please help me asap!!
8. Compare the function g(x) modeled by the graph and the functionf (x) =
21x + 2) + 3.
True or false. Explain.
a) f(x) has a greater y intercept
b) g(1) > f(-1)
c) f(x) increases at a faster rate than g(x)over interval [0, 3).
Answers
Answer:
a) false
b) true
c) true
Step-by-step explanation:
Part (a)The y-intercept of a function is the point when x = 0
⇒ f(0) = 2|0 + 2| + 3
= 2|2| + 3
= 4 + 3
= 7
From inspection of the graph, the y-intercept of g(x) is (0, 7)
Therefore, the y-intercepts of f(x) and g(x) are the same.
"f(x) has a greater y-intercept" → false
Part (b)
From inspection of the graph, g(1) = 6
⇒ f(-1) = 2|-1 + 2| + 3
= 2|1| + 3
= 2 + 3
= 5
Therefore, g(1) > f(-1) → true
Part (c)The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
From inspection of the graph:
g(0) = 7
g(3) = 4
[tex]\textsf{average rate of change of g(x)} \implies \dfrac{4-7}{3-0}=-1[/tex]
f(0) = 7 (from part (a))
f(3) = 2|3 + 2| + 3
= 2|5| + 3
= 10 + 3
= 13
[tex]\textsf{average rate of change of f(x)} \implies \dfrac{13-7}{3-0}=2[/tex]
Function g(x) decreases over [0, 3] at the rate of -1
Function f(x) increases over [0, 3] at the rate of 2
Therefore, "f(x) increases at a faster rate than g(x) over interval [0, 3]" is true
**Please see the attached graph for reference**
The interval [0, 3] is shaded in grey
f(x) is shown in red
The added 2 points are f(-1) and g(1)
Related Questions
Write an equation of the line that passes through the point (6,-9) with the given slope m= 3
Answers
Answer:
y=3x-27
Step-by-step explanation:
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Write an equation of the line passing through (6, -9) and has a slope of -3.
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
First, we need to write the equation in point-slope form:-
[tex]\hookrightarrow\sf{y-y_1=m(x-x_1)}[/tex]
Replace y₁ with -9, m with 3, and x₁ with 6:-[tex]\hookrightarrow\sf{y-(-9)=3(x-6)}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\hookrightarrow\sf{y+9=3(x-6)}[/tex]
[tex]\bigstar[/tex] On further simplification,
[tex]\hookrightarrow\sf{y+9=3x-18}[/tex]
[tex]\star[/tex] Subtract 9 from both sides, which results in:-
[tex]\hookrightarrow\sf{y=3x-27}[/tex]
So we conclude that Option B is correct.
Good luck with your studies.
[tex]\rule{300}{1}[/tex]
A concession stand owner bought some bottles of water for $0.75 each and began selling them for $1.25 each. When he made back all the money he spent, he still had 20 bottles left to sell. What equation can be written to determine the amount of money the owner spent?
Answers
helppppppppppppppppppppppppppppppppppppppppppppp
Answers
So you divide the price by the unit (kg)
And find the better buy by looking at which price is cheapest.
Your answer is the 7.48 kg bag
Hope this helps and good luck!!
Give the value of x .
A. 60 degrees
B. 180 degrees
C. 120 degrees
D. 45 degrees
Answers
Answer:
x=120°
Step-by-step explanation:
sum of all angles in a triangle is equal to 180
let the unknown angle be
[tex] \alpha [/tex]
[tex]60 + 60 + \alpha = 180 \\ \alpha = 180 - 60 - 60 \\ \alpha = 60 \\ [/tex]
[tex] \alpha + x = 180 \\ x = 180 - \alpha \\ x = 180 - 60 \\ x = 120[/tex]
A pet store has three fish tanks each holding a different volume of water in a different number of fish to a holds 4 L and five fish tank bee holds 100 L in office tanks tea or 108 L and 23 fish. order the tanks by volume per fish from least to greatest.
Answers
Annie bought a package of 100 pens for $167.00. How much did each
pen cost?
Answers
Answer:
Step-by-step explanation:
167.00 / 100 = $1.67
How do I solve 15=3p/6 ?
Answers
=> 15 x 6 = 3p
=> 90 = 3p
=> p =90/3
=> p = 30
Hope this helps you :)
Help asap pleaseeeeeeeee
Answers
Answer:
√5
Step-by-step explanation:
Given:
[tex]\displaystyle \large{5\div \sqrt{5}}[/tex]
Which can be rewritten as:
[tex]\displaystyle \large{\dfrac{5}{\sqrt{5}}}[/tex]
To find:
Simplified formTo find simplified form of the expression, keep in mind that surds should not remain as denominators. Therefore, what we have to do is to multiply both numerator & denominator by the surd itself so the denominator will be cleared as rational number.
[tex]\displaystyle \large{\dfrac{5\cdot \sqrt{5}}{\sqrt{5}\cdot \sqrt{5}}}[/tex]
We know that if same surds multiply each other, the surd will be canceled and remains only the insides. To express it in math, it can be as:
[tex]\displaystyle \large{\sqrt{a}\cdot \sqrt{a} = \left(\sqrt{a}\right )^2 =a}[/tex]
Therefore:
[tex]\displaystyle \large{\dfrac{5\sqrt{5}}{5}}[/tex]
Cancel 5:
[tex]\displaystyle \large{\sqrt{5}}[/tex]
Henceforth, the simplified expression is √5
PJ is Decorating Pupcakes for Rocky´s Birthday Party. Her Color Scheme is Black, Purple, and Green. She Will use This Spinner to Determine the Color of Spinkles on each Pupcake. if Pj decorates 60 pupcakes, about how many can she expect to be purple?
A:15 pupcakes
B: 30 pupcakes
C: 20 pupcakes
D: 25 pupcakes
Answers
If there is no picture for the spinner and we assume that it is completely fair, meaning that you have an equal chance of landing on any spot: You will expect to get a certain color every 3 spins because you have 3 different colors. In this case the answer would be 20 pupcakes.
The population of a city decreases by 4.4% per year. If this year's population is
135,000, what will next year's population be, to the nearest individual?
Answers
Answer:
129060
Step-by-step explanation:
135 000 - .044(135000) = 129 060
Rearrange the formula below to make x the subject. α y+1=2x - 10/x+1
Answers
Answer:
cross multiplication
x
what plus what equals -20
Answers
Here you are adding but since you have a negative 40, adding 20 (which is less than 40) the sum is still negative.
Find x. Round to the nearest tenth:
Answers
Find the vertex, axis of symmetry, and y-intercept of the quadratic function.
Answers
Answer:
See below ~
Step-by-step explanation:
Details of Graph
Maximum = 2Domain : all real numbersRange : y ≤ 23
6
2
•
3
12
O y=2x+:
O y = 3x
O y =3x+3
O y=x+3
Which equation represents the relationship shown in the table? •
Answers
Answer:
y = 3x + 3
Step-by-step explanation:
when you check, only that equation delivers the correct x and y pairs.
x = 0, => y = 3×0 + 3 = 3
x = 1, y = 3×1 + 3 = 3+3 = 6
x = 2, y = 3×2 + 3 = 6 + 3 = 9
x = 3, y = 3×3 + 3 = 9 + 3 = 12
it all fits.
Use the t-distribution to find a confidence interval for a difference in means μ1−μ2 given the relevant sample results. Give the best estimate for μ1−μ2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed.
A 99% confidence interval for μ1−μ2 using the sample results x⎯⎯1=535, s1=103, n1=380 and x⎯⎯2=465, s2=86, n2=200
Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places.
Answers
The best estimate and the degree of freedom when the t-distribution is used to find a confidence interval is 7 and 56 respectively.
How to illustrate the research?The best estimate from the information given in the research will be:
= X1 - X2
= 53.5 - 46.5
= 7
The degree of freedom will be:
= 38 + 20 - 2
= 56
Learn more about research on:
https://brainly.com/question/968894
#SPJ1
There is 1 2 of a pizza left for 4 friends to share. What fraction of a pizza will each friend get to eat? please help.
Answers
Answer:
1/3
Step-by-step explanation:
Number of pizza=12
Number of students=4
Therefore,4/12=4/4
=1/3
Solve the problem.
A recipe calls for 6 ounces of unsweetened chocolate for 20 brownies. How much of unsweetened chocolate is needed to make 30 brownies?
Answers
solve 4(x-7)+10=-10 A=X-2 B=X=4 C=X=1 D=X=3
Answers
Answer:
A. -2
Step-by-step explanation:
Find an equation of a line through (2, 1) and perpendicular to - 2x + 4y = 8.
y = -2x - 1
y = -2x + 5
О.
y = -2x - 3
O
y = -2x + 3
Answers
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]-2x+4y=8\implies 4y=2x+8\implies y=\cfrac{2x+8}{4} \\\\\\ y=\cfrac{2x}{4}+\cfrac{8}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x+2\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
since we know that's its slope, then
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]
so then we're really looking for the equation of a line whose slope is -2 and passes through (2 , 1)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad \qquad \stackrel{slope}{m}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-2}(x-\stackrel{x_1}{2}) \\\\\\ y-1=-2x-4\implies y=-2x-3[/tex]
-9v -6(8-7v)
Explain please
Answers
Answer:
33v - 48
Step-by-step explanation:
- 9v - 6(8 - 7v) ← multiply each term in the parenthesis by - 6
= - 9v - 48 + 42v ← collect like terms
= 33v - 48
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - 9v - 6(8 - 7v)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 9v - [(6 \times 8) - (6 \times 7v)][/tex]
[tex]\qquad \sf \dashrightarrow \: - 9v - (48 - 42v)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 9v - 48 + 42v[/tex]
[tex]\qquad \sf \dashrightarrow \:33v - 48[/tex]
Hope it helps ~
I have to choose 2 tools
Answers
Answer:
scale
Step-by-step explanation:
it would be used to measure
A(5, 10) and B(13,-2) are two points on the line AB.
The perpendicular bisector of the line AB has gradient
Find the equation of the perpendicular bisector of AB
Answers
Answer:
hope you understand......
Help me please I need this done quick
Answers
1058.4 in^2
Step-by-step explanation:
Find the surface areas of the rectangular prism and the triangular prisms separately.
Triangular: S = (1/2)lP+B, where l is slant height, P perimeter, and B base area.
14(4)= 56 perimeter of base
13 slant height
B = 14x14 = 196
put together:
S = (1/2)(13 x 56) + 196
S = 560 in^2
Now the rectangular prism
S = 2lw + 2lh + 2wh, where l is length, h height, w width. (delete the first 2lw since they share one side/they're combined shapes.
S = 2(14x8.9) + 2(14x8.9)
S = 498.4 in^2
Add them together: 498.4 + 560 = 1058.4 in^2
Someone show me step for step please!
Answers
[tex]\csc \theta \tan \theta - \tan \theta \sin \theta \\\\\\=\dfrac 1{\sin \theta} \cdot \dfrac{\sin \theta }{\cos \theta }- \dfrac{\sin \theta }{\cos \theta} \cdot \sin \theta\\\\\\=\dfrac{1}{\cos \theta}-\dfrac{\sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{1- \sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{\cos^2 \theta}{\cos \theta}~~~~~~~~~~~~~~;[\sin^2 \theta + \cos^2 \theta =1 ]\\\\\\=\cos \theta[/tex]
Let's write out some trigonometric identities that we can use:
[tex]tan(x)=\frac{sin(x)}{cos(x)} \\[/tex][tex]csc(x)=\frac{1}{sin(x)}[/tex][tex]sin^2(x)+cos^2(x)=1[/tex] ⇒ [tex]cos^2(x)=1-sin^2(x)[/tex]Now let's try solving them out:
[tex]csc(x)tan(x)-tan(x)sin(x)=\frac{1}{sin(x)}tan(x)-sin(x)tan(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)}-sin(x))\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)} -\frac{sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=tan(x)*(\frac{1-sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{cos(x)}*\frac{cos^2(x)}{sin(x)} \\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{sin(x)}*\frac{cos^2(x)}{cos(x)}\\\\csc(x)tan(x)-tan(x)sin(x)=1 * cos(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=cos(x)[/tex]
*I used a different variable, but that doesn't change the answer
Answer: cos(x)
Hope that helps!
Pre-calc/trig
Suppose that θ=arcsin(1/7) in the first quadrant. What is cos(θ/2)? (round to 4 decimals)
Answers
Answer:
0.9974
Step-by-step explanation:
[tex]arcsin( \frac{1}{7} ) = 0.1433 \\ cos( \frac{0.1433}{2} ) = 0.9974[/tex]
Jackie has 3 brothers. Maria has 2 brothers. Keri has 1 brother. Harriet has 2 brothers. Between the four girls, what is the mean number of brothers? Median? Mode?
Answers
Answer:
mean is 2 brothers.
mean, means average
Calculate the amount of work done when moving a 567 N crate a distance of 20 meters
Answers
Answer:
W = 11340 J
Step-by-step explanation:
Given,
Force ( F ) = 567 N
Distance ( s ) = 20 N
To find : Work done ( W )
Formula : -
W = Fs
W = 567 x 20
W = 11340 J
Hence,
the amount of work done is 11340 J.
To graph the inequality x > -3, draw an open circle on -3 and shade to the left.
TrueFalse
Answers
BOOM Creations has offered to sell its balloon
bouquets for a fixed down payment of $65 and an
additional charge of $2.75 per bouquet.
Answers
Answer:
y intercept: 65
rate of change: $2.75
Step-by-step explanation:
Really quite simple lad. Your equation is y=2.75x+65. 65 is your y-intercept, and you have a rate of change of 2.75 per bouquet.
