Find the y-intercept of the following function. f(x)=21x2−31x−68

Answer:

positive, positive, zero, zero, negative, negative, positive

Step-by-step explanation:

The derivative is positive when a function is increasing.

The derivative is zero when a function is neither increasing nor decreasing.

The derivative is negative when the function is decreasing.

Answer:

  240 cm by 288 cm

Step-by-step explanation:

You want the dimensions of a 150 cm by 180 cm poster enlarged by the ratio 8:5.

The enlargement ratio, expressed as a fraction, multiplies each of the original dimensions to get the new dimensions. The new dimensions are ...

  (8/5)·150 cm by (8/5)·180 cm = 240 cm by 288 cm

Answer:

4

Step-by-step explanation:

Solution by separating parts

Rewriting our equation with parts separated

=1 + 1/2 + 2 + 1/2

Solving the whole number parts

1 + 2 = 3

Solving the fraction parts

1/2 +1/2 = 2/2

Reducing the fraction part, 2/2,

2/2 = 1/1

Simplifying the fraction part, 1/1,

1/1 = 1

Combining the whole and fraction parts

3 + 1 = 4

Answer:

4 miles

Step-by-step explanation:

1 1/2 = 1.5
2 1/2 = 2.5

1.5 + 2.5 = 4 miles

Answer:

[tex]33[/tex]

Step-by-step explanation:

Define functions:

[tex]r(x) = 2x+1\\s(x) = -x^2[/tex]

Substitute [tex]s(x)[/tex] into [tex]r(x)[/tex]:

[tex]2(-x^2) + 1[/tex]

Solve for value:

[tex]= 2((-4)^2)+1\\= 2(16) + 1\\= 32 + 1\\= 33[/tex]

** assuming that the function of [tex]s(x)[/tex] the x value is squared with the negative sign.

Using the normal distribution, it is found that:

a) The probability that a randomly selected person spent more than ​$​25 is of 0.3446 = 34.46%.

b) The probability that a randomly selected person spent between ​$12 and ​$​21 is of 0.3307 = 33.07%.

c) The middle 95% of the amounts are between $13.2 and $32.8.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

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

The mean and the standard deviation for the costs of the meal are given as follows:

[tex]\mu = 23, \sigma = 5[/tex]

The probability that a randomly selected person spent more than ​$​25 is one subtracted by the p-value of Z when X = 25, hence:

Z = (25 - 23)/5

Z = 0.4

Z = 0.4 has a p-value of 0.6554.

1 - 0.6554 = 0.3446 = 34.46%.

The probability that a randomly selected person spent between ​$12 and ​$​21 is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 12, hence:

X = 21:

Z = (21 - 23)/5

Z = -0.4

Z = -0.4 has a p-value of 0.3446.

X = 12:

Z = (12 - 23)/5

Z = -2.2

Z = -2.2 has a p-value of 0.0139.

0.3446 - 0.0139 = 0.3307 = 33.07%.

The normal distribution is symmetric, meaning that the bounds of the middle 95% of values are given as follows:

-1.96 = (X - 23)/5

X - 23 = -1.96 x 5

X = $13.2

1.96 = (X - 23)/5

X - 23 = 1.96 x 5

X = $32.8

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The function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.

A competitive water skier's heights y, x seconds after soaring off a ramp.

For x = 0, y = 22

for x = 0.25, y = 22.5

For x = 0.75, y = 17.5

For x = 1, y = 12

For x = 1.1, y = 9.24

The general equation of a quadratic equation is y = [tex]ax^{2} + bx +c[/tex]

Putting x = 0 and y = 22 in the equation, we get :

[tex]y = ax^{2} +bx +c[/tex]

c = 22

Now, putting x = 1 and y =12, we get,

12 = a*1 + b*1 + 22

a +b = 12 - 22 = -10 equation (1)

Putting x = 0.25, y = 22.5,

22.5 = a* [tex]22.5^{2}[/tex] +b*22.5 +22

506.25 a +22.5b = 0.5 equation(2)

Solving equation (1) and equation(2), we get :

a = -16 and b = 6 and c = 22

So, the quadratic equation becomes,

[tex]y = -16x^{2} + 6x +22[/tex]

Now, Time when the skier is 5 feet above the water,

[tex]x = \frac{3 +\sqrt{281} }{16} = 1.23 seconds[/tex]

Hence, the function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.

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Answer:

snap to solve

Step-by-step explanation:

u can use snap to solve to get ur answers

Answer:

Step-by-step explanation:

cost price = $640

sell price = $940

percentage = ?

Rate * Base = Amount

Percent * Sell Price = Cost Price

P * 940 = 640

P940 = 640

P940/940 = 640/ 940

P = 0.66666667

Percent = (0.66666667 × 100)/100 = 66.666667

Correct Answer is 66 2/3%

Answer:

a. )

Step-by-step explanation:

There are 15 balls  ......  two are green with a star

2 out of 15 = 2/15 = .1333

Answer:

191=266+109x

Step-by-step explanation:

It says 191 is the same as 266 added to the product of 109 and _____. i am guessing you meant to say a variable.

The sample statistic when the nursing administrator went through a sample of hospital records is 217.

A statistic is a metric used to describe a sample. Estimation or hypothesis testing can be used to determine how likely it is that a sample statistic differs from the population parameter.

A sample is an analytic subset of a larger population in statistics. The use of samples enables researchers to conduct studies with more manageable data and more quickly. Randomly drawn samples have little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.

A sample statistic is a piece of statistical data derived from a small number of items. A sample is merely a subset of a population. Therefore, the 217 of the patients had been admitted for heart issues is the sample.

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The percentage is the indicating hundredth is  12.5%.

A specific number in every hundred is what is meant by the percentage. It is a fraction with 100 as the denominator, and one percent is used to symbolize it.

Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

A student was marked tardy five different times in a 40-day period.

Percentage of 5 among 40

= (5/40) x 100

= 12.5%

Hence, The percentage of times the students marked will be 12.5%".

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Answer:

[tex]\hat{y}=-0.29x+5.67[/tex]

Step-by-step explanation:

Given points on the scatter plot:

Plot the given points and draw a line of best fit (see attachment).

As the y-values decrease as the x-values increase, the slope of the line of best fit is negative.

From inspection of the plotted line of best fit, we can see that the y-intercept is approximately 5.7.

Therefore, the equation that is appropriate for the line of best fit is:

[tex]\boxed{\hat{y}=-0.29x+5.67}[/tex]

Answer:

y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.

Step-by-step explanation:

i took the test :)

Answer:

First, find the number of boys: [tex]78-60=18[/tex]

The ratio of the number of girls to boys would be 60 : 18.

The length of NM is 10 units

What are similar triangles?

If two triangles' corresponding angles and sides are identical and their corresponding sides are proportional, or if the ratios between the lengths of the corresponding sides are comparable, then two triangles are said to be similar.

Similar triangles are triangles with the same shape but different sizes. Examples of related objects are all equilateral triangles and squares with any side length.

The triangles ONP and LNM are similar triangles.

So, the following is true.

(ON/LN)=(NP)/(NM)

(3.6/6)=(6)/(NM)  ( LN=LO+ON=2.4+3.6=6 )

3.6 NM=6*6 =36

NM=36/3.6 = 10

So, the length of NM is 10 units

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The slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.

First, let us understand the slope intercept form;

The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.

We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.

We are given:

y = 2 + 34x

y = 34x + 2

Compare with y = mx + c, we will get;

m = 34

b = 2

So, the slope is 34 and the y-intercept is 2.

Thus, the slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.

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Answer:

I believe the answer is c

Answer:

x = 18. y = 54

Step-by-step explanation:

first we we figure out the degrees of the spot where N is.

(I know N references the line but ill be using it to call the spot)

72 + N = 90

subtract 72 from both sides

N = 18

So since opposite angles are the same

2x + N = 3x

2x + 18 = 3x

subtract 2x from both sides

18 = 1x

divide by 1 both sides

18 = x

______

now we add all the angles from the left sides to make 180

2x + N + 72 + y = 180

we know x is equal to 18 and N is also 18

2(18) + 18 + 72 + y = 180

simplify

36 + 18 + 72 + y = 180

add

126 + y = 180

subtract both sides by 126

y = 54

Respuesta:

5 millas

Explicación paso a paso:

Si hay 2 personas y cuesta 12 dólares primero restarás 2 dolars por cada persona dejándote con 10 dólares. Después de eso, dividirá 10 por 2 para las millas porque cada milla cuesta 2 dólares. que te llevará a 5 millas

GRACIAS

The time it takes the object to attain maximum height is 2 seconds

To find the time it takes the object to attain maximum height, we have to use the quadratic equation to do so. The formula can be given as

t = -b/2a

But let's write and define our quadratic equation with it's variables.

S = 64t - 16t²

To attain maximum height;

t = -b/2a

a = -16, b = 64,c = 0

Substituting the values

t = -64/2(-16)

t = 2

The time is 2 seconds

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25. doubled

26. doubled

27. increases 4 times

28. remains unchanged

29. increases 6 times

Answer: 6

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent, so both angles are equal to [tex](13x-6)^{\circ}[/tex].

Since angles in a triangle add to [tex]180^{\circ}[/tex], so:

[tex]36+2(13x-6)=180\\\\2(13x-6)=144\\\\13x-6=72\\\\13x=78\\\\x=6[/tex]

(16, 36)  is the image point .

What is  image point?

Reflecting (-6, -4) in the line y= - x yields the point (4, 6).

Dilating (4, 6) by a factor of 4 gives the point (16, 36).

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Answer:

Step-by-step explanation:

Perimeter formula from Area =

4√Area units.

4√250 =

4 × 15.8 =

63.2 cm

A student 6ft tall is standing 20ft away from a 35ft tall flagpole.

The flagpole is 60ft away from a building.

From the students point of view, the flagpole is lined up perfectly with the top of the building.

What's the height of the building?

For the given equation y  = 3x² -7x + 4 the vertex form is given by

( 7/6, -1/12).

As given in the question,

Equation is given by :

y  = 3x² -7x + 4

Standard form of the equation to get the vertex form is given by :

y = a ( x - h )² + k

Where ( h, k ) represents the vertex of the equation,

Now,

Simplify the given equation y  = 3x² -7x + 4 into standard form to get vertex form,

y  = 3x² -7x + 4

⇒ y = 3 [x² -2×(7/6)] + 4

⇒ y = 3 [ x² - 2×(7/6) + (49/36) - (49/36) ] + 4

⇒ y = 3 [ x² - 2×(7/6) + (49/36) ] - 3(49/36) + 4

⇒ y = 3 [x - (7/6)]² - (49/12) + 4

⇒ y = 3[x - (7/6)]² - (1/12)

Compare it with standard form ,

a = 3, h = (7/6) , k = -(1 /12)

Vertex form ( h, k) = ( 7/6 , -1/12 )

Therefore, for the given equation y  = 3x² -7x + 4 the vertex form is given by ( 7/6, -1/12).

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Answer:

25%

Step-by-step explanation:

divide the number by the total then multiply by 100 and add a percent sign

350/1400*100=25%

Answer of the given question are respectively,

[tex]-x^2y , 2w ,\\\\h^6 , -14a^5b^2\\x^6 , 4m^8\\9x^4/14 , y^2\\-5/x^2 , 1/2k\\7 , 1[/tex]

Exponent:

                          A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.

        Example:

                             [tex]2^3[/tex] = 2 × 2 × 2

Combine like term:

 1. [tex]9x^2y -10x^2y[/tex] = [tex]-x^2y[/tex]

 2. Subtract 6w from 8w

          8w -6w = 2w

Rule:

          [tex]x^{a} * x^{b} = x^{a+b} \\\\[/tex]

1.

        [tex]h^2 * h^4 = h^{2+4} \\ \\\\= h^6[/tex]              

2.  

        [tex](-2a^2b).(7a^3b)\\\\-14 a^{2+3} b^{1+1} \\\\= -14 a^5 b^2[/tex]

Rule:

       [tex](x^a)^b = x^{ab}[/tex]

  1.  [tex](x^2)^3 = x^6[/tex]

  2.

         [tex](-2m^3)^2 * m^2 \\\\4m^6*m^2\\\\4m^8[/tex]

Rule:

           [tex]x^a/x^b = x^{a-b}[/tex]

1.

   [tex]27x^5/42x\\\\= 9x^4 /14[/tex]

2.

          [tex](y^3)^2/y^4\\\\y^6/y^4\\\\y^2\\[/tex]        

Rule:

            [tex]x^{-a}= 1/x^a[/tex]

1.

    [tex]-5x^{-2} \\\\= -5/x^2[/tex]

2.

    [tex]4k^2/8k^3\\\\= k^{-1} /2\\\\= 1/2k[/tex]

Rule:

           [tex]x^0 =1[/tex]

1.

         [tex]7x^0\\\\= 7[/tex]

2.

         [tex](w^4)^2/w^8\\\\w^8/w^8\\\\w^0\\\\=1[/tex]

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The new coordinates of House B and House C are
B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively

What is Translation?

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the 3 houses be A , B ,C

The coordinate of House A = A ( 1 , -1 )

​The coordinate of House B = B ( 1 , -2 )

The coordinate of House C = C ( 2 , -1 )

Now , the houses are relocated to new coordinates with

The new coordinate of House A = A' ( 3 , -4 )

The translation of Point A can be expressed in the form of x and y coordinate as there is a translation occurred with a scale factor

So ,

A ( x₁ , y₁ ) to A' ( x₂ , y₂ )

A ( 1 , -1 ) to  A' ( 3 , -4 )

x₂ = x₁ + 2

y₂ = y₁ - 3

From the figure , we can clearly see that the coordinates of the houses A , B and C are translated by a scale factor and the new coordinates are

x₂ = x₁ + 2

y₂ = y₁ - 3

Therefore ,

B ( x₁ , y₁ ) to B' ( x₂ , y₂ )

B' ( x₂ , y₂ ) = B' ( 3 , -5 )

C ( x₁ , y₁ ) to C' ( x₂ , y₂ )

C' ( x₂ , y₂ ) = C' ( 4 , -4 )

Hence , the new coordinates of House B and House C are B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively

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Answer:

13685

Step-by-step explanation:

8050 + .7(8050)

8050 + 5635

13685

By solving a linear equation we will see that there were 6 hours of labor.

We know that the total cost is composed by a fixed amount of $365 plus $89 per hour of labor, so if there are x hours of labor, the total cost will be:

c(x) =  $365 + x*$89

We know that the total cost is $899, then we can write the linear equation:

$899 = $365 + x*$89

$899 - $365 = x*$89

($899 - $365)/$89 = x = 6

So there were 6 hours of labor.

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