Answer:
it is 3.2.5
Step-by-step explanation:
yw
Given f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3, determine whether or not x-a and x+a are factors of f(x). Hence, find, in terms of a, the roots of f(x) = 0.
thankyou so much
Answer:
Step-by-step explanation:
f(x) = 2x³ + ax² - 7a²x - 6a³
= 2x³ - 2a²x + ax² - a³ - 5a²x - 5a³
= 2x(x² - a²) + a(x² - a²) - 5a²(x+a)
= (2x+a)(x - a)(x + a) - 5a²(x + a)
= (x + a)[(2x + a)(x - a) - 5a²]
= (x + a)(2x² - ax - 6a²)
= (x + a)(2x + 3a)(x - 2a)
x-a is the factor of the equation and x + a is not a factor of the equation,
All the roots of the equation are x + a, 2x+3a, x-2a.
What is a cubic equation ?"In algebra, a cubic equation in one variable is an equation of the form
ax^3+bx^2+cx+d=0
in which a is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). "
Given equation is [tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3[/tex]
Now,
[tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3\\\\= 2x^3 - 2a^2x + ax^2 - a^3 - 5a^2x - 5a^3\\\\= 2x(x^2 - a^2) + a(x^2 - a^2) - 5a^2(x+a)\\\\= (2x+a)(x - a)(x + a) - 5a^2(x + a)\\\\= (x + a)[(2x + a)(x - a) - 5a^2]\\\\= (x + a)(2x^2 - ax - 6a^2)\\\\= (x + a)(2x + 3a)(x - 2a)[/tex]
Hence, the roots of the equation are x + a, 2x +3a, x - 2a.
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write 28 + 24 as a product of two factors using the GCF and the distributive property
Answer:
4 x 13
Step-by-step explanation:
GCD of 28 and 24 is 4
28 = 4 x 7
24 = 4 x 6
u take the 4 out
4 (7 + 6)
4 x 13
The product of two factors using the GCF and the distributive property is 4(13).
What is the meaning of the greatest common divisor/factor?
The largest integer of highest degree that is an exact divisor of each of two or more integers.
The greatest common divisor of 24 and 28
24=2×2×2×3
28=2×2×7
We can see that the 2 and 2 is common in 24 and 28
The GCD of 28 and 24 is=2×2= 4
For the distributive property we have
28 = 4 x 7
24 = 4 x 6
we take the 4 out
4 (7 + 6)
=4 x 13
Therefore the GCD is 4 and by distributive property product is 4(13).
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Chloe was given a box of assorted chocolates for her birthday. Each night, Chloe treated herself to some chocolates. There were originally 30 chocolates in the box and after 2 nights, there were 24 chocolates remaining in the box. Write an equation for
C
,
C, in terms of
t
,
t, representing the number of chocolates remaining in the box
t
t days after Chloe's birthday.
Answer:
the answer would be
Step-by-step explanation:
i hope this helped
A placekicker for a football team makes field goals 85% of the time when kicking from the 20-yard line. Assuming that field goal attempts can be considered random events, what is the probability that the placekicker will make 4 of his next 5 attempts from the 20-yard line?
Answer:
Step-by-step explanation:
answer should be 0.39
The probability that the placekicker will make 4 of his next 5 attempts from the 20-yard line is 0.39.
What is the probability?Probability in mathematics is the possibility of an event in time. In simple words how many times does that incident is happening in any given time interval?
Given:
A placekicker for a football team makes field goals 85% of the time when kicking from the 20-yard line.
Assuming that field goal attempts can be considered random events.
P = 0.85
n = 5
Standard deviation = √{5 x 0.85 x (1 - 0.85) = 0.79
The probability that the placekicker will make 4 of his next 5 attempts from the 20-yard line is,
= P (X ≥ 4)
= P (X ≥ 3.5)
= 1 - P(X < 3.5)
= 0.39
Therefore, the probability is 0.39.
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Noah says that to find 20% of a number he divides the number by 5. For example, 20% of 60 is 12, because 60 - 5 = 12. Complete the
statement about whether Noah's method always works.
His method never
works because multiplying by does not give the same result as dividing by 5.
Answer:
he is correct because 20% is the same thing as 1/5 amd 1/5 is the same thing as dividing by 5
Step-by-step explanation:
What is the interquartile range of the following data set? 3,8, 14, 19, 22, 29, 33, 37, 43, 49. A. 26 B. 23 C. 19 D. 18
Answer:
I think the answer is B.23
what is f(x)=5x-12 what is f(2)?
Answer:
f(2) = -2
General Formulas and Concepts:
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
f(x) = 5x - 12
f(2) is x = 2
Step 2: Solve
Substitute: f(2) = 5(2) - 12Multiply: f(2) = 10 - 12Subtract: f(2) = -2Answer:
f ( 2 ) = - 2
Step-by-step explanation:
Step 1:
f ( x ) = 5x - 12 Function
Step 2:
f ( 2 ) = 5 ( 2 ) - 12 Input x
Step 3:
f ( 2 ) = 10 - 12 Multiply
Answer:
f ( 2 ) = - 2
Hope This Helps :)
3(4x+2)=8x+24−2x hhhhhhhh
Answer: x=3
Step-by-step explanation:
1. First lets do the parenthesis 3(4x+2) to get 12x+6
2. 12x+6=8x+24-2x (combine like terms) first lets do 8x and 2x first so its 8-2= 6x
3. 12x+6=6x+24 (now subtract 12x by 6x to get 6x)
4. 6x+6= 24 (now subtract 24 by 6 to get 18)
5. 6x= 18 (now divide 18 by 6 to get 3)
Answer:
x = 3Step-by-step explanation:
[tex]3(4x+2)=8x+24−2x[/tex]
Expand and simplify
We have
[tex]12x + 6 = 8x + 24 - 2x \\ 12x + 6 = 6x + 24[/tex]
Move 6x to the left side of the equation
[tex]12x - 6x + 6 = 24 \\ 6x + 6 = 24[/tex]
Move 6 to the right side of the equation
[tex]6x = 24 - 6 \\ 6x = 18[/tex]
Divide both sides by 6
[tex] \frac{6x}{6} = \frac{18}{6} \\ [/tex]
We have the final answer as
x = 3Hope this helps you
2 (x - 2/3) = 0
solve for x
Answer:
x = 2/3
Step-by-step explanation:
2(x-2/3)=0
2x-1 1/3=0
2x=1 1/3
Devide both sides by 2
x=2/3
r
–4=-3+
+
10
Answer?
Answer:
r = 11
Step-by-step explanation:
Is the question
r - 4 = - 3 + 10
So what's r
r - 4 = -3 + 10 Combine the right
r - 4 = 7 Add 4 to both sides
r - 4 + 4 = 7 + 4
r = 11
The value of which number lies between 14 and 15?
Answer: 69 hope this helps!
If 2 (3t - 10) + t = 40 + 4t, what is the value of 3t?
Answer:
3t = 60
Step-by-step explanation:
2(3t - 10) = 40 + 3t
6t - 20 = 40 + 3t
3t - 20 = 40
3t = 60
If you need to simplify that then the answer would be t = 20.
68/125 Write a fraction as an equivalent fraction with a power of 10 in the denominator.Then write the fraction as a decimal
Answer:
[tex]\huge\boxed{\dfrac{68}{125}=0.544}[/tex]
Step-by-step explanation:
[tex]\dfrac{68}{125}=\dfrac{68\cdot8}{125\cdot8}=\dfrac{544}{1,000}=0.544[/tex]
PLEASE HELP I HAVE 5 MIN TO TURN THIS IN!!!!
There are two gardens, garden A and garden B are shown in the image below.
Is there more than one expression that can be used to represent the perimeter of each garden?
Step-by-step explanation:
garden a:
perimeter=2xlength+2xwidth = 2x(5x(2x-3))+2x(2x-3) = 20x-30 + 4x-6 = 24x-36 / 12(2x-3) feet
garden b:
perimeter= 5x+5 + 4x+2 + 8x-8 = 17x - 1 feet
Answer:
Perimeter A = 24x - 36Perimeter B = 17x - 1Step-by-step explanation:
garden A
Width (W) = 2x - 3
Length (L) = 5(W)
= 5 (2x - 3)
= 10x - 15
Perimeter A = 2L + 2W (perimeter of a rectangular garden)
= 2(10x - 15) + 2(2x - 3)
= 20x - 30 + 4x - 6
= 24x - 36
garden B
side 1 = 5x + 5
side 2 = 4x + 2
side 3 = 8x - 8
Perimeter B = sides (1 + 2 + 3)
= 5x+5 + 4x+2 + 8x-8
= 5x + 4x + 8x + 5 + 2 - 8
= 17x - 1
Simplify 56yz^2/48y^5z^2
Step-by-step explanation:
10
What’s the quotient
Answer:
a) 3/40
Step-by-step explanation:
Answer:
3/40 (3 over 40 )
Step-by-step explanation:
3 / 5 ÷ 8
3 / 5 × 1 / 8 ( when dividing fractions you need to invert and multiply invert the seccond fraction )
3 * 1 = 3 and 5 * 8 is 40
So the answer is 3/40
Students are making ornaments and each takes 1/4 of a piece of Bristol board. They go to the cupboard and find 2 1/2 pieces of Bristol board. How many ornaments can they make?
Answer: 10 ornaments
Step-by-step explanation:
From the question, we are informed that students are making ornaments and each takes 1/4 of a piece of Bristol board. We are further told that they go to the cupboard and find 2 1/2 pieces of Bristol board.
The number of ornaments that they make will be gotten by dividing 2 1/2 by 1/4. This will be:
= 2 1/2 ÷ 1/4
= 5/2 ÷ 1/4
= 5/2 × 4/1
= 10
They can make 10 ornaments
Simplify this expression.
2(10) + 2(x – 4)
explain your steps. will give brainliest for right answers.
Answer:
12 + 2x OR 2x + 12
Step-by-step explanation:
2(10) + 2(x - 4)
Distribute;
20 + 2x - 8
Collect like terms;
12 + 2x OR 2x + 12
What is the answer to this pre-algebra equation 7x+10=3x+120
Answer:
=[tex]\frac{55}{2}[/tex]
Please answer !!!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
<A = 117degrees
Step-by-step explanation:
<A and <B are verticle angles, as given. Hence they will be of equal measures. It is given that <A = 5x -3, and <B = 4x + 21.
Using this, set up an equation;
<A = <B
5x - 3 = 4x + 21
Inverse operations,
5x - 3 = 4x + 21
+3 +3
5x = 4x + 24
-4x -4x
x = 24
Now substitute back in, to find the measure of <A,
5x - 3
x = 24
5 ( 24 ) - 3
120 - 3
117
A turtle is swimming 3 feet below sea level. A seagull is flying 9 feet above sea level. Create a number line with an appropriate scale that could be used to graph the situation.
Answer:
3 tick marks to the left of 0 would be 3 ad 9 tick marks to the right of 0 would be 9
Step-by-step explanation:
Angel bought a plant and planted it in a pot near a window in his house. The plant grew at a rate of 3 inches per month and its height at the time of purchase was 15 inches. Write an equation for
H
,
H, in terms of
t
,
t, representing the height, in inches, of the plant
t
t months after Angel bought the plant.
H = 15 + 3t, is the equation representing the height, in inches, of the plant tt months after Angel bought the plant.
What is an equation?Equation is a mathematical and physical statement that describes physical occurrences and the relationship between various physical quantities. It usually consists of basic variables that show physical quantities, but it may also point to a personal variable like your energy.
An equation that has a "equal to sign (=)" either reveals the answer or represents the value of the variable. However, since there is no equal sign in the case of an expression, there can be no clear answer and the value of the concerned variable cannot be displayed.
Given that,
H representing the height, in inches, of the plant
t months after Angel bought the plant
Thus, equation becomes: H = 15 + 3t
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can u tell which is true or false or not enough info
Answer:
I'm going to list the answers below in the explanation.
Step-by-step explanation:
JL = 36 False
ML = 36 True
MP = 48.5 Not enough info
Angle JLK = 102 True
Angle PNK = 102 False
MP || PK False
The only one I'm not 100% positive about is MP = 48.5 but I'm pretty sure!
Good luck and I hope this helps.
9514 1404 393
Answer:
F, T, T, T, T, F
Step-by-step explanation:
PM and PN are "midlines" of the triangle JKL. As such, they are parallel to and half the length of the side of ΔJKL they don't intersect. The relationships of angles and transversals of parallel lines apply. LMPN is a parallelogram, so opposite sides are the same length.
a) JL is not 36, it it twice that. (F)
b) ML is the same length as PN, 36. (T)
c) MP is half of LK, so is 97/2 = 48.5. (T)
d) ∠JLK corresponds to ∠JMP, so is congruent. (T)
e) ∠PNK corresponds to ∠JLK, so is congruent. (T)
f) MP intersects PK at point P, so cannot be parallel. (F)
am • an = am + n, where a is a real number and m and n are integers
Use the product of powers property to simplify the expression –2x3y4x2y3.
–2(xy)12
–2(xy)72
–2x6y12
–2x5y7
Answer:
it's D i just took it.
Step-by-step explanation:
Answer:
D. -2x^5y^7 on edge
Step-by-step explanation:
(5x^3-3x^4-2x-9x^2-2)+(3x^3+2x^2-5x-7)
Answer:
-3x⁴ + 8x³ - 9x² - 7x - 9
General Formulas and Concepts:
Combining like termsStep-by-step explanation:
Step 1: Define expression
(5x³ - 3x⁴ - 2x - 9x² - 2) + (3x³ + 2x² - 5x - 7)
Step 2: Simplify
Combine like terms (x³): -3x⁴ + 8x³ - 9x² - 2x - 5x - 2 - 7Combine like terms (x): -3x⁴ + 8x³ - 9x² - 7x - 2 - 7Combine like terms (constants): -3x⁴ + 8x³ - 9x² - 7x - 9PLEASE PLEASE HELP ILL MARK AS BRANLIEST
Answer:
[tex]x=7[/tex]The length of MN = 13The length of NO = 13The length of OM = 13Step-by-step explanation:
As the given triangle is equilateral as all the sides of the triangle are equal.
[tex]MN = 3x-8[/tex]
[tex]NO=2x-1[/tex]
[tex]OM=5x-22[/tex]
As all the sides are equal, i.e.
[tex]MN=NO=OM[/tex]
as
[tex]MN=NO[/tex]
[tex]3x-8=2x-1[/tex]
Add 8 to both sides
[tex]3x-8+8=2x-1+8[/tex]
[tex]3x=2x+7[/tex]
[tex]x=7[/tex]
Hence, the value of x = 7
so putting the value of x to determine the lengths of the
segments MN, NO, and MO
[tex]MN = 3x - 8[/tex]
[tex]= 3(7)-8[/tex]
[tex]=21-8[/tex]
[tex]=13[/tex]
Hence, the length of MN = 13
[tex]NO = 2x-1[/tex]
[tex]=2(7)-1[/tex]
[tex]=14-1[/tex]
[tex]=13[/tex]
Hence, the length of NO = 13
[tex]OM = 5x-22[/tex]
[tex]= 5(7)-22[/tex]
[tex]= 35-22[/tex]
[tex]=13[/tex]
Hence, the length of OM = 13
Someone help me plz!!
Answer the question in the photo
Answer:
B and C
Step-by-step explanation:
Both B and C
B)
2/5 = 0.4 (which terminate as decimals)
Similarly
C)
-1/4 = -0.25 (also terminates)
But A and D do not terminate
As for A) 1/3= 0.33333333..........
and for D) 7/9= 0.777777777......
In both cases the decimals are a never ending sequence or in other words does not terminate at all. They are irrational numbers.
Hope you understand. Thank you.
10 po
8. A square with a perimeter of 20 is dilated
with a scale factor of 0.4. How would the
area of the new square be affected?
a) It would be 20 times bigger.
b) It would be 0.4 times smaller.
c) It would be 0.16 times smaller.
d) It would be 400 times bigger.
O a)
Answer:
the answer is c 0.16
Step-by-step explanation
I just took the test
What is an equation of the line that passes through the points (8, -3) and (8,4)?
Answer:
undefined
x = 0
General Formulas and Concepts:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
(8, -3)
(8, 4)
Step 2: Find slope m
Substitute: [tex]m=\frac{4-(-3)}{8-8}[/tex]Subtract: [tex]m=\frac{4-(-3)}{0}[/tex]Simplify: m = undefined