Answer:
The piecewise equation is given as :[tex]A(t)=\begin{cases} 25x& \text{ if } 0 \leq x \leq 3 \\ 75& \text{ if } 3<x<4 \\ 75+20(x-4) & \text{ if } 4 \leq x \leq 6\end{cases}[/tex]
Step-by-step explanation:
Let x be the time in hour and A(x) be the amount of accumulating rainfall at time x.
We are given that in the first three hours the rain fell at a constant rate of 25mm per hour
Amount of rainfall in 1 hour = 25
Amount of rainfall in t hours = 25x
[tex]A(x) = 25x ; 0 \leq x \leq 3[/tex]
The rain then slows down and remains constant
So, Amount of rain for that hour = [tex]25 \times 3 = 75 mm[/tex]
75 mm ; 3
Now we are given that started again at a constant rate of 20 mm per hour for the next two hours.
Amount of rain after 4 hours = [tex]75+20(x-4) ; 4 \leq x\leq 6[/tex]
The rain increases at a rate of 20t from 4 ≤ x ≤ 6.
Hence the piecewise equation is given as :[tex]A(t)=\begin{cases} 25x& \text{ if } 0 \leq x \leq 3 \\ 75& \text{ if } 3<x<4 \\ 75+20(x-4) & \text{ if } 4 \leq x \leq 6\end{cases}[/tex]
if △ ABC ~ △A'B'C' and AC=20cm,A'C'=15cm,B'C'=12cm andA'B'=9cm find the lengths of the other sides of △ABC.
Answer:
AB=12 BC=9
Step-by-step explanation:
Any side of a triangle must be shorter than the other two sides added together.
AB and A'B' must measure LESS than the other 2 sides
15 is 3/4 of 20
12 is 3/4 0f 9
20/15 12/9 = 1.3333333........
What is an equation of the line that passes through the points (3, -1),(-3,1)
Answer: y=-x/3
Step-by-step explanation:
A right triangular prism is sliced perpendicular to its base. What is the shape of the resulting two-dimensional cross section?
trapezoid
rhombus
rectangle
square
Answer:
answer is C. Rectangle
Step-by-step explanation:
The shape of the resulting two-dimensional cross section is a rectangle.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A right triangular prism has a base that is a right triangle, and the prism has three perpendicular rectangular faces that join the two congruent triangles.
When this prism is sliced perpendicular to its base, the resulting two-dimensional cross-section will always be a rectangle.
This is because the cut will be perpendicular to the rectangular faces of the prism and the base triangle, resulting in a rectangle.
The length of the rectangle will be equal to the base of the triangle, and the width of the rectangle will be equal to the height of the prism.
Hence, shape of the resulting two-dimensional cross section is a rectangle.
To learn more on Three dimensional figure click:
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What is 45,803 in expanded form
Answer:
Step-by-step explanation:
The angle of a pentagon are x, x+10,x+20,x+30 and x+40 degree find all the angle of the pentagon
Answer:
59
Step-by-step explanation:
You have to add your numbers then subtract the last number you had.
Hope this doesn't help
(06.06 MC)
A student attempted to generate an equivalent expression using the distributive property, as shown below:
3(p − 4) = 3p − 4
What was the mistake made? (1 point)
a
3 was not multiplied by p
b
3 was not multiplied by −4
c
Incorrect sign was used for the first term
d
Incorrect sign was used for the second term
20 POINTS HELP ASAP
Answer:
b 3 was not multiplied by −4
Step-by-step explanation:
The correct way to apply the distributive property is to multiply 3 by p and multiply 3 by -4 as shown below.
3(p − 4) = 3p + 3 × (-4) = 3p - 12
His attempt is
3(p - 4) = 3p - 4
He did multiply 3 by p, but h did not multiply 3 by -4.
Answer: b 3 was not multiplied by −4
Segment AB falls on line 6x + 3y = 12. Segment CD falls on line 4x + 2y = 8. What is true about segments AB and CD?
They are parallel because they have the same slope of -2.
1
They are parallel because they have the same slope of
2
They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.
They are lines that lie exactly on top of one another because they have the same slope and a different y-intercept.
Answer: C
Step-by-step explanation:
The slope-intercept form of a line is given by
y = mx + b
m - slope
b - y-intercept
Segment AB lies on the line 6x + 3y = 12
6x + 3y = 12
3y = -6x + 12
y = -6/3x + 12/3
y = -2x + 4
Comparing with the slope-intercept form,
Slope = - 2
y-intercept = 4
Segment CD lies on the line 4x + 2y = 8
4x + 2y = 8
2y = -4x + 8
y = -4/2x + 8/2
y = - 2x + 4
Comparing with the slope-intercept form,
Slope = - 2
y-intercept = 4
Both the line segments have the same slope and the same y-intercept, so the two line segments will lie exactly on top of one another.
Therefore, the correct option is (c)
Find the GCF of each pair of terms.
3 and 9
Answer:
The GCF is 3.
Step-by-step explanation:
All you do is list out the factors of the numbers and find the greatest factor that they have in common.
Like the GCF of 3 and 9. We list the factors.
Factors of 3:
1, 3
Factors of 9:
1, 3, 9
As we can see, 3 is the GCF because it is the highest factor that the numbers have in common.
Hope this helps!
5x-x/y when x=4 and y=2
Plug it in!
5x - x/y
5(4) - 4/2
20 - 2
18
18Answer:
8
Step-by-step explanation:
Write the equation of the line going through the points A(0, -4) and B(-1, -6). Then graph.
Answer:
y=2x-4
Step-by-step explanation:
Miss Alison drew a box and whisker plot to represent her students scores on a midterm test. James received 47 on the test. How does James score compare to his classmates?
Answer: A
Step-by-step explanation:
About 25% scored higher; about 75% scored lower.
A line passes through the point (-8,8) and has a slope of -5/4
What’s the name of the transformation???
Answer:
Translation
Step-by-step explanation:
Remember Translation as a 'Slide'
Answer:
translation
Step-by-step explanation:
hopes this help
Hillary swam 24 seconds faster than her last race. She wam the last race in 4 minutes and 12 seconds. How long did it take Hillary to swim this race!
Answer:
3 minutes and 48 seconds
Step-by-step explanation:
Answer: 4 minutes 36 seconds
Step-by-step explanation:
Add the 24 seconds to 4 minutes 12 seconds. 24 + 12 = 36
4 minutes 36 seconds
Find the point slope formula of negative (-6,0) and slope of 2/3
Answer:
[tex]y-0=\frac{2}{3}(x+6)[/tex]
Step-by-step explanation:
The point-slope formula is [tex]y-y_{1}=m(x-x_{1})[/tex]. Plug in the values from the given information and you have your answer.
Suppose a jar contains 8 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Round your answer to 4 decimal places.
it would most likely be blue because its more
it would be a 57.1429%. of blue
#18 please help gang gang
Answer:A
Step-by-step explanation:
270/630 x 100= 43
answer: A
Step-by-step explanation:
270/630x100 =45
Keith bought 4 shirts for $36. At this rate, what would his cost be for 7 shirts?
Answer:
Your cost will be $63
Step-by-step explanation:
How many seconds are in 7 hours?
someone please help me!
Answer:
25200
Step-by-step explanation:
ez
Answer: There is 25,200
Step-by-step explanation:
60 seconds in an hour
70x60=25,200
100 POINTS HEELP PLSSS!!!
Answer:
See below.
Step-by-step explanation:
1.
y = 100 + 65x
y = 40 + 80x
100 + 65x = 40 + 80x
-15x = -60
x = 4
y = 100 + 65x = 100 + 260 = 360
(4, 360)
2.
The lines intersect at the point (4, 360).
At the point of intersection, where x = 4, it shows that by doing 4 hours of labor, both shops cost the same.
3.
Mike's:
y = 100 + 65x = 100 + 65(3) = 100 + 195 = 295
Amy's:
y = 40 + 80x = 40 + 80(3) = 40 + 240 = 280
For 3 hours of labor, Amy's shop is cheaper at $280. Mike's costs $295.
Answer:
1. (4, 360)
2. total cost at both repair shops is the same
3. Amy's Auto Repair: $280
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=100+65x\\y=40+80x\end{cases}[/tex]
Question 1
Solve by using the Substitution Method:
[tex]\implies 40+80x=100+65x[/tex]
[tex]\implies 40+80x-65x=100+65x-65x[/tex]
[tex]\implies 40+15x=100[/tex]
[tex]\implies 40+15x-40=100-40[/tex]
[tex]\implies 15x=60[/tex]
[tex]\implies 15x \div 15=60 \div 15[/tex]
[tex]\implies x=4[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\implies y=40+80(4)[/tex]
[tex]\implies y=40+320[/tex]
[tex]\implies y=360[/tex]
Therefore, the point of intersection is (4, 360)
Question 2
The two lines intersect at (4, 360). This means that the total cost at both repair shops is the same when it takes 4 hours to repair the car. The cost at this time is $360.
Question 2
To find the cost at both repair shops if it takes 3 hours to fix the car, substitute x = 3 into both equations and solve for y:
Mike's Repair shop:
[tex]\implies y=100+65(3)[/tex]
[tex]\implies y=100+195[/tex]
[tex]\implies y=295[/tex]
Amy's Auto Repair:
[tex]\implies y=40+80(3)[/tex]
[tex]\implies y=40+240[/tex]
[tex]\implies y=280[/tex]
Therefore, Amy's Auto Repair company is the cheapest at a cost of $280.
n/7; evaluate, when n=35
Answer:
5
Step-by-step explanation:
35/7 = 5
Answer:5
Step-by-step explanation:
Place parentheses in the expression to find a value other than 18. Then find the value of the new expression.
Answer:
I need a picture
Step-by-step explanation:
but if not then 3 +(1 + 14)
Pls answer pls pls
It would really help
Answer:
Step-by-step explanation:
When you're drawing an inequality on a number line there are a few things to focus on:
- Whether your variable is greater than or less than the number
- Whether it can be equal to the number or not
If it can be equal to the number your first dot will be filled in, if not it will be hollow
When it's less than it means you're moving to the left on your number line, if it's greater than you move right
Find the surface area of the figure above:
15 inches
the red part is the same as the bottom part of the shape, you do 3 x 5 because thats the measurements of the rectangle shaded in red
Courtney is twice as old as Andre and three yoars older than Natalio Courtnoy is half Shar's ago Tho differenco between Shani's age and Natale's age is the same as tho sum of Courtnoy's ago and Andro's ago The oquation below represents their ages 2x-(x-3)-X+ In the equation, tho variable x represents ____age
•Courtenys
•Andre's
•Natalie's
•Shari's
Answer:
Andre's
Step-by-step explanation
I think its Andre. I apologize if it is not.
A certain health insurance plan costs $3000 per year for a family of six. If each member of the family has $750 in medical expenses in a year, and the plan pays 100 percent of those expenses, how much will the family save by purchasing the plan?
Answer:
I think its $1,500
Step-by-step explanation:
6 times 750 = 4,500
4,500- 3,000= 1,500
Please help me find the slope and y-intercept of these two equations. And please tell me if they are proportional. or not
Answer:
Take a look at the image, my edits are in red color.
Step-by-step explanation:
Proportional because it follows y=kx
lmk if you dont understand smth
Pls mark brainliest!
Similarity.
Please help
Need help I’m confused question is 7.50 per hour washing cars Graph the relationship between the number of hours Gilbert works and the total amount of money he earns .
Answer:
You would start your graph at (1,7.5) (2, 15) (3, 22.5) (4, 30) (5, 37.5)
Step-by-step explanation:
What you do is for every hour you add 7.50. I don' know how many hours you need to graph so I just gave you the first five, But you should start to see a pattern, just continue with the pattern and you will get it right! Hope this helps!
What is the system of equations for the solution (4,8) I need step by step.