What is the value of x?

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!

Explanation

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

Answer: 0.27 cubic feet

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)

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

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!!!

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:

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.

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)

12.5% as a decimal is 0.125.

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

We have

In order to convert a fraction to a decimal, we divide the numerator between the denominator.

ANSWER

2/5=40%

0.82=41/50

13/25=0.52

76%=38/50

7/20=0.35

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.

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?

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)

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.

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

1)

then the solution is

It is an identity property

Any number plus zero will give that number

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:

First it is important to remember that, by definition, the result of a subtraction is called "Difference".

In this case you need to subtract 14 from 11. This can operation can be expressed as following:

Notice that , since 14 is greater than 11 and it is also a negative number, the sign of the result (the difference) must be negative too.

Therfefore, keeping the above on mind, you obtain that the difference is the following:

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]

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.

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

Equation of the Line

Let's use the following variables:

x = pounds of sugar

y = pounds of strawberries

Angela spent a total of $19.40 to make strawberry jam, thus:

1.80x + 2.50y = 19.40

The equation of the line represents the relationship between x and y. Any point that solves the problem must lie in the line.

The image shows the graph of a line, but we need to be sure it represents the equation above. A small checkup will be done as follows:

For x = 0, solve for y:

1.80*(0) + 2.50y = 19.40

y = 19.4 / 2.5 = 7.76

This point corresponds to the y-intercept (0, 7.76). It can be correctly found on the graph.

For y = 0, solve for x:

1.80x + 2.50*(0) = 19.40

x = 19.40 / 1.8 = 10.78

This point corresponds to the x-intercept at (10.78, 0). It can also be found on the graph.

Now we are sure the line is the representation of our equation, the only point that lies on that line is B(8, 2).

If we substitute x = 8, y = 2:

1.80*(8) + 2.50*(2) = 19.40

14.4 + 5 = 19.40

19.40 = 19.40

The equation is satisfied, thus, the answer is:

Point B

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.

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.

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:

-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]

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.