A painter leans a ladder against a vertical wall. The top of the ladder is 7 meters above the ground. When the bottom of the ladder is moved 1 meter
farther away from the wall, the top of the ladder is now 5 meters above the ground. What is the length of the ladder?
O There is not enough information to solve this problem.
O the ladder is 7.89 meters long
O the ladder is 8.60 meters long
O the ladder is 13.46 meters long

If the domain of a​ one-to-one function f is ​[6​,&​), the range of its​ inverse, f-1 ​of the one to one function is [6​, &​)

In mathematics, functions are said to be one-to-one functions, when one input value only give an output. No two input values give same output value in a one to one function

Usually in mathematics, functions may have two inputs which give same outputs however for one to one functions one input value gives only one output value

Relating this to domain (input values) and range (output values) and inverse.

The domain of a one to one function will be the range of inverse of the one to one function

This is among the property of one to one function

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Answer:

52 / (1/2)

Step-by-step explanation:

Divide the total height by the thickness of each book.

52 / (1/2)

The height of the CN Tower on scale drawing is 0.05.

A scale is a group of levels or numbers that are applied to a certain system of measurement or comparison.

Given that,

The height of CN Tower = 550 m,

Also, the scale is 1/11000

Let the height of the CN Tower in the scale is x,

Then,

x/550 = 1/11000

⇒x= =550/11000

⇒x = 0.05

The height of the CN Tower on scale drawing is 0.05.

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Answer:

a.) The relation is linear

b.) Plot the given (x,y) coordinates on the given graph and connect them.

c.) The y-intercept is at y=2.

d.) m=4

e.) y=4x+2

Step-by-step explanation:

a.) The relation is linear because the values in the sequence of first differences are all equal:

6-2=4   10-6=4   14-10=4   18-14=4

c.) The y-intercept is the point on the graph where x=0.  According to the given points, the y-intercept must be y=2.

d.)

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\(x_1,y_1)=(0,2)\\(x_2,y_2)=(4,18)\\m=\frac{18-2}{4-0}\\m=4[/tex]

e.) Plug slope (m) and y-intercept into the slope-intercept form to get y=4x+2.

1. If you multiply the first equation by 2, the number to multiply the second equation by eliminating the y terms when making a linear combination is -3.

2a) The price per pound of apples is $1.25.

b) The price per pound of bananas is $0.75.

A system of equations involves two or more equations solved together.

Such equations are also known as simultaneous equations.

5x + 3y = 8.5 ... Equation 1

3x + 2y = 5.25 ... Equation 2

Multiply Equation 1 by 2:

5x + 3y = 8.5 ... (x 2)

= 10x + 6x = 17 ... Equation 3

Multiply Equation 2 by -3:

3x + 2y = 5.25 ... (x -3)

-9x -6y = -15.75 ... Equation 4

Add Equations 3 and 4:

10x + 6x = 17

+

-9x -6y = -15.75

= x = 1.25

Substitute x = 1.25 in Equation 1:

5x + 3y = 8.5

6.25 + 3y = 8.5

3y = 2.25

y = 0.75

Check variables in Equation 2:

3x + 2y = 5.25

= 3(1.25) + 2(0.75) = 5.25

= 3.75 + 1.5 = 5.25

5.25 = 5.25

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5x + 3y = 8.5

3x + 2y = 5.25

1. If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination?

2. Complete the multiplication and add the equations. What is the result?

What is the price per pound of apples? $

What is the price per pound of bananas?

Answer: -√7 because it will cancel out to equal 0

The volume, to the nearest cubic inch, of the tower is 2,347.

Brandon made a model of a tower, as shown in the figure. The tower is composed of a square prism and a square pyramid. The height of the pyramid is 2 inches. The height of the prism is 3 feet = 36 inches and the base of the prism is 8 inches long. Let the volumes of the tower, prism, and pyramid be represented by the variables V, V1, and V2.

V1 = L*B*H

V1 = 8*8*36

V1 = 2,304

The volume of the square prism is 2,304 cubic inches.

V2 = (1/3)a²h

V2 = (1/3)(8)²(2)

V2 = 42.67

The volume of the square pyramid is 42.67 cubic inches.

The volume of the tower is the sum of the volumes of the square prism and the square pyramid.

V = V1 + V2

V = 2,304 + 42.67

V = 2,346.67

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Answer:

0.41

Step-by-step explanation:

$4.94/12=0.41

Answer: $0.39.

Step-by-step explanation: $4.94. Divided by 13 = $0.38

(18a + 43) is an equivalent expression for the given expression i.e.

4(3a + 7) + 3(2a + 5).

Yes, the answers are same from both the expressions i.e. 133.

Given, an expression i.e. 4(3a + 7) + 3(2a + 5)

Now, we are asked to find an equivalent expression for the given expression.

So, on simplifying the given expression, we get

4(3a + 7) + 3(2a + 5)

12a + 28 + 6a + 15

12a + 6a + 28 + 15

18a + 43

So, (18a + 43) is an equivalent expression for the given expression i.e.

4(3a + 7) + 3(2a + 5)

Now, On putting the value of a = 5 in both the expressions, we get

4(3(5) + 7) + 3(2(5) + 5)

= 4(15 + 7) + 3(10 + 5)

= 4(22) + 3(15)

= 88 + 45

= 133

also in (18a + 43),

= 18(5) + 43

= 90 + 43

= 133.

Hence, (18a + 43) is an equivalent expression for the given expression i.e.

4(3a + 7) + 3(2a + 5).

Yes, the answers are same from both the expressions i.e. 133.

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Answer:

-3x + 4y = 3

Step-by-step explanation:

Ax + By = C  standard form

y + 3 = 3/4 (x + 5)        | ×4

4(y + 3) = 3(x + 5)

4y + 4·3 = 3x + 3·5

4y + 12 = 3x + 15

-3x + 4y = 15 - 12

The equation in standard form is    -3x + 4y = 3

The warmest temperature or "maximum" temperature means we need to find the derivative of the function.

T = -(t^2)/2 + 8t + 32

dT/dt = -t +8

A maximum/minimum occurs when the derivate(gradient) = 0

Therefore, dT/dt = 0

0 = -t + 8

t = 8

Putting t = 8 back into the original equation gives.

T(8) = 64 degF

So the warmest temperature is 64 degF 8 hours after 6am so at 2pm

The depth of the deep end of the swimming pool is 9.50 feet.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Since the shallow end of a swimming pool is 3.75 feet below the pool's surface and the deep end of the pool is 5.75 feet deeper, the depth will be:

= -3.75 - 5.75

= - 9.50

It is 9.50 feet deep.

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[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{10}\\ a=\stackrel{adjacent}{8}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{10^2-8^2}=b\implies \sqrt{36}=b\implies 6=b[/tex]

An investment that takes 2 years to increase in value by $50 and

10 years to increase in value by $250 situation is best modeled by an exponential function with time as the independent variable

Two or more expressions with an Equal sign is called as Equation.

We need to find the exponential function with time as the independent variable.

Exponential growth refers to the original value from the range increases by the same percentage over equal increments found in the domain.

an investment that takes 2 years to increase in value by $50 and

10 years to increase in value by $250

an investment that increases by a constant factor of 1.03, or at a

rate of 3%, every year

an investment that increases by $30 every year

an investment that increases by $1 every 2 weeks

Hence, an investment that takes 2 years to increase in value by $50 and

10 years to increase in value by $250 situation is best modeled by an exponential function with time as the independent variable

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Answer:

$0

Step-by-step explanation:

Answer:

She will owe 2,391

Step-by-step explanation:

760-60x12

Answer: 12

Equation: 12 times 5 - 7.

Step-by-step explanation: 12 times 5 is 60 and take away 7 would be 53.

Hoped This Helped!

Mars travels at a rate of 24 km per second.

At this rate, Mars travel 480 km in 20 seconds.

What is speed?

The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time.

Here, we have

Mars revolves around the sun, it travels at a rate of approximately 15 miles per second.

1 mile = 1.6 km (given)

15 miles = 15 ×1.6 = 24 km

So, Mars travels at a rate of 24 km per second.

In 20 seconds, Mars will travel 24×20 =480km

Hence, Mars travels at a rate of 24 km per second.

At this rate, Mars travel 480 km in 20 seconds.

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a. Roster form: { 3, 4,5, 6}

b. Set-builder form : {x | x is an integer, where x ≥ -5}

What is a Roster form?

A list of the elements of a set, each separated by a comma, enclosed in a group of curly brackets, can be used to describe the contents of the set. Roster form is the term for this method of describing a collection.

What is a set-builder form?

Set builder notation is defining a set by expressing its properties rather than simply listing its constituents. One or more variables and a rule specifying which elements are part of the set and which are not are included in the set builder notation.

Here,

a. It is given the set is A={x:x is an integer 3 ≤ x ≤ 6}.

Then the integers lying between 3 and 6 are 3,4,5,6.

So the roster form is

A={3,4,5,6}.

b. It is given that  A = { -5, -4, -3, -2......}

then the set-builder form is

A = {x | x is an integer, where x≤ -5}

Hence,

a. Roster form: { 3, 4,5, 6}

b. Set-builder form : {x | x is an integer, where x ≥ -5}

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Regarding the data-set, we have that:

The dot plot shows the absolute frequencies of each observation, hence we have that:

The distribution is analyzed considering the mean and the median.

The mean is given by the sum of all observations divided by the number of observations, hence:

Mean = (2 x 3 + 3 x 2 + 4 x 3 + 5 x 5 + 6 x 4 + 7 x 2 + 10 x 1)/(3 + 2 + 3 + 5 + 4 + 2 + 1) = 4.85.

There are 20 observations, hence the median is composed by the mean of the 10th and of the 11 observation, which are both of five, hence the median is of five.

Since the median is greater than the median, the data distribution is left skewed.

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Answer:

5, skewed right

Answer:

1. A

2. A, B, D

Step-by-step explanation:

The first one is pretty straightforward, divide 7^2 to both the denominator and numerator, so you get 1/7^2. 7^2 is 49, which is not 14, so A is false. Everything else produces 1/49 in some shape or form.

The second question is also relatively easy. A is correct because 1/4 is 4^-1 and (4^-1)^-1 is 4^1. B is also right because if you add all the exponents up, you basically get -5+6+1=2, and 2^2 is 4. C is wrong because (1/2)^2 is 1/4, not 4. D is correct because 2^(5-3) is 2^2, which is 4. E is wrong because 4^(4-2) is 4^2, which is 16, not 4.

Overall, it's not hard, nor does it take time, you just need to remember the basic formulas: [tex]\frac{1}{x^a} =x^{-a[/tex], [tex]x^a * x^b=x^{a+b[/tex], and [tex]\frac{x^a}{x^b} = x^{a-b[/tex]

The regression line, considering the points given in this problem, is defined as follows:

y = 2.16x + 13.61.

The linear regression equation is obtained inserting the points of the data, that can be given in a table or a in a scatter plot, into a linear regression calculator.

These points are composed by a value of x and a value of y, and these values are listed as follows:

Inserting these points into the linear regression calculator, the equation is given as follows:

y = 2.16x + 13.61.

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The whole plots he can make are 43/6=7.1666

A ratio in mathematics displays the multiplicative relationship between two numbers. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the proportion of oranges to the overall amount of fruit is 8:14, while that of lemons to oranges is 6:8 (or 3:4). (or 4:7).

A ratio can include any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values. Both numbers must be positive in the majority of situations.

Given, the covering land is 5(3/8) acres

That is 43/8 acres

By dividing the plots as 3/4 each, we get

(43/8)*(4/3)=43/6=7.1666

The whole plots he can make are 43/6=7.1666

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Answer: a.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/4 is already less than 1.

When you divide 1/4 by 274, you get much less than 1.

Much less than 1

Using the concept of scientific notation we can write 5.14*10^5 to convert from 5.14*10^5.

What is scientific notation?

Using scientific notation, one can express extremely big or extremely small values.

When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.

For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.

The scientific notation consists of a coefficient multiplied by 10 and raised to an exponent.

To convert to a real number, start with the base and multiply by 5 tens like this: 5.14 × 10 × 10 × 10 × 10 × 10 = 514000(there are only 4 zeros because you cancel one zero to remove the decimal) so we write 5.14*10^5 to convert from 5.14*10^5.

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Answer:

15

Step-by-step explanation:

1. 2x + 3 = 33

2. 2x = 33 - 3

3. 2x = 30

4. x = 15

The measures of the angles are m∠1 = 69° and m∠2 = 29°

How to find the measures of an angle?

*Triangles always have angles that add up to 180 degrees. As a result, you may find the unknown angles by taking the specified angles of a triangle and subtracting them from 180.

*Finding Unknown Measurements Using Exterior Angles

Two angles that together total 180 degrees are known as supplementary angles. These two angles combine to form a straight angle when put side by side

m∠1 = (4x-7)°

m∠2 = (x+12)°

As the two angles are complementary

4x-7+x+12=90°

5x+5=90°

5x=90-5

5x=85

x=[tex]\frac{85}{5}[/tex]

x=17

Therefore

m∠1 = 4(17)-7

m∠1 = 61°

m∠2 = 17+12

m∠2= 29°

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Answer:

3/5 elimination

Step-by-step explanation:

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