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A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles.

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The car is 120 miles away when the motorcycle starts.

The bike gains on the car at 30 mph (70-40).

It takes 4 hours for the bike to close the gap (120/30).

In 4 hours, the bike and the car are 280 miles from the starting point.

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4*70 = 280

7*40 = 280

Since Distance = Speed x Time, and in this case, the distances are equal, we, therefore, have: 70T = 40(T + 3)

70T = 40T + 120

30T = 120

T=4, which makes the distance that both vehicles traveled, highlight_green280miles, calculated as (70 * 4), or (40 * 7).

It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.

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If m has exactly 5 positive divisors then there can only be one prime factor.

According to statement

m has exactly 5 positive divisors AND

Let A^p,B^q,.... are the possible factors of integer m then

assume that p and q ≥ 1.

then the number of possible divisors cannot be 5 because there are no two integers  p, q ≥ 1, such that (p +1)(q + 1) = 5

So, If m has exactly 5 positive divisors then there can only be one prime factor.

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A bisector is a line that divides a given line or angle into two equal parts or measures. So that the required statements and reasons are given below:

              STATEMENT                                                 REASONS

1. BC bisects <ABD                                 Given

2. m<ABC = [tex]26^{o}[/tex]                                       Bisection property of an angle

3. 2(m<ABC) = [tex]52^{o}[/tex]                                   Sum of angles of a bisected angle

4. m<ABC = m<CBD                                Congruent parts of a bisected angle

5. <mABC + m<ABC =  [tex]52^{o}[/tex]     Sum of an individual angle of a bisected angle

6.  m<ABC + m<CBD = [tex]52^{o}[/tex]                      Sum of angles of a bisected angle

7. m<ABC + m<CBD = m<ABD          Sum of the angles of a bisected angle

The above statements and reasons are majorly centered on a bisector, the angles formed due to the bisection of a given angle, and the bisected angle.

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Answer:

1. BC bisects <ABD | Given

2.m<ABD=52 | Given

3.m<ABC = m<CBD | Definition of Bisector

4.m<ABC + m<CBD = m<ABD | Angle Addition Postulate

5.m<ABC + m<CBD =52 | Substitution Property

6.m<ABC + m<ABC =52 | Substitution Propery

7.2(m<ABC)=52 | Addition

8.m<ABC=26 | Division Property

Step-by-step explanation:

Edge 2022

The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time

An equation is an expression that shows the relationship between two or more numbers and variables.

The distance travelled in 30 minutes is:

Distance = speed * time = 4 mph * 0.5 h = 2 miles

The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time

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Answer:

32...................

Answer:

(x - 5)(x + 5)

Step-by-step explanation:

x² - 25 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

x² - 25

= x² - 5²

= (x - 5)(x + 5)

Answer:

Step-by-step explanation:

(x-5) +(x+5)

Answer:

Step-by-step explanation:

Maybe..

8/10

12/15

16/20

20/25

24/30

28/35

32/40

36/45

40/50

Any one of these is equal to the ratio of 4 over 5.

Answer:

No, the person who answered first is wrong

I'll give you the correct answer

Step-by-step explanation:

He the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.

thank you, this is the correct answer

hope that hepls

The linear equation that best fits the data is: y = 10x + 15.

First, find the slope/unit rate (m) and the y-intercept/starting value, then substitute the values into y = mx + b.

Using two points on the graph, (1, 25) and (2, 35), find the slope (m):

Slope (m) = (35 - 25)/(2 - 1)

Slope (m) = 10/1

Slope (m) = 10

Substitute (x, y) = (1, 25) and m = 10 into y = mx + b to find b

25 = 10(1) + b

25 - 10 = b

b = 15

Substitute m = 10 and b = 15 into y = mx + b

y = 10x + 15

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Answer:

The equation representing the proportional relationship between j and m is m = 3j/4 .

Step-by-step explanation:

Writing an Equation to Represent a Proportional Relationship

What is proportional relationship?

A proportional relationship between two quantities is when the two quantities vary directly with one and other. Meaning if one item is doubled, the other item is also doubled.

Going back to the given problem above, we have the table showing the proportional relationship between j and m.

j | 4 | 12 | 20 |

m | 3 | 9 | 15 |

Solution:

Step #1

The proportional relationship can be written as:

m/j = ¾ = ‌9⁄12‌ = ‌15⁄20‌ = ¾

Step #2

So, the equation representing this proportional relationship is:

m = ¾ × j/1 = 3j/4

Final Answer:

The equation representing the proportional relationship between j and m is m = 3j/4 .

Step-by-step explanation:

Number of shirts = dependent variable

Cost of the purchases = independent variable

The amount of aspirin that would be in the patient's body is; 281.25.

A) The amount of aspirin in the patient's body after 2 hours can be evaluated as follows;

a = 500×(3/4)² = 4500/16 = 281.25.

B) The number 500 as used in the equation represents the amount of aspirin in the patient's body prior to taking the medicine, at time, t= 0.

C) The fraction 3/4 as used in the task content is the factor of change in aspirin content in the patient's body.

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Using a linear function, it is found that you would need roughly 24 hours of training to have a monthly pay of $1500.

A linear function is modeled by:

y = mx + b

In which:

Looking at the table, the pay increases $200 each 10 hours of work, hence the slope is:

m = 200/10 = 20

Then:

y = 20x + b

When x = 10, y = 1220, hence:

y = 20x + b

1220 = 20(10) + b

b = 1020.

Then the pay for x hours of training is:

y = 20x + 1020.

For a pay of $1500, we have that:

y = 20x + 1020.

1500 = 20x + 1020.

20x = 480

x = 24

You would need roughly 24 hours of training to have a monthly pay of $1500.

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Answer:

(- 9, 2 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(9, 2 ) → (- 9, 2 )

Answer:

Que is talking about a syrup which contains 50% of sugar .

Que asked : amount of sugar syrup from X grams of sugar.

Explanation :

if a sugar syrup contains 50% of sugar , that means that the half of the solution contains sugar and half is solvent .

means , 2 × amount of sugar = solution (syrup)

now , we are given x grams of sugar

then , solution can be made with x grams of sugar = 2 × (X grams) = 2X gram of solution or sugar syrup.

.

.

Mark BRAINLIEST!

Answer:

1/49.

Step-by-step explanation:

(−7)^-2

=  1 /(- 7)^2

= 1/49.

Step-by-step explanation:

Answer:

2.50x+1.25y=z

Step-by-step explanation:

Let the number of juice bottles = x

And the number of containers of popcorns=y

And the total number of juice bottles and containers of popcorns=z

Total number of juice bottles=x times $2.50

Total number of containers of popcorn= y times $ 1.25

equation; 2.50x+1.25y=z

Answer:

28 ft^2

Step-by-step explanation:

The room is in the shape of a square.  That means the base of the room (width and length) will have the same dimensions.

Length x Width = 49 ft^2

Length = Width

Length^2 = 49 ft^2

Length  = 7 feet

Width is also 7 feet

The height of the room is 4 feet, plenty for non-humans.  One wall area would be (7 ft)*(4 ft) = 28 ft^2

Answer:

10

Step-by-step explanation:

This is because you would have to start with 109 = 23x

then solve it using logarithms

Then once you get the x value, it becomes

X>_10__(whatever number you found)

Answer:

CD = 13

Step-by-step explanation:

since Δ ABD and Δ CBD are congruent , then corresponding sides are congruent, so

CD = DA = 13

Answer:

13

Step-by-step explanation:

We know that if two triangles are congruent, the corresponding element of those are also equal.

Given that,

ABD Δ ≡ CBD Δ

Therefore, the corresponding elements are also equal.

AD = CD

AD = 13 units

∴ CD = 13 units

Answer:

choice C

Step-by-step explanation:

The circle is circumscribed because circles drawn on the outside is known as circumscription. The circle is clearly outside touching the three vertices of the triangle.

Answer:

f(x)=2x-3

Step-by-step explanation:

cause fir example if you put x=2 the y became 1.

The formulas and the equivalent formulas are

W = X - Y                                    X = W +Y

W = X/Z - Y                                 X = Z(W + Y)

W = (X - Y)/Z                               X = WZ+Y

W = XY                                       X =W/Y

To do this, we simply make X the subject of the formula in expressions on the left.

So, we have:

W = X - Y

This gives

X = W + Y

W = X/Z - Y

This gives

X/Z = W + Y

X = Z(W + Y)

W = (X - Y)/Z

This gives

X - Y = WZ

X = WZ + Y

W = XY

This gives

X =W/Y

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Complete question

Match each formula on the left with an equivalent formula on the right.

W = X - Y                                     X =W/Y

W = X/Z - Y                                 X = Z(W + Y)

W = (X - Y)/Z                               X = WZ+Y

W = XY                                       X = W +Y

The scale of the diagram as described in the task content is; 1: 8 where k= 8.

It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.

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Answer:

10

Step-by-step explanation:

Plugin your answer: -4 + 10 = 6

Answer:

10

Step-by-step explanation:

The value of the angle ∠BCA when approximated to 3 significant figures is;  20.4°

From the attached image of the triangle ABC showing the side lengths x and y, we can see clearly that it is a right angle triangle.

Now, since we want to find the value of the angle ∠BCA, then it means we have to use trigonometric ratio to get;

x/y = sin BCA

Plugging in the relevant values gives us;

8/23 = sin BCA

∠BCA = sin⁻¹(8/23)

∠BCA = 20.355

Approximating to 3 significant figures gives us;

∠BCA = 20.4°

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Answer:

[tex] \frac{8}{24} [/tex]

Step-by-step explanation:

If Adam's family uses 8lb of apples to make pie. We know that 3 x 8 = 24, so it's probably approximately 3 out of 18.