Which statement is sufficient evidence that ∆DEF is congruent to ∆ABC?

Kevin is 4 times as old as Daniel and is also 6 years older than Daniel

MAXImum [283]

Answer:

Part a) Daniel's age is 2 years

Part b) Kevin's age is 8 years

Step-by-step explanation:

The question is

Part a) How old is Daniel?

Part b) How old is Kevin?

Let

x ----> Kevin's age

y ----> Daniel's age

we know that

$x=4y$ -----> equation A

$x=y+6$ ----> equation B

Equate equation A and equation B

$4y=y+6$

solve for y

$4y-y=6$

$3y=6$

$y=2$

therefore

Daniel's age is 2 years

Find the value of x

substitute the value of y in any of the two equations

$x=4(2)=8\ years$

$x=2+6=8\ years$

therefore

Kevin's age is 8 years

6 0

3 years ago

Please help with solving this

gizmo_the_mogwai [7]

Answer:

x=-7

Step-by-step explanation:

5x-2x+1=3x-6-x first combine like terms

3x+1=2x-6 combine like terms by subtracting 2x from both sides

x+1=-6 subtract 1 from both sides

x=-7

4 0

3 years ago

P(A)=.50 P(B)=.40, and P(A and B) = .15 what is P(a and B)

seropon [69]

Answer:

0.75

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

1. Given f(x) =1/4 (x – 8), what is the value of f(24)?

goldenfox [79]

Hi there!

»»————-　★　————-««

I believe your answer is:

$f(24)=4$

»»————-　★　————-««

Here’s why:

⸻⸻⸻⸻

$f(x)=\frac{1}{4}(x-8)\\-----------\\\rightarrow f(24)= \frac{1}{4}(24-8)\\\\\rightarrow f(24) = \frac{1}{4}( 16)\\\\\rightarrow\boxed{f(24)=4}$

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

8 0

2 years ago

Read 2 more answers

Need help please help me

ANTONII [103]

Megan:
x to the one third power = $x ^{1/3}$
x to the one twelfth power = $x ^{1/12}$

The quantity of x to the one third power, over x to the one twelfth power is:
 $\frac{x ^{1/3}}{x ^{1/12}}$

Since $\frac{ x^{a} }{ x^{b} } = x ^{a-b}$
then $\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12}$

Now, just subtract exponents:
1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4

$\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12} = x^{1/4}$

Julie:
x times x to the second times x to the fifth = x * x² * x⁵

The thirty second root of the quantity of x times x to the second times x to the fifth is
 $\sqrt[32]{x* x^{2} * x^{5} }$

Since $x^{a}* x^{b}= x^{a+b}$
Then $\sqrt[32]{x* x^{2} * x^{5} }= \sqrt[32]{ x^{1+2+5} } =\sqrt[32]{ x^{8} }$

Since $\sqrt[n]{x^{m}} = x^{m/n} }$
Then $\sqrt[32]{ x^{8} }= x^{8/32} = x^{1/4}$

Since both Megan and Julie got the same result, it can be concluded that their expressions are equivalent.

3 0

3 years ago