Help with the question attached, thank you!!

Answer:

[tex]\huge \boxed{\sf \ \ x=-\dfrac{1}{2} \ \ }[/tex]

Step-by-step explanation:

Hello,

We need to express this parabola using this kind of expression

   [tex]y=a(x-b)^2+c[/tex]

and then, the line of symmetry will be the line x = b

Let's do it !

[tex]\text{*** Complete the square ***} \\ \\ x^2+x=x+2\cdot \dfrac{1}{2}\cdot x=(x+\dfrac{1}{2})^2-\dfrac{1^2}{2^2}=(x+\dfrac{1}{2})^2-\dfrac{1^2}{4} \\ \\ \text{*** Apply it to our parabola } \\ \\y=-x^2-x+2=-(x^2+x)+2=-[(x+\dfrac{1}{2})^2-\dfrac{1}{4}]+2 = -(x+\dfrac{1}{2})^2+\dfrac{1+2*4}{4}= -(x+\dfrac{1}{2})^2+\dfrac{9}{4} \\ \\ \text{*** It comes ***} \\ \\ \Large \boxed{\sf \ \ y=-(x+\dfrac{1}{2})^2+\dfrac{9}{4} \ \ }[/tex]

So the line of symmetry is

[tex]\huge \boxed{\sf \ \ x=-\dfrac{1}{2} \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

the hypotenuse(b) is 50 if that helps

Step-by-step explanation:

a=40 & c=30 if you square these two numbers, add them and find the square root you get the hypotenuse(a^2+b^2=the square root of c^2)

Answer:

18

Step-by-step explanation:

3/4 of 24 is 18

Answer:

Step-by-step explanation:

Distance traveled by Mike in 12 hours = 4 * 12 = 48 km

This will become the radius of the circle

r = 48 km

Area of the circle to be searched = πr²

                                                       = 3.14 * 48 * 48

                                                       = 7234.56 square km

Answer:

y= x^2 + 6

Step-by-step explanation:

y= x2 + 6 (which should be written as y= x^2 + 6) has the form y - k = a(x - h)^2.  For y= x^2 +  6, h = 0 and k  = 6.  Thus the vertex is (0, 6)

Answer:

The nth term of the sequence is

Step-by-step explanation:

The sequence above is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 7

d = 9 - 7 = 2 or 11 - 9 = 2

So the nth term for the sequence is

A(n) = 7 + ( n - 1)2

= 7 + 2n - 2

Hope this helps you

Answer:

sequence is arithmetic

Step-by-step explanation:

A geometric sequence has a common ratio r between consecutive terms.

An arithmetic sequence has a common difference d between consecutive terms, thus

11 ÷ 14 ≠ 8 ÷ 11 ≠ 5 ≠ 8 ← not geometric

11 - 14 = - 3

8 - 11 = - 3

5 - 8 = - 3

There is a common difference d between consecutive terms

Thus sequence is arithmetic.

Answer:

Step-by-step explanation:

This is an arithmetic sequence.

First term = a = 14

Second term = 11

Common difference = second term -  first term

                                 = 11 - 14

                                =  - 4

Each term is got by adding (-4) to the previous term

Third term = 11 + (-4) = 11 -4 = 8

Answer:

asDawas

Step-by-step explanation:

sadasda

Answer: -28, -17, 22.4, 27

hope this helps

Answer:

  6 < x < 8

Step-by-step explanation:

The compound inequality in this instance represent the "and" condition, not the "or" condition.* We might solve it like this.

  -47 > 1 -8x > -63 . . . . given

Multiply by -1:

  47 < -1 +8x < 63

Add 1:

  48 < 8x < 64

Divide by 8:

  6 < x < 8

______

* You can tell this is the case by looking at the ends of the given statement:

  -47 > -63 . . . . a true statement, so the solution set will be an intersection, not a union.

The equation turns into:

400+70+6+0.6+0.03+0.07

which equals:

476.637

The second equation becomes 4+ 68/1000, which becomes 4.068.

Hope this helps!

Answer:

[tex]area = \frac{8}{3}pie ft^2[/tex]

Step-by-step explanation:

Area of sector is given as θ/360*πr²

Where,

θ = central angel of sector, m < DCE = 60°

r = radius = 4 feet

Area of sector = [tex] \frac{60}{360}*pie*4^2[/tex]

[tex] area = \frac{1}{6}*pie*16[/tex]

[tex] area = \frac{1*16}{6}*pie[/tex]

[tex] area = \frac{16}{6}*pie[/tex]

[tex]area = \frac{8}{3}pie ft^2[/tex]

Area of the sector = 8/3π ft²

Answer:

6/7

Step-by-step explanation:

Ruth has played 7 games.  She has scored 9 or more points in 6 of them.  That means she has a 6/7 probability of doing so again.

Answer:

6/7

Step-by-step explanation:

Answer:

y = 4/3

Step-by-step explanation:

The required value of fraction y is 4/3.

Given that,

[tex]\frac{y}{1\frac{7}{9} } = 3/4[/tex]
Fraction y is to be determined by simplification.

The process in mathematics to operate and interpret the function to make function simple or more understandable is called simplifying and the process is called simplification.

Fraction is defined as the number of compositions that constitute the Whole. Fraction is represented as x = a / b where the upper value is termed as the numerator and the lower value is the denominator.

⇒Simplification

[tex]\frac{y}{1\frac{7}{9} } = 3/4[/tex]                                                                          ( 1 + 7 / 9 = 16 / 9)
[tex]\frac{y}{\frac{16}{9} } = 3/4[/tex]               (Transposition of 16/9 from the denominator to the right)
y  = 3 / 4 * 16 / 9
y = 4 / 3

Thus, the required value of fraction y is 4/3.

Learn more about simplification here:
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Answer:

  D) G

Step-by-step explanation:

E evaluates to 3.8 +0 = 3.8 . . . not an integer

F evaluates to 0 +0.5 = 0.5 . . . not an integer

G evaluates to -8 +0 = -8 . . . an integer

H evaluates to 9/0 = undefined . . . not an integer

__

Expression G evaluates to an integer.

Answer:

3 + 6 = 1/2(#grapes)

3 + 6 = 9

9 = 1/2(#grapes)

2(9) = 1(#grapes)

18 = # of grapes

Step-by-step explanation:

Answer:

The graph of the equation y=3x-2 is shown in the picture below!!

Step-by-step explanation:

I hope this helps, if it does please mark brainliest!! Thank you!! Have a great day!

Answer:

y>x+4 (A,B)

y≤3x (B,C,D,E,F)

x≥7(A,B,D)

i realllyyyyyyyy HOPE THIS HELPS YOUUU!!!

Answer:

Step-by-step explanation:

A =3x² + 4x + 1

B = 5x² - 3x + 8

C = 4x² - 7x - 3

B + C –A is

5x² - 3x + 8 + 4x² - 7x - 3 - ( 3x² + 4x + 1)

Expand and simplify

We have

5x² - 3x + 8 + 4x² - 7x - 3 - 3x² - 4x -1

Group like terms

5x² + 4x² - 3x² - 3x - 7x - 4x + 8 - 3 - 1

We have the final answer as

Hope this helps you

Answer:

5

Step-by-step explanation:

When squaring the number 5 (i.e [tex]5^2[/tex] ) the answer is 25. [tex]5^{2}[/tex] is the same thing as 5 times 5. Basically with the square root, you are going backwards, so you are therefore finding the base of it all.

We have a square that has area of 25 square units. The question is: what is the side length? That would be 5 since 5*5 = 25. You would use guess and check if you weren't familiar with square roots. A better option is to use the square root function on the calculator.

Note: the square root undoes the squaring operation

This is the same as h(x) = x/4

In decimal form, it would be h(x) = 0.25x

=============================================

Explanation:

Inverses undo the original function. The original function tells us to take any input (x) and multiply by 4 to get the output y = f(x) = 4x

To get the inverse, we reverse the operation applied here. The opposite of multiplication is division. So we'll divide by 4 instead of multiply by 4. This is why the answer is x/4 or (1/4)x

-----------

Another approach is to do the following: Replace f(x) with y. Swap x and y. Solve for y

f(x) = 4x

y = 4x

x = 4y

4y = x

y = x/4

h(x) = x/4

We end up with the same result as before.

-----------

Extra info:

For any real number x, the following two equations are true

h( f(x) ) = x

f( h(x) ) = x

Explanation:

Use the slope formula. We subtract the y values together, and do the same for the x values as well. Subtract in the same order each time. Then you divide the two results. Reduce the fraction if possible.

m = (y2 - y1)/(x2 - x1)

m = (14 - 18)/(30 - (-20))

m = (14 - 18)/(30 + 20)

m = -4/50

m = -2/25

Answer:

[tex]-\frac{2}{25}[/tex]

Step-by-step explanation:

Slope is rise over run.

[tex]m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]

We are given the points (–20, 18) and (30, 14).

[tex]m=\frac{14-18}{30+20}=\frac{-4}{50}=-\frac{4}{50}=-\frac{4/2}{5/2}=\boxed{-\frac{2}{25}}[/tex]

The slope is -2/25.

Brainilest Appreciated.

Answer:

multiply by a factor of 7/8

Step-by-step explanation:

sphere A radius is 24 and Sphere B radius is 21

24x=21

x = 7/8

Answer:

multiply by a factor of 7/8

Answer:

variation constant = k = 8

equation of variation : y = 8x

Step-by-step explanation:

Any relationship of variation can be written as y = kx

where k is the variation constant.

_______________________________________

Let the equationof relation between y and x be y =kx here as well

given

y = 16 when x = 2

substituting this value in the equation y = kx

16 = k*2

=> k = 16/2 = 8

Thus,

variation constant = k = 8

equation of variation : y = 8x

Answer:

Towards the left

Step-by-step explanation:

Answer:

2.7

Step-by-step explanation:

2.5/5.8 = BD/6.2

BD = 2.7

Answer: 2.7

Step-by-step explanation: 2.5/5.8 = BD/6.2

BD = 2.7

Answer:

See below.

Step-by-step explanation:

The y intercept is 4 so you can mark a point on the line at (0, 4).This is a point on the y-axis 4 units up from the origin (origin is where the axis cross).

The slope is negative so the line will rise to the left.

Mark a point which is  1 unit  horizontally to the left of point (0, 4) and 5 units vertically upwards.

Then draw the line to pass through this point  and the point (0, 4)

The equation of the line is y = -5x + 4.

See the attached picture:

The formula for calculating the size of the population after t years using continuous growth is [tex]A = 100e^{2t}[/tex], making option B the right choice.

Continuous growth in the initial amount P, after time period t, and at the rate of r per time period gives the final amount as: [tex]A = Pe^{rt}[/tex]

In the question, we are asked to suppose that a population begins at a size of 100, and grows continuously at a rate of 200% per year, and are asked for the formula for calculating the size of that population after t years.

The given case can be shown as a continuous growth, with:

Initial population, P = 100,

Rate of growth, r = 200% = 2, and,

The time period, t years.

Thus, the formula for calculating the size of that population after t years can be shown using the formula: [tex]A = Pe^{rt}[/tex], as:

[tex]A = 100e^{2t}[/tex].

Hence, the formula for calculating the size of the population after t years using continuous growth is [tex]A = 100e^{2t}[/tex], making option B the right choice.

Learn more about continuous growth at

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Answer:

Step-by-step explanation:

Displacement vector R = 2i + j +  3k

Unit vector along displacement vector

= R / I R I

= ( 2i + j +  3k )  / √ ( 2² + 1² + 3² )

= ( 2i + j +  3k )  / √ 14

Now force F acts in the direction of this unit vector . It is magnitude of 20 N

So this vector can be represented by the following expression

F = 20 [  ( 2i + j +  3k )  / √ 14 ]

[tex]F= \frac{20}{\sqrt{14} } \times ( 2i+j+3k)[/tex]

Answer:

Jared attempted 60 shots.

Zach attempted 70 shots.

Step-by-step explanation: