99 newspapers in 3 piles

Write the quadratic equation whose roots are 1 and -5, and whose leading coefficient is 3.

Anna35 [415]

Step-by-step explanation:

they're is a neat little trick.

but first of all, "roots" means the 0 solutions of the equation. like

ax² + bx + c = 0

there are 2 solutions for x to make the whole expression equal 0.

these are the "roots".

now to the little trick :

when is a multiplication resulting in 0 ?

when at least one of the factors is 0.

and any quadratic expression can be written as multiplication of 2 factors. like

c(x - a)(x - b) = cx² - cax - cbx + cab

what are the "roots" or 0 points ?

either

c = 0

x - a = 0 | x = a

x - b = 0 | x = b

the leading coefficient = 3.

that means nothing else than c = 3.

root = 1 means (x - 1) is one factor.

root = -5 means (x + 5) is the other factor.

so, we have

3(x - 1)(x + 5) = 3x² + 12x - 15

and the equation is

3x² + 12x - 15 = 0

or

3x² + 12x = 15

7 0

2 years ago

If you have 8 batteries cost $40 [cost per battery]

Finger [1]

Answer:

the answer is 5 because 40 divided by 8 is 5

5 0

3 years ago

Read 2 more answers

M. Score: 0 of 1 pt

beks73 [17]

Answer:

3×5×53

Step-by-step explanation:

You can use divisibility rules to find the small prime factors.

The number ends in 5, so is divisible by 5.

795/5 = 159

The sum of digits is 1+5+9 = 15; 1+5 = 6, a number divisible by 3, so 3 is a factor.

159/3 = 53 . . . . . a prime number,* so we're done.

795 = 3×5×53

_____

* If this were not prime, it would be divisible by a prime less than its square root. √53 ≈ 7.3. We know it is not divisible by 2, 3, or 5. We also know the closest multiples of 7 are 49 and 56, so it is not divisible by 7. Hence 53 is prime.

5 0

3 years ago

A cigarette industry spokesperson remarks that current levels of tar are no more than 5 milligrams per cigarette. A reporter doe

d1i1m1o1n [39]

Answer:

$t=\frac{5.63-5}{\frac{1.61}{\sqrt{15}}}=1.516$

$df=n-1=15-1=14$

Since is a right tailed test the p value would be:

$p_v =P(t_{14}>1.516)=0.076$

If we use a significance level of 0.05 we see that $p_v > \alpha$ and then we can conclude that we don't have evidence in order to conclude that the mean is higher than 5.63, so then the claim makes sense.

Step-by-step explanation:

Data given and notation

$\bar X=5.63$ represent the sample mean

$s=1.61$ represent the standard deviation for the sample

$n=15$ sample size

$\mu_o =15/tex] represent the value that we want to test 
[tex]\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the average is more than 5.63, the system of hypothesis would be:

Null hypothesis: $\mu \leq 5.63$

Alternative hypothesis: $\mu > 5.63$

Compute the test statistic

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$t=\frac{5.63-5}{\frac{1.61}{\sqrt{15}}}=1.516$

Now we need to find the degrees of freedom for the t distribution given by:

$df=n-1=15-1=14$

P value

Since is a right tailed test the p value would be:

$p_v =P(t_{14}>1.516)=0.076$

If we use a significance level of 0.05 we see that $p_v > \alpha$ and then we can conclude that we don't have evidence in order to conclude that the mean is higher than 5.63, so then the claim makes sense.

3 0

3 years ago

Apr 17, 1:42:09 AM

SVEN [57.7K]

Answer:

(-1, 5)

Step-by-step explanation:

3 [x + y = 4]

3x + 3y = 12

- 3x + 7y = 32

-4y = -20

y = 5

x + 5 = 4

x = -1

3 0

2 years ago