The principal is trying to come up with a playground policy to protect students from the risk of getting heatstroke on especially hot and humid days. If that's her goal, at which temperature should students stop being allowed outside for recess?A 80 degrees B 90 degrees C 105 degreesD 130 degrees

Question 13.

Part (a).

Given the solution:

All real numbers

We have the expression:

3(4x + 2) = ________

Let's complete the equation in order to obtain the indicated solution.

For a solution to be all real numbers, the equation must be true.

hence, we have:

After solving we have:

0 = 0

This means the system has infinitely many solutions, therefore, the solution is all real numbers.

ANSWER:

3(4x + 2) = 3(4x + 2)

By definition, the Slope-Intercept Form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

The equation of a line that passes through the Origin has the following form:

Where "m" is the slope of the line.

In this case, you have the first line that passes through the Origin:

You can identify that its slope is:

You also know the second equation, which is written in Slope-Intercept form:

You can identify that:

By definition, the slopes of parallel lines are equal. Then, since:

These lines are parallel.

The answer is: True.

The equation for a hyperbola that opens up and down has the following general form:

Where the foci of the hyperbola are located at (h,k+c) and (h,k-c) with c given by:

And asymptotes with slopes given by a/b and -a/b.

The hyperbola with the equation that we have to find has these two foci:

This means that:

So we get h=3, k=2 and c=√26.

The slope of the asymptotes have to be 5 and -5 which means that:

Using the value of c we have:

So we have two equation for a and b. We can take the first one and multiply b to both sides:

And we use this in the second equation:

We divide both sides by 26:

Which implies that b=1. Then a is equal to:

Now that we have found a, b, h and k we can write the equation of the hyperbola. Then the answer is:

12.5% as a decimal is 0.125.

To convert a percentage in to a decimal, we divide the percentage by 100:

Solution:

Given the equation below

Applying the completing the square method

Where the general form of a quadratic equation is

For the completing square method,

Where

The number that should be added to both sides of the equation to complete the square is

Hence, the number is 9 (option B)

Explanation

To find the displacement in cubic feet, divide the volume value by 1728.

Answer: 0.27 cubic feet

Given:

Let's differentiate the equation.

To differentiate since -8 is constant with resppect to x, the derivative will be:

Where:

derivative of ln(x) with respect to x = 1/x

Thus, we have:

ANSWER:

Given:

Total number of members in a club is 12

Each member pays $12.60 on every month.

Money collected on the second day of the month is $100.80

Answer:

100.8

Step-by-step explanation:

12-4 = 8

the 4 is the people who payes the first day the 8 is the people who payes the second day

12.60 eight times = 12.60•8= 100.8

the eight people each payes 12.60 so that would be 12.60 8 times

SOLUTION:

Winston =

Upon simplification, the number of miles wayne walked was 3

Substituting wayne = 3 into the second equation

Wilfred = 2.5

Since Wilfred and Winston walked the same number of miles,

Winston = 2.5

The first drop menu is Wilfred

The second drop menu is 3

The third drop menu is 2.5

The fourth drop menu is faster than.

Answer:

-1

Step-by-step explanation:

[tex]\frac{\frac{64}{-12+4}}{(6)^2+(-30)+2} \\ \\ =\frac{\frac{64}{-8}}{36-30+2} \\ \\ =\frac{-8}{8} \\ \\ =-1[/tex]

We can add the minutes from 7:20 AM to the next hour (8:00 AM), that is 40 minutes.

Then, from 8:00 AM to 9:00 AM we have 60 more minutes.

Then, from 9:00 AM to 9:49 AM we have 49 additional minutes.

We add all three segments as:

As 60 minutes is 1 hour, 120 minutes is 2 hours. Then, 149 minutes are 2 hours and 29 minutes.

Answer: the time elapsed us 149 minutes (or 2 hours and 29 minutes)

To solve the question, choose values for x to find its corresponding image y. Then, plot the points and connect them.

Step 01: Choosing x = -2.

Substituting x by -2 in the equation:

So, the first point is (-2, 2/9).

Step 02: Choosing x = -1.

Substituting x by -1 in the equation:

So, the second point is (-1, 2/3).

Step 03: Choosing x = 0.

Substituting x by 0 in the equation:

So, the third point is (0, 2).

Step 04: Choosing x = 1.

Substituting x by 1 in the equation:

So, the fourth point is (1, 6).

Step 05: Write the points in a table.

x y (x, y)

-2 2/9 (-2, 2/9)

-1 2/3 (-1, 2/3)

0 2 (0, 2)

1 6 (1, 6)

Step 06: Plot the points and connect them.

The figure below shows the points and the graph.

Done! Your question is solved!

Answer:

A. (6,7)(6,2)(3,7)

Explanation:

From the graph, the coordinates of J, K and L are:

When a point (x,y) is rotated 180° around the origin, we have the transformation rule:

Therefore, the coordinates for Triangle J'K'L' are:

The correct choice is A.

To answer this question, we need to find the unit rate in this case. For this, we need to divide the given liters by the hours. Then, we have:

Then, the dairy produces 4.05 liters per hour.

the amount of money a worker earns is directly proportional to the number of hours worked.at this rate.thag worker makes $104 in an 8 hour shift.weite a direct variation equation that relates the earnings (e) of the worker to the number of hours (n) worked. use the correct lowercase variables given ,and use no spaces​

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form e=kn

In this problem we have

e -----> amount of money a worker earns

n -----> number of hours worked

k is the constant of proportionality

k=e/n

Find the value of k

we have

For n=8 hours, e=$104

sibstitute

k=104/8

k=$13 per hour

The linear equation is

We are asked to describe a situation that could be represented by the equation

Suppose that y is the number of liters of water in a tank.

And x is the number of hours.

Each hour, 30% (0.3) of the water is evaporated from the tank. (subtracted)

So the equation completely models the above scenario.

For example:

What will be the amount of water in the tank after 10 hours?

We have the following sets:

A = {3, 5, 7, 9, 11, 13}

B = {3, 5, 11, 13}

If we look closely, all the elements of B are in A. But each element of A does not belong to B, therefore the statement is totally false.

Answer :x=4

Step-by-step explanation:

x equals a point. If you are in the same exact area but at a different x, you dont know how to get to the area where x is. It is important to note that x does not equal a point, but a location.

In an expression, two or more terms are like terms if they have the same variable and exponents.

For example the terms:

2a and -8a → these terms have the same variable "a" and the same exponent "1"

9y³ and 8x⁴ → these terms have different variables "y" and "x" and different exponents "3" and "4", so they are not like terms.

Constants, for example, -10 or 6, are also considered to be like terms.

The correct option is Yes, which is option A

Why?

The reason is that the probability that marble is removed from the box does not affect the probability that a marble is drawn from the same box. i.e the two events do not affect each other

ANSWER:

Domain: (-∞, ∞)

STEP-BY-STEP EXPLANATION:

We have the following function:

The domain of a function is the set of all possible input values of the function. In this case, it would be the interval of values that x can take.

In this function, x can take any value in real numbers.

Therefore, in that case, it will be:

Solution:

Step 1: Find the equation of the line in the graph.

Two points the line pass through are (0, -4) and (2, -3)

Thus,

The equation of the graph is 2y = x - 8

Step 2:

Solve the two equations simultaneously to detemine the solution to the systems of equations

2y = x - 8 ------------------------equation (1)

y = -x + 2 ----------------------equation (2)

Add both equations to eliminate x

2y + y = x - 8 + (-x) + 2

3y = x -8-x+2

3y = -8 + 2

3y = -6

y = -6/3

y = -2

Substitute y = -2 into equation (2)

y = -x + 2

-2 = -x + 2

-2 -2 = -x

-4 = -x

-x = -4

Divide both sides by -1

x = 4

Hence, the solution to the system of equations is (4, -2)

The correct option is option D

Answer:

[tex]x= \dfrac{\sqrt{2}}{2}, \quad x=-\dfrac{\sqrt{2}}{2},\\\\x=\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x=-\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x= \dfrac{\sqrt{2 + \sqrt{2}}}{2}, \quad x= -\dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]x^2+(4x^3-3x)^2=1[/tex]

Expand and equal the equation to zero:

[tex]\begin{aligned}x^2+(4x^3-3x)^2&=1\\x^2+(4x^3-3x)(4x^3-3x)&=1\\x^2+16x^6-24x^4+9x^2&=1\\16x^6-24x^4+x^2+9x^2-1&=0\\16x^6-24x^4+10x^2-1&=0\end{aligned}[/tex]

Let u = x²:

[tex]\implies 16u^3-24u^2+10u-1=0[/tex]

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a)  is a factor of f(x)

[tex]\textsf{As\;\;$f\left(\dfrac{1}{2}\right)=0$\;\;then\;$\left(u-\dfrac{1}{2}\right)$\;is a factor of $f(u)$}.[/tex]

Therefore:

[tex]\implies \left(u-\dfrac{1}{2}\right)\left(16u^2+bu+2\right)=0[/tex]

Compare the coefficients of u² to find b:

[tex]\implies b-8 = -24[/tex]

[tex]\implies b = -16[/tex]

Therefore:

[tex]\implies \left(u-\dfrac{1}{2}\right)\left(16u^2-16u+2\right)=0[/tex]

Factor out 2:

[tex]\implies 2\left(u-\dfrac{1}{2}\right)\left(8u^2-8u+1\right)=0[/tex]

[tex]\implies \left(u-\dfrac{1}{2}\right)\left(8u^2-8u+1\right)=0[/tex]

Zero Product Property

If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for u.

[tex]\implies u-\dfrac{1}{2}=0 \implies u=\dfrac{1}{2}[/tex]

Use the quadratic formula to solve the quadratic:

[tex]\implies u=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(8)(1)}}{2(8)}[/tex]

[tex]\implies u=\dfrac{8 \pm \sqrt{32}}{16}[/tex]

[tex]\implies u=\dfrac{8 \pm 4\sqrt{2}}{16}[/tex]

[tex]\implies u=\dfrac{2 \pm \sqrt{2}}{4}[/tex]

Therefore:

[tex]u=\dfrac{1}{2}, \quad u=\dfrac{2 - \sqrt{2}}{4}, \quad u=\dfrac{2 + \sqrt{2}}{4}[/tex]

Substitute back u = x²:

[tex]x^2=\dfrac{1}{2}, \quad x^2=\dfrac{2 - \sqrt{2}}{4}, \quad x^2=\dfrac{2 + \sqrt{2}}{4}[/tex]

Solve each case for x:

[tex]\implies x^2=\dfrac{1}{2}[/tex]

[tex]\implies x=\pm \sqrt{\dfrac{1}{2}}[/tex]

[tex]\implies x=\pm \dfrac{\sqrt{2}}{2}[/tex]

[tex]\implies x^2=\dfrac{2 - \sqrt{2}}{4}[/tex]

[tex]\implies x=\pm \sqrt{\dfrac{2 - \sqrt{2}}{4}}[/tex]

[tex]\implies x=\pm \dfrac{\sqrt{2 - \sqrt{2}}}{2}[/tex]

[tex]\implies x^2=\dfrac{2 + \sqrt{2}}{4}[/tex]

[tex]\implies x=\pm \sqrt{\dfrac{2 + \sqrt{2}}{4}}[/tex]

[tex]\implies x=\pm \dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]

Solutions

[tex]x= \dfrac{\sqrt{2}}{2}, \quad x=-\dfrac{\sqrt{2}}{2},\\\\x=\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x=-\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x= \dfrac{\sqrt{2 + \sqrt{2}}}{2}, \quad x= -\dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]

Answer:

Interior angle = 81°; exterior angle = 99°.

Step-by-step explanation:

For triangle XYZ:

Angle X and its exterior angle form a straight line.

Angles on a straight line sum to 180°.

Therefore:

⇒ (4g + 13)° + (3g + 48)° = 180°

⇒ 4g + 13 + 3g + 48 = 180

⇒ 7g + 61 = 180

⇒ 7g + 61 - 61 = 180 - 61

⇒ 7g = 119

⇒ 7g ÷ 7 = 119 ÷ 7

⇒ g = 17

To find the measure of ∠X and its exterior angle, substitute the found value of g into the angle expressions:

⇒ m∠X = (4(17) + 13)°

⇒ m∠X = (68 + 13)°

⇒ m∠X = 81°

⇒ exterior angle to ∠X = (3(17) + 48)°

⇒ exterior angle to ∠X = (51 + 48)°

⇒ exterior angle to ∠X = 99°

Therefore:

Answer: C

Step-by-step explanation: did the practice test!

We know that the calculator price (x) was 25 more than 3 times the price of the textbook (y).

This can be represented as:

We also know that the sum of the prices of the two items is equal to $165:

We have to solve this system of equations with the method of substitution.

We can use the first equation, as we have already clear the value of x, to substitute x in the second equation and then solve for y:

With the value of y we can calculate x using the first equation:

Answer: the solution as ordered pair is (x,y) = (130, 35)

1)

then the solution is

Answer

The statement istrue.

Natural numbers are also whole numbers.

Explanation

Natural numbers are counting numbers.

They are the numbers that are numerically used to count things.

Hence, all natural numbers (counting numbers) are whole numbers.

Hope this Helps!!!