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3 years ago

Write 1-2log7x as a single logarithm

Mathematics

1 answer:

slavikrds [6]3 years ago

4 0

Answer:

$log_{7} \frac{7}{x^{2} }$

Step-by-step explanation:

We need to write $1 - 2log_{7}x$ as a single logarithm.

We know that

$log_{7}7 = 1$

Therefore we have:

$log_{7}7 - 2log_{7}x$

→ $log_{7}7 - log_{7}x^{2}$

→ $log_{7} \frac{7}{x^{2} }$

The solution is: $log_{7} \frac{7}{x^{2} }$

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A line with a slope of 2 passes through (3,9). Which choice is an equation of this line?

Veronika [31]

Answer:

The answer to your question is number 3.

Step-by-step explanation:

Data

slope = m = 2

Point = (3, 9)

Process

1.- Write the equation of the line in the form point-slope

y - y1 = m(x - x1)

2.- Identify the values of x1 and y1

x1 = 3 y1 = 9

3.- Substitution

y - 9 = 2(x - 3)

4.- Simplify

y - 9 = 2x - 6

y = 2x - 6 + 9

5.- Result

y = 2x + 3 slope y-intercept form

6 0

3 years ago

ASAPPP!!!! HELP I WILL GIVE 100POINTS AND BRAINLIST Question 9 (Essay Worth 10 points)

Luda [366]

Answer:

Part A)

The x-intercepts are (-1/4, 0) and (4, 0).

Part B)

The vertex is a maximum because the leading coefficient is negative.

The vertex is (1.875, 72.25).

Part C)

We can plot the zeros and the vertex, and connect them with a curve.

Step-by-step explanation:

The function given is:

$f(x)=-16x^2+60x+16$

Part A)

To find the x-intercepts of the function, set the function equal to 0 and solve for x:

$0=-16x^2+60x+16$

We can divide both sides by negative four:

$0=4x^2-15x-4$

Factor:

$0=(4x+1)(x-4)$

Zero Product Property:

$x-4=0\text{ or } 4x+1=0$

Solve for each case:

$\displaystyle x=-\frac{1}{4}\text{ or }x=4$

Hence, our zeros are:

$\displaystyle \left(-\frac{1}{4}, 0\right)\text{ and } \left(4, 0\right)$

Part B)

Note that the leading coefficient of our function is negative.

So, our function will be concave down.

Hence, our vertex will be the maximum.

The vertex is given by:

$\displaystyle \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -16, b = 60, and c = 16.

Find the x-coordinate of the vertex:

$\displaystyle x=-\frac{(60)}{2(-16)}=\frac{15}{8}=1.875$

Substitute this back into the function to find the y-coordinate:

$f(1.875)=-16(1.875)^2+60(1.875)+16=72.25$

Hence, our vertex is:

$(1.875, 72.25)$

Part C)

Since we already determined the zeros and the vertex, we can plot the two zeros and the vertex and draw a curve between the three points.

The graph is shown below. Again, to do this by hand, simply plot the three points and connect them with a parabola. If necessary, we can also find the y-intercept.

7 0

3 years ago

Correct answer gets brainliest what is 17/12 + 11/12

Diano4ka-milaya [45]

Answer:

$\frac{28}{12} = \frac{7}{3}$ (they're the same)

Step-by-step explanation:

$\frac{17}{12} + \frac{11}{12} = \frac{28}{12}$

3 0

3 years ago

Yasmine bought 4 bracelet. Each bracelet cost $ 3

Morgarella [4.7K]

She spent a total of $12

5 0

3 years ago

Solve each of the following equations for the given variable using proper algebraic notation. Show ALL work for full marks.

icang [17]

Answer:

3x=42

Divide 3x to both sides

14=x

56=8x

Divide 8 to both sides

7=6

6x+4=40

subtract 4 to both sides

6x=36

divide 6 to both sides

x=6

58=4x-6

add 6 to both sides

64=4x

divide 4 to both sides

16=x

Step-by-step explanation:

6 0

3 years ago