Age of Jen is 13.6 years old
Solution:
Let "x" be the age of Jack and "y" be the age of Jen
Given that This Christmas, your brother Jack will be 2 years from being twice as old as your sister Jen
The above sentence can be written mathematically as:
Jack age + 2 = twice of age of Jen
[tex]x + 2 = 2y\\\\x = 2y - 2---- eqn 1[/tex]
The sum of Jacks age and three times Jen's age is 66
Jack age + three times Jen age = 66
x + 3y = 66 ---- eqn 2
Substitute eqn 1 in eqn 2
2y - 2 + 3y = 66
5y - 2 = 66
5y = 68
y = 13.6Thus age of Jen is 13.6 years old
Six cars pull up to a red light, one at a time. At the light, there are three lanes, one left-turn lane, one straight-going lane, and one right-turn lane. How many ways can the cars stack up so that all three lanes are occupied? Note that if the first car turns left and the second goes straight, this is considered different from the first car going straight and the second car turning left. In other words, the cars are distinguishable, but pull up to the intersection in a fixed order.
Answer: [tex]540[/tex]
We count the number of ways that some lane can be left empty, and subtract from the total:
Each driver has three choices, so it's [tex]3^6 = 729[/tex].
Now, we count the ways where at least 1 lane is left empty:
But we have double-counted the situations where two lanes are left empty. Since each driver only has one choice, there are [tex]3(1^6)[/tex] situations we overcount. This leaves [tex]729 - (192 - 3) = 540[/tex] ways to fill all three lanes.
Also, you took this question directly from Alcumus. The source is AoPS Staff they wrote this problem, and might request this post be taken down since you technically are not allowed to post Alcumus problems on the internet or their own forums.
Given the function ƒ(x) = 3x + 5, find ƒ(4) and x such that ƒ(x) = 38.
Select one:
A. 17; 11
B. 20; 13
C. 12; 15
D. 24; 9
Answer:
A. 17 , 11
f(4)=3(4) + 5
=17
f(x)= 38
38 = 3x + 5
38 - 5 = 3x
33 = 3x
x =11
-3W + 2(8x -9) use x = 5 and w = 7
Answer:
41
Step-by-step explanation:
Substitute in 5 and 7 into the correct spots:
(-3)(7)+2((8)(5)-9)
Multiply and simplify:
-21+2(40-9)
-21+2(31)
-21+62
41
:)
Answer:
50
Step-by-step explanation:
-21 + 16x - 9
-21 + 80 - 9
59 - 9
50
Two cars travel at the same speed to different destinations. Car A reaches its destination in 15 minutes. Car B reaches its destination in 35 minutes. Car B travels 15 miles farther than Car A. How fast do the cars travel? Write your answer as a fraction in simplest form.
Answer:
The cars are travelling ar the speed 45 mph.
Step-by-step explanation:
Let the two cars are moving at the speed of x mph.
Now, Car A reaches its destination in 15 minutes i.e. [tex]\frac{15}{60} = 0.25[/tex] hours.
Therefore, Car A travels in 15 minutes by 0.25x miles.
Again, Car B reaches its destination in 35 minutes i.e. [tex]\frac{35}{60} = 0.583[/tex] hours.
Therefore, Car B travels in 35 minutes by 0.583x miles.
Given that, (0.583x - 0.25x) = 15
⇒ 0.333x = 15
⇒ x = 45 mph
Therefore, the cars are travelling ar the speed 45 mph. (Answer)
The cars travel at a speed of 3/4 miles per minute.
Explanation:To find the speed of the cars, we can use the formula Speed = Distance/Time. Let's assume that Car A's speed is x miles per minute. Since Car B travels 15 miles farther than Car A and takes 35 minutes to reach its destination, Car B's speed would also be x miles per minute. Now, using the given information, we can set up two equations:
x * 15 = x * 35 - 15
Simplifying the equation, we get:
15x = 35x - 15
20x = 15
x = 0.75
Therefore, the cars travel at a speed of 0.75 miles per minute or the fraction 3/4 miles per minute.
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An electronics store makes a profit of $72.00 for every television sold and $90.00 for every computer sold. The manager’s target is to make at least $360.00 a day on sales from televisions and computers. Let x = the number of televisions sold. Let y = the number of computers sold. Which of the following represents three possible solutions to the problem?
A. 72x+90y>360 (5,2),(3,3) and (1,4)
B. 72x+90y<360 (4,0),(2,2) and (1,1)
C. 72x+90y>360 (3,1),(2,2) and (1,0)
D 72x+90y>360 (4,0),(3,3) and (1,4)
Answer:
Option A, C and D is the three possible solution.Step-by-step explanation:
Each Television earns $72 and each Computer earns $90.
The manager’s target is to make at least $360.00 a day.
It is not clarified the exact number of Televisions and Computers.
Hence, as per the given condition, [tex]72x + 90y \geq 360\\8x + 10y \geq 40\\4x + 5y \geq 20[/tex].
Now we just need to check the given options, whether they satisfy the above equation, or not.
Except the option B, each inequality indicates a value greater than 360.
Hence, option B can not be the possible solution.
To meet the profit target of 72x + 90y ≥ 360, the correct points are listed in Option A: (5, 2), (3, 3), and (1, 4). These points meet the required profit condition.
To solve this problem, we need to find the inequality that represents the manager's profit target and identify the solutions that meet this condition. Given:
The profit per television is $72 (x represents the number of televisions sold).The profit per computer is $90 (y represents the number of computers sold).The manager’s goal is to make at least $360. This can be represented by the equation: 72x + 90y ≥ 360.
We need to check which option lists points that satisfy this inequality. Let's test the points:
Option A: 72x + 90y > 360 (5, 2), (3, 3), and (1, 4)
(5, 2): 72(5) + 90(2) = 360 + 180 = 540 (satisfies ≥ 360)(3, 3): 72(3) + 90(3) = 216 + 270 = 486 (satisfies ≥ 360)(1, 4): 72(1) + 90(4) = 72 + 360 = 432 (satisfies ≥ 360)Option B: 72x + 90y < 360 (4, 0), (2, 2), and (1, 1)
(4, 0): 72(4) + 90(0) = 288 (does not satisfy ≥ 360)(2, 2): 72(2) + 90(2) = 144 + 180 = 324 (does not satisfy ≥ 360)(1, 1): 72(1) + 90(1) = 72 + 90 = 162 (does not satisfy ≥ 360)Option C: 72x + 90y > 360 (3, 1), (2, 2), and (1, 0)
(3, 1): 72(3) + 90(1) = 216 + 90 = 306 (does not satisfy ≥ 360)(2, 2): 72(2) + 90(2) = 144 + 180 = 324 (does not satisfy ≥ 360)(1, 0): 72(1) + 90(0) = 72 (does not satisfy ≥ 360)Option D: 72x + 90y > 360 (4, 0), (3, 3), and (1, 4)
(4, 0): 72(4) + 90(0) = 288 (does not satisfy ≥ 360)(3, 3): 72(3) + 90(3) = 216 + 270 = 486 (satisfies ≥ 360)(1, 4): 72(1) + 90(4) = 72 + 360 = 432 (satisfies ≥ 360)Only Option A lists points that all satisfy the inequality 72x + 90y ≥ 360. Therefore, Option A is the correct answer.
Pheonix ran 4.5 miles per hour for three fourths of an hour. How did Aliyah run today?
Answer:
3.375 miles
Step-by-step explanation:
3/4 can be changes to 0.75. SO multiply 4.5 times 0.75 to get your answer
An artist needs to purchase jars of paint. The table shows Which quantity container is the better buy?
different sizes of paint jars and their prices.
2-oz jar
4-oz jar
Paints
Total Price
4OZ jar
8-oz jar
2-oz jar
$1.50
16-oz jar
4-oz jar
$2.92
8-oz jar
$5.68
16-ozjar
$11.62
Answer:8-oz jar
First, we have to find out what is the unit rate of the 2-oz jar. $1.50÷2 is $.75.
Second, we have to find the unit rate of the 4-oz jar. $2.92÷4=$73.
Third, we have to find the unit rate of the 8-oz jar. $5.68=$.71.
Fourth, we have to find the unit rate of the 16-oz jar. The division for this one may be tricky. From dividing $11.62 by 16, is stopped at the 3rd number I got from dividing. I got $.726. This is not a value of cents and the value can't go in the thousandths place. So, I rounded .726. I got $.73. So $11.62÷16=$.73.
Lastly, you have to compare the amounts.
The lowest amount or better buy, is $.71 or 8-oz jar.
Answer:
8-oz
Step-by-step explanation:
had the same question on the same assignment:)
Sunil takes 5 more days than Anil to a certain work . Anil left the work after 4days,Sunil takes 5days to complete the rest work . How many days they took to complete the work
Answer:
Anil would take 10 days and Sunil would take 15 days to complete the work.
Step-by-step Explanation:
To Determine:
How many days they took to complete the work?
Information Fetching and Solution steps:
Sunil takes 5 more days than Anil to a certain workAnil left the work after 4 daysSunil takes 5 days to complete the rest workLet is consider,
The number of days taken by Anil to complete the required work = d.
The number of days taken by Sunil to complete the required work = d + 5
Work done by Anil in one day = 1÷d
Work done by Sunil in one day = 1÷ (d+5)
Work done together by Anil and Sunil for one day = 1/d + 1/(d+5)
= (d+5+d)/d(d+5)
= (2d+5)/d(d+5)
Work done together by Anil and Sunil for 4 days = 4×(2d+5)/d(d+5) ....[A]
Work done by Sunil in 5 days = 5÷ (d+5) ....[B]
By adding equation [A] and [B], we can determine the complete work
[A] + [B] = 1
((4×(2d+5)/d(d+5))) + (5÷ (d+5)) = 1
8d+20+5d=1d(d+5)
13d+20=d²+5d
−d²+8x+20=0
(−d−2)(d−10)=0
d=−2 or d=10
As number of days can not be negative. So, d = 10. Therefore,
The number of days taken by Anil to complete
the required work = 10 days
The number of days taken by Sunil to complete
the required work = d+5 = 15 days
Hence, Anil would take 10 days and Sunil would take 15 days to complete the work.
Keywords: days, work
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Find the values of x and y.
X is a right angle so 90 degrees.
The B will be equal to C so B is 47 degrees.
The Y is 180 degrees - X - C so Y is 43 degrees.
Hope this helps.
You mix 1/3
quart of blue paint for every 1/2
quart of red paint to make 2 1/2
quarts of purple paint. How much blue paint and how much red paint do you use?
Answer:
1 quart blue + 1 1/2 quart red
Step-by-step explanation:
Given:
Ratio of blue paint : red paint = 1/3 : 1/2
simplifying this ratio into whole numbers by multiplying both sides by 2 and 3, we get:
(1/3) x (3x2) : (1/2) x (3x2)
2 : 3
From this we can determine the fractions of red and blue paint used in any total purple mix
fraction of blue paint = 2/(2+3) = 2/5 of purple mix
fraction of red paint = 3/(2+3) = 3/5 of purple mix
we are given that we want to make 2 1/2 (= 5/2) quarts of purple paint
hence
amount of blue paint
= fraction of blue paint in purple mix x total amount of purple paint
= (2/5) x (5/2) = 1 quart
amount of red paint
= fraction of redpaint in purple mix x total amount of purple paint
= (3 /5) x (5/2) = 3/2 quart = 1 1/2 quart
A typical marathon is 26.2 miles. Allan averages 12 kilometers per 1 hour when running in marathons. How long does it take for Allan to complete a marathon, to the nearest tenth of an hour.
Answer:
3.5 hours
Step-by-step explanation:
Given: Distance= 26.2 miles
Speed= 12 km/h
First lets convert the unit of speed from kmh to mph.
Remember, 1 mile= 1.609 km
∴ For speed of 12 km/h= [tex]\frac{12}{1.609}= 7.45\ mph[/tex]
Speed= 7.45 mph
Next, find time taken by Allan to complete a Marathon.
[tex]Time= \frac{Distance}{speed}[/tex]
⇒ Time= [tex]\frac{26.2}{7.45}[/tex]
∴ Time= 3.516 hours ≅ 3.5 h (nearest tenth)
∴ Allan took 3.5 hours to complete marathon.
Allan takes approximately 3.5 hours to complete a marathon. This is determined by converting the marathon distance to kilometers and dividing it by his running speed.
To determine how long it takes Allan to complete a marathon, we need to convert the marathon distance from miles to kilometers and then find the time it takes based on his running speed.
1 mile is approximately 1.60934 kilometers, so:
26.2 miles × 1.60934 km/mile ≈ 42.164 km
Allan runs at an average speed of 12 kilometers per hour. The time (t) needed to complete the marathon can be calculated as:
t = distance / speed
t ≈ 42.164 km / 12 km/h ≈ 3.514 hours
Rounding to the nearest tenth of an hour, Allan takes approximately 3.5 hours to complete the marathon.
Liu deposited 3,500 into a savings account . The simple interest rate is 4%. How much interest will the account earn in 2 years .
Interest = interest rate x principal x time
Answer:
$280
Step-by-step explanation:
Interest = Interest Rate x Principal x time
Interest = 0.04 x $3,500 x 2
Interest = $280
Please help, brainliest!!
Write an expression equivalent to 4(6x + 12), and state the property you used to write it.
Answer:
4(6x) + 4(12)
Distributive property
4(6x + 12) = 4(6x) + 4(12)
To see if the answer is correct, we can solve the equations
24x + 12 = 24x + 12
The expressions are equal, so the equivalent expression provided is correct
Hope this helps :)
Answer:
By applying the Distributive Property, I can generate these equivalent expressions: 24x + 48, 24(x + 2), and 12(2x + 4).
15) Write an equation in slope-intercept form for the line that is parallel to the given line and passes
through the given point ----> (2,7)
y = 4x + 6
Answer:
[tex]\displaystyle y = 4x - 1[/tex]
Step-by-step explanation:
7 = 4[2] + b
8
[tex]\displaystyle -1 = b \\ \\ y = 4x - 1[/tex]
* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so 4 remains the way it is.
I am joyous to assist you anytime.
A room has dimensions 6.8m x 9.2m. Steven wants to paint the walls of the room. A large tin of paint covers 20m^2 and cost £11.75. Ignoring windows and doors, and allowing for 2 coats of paint, how much will it cost Steven to paint the room.
Answer:
Total cost to paint the room = £73.51
Step-by-step explanation:
Given:
Dimensions of the room = 6.8 m [tex]\times[/tex] 9.2 m
Cost of tin of paint = £11.75
A tin of paint covers an area = 20 [tex]m^2[/tex]
To find the cost of painting the room with two coats of paint.
Solution:
Area of the room = [tex]length\times width=6.8\ m\times 9.2\ m= 62.56\ m^2[/tex]
We will use unitary method to find the amount of paint required for the room.
If [tex]20\ m^2[/tex] of area is covered by 1 tin of paint.
For [tex]1\ m^2[/tex] of area, amount of paint required = [tex]\frac{1}{20}[/tex] of a tin
Then, for [tex]62.56\ m^2[/tex] amount of paint required = [tex]\frac{62.56}{20}=3.128[/tex] tins of paint.
For double coats twice paint must be required.
So, total amount of paint required for painting the room with two coats of paint = [tex]3.128\times 2=6.256[/tex] tins of paints.
Using unitary method to find total cost.
If 1 tin of paint costs = £11.75
6.256 tins of paint will cost = [tex]6.256\times \£11.75=\£73.508\approx\£73.51[/tex]
Total cost to paint the room = £73.51
In the equation 3/4y+1/2=3 1/4, the fractional coefficient is
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]
In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.
coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.
Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].
Final answer:
The fractional coefficient in the equation 3/4y+1/2=3 1/4 is 3/4.
In the given equation, the fractional coefficient is 3/4, which is the fraction that multiplies the variable y.
Explanation:
The fractional coefficient in the equation 3/4y+1/2=3 1/4 is 3/4.
In the equation 3/4y + 1/2 = 3 1/4, the fractional coefficient refers to the fraction that is multiplied by the variable y.
In this case, the coefficient is 3/4.
When working with algebraic expressions and equations, understanding how to identify and manipulate coefficients is essential for problem-solving.
The student's query seems to be aimed at identifying the coefficient of the variable in the equation. In algebra, fractions like 3/4 can be seen as coefficients when they are directly next to a variable.
No unit cancellations are needed here as the question pertains to pure algebra and not to unit conversions or applied mathematics.
what is the sum of 7.09 + 13.95
Answer:
21.04
Step-by-step explanation:
Start by adding the hundredths category. 0.09 + 0.05 = 0.14, this means that your hundredths column will be a 4, and you will carry the 1 over to the tenths.
Now add your tenths. 0.0 + 0.9 + 0.1 = 1.0, which means that your tenths column is a 0. Carry the 1 over to the whole numbers.
Now add your whole numbers. 7 + 13 + 1 = 21. Combine your terms and you get 21.04
Final answer:
21.04
Explanation:
To find the sum of 7.09 and 13.95, we simply add the two numbers together, aligning the decimal points vertically.
Add the hundredths place: 9 (from 7.09) + 5 (from 13.95) = 14. Write down 4 and carry over 1 to the tenths place.Add the tenths place: 0 (from 7.09) + 9 (from 13.95) + 1 (the carryover) = 10. Write down 0 and carry over 1 to the ones place.Add the ones place: 7 (from 7.09) + 3 (from 13.95) + 1 (the carryover) = 11. Hence, write down 1 and carry over another 1 to the tens place.Add the tens place, which is just the carryover: 1 (from the carryover) + 1 (from 13.95) = 2. So, write down 2.Putting it all together, we get 21.04 as the final sum.
A boat travels 12 Mph in still water. It can travel 18 miles upstream in the same time that it can travel 24 miles downstream. What is the current of the water?
Answer:
[tex]1 \dfrac{5}{7}\ mph[/tex]
Step-by-step explanation:
Let x mph be the current's rate.
Upstream:
Distance = 18 miles
Rate = 12 - x mph
Time [tex]=\dfrac{18}{12-x}[/tex] hours
Downstream:
Distance = 24 miles
Rate = 12 + x mph
Time [tex]=\dfrac{24}{12+x}[/tex] hours
Time is the same, so
[tex]\dfrac{18}{12-x}=\dfrac{24}{12+x}\\ \\18(12+x)=24(12-x)\\ \\216+18x=288-24x\\ \\18x+24x=288-216\\ \\42x=72\\ \\x=\dfrac{12}{7}=1 \dfrac{5}{7}\ mph[/tex]
An airplane has 29 seats. The price for a coach seat is $600 in the price for a first class seat is $1050. The airline collected a total of $21,900 for the flight. How many coach seats were sold
Answer:
19 coach seats
Step-by-step explanation:
let the number of coach seats be C and number of first class seats be F
given that the total number of seats is 29,
C + F = 29 ---------(eq 1)
also given that each coach seat = $600, each 1st class seat is $1050 and a total of $21900 was collected,
600C + 1,050F = 21,900 -------(eq 2)
we have 2 equations and 2 unknowns, we can solve the system of equations by elimination
(eq 1) x 1,050 gives us:
1,050 (C + F) = 1,050(29)
1,050C + 1,050F = 30,450 ----- (eq 3)
by elimination, subtract eq 2 from eq 3
(1,050C + 1,050F) - (600C + 1,050F) = 30,450 - 21,900
1,050C - 600C = 8,550
450C = 8550
C = 855 /450
C = 19
Simplify the expression 8(5x- 3y)
Answer:
40x-24y
Step-by-step explanation:
What is the answer ? Please
Subtract the length of the tail from the whole length.
3/5 - 1/5 = 2/5
The answer is 2/5
3/5 - 1/5 = 2/5
so your answer is 2/5
What is 100% written as a decimal?
O
0.01
O 0.1
O
1
O
10
Answer: 1.0
Step-by-step explanation: Since a percent is a ratio that compares a number to 100, think of 100% as the ratio 100/100 or 100 divided by 100.
Now, dividing a number by 100 moves the decimal point two places to the left so 100 divided by 100 will move the decimal point two places to the left which will gives us 1.0 or simply just 1.
So 100% can be written as the decimal 1.0.
Answer:
1
Step-by-step explanation:
Take 100 and add a decimal point at the end -> 100.Move the decimal over [left] two decimal pointsPut your numbers together and get rid of the 0'sYou get 1Byeeee, get a hundred!
Given: JP = KP; PX = PY
Prove: APYJ - APXK
Which best describes the missing reasons?
Answer:
SAS Reflective property
Step-by-step explanation:
By reflexive property and SAS, we prove that ΔPYJ and ΔPXK are congruent.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given, JP = KP and PX = PY.
∴ JX = KY.
Hence Z is the midpoint of JY and XK.
∴ JY = XK.
Reflexive property.
And the included ∠P is common to both the ΔPYJ and ΔPXK.
Side angle side congruency.
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Help, I know D2 is the dilation of 2? And I know the rotation is 90 degrees but I’m not to sure on how to find my answer? Help please
Answer:
(-18, 2)
Step-by-step explanation:
To rotate a point by 90°:
R₉₀ (x, y) = (-y, x)
R₉₀ (1, 9) = (-9, 1)
To dilate by 2:
D₂ (x, y) = (2x, 2y)
D₂ (-9, 1) = (-18, 2)
Drag each number to the correct location on the table. Each number can be used more than once, but not all numbers will be used.
Simplify the given polynomial expressions, and determine the degree and number of terms in each expression.
Degree
Degree
Number of
Terms
4x + 2.2(3x - 5)
(-304 +503 - 12) + (7x3 - 25 + 6)
(3x2 – 3)(3x2 + 3)
Answer:
1. [tex]12x^2-13.4x-11[/tex]
- Degree: 2
- Number of terms: 3
2. [tex]7x^3+168[/tex]
- Degree: 3
- Number of terms: 2
3. [tex]9x^4-9[/tex]
- Degree: 4
- Number of terms: 2
Step-by-step explanation:
For this exercise you need to remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]
1. Given:
[tex](4x + 2.2)(3x - 5)[/tex]
Apply the Distributive property:
[tex]=12x^2+6.6x-20x-11[/tex]
Add the like terms:
[tex]=12x^2-13.4x-11[/tex]
You can idenfity that:
- Degree: 2
- Number of terms: 3
2. Given:
[tex](-304 +503 - 12) + (7x^3 - 25 + 6)[/tex]
Add the like terms:
[tex]=187 + 7x^3 - 25 + 6=7x^3+168[/tex]
You can idenfity that:
- Degree: 3
- Number of terms: 2
3. Given:
[tex](3x^2 - 3)(3x^2 + 3)[/tex]
Apply Distributive property:
[tex]=9x^4-9x^2+9x^2-9[/tex]
Add the like terms:
[tex]=9x^4-9[/tex]
You can idenfity that:
- Degree: 4
- Number of terms: 2
How does the value of an expression change when it is expanded
Answer:
The value remains the same.
Step-by-step explanation:
using the expression: [tex](x + 1)^{2}[/tex],
where x = 2
substitute for x in the expression;
[tex](2 + 1)^{2}[/tex]
= [tex](3)^{2}[/tex]
=9
The value of the expression before expansion = 9
Lets expand the expression: [tex](x + 1)^{2}[/tex]
= (x + 1) (x + 1)
= [tex]x^{2}[/tex] + 2x + 1
substitute for x in the expression
= [tex]2^{2}[/tex] + 2(2) + 1
= 4 + 4 + 1 = 9
The value of the expansion after expansion = 9
The value remains the same before and after expansion.
The value of an expression, before and when it is expanded will be always same.
Let us consider that an expression,
[tex]f(x)=(x-1)^{2}[/tex]
Substitute x = 2 in above relation.
[tex]f(2)=(2-1)^{2}=1[/tex]
Now expand,
[tex]f(x)=(x-1)^{2}=x^{2} -2x+1\\\\f(2)=2^{2}-2*2+1\\\\f(2)=4-4+1\\\\f(2)=1[/tex]
Hence, the value of an expression, before and when it is expanded will be always same.
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4. Find the slope of the line between the points (9,-12) and (5,4)
The slope of the line is -4.
Work is provided in the image attached.
Answer:
[tex]m=-4[/tex]
Step-by-step explanation:Using the Slope Formula:
[tex]m= \frac{4+12}{5-9}=\frac{16}{-4} =-4[/tex]
Suppose you have $30 to spend on a bag is tootsie rolls that are worth $3 and bags of lolli-pops worth $5.If you have to use all of their money , What combinations of candy bags can they buy ? Construct a liner equation and find /explain the y -intercept,x-intercept ,and slope
Answer:
Part a) [tex]3x+5y=30[/tex]
Part b) see the explanation
Part c) see the explanation
Step-by-step explanation:
Part a) Construct a liner equation
Let
x ----> the number of bags of tootsie rolls
y ----> the number of bags of lolly-pops
we know that
The number of bags of tootsie rolls bought multiplied by their price ($3) plus the number of bags of lolly-pops bought multiplied by their price ($5) must equal $30
so
The linear equation that represent this problem is
[tex]3x+5y=30[/tex]
Part b) Find the intercepts
Find the y-intercept
The y-intercept is the value of y when the value of x s equal to zero
In this context, the y-intercept is the number of bags of lolly-pops that i can buy when the number of bags of tootsie rolls is equal to zero
For x=0
[tex]3(0)+5y=30[/tex]
[tex]y=6[/tex]
The y-intercept is the point (0,6)
so
I can buy 6 bags of lolly-pops and 0 bags of tootsie rolls
Find the x-intercept
The x-intercept is the value of x when the value of y s equal to zero
In this context, the x-intercept is the number of bags of tootsie rolls that i can buy when the number of bags of lolly-pops is equal to zero
For y=0
[tex]3x+5(0)=30[/tex]
[tex]x=10[/tex]
The x-intercept is the point (10,0)
so
I can buy 10 bags of tootsie rolls and 0 bags of lolly-pops
Part c) Find the slope
we have
[tex]3x+5y=30[/tex]
isolate the variable y
[tex]5y=-3x+30[/tex]
[tex]y=-\frac{3}{5}x+6[/tex]
The slope is m=-3/5 ---> is negative because is a decreasing function
That means ---> For every three less lollipops you get, you can have 5 more tootsie rolls
school spirit club wants to raise money by selling t-shirts. one local company charges a fixed fee of $75 for creating the design and $5 for each shirt that they print. Write an equation describing the spirit club's income if they sell each t-shirt for $8
Answer:
The profit = $(3x - 75) where x = number of t-shirts sold
Step-by-step explanation:
School spirit club wants to raise money by selling t-shirts. one local company charges a fixed fee of $75 for creating the design and $5 for each shirt that they print.
We have to find the club's income if they sell each t-shirt for $8.
Let the number of t-shirts that the club sell be equal to x.
So the cost of making x t-shirts = 75 + 5x
If the club sells x t-shirts , then the money they earn = 8x
Profit = selling price - cost price
= 8x - (75 + 5x)
= $(3x - 75)
The club also needs to sell at least 25 t-shirts to make a profit and from then on makes a profit of $3 on each t-shirt they sell.
Algebra 2! Height is 256.
Answer:make a graph
Step-by-step explanation: