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
Answer:
Step-by-step explanation:
Given:
Rewrite the function so it is a <u>rational function</u>
Convert the mixed numbers to improper fractions:
Make the denominators the same:
Combine:
The inverse of a function is its <u>reflection in the line y = x</u>
To <u>find the inverse</u>, make x the subject
Replace f(x) with y:
Replace x with and y with x:
If necessary, convert back into the same format as the original function:
The x-intercept of the inverse function is the point at which it crosses the x-axis, so when
Therefore, the x-intercept is:
Answer:
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Step-by-step explanation:
Answer: 5
0 Remainder
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 8 on the left side and the dividend 40 on the right side like this:
8 ⟌ 4 0
Step 2:
The divisor (8) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:
0
8 ⟌ 4 0
Step 3:
Multiply the divisor by the result in the previous step (8 x 0 = 0) and write that answer below the dividend.
0
8 ⟌ 4 0
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.
0
8 ⟌ 4 0
- 0
4
Step 5:
Move down the 2nd digit of the dividend (0) like this:
0
8 ⟌ 4 0
- 0
4 0
Step 6:
The divisor (8) goes into the bottom number (40), 5 time(s). Therefore, put 5 on top:
0 5
8 ⟌ 4 0
- 0
4 0
Step 7:
Multiply the divisor by the result in the previous step (8 x 5 = 40) and write that answer at the bottom:
0 5
8 ⟌ 4 0
- 0
4 0
4 0
Step 8:
Subtract the result in the previous step from the number written above it. (40 - 40 = 0) and write the answer at the bottom.
0 5
8 ⟌ 4 0
- 0
4 0
- 4 0
0
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 40 divided by 8 calculated using Long Division is:
5
0 Remainder
Answer:
10 + .25t
Step-by-step explanation:
The total amount spent is equal to the amount to get in plus the cost of the tickets times the number of tickets
cost = 10 + .25t