Answer:
20x + 17y
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyStep-by-step explanation:
Step 1: Define
-(-20x - 17y)
Step 2: Simplify
Distribute: -(-20x) - (-17y)Simplify: 20x + 17yWhich expression has the same sum as the one below - 15 + 16
Answer:
6+(-15)
Step-by-step explanation:
In 1992, Disney created a one-of-a-kind special pin. Each year, the pin’s value appreciates by a constant amount. In 1997, the pin was valued at $350. In 2002, it was valued at $600. Let x be the number of years since 1992 and y be the value of the pin in dollars. Write a linear equation in slope-intercept form that models this situation.
Answer:
[tex]y = 50x + 50[/tex]
Step-by-step explanation:
Given
x = years since 1992.
y = value of pin
This means that
[tex]x = 1[/tex] ----- in 1992
[tex]x_1 = 6[/tex]; [tex]y_1 = 350[/tex] ---- in 1997
[tex]x_2 = 11;[/tex] [tex]y_2 = 600[/tex] ---- in 2002
Required
Determine the line equation in slope intercept form
First, we need to determine the slope (m) of the line
[tex]m = \frac{y_2 - y_1}{x_2- x_1}[/tex]
[tex]m = \frac{600 - 350}{11- 6}[/tex]
[tex]m = \frac{250}{5}[/tex]
[tex]m = 50[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Recall that
[tex]x_1 = 6[/tex]; [tex]y_1 = 350[/tex]
[tex]m = 50[/tex]
So, we have:
[tex]y - 350 = 50(x - 6)[/tex]
[tex]y - 350 = 50x - 300[/tex]
[tex]y = 50x - 300 + 350[/tex]
[tex]y = 50x + 50[/tex]
A Rental Car Agency charges a flat fee of $25 per day plus $0.15 for each mile driven. The total charge for one day's rental was $75.30. Which equation below can be used to solve this problem?
Answer:
Step-by-step explanation:
75.30-25 for a day leaves 50.30 for mileage.
50.30/.15 per mile= 335.3 miles driven.
75.30>=25+0.15m. m=335.3
Please help me out with this please
Answer:
2nd from the bottom
Step-by-step explanation:
Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet Jane at the end of her run. How much farther does Jane travel than her trainer? Answer the questions to find out. 1. What is the total distance Jane travels biking and running? Include units with your answer. Write your answer in the space below. 2. Use the Pythagorean theorem to write an equation for the distance Jane's trainer bikes. Write your answer in the space below. 3. Solve your equation to find the distance Jane's trainer bikes. Show your work. Write your answer in the space below. 4. How much farther does Jane travel than her trainer? Write your answer in the space below.
Answer:
can you Please put screen shot in there
Step-by-step explanation:
22.34 miles much farther does Jane travel than her trainer.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
Here, given that,
she leaves the health club and bikes 16 miles south.
Then, She then runs 12 miles west.
so, we have,
It must be, hypotenuse = 16 miles
base= 12 miles
We have to find, the height.
by Pythagorean theorem, we get,
the distance Jane's trainer bikes=√16²-12² miles
=√32 miles
=5.66 miles
So. she travels in total = 28 miles
22.34 miles much farther does Jane travel than her trainer.
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A farmer grows a particular plant that has a gene that can be manipulated to control the age t at which the plant matures. The number of seeds S(t) produced by a plant maturing at age t is S(t)=−0.3t2+30t+0.2 seeds per mature plant A farmer asks the geneticists to genetically engineer a plant line that accounts for the fact that on his farm, only P(t)=90000t+100, plants mature to age t. What age of maturity should the geneticist select for the plants to maximize the seed production of the farmer's crop?a. Between 130 and 140 days b. Between 120 and 130 days
Answer:
The correct option is;
Between 40 and 50 days
Step-by-step explanation:
The number of seeds that are produced by a plant maturing at age t, S(t), is given as follows;
S(t) = -0.3·t² + 30·t + 0.2
The proportion of plants maturing at age (t) in the plants to be engineered by the geneticist P(t) = 90000/(t + 100)
The number of seeds produced by the plants = S(t) × P(t) = (-0.3·t² + 30·t + 0.2)×(90000/(t + 100))
To find the maximum number of seeds, we differentiate using an online tool, and equate to zero to get;
d((-0.3·t² + 30·t + 0.2)×(90000/(t + 100)))/dt = (-27000·t² - 5400000·t + 269982000)/(t + 100)² = 0
(-27000·t² - 5400000·t + 269982000)/(t + 100)² = 27000(t - 41.419)(t + 241.419)/(t + 100)² = 0
t = 41.419 or t = -241.419
Therefore, in order to maximize the production of seed of the crops of the farmer, the geneticist should select between 40 and 50 days.
Alex rode his bike 25 kilometers. About how many miles did Alex ride his bike?
Answer:
Alex rode 15.5343 miles in his bike
Step-by-step explanation:
1 kilometer is 0.621371 miles, multiply 0.621371 with 25. Hope this helps!
Alex rode his bike for 15.535 miles.
What is unit conversion?Unit conversion means the conversion between different units and measurements of the same quantity done by the process of multiplication or division.
Given
Alex rode his bike 25 kilometers
1 kilometer = 0.6214 miles
25 kilometers = 0.6214 × 25 = 15.535 miles
Hence, ride distance is 15.535 miles.
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AB=CD what is the property
Answer me plzzzz fast ASAP
Answer:
this is payback for what you did here
Step-by-step explanation:
Select all lines with a slope of 2/5
Answer:
C and D
Step-by-step explanation:
Answer:
Pull a mil' in a day, ain't even have the bill
On your pill, everyday I just be sippin' Chamomile
Mass appeal, everybody show up 'cause they know I'm here
Every week, I be on the face, she think it's Cetaphil
Up in my business, pull up in my crib
I got people locked and loaded like they trained for ISIS
Askin' for forgiveness, I never said you have it
Pullin' all these dimes like, do you really want attention?
Step-by-step explanation:
A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week.
a. create a system of equations or inequalities that models the situation. define the variables you use.
b. the graph shows one of the relevant equations in this situation. Draw the graph of the other relevant equation.
c. show all the points that represent the number of hours the student can work at each job and meet his goal.
Answer:
:)
Step-by-step explanation:
15x=300
x will equal 20
20x=300
x will equal 15
Inequalities are used to represent unequal expressions
System of equationsRepresent the number of lawns mown by x, and the number of gardens with y.
So, the system of inequalities are:
[tex]x + y \le 20[/tex] --- the number of hours worked, weekly[tex]15x + 20y \le 300[/tex] --- the earnings weeklyGraphSee attachment for the system of inequalities, and all the points that represent the hours worked
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The formula for the area of a triangle is A =12bh, in which b represents the length of the base and h represents the height. If a triangle has an area of 232 mm 2 and the height is 16 mm, what is the measure of the base? The measure of the base is mm.
Answer:
Step-by-step explanation:
Write it out: A = 1/2(bh)
substitute values: 232 = 1/2(16b)
Simplify: 232 = 8b
Divide each side by 8: b = 29
The base is 29 millimeters
Translate the sentence into an inequality..
The quotient of y and 7 is at least 18.
Answer: [tex]\frac{y}{7} \geq 18[/tex]
Step-by-step explanation:
Key things to remember:
- quotient signals dividing
- at least means greater than or equal to, so we use the greater than or equal to sign
Applying this to the problem, we can translate into a simpler sentence:
y divided by 7 is greater than or equal to 18 --> which leads us to the inequality above
What is the measure of angle a?
A) 54
B) 46
C) 126
D) 136
Answer:
Step-by-step explanation: 54+54=108
360-108=252 divide by 2
Answer:
C
Step-by-step explanation:
a and 54° are adjacent angles and are supplementary, thus
a = 180 - 54 = 126 → C
a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an inital speed of 120 feet per second. which equation correctly models the balls height as a function of time
Answer:
An equation that correctly models the ball's height as a function of time is:
h (t) = - 16t ^ 2 + 130t + 2
Step-by-step explanation:
i hope this helps !
Answer:
h(t) = -16t^2 + 120t + 2
Step-by-step explanation:
Multiple Choice
What are the equivalent fraction and decimal for 25%?
A. one over twenty-fiveand 0.25
B. twenty-five over twenty-fiveand 4
C. one-fourthand 0.25
D. three-fourthsand 0.4
A fitness center charges a monthly fee to use the facilities plus $3 for each fitness class. One month Sara took 6 classes and paid $30 for the month. If she paid $48 for the next month how many classes did she take?
Answer:
12
Step-by-step explanation:
3x6 = 18
30-18 = 12 so the monthly fee is twelve
-----------------------------------------------------------------
48- 12 = 36 (cost of classes)
36/3= 12
If a=1, b = 2 and c=-3, find the value of 4a3b2
Answer:
48
Step-by-step explanation:
(4*1)(3*2)*2
4*6*2
48
If you have 3.15 pieces of chocolate and you give 1.6 pieces to your friend how many pieces of chocolate do you have left?
Answer:
1.55
Step-by-step explanation:
Which correctly describes how the graph of the inequality 4x − 2y > 20 is shaded?
Above the solid line
Below the solid line
Above the dashed line
Below the dashed line
Answer:D Below the Dashed line
Step-by-step explanation:
Just took the test
Answer:
Below the dashed line so the answer is D
Step-by-step explanation:
just finished taking the quiz with this same answer!!
What is the volume of a cone (in cubic inches) with a radius of 3 inches and a height of 6 inches?
Use 3.14 for π. Round your answer to the nearest hundredth.
Answer:
V≈56.55in³
Step-by-step explanation:
Answer:
56.55
Step-by-step explanation:
just took the test dattebayo.
A class has 5 girls and 9 boys. Select all associated ratios for this class.
A. 5:4
B. 5:14
C. 9:14
D. 14:11
E. 5:4
F. 9:5
G. 4:9
H. 5:9
Mr. Omar assigns homework to his class and the homework requires students to
find the prime factorization of 648 using the factor tree method. Kumar wrote the
following. Is he correct? If not, explain why and show the correct method.
Kumar’s solution: 162 X4
Need rn! worth 30
Evaluate the function T(x)=19−x, when x=−3.
a.) 57
b.) 22
c.) 16
d.) −16
Answer:
b
Step-by-step explanation:
Which of the following options is an equivalent function to f(x) = 4(3)2x? (2 points) f(x) = 36x f(x) = 4(9)x f(x) = 144x f(x) = 4(6x)
Answer:
f(x) = 4(9)x
Step-by-step explanation:
I took the test!!!
Answer:
Answer Down BelowStep-by-step explanation:
Q's Asked: Which of the following options is an equivalent function to f(x) = 4(3)2x?
Possible answers:
f(x) = 36^x
f(x) = 4(9)^x
f(x) = 144^x
f(x) = 4(6x)
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My answer: I Think the correct answer is (B) .The reason why I think the answer is (b) is bc:
[tex]f(x) = 4(3)^{2x}[/tex] =36
Calculations on How I got 36.
Frist we calculate the exponents [tex]\left(3\right)^2[/tex] --> [tex]\left(3\right)^2=9[/tex]---> =9
then we Multiply 4*9 which gives us : 36.
The reason why Its (B) is bc:
f(x) = 4(9)^x
which means 4 times nine is...... 36. thats the answer (B) f(x) = 4(9)^xHope this helps :3
~~Wdfads~~Whats the slope ?.please help me
Answer:
The slope is -3.
What is slope intercept form?
O
a + b =C
O y = 3m + b
O
y = mx + b
Answerc
Step-by-step explanation:
Answer:
Step-by-step explanation: a
Solve y = x2-5 for x.
O A. x = +/-5
B. X = y + 5
C. X = +/y+5
O D. x = y-5
help what goes where? correct answer only pls :)
Answer:
2(3 + w) = 6 + 2w
2(1 + w) = 2 + 2w
3(2 + w) = 6 + 3w
6(1 + w) = 6 + 6w
Step-by-step explanation:
2 x 3 = 6 and 2 x w = 2w: Therefore your answer is 6 + 2w
2 x 1 = 2 and 2 x w = 2w: Therefore your answer is 2 + 2w
3 x 2 = 6 and 3 x w = 3w: Therefore your answer is 6 + 3w
6 x 1 = 6 and 6 x w = 6w: Therefore your answer is 6 + 6w
Polygon R and polygon S are similar. The perimeter of polygon R is 72 cm, and the perimeter of polygon S is 36 cm. If one side of polygon S is 6 cm, what is the length of the corresponding side in polygon R?
Answer:
the answere is 10
Step-by-step explanation: