daniel sits closer to mia
Given f(x)=4x^2-9 and g(x)=2x+3 find each value
Given f(x)=4x^2-9 and g(x)=2x+3 find each value
FIND EACH VALUE
1. (f+g)(x)
2. (f-g)(x)
3. (fg)(x)
4. f(g(3))
5. g(f(3))
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:
Is 6.610 a rational number
Answer:
yes
Step-by-step explanation:
A rational number can be expressed in the form
[tex]\frac{a}{b}[/tex], where a, b are integers
6.610 can be expressed as
6 [tex]\frac{610}{1000}[/tex] = [tex]\frac{6610}{1000}[/tex] ← a rational number
6.610 is a rational number.
What is a rational number ?A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Or in other words, any number that can be written as a ratio (or fraction) of two integers is a rational number.
Thus 6.610 is definitely a rational number as it satisfies the definition of a rational number.
We have, 6.610 = 661/100 which is expressed as the ratio of two integers.
Therefore, 6.610 is a rational number.
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(3Q) Find the amplitude and period of f(t)= -tan.0t
Answer:
It has no amplitud and the period is 5pi/2
Step-by-step explanation:
Given a function of the following type:
f(t) = AtanB(t + C)
The function has no amplitud, given that it doesn't have maximum or minimum value. And the period is given by: pi/B
In this case, we have f(t)= -tan0.4t. Then:
B = 0.4
⇒ Period = pi/0.4 = 5pi/2
Therefore, the answer is: It has no amplitud and the period is 5pi/2
In Circle C below, is measured in radians
Which Expression can be used to find the area of the shaded sector
Answer:
Step-by-step explanation:
D is correct. The area of the whole circle is (360/360)πr^2. That of the unshaded sector is (theta/360)πr^2.
The expression which can be used to find the area of the shaded sector when the angle is measured in radians, is (θ/2)×r². Option A is correct.
What is the area of a circular sector?Area of the circular sector is the space occupied by it. The area of the circular sector is the half of the product of angle of the sector and the radius of the circle.
When the angle is measured in degree it be given as,
Area of sector=(θπr²)/360
Here, r is the radius of the circle and θ is the angle of the sector.
When the angle is measured in radian it be given as,
Area of sector=(θ/2)×r²
Here, r is the radius of the circle and θ is the angle of the sector.
Hence, the expression which can be used to find the area of the shaded sector when the angle is measured in radians, is (θ/2)×r². Option A is correct.
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How do you solve #5? Show your work...
Answer: 162
Step-by-step explanation:
3(2+4(5+2^3)]
3(2+4(5+8)
3(2+(4)(13))
3(2+52)
(3)(54)
=162
what is (-5/8)×(2/3)
[tex]\frac{-5}{8} * \frac{2}{3}[/tex]
Multiply the top with the top and the bottom with the bottom:
[tex]\frac{(-5)*2}{8*3}[/tex]
[tex]\frac{-10}{24}[/tex]
Then you can simplify:
[tex]\frac{-5}{12}[/tex]
Hope this helped!
Answer:
-5/12
Step-by-step explanation:
Multiply the top of both fractions and the bottom of both fractions, -5*2=-10,8*3=24
so -10/24 can be simplified to -5/12
student tickets for the football game cost $12 each and adult ticket cost $20 $1,720 was collected for the 100 tickets sold at the last game which system of equations can be used to solve for the numbers of each kind of ticket sold
Answer:
B) x+y=120; 12x+20y=1720
Step-by-step explanation:
If variables are defined as ...
x = number of student tickets sold
y = number of adult tickets sold
then the problem statement can be modeled by ...
x + y = 120 . . . . . . the total number of tickets sold is 120
12x + 20y = 1720 . . . . . the total collected from ticket sales was $1720
___
Total revenue is the sum of the revenues from sales of each ticket type. The revenue from a given ticket type is the product of that ticket price and the number sold.
Please help!!!
A shooting star forms a right triangle with the Earth and the Sun, as shown below: A right triangle is shown with the vertices labeled Earth, Sun, and Shooting Star. The angle formed by the Sun is labeled x deg A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star. (10 points)
Answer:
- The scientist can use these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.
- The scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for the distance between the Sun and the shooting star (which would be the hypotenuse of the righ triangle).
Step-by-step explanation:
You can observe in the figure attached that "AC" is the distance between the Sun and the shooting star.
Knowing the distance between the Earth and the Sun "y" and the angle x°, the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.
This is:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
In this case:
[tex]\alpha=x\°\\\\adjacent=BC=y\\\\hypotenuse=AC[/tex]
Therefore, the scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] , and solve for the distance between the Sun and the shooting star "AC":
[tex]cos(x\°)=\frac{y}{AC}[/tex]
[tex]AC=\frac{y}{cos(x\°)}[/tex]
The scientist can use the two measurements by applying the knowledge of trigonometry, particularly Cosine (cos).
[tex]cos x = \frac{adjacent (y)}{hypotenuse (AC)}[/tex]
AC = [tex]\frac{y}{cos x}[/tex]
where the distance between the shooting star and the sun is AC
and the distance between Earth and Sun is BC = y
the right angled triangle has three sides
Hypotenuse (hyp): longest sideOpposite (opp): the side facing the angle of interestAdjacent (adj): the remaining sidecosine (θ) = [tex]\frac{adj}{hyp}[/tex]
sine (θ) = [tex]\frac{opp}{hyp}[/tex]
tan (θ) = [tex]\frac{opp}{adj}[/tex]
where (θ) = angle of interest
What is trigonometry?This is the branch of mathematics that is concerned with angles of triangles as well as the length of it's sides.
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Input in standard form the equation of the given line.
The line through (0, -3) and (3, 0)
Answer:
x-y-3=0
Step-by-step explanation:
The slope of the line that passes through the points (0,-3) and (3,0) is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\ \\=\dfrac{0-(-3)}{3-0}\\ \\=\dfrac{3}{3}\\ \\=1[/tex]
The equation of the line is
[tex]y=m(x-x_1)+y_1\\ \\y=1\cdot (x-0)+(-3)\\ \\y=x-3\\ \\x-y-3=0[/tex]
A gym membership at Gym A costs $12 every month plus a one-time membership fee of $36, and a gym membership at Gym B costs $20 every month plus a one-time $20 membership fee. After about how many months will the gym memberships cost the same amount?
After 2 months, the gym memberships at Gym A and Gym B will cost the same amount, based on the membership cost equations of each gym.
Explanation:We need to determine after how many months the total costs of gym memberships at Gym A and Gym B will be the same. The cost of a gym membership at Gym A is described by the equation C = 12m + 36, where C represents the total cost and m represents the number of months. For Gym B, the cost is given by the equation C = 20m + 20.
To find the number of months where the costs are equal, we set the two equations equal to each other:
12m + 36 = 20m + 20
Subtracting 12m from both sides gives us:
36 = 8m + 20
Subtracting 20 from both sides gives us:
16 = 8m
Dividing both sides by 8 gives us:
m = 2
Therefore, after 2 months, the total costs for gym memberships at both Gym A and Gym B will be the same.
What is the standard form of this complex number (1+2i)/(1+I)
Answer: 3/2 + i/2
Step-by-step explanation: Simplify and write eht enaswer in standard form, a + bi.
Hope this helps! :) ~Zane
Camryn practices the trumpet every 11^\text{th}11
th
11, start superscript, t, h, end superscript day and the flute every 3^\text{rd}3
rd
3, start superscript, r, d, end superscript day.
Camryn practiced both the trumpet and the flute today.
How many days until Camryn practices the trumpet and flute again in the same day?
Answer:
10
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
I hope this helped it took so long to find.
Ginny gets out of school at
3:50 P.M. After her lunch period
ends, she spends 45 minutes
in math class, 60 minutes in
advanced creative writing, and
40 minutes in industrial arts. At
what time does her lunch period
end? Work backward to solve,
and then check your answer.
Thank you this is right
Find the value of each variable. Line / is a tangent
Answer:
a° = 118° , b° = 49° , c° = 144° , d° = 98°
Step-by-step explanation:
* Lets study the figure and take the information to solve the question
- There is a circle
- There is an inscribed triangle in the circle
- Each vertex of the triangle is an inscribed angle in the circle
- Each vertex subtended by an arc
- The measure of any inscribed angle is half the measure of its
subtended arc
* Now lets solve the question
- The sum of the measures of the interior angles of a triangle is 180°
∵ The triangle has angle of measure 59° and another angle of
measure 72°
∴ The measure of the third angle = 180° - (59° + 72°) = 49°
∵ b° is the measure of the third angle in the triangle
∴ b° = 49°
- The arc of measure a° is intercept the angle of measure 59°
∵ The measure of the angle is half the measure of the arc
∴ 1/2 a° = 59° ⇒ multiply both sides by 2
∴ a° = 118°
- The arc of measure c° is intercept the angle of measure 72°
∵ The measure of the angle is half the measure of the arc
∴ 1/2 c° = 72° ⇒ multiply both sides by 2
∴ c° = 144°
- The arc of measure d° is intercept the angle of measure 49°
∵ The measure of the angle is half the measure of the arc
∴ 1/2 d° = 49° ⇒ multiply both sides by 2
∴ d° = 98°
The triangles are similar. What is the value of x? 48,52,20 / 12,x,5
Answer:
The value is 13
Step-by-step explanation:
You can notice that 48/12 is 4 and 20/5 is 4. Therefore, divide 52 by 4
The value of x is 13.
Similar triangle :Two triangles are said to be similar when corresponding angles of both triangles are congruent and ratio of corresponding sides are in equal proportion.
Given that, sides of one triangle are 48, 52, and 20.
Sides of other triangle are, 12, x and 5
Since, corresponding sides are in the proportion.
[tex]\frac{48}{12}=\frac{20}{5}=\frac{52}{x} \\\\x=\frac{52}{4}=13[/tex]
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Write an equation of the line that is perpendicular to the line y =
1
3
x + 6 that passes through the point (2,-3).
Answer:
y = -3x + 3Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]
[tex]\text{We have the equation}\ y=\dfrac{1}{3}x+6\to m_1=\dfrac{1}{3}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{3}}=-3.\\\\\text{We have the equation}\ y=-3x+b.\\\\\text{Put the coordinates of the point}\ (2,\ -3):\\\\-3=-3(2)+b\\-3=-6+b\qquad\text{add 6 to both sides}\\3=b\to b=3\\\\\text{Finally:}\\\\y=-3x+3[/tex]
In the inequality, y > -5x + 1 What is the slope? ___________ What is the y-intercept? _____________ Is it a dashed or solid line? ______________ Do you shade above or below? _____________ Graph the inequality. Make sure to include the shading to indicate the solutions to the inequality.
Answer:
See below
Step-by-step explanation:
The given inequality is
[tex]y\:>\:-5x+1[/tex]
The corresponding linear equation is y=-5x+1.
This line is of the form y=mx+b
The slope of this line is m=-5 and b=1 is the y-intercept.
Since the inequality sign is '>' the boundary line is a dashed line.
We test the origin to see if the inequality will be satisfied.
[tex]0\:>\:-5(0)+1[/tex]
[tex]0\:>\:1[/tex]
This statement is false so we shade above the dashed line.
The graph of the inequality is shown in the attachment.
identify the correct trigonometry formula do you use to solve for the given angle
The correct trigonometry formula [tex]tan^{-1}[/tex] (71°) . Therefore , [tex]tan^{-1}[/tex](71°) is correct .
The correct trigonometry formula to use to solve for the given angle is the tangent formula.
This is because you are given the side opposite to the angle (48) and the side adjacent to the angle (34), and you need to solve for the angle itself (71°).
The tangent formula is:
tan(angle) = opposite / adjacent
In this case, you would have:
[tex]tan^-1[/tex] = 48 / 34
[tex]tan^-1[/tex] = 0. 708333 degree
[tex]tan^-1[/tex] = 0.71 degree
[tex]tan^-1[/tex] (0.71)
= 35.3112 degree.
Therefore, the correct answer is tan(71°).
PLEASE HELP!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
B is the only graph that starts at both intervals of 2, which would be 2, and -2
What is the value, after 7 years, of a 2014 Ford Mustang that originally cost $25,000.00 if the depreciate at a rate of 8% per year? Round your answer to the nearest dollar.
Answer:
$14,236
Step-by-step explanation:
25000 x 0.92 = 23000 = 1 Year
23000 x 0.92 = 21600 = 2 Years
19872
18282.24
16819.66
15474.09
14236 = 7 Years
The answer would be 14000
what is 75% of 180?
Hello There!
75% of 180 is 135.
Converting Percent To Decimal.
p = 75%/100 = 0.75
Y = 0.75 * 180
Y = 135
Make a proportion ([tex]\frac{part}{whole}[/tex])...
The whole is 180 but we need to find the part which would be x
75 % is also a part of 100% (the whole)
The proportion would look like this...
[tex]\frac{x}{180} =\frac{75}{100}[/tex]
Now cross multiply to solve for x. The work for this is below.
100x = 13500
To isolate x divide 100 to both sides
100x/100 = 13500/100
x = 135
So...
135 is 75% of 180
Hope this helped!
A survey was conducted among 100 students of age groups 7−12 years and 13−18 years to find their favorite book genre. The students had to select any one genre out of detective, adventure, and biography. Out of the 50 students in the age group 7−12 years who participated in the survey, 23 liked adventure or biography. The total number of students of both age groups who liked detective books was 28.
Using a two-way table, compute the total number of students in the age group 13−18 years who liked adventure or biography.
23
27
49
51
The correct answer is C. 49.
Remember that there are 100 students divided into 7-12 and 13-18 age group. So there should be 50 for each. The table should go like this:
7-12 age group
23 adventure or biography
27 - detective
so you just have to subtract 50 from 23, which makes it 27. The remaining belongs to the 13-18 age group.
13-18 age group
1 - detective
49 - adventure or biography.
Answer:
49
Step-by-step explanation:
Total number of students =100
Out of the 50 students in the age group 7−12 years who participated in the survey, 23 liked adventure or biography.
So, 50-23 = 27 Out of the 50 students in the age group 7−12 years who participated in the survey liked detective
Now we are given that The total number of students of both age groups who liked detective books was 28.
No. of students of age group 13-17 who like detective books = Students of both age group like detective - No.of students of 7−12 years who liked detective = 28-27 =1
So ,The total number of students of both age groups who liked adventure or biography was 100-28 = 72
Since the age group 7−12 years who participated in the survey, 23 liked adventure or biography.
So, the age group 13-17 years who participated in the survey liked adventure or biography = 72-23=49
Age group Adventure or Biography Detective Total
7-12 23 27 50
13-18 49 1 50
Total 72 28 100
So, Option C is true.
The total number of students in the age group 13−18 years who liked adventure or biography. is 49
An animal shelter spends $3.50 per day to care for each bird and $4.00 per day to care for each cat. Makayla noticed that the shelter spent $161.50 caring for birds and cats on Wednesday. Makayla found a record showing that there were a total of 43 birds and cats on Wednesday. How many birds were at the shelter on Wednesday?
By setting up and solving a system of equations based on the total costs and number of animals, it is determined that there were 21 birds at the shelter on Wednesday.
To solve how many birds were at the shelter on Wednesday, we can set up a system of equations based on the costs and the total number of animals. Let the number of birds be b and the number of cats be c.
The total cost for birds and cats is $161.50, and there are 43 birds and cats together. This gives us two equations:
$3.50b + $4.00c = $161.50
b + c = 43
We can solve this system of equations by first expressing c in terms of b from the second equation:
c = 43 - b
Now we can substitute c into the first equation:
$3.50b + $4.00(43 - b) = $161.50
After simplifying:
$3.50b + $172.00 - $4.00b = $161.50
Combining like terms:
-$0.50b = -$10.50
Dividing by -0.50:
b = 21
So, there were 21 birds at the shelter on Wednesday.
What is the product of (4x)(-3x^8)(-7x^3)
(4x)(-3x^8)(-7x^3)
4 (-3)(-7) = 84
x(-x^8)(-x^3) = x^(1 + 8 + 3) = x^12
Answer: 84x^12
Answer:
C
Step-by-step explanation:
Please help will give brainliest
Answer:
19°
Step-by-step explanation:
In triangle ABC, ∠A=120°, a=8, b=3.
Use the sin rule:
[tex]\dfrac{a}{\sin \angle A}=\dfrac{b}{\sin \angle B}\\ \\\dfrac{8}{\sin 120^{\circ}}=\dfrac{3}{\sin \angle B}\\ \\8\sin \angle B=3\sin 120^{\circ}\\ \\8\sin \angle B=3\cdot \dfrac{\sqrt{3}}{2}\\ \\\sin \angle B=\dfrac{3\sqrt{3}}{16}\approx 0.3248\\ \\\angle B\approx 18.95^{\circ}\approx 19^{\circ}[/tex]
which sampling method is the most popular way to sample?
A. simple random sampling
B. systematic random sampling
C. stratified random sampling
D. Cluster sampling
Answer:
simple random sampling
Step-by-step explanation:
Simple random sampling is the fundamental sampling technique in which a group of subjects is selected for a particular study from a larger group, the population. Each subject is chosen purely by chance and each individual of the larger group (population) has an equal probability of being included in our sample.
Ann took a taxi home from the airport. The taxi fare was
$
2
.
1
0
$2.10dollar sign, 2, point, 10 per mile, and she gave the driver a tip of
$
5
$5dollar sign, 5. Ann paid a total of
$
4
9
.
1
0
$49.10dollar sign, 49, point, 10.
Write an equation to determine the distance in miles
(
x
)
(x)left parenthesis, x, right parenthesis between the airport and Ann's home.
Find the distance between the airport and Ann's home.
miles
Answer:
20.9, rounded answer: 21 miles
Step-by-step explanation:
x= distance between the airport and Ann's home.
since Ann is paying $2.10 per mile let 2.10 be the coefficient
our equation:
5 is our constant since that's how much Ann trips the driver
since the total is equal to 49.10, that's what our equation will be equal to
2.10x+5=49.10
sub "5"
2.10x+5-5=49.10-5
2.10x=44
divide both sides by "2.10"
2.10/2.10x=44/2.10
x=20.9
we can round 20.9 to 21
I don’t know what the answer is I wish I could help
What is 1/8 divided by 6
Answer:
0.75 I think
Step-by-step explanation:
For v=-3i-7j, find the unit vector in the same direction of v, and write your answer as a linear combination of the standard unit vectors I and j.
Answer:
[tex]-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}[/tex]
Step-by-step explanation:
The given vector is:
v = -3i-7j
The unit vector is found by dividing the vector by its magnitude
[tex]Unit\ vector\ of\ v=\frac{v}{||v||}[/tex]
We have to find the magnitude first
So,
[tex]||v||=\sqrt{(-3)^{2} +(-7)^{2}}\\ =\sqrt{9+49}\\ =\sqrt{58}[/tex]
The unit vector is:
[tex]\frac{-3i-7j}{\sqrt{58} } \\=>-\frac{3i}{\sqrt{58}}-\frac{7j}{\sqrt{58}}\\=>(-\frac{3i}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}}) -(\frac{7j}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}})\\=>-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}[/tex]
Therefor the last option is the correct answer ..
The unit vector in the same direction as v = -3i-7j is found by calculating the magnitude of v and then dividing v by its magnitude. The result is (-3/sqrt(58))i + (-7/sqrt(58))j.
Explanation:Finding the Unit VectorTo find the unit vector in the same direction as v = -3i-7j, we first need to calculate the magnitude (length) of v. The magnitude of a vector can be calculated using the Pythagorean theorem as applied to vector components, so for our vector v, the magnitude |v| would be sqrt((-3)^2 + (-7)^2) = sqrt(9 + 49) = sqrt(58).
Next, we find the unit vector by dividing the vector by its magnitude. This gives us: (-3/sqrt(58))i + (-7/sqrt(58))j.
Therefore, the unit vector in the same direction as v is (-3/sqrt(58))i + (-7/sqrt(58))j.
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Two people are looking up at the Eiffel Tower. The people are 8 miles apart, and the Eiffel Tower is between them. The angle of elevation to the top of the Eiffel Tower is 12° for one person and 3° for the other. What is the approximate height of the Eiffel Tower?
the approximate height
Answer:b
Step-by-step explanation: I took the test