Mathematics College

Jessie is building a cabinet door, which is pictured below. The center of the cabinet door is 12 inches by 16 inches, and the border of the cabinet door has a width of x inches. The entire cabinet door has an area of exactly 396 square inches.
Clockwise from the top, the picture reads, x, 12 inches, 16 inches, x, Figure not drawn to scale.

Write an equation in standard form that can be used to find x , the width of the border.

Answers

Answer 1

Answer:

[tex]x^2+14x-51=0[/tex]

Step-by-step explanation:

Since the entire cabinet door is a rectangle, its area is given by:

[tex]A=w\ell[/tex]

The center of the cabinet door measures 12 inches by 16 inches.

And the border of the cabinet door has a width of x inches.

Therefore, the total width of the cabinet door will be (12 + 2x).

Likewise, the total length of the cabinet door will be (16 + 2x).

Thus, the area of the entire cabinet door will be:

[tex]A=(2x+12)(2x+16)[/tex]

We are given that this entire area is 396 square inches. Thus:

[tex]396=(2x+12)(2x+16)[/tex]

Simplify. We can factor out a two from both of the factors on the right-hand side:

[tex]396=2(x+6)(2)(x+8)[/tex]

So:

[tex]396=4(x+6)(x+8)[/tex]

Dividing both sides by four yields:

[tex]99=(x+6)(x+8)[/tex]

Distribute the right-hand side:

[tex]x^2+14x+48=99[/tex]

Therefore, our equation in standard form is:

[tex]x^2+14x-51=0[/tex]

Edit:

We want to find the width of the board. So, we simply have to solve for x. We previously obtained:

[tex]x^2+14x-51=0[/tex]

We can factor:

[tex](x+17)(x-3)=0[/tex]

By the Zero Product Property:

[tex]x+17=0\text{ or } x-3=0[/tex]

Solve for both cases:

[tex]x=-17\text{ or } x=3[/tex]

Length/width cannot be negative. So, we can reject the first solution.

Thus, our only solution is:

[tex]x=3[/tex]

Step-by-step explanation:

inside the parentheses means left or right, and it also means opposite direction.

Answer:

this question answer Iis left 26 units..

elijah used 3/4 of the memory on his cell phone memory card if the memory card can hold 32 gigabytes how many gigabytes did elijah used

Answers

Elijah used 24 gigabytes memory on his cell.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Elijah used 3/4 of the memory on his cell phone memory card.

And, The memory card can hold 32 gigabytes.

Now,

Since, The memory card can hold 32 gigabytes.

And, She used 3/4 of the memory on his cell phone memory card.

Hence. The used memory = 3/4 of 32

= 3/4 × 32

= 3 × 8

= 24 gigabytes

Thus, Elijah used 24 gigabytes memory on his cell.

Learn more about the divide visit:

brainly.com/question/28119824

#SPJ1

4. There are 36 units in a case. You have 90 loose units of stock in the store. The store manager has requested a stock count in CASES. How many cases of stock will 90 units fill? CALCULATION:

Answers

There are 36 pieces in one case. The store has 90 loose storage units. The store manager requested an inventory count where 2.5 units would fill her 90 units.

What is the inventory process like?

Typically, this process involves the retailer (or team of employees) walking through the retailer's warehouse and storefront, counting each item. Information is captured manually using pen and paper or electronically using a mobile device.

Create a storage location map showing each shelf, bin, drawer, receiving dock, and return area. Place geographic divisions, not product lines, between each storage area. Let's start counting! After each counter completes a certain range, allow a manager or someone else to check the count.

90/36 = 2.5

To learn more about stock visit:

brainly.com/question/25818989

#SPJ1

In a survey of 1,000 women aged 22 to 35 who work full time, 545 indicated that they would be willing to give up some personal time in order to make more money. The sample was selected in a way that was designed to produce a sample that was representative of women in the targeted age group.
a. Do the sample data provide convincing evidence that the majority of women age 22 to 35 who work full-time would be willing to give up some personal time for more money? Test the relevant hypotheses using α = .01.
b. Would it be reasonable to generalize the conclusion from Part (a) to all working women? Explain why or why not.

Answers

Answer:

Yes, there is convincing evidence that the majority of women age 22 to 35 who work full-time would be willing to give up some personal time for more money.

No ;

Step-by-step explanation:

n = 1000

x = 545

Phat = x / n = 545/1000 = 0.545

H0: p ≤ 0.5

H1: μ > 0.5

The test statistic :

(phat - p0) ÷ √(p(1 - P0) / n)

Test statistic :

(0.545 - 0.5) ÷ √(0.5(0.5) / 1000)

0.045 / 0.0158113

Test statistic = 2.846

α = 0.01

Decison :

Reject H0 ; if Pvalue < α

Using the Pvalue from Test statistic (Z) calculator :

Pvalue = 0.002214

With Pvalue < α ; We reject H0 and conclude that there is convincing evidence that the majority of women age 22 to 35 who work full-time would be willing to give up some personal time for more money.

No, making generalization about all women would not be reasonable as the data employed for the research mainly focuses on a particular

I need to evaluate the limit and I also need to show the work for it. Please help me out if you can.

Answers

Answer:

-6

Step-by-step explanation:

You can solve all math problems via Photo math application, you can download it from the store for free, it is easy to write the question via the camera and quickly display the final result with the solution steps.

Find the area of the parallelogram below.

Answers

Answer: 58 i think

Step-by-step explanation: i guess you have to add sorry if it wrong

33 hope this helps and sorry if it’s wrong

please help me this is. big

Answers

Answer:

C. = 69.5

Step-by-step explanation:

The median or the average between 80 and 59 is 69.5

Hope this helps! :)

In the sample compound interest rate tables presented in your reading material, the first column on the left-hand side of each table shows you the __________. a. 1% rate, b. principal, c. number of periods, d. maturity values

Answers

In the sample compound interest rate tables presented in your reading material, the first column on the left-hand side of each table shows you the number of periods. Option C

What is the compound interest?

When interest is computed, it is done so on the initial principal as well as all of the accrued interest from prior periods.

The ability of compound interest is defined as producing "interest on interest."

Any frequency schedule, including continuous, daily, and yearly, can be used to compound interest.

Money increases more quickly when compounded.

Formula is given as :
[tex]A = P(1 + \frac{r}{n})^n^t[/tex]

Read more on compound interest rate here:https://brainly.com/question/28020457

#SPJ1

help pls with the question

Answers

Answer:

fart

Step-by-step explanation:

Maya is solving the equation 2(1+7x)=72. She lists an explanation for each step as shown. Which is the missing explanation for Maya's first step after writing the given equation?

Answers

Answer:

apply the distrbutive property

Step-by-step explanation:

...........................

Is a function that can be graphed
as a solid line discrete or continuous?

Answers

Linear function Is a function that can be graphed as a solid line discrete or continuous

What is a linear function?

Linear functions are simply known as functions whose graph is a straight line.

They have one dependent variable and one independent variable.

These functions have either one or two variables without exponents.

Continuous graphs are used to represent functions that are continuous along their entire or whole domain.

Whereas, discrete graphs are used to represent values at specific points along the number line from different directions.

Types of the linear function;

Direct variationslope-intercept formstandard formpoint-slope form

Hence, it is a linear function

Learn more about linear functions here:

https://brainly.com/question/15602982

#SPJ1

The following table shows the coordinates for a triangle and the coordinates for its image. The triangle is mapped
onto its image by a dilation. Draw the triangle and its image on a coordinate plane.
Pls help! Thanks

Answers

Answer:

Th (0,0)

the centre of dialation

Johnny bought 8 toy cars. The cars came in p packages. Write an expression that shows how many toy cars were in each package.

Answers

Answer:

p=8+x

Step-by-step explanation:

c=t/8 where c is the number of cars in each package.

Edgar accumulated $9,000 in credit card debt. If the interest rate is 30% per year and he does not make any
payments for 2 years, how much will he owe on this debt in 2 years by compounding continuously?

Answers

Answer:

$16399.06

Step-by-step explanation:

Given

Debt amount P = $9000Interest rate r = 30% = 0.3Time t = 2 yearsCompound number = continuous

Use formula

A = Pe^(rt)A = 9000*e^(0.3*2) = $16399.06

Mr Paul has 4 bars of chocolate. He distributes 1/3
of each bar to 4 children.
a) Write the fraction of chocolate distributed.
b) Write the fraction of cholates left with Mr. Paul

Answers

a) The fraction of chocolate distributed is given as follows: 4/3.

b) The fraction of chocolates left with Paul is given as follows: 8/3.

How to obtain the fractions?

The fractions are obtained applying the proportions used in the context of this problem.

He distributes 1/3 of each bar to 4 children, hence the total number of bars distributed is given as follows:

4 x 1/3 = 4/3.

(multiplication of fractions, multiply the numerators and the denominators, keeping the quotient).

The total number of bars that Paul had initially is given as follows:

4 bars.

Then the fraction of chocolate remaining with Paul is given by the subtraction of the total amount of bars by the amount given to the children, as follows:

4 - 4/3 = 12/3 - 4/3 = 8/3 bars.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

What is the value of the expression below when x=2x=2?
8x^2 +6x-8
8x
2
+6x−8

Answers

The value of the expression 8x² + 6x - 8 below when x=2 is 36.

The value of the expression when x = 2

The expression can be evaluated by following the steps below:

8x² + 6x - 8 in x = 2 means that the variable x will be replaced by the given number which is 2.

8*2² + 6*2 - 8

8*4 + 12 - 8

32 + 16 - 8 = 36

This therefore means that when x= 2 in 8x² + 6x - 8 , the value gotten will be 36.

Read more about Evaluation of expressions here brainly.com/question/4344214

#SPJ1

What would y be? If x is 9 m

Answers

The answer is 30 because you do big side over small side and cross multiply.

For every boy taking classes at the music school, there are 3 girls who are taking classes at the school. If there are 128 students taking classes, write and solve a proportion to predict the number of girls taking classes at the school.

Answers

Answer:

Step-by-step explanation:

the sum of three numbers is 124. the third number is 4 times the first. the second number is 10 more than the first what are the numbers

Answers

Answer:

19,29,76

Step-by-step explanation:

x=first number

x+10=second number

4x=third number

add three numbers to equal 124.

x+(x+10)+4x=124

6x=114

x=19 first number

x+10 0r

19+10=29 second number

4x or

4(19)=76 third number

19+29+76=124

124=124

Find the exact value of x.

Answers

Answer:

[tex]x = 4 \sqrt{3} [/tex]

Step-by-step explanation:

[tex] \frac{8}{2} = 4 \\ 4 \times \sqrt{3} = 4 \sqrt{3} [/tex]

What is 1653.78367 to the nearest ten square meter? Please help

Answers

Answer: 1653.8

Step-by-step explanation: Find the number in the tenth place 7 and look one place to the right for the rounding digit 8 . Round up if this number is greater than or equal to 5 and round down if it is less than 5.

Pls answer will mark brainliest! Ashlyn is having new hardwood flooring installed at the living room kitchen and dining room if the flooring cost $4.25 per square foot, how much will she spend?

Answers

Answer:

$580.13

Step-by-step explanation:

The area of the flooring:

A = 1/2*8*(13.5 - 7.5) + 1/2(8 + 4 + 18)(7.5) = 136.5 ft²

Cost of flooring:

136.5*$4.25 = $580.13

Idil owns a small business selling clothing. She knows that in the last week 3
customers paid cash, 25 customers used a debit card, and 53 customers used a credit
card.
with
Based on these results, express the probability that the next customer will pay
cash or a credit card as a percent to the nearest whole number.

Answers

The probability that the next customer will pay cash or a credit card is 56%, since 3 customers paid cash and 53 customers used a credit card out of a total of 81 customers.

What is customers?

Customers are individuals or organizations who purchase goods and services from a business. They play an important role in a company's success as they provide the revenue needed to sustain and grow the business. Customers become loyal to a business when they are provided with quality products, excellent customer service, and competitive prices. Companies that focus on customer satisfaction often develop long-term relationships with their customers, as they understand the importance of customer loyalty. Companies must strive to continually meet the changing needs of their customers in order to remain successful in the long term.

To learn more about customers
https://brainly.com/question/27155914
#SPJ1

What is the area of a circle with a diameter of 14 meters? Leave the answer in terms of π.

49π square meters
7π square meters
196π square meters
14π square meters

Answers

Therefore , the solution of the given problem of circle comes out to be Area = 154 meter square or 49π meter square option 1 is correct.

Circle – what is it?

A moving point on a plane is followed so that its distance from a specific point remains constant to produce the circular form known as a circle. The English term circle derives from the Greek word kirkos, which meaning hoop or ring. Area of circle= πr²

Here,

Given :

Diameter of circle : 14

Radius =14/2 = 7 meters

and

Using formula

Area= πr²

=> Area = π7²

=>Area = 22/7 * 7²

=> Area = 22*7

=> Area = 154 meter square or 49π meter square

Therefore , the solution of the given problem of circle comes out to be Area = 154 meter square or 49π meter square option 1 is correct.

To know more about circle , visit

brainly.com/question/29142813

#SPJ1

Answer: A the first one 49π square meters

If you can help me with these four questions I'll give you brainliest :))

Answers

Answer:

13. The mode is 265

14. The range is 42

15. The median is 250

16. The mean is 249

Mark's school is 5 kilometers away from his home. There are about 0.62 miles in 1 kilometer. About how many miles is Mark’s school from his home?

Answers

Answer:

3.1 miles

Step-by-step explanation:

(5 km)(0.62 mi/km) = 3.1 miles

3.1 miles! 3.10686 exactly

Other Questions

How might developing positive social identities lead to tolerance? I dont know help m/12-8=4 Why did we put Japanese in internment camps? how do you say "she was raised in South Africa and England" in chinese?(no links please) I need help on this question 29 POINTS TO WHOEVER GETS THIS RIGHT What is the value of the expression below when w=7 and x=5 3w + 10x 3 pounds of peanuts for 7.50. how much is one pound PLEASE HELPRead the passage from The Phantom Tollbooth."For instance, from here that looks like a bucket of water," he said, pointing to a bucket of water; "but from an ant's point of view it's a vast ocean, from an elephant's just a cool drink, and to a fish, of course, it's home. So, you see, the way you see things depends a great deal on where you look at them from. Now, come along and Ill show you the rest of the forest."What conclusion about Alec's perspective does the passage support? He spends very little time thinking about his own perspective or other people's perspectives.He spends a lot of time thinking about his own perspective as well as other people's perspectives.He spends most of his time thinking about his own perspective and ignoring other peoples perspectives.He spends an equal amount of time thinking about his own perspective and other people's perspectives. -5(i-30)=-10what does i equal? Read the passage.Ocean NoiseWhen we think about the pollution of our oceans, many of us think of oil spills that dirty the waters and harm a variety of ocean life. Or, we might think of people in boats who litter the waters with their trash. After all, how many times in the news do we hear about ships that leak dangerous chemicals into the water? What we may not realize, though, is that there is another danger that is just as harmful to ocean life as any chemical or other dangerous material: ocean noise.Many of us think of the oceans as silent places. On the contrary, they are filled with a variety of sounds. On any given day, one might hear the calls of dolphins as they swim through the waters. Whales use sounds to keep track of each other. Sea lions talk to each other to find food. Even the tiniest of shrimp make a snapping sound. There are also sounds caused by wind or rain upon the waters. Sound also plays an important role in the daily life of various ocean animals, many of which depend upon their sharp sound detection skills to survive. With increased activities by people on many of the oceans waters, the noise has increased so much that it is beginning to cause damage to the oceans as well as to the animals that live in them.Ocean noise is the term used to describe the human-made noise occurring at increasing rates in the ocean. The noise comes from many different sources: large ships, small boats with motors, and jet skis, among others. There are also underwater exploration activities such as mining, as well as radar activities of ships. One of the most harmful types of ocean noise occurs with offshore oil drilling and seismic oil explorations. Air guns are instruments that are used to determine the location of oil and natural gas beneath the sea floor. They make a sound that can damage the hearing of ocean animals.We know that sound travels faster in water than it does in air. This means that sounds in the oceans can travel for many, many miles in a short period of time. Unfortunately, sounds made by people are much louder than sounds made by ocean animals.What this means is that sounds caused by noisy engines or radar equipment used by ships can upset the everyday activities of the creatures that live in the ocean. For instance, humpback whales use songs to talk to each other. Scientists have discovered that the whales system of talking can be disturbed by loud noises. This makes it harder for the whales to find each other. The stranding of whales and dolphins has been found to increase immediately after naval sonar maneuvers. Sea lions are another type of animal that depends on sounds to communicate with other sea lions. Ocean noise can make it difficult for them to find food. Ocean noise can disturb migration routes of whales and other animals that travel to different places.However, scientists and other researchers are working hard to find a solution to this threat to marine life. Since 2003, the use of low-frequency active (LFA) sonar equipment by the United States Navy has been tightly limited because its effects have been shown to cause harm to many ocean animals. NOAA (National Oceanic and Atmospheric Administration) has released a plan to reduce ocean noise that will work better than past attempts to reduce the noise.Other people are helping as well. Some fishing companies use special equipment that makes a pinging sound to keep certain kinds of ocean life from getting caught in its fishing nets. The National Park Service completed a study that tracked tour cruise ships and made an effort to reduce the number of tours. They also tried to increase the quiet time for humpback whales by scheduling tours farther apart.Local conservation groups are also asking people to be more careful about using jet skis, motorboats, and other equipment that might disturb areas where ocean life is particularly fragile. Also, closer attention is being paid to where ships are traveling to make sure that, whenever possible, they stay away from waters where large numbers of ocean animals live.With the increase in ocean noise, measures must be taken to control or, at the very least, curb its growth.What argument does the author make in "Ocean Noise"?The ocean noise created by marine life is more detrimental than noise created by humans.Oil spills are still much more dangerous than ocean noise.Ocean noise has increased slightly. but it is not affecting marine life.Human activity has greatly increased ocean noise to the detriment of marine life. 25, 22, 21, 23, 24 find the mean What measure do we use to determine the amount of potential energy in a battery? Olivia, Nicholas, Chloe, and Ethan each took many samples from the samepopulation of students. The number of students in each of their samples isshown in the table below. Which person's sampling distribution is most likelyto closely approximate the population distribution?Person taking sample Number of students in each sampleOlivia29Nicholas70Chloe56Ethan91A. OliviaB. ChloeC. EthanD. Nicholas 20 points !! NEED HELPWhat is the variable being tested in an experiment?A. explanatory variableB. placeboC. response variableD. control variable Write 2,023 in word form Examine the scenario below. Select the letter of the correct answer. The Article primarily discusses __________. Press enter to interact with the item, and press tab button or down arrow until reaching the Submit button once the item is selected A. how people began using wheels for transportation by putting a pole through a wheel about 300 years after the wheel was invented B. how the wheel, which was invented as a potter's tool, evolved to be used in transportation, agriculture, irrigation, and more over the course of 5,000 years C. how people have invented different types of wheels for agricultural use that can be powered by people, animals, wind, or flowing water D. how around 3500 BCE, potters in ancient Mesopotamia created the first wheel, which was used to spin clay to make it easier to shape their plates, bowls, and sculptures SUBMIT The product of (4x + 3)2 is: Answer fully pls!!!!!!!!!!! What is the acceleration of the particle at t 0?