Factor completely AND solve for the solutions of the quadratic.

The banner attached to the archway will be at (1, 5) and (5.25, 3.938).

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The archway of the main entrance of a university is modeled by the quadratic equation

y = -x² + 6x ....1

The university is hanging a banner at the main entrance at an angle defined by the equation

4y = 21 − x ....2

Then the banner attached to the archway will be

From equations 1 and 2, we have

              4(-x² + 6x) = 21 - x

              -4x² + 24x = 21 - x

        4x² - 25x + 21 = 0

  4x² - 21x - 4x + 21 = 0

x(4x - 21) - 1(4x - 21) = 0

          (4x - 21)(x - 1) = 0

                             x = 5.25, 1

Then the value of y will be

When x = 5.25, then we have

y = -(5.25)² + 6(5.25)

y = 3.938

When x = 1, then we have

y = -(1)² + 6(1)

y = 5

The banner attached to the archway will be at (1, 5) and (5.25, 3.938).

The graph is given below.

More about the parabola link is given below.

https://brainly.com/question/8495504

#SPJ1

[tex]\textbf{a)}\\\\~~~(x+8)(2x-3)\\\\=2x^2 -3x + 16x - 24\\\\=2x^2 +13x -24\\\\\textbf{b)}\\\\~~~(x-5)^2\\\\=(x-5)(x-5)\\\\=x^2 -5x -5x+25\\\\=x^2 -10x +25[/tex]

One possible interpretation of the results is that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts to achieve a total cost of $118.

To determine the amount of each type of nut the customer buys, we can set up a system of equations based on the given information.

Let's use the variables:

A = pounds of almonds

C = pounds of cashews

W = pounds of walnuts

From the given information, we can create the following equations:

A + C + W = 12 (since the customer buys a total of 12 pounds of mixed nuts)

7A + 10C + 12W = 118 (since the total cost of the nuts is $118)

W = C + 2 (since the customer buys 2 more pounds of walnuts than cashews)

We can now represent this system of equations as a matrix:

[1   1   1   12]

[7   10  12  118]

[0   -1  1   2]

To find the reduced row echelon form of this matrix, we can use Gaussian elimination or a similar method. Solving the system of equations represented by the matrix, we obtain the following reduced row echelon form:

[1   0   2   6]

[0   1   -3  4]

[0   0   0   0]

Now, let's interpret the results:

From the reduced row echelon form, we can deduce that there are infinitely many solutions to this system of equations. This means that there are multiple possible combinations of almond, cashew, and walnut quantities that satisfy the given conditions.

One possible interpretation of the results could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 0 pounds of walnuts. This satisfies the equation A + C + W = 12, and the total cost of nuts is $7 * 6 + $10 * 4 + $12 * 0 = $42 + $40 + $0 = $82. However, since the given total cost is $118, this interpretation is not valid.

Another possible interpretation could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts. This satisfies all the given conditions. The equation A + C + W = 12 holds true, and the total cost is $7 * 6 + $10 * 4 + $12 * 2 = $42 + $40 + $24 = $106, which matches the given total cost of $118.

For more such questions on interpretation visit:

https://brainly.com/question/25667250

#SPJ8

Answer:

66

Step-by-step explanation:

A=12×11/2=66

Hope this helps:)

if its diameter is 9, that means its radius is half that, or 4.5.

[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies \begin{array}{llll} SA=4\pi (4.5)^2\implies SA=81\pi \\\\\\ SA\approx 254.47~in^2 \end{array}[/tex]

The surface area of the basketball with diameter of 9 in will be 254.34 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given that, a basketball has a diameter of 9 inches we need to find its surface area,

Since, the basketball is in the shape of the sphere and the surface area of the sphere = 4π×radius²

Therefore, the surface area of the basketball =

= 4×3.14×(9/2)²

= 4×3.14×4.5×4.5

= 254.34 in²

Hence the surface area of the basketball with diameter of 9 in will be 254.34 in².

Learn more about surface area click;

https://brainly.com/question/29101132

#SPJ2

It looks like the series could be

[tex]\displaystyle 1 + 3x + \frac{9x^2}{2!} + \frac{27x^3}{3!} + \cdots = \sum_{n=0}^\infty \frac{3^nx^n}{n!} = \sum_{n=0}^\infty \frac{(3x)^n}{n!}[/tex]

Recall that

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]

It follows that the given series is the power series expansion for [tex]\boxed{e^{3x}}[/tex].

Answer:

this is the answer I got hope it helps

Answer:

7 and one-half feet squared

Step-by-step explanation:

3 x 2.5 = 7.5

Answer:

A.) True

Step-by-step explanation:

A set of outputs and inputs becomes a function when there is only one output per input. In this case, each "x" value only has one "y" value, making it a function.

Answer:

16 1/50

Step-by-step explanation:

First, turn the fractions into improper fractions.

8 9/10 can be 89/10 and 1 4/5 can be 9/5.

Then you multiply them together:

89/10 * 9/5= 801/50

Now, since 801/50 is 16.02 turn that into a mixed fraction. It becomes 16 1/50.

That's your answer.

The value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9

From the question, we are to determine the values of the missing sides

From the diagram,

Opposite = 9

Adjacent = y

Hypotenuse = x

Included angle = 45°

Using SOH CAH TOA, we can write that

[tex]tan 45^\circ= \frac{9}{y}[/tex]

[tex]1 = \frac{9}{y}[/tex]

∴ y = 9

Since the triangle is a right triangle, we can write that

x² = y² + 9² (Pythagorean theorem)

x² = 9² + 9²

x² = 81 + 81

x² = 162

x = √162

x = 12.7

Hence, the value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9

Learn more on Trigonometry here: https://brainly.com/question/24259483

#SPJ1

Answer:

4 I promise

jhjhhhhjjj bug check txt TC gym c rectify txt

Answer:

a) Undefined.

Step-by-step explanation:

[tex]f(x) = \dfrac 3{6x+6} = \dfrac{3}{6(x+1)} = \dfrac{1}{2(x+1)}\\\\\\f(-1) =\dfrac{1}{2(-1+1)}= \dfrac{1}{0}[/tex]

Using a t-distribution calculator, it is found that the critical value for the hypothesis test is of t = 1.3277.

The critical value is found considering three inputs:

Hence, for a two-tailed test, with a 0.2 significance level and 19 df, the critical value is of t = 1.3277.

More can be learned about the t-distribution at https://brainly.com/question/16162795

#SPJ1

Step-by-step explanation:

|...| means absolute value of "...". that means always the "+" value of "...", even if it is negative.

in other words

|-x| = x

|x| = x

|-x - 2y| for x = -2 and y = 3

|- -2 - 2×3| = |2 - 6| = |-4| = 4

Answer:

yes it is

Step-by-step explanation:

It is a rational number, as it can be written as a fraction.

Answer:

for the x values: -2,-1,0,1,2

y-values: 13, 6, 5, 4, -3

Step-by-step explanation:

The number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be 3.5 hours.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

David's phone battery level drops 6 percentage points each hour when he is not playing a game on it.

When David does play a game on his phone, the phone battery level drops 18 percentage points each hour.

On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M.

If David did not charge his phone during this time.

Then the number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be

Let x be the number of no gaming hours and y be the number of gaming hours.

Then the equation will be

6x + 18y = 100 - 22

6x + 18y = 78

  x + 3y = 13 ...1

    x + y = 6 ...2

By solving the equations 1 and 2, we have

x = 2.5 hours and y = 3.5 hours

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ1

Answer:

A

Step-by-step explanation:

Pick any two sides....their sum must be greater than the third side....

  a+b > c

  a+c > b

  c + b > a

The two true statements are the second statement (both lines contain the point (0,0)) and the fourth statement (If the Wilson family buys 3 pizzas, they will get more slices than the Hernandez family).

First, we know that the Hernandez family orders 3 large pizzas, such that they cut each pizza in the same number of slices, getting a total of 24 slices.

Then the number of slices that they get for each pizza is:

24/3 = 8

So from each large pizza, they get 8 slices.

So the relation between the number of pizzas bought (x) and the number of slices (y) is:

y = 8*x

In the other hand for the Wilson family we have the relation:

y = 10*x

Where y and x are the same ones as the defined above.

Then the true statements are:

"If the Wilson family ordered 3 large pizzas from the same restaurant as the Hernandez family, they would have more slices than the Hernandez family after each family cut their pizzas into slices."

This is true because Wilson family cuts each pizza in 10 slices, while the Hernandez family cuts each pizza in 8 slices.

"For each family, a graph of the relationship between number of pizzas, x, and number of slices, y, goes through the point (0, 0) and is a straight line."

The point (0, 0) means that if they buy 0 pizzas, they get 0 slices, which is true, so both relations contain this point.

If you want to learn more about linear relationships:

https://brainly.com/question/4025726

#SPJ1

Answer:

g = 15

Step-by-step explanation:

Rearrange unknown terms to the left side of the equation: 3g - 2g = 15

Combine like terms: g = 15

Answer: g = 15

Answer:

D. The larger multiple

Step-by-step explanation:

n7nj7j

The volume of the rectangular prism is 17 cubic units

The given parameters are:

The volume is calculated as:

Volume = Length * Width * Height

Substitute known values

Volume = 5 * 2 * 1.7

Evaluate

Volume = 17

Hence, the volume of the prism is 17 cubic units

Read more about volumes at:

https://brainly.com/question/1972490

#SPJ1

Since the square root of

x=√x

and the cube root of

x=3√x

and their product

=√x × 3√x

= x1/2 × x1/3 [Since, n√a =a 1/n]

=x1/2+1/3 [Since, a^m ×a^n =a^m+n]

=x^3+2 /6

= x 5/6

Therefore, required product is

=√6x5

Answer:

[tex]x^2y^3[/tex]

Step-by-step explanation:

[tex]\text{Square of}~ x =x^2\\\\\text{Cube of}~ y = y^3\\\\\text{Product} = x^2y^3[/tex]

Using the z-distribution, it is found that the margin of error for the 95% confidence interval is of 0.0889.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate and the sample size are given as follows:

[tex]\pi = 0.71, n = 100[/tex]

Hence, the margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.71(0.29)}{100}}[/tex]

M = 0.0889.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

B

Step-by-step explanation:

the hypotenuse........

Answer:

B

Step-by-step explanation:

The hypotenus is always opposite to the right and angle and always the longest side

Answer: y=-1/5x+4

Step-by-step explanation: use the equation y=mx+b (x,y)->(5,3) 5 is an x value and 3 is a y value so you want to plug in these values into the equation. 3=-1/5(5)+b. We already know our slope so just plug it into m. Now multiply -1/5 and 5 which is -1. 3=-1+b you want to isolate b so you can find the intercept. Add one to both sides so it cancels out. 4=b we found our y-intercept so we can write the equation now. y=-1/5x+4

Answer:

1/20

Step-by-step explanation:

number of favourable outcomes/number of outcomes

Answer:

They are identical triangles.

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

The triangle with 39 and 90 has a missing angle of 51 degrees, and the triangle with 51 and 90 vice versa.

✎ let's answer it

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

it's ↓

( identical triangle)