Divide.
(4x²-24x+15)÷(x−5)
Your answer should give the quotient and the remainder.
Answers
In the problem given, the result of the polynomial long division shows that the quotient is 4x - 4 and the remainder is -5.
How to Perform the Division?To perform polynomial long division of (4x²-24x+15) by (x-5), we follow these steps:
4x - 4
--------------
x - 5 | 4x² - 24x + 15
4x² - 20x
------------
-4x + 15
-4x + 20
----------
-5
Therefore, the quotient is 4x - 4 and the remainder is -5.
We can check our answer by verifying that:
(4x - 4) * (x - 5) + (-5) = 4x² - 24x + 15
which is indeed the original polynomial.
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Related Questions
What is the area of figure?
A. 56 square meters
B. 80 square meters
C. 120 square meters
D. 136 square meters
E. 152 square meters
(quiz help )
Answers
Answer:
D
Step-by-step explanation:
8×16=128
2×4=8
128+8=136m^2
answer: D
Given AC and BD bisect each other at O prove AC is congruent to c
Answers
The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .
Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.
We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.
Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)
Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.
Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD
Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC
Therefore, AC is congruent to c .
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Complete each ratio table.
28
42
56
3.5
14
112.8
56.4
14.1
2,820
1,410
Answers
Answer: i don’t know
Step-by-step explanation:
Answer:34
Step-by-step explanation:
PLEASE ANSWER... im not sure if 'no solution' is the correct answer, i just clicked it on accident!!!!!!!!
Answers
Answer:
d the last one 3 and -3 pls brainlist
Step-by-step explanation:
Stella has $500 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• She buys a new bicycle for $402.96.
• She buys 3 bicycle reflectors for $4.56 each and a pair of bike gloves for $28.21.
• She plans to spend some or all of the money she has left to buy new biking outfits
for $65.69 each
Which inequality can be used to determine o, the maximum number of outfits Stella
can purchase while staying within her budget
Answers
Answer:
65.69o+444.85≤500
Step-by-step explanation:
Construction workers are paving a road. The road must drop 4 cm for every 650 cm measured horizontally.
a) What is the slope of the road?
b) Suppose a section of the road drops 24.5 cm. How long is this section of the road measured horizontally?
Answers
Answer:
a)
slope = (-4 cm) / (650 cm)
slope ≈ -0.00615
b) the section of the road measured horizontally is approximately 3983.74 cm long.
Step-by-step explanation:
change in horizontal distance = (change in vertical distance) / slope
change in horizontal distance = (-24.5 cm) / (-0.00615)
change in horizontal distance ≈ 3983.74 cm
help, I don't know if its right or wrong
Answers
Answer:
its 10 inches
Step-by-step explanation:
Answer: 62.5
Step-by-step explanation:
you do the base times the area which is 25x5=125 and then do half of 125 which is 62.5
What is the answer?? 3(b-5)<-2b
Answers
Answer:
b < 3
Step-by-step explanation:
3 ( b - 5 ) < - 2b
3 ( b ) - 3 ( 5 ) < - 2b
3b - 15 < - 2b
3b + 2b < 15
5b < 15
b < 15/5
b < 3
3(b-5)<-2b
3b<-2b+5
Add the 2b over.
5b<5
Divide by 5.
b<1
Check by plugging in.
3(1-5)<-2(1)
3(-4)<-2
-12<-2
1 is a possibly solution to the inequality.
1. The proportion, p, of consumers who shop with coupons
is the ratio of the number, C, of consumers who use coupons
to the number, N, of consumers asked. Write an equation
for the proportion of consumers who shop with coupons.
Answers
The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.
What is equation?An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.
Here,
This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.
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what is the new equation of the quadratic function
Answers
Answer:
cant really see it
Step-by-step explanation:
A plane flies 1.4 hours at 150 mph on a bearing of 10. It then turns and flies hours at the same speed on a bearing of . How far is the plane from its starting point?
Answers
Answer:
The answer is "1035.76 miles"
Explanation:
The aircraft flies at 120 mph for 1.5 hours at a \(10^{\circ}\) bearing, then flies at the very same speed at \(100^{\circ}\) bearings for 8.5 hours.
However an angle of \(100-10 = 90^{\circ}\) between displacements
First shifts\(= 1.5 \times 120 = 180\ miles.\)
Second shift \(= 8.5\times 120 = 1020\ miles.\)
These two shifts are at \(90^{\circ}\) and therefore the final shift is:
\(\to \sqrt{180^2+1020^2}=1035.76 \ miles\)
Two teams are going on a trip to playa game. There will be
2 buses to take the students. On each bus, there are 60
seats. Teachers and parents will sit in 10 of the seats on
each bus.
How many seats are available for students on the buses?
OA. 110
OB. 50
OC. 70
OD. 100
Answers
Answer:
100
Step-by-step explanation:
60*2=120
10 seats taken up on 2 buses=20
120-20=100
Answer:
the last one (100) 60+60 equals120 10+ 10 equals 20 120-20 equals 100
What is the least common multiple of the numbers 3 16 and 20 
Answers
Answer:
240
Step-by-step explanation:
See photo below
Credit goes to: calculatorsoup.com
A paint manufacturer discovers that the mean volume of paint in a gallon-sized pail is 1 gallon with a standard deviation of 0.05 gallons. The paint volumes are approximately bell-shaped. Estimate the percent of pails with volumes between 0.95 gallons and 1.05 gallons.
Answers
Answer:
Approximately 68%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 1, standard deviation = 0.05.
Estimate the percent of pails with volumes between 0.95 gallons and 1.05 gallons.
0.95 = 1 - 0.05
1.05 = 1 + 0.05
So within 1 standard deviation of the mean, which by the Empirical Rule, is approximately 68% of values.
68.29% of pails have volumes between 0.95 gallons and 1.05 gallons.
Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
\(z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation\)
Given that:
μ = 1, σ = 0.05
\(For\ x=0.95:\\\\z=\frac{0.95-1}{0.05} =-1\\\\For\ x=1.05:\\\\z=\frac{1.05-1}{0.05} =1\)
P(0.95 < x < 1.05) = P(-1 < z < 1) = P(z < 1) - P(z < -1) = 0.8413 - 0.1587 = 68.29%
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What is an equation in point-slope form of the line that passes through (-7, 1) and (-3, 9)?
Answers
writing the linear equation can be used by any any of those coordinates that are given
y - y1 = m(x - x1)
m = Gradient
Making m the subject of the formulam = y - y1 / x - x1
Where:
(-7, 1) = (x, y)
(-3, 9) = (x1, y1)
Solving for mm = (1 - 9) /( -7 + 3)
m = -8/- 4
m = 2
Inputing this into our point slope form equation : y - y1 = m(x - x1)
We have:
y - 9 = 2(x + 3)
Therefore, Option D is the correct option
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In a study of texting speed, 45 adults aged 18-22 were randomly chosen. Each person was asked to the following phrase exactly "Hi! What's up?" on a cell phone. The average time it took was 2.72 seconds. This was found to happen with about a 25% chance when compared to someone saying it takes less than 3 seconds to type. 1.) Identify the following: a. Population: 1. b. Sample: c. Unit/individual: d. Response variable: 2.) What type of variable is the response variable? And what is the level of measurement?
Answers
From the given data in the study of texting speed, we can identify the following
1)
a) population; is all the individuals belonging to the age group of 18-22 years
b) sample; is the selected 45 adults in the age group of 18-22 years
c) unit / individual: adults
d) Response: time taken to write "hi! what's up?"
2)
The response variable is A continuous - quantitative variable.It is a continuous variable as it can take an infinite number of possible values.
The level of measurement isMeasured by the ratio scale of measurement.variables measured by the ratio scale of measurement have equal differences between scale values and equal quantitative meaning. They also have a true zero point
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what is the slope intercept form of 4x+y=-3
Answers
Answer:
Step-by-step explanation:
-4x-3=y
What are the coordinates of the endpoints of the midsegment for A RST that is parallel TS? Enter your answer by filling in the boxes. (_ , _) and (_ , _)
Answers
Answer:
2,4 3,5
Step-by-step explanation:
A boy walks 5km due north and then 4km due east. Find the bearing of his current position from the starting point, how far is the boy now from the starting point
Answers
To assess the accuracy of a laboratory scale a standard weight that is known to weigh 1 gram is repeatedly weighed 4 times. The resulting measurements (in grams) are:
0.95, 1.02, 1.01, 0.98.
For the actual weight
i) write a pivot random variable that can be used for finding confidence interval, which
distribution does this pivot have, explain your answer;
ii)find the 90% and 95% confidence intervals, state the intervals using notion of margin
of error.
Answers
Answer:
Step-by-step explanation:
how dare youuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu
Answer:
(0.9464,1.034)
Step-by-step explanation:
First find the mean μ of all values as;
(0.95+1.02+ 1.01+ 0.98 ) /4 =0.99
μ=0.99
Find the standard deviation as;
-For each value subtract the mean and square the results
0.95-0.99 = -0.04 , -0.04² = 0.0016
1.02-0.99= 0.03, 0.03²=0.0009
1.01-0.99= 0.02, 0.02²= 0.0004
0.98-0.99 = -0.01, -0.01²=0.0001
Find mean of squared deviations as;
(0.0016+0.0009+0.0004+0.0001)/4 =0.00075 ----variance
Standard deviation = √0.00075 = 0.0274
δ = 0.0274
n=4
Thus n< 30 , confidence interval for μ = x ± t*δ/√n ---------(i)
Degree of freedom (df) = n-1 =4-1 =3
The t value for 95% confidence with df= 3 is t=3.182
Substituting the values in equation (i)
0.99 ± 3.182 * 0.0274/√4
0.99 ± 3.182 * 0.0274/2
0.99 ± 3.182 * 0.0137
0.99 ± 0.0436
(0.9464,1.034)
Hope it helps...
Have a great day :P
Answer the questions below about the quadratic function.
g(x) = x^2+2x+5
Does the function have a minimum or maximum value?
- Minimum
- Maximum
Where does the minimum or maximum value occur?
x =
What is the function's minimum or maximum value?
Answers
Answer:
Minimum, x = -1, (-1,4)
Step-by-step explanation:
Respond if you need an explanation
Help I don’t understand!
Answers
As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of depression increases.
what is angle of depression?the arc formed as the line of sight drops from the horizon. The angle of depression is the angle formed when an object is perceived below the observer's height between the horizon and the line of sight of the observer. The depression angle is the angle formed between the line of sight looking down at the object and the horizontal line of sight. If you are on a hill or a building and you are looking down at something, you can tell the slope. To measure these angles, a theodolite or an inclinometer might be employed.
As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of the depression increases.
∠x = 65° ≤ ∠XYZ
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Christopher is deciding between two landscaping companies for his place of business. Company A charges $30 per hour and a $200 equipment fee. Company B charges $50 per hour and a $100 equipment fee. Let
A
A represent the amount Company A would charge for
t
t hours of landscaping, and let
B
B represent the amount Company B would charge for
t
t hours of landscaping. Write an equation for each situation, in terms of
t
,
t, and determine the number hours,
t
,
t, that would make the cost of each company the same.
Answers
The equations for each situation is A = 200 + 30t and B = 100 + 50t. Cost of each company would be same for 5 hours of landscaping.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Let t represent the hours taken for landscaping.
Let A represent the amount Company A would charge for t hours of landscaping, and let B represent the amount Company B would charge for t hours of landscaping.
Company A charges $30 per hour and a $200 equipment fee.
Total amount charged for t hours = 200 + 30t
A = 200 + 30t
Company B charges $50 per hour and a $100 equipment fee.
Total amount charged for t hours = 100 + 50t
B = 100 + 50t
Cost of each company would be same, when,
A = B
200 + 30t = 100 + 50t
30t - 50t = 100 - 200
-20t = -100
t = 5
Hence each of the equation is A = 200 + 30t and B = 100 + 50t and the cost would be same when t = 5 hours.
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Solve
x^2-4=77
E2020
Answers
Answer:
Step-by-step explanation:
Answer:
x = 9 or x = -9
Step-by-step explanation:
x² - 4 = 77
then
x² - 4 + 4 = 77 + 4
then
x² = 81
then
x² - 81 = 0
then
x² - 9² = 0
then
(x - 9)(x + 9) = 0
then
x - 9 = 0 or x + 9 = 0
then
x = 9 or x = -9
__________________________
:)
Which symbol correctly relates 23 ? 16 check all that apply
Answers
Answer:
C and E
Step-by-step explanation:
23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.
which expression is equivalent to the following 6(y+4)
Answers
Given:
6(y + 4)
Let's find the equivalent expression.
To find the equivalent expression, apply distributive property.
Distribute 6 to the numbers in the parentheses.
We have:
6(y + 4)
= 6(y) + 6(4)
= 6y + 24
Therefore, the equivalent expression is: ^
WILL GIVE 5 STARS
Angela plays soccer and golf for a total of 125 minutes every day. She plays soccer 45 minutes more than she plays golf.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Angela plays soccer (x) and the number of minutes she plays golf (y) every day. (5 points)
Part B: How much time does Angela spend playing golf every day? (3 points)
Part C: Is it possible for Angela to have spent 80 minutes playing soccer every day? Explain your reasoning.
Answers
A: The linear equations are x + y = 125 and x = y + 45.
B: Everyday Angela spends 40 minutes in playing golf.
C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Part A:
Let x be the number of minutes Angela plays soccer every day
Let y be the number of minutes Angela plays golf every day
According to the problem statement the linear equations are -
x + y = 125 (total time playing both sports is 125 minutes)
x = y + 45 (Angela plays 45 more minutes of soccer than golf)
Part B:
Substitute x = y + 45 into the first equation -
(y + 45) + y = 125
Use the addition operation -
2y + 45 = 125
2y = 80
y = 40
Angela spends 40 minutes playing golf every day.
Part C:
If Angela spends 80 minutes playing soccer every day, then
x = 80
y + 45 = 80 (using the equation x = y + 45)
y = 35
But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.
This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.
Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.
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10
12
15
18
Are my choices
Answers
Answer:
y=10 x=30
Step-by-step explanation:
3x=90
x=30
2(30)+3y=90
60+3y=90
3y=30
y=10
Answer:
y= 10
Step-by-step explanation:
we have to find x first
∠ABD= 90° because its a right angle
3x°=90°
divide by on both sides
x= 30°
∠CBD must equal 90° degrees as well because a line is 180°
60+3y= 90
-60
3y=30
/3
y= 10
Determine if triangle PQR is similar to triangle LMK. If they are similar enter the scale factor from triangle LMK to triangle PQR.
Answers
Triangles PQR and LMK are not similar. Thus none.
What are similar triangles?Two or more triangles are said to be similar if on comparing their corresponding properties, some common relations holds. One important relation is the scale factor that relates one triangle with the other.
In the diagram given, we have;
scale factor = LK/ PR
= 18/ 10
scale factor = 1.8
But this scale factor can not be used to determine the side LM correctly.
That is,
LM ≠ 1.8*8
LM ≠ 14.4
since LM = 13
Therefore, it can be deduced that triangles PQR and LMK are not similar. Thus none.
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the price of an item has been reduced by $1.09. The new sale price is $71.86. What was the original price?
Answers
Answer:
The original price is 70.77
But I'm not sure
Step-by-step explanation:
71.86 - 1.09= 70.77$