What is the range of the function f(x) = 2x + 1 given the Domain D = {-1,0, 1, 2}?
R = {0, 1,3,5)

R= {-1,1,3,5)

R = {-5, -3,-1,1)

R = {0, 1,3,6}

Answer:1/4

Step-by-step explanation:

Each term is multiplied by 1/4 to get to the next

Therefore 1/4 is the common ratio

Answer:

AB║CD and AD║BC

Step-by-step explanation:

By the property of a parallelogram,

" Consecutive angles of a parallelogram are supplementary"

In the figure attached,

∠DCB and ∠CDA are the supplementary angles. Therefore ABCD will be a parallelogram.

[Given: m(∠DCB) + m(∠CDA) = 180°]

And the pair of opposite sides of the parallelogram ABCD will be parallel.

AD║BC and AB║CD

Answer: subtract 85 with a hundred because you are trying to see how many students out of 100% are good students after that you should get your answer

Step-by-step explanation:

Answer:

77% (rounded)

Step-by-step explanation:

1. Find 85% of 100

           100 x 0.85 = 85

     SO 85 students out of 100 students are good students.

2. Add the 10 more students to the total number.

             100 + 10 = 110 total students

3. Find the percent of good students in the total number of current students.

          85/110 = 0.77 * 100 (to convert to percent) = 77%

Answer:

d) 405 = 15 times 4.5 times h

The height of the prism 'h' = 6 inches

Step-by-step explanation:

Explanation:-

Given Volume of prism

                            V = 405 cubic inches

Given length of the prism

                         L = 15 inches

Given width of the prism

                       W = 4.5 inches

The volume of the prism

                        V = l w h

                       405 = 15 ×4.5× h

                       405 = 67.5 h

Dividing '67.5' on both sides , we get

                      h = 6 inches

Final answer:-

The height of the prism 'h' = 6 inches

Answer: V = l w h. 405 = 15 times 4.5 times h

Step-by-step explanation:

Given the following :

Volume of prism = 405 in^3

Length = 15 inches

Height = h

Width = 4.5 inches

Recall :

The volume of a prism is the product of the Base and the height.

That is;

Volume = Base × height

However, Base of prism is given by the area of the base shape of the prism.

From our parameters Base shape of the prism is a rectangle.

Therefore, Area of rectangle = Length × width

= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism

Therefore, Volume of prism equals ;

Volume = 15 × 4.5 × h

Volume = 405in^3

Volume = Base × height

405 = 15 × 4.5 × h

the correct answer is:

A. 9/-6

Step-by-step explanation:

V= π*r²*h

V/π = r²*h

v/(π*r²) = h

[tex]\frac{x+y}{3}[/tex] = 5

x+y = 15

x = 15-y

Answer:

45

Step-by-step explanation:

From the figure given, TV and RS are parallel.

Therefore, angle VTS and angle RST equal (Alternate angles)

Thus, angle VTS = angle RST = x

Angle T + angle S + angle R = 180° (sum of angles in a triangle)

2x + x + x = 180

4x = 180

Divide both sides by 4 to solve for x

x = 180/4

x = 45

The value of x in each case is 45

If we input 45 as a value of x in the angles in the triangle, the sum of what we have will give us 180°.

Answer:45

Step-by-step explanation:

Answer:

Solution,

[tex]5 \frac{3}{4} \div 1 \frac{1}{2} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{23}{4} \div \frac{3}{2} [/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \frac{23}{4} \times \frac{2}{3} [/tex]

Reduce the numbers with the GCF 2

[tex] \frac{23}{2} \times \frac{1}{3} [/tex]

Multiply the fraction

[tex] \frac{23}{6} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

(Change in y)/(change in x) is defined as the average rate of change.

For a linear equation:

y = a*x + b

A is the average rate of change, and is called the "slope" of the linear equation, and this is a constant.

Then the sentence will be:

"The average change between two ordered pairs (x,y) is the ratio (change in x)/(change in y)

In a linear function, this is called the slope, and it is constant"

Answer:

0.5

Step-by-step explanation:

Let D be the event of selecting a marble with dots.

Let P be the event of selecting a purple marble.

The probability of selecting a marble with dots, P(D)=0.2

The probability of selecting a marble that is both purple and has dots, [tex]P(D \cap P)=0.1[/tex]

We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)

By the definition of conditional probability:

[tex]P(P|D)= \dfrac{P(P \cap D)}{P(D)} \\= \dfrac{0.1}{0.2}\\ =0.5[/tex]

The probability of selecting a purple marble given that the marble has dots on it is 0.5.

Answer:

answer is 8x+10x

18x

is the answer

Answer:

6-3/0-(-4)

=3/4

Step-by-step explanation:

Given two points of a line to find the slope, we use the formula.y2-y1/x2-x1 hence the answer above. Our xs are x2=0 x=-4 y2=6 y1=3

To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.

Answer:

c/3, the sequence is NOT geometric because 2/3 was added to each term to get the next term.

Step-by-step explanation:

geometric sequences are multiplying, arithmetic sequences are addition.

1/3

1/3+2/3= 1 (or 3/3)

3/3+2/3= 5/3

5/3+2/3= 7/3

this is arithmetic, not geometric

Answer:

2x^2+x-1/x^2-1

x^2+11x+18/x^2-11x+18

2x^2-5x+3/x^2+4x+3

Step-by-step explanation:

1.2 and 5

Answer:

second option

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex] πr³ ( where r is the radius )

Here r = 6 , thus

V = [tex]\frac{4}{3}[/tex]π(6)³

Answer:

Second option

Step-by-step explanation:

Volume of a sphere =  [tex]\frac{4}{3}*\pi *r^{3}[/tex]

→ Substitute in the value of radius

Volume of a sphere =  [tex]\frac{4}{3}*\pi *6^{3}[/tex]

Answer:

[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]

Step-by-step explanation:

In the attached diagram

CA=CO+OA

CO=DB

Therefore:

5=2+OA

OA=3 Units

The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:

OB=12 units

OA=3 units

Using Pythagoras theorem

[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]

Answer:

Option (D)

Step-by-step explanation:

Sum of interior angles of a polygon is represented by the expression,

Sum of interior angles = n(n - 1)×180°

Here n is the number of sides of a polygon

If n = 18,

Sum of 18 sided polygon = (18 - 1) × 180°

                                         = 7 × 180°

                                         = 3060°

Therefore, sum of interior angles of a 18 sided polygon will be 3060°.

Option (D) will be the answer.

Answer:

2880

Step-by-step explanation:

SUM=_-2=

18-2=16

16*180 = 2880 OR

18*160 = 2880 degrees

Answer:

2310cm³

Step-by-step explanation:

volume= πr²h

22/7× radius of circle × height

circumference= πd

44cm=22/7×d, diameter= 7 cm, radius= 3.5cm

v= 22/7× 3.5× 21 = 2310cm³

Initial length = 72 cm

Stretched length = 90 cm

Find the increased in length:

increase = 90 - 72 = 18

Find the percentage increase:

Percentage increase = change/original x 100

Percentage increase = 18/72 x 100 = 25%

Answer: The elastic band's length is increased by 25%

Answer:

the slope of the perpendicular bisector is -2/3

Step-by-step explanation:

The slope of the line joining the two points P1(0,3), P2(6,12) is given by

m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5

The slope m2 of a line perpendicular to the previous line is given by

m1*m2 = -1

solving

m2 = -1/m1 = -1/ (3/2) = -2/3

THerefore the slope of the perpendicular bisector is -2/3

Answer:

48 miles.

Step-by-step explanation:

Her average speed was 12 miles per hour. She traveled for 4 hours. We can set up a proportion that shows that she traveled 12 miles over 1 hour, so she traveled x miles over 4 hours.

[tex]\frac{12}{1} =\frac{x}{4}[/tex]

1 * x = 12 * 4

x = 48

So, the cyclist traveled 48 miles.

Hope this helps!

Answer: 48 miles

Explanation: Well obviously if you've been on the road for 4 hours and you're traveling at 12 miles per hour, you end up going 48 miles.

Mathematically speaking we get that

by multiplying 12 × 4 to equal 48.

This 12 represents our rate.

This 4 represents the number of hours or our time.

The 48 represents the 48 miles or our distance we've travelled.

So our rate × time = distance.

This formula is a very popular one in algebra.

Answer:

10

Step-by-step explanation:

This is an arithmetic sequence.  The common difference is -6, and the first term is 52.

a = 52 − 6(n − 1)

When n = 8:

a = 52 − 6(8 − 1)

a = 52 − 42

a = 10

Answer & Step-by-step explanation:

When we see the phrase "rate of change" then it means that we are looking for the slope. So, we will need to know the formula for finding slope or the rate of change.

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, let's use this equation to solve for the rate of change of each question.

Problem 1:

[tex]Slope=\frac{2-\frac{4}{3}}{0-(-1)}\\\\Slope=\frac{\frac{2}{3}}{1}\\\\Slope=\frac{2}{3}[/tex]

The rate of change of this equation is 2/3

Problem 2:

[tex]Slope=\frac{4-2}{1-0}\\\\Slope=\frac{2}{1}\\\\Slope=2[/tex]

The rate of change for this equation is 2

Problem 3:

[tex]Slope=\frac{10-4}{2-1}\\\\Slope=\frac{6}{1}\\\\Slope=6[/tex]

The rate of change for this equation is 6

Answer:

Of the 5000​ surveys, 14​% were returned. This response rate APPEARS to be low.

Step-by-step explanation:

Given:

Total sample collected = 5000

Survey returned = 700

i) What percentage of the 5000 surveys were​ returned?

To find percentage returned, we have:

[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]

Percentage returned = 14%

ii) Does that response rate appear to be​ low?

Yes, the response is significantly low as only 14% is returned out of expected 100%

iii) In​ general, what is a problem with a very low response​ rate?

The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.

Therefore, of the 5000​ surveys, 14​% were returned. This response rate APPEARS to be low.

Answer:

[tex]\dfrac{2}{3}.[/tex]

Step-by-step explanation:

It is given that a box contains 2 dozen pairs of contact lenses ,of which 8 pairs are tinted.

1 dozen = 12 units

Total pairs of contact lenses [tex]=2\times 12 = 24[/tex]

Tinted pairs of contact lenses = 8

Pairs of contact lenses not tinted = 24 - 8 = 16

If a pair of contact lenses is drawn at random from the box, then we need to find the probability that it is not tinted.

[tex]P(\text{Not tinted})=\dfrac{\text{Pairs of contact lenses not tinted}}{\text{Total pairs of contact lenses}}[/tex]

[tex]P(\text{Not tinted})=\dfrac{16}{24}[/tex]

[tex]P(\text{Not tinted})=\dfrac{2}{3}[/tex]

Therefore, the required probability is [tex]\dfrac{2}{3}.[/tex]

Answer:

A. Net

Step-by-step explanation:

Answer:

a. net

Step-by-step explanation:

The net of a 3D shape is how it looks unfolded. A net can easily be put back together.

Hope this helps! :)

Answer: k = 4

Step-by-step explanation:

For this division, to determine the value of k, use the Remainder Theorem, which states that:

polynomial p(x) = dividend (x-a) * quotient Q(x) + remainder R(x)

Knowing the degree of quotient is

degree of Q = degree of p(x) - degree of (x-a)

For this case, Q(x) is a third degree polynomial.

Using the theorem:

[tex]x^{4}-3x^{2}+kx-2 = (x-2)(ax^{3}+bx^{2}+cx+d) + 10[/tex]

[tex]x^{4}-3x^{2}+kx-2 = ax^{4} + x^{3}(b-2a)+x^{2}(c-2a)+x(d-2c)-2d+10[/tex]

a = 1

b - 2a = 0 ⇒ b = 2

c - 2b = -3 ⇒ c = 1

-2d + 10 = -2 ⇒ d = 6

d - 2c = k ⇒ k = 4

Therefore, k = 4 and Q(x) = [tex]x^{4} -2x^{2} + 4x + 2[/tex]

Step-by-step explanation:

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