Answer:
y = -3x
Step-by-step explanation:
(a) Slope
y = mx + b
Choose points (-3, 9) and (3, -9)
m = (-9 - 9)/(3 – (-3))
m = -18/(3 + 3)
m = -18/6
m = -3
=====
(b) y-intercept
y = mx +b
Choose point (0,0).
0 = 0 + b
b = 0
=====
(c) Equation of line
y = mx + b
y = -3x
Karla, Ruby, Anna, and Megan each had a balance of $0 in her bank account on the first day of April. Here are their account balances on the second day:
Karla: $43
Ruby: -$25
Anna: -$48
Megan: $42
Whose account had the greatest change between the first and second days?
A.
Karla's
B.
Ruby's
C.
Anna's
D.
Megan's
PLZZ Healp
Answer:
Anna
Step-by-step explanation:
Compare the answers, and when you do that then you can see that anna had more money come in then the others.
Please help and show work!!
A(1, 1), B(7, 1), C(1, 9)
AB = 7 - 1 = 6
AC = 9 - 1 = 8
Use the Pythagorean theorem:
AB² + AC² = BC²
Substitute:
BC² = 6² + 8²
BC² = 36 + 64
BC² = 100 → BC = √100 → BC = 10
The perimeter of ΔABC:
P = 6 + 8 + 10 = 24
Answer: 24 unitsThe box plots below show the ages of college students in different math courses
Answer:
The statement that most accurately represents the data given is the 'The mean and median age are more likely to be the same for the students in Math 1.'
Step-by-step explanation:
The box and whisker plots given for the two sets of data show a few different things. Box and whisker plots first show us the median in a given set of data, which is the line in the middle of the box. For both Math 1 and Math 2, this line occurs at 19. The whiskers that extend from the box on either side represent the range, or lowest and highest numbers, in the data. For Math 1, the range is 17-21 and for Math 2, the range is 17-23. Since the range is more evenly distributed in Math 1, we can conclude that the mean, or average of the data, is most likely the same as the median of the data, which is 19.
Answer:
its d
Step-by-step explanation:
its d
Ari stocks shelves at a grocery store.He puts 35 cans of juice in each display case.The case has 4 shelves with an equal number of cans,and one shelf with only 3 cans.How many cans are on each of the equal shelves?
Answer:
There are 8 cans on each of the equal shelves
Step-by-step explanation:
Total number of cans put in display = 35
Shelves with equal no of cans = 4 Shelves
And one shelf displays only 3 cans
Therefore, 4 shelves with equal no of cans + 1 shelf with 3 cans = 35 cans
Let us assume equal no. of cans be x
We get, 4x + 3 = 35
4x = 35 - 3
4x = 32
x = 32 ÷ 4
x = 8
Thus, 4 shelves with equal no of cans contains 8 cans each.
I'm doing test corrections rn but I need to show the work for this answer. The problem is that the this doesn't show the work and I need it for full credit, can someone show me the work please?
The two angles are corresponding angles, so they are congruent (due to the horizontal lines being parallel)
x+15 = 102
x+15-15 = 102-15 .... subtract 15 from both sides
x = 87
Does (-2,0 ) make the equation y=x true ?
Answer:
False
Step-by-step explanation:
(-2,0) x is equal to -2 and y = 0
y=x
Substitute the values in.
-2 =0
False
m ∠E = 60° and m ∠G = 85° what is m ∠L?
A: 180°
B: 45°
C: 35°
D: 85°
Answer:
The answer is C: 35°
Step-by-step explanation:
The sum of all angles in a triangle is 180°
So, 180°-(60°+85°)
= 180°-145°
= 35°
m∠L = 35°
Hope it helps!
Simplify each expression by combining like terms.
x^2 + x(x - y) + 10xy
x^2 + x(x - y) + 10xy
Distributive property.
x^2 + x^2 - xy + 10xy
Combine like terms.
2x^2 + 9xy
Factor x out of each term.
x(2x + 9y) is the fully simplified form of the original expression.What is the equation of a line with a slope of -4 and a point (-2,5) on the line
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept
Answer:
The equation of the line would be y = -4x - 3
Step-by-step explanation:
To find any equation when you have the slope and a point, start with point-slope form and then solve for y.
y - y1 = m(x - x1)
y - 5 = -4(x + 2)
y - 5 = -4x - 8
y = -4x - 3
A box of spaghetti at the grocery store is purchased for $1.60 wholesale and is marked up by 60 percent. Then, the store marks down the item by 20 percent. A customer wants to buy three boxes of spaghetti. How much will the customer pay, including paying 8 percent sales tax? Round your answer to the nearest cent.
Answer:
the answer is $8.29
Step-by-step explanation:
1.60 marked up by 60% in decimal form is .60
multiply that .60 by 1.60 and you get .64
you add .64 to 1.60 and you get 2.56
you multiply 2.56 by 3 and you get 7.68
you have a 8% sales tax so you multiply 0.08 by 7.68
you will get .61 you add that to 7.68 to get $8.29
Answer:
$6.64
Step-by-step explanation:
When the price of an item is marked up by a percentage, the new price (after markup) is result when the product of the percentage and the original price added to the original price.
The price after markdown is similar to the mark up except that the product of the percentage and the original price is subtracted from the original price.
Hence when a box of spaghetti at the grocery store is purchased for $1.60 wholesale and is marked up by 60 percent, the new price
=60% * $1.60 + $1.60
$2.56
If the store marks down the item by 20 percent, then the new price becomes
= $2.56 - 20% * $2.56
= $2.048
If a customer wants to buy 3, the price
= $2.048 * 3
= $6.144
Including 8% tax, the price becomes
=$6.144 + 8% * $6.144
= $6.63552
To the nearest cent
= $6.64
please!!! help, urgent math problem!
Answer:
1
Step-by-step explanation:
Slope = change in y / change in x
Y-values: 9 and 2
x-values: 3 and -4
Change is the difference
9-2)/(3- (-4)) = 7/7 = 1
Answer:
The slope is 1
Step-by-step explanation:
To find the slope, we use the formula
m = (y2-y1)/(x2-x1)
where (x1,y1) and (x2,y2) are the points on the line
m = (9-2)/(3--4)
= (9-2) /(3+4)
= 7/7
=1
The slope is 1
If the Greatest Common Factor of L and M is 6, write the expression for the Least Common Multiple of these numbers.
Answer:
[tex]\frac{(L x M)}{6}[/tex]
Step-by-step explanation:
The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.
The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.
We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.
As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.
We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.
[tex]\frac{(L x M)}{6}[/tex]
find the equation of a line with the given points.(put your answers in the form y=mx+b)(6,2)(5,5)
The slope-intercept form: y= mx + b
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (6, 2) and (5, 5). Substitute:
[tex]m=\dfrac{5-2}{5-6}=\dfrac{3}{-1}=-3[/tex]
Therefore we have y = -3x + b.
Put the coordinates of the point (5, 5) to the equation:
5 = -3(5) + b
5 = -15 + b add 15 to both sides
20 = b
Answer: y = -3x + 20Answer:
y = -3x + 20
Step-by-step explanation:
(a) Slope
The point-slope formula for a straight line is
y₂ - y₁ = m(x₂ - x₁) Insert the points
2 - 5 = m(6 - 5)
-3 = m×1
m = -3
=====
(b) y-intercept
y₂ - y₁ = m(x₂ - x₁)
y₂ - 5 = -3(x₂ - 5) Remove parentheses
y₂ - 5 = -3x₂ - 15 Add 5 to each side
y = -3x + 20
WILL MARK BRAINLIEST!!!!
can anyone please answer all 6 questions? please it's realky important :) thank you so much xx
i will also give you a follow :)
The area of the square embedded in the circular base of the cylinder is 18 in^2. If the cylinder is 10 inches long, what is the surface area of the cylinder
The surface area of the cylinder is approximately 191.9 square inches.
Describe Surface Area of cylinder?The surface area of a cylinder is the sum of the areas of its curved surface and its two circular bases. The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
where SA is the surface area, r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14159).
The first term on the right-hand side of the equation (2πr²) represents the area of the two circular bases of the cylinder. The second term (2πrh) represents the area of the curved surface of the cylinder.
The area of the square embedded in the circular base of the cylinder is 18 in², which means each side of the square has a length of √18 in = 3√2 in. Since the square is embedded in the circular base, the diameter of the base of the cylinder is equal to the diagonal of the square, which is 2 times the length of one side, or 6√2 in.
The radius of the circular base is half the diameter, or 3√2 in. The surface area of the cylinder consists of the area of the top circular base, the area of the bottom circular base, and the lateral area (the curved surface area) of the cylinder.
The area of each circular base is πr² = π(3√2)² = 18π in².
The lateral area of the cylinder can be found by multiplying the height (which is given as 10 inches) by the perimeter of the circular base (which is 2πr). The perimeter of the circular base is 2π(3√2) = 6π√2 in. Therefore, the lateral area is 10(6π√2) = 60π√2 in².
The total surface area of the cylinder is the sum of the areas of the two circular bases and the lateral area:
Surface area = 2(18π) + 60π√2
= 36π + 60π√2
≈ 191.9 in² (rounded to one decimal place)
Therefore, the surface area of the cylinder is approximately 191.9 square inches.
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A 3 mi cab ride cost $3.00 . A 6 mi can ride cost $4.80 find a linear equation that modes cost c as a function of distance d.
Answer:
c = 0.6d + 1.2
Step-by-step explanation:
Use distance as the independent variable and cost as the dependent variable. Each point (x, y) is (distance, cost).
The 3 mile ride for $3.00 gives you point (3, 3).
The 6 mile ride that cost $4.80 gives you point (6, 4.8).
Now you need to find the equation of the line that passes through points
(3, 3) and (6, 4.8).
y = mx + b
m = slope = (y2 - y1)/(x2 - x1) = (4.8 - 3)/(6 - 3) = 1.8/3 = 0.6
Use point (3, 3).
y = 0.6x + b
3 = 0.6(3) + b
3 = 1.8 + b
b = 1.2
The equation is
y = 0.6x + 1.2
Use c for cost and d for distance to get
c = 0.6d + 1.2
Which models can be used to solve the problem
Consider functions f and g below.
f(x) = -9x^2 - 7x + 12
g(x) = 3x^2 - 4x - 15
Find f(x) - g(x).
A. -12x^2 - 11x - 3
B. 6x^2 - 11x + 27
C. -6x^2 + 3x - 3
D. -12x^2 - 3x + 27
Answer:
D
Step-by-step explanation:
f(x) - g(x) = -9x^2 - 7x + 12 - (3x^2 - 4x - 15) Remove the brackets
f(x) - g(x) = -9x^2 - 7x + 12 - 3x^2 + 4x + 15
f(x) - g(x) = -9x^2 - 3x^2 - 7x + 4x + 12 + 15
f(x) - g(x) = -12x^2- 3x + 27
Answer D
Answer:
Option D. -12x² - 3x + 27
Step-by-step explanation:
The given functions are f(x) = -9x² - 7x + 12 and g(x) = 3x² - 4x - 15
We have to find the value of f(x) - g(x)
f(x) - g(x) = (-9x² - 7x + 12) - (3x² - 4x - 15)
= -9x² - 7x + 12 - 3x² + 4x + 15
= (-9x² - 3x²) - (7x - 4x) + 12 + 15
= -12x² - 3x + 27
This value of f(x) - g(x) matches with option D.
Therefore, Option D. is the correct option.
Can you help me on this?
Answer:
y = 30
Step-by-step explanation:
We can use ratio's to solve this
40 20
----- = -----------
100 20 + y
Using cross products
40 * (20+y) = 20*100
Distribute
800 + 40y = 2000
Subtract 800 from each side
40y = 2000-800
40y = 1200
Divide by 40
y = 1200/40
y =30
School cafeteria holds 200 students mr Thompson’s class has 22 students who eat lunch in the cafeteria how many more students can still eat in the cafeteria when mr tomposons class has lunch
Answer: 198 students
Step-by-step explanation:
220-22=198students
Final answer:
After subtracting Mr. Thompson's class size of 22 students from the school cafeteria's capacity of 200, 178 students can still eat in the cafeteria.
Explanation:
The student's question pertains to the capacity of the school cafeteria and how many more students can be accommodated when a specific class is having lunch. If the cafeteria holds 200 students and Mr. Thompson's class has 22 students, we can calculate the number of additional students that can still eat in the cafeteria by subtracting Mr. Thompson's class size from the total capacity of the cafeteria.
To solve this, we perform the following subtraction:
Capacity of cafeteria - Number of students in Mr. Thompson's class = Number of remaining spots
200 - 22 = 178
Therefore, 178 students can still eat in the cafeteria when Mr. Thompson's class is having lunch.
Roger Ratkin, the owner of Roger’s Subs, has three employees who earn $500, $550, and $700, respectively. How much does Roger owe for the first 12 weeks for SUTA and FUTA? Assume a SUTA rate of 5.3% and a FUTA rate of .8%.
To calculate SUTA and FUTA for the first 12 weeks, calculate the taxable wages for each employee. Multiply the taxable wages by the respective tax rates to find the amount owed. Roger owes $371 for SUTA and $56 for FUTA for the first 12 weeks.
Explanation:To calculate the amount that Roger owes for SUTA (State Unemployment Tax Act) and FUTA (Federal Unemployment Tax Act) for the first 12 weeks, we need to calculate the taxable wages for each employee. The taxable wages for SUTA is the first $7,000 and for FUTA is the first $7,000 as well.
Since the three employees earn $500, $550, and $700 respectively, their total wages for the first 12 weeks would be $17,100 (12 weeks x ($500 + $550 + $700)). However, since SUTA and FUTA only consider the first $7,000 of wages, we can calculate the amount for each tax.
For SUTA, the total taxable wages would be $7,000. Using the SUTA rate of 5.3%, we can calculate the amount owed: $7,000 x 0.053 = $371.
For FUTA, the total taxable wages would also be $7,000. Using the FUTA rate of 0.8%, we can calculate the amount owed: $7,000 x 0.008 = $56.
Therefore, Roger owes $371 for SUTA and $56 for FUTA for the first 12 weeks for his three employees.
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Find the product write your answer in exponential form 6^9*6^9
Answer:
[tex]6^{18}[/tex]
Step-by-step explanation:
if the base is same we can add the exponential terms
her base is same which is 6. so we can add exponential terms
therefore
[tex]6^{9+9}[/tex]
[tex]6^{18}[/tex]
Hi! See the image attached
What is the slope and y-intercept of the line represented by the equation below? 13x+8y=12
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 13x + 8y = 12 into this form
subtract 13x from both sides
8y = - 13x + 12 ( divide all terms by 8 )
y = - [tex]\frac{13}{8}[/tex] + [tex]\frac{3}{2}[/tex] ← in slope-intercept form
with slope m = - [tex]\frac{13}{8}[/tex] and y-intercept c = [tex]\frac{3}{2}[/tex]
What is the slope of y = -2x?
Answer:
slope = - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - 2x is in this form
with slope m = - 2 and c = 0
Can someone please help me with these 3 answers. aiaf you can not see them make sure to click on the image.
1.) There are 16 juniors and 8 seniors in the Chess Club. If the club
members decide to send 9 juniors to a tournament, how many different
possibilities are there?
2.) How many different ways can 3 cards be drawn from a deck of 52
cards without replacement?
3.) How many different ways can 3 cards be drawn from a deck of 52
cards with replacement?
4.) A corporation has 5 officers to choose from which 3 are selected
to comprise the board of directors. How many combinations are there?
5.) A combination lock has the numbers 1 to 40 on each of three
consecutive tumblers. What is the probability of opening the lock in
ten tries?
Answer:
1.) There are 16 juniors and 8 seniors in the Chess Club. If the club members decide to send 9 juniors to a tournament, how many different possibilities are there?
(16 over 9) = 16!/(9!*7!) = 11440
2.) How many different ways can 3 cards be drawn from a deck of 52 cards without replacement?
52*51*50 = 132600
3.) How many different ways can 3 cards be drawn from a deck of 52 cards with replacement?
52^3 = 140608
4.) A corporation has 5 officers to choose from which 3 are selected to comprise the board of directors. How many combinations are there?
(5 over 3) = 5!/(3! * 2!) = 10
5.) A combination lock has the numbers 1 to 40 on each of three consecutive tumblers. What is the probability of opening the lock in ten tries?
10/40^3 = 1/6400
The questions deal with computing combinatorial possibilities such as selecting members for a Chess Club tournament, drawing cards from a deck with and without replacement, determining the number of combinations for a board of directors, and calculating the probability of opening a combination lock within a limited number of tries.
1. Chess Club tournament possibilities: This can be calculated using the combination formula. The number of ways to select 9 juniors from 16 is given by the formula C(n, k) = n! / (k!(n-k)!) where n is the total number of items, and k is the number of items to choose. In this case, it is C(16, 9).
2. Ways to draw 3 cards without replacement: This also uses the combination formula because the order of drawing doesn't matter. It is C(52, 3).
3. Ways to draw 3 cards with replacement: Since each draw is independent and the card is replaced each time, it's simply 52 x 52 x 52 = 1,40,608.
4. Combinations for a board of directors: Choosing 3 officers from 5 to form a board is C(5, 3).
5. Probability of opening a combination lock: The total number of combinations is 40 x 40 x 40. With ten tries, the probability of opening the lock on each try is 1/64000.
Thus the probability of opening within ten tries is 10/64000.
How many cubes with an edge length of 1/3 inch are needed to build a cube with an edge length of 1 inch?
The number of cubes needed with an edge length of [tex]\bold{\dfrac{1}{3}}[/tex] inches is needed to build a cube with an edge length of 1 inch is 27.
Given to us,the edge length of smaller cube, a = [tex]\bold{\dfrac{1}{3}}[/tex] inches
the edge length of the cube to be built, S = [tex]\bold{\dfrac{1}{3}}[/tex] inches
Volume of a Cubewe know that volume of a cube is given by (side)³.
[tex]\bold{Volume\ of\ cube = (side)^3}[/tex]
Volume of the smaller cubeVolume of the smaller cube = (edge length of the smaller cube)³
= a³
= [tex]\bold{(\dfrac{1}{3})^3}[/tex]
= [tex]\bold{\dfrac{1}{27}}[/tex] in.³
Volume of the cube to be buildVolume of the cube to be build = (edge length of the cube to be built)³
= S³
= 1³
= 1 in.³
solving,
Cubes of smaller length are needed for the larger cube
[tex]\bold{=\dfrac{Volume\ of\ the\ Larger\ cube}{Volume\ of\ the\ Smaller\ cube}}[/tex]
[tex]\bold{=\dfrac{1}{\dfrac{1}{27}}}[/tex]
[tex]\bold{=27}[/tex]
Hence, the number of cubes needed with an edge length of [tex]\bold{\dfrac{1}{3}}[/tex] inches is needed to build a cube with an edge length of 1 inch is 27.
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On an architects blueprint, 1 inch corresponds to 4 feet. Find the length of a wall represented by a line that is 3 7/8 inches long on the blueprint
To find the length of the wall represented by a line that is 3 7/8 inches long on the blueprint, we can use the scale conversion. The length of the wall is 15 1/2 feet.
Explanation:To find the length of the wall represented by a line that is 3 7/8 inches long on the blueprint, we need to use the scale conversion.
The given scale is 1 inch corresponds to 4 feet.
So, we can set up a proportion:
1 inch − 4 feet
3 7/8 inches − x feet
To solve for x, we can cross-multiply:
1 × x = 4 × 3 7/8
Multiply 4 by the whole number 3 and then add the product to the result of 4 multiplied by the fractional part 7/8.
x = 12 + 28/8
x = 12 + 3 1/2
x = 15 1/2 feet
Therefore, the length of the wall represented by a line that is 3 7/8 inches long on the blueprint is 15 1/2 feet.
Which of the following expressions is equal to 2x^(2)+8?
(2x-4i)(x-2i)
(2x-4i)(x-2i)
(2x+4i)(x+2i)
(2x_2i)(x+6i)
Answer:
The expression equal to 2x^(2)+8 is:
First option (2x-4i)(x+2i)
Step-by-step explanation:
If we multiply
(2x-4i)(x+2i)=(2x)(x)+(2x)(2i)-(4i)(x)-4i(2i)
(2x-4i)(x+2i)=2x^(1+1)+4xi-4xi-8i^(1+1)
Simplifying:
(2x-4i)(x+2i)=2x^2-8i^2
and i^2=-1, then:
(2x-4i)(x+2i)=2x^2-8(-1)
Multiplying:
(2x-4i)(x+2i)=2x^2+8
Answer: (2x-4i)(x+2i)
Step-by-step explanation:
Darragh has a Golden Eagle coin in his collection with a mass of 13.551. An uncirculated Golden Eagle coin has a mass of 13.714g.
Answer:
0.163
Step-by-step explanation:
The mass difference between Darragh's Golden Eagle coin and an uncirculated one is 0.163g. This difference could be from various factors including wear and tear, oxidation, or minor variations in the minting process.
Explanation:The question relates to the difference in mass of an uncirculated Golden Eagle coin and one that is in Darragh's collection. First, we need to calculate the difference in mass. The mass of the uncirculated Golden Eagle coin is 13.714g and the mass of Darragh's Golden Eagle coin is 13.551g. By subtracting Darragh's coin mass from the uncirculated coin mass, we get a difference of 0.163g.
This means that Darragh's Golden Eagle coin is 0.163g lighter than an uncirculated one. This difference could be due to factors like wear and tear from handling the coin over time, oxidation, or even from slight variations within the minting process itself. As with any other measurement, there will be a minor uncertainty that should be considered in scientific contexts.
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