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3 years ago

4. Which of the following is a true statement?

Mathematics

2 answers:

Anna [14]3 years ago

8 0

B. Is the true statement

umka21 [38]3 years ago

3 0

Answer: B) -7(4x - 8) = -28x + 56

Step-by-Step Explanation:

=> -7(4x - 8) = -28x + 56
On opening the brackets on L.H.S,
= -28x + 56 = -28x + 56
=> L.H.S = R.H.S

Therefore this is a True Statement

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The standard form of the equation of a parabola is y= x2 - 6x + 14.

Bas_tet [7]

<h3><u>Option C</u></h3><h3><u>The vertex form of the equation is:</u></h3>

$y = (x - 3)^2 + 5$

<em><u>Solution:</u></em>

<em><u>The vertex form of equation is given as:</u></em>

$y = a(x- h)^2 + k$

Where, (h, k) is the vertex

Given that,

$y = x^2 - 6x + 14$

We have to find the vertex form of equation

Step 1:

Complete the square for $x^2 - 6x + 14$

$\text{ Use the form } ax^2 + bx + c \text{ to find values of a, b, c }$

a = 1

b = -6

c = 14

Consider the vertex form of a parabola.

$a(x + d)^2 + e ----- eqn 1$

Substitute the values of a and b into following:

$d = \frac{b}{2a}\\\\d = \frac{-6}{2 \times 1}\\\\d = -3$

Find the value of "e" using following formula:

$e = c - \frac{b^2}{4a}\\\\e = 14 - \frac{(-6)^2 }{4 \times 1}\\\\e = 14 - 9\\\\e = 5$

Substitute the values of a, d, e in eqn 1

$y = 1(x -3)^2 + 5\\\\y = (x - 3)^2 + 5$

Thus vertex form form is found. Option C is correct

3 0

3 years ago

About 78% of the US, population claims that they visit the dentist at least once a year. simple random sample of 200 people is s

Blababa [14]

Answer:

D) 0.78, 0.029

Step-by-step explanation:

Central Limit Theorem:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

About 78% of the US, population claims that they visit the dentist at least once a year.

This means that $p = 0.78$

Random sample of 200 people:

This means that $n = 200$

Mean and standard deviation of the sampling distribution:

By the Central Limit Theorem

Mean $\mu = 0.78$

Standard deviation $s = \sqrt{\frac{0.78*0.22}{200}} = 0.029$

So the correct answer is given by option D.

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3 years ago

PLS HELP LOOK AT PIC

zepelin [54]

31 trust In me I learned this last week

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4 years ago

A student worked on the problem 35.8 x 9.3. The student's answer was 3,329.4. Use estimation to check whether this answer is rea

melomori [17]

The answer is not reasonable.

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3 years ago

Why the order of the coordinates does not matter when calculating length

Rudiy27

The formula for calculating length is:
$\sqrt{ (x_b-x_a)^{2} + (y_b-y_a)^{2} }$

We can also write $x_a - x_b$ or $y_a - y_b$
Why it does not matter?
Let's assume we have 2 numbers, a and b.
When we perform a subtraction:
$a-b$ , we get another number $c$
When we perform another subtraction:
$b-a$ , we get a number $-c$

When we raise $c$ or $-c$ to the power of 2, the result is the same, $c^{2}$ .

4 0

4 years ago