Given m∠D = 70°, m∠E = 42, and m∠EHG = 68°, prove DF is parallel to GH.

Answer is (3,1)

x + y = 4

2x + 3y = 9

We multiply the first equation by -2  to eliminate x

-2x - 2y = -8

2x + 3y = 9

-------------------(add both equations)

0 + y = 1

So y =1

Now plug in 1 for y in first equation

x + y = 4

x + 1 = 4

Subtract 1 on both sides

x = 3

Answer is (3,1)

[tex](f+g)(x)=4x^2+\frac{3}{2}x-7[/tex]

Answer:

[tex]h(x)=4x^2+\dfrac{3}{2}x-7[/tex]

Step-by-step explanation:

Given:  

[tex]f(x)=\dfrac{x}{2}-3[/tex]

[tex]g(x)=4x^2+x-4[/tex]

To find: (f+g)(x)

It is a composite function. Sum of f and g function.

[tex]h(x)=f(x)+g(x)[/tex]

[tex]h(x)=\dfrac{x}{2}-3+4x^2+x-4[/tex]

Combine the like term

[tex]h(x)=4x^2+\dfrac{3}{2}x-7[/tex]

Hence, The sum of f(x) and g(x) would be [tex]h(x)=4x^2+\dfrac{3}{2}x-7[/tex]

The answer to the question is 10 + 9i, B.

The phrase 'five more than twice the square root of four' is a mathematical expression which evaluates to 9. The operation uses addition, multiplication, and square root.

The student is asking for the result of a mathematical expression combining addition, multiplication, and square root operations. It can be written like "5 + 2(sqrt(4))". The square root of four (sqrt(4)) is two. So, the expression becomes "5 + 2*2", which equals 5 plus 4, resulting in 9. Therefore, five more than twice the square root of four equals nine.

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First take not of the total sales and the cost of each ticket.

1,824 and 16

Now setup the equation

16x=1824

To solve this divide 1824 by 16 getting

X=144

x is the total tickets sold

Each ticket (t) costs $16. The band made a total of $1,824 from ticket sales, meaning that 16t=1,824, because the total amount of 16 dollar tickets sold is equal to the total made from ticket sales.

The equation is:

16t=1,824.

You are trying to find the amount of tickets sold by solving the equation.

t stands for the total amount of tickets sold.

Solving the equation:

16t=1,824

Divide both sides by 16.

t=114

114 tickets were sold. 114*16=1,824. This means that when 114 $16 tickets were sold, the band did make $1,824, which shows that 114 is the correct answer.

I hope this helps :)

B and D are both wrong. B has +4 outside the brackets. It is - 4

D is wrong because there is no 4 of any kind outside the brackets.

A is incorrectly represented inside the brackets as 16. That's not right

That only leaves  C. <<<< Answer

Graphs

Notice that the red parabola and the green one are the same thing.

Red: y = -4x^2 - 16x - 14

Green: y = -4(x + 2)^2 + 2

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (4, -5) and (0, -13).

Substitute:

[tex]m=\dfrac{-13-(-5)}{0-4}=\dfrac{-13+5}{-4}=\dfrac{-8}{-4}=2[/tex]

Answer:

Dodecahedron

Step-by-step explanation:

The completed statement with regards to the area of the rectangle WXYZ can be presented as follows;

AD/WZ = 1/2, AB/WX = 1/2 Because the ratio of the corresponding side lengths is 1/2, the ratio of the areas is equal to ( 1 / 2 ) to the second power. To find the area, solve the proportion 30/x = 1 / 4 to get x = 120

The steps by which the area of the rectangle WXYZ is found can be presented as follows;

The area of the rectangle ABCD = 30 square inches

AD/WZ = 1/2, and AB/WX = 1/2

The ratio of the corresponding sides in the rectangles ABCD and WXYZ is 1/2

Therefore, scale factor of the lengths of the sides of rectangle ABCD to the lengths of the sides of the rectangle WXYZ is 1/2

The scale factor of the lengths = 1/2

The scale factor of area = (Scale factor for length)²

The scale factor for the area of the rectangles is therefore; (1/2)² = 1/4

Area of rectangle ABCD/(Area of rectangle WXYZ) = 1/4

30/x = 1/4

x is; 30/(1/4) = 120

Area of the rectangle ABCD is about 120 square inches

The complete question found from a similar question on the website can be presented as follows;

Rectangle ABCD is similar to rectangle WXYZ. The area of ABCD is 30 square inches. Explain how to find the area x of WXYZ. AD/WZ = 1/2

AB/WX = 1/2. Because the ratio of corresponding side lengths is 1/2, the ratio of the area is equal to (___/___) to the second power. To find the area, solve the proportion 30/x = __/___ to get x = ___

Answer:

Distance Maria had to walk in the afternoon is [tex]2\frac{7}{8}[/tex]

Step-by-step explanation:

Lets take that Maria walked [tex]x[/tex] miles in the afternoon.

Distance walked in the morning + distance walked in the afternoon = [tex]10\frac{1}{8}[/tex]

⇒[tex]7\frac{2}{8} +x=10\frac{1}{8}[/tex]

[tex]\frac{58}{8} +\frac{8x}{8} =\frac{81}{8}[/tex]

[tex]\frac{58+8x}{8} =\frac{81}{8}[/tex]

[tex]58+8x=81[/tex]

[tex]8x=81-58\\[/tex]

[tex]8x=23[/tex]

[tex]x=\frac{23}{8}[/tex]

[tex]x=2\frac{7}{8}[/tex]

The first one is correct it is a Quadratic Polynomial.

Every time you divide something by something else, you already have a fraction. A fraction is simply a different way to visualize a division. So, the following writings express the same concept:

[tex] 72\div 24 = \dfrac{72}{24} [/tex]

There's no conceptual difference between the two expressions, so you're not actuall "turning" 72 divided by 24 "into" a fraction, you're just writing it in another way.

Answer in the attachment.

Used:

[tex]\sec x=\dfrac{1}{\cos x}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x[/tex]

The slope of the linear equation C(x) = 8x + 50 is 8, indicating an $8 charge per mile, and the y-intercept is 50, the flat towing fee. Similar service-based costs from other examples also follow this linear model, with their unique slopes and y-intercepts corresponding to the per-hour or per-mile charges and flat fees.

The function C(x) = 8x + 50 represents the cost of towing a vehicle, where C is the cost in dollars, and x is the number of miles the vehicle is towed. The slope of this line is 8, which indicates that the cost increases by $8 for every mile the vehicle is towed. The y-intercept is 50, representing the flat fee charged regardless of the distance towed, which is the cost when x (the number of miles) is 0.

Relating to the other examples provided, we can see a pattern in how these equations are structured for service-based costs. For instance, in Aaron's Word Processing Service, the total cost equation is y = 32x + 31.50, where the slope is 32 representing the hourly charge, and the y-intercept is 31.50, the fixed cost. Similarly, for Ethan's household appliance repairs, the equation is y = 20x + 25, with a slope of 20 and a y-intercept of 25. All these models illustrate how fixed fees and variable rates per service hour or mile can be represented in a linear equation format.

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Answer:A)The conditional relative frequency among widowed employees of those widowed working at grade 2 or below= 28/42 = 66.67%

Step-by-step explanation:

In a  two way frequency table, conditional relative frequency is it’s a fraction that tells us how many elements of of a group have a certain characteristic.

Here In a study about the relationship between marital status and job level, 8,235 males at a large manufacturing firm reported their job grade (from 1 to 4, with 4 being the highest) and their marital status.

from the given two way frequency table,

Number of widowed employees at grade 1 =8

Number of widowed employees at grade 2=20

∴ Number of widowed employees at grade 2 or below=8+20=28

And the total widowed employees working =42

Now the conditional relative frequency among widowed employees of those widowed working at grade 2 or below=[tex]\frac{\text{Number of widowed employees at grade 2 or below}}{\text{Total widowed employees}}=\frac{28}{42}=0.6667=66.67%[/tex]

Therefore, the conditional relative frequency among widowed employees of those widowed working at grade 2 or below= 28/42 = 66.67%

To calculate the conditional relative frequency among widowed employees for those at grade 2 or below, the number of widowed employees at these grades (28) is divided by the total number of widowed employees (42), yielding a frequency of approximately 66.67%. The answer is option A.

The question asks us to find the conditional relative frequency among widowed employees of those working at grade 2 or below at a large manufacturing firm. To find this, we look at the two-way table provided and sum the number of widowed employees in job grades 1 and 2, which gives us

8 + 20 = 28 widowed employees. We then divide this number by the total number of widowed employees to get the conditional relative frequency:

28/42*100 =  66.67%.

Therefore, among widowed employees, approximately 66.67% work at job grade 2 or below. The answer is option A.

Hello,

Please, see the attached file.

Thanks.

Answer : option A

[tex]P(t)= -16t^2 -88t +720[/tex]

Top of a tall boulder = 57 foot

To find the time taken for the pebble to hit the boulder

We set p(t) = 57  and solve for t

[tex]57= -16t^2 -88t +720[/tex]

Subtract 57 on both sides

[tex]0= -16t^2 -88t +720-57[/tex]

[tex]0= -16t^2 -88t +663[/tex]

[tex]0= -(16t^2 +88t -663)[/tex]

apply quadratic formula to solve for t

[tex]t= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

plug in the values a = 16, b= 88 and c= -663

[tex]t = \frac{-88+-\sqrt{88^2-4(16)(-663)}}{2*16}[/tex]

[tex]t= \frac{-39}{4}[/tex] and  [tex]t= \frac{17}{4}[/tex]

t= -9.75  and t = 4.25

Time cannot be negative. So we ignore negative answer

the time taken for the pebble to hit the boulder is 4.25 seconds

The first transformation that is applied first is vertical shift.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

To apply the transformation on the function the order should be follow is

e than one transformation. Apply the transformations in this order:

1. Start with parentheses (look for possible horizontal shift)

(This could be a vertical shift if the power of x is not 1.)

2. Deal with multiplication (stretch or compression)

3. Deal with negation (reflection)

Hence, the transformation applied is vertical shift.

Learn more about transformation here:

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2. Linear Pair Postulate

4. 60° + m∠ACB = 180°

5. m∠ACB = 120°

6. definition of obtuse angle

Answer: ∠Z = 117.2°

Step-by-step explanation:

∠X and ∠Y are isosceles so they are congruent (equal to each other)

5x + 33 = 33x + 42

-5x           -5x          

         33 = 28x + 42

        -42            -42

        -9   =  28x

        [tex]\frac{-9}{28} = \frac{28x}{28}[/tex]

        [tex]-\frac{9}{28} = x[/tex]

************************************************************

∠X + ∠Y + ∠Z = 180°                Triangle angle sum theorem

5x + 33 + 33x + 42 + ∠Z = 180°

38x + 75 + ∠Z = 180°

        -75              -75

38x          + ∠Z = 105°

38[tex](-\frac{9}{28})[/tex]      + ∠Z = 105°

-12.2         + ∠Z = 105°

+12.2                     +12.2

                     ∠Z = 117.2°

Answer:

your answers C

Step-by-step explanation:

The factored form of the expression [tex]27x^3+y^6[/tex] is [tex](3x+y^2)(9x2-3xy^2+y^4)[/tex]. The correct answer of the factored expression is option A

Given the expression;

[tex]27x^3+y^6[/tex]

This can be expressed as the sum of cubes

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

The given expression can also be written as the sum of cubes as shown:

[tex]27x^3+y^6 = (3x)^3+(y^2)^3[/tex]

We can see that:

a = 3x

b = y²

Substituting the given parameters into the formula above;

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\(3x)^3+(y^2)^3=(3x+y^2)((3x)^2-3xy^2+(y^2)^2)\\(3x)^3+(y^2)^3=(3x+y^2)(9x2-3xy^2+y^4)\\[/tex]

Hence the factored form of the expression is [tex](3x+y^2)(9x2-3xy^2+y^4)[/tex]

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3° and 177°

supplementary angles sum to 180°

let x be an angle then the other angle is 59x

x + 59x = 180

60x = 180 ( divide both sides by 60 )

x = [tex]\frac{180}{60}[/tex] = 3

the angles are 3° and (59 × 3 )= 177°

To find the measures of two supplementary angles where one is fifty-nine times larger than the other, set up an equation x + 59x = 180, and solve for x. The smaller angle is 3 degrees, and the larger angle is 177 degrees.

The measure of an angle is fifty-nine times the measure of a supplementary angle. To solve this, we can set up an equation where x is the measure of the smaller angle, and therefore, 59x is the measure of the larger angle. Since angles are supplementary, their sum is 180 degrees. So, our equation is x + 59x = 180. Solving for x, we find that x = 3 degrees and 59x = 177 degrees.

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D the 2 represents the two sets of length and width pairs

2(l + w) = 2l + 2w , that is 2 times length + 2 times width

The average total cost of manufacturing scented candles is given by the formula A(b) = C(b)/b = (250 + 3b)/b, where b is the number of candles manufactured.

The concept of average total cost is key in the calculation. Given the function for total cost of the candles, C(b) = 250 + 3b, the average cost, A, can be calculated by dividing the total cost by the number of candles, b. Therefore, the function representing the average cost, A, in terms of b is given by A(b) = C(b)/b = (250 + 3b)/b. It's important to note that this function also signifies the 'economies of scale', stating as output number increases, the average cost falls.

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In a generic rectangle, split 54 into 50 and 4, and 32 into 30 and 2. Set up these numbers around a rectangle divided into four boxes. Each box is the product of the row and column which intersect at the box. Adding up the values in the boxes gives you the product of 54 and 32.

To use a generic rectangle in multiplying 54 by 32, you first need to break both numbers down. This is part of a strategy known as partial products.

For example, think of 54 as (50 + 4) and 32 as (30 + 2). Then, set up these numbers around a rectangle, splitting it into four sections or boxes. On one side of the rectangle, put 50 and 4, and on the other side put 30 and 2. Each box represents the product of the row and column that intersect at that box.

Now, calculate the content of each box. For instance, the top left box would have 50 x 30 = 1500. The top right box would have 50 x 2 = 100. The bottom left box would have 4 x 30 = 120, and the bottom right box would have 4 x 2 = 8. The sum of the values inside the boxes (1500 + 100 + 120 + 8) results in 1728, which is the product of 54 and 32.

Using the generic rectangle to multiply numbers is a visual strategy that helps with breaking down more complex multiplication, especially when it involves larger numbers.

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Each 1/8 is 0.125, so 7*0.125 in relation to 7/8 as a decimal is 0.875.  Answer C.