Find (g o f)(-3). *
f(x) = 5x – 4
g(x) = x^2 – 1
O A. 36
O B.-9
O c. 1
O D.-54
Answers
Answer:
(g o f)(-3) = 360 Maybe answer A is a typo
Step-by-step explanation:
(g o f)(-3) = g(f(-3))
f(-3) = 5(-3) - 4
= -15 - 4
= -19
Now find g(-19) = [tex](-19)^{2}[/tex] - 1
= 361 - 1
= 360
Related Questions
The height of a sunflower increases from 160cm to 2 metres in a week. Find the percentage increase in height
Answers
Answer:
25%
Step-by-step explanation:
We are given that
Initial height of sunflower=160 cm
After increasing
Final height of sunflower=2m
We have to find the percentage increase in height.
1 m=100 cm
[tex]2m=2\times 100=200cm[/tex]
Increase in height of sunflower=Final height of sunflower-initial height of sunflower
Increase in height of sunflower=200-160=40cm
Percentage increase=[tex]\frac{Increase\;value}{Initial\;value}\times 100[/tex]
Using the formula
Percentage increase in height=[tex]\frac{40}{160}\times 100[/tex]
Percentage increase in height=25%
the line containing the points (-3,k) and (4,8) is parallel to the line containing the points (5,3) and (1,-6) what is the value of k ?
Answers
Answer:
The value of k is:
[tex]k=-\frac{31}{4}[/tex]
Step-by-step explanation:
Given
The line containing the points (-3,k) and (4,8) is parallel to the line containing the points (5,3) and (1,-6).
To determine
what is the value of k?
To determine the value of k, the first step we need to do is to find the slope of the line containing the points (5,3) and (1,-6) using the formula
[tex]\mathrm{Slope}=m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here:
[tex]\left(x_1,\:y_1\right)=\left(5,\:3\right)[/tex][tex]\left(x_2,\:y_2\right)=\left(1,\:-6\right)[/tex]now substituting (x₁, y₁) = (5, 3) and (x₂, y₂) = (1, -6) in the formula
[tex]m=\frac{-6-3}{1-5}[/tex]
[tex]m=\frac{-9}{-4}[/tex]
Apply the fraction rule: [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]
[tex]m=\frac{9}{4}[/tex]
Thus, we conclude that the slope of the line containing the points (5,3) and (1,-6) will be:
[tex]m=\frac{9}{4}[/tex]
Importing Tip:
We know that the parallel lines have the same slopes, so the slope of the line containing the points (-3,k) and (4,8) will also be 9/4.Thus, using the slope formula for the line containing the points (-3,k) and (4,8).
[tex]\mathrm{Slope}=m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here:
[tex]\left(x_1,\:y_1\right)=\left(-3,\:k\right)[/tex][tex]\left(x_2,\:y_2\right)=\left(4,\:8\right)[/tex]As we know that the parallel lines have the same slopes.
Thus, the second step we need to do is to substitute m = 9/4 in the slope formula
[tex]\frac{9}{4}=\frac{y_2-y_1}{x_2-x_1}[/tex]
now substituting (x₁, y₁) = (-3, k) and (x₂, y₂) = (4, 8) in the formula
[tex]\:\:\:\frac{9}{4}=\:\frac{8-k}{4-\left(-3\right)}[/tex]
switch sides
[tex]\frac{8-k}{4-\left(-3\right)}=\frac{9}{4}[/tex]
Multiply both sides by 7
[tex]\frac{7\left(8-k\right)}{4-\left(-3\right)}=\frac{9\cdot \:7}{4}[/tex]
Simplify
[tex]8-k=\frac{63}{4}[/tex]
Subtract 8 from both sides
[tex]8-k-8=\frac{63}{4}-8[/tex]
Simplify
[tex]-k=\frac{31}{4}[/tex]
Divide both sides by -1
[tex]\frac{-k}{-1}=\frac{\frac{31}{4}}{-1}[/tex]
Simplify
[tex]k=-\frac{31}{4}[/tex]
Therefore, the value of k is:
[tex]k=-\frac{31}{4}[/tex]
VERIFICATION:
As the value of k = -31/4.
So the first line will contain the points:
(-3, -31/4)(4, 8)Finding the slope between (-3, -31/4) and (4, 8) using the slope formula
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here:
[tex]\left(x_1,\:y_1\right)=\left(-3,\:-\frac{31}{4}\right)[/tex][tex]\left(x_2,\:y_2\right)=\left(4,\:8\right)[/tex]so substituting (x₁, y₁) = (-3, -31/4) and (x₂, y₂) = (4, 8) in the formula
[tex]m=\frac{8-\left(-\frac{31}{4}\right)}{4-\left(-3\right)}[/tex]
Apply rule: [tex]-\left(-a\right)=a[/tex]
[tex]m=\frac{8+\frac{31}{4}}{4+3}[/tex]
Add the numbers: [tex]4+3=7[/tex]
[tex]m=\frac{8+\frac{31}{4}}{7}[/tex]
[tex]m=\frac{\frac{63}{4}}{7}[/tex] ∵ [tex]8+\frac{31}{4}=\frac{63}{4}[/tex]
Apply fraction rule: [tex]\frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}[/tex]
[tex]m=\frac{63}{4\cdot \:7}[/tex]
[tex]m=\frac{63}{28}[/tex]
Cancel the common factor: 7
[tex]m=\frac{9}{4}[/tex]
So, the slope of the line containing the points (-3,k) and (4,8) is m = 9/4. It means both lines have the same slopes. Hence, they are parallel.
Therefore, we conclude that the value of k = -31/4 is true.
18 -(-6)-9
Please answer now
Answers
Answer:
99
Step-by-step explanation:
-x-=+
18x6=108
108-6=99
Find the measure of segment WC if YW = 4.4 in., and YC = 7 in.
Answers
Answer:
WC = 2.6in
Step-by-step explanation:
If YW = 4.4 in, and YC = 7 in.
And YW + WC = YC.
WC = YC - YW
WC = 7in - 4.4in
WC = 2.6in
6th grade math help me pleaseee
Answers
Answer:
Its the second one, the one on the bottom left.
Step-by-step explanation:
You just need to find the answer to one of the coordinates, then it will be easier.
when x = is 0, then y =8 and when x = 1, then y = 7.5
in a group of 20 people 7 own a dog 4 own a cat 12 do not own a dog or a cat complete the venn diagram to show this diagram
Answers
4
Both (centre)
3
Cat (B)
1
None (outside)
12
what is the area of the triangle with base 5.8cm and height 4.6cm?
Answers
Explanation:
Area of triangle = base * height ÷ 2
5.8 * 4.6 ÷ 2
= 26.68 ÷ 2
= 13.34 cm²
what sign can i use for division
Answers
y= -2x-2, -2x+4y=12 please help i'll give 100 points.
solve it in substitution
Answers
Answer:
x = -2 and y= 2
Step-by-step explanation:
y=-2x-2 and -2x+4y=12
Substitute: -2x+4(-2x-2)=12
Distribute: -2x-8x-8=12
Combine like terms: -10x-8=12
Simplify: -10x=20
20/-10 = -2
Use that value to solve for y
y=-2x-2
Substitute x value: y=-2(-2)-2
Simplify: y=2
Please help with this!! Explain your answer I will mark brainliest!!!
Answers
Answer:
asa
Step-by-step explanation:
it says that angle 6 and angle 9 are congruent and side om is congruent to side em and then the angle 7 and 8 are congruent because they are vertical angles and vertical angles are equal to each other. so it gives you angle side angle which is why the correct answer is asa
In a supermarket, bottles of lemonade are on a buy one get one half price offer.
The normal price of lemonade is 68p.
How much would it cost to get exactly three bottles of lemonade using this offer?
Answers
Answer:
68/2 = 34
68+34+68=170
||| answ=170p |||Step-by-step explanation:
.Write the Pythagorean triplets whose smallest number is 8.
Answers
Answer:
8, 15, 17
Step-by-step explanation:
8^2 + 15^2 = 64 + 225 = 289 = 17^2
I need help with this please
Answers
9514 1404 393
Answer:
8. (d) 19
9. 94°
Step-by-step explanation:
8. The similarity statement tells you corresponding sides are proportional.
CB/CA = FE/FD
g/9 = 95/45
g = 9(95/45) = 9(19/9)
g = 19
__
9. The similarity statement tells you ∠J ≅ ∠M.
∠M = 180° -∠P -∠K = 180° -32° -54° = 94°
∠J = 94°
BRIDGE CONSTRUCTION
Your team is working for the transport authorities of a certain city. You have to
analyze two construction projects for a new bridge over the river in said city. The
spacing between the bridge supports needs to be 1050 feet and the height at the center of the arch
350 cakes. One company has suggested that the structure be in the shape of a parabola; other
company suggests a semi-ellipse. The engineering team will determine the relative resistances of
the two projects; your job is to find if there is any difference in the widths of the
channel.
An empty oil tanker needs a clearance of 280 feet to pass under the bridge.
You must find the width of the channel in each of the proposals.
1. To determine the equation of a parabola with these characteristics, first place the
parabola on coordinate axes in a convenient position and draw it.
2. What is the equation of the parabola? (If you use decimal point in the equation, approximate to
six decimal places. If you use fractions, your answer will be more exact.)
3. If the shape of the satellite dish supports, how wide will the channel it will pass through
the oil tanker?
4. To determine the equation of a semi-ellipse with these characteristics, place the
semi-ellipse on coordinate axes in a convenient position and draw it.
5. What is the equation of the ellipse? How wide will the canal need to be for the
Petroleum ship?
6. Now that you know which of the two alternatives provides the widest channel, consider other
factors. His department is also in charge of verifying the depth of the channel, the
amount of river traffic and other details. For example, if there was a flood in the river and
the water level will rise 10 feet, how would free space be affected? Take a decision
about which project you think would be best as far as your department is concerned and
explain your decision.
Answers
Answer:
I'll answer your questions if you answer my questions.
Step-by-step explanation:
Will give brainliest please help
Answers
Answer: straight line is the answer hope this helps!!
Step-by-step explanation:
If the quadratic equation x2 + 6x - 7 = 0 is rewritten in the form (x - p)2 = q , what is the value of q?
Answers
Answer:
q=16
Step-by-step explanation:
here ya goooooooojgjfjdhdf
2^3 . 2^4
i need help with this
Answers
2^4 makes 16
Does this help... Or are you looking for 2^3 times 2^4 makes?
Answer:
So, what I think you might have meant is 2^3 x 2^4, so I'll solve that
2^3 = 8
2^4 = 16
16 x 8 = 128
Step-by-step explanation:
Hope this helps! Have a great day
PLEASE HELP ASAP I AM GIVING 40 POINTS! just answer like this:
a:
b:
c:
Answers
Answer:
Step-by-step explanation:
(a) f(-4) = 7 - 8(-4) = 7 + 32 = 39
(b) f(0) = 7 - 8(0) = 7 - 0 = 7
(c) f(3) = 7 - 8(3) = 7 - 24 = 17
You deposit $300 in an account that account and $54 simple interest in for years what is the annual interest rate
Answers
Answer:
principal=$300
time=1 year
simple interest=$54
rate=?
Step-by-step explanation:
rate=(simple interest×100)/(principal×time)=(54×100)(300×1)=5400/300=54/3=18% is rate
Find the value of x and y.
Answers
Step-by-step explanation:
x= 180-109 = 71°
y= 360-81-71-100= 108
Calculate the distance between points (1,10) and (5,15)
Only an ap student can solve it
Answers
Answer:
[tex]\displaystyle d = \sqrt{41}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (1, 10)
Point (5, 15)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(5-1)^2+(15-10)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{(4)^2+(5)^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{16+25}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{41}[/tex]Manny makes dinner using 1 box of pasta and 1jar of sauce .If pasta is sold in oackage if 6 boxes and sauce is sold in in packages of 3 jjara what is the least number of dinners that manny can make without any supplies leftover
Answers
Answer:
The least number of dinners that manny can make without any supplies leftover is 6 dinners
Step-by-step explanation:
Dinner = 1 box of pasta + 1jar of sauce
pasta is sold in package of 6 boxes
sauce is sold in in packages of 3
jars
what is the least number of dinners that manny can make without any supplies leftover?
Find the lowest common multiple of 6 boxes and 3 jars
6 boxes = 6, 12, 18, 24, 30, 36, 42,48
3 jars = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
The lowest common multiple of 6 boxes and 3 jars = 6
The least number of dinners that manny can make without any supplies leftover is 6 dinners
Using:
Pasta = 6 dinners / 6 boxes
= 1 package
Pasta = 1 package
Sauce = 6 dinners / 3 jars
= 2 package
Sauce = 2 package
49/5
into mixed fraction
will mark you brainliest and will give you 14 points(this is for my younger sister's exams so please give her an answer) please tell her how to do it with an explanation
Answers
Tell Her/Ask Her This:
You Can Use Long Division.
How Many Time Does 49 Go In To 5?
A little help here?????????????????????????????? (please help I really need it)
Answers
Answer: 2 1/4 inches.
Step-by-step explanation:
3 * 3/4 = 9/4 = 2 1/4
hope it helps pls mark me brainliest
Answer:
2 1/4 inches
Step-by-step explanation:
[tex]x^{2} -7x+8\leq 5[/tex]
Answers
Answer:
x^2-7x+3=0
Step-by-step explanation:
A meal has 756 calories in 6 servings. Find the unit rate.
Answers
Answer:
126 calories per servings
Step-by-step explanation:
756/6=126
URGENT!!!
Which of the following equations could represent a town with an initial population of 875 people and an annual growth rate of approximately 2%?
A. y = 875 ⋅ x1.02
B. y = 875 (1.02)x
C. y = 875(2)x
D. y = 875 • 1.02x
Answers
Answer:
B
Step-by-step explanation:
1+0.02=1.02
875(1.02)^x
The equation is y = 875 (1.02)ˣ represents a town with an initial population of 875 people and an annual growth rate of approximately 2%. which is the correct answer would be an option (B).
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
Initial population = 875 people
Growth rate = 2%
The growth rate is the base of the exponent instead of the initial population.
As per the given situation, the required equation would be as:
y = 875 (1 + 2%)ˣ
y = 875 (1 + 0.02)ˣ
y = 875 (1.02)ˣ
In this equation, x represents the number of years after the initial population of 875 people.
Hence, the correct answer would be option (B).
Learn more about exponential function here:
brainly.com/question/11487261
#SPJ2
Mark point C at (3, 3), point D at (-5, 3), point E at (-5, 1), and point F at (-1, -2). How many steps do you need to take to walk the path
Answers
Answer:the answer is 23 steps
Answer:
23 steps
Step-by-step explanation:
If A(2, 2) and B(14, 10) find the point that will divide AB into a ratio of 3:1 starting from point A.
Answers
Answer:
Point [tex](11,8)[/tex] divides [tex]AB[/tex] into a ratio of [tex]3:1[/tex] .
Step-by-step explanation:
Given: Points are [tex]A(2,2)\,,\,B(14,10)[/tex]
To find: point that will divide [tex]AB[/tex] into a ratio of [tex]3:1[/tex] starting from point [tex]A[/tex].
Solution:
If the point [tex](x,y)[/tex] divides the line joining points [tex]A(u,v)[/tex] and [tex]B(p,q)[/tex] in ratio [tex]m:n[/tex] then
[tex](x,y)=(\frac{mp+nu}{m+n},\frac{mq+nv}{m+n} )[/tex]
Put [tex](u,v)=(2,2)\,,\,(p,q)=(14,10)\,,\,m:n=3:1[/tex]
Therefore,
[tex](x,y)=(\frac{3(14)+1(2)}{3+1} ,\frac{3(10)+1(2)}{3+1} )=(\frac{42+2}{4},\frac{30+2}{4})=(\frac{44}{4},\frac{32}{4})=(11,8)[/tex]
Therefore,
point [tex](11,8)[/tex] divides [tex]AB[/tex] into a ratio of [tex]3:1[/tex] .
what is the solution to 3(x-5)=-x+7
Answers
Answer:
11/2
Step-by-step explanation:
3(x-5)=-x+7
3x-15=-x+7
3x-(-x)-15=7
3x+x=7+15
4x=22
x=22/4
simplify
x=11/2
Answer:
11/2
Step-by-step explanation: