John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $5.95 per pound, and type B coffee costs $4.65 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $656.70. How many pounds of type A coffee were used?

Answer: x = 3.5

Step-by-step explanation:

Given

x/3 + x/7 = 5/3

Determine the Least Common Multiple (LCM) of the denominators

First 10 multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

First 5 multiples of 7: 7, 14, 21, 28, 35

Since 21 is the first overlapping term in both lists, therefore, 21 is the LCM of 3 and 7.

Multiply Least Common Multiple (LCM) of the denominators on both sides

21 (x/3 + x/7) = 21 × 5/3

Expand parentheses and apply the distributive property

7x + 3x = 35

Combine like terms

10x = 35

Divide 10 on both sides

10x / 10 = 35 / 10

[tex]\boxed {x=3.5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The perimeter of the figure is 4a.

The perimeter of a polygon is defined as the addition of the lengths of the polygon's each side.

The perimeter of a polygon = sum of all sides

To determine an expression for the perimeter of the figure as the sum of the lengths of its sides.

The perimeter of the figure as

The perimeter of  the figure = sum of all sides

⇒ 2(a-b) + a +2b +2c + a - 2c

Rearrange the likewise terms in the expression

⇒ 2a - 2b +2a + 2b

Apply the arithmetic operations in the expression

⇒ 4a

Thus, the perimeter of the figure is 4a.

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a = 2 cm

b = 55 mm = 5,5 cm

c = 10 cm

d = 60 mm = 6 cm

Perimeter: 2 + 5,5 + 10 + 6 = 23,5 cm

Answer:

According to question, we get the following equation:

n-35% = 117

n-35/100 = 117

(100n-35)/100 = 117 ........... Took LCM

100n-35 = 117*100

100n-35 = 11700

100n = 11700-35

100n = 11665

n = 11665/100

n = 116.65 .......... ANSWER

I think the given figure will help you....

Answer:

3.3

Step-by-step explanation:

Find all the numbers and find the mean

The x means that there are that many of each number

1 + 1 + 2 + 3 + 3 + 4 + 4+ 5 + 5 + 5

33

We have to divide that by the total amount of numbers present

33/10 = 3.3

Answer:

[tex] \frac{5i}{3 + 2i} \times \frac{3 - 2i}{3 - 2i} \\ \frac{15i - 10 {i}^{2} }{9 - 4 {i}^{2} } \\ \frac{15i - 10( - 1)}{9 - 4( - 1)} \\ \frac{15i + 10}{9 + 4} \\ \frac{15i + 10}{13} \\ \frac{10}{13} + \frac{15i}{13} [/tex]

Answer:

1. 0.832

832/1000

Can be simplified as

416/500

104/125

2. 1.2

12/10

Can be simplified as

6/5

3. 0.1

1/10

4. 0.459

459/1000

5. 1.51

151/100

6. 0.9

9/10

Which were the required answers

Answer:

120/100

Step-by-step explanation:

120÷20= 6

100÷20=5

6/5 = 1⅕

Answer:

1) -3x + 90

=(3)(30+−x)

=(3)(30)+(3)(−x)

=90−3x

=−3x+90

2) 37x+90

=40x+(3)(30)+(3)(−x)

=40x+90+−3x

Combine Like Terms:

=40x+90+−3x

=(40x+−3x)+(90)

=37x+90

Answer:

50,27

Step-by-step explanation:

let the parts be x and y

x+y=77

x=2y-4

substitute

2y-4+y=77

3y=77+4

3y=81

y=81/3=27

x=2×27-4=54-4=50

Answer:

no, y=3x+3

Step-by-step explanation:

plug both points into the equations:

one works but the other doesn't so now we find a line through both points

use the formula (y_2-y_1)/(x_2-x_1) to find the slope:

y=3x+b, plug in a point to find b:

Answer:

g=Xs+t

Step-by-step explanation:

please love math

to learn math, to look for topics you don't know in the internet

Answer:

Step-by-step explanation:

Answer:

V = 1188 yd^3

Step-by-step explanation:

The volume or a rectangular prism is given by V = l*w*h V = 12 (9) * 11 V = 1188 yd^3  

Read more at Answer.Ya.Guru – https://answer.ya.guru/questions/6458403-msferris-owns-a-barn-12-yards-long-9-yards-high-and-11-yards.html

Answer:

Step-by-step explanation:

y = 2x + 2

x = [tex]\frac{y-2}{2}[/tex]

y = [tex]\frac{x-2}{2}[/tex]

[tex]g^{-1}[/tex] (x) = [tex]\frac{x-2}{2}[/tex]

Answer:

___-5___is 3 units left from -2 on a number line.

___1___- is 3 units right from -2 on a number line

Answer:

well since you said 32 per home since that wasnt a hour he was there, i took off 32 from the 128.69 and got 96.69 and divided that by 22.75 and got 4.2 hours but if that's not what you are talking about ill also give the answer for 128.69 divided by 22.75 and the answer for that is 5.6

Step-by-step explanation:

so just add 4.2 or 5.6 to hours and you will get you question at what time he left

Answer:

first option

Step-by-step explanation:

congruency has its own symbol and it's a ~ top of a = sign. and the expression doesn't have the symbol. so we can eliminate two options out meaning it's a.

The correct answer would be an option (A) the measure of segment DE is equal to the measure of segment FG.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

SSS stands for Side-Side-Side criterion. According to this, two triangles are congruent if three sides of a triangle are equal to the corresponding sides of the other triangle.

SAS stands for Side-Angle-Side criterion.  According to this, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

Given that, DE = FG

Congruency is represented by its own symbol, which is a ~ sign on top.

Here, Segment FG's measure is equal to segment DE's measure.

There is no symbol assigned to the expression. Since two possibilities are no longer an option, it must be Option (A).

Hence, the measure of segment DE is equal to the measure of segment FG

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Answer:

It is 1/5

Step-by-step explanation:

0.2 is a decimal ( tenth value [1/10] )

[tex]0.2 = \frac{2}{10} [/tex]

divide the fraction ( numerator and denominator ) by 2:

[tex] = \frac{2 \div 2}{10 \div 2} \\ \\ = \frac{1}{5} [/tex]

Answer:

n=-1

Step-by-step explanation:

Writing out the problem

8=-6n-2n

Simplifying "-6n-2n," which is -8n

8=-8n, or -8n=8

-8n=8

Divide both sides by -8

-8n/-8=8/-8

So, therefore, you get n=-1.

Hope this helps! Enjoy your day, and take care!

Answer:

Step-by-step explanation:

From what I can come up with with no actual factual information is that the equation is

[tex]\frac{1+sin^4x-cos^4x}{1-sin^6x-cos^6x}=\frac{2cos^2x}{3}[/tex] I'm going with that because it actually solves pretty easily, which is usually the way this goes. Begin by cross multiplying:

[tex]3(1+sin^4x-cos^4x)=2cos^2x(1-sin^6x-cos^6x)[/tex] and distribute:

[tex]3+3sin^4x-3cos^4x=2cos^2x-2cos^2xsin^6x-2cos^8x[/tex] and then break up the powers of sin into squared sines:

[tex]3+3[sin^2x*sin^2x]-3cos^4x=2cos^2x-2cos^2x[sin^2x*sin^2x*sin^2x]-2cos^8x[/tex]  and use the Pythagorean identity to change those sines into cosines:

[tex]3+3[(1-cos^2x)(1-cos^2x)]-3cos^4x=2cos^2x-2cos^2x[(1-cos^2c)(1-cos^2x)(1-cos^2x)]-2cos^8x[/tex]

and the FOIL out those terms inside the square brackets:

[tex]3+3[1-2cos^2x+cos^4x]-3cos^4x=2cos^2x-2cos^2x[1-3cos^2x+3cos^4x-cos^6x]-2cos^8x[/tex]

and distribute again on both sides to get rid of the brackets entirely:

[tex]3+3-6cos^2x+3cos^4x-3cos^4x=2cos^2x-2cos^2x+6cos^4x-6cos^6x+2cos^8x-2cos^8x[/tex]

and combining like terms cancels a lot of that out to leave:

[tex]6-6cos^2x=-6cos^6x+6cos^4x[/tex] and get everything on one side to factor:

[tex]0=-6cos^6x+6cos^4x+6cos^2x-6[/tex] and factor out the -6:

[tex]0=-6(cos^6x-cos^4x-cos^2x+1)[/tex] and now we'll factor by grouping, so grouping everything together to get ready for that:

[tex]0=-6[(cos^6x-cos^4x)-(cos^2x+1)][/tex] and begin the factoring:

[tex]0=6[cos^4x(cos^2x-1)-1(cos^2x-1)][/tex] and continuing the factoring:

[tex]0=-6(cos^2x-1)(cos^4x-1)\\0=-6(cos^2x-1)(cos^2x-1)(cos^2x+1)[/tex] and by the Zero Product Property (and we won't list that duplicated factor cuz it's not necessary):

[tex]cos^2x-1=0[/tex]     or       [tex]cos^2x+1=0[/tex]

Solving the first:

[tex]cos^2x=1[/tex] so

x = 0 + 2kπ  and solving the second one:

[tex]cos^2x=-1[/tex] which is not solvable over the real number system.

So x = 0 + 2kπ

and I really hope that's what you were looking for!

Answer:

may be 5 unit is the distance is between then

Answer:

5 units

Step-by-step explanation:

use distance formula kid

Answer:

yes it is

rational number is any number that can be expressed as a ratio of two integers (hence the name "rational"). It can be written as a fraction in which the the top number (numerator) is divided by the bottom number (denominator).

plsmark me brilliant

Answer:

SEE IMAGE FOR SOLUTION

Hope it helps

Have a great day

Answer:

$14.93

Step-by-step explanation:

she works 7+8=15 hours.

she earns in total per day

7×$23.46 + 8×$7.47 = $223.98

on average she makes per hour

223.98 / 15 = $14.93

She make on average 223.98 per hour for the day.

Given that,

She usually works at a retail store for 7 hours during the day and is paid $23.46 per hour by the store.

In the evening she works at a restaurant as a manager for 8 hours and is paid $7.47 per hour.

We have to determine,

How much does she make on average per hour for the day.

According to the question,

She usually works at a retail store for 7 hours earn = $23.46 per hour.

She works at a restaurant as a manager for 8 hours = $7.47 per hour

Total number of hours she works = 7hours + 8hours = 15hours

Therefore,

She make on average per hour for the day =

7×$23.46 + 8×$7.47 = $223.98

Hence, she make on average 223.98 per hour for the day.

To know more about Addition click the link given below.

https://brainly.com/question/24442197

Answer:

$4000 net profit

Step-by-step explanation:

Profit adds to the net revenue, while loss subtracts from it.

So 6500 is positive but 1200 and 1300 are negative.

+6500 - 1200 - 1300 = 5300 - 1300 = 4000

$4000 profit