Write a linear function for the graph, and state and interpret the slope and y-intercept for the given scenario:

Water pressure can be measured in atmospheres (atm). Use the infomation in the graph to write an equation that models the pressure (y) at depth (x).

Triangles AED and BEC are congruent by AAS rule, so DE ≅ CE by CPCTC

When corresponding sides and angles of two triangles are congruent, they are said to be congruent triangles.

Given is figure of triangles,

In Δ ADC and Δ BCD,

AD ≅ BC (given)

∠ BCD ≅ ∠ ADC (given)

DC is common segment in both,

Therefore,  Δ ADC ≅  Δ BCD by SAS rule

∠ DAE ≅ ∠ CBE by CPCTC

∠ AED ≅ ∠ BEC by vertically opposite angles postulate.

Δ AED ≅ Δ BEC by AAS rule

DE ≅ CE by CPCTC

Hence, Triangles AED and BEC are congruent by AAS rule, so DE ≅ CE by CPCTC

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Answer:

4.) m > 7

5.) k + (-5) > 30 (The ">" has a line under It)

6.) 0.875

I don't know what it means when it says "graph the solution set" but I simplified it for you!

Answer: y=7x+1

Step-by-step explanation:

y=mx+b

Given:

slope= 7

point is (1,8)

Replace x and y for those numbers:

8=7(1)+b

Solve for b:

8=7+b

b=1

Final equation:

y=7x+1

The inequality for the annual family income is:

y < 1240x + 48,200

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Let x=0 be the year 2006

The inequality is:

y < 1240x + 48,200

Graphing:

Consider equal sign in place of < symbol

Take random values for x, find corresponding y values and plot them

Mark it as dashed line as shown in the graph because of the inequality symbol "< "

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The ratios are as follows

Ratio of boys to girls = 2:3

Ratio of girls to boys = 3:2

Ratio of tomato plants to lettuce plants = 1:2

Ratio of lettuce plants to cucumber plants = 4:1

Unit rate = $4

Cost of buying 20 copies = $80

What are ratios?

Ratios compare two numbers, usually by dividing them.

If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B.

For example, if A is five and B is 10, your ratio will be 5/10.

According to the given question:

1) There were 6 boys and 9 girls on the camping trip.

Ratio of boys to girls = 6:9 = 2:3

Ratio of girls to boys = 9:6 = 3:2

2) There are 4 tomato plants, 8 lettuce plants, and 2 cucumber plants in Jill's garden.

Ratio of tomato plants to lettuce plants = 4:8 = 1:2

Ratio of lettuce plants to cucumber plants = 8:2 = 4:1

3)  If Jan can buy 10 copies of a certain book for $40

Unit rate = 40/10 = $4

Cost of buying 20 copies = 20 x 4 = $80

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Answer: The sale price per dozen would we around $6.80 with no tax included.

Step-by-step explanation:

The altitude of the balloon found using Pythagorean Theorem is 40·√3 feet, the best correct option is option C)

C) 40·√3 ft

The Pythagorean Theorem states that the square of the hypotenuse side of a right triangle is the same as the sum of the square of each of the two legs of the right triangle.

15) The parameters in the question includes;

Horizontal distance of the flag pole from the point the rope is staked down = 40 feet

Length of the rope to which the balloon is secured = 80 feet

Location of the balloon = directly above the flag pole

Therefore, the altitude of the balloon, the length of the rope, and the horizontal distance from the flag pole from the point the rope is staked form a right triangle, with the length of the rope representing the hypotenuse side.

Let h represent the altitude of the flag pole, using Pythagorean Theorem, we get;

80² = 40² + h²

Therefore; h² = 80² - 40² = 4800

The altitude of the balloon, h = √(4800) = 40·√3

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Answer:

Step-by-step explanation:

Answer: I'm pretty sure the answer is either 18.6, or 90

Tell me in the comments if I'm wrong

The number of cars sold that were not white based on the dot plot is 19

From the question, we have the following parameters that can be used in our computation:

The dot plot represents the given parameter

From the dot plot, we have the following values represented as follows:

The above parameters means that the following cars are not white cars

So, we have the following representation

When these frequencies are added, we have

Total = 5 + 8 + 1 + 4 + 1

Evaluate the sum

Total = 19

Hence, the number of cars is 19

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Answer:

Step-by-step explanation:

2+0 is zero I mean two and 1+1 is two and 5+ I forgot something and you know you just need to add them up together in it at all your answer

Answer: 3 [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Answer:

7 1/5

Step-by-step explanation:

Step-by-step explanation:

Step 1: 2x²--7x²=9x²

Step 2: 2x--7x=9x

Step 3: -7-+2=-9

Overall answer: 9x²+9x-9

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The weight of the male that has a body surface area of 2.3 would be = 108kg

The body surface area (BSA) is defined as the parameter that can be used to estimate the surface area of a person's body based on body weight and height.

The formula for BSA = √w×h/3600

The weight of the male = X

The height of the male = 176cm

The BSA = 2.3

From the formula, make w the subject of formula;

w = BSA²× 3600/h

w = 2.3²× 3600/176

w= 5.29×3600 /176

w = 19044/176

w = 108kg

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Answer:

-4 acceleration

Step-by-step explanation:

: )

Answer: 7

Step-by-step explanation:

The values of the unknown angles are ∠1 = 92°, ∠2 = 24°, ∠3 = 64°, ∠4 = 35°, ∠5 = 81°

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal). For example, in the below-given figure, angle p and angle w are the corresponding angles.

∠1 + 88 = 180°( angles on a straight line)

∠1 = 180 - 88 which is 92°

∠3 = 64°( corresponding angles are equal)

∠2 + ∠1 + ∠3 = 180( sum of angles in a triangle)

∠2 + 92° + 64° = 180

∠2 = 180 - 92 - 64

∠2 = 24°

∠4 + 81 + ∠3 = 180 ( angles on a straight line)

∠4 + 81 + 64 = 180

∠4 = 180 - 64 -81

∠4 = 35°

∠5 = 81°( alternate angles are equal)

In conclusion the values of ∠1, ∠2, ∠3, ∠4, ∠5 are 92°, 24°, 64°, 35° and 81° respectively.

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The main differences between the place value of the whole number and the decimal is given below

What is decimal ?

Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the term used to describe how numbers are represented using the decimal system.

A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.

Decimals can be classified as non-recurring (as in not repeating or ending), recurring (as in repeating or not terminating), and decimal fractions (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).

The whole number part of the decimal number is the part that lies strictly to the left of the decimal point, and the place value of each digit in the whole number part is given .

The fractional part of the decimal number is the part that lies strictly to the right of the decimal point.

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I guess it sort of depends on whether you are folding the rectangle in half "long-ways" or "short-ways", however, if the rectangle is folded "long-ways", then the length of the new long side would be 5.5, with the shorter end being 4.25, or just 4.2.

Hope this helps!

Answer:

4.5 or equivalently 4 1/2 or 9/2

All are equivalent

Units are miles/hour

Step-by-step explanation:

Take any two points on the graph. Divide the change in y values to the change in x values and you get the rate

Chosen points: (0, 0) and (2, 9)

Rate of change = (9-0)/(2-0) = 9/2 = 4.5

Answer:

The correct answer is 514.90

Step-by-step  

The expression that shows the number of miles he drove and trips he made to San Diego is; 3850 + yb

Let a round trip to Los Angeles be denoted by the variable; x

Let the number of miles in a round trip to Los Angeles be denoted by the variable a

Let a round trip to San Diego be denoted by the variable: y

Let the number of miles in a round trip to San Diego be denoted with the variable: b

This means that our algebraic equation representing the number of miles driven in all to be: xa + yb

Since the truck driver made 5 round-trips to Los Angeles, then it means that, we have the equation;

5a + yb as the total miles driven in all.

However, from the table attached, a round trip to  Los Angeles  is 770 miles. Thus;

Total miles driven = 5(770) + yb = 3850 + yb

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Answer: it is A.

Step-by-step explanation: I did the quiz

Answer:

16

Step-by-step explanation:

You must use the Pythagorean theorem to find w. Because you are looking for a leg, you must do a² - b² = c². This translates to 20² - 12² = w². If you enter the numbers into your calculator 20²- 12² = 256. You must then square root 256, and if you input √256 into your calculator you will get your final answer of w = 16.

The value of x is 1.2

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

6-4x = 6x-8+2

group the variable and constant terms

6 +8 -2 = 6x +4x = 10x

12= 10x

=> x= 12/10 = 1.2

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Answer:

520

Step-by-step explanation:

390/3=130, 130x4=520

Answer:

5/3 is the slope

Step-by-step explanation:

Use the slope formula

m = y2 - y1/ x2 -x1

Answer:

Slope = 5/3

Step-by-step explanation:

Formula we use,

→ Slope = (y2 - y1)/(x2 - x1)

Now the required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (12 - 7)/(5 - 2)

→ [ m = 5/3 ]

Hence, required slope is 5/3.