a) [tex]x^5-x^3[/tex]
[tex]x^3\left(x^2-1\right)[/tex] ........take out x³
[tex]x^3\left(x+1\right)\left(x-1\right)[/tex] ......separated (x²-1)
b) [tex]3x^2-75[/tex]
[tex]3\left(x^2-25\right)[/tex] ........took out 3.
[tex]3\left(x+5\right)\left(x-5\right)[/tex] .......separated (x²-25)
c) [tex]3x^5y+4x^4y-5x^2y[/tex]
[tex]x^2y\left(3x^3+4x^2-5\right)[/tex] ............takeout x²y at the front.
d) [tex]81x^3-125[/tex]
[tex]81x^3-125[/tex] ......cannot be factorised much more further.
Solution:
Part - A:
To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x⁴ (GCF), which can factorize completely. This will subtract 4 from the exponents.
=> x⁵ - x³=> x⁴(x - 1)Part - B:
To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by 3 (GCF), which can factorize completely. This will divide 3 from the terms.
3x² - 753(x² - 25)3(x + 5)(x - 5)Part - C:
To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x²y (GCF), which can factorize completely.
3x⁵y + 4x⁴y - 5x²y=> x²y(3x³ + 4x² - 5)Part - D:
Unfortunately, this expression can't factor with rational numbers. The expression results in 81x³ - 125.
Expand and simplify this equation plz, 4(3x+5) - 5(8x+2)
[tex]4(3x + 5) - 5(8x + 2) \\ 12x + 20 - 40x - 10 \\ 12 x - 40x + 20 - 10 \\ - 28x + 10[/tex]
Make d the subject of the formula h=d/3 +2
Answer:
d =3h - 6
Step-by-step explanation:
[tex]h = \frac{d}{3} + 2 \\ \\ \implies \: 3h = d + 6 \\ \\ \implies \: 3h - 6= d \\ \\ \implies \: \huge \: d = 3h - 6 \\ \\ [/tex]
The difference between two numbers is 10 and their sumis four times the smaller number. Find the two numbers.
Answer:
5 and 15
Step-by-step explanation:
15+5=20
5x4=20
can someone please help me with this
Answer:
m∠Q = 121°
m∠R = 58°
m∠S = 123°
m∠T = 58°
Step-by-step explanation:
The sum of the interior angles of a quadrilateral = 360°
Create an expression for the sum of all the angles and equate it to 360, then solve for x:
∠Q + ∠T + ∠S + ∠R = 360
⇒ 2x + 5 + x + 2x + 7 + x = 360
⇒ 6x + 12 = 360
⇒ 6x = 360 - 12 = 348
⇒ x = 348 ÷ 6 = 58
So now we know that x = 58, we can calculate all the angles:
m∠Q = 2x + 5 = (2 x 58) + 5 = 121°
m∠R = x = 58°
m∠S = 2x + 7 = (2 x 58) + 7 = 123°
m∠T = x = 58°
A student graphed f(x) = x and h(x) = f(x + 5) on the same coordinate grid. Which statement describes how the graphs of f and are related? helpppp
Answer:
Here we have a problem with translations, where we define a translation as an operation that moves the graph of a function in a given direction.
We will see that the correct option is A.
"The graph of f is shifted 3 units up to create the graph of g."
To get this, we first need to describe vertical translations.
For a function f(x) we define a vertical translation (or vertical shift) of N units as:
g(x) = f(x) + N
If N is positive, the translation is upwards
if N is negative, the translation is downwards.
So here we have:
g(x) = f(x) + 3
So we can see that this is a translation of 3 units upwards, then the correct option is A, the graph of f(x) is shifted (or translated) 3 units up to greater the graph of g(x).
And the graphs of g(x) = x + 3 and f(x) = x can be seen below, where you can see this, where the grey line is g(x).
Step-by-step explanation:
What is the nth term in algebra?
The nth term of an arithmetic sequence is given by:—
an = a + (n – 1)d
So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula
will stopped by the grocery store for his wife he bought a pizza for 5.99 and 3 avacodos his total was 8.54 write an equation to find the cost if each avacodo
Answer:
each avocado is 0.85 cents
Step-by-step explanation:
you will subtract $8.54 and $5.99 and you will get $2.55 then, when you get that and you will divide $2.55 by 3 and the total will come out to 0.85 so that means that each avocado is 84 cents
Find the ratio of 30 minutes to 15 hours. method needed.
Answer:
2.1
Step-by-step explanation:
Here we will simplify the ratio 30:15 for you and show you how we did it.
To simplify the ratio 30:15, we find the greatest common divisor of 30 and 15, and then we divide 30 and 15 by the greatest common divisor.
The greatest common divisor that you can use to simplify 30:15 is 15. Which means the answer to ratio 30:15 simplified is: 2.1
How many significant figures are in the measurement 1. 050 L? a. 1 b. 2 c. 3 d. 4.
Answer:
C) 3
Step-by-step explanation:
The number of significant figures in a measurement basically means how many decimal digits there are after the decimal point. Since the decimal portion of the measurement is 050, there are 3 digits, so there are 3 significant figures in the measurement
Really need help and ALL CAPS NO SPACES
Step-by-step explanation:
1. [tex]x+6 + 3x + 2 + 2x + 4[/tex]
Combine Like Terms:
Answer: [tex]6x+12[/tex]
G
2. [tex]6x + 4 + 7x + 1 + 5x + 7[/tex]
Combine Like Terms:
Answer: [tex]18x+12[/tex]
B
3. [tex]4x-3 + 3x + 5x - 6[/tex]
Combine Like Terms:
Answer: [tex]12x-9[/tex]
I
4. [tex]6x - 8 + 3x + 7 + 5x - 3[/tex]
Combine Like Terms:
Answer: [tex]14x-4[/tex]
H
Your code is, GBIH
The graph represents a map where each unit is 0.75 miles. Use the map to answer the question. Round to the nearest hundredth, if necessary.
How many miles is the most direct path from Jim's house to the mall?
(HINT: That means when you get the length of what they're asking for, you're going to multiply it by 0.75.)
Answer:
Try 11.25 miles
Step-by-step explanation:
Show and explain how you will estimate the answer to the problem 4 3/8 + 5 6/10. • Explain in sentence form. Find the estimated answer to the problem.
no links pls this is important im also timed
Answer:
4 (3)/(8) + 5(6)/(10)
Step-by-step explanation:
4 3/8= 35/8
5 6/10 = 28/5
= 9 39/40
Answer:
did yall ever find the answer
Step-by-step explanation:
4. If they make $404,300, how many tickets have they sold?
Answer:
Hello again, as I said in your previous question, I don't have any other information to possibly answer this. They must have sold a lot of tickets to get that much money. How many people bought the tickets? How much does one ticket cost?
Hope this helped, please provide more information next time to properly answer you :)
the outer diameter of a spherical shell is 10 cm and the inner diameter is 9 cm . find the volume of the metal used in the shell
Three-dimensional objects
the outer diameter: 10 cm, r₁ = radius = 5 cm
the inner diameter: 9 cm, r₂ = 4.5 cm
volume of metal:
[tex]\tt =\dfrac{4}{3}\pi(r_1^3-r_2^3)\\\\=\dfrac{4}{3}\pi(5^3-4.5^3)\\\\=141.952\:cm^3[/tex]
Select the outlier in the data set.
then
If the outlier were removed from the data set, would the mean increase or decrease?
====================================================
Explanation:
The set of given numbers sorts to this
11, 50, 72, 78, 80, 81, 85, 89, 94, 96, 97, 98
The majority or main cluster of the values are between 50 and 98. The outlier 11 is off on its own pretty far from the main cluster.
Let's find the mean of every value in this set. If you added up all the numbers, then you should get 931. Divide this over the number of values (12) and the mean of this set is roughly 931/12 = 77.5833
Now let's kick out the outlier 11. The 931 will drop to 931-11 = 920. Divide that new smaller sum over the 12-1 = 11 items left to get 920/11 = 83.6364 approximately.
--------------
To summarize so far:
old mean = 77.5833 approximatelynew mean (removed outlier) = 83.6364 approximatelyWe see that the mean has increased. This is because the outlier was pulling down on the mean to make it smaller than it should be. Once the outlier is out of the picture, the new mean will increase and better represent the center of the main cluster.
The three sides of AJKL
measure 11.2 feet, 21 feet, and
23.8 feet. IS AJKL an acute,
right, or obtuse triangle?
Answer:
right triangle
Step-by-step explanation:
I find it convenient to answer questions like this by computing a "form factor" that subtracts the square of the long side from the sum of the squares of the shorter sides. The sign of this value is the sign of the cosine of the largest angle in the triangle.
f = a² +b² -c²
f = 11.2² +21² -23.8²
f = 125.44 +441 -566.44 = 0
The cosine of the largest angle is 0, so that angle is 90° and the triangle is a right triangle.
16
Given the circle,
M
X
80°
4
ү°
A
25°
2
N
8
What is the value of y?
y=
degrees
Answer: the asnwer is 80 degrees
Step-by-step explanation:
Paulo has R$45.00 and Carlos has 5/9 of that amount. How many Carlos has? How many do the two have together?
We are given –
Paulo has R$45.00 and Carlos has 5/9 of that amount.We are asked to find, how much Carlos owns and how much they have together.
Explanation :-
At first, we just need to multiply 45 by 5, and then we will divide the value by 9, so we find that:
[tex]\qquad[/tex][tex] \bf \longrightarrow 45 \times 5 = 225[/tex]
[tex]\qquad[/tex][tex] \bf \longrightarrow \dfrac{225}{9} = 25[/tex]
Therefore, we find that Carlos has 25 R$.Now to find out how much they have together. We have to add Paul's amount to Carlos' amount for that.
[tex]\qquad[/tex][tex] \bf \longrightarrow 25 + 45 = 70[/tex]
Henceforth, they both have 70 R$. together.Marta sells Sue Ann Cosmetics and gets
20% commission on all her sales. Last
month, she sold $560.00 worth of
cosmetics. How much was her
commission?
Please help it’s urgent
Answer: $112
Step-by-step explanation:
o get the solution, we are looking for, we need to point out what we know.
1. We assume, that the number 560 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 560 is 100%, so we can write it down as 560=100%.
4. We know, that x is 20% of the output value, so we can write it down as x=20%.
5. Now we have two simple equations:
1) 560=100%
2) x=20%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
560/x=100%/20%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 20% of 560
560/x=100/20
(560/x)*x=(100/20)*x - we multiply both sides of the equation by x
560=5*x - we divide both sides of the equation by (5) to get x
560/5=x
112=x
x=112
now we have:
20% of 560=112
Please help meeee (1 image)
The Statue of Liberty is approximately 300 feet high, including the base upon
which the statue stands. If the base is 150 feet high, what percent of the total
height is the statue itself?
Answer:
The state itself is 50% of the total height.
Explanation:
Well, if the height including the base is 300 ft, that'd mean the total height of the statue itself is (300-150) ft = 150 ft.
Thus, it is (150/300)*100% = 50% of the total height.
-15 equals an unknown number
tripled.
Answer:
The unknown number is -5
Step-by-step explanation:
Let n represent the unknown number then...
3n=-15
Divide both sides by 3
(3n)/(3)=(-15)/(3)
n=-5
may someone help me with this pls
Answer:
PQRS - a parallelogramGHJI - not necessarilyRSUT - a parallelogramABDC - a parallelogramStep-by-step explanation:
A parallelogram has these characteristics that can be useful for answering this question:
opposite sides are the same lengthopposite sides are parallelthe diagonals bisect each other__
PQRSOpposite sides are the same length: a parallelogram
__
GHJITwo isosceles triangles share a base segment. Not necessarily a parallelogram.
__
RSUTThe diagonals bisect each other: a parallelogram
__
ABDCOpposite sides are parallel: a parallelogram. We know BD║AC from the converse of the alternate interior angles theorem. AB and CD are marked parallel.
what is the volume of the prism?
substitution method
x-2y=8
8x+6y=42
Answer:
(6,-1)
Step-by-step explanation:
Hi there!
We are given the following system:
x-2y=8
8x+6y=42
And we want to solve it by substitution
Substitution is where we solve one of the equations in the system for a variable for an expression containing the other variable, then substitute that expression into the other equation, then solve the equation for that variable, then use the value of the solved variable to find the value of the first variable.
It's easier to solve a system for a variable if the leading coefficient in front of a variable is 1, like with x in x-2y=8
So let's solve the equation for x.
add 2y to both sides
x-2y=8
+2y +2y
________________
x=2y+8
Now substitute 2y+8 as x in 8x+6y=42
8(2y+8)+6y=42
Multiply
16y+64+6y=42
Subtract 64 from both sides
16y+6y=-22
Add 16y and 6y together
22y=-22
Divide both sides by 22
y=-1
Substitute -1 as y into x=2y+8 to solve for x
x=2(-1)+8
Multiply
x=-2+8
x=6
The answer is x=6, y=-1, or as a point, (6, -1)
Hope this helps!
See more on solving systems of equations by substitution here: https://brainly.com/question/26559381
HELP BEFO 7 PLEASE...
What is the measure of the central angle of a sector of the sector has a radius of 3cm and an area of 63/8 pi cm^2
Answer:
Ans=0=315⁰
Step-by-step explanation:
Hope this helps :)
When both equations begin with y='s you
A- E LIM ININATE ONE PROBLEM
B - YOU DO GUESS AND CHECK FOR ONE PLUG INS
C - YOU SET BOTH EQUATIONS UP EQUALTO EACH OTHER
It
z²+1/z3= 34, find
z3+1/z3 using only
positive value of z+1/z
Answer:
5330
------------
73
Step-by-step explanation:
1- Transform the expression
2- Calculate
Allison measured a line to be 5.4 inches long. If the actual length of the line is 5.5 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
1.85%
Step-by-step explanation:
→ Find the difference between the actual and predicted
5.5 - 5.4 = 0.1
→ Divide answer by 5.4
0.1 ÷ 5.4 = 0.01851851851
→ Multiply answer by 100
0.01851851851 × 100 = 1.85%