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3 years ago

Find the values of p and q

Mathematics

1 answer:

VashaNatasha [74]3 years ago

6 0

Answer:

p = 2 and q = 14

Step-by-step explanation:

Evaluate f(g(x)) by substituting x = g(x) into f(x), that is

f(px + 4)

= 3(px + 4) + p = 3px + 12 + p

f(g(x)) = 3px + 12 + p and f(g(x)) = 6x + q

Equating the 2 expressions gives

3px + 12 + p = 6x + q

Compare the coefficients of like terms and the constant term

For the 2 expressions to be equal then

3p = 6 ⇒ p = 2 , and

q = 12 + p = 12 + 2 = 14

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Mae Ling earns a weekly salary of $330 plus a 7.5% commission on sales at a gift shop. How much would she make in a work week if

notka56 [123]

Answer:

$690

Step-by-step explanation:

The amount she makes in a week=her weekly salary + the commission on sales.

Amount=330 + 7.5% of 4800.

Amount = 330+ 360=690.

The she would make if she sold $4,800 of merchandise is $690.

3 0

3 years ago

What is the factored form of x^2-x-2

tekilochka [14]

For this case we have:

By definition, the factorization is an algebraic expression that is used to find two or more factors, taking into account that the product of these factors must be equal to the given expression.

That is to say:

Given an expression of the form $x ^ 2 + (a + b) x + ab$

We can factor in the following way:

$(x + a) (x + b)$

Since, its product is: $x ^ 2 + bx + ax + ab = x ^ 2 + (a + b) x + ab$ ,

checking the given definition.

If we have:

$x ^ 2-x-2$

We can factor:

$(x-2) (x + 1)$

When making your product we obtain: $x ^ 2 + x-2x-2 = x ^ 2-x-2$

Answer:

$(x-2) (x + 1)$

6 0

3 years ago

Is a triangle with sides of length 6ft, 21 ft, 23 ft. A right triangle?

gayaneshka [121]

Answer:

Step-by-step explanation:

By using the Pythagoras theorem, it can be easily determined that whether the triangle is right triangle or not.

Thus, $a^{2}+b^{2}=c^{2}$ where where a and b are the legs and c is the hypotenuse.

Let a=6ft, b=21ft and c=23ft, then

$a^{2}+b^{2}=c^{2}$

$(6)^{2}+(21)^{2}=(23)^{2}$

$36+441=(23)^{2}$

$477=529$

which is not possible, therefore the given triangle is not right triangle because it does not satisfy the Pythagoras theorem.

7 0

3 years ago

Suppose a researcher is testing the hypothesis Upper H 0: pequals0.4 versus Upper H 1: pless than0.4 and she finds the P-valu

andre [41]

Answer:

D. If the P-value for a particular test statistic is 0.33, she expects results at least as extreme as the test statistic in exactly 33 of 100 samples if the null hypothesis is true.

D. Since this event is not unusual, she will not reject the null hypothesis.

Step-by-step explanation:

Hello!

You have the following hypothesis:

H₀: ρ = 0.4

H₁: ρ < 0.4

Calculated p-value: 0.33

Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

In this case, you have a 33% chance of getting a value as extreme as the statistic value if the null hypothesis is true. In other words, you would expect results as extreme as the calculated statistic in 33 about 100 samples if the null hypothesis is true.

You didn't exactly specify a level of significance for the test, so, I'll use the most common one to make a decision: α: 0.05

Remember:

If p-value ≤ α, then you reject the null hypothesis.

If p-value > α, then you do not reject the null hypothesis.

Since 0.33 > 0.05 then I'll support the null hypothesis.

I hope it helps!

3 0

3 years ago

A city planner designs a park that is a quadrilateral with vertices at J(-3,1), K(1,3), L(5,-1), and M(-1,-3). There is an entra

Ksivusya [100]

The Quadrilateral is JKLM,

let $M_{JK}, M_{KL}, M_{LM}, M_{JM},$ be the midpoints of JK, KL, LM and JM respectively.

---------------------------------------------------------------------------------------------------------

Given any 2 point P(m,n) and Q(k,l),<span>

the coordinates of the midpoint of the line segment PQ are given by the formula:

$M_{PQ}=( \frac{m+k}{2} ,
\frac{n+l}{2})$ , </span>

-------------------------------------------------------------------------------------------------

thus the coordinates of points $M_{JK}, M_{KL}, M_{LM}, M_{JM},$

are as follows:

$M_{JK}= (\frac{-3+1}{2}, \frac{1+3}{2})=(-1,2), \\\\M_{KL}= (\frac{1+5}{2}, \frac{3-1}{2}=(3,1), \\\\M_{LM}= (\frac{5-1}{2}, \frac{-1-3}{2})=(2, -2),\\\\ M_{JM}= (\frac{-3-1}{2}, \frac{1-3}{2})=(-2,-1)$

------------------------------------------------------------------------------------------------

The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:<span>

$|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2}
}$ </span>

------------------------------------------------------------------------------------------------

thus the distances connecting the opposite entrances can be calculated as follows:

$|M_{JK},M_{LM}|= \sqrt{ (-1-2)^{2} + (2-(-2))^{2} }= \sqrt{9+16}=5$

$|M_{KL}M_{JM}|= \sqrt{ (3-(-2))^{2} + (1-(-1))^{2}}= \sqrt{25+4}= \sqrt{29}=5.39$

Thus the total distance of the paths joining the opposite entrances is

5+5.39 units = 50 m + 53.9 m = 104 m (rounded to the nearest meter)

Answer: 104 m

8 0

3 years ago