides of a square are equal, we simply need to simplify the given expression and use it to represent each side. The given expression is 6(3x+8)+32+12x.

First, we can simplify this by distributing and combining like terms:

6(3x+8) becomes 18x + 48

Adding the 32 gives us 18x + 48 + 32

Finally, add the 12x to get 18x + 12x + 48 + 32

Combining like terms results in 30x + 80.

Now we have our simplified expression, which is 30x + 80, to represent the length of each side of the square. For different but equivalent forms:

As two terms: 30x + 80 (this meets the requirement of containing only two terms)

Factored form: 10(3x + 8)

Expanded form by distributing a common factor: 2(15x) + 2(40)

These are three different equivalent expressions we can use to represent the lengths of each side of the square.

Lionel is planning a one-day outing

Answers

The answer is C. If we want to go on x rides, we need to pay 40+5x dollars at Thrill Park, and 60+3x dollars at Splash Park. The average money needed for each ride is (40+5x)/x at Thrill Park, (60+3x)/x at Splash Park. Therefore, the system of equations is y=(40+5x)/x, and y=(60+3x)/x.

A polygon that has all sides the same measure and all angles the same measure is called what? A. Convex polygon B. Concave polygon C. Irregular polygon D. Regular polygon

Answers

D. Regular polygon.

A polygon that has all sides the same measure and all angles the same measure is called Regular polygon.

Hoped I helped!

caros ran 5.25 miles each day for d days. h ran a total of 157.5 miles. which eqution represents the number of days carlos ran?

Answers

The answer to your question is A.

What are the lower, middle, and upper quartiles of this data? 122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77

Answers

Answer:

The lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.

Step-by-step explanation:

The given data set is

122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77

Arrange the data set in ascending order.

71, 71, 77, 84, 85, 98, 98, 104, 111, 114, 122, 147, 164

Divide the data set in equal parts.

(71, 71, 77, 84, 85, 98), 98, (104, 111, 114, 122, 147, 164)

Now divide each parenthesis in two equal parts.

(71, 71, 77), (84, 85, 98), 98, (104, 111, 114), (122, 147, 164)

Lower quartile is

[tex]Q_1=\frac{77+84}{2}=80.5[/tex]

Middle quartile is

[tex]Median=Q_2=98[/tex]

Upper quartile is

[tex]Q_3=\frac{114+122}{2}=118[/tex]

Therefore, the lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.

Find the two numbers that have a
difference of 3 and a sum of 27.

Answers

12 and 15

15-12=3
15+12=27

The larger one is (27+3)/2 = 15.
The smaller one is 3 less, 12.

The two numbers are 12 and 15.

_____
This is what I call a "sum and difference" problem. You are given the sum of two numbers and the difference between them. Since you see this kind of problem many times and many ways in Algebra courses, it can be worthwhile to remember the solution--or at least, the derivation of the solution.

Let "a" and "b" represent the numbers. Let "s" and "d" represent their sum and difference, respectively. You are given
.. a +b = s
.. a -b = d
Add these two equations.
.. 2a = (s +d)
Divide by 2.
.. a = (s +d)/2 . . . . . . . . . one of the numbers, as computed above

If you subtract the second equation from the first, you get
.. 2b = s -d
.. b = (s -d)/2 . . . . . . . . . the other number

Of course, you also know
.. b = s -a
.. b = a -d
.. a = s -b
.. a = b +d
so that once you have found either of the numbers, you have several ways to find the other one.

(I will give Brainliest/5 stars to correct answer)
Find a ⋅ b.

a = 7i - 4j, b = 4i + 3j

A) <28, -12>
B) 16
C) -40
D) <11, -1>

Answers

a•b = 7*4 +(-4)*3
= 28 -12
= 16 . . . . . matches selection B

To find the dot product you multiply the corresponding coordinates and then add up the products

a dot b = dot product between the vectors 'a' and 'b'
a dot b = 7*4 + (-4)*3
a dot b = 28 - 12
a dot b = 16

Answer: Choice B) 16

Of the four choices given, which two, when written as a system, have a solution of (–4, 5)?

Answers

It's A i just took the test.

Juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x) = 10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container. Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?

Answers

Answer: There is approximately 8.2 amount of radioactive material that will remain after 10 hours.

Step-by-step explanation:

Since we have given that

[tex]f(x)=10(0.98)^x[/tex]

where, f(x) represents the amount of radioactive material that will remain after x hours in the container.

Since we have given that x = 10 hours.

So, our equation becomes,

[tex]f(10)=10\times (0.98)^{10}\\\\f(10)\approx 8.17\\\\f(10)\approx 8.2[/tex]

Hence, there is approximately 8.2 amount of radioactive material that will remain after 10 hours.

Each statement describes a transformation of the graph of y = log2x.
Which statement correctly describes the graph of y = log2(x + 3) - 9?

It is the graph of y = log2x translated 3 units down and 9 units to the left.

It is the graph of y = log2x translated 9 units down and 3 units to the right.

It is the graph of y = log2x translated 9 units down and 3 units to the left.

It is the graph of y = log2x translated 3 units up and 9 units to the left.

Answers

I take it this is in base 2? It really doesn't matter for this question, but I will interpret it that way. The easiest way to do this is with a graphing calculator to see what happened. You can do it on the internet by going to wolframalpha and putting the equations in like this.

y = log_2(x); y = log_2(x + 3) - 9

You will see the picture clearly when you do this. The answer is that it moves 3 units towards the left and 9 units down.

Answer: Third one down.

Comment: Anything you put inside the brackets with an x moves the graph left or right depending on the sign. (x + 3) moves 3 units to the left. (x - 3) moves the graph 3 units to the left.

Anything outside the brackets moves the graph up or down. minus goes down. Plus goes up. The number must be on the right. - 9 goes nine units down.

it's C: It is the graph of y = log2x translated 9 units down and 3 units to the left.

The table below shows the distance d(t) in feet that an object travels in t seconds:

t
(seconds)
d(t)
(feet)
3
126
4
224
5
350
6
504

What is the average rate of change of d(t) between 3 seconds and 5 seconds, and what does it represent?

Answers

Average change of d(t) between 3s and 5s=(d(5)-d(3))/(5-3)=(350-126)/2=224/2=112 ft/t. This represents the average speed of the object between 3s and 5s.

The tennis ball has a radius of 10 cm. Calculate the approximate volume of the tennis ball. Round to the nearest tenth

A. 4,186.7 cubic centimeters

B. 523.3 cubic centimeters

C. 2,356.2 cubic centimeters

D. 658.9 cubic centimeters

Answers

The formula is V = (4/3) pi * r^3
r = 10 cm^3 = 1000 cm^3 That let's out D
V = (4/3) * 3.14 * 1000
V = (1.3333) * 3.14 * 1000
V = 1333 * 3.14
V = 4185 cm^3
A <<<< ==== answer

these are so hard please help me and answer the last 4 I posted

Answers

kai:
6 days = 1 shed
1 day = 1/6 shed

Mark:
8 days = 1 shed
1 day = 1/8 shed

Together:
1 day = 1/6 + 1/8 shed

Ans: 1/6d + 1/8d = 1

The first thing you should know is that the rate of each one is:
Kaitlyn = 1/6
Mark = 1/8
Then,
d = number of days.
The equation then if they work together is:
1 / 6d + 1 / 8d = 1
answer:
the equation for number of days it would take to build the sheld together is
1 / 6d + 1 / 8d = 1

Brandon sights a helicopter above a building that is 200 feet away at an angle of elevation of 30 degrees. To the nearest foot, How high above the ground the is the helicopter

Answers

For this case what you should know is that you should model the problem as a triangle with a right angle.
We then have the following trigonometric relationship:
Tan (30) = y / 200
Clearing the value of and we have:
y = 200 * tan (30)
y = 115.4700538
Nearest foot:
y = 116 feet.
Answer:
the helicopter is 116 feet above the ground

Need Help! I don't get it

Answers

well hmmm let's say you take the car and go in the city for 60 miles with it, well, the car can do 60 miles per gallon, since you just drove it for 60 miles, you only spent 1 gallon of gasoline then.

that only happens if you drive it for 60 miles, what if you drive it for more, let's do a quick table on that,

[tex]\bf \begin{array}{ccll} miles&cost\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 60&3.6(1)\\\\ &3.6\left( \frac{60}{60} \right)\\\\ 120&3.6(2)\\\\ &3.6\left( \frac{120}{60} \right)\\\\ 180&3.6(3)\\\\ &3.6\left( \frac{180}{60} \right) \end{array}[/tex]

and so on, now let's check if you less than 60 miles,

[tex]\bf \begin{array}{ccll} miles&cost\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 40&3.6\left( \frac{40}{60} \right)\\\\ 20&3.6\left( \frac{20}{60} \right)\\\\ 10&3.6\left( \frac{10}{60} \right) \end{array}[/tex]

so, if you divide the amount of miles driven, by 60, when you have driven it for 120 miles, 120/60 is just 2, and the cost is for 2 gallons, or 3.6 * 2, which is 7.2 bucks, for 180 miles is 180/60 or 3 gallons for 3.6 * 3 bucks, and so on.

now, what if you drive it instead for "m" miles?

[tex]\bf \begin{array}{ccll} miles&cost\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ m&3.6\left( \frac{m}{60} \right)\\\\ \end{array}\implies c=3.6\left( \cfrac{m}{60} \right)\implies c=\cfrac{3.6m}{60} \\\\\\ c=\cfrac{3.6}{60}m\implies c=0.06m[/tex]

Find the probability that when a couple has three children, at least one of them is a girl. (Assume that boys and girls are equally likely.)

Answers

Consider this option (2 ways for this):
1. Probability=1-[probability_all_boys].
for [probability_all_boys]=1/[all_possible_combinations];
for [all_combinations]=2³=8. It means that
Probability=1-(1/8)=7/8=0.875.
2. Probability=[needed_cases]\[all_possible_cases];
all possible combinations are:
bbb;ggg;bgg;bgb;bbg;gbg;gbb;ggb; - (where 'g' - girl, 'b' - boy) total 8.
needed cases: ggg;bgg;bgb;bbg;gbg;gbb;ggb, - total 7.
Probability=7/8=0.875

Final answer:

The probability of having at least one girl when a couple has three children can be found by calculating the probability of having all boys and subtracting it from 1.

Explanation:

Probability that at least one child is a girl:

Find the probability of having all boys: (1/2)³ = 1/8

Subtract this from 1 to get the probability of having at least one girl: 1 - 1/8 = 7/8

The base of a triangle is 12 in. The height is 7 in. What is the area of the triangle? A) 19 in2 B) 28 in2 C) 42 in2 D) 84 in2

Answers

The area of triangle formula is 1/2bh.

1/2(12)(7) = 42 in²

Hope this helps :)

Answer:

C. 42

Step-by-step explanation:

A total of 60% of the customers of a fast food chain order a hamburger, french fries, and a drink. if a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?

Answers

This is called a binomial probability experiment.

Let n = 15.

Let p = 0.6

The binomial distribution formula is represented by:

p = (n r) [tex] p^{r} [/tex] [tex] q^{n-r} [/tex]

After plugging p and n into our distribution, we have 0.403. This means that the probability that 10 or more will show that the above three food items were ordered.

The probability that 10 or more will show that the above three food items were ordered is 0.403.

What is Binomial Distribution?

The binomial distribution summarises the number of trials or observations where each trial has the same chance of achieving a specific value. The binomial distribution indicates the likelihood of observing a given number of successful outcomes in a given number of trials.

Given:

n= 15

p= 0.6

q= 1-0.6= 0.4

r= 10

Now, P(10<=x<=15) = 1 - binomcdf (15,0.6,9) = 0.4032

Then, P (x≥0) = [tex]\sum_{x=0}^n[/tex][tex]^{15}C_{10}(0.6)^{10}(0.4)^{10}[/tex]

= [tex]\sum_{x=0}^{15[/tex] 3003 x (0.0060466176) (x 0.0001048576)

= 0.403

Hence, the probability is 0.403.

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The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas?

Answers

10.63

Hope this helped!

What are the coordinates of the vertex of the table? Is it a minimum or a maximum? X Y 0 1 -1 -2 -2 -3

Answers

First, We observe that the function is a parabola that grows
For this case, we must first graph the function to observe the behavior of the same.
We see that the vertex of the function is located at the point:
(x, y) = (- 2, -3)
The point is a minimum.
Answer:
(x, y) = (- 2, -3)
It is a minimum.
See attached image.

a cookie recipe calls for 2/3 cup of sugar if you have three cups of sugar in your pantry how many batches of cookies can you make

Answers

Hello!

2/3 × 3 = 2

You can make 2 batches of cookies.

Write a number with one decimal place,that is bigger than 6 4/5 but smaller than 7 how can I solve this

Answers

Hello!

The easiest way to solve this would be to convert 6 4/5 to a decimal. We know that to convert a fraction to a decimal, we must divide the numerator by the denominator.

4 / 5 = 0.8

0.8 + 6 = 6.8

So, 6 4/5 is 6.8 as a decimal.

See how it's easier now that we've converted the mixed number to a decimal?

There could be many numbers between 6.8 and 7. Some examples are:

6.81, 6.82, 6.83, 6.9, etc.

Which of the following is not a way to represent the solution of the inequality 2(x − 2) less than or equal to 2?

A number line with a closed circle on 3 and shading to the right
A number line with a closed circle on 3 and shading to the left
3 greater than or equal to x
x less than or equal to 3

Answers

The answer is A A number line with a closed circle on 3-

Answer:

The correct option is 1.

Step-by-step explanation:

The given inequality is

[tex]2(x-2)\leq 2[/tex]

Divide both the sides by 2.

[tex]\frac{2(x-2)}{2}\leq \frac{2}{2}[/tex]

[tex](x-2)\leq 1[/tex]

Add 2 on both the sides.

[tex]x-2+2\leq 1+2[/tex]

[tex]x\leq 3[/tex]

The value of x is than or equal to 3. In other words 3 greater than or equal to x.

Since the sign of inequality is ≤, therefore a number line with a closed circle on 3 and shading to the left represent the above inequality.

Only the statement "A number line with a closed circle on 3 and shading to the right" is not is not a way to represent the solution of the given inequality.

Therefore the correct option is 1.

The semicircle shown at left has center X XX and diameter W Z ‾ WZ start overline, W, Z, end overline. The radius X Y ‾ XY start overline, X, Y, end overline of the semicircle has length 2 22. The chord Y Z ‾ YZ start overline, Y, Z, end overline has length 2 22. What is the area of the shaded sector formed by obtuse angle W X Y WXYW, X, Y?

Answers

Triangle XYZ is equilateral, so the central angle of the sector is 120°, or 2π/3 radians. The area of a sector of central angle β is given by
.. A = (1/2)r^2*β . . . . . . β in radians
Your sector's area is
.. A = (1/2)*2^2*(2π/3) = 4π/3 . . . . square units

The area of the shaded region is 4π/3 square units.

We have given that x= center diameter =wz w and z end over line radius=2

Triangle XYZ is equilateral,

What is the central angle of equilateral ?

120 degrees

so the central angle of the sector is 120°,

In radian

=120×[tex]\pi[/tex]/180

=2π/3 radians.

The area of a sector of central angle β is given by,

[tex]A = (1/2)r^2(\beta )[/tex] . . . . . . β in radians

[tex]A = (1/2)*2^2*(2\pi /3)[/tex]

= 4π/3 . . . . square units

Therefore the area of the shaded region is 4π/3 square units.

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if the legs of a right triangle are 8 and 10, find the length of the hypotenuse

Answers

Hello there!

You need to use the Pythagorean theorem.

a² + b² = c²

8² + 10² = c²

64 + 100 = c²

164 = c²

c = √164

c = 2√41

Decimal is 12.8

Thus, the length of the hypotenuse is 12

Let me know if you have any misunderstanding about the answer!

As always, I am here to help!

Hello!

We can use Pythagoras' Theorem to solve this problem. The Pythagorean Theorem:

a² + b² = c², where c is the hypotenuse.

Your two legs measure 8 and 10; substitute them into the theorem:

a² + b² = c²
8² + 10² = c²
64 + 100 = c²
164 = c²
12.81 ≈ c

Answer:
The length of the hypotenuse is approximately 12.81 units.

Can someone please help me with this assignment

Answers

These are 8 questions and 8 answers.

Page 1:

1) Triangle ABC has vertices A(-2,1), B(0,5), and C (8,1). What type of triangle is triangle ABC

Answer: option A. acute triangle.

Explanation:

Determine the lengths of the three sides:

Side AB: √[(0+2)^2 + (5-1)^2 ] = √ [4 + 16] = √(20)

Side BC: √ [ (8-0)^2 + (1 -5)^2 ] = √ [ 64 + 16 ] = √(86)

Side AC: √ [ (8 + 2)^2 + (1 - 1)^2 ] = √100 = 10

Compare the square of the side length of the largest side with the sum of the squares of the other two sides.:

AC^2 = 100
BC^2 = 86
AB^2 = 20

BC^2 + AB^2 = 86 + 20 = 106

100 < 106 => AC^2 < BC^2 + AB^2 =>

all the angles are less than 90°, which means the triangle is actue.

That is becasue when the square of the largest side is equal to the sum of the squares of the smaller sides, there is a right angle and the triangle is a right triangle (Pytaghorean theorem). When the square of the largest side is less than the sum of the squares of the other two sides, the angle is less than 90°, and the triangle is acute.

2) Which set represents the side lengths of a right trianle?

Answer: option C: 9, 12, 15

Explanation:

Check whic set obeys Pythagorean theorem.

15^2 = 225
12^2 = 144
9^2 = 81
.
144 + 81 = 225 => 15^2 = 12^2 + 9^2 => right triangle

3) Which property disproves the statement in the student's notes?

Answer: option B) all angles of a rhombus are not congruent.

Explanation:

A rhombus is a quadrilateral whose four sides all have the same length. It is a quadrilateral.

The angles do not need to be congruent. Only the square, which is only one special case of rhombus, has the four angles congruent, but the masure of the angles of other rhombus are not equal.

4) What is the are of the figure?

Answer: 85 unit^2

Explanation:

1) Area of the rectangle = base * height = 4 * 9 = 36
2) area of the trapezoid = height * half of the sum of the bases = 7 * (3+7)/2 = 35
3) area of the rhombus = half the product of the diagonals = 7 * 4 / 2 = 14

Result: 36 + 35 + 14 = 85

That option is not among the choices. The nearest one is 84 unit^2.

Page 2 is the same page 1.

Page 3:

5) Question 8:

What line can be used to draw the altitude of the triangle FGH

Answer: option D: 3y = 7x + 16

Explanation:

1) All triangles have 3 altitudes (one for each vertex).

2) Now I am going to find the altitude of the vertex H (respect to base FG.

3) First calculate the slope of the segment FG:

slope = [y2 - y1] / [x2 - x1]

x2, y2 are the coordinates of the point G (6, -2) and x1, y1 are the coordinates of the point F (-8,4)

=> slope = [ -2 - 4] / [6 - (-8) ] = [-6] / [14] = - 3/7

4) Now calculate the slope of the perpendicular line (because the altitude is perpendicular to the base).

The lines of perpendicular lines obey the rule: slope line A = - slope line B / 2

So, the slope of the line perpendicular to the base is - [1 / (-3/7) ] = 7/3

5) The equation of the line with slope 3/7 that contains the point H (-4, - 4) is:

y - (-4) 7
--------- = -----
x - (-4) 3

=> 3(y + 4) = 7(x + 4)

=> 3y + 12 = 7x + 28

=> 3y = 7x + 28 - 12

=> 3y = 7x + 16 which is the answer

6) Question 8. How will be the volume affected

Answer: option c. the volume will be 9 times larger.

Explanation:

1) Formula of the volume of rectagular prism

Volume = length * width * height

2) Name, V the volume, l the length, w the width, h the heigth => V = l * w * h

3) Triple the length and the width:

New volume = 3l * 3w * h = 9 l * w * h = 9V

4) You have proved that the new volumen is 9 times the original volume, which is the option c.

7) Question 9

What is the approximate length of the median of the trapezoid ABCD.

Answer: option b. 7.8 units

Explanation:

1) The median of a trapezoid is half the sum of the two parallel segments

2) The two parallel segments are AB and CD

3) The length of the segment AB is:

AB^2 = (3+7)^2 + (7-2)^2 = 10^2 + 5^2 = 100 + 25 = 125

=> AB = √125 ≈ 11.18

4) The length of the sement CD is:

CD^2 = (3 + 1)^2 + (1+1)^2 = 4^2 + 2^2 = 16 + 4 = 20

=> CD = √20 ≈ 4.47

5) The median is [11.48 + 4.47] / 2 ≈ 7.83 => option b.

8) Question 10. Problem

Answer: option B. 34.8 feet

Explanation:

1) Variables:

Ha = 4 ft (heigth of Abigail)
α = 38°
s = 50 ft (length of the string)
Hk = ? (altitude of the kite)

2) formula of sine ratio:

sin α = opposite-leg / adjacent leg

3) solution

sin α = x / s => x = sinα * s = sin(38°) * 50 ft = 30.78 ft

Hk = x + Ha = 30.78 ft + 4 ft = 34.78 ft => aption B. 34.8 feet

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