[tex]\bf \stackrel{\textit{solving for \underline{y}}}{3y+12=2x}\implies 3y=2x-12\implies y=\cfrac{2x-12}{3}\implies y=\cfrac{2x}{3}-\cfrac{12}{3} \\\\\\ y=\cfrac{2}{3}x-4\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
The value of the digit 4 in 24, 601 is how many times greater then the value digit 4 in 437
Answer:
The Answer is 10 times as much.
Step-by-step explanation:
We know that the 4 in 24,601 is 4000. We also know that the 4 in 437 is 400. If we do 4000/400, we get 10 times as much!
I hope this helps.
What is the diameter in inches of a circle that has an area of 16pi square inches
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=16\pi \end{cases}\implies 16\pi =\pi r^2\implies \cfrac{16\pi }{\pi }=r^2\implies 16=r^2 \\\\\\ \sqrt{16}=r\implies 4=r~\hfill \stackrel{\textit{diameter is twice the radius}}{d=8}[/tex]
Need help with #18 ASAP. Will pick brainliest and question worth 20 points.
Answer:
scoops 1 1/2 5 12.8 1.5 1.05 20 12.25
milk 10 5 50 128 15 10.5 200 122.5
Step-by-step explanation:
The problem states 1 scoop per 10 oz of milk
1 scoop x scoops
------------ = ------------
10 oz 5 oz
Using cross products
1 *5 = x * 10
Divide by 10
5/10 =x
1/2 scoops
1 scoop 5 scoops
------------ = ------------
10 oz x oz
Using cross products
1 *x = 5 * 10
x =50
50 oz
1 scoop x scoops
------------ = ------------
10 oz 128 oz
Using cross products
1 *128 = x * 10
Divide by 10
x =128/10
12.8 oz
1 scoop 1.5 scoops
------------ = ------------
10 oz x oz
Using cross products
1 *x = 1.5 * 10
x =15
15 oz
1 scoop x scoops
------------ = ------------
10 oz 10.5 oz
Using cross products
1 *10.5 = x * 10
Divide by 10
x =10.5/10
1.05 oz
scoop 20 scoops
------------ = ------------
10 oz x oz
Using cross products
1 *x = 20 * 10
x =200
200 oz
scoop 12.25 scoops
------------ = ------------
10 oz x oz
Using cross products
1 *x = 12.25 * 10
x =122.5
122.5 oz
Answer:
[tex]\underline {\text{P}\ \ |\quad1\quad| \quad\frac{1}{2}\quad|\quad5\quad|\quad12.8\quad| \quad1.5\quad| \quad1.05\quad|\quad20 \quad|\quad12.25\quad|}\\{\text{M}\ |\quad10\ \ | \quad 5\quad|\quad50\ \ |\quad128.\quad|\quad15\quad| \quad10.5\quad|\quad200\ |\quad122.5\quad|}[/tex]
Step-by-step explanation:
Set up the proportion as [tex]\dfrac{1 \text{ powder}}{10 \text{ milk}}=\dfrac{P}{M}[/tex], then cross multiply and solve for the variable.
Column 1: [tex]\dfrac{1}{10} =\dfrac{1}{M}[/tex] → M = 10
Column 2: [tex]\dfrac{1}{10} =\dfrac{P}{5}[/tex] → 5 = 10P → [tex]\frac{1}{2} = P[/tex]
Column 3: [tex]\dfrac{1}{10} =\dfrac{5}{M}[/tex] → M = 50
Column 4: [tex]\dfrac{1}{10} =\dfrac{P}{128}[/tex] → 128 = 10P → 12.8 = P
Column 5: [tex]\dfrac{1}{10} =\dfrac{1.5}{M}[/tex] → M = 15
Column 6: [tex]\dfrac{1}{10} =\dfrac{P}{10.5}[/tex] → 10.5 = 10P → 1.05 = P
Column 7: [tex]\dfrac{1}{10} =\dfrac{20}{M}[/tex] → M = 200
Column 8: [tex]\dfrac{1}{10} =\dfrac{12.25}{M}[/tex] → M = 122.5
what scale factor was used in dilation
Answer: (c) [tex]\bold{\dfrac{3}{4}}[/tex]
Step-by-step explanation:
Chooe any point I am choosing point W.
The W' is closer to C than W so the dilation is less than 1
The only answer choice that is less than 1 is option c.
Why is this the answer? because the side lengths are proportional
[tex]\dfrac{CW'}{CW} = \dfrac{WX'}{WX}= \dfrac{3}{4}[/tex]
The perimeter of a rhombus is 180 cm and one of its diagonals is 72 cm. Find the length of the other diagonal and area of the rhombus
Hi there! :)
Answer:
Length of the second diagonal: 54 cm
Area of the rhombus: 1,944 cm²
Step-by-step explanation:
1) To find the value of the second diagonal, you first need to know some important properties of rhombuses:
Since the perimeter is 180, and by definition a rhombus has four congruent sides (of equal length), each side length of the rhombus is equal to 45.
The diagonals of rhombuses also form four right triangles, with hypotenuses equal to the side length of the rhombus and legs equal to half the lengths of the diagonals. In this case one hypotenuse would be equal to 45 and one leg would be equal to 36 (72 ÷ 2 = 36).
We can therefore use the Pythagorean Theorem to solve for one-half of the unknown diagonal:
c² = a² + b² → Where "c" is the hypotenus & "a" and "b" are the two other sides.
45² = 36² + b² → Where "b" is the half of the unknown diagonal.
We can now solve this equation for "b":
45² = 36² + b²
45² = 2,025
36² = 1,296
2,025 = 1,296 + b²
Subtract "1,296" from each side of the equation → 2,025 - 1,296 = 729
729 = b²
Square root on each side of the equation → √729 = 27
27 = b
Since "b" represents half of the unknown diagonal, we need to multiply by 2 to find the full length of the diagonal:
27 × 2 = 54 ⇒ Length of the other diagonal.
2) To find the area of the rhombus, you need to multiply the length of the 2 diagonals and divide the answer by 2:
(72 × 54) ÷ 2 = A
Multiply "72" & "54" together → 72 × 54 = 3,888
3,888 ÷ 2 = A
1,944 = A
There you go! I really hope this helped, if there's anything just let me know! :)
There are 25 students acting in a high school play. They make up 2% of the high school students. Hoy many students attend at the high school play
Answer:
1250
Step-by-step explanation:
since 2% of the school is 25 students that means every 2% there is 25 students.
100/2 = 50
50*25 = 1250 students
Answer:
1250 = total students
Step-by-step explanation:
Students in the play = total students * percent in play
We know that the students in the play =25
We know the percent in the play is .02
Substitute what we know into the equation
25 = total students * .02
Divide each side by .02
25/.02 = total students *.02/.02
1250 = total students
Brandon draws a reflection of the point (-4, -6). He gets the point (-4, 6). Across which axis did he reflect the point. Explain how you know
When you reflect a point across an axis, either the x value or the y value flips signs.
When you reflect across the x axis, the sign of the y value changes(+ to -) or (- to +)
When you reflect across the y axis, the sign of the x value changes (+ to -) or (- to +)
The point reflected across the x-axis because the sign of the y value changed/flipped, while the sign of the x value stayed the same.
Final answer:
Brandon reflected the point (-4, -6) across the x-axis to get the point (-4, 6), which is recognized by the unchanged x-coordinate and the sign reversal of the y-coordinate.
Explanation:
Brandon reflected the point (-4, -6) to get the point (-4, 6). This reflection occurred across the x-axis. We know this because the x-coordinate of the point remained unchanged, indicating that the point was not moved left or right. However, the y-coordinate changed from -6 to 6, which signifies that the point was reflected over the x-axis and moved from below the axis to an equal distance above the axis.
In reflections across the x-axis, the x-coordinate remains the same while the sign of the y-coordinate is reversed. Conversely, a reflection across the y-axis would keep the y-coordinate the same and reverse the sign of the x-coordinate.
In a coordinate system, negative or positive values for x and y are determined by their position relative to the origin. Points to the right of the origin and above the origin are usually considered to have positive coordinate values, with directions indicated by arrows on the axes. In Brandon's case, the negative y-coordinate became positive, affirming the x-axis as the axis of reflection.
simplify the expression. 16-4[3+2÷(9-7)]
Answer:
0
Step-by-step explanation:
Answer:
IT ALL EQUALS TO 0.
Step-by-step explanation:
Step 1: Parenthesis:
16 - 4[3 + 2 / 2]
Sep 2: dO DIVISION IN THE BRACKETS:
16 - 4[3 + 1]
Step 3: Add what is in the brackets
16 - 4[4]
Step 4: Multiply
16 - 16
Step 5: Simplify
0
There is a café at the park.
It is 13 metres long and 8 metres wide. What is the area of the café?
Answer:
42 meters
Step-by-step explanation:
because 13 + 13 + 8 + 8 = 42. and that's your answer
Final answer:
The area of the café is calculated by multiplying the length (13 meters) by the width (8 meters), resulting in an area of 104 square meters (104 m²).
Explanation:
The area of the café at the park can be calculated using the formula for the area of a rectangle, which is the product of its length and width. Given that the café is 13 meters long and 8 meters wide, we multiply these two dimensions to find the area.
Step-by-Step Calculation
Identify the length (13 meters) and the width (8 meters) of the rectangle.
Multiply the length by the width: Area = length × width.
Calculate: 13 meters × 8 meters = 104 square meters (104 m²).
Therefore, the area of the café is 104 m².
What is the simplified form of (−7x3 + 5x2 − x + 6) − (−8x3 + x2 + 3)?
A. −x3 + 4x2 − x + 3
B. x3 + 4x2 − x + 3
C. x3 − 4x2 − x − 3
D. −15x3 + 6x2 − x + 9
Answer:
B. x3 + 4x2 − x + 3
Step-by-step explanation:
(−7x^3 + 5x^2 − x + 6) − (−8x^3 + x^2 + 3)
Distribute the negative sign
(−7x^3 + 5x^2 − x + 6) + (8x^3 - x^2 - 3)
I like to line them up vertically.
−7x^3 + 5x^2 − x + 6
8x^3 - x^2 - 3
----------------------------------
x^3 +4x^2 -x +3
The simplified form of the expression ( –7x³ + 5x² – x + 6) – (–8x³ + x² + 3) is x³ + 4x² – x + 3, corresponding to option B.
To simplify the expression ( –7x³ + 5x² – x + 6) – (–8x³ + x² + 3), we need to remove the parentheses and then combine like terms.
First, distribute the negative sign through the second set of parentheses: –7x³ + 5x² – x + 6 + 8x³ – x² – 3.
Next, combine like terms: (–7x³ + 8x³) + (5x² – x²) – x + (6 – 3).
This simplifies to x³ + 4x² – x + 3.
So, the correct simplified form of the expression is option B. x³ + 4x² – x + 3.
Michelle’s annual take-home pay is $29,000. What is the maximum amount that she can spend per month paying off credit cards and loans and not be in danger of credit card overload?
Answer:
242 dollars / month. See guidelines below
Step-by-step explanation:
That depends largely on where she lives. The rule of thumb is to allow about 1/3 for rent after the government takes it's cut (that's all governments).
Here is an actual breakdown of how budgeting should be done.
Rent 33%Transportation 15% No carFood 10% very low. That means 240 / monthDebt 10%Personal 5%Savings 10% Utilities 10%Clothing 3%Medical 4% very low. Particularly if she is American.Total 100%These numbers are meant for Canada and are meant as a guide. In reality, if you live in the United States you will have to be spending more on medical for example and less somewhere else.
Now to your question. She has 29000 dollars. Debt is listed at 10%
10% of 29000 = (10/100) * 29000 = 2900 dollars.
Like most numbers having to do with money, most people don't understand large numbers and have to have them broken down. In monthly terms, she can spend 2900 / 12 = 241.67 dollars / month on debt. That does not mean that she can add 241.67 of new debt every month. It means that she must first pay off what she owes, and then she gets to spend the balance on debt, but that is a very dangerous way to think. What she should say is if she has left over money that money can be transferred over to another category.
I know of very few people that can consider themselves debt free. Fewer of our American friends can make the claim.
The sources of these %s come from Credit Counselling Society (of Canada)
Chris need a graphing calculator for math class c find a $60 model on sale for 15% off if you decide to buy this calculator how much will the sale price be
A)9
B)12
C)51
D)69
Answer:
C) $51
Step-by-step explanation:
Step 1. Calculate the discount
The discount is 15 % of $60
Discount = 60 × 0.15
Discount = $9
===============
Step 2. Calculate the sale price
Sale price = original price - discount
Sale price = 60 - 9
Sale price = $51
The sale price will be $51.
The family size bottle of sunscreen holds 12 fluid ounces (fl oz) of sunscreen. The regular bottle holds 75% less. How many fewer fluid ounces does the regular bottle of sunscreen hold?
Answer:
9
Step-by-step explanation:
what is the 52nd term for the following sequence ? 14,6,-2,-10,-18
It's an arithmetic sequence:
[tex]a_1=14\\a_2=14-8=6\\a_3=6-8=-2\\a_4=-2-8=-10\\a_5=-10-8=-18\\\vdots\\\text{The general formula for nth term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\\\\\text{We have}\ a_1=14,\ d=-8.\\\\\text{Substitute:}\\\\a_n=14+(n-1)(-8)=14-8n+8=22-8n\\\\\text{We need}\ a_{52}.\ \text{Put n = 52 to the formula}:\\\\a_{52}=22-8(52)=22-416=-394[/tex]
In Maria's store, the customer count this week is 3000. Maria is planning a promotion and expects a 5% increase in customers next week. How many additional customers is Maria expecting?
Answer:
150
Step-by-step explanation:
3000 * 0.05 = 150
A particular computer takes 13-minutes to download a 52-minute TV show. How long will it take the computer to download a 1.5-hour movie?
The particular computer will take approximately 22.5 minutes to download a 1.5 hour movie.
Explanation:In this particular problem, we need to figure out how long a computer will take to download a movie. The computer in question takes 13 minutes to download a 52 minute TV-show, establishing a rate of downloading. We can therefore calculate how long the computer takes to download a minute of TV-show by dividing the download time by the length of the show: 13/52 = 0.25 minutes per minute of show. Next, we convert 1.5 hours (the length of the movie) into minutes, because our rate is in terms of minutes: 1.5*60 = 90 minutes. We then multiply this by our download rate (0.25) to get our answer: 90*0.25 = 22.5 minutes. Thus, this particular computer will take approximately 22.5 minutes to download a 1.5 hour movie.
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What's the lateral area of a right cylinder if the radius of the base is 12mm and the altitude of the cylinder is 5 times the base radius? Use the π key to calculate and round your answer to the nearest whole number.
Answer:
1440π squared mm.
Step-by-step explanation:
Given is the radius of base of cylinder, r = 12mm.
The altitude is five times the base radius, h = 5 times 12mm = 60mm.
The lateral area of the cylinder is the curved surface area of the cylinder.
The formula for curved surface area of cylinder is as follows:-
Curved Surface Area = Circumference of base x altitude of cylinder.
SA = 2πrh = 2π•12•60 = 1440π sq. mm.
Hence, Lateral area of cylinder is 1440π squared mm.
Answer:
1440π
Step-by-step explanation:
We are given the radius of the base of a right cylinder to be 12 mm and its altitude or height to be 5 times the base radius which is equal to (12 x 5) = 60 mm.
We know the formula for the lateral area of a right cylinder:
[tex]A = 2\pi rh[/tex]
So putting in the given values with [tex]\pi[/tex] as it is to get:
[tex]A=2\pi *12*60[/tex]
[tex]A=2(720)\pi[/tex]
[tex]A=1440\pi[/tex]
Therefore, the lateral area of this right cylinder is 1440π.
An alligator is 6 inches long and grows 8 inches per year. Write an equation that represents the length y (in feet) of an alligator that is x years old. How long will the alligator be after 7 years?
Answer:
y=[(8in*x)+6in]/12in
A rescue helicopter is used to help victims who fell in a ditch. The helicopter begins at sea level, which is an elevation of 0 feet. It then travels down for 100 seconds at a speed of 10.5 feet per second. It then travels directly up for 150 seconds at a speed of 5.2 feet per second. After this 250 second period, how much time, in seconds, will it take for the rescue helicopter to travel back to sea level at the helicopter's maximum speed of 15.8 feet per second?
Answer:
The helicopter still needs to fly up sec 17.0886 at maximum speed.
Step-by-step explanation:
To find out how far the helicopter went down do 100(seconds) * 10.5 and get 1050
Then how much he traveled back up same thing 150 (seconds) * 5.2 and get 780
Next find the difference 780-1050 and get -270 ft it is negative because it is still BELOW GROUND ( That's how you know if it need to fly up or down)
Last to find how many seconds you need you work backwards so instead of multiplying you do the opposite witch is dividing so you take your feet (270) and divide by the maximum speed (15.8). 270/15.8 is 17.08
Identify the domain and range of the relation. Represent the relation with a
mapping diagram. Is the relation a function?
{(−1, 1), (−2, 2), (4, −4), (7, −7)}
The domain and range of the relation {(-1, 1), (-2, 2), (4, -4), (7, -7)} are {-1, -2, 4, 7} and {1, 2, -4, -7} respectively.
What is relation in function?Not every relation is a function, but every function is a relation.
A function is a relation with clear boundaries.
When we say that something is well-defined, we mean that each element has been assigned a specific image.
The given set is,
{(-1, 1), (-2, 2), (4, -4), (7, -7)}
The domain of a set is the values of x,
Domain = {-1, -2, 4, 7}
The range of a set is the values of y,
Range = {1, 2, -4, -7}
The relation makes the function because for every value of x the sign of function y is negative,
The required function is,
y = -x.
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Mateo wrote the equation 8-2(3-x)=4x-2(x+1).How many solutions are there to Mateo’s equation?
A. No solution
B. exactly one solution
C. exactly two solutions
D. exactly many solutions
After simplifying Mateo's equation, we find that it results in an impossibility (2=-2), which means that the equation has no solution.
Explanation:In order to find the number of solutions to Mateo's equation, we first need to simplify it. The equation given is 8-2(3-x)=4x-2(x+1). Distributing the numbers on each side of the equation, it turns into 8-6+2x = 4x -2x -2. Simplify it further into 2x + 2 = 2x - 2. If we subtract 2x from both sides, we get 2 = -2.
This result, 2 = -2, is not possible or true. Therefore, the given equation has no solutions. The correct answer to the question is therefore option A: No solution.
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Tim answered all the questions on his math test but got 10 answers wrong . He revived 4 points for every correct answer , and there was no penalty for wrong answers . His score was 76 points .
Write an equation to determine the total number of question (q) on Tim’s math test .
76 points/ 4 points per questions means he answered 19 questions correctly
plus the 10 he answered incorrectly
76/4+10=x
19+10=x
29=x
Rewrite the following expression using the associative property
(4x+9x)+12x
Solve the equation -18=p/2?
Answer:
p=-36
Step-by-step explanation:
-18=p/2
______________________
Multiply both sides by 2
-18(2)= p/2 (2)
______________________
-36 = p
switch the sides of the equation
______________________
p=-36
Ben made a model that was 5 3/4 inches tall. Laquisha made a model that was 70 11/12 inches tall. How many times as tall was Laquisha’s model?
To determine how many times taller Laquisha's model is compared to Ben's model, convert their heights to improper fractions and divide, simplifying the result to find the ratio.
Explanation:To find out how many times taller Laquisha's model is compared to Ben's model, we divide their heights. Laquisha's model height is
70 11/12 inches, and Ben's model height is 5 3/4 inches. First, convert the mixed numbers to improper fractions. Ben's height as an improper fraction is 23/4 inches. Laquisha's height as an improper fraction is 851/12 inches. Next, divide Laquisha's model by Ben's: (851/12)
÷ (23/4). To divide fractions, we multiply by the reciprocal of the second fraction: (851/12)
× (4/23). Simplify to find the ratio, which represents how many times taller Laquisha's model is.
F(x)= (x-2)^2 (x+2)(x+3)
Answer:
[tex]x^{4}[/tex] + x³ - 10x² + 20x
Step-by-step explanation:
expand (x - 2)² and (x + 2)(x + 3) using FOIL
= (x² - 4x + 4)(x² + 5x + 6)
multiply each term in the second factor by each term in the first factor
= [tex]x^{4}[/tex] + 5x³ + 6x² - 4x³ - 20x² - 24 + 4x² + 20x + 24 ← collect like terms
= [tex]x^{4}[/tex] + x³ - 10x² + 20x
Jesse earns $3 each time he walks a dog. Last Monday and Tuesday, he earned a total of $45. He walked 8 dogs on Tuesday. How many dogs did Jesse walk on Monday?
Answer:
7
Step-by-step explanation:
3*8=24 and so 3*7 would =21 and 21+24=45
Jesse walked 7 dogs on Monday.
To find this answer, you must first find out how much money he made for walking dogs on Tuesday. To do so, multiple 8 (number of dogs) by 3 (amount of money earned per dog. This will give you 24, which you subtract from the total (45). 45 - 24 = 21. Finally, divide 21 (amount he made on Monday) by 3 (amount of money earned per dog) to get 7 dogs on Monday.
I hope this helps!
What is 3.2 m converted to centimeters?
A. 3.2 cm
B. 32 cm
C. 320 cm
D. 0.032 cm
Answer:
C. 320 Cm
Step-by-step explanation:
To convert any value in meters to centimeters, just multiply the value in meters by the conversion factor 100.
3.2 meters=3.2*100=320 centimeters
HELP ME PLEASE
12*8+(12^3)=
Answer:
1824
That would be your total
Answer:
1824
Step-by-step explanation:
12*8+(12^3)=
We need to work these in the order of PEMDAS. First is the parentheses and exponents.
12*8 + 1728
Next is multiplication.
96+1728
Now add.
1824
In the diagram below which distance represents the distance from point d to ab
Answer:
CD
Step-by-step explanation:
The fastest way to get from D to AB is to go down CD
The distance from the point D to line AB is represented by the distance CD.
How to find the distance from a point to a line?To find out the distance from a point to a line we have to draw a perpendicular to the line from a given point, this distance will be considered as the distance between the point and line.
Hence the distance from point D to line AB is CD(option A).
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