Answer:
[tex]x^3-3x^2+2x-\frac{3}{2}[/tex]
Step-by-step explanation:
We can divide polynomials by other polynomials by dividing each term by the denominator. Remember, when we divide a variable by itself, we must change the exponent in our answer according to exponent rules.
[tex]\frac{ (2x^4-6x^3+4x^2-3x)}{2x}=\frac{2x^4}{2x} -\frac{6x^3}{2x} +\frac{4x^2}{2x} -\frac{3x}{2x} =x^3-3x^2+2x-\frac{3}{2}[/tex]
Answer:
3/2
Step-by-step explanation:
A dress is selling for $100 after a 20 percent discount. What was the original selling price?
SHOW ALL WORK
Answer:
$125
Step-by-step explanation:
original cost - discount = discounted price
discount = original cost * .2
original cost - original cost *.2 = 100
Factor out the original cost
original cost ( 1-.2) = 100
original cost *.8 = 100
Divide each side by .8
original cost *.8/.8 = 100/.8
original cost = 125
Plz help! 25 points!
10. Soda is on sale for $0.75 a can, and you have a coupon for $0.50 off your total purchase. Write a function rule for the cost of n sodas. How much would 10 sodas cost?
A. C(n) = 0.5n - 0.75; $4.25
B. C(n) = 0.75n - 0.5; $7.00
C. C(n) = 0.5n - 0.5; $4.50
D. C(n) = 0.75n; $7.50
12. The function b(n) = 6n represents the number of light bulbs b(n) that are needed for n chandeliers. How many lightbulbs are needed for 15 chandeliers?
A. 90 lightbulbs
B. 2 lightbulbs
C. 96 lightbulbs
D. 80 lightbulbs
Answer:
10.: B. C(n) = 0.75n - 0.5; $7.00
12.: A. 90 light bulbs
Step-by-step explanation:
10. One soda costs 0.75. n sodas cost 0.75n. Then you subtract the coupon amount, so you pay 0.75n - 0.5.
The cost function is:
C(n) = 0.75n - 0.5
The cost of 10 sodas is:
For 10 sodas, n = 10.
C(10) = 0.75 * 10 - 0.5
C(10) = 7.5 - 0.5
C(10) = 7
Answer: B. C(n) = 0.75n - 0.5; $7.00
12. b(n) = 6n
The number of chandeliers is n.
If n = 15, then you have:
b(15) = 6 * 15
b(15) = 90
Answer: A. 90 light bulbs
Answer:
10. B. C(n) = 0.75n - 0.5; $7.00
12 A. 90 lightbulbs
Step-by-step explanation:
10. Cost of the purchase = number of cans * cost per can - coupon
We know the cost per can is .75 and the coupon is a one time coupon for .50
C(n) = n * .75 - .5
If we let n=10 to buy 10 cans
C(10) = 10*.75 -.50
= 7.50 - .5
= 7.00 is the cost of 10 cans
12. b(n) = 6n where n is the number of chandeliers
b(n) is the number of light bulbs
If we have 15 chandeliers how many light bulbs do we need?
b(15) = 6*15 = 90
We will need 90 light bulbs
Find the next term given in the sequence. 1.31, 2.54, 3.77, ....
Answer: The next term in the sequence is 5.
Step-by-step explanation: We are given to find the next term in the following sequence :
1.31, 2.54, 3.77, . . . .
We can see the following pattern in the consecutive terms of the given sequence :
[tex]2.54=1.31+1.23,\\\\3.77=2.54+1.23,\\\\\\\vdots~~~~~\vdots~~~~\vdots[/tex]
Therefore, the next term in the given sequence will be the last given term plus 1.23.
That is, the next term will be
[tex]3.77+1.23=5.00.[/tex]
Thus, the next term in the sequence is 5.
Which number(s) are 6 units from zero on a number line?
-6
12
6
3
Answer: 6 and -6
Step-by-step explanation:
6 Is the distance from zero, since distance cannot be negative, it does not matter if we go left or right on the number line, it will still be 6 units away from zero.
The numbers 6 units from zero on a number line are -6 and 6. These numbers are at an equal distance from zero but in opposite directions, with -6 being on the left (negative side) and 6 on the right (positive side) of zero.
The numbers that are 6 units from zero on a number line are -6 and 6. Both of these numbers are at an equal distance from zero, but in opposite directions. The number -6 is to the left of zero, representing a negative value, and the number 6 is to the right of zero, representing a positive value.
Therefore, the correct answers are -6 and 6.
The numbers 12 and 3 mentioned in the question are not 6 units from zero; 12 is much farther than 6 units away, and 3 is closer than 6 units to zero.
56 < 4x
Which phrase translates this expression?
A) 56 less than four times a number
B) four times a number less than 56
C) four times a number is less than 56
D) 56 is less than four times a number
what the answer
56 is less than four times a number representing the inequality 56 < 4x thus option (D) is correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given inequality,
56 < 4x
The sign "<" indicates that the value at the left of this sign will be smaller than the right.
Thus, 56 is less than four times the number.
Hence "56 is less than four times a number representing the inequality 56 < 4x".
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The phrase that accurately translates the expression "56 < 4x" is:
56 is less than four times a number.
The correct option is D.
We have the inequality
56 < 4x
Here, the symbol '<' shows less than relation.
So, this phrase represents the inequality statement correctly, stating that 56 is smaller than the result of multiplying four times a certain number (x).
Thus, 56 is less than four times a number.
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Karl drove 617.3 miles. For each gallon of gas the car can travel 41 miles.Select a reasonable estimate of the number of gallons of gas karl used.
Nina buys a used car from Leon’s Used Cars and pays a $500 down payment and $299 per month for 48 months. The cash price is $12,500.00. How much interest does Nina pay if she chooses NOT to pay the cash price?
Answer:
The interest is $1852
Step-by-step explanation:
We are given
down payment = $500
$299 per month for 48 months
per month installment =$299
total months =48
total amount paid = (per month installment)*( total months)
now, we can plug values
total amount paid is
[tex]=299\times 48[/tex]
[tex]=14352[/tex]
total amount paid is $14352
The cash price is $12,500.00
so,
interest = (total amount paid)-( cash price)
so, interest is
[tex]=14352-12500[/tex]
[tex]=1852[/tex]
Rewrite the expression as a multiple of a sum of two numbers with no common factor. 27 + 21
Mrsjones has 1 4/8 pizza left after giving some to Greg she had 7/8 left how much did Greg take
Answer:
5/8
Step-by-step explanation:
well we 1 14/8 so lets turn that to a whole number which is 12/8 (you multiply the denominator by 1 and add the 4)
12/8 - 7/8 = 5/8 ( since both denominators are the same numbers you can simply subtract the numerator )
What can be concluded about a pair of triangles with some congruent corresponding parts? Select all that apply.
The two triangles are always congruent.
The two triangles are never congruent.
The two triangles are sometimes congruent.
A conclusion cannot be made based on the given information.
Answer:
A conclusion cannot be made based on the given information.
Step-by-step explanation:
Take an example of such two triangles where we are given the information that two sides are congruent and an angle that is not enclosed is congruent. These two particular triangles may or may not be congruent. However, they either are or are not - that does not change in time, so the third answer "Two two triangles are sometimes congruent" is non-sense. The only remaining and correct option is the fourth one: conclusion on congruency cannot be made.
Answer:
The answer The two triangles are sometimes congruent.
Step-by-step explanation:
Kenya jumped 7 and 1 sixth feet. Janet jumped 6 and 1 third feet. How much farther did Kenya jump?
Mr. Andrews has a classroom of 45 students. He wants to divide them equally into 5 teams for a group project.
How many students will be on each team?
A) 7
B) 8
C) 9
D) 10 what the answer
Answer:
C) 9
Step-by-step explanation:
well 45/5 would eqaul 9 exactly
To find out how many students will be on each of Mr. Andrews' 5 teams, divide the total number of students, 45, by the number of teams, which results in 9 students per team. C is correct.
To determine how many students will be on each team when Mr. Andrews divides his classroom of 45 students equally into 5 teams, you need to divide the total number of students by the number of teams. This is a division problem in mathematics.
Here is the calculation:
Write down the total number of students: 45.
Write down the number of teams: 5.
Divide the total number of students by the number of teams:
45 ÷ 5 = 9.
So, there will be 9 students on each team, which corresponds to option C.
f(x) = √(3 - x)
f(-1) =
A) 1
B) 2
C) undefined
D) √2
Answer:
B
Step-by-step explanation:
To find the value of f(x) at x=-1, we substitute x=-1 and simplify.
[tex]f(-1)=\sqrt{3-(-1)}=\sqrt{3+1)} =\sqrt{4} =2[/tex]
f(-1)=2.
Answer B.
Answer:
b
Step-by-step explanation:
classify the sequence arithmetic , geometric, or neither
Answer:
Geometric
Step-by-step explanation:
Given terms are {3, -1, 1/3, -1/9............}
If we have common difference between the terms then it is arithmetic
If we have common ratio between the terms then it is Geometric
Difference of 3 and -1 is 4
Difference of 1/3 and -1 is -4/3
Common difference it not same so it is not Arithmetic
Now we check common ratio
we divide second term by first term
first term is 3 and second term is -1
[tex]\frac{-1}{3}[/tex]
now we check with next two terms
[tex]\frac{\frac{1}{3}}{-1}=\frac{-1}{3}[/tex]
common ratio is -1/3
So this is Geometric
Answer:
B so geometric :)
Match the equation with its graph -3x+5y=15
Answer:
The fourth graph.
Step-by-step explanation:
The best way to do this is to first convert the equation to slope-intercept form. Then it is easy to see the slope and y intercept.
-3x + 5y = 15
5y = 3x + 15
y = 3/5x + 3 is slope intercept form.
The slope is 3/5 and the y-intercept is at y = 3.
It is the fourth graph.
Log 6 (1/36)
6 is the base. How to evaluate this?
We can write the argument of the logarithm as a power of 6:
[tex]\log_6\dfrac1{36}=\log_6\dfrac1{6^2}=\log_66^{-2}[/tex]
Then using the property that [tex]\log_ba^n=n\log_ba[/tex], we get
[tex]\log_6\dfrac1{36}=-2\log_66[/tex]
and since [tex]6=6^1[/tex], we have [tex]\log_66=1[/tex], so the value of this expression is simply -2.
The value of [tex]\(\log_6 \left(\frac{1}{36}\right)\)[/tex] is -2.
To evaluate [tex]\(\log_6 \left(\frac{1}{36}\right)\)[/tex], we can use properties of logarithms and exponents.
Let's set up the equation:
[tex]\[\log_6 \left(\frac{1}{36}\right) = x\][/tex]
This equation means:
[tex]\[6^x = \frac{1}{36}\][/tex]
We know that [tex]\(\frac{1}{36}\)[/tex] can be rewritten as [tex]\(6^{-2}\)[/tex] because:
[tex]\[36 = 6^2 \quad \text{so} \quad \frac{1}{36} = 6^{-2}\][/tex]
Thus, the equation [tex]\(6^x = \frac{1}{36}\)[/tex] becomes:
[tex]\[6^x = 6^{-2}\][/tex]
Since the bases are the same, we can equate the exponents:
x = -2
Therefore,
[tex]\[\log_6 \left(\frac{1}{36}\right) = -2\][/tex]
18. What is the quotient of A. 2y ? 17y R ?70 B. 2y ? 17y R 70 C. 2y + 3 D. 2y ? 3
Answer:
you need to provide the statement
Step-by-step explanation:
As a rule of thumb, people should drink 1/2 ounce of water for each pound of body weight per day. How much water should a 145-pound person drink per day?
Answer: 72.5 ounces per day
Solve for y.
y =
Picture in the attached , might have to zoom in
Answer:
Step-by-step explanation:
This is an equilateral triangle, 3 equal sides and 3 equal angles (60°)
so angle C is 60°
you can solve qith an equation
8y - 4 = 60
8y = 60 - 4
8y = 56
y = 56 : 8
y = 7
-------------------
check
8y - 4 = 60
(8 * 7) - 4 = 60
56 = 60 - 4
56 = 56
the answer is good
A standard deck of playing cards has 52 cards: 13 spades, 13 clubs, 13 hearts, and 13 dimonds. What is the probabipity of drawing a spade from a standard 52 card deck, replacing it, then drawing another spade? Show your work or explain how you got your answer.
Final answer:
The probability of drawing a spade, putting it back, and then drawing another spade is 6.25%. This is calculated by multiplying the probability of drawing a spade twice with replacement.
Explanation:
The probability of drawing a spade from a standard deck of 52 cards is 13/52, since there are 13 spades in a deck. If you replace the card and reshuffle, the condition remains the same for the second draw.
Therefore, the probability of drawing another spade is also 13/52. To find the combined probability of two independent events, you multiply the probabilities of both events occurring.
Thus, the probability of drawing a spade, replacing it, and then drawing another spade is:
(13/52) × (13/52)
When you calculate that, you get:
= 169/2704
= 0.0625 or 6.25%
This means that there is a 6.25% chance of drawing a spade, replacing it, and drawing another spade on two consecutive draws from a standard deck of cards.
After one week a music downloading site sold over 80,000 songs. After 4 weeks the music downloading site sold over 300,000 songs. Find the average rate of change of songs per week.
75,000 songs per week
80,000 songs per week
55,000 songs per week
73,334 songs per week
[tex]\bf \begin{array}{ccll} \stackrel{x}{weeks}&\stackrel{y}{songs}\\ \cline{1-2} 1&80000\\ 4&300000 \end{array}~\hspace{10em} (\stackrel{x_1}{1}~,~\stackrel{y_1}{80000})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{300000}) \\\\\\ \stackrel{\textit{average rate of change}}{slope = m\implies} \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{300000-80000}{4-1}\implies \cfrac{220000}{3}\quad \approx \quad 73333[/tex]
3) A regulation basketball has a diameter of 9.4 inches. What is the volume of the ball?
Answer:
Volume = 434.89276543154 inch³
Step-by-step explanation:
volume = 4/3πr³
where r is the radius
r = 9.4/2
r = 4.7³
Volume = 4/3×π×4.73³
Volume = 434.89276543154 inch³
Math help please (80 points)
Answer:
1. x^4 -x^3 -4x^2 -3
a1 = -7.4
an = an-1 -13.8 (choice 1)
Step-by-step explanation:
f(x) = x^4 -x^2 +9
g(x) = x^3 +3x^2 +12
We are subtracting
f(x) -g(x) =x^4 -x^2 +9 - ( x^3 +3x^2 +12)
Distribute the minus sign
x^4 -x^2 +9 - x^3 -3x^2 -12
I like to line them up vertically
x^4 -x^2 +9
- x^3 -3x^2 -12
-------------------------
x^4 -x^3 -4x^2 -3
2. a1 = -7.4
To find the common difference, take term 2 and subtract term 1
-21.2 - (-7.4)
-21.2 + 7.4
-13.8
an = an-1 -13.8
Step-by-step explanation:
f(x) = x^4 -x^2 +9
g(x) = x^3 +3x^2 +12
We are subtracting
f(x) -g(x) =x^4 -x^2 +9 - ( x^3 +3x^2 +12)
Distribute the minus sign
x^4 -x^2 +9 - x^3 -3x^2 -12
I like to line them up vertically
x^4 -x^2 +9
- x^3 -3x^2 -12
-------------------------
x^4 -x^3 -4x^2 -3
2. a1 = -7.4
To find the common difference, take term 2 and subtract term 1
-21.2 - (-7.4)
-21.2 + 7.4
-13.8
an = an-1 -13.8
if you need anymore help just ask and if you wondering i found another question which its the same one as this one so her it is
Graph the following inequality and then select the correct graph below. x + 2 ≥ 1
Answer:
I've done this on Odyssey Ware and it's the second graph
Hope This Helps! Have A Nice Day!!
Which option below best describes the polynomial 10x3 ?
Question 1 options:
third degree polynomial with two terms
first degree polynomial with three terms
third degree monomial
third degree binomial
It is a 3rd degree monomial, meaning it has only one term.
Hope I helped!
Use the substitution method to solve the system of equations. Choose the correct ordered pair. y = 5x + 7 x = 8 A. (8, 47) B. (0, 7) C. (8, 15) D. (0, 8)
Assuming the system is composed of the equations y = 5x+7 and x = 8, then the answer is (8,47) which is choice A
To get this answer, we simply replace x in the first equation with 8, and then compute
y = 5x+7
y = 5*8+7 .... replace x with 8
y = 40+7
y = 47
So together x = 8 and y = 47 pair up to get us the solution (x,y) = (8,47)
After solving the equation by substitution method, the correct pair for x and y will be (8, 47). Hence, option A is correct.
What is an equation?Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given data provided by the question,
The equation is,
y = 5x + 7
Substitute x = 8 in the equation,
y = 5 (8) + 7
y = 47.
So, after substituting the x=8 the value obtained for y is 47.
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Ohn has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he paid the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of his first 20 payments, using complete sentences.
Answer:
Ohn has paid $5730 in first 20 installments
Step-by-step explanation:
As per the question Ohn payed the first installment =$100
Next month Ohn payed the installment = 1.1×$100
Similarly subsequent installment =1.1×1.1×$100
So we can write first 20 installments as
⇒100+100×1.1+100×1.1²+100×1.1³.........+100×[tex]1.1^{20}[/tex]
And we know in geometric series
1+x²+x³+...........[tex]x^{20}[/tex] = (1-[tex]x^{n-1}[/tex])÷(1-x)
Therefore sum of first 20 installments will be
⇒100(1+1.1²+1.1³............[tex]1.1^{20}[/tex] =(1- [tex]1.1^{20}[/tex])÷(1-1.1)
= 100(1-6.73)÷(-.1)
=100×5.73÷.1
= $5730
So Ohn has paid $5730
A point on the unit circle lies on the terminal side of an angle in standard position in Quadrant III .
Select from the drop-down menus to correctly complete each statement.
The cosine of the angle is . Negative or Positive
The sine of the angle is . Negative or Positive
The cosine of the angle is Negative.
The sine of the angle is Negative.
The given angle's terminal side resides in the third quadrant.
In the first quadrant, all trigonometric ratios are positive.
In the second quadrant, only sine and cosecant are positive.
In the third quadrant, only tangent and cotangent are positive.
In the fourth quadrant, only cosine and secant are positive.
In the third quadrant, both sine and cosine of given angle are negative.
Thus, the cosine of the given angle is Negative and
the sine of the given angle is Negative.
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an empty kitchen cabinet has 8 shelves and each shelf can hold no more than 30 cans you want to arrange 40 cans in the kitchen cabinet so that the same number of cans is on each shelf that you use
(a) list the factors of 40
(b) list the factors of 40 that represent the number of cans that could be on each shelf
(c) how many different arrangements of cans are possible
(d) what are the possible arrangements of the cans
Answer:
(a)
[tex]40=1,2,4,5,8,10,20,40[/tex]
(b)
factor=5 can only hold it
(c)
Only one arrangement is possible
(d)
we can put 5 cans into all 8 shelves
(e)
[tex]40=8\times 5[/tex]
Step-by-step explanation:
We are given
an empty kitchen cabinet has 8 shelves
and each shelf can hold no more than 30 cans you want to arrange 40 cans in the kitchen cabinet
so that the same number of cans is on each shelf that you use
(a)
we can find all possible factors of 40
[tex]40=1,2,4,5,8,10,20,40[/tex]
(b)
Since, an empty kitchen cabinet has 8 shelves
so, one of factor of 40 must be 8
so,
[tex]40=8\times 5[/tex]
So, factor=5 can only hold it
(c)
Only one arrangement is possible
because there is only one such possible factor
[tex]40=8\times 5[/tex]
(d)
Since, we got
[tex]40=8\times 5[/tex]
So, we can put 5 cans into all 8 shelves
(e)
Since, there are 8 shelves
and we can put 5 cans on each shelves
so, possible arrangement is
[tex]40=8\times 5[/tex]
Answer:
(a) 40 = 1 x 40, 2 x 20, 4 x 10, or 5 x 8. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
(b) Factors: 5, 8, 10, 20
(c) 4, that is, the quantity of factors in (b)
(d) 5 cans in 8 shelves, 8 cans in 5 shelves, 10 cans in 4 shelves, 20 cans in 2 shelves.
Vanessa earns a base salary of $400.00 every week with an additional 5% comission on everything she sells.Vanessa sold $1650.00 worth of items last week.