All categories

3 years ago

Which of the following are solutions to the equation below?

Mathematics

1 answer:

anastassius [24]3 years ago

4 0

Answer:

C and F

Step-by-step explanation:

Given

(3x - 5)² = 19 ( take the square root of both sides )

3x - 5 = ± $\sqrt{19}$ ← note plus or minus

Add 5 to both sides

3x = ± $\sqrt{19}$ + 5 ( divide both sides by 3 )

x = ± $\frac{\sqrt{\sqrt{19}+5 } }{3}$

Separating the solutions

x = $\frac{\sqrt{19}+5 }{3}$ → C

x = $\frac{-\sqrt{19}+5 }{3}$ → F

You might be interested in

Write the numbers -2.1, -1.8, -2.5 and -2.7 from greatest to least.

Fiesta28 [93]

Answer:

-1.8, -2.1, -2.5, -2.7

Step-by-step explanation:

the bigger the negative number, the smaller it is

5 0

3 years ago

Read 2 more answers

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi

Luden [163]

Answer:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

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

$p_v =P(z>1.768)=0.039$

Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ represent the value that we want to test

$\alpha$ 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 mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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:

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

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

$p_v =P(z>1.768)=0.039$

6 0

3 years ago

What’s the equation of line

ivann1987 [24]

Answer:

y=-x+9

Step-by-step explanation:

5 0

3 years ago

How do you simplify 1/5(10x-25)

kozerog [31]

Answer:2x-5

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

1) What radius of a circle is required to inscribe an equilateral triangle with an area of 15.588 in2 and an altitude of 5.196 i

Andrej [43]

We know that
the distance from the centroid of the triangle to one of the vertices is the radius of the circle <span>required to inscribe an equilateral triangle.

[distance </span>centroid of the triangle to one of the vertices]=(2/3)*h
h=the <span>altitude of the equilateral triangle-----> 5.196 in
so
</span>[distance centroid of the triangle to one of the vertices]=(2/3)*5.196
[distance centroid of the triangle to one of the vertices]=3.464 in----> 3.5 in

the radius is equal to the distance of the centroid of the triangle to one of the vertices
hence
the radius is 3.5 in

the answer is
the radius is 3.5 in

8 0

3 years ago

Read 2 more answers