Determine the domain of (f/g)(x) when f(x)=1/x and g(x)= sqrt x+8
(answer choices in photo)
Answers
Answer:
(−8,0)∪(0,∞)
Step-by-step explanation:
This is composition, which I'm going to assume you've covered (sorry if I use any weird terms because of that).
So, anyway, (f/g)(x) is basically [tex]\frac{f(x)}{g(x)}[/tex].
In this case, the answer would be [tex]\frac{\frac{1}{x} }{\sqrt{x+8} }[/tex]
I'm going to assume we're using the real number system.
In that case, x can't be less than 0 (can't even be equal to because divide by zero error
So, [tex]\sqrt{x+8} > 0[/tex]
Solve for x by squaring.
[tex]\sqrt{x+8} > 0[/tex]
[tex]x > -8[/tex]
However, in the numerator, there is 1/x. A number divided by 0 is undefined. So, x has to be greater than -8, and it can't be 0.
So, with that, the interval notation is like this.
(−8,0)∪(0,∞)
Related Questions
White shapes and black shapes are used in a game some are circles some are squares the ratio of white shapes to black shapes is5:11 the ratio of white circles to white squares are 3:7 the ratio of black circles to black squares are 3:8 work out what fraction of all the shapes are circles
Answers
Answer:
[tex]\frac{9}{32}[/tex]
Step-by-step explanation:
Given:
Ratio of white shapes to black shapes is 5:11
Ratio of white circles to white squares is 3:7
Ratio of black circles to black squares is 3:8
To find: fraction of all the shapes that are circles
Solution:
As ratio of white shapes to black shapes is 5:11,
let number of white shapes be 5 k and number of black shapes by 11 k
As ratio of white circles to white squares is 3:7,
Number of white circles = [tex]\frac{3}{10}(5k)=\frac{3}{2}k[/tex]
Number of white squares = [tex]\frac{7}{10}(5k)=\frac{7}{2}k[/tex]
As ratio of black circles to black squares is 3:8,
Number of black circles = [tex]\frac{3}{11} (11k)=3k[/tex]
Number of black squares = [tex]\frac{8}{11}(11k)=8k[/tex]
Total number of circles = [tex]\frac{3}{2}k+3k=\frac{9}{2} k[/tex]
Total number of shapes = [tex]5k+11k=16k[/tex]
Therefore,
Fraction of circles [tex]=\frac{\frac{9}{2} k}{16k} =\frac{9}{32}[/tex]
please explain the steps to me . i’m genuinely confused
Answers
Answer:See below
Step-by-step explanation:
These angles are equal. All that needs to be done is setting the equations as equal and solving for the variables. Once the variables are found, input them back into the equation to find the angles. Once the variables are put into both equations, the result should be equal.
Answer:
13) 94°
14) 105°
Step-by-step explanation:
13) For this equation, the angles are vertical angles. This means that they equal each other. So the equation would be: 14x-4= 12x+10.
Step 1- Subtract 12x to both sides.
14x-4= 12x+10
-12x -12x
Step 2- Add 4 to both sides.
2x-4= 10
+4 +4
Step 3- Divide both sides by 2.
2x= 14
2 2
x= 7
Now that you know the value of the variable, insert this into the equations.
14(7)-4= 98-4= 94°
12(7)+10= 84+10= 94°
14) For this equation, the angles are alternate exterior angles. This also means that they equal each other. So the equation would be: 16x-7= 15x.
Step 1- Add 7 to both sides.
16x-7= 15x
+7 +7
Step 2- Subtract 15x to both sides.
16x= 15x+7
-15x -15x
This leaves you with: x= 7.
Now, insert the value of the variable into the equations.
16(7)-7= 112-7= 105°
15(7)= 105°
Find the value of x: 19x-4=110
Answers
Answer:
x=6
Step-by-step explanation:
step 1;
19x−4+4=110+4
19x=114
-----------------
step 2;
19x /19 = 114 /19
Find the length of AC if AB = 16 and BC = 12.
Answers
AC = 28
Step-by-step explanation:
Give the digits in the ones place and the hundredths place.
16.89
Answers
Ones place=6
Which translation will change figure ABC to figure A′B′C′? (4 points) A coordinate plane is shown. Figure ABC is composed of coordinates A, negative 4 comma negative 1, B, negative 1 comma negative 1, C, and negative 2 comma negative 3. Figure A prime, B prime, and C prime is composed of coordinates A prime, 0 comma 2, B prime, 3 comma 2, C prime, 2 comma 0. a 3 units right and 3 units up b 4 units right and 3 units up c 4 units right and 4 units up d 4 units left and 3 units down
Answers
Answer:
4 units right and 3 units up.
Hope this help o(*￣▽￣*)o
Answer:
4 units right and 3 units up.
got it right on my test, hope it helps
Find the length of the missing side.
Answers
so do 90-45 and you’ll get 45
to check your answer you can do 45+25+20 which gives you 90
solve 8x-7y=18 for y?
Answers
Answer:
y = 8/7x -18/7
Step-by-step explanation:
8x-7y=18
Subtract 8x from each side
8x-8x-7y=-8x+18
-7y = -8x+18
Divide each side by -7
-7y/-7 = ( -8x+18)/-7
y = 8/7x -18/7
to convert 25 minutes to hours, you would use the ratio 1 hour/60 minutes. true or false
Answers
Answer:
true
Step-by-step explanation:
A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I costs $2.40 per gallon, and milk from dairy II costs $0.80 per gallon. At most $144 is available for purchasing milk. Dairy I can supply at most 50 gallons averaging 3.9% butterfat, and dairy II can supply at most 90 gallons averaging 2.9% butterfat. Answer parts a and b. a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat? The company should buy 40 gallons from dairy I and 60 gallons from dairy II. What is the maximum amount of butterfat? 330 gallons (Type an integer or a decimal.) b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce. The excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons. Is there any way all this capacity
Answers
Answer:
a) i The company should buy 40 gallons from dairy I and 60 gallons from dairy
ii) What is the maximum amount of butterfat? The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%
=5.05%
b.The excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons.
Step-by-step explanation:
a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat?
From the question, we are told that:
Milk from dairy I costs $2.40 per gallon, Milk from dairy II costs $0.80 per gallon.
Let's represent:
Number of gallons of Milk from dairy I = x
Number of gallons of Milk from dairy II = y
At most $144 is available for purchasing milk.
$2.40 × x + $0.80 × y = 144
2.40x + 0.80y = 144........ Equation 1
x + y = 100....... Equation 2
x = 100 - y
2.40(100 - y) + 0.80y = 144
240 - 2.4y + 0.80y = 144
-1.60y = 144 - 240
-1.6y = -96
y = -96/-1.6
y = 60
From Equation 2
x + y = 100....... Equation 2
x + 60 = 100
x = 100 - 60
x = 40
Therefore, since number of gallons of Milk from dairy I = x and number of gallons of Milk from dairy II = y
The company should buy 40 gallons from dairy I and 60 gallons from dairy
II. What is the maximum amount of butterfat?
From the question
Dairy I can supply at most 50 gallons averaging 3.9% butterfat,
50 gallons = 3.9% butterfat
40 gallons =
Cross Multiply
= 40 × 3.9/50
= 3.12%
Dairy II can supply at most 90 gallons averaging 2.9% butterfat.
90 gallons of milk = 2.9% butter fat
60 gallons of milk =
Cross Multiply
= 60 × 2.9%/90
=1.9333333333%
≈ 1.93%
The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%
=5.05%
b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce.
Excess capacity of Diary I =
50 gallons - 40 gallons = 10 gallons
Excess capacity of Diary II =
90 gallons - 60 gallons = 30 gallons
Therefore, the excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons.
(6,11) and (5,9) on a line in standard form
Answers
Answer:
2x - y = 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 11) and (x₂, y₂ ) = (5, 9)
m = [tex]\frac{9-11}{5-6}[/tex] = [tex]\frac{-2}{-1}[/tex] = 2 , thus
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (5, 9) , then
9 = 10 + c ⇒ c = 9 - 10 = - 1
y = 2x - 1 ← in slope- intercept form
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
From y = 2x - 1 ( subtract y and add 1 to both sides )
2x - y = 1 ← equation in standard form
Which statement accurately describes how to perform a 90° clockwise rotation of point A (1,4) around the origin?
A)Create a line perpendicular to the y-axis from point A, and locate a point on the perpendicular line that is equidistant to the
B)Create a circle with the origin as its center and a radius of the origin and point A, then locate a point on the circle that is 90
C)Create a line perpendicular to the x-axis from point A, and locate a point on the perpendicular line that is equidistant to the
D)Create a circle with point A as its center and a radius of the origin and point A, then locate a point on the circle that is 90° CO
Answers
Answer:
B)Create a circle with the origin as its center and a radius of the origin and point A, then locate a point on the circle that is 90 clockwise
Step-by-step explanation:
This is because, to locate a point rotated by 90° from point A, we first draw a circle with the origin as its center and a radius of the origin and point A. We then locate a point on the line that is 90° clockwise from point A. For a 90° clockwise rotation, for a given pair of coordinates, (x,y), the resulting pair of coordinates is (y,-x). So, for the coordinates (1,4), the resulting coordinates we are looking for is (4, -1), which is the point rotated 90° clockwise from point A. The point is thus (4,-1).
Answer:
i think the answer is A
Step-by-step explanation:
if this is wrong plz tell me what the correct answer is.
Plsss help I don’t know how to solve it :)
Answers
Answer:
x= 29
Step-by-step explanation:
These angles equal 180° since they are corresponding angles.
So, the equation would be: (2x-10)+(4x+16)= 180.
Step 1- Add common variables.
(2x+4x)+(16-10)= 180
6x+6= 180
Step 2- Subtract 6 to both sides.
6x+6= 180
-6 -6
6x= 174
Step 3- Divide both sides by 6.
6x= 174
6 6
x= 29
Answer:
x=29
Step-by-step explanation: The two angles for are supplementary, so the equation will be equal to 180 degrees. So to find 180 degrees you need to put (2x-10) and (4x+16) on the same side of the equation.
180=(2x-10)+(4x+16) Combine like terms
180=6x+6 Subtract 6 from both sides
174=6x Divide both sides by 6
29=x
Check:
2*29-10
58-10= 48
4*29+16
116+16=132
132+48=180
easy and quick!
is B the answer to this?
Answers
Answer:
Yes
Step-by-step explanation:
You are correct
Please solve the word problem.
Answers
Answer:
Olga
Step-by-step explanation:
To calculate average speed we can compare their hourly rate
Trisha ran 10km in 2.5 hours which is equal to 4km in an hour
Jason ran 7.5km in 2 hours which is equal to 3.75km an hour
Olga ran 9.5km in 2.25 hours which is equal to 4.2 an hour approximately
If F(x) = -3x-2 , what is F(-5)
A) F(-5)=13
B) F(-5)=-17
C) F(-5)=-13
D) F(-5)= 17
Answers
James earned $816 each year. He earned x dollars less per month than Matt, who earned $80 per month.
Equation: 12(80 – x) = 816
x = 12; monthly earnings = $68
Which strategies will verify that the value for x is correct? Check all that apply.
Answers
Answer:multiply $68 and substitute 12
Step-by-step explanation:
Answer:
its a mutiple choice so click mutiply 68$
and substute 12$
Step-by-step explanation:
i just took the quiz :)
have a good day.
Which table represents a linear function?
2
.
y
y
y
1
0
0
0
0
lo
0
1
1
1
1
1
1
1
1
1
3
AN
2
2.
3
N
0
2
5
3
8
3
3
6
3
1
3
7
.
o
Answers
Answer:
Plz I 'm not sure but I think it is table b
Answer: answer D
Step-by-step explanation:
Simplify.
6.5-7.48 -3.4 + 3.8
Answers
Answer:
-0.58
Step-by-step explanation:
6.5 - 7.48 = -0.98-0.98 - 3.4 = -4.38-4.38 + 3.8 = -0.58I hope this helps!
what is the answer too –5(–2) =
Answers
A Negative number times another negative number will always be positive. So -5 x -2 is 10.
↓This is your answer↓
↓Look down↓
Find the slope and write an equation of the line which passes through the points.
a
(5,6) and (3,4)
b
(−3, 9) and (−3, −5)
Answers
Answer:
a. y=x+1
b. x=-3
Step-by-step explanation:
a. slope= (6-4)/(5-3)=1
substitute (5,6) to y=1x+b; b=1
therefore, y=x+1
b. x=-3
PLEASE HELP!
(Snip it bellow)
Using the vertical line test, determine if the graph above shows a relation, a function, both a relation and a function, or neither a relation nor a function.
A.
function only
B.
both a relation and a function
C.
neither a relation nor a function
D.
relation only
Answers
Answer:
I think it is neither
Step-by-step explanation:
I am not sure but I know it isn't a function
Answer: D Because it does not pass the vertical line test
hope this helps :)
2. What is another name for line m?
Answers
Answer:
slope
Step-by-step explanation:
y = mx + c
where m is the slope of the line
Identify the transformation
Answers
Answer:
The Shape went from Quadrant 1 to Quadrant 3.
Step-by-step explanation:
You just have to look at it.
Answer:
Translation
Step-by-step explanation:
Every point on the figure was moved to a new spot on the graph.
I know, because I did this last year. I hope this helps.
(X-5)^2
Solve for x
Answers
Simplify the expression by combining like terms
7y - 6x + 3 – 2x + 8- y
Answers
hope that helps and plss let me know if you have any questions :))
Answer:
[tex]\boxed{ -8x + 6y + 11}[/tex]
Step-by-step explanation:
[tex]7y - 6x + 3 - 2x + 8- y[/tex]
[tex]= 7y + -6x + 3 + -2x + 8 + -y[/tex]
Combine Like Terms:
[tex]= 7y + -6x + 3 + -2x + 8 + -y[/tex]
[tex]= (-6x + -2x) + (7y + -y) + ( 3 + 8)[/tex]
[tex]= -8x + 6y + 11[/tex]
Hope this helped you!
What equation represents the line that passes through the points (0, 2) and (9, 0)?
Please help me !!
Answers
Answer:
Y = -2/9x +2
Reasoning:
This is because you simply find the slope between the 2 points
I need help with this thing
Answers
There’s a few ways to do this. But you essentially want to find the area for each rectangle and add them together.
We can do the two rectangles on the left, bedroom 1 and 3, by doing 3.5 x (4.25+3.75) = 31.5 in^2
Now do bedroom 2, we have to do 7.5 - 3.5 to get the width of the room since it wasn’t given directly. The width is 4 and we have the length of 3.5. Do 4 x 3.5 to get 14 in^2
31.5 + 14 = 45.5 in^2
We’re not done yet because they want it in ft^2 and we’re given 1 inch = 4 feet
Just do 45.5 x 4 to get 182 ft^2
Help, need to finish thisssssssss
Answers
Answer:
c because 1.8×10=18 so c is correct answer
Explanation
Since x = 10 and is gonna be multiply by a decimal. You move the decimal point 1 place to the right. So in this 1.8 would be 18
line i and line h intersect at what point
Answers
Step-by-step explanation: The intersection of two figures can
be defined as the set of points that is contained in both figures.
In this figure, lines h and i intersect at C or we can
say that C is the intersection of lines h and i.
In this figure, C is the intersection of lines h and i
because C is the point contained by both h and i.
