Answer:
y= 1/18x + 14
Step-by-step explanation:
Well we can first right the equation like : to find the slope
14- 15
____ = -1/-18 = 1/18
0-18
Now we know the slope is 1/18
we can substitute one point in the equation and the slope to find the equation
let's take 0,14
14= 1/18 ( 0 ) + b
14=b
so b= 14
the y-intercept is 14
the equation is
y= 1/18x + 14
What is the area of this triangle?
Working together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in 12 hours. Beatrice and Charlie can build the ant hill in 15 hours. How long, in hours, will it take to build the ant hill if Aran, Beatrice, and Charlie work together?
Here we have a problem of rates of work, we want to know how long will take the 3 ants to build an ant hill if they work together.
We will find that working together, they need to work for 8 hours.
----------------------------------
Let's start by defining the variables that we will use:
A = rate at which Aran worksB = rate at which Beatrice works.C = rate at which Charlie works.Now let's see the given information:
"Aran and Beatrice can build an ant hill in 10 hours"
This can be written as:
(A + B)*10 h = 1 ant hill
"Aran and Charlie can build the ant hill in 12 hours"
This can be written as:
(A + C)*12 h = 1 ant hill
"Beatrice and Charlie can build the ant hill in 15 hours"
This can be written as:
(B + C)*15 h = 1 ant hill.
Then we have 3 equations:
[tex](A + B)*10 h = 1[/tex]
[tex](A + C)*12 h = 1[/tex]
[tex](B + C)*15 h = 1[/tex]
Where for commodity, I removed the "ant hill" unit.
Now we need to solve this system of equations, to do it, we need to isolate one variable in one of the equations and then replace it on another equation.
I will isolate A in the first equation:
[tex]A = \frac{1}{10h} - B[/tex]
Now we can replace it in the second equation to get:
[tex](\frac{1}{10h} - B + C)*12h = 1[/tex]
Now we can isolate C in the last equation to get:
[tex]C = \frac{1}{15h} - B[/tex]
Replacing that in the above equation we get:
[tex](\frac{1}{10h} - B + \frac{1}{15h} - B)*12h = 1\\\\\frac{1}{6h} - \frac{1}{12h}= 2*B\\\\\frac{1}{2}*\frac{1}{12h} = \frac{1}{24h} = B[/tex]
This means that Beatrice alone would construct the hill in 24 hours.
Now that we know the value of B, we can use:
[tex]C = \frac{1}{15h} - B = \frac{1}{15h} - \frac{1}{24h} = \frac{1}{40h}[/tex]
This means that Charlie needs 40 hours to finish the hill alone.
Finally, we can use [tex]A = \frac{1}{10h} - B[/tex] to find the value of A:
[tex]A = \frac{1}{10h} - B = \frac{1}{10h} - \frac{1}{24h} = \frac{7}{120h}[/tex]
Now if the 3 ants work together, the total rate at which they work is:
[tex](A + B + C) = (\frac{7}{120h} + \frac{1}{40h} + \frac{1}{24h} ) = 0.125 h^{-1}[/tex]
This means that they need to work for the inverse of that rate
[tex]\frac{1}{0.125h^{-1}} = 8h[/tex]
Working together, they need to work for 8 hours to complete an ant hill
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Paul won 37 super bouncy balls playing hoops at county fair. At school he gave two to every student in his math class. He only had 3 remaining. How many students are in his class?
Answer:
17 students
Step-by-step explanation:
If he started with 37 and ended with 3 we have to subtract those three first so that we know how many we are actually working with so, 37-3=34. 34 balls is the amount distributed among the class. 34/2 is 17.
1. 10 x ____ = 180
2. 37 x 10 = ____
3. ____ tens = 650
Answer:
1. 18
2. 370
3. 65
Step-by-step explanation:
1. 180/10=18
2. 370 add a zero
3. tens means ·10 so 650/10=65
Answer:
1.)18
2.)370
3.)65 tens yw(:
Evaluate the expression 42 + 5/9y
select all relations that are functions from the choices below.
cos 2 * (x/2) = (sec(x) + 1)/(2sec(x))
Answer:
Answer below
Step-by-step explanation:
I really hope it works
Which postulate proves that the triangles below are similar?
SSS
AA
SAS
These triangles are not similar
Answer:
AA~
Step-by-step explanation:
These triangles are similar but not congruent. One triangle is bigger than the other, meaning none of the side lengths are the same. On the triangles, two angles are given, a 53 degree and a 90 meaning that you would us the AA rule to determine if they are similar. Which they are.
The two triangles are similar triangles using AA postulate.
What are Similar Figures?Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
Given one of the angles in both the triangles is equal to 53°, the other angle is 90°, which are also the vertical angles to each other. As shown below.
Hence, the two triangles are similar triangles using AA postulate.
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Please help due ASAP
Hxhdbdidhdbbr
HELP ASAP!!!! PLEASE HELP!!!!
Step-by-step explanation:
[tex] \sin(c) = \frac{36}{45} = 0.8 \\ \cos(c) = \frac{27}{45} = 0.6\\ \tan(c) = \frac{36}{27} = 1.333[/tex]
What is the solution to the equation? 13 3/4+X= 7 1/ 4
Answer: x=-6 1/4
Step-by-step explanation:
Use complete sentences to describe why postulates are helpful.
Olivia has a points card for a movie theater. She receives 80 rewards points just for signing up. She earns 2.5 points for each visit to the movie theater. She needs at least 105 points for a free movie ticket. Write and solve an inequality which can be used to determine xx, the number of visits Olivia can make to earn her first free movie ticket.
Answer:
10 visits
Step-by-step explanation:
According to the scenario, calculation of the given data are as follows,
Rewards for signing up = 80 points
Reward per visit = 2.5 points
Total points needed = 105
Let, number of visits = x
So, we can calculate number of visits by using following formula,
80 + (2.5 × X) = 105
2.5X = 105 - 80
2.5X = 25
X = 25 ÷ 2.5
X = 10 visits.
Hence, Olivia needs to make 10 visits in order to earn a free movie ticket.
A pair of shoes usually sells for $60. If the shoes are 20% off, and sales tax is 7%, what is the total price of the shoes, including tax?
Answer:
$50.88
Step-by-step explanation:
Adjusted Price without tax = 0.8 * 60,
0.8 * 60 = 48,
With Tax = 1.06 * 48,
1.06 * 48 = 50.88
∴ New Price = 50.88
Answer:
Its $12.84
Step-by-step explanation:
20 percent of $60 is 12, and the sales tax is $.84, so you add those two together and you get $12.84! Hopes this helps and good luck!
what would x equal? (x=___)
Answer:
56mm
Step-by-step explanation:
they are parallelograms so the opposite sides are equal.
in the bottom parallelogram the top side length is 4x the side side length so in the top one the top side length must be 4x the side side length to be similar, so 14*4=56mm
Write the equation of a line through (-1,-5) parallel to 3x-y=5, and in slope intercept form
Answer:
y = 3x -2
Step-by-step explanation:
The general equation form is;
y = mx + b
where m is the slope and b is the y-intercept
For the equation given;
y = 3x -5
the slope from here is 3
If two lines are parallel, they have equal slopes
This mean that the slope of the line we want to calculate too is 3
Now we can use the point slope format to get the correct equation
y-y1 = m(x-x1)
y+ 5. = 3(x+ 1)
y = 3x + 3 -5
y = 3x -2
*PLEASE HELP ME ASAP* Sydnis room is 32 ft by 40 ft. She needs to make a scale drawing of her room that is 8 in. by 10 inc. What is the scale she needs to use?
1 inch = 8ft
1 inch = 4 ft
1 inch = 2 ft
1 inch = 1 ft
Help pls this is timed!!!!!!! Pls and thank you ;P
Who supported the formation of Washington Territory out of a belief that it was America’s destiny to settle the Pacific Northwest?
A.)President Millard Fillmore
B.)Governor Isaac Stevens
C.)Oregon Territory’s northern settlers
D.)Oregon Territory’s southern settlers
Answer:
A. President Millard Fillmore
ratio of width to length is 2:3 if the length 18 meters what is the width
Answer:
12
Step-by-step explanation: 18/3=6 6(2)= 12
Jonathan is building an outdoor staircase for his deck. He uses 8 screws for every 2 steps. If there are 14 steps, how many screws does Jonathan need?
Answer:
56 screws
Step-by-step explanation:
So, first we can find how many screws he needs.
So, if he uses 2 steps for 8 screws, and has 14 steps, that means he puts screws in 7 steps ( 14÷2)
then, if he uses 8 screws, each with 8 steps, we can do 8 times 7, which is 56 screws
The screws does Jonathan need is 56 screws.
It is required to find how many screws does Jonathan need.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Jonathan uses 8 screws for every 2 steps. If there are 14 steps.
So, first we can find how many screws he needs.
According to given question we have
So, if he uses 2 steps for 8 screws, and has 14 steps, that means he puts screws in 7 steps ( 14÷2)
then, if he uses 8 screws, each with 8 steps, we can do 8 times 7, which is 56 screws.
Therefore, the screws does Jonathan need is 56 screws.
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a triangle has sides measuring 31 in 18in and 25 in what is the perimeter of the triangle
38 < 4x - 10
help me out plz n ty
Answer:
Step-by-step explanation:
Bringing like terms on one side
38 + 10 < 4x
48 < 4x
48/4 < x
12 < x
If x : 3 = 5 : 7 , then x = ………
Answer:
the answer is A which 2(1/7)
Plz help me I will give you brainliest and 10 points
Answer:
0.08522
Step-by-step explanation:
What was the price for one notebook?
Answer:
A notebook at the dollar store costs between 1-2 dollars
You brought a magazine for $3 and some candy bars for $2 each. You spent a total of $19. How many candy bars did you buy?
Answer:
8
Step-by-step explanation:
Answer:
Candy bars: $13
Step-by-step explanation:
$3 magazine + $13 total of candy bars = $19
What is the value of
2021
−
2223
+
2425
?
?
Answer:
2223
Step-by-step explanation:
We need to find the value of 2021-2223+2425.
Firstly subtract 2223 from 2021.
2021-2223 = -202
Now add -202 and 2425. So,
2425 +(-202) = 2223
So, the value of 2021-2223+2425 is 2223. Hence, this is the required solution.
The diagram shows a square with a perimeter of 20 cm.
Not drawn
accurately
Eight of these squares fit together to make a rectangle.
Not drawnaccurately
What is the perimeter of the rectangle?
The perimeter of the rectangle is 70cm.
What is perimeter?Perimeter is the total length of the sides of a two-dimensional shape.
What is the formula for the perimeter of square?Perimeter of the square is given by
P = 4a
where,
a is the side length of the square.
P is the perimeter of the square.
What is the formula for the perimeter for the rectangle?Perimeter of the rectangle is given by
P = 2( l + b)
Where,
l is the of the rectangle
b is the breadth of the the rectangle
According to the given question.
We have the perimeter of the square is 20cm.
⇒ 4a = 20
⇒ a = 5cm
⇒ Each side length of the square is 5cm
And a rectangle made of 10 squares.
⇒ length of the rectangle = 5×5 = 25cm
and the breadth of the rectangle = 2 × 5 = 10cm
Therefore, the perimeter of the rectangle = 2(25 + 10) = 2 × 35 = 70cm
Hence, the perimeter of the rectangle is 70cm.
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When multiplying or dividing integers, if the signs are the same, you keep the sign for the answer.
GIVING BRAINLIST PLEASE ANSWER CORRECT!!!
False
True
in the equation x+12=30 does x=16 explain your answer
