By takin common we got that factorization of [tex]x^3+6x^2+8x+48[/tex] is [tex](x+6)(x^2+8)[/tex]
What is factorization ?
factorization is writing a expression as a product of several factors.
Given polynomial
[tex]x^3+6x^2+8x+48[/tex]
We can factorize it as
Taking [tex]x^2[/tex] common from first two terms and 8x common from last two terms
[tex]x^2(x+6)+8(x+6)[/tex]
Taking (x+6) common
[tex](x+6)(x^2+8)[/tex]
By takin common we got that factorization of [tex]x^3+6x^2+8x+48[/tex] is [tex](x+6)(x^2+8)[/tex]
To learn more about factorization visit :
https://brainly.com/question/11579257
Answer:
The answer is D (x+6)(x^2+8)
Step-by-step explanation:
im not the best at explaning but this is the only answer that makes sense have a good day! :)
6. Ava had a rough day on the stock market. Her stocks dropped in value to
one third of what they used to be. If she currently has $140,000 in stock
value, how much were her stocks worth yesterday?
Answer:
420,000
Step-by-step explanation:
If 140,000 is [tex]\frac{1}{3}[/tex] of what she had yesterday, then you just multiply the number by 3 because [tex]\frac{1}{3}[/tex] times 3 is [tex]\frac{3}{3}[/tex], which is 1.
The verbal subtest of the GRE has a population mean of 500 and a population standard deviation of 100 by design (the quantitative subtest has the same mean and standard deviation).
a. Convert the following z scores to raw scores without using a formula:
(i) 1.5,
(ii) -0.5,
(iii) -2.0.
b. Now convert the same z scores to raw scores using symbolic notation and the formula:
(i) 1.5,
(ii) -0.5,
(iii) -2.0.
The z scores of 1.5, -0.5 and -2.0 corresponds with a raw score of 650, 450 and 300
What is z scoreZ score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (x - μ) / σ
Where x = raw score, μ = mean and σ = standard deviation.
Given that σ = 100, μ = 500, hence:
a) For z = 1.5:
1.5 = (x - 500)/100
x = 650
b) For z = -0.5:
-0.5 = (x - 500)/100
x = 450
c) For z = -2:
-2 = (x - 500)/100
x = 300
The z scores of 1.5, -0.5 and -2.0 corresponds with a raw score of 650, 450 and 300
Find out more on z score at: https://brainly.com/question/25638875
If f (x) = –2x – 3 and the domain of f is {-4,0,6} , what is the range of
f (x)?
Answer:
[tex]\lbrace 5,\, -3,\, -15 \rbrace[/tex].
Step-by-step explanation:
The domain of a function includes all the values that this function could accept as inputs. The function would give a (possibly non-unique) output for each of these inputs. The range of this function over this particular domain would be the set of all the possible output values from this function.
In this question, the domain of this function is [tex]\lbrace -4,\, 0,\, 6 \rbrace[/tex], meaning that this function could accept [tex]x = (-4)[/tex], [tex]x = 0[/tex], and [tex]x = 6[/tex] as possible inputs.
[tex]f(-4) = -2 \times (-4) - 3 = 8 - 3 = 5[/tex].[tex]f(0) = -3[/tex].[tex]f(6) = -2 \times 6 - 3 = -15[/tex].In other words, the possible output values of this function over this domain are [tex]5[/tex], [tex](-3)[/tex], and [tex](-15)[/tex]. Hence, the range of this function would be the set [tex]\lbrace 5,\, -3,\, -15 \rbrace[/tex].
A cylinder has a volume of 157 cubic centimeters.
Find the height of the cylinder if its radius is 2.5 cm. Show
work. (2 pts)
Answer:
4.47100222
Step-by-step explanation:
157/2.5=62.8
62.8/pi= 19.98986085
square root the answer above and you get 4.47100222 for the radius
The expressions below model different possibilities for the area of a pool. Identify which of the following expressions have at least the one zero greater than 4.
X^2+11x+30
X^2-5x-14
X^2+5x-24
X^2-5x+6
========================================================
Explanation:
Use a graphing tool like GeoGebra, Desmos, or your graphing calculator to plot each expression given as a separate y equation. Four parabolas should result.
The x intercept is the same as the root or zero of a function.
You should find that only choice B has a root thats larger than 4. That specific root being x = 7.
----------------------------
A non-graphing approach:
You can use the quadratic formula or the factoring method to find the roots.
For choice A, it factors to (x+5)(x+6) = 0. The roots are x = -5 and x = -6 which aren't greater than 4. So we cross choice A off the list. Choices C and D are similar stories.
On the other hand, choice B factors to (x-7)(x+2) = 0 and it has roots of x = 7 and x = -2. This is another way to see why choice B is the answer.
Here are the steps for the quadratic formula for choice B
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-5)\pm\sqrt{(-5)^2-4(1)(-14)}}{2(1)}\\\\x = \frac{5\pm\sqrt{81}}{2}\\\\x = \frac{5\pm9}{2}\\\\x = \frac{5+9}{2} \ \text{ or } \ x = \frac{5-9}{2}\\\\x = \frac{14}{2} \ \text{ or } \ x = \frac{-4}{2}\\\\x = 7 \ \text{ or } \ x = -2\\\\[/tex]
The quadratic formula is handy in case factoring is either not possible, or guess-and-check is too lengthy of a process. As you can probably tell, we could use the quadratic formula's results to help construct the factored form.
A triangle has a base length of 2ac² and a height 6 centimeters more than the base length. Find the area of the triangle if a = 4 and c = 2.
Answer:
608 cm²
Step-by-step explanation:
base = 2ac²
base = 2x4x2²
base = 2x4x4
base = 32cm
height = base + 6cm
height = 32 + 6cm
height = 38cm
Area of triangle = ½ x base x height
Area = ½ x 32 x 38
Area = 1216/2
Area = 608 cm²
Therefore the area of the triangle is 608cm²
Question 7 of 10
Which of the following best describes the slope of the line below?
Answer:
its A
Step-by-step explanation:
PLEASE HELP!!
A fitness trainer decided to track the combined weight loss of
several new customers. She recorded the combined weight loss
each month and kept track for 6 months. Identify the best
mathematical model with its corresponding R2 value and tell
whether it is a good model.
1,2,3,4,5,6
175,120,95,63,44,30
exponential model 0.996. yes, 0.996 is very close to 1
exponential model, 0.996. no, 0.996 is too high an r2 value
quadratic model, 0.994. no 0.994 is too high an r2 value
quadratic model, 0.994. yes 0.994 is very close to 1
Factoring polynomials. Please help I suck at factoring (especially polynomials) Ill give brainiest too
the two numbers are -36 and -2.. thier product is 72 but thier sum is -38..
this one took me time lol
A bucket holds 480 ounces(oz) of water when full. Unfortunately, the bucket has a small hole in it, and is losing 4.8 oz of water per minute. In how many minutes will the bucket be 80% full?
Answer:
20 minutes
Step-by-step explanation:
80% of 480 is 384
480 x .80 = 384
4.8 x 20 = 96
Show why x−3 is a factor of m(x)=x3−x2−5x−3. Justify your answer. You can show this using remainder theorem, long division, synthetic division or any method you choose.
The factors of a polynomial function are the zeros of the function
It is true that x - 3 is a factor of m(x) = x^3 - x^2 - 5x - 3
How to show why the x - 3 is a factorThe function is given as:
m(x) = x^3 - x^2 - 5x - 3
The factor is given as:
x - 3
Set the factor to 0
x - 3 = 0
Solve for x
x = 3
Substitute 3 for x in the function
m(3) = 3^3 - 3^2 - 5(3) - 3
Evaluate
m(3) =0
Since the value of m(3) is 0, then x - 3 is a factor of m(x) = x^3 - x^2 - 5x - 3
Read more about factors at:
https://brainly.com/question/11579257
What is the area of a rectangle with a length of 3 1/3 feet and a width of 1 2/3 feet?
Answer:
area =l×b
= 3⅓ × 1⅔
= 10 × 5
3. 3
50
9
= 5.56feet²
Find the area of the following square. Write your answer in simplest form. Area is 3 2/3
what iis 5.46 ÷ 0.25 (show ur work)
Answer:
21.84
Step-by-step explanation:
5.46/0.25 is actually just 5.46 * 4 but an easier way to do this is just doing
5.46 * 2 which is 10.92
.46 + .46 is .92
5+5 is 10
so thats 10.92
and since we only did times 2 we have to double it
so 10.92 + 10.92
10 + 10 is 20
.92 + .92 is 1.84
20 + 1.84 is 21.84
2 1 . 8 4
2 5 | 5 4 6 .
5 0
------------------------------
4 6 .
2 5 .
-------------------------------
2 1 . 0
2 0 . 0
-----------------------------------
1 . 0 0
1 . 0 0
Therefore, 5.46 divided by 0.25 = 21.84.
how do you solve 1 1/2 × ( − 6/15 ) =?
Answer:
1.5 x -0.4 = -0.6 or -6/10 or -3/5
Step-by-step explanation:
1 1/2= 3/2x(-6/15)
3/2 = 1.5 -6/15 = 0.4
1.5 x -0.4 = -0.6 or -6/10 or -3/5
Help
I don’t understand
Answer:
d
Step-by-step explanation:
If you look up the definition on the internet it says causing great and irreparable harm or damage. so i believe its d causing a great amount of damage! ^.^ may i have brainliest?
Can Anyone help me with this one?
Answer:
1. D
2. A
3. B
4. C
5. i am not sure
Step-by-step explanation:
Hope This Helps!!!
R560 invested at 8% p.a. simple interest for 3 years
Answer:
R 694.4
Explanation:
simple interest = [tex]\sf{\dfrac{PRT}{100}[/tex] → [tex]\sf \dfrac{560*8*3}{100}[/tex] → R 134.4
where p refers to principal, r refers to rate, t refers to time.
total money:
invested money + simple interest
R 134.4 + R 560 → R 694.4
Answer:
R 694.40
Step-by-step explanation:
Simple interest formula:
A = P(1 + rt)
where A is the final amount, P is the initial principal balance, r is the annual interest rate (in decimal format), and t is time (in years)
Given:
P = 560r = 8% = 0.08t = 3⇒ A = 560(1 + 0.08 · 3)
⇒ A = 560(1.24)
⇒ A = 694.40
a book cost for R150 and sold for R180 how much is the profit
Answer:
R30
Step-by-step explanation:
You would subtract R150 from R180 to get the profit.
Hope this helps :)
a) x+4
is a factor of f(x)=x3−x2−20x
Factor completely if so
b) x−6
is a factor of g(x)=x4−6x3−8x+48
Factor completely if so
c) x+7
is a factor of h(x)=x3−37x+84
Factor completely is so
Answer:
a) f(x) = x(x +4)(x -5)
b) g(x) = (x -6)(x -2)(x^2 +2x +4)
c) h(x) = (x +7)(x -3)(x -4)
Step-by-step explanation:
To factor completely generally means to find binomial factors that have integer constants. It is helpful to be familiar with the idea of "greatest common divisor", and what the product of two binomial factors looks like. In particular, there are a couple of special forms that can be useful. One of them is the difference of squares. Another is the difference of cubes.
a² -b² = (a -b)(a +b)
a³ -b³ = (a -b)(a² +ab +b²)
In the general case, the product of binomial factors is ...
(x -a)(x -b) = x² -(a+b)x +ab
The coefficient of the x-terms is the sum of the binomial constants; the constant term is their product.
__
a)The given cubic has no constant term. That is, every term has a factor of x, so that is one of the factors.
f(x) = (x)(x^2 -x -20)
The given factor of x+4 tells you the constant in the other factor is -20/4 = -5.
f(x) = x(x +4)(x -5)
__
b)We observe that the ratios of pairs of coefficients are ...
1 : -6 and -8 : 48 = 1 : -6 . . . . . pairs of coefficients have the same ratio
That means we can factor each pair of terms:
g(x) = x^4 -6x^3 -8x +48
g(x) = x^3(x -6) -8(x -6) = (x^3 -8)(x -6)
Using the difference of cubes formula, the factorization is ...
g(x) = (x -2)(x^2 +2x +4)(x -6)
Note: the quadratic factor has irrational complex roots.
__
c)The quadratic factor of this cubic can be found by dividing it by the given factor. That is most easily accomplished using synthetic division. Explaining how to do that is beyond the scope of this answer. The first attachment shows that the resulting factorization is ...
h(x) = (x +7)(x^2 -7x +12)
The quadratic is factored by finding two factors of 12 that have a sum of -7. The positive sign of their product (12) tells you both will be negative.
12 = (-1)(-12) = (-2)(-6) = (-3)(-4)
The pair of factors with a sum of -7 is -3 and -4. These are the constants in the remaining binomial factors:
h(x) = (x +7)(x -3)(x -4)
_____
Additional comment
A graphing calculator can be an invaluable tool for factoring higher-degree polynomials. The graph of h(x) in the second attachment, for example, shows you the zeros are -7, 3, 4, so the factors are (x+7)(x-3)(x-4).
For a function like g(x), you can find the real zeros from the graph, then you can find the quadratic by factoring out the associated factors. The vertex of the quadratic curve helps you write the expression for that. (see the third attachment)
g(x) = (x -2)(x -6)((x +1)^2 +3) . . . . quadratic factor in vertex form
g(x) = (x -2)(x -6)(x^2 +2x +4)
Find the value of the following expression:
(3∧8 ⋅ 2∧−5 ⋅ 9∧0)−2 ⋅ 2 to the power of negative 2 over 3 to the power of 3, whole to the power of 4 ⋅ 328 (5 points)
Write your answer in simplified form. Show all of your steps. (5 points)
Answer:
The radicand may not always be a perfect square. If a positive integer is not a perfect square, then its square root will be irrational. Consider 5–√ , we can obtain an approximation by bounding it using the perfect squares 4 and 9 as follows:
Step-by-step explanation:
pls brainliest
help me with geometry please
Answer:x=9
Step-by-step explanation:so this is a isosceles triangle so that means the two sides are equal so set up the equation as 3x-7=20. And by moving the 7 over it will be 3x=27 and then you want you separate the x and to do that you have to divide x and 27 by 3 and you answer is x = 9
Hey there!
3x - 7 = 20°
ADD 7 to BOTH SIDES
3x - 7 + 7 = 20 + 7
CANCEL out: -7 + 7 because it give you 0
KEEP: 20 + 7 because it help solve for the x-value
NEW EQUATION: 3x = 20 + 7
SIMPLIFY IT!
3x = 27
DIVIDE 3 to BOTH SIDES
3x/3 = 27/3
CANCEL out: 3/3 because it give you 1
KEEP: 27/3 because it help solve for the x-value
NEW EQUATION: x = 27/3
SIMPLIFY IT!
x = 9
Therefore, your answer is: x = 9
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
help me with this I'm trying to win a bet
8 ÷ 2 (2 +2)
Answer:
16
Step-by-step explanation:
Because of the rule of PE(MD)(AS) the following would be executed like this
8 / 2 (2 + 2)
8 / 2 x 4
4 x 4
16
Therefore, the answer would be 16.
EDIT: This answer was previously incorrect but has been fixed. Calculator confirmed as well. Thank you User emmab2457 in the comments for bringing this to my attention.
The reason the answer is not 1 is because in the term PE(MD)(AS) the Multiply/Divide construct as well as the Addition/Subtraction can be switched, and once reaching this step the equation is solved from Left to Right, no matter if division is before multiplying.
ABCD and PQRS are rectangles. O is the centre of both rectangles. AC is a straight line passing through P, Q and R. BD is a straight line passing through Q, R and S. PQ=8cm and QR=2cm. The perimeter of rectangle ABCD is 60cm. Work out the length of AB and the length of BC.
Answer: See below
Step-by-step explanation:
ΔPQR ≈ ΔABC because PR & AC are same line
So PQ ║ AB & QR ║ BC
In equation form: PQ / AB = QR / BC
8/AB = 2/BC
AB = 4BC
Perimeter of ABCD rectangle = 2(AB + BC)
= 2(4BC + BC)
= 10BC
Perimeter of the rectangle = 60 cm
In equation form: 10BC = 60
BC = 6 cm
AB = 4BC = 24 cm
Length of AB = 24 cm & length of BC = 6 cm
If John takes 2 hours to travel 20km,how many kilometers does he travel in 6 hours?
Answer:
60km
Step-by-step explanation:
There are two ways to look at this
1. Finding the unit rate
We can find how many km he travels in 1 hour by diving both the hours and km by 2. 1 hour = 10km so 6 hours is 60km since we multiply by 6.
2. Multiply by 3
We can multiply both the km and hours by 3, since 2x3=6 hours
20km * 3 hours = 60km
Help me please
Solve the inequality s:
5s+2>7
Answer:
s>1
Step-by-ste:p explanation:
the internet :)
About how many cells are in the human body? HELPP!!!!
You can assume that a cell is a sphere with radius 10-3 cm and that the density of a cell is approximately the density of water which is 1g/cm3.
Answer:
there are 37.2 trillion cells in the human body
1g/cm3.
Step-by-step explanation
A ball is dropped from the top of a building.The table shows its height in feet above ground at the top of each bounce.What is the height of the ball at the top of bounce 5?
Answer:
Here ,
we can see that with each bounce , the height reduces to half .
therefore ,
the fourth bounce will have a height of 6/2 = 3
and ,
the fifth bounce will have a height of 3/2 = 1.5
hope helpful ~
[tex] \\ [/tex]
A dilation is applied to a triangle such that the sides of the image are 1.5 times the length of their corresponding sides in the original triangle.
Then the angles of the image must be 3 times the size of the corresponding angles in the original triangle.
Then the angles of the image must be 1.5 times the size of the corresponding angles in the original triangle.
Then the angles of the image must be congruent to the corresponding angles in the original triangle.
Then the angles of the image must be two-thirds the size of the corresponding angles in the original triangle.
Answer: Then the angles of the image must be 3 times the size of the corresponding angles in the original triangle.
A toy was bought for Rs.564 thereby profit 12%. Find the SP of the toy
Answer:SPssp=631.68
Step-by-step explanation:
Please helppp!
find the surface area of the triangular prism.
2cm
5cm
6cm
4cm
3cm
6cm
Answer:
82 cm^2
Step-by-step explanation:
First, find the formulas for the areas of all of the shapes shown
area of rectangles = base * height
area of triangle = 1/2 * base * height
for the triangle at the top, area = 1/2 * 5 * 2 = 5 cm^2
for the bottom triangle, area = 1/2 * 5 * 2 = 5 cm^2
for the left rectangle, area = 6 * 3 = 18 cm^2
for the middle rectangle, area = 5 * 6 = 30 cm^2
for the right triangle, area = 4 * 6 = 24 cm^2
add all of these together
5 + 5 + 18 + 30 + 24 = 82 cm ^2
