writing polynomial functions write the equation of the polynomial function given the following zeros x= 5 , -2 , -1
Answer:
Step-by-step explanation:1) Find the domain of the given function. f(x) = square root of quantity x plus three divided by quantity x plus eight times quantity x minus two.
using a graphical tool see the attachment
the answer is C) x ≥ -3, x ≠ 2
2. Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 2 - (x - 7)2
using a graphical tool
see the attachment
the answer is C) Increasing: x < 7; decreasing: x > 7
3. Perform the requested operation or operations.
f(x) = 4x + 7, g(x) = 3x2
Find (f + g)(x).
(f + g)(x) = f(x) + g(x)
(f + g)(x) = 4x + 7 + 3x^2
(f + g)(x) = 3x^2 + 4x + 7
The answer is C) 4x + 7 + 3x2
4. Perform the requested operation or operations.
f(x) = x minus five divided by eight. ; g(x) = 8x + 5, find g(f(x)).
f(x)=(x-5)/8 g(x)=8x+5
g(f(x))=8((x-5)/8)+5=x-5+5=x
the answer is B) g(f(x)) = x
5. Find f(x) and g(x) so that the function can be described as y = f(g(x)).y = nine divided by square root of quantity five x plus five.
y=f(g(x))=9/((5x+5) ^1/2)
let do
g(x)=5x+5...........so
f(x)= 9/( x^1/2)
the answer is A) f(x) = nine divided by square root of x. , g(x) = 5x + 5
6. A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?
Original size- >4km*4km=16 km2
4 times its original size---------------4*(16km2)-----64 Km2----------- > 8 km by 8 Km
Therefore
3km----------------------------- 1 sec
(8km-4km)---------------------x
X=4/3=1.33 sec
The answer is D) 1.33 sec
7. Find the inverse of the function.
f(x) = the cube root of quantity x divided by seven. - 9
to solve, replace f(x) with y , switch x and y, solve for y and replace y with f⁻¹(x)
f(x)=((x/7)-9) ^(1/3)
replace f(x) with y
y=((x/7)-9) ^(1/3)
switch x and y
x=((y/7)-9) ^(1/3)
solve for y
x^3=((y/7)-9)
x^3+9=y/7
y=7(x^3+9)
the answer is C) f-1(x) = 7(x3 + 9)
8. Describe how the graph of y= x2 can be transformed to the graph of the given equation.y = (x - 14)2 – 9
using a graphical tool see the attachment the answer is C) Shift the graph of y = x2 right 14 units and then down 9 units
9. Describe how to transform the graph of f into the graph of g. f(x) = alt='square root of quantity x minus nine.' and g(x) = alt='square root of quantity x plus five. '
f(x)=(x-9) ^1/2 g(x)=(x+5) ^1/2
using a graphical tool see the attachment
the answer is C) Shift the graph of f left 14 units
10. If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
f(x) = -16x5 - 7x4 – 6
The answer is B) Degree: 5; leading coefficient: -16
11. Write the quadratic function in vertex form.y = x2 + 4x + 7
Complete the square on the right side of the equation
Use the form ax2+bx+cax2+bx+c, to find the values of a, b, and c.
a=1,b=4,c=7
Consider the vertex form of a parabola.
a(x+d)2+e
Find the value of dd using the formula d=b/2a
d=4/(2*1)=2
Find the value of e using the formula e=c−b2/4a
e=7−4=3
Substitute the values of a, d, and e into the vertex form a(x+d)2+e
(x+2)2+3
The answer is A) y = (x + 2)2+ 3
12. Find the zeros of the function.
f(x) = 3x3 - 12x2 - 15x
using a graphical tool (see the attachment)x1=-1
x2=0
x3=5
The answer is C) 0, -1, and 5
13. Find a cubic function with the given zeros.7, -3, 2
X1=7
X2=-3
X3=2
f(x)=(x-7)(x+3)(x-2)=(x2-4x-21)(x-2)=x3-6x2-13x+42
the answer is C) f(x) = x3 - 6x2 - 13x + 42
14. Find the remainder when f(x) is divided by (x - k).f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3
f(x)=7(3)4+12(3)3+6(3)2-5(3)+16=946
The answer is the B) 946
15. Use the Rational Zeros Theorem to write a list of all potential rational zerosf(x) = x3 - 10x2 + 4x - 24
The constant term of () is -24
The leading coefficient is 1.
We have to only consider the factors of the constant (leading coefficient = 1)
The factors are 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24
The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
HELLPP ASAP THERES A TIMER
Based on this picture, if ∠3 = 50˚then what is m∠8?
SHOW WORK PLEASE
HURRY: 20 POINTS TO THE WINNER
Answer:
1 gallon
Step-by-step explanation:
7/8 + 3/8 + 4/8 = 1 6/8
3/8 + 1/8 + 2/8 = 6/8
1 6/8 - 6/8 = 1
Answer:
Chocolate Sauce: 4/8
Strawberry Sauce: 2/8
Caramel Sauce: 2/8
Chocolate Sauce
Monday, the shop had 7/8, the shop used 3/8 on Tuesday. So we subtract the numerators but the denominator stays the same.
7 - 3 = 4
So it is 4/8
Same thing for Strawberry and Caramel Sauce.
So we add the totals we got from subtracting Monday amount of toppings with Tuesday's amount of toppings.
4/8 + 2/8 + 2/8 =
1 gallon**I hope this helped! :)
- 4y = - 40
please show work if you can
someone plssss help
whats 2 × 2??
Answer:
4 is answerrrrrrrr
Mai is playing a game with a class of second graders. Mai knows she is exactly 120 inches from the mirror on the floor. She has students stand so that she can just see the top of their heads and then guesses their heights. The students are amazed!
Diagram of 2 stick figures.
How is Mai so accurate?
Mia is able to find the height of the students so accurately using the tangent property of trigonometry.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
As it can be seen that there are two right triangles, therefore, using the tangent property of the trigonometry, Mia is able to find the height of the students so accurately.
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sakura bought 72 insches length of fabric for her ninja uniform.the total cost of the fabric is php 285.00 how do you think is the cost of the fabric per centimeter
Answer:
php 3.96
Step-by-step explanation:
If it costs 285.00 per 72 inches, the divide 285.00 by 72 to get per inches. 285.00 divided by 72 = 3.9583. Round 3.9583 to the hundreths place and you get 3.96.
(hope this helps...and why is this question related to naruto??))
Which polynomials are prime? Check all that apply. 15x ^ 2 + 10x - 9x + 7 20x ^ 2 - 12x + 30x - 18 6x ^ 3 + 14x ^ 2 - 12x - 28 8x ^ 3 + 20x ^ 2 + 3x + 12 11x ^ 4 + 4x ^ 2 - 6x ^ 2 - 16
Answer:
15x2+10x-9x+7
8x3+20x2+3x+12
11x4+4x2-6x2-16
Step-by-step explanation:
The prime polynomials are;
⇒ 15x² + 10x – 9x + 7
⇒ 8x³ + 20x² + 3x + 12
⇒ 11x⁴ + 4x² – 6x² – 16
What is an expression?
Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
There are some polynomials.
Now,
Evaluate all options in order to check that the polynomials are prime or not as;
Since, The polynomial is called a prime polynomial if the polynomial has not lower degree factors.
1). 15x² + 10x – 9x + 7
15x² + 10x – 9x + 7 = 5x(3x + 2) - (9x - 7)
Thus, This polynomial can not be factored into lower degree polynomial. Hence, it is a prime polynomial.
2). 20x² - 12x + 30x - 18
20x² - 12x + 30x - 18 = 4x (5x - 3) + 6 (5x - 3)
= (4x + 6) (5x - 3)
Thus, This polynomial is converted into a lower degree polynomial. Therefore, it is not a prime polynomial.
3). 6x³ + 14x² - 12x - 28
6x³ + 14x² - 12x - 28 = 2x² (3x + 7) - 4(3x + 7)
= (2x² - 4) (3x + 7)
Thus, This polynomial is converted into a lower degree polynomial. Therefore, it is not a prime polynomial.
4). 8x³ + 20x² + 3x + 12
8x³ + 20x² + 3x + 12 = 4x² (2x + 5) + 3 (x + 4)
= (4x² + 3) (2x + 5)
Thus, This polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.
5). 11x⁴ + 4x² – 6x² – 16
11x⁴ + 4x² – 6x² – 16 = x² (11x² + 4) - 2 (x² + 8)
Thus, This polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.
Therefore, The prime polynomials are;
⇒ 15x² + 10x – 9x + 7
⇒ 8x³ + 20x² + 3x + 12
⇒ 11x⁴ + 4x² – 6x² – 16
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A bag contains 37 coins consisting of only dimes and quarters.The total amount of money in the bag is $6.85. How many dimes are in the bag ??
Answer:
16 dimes
Step-by-step explanation:
D=number of dimes
Q=number of quarters
D+Q=37
.25 xQ + .10 x D=6.85
sub Q from first equation
.25(37-D) + .10 x D=6.85
D(.10-.25) + .25 x 37 =6.85
-.15D + 9.25=6.85
D= (6.85-9.25)/(-.15)
D=16
can you help me with my homework
ුැේෞඈචොමටඉපගපයිිඅඅේෛෛඑටමවවඈ
-240+370=
what is the sum
Answer:
it would be the same as 370-240 which equals 130
Step-by-step explanation:
Answer:
130
Step-by-step explanation:
give me brainliest (aka the crown) :)
What number means the same as 9,000,000,000 + 900,000,000, + 90,000,000 +9,000,000, + 900,000 + 9,000 +9 PLEASE DO IT QUICKLY
Answer:
9,999,909,009
Step-by-step explanation:
plz mark me brainliest. :0
Answer:
it does not equal the same
Step-by-step explanation:
but heres ur answer 9999909009
Solve the following system of equations.
2x + 5y = -18 and y = -4x
Answer:
x=1 and y= -4
Step-by-step explanation:
step one: plug -4x into y in thi]e first equation.
2x+5(-4)= -18
step two: solve for x
2x-20= -18
(add 20 to both sides to eliminate -20 on the right)
2x=2
(divide both sides by 2 to get x by its self)
x=1
step 3: now that we found the value for x plug it in to either equation and solve for y
y= -4x
y= -4(1)
y= -4
What equation is equivalent to 2(3-y)
A. 2y - 6
B. 6 - 2y
C. 6 + y
D. 6 + 2y
Answer:
The answer is C.6+y
............
Find the area of the square ABCD.
Answer:
Step-by-step explanation:
area of square is basically one side times itself
14 times 14 =196m^2
Answer: 196 meters
Step-by-step explanation: To find the area of any square you must do length(vertical side) times the width(horizontal side). It would look like this: length x width. So in this equation, it would be 14x14=the area. Another thing is that when you have a square when you know one side the other side is always as long or wide as the one you know. So 14x14=196 square meters
say random sentences which make no sense!
ill go
pls stop flying over my barn with you toothbrush I hate when the cows bark
pls say sum nd dont be lame
Answer:
the home is located on a quiet street and is a boy with an enormous advantage in a small area
27 = 54
value that would make it true
Answer:
2
Step-by-step explanation:
27 = 54,
let's say the value that will make it true is x
So then,
27 * x = 54. If we divide both sides by 27, we have
x = 54 / 27
x = 2
The value that will make it true is multiplying 27 by 2
9. A garden has two circles. 1 big circle with sunflowers. 1 smaller circle with a radius of 6yd. Distance between the outside of the smaller circle to the end
of the bigger circle is 3yd. Find the area of the sunflower part of the garden.
Answer:
the answer would be 25
Step-by-step explanation:
since if you add all the following numbers up you make 11 and to taht you double the answer and that would give you 22 and then you add the remaining IP to make 25b
A group of 4 friends bought movie tickets. Each person also bought a large popcorn for $7.50. If they spent a total of $72, how much was each movie ticket (t)?
Answer:
$16.125 but i don't know if you have to round
Step-by-step explanation:
Please help me! (Tangent Ratios) (30 points)
Answer:
Step-by-step explanation:
A = 48/20
B = 20/48
name the missing numerator. ?/9 = 36/81
Answer:
the missing number is 6
Step-by-step explanation:
because is you do 6/9 and multiply it by it self it
equals 36/81
(9x9) and (6x6)
[tex]\frac{2y-1}{15} =\frac{y}{10}[/tex]
Answer:
y = 2
Step-by-step explanation:
Given
[tex]\frac{2y-1}{15}[/tex] = [tex]\frac{y}{10}[/tex] ( cross- multiply )
10(2y - 1) = 15y ← distribute left side
20y - 10 = 15y ( subtract 15y from both sides )
5y - 10 = 0 ( add 10 to both sides )
5y = 10 ( divide both sides by 5 )
y = 2
How do o solve this
Answer:
Step-by-step explanation:
Im not sure if u need to use shapes, but I will since it says in the example
4x - put it in a square box
2x - also in a square box
3 - in a circle box
1 - in a circle box
combine like terms
4x+2x=6x
3+1=4
6x+4
HALP!!! DON'T MIND MY TABS BTW!! JUST NEED HELP!!! SUPER eAsY!!
Answer: cv
Step-by-step explanation:
find the selling price of an $86 item after a 50% markup
Answer:
129
Step-by-step explanation:
the answer is 129 because you do 0.50 times 86 which is 43 so you do 43 + 86 which is 129 so $129 is your answer
The selling price of an $86 item after a 50% markup will be $129.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The price of an item is $86 and the price is increased by 50%.
Let 'x' be the selling price. Then the selling price is calculated as,
50% = [(x - 86) / 86] x 100
Simplify the equation, then we have
50% = [(x - $86) / $86] x 100
0.50 = (x - $86) / $86
$43 = x - $86
x = $86 + $43
x = $129
The selling cost of a $86 thing after a half markup will be $129.
More about the percentage link is given below.
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What is the radius of the circle? cm
What is the circumference of the circle?
help megh ghvgcj bhnbjfvgbn hvcf
Answer:
swap the inequality with the equasion and ur good
PLZ MARK AS BRAINLIEST
Estimate. Show your work. Cam buys 3 CDs for $26.77. If each CD costs the same amount, about how much does each CD cost?
Answer:
$8.92
Step-by-step explanation:
26.77/3 ≈ 8.92
In a bag of sweets, 6 are orange and 9 are lime. Jodi chooses a sweet at random, eats it an
then chooses a second sweet at random.
What is the probability that both sweets are the same flavour?
(3 Points)
Answer:[tex]\frac{17}{35}[/tex]
Step-by-step explanation:
Given
The bag contains 6 orange and 9 lime sweets
For both sweets of the same flavor, Jodi must either choose orange or lime
No. of ways it can be done is [tex]^6C_1\times^5C_1+^9C_1\times^8C_1[/tex]
The total no of ways of selecting two sweets out of 15 is [tex]^{15}C_1\times^{14}C_1[/tex]
The probability that both sweets are the same flavor
[tex]P=\dfrac{^6C_1\times^5C_1+^9C_1\times^8C_1}{^{15}C_1\times^{14}C_1}=\frac{102}{210}=\frac{51}{105}=\frac{17}{35}[/tex]