Answer:
y=2x-16
Step-by-step explanation:
So since we have a point and the slope, we can use the point-slope equation to find our equation of a line
y - y₁ = m(x - x₁)
Here our (x₁, y₁) point is (4, -8) and our m is 2
Plugging in these values to our equation gives us:
y - (-8) = 2(x - (4)) → distributing the negative to the -8 gives y + 8 = 2(x - 4) → distributing the 2 to the (x - 4) gives y + 8 = 2x - 8 → and finally subtracting the 8 from both sides gives our equation of a line y = 2x - 16
An engineer wants to determine how the weight of a​ gas-powered car,​ x, affects gas​ mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts​ (a) through​ (d) below.Weight (pounds), x Miles per Gallon, y3648 163847 172709 253550 183286 202922 233654 172533 253427 183809 173372 19A) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.y with caret = ___x + ___(Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as​ needed.)B) Interpret the slope and​ y-intercept, if appropriate.C) A certain? gas-powered car weighs 3600 pounds and gets 20 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this? weight?D) Would it be reasonable to use the​ least-squares regression line to predict the miles per gallon of a hybrid gas and electric​ car? Why or why​ not?
Answer:
Step-by-step explanation:
Given the following data :
(Weight, miles per gallon) (x, y) = 3648, 19), (1638, 47), (1727, 09), (2535, 50), (1832, 86), (2029, 22), (2336, 54), (1725, 33), (2534, 27), (1838, 09), (1733, 72)
Using the least square regression calculator :
y = -0.00941x + 59.07
B) slope = -0.00941
The slope 'm' of the graphical relationship is -0.009406
Intercept = 59.07 ( where the regression line crosses the x-axis)
C.) Using the regression equation:
y = -0.00941(3600) + 59.07
y = 25.194 gallons (above)
D.) No, because other factors also contribute to gas mileage such as cylinders, Displacement, mdoel e. T. C
What’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
The equation of circle is :
(x−a)² + (y−b)² = r²
So the equation is
(x-3)² + (y-(-2))² = (6)²
Where center = (a,b) = (3,-2) and
Radius = r = 6
The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 8 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Answer:
Step-by-step explanation:
[tex]A = lw \nl\frac{\dA}{\dt}[/tex] =[tex]\frac{\dA}{\text{d}l}\frac{\text{d}l}{\dt} + \frac{\dA}{\text{d}w}\frac{\text{d}w}{\dt}[/tex] =[tex]w\frac{\text{d}l}{\dt} + l\frac{\text{d}w}{\dt}[/tex] [tex]\nll = 20 \text{ cm}[/tex] \;\; [tex]\frac{\text{d}l}{\dt} = 8 \text{ cm/s}[/tex] \;\;w = 10 \text{ cm}, \;\; [tex]]\frac{\text{d}w}{\dt} = 3 \text{ cm/s}[/tex] [tex]\nl\frac{\dA}{\dt} =( 10 \text{ cm} )( 8 \text{ cm/s} ) + ( 20 \text{ cm} )( 3 \text{ cm/s} ) =140 \text{ cm}^2\!\text{/s} [/tex]
Given :
The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 8 cm and the width is 5 cm .To find :-
how fast is the area of the rectangle increasing?Solution :-
As we know that :-
A = lbTo find the rate :-
d(A)/dt = d(lb)/dt .Differenciate :-
dA/dt = l (db/dt ) + b (dl/dt )Substitute :-
dA/dt = 8*8 + 5*4dA/dt = 64 + 20 cm²/s dA/dt = 84 cm²/sAn experienced landscaper thought it would be funny to play a joke on some rookie landscapers. The rookies were given the measurements, l e n g t h equals 4 space cube root of 24 f t space a n d space w i d t h equals 6 space cube root of 3 space f t , and asked to find the exact area (no decimals) of the rectangular region they would be working with. Show the equation and all work needed to find the exact area in simplest form. Be sure to write a sentence explaining your answer. Don’t forget the label! Note: we want the exact area, which is not a decimal. Instead, provide the answer in simplest radical form.
Answer:
48∛9 ft²
Step-by-step explanation:
The length (L) and width (W) are given by:
[tex]L = 4\sqrt[3]{24}\\ W= 6\sqrt[3]{3}[/tex]
Since this is a rectangular region, the area is given by:
[tex]A=L*W=L \\A=4\sqrt[3]{24}* 6\sqrt[3]{3}\\A=24\sqrt[3]{72}\ ft^2[/tex]
The answer can be further simplified by factoring as follows:
[tex]A=24\sqrt[3]{72} = \\A=24\sqrt[3]{2*2*2*3*3}= 24\sqrt[3]{2^3*9}\\A=48\sqrt[3]{9}\ ft^2[/tex]
The exact area is its simplest form is 48∛9 ft²
Determine the slope of the line that passes through the points: x−8,0,4,5,y,−33,−1,15,19
Answer:
The equation of a line y = ax + b passes point (-8, -33) and point (0, -1) can be formulated by:
(Note: we do not need all of 4 points, 2 points are enough)
-33 = a x (-8) + b
-1 = a x 0 + b
From 2nd equation, we have:
b = -1
From 1st equation, we have:
b - 8 x a = -33
=> -1 - 8 x a = -33
=> 8 x a = 32
=> a = 4
=> The equation of line: y = 4a - 1
Hope this helps!
:)
2 sin^2 + sin x - 3 = 0
Answer:
x = 2 π n_1 + π/2 for n_1 element Z
or x = π + sin^(-1)(3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^(-1)(3/2) for n_3 element Z
Step-by-step explanation:
Solve for x:
-3 + sin(x) + 2 sin^2(x) = 0
The left hand side factors into a product with two terms:
(sin(x) - 1) (2 sin(x) + 3) = 0
Split into two equations:
sin(x) - 1 = 0 or 2 sin(x) + 3 = 0
Add 1 to both sides:
sin(x) = 1 or 2 sin(x) + 3 = 0
Take the inverse sine of both sides:
x = 2 π n_1 + π/2 for n_1 element Z
or 2 sin(x) + 3 = 0
Subtract 3 from both sides:
x = 2 π n_1 + π/2 for n_1 element Z
or 2 sin(x) = -3
Divide both sides by 2:
x = 2 π n_1 + π/2 for n_1 element Z
or sin(x) = -3/2
Take the inverse sine of both sides:
Answer: x = 2 π n_1 + π/2 for n_1 element Z
or x = π + sin^(-1)(3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^(-1)(3/2) for n_3 element Z
1.What values could replace the "?" in these equations to make them true?
2. How would you explain to a friend who doesn't know about logarithms what the equation
LaTeX: \log_{10}x\:=\:y
log
10
x
=
y
says about x and y?
Answer:
Remember that logarithms are inverse of exponentials. That means the result of the logarithm is equal to the exponent of a power with the same base.
1. (a)[tex]log_{10} (10)=1[/tex]
Notice that the result is one beacuse [tex]10^{1}=10[/tex]
(b)[tex]log_{10}(10000)=4[/tex]
Because [tex]10^{4}=10000[/tex]
(c)[tex]log_{10}(?) =7 \implies 10^{7} =10000000[/tex]
So, [tex]log_{10}(10000000)=7[/tex]
2.I would say to thim that [tex]x[/tex] and [tex]y[/tex] are variables of the logarithm, which be solved by imagine the logarithm as an exponential like
[tex]log_{10} (x)=y \implies 10^{y}=x[/tex]
In other words, the [tex]y[/tex] is the exponent and the [tex]x[/tex] is the result of the exponential.
Write the correct order of letter to the finish line. HELP ITS URGENT and btw it’s not L
Answer:
M
hope this helps
Answer:3rd row (abcg) skip a line h
Step-by-step explanation:
FOR BRAINLIEST only RIGHT ANWERS
Answer:
Length of arc: 6π
Step-by-step explanation:
~ Let us answer this question in terms of π, remaining so ~
1. Assume that this is a complete circle, for the moment being. The chord with length of 12 units would act as the diameter, and using that information we could determine the circumference of this complete circle...which will help us in the future. Apply the formula π * d as such: π * 12 ⇒ 12π to get the circumference as 12π.
2. Knowing that the length of the complete circle's circumference is 12π, this arc is part of a semicircle, meaning that it's value would be half of that of the complete circle's circumference, or in other words: 12π/2 ⇒ Answer ~ Length of arc: 6π
Answer:Length of arc: 6π
Step-by-step explanation:
The ratio of the number of boys to the number of girls in a class is 12:13 What percentage of the class are boys?
48%
Step-by-step explanation:
add the ratio together which is 25
pick the ratio of boy
divide 12 by 25 and multiply 100
12/25×100= 48%
Answer:
48%
Step-by-step explanation:
b/g=12/13
so b/12=g/13=k
b=12k
g=13k
so b+g=25k so k=b+g/25
b=12*(b+g)/25=12*4*(b+g)/25*4=48(b+g)/100
so 48% are boys
calculo la superficie de las figuras sabiendo que cada cuadrado mide 5m2
A flat object with two sides, one colored red (R), the other green (G), is tossed 2 times. List all possible outcomes of the experiment.
Answer:
3 possible outcomes
Step-by-step explanation
1) R R
2) R G
3) G G
help Marshmello ok xd
Answer:
84
Step-by-step explanation:
We simply plug in 1.75 for x into y = 48x, and when we do so we get y = 48 * 1.75 = 84 cups of coffee. Hope this helps!
Answer:
B) 84
Step-by-step explanation:
48 times x is the cups of coffee sold in x hours.
if x = 1.75, then you times 48 by 1.75
48 x 1.75 = 84
Find x when
-1/2
+
X
=
-21/4
Answer:
-19/4
Step-by-step explanation:
-1/2 + x =-21/4
x=-21/4+1/2
x=-21/4+2/4
x=-19/4
individual health insurance is usually less expensive than group health insurance
true or false?
Answer:
True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
One hundred examiners each marking eighty scripts per day are needed to mark an examination in fourteen days.How many days would two hundred examiners each marking forty scripts per day take to mark the same examination?
Answer:
SOS
Step-by-step explanation:
You must become familiar with these instructions and the associated documents, as well as any
other instructions issued by OCR, or your supervisor. These instructions form part of your
agreement with OCR. Please refer to clause 2 of your agreement and the task descriptor.
b) Please remember the importance of the marking task. The public expects that the task will be
carried out with a high level of responsibility and concentration. You must only carry out marking
in private, and not in any public place. Marking must only be done by the appointed person. You
should not mark whilst you are in your paid employment, unless your employer permits this.
c) Confidentiality and disclosure - Please refer to your agreement clauses 5.1 - 5.6. You should not
communicate with third parties (particularly the media) about your work without the permission of
the Chief Executive of OCR. Do not give any details of your work to any unauthorised people.
You should only mark in conditions that are secure and confidential.
d) On the rare occasions when you may have to take any OCR materials outside the UK, it is your
responsibility to ensure that all such materials are kept secure in transit. OCR materials include
but are not limited to hard copy material, discs, memory sticks, and laptops containing OCR
related information.
The taking of such materials outside the UK and their return to the UK must always be undertaken
by you personally. You must not ask someone else to do this on your behalf.
You must not return materials to OCR whilst you are outside the UK. Once in the UK when you
need to return materials to OCR, please utilise the specified returns service.
e) You should be aware that if checking of your assessment activities reveals variation in
acceptable tolerances OCR may instruct you to stop assessing and may terminate your
agreement in accordance with clause 10.2 of your agreement for the provision of assessment
services. In these circumstances in accordance with clause 5.4 of your agreement for the
provision of assessment services, you must return all confidential assessment material to OCR
as a matter of urgency. You will be paid for assessment completed.
f) You must tell OCR and your marking supervisor as soon as possible of any change of personal
circumstances,
i. any change of address (which must be confirmed in writing),
ii. illness or other circumstances which may prevent you from meeting deadlines for work.
Use the Assessor Support Line on 01223 552556 or email general
assessor enquiries.
Please update your personal details, including your permanent home address and email address,
in the Assessment Specialist Portal:
g) If you wish to use a different address for the delivery of scripts during the examination/marking
period, you should have updated your details in the Assessment Specialist Portal:
no later than 12 October for a November
series, 9 November for a January series and 30 March for a June series.
Sin2x + cos3x expand the expression
Step-by-step explanation:
Use double and triple angle identities:
sin(2x) + cos(3x)
2 sin x cos x + 4 cos³x − 3 cos x
Which type of quadrilatera can have exactly 1 pair of parallel side
A rectangle
B rhombus
C square
D trapezoid
6)
What would you do to find the arc length around 5/8 of a circle?
Answer:
5/8 * 2 * pi *r
Step-by-step explanation:
First find the circumference of the circle
C = 2 * pi *r
Then multiply it by the fraction of the circle ( arc length) you wish to find
5/8 * 2 * pi *r
what does the pythagorean theorem and it’s Converse state? why is this theorem important? what are some real world examples in which this theorem is used?
Answer:
The converse of the Pythagorean Theorem states that: If the square of the longest side of the triangle is equal to the sum of the squares of the other two sides of the triangle, then the triangle is a right triangle.
Step-by-step explanation:
The string of a kite is 100 meters long and it makes an angle of 60° with the ground. What is the height of the kite?
Show your work please)
Answer:
50√3 ≈ 86.6 m
Step-by-step explanation:
The geometry can be modeled by a right triangle with the height of the kite being the leg opposite the 60° angle. The hypotenuse has the given length of 100 m.
The mnemonic SOH CAH TOA reminds you that the relation between angles and the sides of interest here is ...
Sin = Opposite/Hypotenuse
sin(60°) = (kite height)/(100 m)
kite height = (100 m)·sin(60°) = (100 m)(√3)/2
kite height = 50√3 m ≈ 86.6 m
Which figure has a greater area?
19 ft
16.4 ft
.
15 ft
16.1 ft
Answer:
green triangle
Step-by-step explanation:
The green triangle has an area of
A = 1/2 bh
A = 1/2 (15) * 19
A =142.5 ft^2
The blue triangle has an area of
A = 1/2 bh
A = 1/2(16.1) (16.4)
A =132.02 ft^2
The green triangle has a greater area
Carl pays $45 per month for car insurance. How much does he spend on car insurance in 1 year?
Answer:
He spends $540
Step-by-step explanation:
literally just 45 multiplied by 12
I think of a number and I add one and then I double it
Answer:
I think of a number "4"
4+1 = 5
then 5+5 or (5X2) = 10
Step-by-step explanation:
Hope this helped :)
According to the picture, whats the answer?
Answer:
84 meters
Step-by-step explanation:
5 x 6 = 30 hypotenuse side not shown
3 x 4 ÷ 2 x 2 = 12 red (both ends)
3 x 6 = 18 green side
6 x 4 = 24 blue side
Lynn has two jobs. She earns $7.50 per hour as the hostess for a restaurant and earns
$10 per hour babysitting for a neighbor.
Part 1
Which inequality represents the number of hours working as a hostess, h, and the
number of hours babysitting, b, that Lynn needs in order to earn at least $150 in one
week?
A. h + b > $150
B. h + b 2 $150
7.5h + 10b > $150
• D
7.5h + 10b $150
e here to search
Answer:
7.5h + 10b > $150
Step-by-step explanation:
h represents the amount of hours Lynn works as a hostess for a restaurant, and she gets $7.50 per hour. $7.50h is how much money she gets per hour. b represents the amount of hours Lynn spends working as a babysitter, and she gets $10 per hour. $10b is how much money she gets from babysitting per hour. The total amount of money she gets this week must be more than $150. So the answer is 7.5h + 10b > $150. Hope this helped!
What’s the correct answer for this?
Same slopes, different constant, so parallel lines.
Answer: ... parallel because their slopes are equal. Last choice.
Answer:
D
Step-by-step explanation:
Yes, lines l and k are parallel since they are having equal slopes
What is the solution to the equation? 5 = two-fifths a 2 4 and three-fifths 12 and one-half 25
Answer:
12 1/2
Step-by-step explanation:
Multiply the equation by the inverse of the coefficient of a.
5 = (2/5)a
5(5/2) = (2/5)(5/2)a
25/2 = a
12 1/2 = a . . . . written as a mixed number
The solution is 12 1/2.
Answer:
12 1/2
Step-by-step explanation:
PLEASE HELP
Sara and Sam are each working on a science project in which they need to research the individual masses of the nine planets (including the dwarf planet Pluto as the ninth planet). Sara completes her data for the planets' masses in kilograms while Sam's data is in milligrams.
Sara:
Approximate how many times greater Saturn's mass is than Mercury's.
A: 2,000,000
B: 200,000
C: 20,000
D: 2,000
What is the discount for a iPod that’s $75 dollars but labeled “ save 15% “
Discount = [tex]\frac{15}{100}[/tex] x 75
= [tex]\frac{1125}{100}[/tex]
= $11.25