Heather was asked to graph 3x - y = -4 by using slope and y-intercept. Her graph is shown.

Which choice supports the graph that she has drawn?
A) The slope is positive 3 and the y-intercept is (0,4).
B) The slope is negative 3 and the y-intercept is (0,4).
C) The slope is positive 3 and the y-intercept is (0,-4).
D) The slope is negative 3 and the y-intercept is (0,-4).

Final answer:

The measure of ∠CAE is found by adding ∠CAB to half of ∠ABC. Since ∠ABC is 30° (calculated from the triangle angle sum), ∠ADE is 15°. Therefore, ∠CAE is 97°.

Explanation:

To find the measure of m∠CAE, let's use the information provided. Since DE is the perpendicular bisector of AB, we know that ∠ADE is a right angle (90°).

In ΔABC, the sum of the angles is 180°. We have m∠CAB = 82° and m∠C = 68°. To find m∠ABC, we subtract these from 180°:

180° - 82° - 68° = 30°

Since DE is the perpendicular bisector, ∠ADE is half of ∠ABC, thus:

∠ADE = 30° / 2 = 15°

Finally, we find m∠CAE by adding ∠CAB to ∠ADE:

m∠CAE = 82° + 15° = 97°

Final answer:

To find angle CAE, we use the properties of perpendicular bisectors and the given angles to determine that m∠CAE = 41°.

Explanation:

In triangle ABC, the perpendicular bisector of side AB intersects side AB at point D and side BC at point E. To find angle CAE, we need to use the properties of perpendicular bisectors and the given angles.

The perpendicular bisector of AB passes through the midpoint of AB, which is also equidistant from A and B. This means that CD is an angle bisector of angle CAB. Since the perpendicular bisector of AB is also perpendicular to AB, we have m∠CAD = m∠CAB/2 = 41°.

Since AC is a common side, triangles ACD and ACE share two congruent angles (m∠CAD and m∠CAE), making them similar. We can use the property of corresponding angles in similar triangles to find m∠CAE = m∠CAD = 41°.

Answer:

25%

Step-by-step explanation:

Given tanθ = 4/3 and sin θ =-4/5, based on the Pythagorean identity the cos θ is  3/5.

The sine, cosine, and tangent of an angle are related by the Pythagorean identity sin²(θ) + cos²(θ) = 1.

This means we can solve for cosine given the sine value:

cos²(θ) = 1 - sin²(θ)

We know that sin(θ) = -4/5, so:

cos²θ) = 1 - (-4/5)²

cos²(θ) = 1 - 16/25

cos²(θ) = 9/25

Taking the square root of both sides,

we find that cos(θ) could be ±3/5.

However, we need to consider the quadrant in which theta is located. Since the tangent of theta is positive (4/3) and the sine of theta is negative (-4/5), theta must be in the fourth quadrant (where sine is negative and tangent is positive). In the fourth quadrant, cosine is positive.

Therefore, cos(theta) = 3/5.

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You have to multiply the price by the quantity and you will find the total cost.

1.43 * 22 = 31.46

we have

[tex]y=12x-3[/tex]

Step 1

Make a table of ordered pairs for the equation

Assume different values of x and calculate the value of y in the equation

A) For [tex]x=-1[/tex]

[tex]y=12*(-1)-3=-15[/tex]

the ordered pair is [tex](-1,-15)[/tex]

B) For [tex]x=-0.5[/tex]

[tex]y=12*(-0.5)-3=-9[/tex]

the ordered pair is [tex](-0.5,-9)[/tex]

C) For [tex]x=0[/tex]

[tex]y=12*(0)-3=-3[/tex]

the ordered pair is [tex](0,-3)[/tex]          

D) For [tex]x=0.5[/tex]

[tex]y=12*(0.5)-3=3[/tex]

the ordered pair is [tex](0.5,3)[/tex]

E) For [tex]x=1[/tex]

[tex]y=12*(1)-3=9[/tex]

the ordered pair is [tex](1,9)[/tex]     

in the attached figure  see the table

Step 2

Graph the line

Plot the points [tex](0,-3)[/tex]  and [tex](1,9)[/tex]

see the attached figure

Answer:

This is what I got

Step-by-step explanation:

I don't really have an explanation but this is the right answer for my test.

The average rate of change in the cost of the pizza from an 8-inch to a 16-inch pizza is 0.9425.

Given that:

There are five sizes of pizza.

Personal of size 8 inches, small size of 10 inches, medium size of 12 inches, large size of 14 inches, and extra large size of 16 inches.

The cost of the pizza is a function of the diameter.

Also, a table is given that shows the diameter of the pizza and the cost of the pizza based on the diameter.

From the table:

Cost of 8-inch pizza = 2.51

Cost of 16-inch pizza = 10.05

The average rate of change of a function f(x) from points a to b can be found as:

[tex]\text AroC=\frac{f(b)-f(a)}{b-a}[/tex]

The average rate of change in cost is:

[tex]\text AroC=\frac {10.05-2.51}{16-8} \\\text AroC=\frac{7.54}{8} \\\text AroC=0.9425[/tex]

Hence, the average rate of change in cost is 0.9425.

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The table showing the cost as a function of diameter is given below.

The average rate of change in cost from an 8-inch to a 16-inch pizza is 0.9425 dollars per inch.

To find the average rate of change in cost from an 8-inch to a 16-inch pizza, we need to calculate the average rate of change of the cost function [tex]\( C(d) \)[/tex] with respect to the diameter [tex]\( d \).[/tex]

Given data:

[tex]- \( C(8) = 2.51 \)\\- \( C(10) = 3.93 \)\\- \( C(12) = 5.65 \)\\- \( C(14) = 7.70 \)\\- \( C(16) = 10.05 \)[/tex]

The average rate of change of [tex]\( C(d) \)[/tex] from 8 inches to 16 inches is given by:

[tex]\[\text{Average rate of change} = \frac{C(16) - C(8)}{16 - 8}\][/tex]

First, calculate [tex]\( C(16) - C(8) \):[/tex]

[tex]\[C(16) - C(8) = 10.05 - 2.51 = 7.54\][/tex]

Then, calculate [tex]\( 16 - 8 \):[/tex]

[tex]\[16 - 8 = 8\][/tex]

Now, divide to find the average rate of change:

[tex]\[\text{Average rate of change} = \frac{7.54}{8} = 0.9425\][/tex]

Therefore, the average rate of change in cost from an 8-inch to a 16-inch pizza is 0.9425 dollars per inch.

The complete question is:

Pizza palace offers five sizes personal: (8 inches) small:(10 inches) medium:(12 inches) large:(14 inches) and extra large:(16 inches) the cost c(d) of making a pepperoni pizza can be expressed as a function of the diameter D of the pizza. What is the average rate of change in cost from an eight inch to a sixteen inch pizza?

Answer:

The answer is A

Step-by-step explanation:

A) Ramon drive 50 miles per hour

The unit rate of Ramon is A) Ramon drives 50 miles per hour.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Ramon drives his car 150 miles in 3 hours.

Therefore, The unit rate of Ramon can be obtained by dividing the total miles driven by the total time taken which is,

= (150/3).

= 50 miles per hour.

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Answer:

∠DAB

Step-by-step explanation:

A supplement to an angle is one that will sum to 180° with the given angle.  ∠ABC is 110°; this means its supplement will be 180-110 = 70°.

The angle in the quadrilateral that is 70° is ∠DAB.

The width of the rectangle can be any number less than or equal to 15 inches. If the width also must be at least 10 inches and a whole number, then it can be any of the whole numbers between 10 and 15, inclusive.

You're correct, the initial inequality does solve for w, the width of the rectangle. The inequality 80 - 2w ≥ 50 simplifies to 2w ≤ 30 and further simplified to w ≤ 15. This means that the width of the rectangle can be any number less than or equal to 15 inches.

For the second part of the question, if we also know that the width must be at least 10 inches and it must be a whole number, we can adjust the solution to be an integer number between 10 and 15, inclusive. So the possible values for width would be 10, 11, 12, 13, 14, or 15 inches in this case.

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To solve the inequality 80 - 2w ≥ 50 for w, we need to isolate the variable w. If the width must be at least 10 inches and a whole number, then the solution changes.

To solve the inequality 80 - 2w ≥ 50 for w, we need to isolate the variable w. We can do this by adding 2w to both sides of the inequality:

80 - 2w + 2w ≥ 50 + 2w
80 ≥ 50 + 2w
30 ≥ 2w
15 ≥ w

So, the width of the rectangle must be less than or equal to 15 inches.

If the width must be at least 10 inches and a whole number, then the solution changes. In this case, w can only take on whole number values from 10 to 15, inclusive. So, the width of the rectangle can be 10, 11, 12, 13, 14, or 15 inches.

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Hello,

The correct answer is B) |-13 - 17| = 30

Hope this helps!!!!

Answer:

a

Step-by-step explanation:

should be right

Answer:

no its not reasonable

Step-by-step explanation:

8 times 10 is 80 which is really far from 808.632

Answer: Hence, his evening sales were $630.

Step-by-step explanation:

Let the sales in the morning be 'x'

Let the sales in afternoon be x+50

Let the sales in the evening be 3(x+50).

Total sales for the day = $1000

According to question, it becomes

[tex]x+x+50+3(x+50)=1000\\\\2x+50+3x+150=1000\\\\5x+200=1000\\\\5x=1000-200=800\\\\x=\dfrac{800}{5}\\\\x=160[/tex]

So, his evening sales would be

[tex]3(x+50)\\\\=3(160+50)\\\\=3\times 210\\\\=630[/tex]

Hence, his evening sales were $630.

Answer:at least 50 pages

Use 1.75 cups of blue and 1 cup of yellow

The given problem can be placed in the category of ratios and proportions. There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too. Hence adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.