Find the value of X.

Using the given quadratic function, it is found that:

a) The vertex is (-2.5, -15.5).

b) The y-intercept is of -3.

c) The solutions are x = -0.28, x = 5.28.

It is modeled by:

f(x) = 2x² - 10x - 3.

Which means that the coefficients are a = 2, b = -10, c = -3.

It is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Hence:

[tex]x_v = -\frac{-10}{4} = -2.5[/tex]

[tex]y_v = -\frac{(-10)^2 - 4(2)(-3)}{8} = -15.5[/tex]

The vertex is (-2.5, -15.5).

It is the value of coefficient c, hence it is of -3.

[tex]\Delta = b^2 - 4ac = (-10)^2 - 4(2)(-3) = 124[/tex]

[tex]x_1 = \frac{10 + \sqrt{124}}{4} = 5.28[/tex]

[tex]x_2 = \frac{10 - \sqrt{124}}{4} = -0.28[/tex]

The solutions are x = -0.28, x = 5.28.

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The amount $600 would be after 3 years at 8% interest compounded continuously is $755.83

Compound interest are amount of money added on amiunt invested.

Given the following parameters

P = $600
r = 8% = 0.08
t = 3 years

Using the compound interest formula

A(t) = Ao(1+r)^t
A(t) = 600(1.08)^3
A(3) = $755.83

Hence the $600 would amount to after 3 years at 8% interest compounded continuously is $755.83

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Answer:



Step-by-step explanation:

8:11

Answer:

232

Step-by-step explanation:

232, because each has 100 squares so if you add the 2 filled squares you will get 200. Then if you count the last one only 32 is filled, when u add it it gives you 232

Answer:

a rigid motion does not affect the overall shape of an object but  moves an object from a starting location to an ending location the resultant figure in cogruent to the original figure.a rigged motionis when an  object is  moved  from one location to another  and the size and shape have not changed.hope it helps :)

Answer:

1 is alternate exterior

2 is none of these

3 and 5 are corresponding

4 is alternate interior

Step-by-step explanation:

A Z-score helps us to understand how far is the data from the mean. The z-score of a person who scored 470 on the exam is 0.8.

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,

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

Where Z is the Z-score,

X is the data point,

μ is the mean and σ is the standard variable.

Given the mean is 450, while the standard deviation is 25, therefore, the value of the z-score can be written as,

[tex]Z = \dfrac{X- \mu}{\sigma}\\\\Z(X=470) = \dfrac{470- 450}{25} = 0.8[/tex]

Hence,  the z-score of a person who scored 470 on the exam is 0.8.

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Answer:

448.02

Step-by-step explanation:

72% of 2489 is 1,792.08

25% of 1,792.08 is 448.02

Answer:

v=60

Step-by-step explanation:

10=v/3-10

Subtract 10 from both sides the divide ( however really multiply by the reciprocal.

Answer:

A 18c B 2 qt

Step-by-step explanation:

Basically since 1 pt = 2 c then you multiply pt by 2

Since 4 qt = 1 gal then divide qt by 4.

Using it's concept, it is found that there is a 0.0526 = 5.26% experimental probability that the next student Grayson talks to will pick orange.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In an experimental probability, these number of outcomes are taken from previous trials.

In this problem, 2 out of 38 students picked orange as their favorite color, hence the probability that the next student picks orange is given by:

p = 2/38 = 1/19 = 0.0526.

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i need the answer to this lol

Answer:

[tex]2\frac{5}{12}[/tex]

Evaluate. Subtract 3 by 1

[tex]3 - 1 = 2[/tex]

Find the least common denominators of the fractions, multiply them by the least common denominators, then subtract.

[tex]\frac{2 * 4}{3 * 4} = \frac{8}{12}[/tex]

[tex]\frac{1 * 3}{4 * 3} = \frac{3}{12}[/tex]

Now subtract.

[tex]\frac{8}{12} - \frac{3}{12} = \frac{5}{12}[/tex]

Add the whole number you found earlier from subtracting 3 and 1 by the new fraction, 5/12

[tex]2 + \frac{5}{12} = 2\frac{5}{12}[/tex]

Answer:

horizontal stretch

Step-by-step explanation:

For f(x) to turn into g(x), you must divide the function by 8. When we divide a function, this is known as a horizontal stretch because as you can see, the function gets wider. See the help image below with different examples.

Just a future tip: when you're in doubt, graph it out!

Horizontal stretch is the transformation which converts the graph of f(x) = -8x²- 8 into the graph of g(x) = -x² – 1.  Option C is correct.

The general form of the quadratic function is f(x) = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

In this case, for f(x) = -8x² - 8, the vertex is at (0, -8).

For g(x) = -x² - 1, the vertex is at (0, -1).

Comparing the two functions, you can see that the coefficient in front of x² changes from -8 to -1.

This change in the coefficient results in a horizontal stretch or compression of the parabola.

In this case, the graph has been horizontally stretched to transform from f(x) to g(x).

Hence, Option c is correct. Horizontal stretch is the transformation which converts the graph of f(x) = -8x²- 8 into the graph of g(x) = -x² – 1.

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Step-by-step explanation:

12345+12345+12345+12345=12345×49380

I'm not sure if my answer will help, but oh well.

So basically congruent means equal. so with the two photos you should be able to tell if they are congruent by looking and measuring there angles, sizes, etc.

Answer:

The ball was thrown from a height of [tex]3\; {\rm ft}[/tex].

Step-by-step explanation:

The expression for the height of this ball, [tex]h(t) = -16\, t^{2} + 40\, t + 3[/tex], represents a parabola (with respect to time [tex]t[/tex].)

In this expression, "[tex]3[/tex]" represents the [tex]y[/tex]-intercept of the parabola- the output of the parabola when the input is [tex]t = 0[/tex]. The reason is that when [tex]t = 0\![/tex], terms of this parabola that include [tex]t[/tex] ([tex](-16\, t^{2})[/tex] and [tex]40\, t[/tex]) would evaluate to [tex]0[/tex]:

[tex]\begin{aligned}h(0) &= -16\times 0^{2} + 40\times 0 + 3 = 3\end{aligned}[/tex].

In the case of this ball, the term "[tex]3[/tex]" means that height of this ball is [tex]3\; {\rm ft}[/tex] when [tex]t = 0[/tex] (right when the ball was thrown.) Thus, the ball was thrown from a height of [tex]3\; {\rm ft}[/tex].

Answer:

so

Step-by-step explanation:

what I did was count the lines start from 5m and go on from there hope this helps :)

Answer:

1/2 = 0.5 = 50%

Step-by-step explanation:

Given:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

[tex]\implies \sf P(yellow) = \dfrac{4}{8}=\dfrac12[/tex]

This can also be written as 0.5 or 50%

Probability of yellow:-

P(Y):-

Answer:

47 units.

Step-by-step explanation:

You can split the shape into smaller pieces to make it easier to digest.

4*8 is 32 which is the top rectangle.

9-4=5 since you are trying to figure out the second rectangle, not the whole side length.

5*3=15

15+32=47

The area of the figure is 47 square units.

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

We have,

From the given figure,

We see that,

Two rectangles can be considered.

Now,

One rectangle:

Length = 8

Width = 4

Area = 8 x 4 = 32

Another rectangle:

Length = 5

Width = 3

Area = 5 x 3 = 15

Now,

The area of the figure,

= 32 + 15

= 47

Thus,

The area of the figure is 47 square units.

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Answer: -7 , -10

Step-by-step explanation:

the pattern is that every number gets 3 taken away from the last one (8 - 3 is 5, 5 - 3 is 2, etc)

Answer:

-7, -10.

Step-by-step explanation:

Common difference is - 3 so the next term = -4-3 = -7.

[tex] \frac{2 |x - 3| }{5} = 6 \\ [/tex]

[tex]5 \times \frac{2 |x - 3| }{5} = 5 \times 6 \\ [/tex]

[tex]2 |x - 3| = 30[/tex]

[tex] \frac{2 |x - 3| }{2} = \frac{30}{2} \\ [/tex]

[tex] |x - 3| = 15[/tex]

[tex]x - 3 = 15[/tex]

[tex]x - 3 + 3 = 15 + 3[/tex]

[tex]x = 18[/tex]

[tex]x - 3 = - 15[/tex]

[tex]x - 3 + 3 = - 15 + 3[/tex]

[tex]x = - 12[/tex]

Answer:

uhmm i don't know sorry I am just kind of doing this so I get the credit for answering a question:)

Answer:

there is no picture to give an answer

Answer:

I need the picture to answer the question...

Step-by-step explanation:

Answer:

5.32

Step-by-step explanation:

MARK A BRAIN LESS

CARRY ON LEARNING

B BRAIN LY FAST

Answer:

I cannot see the attachment

Step-by-step explanation:

Answer: x=24

Step-by-step explanation:

Step-by-step explanation:

[tex]5. {x}^{3} - xy + {y}^{2} = 4[/tex]

[tex] \frac{dy}{dx} ( {x}^{3} - xy + {y}^{2} ) = \frac{dy}{dx} (4)[/tex]

[tex]3 {x}^{2} - x(1) \frac{dy}{dx} + 1(y) + 2y \frac{dy}{dx} [/tex]

Combine the dy/dx.

[tex] \frac{dy}{dx} ( - x + 2y) + y + 3 {x}^{2} [/tex]

[tex] \frac{dy}{dx} ( - x + 2y) = - 3 {x}^{2} - y[/tex]

[tex] \frac{dy}{dx} = \frac{ - 3 {x}^{2} - y}{ - x + 2y} [/tex]

[tex] \frac{3 {x}^{2} + y }{x - 2y} [/tex]

Answer:

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{y-3x^2}{2y-x}[/tex]

Step-by-step explanation:

using the product rule to differentiate - xy then

3x² - (x[tex]\frac{dy}{dx}[/tex] + y(1) ) + 2y[tex]\frac{dy}{dx}[/tex] = 0

3x² - x[tex]\frac{dy}{dx}[/tex] - y + 2y[tex]\frac{dy}{dx}[/tex] = 0

3x² + [tex]\frac{dy}{dx}[/tex] (2y - x) - y = 0 (subtract 3x² - y from both sides )

[tex]\frac{dy}{dx}[/tex] (2y - x) = y - 3x² ← divide both sides by (2y - x)

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{y-3x^2}{2y-x}[/tex]

Answer:

in a triangle,

G+E+F = 180°

or, 24°+17°+F = 180°

or, 41°+F = 180°

or, F= 180-41

F = 139°