Suppose that y=f(x) is an even function such that (2,−3) is a point on the graph of . Which of the following points belong to the graph of ?


a) (−3,−2)


b) (2,3)


c) (3,−2)


d) (−2,−3)


e) (−2,3)


f) None of the above

Answer: m = 1/2

Step-by-step explanation: To find the slope of the line, we would first put the equation in y = mx + b form to get y by itself on the left side.

So divide both sides by 2 to get y = 1/2x - 4.

Now the slope is the coefficient of the x term which is 1/2.

This is a positive slope.

2.5 inches steel wire

We can use an equation to find the answer. 750/300 = 2.5

Answer:

2.5 inches of steel wire are needed to make one spring.

Step-by-step explanation:

In order to answer this, we can set up a proportion (setting two fractions equal to each other) to solve for how many inches of steel wire are needed to make one spring.

We are given a ratio: 750 inches of steel wire are required to make 300 springs. Therefore, this is represented as:

\(\bullet \ \ \ \text{750 inches of steel wire : 300 springs}\)

This can be rewritten in fraction form:

\(\displaystyle \bullet \ \ \ \frac{\text{750 inches of steel wire}}{\text{300 springs}}\)

Therefore, we have our first proportion.

We want to make one spring, so we need to find how much steel is required to make one spring. Therefore, for our second fraction, the inches of steel wire is unknown. We can define this as x.

\(\bullet \ \ \ \text{x inches of steel wire}\)

Finally, our ratio can be written in the same manner as the previous ratio:

\(\bullet \ \ \ \text{x inches of steel wire : 1 spring}\)

This can be rewritten in fraction form:

\(\displaystyle \bullet \ \ \ \frac{\text{x inches of steel wire}}{\text{1 spring}}\)

Now, we need to set up our proportion. We do this by setting our two ratios equal to each other.

\(\displaystyle \bullet \ \ \ \frac{\text{750 inches of steel wire}}{\text{300 springs}} = \frac{\text{x inches of steel wire}}{\text{1 spring}}\)

To solve a proportion, we need to cross multiply. We can flip our fractions and solve for the reciprocal since there is not really a way to represent cross-multiplication.

\(\displaystyle \bullet \ \ \ \frac{\text{750 inches of steel wire}}{\text{300 springs}} = \frac{\text{1 spring}}{\text{x inches of steel}}\)

First, we can drop our labels/units.

\(\displaystyle \bullet \ \ \ \frac{750}{300} = \frac{1}{\text{x}}\)

Then, we can multiply across.

\(\displaystyle \bullet \ \ \ 750 = 300x\)

Finally, we can solve for x.

\(\displaystyle 750 = 300x\\\\\frac{750}{300}=\frac{300x}{300}\\\\2.5 = x\\\\x = 2.5\)

Therefore, to make one spring, exactly 2.5 inches of steel wire are needed.

Answer:

The test statistic for Norah's test is \(t = -2\)

Step-by-step explanation:

Norah is in charge of a quality control test that involves measuring the amounts in a sample of bottles to see if the sample mean amount is significantly different than 500 ml.

This means that at the null hypothesis we test if the sample mean is 500 ml, that is:

\(H_0: \mu = 500\)

At the alternate hypothesis, we test if it is differente than 500 ml, that is:

\(H_a: \mu \neq 500\)

The test statistic is:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

500 is tested at the null hypothesis:

This means that \(\mu = 500\)

She takes a random sample of 16 bottles and finds a mean amount of 497ml, and a sample standard deviation of 6ml.

This means that \(n = 16, X = 497, s = 6\)

Calculate the test statistic for Norah's test.

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{497 - 500}{\frac{6}{\sqrt{16}}}\)

\(t = -2\)

The test statistic for Norah's test is \(t = -2\)

Answer: -2

Step-by-step explanation: Khan

The score that is one and a half standard deviation is 182.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

\(z=\frac{x-\mu}{\sigma} \\\\where\ x\ is\ raw\ score, \mu\ is\ mean, \sigma\ is\ standard \ deviation\)

Given that:

μ = 140, σ = 28. For a z score of 1.5(one and a half):

\(1.5=\frac{x-140}{28} \\\\x-140=42\\\\x = 182\)

The score that is one and a half standard deviation is 182.

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The value(s) of x that satisfy the given solution is  (5, 7).

Power on both sides: (√4x-5)²-(2x-10)

2 Simplify using exponent power rule (a")=am

x²-4x-5-(2x-10) 2

Expand the expression using (a+b)

2-a2+2ab+

b2: 2-4x-5-(2x) 2-2×2×10+10²

Multiply the monomials: 2-4-5-(2) 2-40

+102 Calculate the power: 2-4-5-(2x) 2-40x+ 100

Simplify using exponent rule with same exponent

(ab)"a"-b" 2-4x-5-22-2-40x+100 Calculate the power: 2-4-5-4x-40+

100

equation: 2-4-5-4x²+40x-100-0 Combine like terms: -3x²+36-105-0

12r+35-0

Rearrange all nonzero terms to the left side of the Reduce the greatest common factor on both sides of the equation: -2+12-35-0 Multiply each term of the equation by -1: 2-

Find two integers: -7-5--12 1-7x (-5)=35

Rewrite the middle term: 2-7x-5x+35-0 Factor the first two terms and the last two terms respectively: (-7) -5(x-7)=0 Apply zero product property that at least one

Extract the common factor: (x-7)(x-5) =0

factor is zero: 2-7-0 or x-5-0 Rearrange unknown terms to the left side of the

equation: -7

Rearrange unknown terms to the left side

equation: =5

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Answer:

4

Step-by-step explanation:

208 ÷ 52 = 4

52 × 4 = 208

Hope this helped a little!

208/52

= 4

you could have simply cancelled out or even use a calculator

The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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Answer:

Step-by-step explanation:

45

Answer:

30

Step-by-step explanation:

The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the sine of angle 41°

sin 41° = 2.5/x {opposite/hypotenuse}

x = 2.5/sin 41° {cross multiplication}

x = 3.8106

Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

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Answer: 5/7 of the kids chose New York or L.A.

Step-by-step explanation:

All you need to do in this problem is add the fraction of people that chose New York and the fraction of people that chose L.A:

4/7 + 1/7 = 5/7

Answer:

x = -11

Step-by-step explanation:

7 - x = 18

+ x on both sides to cancel the negative one

7 = 18 + x

- 18 on both sides to get rid of the 18

solve:

7 - 18 = x

-11 = x

Answer:

collecting like terms

Step-by-step explanation:

step 1. Shift 7 to the right side

-x = 18 - 7

-x = 11

step 2. divide by -1 both sides

-x/-1 = 11/-1

x = -11

Answer:

correct choice is the last one

Step-by-step explanation:

let h = cost of 1 hamburger meal

let c = cost of 1 chicken nugget meal

5h + 6c = 39

9h + 2c = 35

Answer:

See below

Step-by-step explanation:

9 and 8.4 are less than 1 apart, so 9-8.4 must be less than 1. The actual difference is 9-8.4=0.6 which verifies that our answers are true since 0.6<1.

The function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4 is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

A function is said to be continuous if there are no breaks or jumps in the functions

Conditions for continuity of a function

Now, for the given function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4

We need to determine the interval of continuity, We proceed as follows.

Since f(x) = sin⁻¹x, x ≠ π/4 , we know that the minimum value of x is - 1 and its maximum value is 1.

So, x must lie in the interval (-1, 1) for x ≠ π/4,

Now, when x = π/4 f(x) = sinx. We know that x = π/4 lies in the interval (-1, 1).

But we know that f(x) = sinx at x = π/4. So, there is a removable discontinuity at x = π/4.

So, from the left, f(x) is continuous on the interval [-1, π/4) and  from the right, f(x) is continuous on the interval (π/4, 1]

So, combining both intervals, we have f(x) is continous on the interval [-1, π/4) ∪ (π/4, 1] and since f(x) = sinx at x = π/4, there is a removable discontinuity at x = π/4

So, the function f(x) is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

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Using point-slope form, the equation is \(\boxed{y-2=2(x-1)}\).

Answer:

875 books

Step-by-step explanation:

1st machine 700 books/40 hours = 17.5 books/hr

2nd machine printed 2x or 35 books/hr

25 hours x 35 books/hr = 875 books

9514 1404 393

Answer:

  see beow

Step-by-step explanation:

When x=0, y=-5. The y-intercept is (0, -5).

When y=0, x-5=0, so x=5. The x-intercept is (5, 0).

Plot these two points and draw the line through them.

Answer:

16. 12√5

17. 3 2/2 as it actually equal 4!

Answer:

A=pq

2

Step-by-step explanation:

A=35

Answer:

70KM

Step-by-step explanation:

AREA MEANS MULTIPLY SO 10X7=70

Answer:

A) 6 < x < 12

Step-by-step explanation:

Answer:

Answer= -2x-6

Step-by-step explanation:

Rewrite and remove parenthesis

3x-5-5x-1

collect like terms, then calculate

-2x-6

Answer:

B. -2x - 6

Step-by-step explanation:

(3x - 5) - (5x + 1)

3x - 5 + 5x - 1

Then rearrange into the standard form

3x - 5x + 5 - 1

- 2x + 6

i tried to make an explanation but i am intellectually lacking and/or challenge, so as a result it doesnt match up with my result

Answer:

5 m

Step-by-step explanation:

Answer: 4x+1

Step-by-step explanation:

(f+g)(x)=f(x)+g(x)=(3x-1)+(x+2)=3x-1+x+2=4x+1

Trapezoid Area =

[ ( Sum of the rules ) × ( height ) ] ÷ 2

_________________________________

Area = [ ( 2 + 3 ) × 3 ] ÷ 2

Area = [ 5 × 3 ] ÷ 2

Area = 15 ÷ 2

Area = 7.5 m^2

Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.

Step-by-step explanation:

Answer:

The slope is -3/8

Step-by-step explanation:

(6,−6);(−18,3)

(x1,y1)=(6,−6)

(x2,y2)=(−18,3)

Use the slope formula:

m= y2−y1 /x2−x1

3−−6 /−18−6  

9 /−24

−3 /8

Answer:

4x-2

Step-by-step explanation:

6x-6-2x+4

=4x-2

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

C. y = 66

Step-by-step explanation:

this is a equal triangle so you know you have to find out what that one angle is to get the rest

180 - 114 = 66