Step-by-step explanation:
General line equation: y = mx + c.
2y + 3x = 5
2y = -3x + 5
y = -1.5x + 2.5
Hence m = -1.5 and c = 2.5.
[tex]\tt m=-\dfrac{3}{2}\\\\c=\dfrac{5}{2}[/tex]
Further explanationGiven
The line equation
2y+3x=5
Required
m(gradient) and c(constant)
Solution
The two-variable linear equation is a linear equation that has 2 variables and the exponent is one
ax+by=c
We change the equation in standard form : y = mx + c
[tex]\tt 2y=-3x+5\\\\y=-\dfrac{3}{2}x+\dfrac{5}{2}[/tex]
Gradient :
[tex]\tt -\dfrac{3}{2}[/tex]
Constant :
[tex]\tt \dfrac{5}{2}[/tex]
Is -8 a solution to the equation 8x +2=3x + 13
Answer:
No.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
8x + 2 = 3x + 13
Step 2: Solve for x
Subtract 3x on both sides: 5x + 2 = 13Subtract 2 on both sides: 5x = 11Divide 5 on both sides: x = 11/544 is 2 thirds of a number, what is the number?
Answer:
The number is 66
Step-by-step explanation:
Since 44 is two thirds of a number, 44/x = 2/3
If you multiply the numerator and denominator of 2/3 by 22, you get 44/66
Since 44/x = 44/66,
x=66
If 44 is 2 thirds of a number, then the number is 77.
We can solve this problem by setting up the following equation:
2/3 * x = 44
Where x is the unknown number.
To solve for x, we can multiply both sides of the equation by 3/2. This gives us the following equation:
x = 44 * (3/2)
Simplifying the right side of the equation, we get x = 77.
Therefore, the number is 77.
Here is the solution in more detail:
Define the variables.
x: The unknown number.
Set up the equation.
We know that 2/3 of the number is 44, so we can set up the equation 2/3 * x = 44.
Solve for x.
To solve for x, we can multiply both sides of the equation by 3/2. This gives us the equation x = 44 * (3/2).
Simplifying the right side of the equation, we get x = 77.
The answer.
Therefore, the number is 77.
To learn more about number here:
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Billy has 2.4 m of ribbon for crafts. He wants to share it evenly with 12 friends. Billy has been making craft projects for several years now. How many centimeters of ribbon would 7 friends get?
Answer:
140 cm
Step-by-step explanation:
Given that:
Total length of ribbon present with Billy = 2.4 m
This ribbon is to be shared with 12 friends evenly.
Billy is doing this work of making craft for the past many years.
To find:
How many centimeters of ribbon that 7 friends will get?
Solution:
First of all, let us find out what length of ribbon will each person get.
Length of ribbon to be shared with each person = Total length of ribbon divided by total number of persons
Length of ribbon to be shared with each person = [tex]\frac{2.4}{12} = 0.2\ m[/tex]
Now, The length of ribbon that 7 friends will get = 7 [tex]\times[/tex] 0.2 = 1.4 m
1 m = 100 cm
1.4 m = 1.4 [tex]\times[/tex] 100 cm = 140 cm
Sara says, "If you subtract 14 from my number and multiply the difference by - 4, the result is - 44."
What is Sara's number?
Answer: I believe that the answer would be 25.
Step-by-step explanation:
HOPE IT HELPS :)
Which inequality is shown in this graph?
Answer:
the constant inequality of my life, always close but never there
A triangle has two sides of length 5 and 19. What is the smallest possible whole-number length for the third side?
Answer:
13
Step-by-step explanation:
Given 2 sides of a triangle then the third side x is
difference of 2 sides < x < sum of 2 sides , that is
19 - 5 < x < 19 + 5
14 < x < 24
Thus the smallest whole number length of the third side is 13
Plz help me my maths hw is due in a couple of hrs!!!
Find the value of x.
m22 = 3x + 13
40°
N
X=
Step-by-step explanation:
ttgiffkydfhigdfgkfee FM 8
Jason was hired to mow a lawn that covers an area of 2 3/4 acres. It took him 4 1/8 hours to complete the job. What was his unit rate in hours per acre?
In this activity, you will multiply the numerator in a complex fraction by the reciprocal of the denominator to calculate a unit rate involving fractions. Answer the questions below to calculate Jason’s unit rate as he mowed.
Answer:
2 3/4 = 11/4
4 1/8 = 33/8
11/4 / 33/8 = 11/4 * 8/33 = 88/132 = 2/3
He mowed 2/3 of an acre per hour
Step-by-step explanation:
Mrs Shakya sold a jewellery at a loss of 5%.If she had sold it at Rs,5200 more she would have gained 8% .Find the cost price of the jewellery.
Answer:
40,000
Step-by-step explanation:
Given that:
Percentage Cost price of jewelry = 100%
Jewelery was sold at loss of 5% = (100%- 5%) = 95%
If sold at 5200 more ; profit made = 8%
That is ; (100% + 8%) = 108%
Difference between loss percentage and profit percentage = change in price sold
(108% - 95%) = 5200
13% = 5200
If ;
0.13 = 5200
The percentage cost price = 100% will be;
0.13 = 5200
1 = x
0.13x = 5200
x = 5200 / 0.13
x = 40,000
Use the functions to answer the question: What is f(x)-g(x)?
Answer:
4x^2 + 6x - 6
Step-by-step explanation:
x^2 + 2x - 5 - (-3x^2 - 4x + 1)
x^2 + 2x - 5 + 3x^2 + 4x - 1
4x^2 + 6x - 6
Plug in the equations and combine like terms.
Hope this helps!
A hot air balloon is dropping from a height above the ground at a steady rate of 8 feet per second. It starts from a height of 765 feet. After t-seconds it has hit a height of 421 feet. Set up and solve an equation for the value of t.
PLEASE PLEASE ANSWER THIS FOR ME I REALLY NEED TO UNDERSTAND IT
"FIND THE COLOURED AREA IN THE FOLLOWING SHAPES"
HELP PLEASE
Answer:
See answers below for explanations (answers are in bold)
Step-by-step explanation:
Problem 1 (Top left):
Assuming that the shape is an ellipse, we will use the formula A=πab where a and b are both half the major and minor axis respectively. Since a=9 and b=6, then we have A = π(9)(6) = 54π = 169.646 units^2 as our final answer
Problem 2 (Top right):
Again, we use the same equation as in Problem 1 but this time, a=12 and b=8, so we then have A = π(8)(12) = 96π = 301.593 units^2 as our final answer
Problem 3 (Bottom left):
We can make this irregular shape into a half-ellipse and a rectangle. We would find their separate areas and add them up. The area of the half-ellipse would be A=1/2πab. The value of "a" would be 13.8/2=6.9 since that's the length of the rectangle. The value of "b" would be 3.5, so that means the area of the half-ellipse would be A = 1/2(π)(6.9)(3.5) = 12.075π = 37.935 units^2. The width and length of the rectangle are 5.4 and 13.8 respectively, so this means the area of the rectangle is 5.4*13.8 = 74.52 units^2. Combining both areas, we get 37.935+74.52 = 112.455 units^2 as our final answer
Problem 4 (Bottom right):
This irregular shape is an ellipse, but a circle is missing from its center. Thus, we must find the area of the circle and ellipse and then subtract the circle's area from the ellipse's area. For the area of the ellipse, a=(15.5/2)=7.75, and b=(7/2)=3.5, making its area A = π(7.75)(3.5) = 27.125π = 85.216 units^2. The area of a circle is A=πr² where "r" is the radius. The radius would be 7/2=3.5, making the circle's area A = π(3.5²) = 12.25π = 38.485 units^2. This means that the shaded area is 85.216-38.435 = 46.781 units^2
Find the product of 6/7•5/7
Hey there!
The word “product” simply means the result of a multiplication equation
MULTIPLY the NUMERATORS (TOP numbers) from each other and also MULTIPLY the DENOMINATORS (BOTTOM number) from each other
6(5) / 7(7) = ?
6(5) = 30 ⬅️ NUMERATOR
7(7) = 49 ⬅️ DENOMINATOR
Possible ANSWER: 30/49
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Midway through the fundraiser, Mrs Little, the sponsor, discovers a container of buttermilk in the back of the fridge. It has 6 cups of buttermilk in it. How many recipes will this make? each recipe calls for 7/8. cup of butter milk.
Answer: 6 recipes
Step-by-step explanation: Just divide the 6 cups of buttermilk by 7/8 because each recipe need 7/8 cup of butter milk. You will get a number like this 6.857142857142857 (there are probably more decimals that come after it.) But, all the numbers after the 6 are useless because more recipes can't be made with those because you need at least 7/8 cups for one recipe. So, this will make 6 recipes. Hope this helps!
if you can buy three loaves of bread for $5 how many loaves can you buy with $12.
Answer:
45
Step-by-step explanation:
What is the value of p
Answer:
p = 2
Step-by-step explanation:
p + 4/p - 4
multiplying through by p,
p×p + 4/p ×p - 4×p
p² + 4 - 4p = 0
p² - 4p + 4 = 0
factorizing,
p(p - 2) -2(p - 2) =0
(p -2)(p -2) =0
p-2 =0
p=2
The local high school is having tryouts for the cross country team. The school does not have a track, so the runners run around the school’s football field. The cross country coach determines that the width of the field is seventy yards shorter than the length.
Complete Question
The local high school is having tryouts for the cross country team. The school does not have a track, so the runners run around the school's football field. The cross country coach determines that the width of the field is seventy yards shorter than the length.
Part A
Write an expression that represents the perimeter of the football field. Let x Represent the length of the football field. Include parentheses in your expression. Next, write an equivalent expression that does not include parentheses.
Part B
The cross country coach later determines that the length of the football field is 120 yards. All students must run five laps. Using your answer from Part A, determine the actual number of yards that each athlete must run in the tryouts. In order to make the team, students must complete the laps in 6 minutes. How quickly must they run each lap?
Answer:
[tex]p=4A-140[/tex]
[tex]T =or 62sec[/tex]
Step-by-step explanation:
From the question we are told that
The width of the field is seventy yards shorter than the length.
a) Generally the equation for width and length is given as
[tex]B=x-70[/tex]
Mathematically in finding the perimeter [tex]p[/tex] around the field
[tex]p=2(A+B)[/tex]
[tex]p=2(2A-70)[/tex]
[tex]p=4A-140[/tex]
b)Generally[tex]A=120[/tex]
Mathematically
[tex]p= 4(120) -140[/tex]
[tex]p=480-140[/tex]
[tex]p= 340[/tex]
Therefore
Yards ran by individual athlete[tex]Y[/tex]
[tex]340*5=1700\\Y=1700[/tex]
Time elapsed in a lap T
[tex]T=\frac{340}{1700} *6\\T=1.2min[/tex]
[tex]T =or \hspace 662sec[/tex]
From where Kiana is standing she must look up at a 50° angle to see the top of a building she backs up 50 feet she will need to look up a 40° angle to see the top of the same building approximately how tall is the building
For this case, what we must do is solve the following system of equations: tan (50) = h / x tan (40) = h / (x + 50)
Solving the system we have: (x + 50) * tan (40) = h (x) * tan (50) = h
Matching: (x + 50) * tan (40) = (x) * tan (50)
Rewriting: x (tan (50) - tan (40)) = 50 * tan (40) x = 50 * tan (40) / (tan (50) - tan (40)) x = 118.9692621
Substituting: h = (x) * tan (50) h = (118.9692621) * tan (50) h = 141.7820455
B. 141.8ft
Question 9 of 10
What is the slope formula?
Answer:
Step-by-step explanation:
D
HAPPY NEW YEAR EVERYONE. HERE IS TODAY'S OPTIONAL CHALLENGE
What is 1567238932 * 1456788345
Try to do this on paper and not with a calculator.
This is optional and if you decide to do it, good luck.
Answer:
This is a bit complicated, but the answer would be 2.28831354(v)x10(^)18, or otherwise known as 2283135409967847400.
Step-by-step explanation:
Answer:
D A N G uh,
Step-by-step explanation:
i dont think any person can physically do that
proof i tried ;-;
Romb ma obwód równy 32 cm. Jakie jest pole tego rombu, jeżeli jego wysokość ma 3 cm?
Answer:
24 cm²
Step-by-step explanation:
Z zadanego powyżej pytania uzyskano następujące dane:
Obwód (obwód) = 32 cm
Wysokość (h) = 3 cm
Obszar rombu (A) =?
Następnie określimy długość boku rombu. Można to uzyskać w następujący sposób:
Obwód, czyli obwód (P) = 32 cm
Strona (y) =?
P = 4 s
32 = 4 s
Podziel obie strony przez 4
s = 32/4
s = 8 cm
Stąd długość boku rombu wynosi 8 cm
Na koniec określimy obszar rombu w następujący sposób:
Długość boków = 8 cm
Wysokość (h) = 3 cm
Obszar rombu (A) =?
A = sh
A = 8 × 3
A = 24 cm²
Dlatego obszar rombu jest
24 cm².
PLEASE HELP THIS IS THE THRID TIME I POSTED THIS
equation: f(x) = 3/2x - 3
the line is linear and proportional
the line is linear because it has a steady rate of change, which is 3/2, and the equation is in the y=mx+b form. it is also proportional because as the x value increases, the y value also increases.
slope: 3/2
the y intercept is -3
Pls help I put a pic of problem
Answer:
a
Step-by-step explanation:
Which measure Is the sarne as the standard error of the mean?
A. Standard devlation of the population
B. Standard devlation of the sample means
C. mean of the sarnple
D. mean of the population
Answer:
The answer is B.
Step-by-step explanation:
The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution.
Formula of the standard error of the means is standard deviation divided by square root of the sample size.
SE = δ/√n
This formula also gives the standard deviation of the sample means.
The answer is standard deviation of the sample (B).
For example, "The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean)."
3 lines are shown. A line with points T, R, W intersects a line with points S, R, W at point R. Another line extends from point R to point U between angle T, R, V. Angle V R W is (3 x) degrees and angle T R S is (2 x + 18) degrees.
What is m∠SRW?
18
54
126
108
Given:
Consider the three point of second line are S, R, V instead of S, R, W.
A line with points T, R, W intersects a line with points S, R, V at point R. Another line extends from point R to point U between angle T, R, V.
[tex]\angle VRW=(3x)^\circ[/tex]
[tex]\angle TRS=(2x+18)^\circ[/tex]
To find:
The m∠SRW.
Solution:
The figure according to the given information is shown below (not to scale).
From the below figure it is clear that, [tex]\angle VRW[/tex] and [tex]\angle TRS[/tex] are vertically opposite angles. So, their measures are equal.
[tex]3x=2x+18[/tex]
Subtract 2x from both sides.
[tex]3x-2x=18[/tex]
[tex]x=18[/tex]
Using x=18 the measure of angle VRW is
[tex]\angle VRW=(3x)^\circ[/tex]
[tex]\angle VRW=(3\times 18)^\circ[/tex]
[tex]\angle VRW=54^\circ[/tex]
Now,
[tex]\angle VRW+\angle SRW=180^\circ[/tex] [Linear pair]
[tex]54^\circ+\angle SRW=180^\circ[/tex]
[tex]\angle SRW=180^\circ-54^\circ[/tex]
[tex]\angle SRW=126^\circ[/tex]
Therefore, the correct option is C.
Answer:
126
Step-by-step explanation:
i just got the right answer
Consider the function represented by the equation x – y = 3. What is the equation written in function notation, with x as the independent variable?
f(x) = y + 3
f(x) = –y – 3
f(x) = –x + 3
f(x) = x – 3
Answer:
f(x) = x – 3
Step-by-step explanation:
The equation that is written in function notation, with x as the independent variable is D. f(x) = x – 3
Calculations and ParametersTo write the equation as an independent variable, we simply need to isolate y.
The next step would be to subtract x from both sides:
-y = 3 - x
To eliminate the -ve sign in y, we would divide both sides by -1
y= -3+x
If we rearrange, the answer would be:
f(x) = x – 3
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What is the smallest integer value of r for which it is true that -2.5 < r < 7?
Answer:
[tex]r = -2[/tex]
Step-by-step explanation:
Given
[tex]-2.5 < r < 7[/tex]
Required
Determine the smallest value or r
For an inequality [tex]a < r < b[/tex]
The smallest value is represented as:
[tex]r>a[/tex]
In this case:
[tex]a = -2.5[/tex]
[tex]b = 7[/tex]
So:
[tex]r>a[/tex] becomes
[tex]r > -2.5[/tex]
r > -2.5 implies that the value of r is greater than -2.5
The smallest integer value after -2.5 is -2
Hence, the smallest value of r in this case is:
[tex]r = -2[/tex]
The small zoo at Nichols Park charges $8 for adult admission, $5 for child admission (18 years old and under), and $3 for senior admission (60 years old and over). For one day, the zoo collected $539 and admitted 96 visitors. If the adult admission is 9 more than the senior admission, how many persons of each category were admitted on this particular day?
Answer:
32 seniors, 41 adults, and 23 children were admitted.
Step-by-step explanation:
To make things a bit simpler, we can represent all three kinds of tickets in terms of one variable, [tex]x[/tex]. Let the number of senior visitors be [tex]x[/tex]. Then, since 9 more adults were admitted as compared to the seniors, we can let the number of adult visitors be [tex]x+9[/tex]. Therefore, since there were 96 visitors in total, we know that the number of child visitors is 96 subtracted by the total number of adult and senior visitors. The total number of adult and senior visitors is [tex]x+x+9=2x+9[/tex]. Thus, the number of child visitors is [tex]96-(2x+9)=96-2x-9=-2x+87[/tex].
Now, all we have to do is write an equation to solve for [tex]x[/tex]. Since senior admission costs $3, we can represent the money earned from it as [tex]3*x=3x[/tex]. Since adult admission costs $8, we can represent the money earned from it as [tex]8*(x+9)=8x+72[/tex]. Finally, since child admission costs $5, we can represent the money earned from it as [tex]5*(-2x+87)=-10x+435[/tex]. Since we know that the zoo collected $539 in total, we can write the following equation to solve for x:
[tex]3x + 8x+72-10x+435=539[/tex]
[tex]x+507=539[/tex] (Simplify LHS)
[tex]x=32[/tex] (Subtract 507 from both sides)
Therefore, 32 seniors were admitted. Since [tex]x=32, x+9=32+9=41[/tex], so 41 adults were admitted, and finally, since [tex]x=32,-2x+87=-2*32+87=-64+87=23[/tex], so 23 children were admitted. Hope this helps!
2.3 + 12.3x = 14.6 whats x?
Answer:
x = 1
Step-by-step explanation:
12.3 + 2.3 = 14.6
If you multiplied 12.3 by 1 it would still be 12.3