MATHEMATICS HIGH SCHOOL

1.What is the simplified form of each expression?7x^–8 × 6x^3

a. 42/x^5
b. 1/42x^5
c. 42x^11
d. 13x^–5

(–2x8) · 3y9 · 2x4

a. 3x^12y^9
b. –12x^72y^9
c. –12xy^21
d. –12x^y^9

2. Find the simplified form of the expression. Give your answer in scientific notation.

(8 x 10^7) (7 x 10^4)

a. 1.5 × 10^12
b. 5.6 × 10^12
c. 1.5 x 10^29
d. 5.6 x 10^29

(7 × 10^–4)(9 × 10^–10)

a. 6.3 × 10^–13
b. 63 × 10^–13
c. 6.3 × 10^–15
d. 6.3 × 10^–16

Answers

Answer 1

Answer:

Answer with explanation:

Ques 1)

We are given a expression as:

$7x^(-8)* 6x^3$

It could also be written as:

$(7* 6)* x^(-8)* x^3\n\n\n=42* x^(-8+3)\n\n\n=42x^(-5)\n\n\n=(42)/(x^5)$

Option: a is the answer.

$(-2x^8)* 3y^9* 2x^4$

which is solved as follows:

$(-2* 3* 2)* x^8* y^9* x^4\n\n\n=-12x^(8+4)* y^9\n\n\n=-12x^(12)y^9$

Ques 2)

The expression is:

$(8* 10^7)(7* 10^4)$

It is solved as:

$=(8* 7)* 10^7* 10^4\n\n\n=56* 10^(7+4)\n\n\n=56* 10^(11)\n\n\n=5.6* 10^(12)$

Option: b is the answer.

$(7* 10^(-4))(9* 10^(-10))$

On simplifying:

$=7* 9* 10^(-4)* 10^(-10)\n\n\n=63* 10^(-4-10)\n\n\n=63* 10^(-14)\n\n\n=6.3* 10^(-14+1)\n\n\n=6.3* 10^(-13)$

Option: a is the answer.

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Mateo is doing an experiment for Physics class. He drops a bouncy ball off abalcony from a height of 12 meters. The ball's next bounce is always 75% ofthe height of the previous bounce. Let n = bounce number. Before the ball isdropped, n = 0, because the ball has not yet bounced. Which explicit formularepresents the height of the ball after n bounces?
Find the missing coordinate to complete the ordered-pair solution to the given linear equation: A) y+6x=5 (a) (-1,?) (b) (3,?) B) 3x+2y=-6 (a) (-2,?) (b) (?,3) C) 2x+1/3y=5 (a) (?,18) (b) (8/3,?)
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What restriction may be necessary to the domain and range of linear equations?

Answers

If x is under a square root ( $√(x)$ ) then x cannot equal a negative number. If x is in the denominator of a fraction ( $(y)/(x)$ ) then x cannot equal zero.

A bakery has 72 half-gallons of milk. It takes 1 2/3 cups of milk to make a cake. Note that 1 cup=1/8 half- gallon. How many cakes can the bakery make?

Answers

Answer:

345

Step-by-step explanation:

To find out how many cakes the bakery can make, you'll need to convert the amount of milk they have into cups and then divide by the amount of milk needed to make one cake.

First, let's convert the 72 half-gallons of milk into cups:

1 half-gallon = 8 cups (since 1 cup is 1/8 of a half-gallon)

So, 72 half-gallons = 72 x 8 cups = 576 cups of milk.

Now, you mentioned that it takes 1 2/3 cups of milk to make a cake.

Let's convert this mixed number into an improper fraction: 1 2/3 = (3 x 1 + 2)/3 = 5/3 cups of milk for one cake.

Now, we can find out how many cakes the bakery can make by dividing the total cups of milk by the amount needed for one cake: 576 cups of milk ÷ (5/3) cups per cake = 576 cups ÷ (5/3) ≈ 345.6 cakes.

Since you can't make a fraction of a cake, the bakery can make approximately 345 cakes with the milk they have.

Perpendicular Vectors:Find v x w if v=5i -4j +4k & w=-6i +3j -2k.
A. 3i-4j-2k
B. -14i-9j-4k
C. 5i +3j -4k
D. -4i -14j -9k

Find v x w if v=-3i-4j-8k & w=2i+6j+4k.
A. 12i -2j +3k
B. 8i +12j +32k
C. 32i -4j -10k
D. 10 i -8j +3k

Find the cross product <-6, 7, 2> x <8, 5, -3>. Is the resulting vector perpendicular to the given vectors?
A. <-31,-2,-86>;yes
B. <-37,-2,0>; no
C. <0,-86,-37>; yes
D. <-37, 0, -80>;no

Answers

1.
v x w = 8 i - 24 j + 15 k + 10 j - 12 i - 24 k =
= - 4 i - 14 j - 9 k
Answer: D )
2.
v x w = -16 i - 16 j - 18 k + 12 j + 48 i - 8 k =
= 32 i - 4 j - 10 k
Answer: C )
3.
The cross product:
< - 6, 7, 2 > x < 8, 5, -3 > =
= - 21 i + 16 j - 30 k - 18 j - 10 i - 56 k =
= - 31 j - 2 j - 86 k = < - 31, - 2, - 86 >
Vectors are perpendicular if: cos ( u, v ) = 0
< - 6 , 7. 2 > * < -31, - 2, - 86 > = 186 - 14 - 172 = 0
< 8, 5 , - 3 > * < - 31, - 2, - 86 > = -248 - 10 + 258 = 0
Answer: A ) < - 31, - 2 , - 86 >, yes.

The volume of a cylinder is 288 cubic inches. The radius of the circular base is 4 inches. What is the height of the cylinder? 9 inches
12 inches
18 inches
36 inches

Answers

Answer:

Its 9 just so you know

V = πr2h

h =V / πr2

H = 288 / 3.14 x 4 x 4

H = 288 / 50.24

H = 5.73.

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Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (3x – 4) feet, (x2 – 1) feet, and (2x2 – 15) feet. What is the perimeter of the triangle if x = 4?

Answers

Given:
edge 1 = 3x - 4
edge 2 = x² - 1
edge 3 = 2x² - 15

perimeter if x = 4

edge 1 = 3(4) - 4 = 12 - 4 = 8
edge 2 = 4² - 1 = 16 - 1 = 15
edge 3 = 2(4²) - 15 = 2(16) - 15 = 32 - 15 = 17

Perimeter = 8 + 15 + 17 = 40 feet.

Answer:

40 feet

Step-by-step explanation:

Use the quadratic equation y = x^2 – 6x + 9.Where does the vertex of the parabola lie?

A.below the x-axis

B.on the x-axis

C.on the y-axis

D.above the x-axis

Calculate the discriminant to determine the number of real roots.
y = x^2 + 3x + 9

How many real roots does the equation have?

A.one real root

B.no real roots

C.two real roots

D.no solution to the equation

Answers

Part 1- B, on the X axis.
Part B- A, the answer is one real root, and one non-real root.

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