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3 years ago

Write using exponent! will give brainliest

Mathematics

2 answers:

S_A_V [24]3 years ago

8 0

Step-by-step explanation:

1/(7^6)*1/1/(7^2)

1/(7^6)*(7^2)/1

(7^2)/(7^6)

7^(2-6)

7^(-4)

1/7^4

katen-ka-za [31]3 years ago

3 0

Answer:

$\frac{7^2}{7^6}$

If you have a negative exponent you must place it in the opposite part of the fraction.

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What is the measure of the arc represented by the numbers 6 and 11 on a clock face?

Marat540 [252]

150; because 6-11 is almost 180, but it’s not quite there, so it’s a little less

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3 years ago

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Can I get some help with proofs? Picture is attached

aleksandr82 [10.1K]

Give a reason for each step of the proof.

Given: <1 and <2 are complimentary

<1 is congruent to <3,

<2 is congruent to <4

Prove: <3 and <4 are complimentary

Statements: Reasons:

1. <1 and <2 are complimentary 1.Given

2. m<1 + m<2=90* 2.DEFINITION OF COMPLEMENTARY ANGLES

3. <1 is congruent to <3, <2 is congruent to <4 3.__GIVEN______

4. m<1=m<3, m<2=m<4 4.DEFINITION OF CONGRUENT ANGLES_

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3 years ago

2b^2+4b–2=0 what is the answer?

s2008m [1.1K]

$2b^2+4b-2=0\\
2(b^2+2b-1)=0\\
2(b^2+2b+1-2)=0\\
2((b+1)^2-2)=0\\
2(b+1)^2-4=0\\\
2(b+1)^2=4\\\
(b+1)^2=2\\
b+1=-\sqrt2 \vee b+1=\sqrt2\\
b=-1-\sqrt2 \vee b=-1+\sqrt2

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3 years ago

Solve for x : log(3x) + log(x + 4) = log(15). Please explain it to me.

zlopas [31]

Answer:

x = 1

Explanation:

$\sf \rightarrow log(3x) + log(x + 4) = log(15)$

Rule: log(a) + log(b) = log(ab)

$\sf \rightarrow log(3x(x + 4)) = log(15)$

cancel out log on both sides

$\sf \rightarrow 3x(x + 4) = 15$

relocate constant variable

$\sf \rightarrow 3x^2 + 12x -15 = 0$

take 3 as a common factor

$\sf \rightarrow 3(x^2 + 4x -5) = 0$

divide both sides by 3

$\sf \rightarrow x^2 + 4x -5 = 0$

middle term split

$\sf \rightarrow x^2 + 5x -x-5 = 0$

factor common terms

$\sf \rightarrow x(x + 5) -1(x+5)= 0$

collect into groups

$\sf \rightarrow (x-1)(x+5)= 0$

set to zero

$\sf \rightarrow x-1 = 0 , \ x+5= 0$

relocate variables

$\sf \rightarrow x = 1, \ x = -5$

There must be a positive solution for log, so the solution is only x = 1

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2 years ago

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F(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, ∞) and g(x) = 2x2 + 8x + 6,

svetlana [45]

Answer:

B) Both functions have the same domain.

C) Both functions have the same x-intercepts.

D) Both functions are decreasing on the interval (−∞, −2).

Step-by-step explanation:

step 1

Find the vertex of f(x)

we know that

The x-coordinate of the vertex is the midpoint of the roots

we have

x=-1 and x=-3

the midpoint is

(-1-3)/2=-2

The y-coordinate of the vertex is -4 (because the range is [−4, ∞))

therefore

The vertex of f(x) is the point (-2,-4)

Is a vertical parabola open upward

The vertex is a minimum

The domain is all real numbers

step 2

we have

$g(x)=2x^2+8x+6$

Find the vertex

Factor the leading coefficient

$g(x)=2(x^2+4x)+6$

Complete the square

$g(x)=2(x^2+4x+4)+6-8$

$g(x)=2(x^2+4x+4)-2$

Rewrite as perfect squares

$g(x)=2(x+2)^2-2$

Is a vertical parabola open upward

The vertex is the point (-2,-2)

The domain is all real numbers

The range is the interval [−2, ∞)

Find the x-intercepts

For g(x)=0

$0=2(x+2)^2-2$

$2(x+2)^2=2$

$(x+2)^2=1\\x+2=\pm1\\x=-2\pm1$

The roots or x-intercepts are

x=-1 and x=-3

Verify each statement

A) Both functions have the same vertex

The statement is false

The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)

B) Both functions have the same domain.

The statement is true

The domain is all real numbers

C) Both functions have the same x-intercepts

The statement is true (see the explanation)

D) Both functions are decreasing on the interval (−∞, −2)

The statement is true

Because the x-coordinate of the vertex is the same in both functions, and both functions open upward

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3 years ago

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