MATHEMATICS HIGH SCHOOL

What are the solutions to the quadratic equation 4x^2 = 64? A. x = −16 and x = 16
B. x = −8 and x = 8
C. x = −4 and x = 4
D. x = −2 and x = 2

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Given

4x² = 64 ( divide both sides by 4 )

x² = 16 ( take the square root of both sides )

x = ± $√(16)$ = ± 4

Solutions are x = - 4 and x = 4 → C

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The function t(x) = x + 6 determines how many cans of soup a food truck needs to stock, where x is the number of shifts the crew is going to work in the truck. The crew uses c(t(x)) to find the amount of money to spend on soup. The function c(x) = 2x + 4. Solve for how much money must be spent when the crew is going to work 4 shifts.(A. 24; B. 28; C. 30; D. 34)

The following question references the novel Jane Eyre by Charlotte Bronte.How does Jane gain financial independence?
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c. She write a book that is published
b. Parent's from the school reward her for her work
Please select the best answer from the choices provided

Answers

The answer is:

A: Her uncle leaves her 20,000 pounds

Her uncle leaves her 20 thousand pounds yet she gives 15 thousand pounds to her cousins the Rivers.

115% of what number is 120

Answers

115% is the same as 1.15
some number = x

115% of some number is 120
1.15 of x is 120
1.15 * x = 120

x = 104.3478
x ≈ 104.3

Which of the following arguments correctly justifies the second step of the flow proof of the triangle angle sum theorem below

Answers

We need to see the second step of the proof, so we know what needs to be justified. It would also be nice to see the list of answer choices. I'll never understand how someone who can't answer the question and has to ask someone else can then go ahead and decide that the person helping him only needs to see parts of the question.

Answer:

I JUST TOOK THE TEST THE ANSER IS D.

Alternate interior angles theorem

Step-by-step explanation:

4.5.11Mohamed wrote the paragraph proof to show that ADEG AEFG. What mistake did he make?
ADEG and AEFG are right triangles.
The figure shows DE = EF, AND
EG EG by the Reflexive Property.
Therefore, by the HL theorem,
ADEG AEFG
G
X Х
Choose the correct answer below.
O A. The two triangles are congruent by SAS, not the HL Theorem.
O B. In AEFG, EF is a leg and in ADEG, DE is the hypotenuse, so they cannot be corresponding sides.
O C. The two triangles are congruent by SSS, not the HL Theorem.
OD. In AEFG, EG is a leg, and in ADEG, EG is the hypotenuse, so they cannot be corresponding sides.

Answers

The two triangles are congruent by SAS, not the HL theorem. Therefore, the correct answer is option A.

Triangle DEG and triangle EFG are right triangles.

The figure shows DE=EF (Given)

EG=EG by the reflexive property.

Therefore, by the HL theorem, Triangle DEG and triangle EFG are congruent.

Here, Mohamed stated postulate wrong.

By SAS postulate, Triangle DEG and triangle EFG are congruent.

Therefore, the correct answer is option A.

To learn more about the congruent theorem visit:

brainly.com/question/24033497.

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Answer:B?

Step-by-step explanation:

Publishing scientific papers online is fast, and the papers can be long. Publishing in a paper journal means that the paper will live forever in libraries. The British Medical Journal combines the two; it prints short and reasonable versions, with longer versions available online. Is this OK with authors? The journal asked about a random sample of 104 of its recent authors' several questions. One question was, "Should the journal continue using this system?"
In the sample, 72 said "yes."
(a) do the data give good evidence that more than two-thirds (67%) of authors support continuing this system? carry out an appropriate test to help answer this question.
(b) interpret the p-values from your test in the context of the problem.

Answers

Answer:

There is no significant evidence that more than two-thirds (67%) of authors support continuing this system.

Step-by-step explanation:

Let p be the proportion of authors who support continuing the system

Then hypotheses are:

$H_(0)$ : p=0.67

$H_(a)$ : p>0.67

To calculate the test statistic:

z= $\frac{p(s)-p}{\sqrt{(p*(1-p))/(N) } }$ where

p(s) is the sample proportion of authors who support the publishing system ( $(72)/(104)$ ≈0.692)

p is the proportion assumed under null hypothesis. (0.67)

N is the sample size (104)

Then z= $\frac{0.692-0.67}{\sqrt{(0.67*0.33)/(104) } }$ ≈ 0.477

p-value of test statistic is ≈0.317

Assuming a significance level 0.05, since 0.317>0.05 we fail to reject the null hypothesis.

p-value 0.317 is the probability that the sample is drawn from the distribution assumed under null hypothesis, that is where the proportion of authors supporting the new publishing system is at most 0.67

Final answer:

A hypothesis test for a proportion is used to determine whether more than two-thirds of authors support continuing the system. The p-value associated with the test is less than 0.0001, indicating that the data provide good evidence in favor of the alternative hypothesis. Therefore, the majority of authors support continuing the system.

Explanation:

To determine whether the data provides evidence that more than two-thirds (67%) of authors support continuing the system, we can use a hypothesis test for a proportion. We will use a significance level of 0.05.

Let's set up our hypotheses:

Null hypothesis (H0): p ≤ 0.67 (less than or equal to two-thirds support)
Alternative hypothesis (Ha): p > 0.67 (more than two-thirds support)

Using the normal approximation to the binomial, we can calculate the test statistic and p-value. With a sample size of 104 and 72 authors in favor, the test statistic is:

z = (72 - 0.67 * 104) / sqrt(0.67 * (1 - 0.67) * 104) ≈ 3.79

The p-value associated with a z-score of 3.79 is less than 0.0001. Since this p-value is less than 0.05, we reject the null hypothesis.

Therefore, the data provide good evidence that more than two-thirds of authors support continuing the system.

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Simplify the expression 10-4x(6+5-1) divided by 8+7

Answers

Simple,

writing out the problem...

$(10-4x(6+5-1))/(15)$

Simplify it...

-4x(6+5-1)

-4x(11-1)

-4x(10)

-40x

Making it look like...

$(10-40x)/(15)$

Cancel out the common factors...

Thus making the answer:

$- (2(4x-1))/(3)$ .

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If a = b + 2, then (b - a)⁴ = ?

A spinner with 6 equally sized slices has 1 blue slice, 2 red slices, and 3 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a blue or red slice? Write your answer as a fraction in simplest form.