Given,
f(x)=4x^2-9
g(x)=2x+3
1.
(f+g)(x)=f(x) + g(x)
=4x^2-9+2x+3
=4x^2+2x-6
2.
(f-g)(x)=f(x)-g(x)
4x^2-9-2x-3
=4x^2-2x-12
when x=3, then,
f(3)=4×(3)^2-9=27
g(3)=2×3+3=9
5.
f(g(3))=f(9)=4×(9)^2-9
=312
5.
g(f(3))=g(27)=2×27+3=57
Answer:
listen to romap they are correct
Step-by-step explanation:
Solve |x| > 3
{-3, 3}
{x|x < -3 ∪ x > 3}
{x|x < -3 ∩ x > 3}
Answer: Second Option
{x| x< -3 ∪ x > 3}
Step-by-step explanation:
To solve the inequality
[tex]| x | >3[/tex] there are two cases:
Case 1. [tex]x>0[/tex]
[tex]x > 3[/tex]
Case2. [tex]x<0[/tex]
[tex]-x > 3[/tex]
[tex]x < -3[/tex]
The final solution is the union of the solution of each case
This is:
[tex]x < -3[/tex] or [tex]x > 3[/tex]
{x| x< -3 ∪ x > 3}
A student reads 65 pages per hour.
3 hours equals 195.
5 hours equals 325
9 hours equals 585
10 hours equals 650
To find this I multiplied the hours by 65 pages.
Hope this helps :)
Find the product , select the simplest form
Answer:
the answer is 3
Step-by-step explanation:
21/8 simplify is 3
Yeah, The answer is 3
What is the equation of the line that passes through the point (3, 0) and is perpendicular to the line 2x – y = 5?
Answer:
[tex]\large\boxed{y=-\dfrac{1}{2}x+\dfrac{3}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ 2x-y=5.\\\\\text{Convert to the slope-intercept form y = mx + b:}\\\\2x-y=5\qquad\text{subtract 2x from both sides}\\\\-y=-2x+5\qquad\text{change the signs}\\\\y=2x-5\to m_1=2\\\\\text{Therefore}\ m_2=-\dfrac{1}{2}.[/tex]
[tex]\text{The equation of the searched line:}\ y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through }(3,\ 0).\\\\\text{Put the coordinates of the point to the equation.}\ x=3,\ y=0:\\\\0=-\dfrac{1}{2}(3)+b\\\\0=-\dfrac{3}{2}+b\qquad\text{add}\ \dfrac{3}{2} \text{to both sides}\\\\b=\dfrac{3}{2}[/tex]
What statement helps answer this question
I would say option A best proves it is a parallelogram.
I need all the help I can get from you all
If 9(x - 9) = -11, then x = ?
-90
-2/9
70/9
108
Answer:
70/9
Step-by-step explanation:
multiply the parenthesis
add the constant together then divide
Answer:
70 / 9
Step-by-step explanation:
9(X - 9) = -11
9X - 81 = -11
9X = -11 + 81
9X = 70
X = 70 / 9
Suppose f varies directly as g, and f varies inversely as h. Find g when f = 12 and h = 10, if g = 198 when h = –11 and f = –6. Round your answer to the nearest hundredth, if necessary.
Question 5 options:
–360
–40
40
360
Answer:
360
Step-by-step explanation:
f varies directly as g
f = kg where k is the constant of variation
f varies inversely as h
f = kg/h
We know g = 198 when h = –11 and f = –6. Substituting in
-6 = k*198/(-11)
-6 =k*(-18)
Dividing each side by -18
-6/-18 = k*-18/-18
1/3 =k
Our equation is
f = 1/3 g/h
Letting f = 12 and h = 10
12 = 1/3 g/10
Multiply each side by 10
12*10 =1/3 g/10*10
120 = 1/3 g
Multiply each side by 3
120*3 =1/3 g *3
360 =g
What is the midpoint of the segment shown below A. 10,-4 B 5,-4 C.5,-2 D.10-2
Answer:
C. (5, -2)
Step-by-step explanation:
Midpoint:
x = (x1+x2)/2 = (16-6)/2 = 10/2 = 5
y = (y1+y2)/2 = (5 - 9)/2 = -4/2 = -2
Answer
Midpoint (5, -2)
The midpoint of the graphed line segment is (5, -2)
The correct option is C) (5, -2).
What is the midpoint of the line segment?The midpoint formula is expressed as;
Midpoint = ( ( x₁+x₂ )/2, ( y₁+y₂ )/2 )
From the graph:
Point 1 (16, 5)
x₁ = 16
y₁ = 5
Point 2 (-6,-9)
x₂ = -6
y₂ = -9
Plug the coordinates into the above formula and solve for the midpoint:
Midpoint = ( ( x₁+x₂ )/2, ( y₁+y₂ )/2 )
Midpoint = ( ( 16+(-6) )/2, ( 5+(-9) )/2 )
Midpoint = ( ( 16 - 6 )/2, ( 5 - 9 )/2 )
Midpoint = ( 10/2, -4/2 )
Midpoint = ( 5, -2 )
Therefore, the midpoint is (5, -2).
Option C) (5, -2) is the correct answer.
Learn more about the midpoint formula here: https://brainly.com/question/28577846
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convert 0.5 to a percent value
0.5 as a percent is 50%
0.5 to a percent value is 50%
What is the value of x if line a is parallel to line b and is cut by a transversal?
Answer:
x=35
Step-by-step explanation:
The angles are alternate interior angles. Alternate interior angles are equal if the lines are parallel.
3x+16 = 5x-54
Subtract 3x from each side
3x -3x+16 = 5x-3x-54
16 = 2x-54
Add 54 to each side
16+54 = 2x-54+54
70 = 2x
Divide each side by 2
70/2 = 2x/2
35 =x
Can someone help me with this
Answer:
Yes
Step-by-step explanation:
Try the points and see:
(x, y) = (-1, 3) . . . . x + y = -1 + 3 = 2 . . . . yes
(x, y) = (3, -1) . . . . x + y = 3 + (-1) = 2 . . . yes
The remaining points lie on the line connecting these points, so they, too will be on the graph of that line.
Helppp simplify (3^-2)^4
For this case we must simplify the following expression:
[tex](3 ^ {-2}) ^ 4[/tex]
By definition of power properties we have to:[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
So, rewriting the expression we have:
[tex](\frac {1} {3 ^ 2}) ^ 4 = \frac {1 ^ 4} {(3 ^ 2) ^ 4} = \frac {1} {(3 ^ 2) ^ 4}[/tex]
By definition of power properties we have:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So:
[tex]\frac {1} {(3 ^ 2) ^ 4} = \frac {1} {3 ^ 8}[/tex]
Answer:
Option D
Write a second inequality with the same meaning. −18 ≤ b
ANSWER
[tex]b \geqslant - 18[/tex]
EXPLANATION
The given inequality is:
[tex] - 18 \leqslant b[/tex]
We can rewrite this as:
[tex]b \geqslant - 18[/tex]
The above two inequalities have the same meaning.
Reading from right to left, the first inequality says, "b is greater than or equal to negative 18."
Reading from left to right, the second inequality says, "b is greater than or equal to negative 18."
Therefore the two inequalities have the same meaning.
Step-by-step Answer:
Many inequalities are possible, for example:
Keeping the less than or equal to sign, we could write
-18-b<=0
or, switching sides,
b>= -18 (just by switching sides)
b+18>=0 (by transposing -18 to the left)
Then again, we can multiply both sides by -1, but we need to change the direction of the inequality:
18>=-b
or equivalently, by transposing 18 to the other side
0>=-b-18
and similarly
b+18>=0 (we already had this above)
Guess time to stop!
What is the positive square root of 0.81
Enter your answer in the box.
[tex] \sqrt{0.81} = (0.9)[/tex]
Answer:
the correct answer is .9
.9 times .9 is .81
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Consider the graph of Miriam's bike ride to answer the
questions,
How many hours did Miriam stop to rest?
How many hours did it take Miriam to bike the initial 8
miles?
Answer:
1) 45 minutes or 0.75 hours
2) 45 minutes or 0.75 hours
Step-by-step explanation:
We are given the graph that shows Miriam's bike ride.
The x-axis represents the time (in minutes) and the y-axis represents the distance traveled in miles.
1) How many hours did Miriam stop to rest?
The graphs stays the same from 45 minutes to 90 minutes, where he took the rest. No distance covered in that time.
Rest time = 90 minutes - 45 minutes = 45 minutes
He took rest for 45 minutes.
In hours, it is 45/60 = 0.75 hours
2) How many hours did it take Miriam to bike the initial 8 miles.
Look at the graph, the graph reached 8 miles when the time was 45 minutes.
It took 45 minutest to reach 8 miles initially.
In hours, it is 45/60 = 0.75 hours
PLEASE HELP ASAP!!!
The number of bacteria in a petri dish increases according to the function
y = 1000(3.7^x), where x is the number of hours. How many bacteria will
there be after 3 hours?
OA) 3700
OB) 35,650
OC) 50,653
OD) 63,505
Answer:
C) 50,653
Step-by-step explanation:
y = 1000(3.7)^x
After 3 hours x=3
y = 1000(3.7)^3
y = 1000(50.653)
y =50653
Answer: OPTION C
Step-by-step explanation:
You know that in the function [tex]y = 1000(3.7^x)[/tex] the variable "y" is the number of bacterias in a petri dish and the variable "x" is the number of hours.
Then, to answer the question "How many bacteria will there be after 3 hours?", you need to substitute [tex]x=3[/tex] into the function.
Therefore, the number of baterias after 3 hours will be:
[tex]y = 1000(3.7^3)[/tex]
[tex]y = 1000(50.653)[/tex]
[tex]y = 50,653[/tex]
This matches with the option C.
Cari owns a horse farm and a horse trailer that can transport up to 8,000 pounds of livestock and tack. She travels with 5 horses whose combined weight is 6,240 pounds. Let t represent the average weight of tack per horse. Which of the following inequalities could be used to determine the weight of tack Cari can allow for each horse?
Answer:
5(1248 lb/horse + t lb) ≤ 8000 lb
Step-by-step explanation:
One way to do this is to find the average weight of the 5 horses:
It is:
6,240 lb
---------------- = 1248 lb/horse
5 horses
and to this, for each horse, we must add t lbs tack.
Thus, 5(1248 lb/horse + t lb) ≤ 8000 lb
would be an appropriate inequality.
Please note that your question mentions "the following inequalities;" that means you are expected to share them! Please do so next time. Thanks.
what is the volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches please help
Answer:30
Step-by-step explanation: V=1/3 Bh, 9x10=90 divide that by 3 for 30
The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches is 30 cubics in.
What is a triangular pyramid?Take a triangle. This is a base.
Now take 3 triangles such that each of them is connected to the one-one side of the first triangle and when they're taken together, they form a closed object, called a triangular pyramid.
The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches
The volume of a triangular pyramid
V = 1/3 x B x h,
V = 1/3 x 9 x 10
V = 3 x 10
V = 30
Hence, the volume will be 30 cubics in.
Learn more about triangular pyramids here:
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Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola.
y = x 2 + 1
Answer:
The equation [tex]y=x^2+1[/tex] will be a parabola when it is graphed
Answer:
It's a parabola
Step-by-step explanation:
The equation seems to a parabolic function. The parabola is defined as:
[tex]y=Ax^2+b[/tex]
where b is a displacement, we can notice that in our case A=1 and b=1
so it is a parabola with a vertical displacement of one unit.
the hypotenuse of a right triangle is 20 centimeters. one of the legs is 4 cm longer than the other leg. find the area of the triangle.
Answer:
hypotenuse = 20
leg = x + 4
other leg = x
From the Pythagorean Theorem we know that
20^2 = (x + 4)^2 + x^2
400 = x^2 + 8x + 16 + x^2
2 x^2 + 8x -384 = 0
Solving the quadratic equation we get
x = 12 and x = -16
x = 12 and so the lengths of the 2 legs are:
12 and 16
Right Triangle Area = (leg1 * leg2) / 2
Right Triangle Area = (12 * 16) / 2
Area = 192 / 2
Area = 96 square centimeters
Step-by-step explanation:
To find the area of the triangle, we used the Pythagorean theorem to solve for the legs, obtaining lengths of 16 cm and 12 cm. The area is then calculated using the formula for the area of a right triangle (1/2 * base * height), resulting in an area of 96 cm².
We are given a right triangle with a hypotenuse of 20 cm and two legs where one leg (let's call it a) is 4 cm longer than the other leg (let's call it b). Using the Pythagorean theorem, we can express the relationship between the legs and the hypotenuse: a² + b² = 20². We know that a = b + 4, so if we substitute a into the equation, we get:
(b + 4)² + b² = 400
b² + 8b + 16 + b2 = 400
2b² + 8b - 384 = 0
Dividing everything by 2, we get:
b² + 4b - 192 = 0
Using the quadratic formula or factoring, we find that b = 12 (b can't be negative). Consequently, a = 16. The area of the triangle is given by 1/2 * base * height, which is:
Area = 1/2 * a * b
Area = 1/2 * 16 * 12
Area = 1/2 * 192
Area = 96 cm²
In a jar, the numbers of white, black and red marbles are in ratio of 5:11:8. If the total number of marbles is 144, then how many red marbles are there?
Answer:48 red marbles
Step-by-step explanation:
144÷24= 6
6*5= 30 white
6*11= 66 black
6*8= 48 red
Answer: The number of red marbles in the jar is 48.
Step-by-step explanation: Given that the number of white, black and red marbles in a jar are in the ratio 5 : 11 : 18. And the total number of marbles in the jar is 144.
We are to find the number of red marbles in the jar.
Let, 5x, 11x and 8x be the number of white, black and red marbles in the jar.
Then, according to the given information, we have
[tex]5x+11x+8x=144\\\\\Rightarrow 24x=144\\\\\Rightarrow x=6.[/tex]
Therefore, the number of red marbles will be
[tex]8x=8\times6=48.[/tex]
Thus, there are 48 red marbles in the jar.
Which linear function represents the line given by the point-slope equation y + 7 = –(x + 6)?
After distributing the -1, you will find
y+7= -x-6
Finally, isolate y to find your answer in the linear form of
y= -x-13
helped needed asap 20 points!! and brainliest
ANSWER
1. No solution
2. 4 and 6
3. 81
EXPLANATION
1. The given quadratic equation is
[tex] {x}^{2} + 1 = 0[/tex]
This implies that:
[tex] {x}^{2} = - 1[/tex]
There is no real number whose square is negative one.
This quadratic equation has no solution.
2. The given quadratic equation is
[tex] {x}^{2} - 10x + 24 = 0[/tex]
We split the middle term with -6,-4 because their product is 24 and their sum is -10
[tex]{x}^{2} - 6x - 4x+ 24 = 0[/tex]
We factor by grouping
[tex]{x}(x - 6)- 4(x - 6)= 0[/tex]
[tex](x - 6)(x - 4)= 0[/tex]
We have x=4 and x=6.
3. The given quadratic equation is
[tex] {x}^{2} - 18x = 7[/tex]
We the square of half the coefficient of x to both sides of the equation.
[tex]( - \frac{18}{2} )^{2} = ( { - 9)}^{2} = 81[/tex]
The correct choice is C.
What is the solution to the equation x + 5.7 = 6.1?
x = 0.4
x = 0.6
x = 1.4
x = 11.8
The solution is X=0.4
The answer is the first one
Quinn and Derek bought office supplies together. Quinn bought 10 packs of paper and 12 boxes of pens for a total cost of $33. Derek bought 15 packs of paper and 7 boxes of pens for a total of $27.50. How much was one pack of paper? How much was one box of pens?
Answer:
The cost of one pack of paper was $0.90 and the cost of one box of pens was $2.00
Step-by-step explanation:
Let
x----> the cost of one pack of paper
y---> the cost of one box of pens
we know that
10x+12y=33 ----> equation A
15x+7y=27.50 ---> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (0.9,2)
see the attached figure
Therefore
The cost of one pack of paper was $0.90
The cost of one box of pens was $2.00
Answer:
pens = $2
paper = .9
Step-by-step explanation:
p = price of a pack of paper
n = price of a box of pens
10p + 12n = 33
15p + 7n = 27.50
Multiply the first equation by 3
3(10p + 12n )= 33*3
30p +36n = 99
Multiply the second equation by -2
-2(15p + 7n) = 27.50*-2
-30p -14n = -55
Add the 2 modified equations together
30p +36n = 99
-30p -14n = -55
--------------------
22n = 44
Divide each side by 22
22n/22 = 44/22
n =2
Each box of pens is $2
Now we can find the price of the paper
10p + 12n = 33
10p +12(2) = 33
10p +24 =33
Subtract 24 from each side
10p+24-24=33-24
10p = 9
Divide by 10
10p/10 =9/10
p = .9
If the ratio of a circle’s sector to its total area is 1/3, what is the measure of its sector’s arc?
1/3 = 33%
33% * 390 = 118.8
Your answer 118.8 degrees
Answer: 120 degrees
Step-by-step explanation:
Just did it.
Blake and Ned work for home remodeling business they are putting the final touches on a home they renovated. working alone Blake and paint one room in nine hours, Ned can paint the same room in six hours. how long will it take them to paint the room if they work together
Answer:
3.6 hours
Step-by-step explanation:
Blake can do work in hours = 9
Blake can do a part of work in 1 hour = [tex]\frac{1}{9}[/tex]
Ned can paint the same room in six hours.
Ned can do a part of work in 1 hour = [tex]\frac{1}{6}[/tex]
They can do a part of work together in 1 hour = [tex]\frac{1}{9}+\frac{1}{6}[/tex]
= [tex]\frac{5}{18}[/tex]
Now they can do [tex]\frac{5}{18}[/tex] part of work in hour = 1
So, they can do whole work in hours = [tex]\frac{1}{\frac{5}{18}}[/tex]
= [tex]3.6[/tex]
Hence it will take 3.6 hours to paint the room if they work together.
the sum of two numbers is 52 and the difference is 14. What are the numbers?
14+38=52
52-38= 14
Answer: 38 and 14.
I think this is the answer.
33 and 19
33+19=52
33-19=14
Lisa has an online jewelry shop where she sells earrings and necklaces. SHe sells earrings for $30 and necklaces for $40. It takes half an hour to make a pair of earrings and 1 hour to make a necklace. Lisa only has 10 hours a week to make jewelry. In addition, she only has enough materials to make 15 total jewelry items per week. She makes a profit of $15 on each pair of earrings and $20 on each necklace. How many pairs of earrings and necklaces should Lisa make each week in order to maximize her profit, assuming she sells all her jewelry?
Answer:
10 pairs of earrings and 5 necklaces (the maximum profit will be $250)
Step-by-step explanation:
Let x be the number of earrings and y be the number of necklaces Lisa makes.
1. Lisa only has enough materials to make 15 total jewelry items per week, then
[tex]x+y\le 15.[/tex]
2. It takes half an hour to make a pair of earrings, so it takes her [tex]\dfrac{1}{2}x[/tex] hours to make x earrings. It takes her 1 hour to make a necklace, so it takes her y hours to make y necklaces. Lisa only has 10 hours a week to make jewelry, thus
[tex]\dfrac{x}{2}+y\le 10[/tex]
3. Lisa makes a profit of $15 on each pair of earrings and $20 on each necklace. In total her profit is
[tex]P=15x+20y.[/tex]
You have to find the maximum value of the function [tex]P=15x+20y[/tex] with respect to inequalities
[tex]x+y\le 15\\ \\\dfrac{x}{2}+y\le 10[/tex]
Draw the solution set on the coordinate plane (see attached diagram). The maximum value of the efunction P is at point (10,5) and is
[tex]P=15\cdot 10+20\cdot 5=150+100=\$250[/tex]
If f(x)=3x-1+4 and g(x)=4x-7 what is (f-g)(x)
Answer: [tex](f-g)(x)=-x+10[/tex]
Step-by-step explanation:
Given the function f(x):
[tex]f(x)=3x-1+4[/tex]
And given the function g(x):
[tex]g(x)=4x-7[/tex]
You must subtract both functions is order to find [tex](f-g)(x)[/tex].
You need to remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]
Then:
[tex](f-g)(x)=3x-1+4-(4x-7)[/tex]
Now, you must distribute the negative sign:
[tex](f-g)(x)=3x-1+4-4x+7[/tex]
And finally, add the like terms. Then you get that [tex](f-g)(x)[/tex] is:
[tex](f-g)(x)=-x+10[/tex]