1. what is ad/ab in simplest form
a. 10/3
b. 1/3
c. 17/5
d. 3

what is slope of be/ slope of ae in simplest form?
a. 4
b. 5/4
c. 25/4
d. 5

3. what is the value of x in the proportion (x-1)/5= (4x+2)/35?
a. 1/3
b. 1/5
c. 1/4
d. 3

4. what is the value of x in the proportion
x+1 = 15

x+3 = 21

5. the lengths of the sides of a triangle are in the extended ratio 3 : 10 : 12. the perimeter is 400 cm. what is the length of the longest side in centimeters? ?
a. 16 cm
b. 192 cm
c. 160 cm
d. 48 cm

This is the concept of algebra: The answers to the questions will be as follows:
1. What is AD/AM in the simplest form:
AD/AB is the ratio of AD to AB. This will calculated as follows:
AD=9 units
AB=3 units
thus:
9/3=3
Hence, we conclude that the answer is D. 3

2] What is slope of BE/ slope of AE in simplest form:
slope=(Δy-axis)/(Δx-axis)
slope of AE
=(5-0)/(4-0)
=5/4
slope BE
slope=(5-0)/(4-3)=5/1=5
therefore the ratio of the two slope will be:
BE/AE
=5/(5/4)
=4
The answer is A.4

3. What is the value of x in the proportion (x-1)/5=(4x+2)/35?
To get the value of x we solve the above proportion:
(x-1)/5=(4x+2)/35
35(x-1)=5(4x+2)
35x-35=20x+10
putting like terms together we get:
35x-20x=10+35
15x=45
dividing both sides by 15
x=45/15
x=3
Hence the answer is B.3

4. What is the value of x in the proportion:
(x+1)/(x+3)=15/21
to get the value of x we solve the above:
first we begin by cross multiplying the proportion, this will give us:
21(x+1)=15(x+3)
21x+21=15x+45
putting like terms together we get:
21x-15x=45-21
6x=24
dividing both sides by 6 we get
x=4
∴ x=4

5. The lengths of the sides of a triangle are in extended ratio 3:10:12. The perimeter is 400 cm. What is the length of the longest side in cm.
solution:
Here we introduce the variable x such that the perimeter is:
3x+10x+12x=400
25x=400
x=400/25
x=16
The longest side will be:
12×16=192 cm

All the ratios for  all the given questions have their answers as;

1) Option D; 3

2) Option A; 4

3) Option D; 3

4) X = 4

5) Option B; 192 cm

From the given graph, we have the following dimensions;

AB = 3

AC = 5

AD = 9

1) We want to find AD/AB;

From the given dimensions;

AD = 9 and AB = 3.

Thus;

AD/AB = 9/3

AD/AB =3

Option D; 3

2) We want to find the slope of BE/slope of AE;

Formula for slope between two points is;

m = (y₂ - y₁)/(x₂ - x₁)

Thus;

Slope of AE;

m_ae = (5-0)/(4-0)

m_ae =5/4

Slope of BE

m_be = (5-0)/(4-3)

m_be = 5/1

m_be = 5

Thus; slope of BE/Slope of AE is;

M_be/m_ae = 5/(⁵/₄)

M_be/m_ae = 4

Option A; 4

3) We want to find the value of x in the proportion (x - 1)/5 = (4x + 2)/35.

We will cross multiply to get;

35(x - 1) = 5(4x + 2)

35x - 35 = 20x + 10

Rearranging to get;

35x - 20x = 10 + 35

15x = 45

divide both sides by 15 to get;

15x/15 = 45/15

x = 3

Option B; 3

4) We want to find the value of x in the proportion:  (x + 1)/(x + 3) = 15/21

We will cross multiply to get;  

21(x + 1) = 15(x + 3)

21x + 21 = 15x + 45

Rearranging to get;

21x - 15x = 45 - 21

6x = 24

divide both sides by 6 to get;

x = 4  

5) We are told that the lengths of the sides of a triangle are in extended ratio 3:10:12 and that the perimeter is 400 cm.

Thus;

This means the original lengths were all divided by a common number. Let us call this number x. Since perimeter is sum of all sides, then;  

3x + 10x + 12x = 400

25x = 400

Divide both sides by 25 to get;

x = 400/25

x = 16

The longest side =  12 × 16

Longest side = 192 cm

Option B; 192 cm

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Step-by-step explanation:

Step 1. 95-8=86 (bought 1 plane kit)

Step 2. Find how many planes he can buy with the remainder of the money

86/8=10.75

Therefore he can only buy 10 planes to donate to the animal shelter as he will won't have enough money to by 11 planes.