Given the figure, find the values of x and z.

Answer: (-9,125)

When you graph this the intersection point is that.

Answer: y= -55, 135

X= -10, -9

Step-by-step explanation:

Here is a picture of my work. With this type of problem there are a multiple ways of finding your x and y values.

For the point 13. we have that the line passes through the points (-1,-2) and (0,1) then the slope is

and the line equation will be:

For the point 14: we have that the line passes through the points (-1,0) and (0,-1) then the sslope is:

and the line equation will be:

For the point 15: the line equation is y=-3 because the y coordinate will be always the same (-3) and the slope of the line will be equal to zero

Answer: t∈[0.6]     0 c≤t≤6 c

Step-by-step explanation:

h=316+48t-16t²

-16t²+48t+316≥28

-16t²+48t+316-28≥28-28

-16t²+48t+288≥0

Divide both parts of the equation by 16 :

-t²+3t+18≥0

Multiply both parts of the equation by -1 (in this case, change the sign of the inequality to the opposite)

-(-1)t²+(-1)3t+(-1)18≤0

t²-3t-18≤0

t²-6t+3t-18≤0

t(x-6)+3(t-6)≤0

(t-6)(t+3)≤0

Find the zeros of the function:

t-6=0

t-6+6=0+6

t=6

t+3=0

t+3-3=0-3

t=-3

⇒  - ∞__+__-3__-__6__+__+∞

⇒ t∈[-3;6]

t≥0

⇒  t∈[0,6]

Answer:

c

Step-by-step explanation:

the number(1) with the place value hundreth has nothing after it so it stays the same

Answer:

I believe the answer would be 717. Correct me if I'm wrong but that is what I believe the answer is.

Step-by-step explanation:

Since the answer is talking about hundredth, you would look at the decimal.

The decimal states that its .51, which means it could not be 716, since the decimal is less than 50, so your answer SHOULD be B). 717

Answer:

where x=0 , y=-3

where x=2 ,y =-3

where x= -2 ,y =5

where x= 4 , y = 5

There are 4 liters of solution are needed for the 10% acid solution.

Unitary method:

Unitary method is the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Given,

In a chemistry class, 8 liters of a 4% acid solution must be mixed with a 10% acid solution to get a 6% acid solution.

Here we need to find how many liters of the 10% acid solution are needed.

First, we have to convert the percentage into decimal,

4% = 4/100 = 0.04

10% = 10/100 = 0.10

6% = 6/100 = 0.06

Let x be the required liter of solution.

So, based in the given details,

We have to write the equation as,

=> 0.04*8 + 0.10x = 0.06(8+x)

=> 0.32 + 0.10x = 0.48 + 0.06x

=> 0.10x - 0.06x = 0.48 - 0.32

=> 0.04x = 0.16

=> x = 0.16/0.04

=> x = 4

x = 4 liters of 10% solution is used.

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Paying a bill amount through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

1. Paying a bill amount through the mail without check is a convenient and secure way of making payments.

2. It allows for payment to be made without having to visit a physical location to do so.

3. It also allows for payment to be made without having to use a credit or debit card.

4. Therefore, an advantage of paying a bill through the mail without check is that it is convenient and secure.

Paying a bill through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

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You have the following expression:

where

c = -7.6

d = -8.2

reaplace the previous values into the given expression, and simplify, as follow:

where it has been taken into account the law of signs.

Then, the anwe

Answer:

4 dollars 50 cents

Step-by-step explanation:

60*0.075=4.50

The missing sides of the triangle are

The length of the sides is solved using sine rule.

This represented by the formula

Sine A / a = Sine B / b = Sine C / c

Solving for angle x

= 180 - 130 - 27 sum of angels in a triangle

= 23

applying the formula for the problem

Sine X / WY = Sine Y / WX

Sine 23 / 8 = Sine 27 / WX

cross multiplying

WX = 8 * Sine 27 / Sine 23

WX = 9.295

WX = 9.3 to the nearest tenth

Sine W / XY = Sine Y / WX

Sine 130 / XY = Sine 27 / 9.3

cross multiplying

XY = 9.3 * Sine 130 / Sine 27

XY = 15.692

WX = 15.7 to the nearest tenth

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Answer:

The equation of the straight line passing through the point ( 3,1 )

                      \(\frac{x}{2} + \frac{y}{-2} = 1\)

Step-by-step explanation:

Step(i):-

The equation of the straight line passing through the point ( 3,1 )

                      \(\frac{x}{a} + \frac{y}{b} = 1\)

                     \(\frac{3}{a} + \frac{1}{b} = 1\)

                    3b + a = ab ...(i)

Given the difference of length is  4

                      a-b = 4

                       b =  a - 4 ...(ii)

Step(ii):-

substitute b=a-4 in equation (i) , we get

                3( a-4 ) + a = a (a-4)

               3a - 12+ a =  - 4 a + a²  

                 a² - 8 a + 12 =0

Find the factors of 'a'

                 a² - 6a -2a +12 =0

                a (a-6) -2(a-6) =0

             a =2 and a=6

                  we know that a-b =4

             put       a = 2

                          2 - b =4

                            b = -2

The equation of the straight line whose intercepts on the axes

                    \(\frac{x}{a} + \frac{y}{b} = 1\)

                   \(\frac{x}{2} + \frac{y}{-2} = 1\)

The equation of the straight line

                      \(\frac{x}{2} + \frac{y}{-2} = 1\)

Verification:-

The equation of the straight line passing through the point (3,1)

                      \(\frac{x}{2} + \frac{y}{-2} = 1\)

Put x =3 and y=1

                  \(\frac{3}{2} + \frac{1}{-2} = 1\\\frac{2}{2} =1\\\)

                 1 = 1

∴  The point (3,1) is satisfies the equation

Answer:

3a² + 6ax + 5a

Explanation:

Given the following function

g(x) = 3x² - 5x

Determine g(x+a)

g(x+a) = 3(x+a)² - 5(x+a)

Expand the result

g(x+a) = 3(x² + 2ax + a²) - (5x - 5a)

g(x+a) = 3x² + 6ax + 3a² - 5x + 5a

Determine g(x + a) - g(x)

g(x + a) - g(x) = 3x² + 6ax + 3a² - 5x + 5a - (3x² - 5x)

g(x + a) - g(x) = 3x² + 6ax + 3a² - 5x + 5a - 3x² + 5x

Collect the like terms

g(x + a) - g(x) = 3x² - 3x² - 5x + 5x + 6ax + 3a² + + 5a

g(x + a) - g(x) = 6ax + 3a² + 5a

g(x + a) - g(x) = 3a² + 6ax + 5a

Hence the required result for the function g(x + a) - g(x) is 3a² + 6ax + 5a

The probability that Sergio's number is larger than the sum of the two numbers chosen by Tina is 0.4

We can calculate the probability by finding the number of favorable outcomes, i.e., the number of ways that Sergio can choose a number that is larger than the sum of the two numbers chosen by Tina, and dividing it by the total number of possible outcomes, which is

5C2 * 10C1 = (5!/(2! * 3!)) * 10

= 100

Tina's sum   Sergio's favorable outcomes  

3           7

4           6

5           5

6           4

7           3

8           2

9           1

For example the sum 5 can be achieved by two ways, that is 1+4 and 2+3. So

Tina's sum   Number of ways to achieve that sum

3           1

4           1

5           2

6           2

7           2

8           1

9           1

The number of favourable outcomes is

= 1*7 + 1*6 + 2*5 + 2*4 + 2*3 + 1*2 +1*1

= 40

So probability is

= 40/ 100

= 0.4

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Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

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Answer:

the measure of its compliment degree would be 146.6!!

Step-by-step explanation:

this is because, when talking about compliment degrees, its stating a 180 degree angle (which is just a straight line)  so if one angle is 33.4 degrees, then you would subtract that from 180 to get ur complimentary degree (146.6)

hope this was useful!!

Answer:

g

Step-by-step explanation:

The sample mean in random samples of size n from a given population can be considered a random variable because it varies from sample to sample. This means that the value of the sample mean will not be the same for every random sample taken from the same population. Therefore, it can be considered a random variable.

A random variable is a variable whose value is determined by chance, or randomness. In the case of the sample mean, its value is determined by the values of the individual data points in the sample. Since these data points can vary from sample to sample, the sample mean can also vary. As a result, it is considered a random variable.

The distribution of the sample mean can also be considered a random variable, since it is also affected by chance. The shape and characteristics of the distribution will depend on the population from which the sample is drawn, as well as the sample size. Therefore, the sample mean and its distribution are both random variables in the context of random sampling.

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The standard error of the mean is 2.63.

The standard error simply means the statistical term that's used to measure the accuracy through which the sample distribution illustrates a population by using the standard deviation.

In this case, the effect of using standing height desks on the energy expended by nine elementary school students was studied.

The standard error will be:

= s /✓n

where

s = standard deviation

n = number of students = 9

= 7.9 / ✓9

= 7.9 / 3

= 2.63

The standard error is 2.63.

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SSS - Side - Side - Side

SAS - Side - Angle - Side

ASA - Angle - Side - Angle

AAS - Angle - Angle - Side

The above theorems can be used to compare two triangles.

SSS, which stands for "side, side, side," represents two triangles having identical angles on each of their three sides. Two triangles are said to be congruent if their third sides coincide with those of another triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle match the two sides and included angle of the other triangle. Any angle that may be made by two particular sides is regarded as an included angle.

A triangle is comparable to another if its two matching angles are congruent, according to the AAA postulate of Euclidean geometry. The AAA postulate is derived from the observation that the total internal angle of a triangle is always equal to 180°.

While in case of ASA the angle - side and another angle of first triangle is equal to the corresponding angle - side - angle of other triangle.

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SSS, SAS, ASA, and AAS are four types of triangle congruence.

SSS (Side-Side-Side) is the congruence of three sides of a triangle. This means that all three sides of the triangle have the same length. To prove SSS congruence, you need to show that the corresponding sides of the two triangles have the same length. This can be done by calculating the length of each side and comparing them.

SAS (Side-Angle-Side) is the congruence of two sides and the included angle of a triangle. This means that the two sides of the triangles must have the same length, and the angles between those two sides must also be the same. To prove SAS congruence, you need to show that the corresponding sides of the two triangles have the same length, and that the angles between those two sides are also the same.

ASA (Angle-Side-Angle) is the congruence of two angles and the included side of a triangle. This means that the two angles of the triangles must have the same measure, and the side between those two angles must also be the same length. To prove ASA congruence, you need to show that the corresponding angles of the two triangles have the same measure and that the side between those two angles is also the same length.

AAS (Angle-Angle-Side) is the congruence of two angles and a non-included side of a triangle. This means that two angles of the triangles must have the same measure, and the side not included between those two angles must also be the same length. To prove AAS congruence, you need to show that the corresponding angles of the two triangles have the same measure, and that the side not included between those two angles is also the same length.

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Answer:

1. ∠YZX = 37°

2. ∠YXZ = 53°

3. XZ = 30 meters

Step-by-step explanation:

1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.

⭐What are the inverses of the trigonometric functions?

To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)

We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use \(tan^-1 (opposite/adjacent) =\)

Substitute the values we are given into the function:

\(tan^-1 (18/24) =\)

Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:

\(= 37\)

∴ ∠YZX = 37°

2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.

⭐ What is the triangle sum theorem?

Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.

\(< YZX + < ZYX + < YXZ = 180\)

\(37 + 90 + YXZ = 180\)

\(127 + YXZ = 180\)

\(< YXZ = 53\)

∴ ∠YXZ = 53°

3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.

⭐ What is the Pythagoras' theorem?

Substitute the values of the side lengths into the formula:

\((XZ)^2 = (XY)^2 + (ZY)^2\)

\((XZ)^2 = 18^2 + 24^2\)

Solve for XZ:

\((XZ)^2 = 324 + 576\)

\((XZ)^2 = 900\)

\(\sqrt{(XZ)^2} = \sqrt{900}\)

\(XZ = 30\)

∴ XZ = 30 meters

9514 1404 393

Answer:

  2√5

Step-by-step explanation:

The side ratios in a 30-60-90 triangle are ...

  1 : √3 : 2

The longest side (x) is 2 times the length of the shortest side (√5), so ...

  x = 2√5

Answer:

\(\displaystyle 2\sqrt{5}\)

Step-by-step explanation:

In a \(\displaystyle \frac{π}{6}-\frac{π}{3}-\frac{π}{2}\:OR\:30°-60°-90°\) triangle, the shorter leg is ALWAYS half of the hypotenuse, and the longer leg is \(\displaystyle x\sqrt{3}.\)

I am joyous to assist you at any time.

Answer:

64 cm

Step-by-step explanation:

take the

cube root of 262144

The portion of the parabola from t=-1 to t=1 can be parametrized as x=2t²-4 and y=t.

A parabola is a symmetrical and U-shaped curve that is defined by a mathematical equation.

In this case, we will use the variable t to represent the y-coordinate and find the corresponding x-coordinate. The equation becomes y=t, and substituting this into the original equation, we get

=> x=2t²-4.

To find the portion of the parabola where -1≤t≤1, we can plot the points (x, y) for various values of t in this range.

when t=-1,

=> x=2(-1)²-4 = 0.

And when

t=1, x=2(1)²-4 = -2.

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Answer:

The second one. (top to bottom)

Step-by-step explanation:

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Thus, the part of the trinomial that's equal to the product of p and q is the constant

term!

B: The Constant Term

Step-by-step explanation:

Answer:

a is correct and b is incorrect

These tasks involve analyzing various aspects of cost-volume-profit relationships, sensitivity to changes, and resource constraints to gain insights into the financial performance and operational efficiency of the company.

1) To prepare a contribution margin income statement, you need to classify the costs as variable or fixed and calculate the contribution margin for each product. Subtracting the total variable costs from the total sales revenue will yield the contribution margin, which can be used to determine the operating profit.

2) The weighted average contribution margin ratio can be calculated by dividing the total contribution margin by the total sales revenue. This ratio indicates the average contribution margin earned per dollar of sales.

3) The break-even point in sales dollars can be determined by dividing the total fixed costs by the contribution margin ratio. It represents the level of sales required to cover all costs and achieve a zero-profit position.

4) To earn an annual profit of $400,000, you would need to add this profit amount to the total fixed costs and divide the sum by the contribution margin ratio to find the required sales dollars.

5) By increasing or decreasing the plane sales price by 10 percent while keeping the total sales units constant, you can calculate the impact on the operating profit by multiplying the change in sales price by the total sales units and the contribution margin ratio.

6) If the sales mix shifts more towards the car product, the break-even point in units may decrease. This is because the car product has a lower labor hour requirement per unit compared to the other two products, potentially reducing the total fixed costs and contributing to a lower break-even point.

7) To optimize the use of limited labor hours, you would calculate the contribution margin per labor hour for each product by dividing the contribution margin by the labor hours required per unit. This information can guide decision-making on the allocation of labor hours to maximize profitability.

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The length of each arc intercepted by each slice is 2.09 inches.

The area of each slice 18.85 square inches .

To find the length of each arc intercepted by each slice and the area of each slice of a pizza that is 12 inches in diameter, follow the steps below. Length of each arc intercepted by each slice

The formula to find the length of each arc is given by:

L = θ/360 * 2πr

WhereL = length of arc

θ = angle of arc in degrees

r = radius of circle (diameter/2)

Given, diameter of pizza = 12 inches

So, radius of pizza = 12/2 = 6 inches

Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.

Now, substituting the given values in the formula:

L = 60/360 * 2π* 6L = 1/6 * 12πL = 2π/3 ≈ 2.09 inches

The formula to find the area of each slice is given by:

A = θ/360 * πr²

Given, diameter of pizza = 12 inches

So, radius of pizza = 12/2 = 6 inches

Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.

Now, substituting the given values in the formula:

A = 60/360 * π* 6²A = 1/6 * 36π

A = 6π ≈ 18.85 square inches

Thus, the length of each arc intercepted by each slice is approximately 2.09 inches and the area of each slice is approximately 18.85 square inches.

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The elevation after three seconds is 108 feet.

It should be noted that elevation simply has to do with the height above sea level.

From the information, the elevation h (in feet) of the balloon is modeled by the function h(x) = 6x + 90, where x is the time (in seconds).

After three seconds, the elevation will be:

h(x) = 6x + 90,

h(3) = 6(3) + 90

h(3) = 18 + 90

h(3) = 108 feet

The elevation is 108 feet.

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Complete question

You notice a hot air balloon ascending. The elevation h (in feet) of the balloon is modeled by the function h(x)=6x+90, where x is the time (in seconds) since you first noticed the hot air balloon. What is the elevation after three seconds?