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
Miguel places an 18-foot ladder 8 feet from the base of his house and leans it up
against the side of his house. Find, to the nearest degree, the measure of the
angle the bottom of the ladder makes with the ground.
*
18 ft
o
8 ft
Answer:
18 ft
Step-by-step explanation:
What is the volume of the rectangular prism?
90 cm
20 cm
30 cm
Kathy uses 8.6 pints of blue paint and white paint to paint her bedroom walls. 4 5 of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Answer:Kathy uses 1.72 pint of white paint
Step-by-step explanation:
Total amount of paint ( Blue and white paint)= 8.6 pints
Amount of blue paint=4/5 x 8.6 = 6.88 Pints
amount of white paint = Total amount of paint - amount of blue paint
= 8.6 pints - 6.88 pints
=1.72 pint of white paint
Answer:274707
Step-by-step explanation:
Which scatterplot suggests a linear relationship between x and y?
I need help asap
When Dalvin runs the 400 meter dash, his finishing times are normally distributed with a mean of 65 seconds and a standard deviation of 1 second. Using the empirical rule, what percentage of races will his finishing time be between 64 and 66 seconds?
Answer:
68%.
Step-by-step explanation:
Dalvin's finishing time is normally distributed with a mean of 65 seconds and a standard deviation of 1 second.
Under the empirical rule, 68% of the results will be within 1 standard deviation.
Since the standard deviation is 1 second, 68% of Dalvin's finishing time will be between 64 and 66 seconds.
What is the exact value of sine of 8 pie/3
Answer:
0.1456858
Step-by-step explanation:
Hope it help
Answer:
−1/2
Explanation:
cos(8π/3)
=cos(8π/3 − 2π)
=cos(2π/3) = − cos (π/3) = −1/2
[tex]y = - \frac{1}{2}x + 9[/tex]
please help me :(.
I need this asap ty:p
Which of the following equations are equations of a direct variation? Choose all that apply.
(a) x=−2y
(b) x+2y=12
(c) 3x−2y=0
(d) 5x^2+y=0
(e) y =0.3x +1.6
(f) y−2=x
Answer:
(a) x = -2y
(c) 3x - 2y = 0
Step-by-step explanation:
You can tell if an equation is a direct variation equation if it can be written in the format y = kx.
Note that there is no addition and subtraction in this equation.
Let's put these equations in the form y = kx.
(a) x = -2y
y = x/-2 → y = -1/2x This is equivalent to multiplying x by -1/2, so this is an example of direct variation.(b) x + 2y = 12
2y = 12 - x y = 6 - 1/2x This is not in the form y = kx since we are adding 6 to -1/2x. Therefore, this is NOT an example of direct variation.(c) 3x - 2y = 0
-2y = -3x y = 3/2x This follows the format of y = kx, so it is an example of direct variation.(d) 5x² + y = 0
y = -5x²This is not in the form of y = kx, so it is NOT an example of direct variation.(e) y = 0.3x + 1.6
1.6 is being added to 0.3x, so it is NOT an example of direct variation.(f) y - 2 = x
y = x + 2 2 is being added to x, so it is NOT an example of direct variation.The following equations are examples of direct variation:
x = -2y 3x - 2y = 0Answer:
(a) x = -2y
(c) 3x - 2y = 0
Step-by-step explanation:
You can tell if an equation is a direct variation equation if it can be written in the format y = kx.
Note that there is no addition and subtraction in this equation.
Let's put these equations in the form y = kx.
(a) x = -2y
y = x/-2 → y = -1/2x
This is equivalent to multiplying x by -1/2, so this is an example of direct variation.
(b) x + 2y = 12
2y = 12 - x
y = 6 - 1/2x
This is not in the form y = kx since we are adding 6 to -1/2x. Therefore, this is NOT an example of direct variation.
(c) 3x - 2y = 0
-2y = -3x
y = 3/2x
This follows the format of y = kx, so it is an example of direct variation.
(d) 5x² + y = 0
y = -5x²
This is not in the form of y = kx, so it is NOT an example of direct variation.
(e) y = 0.3x + 1.6
1.6 is being added to 0.3x, so it is NOT an example of direct variation.
(f) y - 2 = x
y = x + 2
2 is being added to x, so it is NOT an example of direct variation.
The following equations are examples of direct variation:
x = -2y
3x - 2y = 0
What symbol should I use?
Answer:
>
Step-by-step explanation:
6.25 L is the same as 6250 mL, which is greater than 625 mL.
Hope it helps!
HERES ANOTHER ONE PLEASE HELPPP
Answer:
30.
Step-by-step explanation:
you get tot the 180-50=120.
120÷2=60
90-60=30
3c + 2 = 3c + 2
please help me
Answer:
3c+2=2+3c
Step-by-step explanation:
y=2x-7[tex]x^{2}[/tex]
x1=0,x2=2/7 that is the answer
Answer:
This is not solvable.
Step-by-step explanation:
Is there a second equation? You cannot solve an equation with two variables.
What’s the value of X
Answer:
37
Step-by-step explanation:
The angle with a red square is 90, because it's a right angle. 53 + 90 is 143. 180 is the sum of all the angles in a triangle, so you do 180-143. 180-143=37
Answer:
37
Step-by-step explanation:
90+53=143
a triangle is 180 degrees.
180-143=37
3x − x − 1 = 15
What is x
Answer: x=8
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x−x−1=15
3x+−x+−1=15
(3x+−x)+(−1)=15(Combine Like Terms)
2x+−1=15
2x−1=15
Step 2: Add 1 to both sides.
2x−1+1=15+1
2x=16
Step 3: Divide both sides by 2.
2x /2 = 16 /2
x=8
Answer:
3x-x=15+1
2x=16
x=16/2
x=8
✨HeHeHe~ moooore mathhhh✨
Answer:
The answer of this should be c
Answer:
C: M=10
Step-by-step explanation:
4M+40=7M+10
-7M -7M
-3M +40=10
-40 -40
-3M=-30
/-3 /-3
M=10
HOPE I HELPED:)
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!
Can somebody tell me the answer to this please
Answer: D
Step-by-step explanation: We first need to solve the inequality.
First subtract 10 from both sides to get -x < -8.
Now divide both sides by -1, but watch out.
If you multiply or divide both sides of an inequality by
a negative number, you must switch the direction of the inequality sign.
So we have x > 8.
Start with an open dot at 8 and draw and arrow to the right.
We use an option dot since x is greater than but not equal to 8.
So option D is your answer.
Answer:
The correct answer is D
Step-by-step explanation:
(4 + 12i) + (16 - 8i)
Answer:
Answer is 20+4i
Step-by-step explanation:
I hope it's helpful!
Answer:
20 + 4i
Step-by-step explanation:
[remove brackets]
(4+12i) + (16-8i) --> 4+12i+16-8i
[collect like terms]
4 + 16= 20
12i - 8i= 4i
20 + 4i
How can 33 ninths be expressed as a decimal
Hey there!
Given:
[tex]\frac{33}{99}[/tex]
First, we can simplify it by dividing the numerator and denominator by [tex]33[/tex]:
[tex]\frac{1}{3}[/tex]
And, using common knowledge, we know that [tex]\frac{1}{3}[/tex] as a decimal is [tex]0.333...[/tex]
Have a great day!
Answer:33/9 is equal to 3 2/3.
Step-by-step explanation:
I hope this helped<3
During a basketball practice, Mai attempted 40 free throws and was successful on 25% of them. How many successful free trows did she make?
Answer:
She made 10 free throws
Step-by-step explination:
I found it on this website: https://staff.4j.lane.edu/~ruzicka/Cal_Young/math/Illustrative%20Math/Unit%203%20Rates%20and%20Percents/Lesson%2011/L11%20HW%20Key%20Corrected.pdf
Try it and see if you are right
I Need help please I only have a little bit of time
Answer:
30
Step-by-step explanation:
if its asking for inches
Use the Distributive Property to expand the expression: z(-6.4 - 3.5x) *
help plz
Answer:
I think this is it -6.4z -3.5xz
Step-by-step explanation:
Answer:
=−3.5xz−6.4z
Step-by-step explanation:
BRAINLIEST for anyone who can answer
Answer: a) -2,1 , 0,1 , 2,1
b) C
Step-by-step explanation:
Simplify the ratio 25:35
Answer:
5:7
Step-by-step explanation:
Step-by-step explanation:
5:7 is the simplified fraction of 25:35
30 POINTS
Find the rectangular coordinates of the point with the polar coordinates ordered pair negative 3 comma 5 pi divided by 3 . (1 point)
ordered pair negative 3 divided by 2 comma 3 divided by 2
ordered pair 3 square root 3 divided by 2 comma negative 3 divided by 2
ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2
ordered pair 3 divided by 2 comma negative 3 divided by 2
express 4.67 as a mixed number
Answer:
4.671 = (4.67 × 100)(1 × 100) = 467100.
Step-by-step explanation:
As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 467100 is also equal to 467100 when expressed as a mixed number.
Answer:
4 67/100
Step-by-step explanation:
From the info we have, we now that the whole number is 4.
.67 ends in the hundredths place which means it will be a decimal over 100.
Now you have 67/100 and since 67 is prime it can't be simplified.
Put them together and you get 4 67/100
I hope this helps, and have a great day! :)
Classify the expression: 5x3+2x-3
Quadratic expression
Linear expression
Cubic expression
Exponential expression
Considering that it's highest exponent is of 3, the expression 5x³ + 2x - 3 is a cubic expression.
What is the degree of a polynomial?The degree of a polynomial is given by the highest exponent.
The highest exponent of the expression 5x³ + 2x - 3 is a 3, hence it is a cubic expression.
More can be learned about the degree of a polynomial at https://brainly.com/question/24380382
#SPJ1
Answer: C: cubic expression
Step-by-step explanation:
Classify the expression: 5x³ + 2x − 3
we know that
Polynomials can be classified two different ways - by the number of terms and by their degree.
so
a) By the number of terms is a trinomial, because has three terms
b) By their degree The degree of the polynomial is found by looking at the term with the highest exponent on its variable
The highest exponent is 3 so this is a 3rd degree trinomial
therefore
Is a cubic expression
A recipe for peach cobbler requires 10 peaches for each cobbler.
Sarah has 38 peaches. Which expressions shows at most the
number of cobblers Sarah can make?
Answer:
3
Step-by-step explanation:
38 / 10 = 3.8 so that means you only have 3 whole numbers
Gina Wilson unit 4 homework 6
What do you mean????
The zurn family ate at a restaurant that was having 15% discount on that day .Their meal costs 64.75,and they left a 20% tip .What is the total cost of the meal
Answer:
[tex]66.05[/tex]
Step-by-step explanation:
Cost of meal = [tex]64.75[/tex]
Cost of meal after discount of [tex]15\%[/tex]
[tex]64.75-64.75\times 0.15[/tex]
[tex]=64.75(1-0.15)[/tex]
[tex]=55.0375[/tex]
Cost of the meal after tip of [tex]20\%[/tex]
[tex]55.0375\times (1+0.2)[/tex]
[tex]=66.045\approx 66.05[/tex]
The total cost of the meal was [tex]66.05[/tex].