A rectangular picture frame is 6 inches wide and 10 inches tall. You want to make the area 7 times as large by increasing the length and width by the same amount. Find the number of inches by which each dimension must be increased. Round to the nearest tenth.

Answers

Answer 1

Answer:

  12.6 inches

Step-by-step explanation:

You want the increase in each dimension necessary to make a 6" by 10" frame have an area that is 7 times as much.

Area

The area of the original frame is ...

  A = LW

  A = (10 in)(6 in) = 60 in²

If each dimension is increased by x inches, the new area will be ...

  A = (x +10)(x +6) = x² +16x +60 . . . . . square inches

We want this to be 7 times the area of 60 square inches:

  x² +16x +60 = 7(60)

Solution

Subtracting 60, we get ...

  x² +16x = 360

Completing the square, we have ...

  x² +16x +64 = 424 . . . . . . . add 64

  (x +8)² = ±2√106 ≈ ±20.6

  x = 12.6 . . . . . . . . subtract 8; use only the positive solution

Each dimension must be increased by 12.6 inches to make the area 7 times as large.

A Rectangular Picture Frame Is 6 Inches Wide And 10 Inches Tall. You Want To Make The Area 7 Times As

Related Questions

The church's goal for the fundraiser was $18,000. They exceeded their goal by 8%. How much money did they raise?

Answers

Answer:

Step-by-step explanation:

18000(1+8/100)

18000(108)/100

19440

a. a triangle with one right angle and two congruent sides​

Answers

Answer:

is an isosceles right triangle, angles 45, 45, & 90 degrees

Step-by-step explanation:

what will A scale factor that is less than one produce

Answers

Answer:

When the absolute value of the scale factor is less than one, a compression occurs. When the absolute value of the scale factor is equal to one, neither an expansion nor a compression occurs.

Step-by-step explanation:

:)

The sum of 2 of the exterior angles of a triangle is 222 degrees. What is the measure of the third exterior angle?

Answers

Answer:

Exterior angles always add up to 360 degrees, therfore 360 - 222 = 138

Step-by-step explanation:

360 - 222 = 138

the answer to your question is 138degrees.

For any shape the exterior angles will always add up to 260 degrees.

Hope this helps in the future!

Answer:

360 - 222 = 138

the answer to your question is 138degrees.

For any shape the exterior angles will always add up to 260 degrees.

Step-by-step explanation:

What is the root of 320 simplified?

Answers

Answer:

17.9 i think is the answer

Step-by-step explanation:

Which of the following is equivalent to sec x ?
A)adj/opposte
B)hypotenuse/adjacent
C)hypotenuse/opposite

Answers

ANSWER: B.) Hypotenuse/adjacent
The secant is a reciprocal of cosine.

I need help with these 2

Answers

For the first one you need to do
x+2+x+2+2x+4+2x+4
=6x+12

When doing this kind of problem you should use FOIL
First, Outer, Inner, Last
(x+2)(2x+4)
First- x•2x= 2x^2
Outer- x•4= 4x
Inner- 2•2x= 4x
Last- 2•4= 8

Combined you have
=2x^2+8x+8

CALCULUS: Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and v(0) = 3.

A. v(t) = sin(t) + cos(t) + 3
B. v(t) = sin(t) + cos(t) + 2
C. v(t) = sin(t) - cos(t) + 3
D. v(t) = sin(t) - cos(t) + 4

I picked A., which was marked wrong, although I truly believe that is the answer because I got sin(t) - (-cos(t)) + 3. Please tell me whether you believe this is right or am I doing something wrong. I really want to learn/master this concept. Thanks is advance.

Answers

Answer:

B. v(t) = sin(t) + cos(t) + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right  

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra I

Function Notation

Calculus

Antiderivatives - Integrals

Integration Constant C

Solving Integration Equations

Integration Property [Addition/Subtraction]:                                                         [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Step-by-step explanation:

*Note: Remember that the velocity function is the integral of the acceleration function/acceleration is the derivative of velocity.

[tex]\displaystyle v'(t) = a(t)\\v(t) = \int {a(t)} \, dt[/tex]

Step 1: Define

a(t) = cos(t) - sin(t)

v(0) = 3

Step 2: Integrate

Set up integral:                                                                                               [tex]\displaystyle v(t) = \int {cos(t) - sin(t)} \, dt[/tex][integral] Rewrite [Integration Property - Subtraction]:                                 [tex]\displaystyle v(t) = \int {cos(t)} \, dt - \int {sin(t)} \, dt[/tex][Integral] Trig integration:                                                                              [tex]\displaystyle v(t) = sin(t) - [-cos(t)] + C[/tex][Velocity Integration] Simplify:                                                                          [tex]\displaystyle v(t) = sin(t) + cos(t) + C[/tex]

Step 3: Find Function

We need to solve for the entire function, meaning we need to find constant C.

Substitute in given point [Velocity Integration]:                                           [tex]\displaystyle v(0) = sin(0) + cos(0) + C[/tex][Velocity Integration] Substitute:                                                                   [tex]\displaystyle 3 = sin(0) + cos(0) + C[/tex][Velocity Integration] Evaluate trig:                                                               [tex]\displaystyle 3 = 0 + 1 + C[/tex][Velocity Integration] Add:                                                                             [tex]\displaystyle 3 = 1 + C[/tex][Velocity Integration] Isolate C [Subtraction Property of Equality]:              [tex]\displaystyle 2 = C[/tex][Velocity Integration] Rewrite:                                                                       [tex]\displaystyle C = 2[/tex][Velocity Function] Substitute in C [Velocity Integration]:                           [tex]\displaystyle v(t) = sin(t) + cos(t) + 2[/tex]

Topic: Calculus

Unit: Basic Integration

Book: College Calculus 10e

SO HARDDD
What is the square root of 267.8?

lol

“Stay close to anything that makes you glad you are alive.” – Hafez.

C h a t here Bradyn and Lis, plz. I keep getting logged out when I use the other one :p

Answers

Answer:

16.3645959315

Step-by-step explanation:

On average, A person spends $240 every 3 months on their cell phone bill... What would the price be for 1 month be?... How much would this person pay over the course of one year?
Pls help me asap!!

Answers

Answer:

$81 for 1 month

$972 for 1 year

Step-by-step explanation:

Answer:

$80 for one month and $960 over the course of one year

Step-by-step explanation:

240 / 3 = 80

12 x 80 = 960

There are 5 4/5 cups of milk left in a carton. Write 5 4/5 as an improper fraction. Explain what the fraction represents in this situation.

Answers

Answer:

29/5

Step-by-step explanation:

multiple 5 times 5 to get 25 then at the 4 to get 29.

there are 29/5th cups of milk

The sail of a boat is in the shape of a right triangle. Which expression shows the height, in meters, of the sail?

The sail of a boat is a right triangle with an acute angle equal to 35 degrees and the side of the sail which is the hypotenuse to the right triangle is 8 meters long.

cosine 35 degrees over 8
8(tan 35°)
tangent 35 degrees over 8
8(cos 35°)

Answers

Answer:

8(cos35)

Step-by-step explanation:

Your welcome.

The expression that models the height is  8 cos35

SOH CAH TOA identity

From the given information, we have the following

Hypotenuse = 8metersHeight  = adjacent

Using the SOH CAH TOA identity

cos theta = adj/hyp

cos 35 = adj/hyp

cos 35 = adj/8

Hyp  = 8 cos35

Hence the expression that models the height is  8 cos35

Learn more on SOH CAH TOA here: https://brainly.com/question/22307176

A group of friends were working on a student film that had a budget of $900. They used 33% of their budget on equipment. How much money did they spend on equipment?​

Answers

They used 33/100 of their money on equipment which means if they have a budget of 900 dollars they used...

900*33/100=9*33=297 dollars on equipment.

The amount used on equipment is $297.

What is a percentage?

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying it by 100.

The percentage change is also calculated using the same method.

In percentage change, we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Budget = $900

Percentage of the budget used.

= 33%

Now,

The amount of budget used.

= 33% of 900

= 33/100 x 900

= $297

Thus,

The amount used on equipment is $297.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ6

Br uh don’t even type “I can’t see the pic” Solve both problems and show ur work

Answers

Answer:

1.22

53.08

Step-by-step explanation:

4. We can find the quarter circle, we can find the whole triangle, lets do that

The circle is, 1/4*(1)^2*pi, which is 1/4pi

The triangle is, 2 * 2 divided by 2, which is 2

2 - 1/4pi gives us the shaded part or

2 - 1/4*3.14

2 - 0.785 = 1.215 rounded to 1.22

5. The area of a cylinder is pir^2h. r is 10, h is 1.2

12pi cm^3

we have 20 m^3 which is 2000 cm^3

Let's divide,

2000/37.68 = 53.078, rounded gives us 53.08

Math problem please help

Answers

Answer:

The second one and the last one

Step-by-step explanation:

The third quadrant is of all negitive. The reason it is, is because it is on the left side of the x axis which makes it go lower like subtracting and dividing, then it is on the bottom half of the y axis which again is the same reason

i hope i helped and have a great day!

Answer:

B and D

Step-by-step explanation:

because in the 3rd quadrant both the x and y will be negative

1st quadrant all x and y are positive

2nd quadrant y are positive but x are negative

and in 4th quadrant x are positive and y are negative.

if brainiest is earned its greatly appreciated

I really don't understand help

Answers

Answer:

128 ft sq.

Step-by-step explanation:

The way you find the area of a square is by multiplying one side by another, and since it is a square, the sides are the same. This means that if we have a square with a side length of x, the way to find the area of that square is to multiply x by x, which can be written as [tex]x^2[/tex]. Now, since we're doubling this, we can say that double Mary's garden is [tex]2 * x^2[/tex]. If we substitute 8 in for x, we have to multiply [tex]8^2[/tex] by 2 or 8 by 8 by 2 to find our answer. 8 times 8 is 64 and 64 times 2 is 128.

Question: 2 out of 10
~!¡! Volume !¡!~
(Pleaaase go try to answer the first one- )

Answers

Answer:

B) 2,340

Step-by-step explanation:

3. What do you call a polynomial with 3 terms?

Answers

Answer:

it's called a trinomial

In AHIJ, h = 38 inches, i = 45 inches and j=61 inches. Find the measure of ZH to the nearest degree.

Answers

Answer:

38°

Step-by-step explanation:

Delta math

Mary ate x pounds of cherries. Leslie ate LaTeX: \frac{6}{9}6 9 more. Write an expression to represent how many pounds of cherries Leslie ate.

Answers

Answer:

The expression to represent number of cherries Leslie ate = ( x + [tex]\frac{6}{9}[/tex] ) pound.

Step-by-step explanation:

As given,

Mary ate cherries = x pound

And

Leslie ate [tex]\frac{6}{9}[/tex] more.

⇒Leslie ate cherries = ( x + [tex]\frac{6}{9}[/tex]  ) pound.

Use the volume formula to find the volume of the prism.

A. 21 cubic units
B. 27 cubic units
C. 42 cubic units
D. 9 cubic units

Answers

For prisms, the formula is b * h * w. You multiply the three numbers you are given to get 21 cubic units.

Answer: A

Step-by-step explanation:

Ax

I need help with math

Answers

Answer:

0,-2        0,-5

2,-3          1,-4

Step-by-step explanation:

Like seriously I gat no idea what the the answer is

Answers

The answer 25 bro good luck

For every pound a company spends on advertising, it spends £0.45 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.

Answers

equals 1 dollar usdddddf 877

Can someone help me with my this?!

Answers

BC=54
Set 6x = 9x-27
Then solve

umm pls help me ik how to do it but not sure on this specific one

Answers

9514 1404 393

Answer:

  -8, +9

Step-by-step explanation:

You need factors of (6)(-12) = -72 that have a sum of +1.

From your knowledge of multiplication tables, you know that 72 = 8·9. Then -72 = (-8)(9), and those two factors have a sum of +1.

  6x^2 +x -12

  = 6x^2 +9x -8x -12

  = 3x(2x +3) -4(2x +3)

  = (3x -4)(2x +3)

A boy visiting New York City views the Empire State building from a point on
the ground, A, which is 940 feet from foot, C, of the building. The angle of
elevation of the top, B, of the building as seen by the boy is 53 degrees. Find the
height of the building to the nearest foot.

Answers

Answer:

49,820

Step-by-step explanation:

so what you were going to do first is you're going to do 940 * 53 there is which equals 2820 and then you're going to do turtle messes so then you're going to do 5 * 0 which equals zero then five times for which equals 20 + 5 * 9 which equals 45 + 2 which 45 + 2 equals 47 so you have 2820 + 47000 which equals 49,820

The sum of the real numbers x and y is 25. Their difference is 13. What is the value of xy ? G. 100 H. 104 J. 114 K. 124

Answers

Answer:

J. 114

Step-by-step explanation:

x + y = 25

x - y = 13

2x = 38

x = 19

x = 25 - 19

x = 6

xy = (6)(19)

xy = 114

Two supplementary angles are in the ratio of 5 to 7. Find positive difference of the measure of the two angles. Do the same problem, only do it for complementary angles instead of supplementary angles.​

Answers

Answer:

30° is the difference if they are supplement

15° is the difference if they are complementary

Step-by-step explanation:

Let 5x = the measure of the smaller angle

and 7x =  the measure of the larger angle

If they are supplementary, then 5x + 7x = 180

                                                        12x = 180

                                                            x = 15

5x = 5(15) = 75 = the measure of the smaller angle

7x = 7(15) = 105 = the measure of the larger angle

105 - 75 = 30 = difference of the measures

Now, if they are complementary, then 5x + 7x = 90

                                                                   12x = 90

                                                                       x = 7.5

5x = 7(7.5) = 37.5 = the measure of the smaller angle

7x = 7(7.5) = 52.5 = the measure of the larger angle

52.5 - 37.5 = 15 = difference of the measures

is the expression a^12 x a^4 equivalent to a^8 x a^8

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Properties of indices.

Here, we have to prove that, if the above exponential equation are equal or not., let's prove it

1.)L.H.S

a^12*a^4 = a^m*a^n ===> a^(m+n)

hence, a^(12+4) ===> a^(16)

2.) R.H.S

===> a^8*a^8 = a^(8+8) ==> a^(16)

since here, LHS = RHS

so both are equal.

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