Answer: [tex]\bold{\pm \{1, 2, 3, 4, 6, 12, \dfrac{1}{2}, \dfrac{3}{2}\}}[/tex]
Step-by-step explanation:
Q P
f(x) = 2x³ - bx² + cx + 12
Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative signs.
[tex]\quad \pm \dfrac{\text{factors of P}}{\text{factors of Q}}\\\\=\pm \dfrac{\text{factors of 12}}{\text{factors of 2}}\\\\=\pm \dfrac{1,2,3,4,6,12}{1,2}\\\\=\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \dfrac{1}{2}, \pm \dfrac{3}{2}\\[/tex]
The selling price of a chair is Rs 980 with a loss of 20%. What is the cost price of the chair?
Answer:
1225
Step-by-step explanation:
a loss of 20% represents 80% ( 100 - 20) of the cost price
100% represents the cost price
To find the cost price divide the selling price by 80 to find 1% and multiply by 100 to find cost price
cost price = [tex]\frac{980}{80}[/tex] × 100 = 1225
Dianna earns $8.50 an hour working as a lifeguard write an equation to find Dianna’s money earned?
y=8.5x
y= money earned
x= hours worked
The equation to find Dianna's money earned as a lifeguard is e = 8.50h.
To find Dianna's money earned, we can write an equation using the formula for calculating earnings:
Earnings=Hourly Rate × Number of Hours Worked
In this case, Dianna's hourly rate is $8.50, and let's denote the number of hours she worked as ℎ.
So, the equation to find Dianna's money earned
E=8.50×h
Where:
E represents the total earnings
8.50 represents Dianna's hourly rate
h represents the number of hours worked
This equation will give us the total amount of money Dianna earned based on the number of hours she worked.
Joshua has $34 in his bank account. With his new job, he deposits the same amount each week into the account. After 35 weeks, Joshua has $909. What function can find the amount in Joshua's account after w weeks?
Answer:
f(x) = 34 + 25w
Step-by-step explanation:
First, we need to find the amount he was paid over the 35 weeks:
909 - 34 = 875
35w = 875
w = 875 / 35 = 25
So every week he is paid $25
The function has to start with 34, as that is the amount already in there, and as w is multiplying by 25, this can be written as 25w
So put these two together:
f(x) = 34 + 25w
James cut three squares lasagnas so that each piece was 1/5 of a lasagna. How many pieces did James cut the lasagna into?
Final answer:
James cuts each of the three lasagnas into five equal parts, resulting in a total of 15 pieces of lasagna.
Explanation:
When James cuts each square lasagna into pieces that are each 1/5 of the lasagna, he's effectively dividing each whole lasagna into five equal parts. Since he has three whole lasagnas, each cut into 1/5-sized pieces, the total number of pieces he would end up with can be found by multiplying the number of pieces per lasagna by the number of lasagnas.
To calculate this, you multiply 5 (the number of pieces from one lasagna) by 3 (the number of lasagnas):
Multiply the number of pieces per lasagna (5) by the number of lasagnas (3).
5 pieces/lasagna × 3 lasagnas = 15 pieces
Thus, James cuts the lasagna into 15 pieces in total.
simplify:
[tex] \sqrt[5]{3} + \sqrt{12} + \sqrt{32} [/tex]
[tex]\sqrt[5]3+\sqrt{12}+\sqrt{32}=\sqrt[5]3+\sqrt{4\cdot3}+\sqrt{16\cdot2}=\sqrt[5]3+\sqrt4\cdot\sqrt3+\sqrt{16}\cdot\sqrt2\\\\=\boxed{\sqrt[5]3+2\sqrt3+4\sqrt2}[/tex]
If sinx is approximately 0.2588, what is the measurement of x to the nearest degree? Approximately, what is the cosine of the angle that is complementary to x? A) 15°; 0.2588 B) 15°; 0.9659 C) 75°; 0.2588 D) 75°; 0.9659
Answer:
A
Step-by-step explanation:
given sin x ≈ 0.2588, then
x = [tex]sin^{-1}[/tex](0.2588) ≈ 15°
using the cofunction identity
cos x = sin(90 - x)
the complement of 15° is 90° - 15° = 75°, hence
cos 75° = sin(90 - 75)° = sin15° ≈ 0.2588
Jason spends 3 1/12 hours biking and 2 1/3 hours at the mall. How much less time does Jason spend at the mall compared to biking?
We must find the difference between 3 1/12 and 2 1/3. So we can first subtract 3 from 2 and we earn 1 whole number. Next we must subtract 1/12 and 1/3. This is the same as 3/36-12/36, which is -9/36 or -1/4. Since we can't have -1/4 we must subtract 1/4 from 1 and earn 3/4 as our answer.
Hope this helps! <3
AB is dilated by a scale factor of 3 to form AB . Point O is the center of dilation, and point O lies on AB . If the slope of AB is 3, what can be said about line A'B' ?
A. The slope of is 6, but does not pass through O.
B. The slope of is 9, and passes through O.
C. The slope of is 9, but does not pass through O.
D. The slope of is 3, and passes through O.
E. The slope of is 3, but does not pass through O.
Option: D is the correct answer.
D. The slope of is 3, and passes through O.
Step-by-step explanation:It is given that:
AB is dilated by a scale factor of 3 to form AB .
Also, the line AB pass through the origin.
So, if AB pass through (0,0) and some point (x,y) then the slope of line AB is:
[tex]Slope=\dfrac{y-0}{x-0}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]
( Since, it is given the slope of AB is 3 )
Now , if AB is dilated to A'B' by a scale factor of 3 then
(0,0) → (0,0)
and
(x,y) → (3x,3y)
i.e. (0,0) and (3x,3y) will lie on A'B'.
Hence, the slope of line A'B' is given by:
[tex]Slope=\dfrac{3y-0}{3x-0}\\\\i.e.\\\\Slope=\dfrac{3y}{3x}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]
Hence, both have the same slope.
The answer is : Option: D
Answer:
Step-by-step explanation:
Factor -.36 out of -1.8w+3.96
[tex]-1.8w+3.96=(-0.36)(5w)+(-0.36)(11)\\\\=\boxed{-0.36(5w+11)}[/tex]
During a recent shopping trip, Erin bought six shirts that cost $15.95 each. How much change did Erin receive if she paid with a $100 bill?
Answer:
4 Dollars and 30 cents
Step-by-step explanation:
15.95 x 6 = 95.7
100-95.7= 4.30
Final answer:
Erin bought six shirts at $15.95 each, totaling $95.70. After paying with a $100 bill, she would receive $4.30 in change.
Explanation:
The question asks us to calculate the total cost of six shirts and then determine the change from a $100 bill. Erin bought six shirts that cost $15.95 each. To find the total cost, we multiply the price of one shirt by the number of shirts:
$15.95 × 6 = $95.70.
Next, we calculate the change Erin would receive if she paid with a $100 bill:
$100 - $95.70 = $4.30.
Therefore, Erin would receive $4.30 in change.
Solve 100 divided by 5 x 4 + 4³
Answer:
144
Step-by-step explanation:
4 x 4 x 4 = 64
100/5 = 20
20 x 4= 80
80 + 64 =144
Answer:
100 /( 5 x 4 + 4³) = 1 4/21
100 / 5 x 4 + 4³ = 144
Step-by-step explanation:
100 /( 5 x 4 + 4³)
PEMDAS tells us to do what is inside the parenthses
We will do the power in side the parentheses first 4^3 = 64
100 /( 5 x 4 + 64)
Now we will multiply
100/(20+64)
Now we add inside the parentheses
100/84
Divide the top and bottom by 4
25/21
Changing from an improper fraction to a mixed number
1 4/21
OR
100 / 5 x 4 + 4³
If the quantity is not in parentheses
We will do the power first 4^3 = 64
100 / 5 x 4 + 64
Then we do the multiplication and division from left to right
20 *4+64
80+64
144
What is the 33rd term of this arithmetic sequence? 7, 17, 27, 37,47
Answer:
327 FOR A FACTTTTT
Step-by-step explanation:
Answer:
the answer would be 327
Step-by-step explanation:
hope this helps :)
Mrs.Barkley has 75 feet ribbon. If each of the 18 students in her class gets an equal length of ribbon, how many inches of ribbon will each student get?
Answer:
Each student would get 4 inches of ribbon
Step-by-step explanation:
Mrs. Barkley has 75 inches of ribbon and is splitting it between 18 students so you would divide 75 by 18. When you divide you get 4.166666... etc. So the answer would be 4
Each of the 18 students in Mrs. Barkley's class will receive 50 inches of ribbon when 75 feet of ribbon are divided equally among them.
The student has asked how many inches of ribbon each student will get if Mrs. Barkley has 75 feet of ribbon and splits it equally among 18 students. To solve this problem, we first need to convert feet to inches because there are 12 inches in a foot. Then we divide the total inches of ribbon by the number of students.
Total length of ribbon for each student= 75/18
The total length of ribbon for each student≈4.1667
So, each student will receive approximately 4.1667 feet of ribbon.
To find out how many inches this is, we'll convert this value to inches. Since 1 foot is equal to 12 inches, we can multiply the total length of the ribbon for each student by 12:
The total length of ribbon for each student (in inches)=4.1667×12
The total length of ribbon for each student (in inches)≈49.9999
Therefore, each student will receive approximately 50 inches of ribbon.
Sally and her husband Jim left their house at the same time traveling in the same direction. Sally drove at 55mph and Jim drove at 65mph. How many hours was it before Jim was 100 miles ahead of Sally?
Answer:
It will take 10 hours.
Step-by-step explanation:
We know distance = rate * time
Sally's rate = 55
Jim's rate = 65
We want Jim to be 100 miles ahead of Sally
The time will always be the same.
d =Sally's distance
Sally
d = 55t
Jim
d+100 = 65 t
We know have 2 equations with 2 unknowns. Substitute d= 55t into Jim's equations
55t + 100 = 65t
Subtract 55t from both sides.
55t-55t + 100 = 65t-55t
100 = 10t
divide each side by 10
100/10 = 10t/10
10 = t
Answer:
It will take exactly 10 hours
Step-by-step explanation:
the equation of a circle is given below x^2 + (y+4)^2 = 64. What is its center? what is its radius?
The center of the circle described by the equation x^2 + (y+4)^2 = 64 is at the point (0,-4), and the radius is 8.
Explanation:In the context of a circle, the general equation form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Looking at your given equation x^2 + (y+4)^2 = 64, it is in this general format.
Here, the value of a is 0 (as there is no number being subtracted from x) and b is -4 (the y coordinate has been shifted 4 units down). Therefore, the center of the circle is at point (0,-4).
For the radius, since r^2 = 64, the radius r will be the square root of 64 which is 8.
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Which algebraic rule describes the transformation?
A) (x, y) → (x + 1, y − 3)
B) (x, y) → (x + 3, y − 1)
C) (x, y) → (x − 1, y + 3)
D) (x, y) → (x − 3, y + 1)
Answer:
B
Step-by-step explanation:
To get to to triangle Y'X'Z', you need to move triangle YXZ 3 units to the right (+3), and 1 unit down (-1). So (x+3,y-1)
Answer:
b
Step-by-step explanation:
Carlos has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Answer:
25
Step-by-step explanation:
Which of the following is an irrational number?
Answer:
7.25252525
Step-by-step explanation:
Irrational numbers are numbers that never end, therefore 7.25 is an irrational number. also, none of the other ones are never ending
Ms. Valenzuela had her students design a snake house for the zoo. In the de3sign shown, the anaconda has 538 more square feet than the python. The python has twice as many square feet as the rattlesnake. How much area does each snake have?
Answer:
If the python has the area x sq. ft, they all have the area [tex]\dfrac{5x}{2}+538\ sq. ft.[/tex]
Step-by-step explanation:
Let x sq. ft be the area the python has.
1. If the anaconda has 538 more square feet than the python, then the anaconda has (x+538) sq. ft.
2. If the python has twice as many square feet as the rattlesnake, then the rattlesnake has the area [tex]\dfrac{x}{2}\ sq. ft.[/tex]
In total they have the area
[tex]x+(x+538)+\dfrac{x}{2}=\dfrac{5x}{2}+538\ sq. ft.[/tex]
Norah has 2/3 ton of stone to spread equally in 4 square yards. How many tons of stone will be spread in each square yard?
Answer:
The answer is 1/6.
In each square yard, Norah would spread 1 / 6 ton of stone.
Given that,
Norah has 2/3 tons of stone to spread equally in 4 square yards, how many tons of stone will be spread in each square yard is ot be determined.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Quantity if Stone = 2/3 ton
Area = 4 square yards
Quantity per yard = [2/3] / 4= 1 / 6
Thus, in each square yard, Norah would spread 1 / 6 ton of stone.
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What is 90/70
Simplified
As an improper fraction, the simplified answer would be 9/7 after you divide both top and bottom by 10
------------------------
If you need a mixed number, then 9/7 converts to 1 & 2/7 because
9/7 = 1 remainder 2
If you had 9 cookies and 7 friends, then each friend gets 1 whole cookie, and there will be 2 left over.
Answer:
The answer would be 9/7 as improper, but if you want the mixed number it would be 2 2/7. Glad I could help let me know if I can do anything else
Step-by-step explanation:
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.
Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
Let x = the number of packages of pasta and y = the number of jars of pasta sauce.
Identify each point as either a solution to the system or not a solution to the system of inequalities.
(1, 12) Solution or Not a Solution
(2, 10) Solution or Not a Solution
(4, 5) Solution or Not a Solution
(6, 10) Solution or Not a Solution
(12, 8) Solution or Not a Solution
(18, 6) Solution or Not a Solution
Answer:
1,12/ Not a solution
2,10/ solution
4,5/ solution
6,10/ not a solution
12,8/ not a solution
18,6/ not a solution
Step-by-step explanation:
all you have to do is put it into the equation.
for example:
1,12
1x1+12x3= $37
1x1+12x1.5= 19lbs
This is not a solution because he can carry it but doesn't have the money to buy it.
Answer:
(1,12)=no solution
(2,10)=Solution
(4,5)=Solution
(6,10)=no solution
(12,8)=no solution
(18,6)=no solution
Step-by-step explanation:
You have to add the money and pounds each together. For example, the equation you would set up would be, for money: 1(1)=1 and the jars 3(12)=36. Together, it equals 37, which would be over the total amount that Tyler may buy. If you do all of these to show your work, then the answers are the ones shown above.
Choose all of the equations that graph as an increasing function.
2
A. y = -- x + 7
3
B. y = -3x - 4
C. y = -5x
D. = 0.05x + 10
Answer:
A. y = -(-x) +7 = x + 7
D. y = 0.05x + 10
Sneakers normally cost $89.99, but on sale, they are marked down to $56.49. What percent off is the sale price?
Answer:
60%
Step-by-step explanation:
Use the equation a=pw. A= Part P= Percent. W= Whole
A= $56.49
P = x (unknown)
W= $ 89.99
Equation = 56.49=89.99x
You divide 89.99 on both sides to be equal and isolate the variable x. You would divide 56.49 by 89.99 and will get 0.627736415. You would round it to the nearest tenth , 0.6 so the percent is 60%
The percent off is 37.2263 % of the sale price.
What Is Percentage Change?In finance, percentage change is frequently used to denote the percentage-based price change of a stock over time. Depending on whether the change is an increase or a reduction, a simple mathematical formula is employed to quantify this change as a percentage.The most common use of percentage change in finance is to monitor changes in stock and market index prices.Comparing the values of several currencies also involves using change expressed as a percentage.Additionally, balance sheets with comparative financial statements contain percentage change.Depending on whether there is an increase or decrease, there are slight differences in how to calculate percentage change.Calculations :
According to the given conditions, state = 33.5/89.99 Multiply the numerator and denominatorwith the same whole number = 3350/8999
Rewrite a fraction as a decimal = 0.372263Multiply a number for both thenumerator and the denominator = 0.372263 x [tex]\frac{100}{100}[/tex]
Write as a simple fraction = 0.372263 x 100 / 100Calculate the product or coefficient = 37.2263 / 100Rewrite a fraction with the denominatorequal to 100 as a percent = 37.2263 %
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Find the area of this trapezoid. Be sure to include the correct unit in your answer.
Answer:
the area of this trapezoid= 81 square inches
Step-by-step explanation:
To find area of trapezoid , we use formula
[tex]Area = \frac{a+b}{2} * h[/tex]
Where a,b are the base of the trapezoid
h is the height of the trapezoid
Here a= 3 in
b = 15 in
h = 9 in
Plug in all the values in the formula
[tex]Area = \frac{a+b}{2} * h[/tex]
[tex]Area = \frac{3+15}{2} * 9[/tex]
[tex]Area = \frac{18}{2} * 9[/tex]
Area = 9 * 9 = 81
the area of this trapezoid= 81 square inches
David sells two calculators for ₹1500 each .He earns a profit of 25% on
one and suffers a loss of 25% on the other. Find his total profit or loss on
the whole deal. Also calculate it as a percentage
Answer:
100% profit of 1500
Step-by-step explanation:
One the first calculator David earns 25% profit:
25% + 1500 = 1,875
He gets a 25% on the second calculator:
1500 - 25% = 1,125
In total he receives 1125 + 1875 = 3000
Therefore he has 100% profit
the first five terms of a sequence are 7,10, 13 , 16 and 19. which of the following functions define this sequence for all integers n>or equal to 1?
A. f[n]= 3n=7
B.f[n]= 4+3n
C. f[n]= 4[3]^n-1
D.f[n]=7[3]^n-1
Answer:
Option B is correct
For [tex]n\geq 1[/tex] , the function for the given sequence is defined as; [tex]f[n] = 4 +3n[/tex]
Step-by-step explanation:
An arithmetic sequence is a sequence in which the difference between each consecutive term is constant.
An explicit formula for this arithmetic sequence given by;
[tex]a_n = a+(n-1)d[/tex] where a represents first term
Since, the given sequences; 7 , 10 , 13 , 16 and 19
⇒ common difference(d) = 3 and a = 7
Since.
10 -7 = 3
13- 10 = 3 ....
The function which defined this sequence is;
[tex]f[n]=a_n = 7 +(n-1)(3)[/tex]
using distributive property:
[tex]f[n] = 7 + 3n -3[/tex]
[tex]f[n] = 4 +3n[/tex]
therefore, the function for the given sequence for all integers [tex]n\geq 1[/tex] is; [tex]f[n] = 4 +3n[/tex]
The correct option is D) f(n) = 4 + 3n.
Step-by-step explanation:
Given :
Arithmetic Sequence -- 7,10,13,16,19
Solution :
The explicit formula of arithmetic sequence is given by,
[tex]T_n = a+(n-1)d[/tex] ------- (1)
where, common difference (d) = 10 - 7 = 3
first term (a) = 7
So from equation (1),
[tex]T_n = 7+(n-1)3 = 7+3n-3[/tex]
[tex]T_n = 4 + 3n[/tex]
Therefore, the correct option is D) f(n) = 4 + 3n.
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Use what you know about the sum of the angles of a triangle to find m
Answer:
Angle ABC is 22 degrees
Angle BAC is 68 degrees
======================================
Work Shown:
Because there are just 3 points, we can refer to "angle BAC" as "angle A" and "angle ABC" as "angle B". Focus on the middle letter of each three-letter sequence.
The three angles A, B, C add up to 180 degrees. This is true for any triangle.
A+B+C = 180
(6x+8) + (2x+2) + 90 = 180 ... substitution
6x+8 + 2x+2 + 90 = 180
8x+100 = 180
8x+100-100 = 180-100 ... subtract 100 from both sides
8x = 80
8x/8 = 80/8 ... divide both sides by 8
x = 10
If x = 10, then angle BAC is
angle BAC = 6x+8
angle BAC = 6*10+8
angle BAC = 60+8
angle BAC = 68
Use x = 10 to find angle ABC as well
angle ABC = 2x+2
angle ABC = 2*10+2
angle ABC = 20+2
angle ABC = 22
The three angles of this triangle are A = 68, B = 22, C = 90
As a check, the three angles must add to 180
A+B+C = 180
68+22+90 = 180
180 = 180
Answers are confirmed
Another thing to notice is that A+B = 90 meaning that A and B are complementary angles. A+B = 68+22 = 90.
What is the decimal equivalent of four over nine ?
Answer: 0.44444444444....
Step-by-step explanation: 4/9 is the same as 4 ÷ 9. 9 does not divide into 4, so we add a 0 and bring down a 0 to get 9 divided by 40. 9 can be multiplied by 4 to get 36, 40 - 36 = 4, bring down another 0, 9 can be multiplied by 4 to get 36, 40 - 36 = 4.... this is a never ending decimal.
For f(x)=-2x-13, find f(x) when x=5
Can someone please help me?
Answer:
f(x) = -38
Step-by-step explanation:
well f(x) is the same thing as y so just write it as y so its easier to understand.
y = -2x -13
take the x value they give you which in this case is 5 and plug it in to the x in your equation.
y = -2(5) -13
now just use a calculator or something and find that
y = -25 - 13
and finally
y = -38
now just change y back to f(x) if needed
hope this helps :)