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dimulka [17.4K]
3 years ago
13

Write an algebraic expression for the given quantity. Let x represent the unknown value. One-eight of the sum of a number and th

ree. The algebraic expression for the given quantity is ___
Mathematics
1 answer:
Mashcka [7]3 years ago
7 0

<u>Answer: </u>

Required expression for one-eight of the sum of a number and three is \frac{x}{8} + 3

<u>Solution: </u>

Given that unknown value is represented by variable x.

Need to create algebraic expression for One-eight of the sum of a number and three.

Let’s first find one eight of the number that is 1/8th of x = \frac{x}8}

Now on adding three we get  

\frac{x}{8} + 3

Hence required expression for one-eight of the sum of a number and three is \frac{x}{8} + 3

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Find the value of c so that the polynomial p(x) is divisible by (x-3). p(x) =-x^3+cx^2-4x+3. c=?
Vilka [71]

Answer:

\boxed{\textsf {The value of c is $\sf \dfrac{-14}{3}$. }}

Step-by-step explanation:

A polynomial is given to us . We need to find the value of c so that it is divisible by (x-3 ) .The given polynomial to us is ,

\sf \implies p(x)=- x^3+cx^2-4x+3

And the factor is ,

\sf \implies g(x) = x + 3

Now , according to factor theorem , p(x) will be divisible by g(x) if p(-3) = 0

\sf \implies p(x)= - x^3+cx^2-4x+3 \\\\\implies\sf p(-3) = 0 \\\\\sf\implies -(-3)^3+c(-3)^2-4(-3)+3 = 0 \\\\\sf\implies 27 + 9c +12+3=0 \\\\\sf\implies 9c +42=0 \\\\\sf\implies 9c = (-42) \\\\\sf\implies c = \dfrac{-42}{9}\\\\\sf\implies \boxed{\pink{\sf c = \dfrac{-14}{3}}}

<h3><u>Hence </u><u>the </u><u>value </u><u>of </u><u>c </u><u>is </u><u>(</u><u>-</u><u>1</u><u>4</u><u>)</u><u>/</u><u>3</u><u> </u><u>.</u></h3>
4 0
3 years ago
At Ralph's fruit stand X pound of grapes cost 90 cents. You want to buy 5 pounds of grapes. How
diamong [38]

Answer:At Ralph’s fruit stand ½ pound of grapes cost 90 cents. You want to buy 5 pounds of grapes.

How much will they cost?

1. What are the two possible rates for this problem?

Solution: ½ pound/90 cents 90 cents/ ½ pound

2. Show each rate as a unit rate.

Solution: . pounds of per 1 cent 180 cents per 1 pound of grapes

3. What does each unit rate tell you?

Solution: The pounds of grapes for 1 cent

The number of cents for one pound of grapes

4. Which unit rate will help you solve the problem?

Solution: 180 per 1 pound of grapes

5. If it costs 180 cents to buy 1 pound of grapes, how much will 2 pounds cost? 4 pounds?

Complete the table below.

POUNDS

OF

GRAPES

COST IN CENTS

1 180

2 360

3 540

What pattern do you see? The cost in cents increases by 180 cents each time.

Multiply the pounds of grapes by 180 cents to get the total cost

6. Since you know the unit price, write a number sentence for the cost of five pounds of

grapes. Write an equation for the cost of any pounds of grapes.

(180 cents per pound)(5 pounds) = $9.00

(Unit rate)(pounds of grapes) = total cost

180x = y where x is the cost per pound of grapes and y is the number of pounds.

Step-by-step explanation:

8 0
3 years ago
Question 2
Liono4ka [1.6K]

Answer: The answer is 110 cookies

Step-by-step explanation: 176 divided by 8 = 22 cookies per cup.

22 x 5 = 110 cookies

Hope this helps ^o^

8 0
3 years ago
Read 2 more answers
Complete function tables part 3<br><br><br><br><br><br><br>please help me ​
Paraphin [41]

Answer:

2 8 15 50

Step-by-step explanation:

h~mmmmm maybe im wrong

8 0
3 years ago
The second on a watch is 14mm long. What area does it sweep through in 30 seconds
skad [1K]

Exact Area = 98pi  

Approximate Area = 307.8760800518 (use calculator stored version of pi)

Approximate Area = 307.72 (using pi = 3.14)

Units are in square millimeters

======================================================

Explanation:

In 60 seconds, the hand sweeps out a full circle of radius 14. The area of this circle is

A = pi*r^2 = pi*14^2 = 196pi

Half of this is what the hand sweeps out in 30 seconds, so A/2 = (196pi)/2 = 98pi is the exact area it sweeps out. Your calculator would then show 98pi = 307.8760800518 approximately

If instead you use pi = 3.14, then the approximate area is 98*3.14 = 307.72

3 0
3 years ago
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