A rectangular picture frame measures 10 cm by 12 cm. Do you want to triple the frames area by adding the same distance "x" to the length and the width. Write and solve an equation to find the value of "x". What are the new dimensions of the picture frame?

Answers

Answer 1
If the original frame area is x, then length*width=12*10=120=area=x. By tripling the frame's area, we get 120*3=360. However, we need to add a number x to both the length and width to equal the new area. Since length*width=area, and 10+x is the width and 12+x is the length, we get (10+x)*(12+x)=360. Expanding using the Distributive Property, we get 120+10x+12x+x^2=x^2+22x+120=360. Subtracting 360 from both sides, we get x^2+22x-240=0.Finding 2 numbers that add up to 22 and multiply to -240, we do a bit of guess and check ( we COULD use the quadratic formula too) to find 30 and -8 fit the bill. Therefore, x^2+30x-8x-240=0=
x(x+30)-8(x+30)=(x-8)(x+30). To make the expression equal to 0, since 0 multiplied by anything is 0, we have to figure out when x-8 and x+30 equal 0, which is when x=8 and -30 respectively (To do this, you could add 8 from both sides to turn x-8=0 to x=8, and something similar to -30). Plugging each one in, we get (10+(8))*(12+(8))=18*20=360. To make sure there aren't 2 solutions, we get that the new width is 10-30=-20, which clearly can't be negative , making x equal to 8. 

Related Questions

Work out the total amount Adam earned last week

Answers

Okay, so we know that Adam earns £200, plus 10% of (42*8) and 15% of (15*14)
To work out the payment for the magazines, you multiply 42 and 8, which gives 366 and find 10% of that, which is £36.60
To work out the payment for the books, you multiply 14 by 15, which gives 210 and find 15% of that, which is £31.50
Then add all the amounts together
£200+ £36.60+ £31.50= £268.10

The force of gravity is less on Mars than it is on Earth. As a result, the weight of an object on Mars m is 40% of its weight on Earth w. Determine which function you would use to find the weight on Mars of a space probe that weighs 15 lb on Earth. Then find the objects weight on Mars.

Answers

If the weight of an object on Mars (m) is 40% of its weight on Earth(w), then our equation would be:

m = 0.4w

Space probe:
m = 0.4(15)
m = 6 lb
The general function is y =0.4.(x), where:

y = the weight on Mars
x = the weight on earth
and 0.4 a coefficient (given = 40% = 0.4)

Now if x = 15lb then on mars it weights y = 0.4.(15) = 6 lb

Splane how you would decide whether the product of three numbers is positive or negative

Answers

Since a positive number times a negative number is negative, but a negative number times a negative number is positive, if there are an odd number of negative numbers it is negative but it is otherwise positive (so if there are an even number of negative numbers it's positive)

Multiply (8 + 3i)(3 + 5i).

Answers

Greetings!

Expand.
[tex](8 + 3i)(3 + 5i)[/tex]
Distribute the parenthesis:
[tex]3(8 + 3i)+5i(8 + 3i)[/tex]
[tex]24+ 9i+40i + 15i^2[/tex]
Combine Like Terms.
[tex]24+ 49i + 15i^2[/tex]
Rearrange to follow proper form.
[tex]15i^2+49i+24[/tex]

Hope this helps.
-Benjamin

Answer:

15i² + 49i + 33.

Step-by-step explanation:

Given : (8 + 3i)(3 + 5i).

To find : Multiply .

Solution : We have given (8 + 3i)(3 + 5i).

Distribute 8 over (3 + 5i) and 3i over (3 + 5i).

8 (3 + 5i) + 3i(3 + 5i).

8 *3 + 8 * 5i + 3 *3i + 3i *5i.

24 + 40 i + 9i + 15 i².

Combine like terms

24 + 9i +40i + 15i².

24 + 49i + 15i².

Therefore,15i² + 49i + 33.

What is 625 written as a single power number of 5

Answers

5 power 4
I mean 5⁴ = 625
625 = 5 × 125 = 5 × 5 × 25 = 5 × 5 × 5 × 5 = 5⁴

Hence, the answer is 5⁴.

Nate solves the problem 3*5=15 by writing and solving 15÷5=3. Explain why Nate's method works

Answers

Nathan method worked because...

multiplication and division are the inverse of each other. 

Write a true conditional statement about yourself. Then write the converse of your statement in if-then form. Is the converse true?

Answers

If pizza is available, then I will eat pizza is my statement - it's conditional in that I will eat pizza if pizza is available.

The converse is pretty much switching the if and then, so I get 'If I eat pizza, then pizza is available', which is true .


Our teacher had1/2 of an eraser left.she gave that to her 2 students equally.how much of the eraser did every student take home

Answers

Hello,

If the teacher has 1/2 of an eraser, and she divides it into 2 pieces to give 1 to each of her students, she gives (1/2) / 2 = (1/2) * (1/2) = 1/4 of the eraser to each student.

Each student takes home 1/4 of the eraser.

Hope this helps!
1/2 an eraser is equally divided among 2 students......
1/2/2= 1/4 

Thus each student receives 1/4 of the eraser

A bag of marbles has 5 green, 2 yellow, 8 red, and 3 purple marbles. What is the probability of picking a green marble, not replacing it, and then picking a red marble?

Answers

the probability of picking a green marble is 1/51

The sum of three consecutive integers is 72. What are the integers?

Answers

23 24 25 sum up to 72
I: x+y+z=72
II: y=x+1
III: z=x+2

-> substitute y and z in I with the definitions II and III:
x+(x+1)+(x+2)=72
3x+3=72
3x=69
x=23

-> insert x into II and III
y=x+1=23+1=24
z=x+2=23+2=25

-> x+y+z=23+24+25=72

25. Find the measure of an angle that is 10 more than three times its complement. Show all work in order to receive credit.

Answers

3x+10+x=90

4x=80

x=20

Answer=70

Tony started a blanket business. He purchased a sewing machine and some fabric to get started, and then sold each blanket for the same price. The expression −450+12x represents the profit that Tony has earned based on the number of blankets sold.

Which expression represents the total amount Tony earns from selling blankets?



12x

12

−450+12x

x

Answers

−450+12x


you want the total amount of money he earns, which means the amount he makes from selling. If he doesn't sell enough, he will lose money

hope this helps

Find the sum of the first 30 terms of the sequence, An = 3n + 2

Answers

To find the answer above you would have to use a graph

Answer:

The sum of the first 30 terms of the sequence [tex]\( A_n = 3n + 2 \)[/tex] is 1455.

Explanation:

To find the sum of the first 30 terms of the sequence [tex]\( A_n = 3n + 2 \),[/tex] we need to substitute the values of [tex]\( n \)[/tex] from 1 to 30 into the formula and then add them together.

The formula for the [tex]\( n \)[/tex]th term of the sequence is [tex]\( A_n = 3n + 2 \).[/tex]

Let's find the first 30 terms of the sequence:

[tex]\[ A_1 = 3(1) + 2 = 5 \][/tex]

[tex]\[ A_2 = 3(2) + 2 = 8 \][/tex]

[tex]\[ A_3 = 3(3) + 2 = 11 \][/tex]

[tex]\[ \vdots \][/tex]

[tex]\[ A_{30} = 3(30) + 2 = 92 \][/tex]

Now, we need to find the sum of these terms:

[tex]\[ \text{Sum} = A_1 + A_2 + A_3 + \ldots + A_{30} \][/tex]

To find the sum, we can use the formula for the sum of an arithmetic series:

[tex]\[ \text{Sum} = \frac{n}{2}(A_1 + A_{30}) \][/tex]

Where:

- [tex]\( n \)[/tex] is the number of terms (30 in this case)

- [tex]\( A_1 \)[/tex] is the first term (5)

- [tex]\( A_{30} \)[/tex] is the 30th term (92)

Now, let's calculate the sum:

[tex]\[ \text{Sum} = \frac{30}{2}(5 + 92) \][/tex]

[tex]\[ \text{Sum} = \frac{30}{2}(97) \][/tex]

[tex]\[ \text{Sum} = 15 \times 97 \][/tex]

[tex]\[ \text{Sum} = 1455 \][/tex]

Arthro is making 5 pounds of snack mix from raisins and almonds. the raisins cost $3 per pound, and the almonds cost $8 per pound. he wants the cost of the snack mix to be $6.50 per pound. how many pounds of each item should he use?

Answers

This is a system of equations problem.
Let r = pounds of raisins
and a = pounds of almonds
We know that r + a = 5. this is our first equation
The second one is more tricky, 3r + 8a = 6.5*5
Now solve:
r = 5 - a
3(5 - a) + 8a = 6.5*5
15 - 3a + 8a = 32.5
5a = 17.5
a = 3.5
r = 5 - 3.5
r = 1.5
He should use 3.5 pounds of almonds and 1.5 pound of raisins

Fifteen marbles are in a row . 20% are blue.one third are green. Yellow marbles account for 0.2 of the row . The remaining marbles are red. Explain how to find out how many of each color of marbles are in the row

Answers

15(.20)= 3 marbles are blue.

15(1/3)= 5 are green

15(.20)= 3 are yellow

3+5+3=11 marbles

15-11= 4 that means the rest of them are red.

Evaluate u + xy, for u = 18, x = 10 and y = 8

Answers

Salutations!

Evaluate u + xy, for u = 18, x = 10 and y = 8

This is just substituting values.

 u = 18

x=10

y = 8

18 +10 * 8 = ?

Multiply 10 and 8

18 + 80 = 98.

Hope I helped (:

Have a great day!

U+xy

Where u=18,x=10,y=8

Sub in all these values

18+10(8)

18+80

98

Hope this helps!

One positive number is 7 times another positive number. the difference between the two numbers is 24. find the two numbers.

Answers

28 and 4 because 4x7 = 28 and 28-4 =24

The golf ball is at the point (2.5,2) and the hole is at the point (9.5,2) the golfer wants to bank off the side wall of the green at the point (x,y)

Is the square root of 2,500 irrational or rational

Answers

It is a  rational because it equals 50 [tex]\sqrt{2500} = 50 [/tex]
The square root of 2,500 is rational

Susan will rotate triangle  ABC 180°about one of the labeled points. Susan says, "The image will not touch the pre-image at all."

Which points could be her center of rotation?

Select each correct answer.

point C

point D

point E

point F

Answers

Answer:

point E and F

Step-by-step explanation:

the only ones that make sense

please help!!!! asap

Answers

It would be D because in order to get rid of the fraction and the value of k you need to multiply -4 to the entire equation. Hope this helps love!

Can yall show work i need help quick

Answers

Looking at the attached image, we start with 3 red circles (representing 3) and 2 green ones (representing 2p) on one side and 7 red circles (representing 7) on the other side. We then cross out 3 red circles from each, and since 2 green circles are left, we split the remainder of each side into half represented by grey lines (as 1*2=2). Crossing out half from each side, we end up with one green circle (p)=2

Holly wants to save money for an emergency. Holly invests 1,500 in an account that pays an interest rate of 6.75%. How many years will it take for the account to reach 7300? Round your answer to the nearest hundredth.

Answers

The formula is
A=p (1+r)^t
A future value 7300
P present value 1500
R interest rate 0.0675
T time?
7300=1500 (1+0.0675)^t
Solve for t
Divide both sides by 1500
7300/1500=1.0675^t
Take the log for both sides
Log (7300/1500)=t×log (1.0675)
Divide both sides by log (1.0675)
T=log(7,300÷1,500)÷log(1.0675)
T=24.2 years round your answer to get 24 years

Hope it helps!
Although the problem didn't mention it, I guess this is a compound interest, if so, then:

A= P(1+i%)ⁿ , where P is the original capital, i% = interest and n= number of years

7300 = 1500(1 + 0.0675)ⁿ

7300/1500 = (1.0675)ⁿ

4.86666 = (1,0675)ⁿ

log(4.86666)= n.log(1.0675)
0.687231 = n(0.028367)

n = 0.687231 / 0.028367

n = 24.23 years

You have 128 ounces of milk and drink 16 ounces per day. What algebraic expression models the amount of milk you have? Let x equal the amount of days

Answers

128 - 16x

this basically states that u start with 128 oz....and u drink 16 oz for  x number of days

The algebraic expression that the amount of milk has will be 128 - 16x.

What is an expression?

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given,

Total milk = 128 ounces

Rate of drinking milk = 16 ounces/day

x equal the number of days

Then,

Amount remaining = 128 - 16x

Hence, The algebraic expression that the amount of milk has will be 128 - 16x.

To learn more about expression

https://brainly.com/question/14083225

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Sarah has 12 shirts and 3 pairs of pants. How many combinations of outfits can she make

Answers

I wold have to say four because

12÷3=4

Hop this Helps!!
36
12 shirts with each pair of pants
so 12*3=36

What is the rate at which work is done on the refrigerator? carnot?

Answers

Work done = Force x Distance
Work done = Energy converted

The rate at which work is done on the refrigerator and Carnot refrigerator depends on the cooling effect desired and the efficiency of the refrigerator.

For a refrigerator,

The coefficient of performance is Qc / W

For a Carnot refrigerator,

The coefficient of performance is Tc / (Th - Tc).

We have,

The rate at which work is done on the refrigerator depends on the specific context or situation.

In general terms,

Work is done on a refrigerator when an external force or energy is applied to the refrigerator to compress the refrigerant and drive the cooling cycle.

This work is usually done by a compressor, which requires energy input to operate.

The efficiency of a refrigerator, including Carnot refrigerators, is given by the coefficient of performance (COP).

The COP is defined as the ratio of the cooling effect (Qc) to the work input (W):

COP = Qc / W

For a Carnot refrigerator, which is an idealized and reversible refrigerator operating between two temperature reservoirs, the COP is given by:

COP = Tc / (Th - Tc)

Where:

Tc = Temperature of the cold reservoir (inside the refrigerator)

Th = Temperature of the hot reservoir (outside the refrigerator)

Generally, higher-efficiency refrigerators require less work input to achieve a given cooling effect.

However, the actual rate of work done on a specific refrigerator depends on its design, efficiency, and the cooling requirements of the system.

Thus,

The rate at which work is done on the refrigerator and Carnot depends on the cooling effect desired and the efficiency of the refrigerator.

Learn mroe about refrigerators and Carnot refrigerators here:

https://brainly.com/question/13441103

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What are the real and imaginary parts of the complex number? −6−i Enter your answers in the boxes. The real part: The imaginary part:

Answers

Answer:

Real part = -6 and imaginary part = -i

Step-by-step explanation:

A complex number can be written as a + bi,

where both a and b are real numbers,

While, i is an imaginary number ( equals to √-1, because √-1 does not defined as a real number ),

The product of a real number and imaginary number is imaginary number,

∴ bi is called imaginary part of a + bi

Also, a is real number ⇒ a is real part of a + bi

Here, the given complex number,

-6-i

By comparing,

Imaginary part = -i, real part = -6.

We want to see the real and imaginary parts of a given complex number.

The real part is: -6

The imaginary part is: -1

A general complex number is written as:

z = a + b*i

Where a is the real part and b is the imaginary part.

In this case, we have the number:

z = -6 - i

We can rewrite this as:

z = -6 + (-1)*i

Then the real part is the number that is alone, in this case, -6.

The imaginary part is the coefficient that multiplies the "i", which is -1.

If you want to learn more, you can read:

https://brainly.com/question/20566728

heeeelp me plz i will give brainliest

Answers

Most of the time, plants are producers because they get their food from photosynthesis. Lily pads do, so it is a producer.

Hope this helps!
I think primary consumer because it does not work as a decomposer either a producer. 

A person is strolling along a moving walkway at a constant velocity of +1.00 m/s with respect to the walkway, which moves at a constant velocity of +0.50 m/s with respect to the ground. an observer on the ground is walking at a constant velocity of -0.2 m/s. what is the velocity of the person on the walkway with respect to the observer on the ground?

Answers

Refer to the diagram shown below.

The velocity of the person on the walkway relative to the ground is the velocity of the walkway (relative to the ground) plus the velocity of the person relative to the walkway.
It is
1.0 + 0.5 = 1.5 m/s

The person on the ground moves at - 0.2 m/s, which is in the opposite direction to that of the walkway and the person on the walkway.
Therefore the velocity of the person on the walkway relative to the person on the ground is
105 - (-0.2) = 1.7 m/s

Answer: 1.7 m/s

Hurry Please!!!! IF ANSWER WILL MAKE BRAINIEST ANSWER
Which expression is equivalent to

Answers

see attached picture for answer
[(x⁴/³ . x²/³]¹/³

1st: x⁴/³ . x²/³ = x⁴/³ ⁺²/³ = x⁶/³ = x² (Remember xᵃ . xᵇ = xᵃ⁺ᵇ)

2nd: (x²)¹/³ = x²/³ (Remember (aᵃ)ᵇ = aᵃᵇ)

Answer: x²/³

One survey estimates that, on average, the retail value of a mid-sized car decreases by 8% annually. If the retail value of a car is V dollars today, which expression represents the car’s value 1 year later?

Answers

value in 1 year = V*0.92

Answer: 0.92v

Step-by-step explanation:

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