Mathematics College

The length of a rectangular picture frame is 2 inches shorter than its width. If the perimeter of
the picture frame is 52 inches, what is the length, l, and width, w, of the frame? Write and
solve an equation to model the problem. Explain the meaning of the solution.

Answers

Answer 1

Answer:

Length = 12 inches

Width = 14 inches

Step-by-step explanation:

Formula for perimeter of a rectangle is;

P = 2(L + W)

Where;

L is length

W is width

We are told that the length is 2 inches shorter than its width. Thus;

L = (W - 2)

Thus,perimeter is now;

P = 2(W - 2 + W)

P = 2(2W - 2)

P = 4W - 4

We are told that the perimeter is 52. Thus;

4W - 4 = 52

4W = 52 + 4

4W = 56

W = 56/4

W = 14 inches

From L = (W - 2) ;

L = 14 - 2

L = 12 inches

Related Questions

72 marble and 75% are red

Answers

uh what do you mean by this?

Belle's dad lends her $10. Then Belle borrows another $15 from him. Write and evaluate an expression that shows the change in the amount of money Belle's dad has.

Answers

The expression that shows the change in the amount of money Belle's dad has is (x - 25) and this can be determined by forming the linear equation in one variable.

Given :

Belle's dad lends her $10. Then Belle borrows another $15 from him.

The following steps can be used to determine the expression that shows the change in the amount of money Belle's dad has:

Step 1 - Let the total amount of money Belle's dad have be 'x'.

Step 2 - Then it is given that Belle's dad lends her $10. So the expression becomes:

= x - 10b

Step 3 - Now, it is also given that Belle borrows another $15 from her dad. So, the above expression becomes:

= x - 10 - 15

Step 4 - Simplify the above expression.

= x - 25

So, the expression that shows the change in the amount of money Belle's dad has is (x - 25).

For more information, refer to the link given below:

https://brainly.com/question/13101306

what is the common denominater of 1/5 and 7/10

Answers

Answer:

10 010 10 10 10 10 101 01 mo1

Step-by-step explanation:

The LCD is 10 between the two of you can mark this as brainlest I’ll be very grateful

¿Cuántas placas diferentes de autos se pueden formar con 3 letras, seguidas de 4 números del 0 al 9? Considere que el alfabeto letras. cuenta con 27

Answers

Answer: Se pueden hacer 196,830,000 placas distintas.

Step-by-step explanation:

Cada placa va a tener 3 letras y 4 números.

Lo primero que tenemos que hacer es contar el numero de opciones que tenemos para cada selección, donde las selecciones van a ser.

Primera letra, segunda letra, tercera letra, primer numero, etcétera.

Entonces.

Para la primera letra tenemos 27 opciones.

Para la segunda letra también tenemos 27 opciones.

Para la tercera letra también tenemos 27 opciones.

Para el primer numero tenemos 10 opciones (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

para el segundo numero también hay 10 opciones.

Para el tercer numero también hay 10 opciones.

Para el cuarto numero también hay 10 opciones.

El numero total de posibles combinaciones va a ser igual al producto de todos los números de opciones, en este caso es:

C = 27*27*27*10*10*10*10 = 27^3*10^4 = 196,830,000

Se pueden hacer 196,830,000 placas distintas.

find the measure of the line segment TV

Answers

9514 1404 393

Answer:

Step-by-step explanation:

When chords cross, the product of the lengths of the pieces is the same for each chord:

EU·ES = ET·EV

8·9 = (12x)(6x)

72 = 72x^2

x^2 = 1 ⇒ x = 1

Then the length of interest is ...

TV = ET +EV = 12·1 +6·1

TV = 18

If ∧ ASC ≅ ∧ KSC then ∠8 is congruent to which angle?

Answers

Answer:

B. angle 5

Step-by-step explanation:

A store is having a sale in which the cost of any item is 35% off.
Can the expression be used to find the cost, x, of an item?
Select Yes or No. Please look at your picture.

Answers

Answer:

1. no

2. yes

3. no

4. yes

Step-by-step explanation:

only the second and last expression works. If x is the final cost, and it is 35% off, then you are subtracting 0.35xor keeping 0.65x

please give thanks by clicking heart button! :)

Had three thfk DJ back finding

Answers

The answer is d...........

The table represents the total miles traveled, y, after a number of hours, x.

Hours, x
Miles, y
2.5
150
4.0
240
5.5
330
7.0
420

Which linear equation represents the situation?

y = 60 x
y = 60 x + 480
y = 4 x + 240
y = 270 x

Answers

Answer:

y=60x

Step-by-step explanation:

i did it on edg2020

Answer:

(2.5,150)(4,240)

slope = (240 - 150) / (4 - 2.5) = 90 / 1.5 = 60

y = mx + b

slope(m) = 60

(4,240)...x = 4 and y = 240

now we sub and find b, the y int

240 = 60(4) + b

240 = 240 + b

240 - 240 = b

0 = b

so ur equation is : y = 60x + 0 which is written as : y = 60x <==

A line is a(n)...... for a function if the graph of the function gets closer and closer to touching the line but never reaches it.
A.) asymptote
B.) diagonal
C.) estimation
D.)diagram
E.) array

Answers

your answer would be asymptote

The population of a country grows exponentially at a rate of 1% per year. If the population was 35.7 million in the year 2010, then what is the population size of this country in the year 2015

Answers

Answer:

37.52 million

Step-by-step explanation:

using,

A = A'(1+R/100)ⁿ............................. equation 1

Where A = population size in 2015, A' = Initial population, R = rate in percentage, n = number of times between 2010 and 2015.

Given: A' =35.7 million, R = 1%, n = 5.

Substitute these values into equation 1

A = 35.7(1+0.01)⁵

A = 37.52 million.

Hence the size of the population of the country in the year 2015 is 37.52 million

I need help!!! Please figure it out and type it out.

Answers

Answer:

13 cm wide; 15 cm long

Step-by-step explanation:

Let w represent the original width. Then the original length is (w+2) and the original area is w(w+2). After the decrease, the width is (w-1) and the length is (w+1). The decreased area is (w-1)(w+1). The difference between these areas is 27, so we have ...

w(w+2) -(w-1)(w+1) = 27

w^2 +2w -(w^2 -1) = 27

2w +1 = 27

w = (27-1)/2 = 13

The original piece of cardboard was 13 cm wide and 15 cm long.

Help with quadratic! Really struggling with this

Answers

Answer:

Step-by-step explanation:

The equation

[tex]G(h)=-3h^2+24h+47[/tex]

represents the grade you are going to earn which is represented by G(h) where h in the equation is the hours you study the week before.

Part A) Is totally up to you because in the question it asks What's the best possible grade you can earn with your current study habits lets say if you study around 4 hours the week before the test. Which means the value of h should be 4 because h represents hours in the equation.

so ,

[tex]G(h)=-3h^2+24h+47\\G(4)=-3(4)^2+24(4)+47\\G(4)=-48+96+47\\G(4)=95\\[/tex]

So if you studied for 4 hours the week before the test you are going to score 95 marks which would be an A* grade.

Part B) In this part it asks you the maximum amount of study time you will need to have to earn that grade which means how many maximum hours you would need to earn a total of 95 marks which is 4.

Part C) The y-intercept is the constant in the equation in this case +47 is y-intercept and in the context of the problem it denotes that if you studied for 0 hours you would still earn 47 marks on the test, which would result you failing the test.

Part D) How many hours would you need to complete and still earn a zero would be:

[tex]G(h)=-3h^2+24h+47\\-3h^2+24h+47=0[/tex]

because it says still earn a zero which means the grade is zero so now we solve the equation.

[tex]-3h^2+24h+47=0\\3h^2-24h-47=0\\[/tex]

using the quadratic formula we get two values for h which are

h = 9.627 and h = -1.627 so eventually hours can never be in negative its impossible you can't study for -1.627 so our answer is 9.627 hours and you would still earn a zero after studying approximately 9.6 hours.

Part E) The grade that you will earn if you studied for 5 hours is:

[tex]G(h)=-3h^2+24h+47\\G(5)=-3(5)^2+24(5)+47\\G(5)= -75+120+47\\G(5)=92\\[/tex]

You would earn 92 marks which would result in an A* grade

Answer:

(A) 95

(B) h=4

(D) h=9.63

(E) 92

Step-by-step explanation:

(A) They are asking for the maximum of the graph of the equation which can be found using the vertex formula:

[tex]max= c-\frac{b^2}{4a}[/tex]

where 'a' is the coefficient of the first term, 'b' is the coefficient of the second term and 'c' is the third term.

So we have:

[tex]max=47-\frac{(24)^2}{4(-3)} = 95[/tex]

(B) To find the hours of study required to get 95 we need to set the equation equal to 95:

[tex]-3h^2+24h+47=95[/tex]

which can be rewritten as:

[tex]-3h^2+24h+47-95=0[/tex]

[tex]-3h^2+24h-48=0[/tex]

When we solve for 'h' we get h = 4

Therefore, studying 4 hours gives us a grade of 95, which is the maximum score from the equation.

(C) The function G(h) is our y and h is our x values. To find the y intercept, x (which is h in the equation) must be set to 0 and solved for y. This is because the y intercept is at the point where x =0.

So we have:

[tex]G(h)=-3(0)+24(0)+47\\ =0+0+47\\ =47[/tex]

This is when h=0 and therefore is represents the grade when 0 hours of studying is done.

(D) To find how many hours of study can still produce a grade of 0, we need to set the function equal to 0 and solve for h.

[tex]-3h^2+24h+47=0\\[/tex]

This gives us two results when solved quadratically:

[tex]h=-1.63[/tex] and [tex]h=9.63[/tex]

Obviously, time cannot be negative so the answer is 9.63 hours.

(E) If we study for 5 hours, h should be equal to 5.

So substituting 5 for h we get:

[tex]-3(5)^2+24(5)+47=92[/tex]

So 5 hours of study affords us a grade of 92.

Hope that explains it.

The local authorities in a certain city install 10,000 electric lamps in the streets of the city. If these lamps have an average life of 1000 burning hours with a standard deviation of 200 hours, assuming normal distribution, what number of lights might expected

Answers

Step-by-step explanation:

It is given:

[tex]\mu=1000[/tex], [tex]\sigma=200[/tex]

Let x be the random variable that denotes the number of hours the lamp lights up.

what number of lights might expected to fail in the first 800 burning hours

Answer: We are required to find the expected number of lights to fail in the first 800 burning hours.

First, we have to find the probability as:

P(Z < 800)

Using the z-score formula, we have:

[tex]P(x <800)=P \left(z<\frac{800-1000}{200} \right )[/tex]

=P(z<-1)

Now using the standard normal table, we have:

P(x<800)=P(z<-1)=0.1587

Therefore, the expected number of lights to fail in the first 800 burning hours is:

[tex]\boldsymbol{0.1587 \times 10000=1587}[/tex]

After how many burning hours 10% of the lamps would be still burning?

We first need to find the z-value corresponding to area = 1- 0.10 = 0.90. Using the standard normal table, we have:

z(0.90)=1.28

Now using the z-score formula, we have:

[tex]z= \frac{x-\mu}{\sigma}[/tex]

[tex]1.28= \frac{x-1000}{200}[/tex]

[tex]1.28 \times 200= x-1000[/tex]

[tex]256= x-1000[/tex]

x= 1000+256

[tex]\boldsymbol{x= 1256 }[/tex]

Using the Zscore principle, the number of bulbs expected to Fail in the first 800 burning hours is 1587

Given the Parameters :

σ = 200μ = 1000x = 800

The number of Lamps that might be expected to fail in the first 800 burning hours :

Recall:

Zscore = (x - μ) ÷ σ

Zscore = (800 - 1000) / 200 = -1

Using the normal distribution table :

P(Z < -1) = 0.15866

The number of bulbs expected to fail :

P × total number of bulbs

0.15866 × 10000 = 1586.6

Hence, 1587 bulbs are expected to fail in the first 800 burning hours.

Learn more : https://brainly.com/question/25226377

Help me out here pleaseeeeeeeee

Answers

Answer:

1 1/5

Step-by-step explanation:

1 and 1 fifth as a fraction.

The last one 1 1/5 is the answer ;)

(5x+3)(-5x+6) box method to distribute and simplify

Therefore, if the homogeneity of variance assumption is violated in an independent groups t-test, this means "the populations from which the samples were drawn have different standard deviations."

Select the correct statement about the function represented by the table.

Answers

B is the correct answer

Answer:

the answer is d because it

Answer this question if cool

Answers

Answer:

The answer to your question is given below

Step-by-step explanation:

From the question given above, the mean score is 23.

Thus, we can obtain the distance from the mean (absolute deviation) by using the following formula: