Car A is traveling east at a steady speed of 50 miles per hour. After 2 hours, it is 140 miles east of Johnstown.
Car B is traveling east on the same road. its distance east of Johnstown is represented by the graph.
Where were the two cars in relation to each other when they began traveling?

Using the point-slope equation, the equations that represent the data are:

y - 6 = -1.25(x + 2)

y -3.5 = -1.25x

Given a point (a, b) and slope (m), the point-slope equation is expressed as, y - b = m(x - a).

Find the slope (m) using two pairs from the table of values say, (-2, 6) and (2, 1):

Slope (m) = change in y / change in x = (6 - 1)/(-2 - 2) = 5/-4 = -1.25

Using the point, (a, b) = (-2, 6) and m = -1.25, plug the values into y - b = m(x - a):

y - 6 = -1.25(x - (-2))

y - 6 = -1.25(x + 2)

This cam be rewritten as:

y - 6 = -1.25x - 2.5

y - 6 + 2.5 = -1.25x

y -3.5 = -1.25x

The equations that represent the data in the table are:

y - 6 = -1.25(x + 2)

y -3.5 = -1.25x

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The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.

Total distance if Pete walks from A to B to C:

= 15 + 25 = 40 yards

As we know in the triangle the sum of the two sides is greater than the third side.

25 + 15 > AC

40 > AC

or

AC < 40

The direct distance from A to C is more than 10(25-15) yards.

The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.

Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

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Answer:

40, 10, 30
see picture

Step-by-step explanation:

The total amount of snowfall on the two days combined is 4 3/8 cm

From the question, we are to determine the amount of snowfall on the two days combined

From the given information,

the amount of snowfall was 1/8 cm on Thursday

The amount of snowfall was 4 1/4 cm on Wednesday

Then,

The total amount of snowfall on the two days combined will be

[tex]\frac{1}{8}+4\frac{1}{4}[/tex] cm

= [tex]\frac{1}{8}+\frac{17}{4}[/tex]

= [tex]\frac{1+34}{8}[/tex]

= [tex]\frac{35}{8}[/tex]

= [tex]4\frac{3}{8} \ cm[/tex]

Hence, the total amount of snowfall on the two days combined is 4 3/8 cm

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To eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.

Elimination is a process of solving a system of equations to eliminate one variable and solve for the other.

To eliminate the y terms from the equations,

first equation: 4x - 3y = 34, and

second equation: 3x + 2y = 17,

we take the L.C.M. of the coefficients of y, that is 3 and 2, which is 6, and multiply the equation by the value = (LCM of the coefficients/respective coefficient of y).

That is, for :

the first equation, we multiply the equation by (LCM of the coefficients/respective coefficient of y) = 6/3 = 2.

the second equation, we multiply by (LCM of the coefficients/respective coefficient of y) = 6/2 = 3.

Thus, to eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.

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1) All interior angles of a square are right angles, so angle WER measures 90°

2) All squares are parallelograms, and diagonals of a parallelogram bisect each other, meaning PA=AE=8 cm. Thus, PE=16 cm

3) All squares are rectangles, and diagonals of a rectangle are congruent, meaning WR=16 cm. Then, using the fact that the diagonals bisect each other, we get that WA=8 cm

4) If we consider right triangle WPR, we know it is isoceles because all sides of a square are congruent. So, the length of WP is:

[tex] \frac{16}{ \sqrt{2} } = 8 \sqrt{2} [/tex]

Answer:

.7 I your answer to your question hope it's help

Answer:

[tex]\frac{7}{10}[/tex]

Step-by-step explanation:

35/50 -->    [tex]\frac{7}{10}[/tex]
divide 35 by 5 = 7
divide 50 by 5 = 10

Answer:

270 miles

Step-by-step explanation:

Since the unit rate is 30 miles per hour, the miles on 9 hours will be:

= 30 × 9

= 270 miles.

Answer:

Rs 20

Step-by-step explanation:

140%=Rs 70

100%

(100%×Rs 70)÷140%=50

Rs 70-Rs 50=Rs 20

Work Shown:

[tex]m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5\\\\[/tex]

Therefore,

[tex]\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5\\\\[/tex]

Answer:

A

Step-by-step explanation:

The parabola opens to the left, so this eliminates C and D.

Also, the vertex is at (-17, 2), and out of A and B, the only parabola with this vertex is A.

The complete options are P(opposed the tax or is female) = 0.28, b. P(supports the tax or is male) = 0.15, c. P(is not unsure or is female) 0.025.

Probability refers to a possibility that deals with the occurrence of random events.

(a) The probability that the person opposed the tax or is female.

P(opposed the tax or is female) = 298 / 1052 = 0.28

(b) The probability that the person supports the tax or is male.

P(supports the tax or is male) = 168/1052 = 0.15

(c) The probability that the person is not unsure or is female.

P(is not unsure or is female) = 27 / 1052 = 0.025

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Answer:

False

Step-by-step explanation:

m∆A+m∆C=180°

110°+110°=180°

220°(/=) 180°

A circle can be circumscribed about the given quadrilateral, the answer is true.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

To circumscribe a circle about a quadrilateral means to place the quadrilateral inside the circle, such that the four vertices of the quadrilateral touches the the circumference of the circle.

Opposite angles of a circumscribed polygon are supplementary.

Therefore, a circle can be circumscribed about the given quadrilateral is true

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Step-by-step explanation:

[tex] = {3}^{0} \times {3}^{ - 3} [/tex]

[tex] = 1 \times \frac{1}{ {3}^{3} } [/tex]

[tex] = \frac{1}{3 \times 3 \times 3} [/tex]

[tex] = \frac{1}{27} [/tex]

Answer:

12 Vanilla Frosted Cupcakes

Step-by-step explanation:

30 Cupcakes.

1/5 Of 30 is 6.

30 - 6 = 24.

24/2 = 12.

Step-by-step explanation:

since the two angles from a straight line, they make a linear pair and linear pairs are supplementery. by the angle addition postulate, you can determine that the two angles sum to 180. substituting the one angle mearsure that you are guven and using a bit of simple arithmetic and the subtraction property of equality, you can determine that the other angle,angle YXZ, is 45 degrees. I hope this is helpful

Answer:

[tex]\fbox {b) 50}[/tex]

Step-by-step explanation:

The sum of the exterior angles of any polygon (including a pentagon) is equal to 360 degrees.

Then :

⇒ x + 2x + x + 30 + x - 10 + x + 40 = 360

⇒ 6x + 60 = 360

⇒ 6x = 300

⇒ x = 50

Answer:

[tex]\huge\boxed{\sf x = 50}[/tex]

Step-by-step explanation:

x + 2x + x + 30 + x - 10 + x + 40 = 360

6x + 60 = 360

Subtract 60 to both sides

6x = 360 - 60

6x = 300

Divide 6 to both sides

x = 300/6

x = 50

[tex]\rule[225]{225}{2}[/tex]

Answer:

x = ±√7, ±i√2

Step-by-step explanation:

[tex]x^4-5x^2-14=0\\(x^2-7)(x^2+2)=0\\[/tex]

[tex]x^2 - 7 = 0[/tex] or [tex]x^2 + 2 = 0\\[/tex]

x^2 - 7 = 0

x^2 = 7

x = ±√7

or x^2 + 2 = 0

x^2 = -2

x = ±i√2

Answer: B. The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths.

Step-by-step explanation:

Reflections are congruency transformations, but dilations are similarity transformations.

Answer:

Pease check my assumptions.

Step-by-step explanation:

I will assume that f(x)=x2 is actually f(x) = x^2.

Same for g(x)=(12x)^2  [Is it g(x)=12x^2  ???]

See the attached image.

Note that (12x)^2 results in a narrower, steeper graph.   That's because (12x)^2 can be rewritten as 144x^2, so every value is multiplied by 144, compared to just x^2.

Answer:

[tex]\fbox {B. Exponential Decay}[/tex]

Step-by-step explanation:

As the exponent is applied to a number less than 1, the future values of the function f(x) will become smaller and smaller. Hence, it represents exponential decay.

The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.

Probability, can be define as the ratio of favorable outcomes to the n number of total events.

Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
       p(b) =  temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
                                  =   0.81 + 0.46 -1
                                  =   0.28

The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

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The  polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).

The given polynomial to us is p(x) = x³ + 5x² - x - 5.

We are asked to factor the polynomial by grouping.

We can do this by following these steps:

Therefore, the polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).

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Answer:

Step-by-step explanation:

       [tex]\sf \boxed{\bf y = mx +b}[/tex]

Here, m is the slope and b is the y-intercept

  Find the slope with the given two points.

   [tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

             [tex]\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}[/tex]

Slope = -2/3 and choose any one the given points.

Substitute m = -2/3  and (5,6)  in the above equation and find 'b'

      [tex]\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}[/tex]

Equation of the line:

            [tex]y = \dfrac{-2}{3}x + \dfrac{28}{3}[/tex]

Answer:

The probability that more than 7 weeks pass between accidents is 4.0551 .

Step-by-step explanation:

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes

A Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period.

mean = 5 weeks

rate = 1/5 = 0.2

x = average time

 P(x > 7) = e^(0.2×7) = 4.0551

The probability that more than 7 weeks pass between accidents is 4.0551 .

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