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AfilCa [17]
3 years ago
6

10(2^×) + 7(3^×) = 6^× + 70​

Mathematics
1 answer:
Mkey [24]3 years ago
8 0

Answer:

x = 2.81 and 2.096

Step-by-step explanation:

Given the expression

10(2^x) + 7(3^x) = 6^x + 70​

This can also be expressed as;

10(2^x) + 7(3^x) = (2*3)^x + 70

10(2^x) + 7(3^x) = 2^x*3^x + 70

Let a  = 2^x and b = 3^x

10a + 7b = ab + 70

10a + 7b - ab = 70

10a-ab + 7b - 70 = 0

a(10-b)+7(b-10) = 0

a(10-b)-7(10-b) = 0

a-7 = 0 and 10-b = 0

a = 7 and b = 10

Since a = 2^x

7 = 2^x

log 7 = log2^x

log7 = xlog2

x = log7/log2

x = 2.81

Similarly

10 = 3^x

log 10 = log 3^x

log 10 = xlog3

x = log 10/log 3

x = 1/0.4771

x = 2.096

Hence the values of x that satisfies the equation are 2.81 and 2.096

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In triangle ABC, the measure of the exterior angle at point B is 100°. If m∠A is 4 times larger than m∠c, FIND m∠c
Aleksandr [31]

Answer:

m<c = 20º

Step-by-step explanation:

We use these following definitions:

The sum of an interior angle with its exterior is of 180º.

The sum of the three interval angles of a triangle is 180º.

The measure of the exterior angle at point B is 100°.

This means that the measure of the interior angle is: 180 - 100 = 80º

m∠A is 4 times larger than m∠c

This means that the measure of angle c is x, and the measure of angle a is 4x. The other angle, B, is 80º. So

x + 4x + 80 = 180

5x = 100

x = \frac{100}{5}

x = 20

The measure of angle C is 20º.

5 0
3 years ago
(Statistics)
siniylev [52]
A,
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upper stated limit of class123 to 125 = 125

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upper stated limit of class129 to 131 = 131

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5 0
3 years ago
Which algebraic expression is equivalent to the expression below? [x +2 - (5x + 5)]2
kvv77 [185]
<span>[x + 2 - (5x + 5)] ² =
[x + 2 - 5x - 5]² =
[x - 5x + 2 - 5]² =
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Answer:
</span>\boxed{C = 16x^2 + 24x + 9}<span>



</span>
6 0
3 years ago
What is the slope of a line parallel the the line whose equation is x+y=5. Fully reduce your answer.
goldenfox [79]

Answer:

m = -1

Step-by-step explanation:

Find the slope of this line.

x+y=5

y= (-1)x+5

Slope (m) = -1 <-- from y = mx+b

A line parallel to the line will have the slope -1.

7 0
3 years ago
Convert <br>431 base 10 divided by 112base 10 Then u should convert the final answer to base 5​
Rainbow [258]

Answer:

32115

Step-by-step explanation:

Step1

Converting 431 to base 10.

4*102=400

3*101=30

1*100=1

Adding all to get Ans=43110

Step2 converting 43110 to 5

The equation calculation formula for 43110 number to 5 is like this below.

5|431

5|86|1

5|17|1

5|3|2

5|3|3

Ans:32115

5 0
3 years ago
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