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jeyben [28]
3 years ago
13

1/2x + 6= 3x - 4 Solve the system of equations

Mathematics
1 answer:
shepuryov [24]3 years ago
5 0
1.Combine multiplied terms into a single fraction

2. Multiply by 1

3. Subtract 6 from both sides of the equation

4.Simplify

5.Subtract 3x from both sides of the equation

6.Simplify

7.Multiply all terms by the same value to eliminate fraction denominators

8.Simplify

9.Divide both sides of the equation by the same term

10.Simplify

Solution:x=4
You might be interested in
What is the product in lowest terms? 8/15 x -3/10
Monica [59]
-24/150
-12/75
-4/25

-4/25 is the answer
8 0
3 years ago
D • (-4) = 32 solve for d
RSB [31]

Answer:

d = -8

Step-by-step explanation:

Isolate the variable, d. Note the equal sign, what you do to one side, you do to the other. Divide -4 from both sides of the equation:

d * -4 = 32\\\frac{d * -4}{-4} = \frac{32}{-4}\\d = \frac{32}{-4}\\d = -8

d = -8 is your answer.

~

7 0
2 years ago
Read 2 more answers
In a clinical study of an allergy drug, 108 of the 200 subjects reported experiencing significant relief from their symptoms. Te
DochEvi [55]

Answer:

The decision is to not reject the null hypothesis.

At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50% (P-value = 0.1443).

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion of all those using the drug that experience relief is significantly higher than 50%.

Then, the null and alternative hypothesis are:

H_0: \pi=0.5\\\\H_a:\pi>0.5

The significance level is 0.01.

The sample has a size n=200.

The sample proportion is p=0.54.

p=X/n=108/200=0.54

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035

Then, we can calculate the z-statistic as:

z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.54-0.5-0.5/200}{0.035}=\dfrac{0.038}{0.035}=1.061

This test is a right-tailed test, so the P-value for this test is calculated as:

\text{P-value}=P(z>1.061)=0.1443

As the P-value (0.1443) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50%.

6 0
4 years ago
Select the correct answer.
fenix001 [56]

Answer:

B

Step-by-step explanation:

substitute

6+4=10

12-3=9

4-9=-5

7 0
2 years ago
Which of the following is equivalent to tan2θcos(2θ) for all values of θ for which tan2θcos(2θ) is defined?
Aloiza [94]

Answer:

2sin²θ - tan²θ

Step-by-step explanation:

Given

tan²θcos(2θ)

Required

Simplify

We start by simplifying cos(2θ)

cos(2θ) = cos(θ+θ)

From Cosine formula

cos(A+A) = cosAcosA - sinAsinA

cos(A+A) = cos²A - sin²A

By comparison

cos(2θ) = cos(θ+θ)

cos(2θ) = cos²θ - sin²θ ----- equation 1

Recall that cos²θ + sin²θ = 1

Make sin²θ the subject of formula

sin²θ = 1 - cos²θ

Substitute sin²θ = 1 - cos²θ in equation 1

cos(2θ) = cos²θ - (1 - cos²θ)

cos(2θ) = cos²θ - 1 +cos²θ

cos(2θ) = cos²θ + cos²θ - 1

cos(2θ) = 2cos²θ - 1

Substitute 2cos²θ - 1 for cos(2θ) in the given question

tan²θcos(2θ) becomes

tan²θ(2cos²θ - 1)

Open brackets

2cos²θtan²θ - tan²θ

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

Simplify tan²θ

tan²θ = (tanθ)²

Recall that tanθ =  sinθ/cosθ

So, we have

tan²θ = (sinθ/cosθ)²

tan²θ = sin²θ/cos²θ

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

Substitute sin²θ/cos²θ for tan²θ

2cos²θtan²θ - tan²θ becomes

2cos²θ(sin²θ/cos²θ) - tan²θ

Open bracket (cos²θ will cancel out cos²θ) to give

2(sin²θ) - tan²θ

2sin²θ - tan²θ

Hence, the simplification of tan²θcos(2θ) is 2sin²θ - tan²θ

Option E is correct

7 0
3 years ago
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