Match the expression to its simplified form

Answer:

Vertex form:  y = -2(x - 1)²

Standard form: y = -2x² + 4x - 2

Step-by-step explanation:

Given the x-intercept as the vertex, (1, 0), and the y-intercept, (0, -2) as the two points on the graph of a parabola:

We can determine the equation by substituting these given values into the vertex form of the quadratic equation:

y = a(x - h)² + k

where:

a = determines the direction of where the graph opens, and the wideness or narrowness of the parabola.

(h, k) = vertex

Use vertex: (1, 0) and y-intercept, (0, -2):

y = a(x - h)² + k

-2 = a(0 - 1)² + 0

-2 = a(-1)²

-2 = a(1)

-2 = a

The quadratic equation in vertex form that matches the graph is:

y = -2(x - 1)² + 0 or  y = -2(x - 1)² ⇒ This is the quadratic equation in vertex form.

To transform the vertex form into the standard form, y = ax² + bx + c:

Simply expand the perfect square, (x - 1)², through FOIL method before distributing -2:

y = -2(x - 1)²

y = -2(x - 1)(x - 1)

y = -2(x² -2x + 1)

y = -2x² + 4x - 2 ⇒ This is the quadratic equation in standard form.  

Answer:

Select an answer for each item. If you do not know the answer, you should make an educated guess. At the bottom of the test, you will be given your results. Questions 1-5. Read the following early draft of an essay and then choose the best answer to the question or the best completion of the statement. (1) Seaweed-based fuel could one day power ...

Step-by-step explanation:

Answer:

Is false because the Italian regions are partly bathed by the sea

Step-by-step explanation:

Answer:

The baker baked 375 loaves of bread that day.

Step-by-step explanation:

The baker baked a total of x loaves of bread.

240 loaves were sold by the end of the day.

The baker was then left with 9/25 of the number of loaves that were baked.

We get the equation:

x-240 = 9x/25

When you solve the equation, you will see that x=375.

Therefore, the baker baked 375 loaves of bread that day.

Answer:

(3,4)

Step-by-step explanation:

There are rules for rotations that make it really easy to find the images of any given point for any given rotation. In this case, we have an 180° clockwise rotation, and to find the image of any point rotated this way, we just have to make the x-values and y-values negative.

In this case, we have (-3,-4). Let's make each value negative: (-(-3), -(-4)). Our negative signs cancel out and we get (3,4). And that's the image of the point (-3,-4) at a 180° clockwise rotation about the origin.

Hopefully that's helpful! :)

Answer:

The number of teaspoons in 15 ml is 3 tsp.

Step-by-step explanation:

All you have to do is divide 15 by 5 and get 3. This is because for every 5 ml there is 1 tsp. So for the 15 ml, there is 3 tsp.

Answer:

Step-by-step explanation:

First, you have to use the law of cosines which is c² = a² + b² - 2abcosФ where Ф is the angle measure between sides a and b. So, just plug-in a = 10, b = 12, and Ф = 72 into the equation and you will get (I won't show all the calculations):

c = 13.0321

Then plug that into the area formula to get:

(0.5)(10)(12)(0.225496911)

Which is about:

13.53

we have 9x - 7 ≤ 28 + 4x

⇔9x - 4x ≤ 28 +7

⇔5x ≤ 35

⇔x ≤ 7

ok done. Thank to me :>

Answer:

See answer below

Step-by-step explanation:

  y = one time fee

  35x = hourly rate( hours worked)

  35x + y = $190

   y =  - 35x = 190

  $35 per hours ×  hours work and you did not used the total cost $190

Next time rewrite the sentence and translate into an equation.

The  customers service charges = one-time fee + hourly rate$ ( hours worked)

                                          190   =  y + 35(x)    point slope form

                                        - 35x + 190 = y

Answer:

A

Step-by-step explanation:

876 divided by 43 = 20

and the remainder is 16

in the case of other options, the quotients are correct but the remainders are wrong.

Therefore, A is the option with both correct quotient and remainder.

Answer: 5 1/15 feet

Step-by-step explanation:

For this you have to add fractions.

First find a common denominator between the factions which can be will turn into 15.

The fraction is now: 1 10/15 + 3 6/15

Now that the denominator is the same add the fractions.

1 10/15 + 3 6/15 = 5 1/15

Make the answer negative since its under sea level

Answer = -5 1/15 feet

Answer:

31.35%

Step-by-step explanation:

In the box, there are:

Total number of pens in the box = 6 + 4 + 7

= 17

If we count pens as outcomes the total number of possible outcomes are 17.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Clarissa takes out a black pen from the box.

That reduces the number of black pens by 1 which increases the total number of pens by 1 as well.

So now:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex] \boxed{ \mathsf{probability = \frac{favorable \: outcomes}{total \: outcomes} }}[/tex]

If we want her to pick up a black pen, and she ends up picking one. So, we can say that the outcome is in our favor.

That makes it,

= 5

= 16

[tex] \implies\mathsf{probability = \frac{5}{16} }[/tex]

For showing it as some percent we'll just multiply the fraction by 100

[tex] \implies \mathsf{ \frac{5}{16} \times 100 }[/tex]

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex] \implies \mathsf{ \underline{ 31.25 \: \% } }[/tex]

2500 hot dogs must be sold to  make a profit

If they can sell 5000 hot dogs at $4 per dog, the selling price for the 5000dogs will be expressed as:

SP= 4 * 5000

SP = 4 + 0.25x

Total number hot dog sold = 5000 - 200x

Revenue = Sales price*Total number hot dog sold

When the price is increased by $0.25 then the revenue will be expressed as [tex]g(x) = (4+0.25x) (5000 - 200x)[/tex]

Taking the product, the resulting function will be;

[tex]g(x) = -50x^2 + 1250x + 20000[/tex]

To get the maximum profit, we need to maximize the revenue by differentiating the function and equating it to zero to have:

[tex]g'(x) = -100x + 450\\0=-100x + 1250\\100x = 1250\\x = 12.5[/tex]

Substittute x = 12.5 into the total number hot dog sold function

Recall that n = 5000 - 200x

n = 5000 - 200(12.5)

n = 5000 -  2500

n = 2500

Hence 2500 hot dogs must be sold to  make a profit

Learn more here: https://brainly.com/question/19594550

Answer:

2

Step-by-step explanation:

correct me if i'm wrong

la la la

Multiply the original dimensions by the scale:

8 x 3.5 = 28

6 x 3.5 = 21

New dimensions:  length = 28, width = 21

Answer:

nahhhh why did you report me I did nun wrong

Step-by-step explanation:

y=-4/3x-9

hope it helps

Answer:

(-8.-9) and (14,13).

Step-by-step explanation:

y=x-1

y=117/x-5

As the 2 terms in x are both equal to y:

x-1 = 117/x-5

(x-1)(x-5) = 117

x^2 - 6x + 5 - 117 = 0

x^2 - 6x - 112 = 0

(x + 8)(x - 14) = 0

x = -8, 14.

When x = -8, y = -8-1 = -9

When x = 14, y = 14-1 = 13.

The required coordinate points are (-8.-9) and (14,13).

Given the following equations

y=x-1

y=117/x-5

Equating both function will give

x-1 = 117/x-5

(x-1)(x-5) = 117

x^2 - 6x + 5 - 117 = 0

x^2 - 6x - 112 = 0

(x + 8)(x - 14) = 0

x = -8, 14.

When x = -8, y = -8-1 = -9

When x = 14, y = 14-1 = 13.

Hence the required coordinate points are (-8.-9) and (14,13).

Learn more on intersection of function here: https://brainly.com/question/343077

Answer: 14

Step-by-step explanation:  

x + 9 = 23

   -9     -9

x = 14

Step-by-step explanation:

Rice = 5¾ kg = 23/4kg = 23/4*1000 g = 5750g

Flour = 5725g

Rice > flour

Answer:

lol its rice

Step-by-step explanation:

Answer:

Simple. since we know the weight per given length, we simply need to know the total length of all steel used. the perimeter is easy as it is given, 2×12 and 2×5 for a total perimeter of 24+10 or 34m. now the diagonals must be calculated...

since this is a right triangle, one could easily use a trig function to calculate, but to keep it simple pathag. theorum a2+b2=c2, where the 2 means squared. rearrange to c=sqrt(a2+b2), or 12 squared + 5 squared...giving 144+25=169. then take square rt of 169. this is length of one diagonal, remember to multiply by 2 since there are two diagonal pieces. add this to total perimeter of 34m above.

now that total length is known, simply multiply by weight/m for total weight

**remember units, as problems become complex keeping up with units can help u know if you are using right solving methods, like in heat transfer, energy equations, etc.

Answer: Kim can mow the greens alone in 6 hours.

Step-by-step explanation:

Let K be the rate Kim mows the greens, and S the rate for Shayla.  The rates K and S will be in greens/hour.

We know they can mow 1 green in 4 hours.  We can state this as a sum of their rates times the 4 hours equals one green:

(4 hours)*(K + S) = 1 green

We are told that K = 2S [Kim is twice as fast as Shayla]

Subsititute:

(4 hours)*(K + S) = 1 green

(4 hours)*(2S + S) = 1 green

4*(2S + S) = 1 green

12S = 1 green

Shalya's rate is 1 green/12 hours

Kim is twice as fast:  K = 2S

Kim's rate is 1 green/6 hours.

The opposite of -1.9 on a number line would be 1.9.

The opposite of the opposite of -1.9 would be -1.9.

That is a super weird trick question... what kinda teacher would give that to you???

Answer:

203 i just did it

Step-by-step explanation:

Answer:

the answer is 203

Step-by-step explanation:

Just got it right on edge 22

Answer:

1.8 meters

Step-by-step explanation:

It was easy for me

Answer:

maybe A

Step-by-step explanation:

First one is for number 2 and vice versa.

where is the Question!!!

can you plz give me brainliest I really need it

Your question is incomplete.

Please if you need help I will try to help you :)

Have a Good Day.

Answer:

41 inches

Step-by-step explanation:

To solve for the diagonal length of his television, we can use the formula:

a² + b² = c²

Square the length and width of the TV then add them together. Then find the square root of the sum.

40² = 1600

9² = 81

1600 + 81 = 1681

√1681 = 41