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elixir [45]
3 years ago
10

A restaurant sells a refillable coffee mug for $7.75. Each refill costs $3.25. Last month Keith spent $82.75 on a mug and refill

s. Enter an equation you can use to find the number of refills that Keith bought. Let r represent the number of refills.
Mathematics
1 answer:
labwork [276]3 years ago
3 0

Answer:

82.75 = 3.25r + 7.75

Step-by-step explanation:

$82.75 is the total money spent last month

$7.75 is the cost of a refillable mug

$3.25 is the cost for every refill

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Verdich [7]

Answer:

33

Step-by-step explanation:

first you set up the problem, supplementary angles equal 180 degrees so the equation should look like, 4x+x+15=180. then you solve from there by combining like terms and you should get x equal to 33

4 0
3 years ago
Suppose u = (1,2,3), v = (2, -3, -4), and w = (1,0,-2). (a) Find u-2v + 3w. (b) Write the vector (3,4,5) as a linear combination
marishachu [46]
<h2>Answer with explanation:</h2>

We are given vectors u,v and w as follows:

      u=(1,2,3)\,\ v=(2,-3,-4),\ and\ w=(1,0,-2)

(a)

Now we are asked to find the value of:

  u-2v+3w

The value is calculated as follows:

u-2v+3w=(1,2,3)-2(2,-3,-4)+3(1,0,-2)\\\\i.e.\\\\u-2v+3w=(1,2,3)+(-2\times 2,-2\times -3,-2\times -4)+(3\times 1,3\times 0,3\times -2)\\\\i.e.\\\\u-2v+3w=(1,2,3)+(-4,6,8)+(3,0,-6)\\\\i.e.\\\\u-2v+3w=(1-4+3,2+6+0,3+8-6)\\\\i.e.\\\\u-2v+3w=(0,8,5)

                              Hence,

                 u-2v+3w=(0,8,5)

(b)

We are asked to represent (3,4,5) as a linear combination of u, v, and w.

Let:

(3,4,5)=au+bv+cw

(3,4,5)=a(1,2,3)+b(2,-3,-4)+c(1,0,-2)

i.e.

(3,4,5)=(a,2a,3a)+(2b,-3b,-4b)+(c,0,-2c)\\\\i.e.\\\\(3,4,5)=(a+2b+c,2a-3b,3a-4b-2c)\\\\i.e.\\\\a+2b+c=3----------(1)

2a-3b=4-------------(2)

3a-4b-2c=5------------(3)

on multiplying equation(1) by 2 an then adding equation (1) to equation (3)

5a=11\\\\i.e.\\\\a=\dfrac{11}{5}

on putting the value of a in equation (2) we get:

2\times \dfrac{11}{5}-3b=4\\\\i.e.\\\\\dfrac{22}{5}-3b=4\\\\i.e.\\\\3b=\dfrac{22}{5}-4\\\\i.e.\\\\3b=\dfrac{2}{5}\\\\i.e.\\\\b=\dfrac{2}{15}

Now on putting the value of a and b in equation (1)

\dfrac{11}{5}+2\times \dfrac{2}{15}+c=3\\\\i.e.\\\\\dfrac{11}{5}+\dfrac{4}{15}+c=3\\\\i.e.\\\\c=3-\dfrac{11}{5}-\dfrac{4}{15}\\\\i.e.\\\\c=\dfrac{3\times 15-11\times 3-4}{15}\\\\i.e.\\\\c=\dfrac{45-33-4}{15}\\\\i.e.\\\\c=\dfrac{8}{15}

Hence, we have:

(3,4,5)=\dfrac{11}{5}(1,2,3)+\dfrac{2}{15}(2,-3,-4)+\dfrac{8}{15}(1,0,-2)\\\\i.e.\\\\(3,4,5)=\dfrac{11}{5}u+\dfrac{2}{15}v+\dfrac{8}{15}w

5 0
4 years ago
To all you misguided people out there:
Alla [95]

Answer:

See below.

Step-by-step explanation:

I think you're supposed to solve the problem explaining all steps, and then copy the answer to the top.

5 0
3 years ago
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PLEASE HELP!!!!!!!!!!​
Dovator [93]

Answer:

second

Step-by-step explanation:

\frac{2x}{5} +\frac{1x}{5} +\frac{5}{8} -\frac{2}{8} = \frac{3x}{5} +\frac{3}{8}

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3 years ago
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Given: m∠A + m∠B = m∠B + m∠C Prove: m∠C = m∠A
mel-nik [20]

Answer:

See below.

Step-by-step explanation:

m∠A + m∠B = m∠B + m∠C

Use the subtraction property of equality to subtract m<B from both sides of the equation.

m∠A + m∠B - m<B = m∠B - m<B + m∠C

m∠A = m∠C

8 0
3 years ago
Read 2 more answers
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