MATHEMATICS HIGH SCHOOL

If u(x) = x5 – x4 + x2 and v(x) = –x2, which expression is equivalent to (U/V) (x)?a) x3 – x2
b)–x3 + x2
c)–x3 + x2 – 1
d)x3 – x2 + 1

Answers

Answer 1

Answer:

Answer: C. $-x^3+x^2-1$

Step-by-step explanation:

Given Functions : $u(x) = x^5 - x^4 + x^2$

$v(x) = -x^2$

The expression equivalent to (u/v) (x) will be equivalent to $(u(x))/(v(x))$ , since polynomials allows division.

$\text{Now, }(u/v)(x)=(u(x))/(v(x))\n\n=(x^5 - x^4 + x^2)/( -x^2)\n\n=(x^5)/( -x^2)-(x^4)/( -x^2)+(x^2)/( -x^2)...........\text{Division law of exponents}\n\n=-x^(5-2)+x^(4-2)-x^(2-2)\n\n=-x^3+x^2-x^0\n\n=-x^3+x^2-1$

Hence, $(u/v)(x)=-x^3+x^2-1$

Answer 2

Answer: Hello,

Answer C if x≠0

(x^5-x^4+x²)/(-x²)=-x²(x^3-x²+1)/x²=-(x^3-x²+1)=-x^3+x²-1

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What is the answer 3.5r=3(4+.5r)?

Answers

$3.5r=3(4+0.5r)\n\n3.5r=3*4+3*0.5r\n\n3.5r=12+1.5r\ \ \ \ \ |substract\ 1.5r\ from\ both\ sides\n\n2r=12\ \ \ \ \ \ |divide\ both\ sides\ by\ 2\n\nr=6$

The 'answer' is the number that 'r' must be in order to make the equation a true statement. There's only one number that can do it. Here's how to find it:

Copy the equation: 3.5r = 3(4 + .5r)

Expand the right side: 3.5r = 12 + 1.5r

Subtract 1.5r from each side: 2r = 12

Divide each side by 2 : r = 6

What is the surface area of the rectangular prism below

Answers

Answer: A=490

Step-by-step explanation:

Formula - A = 2 ( wl + hl + hw)

2(7•14+7•14+7•7) = 490

The height of an ostrich is 20 inches more than 4 times the height of a kiwi. If an ostrich is 108 inches tall, how tall is a kiwi?A) 22 inches

B) 27 inches

C) 44 inches

D) 66 inches

Answers

If an ostrich is 108 inches tall. Then the height of the kiwi will be 22 inches. Then the correct option is A.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The height of an ostrich is 20 inches more than 4 times the height of a kiwi.

Let y be the height of the ostrich and x be the height of a kiwi. Then the equation is given as,

y = 4x + 20

If an ostrich is 108 inches tall. Then the height of the kiwi will be

108 = 4x + 20

4x = 88

x = 22

If an ostrich is 108 inches tall. Then the height of the kiwi will be 22 inches. Then the correct option is A.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

h=height of ostrich
k=height of kiwi
h is 20 more than 4 times k
k=20+4k

k=108
108=20+4k
minus 20 from both sides
88=4k
divide both sides by 4
22=k

answer is A

Jalen gets 3 paid vacation days for every 60 days he works. Select all of the expressions that represent the number of vacation days gets per x days worked. (A) x/20 (B) 3/60x (C) x/3 (D) 0.05x (E) 20x

Answers

Answer:

A and D

Step-by-step explanation:

In this question, we are asked to select the expressions that represent the number of vacation days per x days worked.

Now, to do this, what we simply first do is to get the number of days to takes to get one paid vacation. In the question , we are made to know that he gets 3 days paid vacation for 60 days of work. The number of days to get a single paid vacation would thus be 60/3 = 20 days. This means she gets one paid vacation in 20 days.

Now, we are told after working for x days, how many paid days vacation does she get. To know this, what we do is to first know the number of 20 days in x days. That would simply be x/20. This is the number of vacation days she gets in x days.

now, we check if there are similar options to this.

D is also correct. This is because x/20 is same as 0.005x

You take a walk and notice dogs in the dog park. There are a total of 8 small and large dogs. You realize there are 2 more large dogs than small dogs. How many are there of large and small dogs?

Answers

There are 5 large dogs and 3 small dogs

Solution:

Let "S" be the number of small dogs

Let "L" be the number of large dogs

Given that There are a total of 8 small and large dogs

So we can frame a equation as:

number of small dogs + number of large dogs = 8

S + L = 8 ------- eqn 1

You realize there are 2 more large dogs than small dogs

Number of large dogs = 2 + number of small dogs

L = 2 + S -------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "L" and "S"

Substitute eqn 2 in eqn 1

S + 2 + S = 8

2S + 2 = 8

2S = 6

S = 3

Substitute S = 3 in eqn 2

L = 2 + 3 = 5

L = 5

Thus there are 5 large dogs and 3 small dogs

Answer:

5 large dogs and 3 small dogs

Step-by-step explanation:

The lengths of the sides of a quadrilateral are consecutive even integers. twice the length of the shortest side plus the length of the longest side is 248 inches. find the length of the longest side.

Answers

To solve this problem you must apply the proccedure shown below:

1. You have the following information given in the problem above: twice the length of the shortest side plus the length of the longest side is 248 inches.

2. Therefore, keeping on mind the information above, you have:

x: the shortest side
x+6: the longest side

2x+(x+6)=248
3x+6=248
3x=242
x=242/3
x=80.66 (The shortest side)

x+6=80.66+6=86.66 (The longest side)

The answer is: 86.66

Final answer:

The length of the longest side is 86 inches.

Explanation:

To solve this problem, let's represent the lengths of the consecutive even integers as x, x+2, x+4, and x+6. According to the given information, we can write the equation 2x + (x+6) = 248. Simplifying this equation, we get 3x + 6 = 248. Subtracting 6 from both sides, we have 3x = 242. Finally, dividing both sides by 3, we find x = 80. Therefore, the length of the longest side is x + 6 = 80 + 6 = 86 inches.