What is the area of trapezoid ABCD?



Enter your answer as a decimal or whole number in the box. Do not round at any steps.

units²
Trapezoid A B C D on a coordinate plane with vertex A at negative 3 comma 2, vertex B at 1 comma 5, vertex C at negative 7 comma negative 3, and vertex D at 0 comma negative 2. Angle B is shown to be a right angle.

Answer:

See below

Step-by-step explanation:

Plug in x = 3   And  y = 1 to see

3(3) + 10(1)  >= 20 ?

9     + 10 >= 20?

19 >= 20     Not true  ....the point does not make the inequality true

Values needed to complete the X diagram are:

On top -28, On the bottom: -3 and On the sides: -7 and 4.

An algebraic expression is factorised when it is written as the product of its factors.

The given equation is :

F(x) = x²-3x-28

finding factors,

=  x²-7x+4x-28

= x(x-7) +4(x-7)

= (x-7)(x+4)

Given general equation is ax²+bx+c,

on comparing with  x²-3x-28

a = 1

b = -3

c = -28

ac = 1*(-28) = -28

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Answer:

r>9

Step-by-step explanation:

3r-13+13>14+13

3r>27

3r/3>27/3

r>9

Answer:

r > 9

Step-by-step explanation:

Hello!

Treat inequality as an equal sign. The only rule is that when you divide or multiply by a negative number, flip the sign.

The solution is true for any value of r greater than 9.

A graph of the linear equation (3x + 2y = 6) in standard form is shown in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any proportional relationship such as a linear equation is characterized by a straight line as shown in the image attached below.

Next, we would rewrite the linear equation in standard form as follows:

3x + 2y = 6

2y = 3x + 6

Dividing all through by 2, we have:

2y/2 = 3x/2 + 6/2

y = 3x/2 + 3

In conclusion, a graph which represents the linear equation (y = 3x/2 + 3) shows a proportional relationship between the value of x and y.

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Answer:

209km/h

Step-by-step explanation:

4hrs 15mins was the time.

4hrs x 50km/h = 200km/h

15 percent of 60: how many minutes is in an hour, is 9.

Hence, The answer would be 209km/h.

Using division we can calculate that 8 books can fit in the 14 inch long bookshelf .

Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.

length of book shelf = 14 inch

length of each book = 1 3/5 inch = 1.6 inches

Number of books = 14 ÷ 1.6 = 8.75 books

Hence by division we get that 8 book can be put in the  bookshelf.

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The smallest such whole number is 11 which is, Which is divided by 3, the remainder is 2, f it, divided by 4, the remainder is 3

Let the number be x

Here we have to find the whole number which is Divided by 3,4 the remainder is 2,3 respectively,

x+(3–2)= x +1 is multiple of 3

Div by 4 remainder is

3x+(4–3) = x+1 is multiple of 4

So LCM of 3,4 is 3×4 = 12

Hence,x=12 –1 =11

The smallest such whole number is 11 which is divided by 3, the remainder is 2, if it divided by 4, the remainder is 3.

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Answer:

a = $125.36, b = $729.35, c = $49.53, d =$500, f =$3.50, p =$1,450, and w =

$60

Step-by-step explanation:

If Roni has a riding lawn mower and can mow the field in 30 minutes and  Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, about 0.71 of the field will Roni mow.

Time taken by Roni to mow the field = 30 minutes

Time taken by Allie to mow the field = 75 minutes

Work done by the Roni = x/30

Word done by Allie = x/75

Then they are working together

x/30 + x/70 = 1

Solve the equation

[tex]\frac{70x+30x}{2100}=1[/tex]

70x+30x = 2100

100x = 2100

x = 2100/100

x  = 21

Then, the work done by Roni = x/30

= 21/30

= 0.70

Hence, if Roni has a riding lawn mower and can mow the field in 30 minutes and  Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, about 0.71 of the field will Roni mow.

The complete question is

Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, what part of the field would Roni mow?

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We need to know about fraction to solve this problem. The amount Reshma spent on comic books is Rs 165 and the amount that is left with her is Rs 495.

We can solve this problem by calculating what 1/4th of 660 will be. In this question we know that Reshma spends 1/4th of her pocket money on comic books out of Rs 660. We can think of 660 being divided in 4 parts equally and that Reshma spends one part of it. The amount that will be left with Reshma is the rest three parts.

Reshma spends= 1/4x660=165

Amount left= 660-165=495

Therefore the amount Reshma spends on comic books is Rs 165 and the amount that is left with her is Rs 495.

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Using relations in a right triangle and the Pythagorean Theorem, it is found that the missing side lengths are as follows:

There are three relations in a right triangle, given as follows:

For this problem, we have that:

tan(A) = b/a.

Hence:

5/12 = 6/a

Applying cross multiplication, the side a is found as follows:

5a = 72

a = 72/5

a = 14.4.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Hence the hypotenuse c is given as follows:

c² = 5² + 14.4²

c = sqrt(5² + 14.4²)

c = 15.24.

For the triangle, we have that:

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Answer:

Perpendicular lines: Are lines that intersect at right angles (90°)

Parallel lines: Are lines which have no point of intersection.

Step-by-step explanation:

[tex]{}[/tex]

Let

y ----> total charge in a month

x ----> number of minutes

so

Plan A

y=0.21x+11

Plan B

y=0.10x+20

Equate both equations

0.21x+11=0.10x+20

solve for x

0.21x-0.10x=20-11

0.11x=9

x=9/0.11

x=81.82 minutes

Convert to hours and minutes

81.82 minutes=60+21.82=1 hour 22 min

therefore

The statement which is the most reasonable conclusion about the selling prices based on the graph is that: E. the value of maximum minus third quartile is less than the value of first quartile minus minimum.

A box and whisker plot is also referred to as boxplot and it can be defined as a type of graph that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:

In Mathematics, the value of maximum minus third quartile (Max - Q₃) is generally less than value of first quartile minus minimum (Q₁ - Min). Mathematically, this can be represented by this expression:

Data value = (Max - Q₃) < (Q₁ - Min)

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The true statement about the function are;

⇒ The function is positive for all real values of x, where x < –1.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The graph of the function;

f(x) = –(x + 3)(x – 1)

Now,

Graph of the function is shown in attached image.

Which is a parabola, It goes through (- 3, 0), has a vertex at (- 1, 4), and goes through (1, 0).

Clearly, When x < -1

Take x = 0 < -1

The value of function;

f(x) = –(x + 3)(x – 1)

    = - (0 + 3) (0 -1)

    = -3 x -1

    = 3

The function is positive.

Thus, The true statement about the function are;

⇒ The function is positive for all real values of x, where x < –1.

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465/48

Step-by-step explanation:

1 ⅞ miles × 5⅙ = 465/48

________ _______

1 hour × 5⅙ = 5⅙ hours

Answer:

The correct option is (b) truth value. If we are given two statements, the first statement is called the hypothesis and the second is its conclusion.

The complete expression that fills the blank is -5^2 = 0 - 5^2

These are any statements that use variables, operators and coefficients as its representation

The expression is given as

-5^2 = __-5^2

Represent the blank with x

So, we have the following expression

-5^2 = x - 5^2

Add 5^2 to both sides of the equation

So, we have

x = 5^2 - 5^2

Evaluate the difference

x = 0

This implies that -5^2 = __-5^2 gives -5^2 = 0 - 5^2

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Answer:

x = 2, 4

Step-by-step explanation:

[tex](2x-4)^2=2x(x-2)+48 \\ \\ 4x^2 - 16x+16=2x^2-4x+48 \\ \\ 2x^2-12x-32=0 \\ \\ x^2-6x-8=0 \\ \\ (x-2)(x-4)=0 \\ \\ x=2, 4[/tex]

Answer:

total earnings at 6th hour: 111

hourly wage (slope): 18.5

Step-by-step explanation:

A linear function has a linear relationship, which essentially states as x increases by one, the y-value increases by some constant amount yielding a straight line.

The slope, or how much the y-value changes as x changes by 1 is generally written as: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We can choose any two points and this should yield the slope of the function, but it's a lot easier to choose y-values that are only separated by an x-value of one.

Let's say: [tex](x_1, y_1)=(4,\ 74)\text{ and }(x_2,y_2)=(5,\ 92.50)[/tex]

If we plug the values into the slope formula we just get: [tex]\frac{92.50-74}{5-4}=\frac{92.50-74}{1}=92.50-74[/tex]

And this makes sense, since by definition of a slope, it's just the change in y over change in x. This is equivalent to how much the y-value changes as x increases by one, so if we select two values with a difference of one in their x-values, the slope just turns out to be the difference between the two numbers.

Simplifying our expression we get: [tex]92.50-74=18.5[/tex]

This slope in this context represents how earnings increases as the hour increases, or in other words the hourly wage.

To calculate the earnings of the 6th hour we can just use the definition of a slope. From the x-value 5 to the x-value 6, the y-value should simply increase 18.5

So adding 18.5 to the y-value at x=5 we get: [tex]92.5+18.5=111[/tex]

Answer:

System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0

Step-by-step explanation:

Given:

To Find:

Formula used:

According to question, we have

Inequality for dotted line :

(y-1) > (0-1)/(-1-0) * (x-0)

y - 1 > x

x - y + 1 < 0...(1)

Inequality for solid line:

(y-(-3)) < (0-(-3))/(-6-0) * (x-0)

y + 3 < -x/2

x + 2y +6 < 0...(2)

Using (1) and (2), we get

System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0.

The blue portion of the wall in Marcus's bedroom is discovered to be 144(1/15) or 9.6 square feet in size.

Use the standard formula of Length x Width = Area to calculate the area of a wall.

Because square feet is the most commonly used measurement in the world when it comes to wall sizes, the measurement unit will have an impact on how you calculate square footage.

It is given that a wall in Marcus's bedroom is 8 feet high and 18 feet long.

So, the area of a wall = 8 × 18

                                   = 144

Further, 1/15 portion is painted with blue color.

So, the portion that is painted with blue = 144 × 1/15

                                                                   = 9.6

Therefore, the area of the wall  in Marcus's bedroom that is painted with blue color is found to be 144(1/15) or 9.6 square feet.

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Answer:

divide it in half it would be 339.878

Step-by-step explanation:

radius is half of a diameter

Hello

By definition:

 ⇒ the diameter of a circle is twice the length of the radius of the circle

Thus if the diameter is 679.756:

   [tex]\text{radius} = \dfrac{679.756}{2} = 339.878[/tex]

Hope that helps!

Answer: w = -238

Step-by-step explanation:

[tex]34=\frac{-w}{7}[/tex]

Switch sides

[tex]\frac{-w}{7} =34[/tex]

Multiply both sides by 7

[tex]\frac{7\left(-w\right)}{7} =34\cdot \:7[/tex]

Simplify

-w = 238

Divide both sides by -1

[tex]\frac{-w}{-1}=\frac{238}{-1}[/tex]

Simplify

w = -238

If I made any mistakes, please let me know!

 I hope this helped :)

Maggie's mistake on the solution of the expression for x was when she subtracted 7x to both sides, the result should have been -3x and not 3x.

The equation is given as follows, as the angles are congruent, that is, they have the same measure:

4x + 2 = 7x - 25.

First, we isolate x on the left side of the equality, subtracting 7x from both sides, hence:

4x + 2 - 7x = 7x - 25 - 7x

Then the correct expression is:

-3x + 2 = -25

Which is where Maggie's mistake happened, on the subtraction of 4x and 7x.

Then, isolating x, we subtract 2 from both sides of the equality, to remove the +2 term on the left side of the equality.

-3x = -27

3x = 27

x = 27/3

x = 9.

The correct solution is x = 9.

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The sinusoidal function that matches the graph given is:

g(x) = 4cos((π/7)x) - 2.

The cosine function is defined as follows:

g(x) = acos(bx)+d.

The coefficients have these following roles:

For this problem, we use a cosine function because the function is not zero at the origin, while for the sine it is.

From the graph of this function, the maximum value is of 2, while the minimum value is of -6, hence the amplitude is found as follows:

2a = 8 (difference between these values).

a = 4.

Then:

g(x) = 4cos(bx) + d.

A function with amplitude of 4 should oscillate between -4 and 4, while this one oscillates between -6 and 2, meaning that it was shifted 2 units down, hence d = -2 and:

g(x) = 4cos(bx) - 2.

The period is of 14 units, hence:

2π/b = 14

14b = 2π

b = π/7

Hence the function is:

g(x) = 4cos((π/7)x) - 2.

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Answer: pretty sure its B

hope this helps :)