The factorization of the given polynomial is:
p(x) = (x - 2/3)*(x - 1) = (1/3)*(3x - 2)*(x - 1)
How to factorize the polynomial?
We have:
[tex]p(x) = 3x^2 - 5x + 2[/tex]
First, we need to find the two roots for the equation, then we use Bhaskara's formula to get:
[tex]x = \frac{5 \pm \sqrt{5^2 - 4*3*2} }{2*3} \\\\x = \frac{5 \pm 1}{6}[/tex]
So the two solutions are:
x = (5 + 1)/6 = 1
x = (5 - 1)/6 = 4/6 = 2/3
Then the polynomial can be written as:
p(x) = (x - 2/3)*(x - 1)
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Answer: (3x -2) and (x-1)
Step-by-step explanation:
Just took the test
if you borrow 800$ for 10 years and the interest rate is 7% how much do you pay altogether?
Answer:
Answer is
1,760
Step-by-step explanation:
960+800=1,760
Pls HELPPP !!!!!!!!Variables y and x have a proportional relationship, and y = 21 when x = 14. What is the value of x when y = 12?
Answer:
8
Step-by-step explanation:
y=21 divided by x=14 = 1.5 so Y is 1.5 times larger than X so you should divide y=12 by 1.5 to get 8
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
a. Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
b. Both plans cost the same when 22 texts are sent.
c. Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
d. Both plans cost the same when 50 texts are sent.
Answer:
d
Step-by-step explanation:
[tex]20 + .05x = 10 + .25x[/tex]
[tex].20x = 10 [/tex]
[tex]x = 50[/tex]
A Cone has a radius of 3 and a height of 5. solve.
Assuming your looking for volume.
The following formula is used for calculating the volume (V) of a cone.
[tex]\boxed{V=\frac{1}{3}\pi r^{2} h}[/tex]
where r is the radius and h, the height.Substitute r = 3 and h = 5 into the formula.⇒ [tex]V=\frac{\pi *3^{2} *&5}{3} =\frac{45*\pi }{3}[/tex] ≈ [tex]47.124[/tex] [tex]cubic[/tex] [tex]cm[/tex]
How do I find a point on the line whose equation is 3x-8y=54
An equation is formed of two equal expressions. A point that will lie on the line 3x-8y=54 is (5,-4.875).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
To find a point on the line 3x-8y=54, take any random value of x and substitute for the equation, and solve the equation for y. Now, as you have the value of x and y, you have the coordinate of the point.
Let the value of x be 5.
3x-8y=54
3(5)-8y =54
15-8y = 54
-8y = 54 - 15
-8y = 39
y = -4.875
Hence, a point that will lie on the line 3x-8y=54 is (5,-4.875).
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How many buses do you need for 750 people if each bus holds 150 people?
Answer:
5 buses
Step-by-step explanation:
As, 150 people are hold by= 1 bus
therefore,
750 people are hold by=1/150x750 buses
=5buses
Answer:
5 buses
Step-by-step explanation:
Given:
Each bus holds 150 peopleTo find:
Buses for 750 peopleSince each bus or a single bus can hold 150 people, we can represent the sentence in math expression as:
[tex]\displaystyle\large{1B = 150P}[/tex]
B stands for Bus and P stands for People. Therefore we have the equation of:
[tex]\displaystyle \large{B=150P}[/tex]
Next is to find how many buses can hold 750 people so we will have to multiply both sides by 5 since 150*5 = 750.
[tex]\displaystyle \large{5B=150*5}\\\displaystyle \large{5B=750}[/tex]
If one bus can hold 150 people then 5 buses can hold 750 people. Hence the solution is 5 buses.
At the school football game, there are 42 adults
sitting in the bleachers. the ratio of adults to
students in the bleachers is 7 to 9. how many
students are sitting in the bleachers?
Answer:
54 students
Step-by-step explanation:
42 / 7 = 6
9 x 6 = 54
42 : 54 = 7 : 9
Use the information to answer the question.
A data set is normally distributed. The mean of the data is 9.2, and the standard deviation is 1.8.
Using the 68-95-99.7 rule, what percentage of the data points are greater than 11? Enter the answer in the box.
%
Using the Empirical Rule, it is found that 16% of the data points are greater than 11.
What does the Empirical Rule state?It 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, the mean is of 9.8 and the standard deviation is of 1.8.
11 is one standard deviation above the mean. Considering the symmetry of the normal distribution, 32%(more than one standard deviation above the mean)/2 = 16% of the data points are greater than 11.
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Let k = 7.
Drag the expression into the box that makes the comparison true.
Answer:
k^2 ÷ k^2 the third one is correct
Jarell Tarver invested $20,000 in the Boyd Kern Mutual Fund (Type A). The net asset value is $21.34 per share. The fund is front-loaded with a loading rate of 5.25%. How many shares did Jarell purchase?
Answer:
Ok To tell the truth My honest answer is 20026.59
Step-by-step explanation:
I say this because at the end it says how Many shares di Jarrell purchased so you suppose to add so 20,000 then 21.34 then do 5.25 so that's how u got that answer I hope that's correct I'm sorry if it's not I'm not a big fan of math I believe in you tho
Pls help i will give brainliest to whoever gives a good answer
aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. to prepare for the event, she is practicing and keeping track of her time to complete each station.
the x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 3), (2, 6), (3, 12), (4, 24)
part a: is this data modeling an arithmetic sequence or a geometric sequence? explain your answer. (2 points)
part b: use a recursive formula to determine the time she will complete station 5. show your work. (4 points)
part c: use an explicit formula to find the time she will complete the 9th station. show your work. (4 points)
source
stylesnormal
Answer:
(-11,12)
Step-by-step explanation:
add 4 to 7 then subtract 3 and add 25
Colleen owns a house. In the house, on a tile floor is a throw rug and a heavy decorative urn. Most likely to meet the definition of a fixture is Group of answer choices the urn. the throw rug. the tile floor. None of them are fixtures
The item in the Colleen's house that is most likely to meet the definition of a fixture is a tile.
What is a fixture?A fixture is an item in a house that is permanently attached to a house with the use of a glue, nails or bolt. It would not be easy to remove fixtures from a house. Examples of fixtures are tiles, doors and windows.
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If you have 1 apple and add two more apples every 10 minutes for five hours how many apples would you have
Answer: 61 apples
Step-by-step explanation:
Given:
1 apple
+2 apples = +10 minutes
1 hour = 60 minutes
60/10 = 6 x 2 = 12 apples/hr
12 x 5 = 60 apples for 5 hours
60 + 1 = 61 apples
how many turtles die every year because of humans?
save the turtles
Answer:
We found, based on beach strandings, that more than 1,000 turtles are dying a year, after becoming tangled up, but this is almost certainly a gross underestimate. Young turtles and hatchings are particularly vulnerable to entanglement.” In recent years, global turtle population numbers have been falling.
Surface area of a new cereal box with dimensions of
L=8 in
W=1.75in
H=12.125in
Answer:
264.4375
Step-by-step explanation:
Surface area of a box = 2(lw + lh + wh)
L = 8 , W = 1.75 and H = 12.125
==> plug in values
SA = 2((8)(1.75) + (8)(12.125) + (1.75)(12.125))
==> multiply values that are inside parenthesis together
SA = 2(14 + 97 + 21.21875)
==> add values inside of parenthesis
SA = 2(132.21875)
==> multiply 2 and 132.21875
SA = 264.4375in²
hrlppppppppppp asappppp
Answer:
a) 6x + 5x and 11x
b) 6⋅1 + 6⋅4y and 6 + 24y
Step-by-step explanation:
a) 10x - 4x + 5x <== combine like terms
6x + 5x
11x
Ans: 6x + 5x and 11x
b) 6(1 + 4y) <== distribute
6(1) + 6(4y)
6 + 24y
Ans: 6⋅1 + 6⋅4y and 6 + 24y
Hope this helps!
i need an equation with a variable on each side that equals 15
Answer:
2x + 5 = 3x
Step-by-step explanation:
In this equation, x = 5 and both sides equate to 15. Hope this helped!
"Given m = -2/5 and b = -7, write the equation of the line containing these points"
can someone help?
Answer: y = (-2/5)x - 7
This is the same as writing [tex]y = -\frac{2}{5}x-7[/tex]
======================================================
Explanation:
Any linear equation is of the form y = mx+b, known as slope-intercept form
m = slope
b = y intercept
We'll replace m with -2/5 and replace b with -7 to get y = (-2/5)x + (-7) which simplifies to y = (-2/5)x - 7
Find the Mean given Normal Curve Values (please help and explain your answer)
Answer:
mean = 22
Step-by-step explanation:
34 = mean + 2sd
4 = mean - 3sd ==> mean = 4 + 3sd
34 = 4 + 3sd + 2sd
30 = 5sd
sd = 6
mean = 4 + 3*6 = 4 + 18 = 22
Please help. Can't get calculator to work solve for x. Look at the picture.
Hey there!
4/5 = x/9
CROSS-MULTIPLY the fractions
4 * 9 = x * 5
4 * 9 = 5 * x
SIMPLIFY IT!
36 = 5x
5x = 36
DIVIDE 5 to BOTH SIDES
5x/5 = 36/5
SIMPLIFY IT!
x = 36/5
Therefore, the answer should be:
x = 36/5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
[tex] \boxed{ \boxed{\bf x= \cfrac{36 }{5} }\bf \: or\:\boxed{\bf x= 7.2}}[/tex]
Step-by-step explanation:
[tex] \bf \cfrac{4}{5} = \cfrac{x}{9} [/tex]
We first need to multiply both sides by 9.
[tex]\bf \cfrac{4}{5} \times 9 = x[/tex]Let's put 4/5 × 9 as a single fraction.
[tex] \bf \cfrac{4 \times 9}{5} = x[/tex]Multiply 4 and 9 = 36
[tex] \bf x= \cfrac{36 }{5} \: \: or\: \: x=7.2 [/tex]«••••••••••••••«•°•»•••••••••••••••»
what will help a person with power of attorney make good decisions?
A. knowing how to set up a trust
B. understanding the healthcare process
C. knowing why they were chosen to have power of attorney
D. understanding how to care for your family
Answer:
B - understanding the healthcare process
explanation:
I took the quize!
the owners of a company want to invest $12000 for 4 years.a which account should they choose.Explain
account a earns 5% simple interest
account b earns 5% interest compound annually
Answer:
Compound interest
Step-by-step explanation:
Simple interest in 4 years = 5% *4 = 20%
Compound interest in 4 years = 1.05^4 - 1 = 21.55%
Compound interest is higher than simple interest in any case more than 1 year
What is the inverse of the function f(x)=-1/2(x+3)?
The inverse of the function is : [tex]\frac{-1-6x}{2x}[/tex]
What is an inverse function?An inverse function is a function that serves as an eliminator of a given function.
A function that has an inverse is called invertible function and it is denoted as [tex]f^{-1}[/tex].
Analysis:
let y = [tex]\frac{-1}{2(x+3)}[/tex]
so that,
2y(x+3) = -1
2yx + 6y = -1
2yx = -1 -6
x = [tex]\frac{-1 - 6y}{2y}[/tex]
replacing y with x
[tex]f^{-1}[/tex](x) = [tex]\frac{-1-6x}{2x}[/tex]
In conclusion, the inverse of the function is : [tex]\frac{-1-6x}{2x}[/tex]
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What is the extraneous solution to x+2=3x+34
Answer:
4x + 36
Step-by-step explanation:
combine like terms
3x + x = 4x
2 + 34 = 36
4x + 36 Is the full answer
Find the area of the parallelogram. Round to the nearest hundredth if necessary.
6 m
8 m
Area =
cm2
Answer:
48 square cm.
Step-by-step explanation:
The area of a parallelogram is (A = B * H)
Base is 8
Height is 6
8*6 = 48 square cm.
solve the equation
3/4(x-16)=-2(x-3)+4
Answer:
The answer is X equals 8.
Step-by-step explanation:
Solve for X by simplifying both sides of the equation, then isolating the variable. X equals 8.
A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest hundredth. Enter your answer in the box.
Graph the equation. y = 4(x + 6)(x + 4)
There you go I hope its correct
can someone help me with this problem? thank you!
Answer:
242
Step-by-step explanation:
10x3=30
30x2=60
60+42+140=242
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Solve for c in terms of x.
Answer:
c = x + 5
Step-by-step explanation:
using Pythagoras' identity in the right triangle
c² = 5² + ([tex]\sqrt{x^2+10x}[/tex] )²
= 25 + x² + 10x
= x² + 10x + 25 ← a perfect square
c² = (x + 5)²
take the square root of both sides
c = [tex]\sqrt{(x+5)^2}[/tex] = x + 5