A guy wire runs from the top of a cell tower to a metal stake in the ground. Penelope
places a 12-foot tall pole to support the guy wire. After placing the pole, Penelope
measures the distance from the stake to the pole to be 5 ft. She then measures the
distance from the pole to the tower to be 21 ft. Find the length of the guy wire, to the
nearest foot.

Using the equation of slope intercept form, the equation of the given graph is y=x-3.

In the given question we have to find equation of the given graph.

From the given graph the points are (3,0) and (0,-3).

We know the standrd equation of the line is y=mx+c

where m=slope and c=value of y at the y intercept form.

So the value of c= -3

Now finding the value of m.

m={y(2)-y(1)}/{x(2)-x(1)}

From the points, x(1)=3, x(2)=0, y(1)=0, y(2)= -3

Putting the value

m=(-3-0)/(0-3)

m=-3/-3

m=1

Now putting the value of m and c in the equation

y=mx+c

y=1*x+(-3)

y=x-3

Hence, the equation of the given graph is y=x-3.

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a Given:-

A image.

To find the total area of the given image.

So the given image is splitted into three images they are a triangle at the top and a rectangle at the middle and parallelogram at the bottom.

So the formula for triangle is,

So the formula for rectangle is,

So the formula for parallogram is,

So from the given image we have the values as,

Triangle has,

Rectangle has,

Paralleogram has,

So now we substitute the following values. so we get,

For Triangle,

For Rectangle,

For paralleogram,

So the total area is,

So the total area is 46 in.sq.

just the red one, because if we reflect the triangle by the yellow line we won't get the same the same position of triangle

Answer:

$42.50

Explanation:

Cost of the game = $25

The markup rate = 70%

Therefore, the selling price will be:

The selling price of the computer game is $42.50.

Given

Calculating,

Rounding off to ten-thousands place,

The answer is 0.995

Given the following set:

A = {1,2,3,4,5,6}

B = {4,6,8}

∩ means "intersection" of two sets. In other words, the data that the two sets have in common.

Checking the given sets,

A = {1,2,3,4,5,6}

B = {4,6,8}

A∩B or A and B have a common data of 4 and 6. These two are the intersections of A and B.

Among the given choices, only Choice B is correct which is 6.

Therefore, the answer is CHOICE B : 6

Answer: 10.8 seconds

Step-by-step explanation:

[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]

The greatest common factor(gcf) of the given expression is 3xy.

The expression is 6x²y - 12xy + 9x³y².

From all the terms we take the coefficients. 6 ,12 and 9

The GCF of these three numbers is 3 as it divides all the three numbers.

Now for the variable x. the lowest power will be the gcf. Hence the gcf will have x.

Now for the variable y. the lowest power will be the gcf. Hence the gcf will have y.

Therefore the gcf of the given expression will be 3xy .

6x²y - 12xy + 9x³y² = 3xy (2x - 4 + 3x²y)

The HCF, or highest common factor, is the largest number that divides each of the two or more numbers. HCF is also known by the titles The Greatest Common Measure (GCM) and The Greatest Common Divisor (GCD).

The smallest common multiple of any two or more numbers is found using the least common multiple, or LCM. There are two distinct methods: LCM and HCM.  The HCF of two numbers is the highest factor that will exactly any divide two integers equally.

It is the most effective divisor for any pair of integers that may evenly or completely divide the inputted numbers.

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Answer:

$9.60

Step-by-step explanation:

since 1 penny is 1/100th of a dollar,

you would multiply 960 by 1/100 to get the amount in dollars

[tex]960 *\frac{1}{100}[/tex] = [tex]\frac{960}{100}[/tex]

9.6

$9.60

Step-by-step explanation:

We want to identify how to determine the x-factors for the graph of a function.

On some occasions, the x values for the function will be provided for you to solve for the y values. but on other occasions, the x values are not provided and you have to decide them yourself.

For a linear function, most times, you can pick values within any range of values, e.g from 0 to 5, or 2, 4, 6, 8, 10. Since it is a linear function, it will eventually result in a straight line that contains all other points.

For a quadratic function, the best practice is to pick points around the vertex of the function. The vertex of a function is either the minimum or maximum point of the function.

For example, if the vertex of a quadratic function is (4, 10), the x-coordinate of the vertex is 4. To pick your points, pick points that are some values below 4 and some values above 4, like 2, 3, 4, 5, 6 or 0, 2, 4, 6, 8 That way, you get points that are on either side of the vertex and that will make your plot easier.

Hope that helps!

Answer:

9b - 14

Step-by-step explanation:

4(b + 4) + 5(b-6)

==> expand by distributing

4b + 16 + 5b - 30

==> simplify by combing like terms

9b - 14

Recall that:

Answer:

9b - 14

Step-by-step explanation:

Given expression,

→ 4(b + 4) + 5(b - 6)

Let's simplify the expression,

→ 4(b + 4) + 5(b - 6)

→ 4b + 16 + 5b - 30

→ (4b + 5b) + (16 - 30)

→ 9b + (-14)

→ 9b - 14

Hence, the answer is 9b - 14.

Solution

There are 100 units

Brief Explanation

All types of triangles must have a total angle of 220 degrees. Otherwise, it is not a triangle.

A triangle has three sides three corners and three vertices. The sum of all interior angles of a triangle is always 180°. This is called the sum property of the triangle angles. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A triangle is a three-sided polygon with three corners.

The three sides are joined end to end at points forming the corners of the triangle. The sum of the three angles of a triangle is 180 degrees. A true triangle is a shape with three sides and three angles. The sum of the two side lengths must be greater than the third side and the sum of the three angles must be 180°.

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The total cost of a taxi is given by the sum of a fixed amount of $1.00 per ride and an additional amount of $2.30 per mile driven. Then, the total cost f in function of the total number of miles driven x is given by:

Notice that, since there is no sense in considering "negative miles driven" the domain of this function is given by:

This is equivalent to state "x is a real number greater than or equal to 0"

In this case, we'll have to carry out several steps to find the solution.

Step 01:

perimeter = ?

x + 4 = width

2x - 3 = length

Step 02:

perimeter = 2* width + 2*lenght

perimeter = 2 * (x + 4) + 2 * (2x -3)

= 2x + 8 + 4x - 6

= 6x + 2

The answer is:

The perimeter of the bedroom is 6x - 2

Answer:

3. Texas (1), timeline (2), tryouts (3), two-step (4)

4. wail (1), waved (2), wriggled (3), write (4)

Step-by-step explanation:

3. All start with T

go onto the next letter

Texas

Two-step

Tryout

Timeline

Therefore,

Texas (1)

Timeline(2)

Tryout(3)

two-step (4)

4. Same process as before, we are going to the third letters for wail and waved, the fourth letter for wiggled and write.

Wriggled

Write

Wail

Waved

g comes before t

i comes before v

Therefore,

wail (1)

waved (2)

wriggled(3)

write(4)

Answer:

[tex]y - 2 = - \frac{1}{4} (x - 9)[/tex]

Answer:

28.26 units

Step-by-step explanation:

circumference equals 2r times pi. radius is 9 so the circumference is 2 x 9 x pi (which is 3.14). This would give is 56.52 but since its a half circle you divide it by two

The probability of spinning a 4 on the spinner is 1/12.

Given, a spinner having two numbers 4 & 9

the sector having number 9 has an angle of 30°.

We have to find the probability of spinning a 4 on the spinner

So, the probability of spinning a 4 is,

Probability = (Area of sector having number 4)/(Area of the circle)

Probability = (30°/360°×π×r²)/(π×r²)

Probability = 1/12

Hence, the probability of spinning a 4 on the spinner is 1/12.

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We need to find the area of the sector which is given by the next formula:

Area of the sector = ( central angle / total angle ) * area of the circle

First, we need to find the area of the circle:

Now, we can use the formula for the area of the sector

Central angle = 64

The total angle of a circle= 360

Area of the circle = 144π

Replacing using the formula:

Area of the sector = (64/360) * 144π

Area of the sector = 128π/5

Area of the sector = 80.42477

The equation will be 15+x=60 as the definition of equation says, "A mathematical statement known as an equation is made up of two expressions joined together by the equal sign(=)".

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. In mathematics, an equation is an expression or a statement that consists of two algebraic expressions that have the same value and are separated from one another by the equal symbol. It is an otherwise stated statement that has been mathematically quantified. Expressions that add up to one another make up an equation. A formula is an equation with two or more variables that shows how the variables relate to one another. A line with the equation y=mx+b, where m denotes the slope and b the y-intercept, is an example of a linear equation.

Here,

Suppose you want to buy something for $60, and you have $15 saved up so far. Then your grandmother calls and says she will chip in for your purchase. She doesn’t tell you the amount of money she will give you yet, so you just consider it x dollars.

The sum of your saving and grandmother's amount  is $60.

15+x=60

According to the definition of equation, "A mathematical statement known as an equation is composed of two expressions joined together by the equal sign (=)," the equation will be 15+x=60.

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The first step in solving the equation is adding 11 to both sides, as follows:

In this way, we can start solving the equation for y.

Therefore, the correct option is B: add 11 to both sides.

(This is called Addition Property of Equality: adding the same number to both sides in any equation.)

The Simplification of the fractional expression (1/2 - 1/5) / 2/3 is 9/20

A fraction is a number which consists of a numerator and a denominator.

A numerator is the top or upper value of a fraction while a denominator is the bottom or lower value of a fraction.

(1/2 - 1/5) / 2/3

= (5-2) / 10 ÷ 2/3

= 3/10 ÷ 2/3

= 3/10 × 3/2

= (3 × 3) / (10 × 2)

= 9/20

In conclusion, (1/2 - 1/5) / 2/3 when simplified is given by 9/20

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Answer:

1 cone = $1.36

Step-by-step explanation:

125 c + 10 s = $210

100 c + 30 s = $256

make one of the terms the same (easier one = 30 sundaes)

125 × 3 = 375 c

10 × 3 = 30 s

210 × 3 = $630

375 c + 30 s = $630

375 c + 30 s = $630

100 c + 30 s = $256

same sign = subtract

375 - 100 = 275 c

30 - 30 = 0 s

630 - 256 = $374

275 c = $374

÷ 275 on both sides to get c

c = $1.36

to solve this, you need to isolate x,

Step 1

square root in both sides

so, there are two values for h that fit this equation

so, the answers are A and B

Answer:

y = 3? (A) −192 ... If P = a² + a −1 and R = −a − 1, which expression represents P + R.

Step-by-step explanation:

The position of museum relative to hotel will be (9,1) as the starting position will be (0,0) that is her hotel then the position of coffee shop is (-2,4) and at the end position of museum is (7,5).

A set of values indicating an exact position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, and the second number represents the distance up or down. The location in the cartesian plane will be defined by the coordinate points. The distance between two points is known as the x-coordinate, or abscissa, and the distance between two points is known as the y-coordinate. To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to find the y-coordinate.

Here,

The starting coordinate=0,0

The second coordinate=-2,4

The ending coordinate=7,5

The required coordinate will be

=7--2-0,5-4-0

=9,1

The position of the museum in relation to the hotel is (9,1) because the starting point is (0,0) that is her hotel and the position of the coffee shop is (-2,4) and the position of museum is (7,5).

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The area of the rectangle will be 2,348.3824 cm² as "A rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm".

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. Area is the total amount of space occupied by a flat (2-D) surface or an object's shape. On a piece of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

Here,

Length in inches=26

Width in inches=14

area in inches=26*14

=364 inch²

Now,

1 inch=2.54 cm

area in cm,

=364*2.54*2.54

=2,348.3824 cm²

Since "a rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm," the area of the rectangle will be 2,348.3824 cm².

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From the question;

we are to determine if the point (-2, 11) is on the circle with radius 5 and center (2, 13)

The equation of a circle with a radius r and center (a, b) is given as

Hence, the equation of the circle with radius 5 and center (2, 13)

Considering the point (-2, 11), we need to substitute the values for x and y

therefore, x = -2, y = 11

Since LHS is not equal to RHS then the point (-2, 11) is not on the circle.