MATHEMATICS HIGH SCHOOL

What are the solutions to the quadratic equation 4x2 = 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:

x = ±4

Step-by-step explanation:

4x^2 = 64

Divide each by 4

4x^2 /4= 64/4

x^2 = 16

Take the square root of each side

sqrt(x^2) = ±sqrt(16)

x = ±4

Answer 2

Answer:

Answer:

$\boxed{\boxed{x=\pm 4}}$

Step-by-step explanation:

$4x^2 = 64$

Divide both sides by 4.

$(4x^2)/4 = 64/4$

Simplify.

$x^2 =16$

Take the square root on both sides.

$√(x^2 ) =\pm √(16)$

Simplify.

$x=\pm 4$

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Which logarithmic function has x = 5 as its vertical asymptote and (6, 0) as the x-intercept? (x is the variable.). The logarithmic function is f(x) = log ?

Answers

Answer: f ( x ) = log ( x - 5 )

Explanation:

1) Take g(x) = log (x) as the parent function

2) The horizontal asymptote of g(x) is x = 0, and the y-intercept is (1,0).

3) Then, translating the asymptote to x = 5, and the y-intercept to (6,0), means that the graph of the parent function is being shifted 5 units to the right.

4) The rule is that the translation of the function g(x) a constant value to the right, say it is k, results in the function f(x) = g(x - k).

5) Therefore, the logarithmic function searched is f(x) = g(x - 5) = log (x - 5), and that is the answer.

6) You can prove that log (x - 5) meets the two conditions:

i) $\lim_(x \to \n5+) log(x-5) = - \infty$ , which means x = 5 is a vertical asymptote

ii) f(6) = log (6 - 5) = log (1) = 0 ⇒ point (6,0) is the x-intercept

The parent function:
f ( x ) = log x
Domain of a new function: x ∈ ( 5, +∞ )
Answer: f ( x ) = log ( x - 5 )

In Juneau, Alaska, the 30-year annual snowfall average is 86.7 inches with a standard deviation of 40.4 inches. The last four years saw an average annual snowfall of 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Hia performs a hypothesis test on this data to determine if the next 30-year norm will have a different average if the trend from the last four years continues. She uses a significance level of 5%. Which of the following is a conclusion that she may make?a) The z-statistic is 1.44, so the null hypothesis cannot be rejected.
b) he z-statistic is 1.68, so the null hypothesis cannot be rejected.
c) The z-statistic is 1.85, so the null hypothesis should be rejected.
d) The z-statistic is 4.6, so the null hypothesis should be rejected.

Answers

The expected value of the amount of average snowfall for over 30 years is 86.7 inches with a standard deviation of 40.4 inches. To verify if this particular trend continues, we must check the significance value of the amount snowfall for the past four years. Given that the snowfall for past years are as follows: 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Thus the mean of the sample would be: (115.7 + 62.9 + 168.5 + 135.7)/4 = 120.7 inches. To compute for the z-score, we have z-score = (x – μ) / (σ / √n) where x is the computed/measured value, μ is the expected mean, σ is the standard deviation, and n is the number of samples. Using the information we have, z-score (z) = (120.7 - 86.7) / (40.4/ √4) = 1.68 In order to reject the null hyptohesis our probability value must be less than the significance level of 5%. For our case, since z = 1.68, P-value = 0.093 > 0.05. Therefore, the answer is B.

Answer:

its B

Step-by-step explanation:

Mrs. Yan buys 4 red tulips and 5 yellow tulips a : what fraction of the tulip are red? B: what fraction of the tulip are yellow

Answers

First of all do 4+5=9
Then you know that 4/9 are red and 5/9 are yellow.
a) 4/9
b) 5/9

you are saving $30 each month. you have a goal to accumulate $700 in savings. how long will it take you?

Answers

$700 ÷ $30 = approximately 23 months

It will take you 23 1/3 months or rounding 23 months the way you get the answer is you is you divide the goal over the amount of money each month 700/30.

A container has peppermint gum and spearmint gum. There are 18 pieces of peppermint gum in the container and the ratio of peppermint gum to spearmint gum is 2 : 3. Find the number of pieces of spearmint gum in the container.I WILL GIVE YOU BRAINLIEST PLEASE HELP

Answers

The total number of spearmint gums will be 27

What are algebraic expressions?

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that a container has peppermint gum and spearmint gum. There are 18 pieces of peppermint gum in the container and the ratio of peppermint gum to spearmint gum is 2 : 3.

Let the number of spearmint gum be {x}. So, we can write -

2/3 = 18/x

{x} = (18 x 3)/2

{x} = 27

Therefore, the total number of spearmint gums will be 27.

To solve more questions on algebraic expressions, visit the link below -

brainly.com/question/1041084

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Answer:

27 is your answer

Step-by-step explanation:

if 2;3 is your ratio and u have 18 peppermint gum then divide 18 by 2 and u get 9 then u multiply 9 by 3 and u get 27