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3 years ago

21y+7x=56? what is the value of X

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

4 0

Answer:

x = 8 - 3y

Step-by-step explanation:

$21y+7x=56\\\\21y-21y+7x=56-21y\\\\7x=56-21y\\\\\frac{7x=56-21y}{7}\\\\\boxed{x=8-3y}$

Hope this helps.

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Determine the equation of each of the following parabolas

Pani-rosa [81]

Step-by-step explanation:

For graphs where the zeros (x-intercepts) are known, use the factored form of a parabola:

y = a (x − b) (x − c)

where (b, 0) and (c, 0) are the zeros. Plug in a third point to find the value of a.

For graphs where the vertex is known, use the vertex form of a parabola:

y = a (x − h)² + k

where (h, k) is the vertex. Plug in a second point to find the value of a.

I'll do the first three problems as examples.

a) The vertex is (0, 5), and one of the zeros is (4, 0). Since the vertex is halfway between the zeros, we also know the other zero is (-4, 0). So we can use either form.

Using factored form:

y = a (x − 4) (x − (-4))

y = a (x − 4) (x + 4)

Plug in the vertex to find the value of a:

5 = a (0 − 4) (0 + 4)

5 = -16a

a = -5/16

Therefore, the equation is:

y = -5/16 (x − 4) (x + 4)

b) The vertex is (0, 0). It is also the only root. So again, we can use either form.

Using vertex form:

y = a (x − 0)² + 0

y = ax²

Plugging in the second point:

9 = a (-3)²

9 = 9a

a = 1

Therefore, the equation is:

y = x²

c) This time, we don't know the coordinates of the vertex, but we do know the roots are (-7, 0) and (0, 0). Using factored form:

y = a (x − 0) (x − (-7))

y = a x (x + 7)

Plugging in the third point:

4 = a (4) (4 + 7)

4 = 44a

a = 1/11

Therefore, the equation is:

y = 1/11 x (x + 7)

7 0

3 years ago

A company manufactures light bulbs. The lifetime for these bulbs is 4,000 hours with a standard deviation of 200 hrs. What lifet

arlik [135]

Answer:

The company should promote a lifetime of 3589 hours so only 2% burnout before the claimed lifetime

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 4000, \sigma = 200$

What lifetime should the company promote for these bulbs, whereby only 2% burnout before the claimed lifetime?

This is the value of X when Z has a pvalue of 0.02. So it is X when Z = -2.055.

$Z = \frac{X - \mu}{\sigma}$

$-2.055 = \frac{X - 4000}{200}$

$X - 4000 = -2.055*200$

$X = 3589$

The company should promote a lifetime of 3589 hours so only 2% burnout before the claimed lifetime

4 0

3 years ago

Which number sentence is true?

aliya0001 [1]

The answer is A) 1,73<2,1

3 0

3 years ago

Please help due pretty soon

____ [38]

The answer is A) y=-2x+75

6 0

3 years ago

A candy store owner has chocolate candies worth $2.50 per pound and sour candies worth $0.90 per pound. How much of each kind of

SVETLANKA909090 [29]

Answer:

Weight of chocolate candies = 30lbs

Weight of sour candies = 30lbs

Step-by-step explanation:

We are told in the question that :

Chocolate candies worth $2.50 per pound

Sour candies worth $0.90 per pound. How much of each kind of candies should she combine to get 60 lb of mixed candies worth $1.70 per pound?

Let x represent the number of pounds of chocolate candies

Let 60 - x represent the number of pounds of sour candies

Hence, we have the equation

x × $2.50 + (60 - x) × $0.90 = 60 × $1.70

= 2.5x + 54 - 0.9x = 102

Collect like terms

2.5x - 0.9x = 102 - 54

= 1.6x = 48

x = 48/1.6

x = 30 lbs

x represent the number of pounds of chocolate candies,

60 - x represent the number of pounds of sour candies

= 60 - 30

= 30lbs

Weight of chocolate candies = 30lbs

Weight of sour candies = 30lbs

Therefore, she should combine 30lbs of chocolate candies and 30lbs of sour candies to get 60 lb of mixed candies worth $1.70 per pound.

4 0

3 years ago