Emily needs to buy fabric to make curtain panels for her windows. Each panel will be 4 feet long and 1/2 foot wide. Each piece of fabric that she can buy is 4 feet long and 2 feet wide . How many panels can she make from i piece of fabric?

Answers

Answer 1

Answer: Each panel is 4 ft long and 1/2 ft wide

The piece of fabric is 4 ft long and 2 ft wide

So she can therefore fit 4 panels into this. We can calculate this by area
4*1/2=2ft^2

4x2=8ft^2

So 4*2 =8

Answer 2

Answer: The pieces of fabric are already the correct length, so it is just a matter of how many panels will fit into one piece of fabric. 2/(1/2) = 4, so she can make 4 panels from 1 piece of fabric.

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A carpenter purchased 50 ft of redwood and 90 ft of pine for a total cost of $274. A second purchase at the same prices include 80 ft of redwood and 50 ft of pine for a total cost of 335. Find the cost per foot of redwood and of pine

Answers

Answer:

Redwood: $3.50 per foot

Pine: $1.10 per foot

Step-by-step explanation:

The manner that should be approach is by using the substitution method.

Therefore using the information from the question:

50 ft of redwood and 90 ft of pine give a total cost of $274

So we use this information and make a equation using x and y, in this case redwood would be x and pine would be y.

$50x + 90y=274$

We do this for the second purchase also...

$80x+50y=335$

Now, we have two equations that are perfect for the usage of the substitution method.

$50x + 90y=274$

$80x+50y=335$

Using one equation, in this case the top one, we must solve for either x or y (in this case we solved for y)

$90y=274-50x$

$(90y)/(90) =(274)/(90) -(50x)/(90)$

$y=(274)/(90) -(50x)/(90)$

Using this equation from above we insert this into the other equation that deals with the second purchase and solve for x now.

$80x+50((274)/(90) -(50x)/(90))=335$

$80x+152.2-27.8x=335$

$80x-27.8x=182.8$

$(52.2x)/(52.2) =(182.8)/(52.2)$

$x=3.50$

This is the cost of redwood so now we use this answer and plug it in either equation in order to get the cost of pine (y).

$50(3.5)+90y=274$

$175+90y=274$

$(90y)/(90)=(99)/(90)$

$y=1.1$

So therefore you get the two costs by using the substitution method!

~~~~Best!!!

Evaluate each expression for a = -4, b = 3, and c = 2.
3a-1

Answers

Answer:

the answer is -13

Step-by-step explanation:

Can you help with the question

Answers

Step-by-step explanation:

See image

Mario invested $6,000 in an account that pays 5% annual interest compounded annually. Using the formula A = P(1 + r)t, what is the approximate value of the account after 2.5 years?a. $6,075
b. $6,118
c. $6,456
d. $6,778

Answers

The approximate value of the account after 2.5 years is $6778.

Compound interest

The compound interest is given by:

A = P(1 + r)^t

where P is the initial amount, r is the interest rate, t is the period and A is the final amount.

Given that:

r = 5% = 0.05, P = $6000, t = 2.5 years, hence:

A = 6000(1 + 0.05) ^ 2.5 = $6778

The approximate value of the account after 2.5 years is $6778.

Find out more on Compound interest at: brainly.com/question/24924853

Given:
Principal = 6,000
interest rate = 5%
term = 2.5 years

A = P (1+r)^t
A = 6,000 (1 + 0.05)².⁵
A = 6,000 (1.05)².⁵
A = 6,000 (1.1297)
A = 6,778.20 Choice D.

A quadratic equation is written in four equivalent forms below. I. y = (x - 1)2 - 49 II. y = x2 - 2x - 48 III. y = (x + 6)(x - 8) IV. y = x(x - 2) - 48 Which of the forms shown above would be the most useful if attempting to find the x-intercepts of the quadratic equation?

Answers

The x-intercept also known as the root of a quadratic can be found by solving the equation with respect to x.

III is the most useful for finding the roots
you would simply equate each term to

So y= x + 6 AND y= x - 8
0= x + 6 0= x - 8
x= -6 x= 8

: . x-intercepts are x= -6 & x= 8

A two-digit number read from left to right is 20% greater than the same number read from right to left. Find the number.

Answers

Final answer:

The number that is 20% larger when read from left to right than when read from right to left is 24.

Explanation:

The question asks for a two-digit number which is 20% larger when read from left to right than it is when read from right to left. Let's denote the digit in the tens place as 'a' and the one in the units place as 'b', then the two-digit number can be written as 10*a + b. When reversed, this becomes 10*b + a.

According to the question, 10*a + b is 20% (or 1.2 times) greater than 10*b + a. So, we can set up the following equation: 1.2(10*b + a) = 10*a + b.

When you solve this equation, the solution is a = 2 and b = 4, so the number the question is asking for is 24