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3 years ago

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A pair of shoes costs $29.99 and the state sales tax is 5%. Use the formula C = p + rp to find the total cost of the shoes, wher

e C is the total cost, p is the price, and r is the sales tax rate.

1 answer:

Lemur [1.5K]3 years ago

6 0

29.99 + .05 × 29.99 = 31.49

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Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.

sattari [20]

Answer:

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

$x+3y\le 36.$

2. Tyler can carry up to 20 pounds of food in his backpack, then

$x+1.5y\le 20.$

You get the following system of inequalities:

$\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.$

Now substitute the coordinates of each point:

<u>(1,12):</u>

$\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.$

False, because first inequality doesn't hold.

<u>(2,10):</u>

$\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.$

True, both inequalities hold.

<u>(4,5):</u>

$\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.$

True, both inequalities hold.

<u>(6,10):</u>

$\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.$

False, because secondt inequality doesn't hold.

<u>(12,8):</u>

$\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.$

False, because second inequality doesn't hold.

<u>(18,6):</u>

$\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.$

False, because second inequality doesn't hold.

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3 years ago

2, 3, 5, 9, 17...

BARSIC [14]

Answer:

Step-by-step explanation:

i'm sure the answer is C

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3 years ago

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How to factor x^2-49y^2

marishachu [46]

$x^2-49y^2=x^2-(7y)^2=(x-7y)(x+7y)\\\\\\a^2-b^2=(a-b)(a+b)$

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3 years ago

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Can somebody help me please !?

r-ruslan [8.4K]

Answer:

option 4) x = 14 y = 7

Step-by-step explanation:

We are given a side angle and a side length so we can use trigonometry to find the solution

To find x we can use sine because the given side length is opposite to the angle so,

sin(60) = $\frac{7\sqrt{3} }{x}$

solve for x and you get 14 (make sure you check that your calculator is in degrees)

for either use Pythagorean theorem or remove sine by tangent.

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The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same mea

Mrac [35]

Let us start with the unknown. Let us give one of the base angles the value of x. The other base angle is also x since both the base angles in an isosceles triangle will be equal. The remaining angle is 40 more than three times one of the base angles.It is 3x + 40. Here we get the equation

x+x+3x+40=180

5x + 40 = 180

5x = 180 - 40 = 140

Therefore x = 140/5 = 28

So the angles are 28, 28 and 124.

The third angle is 3 times 28 + 40 = 84 + 40 = 124.

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4 years ago