Answer:
f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192
Step-by-step explanation:
We have the function f(x) = x^2 − x − 12 and g(x) = x^2 − 16 and we need to find the multiplication of both functions.
f(x) × g(x) = ( x^2 − x − 12)(x^2 − 16) = x^4 - 16x^2 -x^3 + 16x -12x^2 + 192
Simplifying:
f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192
Answer: [tex]f(x)*g(x)=x^4-x^3-28x^2+16x+192[/tex]
Step-by-step explanation:
Given the function f(x) and g(x):
[tex]f(x)=x^2 - x -12\\\\g(x)= x^2 - 16[/tex]
We need to multiply them. To do this we need to remember the Product of power property, which states:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
And the multiplication of signs:
[tex](+)(+)=+\\(+)(-)=-\\(-)(-)=+[/tex]
Then:
[tex]f(x)*g(x)=(x^2 - x -12)(x^2 - 16)\\\\f(x)*g(x)=x^4-16x^2-x^3+16x-12x^2+192[/tex]
Adding like terms, we get:
[tex]f(x)*g(x)=x^4-x^3-28x^2+16x+192[/tex]
factorise 8y^3 - 15x^3
Answer:
(2y-cubert(15)x)(4y^2+2cubert(15)xy+cubert(15^2)x^2)
Step-by-step explanation:
It almost look like someone possibly meant to write a perfect cube there instead of 51... but we can still factorize this... it just won't be as pretty.
The formula for factoring a difference of cubes is
u^3-v^3
=(u-v)(u^2+uv+v^2).
So the answer here is
(2y)^3-(cubert(15)x)^3
=(2y-cubert(15)x)(4y^2+2cubert(15)xy+cubert(15^2)x^2)
cubert means cube root of
The thing I'm cube rooting is the thing in ( ) next to the cubert.
Make sure you actually write the symbol for cube root instead of my notation.
Write twenty billion,one million thirty thousand and one as a number
Answer:
20,001,030,001
For this case we must express the following phrase in numerical form:
"twenty billion, one million thirty thousand and one as a number"
twenty billion is equivalent to [tex]20,000,000,000[/tex]
one million equals [tex]1,000,000[/tex]
thirty thousand equals [tex]30,000[/tex]
one equals 1
Then, we can express:
[tex]20,001,030,001[/tex]
Answer:
20,001,030,001
Multiply.
(x2 - 5x)(2x + x-3)
Hi there! My name is Zalgo and I am here to help you out today. When you multiply (x2-5x) (2x+x-3), you will get 3x^3-18x^2+15x.
I hope that this info helps! :)
"Stay Brainly and stay proud!" - Zalgo
(By the way, can you mark me Brainliest? I'd greatly appreciate it! Thank you! XP)
In this triangle Cos A / Cos B = ?
For this case we have that by definition of trigonometric relations of rectangular triangles, that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:
[tex]Cos (A) = \frac {3} {4.24} = 0.707547169811\\Cos (B) = \frac {3} {4.24} = 0.707547169811[/tex]
So:
[tex]\frac {Cos (A)} {Cos (B)} = \frac {0,707547169811} {0,707547169811} = 1[/tex]
Answer:
[tex]\frac {Cos (A)} {Cos (B)} = 1[/tex]
Add -4/y + (-7/8y).
please help
Answer:
-39/8y
Step-by-step explanation:
-4/y(2)+(-7/8y)
please help
1. f(x)=3(2)^x
2. f(x)=2(3)^x
3. f(x)=3(1/2)^x
4. f(x)=2(1/3)^x
Answer:
C. f(x)=3(1/2)^x
Step-by-step explanation:
standard form of a function is f(x)=ab^x
a should be 3, or the y value where the x value is 0
the b value is 1/2 because that's the rate of change
24 PTS. MARK AS BRAINY!! Help me... I'm desperate... :(
Point J with coordinates (-2,1) is translated (x-3,y-3) and then reflected on the x-axis. What are the coordinates of J"?
Answer: Its (5,-2)
Step-by-step explanation: When you reflect across the x-axis the y value changes.
2 and 3 are
angles.
complementary
vertical
congruent
supplementary
Answer:
supplementary
Step-by-step explanation:
Angles 2 and 3 form a straight line. Straight lines are supplementary
Answer:
Supplementary
Step-by-step explanation:
1 and 2 are vertical along with 3 and 4 they can't be complementary non of them form right angles but supplementary is a straight line making 180 degrees.
Help me I need to pass so I can go on to the next thing plz someone help me
Answer:
The scale factor is 2
Step-by-step explanation:
AB -->A'B' : enlargement , scale factor is greater than 1
From QA to QA' : 1.25 to 2.5 so the ratio is 1:2
The scale factor is 2
1. Solve |x|>5 A. {-5,5} B. { x|-5 < x < 5 } C. { x|x < -5 or x > 5}
2. Solve |x|>5 A. {-5,5} B. { x|-5 < x < 5 } C. { x|x < -5 or x > 5}
3. Solve |4x-8| <12
1. The given absolute value inequality is:
[tex] |x| \: > \: 5[/tex]
This implies that;
[tex] - x \: > \: 5 \: or \: x \: > \: 5[/tex]
We the first inequality by -1 and reverse the sign to get:
[tex]x \: < - \: 5 \: or \: x \: > \: 5[/tex]
The correct answer is
C. { x|x < -5 or x > 5}
2. The given inequality is:
[tex] |4x - 8| \: < \: 12[/tex]
This implies that,
[tex] - (4x - 8) \: < \: 12 \: or \: (4x - 8) \: < \: 12[/tex]
Divide through the first inequality by -1 and reverse the sign
[tex]4x - 8\: > \: - 12 \: or \: 4x - 8\: < \: 12[/tex]
Group similar terms:
[tex]4x \: > \: - 12 + 8 \: or \: 4x \: < \: 12 + 8[/tex]
Simplify:
[tex]4x \: > \: - 4\: or \: 4x \: < \: 20[/tex]
Divide both sides by 4
[tex]x \: > \: - 1\: or \: x \: < \: 5[/tex]
Find measure jk
Answers are 52, 128, 154 & 180
Answer:
b. 128°
Step-by-step explanation:
arc LJ = 2 (26) = 52°
arc KL = 180° (half circle)
so
arc JK = 360° - (arc LJ + arc KL)
arc JK = 360° - 232°
arc JK = 128°
Answer
b. 128°
What is the solution to the system of equations below? y = 1/4x + 2 and 3y = - 3/4x -6
no solution
infinitely many solutions
(–16, 6)
(–16, –2)
Final answer:
The system of equations y = 1/4x + 2 and 3y = -3/4x - 6 represents two distinct parallel lines with the same slope but different y-intercepts, thus the system has no solution.
Explanation:
To find the solution to the system of equations y = 1/4x + 2 and 3y = -3/4x - 6, we need to check if they have a common solution, indicating the point where they intersect, or if they are parallel, which would mean they have no solution, or if they are the same line, which would translate into infinitely many solutions.
First, simplify the second equation by dividing every term by 3, which gives y = -1/4x - 2. Now we can see that the coefficients of x and the constant terms in both equations are multiples of one another but with opposite signs, which means the lines are parallel and have the same slope but different y-intercepts. Therefore, these two equations represent two distinct parallel lines that never intersect.
The correct answer is that there is no solution to this system of equations because the lines are parallel and will never meet.
Austin has $80 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will he have in 2 years?
Divide -5/12 and -5/8
Answer:
2/3
Step-by-step explanation:
-5/12 ÷ -5/8
Copy dot flip
-5/12 * -8/5
The 5's cancel
-8/-12
Divide the top and bottom by -4
2/3
Answer:
2/3
Step-by-step explanation:
-5/12 divided by -5/8
To solve this you need to change the division sign to a multiplication sign.Then find the reciprocal of the second fraction. It should look like this.
-5/12*-8/5
Then you multiply straight across
5*8=40
5*12=60
40/60
This can be simplified to 2/3
PLS HELP OMG
-
what is the best estimate of a 20% tip if you ordered a meal that cost $29.35?
Answer:
5.87
Step-by-step explanation:
29.35/x=100/20
(29.35/x)*x=(100/20)*x - we multiply both sides of the equation by x
29.35=5*x - we divide both sides of the equation by (5) to get x
29.35/5=x
5.87=x
x=5.87
Answer:
$5.87
Step-by-step explanation:
20% = 20/100 = 1/5
hence 20% tip,
= 20% of the total cost
= 1/5 x $29.35
= $5.87
The value of k so that the sequence k-1, k+3, 3k-1 forms an arithmetic progression is?
Answer:
k = 4.
Step-by-step explanation:
An arithmetic sequence has a common difference.
So for this to be arithmetic:
k + 3 - (k - 1) = 3k - 1 - (k + 3)
k + 3 - k + 1 = 3k - 1 - k - 3
3 + 1 = 2k - 4
4 + 4 = 2k
k = 4.
The sequence is 3, 7, 11.
In the game of blackjack played with one deck, a player is initially dealt 2 different cards from the 52 different cards in the deck. A winning "blackjack" hand is won by getting 1 of the 4 aces and 1 of 16 other cards worth 10 points. The two cards can be in any order. Find the probability of being dealt a blackjack hand. What approximate percentage of hands are winning blackjack hands?
Answer:
[tex]P =4.83\%[/tex]
Step-by-step explanation:
First we calculate the number of possible ways to select 2 cards an ace and a card of 10 points.
There are 4 ace in the deck
There are 16 cards of 10 points in the deck
To make this calculation we use the formula of combinations
[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]
Where n is the total number of letters and r are chosen from them
The number of ways to choose 1 As is:
[tex]4C1 = 4[/tex]
The number of ways to choose a 10-point letter is:
[tex]16C1 = 16[/tex]
Therefore, the number of ways to choose an Ace and a 10-point card is:
[tex]4C1 * 16C1 = 4 * 16 = 64[/tex]
Now the number of ways to choose any 2 cards from a deck of 52 cards is:
[tex]52C2 =\frac{52!}{2!(52-2)!}[/tex]
[tex]52C2 = 1326[/tex]
Therefore, the probability of obtaining an "blackjack" is:
[tex]P = \frac{4C1 * 16C1}{52C2}[/tex]
[tex]P = \frac{64}{1326}[/tex]
[tex]P = \frac{32}{663}[/tex]
[tex]P =0.0483[/tex]
[tex]P =4.83\%[/tex]
Answer:
Probability = 0.0483
Percentage = 4.83%
Step-by-step explanation:
We know that a blackjack hand played with one deck consists of:
1 of the 4 aces = [tex]\frac{4}{52}[/tex]
So 1 out of the 16 cards worth 10 points will be equal to = [tex]\frac{16}{52}[/tex]
Finding the probability of getting a blackjack hand assuming that the cards were not replaced:
P (blackjack hand) = P(1st ace) × P(2nd 10 point card) + P(1st 10 point card) × P(2nd ace)
P (blackjack hand) = [tex]\frac{4}{52} \times \frac{16}{51} + \frac{16}{52} \times \frac{4}{51}[/tex] = 0.04827
Percentage of getting blackjack hand = 4.83%
Which pair of lines is parallel? A. y=4x+1 and y+4=5 B. y=-2+x and 2y-2x=-2 C. y=1/4x + 2 and y-2=1/2x D. y=1/5x+1 and 5y+x= 10
Answer:
B. y=-2+x and 2y-2x=-2
Step-by-step explanation:
Two lines are parallel if they have the same slope.
The equation 0of a line is tipically written as y=mx + b, where 'm' represents the slope and 'b' the y-intercept.
Let's evaluate each of the options:
A. y=4x+1 and y+4x=5
Writing the equations in the slope-intercept form, we get:
y=4x+1 → m=4
y=5-4x → m=-4
Given that they have different slopes, they are not parallel.
B. y=-2+x and 2y-2x=-2
Writing the equations in the slope-intercept form, we get:
y=-2+x → m=1
y=-1 + x → m=1
Given that the equations have the same slope, they are parallel.
C. y=1/4x + 2 and y-2=1/2x
Writing the equations in the slope-intercept form, we get:
y=1/4x + 2 → m=1/4
y=1/2x+2 → m=1/2
Given that they have different slopes, they are not parallel.
D. y=1/5x+1 and 5y+x= 10
Writing the equations in the slope-intercept form, we get:
y=1/5x+1 → m=1/5
5y+x= 10 → y=2 - 1/5x → m=-1/5
Given that they have different slopes, they are not parallel.
–42 ÷ (–6) a.–252 b.–7 c. 7 d. 252
Answer:
a negative multiplied or divided by negative is positive. if its adding or subtracting it takes sign of the bigger number. and it dividing so the number is not going to get bigger. so its positive 7
[tex]\text{Hey there!}[/tex]
[tex]\text{Since, both of your terms (-42 and -6) are negative, we know that your answer}[/tex] [tex]\text{will most likely be a POSITIVE number}[/tex]
[tex]\text{Because. negative \& negative makes positive!}[/tex]
[tex]\text{-42}\div\text{(-6)}=\dfrac{-42}{(-6)}=42\div6=7[/tex]
[tex]\boxed{\boxed{\text{Answer: C. 7}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Anya found the slope of the line that passes through the points (–7, 4) and (2, –3). Her work is shown below. Let (x2, y2) be (–7, 4) and (x1, y1) be (2, –3). m = = = The slope is . What error did she make? She simplified the denominator incorrectly. The denominator simplifies to –7. She labeled the points incorrectly. The point (–7, 4) should be (x1, y1). She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values. She used an incorrect formula. The formula should be the sum of the x-values with respect to the sum of the y-values.
Answer:
She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex](x2,y2)=(-7,4)[/tex]
[tex](x1,y1)=(2,-3)[/tex]
Substitute the values
[tex]m=\frac{4+3}{-7-2}[/tex]
[tex]m=\frac{7}{-9}[/tex]
[tex]m=-\frac{7}{9}[/tex]
therefore
She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values
Answer:
C
Step-by-step explanation:
Which pair of spheres are congruent?
R and S
R and T
S and T
Answer:
S and T
Step-by-step explanation:
I put R&T, that's wrong. It's S and T.
The pair of spheres are congruent is S and T.
What is congruence?Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
As, per the given figure,
Figure R having a radius 3.
Figure S is having a radius 4
Figure T is having radius 4
So, by considering the property of congruence figure S and T will be congruent spheres.
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What is the y-intercept of the function f(x) = 2 · 3*?
А. (2, 0)
в. (0, 6)
с. (0, 3)
D. (0, 2)
Answer:
Option D. (0, 2)
Step-by-step explanation:
we have
[tex]f(x)=2(3)^{x}[/tex]
This is a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
r is the rate of change
In this problem
a=2 ---> the initial value ( value of the function when the value of x is equal to zero)
b=3
b=1+r ----> 3=1+r ----> r=2 ---> r=200%
Remember that
The initial value of the function is equal to the y-intercept
The initial value is the point (0,2)
therefore
The y-intercept is the point (0,2)
x + y = k
2x + 3y = k + 1
The point of intersection of the lines has an x-coordinate of
A.2k + 1
B.-2k + 1
C.2k - 1
Answer: Yes A is correct
Step-by-step explanation:
Multiply the first equation by 3...
2x+3y=k+1 needs to be subtracted by 3x+3y=3k
which equals -x=-2k-1
Then you can multiply the equation by -1 to make them all positive. Resulting in x=2k+1
The correct option is c.
To solve the given simultaneous linear equations x + y = k and 2x + 3y = k + 1 using the elimination method, multiply the equations by suitable constants to eliminate one variable. The values of x and y in terms of k are x = 2k - 1 and y = 1 - k.
Explanation:To solve the given simultaneous linear equations x + y = k and 2x + 3y = k + 1 using the elimination method, we can eliminate one variable by multiplying the equations by suitable constants. Let's multiply the first equation by 2 and the second equation by -1 to eliminate x.
2x + 2y = 2k
-2x - 3y = -k - 1
Adding these equations together, we get:
2y - 3y = 2k - (k + 1)
-y = k - 1
Multiplying both sides by -1:
y = 1 - k
Substituting this value of y back into the first equation:
x + (1 - k) = k
x = 2k - 1
So, the values of x and y in terms of k are x = 2k - 1 and y = 1 - k.
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take 25% off the original. now take off an additional 10% and calculate the new sales cost of this item. what is your total percent of savings?
x = original price, or 100%
if we take off 25% from 100% what's left is 75%, that's the discounted price.
let's then take 10% of that.
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of "x"}}{\left( \cfrac{75}{100} \right)x\implies 0.75x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{10\% of 0.75x}}{\left( \cfrac{10}{100} \right)0.75x\implies 0.075x}~\hfill \stackrel{\textit{total percent savings}}{0.75x-0.075x\implies 0.675x} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{changing that to percent format}}{0.675\cdot 100\implies 67.5\%}[/tex]
Y=81/3x what is the constant of proportionality
Answer:
[tex]\frac{81}{3}[/tex]
Step-by-step explanation:
Given the direct variation equation
y = kx ← k is the constant of proportionality
then for
y = [tex]\frac{81}{3}[/tex] x
k = [tex]\frac{81}{3}[/tex]
A truck can be rented from company A for $40 a day plus $0.30 per mile. Company B charges $20 a day plus $0.70 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for company A and company B are the same.
Despite different rental costs, the rental costs for company A and company B will be the same, after 50 miles.
To solve this, we need to set up an equation based on their pricing structures and solve for the number of miles.
Let m represent the number of miles driven. The cost for company A would be $40 + $0.30m, and the cost for company B would be $20 + $0.70m.
We set these two expressions equal to each other to find the breakeven point:
$40 + $0.30m = $20 + $0.70m
Subtracting $0.30m from both sides gives us:
$40 = $20 + $0.40m
Next, we subtract $20 from both sides:
$20 = $0.40m
Dividing both sides by $0.40, we get:
m = 50
What is the additive inverse of the polynomial? –6x3 + 4x2 – 4x
Answer:
6x³ - 4x² + 4x
Step-by-step explanation:
The additive inverse is the value added to make the expression equal to zero.
Given
- 6x³ + 4x² - 4x , then the additive inverse is
- ( - 6x³ + 4x² - 4x)
= 6x³ - 4x² + 4x
The additive inverse of the polynomial is 6x³ - 4x² + 4x.
What is a Polynomial?They are the algebraic expressions containing constants and indeterminates.The variable part contains exponent which is a whole number.Given: Polynomial
-6x³ + 4x² - 4x
Additive inverse of the polynomial is the polynomial when added to the original polynomial gives the sum zero.
Let, the additive inverse of the given polynomial be P.
⇒ P + -6x³ + 4x² - 4x = 0
⇒ P = 6x³ - 4x² + 4x
Therefore, the additive inverse of the given polynomial is 6x³ - 4x² + 4x.
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In order to solve for the variable in the equation Mikel first applies the distributive property. Which equation is a result of this step?
Answer:
1 - x - 2 + 2x = 10x - 25 - x
Step-by-step explanation:
We have the expression: 1 - (x+2) + 2x = 5(2x - 5) - x
Applying the distributive property we get:
1 - x - 2 + 2x = 10x - 25 - x
So, the following equation is the result of that step: 1 - x - 2 + 2x = 10x - 25 - x
Answer:
The equation is:
[tex]1-x-2 + 2x = 10x-25-x[/tex]
Step-by-step explanation:
The distributive property says that
[tex]c(a+b) = ac + bc[/tex]
In this case we have the following equation
[tex]1-(x+2) + 2x = 5(2x-5)-x[/tex]
Then apply the distributive property as shown below
[tex]1-1*x-1*2 + 2x = 5*2x-5*5-x[/tex]
Now simplify the expression
[tex]1-x-2 + 2x = 10x-25-x[/tex]
So the equation that results after applying the distributive property is:
[tex]1-x-2 + 2x = 10x-25-x[/tex]
will 5x-3y>15 have a solid line
Answer:
The inequality [tex]5x-3y >15[/tex] have a dashed line
Step-by-step explanation:
we have
[tex]5x-3y >15[/tex]
The solution of this inequality is the shaded area below the dashed line
The equation of the dashed line is [tex]5x-3y=15[/tex]
The slope of the dashed line is positive
The y-intercept of the dashed line is -5 ---> point (0,-5)
The x-intercept of the dashed line is x=3 ----> point (3,0)
Graph the solution
see the attached figure
Question 3 (2 points)
Find the area of a regular octagon with a side length of 12 and an apothem of 30.
1440
2880
180
well, this is an OCTAgon, OCTA = 8.
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\ \cline{1-1} a=30\\ p=\stackrel{8\times 12}{96} \end{cases}\implies A=\cfrac{1}{2}(30)(96)\implies A=1440[/tex]