use exterior angle measures to solve for h

The solutions to the quadratic equation x² + 3x - 28 = 0 are 4 and -7.

The quadratic formula is expressed as;

x = (-b±√(b² - 4ac)) / (2a)

Given the equation;

x² + 3x - 28 = 0

Substitute the values of a, b, and c into the formula and solve for x.

x = (-b±√(b² - 4ac)) / (2a)

x = ( -3 ±√( 3² -  ( 4 × 1 × -28) )) / (2×1)

x = ( -3 ±√( 9 -  ( -112) )) / (2)

x = ( -3 ±√( 9 + 112 )) / (2)

x = ( -3 ±√( 121 )) / 2

x = ( -3 ± 11 ) / 2

x = ( -3 - 11 ) / 2, x = ( -3 + 11 ) / 2

x = -14/2, x = 8/2

x = -7, x = 4.

Therefore, -7 and 4 are the solutions to the equation.

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The function of the graph which is not connected with each other is known as a discontinuous function. A function f(x) is said to have a discontinuity of the first kind at x = a, if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.

The function is an expression or law that defines a relationship between one variable and the independent variable and another variable the dependent variable

The independent variable is the variable being controlled in the problem, and the dependent variable is the variable that changes because of this control

Some examples of a discontinuous function

f(x) = 1 / (x - 2)

f(x) = tan x

f(x) = x2 - 1

For x < 1 and f(x) = x3 - 5 for 1 < x < 2

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A relationship between one variable, the independent variable, and another variable, the dependent variable, is defined by an expression or law known as the function.

The variable being controlled in the problem is the independent variable, and the variable that changes as a result of this control is the dependent variable.

f(x) = 1 / (x - 2)

f(x) = tan x

f(x) = x2 - 1

For x < 1 and f(x) = x3 - 5 for 1 < x < 2

Answer:

Sequence:

1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex]

. . . . . . . . . .  ⭐ please take a ruler and measure the distance from AA',    . . .  . . . . . BB', CC', DD', and EE', and then write that distance (it should      . . . . . . . .  be the same for each measurement) in place of 5 in -5. I just     . . . . . . . .  wrote -5 because it was my best approximation for looking at     . . . . . . . .  a laptop screen. ⭐

2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex]

3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex]

Step-by-step explanation:

1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex] means that when you move figure ABCDE down by 5 units, it will map onto the image of A'B'C'D'E.

2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex] means that when you rotate figure A'B'C'D'E' 180 degrees counterclockwise about point B', said figure will map onto the image of A''B''C''D''E''.

3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex] means that when you reflect figure A''B''C''D''E'' across segment D''E'', said figure will map onto the image A'''B'''C'''D'''E'''.

Answer:

62.5%

Step-by-step explanation:

5/8 × 100

should give you 62.6%

No it is not reasonable , because the number of medium T-shirts is not 3 times the number of large T-shirts .

Given :

Let say that the class need x medium and y large t - shirts .

so ,

x + y = 216

x = 3y

substitute

3y + y = 216

4y = 216

divide by 4 on both sides

4y / 4 = 216 / 4

y = 216/4

y = 54

x = 54 * 3

= 162

so here we need 162 medium t - shirts and 54 large t - shirts

given 72 large and 144 medium t - shirts so it not reasonable .

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The margin of error is 0.086 and its C.I is (0.575 , 0.785).

What is margin of error?

n = 117 , x =87

Point estimate for the proportion:

P = x/n

= 81/118

= 0.68644

Confidence = 95%, α = 0.05

From z-table area 0.975 close to z=1.96

Margin of error, E = 1.96 √((0.68*0.55)/130)

= 1.96 * 0.05363

= 0.105

= 0.086

Confidence = P ± E

= 0.68 ± 0.105

=(0.68-0.105 , 0.68+0.105)

= (0.575 , 0.785)

Hence, the margin of error is 0.086 and its C.I is (0.575 , 0.785).

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Yes, a 7th grader may be taken algebra. Depending on the school district, and capacity some 7th graders may be able to take algebra as an elective or as part of their regular curriculum.

Algebra is the branch of mathematics that helps in the rendering of problems or situations in the form of mathematical expressions.

It includes variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Some of the branches of mathematics such as trigonometry, calculus, coordinate geometry, involve the use of algebra. One example is in algebra is 2x + 4 = 8.

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Answer:

75 m

Step-by-step explanation:

three seconds of 25 m/s and 3 x 25 = 75

Answer:

y ≈ 95.7°

Step-by-step explanation:

To solve for the angle a trigonometric function is being used on, we have to use the inverse of the trigonometric function.

Inverse of tan(y°) = 4.12:

[tex]tan^{-1}(-0.10) = y[/tex]

Next, I used a scientific calculator to find the angle measure of y. I recommend using the Desmos Scientific Calculator.

[tex]95.7 = y[/tex]

The number 1. 8 in the form a / b, using integers, to show that it is a rational number is 9 / 5 .

Note that the number 1.8 consists of two parts 1 and 0.8.

The decimal 0.8 can be written as the fraction is 8 / 10

Add these two numbers :

= 1 + 8 / 10

multiply and divide by 10

= 10 / 10 + 8 / 10

= 10 + 8 / 10

= 18 / 10

simplify the number

= 2 * 3 * 3 / 2 * 5

= 1 * 3 * 3 / 1 * 5

= 9 / 5

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In the equation c(n) = 50+4n, the value of c(7) is equal to 78.

Absolutely one element of Y is assigned to every element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function's domain and codomain, respectively.

Al-Biruni and Sharaf al-Din al-Tusi were two Persian mathematicians who developed the earliest known approach to function and its concept. The basic conception of functions was the relationship between fluctuating quantities and other variables. An illustration of this is how time affects a planet's position. In the past, the idea was developed with the infinitesimal calculus around the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable.

This is how the function is defined:

The equation c(n) = 50+4n defines function c, and n is the number of visits.

The function displays the cost in USD per month.

Thus, the following formula can be used to get the value of c(7):

c(7) = 50+4n

c(7) = 50+4(7)

= 50+28

=78

Therefore, c(7)=78

So, the value of c(7)=78.

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Answer:

True

Step-by-step explanation:

Most of the function f(x) has the domain is (- infinity, positive infinity), So I think this is true!

F=9/5C+32 is the required equation and Greg statement is true

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that Greg is expressing temperature in farenheit and Josh expressing it in the celsius.

C=5/9(F-32)

We need to rewrite the formula so that Josh can quicly convert the temperature that Greg describes F.

F=9/5C+32

The temperature where John leaves has 77 F.

Let us convert to celsius.

C=5/9(77-32)

C=5/9(45)

C=5(5)

C=25 degrees.

25 degress< 30 degrees.

Hence, F=9/5C+32 is the required equation and Greg statement is true.

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From the provided sample, The mean variance and standard deviation of the sample is given by [tex]\bar x = \frac{\sum x}{n} , variance = {standard deviation }^2[/tex] and

[tex]\sqrt \frac{\sum {(x-\bar x)^2}}{n-1}[/tex] .

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

sample size =n .

[tex]\sum x[/tex] = sum of sample data.

[tex]\bar x = \frac {\sum x}{n}[/tex] (sample mean)

sample standard deviation(s) = [tex]\sqrt \frac{\sum {(x-\bar x)^2}}{n-1}[/tex]

[tex]variance = standard deviation ^2[/tex]

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ME adds up the variances and divides the result by n. In this context, an error is defined as an uncertainty in a measurement or the difference between the measured value and the true/correct value.

In mathematics and statistics, the mean is the average of a set of variables. The simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean are all ways for calculating the mean. The mean (average) of a data set is computed by adding all of the numbers in the set and dividing by the number of values in the set. When arranging data from smallest to greatest, the median is the value in the middle. The mode is the most commonly occurring number in a data set.

Here,

Subtract each measurement from another.

Find the absolute value of each difference from Step 1.

Add up all of the values from Step 2.

Divide Step 3 by the number of measurements.

Mean Error (ME) is calculated by adding the variances and dividing the result by n. An error in this sense is an uncertainty in a measurement, or the discrepancy between the measured value and the true/correct value.

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Dr. Yung has committed a type l ( false positive) error.

Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually false in the population results in a type II error (false-negative).

A type I error occurs when a null hypothesis that is actually true is mistakenly rejected during statistical hypothesis testing (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"),

Therefore, the error is a type 1 error.

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Speed of object = 40 feet per second

Given data :

Equation represent speed is s = d/t

Assume;

Speed = S

Time taken = T

Distance cover = D

So,

Speed = Distance / Time

S = D / T

Speed of object = 100 / 2.5

Speed of object = 40 feet per second

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To find the total balance in an account that earns a simple interest rate of 8% per year, we can use the formula A = P(1 + rt), where A is the total balance, P is the initial principal (or amount invested), r is the annual interest rate, and t is the number of years. In this case, the annual interest rate is 8%, so we can substitute 0.08 for r in the formula. Since Kadeem wants to find his total balance in one step, we can set t equal to 1 year. So, to find Kadeem's total balance in one year in one step, he needs to multiply his current balance by 1 + 0.08 = 1.08. Therefore, Kadeem should multiply his current balance by 1.08 to find his total balance in a year in one step.

Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.

To find the number of people that need to attend the pancake breakfast, we can set up the following equation:

Number of People x Cost per Person = Total Cost

We know that the total cost is $2,520 and the cost per person is $15, so we can substitute those values into the equation:

Number of People x $15 = $2,520

We can solve for the number of people by dividing both sides of the equation by $15:

Number of People = $2,520 / $15

This gives us the number of people that need to attend the pancake breakfast in order to raise the desired amount of money. In this case, the number of people is 168.

Therefore, Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.

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Solving for two variables (normally denoted as "x" and "y") requires two sets of equations.

Assuming you have two equations, the best way for solving for both variables is to use the substitution method, which involves solving for one variable as far as possible, then plugging it back in to the other equation. Knowing how to solve a system of equations with two variables is important for several areas, including trying to find the coordinate for points on a graph.

Write out the two equations that have the two variables you want to solve. For this example, we will find the value for "x" and "y" in the two equations "3x + y = 2" and "x + 5y = 20"

Solve for one of the variables in on one of the equations. For this example, let's solve for "y" in the first equation. Subtract 3x from each side to get "y = 2 - 3x"

Plug in the y value found from the first equation in to the second equation in order to find the x value. In the previous example, this means the second equation becomes "x + 5(2- 3x) = 20"

Solve for x. The example equation becomes "x + 10 - 15x = 20," which is then "-14 x + 10 = 20." Subtract 10 from each side, divide by 14 and you have end up with x = -10/14, which simplifies to x = -5/7.

Plug in the x value in to the first equation to find out the y value. y = 2 - 3(-5/7) becomes 2 + 15/7, which is 29/7.

Check your work by plugging in the x and y values in to both of the equations.

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The values of the integers lie between 29 and 39 and is 30,31,32,33,34,35,36,37,38.

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Given that the integers lie between the numbers 29 and 39. The numbers will be,

29, { 30,31,32,33,34,35,36,37,38 }, 39

Therefore, the values of the integers lie between 29 and 39 and are 30,31,32,33,34,35,36,37,38.

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Answer:

X is a variable, the value depends on the equation

The relationship between the volume of a sphere and the volume of a cylinder is: the volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.

In this question we need to describe the relationship of the volume between the volume of a sphere and the volume of a cylinder.

Consider  a cylinder with radius r and height h.

we know that the formula for the volume of cylinder is,

V1 = π * r² * h

Consider a sphere with radius r1.

We know that the formula for the volume of sphere is,

V2 = 4/3 * π * r1³

If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r1 = r and h = 2r

V2 = 4/3 * π * r³

And V1 = π * r² * (2r)

V1 = 2 * π * r³

V1 = 2 * 3/4 * V2

V1 = 3/2 * V2

volume of cylinder = 3/2 *  volume of sphere

Therefore, the volume of a sphere = 2/3 * the volume of a cylinder

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Answer:

x = 10

Step-by-step explanation:

7x-22=3x+18

4x -22 = 18

4x = 40

x = 10

The relation between area, height and volume is: volume = area * height

In this question we need to find the relation between area height and volume.

the formula for area and volume are based on height:

volume = base area * height

Let v represents the volume, A represents area and h represents the height.

V = A * h

As we know the volume of rectangular prism is:

volume = length * width * height

i.e., V = l * w * h

and the base area is:

area = length * width

i.e., A = l * w

Substitute A =  l * w in V = l * w * h

Then we get, V = A * h

Therefore, the relation between area, height and volume is: V = A * h i.e., volume = area * height

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The missing number in the pair of equivalent expressions is 9.

To solve this problem, you can use the model provided to represent the expressions 15 + 9 and 5 + 3.

For the expression 15 + 9, you can place 15 in the first row of five squares and 9 in the second row of five squares, like this:

[15] [9]

For the expression 5 + 3, you can place 5 in the first row of three squares and 3 in the second row of three squares, like this:

[5] [3]

Then, you can use the model to find the missing number in the pair of equivalent expressions. Since the two expressions are equivalent, the missing number should be in the same position as the number 3 in the second row of the model.

If you look at the first expression, you can see that the missing number is in the same position as the number 9. Therefore, the missing number in the pair of equivalent expressions is 9.

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My_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .

Now, According to the question:

Create a list containing your 3 variables : my_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .

How do I store multiple values in one variable Python?

append()

We use the append() method for this. You can use this to append single values to the list – value, list, tuple.

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Answer:

see explanation

Step-by-step explanation:

AD = BC = 8 ( opposite sides of a parallelogram are congruent )

DC = AB = 15 ( opposite sides of a parallelogram are congruent )

Consecutive angles in a parallelogram are supplementary , sum to 180° , so

∠ A + ∠ D  = 180° , that is

∠ A + 68° = 180° ( subtract 68° from both sides )

∠ A = 112°

the opposite angles of a parallelogram are congruent , then

∠ B = ∠ D = 68° , and

∠ C = ∠ A = 112°