How do I find the equation of the line y=mx + C, passing through the points M (-2, -3) and T (3, 7)?
How do I find the equation of the line y=mx + C, passing through the points M (-2, -3) and T (3, 7)?
A2A
y = mx + C is often called slope-intercept form.
There are two pieces of information you will need to solve for. #1: The slope, which is m, and #2: the y-intercept, which is C (incidentally I learned this as y = mx + b, instead of y = mx + C, but that is a trivial detail)
Step #1 Find the slope. use the formula slope = (y₂ - y₁)/(x₂ - x₁) => (7 - -3)/3 - -2) = 10/5 = 2. m=2
Step #2 Find the y-intercept. Solve for y = mx + C when x is 2 and x = -2 and y = -3 -3 = 2(-2) + C => -3 = -4 + C add 4 to both sides, 1 = C
Equation: y = 2x + 1.
Check: x = 3 => y = 2(3) + 1 => y = 6 + 1 => y = 7 => (3, 7)
Check: x = -2 => y = 2(-2) + 1 => y = -4 + 1 => y = -3 => (-2, -3)
Let R be the region in the first quadrant bounded by x2 − y2 = 16, the horizontal line y = 0, and the vertical line x = 5. What is the volume of the solid formed by revolving R about the x-axis?
Check the picture below.
so the region is the one bounded by a hyperbola and two straight lines, one of which is the x-axis, or namely y = 0, since the hyperbola has a vertex at x = 4, then our bounds are from 4 to 5.
[tex]x^2-y^2=16\implies x^2-16=y^2\implies \pm\sqrt{x^2-16}=y \\\\\\ \stackrel{I~Quadrant}{+\sqrt{x^2-16}=y}\qquad \qquad \implies \stackrel{\textit{using the disk method}~\hfill }{\displaystyle\int_{4}^{5}~\pi \left( \sqrt{x^2-16} \right)^2\cdot dx\implies \pi \int_{4}^{5}(x^2-16)dx} \\\\\\ \pi \left( \left. \cfrac{x^3}{3} \right]_{4}^{5} ~~ - ~~\left. 16x\cfrac{}{} \right]_{4}^{5}\right)\implies \pi \left[\cfrac{61}{3}~~ - ~~16 \right]\implies \cfrac{13\pi }{3}[/tex]
True or False. A function is increasing if its outputs get larger as the inputs
get larger.*
Answer:
True
Step-by-step explanation:
A function is increasing if its outputs get larger as the inputs is a "true statement" or the first option. If the inputs are getting larger for every input and the outputs are getting larger for every output, if you plot the data on a scatter plot or a coordinate plane of sorts you would see it take shape of a line that is moving from the left to the top right which means the function is indeed increasing when the outputs/inputs get larger.
Hope this helps.
A sundae requires 333 ice-cream scoops and 444 strawberries, and a milkshake requires 222 ice-cream scoops and 666 strawberries. Ramses wants to make sundaes and milkshakes with at most 252525 ice-cream scoops and 373737 strawberries. Let SSS denote the number of sundaes he makes and MMM the number of milkshakes he makes.
Answer:
[tex]3x+2y\leq 25 \\4x+6y \leq 37[/tex]
Step-by-step explanation:
Sunday ice cream :
Ice cream scoops = 3
Strawberries = 4
Milkshake :
Ice cream scoops = 2
Strawberries = 6
Ramses wants to make sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.
Let x be the no. sundaes and y be the no. of milkshakes
So, Equations are :
[tex]3x+2y\leq 25 \\4x+6y \leq 37[/tex]
Now we are supposed to graph the solution
[tex]3x+2y\leq 25[/tex] --- Blue
[tex]4x+6y \leq 37[/tex] --- Green
Refer the attached figure
i finished all of these but i wanted to make sure these were correct! i will be posting others and thank you for answering :)
Answer:
Step-by-step explanation:
Where are your answers?
100 g of fish cost 70¢.
€
(a) Calculate the cost of 180 g.
(b) Mr Tan paid $2.45 for some fish. How
many grams of fish did he buy?
Answer:
a) 100/70 = 1.43 cents for 1 g of fish
180 x 1.43 = 257.4 pennies = 2.57 dollars
b) 2.45 dollars = 245 pennies
245/1.43 = 141.33.... = 141 g
Step-by-step explanation:
whoever answers first gets brainliest!!!!
Answer:
38%
Step-by-step explanation:
Answer:
C. 38%
Step-by-step explanation:
3 ÷ 8 = 0.375
Make it a percent
0.375 x 10 = 37.5
Since it isn't an option, round up. A good rounding rule is: Four or less, let is rest. Five or more, let it soar.
Since this number ends in 5, round up.
37.5 is now 38
38%
The area of a circle is 144pi m2. What is the diameter of the circle?
A. 6m
B. 12m
C. 24m
D. 144m
-6 < 2t - 5 < 3
Solve for T
Answer:
I think it's 7
Step-by-step explanation:
-6 < 2T (-5+5) < 3+5
-6 < 2T < 8
+6 < 2T < 8 + 6
0 < 2T < 14
0 < ÷ 2 < ÷ 2
0 < T < 7
-0 < T < -0
T = 7
Solid metal support poles in the form of right cylinders are made out of metal with a density of 6.1 g/cm 3 3 . This metal can be purchased for $0.62 per kilogram. Calculate the cost of a utility pole with a diameter of 41 cm and a height of 780 cm. Round your answer to the nearest cent.
The cost of a utility for a pole with a diameter of 41 cm and a height of 780 cm is $3894697.41
Density formula
The density formula is given by:
Density = mass/volume
The volume of the cylinder = π * radius² * height
Radius = diameter / 2 = 41/2 = 20.5, height = 780 cm. Hence:
Volume = π * 20.5² * 780 = 1029798 cm³
Density = mass/volume
6.1 = mass/1029798
mass = 6281770 kg
Cost = 6281770 kg * $0.62 per kilogram = $3894697.41
The cost of a utility for a pole with a diameter of 41 cm and a height of 780 cm is $3894697.41
Find out more on Density at: https://brainly.com/question/1354972
F
∝
a
If
F
=
48
when
a
=
3
find,
F
when
a
=
4
Answer:
F(4) = 36
Step-by-step explanation:
F = C/a, where C is a constant
Since 48 = C/3
C = 144
F(a) = 144/a
-----
F(3) = 144/3
F(3) = 48
----
F(4) = 144/4
F(4) = 36
If f(-4) for f(x)=-2x+7 is 15, then what is f^-1 (15)?
let's recall that for a function f(x) that has an inverse function f⁻¹(x), the domain of f(x) corresponds to the range of f⁻¹(x), what the heck does that all mean?
well, it means that for any coordinate pairs (a , b) in f(x), there's a corresponding pair of (b , a) on f⁻¹(x).
we know in this case that f(-4) = 15, or namely that f(x) has a pair of (-4 , 15), well, that means that f⁻¹(x) has a swapped pair of (15 , -4).
the above means that f⁻¹(15) = -4.
Which number line shows the solutions to n > 3?
Answer:
The second one.
Step-by-step explanation:
The hollow dots represent > or < depending the direction of the arrow. The filled dots represent less than or equal to. So the second.
Answer: Your answer would be B
Step-by-step explanation: The open circle means it's not greater than or equal to! So therefore, answer is B! Let me know if I'm wrong. If not have a great day!
8+3(4x-2) anyone know how to solve?
Answer:
x = -1/6
Step-by-step explanation:
Firstly, you need to expand the brackets. So this would give, 8 + 12x - 6.
Then you collect like terms to give, 12x + 2. After this, we solve for x. To do this we need to assume that all this is = 0. Then it's easy to solve:
12x + 2 = 0
12x = -2
x = -2/12
x = -1/6
What are the equation and slope of the line shown on the grid? I give Brainliest Answer!
Answer:I think it’s y = 6; slope is 6
Step-by-step explanation:
Because it’s on the positive side so I think it’s that one
The equation of the line will be x = 6. And the slope of the vertical line is infinite.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation of the vertical line is given as,
x = c
The line is passing through (6, 0). Then we have
6 = c
Then the equation of the line will be x = 6. And the slope of the vertical line is infinite.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
I need to know the answer to this and how to solve it .
Answer:
=> B.125
Step-by-step explanation:
=> 180°- 55°{ linear pair }
=> 125°
The measure of angle COE = 125
Help A costume designer needs to make 12 costumes for the school play.Each costume requires 2 2/3 yards of fabric.How many yards of fabric does the costume designer need to make all costume
Answer:
32
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
Hope this helps! :)
Have a blessed day and remember to keep smiling! :)
[tex][Hello,BrainlyUser][/tex]
Answer:
32 Yards
Step-by-step explanation:
Given;
Length of fabric required for each costume = 2 2/3
Total number of costumes to be made =12
Solve;
12 * 2 2/3
We can multiply mixed numbers by converting it to fractions.
⇒ 12 * 8/3
⇒ 32
Thus, you need 32 yards of fabric.
[CloudBreeze]
Farmer MacDonald has 72 cows and pigs on his farm. The ratio of cows to pigs is 5 to 3. How many cows and how many pigs does he have?
Answer: 45 and 27
Step-by-step explanation:
A lil trick Is that u add 5+3=8 then 72/8 = 9
So then 5x9 and 3x9 because each ratio "unit" Is equal to 9 so ya
gl
Please help me with this math problem!! Will give brainliest!! Please include a drawing in your answer. No links please!!
Answer:
Step-by-step explanation:
AC = 150 Feet
CB = 75 feet.
BD = 100 feet
You use the tangent here.
Tan(A) = opposite/ Adjacent
Opposite = BD = 100 feet
Adjacent = AB = AC + CB = 150 + 75 = 225 feet.
Tan(A) = 100 / 225
Tan(A) = 0.4444
A = Tan-1(0.4444)
A = 23.96 degrees, but the front row of trees cannot be more than 100 feet tall
y=-3x^2-24x-42 in vertex form
Answer:
Step-by-step explanation:
y = - 3x² - 24x - 42
y = - 3( x² + 8x + 14 )
y = - 3( x² + 2·4·x + 16 - 16 + 14 )
y = - 3[ ( x + 4 )² - 2 ]
y = - 3( x + 4 )² + 6
Bob bought some new boots that cost $67.34. He paid 7.5% tax. How much did he pay at the cash register?
A. $3.20
B. $24.78
C. $72.39
D. $33.40
Answer:
72.39
Step-by-step explanation:
Cost of boots: 67.34
Tax: 7.5%
Amount of tax he payed: 67.34 * 7.5/100 = 5.05
Total Amount = 67.34 + 5.05 = 72.39
I spent $4.80 on groceries and $1.20 on vegetables. What is the ratio of:
a. Cost of groceries to cost of vegetables;
b. Cost of vegetables to cost of groceries;
c. Cost of vegetables to total cost;
d. Cost of groceries to total cost?
Help me plz
The required ratio is given as a) 4/1 b) 1/4 c) 1/5 and d) 4/5.
Given that,
Spent $4.80 on groceries and $1.20 on vegetables.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Total cost = 4.80 + 1.20
Total cost = $6.00
a. Cost of groceries to cost of vegetables;
Ratio = 4.80 / 1.20 = 4 / 1
b. Cost of vegetables to cost of groceries;
Ratio = 1.20 / 4.80 = 1 / 4
c. Cost of vegetables to total cost;
Ratio = 1.20 / 6 = 1 / 5
d. Cost of groceries to total cost
Ratio = 4.80 / 6 = 4 / 5
Thus, the required ratio is given as a) 4/1 b) 1/4 c) 1/5 and d) 4/5.
Learn more about ratios here:
brainly.com/question/13419413
#SPJ2
Sylvia’s cat weighs 12 pounds Michele’s cat weights 9 pounds.
How many more ounces does Sylvia’s cat weigh than Michele’s cat?
Answer:
Sylvia's cat weighs 3 pounds more than Michelle's cat
Sylvia’s cat weighs 48 ounces more than Michele’s cat.
What is weight?The downward force exerted by any object due to the effect of the earth's gravity is called weight.
Given that:-
Sylvia’s cat weighs 12 pounds Michele’s cat weighs 9 pounds.The difference between the weight = 12 - 9 = 3 pound
1 pound = 16 ounces
3 pounds = 16 x 3 ounces = 48 ounces
Therefore Sylvia’s cat weighs 48 ounces more than Michele’s cat.
To know more about weight follow
https://brainly.com/question/2337612
#SPJ2
Are the following equations perpendicular y=-1/3x+4 and y=1/3x+12?
Explanation:
Compare each equation to the form y = mx+b
m = slope
The first equation has slope -1/3 and the second equation has slope 1/3
The slopes do not multiply to -1, so the lines aren't perpendicular.
The slopes aren't equal, so the line aren't parallel either.
Solve the system of linear equations in two variables by elimination or substitution.
4x+ 3y=2
2x-3y=1
Answer:
( [tex]\frac{1}{2}[/tex], 0 )
Step-by-step explanation:
Given the 2 equations
4x + 3y = 2 → (1)
2x - 3y = 1 → (2)
Adding (1) and (2) term by term will eliminate the y- term, that is
6x = 3 ( divide both sides by 6 )
x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
Substitute x = [tex]\frac{1}{2}[/tex] into either of the 2 equations and evaluate for y
Substituting into (1)
4([tex]\frac{1}{2}[/tex] ) + 3y = 2
2 + 3y = 2 ( subtract 2 from both sides )
3y = 0 ⇒ y = 0
Solution is ( [tex]\frac{1}{2}[/tex], 0 )
When Amira goes bowling, her scores are normally distributed with a mean of 160
and a standard deviation of 13. What percentage of the games that Amira bowls does
she score less than 192, to the nearest tenth?
Using the normal distribution, it is found that she scores less than 192 in 99.3% of games.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 160, \sigma = 13[/tex].
The proportion of games in which she scores less than 192 is the p-value of Z when X = 192, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{192 - 160}{13}[/tex]
[tex]Z = 2.46[/tex]
[tex]Z = 2.46[/tex] has a p-value of 0.993.
Hence, she scores less than 192 in 99.3% of games.
More can be learned about the normal distribution at https://brainly.com/question/24663213
Which of the following statements are equivalent
to the statement "the price decreased by 25%"?
Choose all the correct answers.
(A) The price doubled.
(B) The price is 150% of the price before.
(C) The price was reduced by a quarter.
(D) The price is half of what it was before.
(E) The price is now 1.5 times greater than what it was before.
(F) The price now is 662 % of what it was before.
F
-
3
(G) The price now is 200% of what it was before.
(H) The price is 75% of what it was before.
Answer:
(C) The price was reduced by a quarter
(H) The price is 75% of what it was before.
Step-by-step explanation:
Let's go through all the answer choices:
(A) The price doubled.
(B) The price is 150% of the price before.
(E) The price is now 1.5 times greater than what it was before.
(F) The price now is 662 % of what it was before.
(G) The price now is 200% of what it was before.
knowing that decreased meaning smaller or fewer.
Thus, it can't be doubled or more than 100% as well was greater.
Hence, the best answer is
(C) The price was reduced by a quarter
(H) The price is 75% of what it was before.
Note:
Reduced = Smaller, Less amount
Greater = More
Doubled = More
Decreased = Smaller, Less amount.
[RevyBreeze]
The statements are equivalent to the statement "the price decreased by 25%" are:
The price was reduced by a quarter.
The price is 75% of what it was before.
We have statement,
"the price decreased by 25%".
So, the statement that follow the statement is
The price was reduced by a quarter.
The price is 75% of what it was before.
Statements are not equivalent to the given statement.
"The price is 150% of the price before" means the price increased by 50%, not by 100% or double.
"The price doubled."
"The price is 150% of the price before."
"The price is now 1.5 times greater than what it was before."
"The price now is 200% of what it was before."
Learn more about Price Relation here:
brainly.com/question/19091385
#SPJ2
HELP QUICK PLSSSSSSSSS
Answer:
I believe the answer is 198
Answer:
791.68135 cubic metres
Step-by-step explanation:
V=πr2h=π·62·7≈791.68135
LOOK AT THE PICTURE
PLEASE PLEASE HELP ASAP THIS TEST IS IMPORTANT I WILL MARK BRAINLIEST AND GIVE 20 POINTS OR MORE LOOK AT THE PICTURE
Maria is trying to estimate 30. She uses this table of values:
What should she do next to find 30 to the nearest hundredth?
A. She should find the squares of numbers between 5.5 and 5.6.
B. She should estimate that 30 is 5.50.
C. She should find the squares of numbers between 5.4 and 5.5.
D. She should find the average of 5.4 and 5.5.
Answer:
A im pretty sure :)
Step-by-step explanation:
The volume of this right prism is 214.5 ft. What is the height, x, of the prism? 5 ft Enter your answer as a decimal in the box. 5 ft 5.8 ft X= ft x A 8 ft. Pls help me!
The volume of the right prism is the product of the length, width and height
The height of the prism is 7.40 ft
How to determine the height of the prism?The given parameters are:
Volume = 214.5 ft cube
Length = 5 ft
Width = 5.8 ft
The volume of the right prism is calculated as:
Volume = Length * Width * Height
So, we have:
214.5 = 5 * 5.8 * Height
Evaluate the product
214.5 = 29 * Height
Divide both sides by 29
7.40 = Height
Rewrite as:
Height = 7.40
Hence, the height of the prism is 7.40 ft
Read more about volumes at:
https://brainly.com/question/1972490
Answer:
6.6
Step-by-step explanation:
simplify the expression 5/6 (-2y + 3) = ?
Answer:
[tex]-\frac{5y}{3}+\frac{5}{2}[/tex]
Step-by-step explanation:
Given Problem;
[tex]\frac{5}{6}\left(-2y+3\right)[/tex]
Solve;
[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac[/tex]
[tex]\frac{5}{6}\left(-2y+3\right)=\frac{5}{6}\left(-2y\right)+\frac{5}{6}\cdot \:3[/tex]
[tex]=\frac{5}{6}\left(-2y\right)+\frac{5}{6}\cdot \:3[/tex]
[tex]\mathrm{Simplify\;=\frac{5}{6}\left(-2y\right)+\frac{5}{6}\cdot \:3:}-\frac{5y}{3}+\frac{5}{2}[/tex]
[tex]=-\frac{5y}{3}+\frac{5}{2}[/tex]
Hence, Answer = [tex]-\frac{5y}{3}+\frac{5}{2}[/tex]
~Learn with Lenvy~