Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar and ^ to indicate an exponent. Find the missing terms and write them in decreasing order of exponents.

Answer:

Please refer to the attached image for the graph of given function.

Step-by-step explanation:

Given the equation:

[tex]-x^{2} +4x+12[/tex]

Let us rewrite by letting it equal to [tex]y[/tex].

[tex]y=-x^{2} +4x+12[/tex]

Now, we can see that it is a quadratic equation and it is known that a quadratic equation has a graph of parabola.

Let us compare the given equation with standard quadratic equation:

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

we get:

[tex]a = -1\\b = 4\\c = 12[/tex]

Coefficient of [tex]x^{2}[/tex] is negative 1, so the parabola will open downwards.

Axis of symmetry: It is the line which will divide the parabola in two equal congruent halves.

Formula for axis of symmetry is:

[tex]x = -\dfrac{b}{2a}[/tex]

[tex]x = -\dfrac{4}{2(-1)}\\\Rightarrow x=2[/tex]

It is shown as dotted line in the image attached in the answer area.

Axis of symmetry will also contain the vertex of the parabola.

It is a downward parabola so vertex will be the highest point on this parabola.

Putting x = 2 in the equation of parabola:

[tex]y=-2^{2} +4\times 2+12\\\Rightarrow y =16[/tex]

So, vertex will be at P(2, 16).

Now, let us find points of parabola to sketch graph:

put x = 0, [tex]y=-0^{2} +4\times 0+12=12[/tex]

Another point is Y(0,12)

Now, let us put y = 0, it will give us two points because the equation is quadratic in x.

[tex]0=-x^{2} +4x+12\\\Rightarrow -x^{2} +6x-2x+12=0\\\Rightarrow -x(x -6)-2(x-6)=0\\\Rightarrow (-x-2)(x-6)=0\\\Rightarrow x = -2, 6[/tex]

So, other two points are X1(-2, 0) and X2(6,0).

If we plot the points P, Y, X1 and X2 we get a graph as attached in the image in answer area.

Answer:

£100

Step-by-step explanation:

if the ratio is 7:3, the difference between them is 7-3 . = 4.

So,

4x = £40

Now, calculate x

x = £10

Now,

we are able to calculate:

7x (Bridget's share) = £70

3x (Caroline's share) = £30

Sum = £100

Hope this helps.

Good Luck

i got this question too as my homework it so hard ill let you know if i find out the answer.

Answer:

Step-by-step explanation:

No of people using both gym and pool that is N( gup ) = 25

No of people using both track and pool that is N( tup ) = 30

No of people using both track and gym that is N( tug ) = 17

No of people using all that is N( gutup) = 6

No of people  using two or three facilities

= 25+30+17- 2 x 6

= 60

Total no of people = 125

No of people using only one facility

= 125 - 60

= 65 .

Ratio of people using only one facility

= 65 / 125

.52

Required probability

= .52 .

probability that the person uses exactly one of the facilities

= .52

Answer:208

Step-by-step explanation:

13 x 16 = 208

<!> Brainliest is appreciated! <!>

Answer:

In this problem, there is multiple choice for every question. The trick is to exclude the answer that unlikely true.

To solve this easier, you need to find the distance of AB first. After that try to match the answer coordinate with the midpoint of AB. 

1.  Answer: Point C(-3.6, -3.4) divides AB in the ratio 2:3

A (-2,-1) and B(-6, -7)The distance between A and B would be:

x= x2-x1 = -6 - (-2)= -4

y= y2-y1 = -7 - (-1)= -6

Since both x and y coordinate of A and B is minus, let's try answer with x and y minus value.

Point C(-3.6, -3.4) divides AB in the ratio 2:3

x3= x1 + AB ratio* AB distance

x3= -2 + (2/2+3)*(-4)= -3.6

y3= y1 + AB ratio* AB distance

y3= -1 + (2/2+3)*(-6)= -1 - 12/5= -3.4

2.  Point C(0, 1) divides AB in the ratio 4:7

A(4,-3) and B(-7,8)

The distance between A and B would be:

x= x2-x1 = -7 - (4)= -11

y= y2-y1 = 8 - (-3)= 11

Since both x and y distance is 11, let's try answer with total ratio 11

Point C(0, 1) divides AB in the ratio 4:7

x3= x1 + AB ratio* AB distance

x3= 4 + (4/4+7)*(-11)= 4- 4=0

y3= y1 + AB ratio* AB distance

y3= -3 + (4/4+7)*(11)= -3 +4= 1

3. Answer: Point C(8, 9) divides AB in the ratio 5:3

A(3,4) and B(11,12)The distance between A and B would be:

x= x2-x1 = 11 - (3)= 8

y= y2-y1 = 12 - (4)= 8

Since both x and y distance is 8, let's try answer with the total ratio 8. Both of x and y also plus, so focus on coordinate with both x and y plus too.

Point C(3.5, -2.5) divides AB in the ratio 1:7-----> total ratio 8,y minus

Point C(-2, 5) divides AB in the ratio 2:6  -----> total ratio 8, x minus

Point C(8, 9) divides AB in the ratio 5:3   -----> total ratio 8, both x and y plus

x3= x1 + AB ratio* AB distance

x3= 3 + (5/5+3)*(8)= 3+ 5=8

y3= y1 + AB ratio* AB distance

y3= 4 + (5/5+3)*(8)= 4 +5= 9

4. Point C(-2, 5) divides AB in the ratio 2:6  

A(-5,2)and B(7, 14)

The distance between A and B would be:

x= x2-x1 = 7 - (-5)= 12

y= y2-y1 = 14 - (2)= 12

Since both x and y distance is 12, it will be hard to use it since 12 has many factors. Both y coordinate is plus, so focus on coordinate with y more than x and plus.

Point C(4, 1.6) divides AB in the ratio 3:2  ----->  x more than y

Point C(-2, 5) divides AB in the ratio 2:6  -------> y plus, y more than xx3= x1 + AB ratio* AB distance

x3= -5 + (2/2+6)*(12)= -5+ 3=-2

y3= y1 + AB ratio* AB distance

y3= 2 + (2/2+6)*(12)= 2 +3= 5

Step-by-step explanation:

Answer:

when y=1 then x=0.5

Step-by-step explanation:

The graph is provided.

The equation y=4x-1 can be graphed by first graphing the -1 which is the y-intercept in the y=mx+b form. 4=m that is our slope. you can find the lines second point by moving 4 up and 1 to the right. rise/run =4/1. So when you move 4 up and 1 right you get another point on the line (1,3).

You can find out x=0.5 when y=1 by just tracing your finger over the graph and the point when y equals 1 the line intercepts x=0.5. Another screenshot is given.

I hope this helps!

Answer:

b,d,e,f and g

Step-by-step explanation:

A binomial is a polynomial with 2 terms

● a has only one term (15)

● b has two terms 15x and 2 so it is a binomial

● c has only one term so it's not a binomial

● d has two terms 512v^5+ 99w^5

● e has also two terms -6y^2 and (-79)x

● f= 2(3x+4) = 6x+8 so f has two terms then it's a binomial

● g has also two terms

Answer:

3  CUPS pints

Step-by-step explanation:

Multiple to get it by doing this (1/2) US pint x 3 = 1.5 US pints *2= 3 cups

Answer:

47

Step-by-step explanation:

It's just aligning each number / line to each matching one.

Answer:

47 degrees

Step-by-step explanation:

The angle that matches the angle U is angle C

The measure of angle U is 47 degrees

Answer:

x = 76 roses

Step-by-step explanation:

Step 1: Define variables

x = # of roses

y = # of tulips

Step 2: Write systems of equations

x = 4y + 8

5x + 2y = 414

Step 3: Use Substitution

5(4y + 8) + 2y = 414

20y + 40 + 2y = 414

22y = 374

y = 17

Step 4: Plug in y to find x

x = 4(17) + 8

x = 68 + 8

x = 76

Answer:

x = 76

Step-by-step explanation:

x = Roses

y = Tulips

x = 4y + 8

5x + 2y = 414

5(4y + 8) + 2y = 414

20y + 40 + 2y = 414

22y = 374

y = 17

x = 4(17) + 8

x = 68 + 8

x = 76

Answer:

  d) 27

Step-by-step explanation:

The expanded form of (a+b)³ is ...

  (a +b)³ = a³ +3a²b +3ab² +b³

When we are expanding (x +3)³, the x-term is ...

  3(x)(3²) = 27x

The coefficient of x in the expansion is 27.

Answer:

Step-by-step explanation:

8d + 4 = 5d + 28

Group like terms

That's

8d - 5d = 28 - 4

3d = 24

Divide both sides by 3

d = 8

[tex] \frac{7(7g + 8)}{4} = 38.5[/tex]

Cross multiply

we have

7(7g + 8) = 38.5(4)

49g + 56 = 154

49g = 154 - 56

49g = 98

Divide both sides by 49

g = 2

Hope this helps you

Answer:

there's only one equation listed, and it has one solution, which is 0

Step-by-step explanation:

Answer: There is only one equation here...

Anyway it's ans is 0

Step-by-step explanation:

Feel pleasure to help u

Answer:

(D) [tex]f^{-1}{(x$) has an x-intercept of (-36, 0).[/tex]

(E)[tex]f^{-1}{(x)[/tex] has a range of all real numbers.

Step-by-step explanation:

Given the function: [tex]f(x)= -\dfrac23x-24[/tex]

[tex]f(x)+24= -\dfrac23x\\$Multiply both sides by $ -\dfrac32\\x=-\dfrac32(f(x)+24)\\f^{-1}(x)=-\dfrac32f(x)-36[/tex]

When y=f(x)=0

[tex]f^{-1}(x)=-\dfrac32(0)-36\\f^{-1}(x)=-36[/tex]

Therefore, [tex]f^{-1}(x)$ has a x-intercept of -36[/tex]

Also, [tex]f^{-1}(x)[/tex] has a range of all real numbers.

Therefore, Options D and E are correct.

Answer:

4 and 5

Step-by-step explanation:

EDGE

Answer:

Below.

Step-by-step explanation:

This is a parabola.

As the coefficient of x^2 is positive it will open upwards ( shaped like a 'U').

If we convert to vertex form we can find the line of symmetry  and the coordinates of the vertex:

f(x) = 3x^2 - 2x + 1

f(x) = 3(x^2 - 2/3 x) + 1

f(x) = 3[(x - 1/3)^2 - (1/3)^2] + 1

f(x) = 3(x - 1/3)^2 - 1/3 + 1

f(x) = 3(x - 1/3)^2 + 2/3

So the line of symmetry is  x = 1/3 and

the vertex ( the minimum of the curve) is at (1/3, 2/3).

Answer:

B. 8

Step-by-step explanation:

Step 1: Find g(-2)

g(-2) = (-2)² + 1

g(-2) = 4 + 1

g(-2) = 5

Step 2: Find f(5)

f(5) = 2(5) - 2

f(5) = 10 - 2

f(5) = 8

Answer:

Option D is the correct option.

Explanation:

Since, there is a solid circle(blue) at X=4 which implies the value '4' is included in the inequality solution.

Hope this helps...

Good luck on your assignment...

Answer:

the answer you are looking for is the letter B. 33

Answer:

72 rocks.

Step-by-step explanation:

A "easier" way to find out the answer, is to find how much rocks Jessica paints in 1 minute.

Divide 12 with 8:

12/8 = 1.5

Next, multiply the number you got (1.5) with 48:

48 x 1.5 = 72

Jessica can paint 72 rocks in 48 minutes.

~

Answer:

72 rocks

Step-by-step explanation:

So let’s create the following ratio 12:8

The 12 is the amount of rocks and the 8 is the time in minutes.

So we have to find how many rocks she can paint in 48 minutes.

So we make the following ratio x:48.

So we need to find x the amount of rocks she can paint in 48 minutes.

So to find x we have to divide 48 by 8 = 6.

So if the ratio is x6 we can just do 12 * 6 which is 72.

So she can  paint 72 rocks in48 minutes.

Answer:

Step-by-step explanation:

Q1: <B = 150 °

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

8x-10 = 3x+90

5x=100 (subtract 3 from both sides)

x=20   (divide both sides by 5)

x = 20

<B= 3x +90

<B = 3 (20) +90

<B = 60 + 90

<B = 150

Q2: 62

An angles complement (not compliment, haha) is what the number that added to the angle equals 90°.

An angle is 34 more than its complement.

Let x represent the angle.

Let y represent its complement.

x= 34 +(90-x)

y= (90-x)

x + y = 90

34 + (90-x) + (90-x) =90

x= 62

Check the answer.

x= 34 more than complement.

62-34=28

62+28=90

Checked!

Words of encouragement:

Good luck!

Answer:

35cm

Step-by-step explanation:

The net of a regular pentagon has 10 sides.

Since each of the faces are equilateral triangles, the side lengths are equal.

Therefore:

Length of each side of the net = 70/10 =7cm

Therefore, the base is a regular pentagon of side length 7cm.

The perimeter of the base of the pyramid = 5 X 7

=35cm

The perimeter of the base of the pyramid is 35cm.

If the plane is flying at an altitude of 21,000 feet, it is perpendicular to the observer's horizontal line of sight. Thus, I concluded that the given information be assigned to the attachment below.

Given -

( Observer at point O, plane flying at point P

( Plane at 55° angle to horizontal line of sight, altitude of 21,000 feet

The distance ( x ), is represented by the line segment OP, with which we have to determine the length of. Therefore we can conclude the following -

[tex]Sin( 55 ) = Altitude / Distance,\\Sin( 55 ) = 21,000 / x,\\----------------\\x = \frac{21,000}{Sin( 55 )},\\x = 21,000 / 0.81915204428\\\\x = ( About ) 25636 feet\\[/tex]

As you can see, the distance from the plane to the observer is about 25,636 ft!

Answer:

25,636 feet

Step-by-step explanation:

I took the test on FLVS and got 100%

Answer:

x=12

Step-by-step explanation:

Intersecting Chords Formula:

(segment piece) x (segment piece) =  (segment piece) x (segment piece)

10 * x =  ( 3+x) *8

10x = 24+8x

Subtract 8x

10x-8x = 24+8x-8x

2x= 24

Divide by 2

2x/2 =24/2

x = 12

Answer:

The answer is 3 11/21

Step-by-step explanation:

Answer:

              [tex]\underlie{\bold{\ 3\frac{11}{21}\ }}[/tex]

Step-by-step explanation:

[tex]2\frac7{15}\cdot1\frac37=\frac{2\cdot15+7}{15}\cdot\frac{1\cdot7+3}{7}=\frac{37}{15}\cdot\frac{10}{7}=\frac{37}{3}\cdot\frac{2}{7}=\frac{37\cdot2}{3\cdot7}=\frac{74}{21}=\frac{3\cdot21+11}{21}=3\frac{11}{21}[/tex]

Answer:

[tex]4^m[/tex]

Step-by-step explanation:

When you exponent an exponent, you multiply the powers together.

When you divide exponents, you subtract the powers.

Step 1: Convert to same base

log₄64 = 3

Step 2: Rewrite equation

[tex]\frac{(4^3)^{0.5m}}{4^{0.5m}}[/tex]

Step 3: Simplify

[tex]\frac{4^{1.5m}}{4^{0.5m}}[/tex]

Step 4: Simplify

[tex]4^m[/tex]

Answer:

when the square on the hypotenuse of a right-angled triangle is equal in to the sum of the squares on the other two sides

Step-by-step explanation:

let's say......

h = ?

o = 4

a = 4

a^2+o^2=32

square root 32

5.65685424949

that is the value for h

Answer:

A^2+B^2=C^2

you use it the find any length of a right angled triangle

Answer:

Hey there!

We have the equation: y2-y1/x2-x1.

So, we have: 8-2/8-6.

6/2, or 3.

Hope this helps!

Complete question:

Dr. Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) is the color of the light produced by the lamp (red, orange, yellow, green, or blue) Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable. The order of the color of the light presentation is to be counterbalanced. Using concepts from the textbook, why would Dr. Lyte need to use counterbalancing in this scenario?

Answer:

Here,

Independent variable (IV) is: the color of the light produced by the lamp (red, orange, yellow, green, or blue)

We are also told only 10 participants are available.

All 10 participants are being exposed to all five levels of the color variable in the same order.

Counterbalancing is said to be a technique used when establishing task order. It helps prevent introduction if cofounding variables.

Dr. Lyte will need to use counterbalancing technique in this scenario because some of the participants may be unable to understand difference in similar colours. Example some participants may not be able to differentiate between orange and red when the red colour comes after orange.

But using counterbalancing technique, Dr. Lyte can avoid such an error.