The prom committee is decorating the venue for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5 feet, EF=39 feet, and m∠GHF=128° , find GE.

Answer:

We can use algebra to find the two consecutive even integers whose product is 168.

Let's call the first even integer x. Since it is consecutive to another even integer, the next one will be x+2. The product of these two integers is:

x * (x+2) = 168

We can solve for x by simplifying the equation:

x^2 + 2x = 168

x^2 + 2x - 168 = 0

We can factor the left side of the equation:

(x-14)(x+12) = 0

So the two solutions for x are -12 and 14.

The negative integers are -12 and -14.

The two integers that multiply to give 168 are -12 and -14, but keep in mind that they are not consecutive integers.

The values of the terms are a₂ = 15, a₃ = 30 and a₄ = 45

The definition of the function is given as

a₁= 0

aₙ = aₙ₋₁ + 15

The above definitions imply that we simply add 15 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₂ = 0 + 15

a₂ = 15

Also, we have

a₃ = 15 + 15

a₃ = 30

Lastly, we have

a₄ = 30 + 15

Evaluate the equation

a₄ = 45

Hence, the value of a₄ is 45

Read more about sequence at

brainly.com/question/7882626

#SPJ1

The distance between the tennis balls and the cans is 49.46 cubic inches.

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

Given: Each ball has a diameter of three inches.

Three tennis balls are contained in each can, which is how they are sold.

Each can has a cylindrical shape.

We start by determining each tennis ball's volume.

Because of their spherical shape, their volume is determined by

[tex]$V=\frac{4}{3} \pi r^3$[/tex]

Where [tex]$r=\frac{d}{2}=\frac{3 \text { in }}{2}=1.5 i$[/tex] in

Replacing the radius and using [tex]$\pi \approx 3.14$[/tex], we have

[tex]$V=\frac{4}{3}(3.14)(1.5 \mathrm{in})^3=14.13 \mathrm{in}^3$$[/tex]

Therefore, the volume of each tennis ball exists 14.13 cubic inches, approximately.

Assuming that the diameter of each ball exists congruent with the diameter of the can, we contain the volume of a cylinder defined by

[tex]$V=\pi r^2 h$[/tex]

Where, r = 1.5 in and h = 3(3 in)=9 in, because each can has three balls, and the height exists the sum of all three diameters.

[tex]$V=3.14(1.5 i n)^2(9 i n)=63.59 n^3$$[/tex]

Therefore, the volume of each can exists 63.59 cubic inches, approximately.

The complete question is:

Tennis balls with a 3 inch Diameter are sold in cans of three. The can is a cylinder

A)what is the volume of one tennis ball ?

B)what is the volume of the cylinder ?

C)how much space is not occupied by the tennis balls in the can?

To learn more about volume refer to:

https://brainly.com/question/14197390

#SPJ1

Two  cards are drawn in succession from a standard deck. The probability that both the drawn cards are diamonds is 143/2,652

Probability is defined as the ratio of the number of favorable events to the the number of possible outcomes. The probability of an event A is defined as:

P(A) = n(A)/n(S)

Where:

n(A) = number of possible ways the event A occurs

n(S) = total possible outcomes

In a standard deck, there are 52 cards. The number of diamond suit = 13 cards.

First drawn: number of diamond = 13

Hence, P1(diamond) = 13/52

In the second drawn, the number of diamonds left is 13 - 1 = 12, and total number of cards left is 52 - 1 = 51.

Hence, the probability of the second card will be a diamond is:

P2(diamond) = 12/51.

Since those 2 events are independent, the probability that both cards are diamonds is:

P(diamonds) = P1 (diamond) x P2 (diamond)

                     = (13/52) x (11/51) = 143/2,652

Learn more about probability here:

https://brainly.com/question/5858025

#SPJ4

The numerical value of x in the function f(x) = -9x + 13 when f(x) = -41 is 6.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

To find the value of x, replace the occurrence of f(x) with -41 in the function and simplify.

f(x) = -9x + 13

-41 = -9x + 13

Collect like terms

9x = 41 + 13

Add 41 and 13

9x = 54

Divide both sides by 9

9x/9 = 54/9

x = 54/9

x = 6

Therefore, the input value x is 6.

Learn more about functions here: brainly.com/question/2541698

#SPJ1

Answer: $10=2.30p

Step-by-step explanation:

By trigonometric functions and trigonometric formulas, the exact value of cot (3π / 2) is equal to 0.

In this problem we have the case of trigonometric function whose exact value must be found by means of trigonometric functions and trigonometric formulas. Now we proceed to present the entire procedure:

cot (3π / 2)

1 / tan (3π / 2)

Rewrite the function in terms of fundamental trigonometric functions: (sine, cosine)

1 / [sin (3π / 2) / cos (3π / 2)]

cos (3π / 2) / sin (3π / 2)

Then, we get the following exact value:

0 / (- 1)

0

To learn more on trigonometric functions: https://brainly.com/question/28483432

#SPJ1

Answer:

125b+2

Step-by-step explanation:

5^3b+2

5x5x5=125

125b+2

Cannot be simplified any futher

Answer: To find the total weight of the bags of topsoil, you can multiply the number of bags by the weight of each bag.

18 bags * 36 pounds/bag = 648 pounds

So, Elayna bought 18 bags of topsoil which is 648 pounds in total.

Step-by-step explanation:

Answer: X has to be greater than or equal to 15/7 for the inequality to be true.

Step-by-step explanation:

here are the steps to solve the inequality 25-2x≤5(2-x):

Start by simplifying the right side of the inequality: 5(2-x) = 10 - 5x

Now we can substitute this back into the original inequality: 25 - 2x ≤ 10 - 5x

Next, we need to combine like terms on both sides of the inequality: 25 - 7x ≤ 10

Now we'll add 7x to both sides: 25 ≤ 10 + 7x

Subtract 10 from both sides: 15 ≤ 7x

Finally, divide both sides by 7: 15/7 ≤ x

The solution set is x ≥ 15/7.

So x has to be greater than or equal to 15/7 for the inequality to be true.

Answer:

-5 ≥ x  or x ≤ -5

Step-by-step explanation:

25 - 2x ≤ 5(2 - x)

distribute the 5 to eliminate the parentheses:

25 - 2x ≤ 10 - 5x

now combine like terms:

15 - 2x ≤ -5x

15 ≤ -3x

-5 ≥ x  or x ≤ -5

the inequality symbol gets switched whenever you multiply or divide by a negative value

No Chase's work is not correct. He has made a mistake in working the brackets out. The BODMAS Rule has to be used here.

We have 2(12 ÷ 2)2 – 14 + 6

Here according to the BODMAS rule which stands for Brackets  Of  Division  Multiplication  Addition  Subtraction, we will first solve the brackets.

Now any number to the left or right of the brackets without any sign in between the bracket and the number has to be multiplied by the answer we get by solving the bracket.

12 ÷ 2 = 6

Hence we get

2 X 6 X 2  -  14  +  6

Now we need to multiply.

2 X 6 X 2 = 12 X 2 = 24

Hence we get

24 - 14 + 6

Now we need to add the numbers up.

24 + 6 = 30 hence we get

30 - 14

= 16

Hence Chase's work is not correct.

To learn more about Elementary Operations visit

https://brainly.com/question/29396321

#SPJ4

We can assume linear inequality 8x>40 for x>8 for an indirect proof.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given,

Quinn ran total distance>40 mile

No. of times he ran=5

average distance for each run>8

also let x>8 where x=average distance for each run

Hence,

           We can assume linear inequality 8x>40 for x>8

To know more about linear inequalities visit the link

https://brainly.com/question/11897796?referrer=searchResults

#SPJ1

Answer:

12.  & 2.5mins

Step-by-step explanation:

2 hours = 120 mins for 48 baguettes.  so 120/48 = 2.5 mins per baguette

30 mins is 1/4 of 2 hours. so 12  baguettes

The statement below about the rocket is true:

A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.

A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

Given, A rocket travels at an approximate speed of 7.9 kilometers per second.

Since, some unit conversion:

1 kilometer = 1000 meteres

1 kilometer = 100000 centimeteres = 10⁵ cm

1 kilometer = 10000000 milimeteres = 10⁷ mm

thus we can say that from the given options only "f" is correct that states:

A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.

Learn more about unit conversion here:

https://brainly.com/question/19420601

#SPJ1

The option that shows how to find 35% of 25 using mental maths is A. 2.5 + 2.5 + 2.5 + 1.25 = 8.75

In Mathematics, a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

In this case, it should be noted that 35% of 25 will be:

= 35% × 25

= 0.35 × 25

= 8.75

Using mental mathematics, the correct option that shows this is A.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

Answer:

23.37

Step-by-step explanation:

There ya go

:)

Ariana earned $708 in 24 hours, so $312 more Ariana earn per hour than Jacob.

We have to find how much more Ariana earn per hour than Jacob.

The equation y = 16.5x represents Jacob's earnings in dollars and cents, y, for working x hours.

Ariana earned $708 in 24 hours.

So the value of x = 24

Now putting the value of x in equation y = 16.5x

y = 16.5 × 24

y = 396

Jacob's earnings = $396

Difference between the Ariana earning and Jacob earning = $708 - $396

Difference between the Ariana earning and Jacob earning = $312

To learn more about solving the equation link is here

brainly.com/question/24945234

#SPJ4

The revenue is maximized when the derivative of R(p) is equal to 0.

R'(p) = -80p + 400 = 0

p = 5

A function is a mathematical relationship between two or more variables, where one variable (the output) is determined by the values of the other variables (the inputs). A function can be expressed as an equation, and it describes how the output changes in relation to the inputs.

Therefore, the maximum revenue is achieved when the price of each ticket is $5.

learn more about function: https://brainly.com/question/17043948

#SPJ1

The third angle of  acute scalene triangle is  41°

Now, According to the question:

The first angle of acute scalene triangle is 93°

The second angle of  acute scalene triangle is 46°

Let the third angle of  acute scalene triangle is x

We know that:

The sum of the interior angles is always equal to 180 degrees.

Now, 93° + 46° + x = 180°

139° + x = 180°

x = 180° - 139°

x = 41°

Hence, the third angle of  acute scalene triangle is  41°

Learn more about Scalene Triangle at:

https://brainly.com/question/4409838

#SPJ4

Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.

What is null hypothesis ?

The null hypothesis is a arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test the null hypothesis, we can use a one-sample t-test. The t-statistic for this test is calculated as:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the population mean (6.7 lbs/square inch in this case), s is the population standard deviation (assumed to be 1), and n is the sample size (280 engines).

The p-value for this test can be calculated using the t-distribution table or a t-test calculator. If the p-value is less than the significance level of 0.1, then we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs below the specifications.

Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.

To learn more about null hypothesis visit : brainly.com/question/28920252

#SPJ4

Steven will have to pay $127. 50 for the insurance per year.

The correct answer is an option (C)

First, we need to find the corresponding value for the all-wood building in the city suburbs.

From given table, we will use the value 0.85 because he wishes to ensure his belongings.

Here, the value of the belongings in the apartment is about $15,000

Steven wants to insure his belongings while renting.

Now we can calculate the amount of money he will have to pay  for insurance per year as follows:

15000 × (0.85 / 100)

= 127. 50 dollars

Therefore, he will have to pay 127. 50 dollars for insurance.

Learn more about insurance here:

https://brainly.com/question/13639768

#SPJ4

Answer:

11/3 or 11/3x

Step-by-step explanation:

Another term for "Rate of change" is slope.

The usual slope equation is (y2-y1)/(x2-x1)

Plugging in the points we get

(3 - (-8)) / (3 - 0)

(3+8)/(3-0)

(11)/(3)

Which makes the slope 11/3 or 11/3x

The area of a circle is 158.3 sq. m.

Consider we need to find the area of the given circle.

The radius of a circle is 7.1 m.

The area of a circle is the place occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the circumference of a circle is called the area of the circle.

The area of the circle is:

[tex]A = \pi r^{2}[/tex] , where r is the circle's radius.

Putting r = 7.1 , π = 3.14, we get

[tex]A = 3.14 *(7.1)^{2}[/tex]

A = 158.2874

A ≈ 158.3

So, the area of a circle is 158.3 sq. m.

Read more about circle:

https://brainly.com/question/20489969

#SPJ4

Answer:

c

Step-by-step explanation:

If the federal income tax withheld is $1080.50 and the federal total tax is $206 , then the tax refund that she expect back is (b) $874.50  .

The Lilly's federal total tax is = $206  ;

the federal income tax withheld is = $1080.50  ;

The amount of the refund is the difference between the federal income tax withheld and federal total tax .

So , the refund is = (federal income tax withheld) - (federal total tax) ;

Substituting the values ,

we get ;

Refund = 1080.50 - 206

= $874.50

Therefore ,  tax refund that she expect back is $874.50  .

The given question is incomplete , the complete question is

As Lily files her taxes, she learns that her federal total tax due ends up being $206. According to her Federal income tax withheld is $1080.50 , how much of a tax refund can she expect back ?

(a) $206.00

(b) $874.50

(c) $1,080.50

(d) $13,369.50

Learn more about Federal Income Tax here

https://brainly.com/question/9569073

#SPJ4

The minimum stopping distance is 800 ft.

Part A: The minimum stopping distance for a driver going at the speed limit (40 mph) is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (40 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 800 ft.

Part B: For a driver going at 45 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (45 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 925 ft, which is 15.6% greater than the stopping distance for the speed limit.

Part C: For a driver going at 50 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (50 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 1250 ft, which is 56.3% greater than the stopping distance for the speed limit.

Learn more about equation here:

https://brainly.com/question/29538993

#SPJ4

Answer:

Step-by-step explanation:

that a huge prob but yah

Answer: x > -5

Step-by-step explanation:

-1.5x < 7.5

x > -5 (When multiplying both sides by a negative, the inequality is flipped)

[tex]-1.5x < 7.5[/tex]

Divide both sides by -1.5:

[tex]\dfrac{-1.5x}{-1.5} < \dfrac{7.5}{-1.5}[/tex]

When dividing by a negative number, the inequality sign will reverse.

Answer:

[tex]x > -5[/tex]