In A ABC, mZA= 15° and m2 B = 120°.
Select the triangle that is similar to AABC.

Answer:

y = - 2x + 17

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 )

Here m = - 2, then

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

To find c substitute (6, 5) into the partial equation

5 = - 12 + c ⇒ c = 5 + 12 = 17

y = - 2x + 17 ← equation of line

The future value of depositing $1,000 every year for 20 years, with payments made at the beginning of each period, at an interest rate of 7% compounded yearly, is approximately $43,865.18.

To calculate the future value of a series of deposits, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value

P is the periodic payment

r is the interest rate per period

n is the number of periods

In this case, the periodic payment is $1,000, the interest rate is 7% (or 0.07), and the number of periods is 20.

Plugging these values into the formula, we get:

FV = 1000 * [(1 + 0.07)^20 - 1] / 0.07

  = 1000 * [1.07^20 - 1] / 0.07

  ≈ 1000 * [2.6532976 - 1] / 0.07

  ≈ 1000 * 1.6532976 / 0.07

  ≈ 43,865.18

Therefore, the future value of this series after 20 years would be approximately $43,865.18.

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Excess capacity (e.g., factories can make more than the optimal industry production quantity) within the industry is not a deterrent to entry into an industry

Barriers to entry is an economics and business term describing factors that can prevent or impede newcomers into a market or industry sector, and so limit competition. Barriers to entry may be caused naturally, by government intervention, or through pressure from existing firms

Common barriers to entry include special tax benefits to existing firms, patent protections, strong brand identity, customer loyalty, and high customer switching costs.

According to the question,

Prevalence of learning curves in the industry , Production that requires expensive machinery that can be resold and High economies of scale in the industry are all deterrent or barriers to entry

But Excess capacity (e.g., factories can make more than the optimal industry production quantity) within the industry is not a deterrent to entry into an industry because when there is excess capacity in the industry , existing firms can cut the prices making it harder for new entrant to make a profit.

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Answer:

The unit rate is $9.20 per toy

Step-by-step explanation:

Since the total of the toys is 46, you divide by 5, to see how much each toy is

We need to prove that if p² divides ab, then p² divides a or p² divides b. Since a and b are relatively prime, p cannot divide both a and b. If p² divides ab, then it must have p in it twice.

Let p be a prime and let a and b be relatively prime integers. Now, we need to prove that if p² | ab, then p² | a or p² | b.Let's assume that p² does not divide a. Then, we can write a = p x c + r, where r is a positive integer less than p. Since a and b are relatively prime, p does not divide b. Thus, we can write pb = pxd + s, where s is a positive integer less than p. Therefore, ab = (pxc + r) (pxd + s) = p²xcd + pxr + pys + rs. Now, p² divides ab, thus, p² divides p²xcd, pxr and pys but p² does not divide rs. Thus, p² divides pxc or p² divides pxd. Hence, either p² divides a or p² divides b. Thus, we have shown that if p² | ab, then p² | a or p² | b.

It can be said that if p² divides the product of two relatively prime integers, then p² must divide either of the integers. Hence, we can prove the contrapositive of the statement: if p² does not divide a and p² does not divide b, then p² does not divide ab.

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Let's use the variable x to represent the price of the television set before taxes.

If the tax rate is 4%, then the original price is multiplied by 1.04, so it is equal 1.04x.

The final price is $520, so we have:

So the price before taxes is $500.00.

Answer:percantage spent on other things = 30%

Step-by-step explanation:

Percentage spent on other things = Money spent on other things/ Total money x `100/ 1

Money spent on rest things = Total money - ( Money spent on ice cream + Money spent on pizza)

100 -(25+ 45)

100-70= Rs 30

Percentage spent on other things = Money spent on other things/ Total money x `100/ 1

= Rs 30/ Rs 100 x 100

0.3 x 100 = 30%

c. 1,256 m³ is the approximate volume of the sphere.

The approximate volume of a sphere can be calculated using the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere. In this case, the diameter of the sphere is given as 10m.

The radius of the sphere is half of the diameter, so the radius would be 10m/2 = 5m.

Plugging the radius value into the formula, we get V = (4/3)π(5m)^3. Simplifying further, we have V = (4/3)π(125m^3).

Calculating the value, V = (4/3)π(125m^3) ≈ 1,256 m³.

Therefore, the approximate volume of the sphere is approximately 1,256 m³.

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Answer:

View the image below

Step-by-step explanation:

Answer:

The payment for driving 80 miles is $78

Step-by-step explanation:

Mathematical model

Mathematical models are used in disciplines like natural sciences and engineering, among many others.

The data provided in the question allows building a model for the charges of the car rental, knowing there are two fees:

A fixed charge of $50

A variable charge or $0.35 per mile driven.

Part A

Using m as the number of miles driven for the day, the model for the payment for the car rental is:

P(m)=50+0.35m

Part B

Find the payment if the car is driven m=80 miles:

P(80)=50+0.35*80

P(80)=50+28=78

The payment for driving 80 miles is $78

The statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is NOT true.

A. The statement is true. The ratios of the vertical rise to the horizontal run, also known as the slopes, of any two distinct nonvertical parallel lines are equal. This is one of the properties of parallel lines.

B. The statement is true. If two distinct nonvertical lines are parallel, then they have the same slope. Parallel lines have the same steepness or rate of change.

C. The statement is true. Given two distinct lines in the Cartesian plane, the two lines will either intersect at a point or they will be parallel and never intersect. These are the two possible scenarios for distinct lines in the Cartesian plane.

D. The statement is NOT true. Given any two distinct lines in the Cartesian plane, they may or may not be parallel or perpendicular. It is possible for two distinct lines to have neither parallel nor perpendicular relationship. For example, two lines that have different slopes and do not intersect or two lines that intersect but are not perpendicular to each other.

Therefore, the statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is the one that is NOT true.

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Answer:

14 feet

Step-by-step explanation:

We solve the above question by using the Greatest Common Factor method

We find the factors of 56 and 98

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

The factors of 98 are: 1, 2, 7, 14, 49, 98

Then the greatest common factor is 14.

Therefore, the greatest possible length you can cut the rope so all pieces will be the same is 14 feet

Applying the ratio test to the given series results in the inequality lim nnÏ 2/17n<1, which implies that the series converges. Therefore, the correct answer is (A).

The ratio test is a method used to determine the convergence or divergence of an infinite series. The test involves taking the limit of the ratio of consecutive terms in the series as n approaches infinity. If this limit is less than 1, then the series converges, and if it is greater than 1, then the series diverges.

In this case, applying the ratio test to the given series involves taking the limit of the ratio of the (n+1)th term and nth term as n approaches infinity. Simplifying this ratio using the given expression for the nth term, we get [(n+1)/n] Ï 2/17. Taking the limit of this expression as n approaches infinity gives us 2/17, which is less than 1. Therefore, the series converges.

The other options presented in the question involve taking the limit of different expressions, which do not correspond to the ratio test for infinite series. Therefore, they do not provide a valid method for determining the convergence or divergence of the given series.

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The equations given are x - 5y = 3 and 3x - 2y = -4. To find the solution to this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

One way to solve this system of equations is by substitution. We can solve one equation for x or y, and then substitute that expression into the other equation to eliminate one variable. Let's solve the first equation for x:

x - 5y = 3

x = 5y + 3

Now we can substitute this expression for x into the second equation:

3x - 2y = -4

3(5y + 3) - 2y = -4

15y + 9 - 2y = -4

13y = -13

y = -1

We can now substitute this value for y back into either equation to find the value of x:

x - 5y = 3

x - 5(-1) = 3

x + 5 = 3

x = -2

Therefore, the solution to the system of equations x - 5y = 3 and 3x - 2y = -4 is (-2, -1). This is the point where the solid line and dotted line intersect, as shown in the image.

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Yes, 3(x-4)-2(2.5x-1) and -2(x+5) are equivalent expressions.

Two expressions are considered equivalent when they produce the same result when evaluated at the same value for the variables involved. For example, the expressions 2x + 3 and 3 + 2x are equivalent because they both produce the same result for any value of x. Therefore, it is necessary to evaluate the two expressions to determine if they are equivalent or not.

First, we will simplify the left-hand side of the equation.

3(x-4)-2(2.5x-1)

= 3x - 12 - 5x + 2

= -2x - 10

Next, we will simplify the right-hand side of the equation.

-2(x+5)

= -2x - 10

Both expressions simplify to -2x - 10, which means they are equivalent.

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Sorry but your screenshot is very blur. please give clear photo so that we can read question and answer it.

Answer: a

Step-by-step explanation:

Version A:

Mean = 20

Median = 20

Mode = 10 and 30

Range = 20

Version B:

Mean = 20

Median = 20

Mode = 20

Range = 20

It is the middles value of the given set of numbers after arranging the given set of numbers in order.

We have,

Version A:

Mean:

It is the average value.

= (5 x 10 + 3 x 15 + 20 + 3 x 25 + 5 x 30) / 17

= (50 + 45 + 20 + 75 + 150) / 17

= 20

Median:

It is the mid-value.

10, 10, 10, 10, 10, 15, 15, 15, 20, 25, 25, 25, 30, 30, 30, 30, 30

= 20

Mode:

The number that occurs most times.

= 10 and 30

Range:

Highest value - Lowest value.

= 30 - 10

= 20

Version B:

Mean:

= (10 + 3 x 15 + 5 x 20 + 3 x 25 + 30) / 13

= (10 + 45 + 100 + 75 + 30) / 13

= 20

Median:

The number that occurs most times.

10, 15, 15, 15, 20, 20, 20, 20, 20, 25, 25, 25, 30

= 20

Mode:

= 20

Range:

= 30 - 10

= 20

Thus,

Version A:

Mean = 20

Median = 20

Mode = 10 and 30

Range = 20

Version B:

Mean = 20

Median = 20

Mode = 20

Range = 20

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Answer:

The vertex is at (5, -9)

Step-by-step explanation:

The vertex is halfway between the zeros

f(x) = (x-8)(x - 2)

0  = (x-8)(x - 2)

x=8 and x=2 are the two zeros

(8+2)/2 = 10/2 = 5

The x coordinate is at 5

The y coordinate is found by substituting the x coordinate into the function

f(5) = (5-8)(5 - 2) = -3 (3) = -9

The vertex is at (5, -9)

Answer:

Step-by-step explanation:

Definitions

In the diagram which is attached below:

Angles ADC are BDC are on a straight line, and they add up to 180 degrees.

Therefore:

\(\angle ADC$ and \angle BDC$ are supplementary.\)

Furthermore,

\(\angle ACB$ is a right angle.\\\angle ACB=\angle ACD+\angle DCB\\$Therefore, \angle ACD$ and \angle DCB$ are complementary.\)

A pair of complementary angles is angles ACD and DCB.

Answer:

Supplementary

ACD & BCD

Step-by-step explanation:

Given:

The vertices of square WXYZ are W(1,7), X(6,5),  Y(4,0), and Z(-1, 2).

Consider the rule of transformation is \((x, y)\to (x-7, y-6)\).

To find:

The new coordinates.

Solution:

We have,

\((x, y)\to (x-7, y-6)\)

Using the above rule of transformation, we get

\(W(1, 7)\to W'(1-7, 7-6)=W'(-6,1)\)

\(X(6, 5)\to X'(6-7, 5-6)=X'(-1,-1)\)

\(Y(4, 0)\to Y'(4-7, 0-6)=Y'(-3,-6)\)

\(Z(-1, 2)\to Z'(-1-7, 2-6)=Z'(-8,-4)\)

Therefore, the new vertices are W'(-6,1), X'(-1,-1), Y'(-3,-6) and Z'(-8,-4).

Answer:

he gets $110 everytime he sells a copy

if he sells 0 copies, he will still have the $1,500 that's unaffected by the book

Step-by-step explanation:

I hope this helps :)

Answer:

18. Huan sold 18 pizza's. 23 - 5 = 18.

You can also start at 23, and count down to 5.

Step-by-step explanation:

Answer:

315

Step-by-step explanation:

So with the ratio, you can tell that 11/18 of the people at the festival are kids, and 7/18 are adults.

Since you want to find the number of adults, just multiply.

7/18 x 810

You can cross multiply to get rid of 18 and 810 will simplify into 45. So then you are left with multiplying

7 x 45

=315

So, 315 is your answer

Answer: 315 Adults.

Step-by-step explanation:

Let the number of adults is x.

Then the number of kids is (810-x).

The ratio of kids to adults is

810 - x/x = 11/7

It is your basic equation, which you get from the condition.

To solve it, cross multiply; then simplify

7*(810-x) = 11x

7*810 - 7x = 11x

7*810 = 11x + 7x

7*810 = 18x

x = 7 x 810/18 = 315.

Answer:

56

Step-by-step explanation:

Answer:

k=56

Step-by-step explanation:

100-44=56

100-56=44

Answer: x is greater than or equal to 18

Step-by-step explanation:

Answer:

x ≤ - 2

Step-by-step explanation:

- x/6 ≤ 3

- x/2 ≤ 1

- x ≤ 2

x ≤ - 2

Using system of linear equations, the law firm employed  7 associate and 9 partners

The system of linear equations can be defined as a set of two or more linear equations that have the same variables. Linear equations can be said as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

In this question, we have to write out two equations and solve for the unknown variable.

let;

x + y = 16 ...eq(i)

400x + 1000y = 11800 ...eq(ii)

From equation 1

x = 16 - y ...eq(iii)

Put eq(iii) into equation (ii)

400(16 - y) + 1000y = 11800

6400 - 400y + 1000y = 11800

6400 + 600y = 11800

600y = 11800 - 6400

600y = 5400

y = 5400 / 600

y = 9

Put y = 9 in equation (i)

x + 9 = 16

x = 16 - 9

x = 7

The firm has 7 associate and 9 partners

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