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BaLLatris [955]
3 years ago
5

Try the numbers 22, 23, 24, 25 in the equation 4/3 = 32/d to test whether any of them is a solution. a. 23 is a solution. c. 24

is a solution. b. 25 is a solution. d. 22 is a solution.
Mathematics
1 answer:
S_A_V [24]3 years ago
4 0

Answer:

c. 24 is a solution

Step-by-step explanation:

Given equation:

\frac{4}{3}=\frac{32}{d}

To test the numbers 22, 23, 24, 25 for the solution.

Solution:

In order to test the given number for the solution, we will plugin each number in the unknown variable d and see if it satisfies the equation.

1) d=22

\frac{4}{3}=\frac{32}{22}

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

\frac{4}{3}=\frac{32\div 2}{22\div 2}

\frac{4}{3}=\frac{16}{11}

The above statement can never be true and hence 22 is not a solution.

2) d=23

\frac{4}{3}=\frac{32}{23}

The fractions can no further be reduced.

The statement can never be true and hence 23 is not a solution.

3) d=24

\frac{4}{3}=\frac{32}{24}

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

\frac{4}{3}=\frac{32\div 8}{24\div 8}

\frac{4}{3}=\frac{4}{3}

The above statement is always true and hence 24 is a solution.

4) d=25

\frac{4}{3}=\frac{32}{25}

The fractions can no further be reduced.

The statement can never be true and hence 25 is not a solution.

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The sides of a right triangle are x, x+21, and x+27. what is the length of the hypotenuse
mina [271]
Answer: 51 uinits

The three numbers are x , x + 21 and x + 27. 
The greatest of the 3 numbers is x + 27, so x + 27 has to be the hypotenuse.

----------------------------------------------
Pythagoras Theorem
----------------------------------------------

a² + b²  = c²

x² + (x+21)² = (x+27)²

x² + x² + 42x + 441 = x² + 54x + 729

x² - 12x -288 = 0

(x - 24)(x + 12) = 0

x = 24 or x = -12 (rejected, length cannot be negative)

----------------------------------------------
Find hypotenuse
----------------------------------------------
 Hypotenuse = x + 27 = 24 + 27 = 51 units

-----------------------------------------------
Answer: 51 units
----------------------------------------------

3 0
3 years ago
Read 2 more answers
When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8 ?
Zanzabum

Answer:

\huge\boxed{f=g(x)\ \text{for}\ x=-\dfrac{16}{3}=-5\dfrac{1}{3}}

Step-by-step explanation:

When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8?

f(x)=g(x)\iff\dfrac{1}{2}x=2x+8\qquad|\text{subtract}\ 2x\ \text{from bpoth sides}\\\\\dfrac{1}{2}x-2x=2x-2x+8\\\\-1\dfrac{1}{2}x=8\qquad|\text{convert the mixed number to the improper fraction}\\\\-\dfrac{2\cdot1+1}{2}x=8\\\\-\dfrac{3}{2}x=8\qquad\text{multiply both sides by}\ -\dfrac{2}{3}\\\\\left(-\dfrac{2\!\!\!\!\diagup}{3\!\!\!\!\diagup}\right)\left(-\dfrac{3\!\!\!\!\diagup}{2\!\!\!\!\diagup}x\right)=\left(-\dfrac{2}{3}\right)\cdot8\\\\x=-\dfrac{2\cdot8}{3}\\\\x=-\dfrac{16}{3}

8 0
3 years ago
The current population of a threatened animal species is 1.2 million, but it is declining with a half-life of 20 years. How many
Allisa [31]
Rate:\frac{1,200,000}{20}
Unit\ Rate:\frac{60,000}{2} = 30,000

25\ Years:750,000
55\ Years:1,650,000

6 0
2 years ago
Please help me i cant get this i. honestly just need someone to give the answers for this lesson
Likurg_2 [28]
Area of the triangle = (1/2)*base* height = (1/2)*3*6 = 9 sm²
We have 4 triangles like this one ,
so area of 4 triangles  = 9*4 = 36 cm².
Area of the square = 3*3 = 9 cm²

Surface area here means area all triangles  + area of the square =36 +9 =
= 45 cm ²

Answer is 45 cm².

7 0
3 years ago
I NEED HELP??? with this math problem?
7nadin3 [17]

Answer:


Step-by-step explanation:

35x + 30 = 22x + 69

<u>-22x  -30    -22x  -30</u>

13x = 39

x=3

6 0
3 years ago
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