Consider this power. (–4) –3 1. Apply the negative exponents rule: 1 (−4)3 2. Expand the exponent: 1 (−4)(−4)(−4) 3.Simplify: What is the value of (–4)–3? Negative StartFraction 1 Over 64 EndFraction Negative StartFraction 1 Over 12 EndFraction StartFraction 1 Over 64 EndFraction StartFraction 1 Over 12 EndFraction

Answer:

5. Rational

6. 4.27 Rational, 0.375 Rational,

0.232342345 Rational, √62 Not rational, 13/1 Rational

Step-by-step explanation:

A rational number is an integer, fraction, terminating decimal, or repeating decimal.

An irrational number  is a number that cannot be expressed as the ratio of two integers.

Hope this helps :)

Answer:

Quadratic coefficient = -14, linear coefficient = 168, constant term = -494

Step-by-step explanation:

Its easiest to first start out with a vertex form equation because it can then be converted to a standard quadratic.

given a vertex at (6,10) , and point of intersection at (7,-4), the equation can be set up like this:

y = a(x-6)^2+10, because we know h and k from the vertex.

We also know y and x from the given point of intersection so a can be solved.

-4 = a(7-6)^2+10

-4 = a + 10

-4-10 = a

a = -14 which is also known as the quadratic coefficient because it is part of a second degree quantity and a Trionomial as a whole(quadratic).

since all the variables are known, you can

expand the equation and set it to standard form

y = -14(x-6)^2+10

y = -14(x^2-12x+36)+10

y = -14x^2+168x-504+10

y = -14x^2+168x-494

For reference, the standard form equation is ax^2+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.

In this instance, -14x^2+168x-494 = ax^2+bx+c

Answer:

f(x) = 3x - 3

Step-by-step explanation:

First, the slope of the line has to be the same for it to be parallel, so the slope(coefficient of x) of the equation is 3.

Next, to make it pass through that specific point, we need to add/subtract a number to make the equation cross that point.

f(x) = 3x at x = 2 evaluates as 6, but the equation needs to pass through the point (2, 3), so we subtract 3 from the equation, leaving us with f(x) = 3x-3.

Answer:

1<x<6

Step-by-step explanation:

subtract 1 from every side: 2<2x<12

divide 2 every side: 1<x<6

Answer:1

Step-by-step explanation:

Answer:

To find : If 21m, 28m and 49m form a right angle or not.

Logic : To find if this triangle is a right angle, we can use the Pythagoras Theorem, which states that the square if the longest side should be equal to the square of the sum of the other two sides.

The name of the longest side is called the hypotenuse, while the others are called legs or one is the perpendicular and the other the base.

Proof : [tex]h^{2} = p^{2} + b^{2}[/tex]

=> [tex]49^{2} = 28^{2} + 21^{2}[/tex]

=> 2401 = 784 + 441

=> 2401 ≠ 1225

Therefore these side lengths cannot be the lengths of a right angled triangle.

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The positive solution would be 4

Answer:

I don't get the question?

Step-by-step explanation:

Answer:

40°

Step-by-step explanation:

Ratio of two supplementary angles = 2 : 7

The angles are 2x , 7x

2x + 7x = 180  {Supplementary}

       9x = 180

         x = 180/9

x = 20

Acute angle = 2x = 2*20 = 40

Answer:

about 22 chocolate pieces

Step-by-step explanation:

total candy - peppermints = chocolate

5/5 - 2/5 = 3/5 chocolates

x/36 = 3/5

cross multiply

x × 5 = 36 × 3

5x = 108

divide both sides by 5

x = 21.6

Answer:

x=24

Step-by-step explanation:

x/4+10=16

x/4=16-10

x/4=6

x=24

Answer:

x=24

Step-by-step explanation:

x/4+10=16

subtract 10 from each side:

x/4=6

multiply by 4 on each side:

x=24

Answer: D

Step-by-step explanation:

For every input there can be only one output. D is the only answer that has one output per input.

Answer:

A. the study had no control group

Answer:

5/

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation: The equation is: 3/8 + 1/4 but these are unlike fractions. Lets make them like fractions.

To make them like fractions you have to find the common denominator.

Common denominator: 8

Like fraction problem: 3/8 + 2/8 =...

5/8!

Answer:

It depends on the equation/coordinates

Step-by-step explanation:

When solving a linear function, you just have to have a straight line in the coordinate plane.

Answer:

1.8z^2

2.6p^5

3.Yes

Step-by-step explanation:

1.You have to use the Quotient Rule and subtract the exponents but sense they do not have the same base number you would divide the bases 24/3=8 and 4-2=2 and leave the variable the same

2.You would multiply 3*2 giving you six and then you would add the exponents together giving you 5 leaving 6p^5 as your final answer

3.When solving an equation like this you have to use The Product Rule meaning exponents with the same base number you would add the exponents which in this case results in 3+7=10 therefore leaving you with a^10

HOPE THIS HELPS!!!

Answer:

449,100 pounds

Step-by-step explanation:

0.2% in decimal form is 0.002

0.002 (percent lost) * 450,000 (weight) = 900 (pounds lost)

450,000 - 900 = 449,100 pounds

Answer:

Slope = 6

Step-by-step explanation:

Reading your description carefully, the equation of line has been given to be

When we compare this with the standard form of a straight line

We immediately see that the slope or gradient m = 6.

Alternatively, when we consider the coordinates of the points mentioned, we have

(1, 5)    ;     (0, -1)     ;     (-1, -7)

We can take any two points out of these three and calculate the slope using the formula

For example, let us consider the points (1, 5) and (-1, -7)

Here x₁ = 1; x₂ = -1 and y₁ = 5; y₂ = -7

Plugging the numbers in the above formula, we have

This agrees with what we calculated directly from the equation of the line!

Hence, slope of the line on the graph = 6

The slope of the line in simplified form is -1

Find the required diagram attached.

The formula for calculating the slope of a line is expressed as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Using the coordinate points (0, -2) and (-2, 0)

Substitute the given coordinates into the formula:

[tex]m=\frac{0-(-2)}{-2-0}\\m=\frac{0+2}{-2}\\m=\frac{-2}{2}\\m=-1[/tex]

Hence the slope of the line in simplified form is -1

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Given:

Consider the two points are B(2,3) and B'(-4,-6).

Center of dilation is the origin.

To find:

The scale factors of this dilation that transformed B into B'.​

Solution:

If a figure dilatated by scale factor k and center of dilation is the origin, then

[tex](x,y)\to (kx,ky)[/tex]

It means, the point after dilation is

[tex](x',y')=(kx,ky)[/tex]

where, k is the scale factor.

[tex]k=\dfrac{x'}{x}[/tex]

x-coordinate of image is -4 and x-coordinate of original point is 2.

[tex]k=\dfrac{-4}{2}[/tex]

[tex]k=-2[/tex]

Therefore, the scale factor is -2. It means, the point and image lie on the opposite sides of center of dilation.

Answer:

The equation is y = 12.5x I believe.

Answer;

The constant of proportionality (known as "speed" in this case) is 12.5 miles per hour.

The equation is

y = 12.5 × t

Explanation:

To find the constant of proportionality, divide one value in each pair by the other. If this relationship is a true direct proportionality , when you repeat these for every pair, your will come up with the same value:

For example

25

miles

÷

2

hours

=

12.5

miles

hour

A direct proportionality will always result in an equation that resembles this:

y = k x where  y and  x are the related quantities and  k is the constant of proportionality. If you draw a graph using the values you have, the graph will show a straight line the passes through the origin. The slope of this line will be the constant of proportionality. And if the values given are real physical quantities, this constant will contain important information about the situation you are studying.

Answer:

the third option: x + 2(2x - 4) = 10

Step-by-step explanation:

the question tells you that y = 2x - 4.

so, instead of writing y in the equation, just replace it with 2x - 4.

x - 2y = 10

becomes

x - 2(2x-4) = 10

Answer:

10 days.

Step-by-step explanation:

Let d represent number of days.

We have been given that ABC Travel offers a plane ticket for $295 and a rental car for $39 per day. The total cost of travelling x days using ABC travel company would be .  

We have been given that M and N Travel offers a plane ticket for $350 and a rental car for $33 per day. The total cost of travelling x days using M and N travel company would be .

To make M and N travel the better deal, we will set an inequality, where total cost of x days using ABC travels is greater than M and N travels as:

Since the closest integer to 9.1677 is 10, therefore, for a vacation of 10 days using M and N travels will be the better deal.

Answer:

1/2

Step-by-step explanation:

Answer:50

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

The y-intercept is the value in the equation without the x and the slope is the value in the equation with the x, it would respond to y = 7.5 - 2

A line's equation is a unified representation of all of the line's points. Any point on a line will satisfy the equation in its general version, which is of the type ax + by + c = 0. The slope of the line and a point on the line are the two essential elements needed to create the equation of a line.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

The y-intercept is the value in the equation without the x and the slope is the value in the equation with the x, it would respond to y = 7.5 - 2

Therefore, the correct answer is option C) y= 7.5x-2.

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