Find the equation of the linear function represented by the table below in slope
intercept form
Answer:
y=x+2.
Step-by-step explanation:
1. if the point A has coordinates (-3;1) and B - (1;3), then it is possible to make up the equation:
[tex]\frac{x-X_A}{X_B-X_A}= \frac{y-Y_A}{Y_B-Y_A}; \ => \frac{x+3}{4} =\frac{y+1}{4};[/tex]
2. if to evaluate the equation, then
x+3=y+1; ⇔ y=x+2 (slope-interseption form).
What value of x satisfies the conclusion of the mean value theorem for f(x) = ln(x3) over the interval [1, e2]?
Answer:
[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].
Step-by-step explanation:
According to the Mean Value Theorem, for all function that is differentiable over the interval [tex][a, b][/tex], there is at a value [tex]c[/tex] within the interval such that:
[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex] (1)
Where:
[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds.
[tex]f(a)[/tex], [tex]f(b)[/tex] - Function evaluated at lower and upper bounds.
[tex]f'(c)[/tex] - First derivative of the function evaluated at [tex]c[/tex].
If we know that [tex]f(x) = \ln x^{3} = 3\cdot \ln x[/tex], [tex]f'(x) = \frac{3}{x}[/tex], [tex]a = 1[/tex] and [tex]b = e^{2}[/tex], then we find that:
[tex]\frac{3}{c} = \frac{3\cdot \ln e^{2}-3\cdot \ln 1}{e^{2}-1}[/tex]
[tex]\frac{3}{c} = \frac{6\cdot \ln e-3\cdot \ln 1 }{e^{2}-1 }[/tex]
[tex]\frac{3}{c} = \frac{6}{e^{2}-1}[/tex]
[tex]c = \frac{1}{2}\cdot (e^{2}-1)[/tex]
[tex]c \approx 3.195[/tex]
[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].
Answer:
C. 1/2(e^2-1)
Step-by-step explanation:
Edge AP Cal 2022
Why is 2/10 equivalent to 1/5?
Answer:
If you divide both top and bottom of [tex]\frac{2}{10}[/tex] by 2, you get [tex]\frac{1}{5}[/tex]
Answer:
because you have to find common denominators
2/10= 1/5
2/10= 1x2/5x2
Whatever you do to the bottom, you do to the top so that is why i also multiplied the numerator by 2.
2/10=2/10
Hope it helped!! Pls mark brainliest :)) Have a good day
Step-by-step explanation:
2 1/2 divided by 3 4/6=?
Please help me.
Answer:
15/22
Step-by-step explanation:
Solve the system of equations –2 + y = 14 and -5x – 7y=10 by combining the
equations.
Submit Answer
attempt out of 2
o
PLEASE ANSWER!!
Answer:
Step-by-step explanation:
-2+y=14
-5x-7y=10
y=14+2
y=16
-5x-7(16)=10
-5x-112=10
+112 +112
-5x=122
x=-24.4
Can someone please tell me the answer ..
Answer:
148
Step-by-step explanation:
Please help me on this question 30 points on the line
Answer:
4(x-3) = 8
Step-by-step explanation:
4 times the difference would be 4(x-y), and we already know what y is, which is 3. Finally, the "is 8" means "equals 8" giving us our equation: 4(x-3) = 8.
Answer:
4(x-3) = 8
Step-by-step explanation:
a. If a spinner is spun twice, are the events
independent or not independent? Justify
your answer.
2
In an A-Frame house, the roof extends to the ground level. If each side of the roof meets the ground at a 62° angle, what will be the measure of the angle where the two sides of the roof meet?
Answer:
36 degrees
Step-by-step explanation:
Angles in a triangle add up to 180.
180-62-62=36
36 degrees
Step-by-step explanation:
Write an equation for a line perpendicular to h(t) = -2t +4 and passing through the point (-4, -1).
Answer:
y=1/2t+1
Step-by-step explanation:
To get a perpendicular line, the slopes have to be reciprocals.
b) Simplify (4ab^2)^3
Answer:
[tex]64a^{3} b^{6}[/tex]
Step-by-step explanation:
[tex](4ab^2)^3[/tex]
=> [tex]4^{3} a^{3} b^{6}[/tex]
=> [tex](4 \times 4 \times 4) a^{3} b^{6}[/tex]
=> [tex]64a^{3} b^{6}[/tex]
The table shows locations on a map.
Place
park
farmers market
Location
•(-2,2)
(-2,3)
(2, 2)
(6,-3)
post office
bus stop
Which places on the map are 4 units apart?
the park and the farmer's market
O the farmers market and the bus stop
O the post office and the park
O the post office and the bus stop
Answer:
The table shows locations on a map.
Place
parkfarmers marketpost officebus stopLocation
(-2,2)(-2,3)(2, 2)(6,-3)Which places on the map are 4 units apart?
O the park and the farmer's market
O the farmers market and the bus stop
✓ the post office and the park
O the post office and the bus stop
Step-by-step explanation:
Distance :---
[tex]→ \sqrt{ {(2 - ( -2 ))}^{2} + {(2 - 2)}^{2} } \\ = \sqrt{ {4}^{2} + {0}^{2} } = \sqrt{ {4}^{2} } = \boxed{4 \: units}[/tex]
Find the value of each angle mentioned above.
Answer:
36°, 42°, 72°, 102°, 108°
Step-by-step explanation:
Angles at a point = 360°
Therefore:
(3x - 6) + x + 3x + 2x + (x + 6) = 360°
Open parthenogenesis
3x - 6 + x + 3x + 2x + x + 6 = 360
Add like terms
10x = 360
Divide both sides by 10
x = 36
✔️Value of each angle:
Plug in the value of x in each expression
x = 36°
3x - 6 = 3(36) - 6 = 102°
3x = 3(36) = 108°
x + 6 = 36 + 6 = 42°
2x = 2(36) = 72°
1. True or false: A function is a rule that assigns each input exactly one
output.
True
False
The size of a jar of coffee is increased by one 1/5. The new size is later reduced by 1/5
Is the new jar smaller, the same size or larger than the original?
Answer:
The new jar would be smaller than the original.
Step-by-step explanation:
First you would have to find one 1/5 of the original size. This gives you the increased size.
Then, you'd find 1/5 of the new size and subtract it from the increased size of the jar.
1/5 of the increased size is larger than 1/5 of the original size, so no matter what number it is, you'll always end up with a smaller-sized jar of coffee at the end.
The new jar would be smaller than the original.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
First, you would have to find one 1/5 of the original size. This gives you the increased size.
Then, you'd find 1/5 of the new size and subtract it from the increased size of the jar.
1/5 of the increased size is larger than 1/5 of the original size, so no matter what number it is, you'll always end up with a smaller-sized jar of coffee at the end.
To know more about scale factors follow
https://brainly.com/question/25722260
#SPJ2
David canoes 20km downstream in 2.5 hours his return trip takes 4 hours find the rate of his current. A 1.5 km/h B 1 km/h C 0.5 km/h D 2.5 km/h
Answer:
1.5 km/hour
Step-by-step explanation:
d is the David's speed in still water
c is the speed of the current
Going with the current, he travels d+c km per hour.
Going against the current, he travels d-c km per hour.
d+c = (20 km)/(2.5 hours) = 8 km/hour
d-c = (20 km)/(4 hours) = 5 km/hour
Add the equations to eliminate the c terms
d+c = 8
d-c = 5
----------
2d = 13
d = 6.5 km/hour
c = 8-d = 1.5 km/hour
Photo attached please help
Answer:
Wow your on apec to?
Step-by-step explanation:
Wait could you show the whole question and the other answers please. I was going to say C.
I noticed a few others answers missing so I can't properly answer your question.
Please Help ASAP
1. Andrew and Griffin both worked hard over the weekend. Together they earned a total of $65. Griffin earned $15 more than Andrew.
(a) Write a system of equations for the situation. Use a for the amount Andrew earned and g for the amount Griffin earned.
(b) Graph the equations in the system.
(c) Use your graph to estimate how much each person earned. (You must solve by graphing, other solving methods will not earn credit)
Answer:
2x-15=65
Step-by-step explanation:
You have to subtract 15 dollars from 65 because it is extra money that Griffin had earned. Now you are left with 40 so now you would divided 2 since its both Griffin and Andrew. At the end, Griffin earned 35 dollars and Andrew earned 20 dollars.
The population of a small town was 1200 people in 1998. In 2008 the population of that same town was recorded as 6,000. What was the percent of increase?
Answer:
The population had a 400% increase
a ship sails 400km in 18hours.how many days will it take to cover 1600km at the same rate?
Answer:
72 hours
Step-by-step explanation:
1600/400=4
so 4 x 18= 72 hours
Two of the known angles in a trianglemeasure 120 and 22 What is the measure of the third angle?
Answer:
120+22+x=180
x=38
120+22+38=180
Step-by-step explanation:
Hope it helps
Mark me as brainiest
Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. The following is the amount ($000) earned per month by a sample of 15 Claiborne models:
$4.7 $3.8 $6.7 $3.8 $3.9 $4.2 $4.0 $4.0 $4.8 $3.1 3.1 5.5 3.4 6.1 4.9
The following is the amount ($000) earned by a sample of 12 Klein models.
$4.0 $3.8 $3.6 $2.5 $4.9 $5.2 $5.9 $4.9 $4.4 $3.6 5.1 4.7
Required:
a. Find the degrees of freedom for unequal variance test.
b. State the decision rule for 0.05 significance level: H0: μLC ≤ μCK; H1: μLC > μCK.
c. Compute the value of the test statistic.
d. Is it reasonable to conclude that Claiborne models earn more? Use the 0.05 significance level.
Answer:
24 ; Tstat > Tcritical ; 0.052 ; Fail to eject the Null
Step-by-step explanation:
Claiborne model:
$4.7 $3.8 $6.7 $3.8 $3.9 $4.2 $4.0 $4.0 $4.8 $3.1 $3.1 $5.5 $3.4 $6.1 $4.9
Sample size, n1 = 15
Using calculator :
Mean, m1 = 4.4
Standard deviation, s1 = 1.056
Klein model:
$4.0 $3.8 $3.6 $2.5 $4.9 $5.2 $5.9 $4.9 $4.4 $3.6 $5.1 $4.7
Sample size, n = 12
Mean, m2 = 4.38
Standard deviation (s) = 0.923
To obtain the degree of freedom for unequal variances test, use the Relation :
Degree of freedom (DF) = (s1²/n1 + s2²/n2)² / { [ (s1² / n1)² / (n1 - 1) ] + [ (s2² / n2)² / (n2 - 1) ] }
(1.056^2/15 + 0.923^2/12)^2 / {[(1.056^2/15)^2 / (15 - 1)] + [(0.923^2/12)^2 / (12 - 1)]}
0.0211226 / (0.0003947 + 0.0004581)
= 24.768527
df = 24 rounded down to the nearest whole number.
Decision region :
α = 1-0.95 = 0.05
Tdf, 0.05 = 1.711
Tcritical = 1.711
Reject Null, if Tstat > Tcritical
The t - test statistic :
(m1 - m2) / (s1²/n1 + s2²/n2)
(4.4 - 4.38) / sqrt(1.056^2 / 15 + 0.923^2 / 12)
0.02 / 0.3812301
= 0.0524617
= 0.052
Since, Tstat < Tcritical, we fail to reject the Null. It is not reasonable to conclude that Claiborne model earns more.
3. Solve for x.
3r + 11
9x-14
how do you solve these problems?
a. (2/7)x + 5= -21 and
b. 1/2(18x-2)=0
Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation.
y - ln y = x^2 + 1, dy/dx = 2xy/y - 1
x^2 + y^2 = 4, dy/dx = x/y
e^xy + y = x - 1, dy/dx = e^-xy - y/e^-xy + x
Answer:
dont know
Step-by-step explanation:
Factorise this expression as fully as possible
2x2 + 6x
Answer:
The factored expression is: [tex]2x(x + 3)[/tex]
Step-by-step explanation:
We are given the following expression:
[tex]2x^2 + 6x[/tex]
To factorize it as fully as possible, we first find the GCF between the numeric values, and the coefficients:
Numeric:
GCF between 2 and 6 is 2, because:
2 - 6| 2
1 - 3|
1 and 3 are not divisible by the same number, so 2.
Coefficient:
Between x² and x, x.
Factorizing:
Simplifying by 2x.
[tex]2x(\frac{2x^2}{2x}+\frac{6x}{2x}) = 2x(x + 3)[/tex]
The factored expression is: [tex]2x(x + 3)[/tex]
Please help!!!!! Explain
Answer:
If the total price of an object is A, and we have a tax of X%, then the new price of the object is:
Price = A + A*(X%/100%) = A*(1 + X%/100%)
In this case, the initial price of the car is:
A = $16,368
a) the tax is 6.6%
In this case, the price will be:
Price = $16.368*(1 + 6.6%/100%) = $17,448.288
b) the tax is 8.25%
In this case, the price will be:
Price = $16.368*(1 + 8.25%/100%) = $17,718.36
c) the tax is r.
we only replace X% by r.
Price = $16.368*(1 + r/100%)
d) We want to solve for r the above equation, we just need to isolate r.
Price/( $16.368) = (1 + r/100%)
Price/($16.368) - 1 = r/100%
(Price/($16.368) - 1)*100% = r
s'ams mother is twice as old as sam in 12 years sam will be as old as his mother was 12 years ago how old are sam and his mother now? sam is?years old his mother is ? years old
Answer:
Sam is 24 years old and his mother is 48 years old.
Step-by-step explanation:
Equations
Let's call
x = Sam's current age
Since Sam's mother is twice as old as Sam:
2x = Sam's mother current age
x + 12 = Sam's age in 12 years
2x - 12 = Sam's mother age 12 years ago
These two last expressions are equal:
x + 12 = 2x - 12
Subtracting x and adding 12:
x = 24
2x = 48
Sam is 24 years old and his mother is 48 years old.
Answer:
Sam is 24 and his mom is 48
Step-by-step explanation:
Jessica cuts a ribbon with a length of 12 inches into three pieces such that the length of
one piece is 3 1/2 inches and the lengths of the other two are the same. What is the length of each of the other two pieces?
A. 2 1/2 inches
B. 4 1/4 inches
C. 7 3/4 inches
D. 8 1/2 inches
Answer:
B 4 1/4
Step-by-step explanation:
Answer:
Its B. 4 1/4
Step-by-step explanation:
How it helps!
a cylindrical water tank has a diameter of 4m and a height of 3m.while a water tank shaped like a rectangular prism has a length of 7m.a width of 2 meters and a height of 2 meters. which of the tanks can hold more water? by how many cubic meters?
Answer:
The cylindrical tank can hold 9.7 cubic meter more water than the rectangular prism shape tank .
Step-by-step explanation:
We are given that
Diameter of cylinderical water tank, d=4 m
Radius of cylinderical water tank,r=d/2=4/2=2 m
Height of cylinderical water tank,h=3 m
Length of rectangular prism, l=7 m
Width of rectangular prism ,w=2 m
Height of rectangular prism, h=2m
Volume of cylinder=[tex]\pi r^2 h[/tex]
Where [tex]\pi=3.14[/tex]
Using the formula
Volume of cylinderical tank=[tex]3.14(2)^2\times 3=37.7m^3[/tex]
Volume of rectangular prism=[tex]lwh[/tex]
Using the formula
Volume of rectangular prism=[tex]7\times 2\times =28m^3[/tex]
Difference between volumes=37.7-28=9.7 cubic meters
Hence, the cylindrical tank can hold 9.7 cubic meter more water than the rectangular prism shape tank .