3. WEDNESDAY (5/20): The minimum of the graph of a quadratic function is located at (-1,2). The point (2, 2015
also on the parabola. Which function represents this?
a) f(x) = x² + 2x + 3
b) f(x)= x² - 2x+3
c) f(x) = 2x²+4x+4
d) f(x)= 2x²- 4x+4​

Answer:

Step-by-step explanation:

2x² - 8x - 24 = 0

2x² - 12x + 4x - 4*6 = 0

2x(x-6) + 4(x - 6) = 0

(x - 6)(2x + 4) = 0

Answer:

65.97

Step-by-step explanation:

Answer:

Side AB has a length of 4, and side BC has a length of 11.7

Answer:

1. segment RT

2. segment QS

3. segment PS

4. < QTR

5. arc QR

6. arc QSR

7. arc QS

These are all by definition.

Radius: distance from the center of a circle to a point on the circle

Diameter: a chord that goes through the center

Chord: any segment whose endpoints are on the circle

Central Angle: an angle at the center of the circle with endpoints on the circle

Minor Arc: arc that is less than 180 degrees

Major Arc: arc that is greater than 180 degrees

Semicircle: Arc of 180 degrees

Answer:

24

Step-by-step explanation:

Answer:

zero=0

Explanation:

-8-2k=-2(k+4)

-8-2k=-2k-8

-2k+2k=-8+8

zero=0

Answer:

8

Step-by-step explanation:

Step 1: Add 19 to both side

b-19+19=-11+19

b=8

Hope I helped:D

Answer: b = 8

Step-by-step explanation: To solve for b in this equation, we want to get b by itself on the left side of the equation.

Since 19 is being subtracted from b, to get b by itself,

we need to add 19 to the left side of the equation.

If we add 19 to the left side, we must also add 19 to the

right side in order to keep our equation balanced.

Notice that on the left side, -19 and +19 cancel

each other out so we're simply left with b.

On the right side, -11 + 19 equals 8.

So we have b = 8.

Answer:

Step-by-step explanation:

The formula for calculating the surface area of a triangular prism is expressed as shown below:

SA= bh + pH

b= base of the triangle

h- height of the triangle

p= perimeter of the triangle

H= height of the prism

Given b = 1foot

h = 2feet

perimeter of the triangle = sum of all its sides = 1ft + 2ft + 2.2ft

p = 5.2ft

H = 3ft

Substituting the values into the formula for finding the surface area:

SA = 1(2)+5.2(3)

SA = 2+15.6

SA = 17.6ft²

The surface area of the triangular prism is  17.6ft²

Answer:

69 ft^2

Step-by-step explanation:

Answer:

sqrt(A /pi ) = r

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

Divide each side by pi

A / pi = r^2

Take the square root of each side

sqrt(A /pi ) = sqrt(r^2)

sqrt(A /pi ) = r

Answer:

sqrt(A /pi ) = r

Step-by-step explanation:

The answer that I got was 7/7

Answer:

The slope of the line is 1

Step-by-step explanation:

the formula for slope is y2-y1 / x2-x1. The point (-4,2) could be labeled as x1 and y1, where x1 is -4 and y1 is 2 and the point (3,9) could be labeled as x2 and y2, where x2 is 3 and y2 is 9. So then the equation would be set up as the following: 9-2 / 3--4. Simplified, the equation equals 1, because when you subtract it comes out as 7/7.

Hope this helps :)

This question is incomplete because it lacks the diagram of the line plot. Find attached to the answer, the diagram of the scatter plot.

Answer:

35/8 inches or 4 3/8 inches.

Step-by-step explanation:

Reading the line plot, the number of objects is plotted vertically while the length of the object is arranged horizontally on the line plot.

The total length is calculated as: summation of the (Number of objects × Length of the objects)

= [(1/8 ×0) + (1/4×0) + (3/8 × 2) + (1/2 ×3) + (5/8 × 1) + (3/4 × 2) +(7/8 × 0)] inches

=[ 0 + 0 + 3/4 + 3/2 + 5/8 + 3/2 + 0] inches

= 35/8 inches or 4 3/8 inches.

Therefore, the total length of the objects if they are connect end to end is 35/8 inches or 4 3/8 inches.

Answer:

5/4=1 1/4

Step-by-step explanation:

you have to turn the bottom number the same as the other one by multiplying it by 2,you have to do the for the top and it together to get your answer

Answer:

1 1/4

Step-by-step explanation:

1/2 + 2/4. 2/4 + 3/4 = 5/4 = 1 1/4

Answer:

the length of the car in Ivan's drawing is 12 cm, or the second option.

Step-by-step explanation:

Scale drawing length : actual car length = 2 cm:1 cm

Since it's the same car, we know that the length would be 6 cm.

Therefore, we can set up a proportion and solve for x.

2/1=x/6

x=12

Therefore, the length of the car in Ivan's drawing is 12 cm, or the second option.

I hope this helped and have a good rest of your day!

Answer:

8/3 hours

Step-by-step explanation:

Sloane drives for 2/3 hours to get grandmother's house

Inorder to arrive at her cousin's house she is required to drive 4 times longer

= 2/3 ×4

= 8/3 hours

Thus, Sloanne needs to drive for 8/3 hours inorder to reach her cousin's house.

Answer:

Step-by-step explanation:

A line parallel to y-axis has no defined slope  and line parallel to x-axis has a slope of zero.

Answer:

[tex] y = 78(0.54)^t[/tex]

And for this case we want to identify the initial amount and for this case would be 78. And the growth rate can be obtained from the term inside of the parenthesis.

The general model is given by this model:

[tex] y = a (1+r)^t[/tex]

And then [tex] 1+r = 0.54[/tex] and [tex] r = 0.54 -1= -0.46[/tex]

And then we want to find the of the function at t=5 and we got:

[tex] y(5) = 78(0.54)^5 = 3.58 \approx 3.6[/tex]

Step-by-step explanation:

For this case we have the following function given:

[tex] y = 78(0.54)^t[/tex]

And for this case we want to identify the initial amount and for this case would be 78. And the growth rate can be obtained from the term inside of the parenthesis.

The general model is given by this model:

[tex] y = a (1+r)^t[/tex]

And then [tex] 1+r = 0.54[/tex] and [tex] r = 0.54 -1= -0.46[/tex]

And then we want to find the of the function at t=5 and we got:

[tex] y(5) = 78(0.54)^5 = 3.58 \approx 3.6[/tex]

Answer:

Initial amount = 78

Rate of growth = -46%

Y(t=5) = 3.6

Step-by-step explanation:

The general form of an exponential function is:

[tex]Y(t) = Y_0*(1+r)^t[/tex]

The initial value (Y0) is the value of Y(t) when t = 0:

[tex]Y(0) = 78*0.54^0=78[/tex]

Comparing the given function to the general form of the exponential function, the rate of growth 'r' is determined as:

[tex]Y(t) = Y_0*(1+r)^t = 78*(0.54)^t\\78*(1+r)^t = 78*(0.54)^t\\1+r=0.54\\r=-0.46=-46\%[/tex]

At t=5, the value of Y(t) is:

[tex]Y(5)=78(0.54)^5\\Y=3.6[/tex]

Step-by-step explanation:

D= rt

Where D is distance r is rate and t is time

15 < r3

15/3 < r

5< r

The inequality is Rate > 15 / 3. And the swimming rate of a manatee swims for 15 miles in 3 hours will be 5 miles per hour.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The swimming rate of a manatee swims for 15 miles in 3 hours is given as,

Rate > 15 / 3

Rate > 5 miles per hour

The inequality is Rate > 15 / 3. And the swimming rate of a manatee swims for 15 miles in 3 hours will be 5 miles per hour.

More about the rate link is given below.

https://brainly.com/question/14731228

#SPJ2

Answer:

-3/4

Step-by-step explanation:

Point A is at (-4,3) and Point B is at (4,-3)

The slope is at

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

   = (-3 -3)/(4 - -4)

   = (-3-3)/(4+4)

    = -6/8

     = -3/4

Answer:

trevon ran 49 miles

Step-by-step explanation:

9+40=49

Answer:

49 miles

Step-by-step explanation:

Norachi ran 40 miles less than Trevon.

So, Trevon ran 40 miles more than Norachi

Distance covered by Trevon = 40 +9 = 49 miles

Answer:

Where (h,k) is the center and r is the radius

Step-by-step explanation:

[tex]r^2 = (x-h)^2+ (y-k)^2[/tex]

Answer:

1) 943.895 mm3

2) 144 cm3

Step-by-step explanation:

1)

First we need to find the volume of the rectangular prism:

Volume_1 = 9 * 11 * 6 = 594 mm3

Then, we can find the volume of the half cylinder above the prism:

Volume_2 = 0.5*(pi * (4.5^2) * 11) = 349.895 mm3

So the volume of the figure is the sum of both volumes:

Volume_total = Volume_1 + Volume_2 = 943.895 mm3

2)

The volume of a pyramid is one third of the base area multiplied by the height, so we have:

Volume = (1/3) * 6 * 8 * 9 = 144 cm3

Answer:

1. Volume of the composite figure is 943.89 mm³

2. The volume, of the is 144 cm³

Step-by-step explanation:

1. The composite figure comprises of a cube and a half cylinder;

Volume of a cube = 9 mm × 11 mm × 6 mm = 594 mm³

Volume of the half cylinder = area of base × length = (π·r²)/2 × l

Where:

r = (Diameter of base)/2 = 9/2 = 4.5 mm

l = 11 mm

Therefore, plugging the values, gives;

Volume of the half cylinder = (π × 4.5²)/2 × 11 = 349.89 mm³

Hence, volume of the composite figure = Volume of the cube + Volume of the half cylinder

Volume of the composite figure = 594 mm³ + 349.89 mm³ = 943.89 mm³

2. The volume, V of a pyramid is given by the following relation;

[tex]V = \frac{l \times w \times h}{3}[/tex]

Where:

l = Length of base = 8 cm

w = Width of the base = 6 cm

h = Height of the pyramid = 9 cm

[tex]V = \frac{8 \times 6 \times 9}{3} = 144 \ cm^3[/tex]

Here we have that a cube of side x, therefore, the area = x·x, integrating we have;

[tex]\int\limits^x_0 {x \cdot x} \, dx = \frac{x^3}{3}[/tex]

Where:

Length, height width of the pyramid = x

It can therefore be shown, that for a pyramid of length, l, width, w, and height, h, the volume, [tex]V = \frac{l \times w \times h}{3}[/tex] .

Answer:

The formula of this perpendicular line is y = 4x - 2

Step-by-step explanation:

In y = -1/4x+3 the gradient is -1/4.

If two lines are perpendicular, then their gradients will multiply together to give -1.

Use this to find the gradient a of the perpendicular line.

-1/4 * a = -1

a = -1 * -4 so the gradient a of the perpendicular line = 4.

Substitute (2,6) in y = 4x + b, to find the value of b.

y = 4x + b

(2,6)

6 = (4*2) + b

b = 6 - (8)

b = -2

So now we have our equation.

The formula of this perpendicular line is y = 4x - 2

Answer:

I'm sorry but I don't see any equations

Step-by-step explanation:

Answer:

20.5 feet

Step-by-step explanation:

Answer:

11 boxes will be fully packed and .25 will be remaining

Our total amount of apples is 135 apples, and the amount that each box can hold is 12.

So, that means we can make an equation for this.

The equation would be 135 = 12x.

Then, to find x we can divide both sides by 12.

135/12 = 11.25

Next, we take 11 and multiply it by 12 to see how many apples it is.

11 x 12 = 132

So, 135-132 equals 3.

3 is 1/4 of 12.

That means 11 boxes will be fully packed and 1/4 of a box will be filled.

Answer:

positive

Step-by-step explanation:

Answer:

size

Step-by-step explanation:

Example: (1 0 2) has 1 row and 3 columns, so m = 1 & n = 3 and the size is 1 x 3.