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Answer:

(w-12)(w+12)

Step-by-step explanation:

Using the identity

a^2-b^2=(a-b)(a+b)

now,

w^2-144=(w)^2-(12)^2=(w-12)(w+12)

Pedro went to bed and slept 14 hours, when he woke up next day it was 10 am, it means he went to sleep 14 hours before 10am, it means he went to sleep at 8 pm

The correct value of the equation that's illustrated will be x² + 14x + 55= (x + 7)² + 6

It should be noted that an equation can be used in order to show the relationship between the variables.

It should be noted that (x + 7)² will be:

= (x + 7)(x + 7)

= x² + 7x + 7x + 49

= x² + 14x + 49

Therefore, x² 14x + 55 - (x² + 14x + 49) = 6

In conclusion, the answer in the box is 6.

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1/4 of the distance between points A(2,5) and B(14,9) is given by the formula:

Answer:

3 yards, 2 feet

Step-by-step explanation:

Convert the measurement as indicated. 11 ft=_yd_ft

There are 3 feet in a yard so 3 yards (equal to 9 feet) and a remainder of 2 feet equal 11 feet so:

11 feet = 3 yards, 2 feet

The system of inequatilies that is represented in the graph is:

y ≥ –x² – x + 1

y > 2x² + 3

We can confirm this statement since the first equation implies that the system doesn't include any point bellow the parabola y = -x² - x + 1, and the second equation implies that the system must include only points above the parabola y = 2x² + 3

Answer:

Answer C
This statement is  not true

Step-by-step explanation:

Logarithms result in real values only for positive values of the argument i.e. log(x) results in a real value only for x > 0 So A is correct

Range is set of all real numbers -∞ < x < ∞ So B is correct

D is also correct. At x = 0, log is not defined

Only C is incorrect. If 0 < a < 1 the graph actually shows a downward trend ie logarithmic decline instead of growth

An additional 36 gallons of water will be pumped into the pool past 13 minutes

Constant rate of flow: The definition of a constant rate of flow rate shows how fluid of a certain volume moves through a segment in a specified amount of time. Instead of measuring how quickly a fluid moves from point A to point B, the motion of fluids is examined by figuring out its flow rate. Specifically, how much fluid volume moves from point A to point B in a given amount of time.

Time for which water has been pumped into the pool = 13 minutes

Rate of flow of water = 24 gal/min

So, water pumped in 1.5 minutes = 24*1.5 = 36 gallons

Total water pumped in the pool in 14.5 minutes = 24*14.5 = 348 gallons

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The horizontal and vertical axes are the two axes of the coordinate plane.

The origin is the location where these two axes come together. What is the y-coordinate of C' if ABC is mirrored across the z-axis to produce AA'B'C'?

Answer :

(-3,2)

Detailed explanation:

The right response is C (-3,2). The bold line moving up and down in the middle of the page is the y axis. If you could take up the triangle and turn it on its side, you could. In Point C's landing zone (-3,2).

Point C is situated two spaces to the right of the y-axis, as you can also see. The x axis is still three spaces below it.

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The radius of the volleyball to the nearest tenth of an inch is 8.3

The formula is

= √ 3v/4π

volume(v) = 288

π = 3.142

= √ 3×288/4×3.142

= √ 864/12.6

Next step is to get the square root of 68.6

= √ 68.6

= 8.29

Hence the radius of the volley ball is 8.3 inches

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The simplified expression of (−4x − 15) + (17 + 7x) is - 11x + 2.

The expression can be simplified as follows:

(−4x − 15) + (17 + 7x)

we have to open the brackets of the expression

(−4x − 15) + (17 + 7x)

−4x − 15 + 17 + 7x

Combine like terms

−4x − 15 + 17 + 7x

- 4x + 7x  - 15 + 17

Do the arithmetic of the like terms

- 4x + 7x  - 15 + 17

Therefore,  the simplified expression is as follows:

- 11x + 2

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Answer: 3x+2

Ex:

(-4x-15)+(17+7x)

-4x-15+17+7x Remove unnecessary parentheses

3x-15+17 Add like terms

3x+2

Answer:

20

Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

Choose any two points on the line. For this, I will use (0, 5) and (1, 25):

[tex]\frac{25-5}{1-0}=\frac{20}{1} = 20[/tex]

Answer:   The answer is 18 Girls and 13 Boys. (18 + 13 = 31)

The ratio for girls to boys would 18:13

Step-by-step explanation:  Confirmed correct.

The standard deviation for the number of people with the genetic mutation in such groups is 3.1305.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Let X be the number of people with genetic mutation is a group of 500,

The formula of standard deviation is given as

[tex]SD=\sqrt{n*p(1-p)} \\SD=\sqrt{500*0.02*0.98} \\SD=3.1305[/tex]

The standard deviation of the given sample is 3.1305

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Answer:

7⁷¹

Step-by-step explanation:

Let's do it this way

7⁴^³ × 7⁷

Let's firstly apply indices since the base is the same

7⁴^³+ (⁷)

(4³ = 4×4×4 can be rewrite)

7⁴×⁴×⁴ + ⁷

7⁶⁴+⁷

= 7⁷¹

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Answer:

Raise 7 to the power of 4

Step-by-step explanation:

2401

Answer:

6 4/6

Explanation:

To sum 2 3/6 and 4 1/6, we first need to convert the mixed numbers to fractions as follows

Now, we can add the numbers as

Finally, when we divide 40 by 6, we get 6 as a quotient and 4 as a remainder, so 40/6 is equivalent to

Therefore, the answer is 6 4/6

1) Finding the zeros of this function f(x) =x² +3x -18

f(x) = x²+3x-18 Factoring this equation, and rewriting it

Which two numbers whose sum is equal to 3 and their product is equal to 18?

6 -3 = 3 and 6 *-3 = -18

So we can rewrite as (x +6) (x-3)

(x+6)(x-3)=0 Applying the Zero product rule, to find the roots

x+6=0,

x=-6

x-3=0,

x=3

S={3,-6}

2) Setting a table, plugging in the values of x into the factored form: (x-6)(x-3)

x | y |

1 | -14 (1 +6)(1-3) =-14

2 | -8 (2 +6)(2-3) =-8

3 | 0

4 | 10

-5 | -8

-6 | 0

3) Plotting the function:

Answer: 37.2

Step-by-step explanation:

The circumference of the bike is [tex]0.3\pi \approx 0.3(3.14)=0.942[/tex] m.

Dividing this by the 35 m traveled, we get the bike turned [tex]\frac{35}{0.942} \approx 37.2[/tex]

Answer:

am pretty sure am correct i hope it helps you

So,

We can identify that the function is increasing when it goes up.

In this graph, we can notice that the graph goes up in the intervals:

Answer:

Step-by-step explanation:

We are asked to graph an inequality . y≥2x - 3

The boundary line of our given inequality will be a solid line as we have greater than or equal to ≥ sign.

The boundary line of our given inequality would be .y=2x - 3

Now, we will test point (0,0) to shade in the correct region as:

0≥2(0)-3

0≥0-3

0≥-3

It should look something like this:

Answer:

four is greater than six times a number t in an inequality sentence is 4 › 6 * t

Given

Answer

Let the side of square be s

s = 10 ft

The linear function passing through points (1,7) and (2.5, 1) is given by:

y = -4x + 11.

A linear function, in slope-intercept format, is modeled according to the rule presented below:

y = mx + b

In which the coefficients are described as follows:

For this problem, the two points that form the function are given as follows:

(1,7) and (2.5, 1).

The slope is given by change in y divided by change in x, hence it is given by:

m = (1 - 7)/(2.5 - 1) = -4.

Then:

y = -4x + b.

When x = 1, y = 7, hence we can find the intercept b of the function as follows:

7 = -4(1) + b

b = 7 + 4

b = 11.

Hence the equation is:

y = -4x + 11.

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Answer:

y = - 2x + 12

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 0 ) and (x₂, y₂ ) = (- 1, 14 )

m = [tex]\frac{14-0}{-1-6}[/tex] = [tex]\frac{14}{-7}[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (6, 0 )

0 = - 12 + c ⇒ c = 0 + 12 = 12

y = - 2x + 12 ← equation of line

Answer:

43 for the first one

Step-by-step explanation:

108+29=

43

From the given data-set, we have that:

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

To find the correlation coefficient, we find the same strategy, inserting these points into a calculator of correlation coefficients.

From the data, the points are given as follows:

(3, 7), (4, 8), (5, 10).

Hence the correlation coefficient is of:

r = 0.982.

The line of best-fit is given by:

y = 1.5x + 2.33.

Which has a slope of 1.5 and an intercept of 2.33.

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SOLUTION

We want to find out at which points the lines

intersect.

To do this, we have to solve the equations simultaneously and look for the values of x and y.

This becomes

Dividing both sides by 1.5, we get x, this becomes

To get y, we substitute the x for 8 into equation 1 or 2. Let us use equation 1, we have

1. a)

Given:

Both numbers are positive.

Aim:

We need to find which one of the two numbers is greater than the other.

Explanation:

On a number line, numbers always increase so numbers to the right are greater than numbers to the left.

Mark the given points on the number line and find which number is right of another. numbers to the right are greater than numbers to the left.

For example.

The positive numbers are 17 and 20.

20 to the right are greater than 17 to the left

20 is greater than 17.

1. b)

Given:

Both numbers are negative.

Aim:

We need to find which one of the two numbers is greater than the other.

Explanation:

On a number line, numbers always increase so numbers to the right are greater than numbers to the left.

If both numbers are negative, the number closer to zero is the bigger number.

For example.

The negative numbers are -10 and -5.

-5 is closer to zero.

-5 is greater than -10.

1, c).

Given:

one number is positive and one number is negative

Aim:

We need to find which one of the two numbers is greater than the other.

Explanation:

On a number line, numbers always increase so numbers to the right are greater than numbers to the left.

The positive numbers are always to the right are greater than the negative numbers to the left.

Positive numbers are greater than negative numbers.

For example.

The positive number is 5 and the negative number is -8.

5 is greater than -8.

The correct answer for the limit expression is √2 (π/4)(π - 5).

What is limit?

In mathematics, the value of the limit of a function always approaches as input and finally it approach to some value. It is used for the calculation of the continuity function, derivatives or calculus.

According to the question, the value of the variable 'x' should be substituted in the limit expression.

Now, the required expression will be:

[tex]\lim_{x \to \\pi /4} (secx)(4x^{2} -5x) = sec(\pi/4)(4(\pi /4)^{2} -5(\pi /4))[/tex]

Now, the value of the sec(pi/4) is √2

⇒ √2((π²/4)-5(π/4)) = √2 (π/4)(π - 5)

Hence, the correct answer for the limit expression is √2 (π/4)(π - 5).

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