The length and width of a 6-inch by 8-inch photograph are reduced by the same amount to make a new photograph whose area is half that of the original. By how many inches will the dimensions of the photograph have to be reduced?

Answers

Answer 1

Answer:

The dimensions have to be reduced by 2 inches

Step-by-step explanation:

Given that the dimensions are: 6 by 8 inches which means that the area is 48 square inches.

Let x be the amount to make a new photo which is half of the area that means

The new dimensions will be: (8-x) by (6-x) and as the area is half

The area of new photo will be: 48/2 = 24

Putting it mathematically

[tex](8-x)(6-x) = 24\\8(6-x)-x(6-x)=24\\48-8x-6x+x^2=24\\48-14x+x^2=24\\x^2-14x+48-24=0\\x^2-14x+24=0\\x^2-12x-2x+24=0\\x(x-12)-2(x-12)=0\\(x-2)(x-12)=0\\x-2=0 => x=2\\x-12=0 =>x=12[/tex]

Subtracting 12 from both dimensions will make them negative so 12 cannot be the solution.

Hence,

The dimensions have to be reduced by 2 inches

Answer 2

We want to see by how much we must reduce the dimensions of the photograph in order to reduce its area to half. We will find that we must reduce each measure by 2 inches.

The original measures of the photograph are:

length = 6 inwidth = 8 in.

Then the area is:

A = (6 in)*(8 in)  = 48 in^2

Now we want to define a new length and a new width:

L' = (6 in - n)W' = (8in - n)

such that:

A' = L'*W' = 24 in^2

      (6 in - n)*(8in - n)  = 24 in^2

      48in^2 - n*14 in + n^2 = 24 in^2

    n^2 - n*14 in + 24in^2 = 0

This is a quadratic equation, we can solve this for n by using Bhaskara's formula, we will get:

[tex]n = \frac{14in \pm \sqrt{(-14)^2 - 4*1*24in^2} }{2*1} \\\\n = 7in \pm 5 in[/tex]

The only solution that makes sense is:

n = 7in -  5in = 2in

This means that we need to reduce each measure by 2 inches.

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Related Questions

HELP!!!!!!
The line graphed by the equation, y =2/3 x +1/4 , has a slope of 1/4 and a y-intercept of 2/3. True False

Answers

Answer:

Um, no lo sé, lo siento, solo necesito los puntos

Step-by-step explanation:

Answer:

False; the slope is 2/3 and the y intercept is 1/4

I hope this is good enough:

After releasing of radioactive material into.The atnosphere from.A nuclear.Powe plant in a country in 1988, the hay in that country was contaminayed by radioactive.Isotope remains, how long did the famers need to.Wait to use this hay

Answers

Answer:

the question is incomplete, so I looked for a similar one:

After the release of radioactive material into the atmosphere  from a nuclear power plant, the hay was contaminated by iodine  131 ( half-life, 8 days). If it is all right to feed the hay to cows  when 10% of the iodine 131 remains, how long did the farmers  need to wait to use this hay?

iodine's half life (we are given x, we need to find b):

0.5A₀ = A₀eᵇˣ

x = 8 days

we eliminate A₀ from both sides

0.5 = eᵇ⁸

ln 0.5 = ln eᵇ⁸

-0.69315 = b8

b = -0.69315 / 8 = -0.08664

since the farmers need to wait until only 10% of the iodine remains (we already calculated b, now we need to find x):

0.1A₀ = A₀eᵇˣ

0.1 = eᵇˣ

ln 0.1 = bx

where b = -0.08664

x = ln 0.1 / -0.08664  = -2.302585 / -0.08664  = 26.58 days

Neil has 3 partially full cans of white paint.They contain 1/3 gallon, 1/5, gallon, and 1/2, gallons of paint About how much paint dose Neil have in all?

Answers

Answer:

1 and 1/30 gallons

Step-by-step explanation:

First, convert all the fractions to a common denominator. I'm choosing 30.

1/3=10/30  1/5=6/30  1/2=15/30

Now, you can add them together to get 31/30, so a little more than a gallon

I need help pls pls pls pt.2

Answers

Answer:

where is the Worksheet

Step-by-step explanation:

there is no Worksheet

How many solutions does 2x + 6 = -2 (x - 3)

Answers

Answer: x=0

Step-by-step explanation:

2x+6=-2x+6

2x+2x=6-6

4x=0

x=0/4

x=0

U GET BRAINLIEST IF U ANSWER
WHICH ONES ARE POSITIVE OR NEGATIVE SUMS
–5 + (–2)
Choose...
5 + (–2)
Choose...
-3 + 4
Choose...
0 + (–3)
SPACE THEM OUT SO I KNOW
THANKSSSSSSSSSSS

Answers

Answer:

Below :)

Step-by-step explanation:

-5+(-2)=     -7

5+(-2)=       3

-3+4=         1

0+(-3)=      -3

1 and 4 are negative sums, 2 and 3 are positive! :)

Answer:

-5+(-2) will be -7 so negative sum

5+(-2) will be 3 so postive sum

-3+4 will be 1 so postive sum

and finally 0 + (-3) is -3 so negative sum

hope this helps!

When 4(0.5x+2.5y - 0.7x- 1.3y +4) is simplifted, what is resulting expersion

Answers

-0.8x + 2y + 1

ya dig

2y - 7 = 35

A
28

B
21

C
14

D
9

Answers

Answer:

Do u know the answer to

Step-by-step explanation:

Triangle ABC is a right triangle.  The length of the legs are 3 in and 6 in, how long is the hypotenuse? (Round to the nearest tenth if necessary)  

A) 3.3 in

B) 6.7 in

C) 7.9 in

D) 9.0 in

Answer:

21

Step-by-step explanation:

2y-7=35

2(21)-7 = 35

42-7= 35

35 =35

what would the answer be?

Answers

Answer:

-2y

Step-by-step explanation:

10x+ -2y = 3

-10            -10

-2y        =  -7

-2              -2


4. How do you solve x2 + 9x - 3 = 0 using the completing-the-square method?

Answers

Answer:

i used to have a problem with this

Step-by-step explanation:


A hobby shop sells small and large toy cars. A small toy car is $5.50, and a large toy car is $9. What is an equation that relates the cost, Cin dollars
with the number of small toy cars, S, and the number of large cars, L. purchased?

Answers

Answer:

C = 5.50S + 9L

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

The equation that relates the cost, Cin dollars with the number of small toy cars, S, and the number of large cars, L is  C = 5.50S + 9L.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A hobby shop sells small and large toy cars. A small toy car is $5.50, and a large toy car is $9.

Let S be the number of a small toy car and L be the number of a large toy car.

The equation can be made:

Total cost:

C = 5.50S + 9L

Thus, the equation that relates the cost, Cin dollars with the number of small toy cars, S, and the number of large cars, L is  C = 5.50S + 9L.

Learn more about the linear equation here:

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Independent Practice : Rectangular Prism
GRAHAM CRACKERS A manufacturer wants to double the volume of the graham cracker box.
The manufacturer will either double the height or double the width.
GRAHAM
CRACKERS
a. Which option uses less cardboard? Justify your answer.
h 9 in
w 2 in
16 in.
b. What is the volume of the new graham cracker box?


Answers

Answer:

a). Amount of cardboard required will be less when manufacturer doubles the width.

b). Volume of the new cracker box = 216 in³

Step-by-step explanation:

Volume of the Graham cracker box = volume of the rectangular prism formed

                                                           = Length × Width × Height

                                                           = 6 × 2 × 9

                                                           = 108 in³

a). To double the volume of the rectangular prism, manufacturer either doubles the height or doubles the width.

When manufacturer doubles the height,  

Amount of cardboard required = surface area of the rectangular prism

                                                      = 2(lw + wh + hl)

                                                      = 2(6×2 + 2×18 + 18×6)

                                                      = 2(12 + 36 + 108)

                                                      = 2(66)

                                                      = 132 in²

When manufacturer doubles the width,

Surface area of the rectangular prism = 2(6×4 + 4×9 + 9×6)

                                                               = 2(24 + 36 + 54)

                                                               = 2(114)

                                                               = 228 in²

Therefore, amount of cardboard required will be less when manufacturer doubles the width.

b). Volume of the new Graham box = 2(Volume of the old box)

                                                           = 2 × 108

                                                           = 216 in³

From A to B a private plane flies 2.8 hours at 110 mph on a bearing of 64 degrees . It turns at point B and continues another 1.7 hours at the same speed, but on a bearing of 154 degrees to point C. Round each answer to three decimal places. a. At the end of this time, how far is the plane from its starting point? b. On what bearing is the plane from its original location?

Answers

Answer:

a. 360.323 m

b. [tex]95.265^{o}[/tex]

Step-by-step explanation:

Distance covered from A to B = speed x time

                                                 = 110 x 2.8

                                                 = 308 m

Distance covered from B to C = speed x time

                                                  = 110 x 1.7

                                                  = 187 m

The sum of angles at B = [tex]64^{o}[/tex] + [tex]26^{o}[/tex]

                                       = [tex]90^{o}[/tex]

a. The distance of the plane from it starting point to C can be determined by applying the cosine rule.

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] - 2ac Cos B

Sot hat;

[tex]b^{2}[/tex] = [tex]187^{2}[/tex] + [tex]308^{2}[/tex] - 2(187 x 308) Cos [tex]90^{o}[/tex]

But, Cos [tex]90^{o}[/tex] = 0

So that,

[tex]b^{2}[/tex] = [tex]187^{2}[/tex] + [tex]308^{2}[/tex]

  = 34969 + 94864

  = 129833

b = [tex]\sqrt{129833}[/tex]

  = 360.323

The distance from A to C is 360.323 m.

b. Applying the sine rule;

[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex]

[tex]\frac{187}{SinA}[/tex] = [tex]\frac{360.323}{Sin90^{o} }[/tex]

[tex]\frac{187}{SinA}[/tex] = [tex]\frac{360.323}{1}[/tex]

Sin A = [tex]\frac{187}{360.323}[/tex]

         = 0.5190

⇒ A = [tex]Sin^{-1}[/tex] 0.5190

       = [tex]31.265^{o}[/tex]

The bearing of the plane from its original location = [tex]64^{o}[/tex] + [tex]31.265^{o}[/tex]

                                                     = [tex]95.265^{o}[/tex]

Using the Sine and Cosine rule on the triangle generated using the information given, the distance and bearing of the plane from its original location are :

360.32 mile 95.26°

Using the Cosine Rule :

= + - 2abCosB

b² = 187² + 308² - 2(187)(308)Cos(90°)

b² = 187² + 308² - 0

b² = 129833

b = √129833

b = 360.32 miles

B.)

Using the Sine rule :

a/sinA = b/SinB = c/SinC

187/sinA = 360.32/sin90

187/sinA = 360.32/1

sinA × 360.32 = 187

sinA = 187 / 360.32

sinA = 0.51898

A = Sin¯¹(0.51898)

A = 31.264

Hence, bearing of C from A = (64° + 31.264) = 95.26°

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URGENT!! I WILL GIVE BRAINLIEST TO CORRECT ANSWER!!
find the length of side x in simplest radical form with a rational denominator​

Answers

Answer:

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

Step-by-step explanation:

Because of 45 45 90 triangle rule, we can see that the length opposite of the right angle is [tex]\sqrt{6}[/tex]. Using the 45 45 90 triangle rule, the side opposite to the right angle is x[tex]\sqrt{2}[/tex]. Then we solve for x and get x=[tex]\sqrt{3}[/tex].

Hope this helps and have a nice day!  

Can someone please help me!?!?!?

Answers

3. Alt. Interior Angles

4. definition of midpoint

3.7(x−5.9)=−26.64
help

Answers

Answer: -1.3

Step-by-step explanation:

2/3(9x-6)= 4x + 10
3
6x-4=4x+10
What is the value of x in the equation?
A X = 7
B X = 8
B X = 3.2
D X = -12

Answers

Answer:

the answer will be A. x=7

Your answer should be 7

Find the slope of the line that passes through the points (2, -3) and (5, -4).

Answers

slope is -1/3 hope this helps
slope is -1/3 please don’t come at me if it’s wrong just tell me

Zahra was given two data sets, one without an outlier and one with an outlier. Data without an outlier: 15, 19, 22, 26, 29 Data with an outlier: 15, 19, 22, 26, 29, 81 How is the median affected by the outlier? The outlier slightly affected the median. The outlier made the median much higher than all the other values. The outlier made the median much lower than all the other values. The median is the exact same number in both data sets.

Answers

Answer:

The outlier slightly affected the median.

Step-by-step explanation:

Given :

Data without an outlier: 15, 19, 22, 26, 29

Data with an outlier: 15, 19, 22, 26, 29, 81

The median :

Data without outlier :

0.5(n + 1) th term

n = 5

0.5(5 + 1) = 0.5(6) = 3rd term

3rd term = 22

Data with outlier :

0.5(n + 1) th term

n = 6

0.5(6 + 1) = 0.5(7) = 3.5th term

(3rd term + 4th term) /2

(22 + 26) / 2

48 / 2

= 24

From the result obtained ; The outlier slightly affected the median.

Answer:

A) The outlier slightly affected the median.

Step-by-step explanation:

Without the outlier, the median is 22, and with the outlier, the median is 24. So the outlier slightly affected the median.

Hope this helps :)

A car covered a certain distance at a speed of 24 mph. While returning, the car covered the same distance at a speed of 16 mph. What was the average speed of the car for the entire journey?


please healp

Answers

Answer:

(96/5) mph, or 19.2 mph

Step-by-step explanation:

Average speed = (total distance traveled) / (total time elapsed)

Here we need to calculate the two elapsed times (going and returning)

Going:  t1 = d/(24 mph)

Returning:  t2 = d/(16 mph)

Less time is required for the outward bound trip.

                                                                            16d + 24d

Total time elapsed:  t = t1 + t2 = d/24 + d/16 = ------------------- = (5/48)*d hr

                                                                                 16*24

Thus, the average speed is (total distance traveled) / (total elapsed time)

                         

                                2d

which here is --------------------- = (96/5) mph, or 19.2 mph

                             (5/48)d

If we take average speed into account in any direction, it equals (24 + 16) / 2 = 40 / 2 = 20mph.

What is average speed?Average speed is calculated by dividing a number by the time it takes to obtain that number. The SI unit of speed is meters per second.The average speed is represented by a scalar value. The magnitude indicates its absence of direction.Since this distances were the same, the average speed can be calculated directly by adding the speeds and dividing by 2. There is no need to weigh anything.

If we consider speed in any direction, the average speed is:

(24 + 16) / 2 = 40 / 2 = 20mph

However, if direction is important, one number must be negative because the directions are opposite:

(24 - 16) / 2 = 8 / 2 = 4mph (in the positive direction)

Depending on the circumstances, either of these could be your response.

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=Evaluate the function f(x) = –2x2 – 3x + 5 for the input value –3.

−22
–4
2
32

Answers

Answer:

The correct answer is -4.

Step-by-step explanation:

have a good day yall

Evaluating the function, f(x) = –2x² – 3x + 5 for x = -3, we would have: f(-3) = -4. (option B).

How do you Evaluate a Function?

To evaluate a function, plug in the given value of the input (x) and simplify.

Thus:

f(x) = –2x² – 3x + 5

Substitute x = -3 into the function

f(-3) = –2(-3)² – 3(-3) + 5

f(-3) = -2(9) + 9 + 5

f(-3) = -4

Therefore, evaluating the function, f(x) = –2x² – 3x + 5 for x = -3, we would have: f(-3) = -4. (option B).

Learn more about evaluation of function on:

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GEOMETRY HELP ILL VOTE YOU BRAINLIEST I PROMISE PLEASE

Answers

Answer:

x=29

Step-by-step explanation:

4x-18+5x-71=180

9x=269

x=29

Each dimension of a parallelogram is multiplied by a positive number n. Write an expression for the area of the new parallelogram. Let b represent the base and h represent the height of the original parallelogram.

what is the expression for the area of the new parallelogram???

Answers

Answer:

b*h

Step-by-step explanation:

therethere are four sides to a parallelogram and two of them would be h and b and you must multiply that by n then each other

New area:

(b*n) * (h*n) = (b*h)n^2

What is 0.8 as a fraction?

Answers

Answer:

8/10

Step-by-step explanation:

Answer: 0.8 = [tex]\frac{4}{5}[/tex]

Step-by-step explanation: We need to change 0.8 into a fraction.

0.8 = [tex]\frac{8}{10}[/tex]

[tex]\frac{8}{10}\\[/tex] = [tex]\frac{4}{5}[/tex]

Therefore, your answer is [tex]\frac{4}{5}[/tex]

hope this helps!

lovelymoonlight

Find the slope (m) and the y intercept please show work

Answers

Answer:

m=2/5

b=3.8

Step-by-step explanation:

To find slope you need to use slope formula which is (y2-y1)/(x2-x1) so you need two points from the table and plug them into this. I'll use the first two points (-2, 3) and (-1, 5)

(5-3)/(3--2)

2/5

our slope is 2/5(m)

now to find the y int(b)

we have out slope intercept formula which is y=mx+b

plug in our slope

y=2/5x+b

now take a random point from our tabell and apply it to our equation I'll use (-2, 3) again.

3=2/5(-2)+b

3=-4/5+b

3=-0.8+b

add 0.8 to each side

3.8=b

b=3.8

Ms. Reyes buys three types of flowers. She buys 20 roses, 24 carnation, and 36 tulips. She plans to group the flowers into more than a bouquet. She wants to put the same number of each type of flower into each bouquet. What is the greatest number of bouquets Ms. Reyes can make?

Answers

Answer:

The greatest number of bouquets Ms. Reyes can make is 4 bouquets

Step-by-step explanation:

Ms. Reyes buys three types of flowers. She buys 20 roses, 24 carnation, and 36 tulips.

To find the greatest number of bouquets she can make, we solve using Greatest Common Factor method.

We find the factors of 20, 24 and 36

The factors of 20 are: 1, 2, 4, 5, 10, 20

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

Then the greatest common factor is 4.

Hence, the greatest number of bouquets Ms. Reyes can make is 4 bouquets

What is the value of k in the equation StartFraction k Over 3 EndFraction minus 5 = 34?

Answers

[tex]\huge\text{$k=\boxed{117}$}[/tex]

[tex]\displaystyle\frac{k}{3}-5=34[/tex]

To find the value of [tex]k[/tex], we need to isolate it on one side of the equation. Add [tex]5[/tex] to both sides of the equation, then multiply both sides of the equation by [tex]3[/tex].

[tex]\displaystyle\begin{aligned}\frac{k}{3}-5+5&=34+5\\\frac{k}{3}&=39\\\frac{k}{3}*3&=39*3\\k&=\boxed{117}\end{aligned}[/tex]

Helppppppppppppppppppp

Answers

Answer:

2^3 * 7 + 7^2

Step-by-step explanation:

1) divide 28 by 2 = 14

2) divide 14 by 2 = 7

3) this means that 2 * 2 * 7 = 28

4) you can then take those 2 twos and multiply them with the first 2 and make 2^3

5) the square root of 49 is 7 so that is just 7^2

6) plug in all these new values for the originals and you get the answer above

Answer:

first you gotta calculate 2 -28 +49

After getting the answer solve the expressions to see which one is equivalent to 2-28 +49 (I think)

which expression has the same value as 7 ÷ 9/10
A) 7 x 10/9
B) 1/7 ÷ 910
C) 7 x 9/10
D) 1/7 ÷ 10/9

Answers

Answer

A.) 7* 10/9

When you divide fraction you change the symbol and flip the fraction and A is that equation.

Answer:

7 ÷ 9/10 = 7.777

a. 7 × 10/9 = 7.777

b. 1/7 ÷910 = 0.000

c. 7 × 9/10 = 6.3

d. 1/7 ÷ 10/9 = 0.128

therefore the answer is a

Step-by-step explanation:

Hope this helped!!! have a wonderful day!! :):):):)

What is the volume of the rectangular prism?

Answers

Answer:

180

Step-by-step explanation:

5 time 6 times 6 is 180

Other Questions
Read the passage from President Barack Obama's back-to-school remarks. And thats what I want to focus on today: the responsibility each of you has for your education. I want to start with the responsibility you have to yourself. Every single one of you has something youre good at. Every single one of you has something to offer. And you have a responsibility to yourself to discover what that is. Thats the opportunity an education can provide. The repetition of responsibility in the passage helps Obama achieve his purpose by providing evidence to support his speech. emphasizing the main idea of the speech. showcasing his expertise at writing a speech. soothing the audience with the rhythm of the speech. i need help to solve please 2037 + 135.5x = 5560 what is x? Please help me I dont know the answer You should read the lifts safety and operating instructions only if you havent used the automotive lift before which detail from the text best supports the answer to part a PLEASEEEEE HELPPPPP ASAPPPP Compare and contrast the relationship American Indians had with the French and the British. How were the relationships similar La mesa ________ quinientos dlares. cuesta; 500 cuestan; 300 cuestan; 5.000 cuesta; 3.000 What is a mission statement? for what value of x do the expressions 2/3x+2 and 4/3x+6 have the same value? Find the greatest common factor of the monomials. Please helpppp and show work 20x, 36x = Young had learned to read before he was two, and by the age of twenty had mastered a dozen foreign languages including Arabic, Persian, and Turkish. Aninheritance from an uncle left him free to pursue his scientific interests. At various times, Young studied the habits of spiders, the surface features of themoon, and diseases of the chest. Then, intrigued by the challenge of the Rosetta Stone, he put aside his other studies and concentrated on attempting todecipher the writing on it. Young had read of de Sacy's and Akerblad's work in Paris, and was determined to succeed where they had failed.Based on the details in the excerpt, James Cross Giblin's attitude toward Thomas Young isA. positive because Young shows the skills and determination to figure out the inscriptions.NeB. positive because Young is wealthy and has plenty of free time to pursue anything that interests him.oc. negative because Young lacks the experience needed to read foreign languages.OD. negative because Young is overconfident in his ability to succeed where others have failed, A function is ????????? what is phylum plsss plss Please help :))) and explain how to do it if you can but if you cant its fine The president can provide a check on Congress's power to create legislation by?a declaring a proposed law unconstitutionalb. overriding a vetoc. refusing to fund a billd vetoing a bill Smoking marijuana:a. can cause psychological dependence.b. has no positive effects.c. has no adverse side effects.d. has been definitively shown to cause lung cancer. For which of the following sample sizes would it not be possible to estimate the mean of a population from the mean and standard deviation of a sample of that population? A. 50 B. 200 C. 100 D. 5 Which expressions are equal to 763? i just dont want to do it189 + 674247 + 516628 + 145435 + 328