Answer:
9 is in the domain of f(g(x))
Step-by-step explanation:
f(g(x)) = -8*g(x) - 4
= -8*( 7x+3) - 4
= -56x - 24 - 4
= -56x - 28
= -28(2x + 1)
f(g(9)) = -28(2*9 + 1)
= -28*19
= -532
Since 9 can be plugged into the compound function, it is in the domain.
How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) = StartFraction 1 Over x EndFraction?
g(x) is shifted 4 units right and 6 units up from f(x).
g(x) is shifted 4 units right and 6 units down from f(x).
g(x) is shifted 4 units left and 6 units up from f(x).
g(x) is shifted 4 units left and 6 units down from f(x).
Answer:
Option D.
Step-by-step explanation:
The given parent function is
[tex]f(x)=\dfrac{1}{x}[/tex]
The given function is
[tex]g(x)=\dfrac{1}{x+4}-6[/tex]
Using the parent function, the given function can be written as
[tex]g(x)=f(x+4)-6[/tex] ...(1)
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex] .... (2)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
[tex]a=4>0[/tex], it means the graph shifts 4 units left.
[tex]b=-6<0[/tex], it means the graph shifts 6 units down.
So, g(x) is shifted 4 units left and 6 units down from f(x).
Therefore, the correct option is D.
Transformation involves changing the form of a function.
The true option is (d) g(x) is shifted 4 units left and 6 units down from f(x).
The functions are given as:
[tex]g(x)= \frac{1}{x + 4} - 6[/tex]
[tex]f(x)= \frac{1}{x}[/tex]
Start by shifting the function to the left, by 4 units.
This is represented as:
[tex](x,y) \to (x + 4,y)[/tex]
So, we have:
[tex]f'(x)= \frac{1}{x + 4}[/tex]
Next, shift the function down, by 6 units.
This is represented as:
[tex](x,y) \to (x,y - 6)[/tex]
So, we have:
[tex]g(x)= \frac{1}{x + 4} - 6[/tex]
Hence, the true option is (d)
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What is the value of this expression when c= -4 and d = 10?
1/4(c3+d2)
The value of the expression using BODMAS rule is 9.
What is simplification?
To simplify the arithmetic expression involving more operators, we need to use BODMAS rule. The full form of BODMAS is Brackets (Parts of a calculation inside the bracket always come first), Precedence of brackets are : [{(bar)}], Orders (powers and square roots), Division, Multiplication, Addition, Subtraction.
For the given situation,
The values are c = -4, d = 10
The expression is 1/4(c^3+d^2)
Substitute the above values,
⇒ [tex]\frac{1}{4}(c^{3}+d^{2} )[/tex]
⇒ [tex]\frac{1}{4} (-4^{3} +10^{2} )[/tex]
⇒ [tex]\frac{1}{4}(-64+100)[/tex]
⇒ [tex]\frac{1}{4}(36)[/tex]
⇒ [tex]9[/tex]
Hence we can conclude that the value of the expression using BODMAS rule is 9.
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Answer: 9
Step-by-step explanation:no clue how I got it but the test marked it correct
Write a quadratic function with a vertex at (-9,13).
Answer:
y = x² + 18x + 94
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 9, 13) and letting a = 1, then
y = (x + 9)² + 13 ← expand (x + 9)² using FOIL
= x² + 18x + 81 + 13
= x² + 18x + 94
Rewrite y = x2 + x - 20 in factorized form.
Answer:
y = x2 + x - 20 factors into
y = (x +5) * (x -4)
Step-by-step explanation:
Answer:
y = (x + 5)(x - 4)
Step-by-step explanation:
Given
y = x² + x - 20
Consider the factors of the constant term (- 20) which sum to give the coefficient of the x- term (+ 1)
The factors are + 5 and - 4, since
5 × - 4 = - 20 and 5 - 4 = + 1, thus
x² + x - 20 = (x + 5)(x - 4)
Solve for s.
9s = –10 + 10s
s = __
Answer:
10
Step-by-step explanation:
9s=-10+10s
Add 10 on both sides,
9s+10=-10+10s+1
9s+10=10s
Subtract 9s on both sides,
9s+10-9s=10s-9s
10=s
Therefore,s=10
What is the unit rate of 405 miles in 8 hours?
Answer:
50.625 miles per hour (mph)
Step-by-step explanation:
Step 1: Divide
405/8
= 50.625
mark as brainliest please, I need a few more :)
Whats the distance between the points (7,3) and (7,-8)?
Also it deosnt come with a picture..
A. 11
B. 5
C. 10
D. 12
Answer:
A
Step-by-step explanation:
These two coordinates in (x,y) form have the same value for x, so they only differ in the y-value. That means if we subtract the y-values, that’s the vertical distance!
-8 - 3 = -11
(It helps me to think of this as -8 + -3.) They’re 11 units apart: think of it like a absolute value.
So the answer is A. 11
Twice Brittany’s age is less than the age of Abraham Lincoln when he died. President Lincoln was 56 years old at the time of his death. Write an inequality to represent Brittany’s age, b. Brittany’s brother, Nate, is two years younger than Brittany. Write an equation for Nate’s age, n, in terms of Brittany’s age, b. Rewrite the expression from Part B to get the variable b alone on one side of the equation. (This is also called isolating b.) Substitute the value of b from Part C into the inequality you found in Part A. Solve the inequalities from parts A and D for the variables b and n, respectively. Could Brittany be 27 years old and Nate 26? Why or why not?
Answer:
2b < 56
n = b - 2
b = n + 2
n < 27
b < 28
No, because the difference between Brittany and Nate's age is 2years
Step-by-step explanation:
A.)
Twice Brittany’s age is less than the age of Abraham Lincoln when he died. President Lincoln was 56 years old at the time of his death
Let Brittany's age = b
Twice Brittany's age = 2 × b = 2b
Lincoln's age = 56
2b < 56
B.)
Nate's age = n
Nate is 2 years younger than brittany who is aged 'b'
n = b - 2
C.) b = n + 2
D.)
If 2b < 56 and b = n + 2
2(n + 2) < 56
2n + 2 < 56
2n < 56 - 2
2n < 54 ; n < 27
2b < 56
b < 56/2
b < 28
No, because the difference between Brittany and Nate's age is 2years
What are the odds against selecting a red marble
Answer: it’s the first one.
Step-by-step explanation:
Rodney spun this five section spinner 80 times. The results of his spins are listed in the table below.
Identify the sample space using the first letter of the color in alphabetical order
{ , , , , }.
What is the theoretical probability for landing on blue?
%
What is the experimental probability for landing on yellow or white?
%
Answer:
Sample space: {B, G, R, W, Y}
20%
40%
Step-by-step explanation:
Theoretical probability of blue:
1/5 × 100 = 20%
Experimental probability (based on observation) of yellow or white:
(20+12)/80 × 100
32/80 × 100
40%
What is the value of y in this triangle?
980
А.
124°
В. 98°
Ос. 56°
OD. 36°
Answer:
D.36
Step-by-step explanation:
you have to subtract them to get your answer.
Suppose (12, 8) and (4, 6) are the endpoints of a diameter of a circle. Which is an equation of the circle?
Answer:
[tex](x-8)^2 + (y-7)^2 - 17 = 0[/tex]
Step-by-step explanation:
The formula for the equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) is the center and r is the radius of the circle.
To first solve solve this, use the endpoints of the diameter to solve for the center of the circle using the midpoint formula, which is known as:
[tex]\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)\ }{2}[/tex]
The points given are (12,8) and (4,6), so plug in the coordinates into the formula.
Center = (1/2)(12+4),(1/2)(8+6)
= (8,7)
Now, to find the radius, we can use the distance formula and use the center (8,7) and one of the endpoints, (12,8). The distance formula is known as:
[tex]\sqrt{(x_{1} -x_{2})^2 +(y_{1} -y_{2})^2 }[/tex]
Radius = √(x₂- x₁)² + (y₂-y₁)²
= √(12- 8)² + (8-7)²
= √(4² + 1²) = √(16+ 1) = √17
= r² = 17
Now that the radius and the center are known, the equation of the circle can be written as:
[tex](x-8)^2 + (y-7)^2 - 17 = 0[/tex]
What if the value of x?
Answer:
x = 5
Step-by-step explanation:
This is a right triangle with hypotenuse x
We can use the Pythagorean theorem
a^2+b^2 = c^2
3^2+4^2 = x^2
9+16= x^2
25=x^2
Take the square root of each side
sqrt(25) = sqrt(x^2)
5 = x
What is the volume of the rectangular pyramid shown below?
9 in.
8 in.
7
in.
Answer:
Step-by-step explanation:
To calculate the volume of a pyramid with a rectangular base, find the length and width of the base, then multiple those numbers together to determine the area of the base. Next, multiply the area of the base by the height of the pyramid. Take that result and divide it by 3 to calculate the pyramid's volume!
I cant do this until I know What number is what.
Which is length?
Which is height?
and which is width?
Answer:
Step-by-step explanation:b
PLEASE ANSWERRRRR! EASY!!!!!!!!!!!!!
People use water to cook, clean, and drink every day. An estimate of 17.2% of the water used each day is for drinking. If a family uses 68.8 gallons of water a day for drinking, how many gallons do they use every day?
What is the value of x? Leave answer in simplest radical form.
8
60°
Answer:
Your answer is A . 8
Step-by-step explanation:
hope it helps !
Perform the addition of polynomials (middle school math pls help!)
Answer: 1/4a - 1/6b + 1/10c
Hope this helped! Have a great rest of your day :)
Solve by completing the square:
x2 + 3x – 9 = 0
Answer:
Step-by-step explanation:
x = 9/5
The solution of the equation [tex]x^2 + 3x - 9 = 0[/tex] by completing the square would be [tex]x = \pm ( \dfrac{\sqrt{45}}{2} - \dfrac{3}{2} )[/tex].
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that the equation is,
[tex]x^2 + 3x - 9 = 0[/tex]
Now completing the square as
[tex]x^2 + 3x - 9 = 0[/tex]
Add and subtract by 9/4,
[tex]x^2 + 3x + \dfrac{9}{4} - \dfrac{9}{4} - 9 = 0[/tex]
[tex]x^2 + 3x + ( \dfrac{3}{2})^2 - \dfrac{9}{4} - 9 = 0[/tex]
[tex](x + \dfrac{3}{2} )^2 - ( \dfrac{9}{4}+ 9) = 0[/tex]
[tex](x + \dfrac{3}{2} )^2 - ( \dfrac{45}{4}) = 0[/tex]
[tex](x + \dfrac{3}{2} )^2 = ( \dfrac{45}{4})[/tex]
Taking square root on both sides,
[tex](x + \dfrac{3}{2} ) = \pm ( \dfrac{\sqrt{45}}{2})[/tex]
Therefore, the solution of an equation is,
[tex]x = \pm ( \dfrac{\sqrt{45}}{2} - \dfrac{3}{2} )[/tex]
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Help me please help me helpm
Answer:
[tex]g(x) = {(x + 9)}^{2} [/tex]
What is the value of b? -8/5b = 8
Answer:
-0.2 or -2/10
Step-by-step explanation:
hope this helps
The difference when 7 less than a number is subtracted from twice the number is 12. What is the number?
Answer:
5
Step-by-step explanation:
2x - ( x - 7 ) = x + 7
x + 7 = 12
x = 12- 7 = 5
the number is 5
Toilet paper has been hard to find lately. You go to the store and are surprised to find that they have some toilet paper in stock. Now you have a different problem. There are two brands of toilet paper you can choose from, Roll A and Roll B. Which roll should you buy in order to get the most toilet paper? Round your answer to the nearest whole number.
Total Volume = (3.14) (2.5) ^2 (4.5) =
Subtract the middle rim.
V = (3.14 ) ( .75 ) ( 4.5 )
TOTAL VOLUME - MIDDLE PART VOLUME =
Answer:
77
Step-by-step explanation:
Total Volume = 88
Middle Part Volume = 11
Total - Middle = 77
Simplify
[tex](5 \frac{1}{6)6} [/tex]
Answer:
simplify the expression
exact form :
5/36
decimal form :
0.138
The mean of four numbers is 85. The four numbers are 86, 83, 81, and .
a) Write an equation to show this information
b) Solve the equation for .
Answer:
90
Step-by-step explanation:
a)
Since, to find the average of a set of numbers, you need to add them all together and divide by the amount of numbers:
[tex]\dfrac{86+83+81+x}{4}=85[/tex]
b)
Multiply both sides by 4:
[tex]86+83+81+x=340\\x=90[/tex]
Hope this helps!
Solve this brain teaser, please!!!
Answer:
0 in the end they all burn out
Step-by-step explanation:
Answer: 10
Step-by-step explanation:
How many servings of
cups are in 33 cups of ice cream?
Answer:
I am 99% sure its 33 servings
Step-by-step explanation:
because the question says that "how many servings of cups are in 33 cups".
(hopefully im right) and HOPEFULLY THIS HELPS. : )
What is the area of a circle with a radius of 6 inches?
Answer:
113.04 inches
use the formula for the area a circle
[tex]A=\pi a^{2}[/tex]
:
A small pouch contains 8 black marbles,5 white marbles, and 12 red marbles. Find the probability of picking a red then a black marble if you do not replace the first marble.
Answer:
4/25
Step-by-step explanation:
Total amount of marbles: 8 + 5 + 12 = 25
With 25 marbles, the probability of picking a red is: 12/25
After 1 red marble is removed, the probability of picking a black is: 8/24 = 1/3
Then, the probability of picking a red then a black marble if you do not replace the first marble is: 12/25 * 1/3 = 4/25
help me with this please I don't exactly get it
Answer:
P = 40.56 in (ANS)
Step-by-step explanation:
radius = 8/2 = 4 in
semi-circle perimeter = pi * R = 3.14 * 4 = 12.56 in
figure perimeter = 12.56 + 10 + 8 + 10 = 40.56 in (ANS)
What’s the missing leg length
Answer:
15
Step-by-step explanation:
pythag theorum
Answer:
15
Step-by-step explanation:
Pythagorean thm. says a^2+b^2=c^2 where a and b are the legs of the triangle and c is the hypotenuse.
The hypotenuse, c = 17
Leg b =8
a^2=c^2-b^2
a^2=17*17-8*8
a^2=289-64
a^2=225
Take the square root of both sides.
a = 15
