Answers
Part-A:-
(f×g)=[tex]\\ \sf\longmapsto x^2+3x-70(4x-12)[/tex]
[tex]\\ \sf\longmapsto 4x^2+12x-280-12x^2+36x+840[/tex]
[tex]\\ \sf\longmapsto -8x^2+48x+560[/tex]
Now
[tex]\\ \sf\longmapsto (f.g)(3)[/tex]
[tex]\\ \sf\longmapsto -8(3)^2+48(3)+560[/tex]
[tex]\\ \sf\longmapsto -72+144+560[/tex]
[tex]\\ \sf\longmapsto 72+560[/tex]
[tex]\\ \sf\longmapsto 632[/tex]
Part-B:-
[tex]\\ \sf\longmapsto f(3)[/tex]
[tex]\\ \sf\longmapsto (3)^2+3(3)-70[/tex]
[tex]\\ \sf\longmapsto 9+9-70[/tex]
[tex]\\ \sf\longmapsto 18-70[/tex]
[tex]\\ \sf\longmapsto -52[/tex]
Now
[tex]\\ \sf\longmapsto g(f(3))[/tex]
[tex]\\ \sf\longmapsto g(-52)[/tex]
[tex]\\ \sf\longmapsto 4(-52-3)[/tex]
[tex]\\ \sf\longmapsto 4(-55)[/tex]
[tex]\\ \sf\longmapsto -220[/tex]
Part:-C
[tex]\\ \sf\longmapsto g(-2)[/tex]
[tex]\\ \sf\longmapsto 4(-2-3)[/tex]
[tex]\\ \sf\longmapsto 4(-5)[/tex]
[tex]\\ \sf\longmapsto -20[/tex]
Now
[tex]\\ \sf\longmapsto f(g(-2))[/tex]
[tex]\\ \sf\longmapsto f(-20)[/tex]
[tex]\\ \sf\longmapsto (-20)^2+3(-20)-70[/tex]
[tex]\\ \sf\longmapsto 400-60-70[/tex]
[tex]\\ \sf\longmapsto 400-130[/tex]
[tex]\\ \sf\longmapsto 270[/tex]
Part-D:-
g×f=f×g[tex]\\ \sf\longmapsto (g.f)(-2)[/tex]
[tex]\\ \sf\longmapsto -8(-2)^2+48(-2)+560[/tex]
[tex]\\ \sf\longmapsto 32-96+560[/tex]
[tex]\\ \sf\longmapsto -64+560[/tex]
[tex]\\ \sf\longmapsto 496[/tex]
Related Questions
Determine the supplement of each angle measure.
63°
Answers
Answer:
117 is the answer of your questions
Step-by-step explanation:
supplement=180
given angle=63
180-63=117
Plz help!! Math isn’t my thing. I’ll give brainliest.
Answers
Answer:
(2, - 6 )
Step-by-step explanation:
Use the mid point formula and equate to each coordinate of the midpoint
with endpoints (x₁, y₁ ) and (x₂, y₂ ) then
midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
let S = (x, y) , then
[tex]\frac{x+0}{2}[/tex] = 1 ( multiply both sides by 2 )
x = 2
and
[tex]\frac{y+2}{2}[/tex] = - 2 ( multiply both sides by 2 )
y + 2 = - 4 ( subtract 2 from both sides )
y = - 6
Then S (2, - 6 )
Find the distance between the two points rounding to the nearest tenth (if necessary).
(5,-5) and (8,-8)
Answers
Answer:
4.2
Step-by-step explanation:
d=sqrt[(x1-x2)^2+(y1-y2)^2]
d=sqrt[(5-8)^2+(-5+8)^2]
d=sqrt[(-3)^2+(3)^2]
d=sqrt[9+9]
sqrt18=4.24
How many meters does a runner cross in a circular runway with radious of 100 meters [R=3, 14]
Answers
circumference (length of the outside of the circle = diameter * pi = 200 * 3.14
= 628m
step by step
6x+1<9-2x
2x-1 less than or equal to 5x+20
3-(2x-7) less than or equal to 34-6x
Answers
Answer:
6x+1<9-2x
6x+2x<9-1
8x<8
x<1
2x-1 ≤ 5x+20
2x-5x≤20+1
-3x≤21
x≥-7
3-(2x-7) ≤ 34-6x
3-2x+7 ≤ 34-6x
-2x+6x ≤ 34-3-7
4x ≤ 24
x ≤ 6
Sin A 4/5.
Find
COSA + tan A
Answers
Answer:
Step-by-step explanation:
The opposite side (the one not connected to A) = 4
The hypotenuse is 5
The adjacent side needs to be found for the cosine and the tangent.
a^2 + b^2 = c^2
a = opposite side = 4
b = adjacent side = ?
c = hypotenuse = 5
4^2 + x^2 = 5^2
16 + x^2 = 25
x^2 = 25 - 16
x^2 = 9
x = sqrt(9)
x = 3
cos(A) = adjacent / hypotenuse = 3/5
Tan(A) = opposite / adjacent = 4/3
cos(A) + tan(A) = 3/5 + 4/3
cos(A) + tan(A) = 9/15 + 20/15 = 29/15
To find: CosA + TanA
Solution:
16/25 + Cos²A = 1 [Sin²A + Cos²A = 1]
Cos²A = 1 - 16/25
Cos²A = 25 - 16/25
Cos²A = 9/25
CosA = 3/5
We know that TanA = SinA/CosA
TanA = (4/5)/(3/5)
TanA = 4/3
CosA + TanA = 3/5 + 4/3 = 29/15
I wrote a cheque for $10 and he threw my 2 dollar how much do I have left
Answers
Answer:
you have $ 8
Step-by-step explanation:
cheque wrote ,=$10
and he threw =$2
then total $ left will be $8
please mark me brainleast
What is 3(x-6)+12=6(x+1)-3x show your work.
Answers
Answer:
No solution.
Step-by-step explanation:
3(x - 6) + 12 = 6(x + 1) - 3x
3x - 18 + 12 = 6x + 6 - 3x
3x - 6 = 3x +6
-6 = 6
-6 ≠ 6
The length of each side of an equilateral triangle having an area of 9√3 cm² is
Answers
Answer:
6 cm
Step-by-step explanation:
Let each side of the equilateral triangle be a.
Given, area of an equilateral triangle = 9√3 cm2
Area of an equilateral triangle = (√3)/4 × (Side)²
=> (√3)/4 × a² = 9√3
[tex] {a}^{2} = \frac{9 \sqrt{3} }{ \frac{ \sqrt{3} }{4} } = \frac{9 \sqrt{3} }{ \sqrt{3} } \times 4 = 9 \times 4[/tex]
=> a² = 36
[tex] \sqrt{ {a}^{2} } = \sqrt{36} \\ a = (+ - )6[/tex]
∴ Side = 6 cm [taking positive square root because side is always positive]
Jamal buys a strip of 25 postage stamps. The strip of stamps is 21 7/8 inches long. How long is each stamp?
Answers
Rewrite the length as an improper fraction.
21 7/8 = 175/8
Write the quantity of stamps as a fraction: 25/1
Divide length by number of stamps:
175/8 / 25/1
When dividing by a fraction change the sign to multiplication and flip the second fraction over:
175/8 x 1/25.
Now multiply numerators and then denominators:
(175 x1) / (8x 25) = 175/200
Simplify to 7/8
Each stamp is 7/8 inches long
Which fractions are equal to 0.375?
Answers
The fraction that is equal to 0.375 is 3/8.
Hope this helps! :)
Point W is on line segment V X. Given VX = 18 and VW = 14 determine the length W X
Answers
Answer: WX = 4
Concept:
Here, we need to know the idea of segment addition postulate.
The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
Given information
VX = 18
VW = 14
Given expression deducted from the segment addition postulate
WX = VX - VW
Substitute values into the expression
WX = 18 - 14
Simplify by subtraction
WX = 4
Hope this helps!! :)
Please let me know if you have any questions
A number line shows 1 1/5, −2 2/5, and −1 3/5. Which statement is NOT true?
Answers
Answer:
The answer Is A 1 1/5 < -2 2/5
Step-by-step explanation:
It says that this statement is true because 1 1/5 is to the left of -2 2/5 on the number line but it is actually to the right because -2 2/5 is negative while 1 1/5 is positive therefore making it larger and the correct statement would be that 1 1/5 > -2 2/5
another easy question pls answer
Answers
Answer:
22.5 degrees and 67.5 degrees
Step-by-step explanation:
complementary angles add up to 90°
x + 3x = 90°
4x = 90
90/4 = x
x = 22.5
The first angle is 22.5
The second angle is 3 times as much
22.5 x 3 = 67.5
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
suppose a 13 foot ladder is leaning against a building. Reaching to the bottom of a second floor window 12 ft above the ground. How far is the base of the ladder from the building? Round your answer to the nearest 10th
5 ft
4ft
3ft
6ft
Answers
Answer: First Choice. 5ft
Step-by-step explanation:
Here we need to know the idea of the Pythagorean theorem.
Since a building is straight, the base angle is a right angle, thus it would be a right triangle.
Pythagorean Theorem: a² + b² = c²
**NOTE** Please refer to the attachment below for the figure. (I drew it, so if it was not clear and understandable for you, please tell me.)
Solve:
Given information
a = 12 ft
c = 13 ft
b = unknow base length
Given formula for Pythagorean Theorem
a² + b² = c²
Substitute values into the formula
12² + b² = 13²
Simplify exponents
144 + b² = 169
Subtract 144 on both sides
144 + b² - 144= 169 - 144
b² = 25
Square root both sides
√b² = √25
[tex]\boxed{b=5}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Gary rents three DVDs each week at Fantastik Flicks. Write an algebraic expression for Wn, the total number of points earned in the nth week
Answers
For the nth week, the total points earned in the DVD rentals is [tex]p_n + 2[/tex]
Your question is not complete, it seems it is missing the following information below;
DVD rentals: 1 2 3
Total DVD points: 3 5 7
The number of points earned is a function of number of DVD rentals.
For the first DVD, the number of points earned;
[tex]n_1 = p_1 + c\\\\where;\\c \ is \ the \ constant \ point \ earned[/tex]
3 = 1 + c
3- 1 = c
2 = c
For nth week the total point earned is given as;
[tex]n_t_h = p_n + c\\\\n_t_h = p_n + 2[/tex]
Thus, for the nth week, the total points earned in the DVD rentals is [tex]p_n + 2[/tex]
Learn more here: https://brainly.com/question/18077111
Here we have a problem with arithmetic sequences.
After a small online search, I've found that:
Fantastik Flicks gives: 3 points for the first rental, 5 points for the second rental, 7 points for the third rental
And so on.
We will find that the total of points in the n-th week is given by:
Wₙ = 15 + (n - 1)*18
Looking at the number of points given for each rental, we can see that we have an arithmetic sequence with an increase of 2, 3, 5, 7, 9, 11, 13, 15,...
We want to find the total of points earned in each week. For example, for the first week the total of points is: W₁ = (3 + 5 + 7) = 15
For the second week, the total of points is: W₂ = (9 + 11 + 13) = 33
For the third week, the total number of points is: W₃ = (15 + 17 + 19) = 51
Now let's see if Wₙ also is arithmetic. To see this, we need to look at the difference between consecutive elements of Wₙ.
W₂ - W₁ = 33 - 15 = 18
W₃ - W₂ = 51 - 33 = 18
So in both cases we got the same difference, this makes a lot of sense, taking in account that we construct the Wₙ with an arithmetic sequence, so is logical that the sequence {Wₙ} is also arithmetical.
Now that we know this, we can see that in the n-th week, the total of points will be: Wₙ = W₁ + (n - 1)*18Wₙ = 15 + (n - 1)*18
If you want to learn more, you can read:
https://brainly.com/question/19007362
Write an equation in slope-intercept form of a line that passes through the point (-4,9) and has a slope of 1/2.
Answers
Answer:
y = 1/2x + 11
Step-by-step explanation:
y = 1/2x + b
9 = 1/2(-4) + b
9 = -2 + b
b = 11
PLZ HELPP
Q: Nitrates are organic compounds that are a main ingredient in fertilizers. When those fertilizers run off
into streams, the nitrates can have a toxic effect on
fish. An ecologist studying nitrate pollution in two
streams measures nitrate concentrations at 42 places on Stony Brook and 42 places on Mill Brook. The parallel dotplots display the data.
1. Explain what the dot above 12 in the Stony Brook graph represents.
Answers
By looking at the dot graph, we can see that the single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was 12 mg/L
To understand this, first I want to give a brief explanation of how these graphs work.
You know that the ecologist did study the Nitrate pollution at 42 places in two lakes.
Each of these 42 places is represented with a dot in the corresponding graph. Now looking at the graph, the position of the dots represents the nitrate concentration (you can see it in the horizontal axis) on one of these 42 places (42 dots for 42 places).
So, having a single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was of 12 mg/L
If you want to learn more, you can read:
https://brainly.com/question/16354226
3. For the sequence defined by tn= 3n + 8,
find each indicated term.
a) t1
b) t7
c) t14
Answers
Step-by-step explanation:
Hi there!
According to the question;
nth term (tn) = 3n+8
a).
T1 = 3*1+8
= 11
b).
t7 = 3*7+8
= 29
c).
t14 = 3*14+8
= 50
Therefore, t1 = 11, t7 = 29, t14 = 50.
Hope it helps!
Answer:
11, 29, 50
Step-by-step explanation:
To find the appropriate term , substitute the term number into the rule, that is
(a) t₁ = 3(1) + 8 = 3 + 8 = 11
(b) t₇ = 3(7) + 8 = 21 + 8 = 29
(c) t₁₄ = 3(14) + 8 = 42 + 8 = 50
HELP!! Use the properties of addition to simplify this expression. 6-8 +6f-2f
Answers
Answer:
-2 + 4f
Step-by-step explanation:
6 - 8 + 6f - 2f
2(3 - 4 + 3f -f) [Distributive Property]
=> 2(-1 + 3f - f)
=> 2(-1 + 2f)
=> -2 + 4f
Answer:
4f-2
Step-by-step explan:
6-8+6f-2f
6-8+4f
4f-2
What 2 divided by 188
Answers
Answer:
1/94
Step-by-step explanation:
2/188 = 1/94
Answer:
0.01063829787.
Step-by-step explanation:
Caculator.
QUICK PLEASE!!!
Consider f(x) Equals StartFraction 8 (x minus 1) Over x squared + 2 x minus 3 EndFraction.
Which statements describe the existence of vertical asymptotes at x = –3 and x = 1?
Answers
Answer:
A
Step-by-step explanation:
edge 2021
Answer:
It is A
Step-by-step explanation:
I got it right on the test Edge 2022.
helpppppp meeeeeee plssssss!!!!!!!!!!!!!!!1
Answers
Answer:
-12
Ydbzushsbsksjsbsksudjeke
What is (x)
9.4x+17.5
Answers
Answer: x=1.8617
Step-by-step explanation: 9.4x+17.5 9.4x/9.4=17.5/9.4 x=1.8617
The GCF of two numbers is 3.
Their LCM of the two numbers is less than 20.
Which could not be the two numbers?
Answers
Answer:
Step-by-step explanation:
Let say a and b the 2 natural integers with 0 < a< b.
Since a*b=GCF(a,b)*LCM(a,b)
a*b < 3*20=60
[tex]\begin{array}{c|c|c|c|c|c}a&b&a*b&GCF&LCM&GCF*LCM\\---&---&---&---&---&---\\3&6&18&3&6&18\\3&9&27&3&9&27\\3&12&36&3&12&36\\3&15&45&3&15&45\\3&18&54&3&18&54\\6&9&54&3&18&54\\---&---&---&---&---&---\\\end {array}[/tex]
Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.
1.Write the linear equation that models the equation?
2.What is the cost per T-shirt?
3.What is the standard shipping and handling bag?
Answers
Step-by-step explanation:
Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.
Then we have to writer a linear equation, for which I got: y-27/4x+25. We also had to find the cost per t-shirt, for which I got: $31.75. The last part I don't understand, however: fidn the shipping and handling charge.
The second word problem is:
It costs Consolidated Cereals Corporation $1050 to produce 100 boxes of corn flakes and $1250 to produce 500 boxes. I found the cost function: c(x)=1/2x+1000 but don't know how to determine the fixed cost and the variable cost per box (mainly because I have no idea what those are.)
Cost= m x+b
x is the cost per shirt, b is the handling charge
295=40m+b
565=80m+b
subtract the first equation from the second:
370=40x solve for m, the cost of each shirt. Then solve for b, put all that into y= mx+b
One the second question,
Cost= variable cost * n + Fixedcosts or
cost= n*v+F
1250=500v+f
1050=100v+f
subtract the second equation from the first
200=400v solve for v, and it is 1/2 dollar. Solve for f, the fixed cost, and it looks as if it is 1000 dollars.
Jim's cat can run 4 blocks in 15 seconds. Juanita says one of her cats can run 3 blocks in 11
seconds. Who has the fastest cat? How did you decide?
Answers
Answer:
Juanita's cat is faster because it can run more blocks in a second
Step-by-step explanation:
Take the number of blocks and divide by the number of seconds
Jim:
4 blocks/ 15 seconds
.26666.... block per second
Juanita
3 blocks / 11 seconds
.2727...... blocks per second
Juanita's cat is faster because it can run more blocks in a second
collection of even numbers is well defined set or not
Answers
Answer:
set of even counting number is well-defined
Write the Roman Numeral CLXIV in standard form. Roman Numeral Standard Number 1 5 10 50 100 500 1,000 X L C D A) 169 B) 166 C) 164
Answers
Answer:
164
Step-by-step explanation:
in standard form CLXIV IS 164
s= zh - 2zt^3 solve for z
Answers
Hi ;-)
[tex]s=zh-2zt^3\\\\z(h-2t^3)=s \ \ /:(h-2t^3)\\\\z=\dfrac{s}{h-2t^3}[/tex]
Answer:
z = [tex]\frac{s}{h-2t^3}[/tex]
Step-by-step explanation:
Given
s = zh - 2zt³ ← factor out z from each term
s = z(h - 2t³ ) ← divide both sides by h - 2t³
[tex]\frac{s}{h-2t^3}[/tex] = z
