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4 years ago

Calculate 7x +5 - 3x - 7 = 10

Mathematics

2 answers:

Tatiana [17]4 years ago

7 0

7x +5 - 3x - 7 = 10 4x-2=10 4x=10+2 4x=12 X=12÷4 X= 3

vredina [299]4 years ago

6 0

You answer is 3 and here's why...

7x + 5 - 3x - 7 = 10

First you must collect like terms

And that gives us

4x - 2 = 10

Next you must simplify by removing additives

4x - 2 + 2 = 10 + 2

4x = 12

Now you must divide

4x/4 = 12/4

x = 3

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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th

Naddika [18.5K]

Answer:

The rocket will hit the ground after about 8.20 seconds.

Step-by-step explanation:

The height of the rocket y, in feet, x seconds after launch is modeled by the equation:

$y=-16x^2+121x+83$

We want to find the time at which the rocket will hit the ground.

If it hits the ground, the height of the rocket y will be 0. Thus:

$0=-16x^2+121x+83$

We can solve for x. Factoring (if possible at all) or completing the square can be tedious, so we can use the quadratic formula:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = -16, b = 121, and c = 83. Substitute:

$\displaystyle x=\frac{-(121)\pm\sqrt{(121)^2-4(-16)(83)}}{2(-16)}$

Simplify:

$\displaystyle x=\frac{-121\pm\sqrt{19953}}{-32}$

Divide everything by -1 and simplify the square root. The plus/minus will remain unchanged:

$\displaystyle x=\frac{121\pm3\sqrt{2217}}{32}$

Therefore, our two solutions are:

$\displaystyle x=\frac{121+3\sqrt{2217}}{32}\approx 8.20\text{ or } x=\frac{121-3\sqrt{2217}}{32}\approx -0.63$

Since time cannot be negative, we can ignore the second solution.

Therefore, the rocket will hit the ground after about 8.20 seconds.

7 0

3 years ago

What is the length of SR? 18 units 9 units 12 units 15 units

Serjik [45]

Answer:

Step-by-step explanation:

RT = sqrt(20^2 - 16^2)

RT = sqrt(400 - 256)

RT = sqrt(144)

RT = 12

SR/ST= QR/QT

SR/12 = 20/16

SR = 12 x 20 / 16

SR = 240/16

SR = 15

answer is C.

15 Units

7 0

4 years ago

A data set lists earthquake depths. The summary statistics are

irinina [24]

Answer:

Step-by-step explanation:

The summary of the given statistics data include:

sample size n = 400

sample mean $\overline x$ = 6.86

standard deviation = 4.37

Level of significance ∝ = 0.01

Population Mean $\mu$ = 6.00

Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

To start with the hypothesis;

The null and the alternative hypothesis can be computed as :

$H_o: \mu = 6.00 \\ \\ H_1 : \mu \neq 6.00$

The test statistics for this two tailed test can be computed as:

$z= \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt {n}}}$

$z= \dfrac{6.86 - 6.00}{\dfrac{4.37}{\sqrt {400}}}$

$z= \dfrac{0.86}{\dfrac{4.37}{20}}$

z = 3.936

degree of freedom = n - 1

degree of freedom = 400 - 1

degree of freedom = 399

At the level of significance ∝ = 0.01

P -value = 2 × (z < 3.936) since it is a two tailed test

P -value = 2 × ( 1 - P(z ≤ 3.936)

P -value = 2 × ( 1 -0.9999)

P -value = 2 × ( 0.0001)

P -value = 0.0002

Since the P-value is less than level of significance , we reject $H_o$ at level of significance 0.01

Conclusion: There is sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 5.00 km.

7 0

3 years ago

QUESTION 4 Factorise fully: 4.1.1 12x² – x - 6

vaieri [72.5K]

Answer:

y = (4x - 3)(3x + 2)

Step-by-step explanation:

Factorization is the process of taking like terms out of number such that one can rewrite an expression by its factors, or as the products of serval smaller expressions.

The first step to factoring an equation is to rewrite the linear term as the sum or difference of two other linear terms. One must do this in such as way that it shares a common factor with one of the other terms in the expression.

$12x^2 -x - 6$