Final answer:
The quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.
Explanation:
To find the quotient when 4x^3 + 2x + 7 is divided by x + 3, we can use long division. Divide the first term, 4x^3, by x which gives 4x^2. Multiply x + 3 by 4x^2 to get 4x^3 + 12x^2. Subtract this from the original expression to get -10x^2 + 2x + 7. Then, divide -10x^2 by x which gives -10x. Multiply x + 3 by -10x to get -10x^2 - 30x. Subtract this from the previous result to get 32x + 7. Finally, divide 32x by x which gives 32. Multiply x + 3 by 32 to get 32x + 96. Subtract this from the previous result to get -89. Therefore, the quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.
If the sum of a number and five is doubled, the results is one less than the number.find the number
The number that satisfies the condition that, when added to five and then doubled, is one less than the number itself is -11. We found this number by setting up an equation and solving for the variable.
Explanation:Let's define x to be the number we're trying to find. According to the question, if the sum of this number and five is doubled, the result is one less than the number.
The equation based on the given information is 2(x + 5) = x - 1. To solve for x, let's distribute the 2 to both terms in the parentheses: 2x + 10 = x - 1.
Next, we need to get all the x terms on one side and the constant terms on the other side. We can do this by subtracting x from both sides, giving us: x + 10 = -1. Then, subtract 10 from both sides to isolate x: x = -11. So, the number we're looking for is -11.
Find the slope of the line that passes through (9,9) and(2,1)
Answer:
8/7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-9)/(2-9)
m=-8/-7
m=8/7
Answer:
m= 8/7
Step-by-step explanation:
the formula to find slope is
m= y2-y1/x2-x1
$7 is what percent of 10$
Answer:
7/10
Step-by-step explanation:
you got 7 out of 10 dollars
Answer:
70%
Step-by-step explanation:
Because the fraction would be 7/10 when you make it to precent form it would be 70/100 which is 70%
During ski season,the owner of ski shop has determined that the number of customers in a day is greater then or equal to 50 more then the temperature(Fahrenheit)
The question is incomplete. Here is the complete question:
During ski season,the owner of ski shop has determined that the number of customers in a day is greater than or equal to 50 more then the temperature(Fahrenheit) . Write an inequality for the problem and determine the constraints on the variables.
Answer:
[tex]N\geq T+50[/tex]
Step-by-step explanation:
Let the number of customers be 'N' and the temperature in Fahrenheit be 'T'.
Given:
Number of customers is related to temperature in Fahrenheit as:
Number of customers is greater than or equal to 50 more than the temperature in Fahrenheit. This means,
[tex]N\geq T+50[/tex]
Now, since 'N' represents number of customers and number can never be a negative quantity. So, the only constraint for this inequality is that the number of customers must be greater than or equal to 0.
So, [tex]N\geq 0[/tex]
n a simple random sample of 219 students at a college, 73 reported that they have at least $1000 of credit card debt.
Which interval is the 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt?
(31.0 ,35.6)
( 30.1 , 36.5)
(25.0 ,41.6)
(27.5 ,39.1 )
Answer:
[tex]0.333 - 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.251[/tex]
[tex]0.333 + 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.416[/tex]
The 99% confidence interval would be given (0.251;0.416).
(25.0 ,41.6)
Step-by-step explanation:
1) Data given and notation
n=219 represent the random sample taken
X=73 represent the students that reported that they have at least $1000 of credit card debt.
[tex]\hat p=\frac{73}{219}=0.333[/tex] estimated proportion of students that reported that they have at least $1000 of credit card debt.
[tex]\alpha=0.01[/tex] represent the significance level
z would represent the statistic (variable of interest)
p= population proportion of students that reported that they have at least $1000 of credit card debt.
2) Confidence interval
The confidence interval would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 99% confidence interval the value of [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2=0.005[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=2.58[/tex]
And replacing into the confidence interval formula we got:
[tex]0.333 - 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.251[/tex]
[tex]0.333 + 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.416[/tex]
And the 99% confidence interval would be given (0.251;0.416).
We are confident that about 25.1% to 41.6% of students have at least $1000 of credit card debt.
And for this case the most accurate option is:
(25.0 ,41.6)
Find the measure of each numbered angle.
Answer:
m∠1 = 50°
m∠2 = 88°
Step-by-step explanation:
Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.
Answer:
2.) m/_1 = 50
3. )m/_2=88
Step-by-step explanation:
2.) the line that the exterior angle 140 is on is a straight line. this means it is 180 degrees. 180 - 140 = 40. the box in the left corner means it is a right angle or 90 degrees. evey triangle is 180 degrees so add 40 and 90 to get 130 and then subtract 130 from 180 to get 50 which is the angle number 1.
3.)the line 120 is on is a straight line so we do 180 minus 120 to get the angle inside. it is 60. 60 +32 = 92. 180 - 92 is 88 degrees.
Consider a simple economy where the basket of goods used to calculate the CPI contains two items: shirts and pants. The basket consists of 3 shirts and 2 pairs of pants. Each item increases in price by $1 in year 2. The pants price is 20$ and the shirt price is 25$. What is the CPI for year 2.
To calculate the CPI for year 2 in a simple economy involving shirts and pants, we first find the total cost of the basket in both years considering the price increase. Then, using the formula for CPI, we find that the CPI for year 2 is 122.45, indicating an increase in the average price level compared to the base year.
Explanation:To calculate the Consumer Price Index (CPI) for year 2 in a simple economy with only shirts and pants in the basket of goods, we first need to understand the concept of CPI. The CPI represents the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. Here, we're given that the price of each item increases by $1 in year 2, with the new prices being $21 for pants and $26 for shirts.
First, calculate the total cost of the basket in year 2:
Cost of 3 shirts in year 2 = 3 shirts * $26 per shirt = $78
Cost of 2 pairs of pants in year 2 = 2 pants * $21 per pants = $42
Total cost of the basket in year 2 = $78 + $42 = $120
To determine the CPI for year 2, we also need to know the base year's total cost, which isn't directly provided here.
However, assuming the base year (year 1) prices were $1 less for each item, the prices would have been $20 for shirts and $19 for pants.
Cost of the basket in year 1:
Cost of 3 shirts = 3 shirts * $20 per shirt = $60
Cost of 2 pairs of pants = 2 pants * $19 per pants = $38
Total cost of the basket in year 1 = $60 + $38 = $98
Finally, to calculate the CPI for year 2, we use the formula:
CPI for year 2 = (Total cost of the basket in year 2 / Total cost of the basket in year 1) * 100
= ($120 / $98) * 100 = 122.45
Therefore, the CPI for year 2 is 122.45, indicating prices have increased on average when comparing year 2 to the base year (year 1). This helps in understanding the inflation rate and cost of living increases for consumers.
(8,4); m=7 what’s the answer in point-slope form
The equation of line in point slope form is y - 4 = 7x - 56
Solution:
Given that m = 7 and point is (8, 4)
We have to find the equation of line in point slope form
It emphasizes the slope of the line and a point on the line
The point slope form is given as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where "m" is the slope of line
Substitute m = 7 and (x, y) = (8, 4) in above point slope form
[tex]y - 4 = 7(x - 8)[/tex]
[tex]y - 4 = 7x - 56[/tex]
Thus equation of line in point slope form is found
We can write the equation in standard form
The standard form of an equation is Ax + By = C. In this kind of equation, x and y are variables and A, B, and C are integers.
[tex]y - 4 = 7x - 56\\\\7x - y -52 = 0[/tex]
Penny reads 12 pages in one-third of an hour. What is the unit rate for pages per hour? For hours per page?
Answer:
The unit rate of pages per hour is 36 pages per hour .
Step-by-step explanation:
Given as :
Penny reads 12 pages in one-third of an hour.
∵ 1 hour = 60 minutes
So , one-third of an hour = [tex]\dfrac{1}{3}[/tex] × 60 min
Or, one-third of an hour = 20 min
Now, According to question
∵ In 20 min , the number of pages read by Penny = 12
So, In 1 min , the number of pages read by Penny = [tex]\dfrac{12}{20}[/tex]
∴ In 60 min , the number of pages read by Penny = [tex]\dfrac{12}{20}[/tex] × 60 min
i.e In 1 hour ,the number of pages read by Penny = 12 × 3 = 36 pages
Hence,The unit rate of pages per hour is 36 pages per hour . Answer
PLEASE HELP!! WILL MARK BRAINLIEST AND THANK YOU!!!
X= ____________
Answer:
x = 26
Step-by-step explanation:
The parallel lines are Line l and Line m. The other line shown is the transversal.
When 2 parallel lines are cut by a trasversal it creates 4 euqual angles and another 4 equal angles of different measure.
The angle "5x + 7" is equal to the angle "8x - 71" since they are alternate exterior angles.
So, we can equate both expressions and use algebra to solve for "x". The process is shown below:
[tex]5x+7=8x-71\\8x-5x=71+7\\3x=78\\x=\frac{78}{3}\\x=26[/tex]
Hence,
the value of x is 26
) An electrician needs 3/4 of a roll of electrical wire to wire each room in a house. How many rooms can he wire with 4 1/2 rolls of wire?
With 4.5 rolls of wire, the electrician can wire up to 6 rooms, assuming a constant wire requirement per room and no additional factors like wastage or special installations.
If an electrician requires 3/4 of a roll of electrical wire to wire one room, then to wire multiple rooms, you can multiply this amount by the number of rooms. In this case, we're dealing with 4 and 1/2 rolls of wire, which is equivalent to 4.5 rolls.
To find out how many rooms can be wired, divide the total amount of wire available by the amount needed for one room:
4.5 rolls ÷ 3/4 roll per room = 4.5 ÷ 3/4 = 6.
So, with 4 and 1/2 rolls of wire, the electrician can wire up to 6 rooms in the house. Keep in mind that this calculation assumes a constant amount of wire is needed for each room and that there are no extra factors like wastage or additional requirements for special installations.
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HELP ASAP NEED THIS.
Answer:
B
Step-by-step explanation:
The 2 part of the ratio represents 39 instructors.
Dividing 39 by 2 gives the value of one part of the ratio, that is
39 ÷ 2 = 19.5 ← value of 1 part of the ratio, thus
number of employees = 12 × 19.5 = 234 → B
Find the value of the greater root of x2 - 6x + 5 = 0.
A) -5
B) -1
C) 1
D) 5
Answer:
D
Step-by-step explanation:
We need to find 2 roots of the quadratic function given and find the greater of the two roots.
We factorize the quadratic and find the two solutions first:
[tex]x^2-6x+5=0\\(x-5)(x-1)=0\\x=1,5[/tex]
So,
x = 1
and
x= 5
Out of the two, x = 5 is the greater root.
D is the correct answer.
What is the answer to 2(x+3)
Using the distributive property...
2(x+3) = 2x+6
answer: 2x+6
Please help with this click on the picture to see the whole thing
A negative exponent means to move the decimal point to the left.
5 x 10^-2 = 0.05
Answer:
5 x 10^-2 = 0.05
Explanation:
A negative exponent means to move the decimal point to the left.
Hope this helped!
Have a wonderful day!
~Lola
Audrey has 400 songs on her MP3 player. Of these songs, 150 are by female vocalists, 75 are by male vocalists, and 175 are by groups. If one song is played at random, what is the probability it is sung by a female vocalist?
Probability for male = 75/400 = 3/16
Probability for groups = 175/400 = 7/16
Probability for female = 150/400 = 3/8
There is a 3/8 probability of the song being sung by a female vocalist.
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A rectangular swimming pool had a length twice as long as it’s width. The pool has a sidewalk around it that is 2 feet wide. Write an expression that would help you find the area of the pool and it’s sidewalk.
Answer:
Area = [tex]2w^2+12w+16[/tex]
Step-by-step explanation:
We let the width of the pool be "w"
We know the length is twice as long as width, so the length is:
2w
So,
Width = w
Length = 2w
Since a sidewalk with 2 feet width goes around the pool completely, the area enclosed by pool + sidewalk would have 2 feet around it, so its length and width would be:
Width = w + 2 + 2 = w + 4
Length = 2w + 2 + 2 = 2w + 4
The area of a rectangular region is always length * width, so the expression for area of pool and sidewalk would be:
[tex](w+4)(2w+4)\\=2w^2+4w+8w+16\\=2w^2+12w+16[/tex]
If we let the width of the swimming pool be "w", the expression for the area of pool and sidewalk is:
Area = [tex]2w^2+12w+16[/tex]
The perimeter of a right triangle is 24 meters, and the area is 24 square
meters. The lengths of the sides are each multiplied by 4. What is the area
of the new triangle?
OA) 136 m
OB) 184 m
OC) 226 m
OD) 384 m
Answer:
D. 384
Step-by-step explanation:
Sorry for the very late response. But if anyone wasn't sure if 384 is correct, it is. I can confirm this because I just took the test. I hope I could help! (:
a point is reflected in the x-axis the new point is (5, -3.5) what is the distance between the two points? Urgent pls help
Distance between two points is 7
Explanation:
This is a question based on reflection of point w.r.t line. During reflection we can see the mirror image with t-shirt print inverted.But the distance from mirror remains same.
Assume a point (x,y), and it reflect in x-axis, then x-axis serves as the mirror, and the new point is (x,-y), because the distance from the mirror remains same. If the reflection of the point is (x,y) in y-axis, then y-axis serves as the mirror, and the new point is (-x,y). And if you reflect (x,y) in y=x line, then new point will be (y,x).
So considering the above question, if new point is (5, -3.5), then the original point must be (5, 3.5)
Distance between two points [tex]P(X_1, Y_1)[/tex] and [tex]Q(X_2, Y_2)[/tex]is given by:
d(P, Q) = [tex]\sqrt{ (X_2-X_1)^{2} + (Y_2-Y_1)^{2}}[/tex]
[tex]Y_2-Y_2 = (3.5) - (-3.5) = 3.5+3.5 = 7\\ \\X_2-X_1 = 5 - 5 = 0[/tex]
[tex]So \sqrt {(Y_2-Y_1)^{2} + (X_2-X_1)^{2}} = \sqrt { 7^{2} + 0^{2}} = \sqrt { 14+0} = \sqrt {14} = 7[/tex]
So distance = 7
Solve:
2(−n−3)−7(5+2n)
Answer:
-16n-41
Step-by-step explanation:
2(-n-3)-7(5+2n)
First begin by expanding the bracket. That is, multiplyingthe brackets by 2 and -7 appropriately.
In doing so we have,
2(-n) x 2(-3) -7(5) x -7 (+2n)
simplifying becomes:
-2n-6-35-14n
collwct like terms becomes -2n-14n-6-35
Final answer becomes Thus: -16n-41
Select all the expressions with a product less than 2/3.
4 and 1/8 x 2/3
2/3 x 2/3
2/3 x 2
5/6 x 2/3
The expressions with a product less than 2/3 are:
2/3 × 2/3 and 5/6 × 2/3 ⇒ 2nd and 4th
Step-by-step explanation:
Let us revise some fact about the product of two numbers
If x is multiplied by y where y > 1, then the product is greater than x (Ex: if x is 3/4 and y is 2, then xy = (3/4)(2) = 3/2 which is greater than 3/4)If x is multiplied by y where 0 < y < 1, then the product is less than x (Ex: if x = 2/5 and y = 1/3, then xy = (2/5)(1/3) = 2/15 which is less than 2/5)We need to select all the expressions with a product less than 2/3
∵ 4 and 1/8 × 2/3
- 4 and 1/8 means mixed number [tex]4\frac{1}{8}[/tex]
∵ [tex]4\frac{1}{8}[/tex] > 1
- That means the product of it and 2/3 will be greater than 2/3
as the first fact above
∴ [tex]4\frac{1}{8}[/tex] × [tex]\frac{2}{3}[/tex] > [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{2}{3}[/tex] is between 0 and 1
- That means the product of it and 2/3 will be less than 2/3
as the second fact above
∴ [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] < [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{2}{3}[/tex] × 2
∵ 2 > 1
- That means the product of it and 2/3 will be greater than 2/3
as the first fact above
∴ [tex]\frac{2}{3}[/tex] × 2 > [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{5}{6}[/tex] × [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{5}{6}[/tex] is between 0 and 1
- That means the product of it and 2/3 will be less than 2/3
as the second fact above
∴ [tex]\frac{5}{6}[/tex] × [tex]\frac{2}{3}[/tex] < [tex]\frac{2}{3}[/tex]
The expressions with a product less than 2/3 are:
2/3 × 2/3 and 5/6 × 2/3
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Only the expressions 2/3 x 2/3 and 5/6 x 2/3 have products less than 2/3, with products of 4/9 and 5/9 respectively.
To determine which expressions have a product less than 2/3, each expression must be evaluated separately:
4 and 1/8 x 2/3 = 33/8 x 2/3
2/3 x 2/3 = 4/9
2/3 x 2 = 4/3
5/6 x 2/3 = 10/18 or 5/9
After simplifying, the expressions that yield a product less than 2/3 are:
2/3 x 2/3 = 4/9, as 4/9 is less than 6/9 (2/3)
5/6 x 2/3 = 5/9, which is also less than 6/9 (2/3)
The expressions 4 and 1/8 x 2/3 and 2/3 x 2 are both greater than 2/3.
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what are the apparent zeroes of the function graphed above?
A. {-1, 2.5}
B. {-17, 5}
C. {-4, 0, 2}
D. {-2, 0 , 4}
Answer:
So the correct option is D
{-2 , 0 , 4}
Step-by-step explanation:
Given:
A Graph
To Find:
Zeroes of the function graph = ?
Solution:
Zeroes of Graph:
Wherever the function graphs line cuts the x-axis are called ZEROES of the function graphs.
Here there are three different points were the function graphs cuts on x-axis. Therefore three zeroes,which are -2 , 0 , 4
i.e x = - 2 , x = 0 (origin),and x = 4
So the correct option is D
{-2 , 0 , 4}
what is the working out for 5x+3=2x+15
The solution is x = 4
Step-by-step explanation:
The given equation is a linear equation so it will have only one equation
Given equation is:
[tex]5x+3=2x+15[/tex]
Subtraction property of equality:
[tex]5x+3-3 = 2x+15-3\\5x = 2x+12[/tex]
Subtraction property of equality:
[tex]5x-2x = 2x-2x+12\\3x = 12[/tex]
Division Property of Equality:
[tex]\frac{3x}{3} = \frac{12}{3}\\x = 4[/tex]
Hence,
The solution is x = 4
Keywords: Linear equation, variables
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Mrs. Jacobs is making several batches of cookies and is using 84 total ounces of chips. The cookies have chocolate chips and peanut butter chips. There are 5 times as many ounces of chocolate chips as peanut butter chips. How many ounces of chocolate chips does Mrs. Jacobs use?
The ounces of chocolate chips used by Mrs Jacob is 70 ounce
Solution:
Given that Jacob is making several batches of cookies and is using 84 total ounces of chips
Let "c" be the ounces of chocolate chips
Let "p" be the ounces of peanut butter chips
To find: ounces of chocolate chips used by Mrs Jacob
Given that There are 5 times as many ounces of chocolate chips as peanut butter chips
Thus we can frame a equation as:
ounces of chocolate chips = 5 x ounces of peanut butter chips
c = 5p -------- eqn 1
Jacob used 84 total ounces of chip. Therefore,
ounces of chocolate chips + ounces of peanut butter chips = 84
c + p = 84 ---- eqn 2
Substitute eqn 1 in eqn 2
5p + p = 84
6p = 84
p = 14Substitute p = 14 in eqn 1
c = 5(14) = 70
c = 70Thus the ounces of chocolate chips used by Mrs Jacob is 70 ounce
What is a positive coterminal angle to -32° that is between 500° and 1000° and a negative
coterminal angle to -32° that is between – 500° and -50°?
Positive coterminal angle = 688 degrees
Negative coterminal angle = -392 degrees
Solution:
Coterminal Angles are angles who share the same initial side and terminal sides.
Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians
Positive coterminal angle:
The positive coterminal angle of [tex]-32^{\circ}[/tex] is given as:
We have to find positive coterminal angle between 500° and 1000°
Between 500° and 1000° there is an angle which is coterminal to 0°:
2 x 360° = 720°
positive coterminal angle = [tex]-32^{\circ} + 720^{\circ} = 688^{\circ}[/tex]
Negative coterminal angle:
We have to find negative coterminal angle between – 500° and -50°
Negative coterminal angle = [tex]-32^{\circ} - 360^{\circ} = -392^{\circ}[/tex]
The area of the net the team uses is no more than 107.25 ft2. The width of the net is 3.25 feet.
Which inequality can be used to find the possible lengths of the volleyball net?
Answer:
The inequality is [tex]l\times (3.25)\leq 107.25[/tex]
Step-by-step explanation:
Given: Area of volleyball net= [tex]107.25 ft^{2}[/tex]
Width of Volleyball net= [tex]3.25 \ ft[/tex]
Considering the volleyball net is in rectangular shape and l and w is length and width respectively.
Area of rectangle= [tex]l\times w[/tex]
Now, using formula to form inequality
⇒ [tex]l\times (3.25)\leq 107.25[/tex]
Next, using the inequality to find length of Volleyball net.
∴ [tex]l\times (3.25)\leq 107.25[/tex]
Dividing both side by 3.25
⇒ [tex]l= \frac{107.25}{3.25} = 33\ ft[/tex]
∴ l= 33 ft
The possible length of Volleyball net is 33 ft.
Answer:
b
Step-by-step explanation:
Four less than the product of two and a number
Answer:
2x - 4
Step-by-step explanation:
Write out the equation:
(2 * x) - 4
Simplify
2x - 4
:)
This table shows equivalent ratios which ratios are equivalent to the ratios in the table check all that apply ?
Answer: 40:8 and 20:4
Step-by-step explanation :It matches up if you multiply both top and bottom with 8 to get 40:8 and multiply with 4 to get 20:4 .
Answer:
A and E
Step-by-step explanation:
A square has a perimeter of 148 inches. How do you find the length of the diagonal of the square?
Answer:
52.33 inches
Step-by-step explanation:
Multiply the length of one side by the square root of 2.
In this case: 37, you would divide that by the square root of 2.
Hope this helps!
What is the space covering the inside of a plane?
Answer:always
Step-by-step explanation: