In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .
What is Standard Form of a Equation ?
Ax+By=C
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).
The standard form of a linear equation is helpful for determining the x and y-intercepts of a graphed equation. It also helps you understand the concept of least common denominators, which is finding the lowest number to multiply and thus convert two fractions into whole numbers.
Given Equation :[tex]y = -\frac{4x}{3} + 2\\[/tex]
To convert it into Standard form , Multiply both sides with 3
[tex]3y = 3(\frac{-4x}{3} +2)[/tex]
[tex]3y = -4x + 6\\4x + 3y = 6[/tex]
Hence , In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .
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for every 8chin ups Melanie can do Theresa can do 5. If Melanie did 48 chin ups, how many fewer did Theresa do
Answer: Theresa did 18 fewer chin-ups.
Step-by-step explanation:
Melanie 8,16,24,32,40,48
Theresa 5,10,15,20,25,30
48-30=18
Danny opened a savings account and deposited $100.00. The account earns 2% interest,
compounded annually. If he wants to use the money to buy a new bicycle in 3 years, how
much will he be able to spend on the bike?
nt
P(1 + 1)^²₁. where A is the balance (final amount), P is the principal
Use the formula A = P 1 +
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Answer: f = p * (1 + r) ^ n
f is the future value.
p is the present value.
r is the interest rate per time period.
n is the number of time periods.
time periods are months.
rate is the percent divided by 100.
p = 100
r = 6% per year / 12 = .5% per month / 100 = .005 per month.
n = 2 years * 12 = 24 months.
formula becomes f = 100 * (1 + .005) ^ 24
solve for f to get:
f = 112.7159776 = 112.72
that's how much Danny will be able to spend on the bike in 2 years.
Step-by-step explanation:
The average mass of 5 boys is 50 kilograms. Another boy’s mass is added and the average goes to 40 kilograms. What was the mass of the sixth boy?
The mass of the sixth boy is 80 kilograms.
What was the mass of the sixth boy?It's important to note that a mean simply means the average of a set of numbers that are given. In this situation, the average mass of 5 boys is 50 kilograms. The total mass will be:
= 50 × 5
= 250 kilograms
In this case, when another boy’s mass is added and the average goes to 55 kilograms. The total mass will be:
= 55 × 6
= 330 kilograms.
The average mass of the last boy will be:
= 330 - 250
= 80 kilograms
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Complete questions
The average mass of 5 boys is 50 kilograms. Another boy’s mass is added and the average goes to 55 kilograms. What was the mass of the sixth boy?
Olivia want to have a 90 average in algebra, where tet count for 55%, quizze count for 30ge % and homework count for 15%. If he ha a 92 tet average and 100% HW average, what mut her quiz average be? Let x = the average of the
In order to score 90 average in algebra her quiz average should be 82%.
It involves calculating the result of multiplying a number of quantities by their sum, then dividing the result by the total number of quantities.
Given,
She has a test grade of 55%, a quiz grade of 30%, and a homework grade of 15%.
If she achieved a score of 92% on the test
Make x the number of tests,
x = (90 - (0.55(92) + 0.15(100)))/0.30
x = 82
To receive a 90 in math, Olivia needs to have a quiz average of 82.
One of the oldest subfields of mathematics, algebra covers number theory, geometry, and analysis. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.
Algebra covers a wide range of topics, from the study of abstractions to the solution of simple equations.
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. if you start with 1/4, you can create an entire class of fractions equivalent to 1/4 like the one above, by multiplying 1/4 by different forms of what number?
If you start with 1/4, you can create an entire class of fractions equivalent to 1/4 by multiplying 1/4 by different forms of the number 1.
What are fractions?The connection between two numbers, known as the numerator and the denominator, is expressed mathematically as fractions. The number of pieces is represented by the numerator, while the total number of components is represented by the denominator. For instance, if a pizza is cut into 8 slices and someone eats 3 of them, the fraction corresponding to the quantity consumed would be 3/8.
Diverse mathematical ideas, including division, ratios, and proportions, can be represented using fractions. They can also be used to represent decimal and percentage values, with the decimal point placed to the right of the numerator and the number of decimal places represented by the denominator.
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Simplify the expression below
7/2h - 3(5h - 1/2)
step by step please
Answer: [tex]-\frac{23}{2}h+\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\frac{7}{2}h-15h+\frac{3}{2}\\\\\frac{7}{2}h-\frac{30}{2}h+\frac{3}{2}\\\\-\frac{23}{2}h+\frac{3}{2}[/tex]
Write a rule for the n th term of the sequence. Then find a_{20}
$51,48,45,42,...$
The rule for the nth term of arithmetic sequence is a + (n - 1)d.
What is the nth term of arithmetic sequence?The difference between consecutive terms in an arithmetic sequence is always the same.An arithmetic sequence's nth term is given by a = a + (n - 1)d. The number d is known as the common difference because any two consecutive terms of an arithmetic sequence differ by d, and it can be found by subtracting any two terms a and an+1.Here also,
We use the definition for the nth term of an arithmetic sequence:
an = a1 + (n - 1) d
Here first term (a1) = 51
common difference (d) = a2 - a1
= 48 - 51
= -3
We have to find 20th term,
a[20] = a1 + (20 - 1) d
= 51 + 19 x -3
= 51 - 57
= - 6
Therefore 20th term of the sequence 51,48,45,42,... is -6.
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Show the work please! Thanks!!
Simplifying
2x + 5y = 2
Solving
2x + 5y = 2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5y' to each side of the equation.
2x + 5y + -5y = 2 + -5y
Combine like terms: 5y + -5y = 0
2x + 0 = 2 + -5y
2x = 2 + -5y
Divide each side by '2'.
x = 1 + -2.5y
Simplifying
x = 1 + -2.5y
Simplifying
5X + 10y = 17
Solving
5X + 10y = 17
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-10y' to each side of the equation.
5X + 10y + -10y = 17 + -10y
Combine like terms: 10y + -10y = 0
5X + 0 = 17 + -10y
5X = 17 + -10y
Divide each side by '5'.
X = 3.4 + -2y
Simplifying
X = 3.4 + -2y
Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1).
1. 1/3
2. 1
3. 2
4. 4/3
Answer:
4. 4/3
Step-by-step explanation:
(-2, -3) (1,1)
1+3/1+2=
4/3
Which equation represents how to determine the speed of an object?
The equation that the speed of an object is speed = distance/time
How to determine the equation of an objectFrom the question, we have the following parameters that can be used in our computation:
Parameter = Object
Argument = Speed
By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object
Mathematically, this can be represented as
Speed = Distance : Time
Express as fraction
Speed = Distance/Time
Hence, the equation is Speed = Distance/Time
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Graph the solution to this inequality on the number line. 1/2x−3<−1 3/8
The solution to the inequality, 1/2x - 3 < -1 3/8, is x < 13/4. See the graph below.
How to Graph the Solution of an Inequality on a Number Line?Given the inequality, 1/2x - 3 < -1 3/8, solve to find the value of x, which is the solution to the inequality.
1/2x - 3 < -1 3/8 [given]
1/2x - 3 < -11/8
Add 3 to both sides of the equation:
1/2x - 3 + 3 < -11/8 + 3 [addition property of equality]
1/2x < 13/8
Multiply both sides by 2:
1/2x * 2 < 13/8 * 2 [multiplication property of equality]
x < 13/4
The solution to this inequality, x < 13/4 is given in the graph below.
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Using the unit circle, on what interval is the cosine function increasing? (0, startfraction pi over 2 endfraction) (0, pi) (startfraction pi over 2 endfraction, startfraction 3 pi over 2 endfraction) (pi, 2 pi)
The interval where the cosine function is increasing is (π, 2π).
Finding the value of the cosine function in different intervals:The cosine function for the interval (0, π/2) gives
cos(x) = cos(0) = 1
cos(x) = cos(π/2) = 0
So, the value of the function is decreasing in this interval.
Then, for the interval (0, π), it gives
cos(0) = 1; cos(π) = -1
So, the value of the cosine function is decreasing in this interval.
Then, for the interval (π/2, 3π/2), it gives
cos(π/2) = 0
cos(π) = -1
cos(3π/2) = 0
So, the value of the function decreases up to x = π and then increases up to the same value as before i.e., cos(π/2) = cos(3π/2).
Then, for the interval (π, 2π), the cosine function gives
cos(π) = -1
cos(2π) = 1
Thus, the cosine function in this interval increase from -1 to 1.
Therefore, in the interval (π, 2π), the cosine function is increasing.
This is explained by using a unit circle below:
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Answer:
D
Step-by-step explanation:
got it right
1/2 - 1/7 =
3/5 - 1/2
Answer:
1/2 - 1/7 = 5/14
3/5 - 1/2 = 1/10
Step-by-step explanation:
Harmony pays $64.00 per month for a base cable package and an additional amount for on-demand programming. Last month, Harmony received a $67.36 cable bill.
$64.00 + x = $67.36
Ignoring sales tax and additional fees, how much did she spend for on-demand programming?
A) $3.36
B) $6.36
C) $70.72
D.) $131.36
choose the best graph to match the given expression.
F(x)= [x+1]
Answer:
Step-by-step explanation:
I don't see a graph from which to choose. Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?
The graph of functions
(F(x) = (x+1), and
(F(x) = |x+1| are both attached.
Algebraic fractions which option is correct
Answer:
A
Step-by-step explanation:
because to solve this question the division would change into multiplication and the second fraction would be converted upside down
PLEASE HELP ASAP!!!!!! I WILL GIVE BRAINIEST!!!!! I only need 2 and 3. Please explain your answer so I can understand this!!
The least expensive per pound is Customer A.
How to illustrate the expression?It should be noted that expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
The rate for the first customer will be:
= $14.50 / 1.75
= $8.29 per pound.
The second Customer rate will be:
= $26.25 / 2.5
= $10.5 per pound
The third Customer will be:
= $5.50 / 0.375
= $14.47 per pound.
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4. The chart below represents the kinematics of a freely falling body.
Time
(seconds t)
Total Distance
meters d (t)
1
5
2
20
45
80
125
3
4
5
a. Is the relationship between time and distance an arithmetic sequence?
Explain.
b. The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt2, where g is constant at 10 m/s². Show, in terms of n, the distance a falling body covers in t = n seconds of movement.
a. The given sequence is not an arithmetic sequence.
b. The distance a falling body covered in t = n seconds of movement is 5n²meters.
What is the distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Here, we have
a. A sequence can be said arithmetic sequence if the difference between any two consecutive terms remains the same.
In this case, the difference between 20 and 5 is 15, and the difference between 45 and 20 is 25, this shows that the difference between two consecutive terms is not the same.
Hence, it can be said that the given sequence is not an arithmetic sequence.
b. To evaluate the distance covered by the body in “n” seconds, Substitute t=n in d(t) then d(n) will represent the distance covered by the body in “n” seconds
d(n)=1/2 g(n)²
d(n) = 1/2(10)(n)²
d(n) = 5n²meters
Hence, the distance a falling body covered in t = n seconds of movement is 5n²meters.
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The angles of a triangle are 44 degrees, 110 degrees, and 26 degrees. Classify the triangle
The measure of angles form an scalene triangle.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
An angle requires two straight line, such that they're connected on one of their endpoints. The point of their joint is called vertex of that angle.
We are given that the angles of a triangle are 44 degrees, 110 degrees, and 26 degrees.
Since we know that angle sum property of a triangle;
44 + 110 + 26
180
Therefore, the measure of angles form an scalene triangle.
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A large pizza at palanzio pizzeria cot $6. 80 plu $. 90 for each topping. The cot of a large pizza at guido' pizza i $7. 30 plu $. 65 for eachtopping. How many topping need ti be added ti a large pizza from palanziod pizzeria and guido' pizza in order for the pizza to cot the ane not including tax
2 toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.
Let x be the number of toppings to be added to each pizza and y be the total cost of pizza.
A large pizza at Palanxio's Pizzeria cot $6. 80 plu $. 90 for each topping.
So, we get an equation,
y = 6.80 + 0.90x
The cot of a large pizza at Guido's Pizza i $7. 30 plu $. 65 for eachtopping.
So, we get an equation,
y = 7.30 + 0.65x
We need to find the number of toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.
Now let's equate the costs of both pizzas and solve for x.
6.80 + 0.90x = 7.30 + 0.65x
0.25x = 0.50
x = 2
Therefore, 2 toppings to be added to each pizza
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At a football stadium, 25% of the fans in attendance were teenagers. If there were 10 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
40 people
Step-by-step explanation:
25% = 10
50% = 20
100% = 40
three solutions of the equation y= -2x
Answer:
three solutions of the equation:
y = -2x - 1
=>
1) (0, -1)
2) (1, -3)
3) ( -1, 1)
Step-by-step explanation:
Are any of these numbers linear expressions? 5x+3, 8xy, 14, or 3x^2
Answer: 5x+3 is a linear expression
Step-by-step explanation:
The linear expression is y=mx+b
5x +3 has a slope and y-intercept, so it is a linear expression!
8xy is not because it is just a variable
3x^2 is not because it has ^2
Jaylen bought 5 pounds of apples for 12.99 and 4 cupcakes for 2.99 each. He went to the store with $48. How much did Jaylen have left after his shopping trip?
23.05
37.94
10.06
24.95
Answer:
$24.95
Step-by-step explanation:
2.99 times 4 is 11.96, and you would add that with 12.99 to get 24.95.
Answer:
Jaylen have left 23.05 $
Step-by-step explanation:
5 pounds of apples = 12.99 $
4 cupcakes = 2.99 $/apple
Total money = 48 $
All the cupcakes costs = 4*2.99 = 11.96 $
Then she bought in total:
48 -(12.99 + 11.96)
48 - 24.95 = 23.05
What is the y-intercept of this line?
Answer: b=13
Step-by-step explanation:
This equation is in point-intercept form: y = mx + b
slope = m = 4/3
y-intercept = b = 13
Ahmad jogged a distance of 3200 m on Saturday and a distance of 1.8 km on Sunday.
(a) Express the distance he jogged on Saturday as a percentage of the total distance jogged on both days.
(b) Find the percentage decrease in the distance he jogged from Saturday to
Sunday.
Answer:
a) 4,000 meters
b) - 56.25% (or -56% with 2 sig figs
Step-by-step explanation:
Calculate the total distance Ahmad jogged on both days. This will require a conversion unit to make the distances the same units.
Sat.: 3200 m
Sun: 1.8 km
(1,000m/km)
(1.8km)*(1,000 m/km) = 1,800 m jogged on Sunday
Total distance jogged = 3,200 m + 1,800 m = 4,000 meters total jogged
a) Percentage jogged on Saturday:
(3,200 m)/(4,000 m) = 0.80 or 80%
b) Percentage Decrease (From Saturday to Sunday):
Sat: 3200 m
Sun: 1800 m
Difference = 1400 m (decrease)
Percentage Decrease = (1800/3200) = 56.25%
Ahmad's distance on Sunday was a 56.25% decrease from Saturday.
there are 5 children on your guest list and 40 people in total. what percentage of the people are children?
Answer: 12.5%
Step-by-step explanation:
5/40
0.125 x 100
12.5%
Answer:
2 children I believe so
Step-by-step explanation:
because you take 40%×5 and u will get 2
Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y =
The solution for the system of equations is the point (3, 5), and the difference x - y gives:
x - y = -2
How to solve the system of equations?Here we have the following system of equations:
5x + 3y = 30
-5x - 2y = -25
Notice that in the two equations we have the "5x", but in one case is positive and in the other negative, then we can just add them so we get:
(5x + 3y) + (-5x - 2y) = 30 - 25
(5x - 5x) + (3y - 2y) = 5
0 + y = 5
y = 5
So we found the value of y, by evaluating the second linear equation in y = 5 we will get:
-5*x - 2*5 = - 25
-5x = -25 + 2*5
-5x = -25 + 10
-5x = -15
x = -15/-5 = 3
So y = 5 and x = 3, the difference x - y gives:
3 - 5 = -2
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The rate of change is how a quantity is changing with respect to a change in another quantity.
True false question.
True
False
Answer: True
Step-by-step explanation:
The rate of change or the slope is the changes to another quantity with a constant.
Jimmy, Johny, and Jolly worked part-time on the weekend to earn some extra money. Three of them together earned $57. If Johny earned twice as much as Jolly did and Jimmy earned $3 less than Johny did, how much did Jimmy earn?
On solving the provided linear equation question - Jolly = $17.4, Jimmy =2x-30 =4.8 and Johnny = 2x=34.8
What is a linear equation?A linear equation has the algebraic form y=mx+b. where m is the slope and b is the y-intercept, consisting of a first-order (linear) term and a constant. If x and y are variables, the above is sometimes called a "two-variable linear equation".
Take Jolly's expenditure as x.
Jimmy would have spent twice as much as Jolly.
Johnny Equals 2x-30 if Johnny spent $30 less than Johnny.
Total amount spent: $57
Therefore,
[tex]x+ (2x-30) + 2x = 57\\ x+ 2x -30 +2x =57.\\ 5x = 57+ 30\\[/tex]
x = 87/5
x= 17.4
Now take is that - X= 17.4.
Jolly is that - x= $17.4
Jimmy is that - =4.8
Johnny is that = =34.8
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