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dem82 [27]
3 years ago
6

8. Corey combines x pounds of

Mathematics
2 answers:
Mariana [72]3 years ago
7 0

Answer:

12x+72=10.50(x+8)

Step-by-step explanation:

Cost of 1 pound of herbal tea = $12

Cost of x pounds of herbal tea = 12x

Cost of 1 pound of regular tea = $9

Cost of 8 pounds of regular tea = 9\times 8 = 72

Now we are given that  He makes a mixture that  averages $10.50 per pound.  

Total weight of mixture = 8 punds + x pounds = x+ 8

So, 12x+72=10.50(x+8)

Hence an equation to model the situation is 12x+72=10.50(x+8)

hram777 [196]3 years ago
4 0

For this case we have to:

x: Let the variable representing the pounds of herbal tea

y: Let the variable representing the pounds of the mixture

According to the data we have:

x + 8 = y

On the other hand, to find the cost of each type of tea it is necessary to multiply the cost per pound, by the amount of pounds of each type of tea, that is:

12x + 9 (8) = 10.50y\\12x + 72 = 10.50y

Thus, we have the following system of equations:

x + 8 = y\\12x + 72 = 10.50y

Substituting the first equation in the second we have:

12x + 72 = 10.50 (x + 8)

ANswer:

The situation can be modeled by the following equation:

12x + 72 = 10.50 (x + 8)

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artcher [175]
You should find the attached graphic to be helpful for what you need to know.

7 0
3 years ago
Solve each inequality, and then drag the correct solution graph to the inequality.
Nesterboy [21]

The correct solution graph to the inequalities are

4(9x-18)>3(8x+12)  →  C

-\frac{1}{3}(12x+6) \geq -2x +14  → A

1.6(x+8)\geq 38.4  →  B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

4(9x-18)>3(8x+12)

First, clear the brackets,

36x-72>24x+36

Then, collect like terms

36x-24x>36+72\\12x >108

Now divide both sides by 12

\frac{12x}{12} > \frac{108}{12}

∴ x > 9

For the second inequality

-\frac{1}{3}(12x+6) \geq -2x +14

First, clear the fraction by multiplying both sides by 3

3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)

-1(12x+6) \geq -6x +42

Now, open the bracket

-12x-6 \geq -6x +42

Collect like terms

-6 -42\geq -6x +12x

-48\geq 6x

Divide both sides by 6

\frac{-48}{6} \geq \frac{6x}{6}

-8\geq x

∴ x\leq  -8

For the third inequality,

1.6(x+8)\geq 38.4

First, clear the brackets

1.6x + 12.8\geq 38.4

Collect likes terms

1.6x \geq 38.4-12.8

1.6x \geq 25.6

Divide both sides by 1.6

\frac{1.6x}{1.6}\geq  \frac{25.6}{1.6}

∴ x \geq  16

Let the graphs be A, B and C from left to right

The first graph (A) shows x\leq  -8 and this matches the 2nd inequality

The second graph (B) shows x \geq  16 and this matches the 3rd inequality

The third graph (C) shows x > 9 and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

4(9x-18)>3(8x+12)  →  C

-\frac{1}{3}(12x+6) \geq -2x +14  → A

1.6(x+8)\geq 38.4  →  B

Learn more here: brainly.com/question/17448505

8 0
2 years ago
The temperature was 68 F .Later that day the temperature was 82 F .How much does the temperature need to rise or fall to return
ruslelena [56]
The answer is A because 82-14=68.
4 0
3 years ago
Suppose the line of best fit is being found for some data points that have an r-value of 0.657. If the standard deviation of the
oksian1 [2.3K]
We are given a line with the following data:

r-value = 0.657 (r)
standard deviation of x-coordinates = 2.445 (Sx)
standard deviation of y-coordinates = 9.902 (Sy)

We are asked to find the slope of the line up to 3 decimal places.

To find the slope of the line, based on the data that we have, we can use this formula:

slope, b = r * (Sy / Sx) 

substitute the values to the formula:

b = 0.657 * ( 9.902 / 2.445 )

Solve for the b.

Therefore, the slope of the line is 

b = 2.66078, round off to three decimal places:

b = 2.661 is the slope of the line. 
5 0
3 years ago
Read 2 more answers
Help asap pls and thx
vazorg [7]

Step-by-step explanation:

from what I can see there are 2 options to make the 2 triangles congruent :

either the opposite sides must be equal or the neighboring sides must be equal.

so, either

5x = 3x + 10

and

5x - 2 = 4x + 3

or

5x = 4x + 3

and

5x - 2 = 3x + 10

for the first

5x = 3x + 10

2x = 10

x = 5

control

5x - 2 = 4w + 3

5×5 - 2 = 4×5 + 3

23 = 23

correct.

for the second

5x = 4x + 3

x = 3

control

5×3 - 2 = 3×3 + 10

15 - 2 = 9 + 10

13 = 19

no, not a valid solution.

so, x = 5

5 0
2 years ago
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