Can someone please help me? And please explain your answer afterwards!

Answer:

[tex]h(t)=-6(t-2)^2+24[/tex]

Step-by-step explanation:

Given function:

[tex]h(t)=-6t^2+24t[/tex]

where:

Rewrite in the form [tex]h(t)=a(t-h)^2+k[/tex]

The quickest way to do this is to expand [tex]h(t)=a(t-h)^2+k[/tex] and compare coefficients with the original function.

[tex]\begin{aligned}h(t)& =a(t-h)^2+k\\ & = at^2-2aht+ah^2+k\end{aligned}[/tex]

Comparing coefficients with [tex]h(t)=-6t^2+24t[/tex]

[tex]\begin{aligned}\implies at^2& =-6t^2\\ a &=-6\end{aligned}[/tex]

[tex]\begin{aligned}\implies -2aht & =24t\\ -2(-6)ht& =24t\\ 12ht & = 24t\\ 12h & = 24\\ h & = 2\end{aligned}[/tex]

[tex]\begin{aligned}\implies ah^2+k & = 0\\(-6)(2)^2+k &=0\\ -24+k & =0\\ k &=24 \end{aligned}[/tex]

Therefore, substituting the found values into the equation:

[tex]h(t)=-6(t-2)^2+24[/tex]

Answer: (2,2)

Step-by-step explanation:

3x+y=8

X=2, y=2

3(2)+2=8

6+2=8

3/4 inch

3 miles

the length of the map

Based on the given conditions, write:

x= 34/ 4 · 25/ 3

Write as a single fraction:

x= 3 × 25/ 4/ 3

Divide a fraction by multiplying its reciprocal:

x= 3 x 25/ 4 × 1/ 3

Write as a single fraction:

x= 3 x 25/ 4 × 3

Reduce fraction to the lowest term by canceling 25 the greatest common factor:

x= 25/4

therefore,the length of the map is 25/ 4.

Answer:

Step-by-step explanation:

Remark

The figure inside the circle is a quadralateral. The 4 angles touch the circumference of the circle. The figure is further defined as a cyclic quadrilateral.

One of the properties of such a figure, is that the opposite angles are supplementary. That is they add to 180.

Equation and solution

? + 100 = 180             Subtract 100 from both sides

? + 100 - 100 = 180 - 100

? = 80 degrees

Answer

? = 80

Answer:

Step-by-step explanation:

In the question it is given that the volume of a sphere is 4,500π cubic yards. And we have to find the radius.

We know that,

Now, Substituting the values in the fomulae :

⇒ 4/3πr³ = 4500π

Cancelling π from both sides :

⇒ 4/3r³ = 4500

⇒ 4r³ = 4500 × 3

⇒ 4r³ = 13500

⇒ r³ = 13500/4

⇒ r³ = 3375

Taking cube root on both sides we get :

⇒ r = 15

Therefore,

Answer:

Step-by-step explanation:

In this question we have provided volume of sphere that is 4500π cubic yards . And we are asked to find the radius of the sphere .

We know that ,

[tex] \qquad \: \frak{Volume_{(Sphere)} = \dfrac{4}{3}\pi r {}^{3} } \quad \bigstar[/tex]

Where ,

Solution : -

As in the question it is given that volume of sphere is 4500π . So equation it with volume formula :

[tex] \dashrightarrow \: \qquad \: \dfrac{4}{3} \pi r {}^{3} = 4500\pi[/tex]

Step 1 : Cancelling π as they are present on both sides :

[tex]\dashrightarrow \: \qquad \: \dfrac{4}{3} \cancel{\pi }r {}^{3} = 4500 \cancel{\pi}[/tex]

We get ,

[tex]\dashrightarrow \: \qquad \: \dfrac{4}{3} r {}^{3} = 4500[/tex]

Step 2 : Multiplying with 3/4 on both sides :

[tex]\dashrightarrow \: \qquad \: \dfrac{ \cancel{4}}{ \cancel{ 3}} r {}^{ 3} \times \dfrac{ \cancel{3}}{ \cancel{4}} = \cancel{ 4500} \times \dfrac{3}{ \cancel{4} }[/tex]

On further calculations, We get :

[tex]\dashrightarrow \: \qquad \: r {}^{3} = 1125 \times 3[/tex]

[tex]\dashrightarrow \: \qquad \:r {}^{3} = 3375[/tex]

Step 3 : Applying cube root on both sides :

[tex]\dashrightarrow \: \qquad \: \sqrt[3]{r {}^{3} } = \sqrt[3]{3375} [/tex]

We get :

[tex]\dashrightarrow \: \qquad \: \purple{\underline{\boxed{\frak{r = 15 \: yards}}}}[/tex]

Answer:

120

Step-by-step explanation:

If Kara earns 3 times as many points completing the next level than she earned the previous level, to find how many points she earned at level 3, triple the amount of points earned in level 2, which is 9.

9 × 3 = 27

We can confirm this is the correct value by multiplt 27 by 3 to see if it equals 81, which it ineed does.

To find how many points she scored in all, find the sum by adding all of the points together.

3 + 9 + 27 + 81 = 120

She scores 120 points in all.

hope this helps!

Answer:

36

Step-by-step explanation:

8x^2 - 7x^2 +14x +40 = 0

x^2 + 14x + 40 = 0

a = 1, b = 14, c = 40

14^2 - 4*1*40

36

Answer:

36

Step-by-step explanation:

you're welcome hope this helps

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

  Future amount = 48(1 + 0.316074)^12

Step-by-step explanation:

You want the exponential equation that can be used to find the number of bacteria in a colony after 12 days if it starts with 48 bacteria and triples in 4 days.

The exponential function can be written in the form ...

  future amount = a·b^(t/p)

where 'a' is the initial amount, 'b' is the growth factor in period p.

The problem statement tells you the initial amount is 48, and the factor by which the amount grows is a factor of 3 in 4 days. This lets you write the function as ...

  future amount = 48·3^(t/4) . . . . . where t is in days.

This equation can be rearranged so the only exponent is t:

  future amount = 48·(3^(1/4))^t = 48·1.316074^t

  future amount = 48·(1 +0.316074)^t

Then the amount in 12 days is ...

  future amount = 48·(1 +0.316074)^12

The numbers that go in the boxes are 0.316074 and 12.

__

Additional comment

Working from our original equation, we would compute the number after 12 days to be ...

  future value = 48·(3)^(12/4)

Putting the growth factor in "1 +" form, this could be ...

  future value = 48·(1 +2)^3

and your box numbers would be 2 and 3. We doubt your answer checker will accept this version of the equation.

Either way, the number of bacteria after 12 days is 1296.

If you use 3^(1/4) -1 as the growth rate in the first box, you need to report it to at least 5 significant digits in order for the future value to come out right. We have shown the value with 6 significant figures.

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Answer:

i think the first and last one.

Step-by-step explanation:

Answer:

y = 9/13

Step-by-step explanation:

x = -4 + y

5(-4 + y) + 4y = 7

-20 + 9y = 7

9y = -13

Answer:

5x + 4y = 7 × -2

-2x - 2y = 8 × 5

-10x - 8y = -14

-10x - 10y = 40

Step-by-step explanation:

2y = -54 ÷2

y = -27

Now substitute the value of y into equation (1)

5x + 4y = 7

5x + 4(-27) = 7

5x = 7 + 108

5x = 115

X = 23

Answer:

-0.25

Step-by-step explanation:

→ Find fg(x)

2 ( x + 1 )² = 2x² + 4x + 2

→ Find gf(x)

2x² + 1

→ Equate them

2x² + 1 = 2x² + 4x+ 2

→ Move everything to the right hand side

0 = 4x + 1

→ Solve

x = -0.25

Answer:

[tex]-\frac{1}{4}[/tex]

Step-by-step explanation:

Work out fg(x)

To work out fg(x), put the g function into the f function so, the x in f(x) is equal to the x+1 (from the g function) so:

[tex]2(x+1)^{2} = 2 (x^{2} +2x+1) = 2x^{2} + 4x +2[/tex]

So fg(x) = [tex]2x^{2} + 4x +2[/tex]

Work out gf(x)

Do this by substituting the f(x) equation into the g(x) which is:

[tex](2x^{2} )+1[/tex]

So gf(x) = [tex](2x^{2} )+1[/tex]

Work out x

And since fg(x) = gf(x),

[tex]2x^{2} + 4x +2[/tex] = [tex](2x^{2} )+1[/tex]

4x = -1

x =[tex]-\frac{1}{4}[/tex]

Answer:

Answers are in bold (in order)

Step-by-step explanation:

For the table, the question is asking us to take our x value and put it into the equation. for example:

y = 8x +1 . if x = 0, we can write this as this

y = 8(0) + 1 -> (the brackets mean times)

8 x0 = 0. 0+1 = 1.

if we follow this rule, the values are: 1, 9, 17, 25, 33.

For the function machine, if x = 1, then we can write 1 where the x is. The function machine is telling us that 1 x3 and then -2 = y, y being a random number we don't know. 1 x 3 = 3. That means 3-2 = y . 3-2 = y. So, y = 1 when x = 1.

When x =-9 we can rewrite x as -9. That means that -9 x 3, then -2 = y.

-9 x 3 = -27.

That means that -27 -2 = y

-27 -2 = -29, so when x = -9, y = -29.

For the third part we need to work out the gradient and the equation of the table. The gradient (how much our values go up by) The gradient can be worked out by diving the change in y (our y value) by the change in x (our x value). So, if we take the first two y values, we have -2 and 8. The difference/chance between these two is 10. (-2+10=8). And for the x values, the first two x values are 0 and 1. The difference/change between these two is 1. (1-0=1.) So, all we need to do is divide these values 10/1 = 10. So our gradient is 10. That means that the first box on the function machine will be “x10” to work out the second, we simply do the first box and go from there. If our x = 1, then 1 x 10 = 10. Our table says that when x = 1, y = 8. So to we need to work out the change between these is, to get our answer. To get from 10 to 8, we minus two. So the final box on the function machine must be “-2”

For the last part of the question, we are just substituting in the values of x.

If t = 1, then 4(t-3) is basically 4(1-3)

1-3 = -2. 4(-2) = -8.

so when t =1, s = -8. If you do this for the next two questions, you should get the answers:

s = -28 when t = -4

s = -12 when t = 0

Answer:

Second option

Step-by-step explanation:

They have two congruent pairs of sides and one congruent pair of angles.

The triangles B can be proven congruent by the SAS theorem

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

From the Option B) , we get

Let the first triangle be ΔABC

Let the second triangle be ΔBDE

Now , the measure of side AB = measure of side BD

And , the measure of side AC = measure of side BE

And , the measure of ∠ABC = measure of ∠DBE

Therefore , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

Hence , the triangles are congruent by SAS theorem

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Answer:

yes because 1/2= .5

and 6/12= .5 so they are equivalent

yes

In order to determine whether or not 6/12 is equivalent to 1/2, we need to reduce the first fraction.

Reduce by dividing the top & bottom by 6 ↓

[tex]^6/_{12}=^1/_2[/tex]

hope helpful ~

Answer:

4

Step-by-step explanation:

3+0+5+0+7+4+3+10 = 32
Mean = sum of numbers / how many numbers
mean = 32/8
mean = 4

Answer:

B =116°

D = 116°

Step-by-step explanation:

one set of opposite angles of a kite equal

Answer:

6441.46 (2d.p.)

Step-by-step explanation:

47×89= 4183÷(845)=0.571×879000=502434.319÷78= 6441.46

Answer:

(x + 4)^2 + (y - 1)^2 = 61.

Step-by-step explanation:

We need to find the square of the radius and the coordinates of the center.

Center = (-10 + 2)/2 , (-4 + 6)/2

= (-4, 1).

Length of the diameter

=  √((-10-2)^2 + (-4-6)^2)

= √(144 + 100)

=√244

So the radius = √244/2

and r^2 = 244/4 = 61,

So the equation of this circle is:

(x - (-4)^2 + (y - 1)^2 = 61

(x + 4)^2 + (y - 1)^2 = 61.

(x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given coordinates of the diameter of circle are  (-10,-4) and (2,6)

Diameter=√(x₂-x₁)²+(y₂-y₁)²

x₂=2,x₁=-10, y₁=-4, y₂=6

Diameter=√(2-(-10))²+(6-(-4))²

=√(12)²+(10)²

=√144+100

=√244

We know that Radius=Diameter/2

R=√244/2

Squaring both sides

R²=244/4

R²=61

So the equation of this circle is:

(x - (-4)² + (y - 1)² = 61

(x + 4)²+ (y - 1)² = 61.

Hence (x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

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Answer:

you have to multiple 5x5x5

Answer:

68.3 cm^2

Step-by-step explanation:

Assuming slant height is 5 cm :  ( the Q does not say)

The base area will be   5 x 5 = 25 cm^2

then you have 4 equilateral triangles of side length 5 cm

  total area = 43.3 cm^2

SUM = 68.3 cm^2

Answer: 23

Step-by-step explanation: 3+7+9+12+X /5 =8

31 + X = 8

X = 23

Answer:

175

Step-by-step explanation:

35 times 5 is 175

Hope This Helped

The surface area of the right triangular prism is : 20,568 [tex]in^{2}[/tex]  

using this formula ;SA = bh + (s1 + s2 + s3)*l

A traingular prisms is a prism that has triangles as its base. It has two triangles which are called the bases and three rectangles called the lateral faces.

Given data:

where; SA means the surface area

Therefore:

SA = 24*12 + ( 13 * 13 * 24 ) * 5

SA = 288 + ( 4056) * 5

SA = 288 + 20280

SA = 20,568 [tex]in^{2}[/tex]

In conclusion, the surface area of the right triangular prisms is 20,568 [tex]in^{2}[/tex]

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Answer:

20,568..............................

Answer:

96

Step-by-step explanation:

The average for the first 6 days was 100, and it ended up dropping overall by 2 for the average.

6 days=x/6=100

4 days=x/4=98/100

You can do 96+100/2 which is 98 degrees.

Answer: 16

Step-by-step explanation:

Answer:

6.6 in (Brainliest please)

Step-by-step explanation:

A= 1/2 b*h

12.87= 1/2 b(3.9)

12.87= 1.95b

12.87/1.95= 1.95b/1.95

6.6=b