a 20-foot ladder is placed against a building. If the top of the ladder will lean against the building 4 square root 7 feet high, how far away from the base of the building is the bottom of the ladder located? include a sketch

Scale factor is given by the formula below:

Using the right-hand side

new length = 1

old length= 3

substitute the values into the formular

Step 1:

Concept:

The cost of wire varies directly to the length in inches

Step 2:

Final answer

14 inches will cost = 14 x 0.04 = $0.56 = 56 cents

56 cents

The number in the word problem is 2

let the number be x

from the question it is deduced that

If a number is tripled and then subtracted from 15 = 15 - 3x

5 more than twice the number = 2x + 5

equating both sides

15 - 3x = 2x + 5

collecting like terms

15 - 5 = 2x + 3x

10 = 5x

x = 2

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The congruent statement for the triangle is ΔVXW ≅ ΔRPQ

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal .

In other words, two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

Therefore, for the two triangles the to be congruent the corresponding sides are and the angles are equals also.

Hence,

∠V ≅ ∠R

∠W ≅ ∠Q

∠X ≅ ∠P

Therefore, ΔVXW ≅ ΔRPQ

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Answer: Width = 5.7 feet, Length = 10.5 feet

Step-by-step explanation:

Let the width be w. Then, the length is 2w-0.9.

[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]

Answer: 196 miles

Step-by-step explanation: speed = 56 = distance / time

time = 3.5 hours

distance = speed x time = 56 x 3.5 = 196 miles

Answer:

196 miles

Step-by-step explanation:

If it drove for 56 miles per hour and rod for 3 1/2 hours the if we multiply 56 by 3 we have 168 miles and 1/2 of 56 is 28.

So the bus drove 196 miles

Answer:

1.75

Step-by-step explanation:

1/4 (5 - -2)

1/4(5 + 2)

1/4(7)

7/4

1 3/4

9=4/t

To solve for t

multiply both-side of the equation by t

That is;

9t = 4

divide both-side of the equation by 9

That is;

Given that:

- Marc sold 500 tickets for the school play.

- Student tickets cost $2.

- Adult tickets cost $5.

- The total amount of money from the sale was $1,789.

a.) Let be "x" the number of student tickets Marc sold for the school play, and "y" the number of adult tickets Marc sold for the school play.

You can represent the total number of tickets he sold with this equation:

You can represent the total amount of money from the sale with this equation:

Now you can set up this System of Equations that can be used to determine how many of each type of ticket Marc sold:

b.) You can solve the System of Equations using the Elimination Method:

1. Multiply the first equation by -2:

2. Add the equations:

3. Solve for "y":

4. Substitute the value of "y" into the first original equation and solve for "x":

Hence, the answers are:

a.)

b.)

The line y = 2x + 6 shown in the data is the line of best fit of the data

What is line of best fit?

There are many points of the data and by plotting the points on the graph, a single line cannot pass through all the points.

Line of best fit minimize the distance between the line and the points of the data

The points which are plotted on the graph in red are the points of the data and y = 2x + 6 is the line of best fit of the data.

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The money owed by the cashier after selling three shirts and two sweatshirts for $203.75 and 6% clothing tax is $215.975.

The percentage tax is the tax amount charged for the item. The tax amount is given by dividing the per cent by 100 and multiplying it by the total amount of the item.

The total cost of three shirts and two sweatshirts is $203.75 and the tax is 6%.

The tax amount will be,

Tax amount = [tex]\frac{6}{100}\times203.75[/tex]

[tex]=12.225[/tex]

So, the total money owed by the cashier will be,

Total money owed by cashier [tex]=203.75+12.225[/tex]

= $215.975

Therefore, the money owed by the cashier after selling three shirts and two sweatshirts is $215.975.

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The mean μ=9 is the setting so that an 8 ounce cup will overflow when only 0.5% of the time.

A Z-score indicates how far a given value is from a standard deviation. A Z-score (standard value) is the number of standard deviations that a particular data point is above or below the mean. Standard deviation essentially reflects the amount of variability within a given data set.

The average is calculated as: From the Z-score formula:

z=(x-μ)/σ

Z-score associated with 0.5% is 0

(8μ)/0.4=0

Solving for x gives:

μ=9

For μ=9, an intermediate setting such that the 8 ounce cup overflows 0.5% of the time.

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The answer will be [tex]4^{30}[/tex]  different ways can the question be answered using permutation.

What is permutation?

A permutation is both an ordered combination and an ordered arrangement of results. For instance, 3 people are to sit in each of the 5 chairs. The first person can be seated in five different ways, the second person in four different ways, and the third person in three different ways. Accordingly, generalising this, we obtain n alternatives to fill the first chair, n-1 options to fill the second, and n-2 options to fill the third chair. As a result, nPr = n! / (n - r)! can be used to represent how many different permutations (arrangements) there are when there are r individuals and n chairs.

Each question has four choices. So, the total number of ways in which the questions can be attempted is [tex]4^{30}[/tex]

Hence the number of ways the question be answered is  [tex]4^{30}[/tex].

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To find if a relation is a function, identify if there is more that one value of y for the same value of x (if there are more than one value for one value of x is not a function)

Ordered pairs (x,y)

1.

x y

1 -2

-2 0

-1 2

1 3

2.

x y

1 1

2 2

3 5

4 10

5 15

The ordered pair (0, 3) does not lie onto any of the four quadrants.

We know in the cartesian plane there are four quadrants.

In the first quadrant (x, y).

In the second quadrant (- x, y).

In the third quadrant (- x, - y).

In the fourth quadrant (x, - y).

Given are some ordered pairs. We know when x = 0 the point lies onto the x-axis and when y = 0 the point lies onto the x-axis.

Out of the given ordered pairs (0, 3) does not belong to any quadrant as it lies onto the y-axis only at 3.

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The expression is given to be:

Recall the rule of logarithms:

Thus the expression becomes:

Recall the rule:

Hence, we have the expression to be:

The answer is 86.

Answer:

Step-by-step explanation:

14-7=7

7-1=6

6=12x

x=0.5

Answer

Angle PST = 80°

Explanation

Opposite angles of a parallelogram are equal.

Angle R = 130° = Angle QPS

The sum of angles on a straight line is 180°.

Angle QPS + Angle SPT = 180°

130° + Angle SPT = 180°

Angle SPT = 180° - 130° = 50°

Then, we were told that ST = SP, so, the the base angles of triangle PST are equal.

Angle SPT = Angle STP = 50°

Sum of angles in a triangle = 180°

Angle SPT + Angle STP + Angle PST = 180°

50° + 50° + Angle PST = 180°

100° + Angle PST = 180°

Angle PST = 180° - 100°

Angle PST = 80°

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The roots of 2x^2+4x+7 are -1 + i√5 and -1 - i√5.

A quadratic function has the generic form f(x)=ax²+bx+c. A parabola, a kind of two-dimensional curve, is the graph of a quadratic function. A polynomial function of degree two in one or more variables is known in algebra as a quadratic function, quadratic polynomial, polynomial of degree 2, or simply a quadratic. The phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms. Latin's word for square is quadratus.

Function:

2x² + 4x + 7 = 0

ax² + bx + c = 0

x = [tex]\frac{-b +-\sqrt{}b^{2}- 4ac }{2a}[/tex]

a = 2

b = 4

c = 7

Using quadratic function,

x = [tex]\frac{-4\sqrt{} 4^{2} -4(2)(7)}{2(2)}[/tex]

x = [tex]\frac{-4+-\sqrt{-40} }{4}[/tex]

So,

i = √-1

x = [tex]\frac{-4+-2i\sqrt{10} }{4}[/tex]

Simplifying,

x = -1 +-√10/2

Roots are:

x = -1 + i√10/2

x = -1 - i√10/2

The roots of 2x^2+4x+7 are -1 + i√5 and -1 - i√5.

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Answer:

201.06 square centimeters.

Explanation:

The formula for finding the area of a circle is:

Given that the diameter = 16 cm

Next, substitute r=8cm into the formula for area.

The area of the circle is 201.06 square centimeters.

Answer:

There are 55 grams of sugar in a 20-ounce bottle of soda.

Step-by-step explanation:

So if your looking for a 68 ounce bottle of soda we know there would be about 165 grams of sugar just in 60 ounces. as then you would find the amount of 8 grams of sugar.

If linear function can be modeled using the equation 2x-y=2. Then x=1 is the Zero of this function

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

2x-y=2

We need to write this in slope intercept form

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

y=2x-2

m=2 and y intercept is -2

Now take the values of x and y

x       0       1         2         3

y       -2      0         2         4

Hence the zero of this function is x=1

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We could state an exponential model.

Number of bateria will be given by:

where k=growth constant and t=time in minutes.

We're given that N0 is the initial population, which is:

We also know that, when t=236 min, N=2(9,085) = 18,170:

We're going to solve this equation to find the value of k:

Then, our expression is:

To find the population of bacteria after 708 minutes, we replace t by 708:

Therefore, the population of bacteria 708 minutes from now, is 72680.

Fruit punch is served during the reception in 154-ounce cups using division.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groupings. When dividing numbers, we divide a bigger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

For instance, 4 2 Equals 2. As a multiplication fact, this can be expressed as 2 + 2 = 4.

The division is represented mathematically by a symbol consisting of a tiny horizontal line with dots above and below the line. The division of two integers is represented by one of two fundamental division symbols.

Total fruit punch foe prepared = 3696 ounces

Number of punch balls = 4

Each serving has = 6 ounces of punch

So, 4 servings will have

4 × 6 = 24

The number of servings of fruit punch available at reception is given by

3696÷24

= 154

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The amount of string that can be stretched by 3 kg weight is 5/ 4× 3

= 15 / 4 = 3.75 cm

Given ; The string is attached to a weigh whose weight is 8 kg

the length of the string which is being stretched is 10 cm

The amount of string that can be stretched by 3 kg weight can be calculated by unitary method

According to the unitary method ;

the string when attached to a 1 kg weight the length will be = 10 / 8 = 5 /4

Thus the amount of string that can be stretched by 3 kg weight is 5/ 4× 3

= 15 / 4 = 3.75 cm

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The coordinates of R are (7, -3).

Therefore,

R are (7, -3)

P are (4,-3)

Q are (4,4)

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We are given the following information.

We also know that the general equation of a line is given by

Where m is the slope of the line and b is the point at which it crosses the y axis.

Since the line given goes through (0,0), b=0. Now we just need to find m.

This can be done via the formula

In this case

And so, the equation of the line given is

Now we simply need to see which of the options fit this equation. We can do this easily, because x and y are equal except for their sign.

As such, the point of the terminal side of 135° is (-1,1).

The equation represent the given situation is y=3x+10.

What is equation?

   A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here let us take the values of time and amount as x and y. Then take any two points ,

[tex](x_1,y_1)=(3,19)\\(x_2,y_2)=(6,28)[/tex]

Now using slope formula,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = 9/3 = 3

Now using equation formula ,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-19=3(x-3)

=>y-19=3x-9

=>y=3x-9+19

=>y=3x+10

Hence the correct option is A)y=3x+10.

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The values of the area of the shaded region are;

1. Area = 36, perimeter = 28

2. Area = 16, perimeter = 16

3. Area = 22, perimeter = 30

4. Area = 29, perimeter = 28

6. Area = 53.9

The area of a figure is the area bounded by the line that serves as the boundary of the figure.

The areas and perimeters of the figures are found as follows;

1. The figure consists of two rectangles

The dimension of the small rectangle at the top are;

Length = 4, Width = 3

Area = 3 × 4 = 12

Dimensions of the larger rectangle are;

Width = 4, Length = 6

Area = 4 × 6 = 12

The area of the composite figure is therefore; A = 3 × 4 + 6 × 4 = 36

The sum of the length of the sides, which is the perimeter, P = 8 + 3 + 4 + 3 + 4 + 6 = 28

2. The figure consists of a right triangle at the top rectangle;

The leg lengths of the right triangle are; 3 and 4

The area of the right triangle = 0.5 × 3 × 4 = 6

The dimension of the rectangle are; Length = 5, width = 2

Area of the rectangle = 5 × 2 = 10

Area of the composite figure is therefore, A = 0.5 × 4 × 3 + 2 × 5 = 16

The perimeter of the composite figure, P = 4 + 3 + 2 + 5 + 2 = 16

3. The figure is a composite figure that is found by subtracting the area of a rectangle from the area of a right triangle as follows;

The dimensions of the triangle are;

Leg lengths; (8 + 4) = 12 and (3 + 2) = 5

Area of the right triangle = 0.5 × (8 + 4) × (3 + 2) = 30

Dimensions of the rectangle left blank are;

Length = 4, width = 2

Area of the rectangle = 4 × 2 = 8

Therefore;

Area of the composite figure = 0.5 × (8 + 4) × (3 + 2) - 4 × 2 = 22

Length of the hypotenuse side = √((8 + 4)² + (3 + 2)²) = 13

The perimeter of the composite figure = 3 + 13 + 8 + 2 + 4 = 30

4. The figure is a composite figure that consist a large rectangle and small rectangle.

Dimensions of the large rectangle are;

Length = 2 + 2 + 3 = 7

Width = 5

Area of the large rectangle = 7 × 5 = 35

Dimensions of small rectangle are;

Length = 3, width = 2

Area of the small rectangle = 3 × 2 = 6

Area of the composite figure = 35 - 6 = 29

The perimeter = 2 × (2 × 2 + 3) + 2 × 5 + 2 × 2 = 28

6. Area of the circle = π × 14²/4

Area of the square = 10 × 10 = 100

The area of the shaded region = π × 14²/4 - 100 ≈ 53.9

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He can buy 5 candy at most with this inequality 2c-3<9 as the inequality will result in c<6 as the definition of inequality says, "In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another".

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. The equation-like form of the expression 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. The greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol () are the five inequality symbols. Take the same amount away from both sides. Add the same positive number to both sides. Subtract the same positive number from both sides. Reverse the sign and multiply both sides by the same negative number.

Here,

2c-3<9

add 3 both side,

2c-3+3<9+3

2c<12

divide both side by 2,

c<6

According to the definition of inequality, "In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another," he can only purchase a maximum of 5 candies with the inequality 2c-3<9.

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