Simple Math Range and domain help

Answer:

f(x)= x + 3

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

[tex]n(J \cap K)=n(J)+n(K)-n(J \cup K) \\ \\ =255+186-429 \\ \\ =12[/tex]

Answer:

(2,-2)

Step-by-step explanation:

The function g(x) reflected along x-axis is |x| + 5.

A modulus function always outputs positive values, hence the outputs are greater than or equal to zero,f(x) ≥ 0.

When a graph is reflected along x-axis f(x) becomes -f(x).

∴ The function f(x) = |x| - 5 when reflected along x-axis it will become

f(x) = - (|x| - 5).

f(x) = - |x| + 5.

Or

g(x) = - |x| + 5.

Graph of g(x) is shown in the image attached.

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The scale factor of the drawing is 1 / 200 or 0.005.

Scale factor is used to scale shapes in different dimensions.

In other words, Scale factor is described as the number or the conversion factor which is used to change the size of a figure without affecting its shape.

Therefore, scale factor can be represented mathematically as follows:

Scale factor = dimensions of the new shape ÷ dimensions of the original shape.

Hence he uses the scale 10 millimetres equals to 2 meters.

We have to convert metres to millimetres to get the scale.

10millimetres = 2meters

Therefore,

1 meter  =  1000 millimetres.

2 meters = ?

cross multiply

length = 2 × 1000 = 2000 millimetres

Therefore, the scale factor of the drawing is as follows:

scale factor = 10 / 2000

scale factor = 1 / 200

scale factor = 0.005

Therefore, the scale factor of the drawing is 1 / 200 or 0.005.

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Answer:

1. He get get to school 10 minutes faster riding by hisself than ridding with Christina.

Step-by-step explanation:

Christina is 22 minutes - Luis 12 minutes = 10 minutes.

Answer:

a = 115°

Step-by-step explanation:

Two angles are supplementary angles because they make a straight line.

The sum of two angles is equal to 180° then to find the measure of the missing angle we simply subtract 65 from 180:

180 - 65 = 115

Answer:

670.05

Step-by-step explanation:

Rounding to the nearest dollar, Serina will have $515 at the end of five years. Therefore, correct option is A.

To calculate the amount Serina will have at the end of five years, we can use the formula for compound interest:

A = [tex]P(1 + r)^{(nt)[/tex]

Where:

A = the future value of the investment/loan, including interest

P = the principal amount (initial deposit)

r = the annual interest rate (in decimal form)

n = the number of times that interest is compounded per year

t = the number of years the money is invested for

In this case, Serina deposits $500 with an annual interest rate of 5%, compounded semiannually (n = 2), and keeps the money in her account for three years (t = 3).

Plugging in the values, we get:

A = 500(1 + 0.05)⁶

A = 500(1.005)⁶

A ≈ 500(1.030)

A ≈ $515

Therefore, correct option is A.

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Answer:

 3x + 7

Step-by-step explanation:

Hope this helps you :)

Answer:

Did you already get the answer?

Step-by-step explanation:

The solutions of given equations are x = 0,b = -3,y = 2 and c = 5 respectively.

A formula known as an equation uses the same sign to denote the equality of two expressions.

The equation must be constrained by =,< or >.

Given the equations,

01) x/4 + 2x/3 - 4 = - 4 + 5x/2

(3x + 8x)/12 = 5x/2

x = 0

02) 3.2b + 10 = -1.7b - 4.7

2.2b + 1.7b = -4.7 - 10

b = -3

03) 6.6y + y + 6.5 = y - 6.7

5.5y = -6.7 - 6.5

y = 2

04) 2c - 7c + 8 = -17

-5c = -25

c = 5

Hence "The solutions of given equations are x = 0,b = -3,y = 2 and c = 5 respectively".

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The side lengths could be used to create a scale drawing of the field is 6600 yard².

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

Given:

A lacrosse field is rectangular with a length of 110 yards and a width of 60 yards.

According to given question we have

We know that

Area of rectangle= Length × width

Area of rectangle= 110 × 60

Area of rectangle= 6600 yard².

Scale ratio can be 1:55

Therefore, the side lengths could be used to create a scale drawing of the field is 6600 yard².

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The certificate will be worth of  $11534.9 on Ruth's 19th birthday.

Compound Interest is calculated using the formula.

[tex]Amount=P*(1+\frac{r}{n} )^{nt}[/tex]

where , P=principal

r = rate of interest

n= number of times interest is compounded

t = no of years

In the given question ;

Principal = $1500

n=1      ...(as it is compounded annually)

t= 18 years ...(as on 19th birthday Ruth will complete 18 years)

r=12%=0.12

Substituting the values of P,n,t,r in the formula we get,

[tex]Amount=P*(1+\frac{r}{n} )^{nt}[/tex]

[tex]=1500*(1+\frac{0.12}{1} )^{1*18}[/tex]

On solving further we get

=[tex]1500*(1.12)^{18}[/tex]

=1500*7.6899

=11534.85

Therefore , On Ruth's 19th birthday the certificate will be of worth $11534.9  .

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Answer:

The graph of  [tex]y=\sqrt{4x+16}+5[/tex]  is the graph of [tex]y=\sqrt{x}[/tex]  translated 4 units left, stretched horizontally by a factor of 1/4, and translated 5 units up.

Step-by-step explanation:

Transformations

[tex]\textsf{For }a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

Given function

[tex]y=\sqrt{4x+16}+5[/tex]

Parent function

Parent functions are the simplest form of a given family of functions.

[tex]y=\sqrt{x}[/tex]

The graph of the parent function is related to the graph of the given function by a series of transformations.  To determine the series of transformations, work out the steps of how to go from the parent function to the given function.

Factor the expression under the square root sign:

[tex]y=\sqrt{4(x+4)}+5[/tex]

Transformations

Parent function:

[tex]f(x)=\sqrt{x}[/tex]

Translated 4 units left:

[tex]f(x+4)=\sqrt{x+4}[/tex]

Horizontally stretched by a factor of 1/4 (compressed by a factor of 4):

[tex]\begin{aligned}f(4(x+4)) & =\sqrt{4(x+4)}\\ & = \sqrt{4x+16} \end{aligned}[/tex]

Translated 5 units up:

[tex]f(4x+16)+5=\sqrt{4x+16}+5[/tex]

Therefore, the graph of  [tex]y=\sqrt{4x+16}+5[/tex]  is the graph of [tex]y=\sqrt{x}[/tex]  translated 4 units left, stretched horizontally by a factor of 1/4, and translated 5 units up.

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Answer:

Yes

Step-by-step explanation:

true, 3:7 is a ratio and is equal to 3/7

The values given in standard form are 8.59 and 7.003

The standard form of a number is a way of writing the number in a form that follows certain rules. Any number that has exponents and decimals is said to be a standard notation.

Given the following statements

eight and fifty-nine hundredths

8 + 59/100

8 + 0.59

8.59

For the expression seven and three thousandths

7 + 3/1000

7 + 0.003

7.003

Hence the values given in standard form are 8.59 and 7.003

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The consecutive odd numbers that sum up to 321 are 105, 107 and 109.

The sum of three consecutive odd integers is 321.

Odd numbers are numbers that when divided by 2 produces a remainder.

let

x = first odd numbers

Therefore,

x + x + 2 + x + 4 = 321

combine the like terms

x + x + x + 2 + 4 = 321

add the like terms

x + x + x + 2 + 4 = 321

3x + 6 = 321

subtract 6 from both sides

3x + 6 = 321

3x + 6 - 6 = 321 - 6

3x  = 315

divide both sides by 3

x = 315 / 3

x = 105

Therefore, the consecutive odd numbers that sum up to 321 are 105, 107 and 109.

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The sequence or pattern [[tex]x_{n}[/tex]] [tex]x_{n}[/tex] Converges to Zero, meaning that the power, limit, and final solution all get closer to zero.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts. The length of the series is the number of elements (potentially infinite).Unlike a set, a sequence may contain the same things more than once at different locations, and unlike a set, the sequence's order is crucial.

According to given information;

First put;

[tex]x_{n}[/tex]−1=−√(1+x[tex]_n_-_2[/tex]+1)

into

[tex]x_{n}[/tex]=(−1+x[tex]_n_-_1[/tex]+1)

You'll notice a general form:

[tex]x_{n}[/tex]=−1+(x[tex]_n_-_r[/tex]+1)^2^−r

Then put r = n-1, and take the limit of both sides with n tending to infinity. On the right hand side, you have

−1 +[tex]\lim_{n \to \infty}[/tex](x+1)^[tex]\frac{1}{2n-1}[/tex]

       n→∞

he power approaches 0, the limit approaches 1 and the final answer approaches 0.

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Answer:

(15 ÷ n) + (n ÷ 15)

Step-by-step explanation:

The sum of 15 divided by a number and that number divided by 15.

15 divided by a number

= (15 ÷ n)

15 is being divided by an unknown number (put n as a variable)

that number divided by 15

= (n ÷ 15)

An unknown number (put n as a variable) is being divided by 15.

The sum

Add (15 ÷ n) and (n ÷ 15)

(15 ÷ n) + (n ÷ 15)

Hope this helped and have a lovely rest of your day! :)

a formula for the perimeter of the rectangle in terms of its length, l will be given as l = P / 2 - b.

We know that the perimeter of rectangle is given by:

Perimeter ( P ) = 2 ( l + b )

Now, we need to represent this formula in terms of length that is l.

So, we get that:

P = 2 l + 2 b

Now subtract 2 b from both the sides:

P - 2 b = 2 l + 2 b - 2 b

P - 2 b = 2 l

2 l = P - 2 b

Divide both the sides by 2:

2 l / 2 = (P - 2 b) / 2

l = P / 2 - b

Therefore, we get that, a formula for the perimeter of the rectangle in terms of its length, l will be given as l = P / 2 - b.

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Answer:

c

Step-by-step explanation:

C is straight forward that the value of the y intercept is 8, unlike the A and B where you must first simply by removing the brackets

Answer:9 citronella and 6 fragrant wood apples

Step-by-step explanation:

Answer:

Step-by-step explanation:

Cost of one rubber = $1

Cost of one pen = 0.25

Answer:

46

Step-by-step explanation:

4x-4=180

4x=184

x=46

Answer:

x=46

Step-by-step explanation:

used by scientific calculator.

There are multiple but here are 2

13+13+11+11 = 42

10+10+14+14 = 42

Using the normal distribution, we have that:

A.

B. Due to the higher coefficient of variation, Company A has the larger dispersion.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For Company A, the mean and the standard deviation are given as follows:

[tex]\mu = 500, \sigma = 40[/tex]

The Empirical Rule is applicable for a normal variable, meaning that 95% of the measures are within 2 standard deviations of the mean, hence:

The middle 95% of the wires from Company A tested between 420 and 580 psi.

The middle 50% is the measures between the 25th percentile(X when Z = -0.675) and and the 75th percentile(X when Z = 0.675), hence:

25th percentile:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

-0.675 = (X - 500)/40

X - 500 = -0.675(40)

X = 473.

75th percentile:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

0.675 = (X - 500)/40

X - 500 = 0.675(40)

X = 527.

The middle 50% of the wires of Company A tested between 473 psi and 527 psi.

The company with the larger dispersion has the highest coefficient of variation, given by the standard deviation divided by the mean.

Hence:

Hence Company A has the larger dispersion.

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Answer:

hey from where are you...