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Harlamova29_29 [7]
3 years ago
15

What are the solutions of the quadratic equation 49x^2=9?

Mathematics
1 answer:
Flauer [41]3 years ago
5 0
<span>Simplifying 49x^2 + -9 = 0
Reorder the terms: -9 + 49x^2 = 0
Solving -9 + 49x^2 = 0 Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9' to each side of the equation. -9 + 9 + 49x^2 = 0 + 9
Combine like terms: -9 + 9 = 0 0 + 49x^2 = 0 + 9 49x^2 = 0 + 9
Combine like terms: 0 + 9 = 9 49x^2 = 9
Divide each side by '49'. x^2 = 0.1836734694
Simplifying x^2 = 0.1836734694
Take the square root of each side: x = {-0.428571429, 0.428571429}

hope this helps!!</span>
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The number of new cars purchased in a city can be modeled by the equation C=20t to the 2nd power, where C is the number of new c
Allisa [31]

Answer:

1998 + 5\sqrt{30}

Step-by-step explanation:

Set up the equation:

Since C(t) gives the number of cars purchased in the t-th year after 1998, then make the number of cars equal to 15 000 and solve for t - the year:

20t^2 = 15000

t^2 = 750

t = \sqrt{750} = \sqrt{10} \cdot \sqrt{25} \cdot \sqrt{3} = 5\sqrt{30}

The year will be simply 1998 + 5 \sqrt{30}

4 0
3 years ago
calculate the power of the pump which can lift 400kg of water to be stored in a water tank at a height of 19m and 40s (take g=10
iren [92.7K]
Hi, here it is !
I hope this help...

5 0
2 years ago
Hypothesis Testing for Means with Small Samples
Scorpion4ik [409]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: volume of root beer in a Windsor Bottling Company can.

A sample of n=24 cans was taken and their contents measured, resulting:

X[bar]= 11.4 oz

S= 0.62 oz

Assuming that the variable has a normal distribution X~N(μ;σ²), the parameter of interest is the average contents of the root beer cans of the Windsor Bottling Company (μ)

The claim is that the population mean content of the cans is different from 12 oz, symbolically: μ ≠ 12

The statistical hypothesis (Null and alternative) have to be complementary, exhaustive and mutually exclusive. The null hypothesis is the "no change" hypothesis and always carries the "=" sign.

If the claim is μ ≠ 12, its complement is μ = 12, the expression carrying the "=" sign will be the null hypothesis and its complement will be the alternative hypothesis:

H₀: μ = 12

H₁: μ ≠ 12

α: 0.05

To test the population mean of this normal population, you have to apply a one sample t-test, with statistic:

t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}

t_{H_0}= \frac{11.4-12}{\frac{0.62}{\sqrt{24} } } = -4.74

This test is two-tailed, using the critical value approach, you have to determine two rejection regions. Meaning, you'll reject the null hypothesis to small values of the statistic or to high values of the statistic.

t_{n-1;\alpha /2}= t_{23;0.025}= -2.069

t_{n-1;1-\alpha /2}= t_{23;0.975}= 2.069

The decision rule is:

If t_{H_0} ≤ -2.069 or if t_{H_0} ≥ 2.069, then you reject the null hypothesis.

If -2.069 < t_{H_0} < 2.069, then you do not reject the null hypothesis.

The value is less than the left critical value, the decision is to reject the null hypothesis.

Then you can say that with a 5% significance level, there is significant evidence to reject the null hypothesis, then the average amount of root beer of the Windsor Bottling Company is different from 12 oz, this means that the claim about the amount of root beer in the cans is correct.

I hope it helps!

6 0
3 years ago
Which of the following statements explains why 0.8 is or is not a rational number?
noname [10]

Answer:

a

Step-by-step explanation:

its 8 bc when u put it under 9 it repeats

7 0
3 years ago
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dsp73

Answer:

by doing it the same way you did with the first one.

Step-by-step explanation:

4 0
2 years ago
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