Answer:
(x - 2)*(x - 1) is the answer
Step-by-step explanation:
We have to divide the polynomial f(x) = x^{3}-8x^{2}+17x-10 by (x-5).
Now, after dividing f(x) gets simplified into (x-5)*(x^{2}-3x+2).
So, we need to factorize the quadratic equation x^{2}-3x+2.
i.e. x^{2} - 3x + 2 = x^{2} - x - 2x + 2 = x(x-1) - 2(x-1) = (x - 2)*(x - 1)
Therefore, f(x) again gets simplified into (x-5)*(x - 2)*(x - 1)
Now eliminating the common factor (x-5).
We get, [tex]\frac{x^{3}-8x^{2}+17x-10}{x-5}[/tex] = (x - 2)*(x - 1)
Answer:
[tex]x^{2}-3x+2[/tex]
Step-by-step explanation:
Use synthetic division.
Reverse the sign of -5 and write the coefficients of the polynomial.Multiply the coefficient by the divisor, then add to the next coefficient.Continue through the last coefficient.5 | 1 -8 17 -10
+ 5 -15 10
1 -3 2 0
The quotient is [tex]x^{2} -3x+2[/tex].
An alligator is 6 inches long and grows 8 inches per year. Write an equation that represents the length y (in feet) of an alligator that is x years old. How long will the alligator be after 7 years?
Answer:
y=[(8in*x)+6in]/12in
first to answer will be the brainliest
Answer: the first question is no. It is not a proportional relationship. Can you tell me what the options for the second question is please?
what is the 52nd term for the following sequence ? 14,6,-2,-10,-18
It's an arithmetic sequence:
[tex]a_1=14\\a_2=14-8=6\\a_3=6-8=-2\\a_4=-2-8=-10\\a_5=-10-8=-18\\\vdots\\\text{The general formula for nth term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\\\\\text{We have}\ a_1=14,\ d=-8.\\\\\text{Substitute:}\\\\a_n=14+(n-1)(-8)=14-8n+8=22-8n\\\\\text{We need}\ a_{52}.\ \text{Put n = 52 to the formula}:\\\\a_{52}=22-8(52)=22-416=-394[/tex]
HELP ME PLEASE. Round the fraction to the nearest 1/2.
1/9. A 0
B 1/2
C 1
Answer:
A.0
Step-by-step explanation:
We can make 1/9 to 2/18
0 is 0/18,
1/2 is 9,18,
1 is 10/18
It is closest to 0/18
Answer:A
simplify the expression. 16-4[3+2÷(9-7)]
Answer:
0
Step-by-step explanation:
Answer:
IT ALL EQUALS TO 0.
Step-by-step explanation:
Step 1: Parenthesis:
16 - 4[3 + 2 / 2]
Sep 2: dO DIVISION IN THE BRACKETS:
16 - 4[3 + 1]
Step 3: Add what is in the brackets
16 - 4[4]
Step 4: Multiply
16 - 16
Step 5: Simplify
0
Michelle’s annual take-home pay is $29,000. What is the maximum amount that she can spend per month paying off credit cards and loans and not be in danger of credit card overload?
Answer:
242 dollars / month. See guidelines below
Step-by-step explanation:
That depends largely on where she lives. The rule of thumb is to allow about 1/3 for rent after the government takes it's cut (that's all governments).
Here is an actual breakdown of how budgeting should be done.
Rent 33%Transportation 15% No carFood 10% very low. That means 240 / monthDebt 10%Personal 5%Savings 10% Utilities 10%Clothing 3%Medical 4% very low. Particularly if she is American.Total 100%These numbers are meant for Canada and are meant as a guide. In reality, if you live in the United States you will have to be spending more on medical for example and less somewhere else.
Now to your question. She has 29000 dollars. Debt is listed at 10%
10% of 29000 = (10/100) * 29000 = 2900 dollars.
Like most numbers having to do with money, most people don't understand large numbers and have to have them broken down. In monthly terms, she can spend 2900 / 12 = 241.67 dollars / month on debt. That does not mean that she can add 241.67 of new debt every month. It means that she must first pay off what she owes, and then she gets to spend the balance on debt, but that is a very dangerous way to think. What she should say is if she has left over money that money can be transferred over to another category.
I know of very few people that can consider themselves debt free. Fewer of our American friends can make the claim.
The sources of these %s come from Credit Counselling Society (of Canada)
What is the diameter in inches of a circle that has an area of 16pi square inches
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=16\pi \end{cases}\implies 16\pi =\pi r^2\implies \cfrac{16\pi }{\pi }=r^2\implies 16=r^2 \\\\\\ \sqrt{16}=r\implies 4=r~\hfill \stackrel{\textit{diameter is twice the radius}}{d=8}[/tex]
Factor the expression using the GCF of 8-22
8 = 2 · 2 · 2
22 = 2 · 11
GCF(8, 22) = 2
8 - 22 = 2 · 4 + 2 · 11 = 2 · (4 + 11)what is 0.00526 in scientific notation
Answer:
5.26 X 10^-3
Step-by-step explanation:
Jesse earns $3 each time he walks a dog. Last Monday and Tuesday, he earned a total of $45. He walked 8 dogs on Tuesday. How many dogs did Jesse walk on Monday?
Answer:
7
Step-by-step explanation:
3*8=24 and so 3*7 would =21 and 21+24=45
Jesse walked 7 dogs on Monday.
To find this answer, you must first find out how much money he made for walking dogs on Tuesday. To do so, multiple 8 (number of dogs) by 3 (amount of money earned per dog. This will give you 24, which you subtract from the total (45). 45 - 24 = 21. Finally, divide 21 (amount he made on Monday) by 3 (amount of money earned per dog) to get 7 dogs on Monday.
I hope this helps!
solve fast pls hh
Solve 8x+3−3(x−1)=x−2.
Answer:
x= -2
Step-by-step explanation:
1-) 8x+3-3x+3=x-2
2-) 5x+6=x-2
3-) 4x=-8
4-)x= -2
Then answer the question(s) below, using complete sentences. . Site 1 How can credit cards be more secure than cash?
Answer:
Step-by-step explanation:
If you lose cash and someone finds it, you've lost it without recourse. If you lose a credit card, usually the issuer of the card can cancel it after your last verified purchase and replace the card for you. That is the main advantage.
You also have a record of what you've spent with a credit card. Sometimes you get a receipt and some sometimes you don't when you use cash.
Cash forces you to carry around coins, especially if you make a lot of small purchases in different places. Getting change for 2.22 cents from a 20 can be a little awkward and soon the big bills turn into many more little ones. Credit cards don't have that disadvantage.
Answer:
There are online services that will help someone monitor their credit and make a note of any changes in their credit score. Credit card monitoring keeps track of all open accounts and monitors hard inquiries. That way, if someone did not make the purchase, they can immediately tell the lender that the card has been compromised.
Step-by-step explanation:
This is an altered version of the information from the website given. I got a 100% on edgenunity.
What is 3.2 m converted to centimeters?
A. 3.2 cm
B. 32 cm
C. 320 cm
D. 0.032 cm
Answer:
C. 320 Cm
Step-by-step explanation:
To convert any value in meters to centimeters, just multiply the value in meters by the conversion factor 100.
3.2 meters=3.2*100=320 centimeters
F(x)= (x-2)^2 (x+2)(x+3)
Answer:
[tex]x^{4}[/tex] + x³ - 10x² + 20x
Step-by-step explanation:
expand (x - 2)² and (x + 2)(x + 3) using FOIL
= (x² - 4x + 4)(x² + 5x + 6)
multiply each term in the second factor by each term in the first factor
= [tex]x^{4}[/tex] + 5x³ + 6x² - 4x³ - 20x² - 24 + 4x² + 20x + 24 ← collect like terms
= [tex]x^{4}[/tex] + x³ - 10x² + 20x
Mateo wrote the equation 8-2(3-x)=4x-2(x+1).How many solutions are there to Mateo’s equation?
A. No solution
B. exactly one solution
C. exactly two solutions
D. exactly many solutions
After simplifying Mateo's equation, we find that it results in an impossibility (2=-2), which means that the equation has no solution.
Explanation:In order to find the number of solutions to Mateo's equation, we first need to simplify it. The equation given is 8-2(3-x)=4x-2(x+1). Distributing the numbers on each side of the equation, it turns into 8-6+2x = 4x -2x -2. Simplify it further into 2x + 2 = 2x - 2. If we subtract 2x from both sides, we get 2 = -2.
This result, 2 = -2, is not possible or true. Therefore, the given equation has no solutions. The correct answer to the question is therefore option A: No solution.
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Find the slope of the line going through the points (5, 2) and (0, -13).
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (5, 2) and (0, -13). Substitute:
[tex]m=\dfrac{-13-2}{0-5}=\dfrac{-15}{-5}=3[/tex]
Answer: slope = 3Answer:
3
Step-by-step explanation:
We are to find the slope of a line which passes through the two given points: (5, 2) and (0, -13).
We know the formula of the slope (m):
[tex]Slope[/tex][tex](m)[/tex]=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
So putting in the values of the coordinates of the given points in the formula to get:
Slope = [tex]\frac{-13-2}{0-5} =\frac{-15}{-5}[/tex] = 3
Therefore, the slope slope of a line which passes through the two given points: (5, 2) and (0, -13) is 3.
Brandon draws a reflection of the point (-4, -6). He gets the point (-4, 6). Across which axis did he reflect the point. Explain how you know
When you reflect a point across an axis, either the x value or the y value flips signs.
When you reflect across the x axis, the sign of the y value changes(+ to -) or (- to +)
When you reflect across the y axis, the sign of the x value changes (+ to -) or (- to +)
The point reflected across the x-axis because the sign of the y value changed/flipped, while the sign of the x value stayed the same.
Final answer:
Brandon reflected the point (-4, -6) across the x-axis to get the point (-4, 6), which is recognized by the unchanged x-coordinate and the sign reversal of the y-coordinate.
Explanation:
Brandon reflected the point (-4, -6) to get the point (-4, 6). This reflection occurred across the x-axis. We know this because the x-coordinate of the point remained unchanged, indicating that the point was not moved left or right. However, the y-coordinate changed from -6 to 6, which signifies that the point was reflected over the x-axis and moved from below the axis to an equal distance above the axis.
In reflections across the x-axis, the x-coordinate remains the same while the sign of the y-coordinate is reversed. Conversely, a reflection across the y-axis would keep the y-coordinate the same and reverse the sign of the x-coordinate.
In a coordinate system, negative or positive values for x and y are determined by their position relative to the origin. Points to the right of the origin and above the origin are usually considered to have positive coordinate values, with directions indicated by arrows on the axes. In Brandon's case, the negative y-coordinate became positive, affirming the x-axis as the axis of reflection.
Graph the line for y+1=−3/5(x−4) on the coordinate plane. Move Line Undo Redo Reset
Answer:
The equation of line is shown below.
Step-by-step explanation:
The equation of line is
[tex]y+1=\frac{-3}{5}(x-4)[/tex]
It is the point slope form of a line, therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the line passing through (4,-1).
Rewrite the above equation in slope intercept form.
[tex]y=\frac{-3}{5}x+\frac{12}{5}-1[/tex]
[tex]y=\frac{-3}{5}x+\frac{12-5}{5}[/tex]
[tex]y=\frac{-3}{5}x+\frac{7}{5}[/tex]
The point slope form of a line is
[tex]y=mx+b[/tex]
Where m is the slope and b is y-intercept.
Therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the y-intercept of the line is [tex]\frac{7}{5}[/tex].
Slope is defined as
[tex]m=\frac{Rise}{Run}[/tex]
Since the slope is negative, therefore the run of the line is considered on the left side. The line rise by 3 and run by 5, therefore we will add 7 in y and subtract 5 from x.
The y-intercept is [tex](0,\frac{7}{5})[/tex].
[tex](0-5,\frac{7}{5}+3)=(-5,\frac{22}{5})=(-5,4.4)[/tex]
Therefore we have three points (4,-1), (-5,4.4) and (0,1.4). Plot the point on the coordinate plane and connect them be a straight line.
The graph line for y+1 = -3/5(x-4)
Plot the y-intercept at (0, 7/5).
From that point, move 5 units to the right and 3 units down to find another point on the line. This gives you the point (5, 4/5).
You can continue this pattern, moving 5 units to the right and 3 units down from the previous point to find more points on the line.
To graph the line with the equation y + 1 = -3/5(x - 4), we can first rearrange it into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Starting with your equation:
y + 1 = -3/5(x - 4)
Let's isolate y:
y = -3/5(x - 4) - 1
Now, we can distribute the -3/5 to both terms inside the parentheses:
y = (-3/5)x + (12/5) - 1
y = (-3/5)x + 12/5 - 5/5
y = (-3/5)x + 7/5
Now that we have the equation in slope-intercept form (y = mx + b), we can see that the slope (m) is -3/5, and the y-intercept (b) is 7/5.
Now, we can plot this line on the coordinate plane. Start by plotting the y-intercept, which is the point (0, 7/5), and then use the slope to find additional points on the line. The slope of -3/5 means that for every 5 units to the right, you go 3 units down.
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The value of the digit 4 in 24, 601 is how many times greater then the value digit 4 in 437
Answer:
The Answer is 10 times as much.
Step-by-step explanation:
We know that the 4 in 24,601 is 4000. We also know that the 4 in 437 is 400. If we do 4000/400, we get 10 times as much!
I hope this helps.
There are 25 students acting in a high school play. They make up 2% of the high school students. Hoy many students attend at the high school play
Answer:
1250
Step-by-step explanation:
since 2% of the school is 25 students that means every 2% there is 25 students.
100/2 = 50
50*25 = 1250 students
Answer:
1250 = total students
Step-by-step explanation:
Students in the play = total students * percent in play
We know that the students in the play =25
We know the percent in the play is .02
Substitute what we know into the equation
25 = total students * .02
Divide each side by .02
25/.02 = total students *.02/.02
1250 = total students
which. is. less. to. greater. 4.054. 4.045.4.405.4.504.4005
The ascending order of the provided numbers is 4.045, 4.054, 4.405, 4.4005, and 4.504. This was achieved by comparing each decimal place from left to right.
Explanation:The numbers 4.054, 4.045, 4.405, 4.504 and 4.4005 can be arranged in increasing order (from less to greater) by comparing each place value from left to right. When we compare these numbers, the arrangement from less to greater would be 4.045, 4.054, 4.405, 4.4005, and 4.504.
To do this, we first compare the numbers at each decimal place (tenths, hundredths, thousandths etc.), and arrange accordingly. We continue this process until we have the complete list in ascending order.
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Identify the domain and range of the relation. Represent the relation with a
mapping diagram. Is the relation a function?
{(−1, 1), (−2, 2), (4, −4), (7, −7)}
The domain and range of the relation {(-1, 1), (-2, 2), (4, -4), (7, -7)} are {-1, -2, 4, 7} and {1, 2, -4, -7} respectively.
What is relation in function?Not every relation is a function, but every function is a relation.
A function is a relation with clear boundaries.
When we say that something is well-defined, we mean that each element has been assigned a specific image.
The given set is,
{(-1, 1), (-2, 2), (4, -4), (7, -7)}
The domain of a set is the values of x,
Domain = {-1, -2, 4, 7}
The range of a set is the values of y,
Range = {1, 2, -4, -7}
The relation makes the function because for every value of x the sign of function y is negative,
The required function is,
y = -x.
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The family size bottle of sunscreen holds 12 fluid ounces (fl oz) of sunscreen. The regular bottle holds 75% less. How many fewer fluid ounces does the regular bottle of sunscreen hold?
Answer:
9
Step-by-step explanation:
Joe filled up his car’s gas tank. After travelling 165 km, 3 8 of the gas in the tank was used. At this rate, approximately how much farther can the car travel before its fuel tank is completely empty?
Answer:
275 km
Step-by-step explanation:
It has 1 - 3/8 = 5/8 of a tank left.
3/8 of a gallon gives 165 km
So 1 gallon gives 165 / 3/8 = 165 * 8/3 km
5/8 gallon gives 168 * 8/3 * 5/8 km
= 165 * 5/3
= 275 km (answer)
HELP ME PLEASE
12*8+(12^3)=
Answer:
1824
That would be your total
Answer:
1824
Step-by-step explanation:
12*8+(12^3)=
We need to work these in the order of PEMDAS. First is the parentheses and exponents.
12*8 + 1728
Next is multiplication.
96+1728
Now add.
1824
To make sandwiches for a picnic, Amy buys 1 loaf of bread for $4.19 and 4 pounds of turkey at $6.95 per pound. Amy calculates the total cost as $31.99. Which equation best shows whether or not Amy’s estimate is reasonable?
Answer: ($4.19 x 1) + ($6.95 x 4) = $31.99
Step-by-step explanation: 4.19 is the price of the loaf of bread, so the first part of the equation ($4.19x), in this case the x is 1 since she bought only one loaf.
6.95 is the price of the turkey per pound, so our second part to the equation, ($6.95y), in this case y is 4 since the turkey weighed 4 pounds.
The complete equation is the combined cost of the turkey and bread so ($4.19x) + ($6.95y) = $?
The we replace the letters, ($4.19 x 1) + ($6.95 x 4) = $?
And then we add and multiply, ($4.19 x 1) + ($6.95 x 4) = $31.99
Answer:
a
Step-by-step explanation:
In the diagram below which distance represents the distance from point d to ab
Answer:
CD
Step-by-step explanation:
The fastest way to get from D to AB is to go down CD
The distance from the point D to line AB is represented by the distance CD.
How to find the distance from a point to a line?To find out the distance from a point to a line we have to draw a perpendicular to the line from a given point, this distance will be considered as the distance between the point and line.
Hence the distance from point D to line AB is CD(option A).
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Which product is negative?
___________________________
a) −3⋅(−2)⋅(−4)⋅(−7)
b) −6⋅(−7)⋅(−8)⋅0
c) −2⋅(−7)⋅12⋅(4)
d) 4⋅(−9)⋅(−3)⋅(−1)
Need help with #18 ASAP. Will pick brainliest and question worth 20 points.
Answer:
scoops 1 1/2 5 12.8 1.5 1.05 20 12.25
milk 10 5 50 128 15 10.5 200 122.5
Step-by-step explanation:
The problem states 1 scoop per 10 oz of milk
1 scoop x scoops
------------ = ------------
10 oz 5 oz
Using cross products
1 *5 = x * 10
Divide by 10
5/10 =x
1/2 scoops
1 scoop 5 scoops
------------ = ------------
10 oz x oz
Using cross products
1 *x = 5 * 10
x =50
50 oz
1 scoop x scoops
------------ = ------------
10 oz 128 oz
Using cross products
1 *128 = x * 10
Divide by 10
x =128/10
12.8 oz
1 scoop 1.5 scoops
------------ = ------------
10 oz x oz
Using cross products
1 *x = 1.5 * 10
x =15
15 oz
1 scoop x scoops
------------ = ------------
10 oz 10.5 oz
Using cross products
1 *10.5 = x * 10
Divide by 10
x =10.5/10
1.05 oz
scoop 20 scoops
------------ = ------------
10 oz x oz
Using cross products
1 *x = 20 * 10
x =200
200 oz
scoop 12.25 scoops
------------ = ------------
10 oz x oz
Using cross products
1 *x = 12.25 * 10
x =122.5
122.5 oz
Answer:
[tex]\underline {\text{P}\ \ |\quad1\quad| \quad\frac{1}{2}\quad|\quad5\quad|\quad12.8\quad| \quad1.5\quad| \quad1.05\quad|\quad20 \quad|\quad12.25\quad|}\\{\text{M}\ |\quad10\ \ | \quad 5\quad|\quad50\ \ |\quad128.\quad|\quad15\quad| \quad10.5\quad|\quad200\ |\quad122.5\quad|}[/tex]
Step-by-step explanation:
Set up the proportion as [tex]\dfrac{1 \text{ powder}}{10 \text{ milk}}=\dfrac{P}{M}[/tex], then cross multiply and solve for the variable.
Column 1: [tex]\dfrac{1}{10} =\dfrac{1}{M}[/tex] → M = 10
Column 2: [tex]\dfrac{1}{10} =\dfrac{P}{5}[/tex] → 5 = 10P → [tex]\frac{1}{2} = P[/tex]
Column 3: [tex]\dfrac{1}{10} =\dfrac{5}{M}[/tex] → M = 50
Column 4: [tex]\dfrac{1}{10} =\dfrac{P}{128}[/tex] → 128 = 10P → 12.8 = P
Column 5: [tex]\dfrac{1}{10} =\dfrac{1.5}{M}[/tex] → M = 15
Column 6: [tex]\dfrac{1}{10} =\dfrac{P}{10.5}[/tex] → 10.5 = 10P → 1.05 = P
Column 7: [tex]\dfrac{1}{10} =\dfrac{20}{M}[/tex] → M = 200
Column 8: [tex]\dfrac{1}{10} =\dfrac{12.25}{M}[/tex] → M = 122.5
which of the following are possible rational roots 3x^2-3x+5
Answer: [tex]\bold{\pm1, \pm5, \pm\dfrac{1}{3},\pm \dfrac{5}{3}}[/tex]
Step-by-step explanation:
Q P
3x² - 3x + 5
Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative values.
[tex]\pm \dfrac{\text{factors of P}}{\text{factors of Q}}[/tex]
[tex]=\pm \dfrac{\text{factors of 5}}{\text{factors of 3}}[/tex]
[tex]=\pm \dfrac{1, 5}{1, 3}[/tex]
[tex]=\pm\dfrac{1}{1}, \pm\dfrac{5}{1}, \pm\dfrac{1}{3},\pm \dfrac{5}{3}[/tex]