A cable TV company charges a flat fee of $25 for basic cable service, plus
extra for each movie a customer watches. Here is some of the pricing
information:
Movies watched 0 1 2 3
Cable TV bill ($) 25 29 33 37
According to this information, how many movies can a customer watch and
still keep his or her bill under $60?

Answer:

The second option.

Step-by-step explanation:

We are trying to find what is W(x) - D(x).

(4x^3 + 6x^2 - 11x + 7) - (x^3 + 2x^2 + 15)

= 4x^3 - x^3 + 6x^2 - 2x^2 - 11x + 7 - 15

= 3x^3 + 4x^2 - 11x - 8

This corresponds to the second option.

Hope this helps!

A function, C(x), to model the water used by the car wash on a shorter day will be 3x³ + 4x² - 11x - 8

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that:-

Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.

We are trying to find what

C(x)  =  W(x)   -    D(x)

C(x)  =   (  4x³   +   6x²  −   11x   +  7, )  -  (  x³   +  2x²  +  15  )

C(x)   =   4x³  -  x²  +  6x²  -  2x³  - 11x  +  7  - 15

C(x)   =   3x³  +  4x²  -  11x  -   8

Therefore A function, C(x), to model the water used by the car wash on a shorter day will be 3x³ + 4x² - 11x - 8

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Answer:

The correct option is;

A. 30

Step-by-step explanation:

Given that the perpendicular bisector forms two other right angled triangles, we have;

For the larger right angled triangle, hypotenuse length = 100

For the smaller right angled triangle, hypotenuse length = 90

We note that;

y² = x² + 10²

z² = x² + 90²

100² = z² + y ²

Therefore we have;

100² = x² + 10² + z² =  x² + 10² + x² + 90² = 2·x² + 90² + 10²

10000 =  2·x² + 8200

2·x² = 10000 -  8200 = 1800

x² = 1800/2 = 900

x = 30

Answer:

(1) P (z > 1.38) = 0.08379

(2) P (z < - 0.42) = 0.33724

(3) P (z < 3.04) = 0.99882

(4) P (z > -2.43) = 0.00755

Step-by-step explanation:

(1)

Compute the value of P (z > 1.38) as follows:

[tex]P(z>1.38)=1-P(z<1.38)\\=1-0.91621\\=0.08379[/tex]

(2)

Compute the value of P (z < -0.42) as follows:

[tex]P(z<-0.42)=1-P(z<0.42)\\=1-0.66276\\=0.33724[/tex]

(3)

Compute the value of P (z < 3.04) as follows:

[tex]P(z<3.04)=0.99882[/tex]

(4)

Compute the value of P (z > -2.43) as follows:

[tex]P(z>-2.43)=1-P(z<2.43)\\=1-0.99245\\=0.00755[/tex]

Answer:

Yesh.

Step-by-step explanation:

3x - 4y = -2

3 * 6 - 4 * 5 = -2

18 - 20 = -2

-2 = -2

So, the ordered pair is a solution to the equation.

Hope this helps!

Answer:

Yes, it is

Step-by-step explanation:

If you add in the numbers, you get

(3*6)- (4*5)=-2.

then solving it, you get

18-20= -2

which is correct. (18-20 IS -2)

so, the ordered pair is a solution to the problem. Hope this helps :)

The number -32 belongs to set : A) integers, rational

Rational numbers are terminating or  repeating real numbers. Whereas, irrational numbers are the complement of rational number with real number being the universal set. These numbers are non terminating non repeating real number.

Integers are a subset of rational number. These are numbers not in fraction or decimal, or say with a denominator 1.

Whole numbers are subsets of integers which are positive, or say integers greater than equal to 1.

Given number : -32.

Since, the number is terminating, it is rational.

Further, it is not a fraction or decimal, hence integer.

But since the number is negative, not a whole number.

Therefore A) Integers, rational is correct option.

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Answer:

The answer is option B.

Step-by-step explanation:

Let < D be x

Since the triangle isosceles < E is also the same as < D

Let < E also be x

Angles in a triangle add up to 180°

x + x + 102 = 180

2x = 180 - 102

2x = 78

Divide both sides by 2

x = 39°

Therefore m < D is 39°

Hope this helps you

Answer: 51.75

Step-by-step explanation: 15 precent of 45 is 6.75

                                              Then add 45+6.75

Answer:

Her total including the bill will be $51.75

Step-by-step explanation:

15% of $45

= $6.75

$45 + $6.75 = $51.75

Answer:

answer is 24

area of triangle=1/2 base*height

1/2*16*3=24

Answer:

24 sq. units

Step-by-step explanation:

Area of a triangle = Base x height ÷ 2

Base = 16

Height = 3

Therefore 16 x 3= 48 ÷2 = 24

I really hope this helps:)

Answer:

4.

Step-by-step explanation:

One line of symmetry is horizontal ( through the centre of the horizontal part of the cross).

Another is a vertical line through the centre of the vertical part.

Then there are 2 diagonal lines of reflectional symmetry.

Answer:

f(x)=2(x-3)^2

Step-by-step explanation:

vertex form: a(x-h)^2+k

so find the vertex (h,k) and use it to turn it into vertex form

Answer:

92

Step-by-step explanation:

E is the midpoint of AC.

F is the midpoint of BC.

FE and AB are parallel by a theorem.

m<DBF = m<EFC = 92 by corresponding angles of parallel lines cut by a transversal.

Answer:

92°

Step-by-step explanation:

Answer:

0.9156

Step-by-step explanation:

In the picture attached, the data is plotted (I made it using MS Excel, you can use similar programmes or a calculator).

The line that best correlates the data has the following equation:

y = 0.1037x + 50.922

and its correlation coefficient is:

R² = 0.9156

Answer:

Correlation coefficient, r = 0.957

Step-by-step explanation:

Let y represent the weight

Let x represent the height

y                        x                       x²                 y²                     xy

99                     61                      3721            9801               6039

104                    61                      3721            10816              6344

110                     62                     3844           12100              6820

133                     64                     4096           17689             8512

130                     65                     4225           16900            8550

142                     68                     4629           20169            9656

146                     66                     4356           21316              9636

153                     67                     4489           23409            10251

184                     69                     4761            33856            12696

185                     70                     4900           34225            12950

[tex]\sum y = 1386[/tex], [tex]\sum x = 653[/tex], [tex]\sum x^2 = 42737[/tex], [tex]\sum y^2 = 200276[/tex], [tex]\sum xy = 91454[/tex]

Correlation coefficient formula,

[tex]r = \frac{n \sum xy - \sum x \sum y}{\sqrt{(n \sum x^2 - (\sum x)^2) (n \sum y^2 - (\sum y)^2)} } \\r = \frac{10* 91454 - 653*1386}{\sqrt{(10* 42737 - (653)^2) (10* 200276 - (1386)^2)} }[/tex]        

Correlation coefficient, r = 0.957

Answer:

4 raised to 4 is 256

Step-by-step explanation:

Answer: 256

Step-by-step explanation:

Remember: to calculate by elevated you have to calculate the same number the same number of times. For example: 4 raised by 4 is: 4 x 4 x 4 x 4 and that multiplication results in: 256. I hope and it has helped you ;)

Answer:

x = -2

Step-by-step explanation:

Step 1: Substitute h(x) for -9

-9 = 4x - 1

Step 2: Solve for x

-8 = 4x

x = -2

Answer:

x = -2.

Step-by-step explanation:

h(x) = 4x - 1, h(x) = -9.

-9 = 4x - 1

4x - 1 = -9

4x = -8

x = -2

Check your work!

4 * (-2) - 1

= -8 - 1

= -9

Since it works out, x = -2.

Hope this helps!

Answer:

Step-by-step explanation:

Hello

first of all we assume that this number is different from 0 as dividing by 0 is not allowed

let's not n this number

its inverse is

[tex]\dfrac{1}{n}[/tex]

and we can write

[tex]n*\dfrac{1}{n}=1[/tex]

hope this helps

Answer:

x * 1/x = 1

Step-by-step explanation:

Let x be the number

1/x is the inverse

x * 1/x = 1

Answer:

[tex]a)41[/tex]

Step-by-step explanation:

[tex]x - 9 < 32[/tex]

[tex]by \: collecting \: like \: terms[/tex]

[tex]x < 32 + 9[/tex]

[tex]x < 41[/tex]

Answer:

B) 24

D) 40

E) 36

Step-by-step explanation:

x - 9 < 32

Add 9 on both parts.

x - 9 + 9 < 32 + 9

x < 41

x is lesser than 41.

24, 40, and 36 are lesser than 41 from the list.

Step-by-step explanation:

Angles and sides go hand-in-hand. Although I don't see the actual triangle that's used, and that can affect my answer, the side opposite of the shortest angle will be the shortest, the side opposite of the middle angle will be the middle, and the side opposite the largest angle will be the largest. For example, if the shortest angle (m∠X = 51) is the top vertex, the base side will be the shortest.

Answer:

  [tex]\dfrac{5}{x^3-12x^2+47x-60}[/tex]

Step-by-step explanation:

Though it is not what you have written, we think you want to simplify ...

  [tex]\dfrac{2(a-3)}{(a-4)(a-5)}+\dfrac{(a-1)}{(3-a)(a-4)}+\dfrac{(a-2)}{(5-a)(a-3)}\\\\=\dfrac{2(a-3)^2}{(a-3)(a-4)(a-5)}+\dfrac{-(a-1)(a-5)}{(a-3)(a-4)(a-5)}+\dfrac{-(a-2)(a-4)}{(a-3)(a-4)(a-5)}\\\\=\dfrac{2(a^2-6a+9)-(a^2-6a+5)-(a^2-6a+8)}{x^3-12x^2+47x-60}\\\\=\boxed{\dfrac{5}{x^3-12x^2+47x-60}}[/tex]

_____

When writing a fraction in plain text, parentheses are needed around the entire denominator. The order of operations tells you that a/bc = (a/b)c, not a/(bc).

Answer:

1/2, 8/10, 0.9

Step-by-step explanation:

Convert to decimals.

8/10 = 0.8

0.9

1/2 = 0.5

Arrange from least to greatest.

0.5, 0.8, 0.9

1/2, 8/10, 0.9

Answer: 72cups

Step-by-step explanation:

there are 8oz in a cup, so 8oz x 3cups = 24oz

[tex]\\ \frac{24}{8} \ = \frac{x}{192} \\(24) (192) = 8x\\(3) (192) = x\\576=x\\[/tex]

[tex]\frac{576}{8} = 72cups[/tex]

The baker will need 72 cups of flour for 192oz of chocolate chips.

Answer:

option 4

Step-by-step explanation:

Given the x- intercepts say x = a, x = b, x - c then the corresponding factors are

(x - a), (x - b), (x - c) and the polynomial is the product of the factors

Here the x- intercepts are x = 3, x = 0, x = - 1, thus the factors are

(x - 3), (x - 0), (x - (- 1) , that is

(x - 3), x and (x + 1) , then

y = ax(x - 3)(x + 1) ← where a is a multiplier

To find a substitute (1, - 8) into the equation

- 8 = a(1 - 3)(1 + 1) = - 4a ( divide both sides by - 4 )

a = 2, thus

y = 2x(x - 3)(x + 1) ← expand factors using FOIL

   = 2x(x² - 2x - 3) ← distribute by 2x

    = 2x³ - 4x² - 6x

Answer:

D) 2x3 – 4x2 – 6x

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sqrt{65}\approx8.062}[/tex]

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have two points (4, 0) and (-3, 4).

Substitute:

[tex]d=\sqrt{(-3-4)^2+(4-0)^2}=\sqrt{(-7)^2+4^2}=\sqrt{49+16}=\sqrt{65}[/tex]

Answer:

A letter T is folded vertically through the middle.

Step-by-step explanation:

Reflectional symmetry refers to the symmetry of line that divides the given shape into two equal halves. The halves represent the mirror reflection of each other. The line of symmetry is drawn to show the reflection and it acts as a mirror. For the letter 'T', the reflectional symmetry will be drawn vertically in the middle of the letter. The line divides the letter into two equal halves with mirror images.

The figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.

A line of reflectional symmetry can be described as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.

When a line divides letter T vertically, two mirror images are created.

Thus, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.

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Answer: b. [tex](x-2)^2+(y+9)^2+(z+1)^2=r[/tex]

Step-by-step explanation:

The general equation of a sphere is : [tex](x - a)^2 + (y - b)^2+ (z - c)^2 = R^2[/tex], where (a, b, c) represents the center of the sphere, R represents the radius, and x, y, and z are the coordinates of the points on the surface of the sphere.

Given, Center of the sphere =  (2,-9,-1)

Radius = √r

Then, the equation of the sphere would be

[tex](x - 2)^2 + (y - (-9))^2+ (z - (-1))^2 = (\sqrt{r})^2\\\\\Rightarrow\ (x-2)^2+(y+9)^2+(z+1)^2=r[/tex]

Hence, the correct option is b. [tex](x-2)^2+(y+9)^2+(z+1)^2=r[/tex] .

THIS IS THE COMPLETE QUESTION BELOW;

The probability of pulling a green marble out of a bag of colored marbles is 2:5. If you were to pull colored marbles out of the bag one at a time, and putting the marble back each time for 600 tries, approximately how many time would you select a green marble?? ( explanation too) 7th grade Math

Answer:

We would approximately pick a green marble 240 times

Step-by-step explanation:

Given from the question the probability of pulling a green marble out of a bag of colored marbles is 2:5

Let us denote the number of trials as X

Now the approximately number of times a green marble can be selected would be

=2/5 times

From the question we are given 600 trials

which implies our x=600

Therefore, the number of times we would pick a green marble is:

2/5 × 600 times

≈ 240 times

Therefore, we would approximately pick a green marble 240 times

Answer:

Can't be determined.

Step-by-step explanation:

From the fact that the quadrilaterals are similar:

Corresponding sides are in proportion and

Corresponding angles are congruent.

We can't create a proportion, so there's nothing else that we can determine.

Answer:

Below.

Step-by-step explanation:

Similar figures have the same size but not necessarily the same size.

The respective sides will be in the same ratio in a similar figure.

So from the information given you can't say what the measure of the perimeter of quadrilateral EFGH is. All you can say is the ratio of the perimeters is the same as the ratio of the respective sides. If the ratio is 1:2 for example then the perimeter of EFGH is 2*4y^2 = 8y^2.

Answer:

Solution,

[tex] {w}^{3} - w( {w}^{2} + 2w - 1) + 2w \\ = {w}^{3} - {w}^{3} - 2 {w}^{2} + w + 2w \\ = - 2 {w}^{2} + 3w[/tex]

Some rules:

[tex]( + ) \times ( + ) \ = ( + ) \\ ( - ) \times ( + ) = ( - ) \\ ( + ) \times ( - ) = ( - ) \\ ( - ) \times ( - ) = ( + )[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

Third Choice: a = 2, b = -3, c = -27

Step-by-step explanation:

The equation to be solved with the quadratic formula must be written in the form

ax^2 + bx + c = 0

2x^2 = 27 + 3x

Subtract 3x from both sides. Subtract 27 from both sides.

2x^2 - 3x - 27 = 0

Now we see we have

a = 2, b = -3, c = -27

Answer: Third Choice

Answer:

The first train travels at 58 mph and the second train travels at 203 mph.

Step-by-step explanation:

The first train left Miami at 3:00 PM.

The second train left Miami at 8:00 PM.

Let the speed of the first train be x.

The second train travels 145 mph faster than the first, that is 145 + x

The second train overtakes the first at 10:00 PM

This means that at 10:00 PM, they were both at the same location.

That is 7 hours after the first train left and 2 hours after the second train left.

Speed is given as:

s = d / t

where d = distance traveled and t = time taken

For the first train, after 7 hours traveling at speed x:

x = d / 7

=> d = 7x _______(1)

For the second train, after 2 hours, traveling at speed 145 + x:

145 + x= d / 2

=> d = 290 + 2x ____(2)

Equating (1) and (2):

7x = 290 + 2x

=> 7x - 2x = 290

5x = 290

=> x = 290/5 = 58 mph

Therefore, the first train travels at 58 mph and the second train travels at 203 mph (58 + 145)

Answer:

Infinitely many linear equations

Step-by-step explanation:

a + 2b + c = 0

x = 1 and y = 2