What integer values for a and b would make the following statement true?

The distance they finishes is 8.6 miles

Given that miles run by Joni is 5 miles and the miles ran by Lori is 7 miles

We need to find the distance they finished

To calculate the total distance along the diagonal line, the Distance Formula first squares the differences between the two x coordinates and the two y coordinates, then adds those squares, and finally calculates their square root.

We know that

According to the Distance formula

= [tex]\sqrt{(5)2+(7)^2}[/tex]

= [tex]\sqrt{25+49}[/tex]

= [tex]\sqrt{74}[/tex]

= 8.6 miles

Therefore the distance finished is 8.6 miles

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The value of angle C in the triangle is 50°.

From the information given, the angle A = 60° while B is given as 70° and we are told to calculate the value of C.

It should be noted that the sum of angles on a triangle is 180°. Therefore, the value of C will be:

= 180° - (60° + 70°)

= 180° - 130°

= 50°

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Answer:

Step-by-step explanation:

The area for a triangle is

[tex]A=\frac{1}{2}bh[/tex]

Our base is given as x, the height is given as 1 more than 6 times the base which looks like this: 6x + 1. We know that the area is 13, so filling in everything:

[tex]13=\frac{1}{2} (6x+1)(x)[/tex]

We can get rid of the denominator of 2 by multiplying it on both sides to get:

[tex]26=(6x+1)(x)[/tex] and simplifying a bit:

[tex]26=6x^2+x[/tex]

Now we can move over the 26 and put the expression into standard quadratic form by setting it equal to 0:

[tex]6x^2+x-26=0[/tex] which is choice C

Answer: 1/5

Step-by-step explanation: You just subtract 4/5 from 1, or 5/5. And BOOM! you get 1/5.

Answer:

12/5

Step-by-step explanation:

to find tan D you need the opposite and the adjacent sides.

12 is opposite D and 5 is adjacent to D

so using the equation tan=Opposite/adjacent

tanD=12/5

The height of the rectangular cereal box is 40 cm.

Volume of a rectangular prism = lwh

where

Therefore,

10000 = 25 × 10 × h

10000 = 250h

h = 10000 / 250

h = 40 cm

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Health club members or were smokers is [tex]334[/tex] from a A survey of [tex]400[/tex] nurses yielded.

How can we find the health club members or were smokers ?

Events of health club members is [tex]P(M)=279[/tex]

Events of smokers is [tex]P(S)=215[/tex]

Probability of health club members and smokers is [tex]p(M and S)=160[/tex]

Probability of health club members or were smokers is =?

So we use the formula

[tex]p(M or S)=p(M)+p(S)-p(M and S)\\ = 279+215-160\\ = 334[/tex]

Probability of health club members or were smokers is [tex]334[/tex]

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The instantaneous rate of change of the function is 5/π

The function is given as

[tex]f(x) =\cos(x - \pi) + 4[/tex]

Where

[tex]x = \pi[/tex]

Calculate f(π) as follows

[tex]f(\pi) =\cos(\pi - \pi) + 4[/tex]

This gives

[tex]f(\pi) =\cos(0) + 4[/tex]

Evaluate the expression

[tex]f(\pi) =5[/tex]

The instantaneous rate of change is then calculated as;

[tex]f'(x) = \frac{f(\pi)}{\pi}[/tex]

This gives

[tex]f'(x) = \frac{5}{\pi}[/tex]

Hence, the instantaneous rate of change of the function is 5/π

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The mean for the given set of data exists at -1 1/3.

Mean exists an arithmetic average of the data set and it can be estimated by dividing a totality of all the data points by the digit of data points in the data set. It exists a point in a data set that exists as the average of all the data points we keep in a set.

Mean = (Sum of terms) / (Number of elements)

To find the mean, we must add all of the numbers and then divide them by the number of values you were given.

-4 + -3 + -1 + -1 + 0 + 1 = -8

There exist a total 6 number of elements in the set of data.

Mean = (Sum of terms) / (Number of elements)

Mean = (-4 + -3 + -1 + -1 + 0 + 1) / 6

-4 + -3 + -1 + -1 + 0 + 1 = -8

Mean = -8 / 6

= -4/3 = -1 1/3

The mean for the given set of data exists at -1 1/3.

Therefore, the correct answer is option a) -1 1/3.

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Answer:

the cat would take 13 steps

Answer:60g

Step-by-step explanation:

Hope this the answer

[tex]3x + 2 = 47 \\ 3x = 47 - 2 \\ 3x = 45 \\ x = \frac{45}{3} = 15[/tex]

Answer:

C. [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex]

Step-by-step explanation:

When you convert a fraction division into multiplication, you convert the divisor into its reciprocal. The reciprocal of [tex]\frac{2}{7}[/tex] is [tex]\frac{7}{2}[/tex]. So you get your answer  [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex].

Answer:

39

Step-by-step explanation:

Answer: 3/2

Step-by-step explanation:

[tex]\frac{7-1}{5-1}=\frac{6}{4}=\frac{3}{2}[/tex]

Answer:

y = x + 2

Step-by-step explanation:

You can find the slant asymptote using polynomial long division because the numerator is one degree higher than the denominator.

(x^2+x+4)/(x-1)

I'm not sure how to show long division but you should get:

x+2 with remainder 6

Then your slant asymptote is y = x + 2

You can graph it on Desmos to verify

Answer:

1425

Step-by-step explanation:

Each notebook costs 40, if she buys 30 you can find the total price of notebooks by multiplying the two numbers:

[tex]40*20=1200[/tex]

Each pen costs 15, the same process can be used, multiply price by quantity:

[tex]15*15=225[/tex]

Now just sum the two numbers to find the final price:

1425

Answer:

Step-by-step explanation:

30*40+15*15=

1200+625=

Rs1625

hope this helps

The coordinates of U after the reflection are: (-5, -3)

By looking at the graph, we can see that the coordinates of point U are:

U = (-1, -3)

And we want to reflect it across the line x = -3.

Notice that because this is a vertical line, the y-component does not change by the reflection. Only changes the x-component, such that the distance between the original coordinates and the final coordinates to the line don't change.

The original x-component is x = -1, the distance to the line is:

d = |-3 - (-1)| = 2 units.

Then the new x-component will also be at 2 units of the line, but in the other direction:

new x-component: x = -3 - 2 = -5

The coordinates of U after the reflection are:

(-5, -3)

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The width of the cooling tower is 36 meters.

A cooling tower is a vent that is built for the purpose of releasing waste heat back to the atmosphere.

Now we can model the system using;  x²/324 - (y² - 90)²/1600. Thus, the width can be obtained from;

2 × ✓324

= 2 × 18

= 36 meters

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Missing parts;

Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.

36 meters

48 meters

80 meters

89 meters

Please see the explanation of this question to see procedure for the dilation of the triangle ABC and the image attached below to know the result.

In this question we must apply a kind of rigid transformation known as dilation. A dilation of a point around a point of reference is defined by the following operation:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]     (1)

Where:

Let assume that the point P is the origin of a rectangular system of coordinates. Then, the coordinates of the three vertices of the triangle ABC respect to the origin are: A(x, y) = (- 1, 2), B(x, y) = (- 1, - 1), C(x, y) = (2, 0).

Then, the vertices of the resulting triangle A'B'C' are, respectively:

A'(x, y) = (0, 0) + 3 · [(- 1, 2) - (0, 0)]

A'(x, y) = (- 3, 6)

B'(x, y) = (0, 0) + 3 · [(- 1, - 1) - (0, 0)]

B'(x, y) = (- 3, - 3)

C'(x, y) = (0, 0) + 3 · [(2, 0) - (0, 0)]

C'(x, y) = (6, 0)

Finally, we draw the resulting triangle with the help of a graphing tool.

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Applying the sine ratio and law of sines, the correct measurements are:

B. m∠B = 15°

E. h ≈ 31.28 ft.

Sine ratio that can be used to determine the side length of a right triangle is, sin ∅ = opposite side/hypotenuse.

Find c using the law of sines:

C = 33°

A = 180 - 48 = 132 [linear pair]

B = 180 - 33 - 132 = 15° [triangle sum theorem]

b = 20 ft

c = ?

Using the law of sines, b/sin B = c/sin C, we have:

20/sin 15 = c/sin 33

(c)(sin 15) = (20)(sin 33)

c = (20 × sin 33)/sin 15

c ≈ 42.09

Use the sine ratio to find h:

∅ = 48°

Hypotenuse = c = 42.09

Opposite = h = ?

sin 48 = h/42.09

h = (sin 48)(42.09)

h ≈ 31.28

The correct measurements are:

B. m∠B = 15°

E. h ≈ 31.28 ft

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Answer:

B. and E.

Step-by-step explanation:

Answer:

Its A or B

Step-by-step explanation:

The coordinates of the new rectangle formed after transformation are; A'(3, -1); B'(6, -1); C'(6, 4); D'(3, 4)

We are told that the original rectangle which I labelled ABCD in the attached image is rotated 90° clockwise about the origin.

Now, from the translation of Rectangle ABCD into A'B'C'D' using the transformation rule in the question, the new coordinates are;

A'(3, -1)

B'(6, -1)

C'(6, 4)

D'(3, 4)

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The graph that represents y= cos(2x - π) +5 is illustrated below.

It should be noted that a graph simply means a series of connections among variables given.

In this case the graph that represents y= cos(2x - π) +5 is illustrated below.

The graph is attached.

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When an arithmetic expression contains two or more different operators, such as * and , the order in which the operations is done is determined by: Operator precedence

Precedence is known to be a kind of rule that tells the order in which a specific operations need to be carry out in an arithmetic expression.

The precedence of an operator specifies how tightly it binds two arithmetic expressions together.

In the arithmetic expression 4 + 5 * 3 , the answer is 19 and not 27 because the multiplication (*) operator has a higher precedence than the addition (+) operator.

Operator associativity is nothing but how operators of the same precedence are evaluated in an arithmetic expression. It can be either from left to right or right to left.

Therefore, when an arithmetic expression contains two or more different operators, such as * and , the order in which the operations is done is determined by: Operator precedence

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Answer:

Step-by-step explanation:

32 = 2 : 5

32/7 = 4

2 x 4 : 4 x 5

8 : 20

The probability you will roll a sum of 9 is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability you will roll a sum of 9 = total times a sum of 9 is derived / total sample spaces

The probability you will roll a sum of 9 = 4/36 = 1/9

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