h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
What is the graph of the function?A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.
Here,
We can draw the graph as
h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)
h(x) = f(x) + 5
The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.
Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
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Question 1-1
Barrett earns $15 per hour cutting grass and $10 per hour tutoring reading. In one month, Barrett needs to save at least $400 for a
new lawnmower but does not want to work more than 35 hours.
Part A: Let z represent the hours cutting grass and y represent the hours tutoring. Given z 20 and y ≥ 0, select all the inequalities
that represent the situation.
On solving the inequality we know, Barrett should work 25 hours tutoring and 10 hours cutting grass to make $400.
What exactly does inequality mean?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality results from a lack of balance.
Solution:-
given,
z=hours of cutting grass
y=hours of tutoring
Two equation can be made using given condition
15z+10y=400
and
z+y=35
Solving both equation simultaneously,
we get
y=25
z=10
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Bea T. Howen, a sophomore college student, lost her scholarship after receiving a D in her "Music Appreciation" course. She decided to buy a snow plow to supplement her income during the winter months. It cost her $6312.50. Fuel and standard maintenance will cost her an additional $8.75 for each hour of use. Find the cost function C(x) associated with operating the snow plow for x hours. C(x)= If she charges $34.00 per hour write the revenue function R(x) for the amount of revenue gained from x hours of use. R(x)= Find the profit function P(x) for the amount of profit gained from x hours of use. P(x)= How many hours will she need to work to break even? hours
Answer:
[tex](a)\ C(x) = 6312.50 + 8.75x[/tex]
[tex](b)\ R(x) = 34x[/tex]
[tex](c)\ P(x) = 6312.50 -25.25x[/tex]
[tex](d)\ Break\ Even = 250\ hours[/tex]
Step-by-step explanation:
Solving (a): The cost function.
Given
[tex]Cost = \$6312.50[/tex] --- cost of saxophone
[tex]Additional = \$8.75[/tex] per hour
The cost function is: sum of the cost of the saxophone and the extra cost per hour.
If an hour costs 8.75, then x hours will cost 8.75x
So, the cost function is:
[tex]C(x) = Cost + Additional[/tex]
[tex]C(x) = 6312.50 + 8.75x[/tex]
Solving (b): The revenue function
Given
[tex]Charges = \$34.00[/tex] per hour
The revenue function is the product of the unit charge by the number of hours.
If in an hour, she charges $34.00, then in x hours, she will cost 34x
So, the revenue function is:
[tex]R(x) = Charges * Hours[/tex]
[tex]R(x) = 34.00 * x[/tex]
[tex]R(x) = 34x[/tex]
Solving (c): The profit function
This is the difference between the cost function and the revenue function
i.e.
[tex]P(x) = C(x) - R(x)[/tex]
So, we have:
[tex]P(x) = 6312.50 + 8.75x - 34x[/tex]
[tex]P(x) = 6312.50 -25.25x[/tex]
Solving (d): The break even hours.
To do this, we simply equate the cost function and the revenue function, then solve for x
i.e.
[tex]C(x) =R(x)[/tex]
[tex]6312.50 + 8.75x = 34x[/tex]
Collect like terms
[tex]6312.50 =- 8.75x + 34x[/tex]
[tex]6312.50 = 25.25x[/tex]
Solve for x
[tex]x = \frac{6312.50}{25.25}[/tex]
[tex]x = 250[/tex]
HELPPPPP! Points scored in a basketball game vary directly with shots taken. If a player scores 50 points , and takes 40 shots , how many would she score if she takes 60 shots? Round your answer down to the nearest points scored
Answer:
Points scored in a basketball game vary directly with shots taken.
This means that this question can be solved
by proportions, using a rule of three.
How many would she have scored if she takes 60 shots?
Using a rule of three:
50 points - 40 shots
x points - 60 shots
Applying cross multiplication:
4x = 50 × 60
Divide from both sides
x = 50 × 1.25 = 75
Answer is 75
Step-by-step explanation:
Here is a easier explanation if you didn't understand clearly:
It asked for how many 60 shots would score.
You would look at the first time he scored which is 50 and took 40 shots. Divide them
50 ÷ 40 = 1.25 or 1.5
So now you know each point scores 1.25 or 1.5
Now you multiply 1.25 or 1.5 with how many shots to see how much was scored and in this case 60 shots.
60 × 1.25 or 60 × 1.5
& They both end up equaling just the same, 75.
Hope it made sense :)
Find the missing length indicated
Unitary method A car can cover a distance of 522km on 36litres of disesel. How far can it travel with 14litres,
Answer:
It can cover 203 km with 14 litres.
Step-by-step explanation:
Given that,
A car can cover a distance of 522km on 36litres of diesel.
522 km = 36 litres
1 l = (522/36) km
We need to find how far can it travel with 14 litres.
We can use the unitary method to solve it.
[tex]14\ L=\dfrac{522}{36}\times 14\\\\=203\ km[/tex]
So, it can cover 203 km with 14 litres.
Given the triangle below what is the length of the third side rounded to the nearest whole number?
Will Give brainliest
No links please.
Sorry I over complicated the answer that i wrote, I think the answer is 18
Helppppppppppppppp!!!!!
Hi there!
[tex]\large\boxed{\text{ UVY} = 65^o, \text{ VYZ }= 65^o}[/tex]
We can begin by finding ∠VUY so we can solve for ∠UVY.
∠VUY is supplementary to ∠TUY, so:
180 = 144 + ∠VUY
∠VUY = 36°
In a triangle, angles sum up to 180°, so:
180 = 36° + 79° + m∠UVY
m∠UVY = 65°
Solve for m∠VYZ by comparing the angle to m∠UVY because the angles are alternating interior angles. Thus:
m∠UVY = m∠VYZ = 65°.
Help plz:)))I’ll mark u Brainliest
Answer:
h = 9
Step-by-step explanation:
cylinder A = [tex]\pi[/tex][tex]3^{2}[/tex]*4 = 113.0973355 [tex]m^{3}[/tex]
Cylinder B = 113.0973355 [tex]m^{3}[/tex]
113.0973355 [tex]m^{3}[/tex] = [tex]\pi[/tex][tex]2^{2}[/tex]*h
113.0973355 [tex]m^{3}[/tex] / 4[tex]\pi[/tex] = h
8.999999999998 = h
I think b/c of the rounding error of rounding off pi, that h= 9
Dan is trying to construct a bigger square by utilizing and putting together pieces of square-shaped pieces of paper with similar dimensions. Without tearing or cutting, what is the minimum number of pieces required to achieve his objective?
The minimum number of pieces dan requires to achieve his objective of constructing a bigger square is; 4 pieces
First of all we need to understand that the 4 sides of a square are equal.We are told that dan is trying to construct a bigger square with a smaller square. That all the smaller square-shaped pieces of paper have similar dimensions.
Now, if the length of a side of the small square shaped pieces is x, it means that if we join 2 of the smaller squares, we will have;Length = 2x
Width = x
Both sides above are not equal and as such we need to join 2 more squares the exact way the above was done. This means that if the 2 new squares are added adjacent to the incomplete side, we will now have;Length = 2x
Width = 2x
Thus, the minimum number of pieces dan will require to construct the bigger square is 4 squares.
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HELP WILL GIVE BRANLIEST! No links!!!
Answer:
11.5
Step-by-step explanation:
[tex]14^{2} - 8^{2} = 132\\\sqrt{132}= 2\sqrt{33} = 11.48912529\\answer-is -11.5[/tex]
Answer:
11.48
Step-by-step explanation:
Pythagoras Therum
8^2 + x^2 = 14^2
64 +×^2 = 196
x^2 = 132
sqrt both sides
11.48
88 student said they watch TV everyday. This number represents 80% of the students body. What is the total number of students in the student body? And i need you to give me the part,whole,and percent
The total number of students in the student body is 110.
How many students are in the student body?Percentage is the ratio of an amount expressed as a number out of 100. The sign that is used to represent percentage is %.
In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.
In order to determine the total number of students in the student body, divide the number of students that watch TV everyday by the given percentage.
Number of students in the student body = number of students that watch TV everyday / percentage
88 / 80%
= 88 / 0.8 = 110
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A hexagon forms a semi-regular tessellation with which of the following
regular polygons?
A. Square and equilateral triangle
B. Dodecagon and equilateral triangle
C. Trapezoid and pentagon
D. Trapezoid and octagon
Answer:
A.
Step-by-step explanation:
The formula for finding the perimeter of a rectangle is P = 2 × l + 2 × w.
For which of the following quadrilaterals could you NOT use this formula to find its perimeter?
A.
Parallelogram
B.
Rhombus
C.
Square
D.
Trapezoid
Answer:
D. trapezoid
Step-by-step explanation:
---------------
Can y’all help me?!
Answer:D
Step-by-step explanation:
3 is on the positive x side and 2 is on the negative y side so it will be (3,-2)
A family went out to dinner. The cost of their meal was $57.50, before sales tax and tip.
A sales tax of 8% was added.
The family then tipped 18% on the amount after the sales tax was added.
Part A:
What was the amount, rounded to the nearest cent, of just the sales tax?
Part B : What was the total amount the family paid , including tax and tip , rounded to the nearest cent ?
PLEASE HELP
Answer:
I hope I got this answer right
A is 4.60 and B is 8.30
pls help djehhxhxhxhxhxjjdndnd
Area of both the triangles :
= ½ × base × prepenicular
= ½ × 3 × 4
= 3 × 2
= 6 × 2 = 12 ( We have two triangles)
Area of semicircle :
= πr²/2
= 3.14 × 3 × 3 /2
= 28.26/2
= 14.13
Total area = 12 + 14.13 = 26.13 = 26.130
onsider the transformation.
Which statement about the transformation is true?
O It is isometric because the side lengths remained the
same,
• It is isometric because all
angle measures remained
the same.
It is not isometric because the side
lengths did not
remain the same.
O It is not Isometric because the
not remain the same.
angle measures did
Mark this and return
Save and Exit
The transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.
What is isometric transformation?An isometric transformation is one that keeps the angles and distances between the original and changed shapes the same. There are numerous techniques that can be used to alter any image in a plane.
The two figures are isometric only if they are congruent. In the given figure the angles remain the same however the lengths of the side are transformed as the figure is dilated.
Hence, the transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.
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Three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally, how much of the candy bar will each person get?
The candy bar will each person get will be 4 / 15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally.
The amount of candy shared by each person will be,
Amount = ( 4 / 5 ) ÷ 3
Amount = 4 / 15
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Can y’all help me?!
Answer:
4 is next in NUMBER OF DAYS
9 is the first in NUMBER OF TADPOLES
41 is the 2nd answer ON NUMBER OF TADPOLES
Step-by-step explanation:
hope this helps a lot!!
In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 2.5 inches. Using the empirical rule, what percentage of the boys are between 61.5 and 76.5 inches tall?
Step-by-step explanation:
plus of yhis number and solve it oksy
Pls help me out here
All of the equations that are true include the following:
B. 56 + 70 = 14(4 + 5).
C. 28 + 49 = 7(4 + 7).
What is the distributive property of multiplication?In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.
How to determine the true equation?In order to determine the true equation, we would apply the distributive property of multiplication and then check whether or not the right-hand side is equal to the left-hand side.
By applying the distributive property of multiplication to the given mathematical expression, we have the following:
32 + 96 = 8(4 + 14)
32 + 96 = 32 + 112 (False).
56 + 70 = 14(4 + 5).
56 + 70 = 56 + 70 (True).
28 + 49 = 7(4 + 7).
28 + 49 = 28 + 49 (True).
27 + 36 = 3(9 + 13)
27 + 36 = 27 + 39 (False).
25 + 35 = 5(5 + 6)
25 + 35 = 25 + 30 (False).
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2 7/8 + 2 7/8 Answer pls
Answer:
5 + 3/4
Step-by-step explanation:
Answer:
23/4
Decimal Form:
5.75
Mixed Number Form:
5 3/4
Step-by-step explanation:
there ya goo
PLEASE HELP!!
For the right triangles below, find the values of the side lengths c and b.
Round your answers to the nearest tenth.
Answer:
[tex]c = 3 \tan(60 \degree) \\ c = 5.2 \\ hypotenuse \: of \: first \: triangle : \\ = \frac{ 5.2 }{ \sin(60 \degree) } \\ = 6 \\ \\ \frac{6}{4} = \frac{c}{b} \\ \frac{6}{4} = \frac{5.2}{b} \\ b = \frac{5.2 \times 4}{6} \\ b = 3.5[/tex]
Determine whether the scenario involves independent or dependent events.
A basket contains seven apples and six peaches. You randomly select a piece of fruit and then return it to the basket. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second piece is a peach.
Combine terms: 12a + 26b -4b – 16a.
Answer:
The answer is -4a + 22b
Step-by-step explanation:
12a + 26b -4b -16a
12a - 16a + 26b - 4b
-4a + 22b
Thus, The answer is -4a + 22b
-TheUnknownScientist
Step-by-step explanation:
[tex] \mathfrak{SOLUTION} _{(By\:Mister360)} \begin{cases} \\ \rm \mapsto \: 12a + 26b - 4b - 16a \\ \\ \rm \mapsto \: 12a - 16a + 26b - 4b \\ \\ \rm \mapsto \: (12 - 16)a + (26 - 4)b \\ \\ \rm \mapsto \: - 4a + 22b \\ \\ \rm \mapsto \: - (4a - 22b) \end{cases}[/tex]
you can use a calculator if you want. No links please help this is very important i will give you brain thing if its correct
Answer:
6a. 0.02623
b. 0.5692
Thank you :)
A bakery sells cupcakes and cookies. No more than 750 total items
can be produced a day. Production costs cannot exceed $1200 per day. It costs
$0.50 to make a cupcake and $0.25 to make a cookie. Given that you have the
constraints0.5x +0.25y < 1200 and 2 + y < 750, how would you
write an additional constraint to represent that the bakery can produce at most 85
cookies?
Answer:
The question doesn't make since so random guess
If you multiply $0.50 by 750 you get 375
If you multiply $0.25 by 750 you get 187.5
divide that by 85 and you get 2.2.
Step-by-step explanation:
Solve: 10y2+57y+35=0.
Answer: y = −0.7, -5
Step-by-step explanation:
7. Sarah draws a card from a standard deck, throws the card away, and then draws another card.
Are these events independent or dependent?
Answer:
dependent
Step-by-step explanation:
Solve for x.
x - 6 = 8
x = [?]
x=14
Step-by-step explanation:
the answer is 14
I just added 8 with 6
:)