During the repair, the mechanics will need to
connect a cable between chairs B and J, and then
continue that cable to chair G. What is the angle
formed by the cable?

It would take Arron 3 hours to travel 18 miles upstream (against the river)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operations.

Speed is the ratio of total distance to total time taken.

Arron boat has a speed of 9 mph in still water and the speed of the river is 3 mph. Since he is travelling upstream, we subtract both speed:

He needs to travel 18 miles upstream at time t, hence:

(9 mph - 3 mph) = 18 miles / t

6t = 18

t = 3 hours

It would take Arron 3 hours

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The required reference angle of 13π/8 is 3π/8.

The reference angle of an angle in standard position is the positive acute angle formed between the terminal side of the angle and the x-axis.

Given an angle of 13π/8, we can determine its reference angle as follows:

Angle: 13π/8

Since the angle is in the fourth quadrant, we subtract it from 2π (one full revolution) to find the reference angle:

Reference angle: 2π - 13π/8 = 3π/8

Therefore, the reference angle of 13π/8 is 3π/8.

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The difference in height is 400 metres.

Height refers to vertical distance from the top to the object's base. Occasionally, it is also labeled as an altitude which measures from down to top of a surface.

To get difference in height, we will subtract the height after the eruption from the height before the eruption:

Given:

Height before eruption = 2.95 kilometers

Height after eruption = 2.55 kilometers

Difference in height = Height before eruption - Height after eruption

Difference in height = 2.95 km - 2.55 km

Difference in height = 0.4 kilometers

0.4 kilometers to metres will be:

= 0.4 * 1000 metres

= 400 metres.

Full question:

Mount St. Helens, located in Washington, erupted on May 18, 1980. Before the eruption, the volcano was 2.95 kilometers high. After the eruption, the volcano was 2.55 kilometers high. Find the difference in height of Mount St. Helens before and after the eruption.

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Answer: Tommy's sister is four meters away from him.

Step-by-step explanation:

If Tommy's older brother is 4 meters ahead and he is 5 meters from his sister,subtract 1 from that since it is described she is right next to him,and you get four.

This is my first time answering anyone so I hope it helps.

a. The constant of variation is k = 45.

b. The equation for the relation is y = 45/x².

c. x = 5, y is approximately equal to 1.8.

d. The equation provided, y = -52 + (5)/(5x²), seems to be incorrect or incomplete as there are misplaced parentheses and missing values.

The constant of variation for the relation "y varies inversely as the square of x," we can use the general form of an inverse variation equation:

y = k/x², where k represents the constant of variation.

The given information, we have y = 5 when x = -3.

Substituting these values into the equation, we get:

5 = k/(-3)²

5 = k/9

k = 45

The constant of variation is k = 45.

The equation for the relation is y = 45/x².

To find y when x = 5, we can substitute the value of x into the equation:

y = 45/(5)²

y = 45/25

y = 1.8

x = 5, y is approximately equal to 1.8.

The equation provided, y = -52 + (5)/(5x²), seems to be incorrect or incomplete as there are misplaced parentheses and missing values. Please clarify the equation and I'll be happy to assist you further.

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Answer:

6 divide by 60 into 100

Step-by-step explanation:

is 10

The prove of the statement is described below.

First of all ,

Labeling the given figure

And draw  a diagonal,

In the quadrilateral PQRS,

The side PQ is equal to the side RS.

Therefore,

PQ = RS

And also, the side PQ is parallel to the side RS.

Then,

PQ || RS.

Now, draw the diagonal PR.

We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.

By the rule of  Side-Angle-Side,

we can show that ∆ PQR ≅ ∆ RSP.

Therefore,

The side QR is parallel to PS

Then,

QR || PS.

Hence,

PQRS is a parallelogram.

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The measures of the following arcs are :

m∡AB = 49°

m∡ABC = 253°

m∡BAC = 156°

m∡ACB = 311°

Note that the sum total of the arcs in a circle is 360°

m∡AB = 49° - Given

m∡ABC =  360°  107° =  253°

m∡BAC =  107 + 49 = 156°

m∡ACB = 360 - 49 = 311°

A curve's arc length is significant because it represents the distance between two locations on the curve. The circumference of a circle is equal to its arc length. The arc length of an ellipse equals the ellipse's perimeter.

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Answer:

$6.06

Step-by-step explanation:

$1.29 x 4.7 = 6.063

Round: 6.06

Answer:

Step-by-step explanation:

To find the difference between the amount of butter and sugar used, we need to subtract the weight of sugar from the weight of butter.

The weight of butter used is 5/8 pounds, and the weight of sugar used is 1/2 pounds. To subtract these fractions, we need to find a common denominator.

The common denominator for 8 and 2 is 8, so we can rewrite the fractions as follows:

5/8 pounds of butter

4/8 pounds of sugar

Now we can subtract the weight of sugar from the weight of butter:

5/8 - 4/8 = 1/8

Therefore, Percy's Desserts used 1/8 pound more butter than sugar.

Answer: Percy's Desserts used 1/8 pounds more butter than sugar in their batch of fresh scones.

Step-by-step explanation:

1. Identify the quantities of butter and sugar used: Percy's Desserts used 5/8 of a pound of butter and 1/2 of a pound of sugar.

2. Convert the quantities to a common denominator: To compare these quantities, we need to express them with a common denominator. The least common denominator of 8 and 2 is 8. So, we express 1/2 as 4/8.

3. Subtract the quantity of sugar from the quantity of butter: Now that both quantities are expressed in eighths of a pound, we can subtract them: 5/8 - 4/8 = 1/8.

4. Convert the result back to a decimal: 1/8 of a pound is equivalent to 0.125 pounds.

So, Percy's Desserts used 0.125 pounds more butter than sugar in their batch of fresh scones.

According to the angles between intersecting secant and tangent, the value of

angle DF is 52 degrees

angle PQR = 49 degrees

The value of angle DF is solved using the angles of intersecting secant out side the circle

The theorem give the formula in the form

44 = 1/2 (140 - DF)

88 = 140 - DF

DF = 140 - 88

DF = 52 degrees

Using intersection of tangents, for the second figure

exterior angle = 1/2 (major arc - minor arc)

major arc = 360 - 131 = 229

PQR = 1/2 (229 - 131)

PQR = 49 degrees

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The exact value of the cosine of θ is given as follows:

a) 3/5.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

Applying the Pythagorean Theorem, the hypotenuse length is given as follows:

x² = 6² + (-8)²

x² = 100

x = 10.

As the x-coordinate is used for the cosine, the cosine is given as follows:

cos(θ) = 6/10

cos(θ) = 3/5.

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The resultant of the force that acts in opposite directions is 7 N.

We have,

We know that the resultant force is the force that has the same effect in magnitude and direction as two or more forces that is acting together. We have to note that the force that is actinmg on an object is a vector quantity. The implication of this is that the magnitude and the direction of the forces that are acting on the body is very important.

By the use of the law of vectors we can be able to write in the case of the question that we have here, we can see that the forces are acting in the opposite directions. The implication of this is that we would have to subtract the forces so as obtain the resultant force.

We have to note that when we have opposite forces, one is said to be positive and the other negative and the resultant force can be found by subtraction. As such the resultant force can be obtained from;

Let the +B force be 12 N

Let the -B force be 5N

12 N - 5 N = 7 N

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The total distance she cover after running is 9600 meters

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

Number of times = 12 times

Dimensions of the playground = 240 m by 160 m

The perimeter of the playground is calculated as

Perimeter = 2 * sum of dimensions

substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (240 + 160)

The total distance she cover is calculated as

total distance = 12 * 2 * (240 + 160)

Evaluate

total distance = 9600 meters

Hence, the total distance she cover is 9600 meters

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Answer:

  (b)  $3564.54

Step-by-step explanation:

You want the new balance showing on a credit card statement if the APR is 27.99%, the old balance is $3109.87, a payment of $159 was made, and purchases were made totaling $532.42.

Apparently, the new balance is computed by subtracting payments, and adding new charges to the old balance, then computing and adding the finance charge on this sum.

  balance before finance charge: $3109.87 -159.00 +532.42 = $3483.29

The finance charge is 1 month's interest at the annual rate:

  I = Prt = $3483.29×0.2799×(1/12) = $81.25

The new balance is the subtotal above, with the finance charge added:

  new balance = $3483.29 +81.25 = $3564.54

Kyle's new balance will be $3564.54.

__

Additional comment

This is a very expensive credit card. Not only is the interest rate of 27.99% very high, but also finance charges are charged on new purchase in the month they are purchased.

Some cards these days have interest rates of 12.75% or lower, with no finance charge for purchases made during the month. Some cards offer a rebate of up to 1.5% of purchases, so a net "negative" finance charge if you pay off the card every month.

The numbers arranged in the correct order are:

-3 = -3

-3 < | -1 |

0 < | 1 |

2 > | 0 |

3 > | 1 |

We have,

-3 = -3:

This is a true statement because -3 is indeed equal to -3.

-3 < | -1 |:

This is also a true statement.

The absolute value of -1 is 1, so we are comparing -3 and 1.

Since -3 is less than 1, the inequality is true.

0 < | 1 |:

Again, this is a true statement.

The absolute value of 1 is 1, so we are comparing 0 and 1.

Since 0 is less than 1, the inequality holds true.

2 > | 0 |:

This is also a true statement.

The absolute value of 0 is 0, so we are comparing 2 and 0.

Since 2 is greater than 0, the inequality is true.

3 > | 1 |:

Once again, this is a true statement.

The absolute value of 1 is 1, so we are comparing 3 and 1.

Since 3 is greater than 1, the inequality holds true.

Therefore,

By arranging the given numbers in this order: -3, -3, -1, 0, 1, 2, 3, all of the number sentences become true.

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Answer:

x+1

Step-by-step explanation:

you have to rewrite the equestion, factor the expression, and than reduce it

The only relation that is a function is the one in option C.

A relation maps elements from a set called the domain into elements of another set, called the range.

Particularly, if each of the elements in the domain is mapped to a single value in the range, then we have a function.

When we have a graph, we can do the vertical line thest, if a vertical line touches the graph more than once, then it is not a function, with that we can discard the two graphs in the left.

And for option D, we can see that the input 22 is mapped into two different values.

The remaining option, C, is the correct one.

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The triangles are not similar

Given data ,

Let the first triangle be ΔJKL

Let the second triangle be ΔMNP

Now , the corresponding sides are

JK / JL ≠ NM / MP

where the corresponding sides of similar triangles are not in the same ratio

And , the common angle to both the triangles is ∠J = ∠M

So , ∠J = ∠M and JK / JL ≠ NM / MP

Hence , the triangles are not similar

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The correct answer is [tex]\dfrac{16\pi }{9}[/tex]

The area of a shaded region is [tex]\sf \dfrac{n\pi r^2}{360}[/tex]

So, applying the formula [tex]\sf \dfrac{n\pi r^2}{360}[/tex]

[tex]\sf =\dfrac{160\pi r^2}{360}=\dfrac{160\pi (2^2)}{360} =\dfrac{160\times\pi \times4}{360} =\dfrac{16\pi }{9}[/tex]

Hence the area of shaded region is [tex]\dfrac{16\pi }{9}[/tex]

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The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.

We have,

The vertex form of a parabola is given by the equation y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

Now,

Given that the parabola passes through (-2, 4) and has a vertex (0, 8), we can substitute these values into the equation to find the value of 'a'.

Using the vertex (0, 8):

8 = a(0 - 0)² + 8

8 = a(0) + 8

8 = 8

Since the coefficient of the squared term is 'a', which remains unchanged, we can conclude that a = 1.

Therefore,

The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.

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The equation can be used to determine how many points Patrick earned is ;5 + 6 + y = 14.

What is an equation?

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

A mathematical equation is a statement with two equal sides and an equal sign in between.  4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that Billy, Kip, and Patrick earned a combined 14 points during their team's game. Billy earned 5 points and Kip earned 6 points.

We can determine the direct answer by taking Billy and Kip's points and subtracting it from the total combined points.

That will give us 11, which means Patrick earned 3 points.

The equation we can use to represent this is ;5 + 6 + y = 14.

The statement "x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex]" is false.

To determine whether x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex], we can use the factor theorem.

According to the factor theorem, if a polynomial p(x) has a factor (x - a), then p(a) = 0.

In this case, we have x + 3 as a possible factor. To check if it is indeed a factor, we substitute -3 for x in the polynomial p(x):

[tex]p(-3) = (-3)^3 - 7(-3)^2 + 15(-3) - 9[/tex]

= -27 - 63 - 45 - 9

= -144

Since p(-3) is not equal to zero, we conclude that x + 3 is not a factor of p(x).

Therefore, the statement "x + 3 is a factor of [tex]p(x) = x^3 - 7x^2 + 15x - 9[/tex]" is false.

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Answer: (-2, -1)

Step-by-step explanation:

Ok since we just have to find A", let's transform only point A.

Point A=(-1, 5).

Now let's translate it: (-1+3, 5-4). Point A' = (2, 1).

Now, we have to do a 180° rotation. The formula is (-x, -y).

Point A'' = (-2, -1)

The algebraic expression for the sentence "5 subtracted from 3 times p" is given as follows:

A. 5 - 3p.

The sentence in the context of this problem is defined as follows:

"5 subtracted from 3 times p"

The expression that represents 3 times p is given as follows:

3p.

(that is, 3 and p are multiplied).

Then 5 subtracted from 3 times p means that the number 5 subtracts the above expression, hence the expression is given as follows:

5 - 3p.

Meaning that option A gives the correct answer in the context of this problem.

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Answer: the woodworker should choose the dimensions of the box to be approximately 3.825 inches by 3.825 inches by 1.603 inches, with a total surface area of approximately 33.512 square inches.

Step-by-step explanation:

Let the side length of the square base be x, and the height of the prism be h. Then the volume of the prism is:

V = x^2h

We're given that V = 61.3 cubic inches, so:

x^2h = 61.3

We want to minimize the surface area of the box, which consists of the area of the two square bases (2x^2) plus the area of the four rectangular faces (4xh). So the total surface area is:

A = 2x^2 + 4xh

We can solve the first equation for h:

h = 61.3/x^2

Substituting this into the equation for A, we get:

A = 2x^2 + 4x(61.3/x^2)

A = 2x^2 + 245.2/x

To minimize A, we take the derivative and set it equal to zero:

dA/dx = 4x - 245.2/x^2 = 0

4x = 245.2/x^2

x^3 = 61.3

x = (61.3)^(1/3)

x ≈ 3.825

So the length of each side of the square base should be approximately 3.825 inches. We can use the equation for h to find the height:

h = 61.3/x^2

h ≈ 1.603

So the height of the prism should be approximately 1.603 inches.

Therefore, the woodworker should choose the dimensions of the box to be approximately 3.825 inches by 3.825 inches by 1.603 inches, with a total surface area of approximately 33.512 square inches.

Answer:

Exponential Growth

Step-by-step explanation:

The base of 1.88 is greater than 1, so there will be exponential growth

Answer:

y=3.5x

Step-by-step explanation:

to find the the feet mary walks per second, divide 14 by 4

14/4=3.5 feet/second

the total distance mary walks can be represented by multiplying the number of feet she walks per second by the number of seconds she walks

y= 3.5x

in this model, x is seconds

For the transformations of the triangle, we have that:

1. The translation of triangle ABC preserves side lengths and angles.

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

A translation involves shift left, shift right, shift down, or shift up, meaning that just the coordinates of the figure change, not the angles or the side lengths,

1. The translation of triangle ABC preserves side lengths and angles.

For a dilation, the coordinates of the vertices are multiplied by a constant, hence the side lengths change while the angles remain constant, thus:

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

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