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2 years ago

4.7.PS-10

Mathematics

1 answer:

denis-greek [22]2 years ago

3 0

Answer:

3x times 24 widgets

Step-by-step explanation:

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For each sentence below, find the value of x that makes each sentence true.

vitfil [10]

ANSWER

1. $x=\frac{1}{2}$

2. $x=1$

QUESTION 1

The first sentence is $(5^{\frac{1}{5}})^5=25^x$ .

Recall that;

$(a^m)^n=a^{mn}$

We simplify the left hand side by applying this property to get;

$5^{\frac{1}{5}\times 5}=25^x$ .

$\Rightarrow 5^{1}=25^x$ .

We now rewrite the right hand side too in an index form to obtain;

$\Rightarrow 5^{1}=5^{2x}$

We now equate the exponents to get;

$\Rightarrow 1=2x$ .

$\Rightarrow \frac{1}{2}=x$

$\Rightarrow x=\frac{1}{2}$ .

QUESTION 2

The second sentence is $(8^{\frac{1}{3}})^2=4^x$

We simplify the left hand side first to get;

$(2^{3\times \frac{1}{3}})^2=4^x$

$2^2=4^x$

We now rewrite the left hand side too in index form to obtain;

$2^2=2^{2x}$

We equate the exponents to get;

$2=2x$

This implies that;

$1=x$

$x=1$

4 0

2 years ago

HELP ASAP BRAINLIEST FOR FIRST CORRECT ANSWER In triangle ABC, m∠A=(5x−10)∘, m∠B=(12x)∘, and the exterior angle at C is (16x)∘.

kirill [66]

Answer:

160

Step-by-step explanation:

5x-10+12x=16x

17x-16x=10

x= 10

exterior angle at C = 16x= 16×10 = 160°

5 0

2 years ago

Read 2 more answers

In a trapezoid, the lower base is 15 cm, the upper base is 7 cm, and each of the two legs is 10 cm. How far must each of the leg

lora16 [44]

Answer:

15 feet apart

Step-by-step explanation:

brainliest?

4 0

2 years ago

Using sigma notation write the geographic series: 6+12+24+48+96

Alika [10]

Answer:

$\sum_{n=1}^{5} 6(2^{n-1})$

Step-by-step explanation:

6 + 12 + 24 + 48 + 96 =

= 6 + 6 * 2 + 6 * 4 + 6 * 8 + 6 * 16

= 6 + 6 * 2^2 + 6 * 2^2 + 6 * 2^3 + 6 * 2 * 4

= 6 * 2^(n - 1)

$\sum_{n=1}^{5} 6(2^{n-1})$

4 0

2 years ago

Solve each equation for the given variable a-2b=-10 for b

Ymorist [56]

A-2b=-10
add 2b on both sides
a=2b-10
add 10 to both sides
a+10=2b
divide both sides by 2
a/2+10/2=a/2+5=b
b=5+a/2

8 0

2 years ago