Question 10
100 pts
Find the area of a trapezoid in which b. - 7cm, b = 12 cm, and h = 5 cm.
Scmn
12 cm
47.5 cm
O 12.5 cm
O 95 cm
O 24 cm2

To verify if the relation is a function, it must be verified if from each value of x only one arrow departs.

A relation represents a function when each input value is mapped to a single output value.

In mapping notation, with the arrows, it must be verified if there is no input from which more than one arrow departs.

The problem is incomplete, hence the general procedure to verify if the relation is a function was presented.

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The values of x is 6 and y is (-6).

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

-4x-5y=6............(1)

9x+7y=12..................(2)

Solving Equation (1) and (2) we get

-36 x  - 45y = 54

36x + 28y = 48

____________

         -17y= 102

              y= -6.

and, -4x -5y= 6

-4x - 5(-6) = 6

-4x + 30 = 6

-4x = 6-30

-4x = -24

x= 6

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Answer:

infinite number of solutions

Step-by-step explanation:

\(\frac{4}{5}\) (x + 9) - \(\frac{1}{5}\) x = \(\frac{3}{5}\) (x + 12)

multiply through by 5 to clear the fractions

4(x + 9) - x = 3(x + 12) ← distribute parenthesis on both sides

4x + 36 - x = 3x + 36

3x + 36 = 3x + 36

since both sides are the same then any value of x will make the equation true.

Thus there are an infinite number of solutions

Answer:

= 12 miles per hour

Step-by-step explanation:

This is a fraction equal to

30 miles ÷ 2.5 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 2.5

30 miles ÷ 2.5

2.5 hours ÷ 2.5

=  

12 miles

1 hour

=  

12 miles

hour

= 12 miles per hour

Answer:

\(1\frac{3}{5}\) meter is the difference in depths of locations diver dove.

Step-by-step explanation:

31.286 i think that its 31.286 bc welp me smart

Answer:

A

Step-by-step explanat

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Based on the set of transformations for trapezoid ABCD, the location of point A after the transformations are complete is: D. (−5, 1).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).

By applying a rotation of 180° to the given point, the coordinates of its image is given by:

(x, y)                           →               (-x, -y)

Points A = (-5, 1)        →     Points A' = (-(-5), -(1)) = (5, -1).

Next, we would reflect the given point over the x-axis as follows;

(x, y)                           →              (x, -y)

Points A' = (5, -1)        →     Points A' = (5, -(-1)) = (5, 1)

Lastly, we would reflect the given point over the y-axis as follows;

(x, y)                           →              (-x, y)

Points A' = (5, 1)        →     Points A' = (-(5), 1) = (-5, 1)

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Answer:

Answer: 5

Step-by-step explanation:

5(x+1)-5x

distribute

=(5)(x)+(5)(1)+ -5x

=5x+5+ -5x

Combine like terms

5x+5+ -5x

= (5x+ -5x) + 5

= 0 + 5

= 5

Solution:

Given:

The equation is the equation of a line in the slope-intercept form.

To get the slope and y-intercept of the equation, we compare it to the equation of a line in slope-intercept form.

Hence,

Therefore,

The slope is -7

The y-intercept is 4

The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²

What is meant by a perfect square trinomial?

By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.

Given expression y² - 13y + ?

Comparing with the general equation

a = 1

b = -13

For perfect square trinomial

b² = 4ac

(-13)² = 4 * 1 * c

169 = 4c

c = 169/4

So the expression becomes,

y² - 13y + 169/4 = (y - 13/2)²

Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.

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Step-by-step explanation:

it's an Equilateral triangle

the base angels are equal

A=100°

B=40°

C=40°

The required vertex angle will be  100° in the given figure.

An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle.

The triangle given in the figure is an Isosceles triangle.

It is given that side AB is equal to side AC.

So ∠B = ∠C = 40°

Now we know that the sum of angles of a triangle is equal to 180°. So here in this triangle ABC. These are the sum of these three angles will be equal to 180.

As per the given figure,

∠A + ∠B +∠C = 180°

∵ ∠B = ∠C = 40°

∠A + 40° +40° = 180°

∠A + 80° = 180°

∠A = 180° - 80°

∠A = 100°

Therefore, the required vertex angle will be  100° in the given figure.

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Answer:

8

Step-by-step explanation:

ANSWER

B 4.003 > 4.03

EXPLANATION

To find out which inequality is not true, the statement in the inequality must be mathematically wrong.

Let us examine each inequality.

A 65.7 < 67.54 is true because 65.7 is actually less thana 67.54.

B 4.003 > 4.03 is not true because 4.003 is actually less than 4.03.

C 26.4 < 26.8 is true because 26.4 is less than 26.8

D. 0.91 > 0.097 is true because 0.91 is greater than 0.097

So, the answer is B.

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =\((1/2) * 54 * 56 = 1512\) square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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Answer:

312

Step-by-step explanation:

Add the area of each face together

Don't forget the units!

Let's start by finding the right face (12 by 3). From your picture, we can tell its 12m long, and 3m tall. To find the aria of any face, we multiply the length, times the width.
12 x 3 = 36.
Now let's look at where it says 8m. Since that face is just as tall as the first one, we can tell its 3m tall.
8 x 3 = 24.

We can continue this for the top face.
Since the width of the second face we did is 8m, and the width of the first one is 12m, we can tell that the top one is 8 x 12. (96).

We can do this again for the other 3 sides.
A shortcut i like to take, is to do 3 of the sides, (Like the ones we did) and add them together, then double the sum.

36+24+96=156.

156x2=312.

This shortcut should work, because by adding the aria of half the sides together, we get exactly half the answer.

When doing this, it only works to do 3 different sides. it will not work if you do the same side twice, or a parallel side.

I encourage you to let me know if this method works for you! I hope this helps!

The number of ways for which the square can be painted is given as follows:

16 ways.

The square is composed by four regions, and for each region the painting is independent of other regions, meaning that the Fundamental Counting Theorem is used to solve this problem.

The Fundamental Counting Theorem states that if there are n independent trials, each with \(n_1, n_2, \cdots, n_n\) possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

In this problem, the square is composed by four regions, each with two possible options for the paint color, hence the number of ways in which the square can be painted is given as follows:

N = 2 x 2 x 2 x 2 = 2^4 = 16 ways.

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Answer:

Velocity is 20

Step-by-step explanation:

well you divide the meters traveled by the time it took and you should get your answer.

1. divide 1200 by 20

2 answer should be 60

Ahab's total change to funds is -$175, which means he spent more than he gained.

Ahab spent 3 tires at $50 each, which is a total of 3 x $50 = $150.

Later, he returned one tire, so he gets $50 back.

He also found a $5 bill, so he has an extra $5.

He then bought 2 jackets at $40 each, which is a total of 2 x $40 = $80.

The total amount Ahab spent is $150 + $80 = $230.

However, he also received $50 back and found $5, so his total change to funds is $50 + $5 - $230 = -$175.

Therefore, Ahab's total change to funds is -$175, which means he spent more than he gained.

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Answer:

A

Step-by-step explanation:

Table 1 shows the linear relationship between the two variables.

A linear relationship is one in which two variables have a direct connection, which means if the value of x is changed, y must also change in the same proportion.

According to the given question.

We have some tables. Which represents the relationship between the two variables x and y.

Since,

If x is linearly related to y then the slope will same for every points.

For the

Table 1.

For the points (9, 13) and (14, 16)

\(slope = \frac{16-13}{14-9}\)

\(\implies slope = \frac{3}{5}\)

For the points (14, 16) and (19, 19)

\(slope = \frac{19-16}{19-14} =\frac{3}{5}\)

So we can see that the slope is same for each pair of points.

Hence, table 1 shows the linear relationship between the two variables.

Table 2:

For the points (-4, 2) and (2, 10)

\(slope = \frac{10-2}{2+4} =\frac{8}{6} =\frac{4}{3}\)

For the points (8, 50) and (2, 10)

\(slope = \frac{10-50}{2-8} =\frac{-40}{-6} =\frac{20}{3}\)

Since, the slope are not same. Therefore, table 2 doesn't shows the linear relationship between the two variables.

For table 3

Since the slope is changing therefore, table 3 doesn't shows the linear relationship between the two variables.

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Answer:

The point estimate for p is 0.2043.

Step-by-step explanation:

The point estimate for the population proportion of accidents that involved faulty equipment is the number of acidents which involved faulty equipment divided by the number of accidents surveyed.

In this question:

700 accidents surveyed

143 involved faulty equipment

143/700 = 0.2043

The point estimate for p is 0.2043.

Answer:

P=x+18

Step-by-step explanation:

a=8

b=x

c=10

P=8+x+10

Answer:

- 4 / 3

Step-by-step explanation:

3 ( x - 4 ) = 12x

Divide 3 on both sides,

3 ( x - 4 ) / 3 = 12x / 3

x - 4 = 4x

x - 4x = 4

- 3x = 4

x = 4 / - 3

x = - 4 / 3