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[tex]sum \: of \: interior \: angles = (5 - 2)180 = 540 \\ each \: angle = \frac{540}{5} = 108 \\ x + bcd = 180 \\ x + 108 = 180 \\ x = 180 - 108 = 72[/tex]

The height of the hill is 12.8 cm.

What is Gravitational potential energy?

The gravitational potential energy of an object is given by:

U = mgh

where,

m is the mass of the object.

g is the acceleration of gravity.

h is the height of the object.

Given that;

The potential energy = 100 J,

In this problem, we have;

The potential energy of the person is = U = 100 J

The mass of the person = m = 80 kg

Now, Solving for h, we find at what height the person is:

h = U /mg

h = 100 / 80*9.8

h = 12.8 cm

Hence, The height of the hill is 12.8 cm.

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Answer:

108°

Step-by-step explanation:

Solving the distance-time problem here, the taken time to reach the restaurant is 196 seconds (approx.)

This is a distance-time problem.

To solve this problem the required formula is, d/t = v or, d/v = t,

where d is the represented distance and t denotes the required time, and v is denoted as the velocity or speed.

Here v, velocity is 32 feet/second, and d, distance is 6271 feet.

So, the taken time to reach the restaurant is 6271/32 = 196 seconds (approx.)

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Answer:

D

Step-by-step explanation:

Answer:

D [tex]y = - 5 - 17[/tex]

Step-by-step explanation:

To make y the subject of formula in:

[tex]5x + y = - 17[/tex]

Mover 5x to the other side of the equation which makes it -5x due to the equality sign

Therefore:

[tex]y = - 5 - 17[/tex]

Correct option is A. Equation for the translation of y=2/x that has asymptotes at x=3 and y=-5  is y=2/x-3 -5.

A curve's asymptote is the point at which the curve converges. In other words, despite being endlessly near, the curve and its asymptote never collide. Asymptotes are utilized in big O notation, are straightforward approximations to complicated equations, and are helpful for charting rational equations, among other uses.

Typically, the limit of a value when the function is not specified can be used to determine the asymptote(s) of a curve. Examples of such points include and as well as the location where the numerator of a rational function equals zero.

Given,

y = 2/x

asymptotes at x=3 and y=-5

⇒ denominator is (x-3)

⇒ y = -5 is highest degree of the equation.

⇒ The equation will be y=2/x-3 -5.

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Length of a side of original square = 5 inches

Let's take the value of the length of the original square be to x.

As it is known that the area of the larger square has  = 49 square inches, and the side are lengthened by 2 inches from the original square side.

So we have the expression:

[tex](x + 2)^{2}[/tex] = 49

x + 2 = 7

x= 5

Therefore the original side of the square is 5 inches.

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The average rate at which Mr. Blade types is 30 words per minute.

Average or mean is a measure of central tendency where it defines the central number of a data set.

Average is calculated by dividing the total sum of the values of the dat set divided by the frequency or the number of data in the set.

Mr. Adi takes 9 minutes.

The average rate of Mr. Adi is 40 words per minute.

So in 9 minutes he writes 40 × 9 = 360 words in total.

Mr. Blade typed the same number of words.

he took 12 minutes to type it.

So average rate = total words typed ÷ time taken (in minutes)

Average rate= 360 ÷ 12 =30 words per minute.

Hence Mr. Blade writes at the average rate of 30 words per minute.

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Eva bought 18 chicken wings with $18

Eva bought 20 chicken wings for $20

The first step is to calculate the cost of one chicken wing

= 20/20

= 1

1 chicken wings cost $1, if Eva spent $18 then the number of chicken wings bought can be calculated as follows

= 18 × 1

= 18

Hence Eva bought 18 chicken wings with $18

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Let [tex]x[/tex] be the "given angle" mentioned here. Then its complement indeed has measure [tex]90-x[/tex], and its supplement [tex]180-x[/tex].

Now translate the following sentence into an equation:

"The supplement of a given angle is 10° more than twice its complement."

[tex]\implies 180 - x = 10 + 2 (90 - x)[/tex]

Solve for [tex]x[/tex].

[tex]180 - x = 10 + (180 - 2x)[/tex]

[tex]180 - x = 190 - 2x[/tex]

[tex]2x - x = 190 - 180[/tex]

[tex]\boxed{x = 10}[/tex]

woah this looks hard

The given equation is 8p + 4 = −9 + 7p.The value of p is -13.

The required solution for the given equation is p = -13

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1.There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.

Now the given equation is,

8p + 4 = −9 + 7p

Solving them,

Taking variables to one side and constant to another, we  get

8p-7p=-9-4

p=-13

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Answer: Yes

Step-by-step explanation:

one is just bigger than the other if you blow the little one up than you can see they are the same!

The distance between two given points (3, −4) and (−2, 5) is √106 units.

Given that, two points are (3, −4) and (−2, 5).

Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates.

The formula for the distance, d, between two points whose coordinates are d=√(x2-x1)²+(y2-y1)²

Now, put two points (3, −4) and (−2, 5) in the distance formula and simplify.

That is, distance = √[(-2-3)²+(5-(-4))²]

=√(25+81)

=√106 units

Therefore, the distance between two given points (3, −4) and (−2, 5) is √106 units.

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The regular price of the sofa if 66% is given off, is $680.00

What is regular price?

The regular price of the sofa is the price at which it is sold without considering the coupon of 66%, in essence, it is 100% of the original price of the sofa, in short, if 66% is given off, then the sale price is 34% of the original price

34% of regular price=$231.20

1% of regular price=231.20/34

1% of regular price=$6.80

100% of regular price=$6.80*100

100% of regular price=$680

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Full question

A sofa is on sale for 66% off. the sale price is $231.20 . what is the regular price?

:

Answer:

11 more yards per minute on Path B.

Step-by-step explanation:

Path A: 672 yards in 6 minutes = 112 yards per minute.

Path B: 984 yards in 8 minutes = 123 yards per minute.

123 - 112 = 11 yards per minute longer on Path B.

Answer:

156 yards per minute

Step-by-step explanation:

first off remember to have a label

it is change in Y over change in X so

984-672/ 8-6

you could get 312/2

which equal 156

I attached a photo to make it clear

Answer:

x<-5

Step-by-step explanation:

Answer:

2,992,646,116

Step-by-step explanation:

I am big brain

Answer:

2992646116

Step-by-step explanation:

multiply starting with 98663

The system of equations that's corresponding to the given function are y = 5 - x and 5 - x = 9x².

According to the statement

We have to find that the linear equation.

So, For this purpose, we know that the

The systems of equations, sometimes called simultaneous equations, are a group of relationships between various unknown variables that can be expressed in terms of algebraic expressions.

From the given information:

Given the systems of equations;

y = 9x²

and

x + y = 5

From equation 2:

y = 5 - x

Substitute into equation 1 to have;

5 - x = 9x²

From the resulting equation, we are able to see that the system of equations that's corresponding to the given function are y = 5 - x and 5 - x = 9x².

So, The system of equations that's corresponding to the given function are y = 5 - x and 5 - x = 9x².

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The inverse of an exponential function with a base e is the logarithm.

A logarithm is defined simply?

How does exponential growth utilise e?

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After the solving equation ln (x-7)=2, the value of x is equal to [tex]e^{2}[/tex] + 7

We have been asked to find x in ln (x-7)=2

⇒ ln (x-7)=2

⇒ x - 7 = [tex]e^{2}[/tex]

⇒ x = [tex]e^{2}[/tex] + 7

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

$780

Step-by-step explanation:

Simple Interest Formula

[tex]\boxed{\sf A = P(1 + rt)}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=650(1+0.05(4))[/tex]

[tex]\implies \sf A=650(1+0.2)[/tex]

[tex]\implies \sf A=650(1.2)[/tex]

[tex]\implies \sf A=780[/tex]

Therefore, the amount in the account now is $780.

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Answer:

honestly i say foundation of math12 ithink it will come more in handy in life

Considering the numeric values of the function, the points and ordered pairs are given as follows:

To find the numeric value of a function, we replace each instance of the variable by the desired value.

An ordered pair is given by:

(x, f(x)).

In which f(x) is the numeric value.

For this problem, the function is given by the following rule:

y = 3x + 1.

When x = 2, the numeric value is given by:

y = 3 x 2 + 1 = 6 + 1 = 7.

Hence the ordered pair is (2,7).

When x = 3, the numeric value is given by:

y = 3 x 3 + 1 = 9 + 1 = 10.

Hence the ordered pair is (3,10).

When x = -1, the numeric value is given by:

y = 3 x -1 + 1 = -3 + 1 = -2.

Hence the ordered pair is (-1,2).

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Answer:

d is the correct answer

Step-by-step explanation:

m∠ABC = 68°; m∠DEF = 112°

Answer:

D is correct

Step-by-step explanation:

Supplemental angles add to 180

6x + 8 + 12x -8 = 180  Combine line terms

18x = 180  Divide both sides by 18

x  = 10

Substitute 10 in for x

ABC

6x + 8

6(10) + 8

60 + 8

68

DEF

12x - 8

12(10) - 8

120 - 8

112

the extraneous solution for the equation √(2 x +9) - √x = 3 is x = 0 or x = 6.

We are given an equation:

√(2 x +9) - √x = 3

√(2 x +9) = 3 + √x

Raise both sides to the power 2, we get that:

2 x + 9 = 9 + x + 6√x

x = 6√x

Squaring both sides again, we get that:

x² = 6 x

x² - 6 x = 0

x ( x - 6) = 0

x = 0 or x = 6.

Therefore, we get that, the extraneous solution for the equation √(2 x +9) - √x = 3 is x = 0 or x = 6.

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Answer:[tex]f\left(x\right)\le \:0[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:0\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:0]\end{bmatrix}[/tex]

Answer:

a. 62

b. 8.8

c. 2.8

Step-by-step explanation:

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