A 30-foot ladder is leaning against a building. The base of the ladder is
18 feet from the side of the building. How high does the ladder reach along the side of the building?

The ladder reaches ___ feet high on the building.

Answer:

rational

Step-by-step explanation:

the square root of 196 is 14 (  whole number) therefor it is rational

Answer:

Step-by-step explanation:

Yes , Are collinearity and betweenness of points maintained under rotation.

A rotation is a transformation that maintains congruence of the original figure and its image.

What does "collinearity" mean?

What is an example of collinearity?

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Answer:

Step-by-step explanation:

Okay so this is fun, let's lable the angle just under 72, but still on the right side B. now, side b is corresponding or equal to (2y+48). So you set them to equal 180 because it makes a straight line....

(2y+48) + 72 = 180

2y + 48 + 72 = 180

2y + 120 = 180

2y = 180 - 120

2y = 60

y = 60/2

y = 30

plug this back in and ...

2(30)+48 =

(60+48) =

108

No we'll use 108 + 72 to make sure that the y is correct and....

108 + 72 = 180 so.. CORRECT! :)

Evaluating the expression 2a + b for a = 3 and b = -5 is equal to -1.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.

Given the expression 2a + b, substitute the value of the variable a and the value of variable b.

2(3) + (-5)

Performing the arithmetic operations, we can have the value of the expression.

2(3) + (-5)

= 6 - 5

= 1

Hence, the expression 2a + b when a = 3 and b = -5 is equal to -1.

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The solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given equation is x³ - 4x² - 7x + 10 = 0. The equation will be solved as,

x³ - 4x² - 7x + 10 = 0

x³ - 3x² - 10x - x² + 3x + 10 = 0

( x² - 3x - 10) ( x - 1 ) = 0

( x² -5x + 2x - 10 ) ( x-  1) = 0

( x - 5 )( x + 2 )( x - 1 ) = 0

Therefore, the solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).

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Using exponent properties we can get two equivalent expressions:

⁸√d^5

d^(5/8)

Here we need to use two properties, these are:

ⁿ√x = x^(1/n)

(x^n)^m = x^(n*m)

Now, if we use the first property, we can rewrite the expression as:

(d^1/8)^5 = ⁸√d^5

Which is an equivalent expression.

If we use the other property we can get:

(d^1/8)^5 = d^( (1/8)*5) = d^(5/8)

Which is another equivalent expression.

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the scale of dilation is 2.5 for the triangle ABC.

We are given the coordinates of triangle ABC as:

A(0, 0), B(0, 4), and C(6, 0)

Coordinates of dilated triangle A'B'C' is:

A' (10, 0), B'(0, 10), and C' (15, 0).

The scale of dilation can be calculated as:

k · ( 0, 0 ) = ( 0 , 0 )

k · ( 0 , 4 ) = ( 0 , 10 )

k · ( 6, 0 ) = ( 15, 0 )

k = 15 / 6 = 10 / 4 = 2.5

The scale of dilation is 2.5 for the triangle.

Therefore, the scale of dilation is 2.5 for the triangle ABC.

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The slope of line passing through points  (2,7) and (-3,11) is -4/5.

Slope of a Line

The slope of a line is defined as the increase divided by the run, or as the ratio of the rise to the run. It describes the slope of the line in the coordinate plane. Calculating the slope of a line and determining the slope between two different points are similar activities.

The following formula is used to determine slope:

The slope of the line between two points is given by y2 - y1 / x2 - x1.

Given points are -

(2,7) and (-3,11)

Slope of the line is -

= 11 - 7 / -3 -2

= 4 / -5

So the slope of the line is -4/5

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Answer:

Piece wise

Step-by-step explanation:

Piecewise function definition A piecewise function is a function that is defined by different formulas or functions for each given interval. Its also in the name: piece. The function is defined by pieces of functions for each part of the domain.

A quadrilateral can be both a square and a rectangle, or a rectangle but not a square, because squares are rectangles but rectangles are not always squares. They do not conflict with one another.

What is termed quadrilateral?

What types of quadrilaterals are examples?

A closed, two-dimensional figure with four sides, four angles, and four vertices is called a quadrilateral. Square, rectangle, and trapezium are a few examples of quadrilaterals.

The two events are mutually exclusive if they cannot occur at the same time.

A quadrilateral can be both a square and a rectangle, or a rectangle but not a square, because squares are rectangles but rectangles are not always squares.

They do not conflict with one another.

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The sum of its integer and fractional parts is (-6) + (-1/3).

Fractions are numerical values that represent a subset of a larger whole. A fraction is a portion or section of a whole quantity, which can be any number, a specific value, or a thing.

A mixed fraction is made up of both a whole number and a fraction. If 8 is a whole number and 1/2 is a fraction, the result is a mixed fraction.

The given expression is -6 1/3.

The integral part is -6, and the fractional part is 1/3.

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The correct question is: " How can - 6 1/3 be expressed as the sum of its integer and fractional parts? "

The Simplified expression for -(2x + y) -2(-x-y) is y.

Like terms in an algebraic expression is defined as those terms that have same variable and that variable has the same power .

Algebraic Operation is only possible with Like terms .

For Example ; 3x , 9x are like terms .

According to the given Algebraic expression

= -(2x + y) -2(-x-y)

= -2x-y+2x+2y

Combining like terms together

We get ,

= (-2x+2x)+(2y-y)

= 0+y

=y

Therefore , the Simplified expression for -(2x + y) -2(-x-y) is y.

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The population of Texas will be 2.9 × 10³.

Population of Austin, Texas = 9.64 × 10.

The population of the state of Texas is 30 times that of Austin.

Therefore the population of Texas will be:

= 30 × 9.64 × 10

= 2900

= 2.9 × 10³

Therefore, the population of Texas will be 2.9 × 10³.

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Answer:

are these time stamps

Step-by-step explanation:

let me know

EN is a radius and the diameter is twice the radius. The diameter of the circle is 26 ft.

In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.

The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.

Here, CF is a radius and the diameter is twice the radius.

Diameter of a circle = 2r

d = 2r

Where, r = 13

Diameter of a circle, d = 2r

Diameter of a circle = 2(13)

Diameter of a circle = 26

Therefore, the diameter of the circle is 26 ft.

Here, EN is a radius and the diameter is twice the radius.

Therefore, the diameter is 26 ft.

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The standard deviation decreases as the sample size increases.

The degree of data dispersion from the mean is measured by the standard deviation. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

A region containing 68 percent of the total number of data points would be defined by one standard deviation, or one sigma, shown above or below the average value on that normal distribution curve. Ninety-five percent of the data would be covered by two sigmas above or below, whereas three sigmas would cover 99.7 percent.

The standard deviation is significant because it reveals the degree of dispersion of the values in a particular dataset. Every time we examine a dataset, we look for the following metrics: the dataset's geographic center.

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Answer:

Step-by-step explanation:

e

Step-by-step explanation:

100x4=400miles

400miles in February

OR

300x4=1200 miles

1200 miles in February

I don't know what is the correct one tho

Answer:

Step-by-step explanation:

1200 miles

Answer:

36/-4+2(10-8)

36/-4+2(2)

-9+2(2)

-9(4)

-36

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Step-by-step explanation:

A=M

B=N

E=P

AB=MB

BE=NP

AE=MP

I don't know about the blanks sorry

Using the rule of exponents, the expression is 12x^4 × 35y^5

The rules of exponents are given as:

Given the expression;

3x^3 * 7y^2 * 4x * 5y ^3

collect the like bases

3x³ × 4x × 7y² × 5y³

Add the powers

12x^3 + 1 × 35^ 2 + 3

We then have;

12x^4 × 35y^5

Thus, using the rule of exponents, the expression is 12x^4 × 35y^5

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The given sequence is arithmetic progression AP. The common difference is found to be (-11).

Arithmetic Progression (AP) is a number sequence in which the difference between two numerical order is a constant value. Arithmetic Sequence is another name for it.

We would then come across some key terms in AP, that are denoted as:

Some formula use in AP are-

Now as per the given question;

The given sequence is  97,86,75,64, ...........

Let the first term is'a₁' = 97.

Let 'a₂' = 86 is the second term.

Let the third term is 'a₃' = 75.

Let the fourth term be 'a₄' = 64.

As we know, in the AP, the difference between two consecutive terms is equal and therefore is referred to as the common difference.

d = a₂ - a₁      

Substitute the values;

d = 86 - 97 = -11     ........(equation 1)

Now consider other pair;

d = a₃ - a₂    

d = 75 - 86 = -11      .......(equation 2)

Put the values;

Thus, both the two equation are equal. It means the common difference is same that is (d  = -11).

Therefore, the stated sequence is found to be in AP and the value of the common difference is found to be (d = -11).

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Kristen will do both the exercises together, 6 days from now.

We are told that Kristen goes hiking every 3 days and swimming every 2 days.

The day she will do both the exercises together will be the day which is a multiple of the LCM of 2 and 3.

Now, since 2 and 3 are both prime numbers, their LCM (lowest common multiple) will simply be their product, which comes out to be-

LCM (2, 3) = 2 * 3

= 6

Thus, Kristen will do both the exercises on every 6th day.

Thus, if she went for both swimming and hiking today, she will do both the exercises together again 6 days from now.

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Answer:

The equation for Brayden and Howard gaining the same number of yards has no solution. So, they could not have gained the same number of yards. Because Brayden and Howard could not have gained the same number of yards, all three could not have gained the same number of yards.

Step-by-step explanation:

(This is straight from Edmentum)

Answer:

There were 27 student tickets sold and 35 parent tickets sold.

Step-by-step explanation:

So first, we have to set up our equations!

s + p = 62 (s is the # of student tickets sold; p is the # of parent tickets sold;  62 is the total # of tickets sold)

1.75s + 3.75p = 178.50 (1.75s is the price for student tickets multiplied by the number of student tickets; 3.75p is the price for parent tickets multiplied by the number of parent tickets; 178.50 is the total amount of money)

Now! We are going to use elimination to solve for the variables, first for "s". To do this, we are going to multiply the first equation by -3.75!

     -3.75 (s + p = 62)

    -3.75s - 3.75 p = -232.50

+     1.75s + 3.75p = 178.50

        -2s = -54

          s = 27

Next! We have to solve for "p" by multiplying the first equation by -1.75!

-1.75 (s + p = 62)

    -1.75s - 1.75 p = -108.50

+     1.75s + 3.75p = 178.50

        2p = 70

          p = 35

Lastly, we know that there were 27 student tickets sold, and 35 parent tickets sold.

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

Step-by-step explanation:

285 dollars.  the left money = 660 - 375 =285