MATHEMATICS HIGH SCHOOL

Kennedy had the expression 3(2x-3x+8). She simplified and rewrote theexpression 3(8+x). If any, what was her error?

Answers

Answer 1

Answer:

Answer:

Kennedy did not distribute the 3 to the numbers in the parentheses.

Step-by-step explanation:

The simplified expression should be -3x+24.

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A motorcycle can travel 70 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 60 km?

Answers

We have the following given
mileage = 70 miles per gallon
distance = 60 km

Required: amount of fuel in gallons

First, we must convert the distance to miles, so
60 km (1 mi/1.6 km) = 37.5 mi

So, the amount of fuel is
37.5 mi / (70 mi/gal) = 0.54 gallons

Answer:

0.54 gallons

Step-by-step explanation:

A package weighs 8 ounces how many pounds does the package weigh

Answers

since a pound is 16 ounces and 8 is half, then the package is half of a pound

Since 1 ounce = 0.0625
Now if we multiply 8 by 0.0625 it equals 0.5

So next time your converting ounces to pounds, you always multiply how many ounces there is to 0.0625

Answer : 0.5 pounds

Hope it helped :)

What is the answer to this problem? 7.5/12=4.2/x

Answers

Answer:

x = 67.2

Step-by-step explanation:

7.5/12 = 4.2/x

First, divide 7.5 by 12.

0.625 = 42/x

Next, multiply both sides by x

0.625x = 42

Next, divide by 0.625

x = 67.2

There's your answer!

Answer:

Answer is 6.720

Step-by-step explanation:

x = 168/25 = 6.720

Add 350 pounds to 4 tons.

4,350 lb.
8,350 lb.
4.5 tons
5 tons

Answers

8,350 lb.

1 ton = 2000 lbs, 2000 x 4 = 8000 + 350 lbs = 8,350 lbs

Answer:

The answer is B your welcome!

Step-by-step explanation:

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its the answer.

Use mathematical induction to prove the statement is true for all positive integers n. The integer n3 + 2n is divisible by 3 for every positive integer n.

Answers

1. prove it is true for n=1
2. assume n=k
3. prove that n=k+1 is true as well

so

1.
$(n^3+2n)/(3)$ =
$(1^3+2(1))/(3)$ =
$(1+2)/(3)$ =1
we got a whole number, true

2.
$(k^3+2k)/(3)$
if everything clears, then it is divisble

3.
$((k+1)^3+2(k+1))/(3)$ =
$((k+1)^3+2(k+1))/(3)$ =
$(k^3+3k^2+3k+1+2k+2))/(3)$ =
$(k^3+3k^2+5k+3))/(3)$
we know that if z is divisble by 3, then z+3 is divisble b 3
also, 3k/3=a whole number when k= a whole number

$(k^3+2k)/(3) + (3k^2+3k+3)/(3)$ =
$(k^3+2k)/(3) + k^2+k+1$ =
since the k²+k+1 part cleared, it is divisble by 3

we found that it simplified back to $(k^3+2k)/(3)$

done

Answer:

We have to use the mathematical induction to prove the statement is true for all positive integers n.

The integer $n^3+2n$ is divisible by 3 for every positive integer n.

for n=1

$n^3+2n=1+2=3$ is divisible by 3.

Hence, the statement holds true for n=1.

Let us assume that the statement holds true for n=k.

i.e. $k^3+2k$ is divisible by 3.---------(2)

Now we will prove that the statement is true for n=k+1.

i.e. $(k+1)^3+2(k+1)$ is divisible by 3.

We know that:

$(k+1)^3=k^3+1+3k^2+3k$

and $2(k+1)=2k+2$

Hence,

$(k+1)^3+2(k+1)=k^3+1+3k^2+3k+2k+2\n\n(k+1)^3+2(k+1)=(k^3+2k)+3k^2+3k+3=(k^3+2k)+3(k^2+k+1)$

As we know that:

$(k^3+2k)$ was divisible as by using the second statement.

Also:

$3(k^2+k+1)$ is divisible by 3.

Hence, the addition:

$(k^3+2k)+3(k^2+k+1)$ is divisible by 3.

Hence, the statement holds true for n=k+1.

Hence by the mathematical induction it is proved that:

The integer $n^3+2n$ is divisible by 3 for every positive integer n.

Lamar is writing a coordinate proof to show that a segment from the midpoint of the hypotenuse of a right triangle to the opposite vertex forms two triangles with equal areas. He starts by assigning coordinates as given.A right triangle is graphed on a coordinate plane. The horizontal x-axis and y-axis are solid, and the grid is hidden. The vertices are labeled as M, K, and L. The vertex labeled as M lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as K lies on begin ordered pair 0 comma 2 b end ordered pair. The vertex labeled as L lies on begin ordered pair 2a comma 0 end ordered pair. A bisector is drawn from point M to the line KL. The intersection point on line KL is labeled as N.

Enter the answers to complete the coordinate proof.
N is the midpoint of KL¯¯¯¯¯KL¯ . Therefore, the coordinates of N are (a,
).

To find the area of △KNM△KNM , the length of the base MK is 2b, and the length of the height is a. So an expression for the area of △KNM△KNM is
.

To find the area of △MNL△MNL , the length of the base ML is
, and the length of the height is
. So an expression for the area of △MNL△MNL is ab.

Comparing the expressions for the areas shows that the areas of the triangles are equal.

Answers

The coordinates of N is (a,b) using the midpoint formula.
The area for △KNM is (1/2)(a)(2b) = ab
The area of △MNL is ab.
Since the area of △KNM = △MNL and the area of △KML is 2ab, then we have proved that a segment from the midpoint of the hypotenuse of a right triangle to the opposite vertex forms two triangles with equal areas.

1. N is a midpoint of the segment KL, then N has coordinates

$\left((x_K+x_L)/(2),(y_K+y_L)/(2) \right) =\left((0+2a)/(2),(2b+0)/(2) \right) =(a,b).$

2. To find the area of △KNM, the length of the base MK is 2b, and the length of the height is a. So an expression for the area of △KNM is

$A_(KMN)=(1)/(2)\cdot \text{base}\cdot \text{height}=(1)/(2)\cdot 2b\cdot a=ab.$

3. To find the area of △MNL, the length of the base ML is 2a and the length of the height is b. So an expression for the area of △MNL is

$A_(MNL)=(1)/(2)\cdot \text{base}\cdot \text{height}=(1)/(2)\cdot 2a\cdot b=ab.$

4. Comparing the expressions for the areas you have that the area $A_(KMN)$ is equal to the area $A_(MNL)$ . This means that the segment from the midpoint of the hypotenuse of a right triangle to the opposite vertex forms two triangles with equal areas.

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