Answer:
Quotient =(3x²-5x-1) and reminder = 1
Step-by-step explanation:
[tex]\frac{9x^3-18x^2+2x+2}{3x-1}[/tex]
3x-1)9x³-18x²+2x+2(3x²-5x-1
9x³-3x²
------------------------
-15x²+2x+2
-15x²+5x
------------------
-3x+2
-3x+1
--------
1
Therefore 9x³-18x²+2x+2=(3x²-5x-1)(3x-1)+1
Quotient =(3x²-5x-1) and reminder = 1
Tim would like to buy a video game that costs $27. He has not saved any money. His parents are willing to pay him $3 for every 2 chores, but will also pay him for completing single chores.
Tim would have to do 18 chores (2 chores 9 times or 1 chore 18 times) to be able to buy the video game.
Step-by-step explanation:
Step 1; Tim's parents will give him $3 for every two chores. This equals $1.50 for a single chore. He wants to save up $27 so that he can buy the video games he wants.
Step 2; The number of times he has to do the chores to be able to but the video game is a division between the money he wants to save up by the money he gets for the chores.
Number of 2 chores he needs to do = Amount of money he wants to save up / money he gets for doing two chores
= $27 / $3 = 9 times.
Number of single chores he has to do =Amount of money he wants to save up / money he gets for doing two chores
$27 / $1.50 = 18 times
Find the final price on a $1,049 television
that is on sale for 12% off of the sales tax is
4.5%
Answer:
$883.40
Step-by-step explanation:
Calculate the amount of money needed to pay after the discount.n
$1049 × 88% = $923.12
Calculate the amount of money needed to pay after the tax.
$923.12 × 104.5% = $883.3684210526
=$883.40(rounded off to nearest cents)
hope this helps
To find the final price of the television on sale, calculate the discount amount, subtract it from the original price, and then add the sales tax amount.
Explanation:To find the final price of the television, we first need to find the discount amount by multiplying the original price ($1,049) by the discount percentage (12%).
Discount amount = $1,049 × 0.12 = $125.88
Next, subtract the discount amount from the original price to get the sale price:
Sale price = $1,049 - $125.88 = $923.12
Finally, add the amount of sales tax to the sale price. To find the sales tax amount, multiply the sale price by the sales tax rate (4.5%):
Sales tax amount = $923.12 × 0.045 = $41.54
Final price = Sale price + Sales tax amount = $923.12 + $41.54 = $964.66
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What place is the 4 at in the number 562,347
Answer: tenth place
Step-by-step explanation:
Answer:
The tens place.
Step-by-step explanation:
In order, the numbers would go as follows:
7 would be in the ones place.
4 would be in the tens place.
3 is in the hundreds place.
2 is in the thousands place.
6 is in the hundred thousands place.
5 is in the millions place.
a hose is coiled into circular loops about 30 inches in diameter. the length of each loop is about...
a. 7 ft
b. 8 ft
c .9ft
D. 10ft
Answer:
b. 8 ft
Step-by-step explanation:
We use the formula for the circumference of a circle to find the length of each loop.
Circumference of a circle = 2πr or Dπ
Where: π = pi
r = radius of the circular loops
D = Diameter
π = [tex]\frac{22}{7}[/tex]
D = 30 inches
Use Circumference of a circle = Dπ
Circumference of a circle = 30 x (22/7)
= 30 x 3.142857143
= 94.28571429 inches
Convert 94.28571429 inches to feet (ft)
12 inches = 1 ft
94.28571429 inches = 94.28571429/12
= 7.857142858 ft
≈ 8 ff
45.6 x 10 to the 2nd power
4,560
10 to the 2nd power is = 100
so 100 × 45.6 =
When 18 is subtracted from 6 times a number the result is -12 what is the number
Answer:
24
Step-by-step explanation:
18-6=12
24=12x2
12-24= -12
Can you help solve this please
50 points for all questions
9) Volume of the cone: [tex]9152 mm^3[/tex]
10) New volume of the cone: [tex]339 mm^3[/tex]
11) The volume of the cone shrinks by a factor of [tex]3^3=27[/tex]
12) Volume of the composite figure: [tex]15 ft^3[/tex]
Step-by-step explanation:
9)
The volume of a cone is given by the equation
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
where
[tex]\pi r^2[/tex] is the area of the base, where
r is the radius of the cone
h is the height of the cone
For the cone in this problem, we have:
r = 18 mm (radius)
h = 27 mm (height)
Therefore, the volume of this cone is
[tex]V=\frac{1}{3}\pi (18)^2 (27)=9152 mm^3[/tex]
10)
In this second exercise, the radius and the height of the cone are divided by 3. Therefore we have:
[tex]r'=\frac{r}{3}=\frac{18}{3}=6 mm[/tex] is the new radius of the cone
[tex]h'=\frac{27}{3}=9 mm[/tex] is the new height of the cone
Therefore, the new volume of the cone is
[tex]V=\frac{1}{3}\pi r'^2 h'[/tex]
And substituting, we find
[tex]V=\frac{1}{3}\pi (6)^2 (9)=339 mm^3[/tex]
11)
We can understand what happened to the volume of the cone after dividing its dimensions by 3 by calculating the ratio of the original volume to the new volume:
[tex]\frac{V}{V'}=\frac{9152}{339}=27[/tex]
This means that the new volume of the cone is 27 times smaller than the original volume.
We see that this "factor of shrinking" corresponds to the total factor of shrinking ofits dimensions, to the power of 3. In fact:
- Each the radius and the height of the cone has shrunk by a factor of 3
- However, the cone is a figure in 3 dimensions, so the total factor of shrinking of its volume is [tex]3^3 = 27[/tex]
12)
The composite figure consists of a squared pyramid + a parallelepiped.
The volume of the square pyramid is given by:
[tex]V_1 = \frac{1}{3}Lwh[/tex]
where
L = 5 ft is the length of the base
w = 1 ft is the width of the base
h = 6 ft is the height of the pyramid
Substituting,
[tex]V_1 = \frac{1}{3}(5)(1)(6)=10 ft^3[/tex]
The volume of the parallelepiped is given by
[tex]V_2=Lwh[/tex]
where
L = 5 ft is the length of the base
w = 1 ft is the width of the base
h = 1 ft is the height
Substituting,
[tex]V_2 = (5)(1)(1)=5 ft^3[/tex]
So, the total volume of the composite figure is
[tex]V=V_1+V_2=10+5=15 ft^3[/tex]
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Answer:
9) Volume of the cone: 9152 mm^3
10) New volume of the cone: 339 mm^3
11) The volume of the cone shrinks by a factor of 3^3=27
12) Volume of the composite figure: 15 ft^3
Step-by-step explanation:
An Expression is shown.
1 3 a 2 + b ÷ 2
What is the value of the expression if a = 3 and b = 8?
Answer:
If you're supposed to be multiplying the first four numbers, the answer is going to be 13.
Step-by-step explanation:
Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10
Given ⇒ 2(x − 4) + 6x = 9x − 10
Step 1 ⇒ 2x − 8 + 6x = 9x − 10
Step 2 ⇒ 2x + 6x − 8 = 9x − 10
Step 3 ⇒ 8x − 8 = 9x − 10
Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Step 5 ⇒ 0 − 8 = x − 10
Step 6 ⇒ −8 = x − 10
Step 7 ⇒ −8 + 10 = x − 10 + 10
Step 8 ⇒ 2 = x + 0
Step 9 ⇒ 2 = x
Which step in solving this equation is justified by the Distributive Property?
A) Step 1 ⇒ 2x − 8 + 6x = 9x − 10
B) Step 2 ⇒ 2x + 6x − 8 = 9x − 10
C) Step 3 ⇒ 8x − 8 = 9x − 10
D) Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Answer:
A I think is the right one
The maximum volume of a cylindrical tank measures 3rs/4 liters. What is one-third of the tank's maximum volume? (1/3)x(3rs/4) (3rs/4) / 1/3 (3rs/4) / 3 9rs/4 rs/4
there is not any slope for this mathematical equation
To find one-third of the tank's maximum volume, multiply the maximum volume by one-third: 1/3 * 3rs/4 = 3rs/12.
Explanation:To find one-third of the tank's maximum volume, we can multiply the maximum volume by one-third:
1/3 × 3rs/4 = 3rs/12
So, one-third of the tank's maximum volume is 3rs/12 liters.
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What ratio is equivalent to 2:9
Answer:
8:36
Step-by-step explanation:
Factors: 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36
GCF: 4
8 ÷ 4 = 2 36 ÷ 4 = 9
The height y of a jumping frog can be modeled by y = -16x^2+ 4x, where x is the time in
seconds) since the frog jumped from the ground. Find the roots of the equation when y = 0
Explain what the roots mean in this situation.
Answer:
roots: 0, 1/4time when the height is zeroStep-by-step explanation:
The roots are the values of x that make y=0.
0 = -16x^2 +4x = -4x(4x -1)
The values of x that make the factors zero are solutions to this equation:
x = 0
x = 1/4 . . . . . makes the factor (4x-1) equal to zero
The roots of the equation are x=0 and x=1/4.
__
Since y is height and x is time, when y=0, the frog is on the ground. The roots, then, are the times when the frog is on the ground.
The smaller root is the time when the frog leapt.
The larger root is the time when the frog landed.
The roots of the equation y = -16x² + 4x are x = 0 and x = 1/4,
The given equation y = -16x² + 4x models the height y of the frog as a function of time x in seconds.
To find the roots of this equation when y = 0, we need to solve:
0 = -16x² + 4x
This is a quadratic equation.
Quadratic equations can be solved by factoring, completing the square, or using the quadratic formula.
In this case, factoring is straightforward:
0 = x(-16x + 4)
This gives us two solutions
x=0
x=4/16=1/4
The roots are x = 0 and x = 1/4 seconds.
Interpreting the Roots
The roots of the equation indicate the times when the frog is at ground level (y = 0). At x = 0, the frog has just jumped, and at x = 1/4 seconds, the frog returns to the ground. Therefore, these roots represent the start and the end of the jump respectively.What does 7 1/2 - 2 3/16 - 1 5/8= as a fraction?
Answer:
3 11/16
Step-by-step explanation:
7 1/2 - 2 3/16 - 1 5/8
turn all to same fractions using multiplication
by this i mean to only multiply the fractions (both numerator and denomenator)
7 8/16 - 2 3/16 - 1 10/16
Turn them into improper fractions
120/16 - 35/16 - 26/16 =
And solve
3 11/16
Four more than half of the students in Bryan’s homeroom have tickets to attend the school’s musical. 20 students have tickets. Select all the equations that can be used to find the number of students in Bryan’s homeroom.
The equation formed by the given problem statement is 0.5*x + 4 = 20, solving this gives x = 32. Hence, there are 32 students in Bryan’s homeroom.
Explanation:The problem statement says that 'Four more than half of the students in Bryan’s homeroom have tickets to attend the school’s musical' and '20 students have tickets'. If we denote the total number of students in Bryan’s homeroom by x, we can write the statement as an equation: 0.5*x + 4 = 20. Simplifying this equation gives us 0.5*x = 20 - 4 = 16, so x = 16 * 2 = 32. Hence, there are 32 students in Bryan’s homeroom.
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Which is larger 17/40 or 8/15
It's easier to figure it out when both fractions have the same denominator, so let's fix that:
17/40*15/15 is 255/600
8/15*40/40 is 320/600
Notice we are multiplying by a factor of 1 to get equivalent fractions
So 8/15 is bigger
Hope this helped!
8/15
when you divide it it comes out to be 0.533 repeating
but when you divide 17/40 it comes out to be 0.425
so .5 is larger then .4
3 1/2, 3 5/6, 4 2/12, ………………, 4 5/6
What is the missing term?
What rule can you create for this pattern?
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
The sequence is [tex]3\frac{1}{2}, 3\frac{5}{6}, 4\frac{2}{12}, .... , 4\frac{5}{6}[/tex].
So, we have to find the missing term.
The sequence can be written in improper fraction as [tex]\frac{7}{2}, \frac{23}{6}, \frac{25}{6}, ... , \frac{29}{6}[/tex].
Therefore, the sequence is in A.P. as the consecutive numbers in the sequence are increasing by [tex]\frac{1}{3}[/tex].
As, [tex](\frac{23}{6} - \frac{7}{2}) = \frac{1}{3} = (\frac{25}{6} - \frac{23}{6})[/tex].
Therefore, the missing number is [tex](\frac{25}{6} + \frac{1}{3}) = \frac{27}{6} = \frac{9}{2} = 4\frac{1}{2}[/tex]. (Answer)
Hahn passes the 0 point running 5 meters per second to the right. where will he be 6 seconds later
Answer:
30 meters away
Step-by-step explanation:
each second is equal to 5 meters, hence meters per second
cual es factor de 8
Answer:
ocho es 8
Step-by-step explanation:
si quieres a saver mas solo necesitas a preguntar ;)
solo estoy jugando no mi mesajas yo no te quiero solo estoy jugando otra ves si te quiero como un amigo
As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable? What one-variable equation is she left with after adding?
5x + 6y = 18
2x – 3y = 12
Factor:________
Equation:________x=_________
Answer:
Yumiko should multiply the other equation by 3.
If she adds the two equations she would be left with the variable 'x'.
Step-by-step explanation:
Given the two equations are as follows:
[tex]$ 2x - 3y = 12 \hspace{5mm} \hdots (1) $[/tex]
[tex]$ 5x + 6y = 18 \hspace{5mm} \hdots (2) $[/tex]
It is given that she multiplies the first equation by 6. Therefore, (1) becomes
[tex]$ 12x - 18y = 72 \hspace{15mm} \hdots (a) $[/tex]
Now, note that the sign of the variable 'y' is negative. So, if we make the co-effecient of 'y' equal in both the cases, add them it would result in the elimination of the variable 'y'.
The co-effecient of y in Equation (2) is 6. To make it 18 like it is in Equation (1), we multiply throughout by 3.
Therefore, Equation (2) becomes:
[tex]$ 15x + 18y = 54 \hspace{5mm} \hdots (b) $[/tex]
Now, we add Equation (a) and Equation (b).
[tex]$ \implies 12x - 18y + 15x + 18y = 72 + 54 $[/tex]
[tex]$ \implies 27x = 126 $[/tex]
Factor: 3
Equation: 27x = 126
how do you do linear models?
Answer:
Identify the input and output values.
convert the data to do coordinate pairs.
find the slope.
write the linear model.
use the model to make a prediction by evaluating the function at the given x-value.
use the model to identify an x value that results in a given y value.
What is the absolute value of | 56-12 |?
Answer: 44! Hope this helps :D
Step-by-step explanation:
Answer:
Step-by-step explanation:
56 - 12 is 44
Buying a Car Math Quiz
QUESTION 2 of 10: According to AAA the average monthly maintenance cost on a used car is 75 per month. You are looking to pay cash for
the exact same Jeep at two different dealers. Dealer "A' wants $4.995.00. Dealer "B" wants 55,595.00 with free maintenance coverage for
one year. Which is the best deal?
Answer:
Dealer B
Step-by-step explanation:
Maintenance cost per year = 75$
Dealer "A' wants $4.995.00.
Dealer "B" wants 55,595.00 with free maintenance cover for a year.
It is obvious that the best deal is what dealer B is offering, with free maintenance cover per year. for example, if i pick dealer A, calculate the maintenance cover for 3years = $2700
whereas for dealer B, a whole year maintenance cost is free, it implies that one will start paying the next coming year i.e a year lesser than dealer A. by that time the one who picked dealer A must have paid $3600 for maintenance while the one who picked dealer B will about to pay $1800.
The best deal is what dealer B is offering coupled with the free maintenance cover for 1year.
Final answer:
After calculating the total costs for one year, Dealer B offers a better deal on the Jeep by saving $300, as it includes free maintenance, contrasting with Dealer A which results in higher overall costs after adding maintenance payments.
Explanation:
To determine which car deal from the dealers is the better option, we need to calculate the total cost of each option over the course of one year, including the average monthly maintenance cost on a used car. According to AAA, this cost is $75 per month.
For Dealer A, the cost of the car is $4,995 with no free maintenance, so the total cost after one year is the price of the car plus 12 months of maintenance:
Cost of the car: $4,995
12 months of maintenance: 12 * $75 = $900
Total cost for Dealer A after one year: $4,995 + $900 = $5,895
For Dealer B, the car costs $5,595 but comes with free maintenance for one year, which means:
Total cost for Dealer B after one year: $5,595
Comparing these totals, we see that Dealer B offers the better deal, with the overall savings being:
Savings: $5,895 - $5,595 = $300
At the fair, you spend $6 for food, then use the rest of your $20 to buy ride tickets. You have
enough money to buy 56 tickets. How much does each ticket cost?
a. $ 0.20 c. $0.35
b. $0.25 d. $ 0.48
what is the product of 2/5 and 2/3
Answer:
4/15 or in decimal form its 0.26
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.26
Harry ate 6 candies. Jake ate 2 fewer candies than Harry. How many candies did jake eat?
Answer:
4
Step-by-step explanation:
6 - 2 = 4
Jake ate 2 less than 6 which is how many Harry ate.
Answer:
4
Step-by-step explanation:
the answer is 4 because 6 minus 2 would be 4 so the answer is four
Your bedroom ceiling is 10 feet high and is 2/3 as high as the living room ceiling. Write and solve an equation to find the height of the living room ceiling
The height of living room ceiling is 15 feet.
Step-by-step explanation:
Given,
Height of ceiling in bedroom = 10 feet
This is 2/3 height of living room ceiling.
Let,
x be the height of living room ceiling.
2/3 of x = 10
[tex]\frac{2}{3}x=10[/tex]
Multiplying both sides by 3
[tex]3*\frac{2}{3}x=10*3\\2x=30[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{30}{2}\\x=15[/tex]
The height of living room ceiling is 15 feet.
Keywords: fraction, division
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The height of the living room ceiling is 15 feet.
Explanation:To find the height of the living room ceiling, we can start by letting 'x' represent the height of the living room ceiling.
Since the bedroom ceiling is 2/3 as high as the living room ceiling, we can write the equation:
10 = (2/3)x
To solve for x, we can multiply both sides of the equation by 3/2:
(3/2)(10) = (3/2)((2/3)x)
15 = x
Therefore, the height of the living room ceiling is 15 feet.
Which Fraction is less than 3/5 3/10 3/4 2/3 or 5/3
Answer:
The fraction less than [tex]\frac{3}{5}[/tex] is [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
Given fractions are
[tex]\frac{3}{5} ,\frac{3}{10} ,\frac{3}{4}, \frac{2}{3}, \frac{5}{3}[/tex]
[tex]\frac{3}{5} =0.6\\\\\frac{3}{10}= 0.3\\\\\frac{3}{4} =0.75\\\\\frac{2}{3}=0.66 \\\\\frac{5}{3}=1.66[/tex]
Arranging the fraction in increasing order of their value
[tex]\frac{3}{10}= 0.3<\frac{3}{5} =0.6<\frac{2}{3}=0.66<\frac{3}{4} =0.75<\frac{5}{3}=1.66[/tex]
So,the fractions less than [tex]\frac{3}{5}[/tex] is [tex]\frac{3}{10}[/tex]
A spherical ball with a volume of 2,304π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?
Answer:
Therefore the volume of the box is 13824 in³
Step-by-step explanation:
Given:
A spherical ball with is packaged in a box that is in the shape of a cube.
Volume of ball = 2304π in³.
Let 'r' be the radius of sphere
To Find:
Volume of Cube = ?
Solution:
Volume of sphere is given by
[tex]\textrm{Volume of sphere}=\dfrac{4}{3}\pi r^{3}[/tex]
Substituting the values we get
[tex]2304\pi=\dfrac{4}{3}\pi r^{3}\\\\\therefore r^{3}=1728\\\\Cube\ Rooting\\\\r=12\ in[/tex]
Now we know that diameter is given by
[tex]diameter=2\times r=2\times 12=24\ in[/tex]
it is given that,
The edge length of the box is equal to the diameter of the ball.
Therefore the length of cube = 24 in
Now the volume of the cube is given by
[tex]\textrm{Volume of cube}=(edge)^{3}[/tex]
substituting the values we get
[tex]\textrm{Volume of cube}=(24)^{3}=13824\ in^{3}[/tex]
Therefore the volume of the box is 13824 in³
A cantaloupe weighs 1/2. A watermelon weighs four times as much as the cantaloupe, how much does the watermelon weighs?
Answer:2
Step-by-step explanation: 1/2=0.5 0.5x4=2
Add. What is the answer
(5b^2-3b+2)+(2b-4)
Answer:
5b²-1b-2
Step-by-step explanation:
-3b and +2b are like terms so you combine them together -3b+2b= -1b
+2 and -4 are like terms so +2-4= -2
5b² has no like terms
then you put your answers together to simplify the equation
5b²-1b-2
The polynomials added together give the result 5b^2 - b - 2. The addition is done by combining like terms in the given polynomials.
Explanation:To add these polynomials, you combine like terms. Like terms are the terms in the polynomial that have the same variable and exponent. Here, our terms are 5b^2, -3b, 2, 2b, and -4.
The term 5b^2 does not have a like term, so it remains as is. The terms -3b and 2b add up to -b because -3b + 2b = -b. And finally, the constants 2 and -4 add up to -2. When we combine these results, we have the final answer: 5b^2 - b - 2.
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