Answer:
y=2x-3
Step-by-step explanation:
y=mx+b
-1=1m+b
3=3m+b
subtract those two ^
-4=-2m
2=m
-1=1m+b
-1=1(2)=b
-1=2+b
-3=b
y=2x-3
Find the simple interest earned to the nearest cent for each principal, interest rate, and time.
$1200 at 3.9% interest over 8 months
AND $580 at 2% interest over 6 months
I'll give you 45 points and mark you brainliest!
Answer:
Interest earned at 3.9 percent rate is $31.2
Interest earned at 2 percent rate is $5.8
Step-by-step explanation:
A = P(1 + rt)
Where 'A' is the amount, 'r' is the rate and 't' is the time in years
When;
P = $1200
r = 3.9%
t = [tex]\frac{8}{12}[/tex] years
Then,
A = $1200(1 + 0.039([tex]\frac{8}{12}[/tex]))
A = $1200 + $31.2 = $1231.2
Interest = Amount - Principal
Interest earned at 3.9 percent rate is $1231.2 - $1200 = $31.2
When;
P = $580
r = 2%
t = [tex]\frac{6}{12}[/tex] years
Then,
A = $580(1 + 0.02([tex]\frac{6}{12}[/tex]))
A = $580 + $5.8 = $585.8
Interest earned = Amount - Principal
Interest earned at 2 percent rate = $585.8 - $580 = $5.8
Thesimple interest, you use the formula I = PRT, with P representing principal, R the annual interest rate in decimal form, and T the time in years. For $1200 at 3.9% over 8 months, the interest is $37.20. For $580 at 2% over 6 months, the interest is $5.80.
The simple interest earned on two separate principals with different interest rates and time periods. To calculate simple interest, we use the formula I = PRT, where I is the interest earned, P is the principal amount, R is the annual interest rate (in decimal form), and T is the time in years. If the time is given in months, we must convert it into years by dividing by 12.
Example 1:
Principal (P) = $1200
Annual Interest Rate (R) = 3.9% = 0.039
Time (T) = 8 months = ({8}{12}) years
Simple Interest (I) = $1200 (times) 0.039 (times) \(frac{8}{12}) = $37.20 to the nearest cent
Example 2:
Principal (P) = $580
Annual Interest Rate (R) = 2% = 0.02
Time (T) = 6 months = ({6}{12}) years
Simple Interest (I) = $580 (times) 0.02 (times) \({6}{12}) = $5.80 to the nearest cent
In conclusion, we have two amounts of simple interest for the different principals, rates, and times provided. To find the total future amount with simple interest, we would add the interest earned to the principal amount.
Simplify 10+6/2+3
16/5
3
7
11/3
Step-by-step explanation:
[tex]\text{If}\ 10+\dfrac{6}{2}+3=10+3+3=16\\\\\text{If}\ \dfrac{10+6}{2+3}=\dfrac{16}{5}[/tex]
To simplify 10+6/2+3, we first perform the division operation (6 ÷ 2 = 3), and then carry out the addition operations in order (10 + 3 + 3), giving us a final result of 16.
Explanation:To simplify 10+6/2+3, we have to follow the order of operations as guided by the mnemonic PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In the given expression, there are no parenthesis, exponents, so we proceed by carrying out division and then addition.
Step 1: Perform the division operation 6 ÷ 2 = 3.
Step 2: Simplify the expression by performing the addition operations in the order from left to right. So, 10 + 3 (from division) + 3= 16.
Therefore, the simplified form of the original expression is 16.
Learn more about Order of Operations here:https://brainly.com/question/15840745
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How are graphs with a nonzero axis misleading? -They distort differences between values. -They rely on faulty data. -They are visually distracting. -The scales on the axes are consistent.
Answer:
They distort differences between values.
Step-by-step explanation:
Non-zero axes distort differences between values, but they are not always misleading.
It depends on who is looking at them.
Consider the bar graphs below, showing the change in interest rates over time.
A naïve reader might conclude that interest rates had risen sharply (the zero-axis shows that they have remained steady).
However, a professional who specializes in interest rates might find the information in the left-hand graph quite useful.
A professional who specializes in interest rates might find the information in the left-hand graph quite useful.
They distort differences between values.
We have given that, a graph
They distort differences between values,
What distort differences between values?Non-zero axes distort differences between values, but they are not always misleading.
It depends on who is looking at them.
Consider the bar graphs below, showing the change in interest rates over time.
A naïve reader might conclude that interest rates had risen sharply (the zero-axis shows that they have remained steady).
However, a professional who specializes in interest rates might find the information in the left-hand graph quite useful.
To learn more about the graph visit:
https://brainly.com/question/25020119
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What is the cube root of 27a^12
ANSWER
[tex]3{a}^{4 } [/tex]
EXPLANATION
The cube root of
[tex]27 {a}^{12} [/tex]
is
[tex] \sqrt[3]{27 {a}^{12} } [/tex]
This is the same as:
[tex](27 {a}^{12} )^{ \frac{1}{3} } [/tex]
[tex]( {3}^{3} ({a}^{4})^{3} )^{ \frac{1}{3} } [/tex]
[tex] = (3{a}^{4} )^{3 \times \frac{1}{3} } [/tex]
[tex] = 3{a}^{4 } [/tex]
y = 5x - 8
y = 4x - 7
ANSWER
(1,-3)
EXPLANATION
The given equations are:
y = 5x - 8
y = 4x - 7
We equate the two equations to get:
5x - 8=4x - 7
Group similar terms:
5x - 4x=-7+8
Simplify bottom sides
x=1
Put x=-15 into the first equation:
y=5(1)-8
y=-3
(1,-3)
The solution is (1,-3)
how to solve for x 4/X=12/7.5
A discount bookstore sells hardcover books for $12 and paperback books for $6. The number of hardcover books, x, sold one day was twice the number of paperback books, y, sold the same day. The total sales that day were $180.
1.What is the system of equations that represents this situation?
2.What is the solution to the system and what does it represent in the context of this situation? Show your work.
Answer:
Part 1) The system of equations that represent this situation is
[tex]12x+6y=180[/tex] and [tex]x=2y[/tex]
Part 2) The number of hardcover books sold was [tex]12[/tex] and the number of paperback books sold was [tex]6[/tex]
Step-by-step explanation:
Part 1) What is the system of equations that represents this situation?
Let
x----> number of hardcover books sold
y----> number of paperback books sold
we know that
The system of equations that represent this situation is equal to
[tex]12x+6y=180[/tex] -----> equation A
[tex]x=2y[/tex] -----> equation B
Part 2) What is the solution to the system and what does it represent in the context of this situation?
Substitute equation B in equation A and solve for y
[tex]12(2y)+6y=180[/tex]
[tex]24y+6y=180[/tex]
[tex]30y=180[/tex]
[tex]y=6[/tex]
Find the value of x
[tex]x=2y[/tex]
[tex]x=2(6)=12[/tex]
The solution of the system of equations is the point (12,6)
That means
The number of hardcover books sold was [tex]12[/tex]
The number of paperback books sold was [tex]6[/tex]
Football helmets are made with padding that helps reduce head injuries when a player collides with an object. Which best explains how the padding reduces injuries? It extends the time of the collision. It reduces the time of the collision. It eliminates the reaction force of the object. It eliminates the action force of the object.
Answer:
It extends the time of the collision
Step-by-step explanation:
The correct option is : It extends the time of the collision.
The padding helmets have cushions inside it that moves inwards when a ball hits the helmets.
When the collision occurs, the time will increase and less force will be exerted on helmet that is why the impact of the collision will be less.
Answer:
A. It extends the time of the collision.
Step-by-step explanation:
the picture
a giant radio Mast is held To The Ground by 8 wires for which are Illustrated the other wires are fixed in the same position on the other sides of The Masque of the wires have to be replaced what length of the wires must be purchased
Answer:
Step-by-step explanation:
Pythagoream theorem applies.
The long wires are [tex]\sqrt{45^2+30^2}m[/tex] long, or about 54m long.
The short ones are [tex]\sqrt{20^2+30^2}m[/tex], or about 36m long. You will need 4 of each, so it's [tex]4* 54m + 4*36m = 540m[/tex] of wire
kayden brought 9 packs of paper for $27 how much will you pay for 11 packs of paper
Answer: $33
Step-by-step explanation: Divide 27/9 which is $3
-so you pay $3 for each pack
-then to find how much you need to pay for 11 packs you just multiply 11*3=33
60 Points Please Help!!!! Been Stuck For Hours!!!!
Perform the indicated operation. What is the numerator in the final expression? Type your answer in the space provided. Do not include spaces in your answer. If the answer requires an exponent, use the ^ key to indicate the power. For example, if the answer is 2x2y, type 2x^2y.
x over 2 + y over 3 - z over 4
Answer:
The Numerator is 6x + 4y - 3z
Step-by-step explanation:
Step 1 :
z
Simplify —
4
Equation at the end of step 1 :
x y z
(— + —) - —
2 3 4
Step 2 :
y
Simplify —
3
Equation at the end of step 2 :
x y z
(— + —) - —
2 3 4
Step 3 :
x
Simplify —
2
Equation at the end of step 3 :
x y z
(— + —) - —
2 3 4
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 3
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 0 1
3 0 1 1
Product of all
Prime Factors 2 3 6
Least Common Multiple:
6
Calculating Multipliers :
4.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 3
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
4.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. x • 3
—————————————————— = —————
L.C.M 6
R. Mult. • R. Num. y • 2
—————————————————— = —————
L.C.M 6
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • 3 + y • 2 3x + 2y
————————————— = ———————
6 6
Equation at the end of step 4 :
(3x + 2y) z
————————— - —
6 4
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 6
The right denominator is : 4
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 2 2
3 1 0 1
Product of all
Prime Factors 6 4 12
Least Common Multiple:
12
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 2
Right_M = L.C.M / R_Deno = 3
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (3x+2y) • 2
—————————————————— = ———————————
L.C.M 12
R. Mult. • R. Num. z • 3
—————————————————— = —————
L.C.M 12
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(3x+2y) • 2 - (z • 3) 6x + 4y - 3z
————————————————————— = ————————————
12 12
Final result :
6x + 4y - 3z
————————————
12
How do you simplify this?
the answer is 2yx^3/(2y^2)^3
generally, who sells goods to the consumers?
Answer:
Retailer
Step-by-step explanation:
A retailer buys goods from the manufactures and wholesalers and then sell these products directly to the consumers or users.In the supply chain retailers are the ones who connect with the customers to obtain information on goods and servicers delivered.
the point (3,-6) lies on the terminal side of angle 0. Find the exact value of the six trigonometric functions of 0. Sin cos tan csc sec cot
ANSWER
See explanation
EXPLANATION
The point (3,-6) is the fourth quadrant.
In this quadrant only the cosine ratio and the secant ratio are positive.
The remaining four trigonometric ratios are negative.
The diagram is shown in the attachment.
We use the Pythagoras Theorem to find the hypotenuse, h.
[tex] {h}^{2} = {6}^{2} + {3}^{2} [/tex]
[tex] {h}^{2} = 36 + 9[/tex]
[tex] {h}^{2} = 45[/tex]
[tex]h = \sqrt{45} [/tex]
[tex]h = 3 \sqrt{5} [/tex]
[tex] \sin( \theta) = - \frac{opp}{hyp} [/tex]
[tex]\sin( \theta) = - \frac{6}{3 \sqrt{5} } [/tex]
[tex]\sin( \theta) = - \frac{2 \sqrt{5} }{ 5 } [/tex]
[tex]\sin( \theta) = - \frac{2}{ \sqrt{5} } [/tex]
[tex]\ cos(\theta) = \frac{adj}{hyp} [/tex]
[tex]\ cos(\theta) = \frac{3}{3 \sqrt{5} } [/tex]
[tex]\ cos(\theta) = \frac{1}{ \sqrt{5} } [/tex]
[tex]\ cos(\theta) = \frac{ \sqrt{5} }{5} [/tex]
[tex]\tan(\theta)= - \frac{opp}{hyp} [/tex]
[tex]\tan(\theta)= - \frac{6}{3} = - 2[/tex]
[tex]\csc(\theta)= - \frac{hyp}{opp} [/tex]
[tex]\csc(\theta)= - \frac{3 \sqrt{5} }{6} = - \frac{\sqrt{5} }{2} [/tex]
[tex] \sec( \theta) = \frac{hyp}{adj} [/tex]
[tex]\sec( \theta) = \frac{3 \sqrt{5} }{3} = \sqrt{5} [/tex]
[tex]\cot( \theta) = - \frac{adj}{opp} [/tex]
[tex]\cot( \theta) = - \frac{3}{6} = - \frac{1}{2}[/tex]
homer wants to identify the center and radius of the circle defined by the equation...
Answer:
Step 2, he didn't add the values he completed the square with to both sides.
Step-by-step explanation:
When you complete the square, you need to add the values to both sides, not just one.
So when Homer added 49 + 1 or 50 to the left side of the equation, he should've also added 50 to the right side of the equation.
Hence, the equation would now be :
(x-7)^2 + (y+1)^2 = 75
Mai mowed fawns for 2 hours and earned $7.50 per hour. Then she washed windows for 3 hours and earned $6.25 per hour. What were Mai's average earnings per hour for all 5 hours?
So you work for 2 hours and each hour you get 7.50
So you do 2*7.50 = 15$
Then you do the windows
3 hours and every hour you earn 6.25
3*6.25=18.75$
Now you add them
15+18.75= 33.75$ but if you want an average then around 34$
heather runs 8 miles in 84 minutes at rhe same rate how many minutes would she take to run 6 miles
Answer:63Minutes
Step-by-step explanation:
Answer: 63.
Step-by-step explanation: In order to find how fast she runs 6 miles, it'd be convenient to know how fast she runs in 1 mile. So:
8 miles = 84 minutes.
8/8 = 1
84 / 8 = 10.5
6 x 1 = 6
10.5 x 6= 63.
What is the area of DeltaSTR?
Answer:
B
Step-by-step explanation:
Answer:
The correct option is A.
Step-by-step explanation:
The area of a triangle is
[tex]A=\frac{1}{2}\times base\times height[/tex]
From the given figure it is clear that the base of the triangle STR is 6 ft and the height of the triangle 10 ft. So, the area of triangle STR is
[tex]A=\frac{1}{2}\times 6\times 10[/tex]
[tex]A=3\times 10[/tex]
[tex]A=30[/tex]
The area of triangle STR is 30 square ft. Therefore the correct option is A.
The diagram shows the dimensions of a triangular garden at the park. If another triangular garden is congruent to this triangle, what is the perimeter of the other garden?
Answer:
b 93
Step-by-step explanation:
Answer:
Step-by-step explanation:
Alright, lets gets started.
The dimensions of the given triangle is 24 , 52 and 17.
The another triangle is given congruent to this triangle.
It means the dimensions of another triangle will also be 24, 52 and 17.
So the perimeter will be addition of these sides.
Hence the perimeter will be = [tex]24+52+17[/tex]
Hence the perimeter will be = 93 feet : Answer
Hope it will help :)
Jenna walks 12 miles in 5 days. Alex walks 7 miles in 3 days. Who walks more miles per day?
Answer:
Alex walks more miles
Step-by-step explanation:
Answer:
Jenna walks more miles per day
Step-by-step explanation:
i got this answer by doing 12 divided by 5 = 2.4 and 7 divided by 3 = 2.33333333333 and 2.4 is more that 2.33333333333 so Jenna walked futher,
i hope that this answer helped you, pls give me good votes if it did, because im new here and trying to get points.
Julio sold half of his comic books and then bought 14 more. he now has 28. with how many did he begin?
Answer:
28
Step-by-step explanation:
We start by doing 28 - 14 which equals 14.
We do this because we want to find out the amount of books before he bought 14. We have 14 which is after he sold half of his comics. A half is 1/2, that means you multiply 14 by 2. You get 28.
Final answer:
Julio initially had 28 comic books, sold half, then purchased 14 more, which resulted in him having a total of 28 comic books. We used a simple algebraic equation to determine the original amount.
Explanation:
Let's denote the original number of comic books that Julio had as x. According to the problem, Julio sold half of his comic books (x/2) and then bought 14 more. Consequently, he now has 28 comic books in total.
To express this situation mathematically, we can create the following equation to represent the changes in the number of comic books Julio has:
x/2 + 14 = 28
If we simplify this equation by subtracting 14 from both sides, we get:
x/2 = 28 - 14
x/2 = 14
By multiplying both sides of the equation by 2, we can find the original number of comic books Julio had:
x = 14 * 2
x = 28
Therefore, Julio began with 28 comic books before he sold half and bought 14 more.
help me plz i need the answer
1st one is 0
2nd one is -3
3rd one is -2
4th one is 5
Combine like terms, isolate the variable, and make the slope of the variable 1 to find all the answers.
What property justifies the work between Step 3 and Step 4?
A) Inverse property of addition
B) Identity property of addition
C) Addition property of inequality
D) Commutative property of addition
I’m awful at properties, please help asap ((:
I think it's B
[tex] - 11 \geqslant n + 0 \\ 1. \: - 11 \geqslant n \\ 2. \: n \leqslant - 11 \\ \\ - 11 \geqslant n \\ 1. \: n \leqslant - 11[/tex]
Answer:
The answer is B. Identity property of Addition
Step-by-step explanation:
The point (4,3) is reflected across the x-axis. What are the coordinates of the new point?
(4, 3)
(4, -3)
(-4, 3)
(-4,-3)
Helpppppp!!!/
Answer:
(4, -3)
Step-by-step explanation:
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is changed to the opposite sign.
The reflection of the point (x, y) across the x-axis is the point (x, -y).
The reflected point across the x-axis of the original point (4,3) would have the coordinates (4, -3), where the x-coordinate remains the same and the y-coordinate changes sign. Hence correct option b.
When a point is reflected across the x-axis, the y-coordinate changes sign, but the x-coordinate remains the same. The reflection of the point across the x-axis means that the x-coordinate (4) does not change, but the y-coordinate (3) becomes its opposite (-3). Thus, the new coordinates of the reflected point are (4, -3).
In ΔPQR, point C is the centroid. If CZ = 8, then QC =
A) 4
B) 8
C) 16
D) 24
Answer:
QC=16 this is correct on usa testprep
Step-by-step explanation:
The centroid of a triangle is the point of concurrency of the median lines of
the triangle.
The length of segment [tex]\overline{QC}[/tex] is C) 16
Reasons:
The given parameters are;
Point C = The centroid of ΔPQR
[tex]\overline{CZ}[/tex] = 8
Required:
The length of segment QC
Solution;
Given that point C is the centroid of the triangle ΔPQR, we have;
[tex]\overline{QC} = \dfrac{2}{3} \times \overline{QZ}[/tex]
[tex]\overline{CZ}= \dfrac{1}{3} \times \overline{QZ}[/tex]
Therefore;
[tex]\overline{CZ}= \dfrac{1}{2} \times \overline{QC}[/tex]
[tex]\overline{QC} = 2 \times \overline{CZ}[/tex]
[tex]\overline{QC} = 2 \times 8 = 16[/tex]
[tex]\underline{\overline{QC} = 16}[/tex]Learn more here:
https://brainly.com/question/1747484
Find the solutions to 2x^2+5x-3=0
Answer:
x=1/2, x=-3
Step-by-step explanation:
2x^2+5x-3 = 0
(2x^2+6x)+(-x-3) = 0
2x(x+3)+-1(x+3) = 0
(2x-1)(x+3)=0
2x-1=0, x+3=0
x=1/2, x=-3
What is the answer to this question??????
Answer:
The answer is A. F(x)=(X+3)^4
Step-by-step explanation:
1. Whenever the function is in parenthesis, the symbol does the opposite then it usually does. So for (X+3)^4, the + in the parenthesis shifts the graph to the left instead of right.
2. Also, when in parenthesis, function shifts horizontally, not vertically. So answers B and C would shift the graph up and down, instead of left or right.
Please feel free to ask me if you have more questions or concerns with this problem!
Answer:
A. F(x) = (x+3)⁴Step-by-step explanation:
f(x) + n - shift the graph n unit up
f(x) - n - shift the graph n unit down
f(x + n) - shift the graph n unit to the left
f(x - n) - shift the graph n unit to the right
=======================================================
F(x) ← G(x) shifted 3 units to the left
F(x) = G(x + 3) → F(x) = (x+3)⁴
If s(x)=x-7 and t(x)=4x^2-x+3 which expression is equivalent to (txs)(x)?
For this case we have by definition that:
[tex](f * g) (x) = f (x) * g (x)[/tex]
In this case we must find[tex](t * s) (x),[/tex] so:
([tex](t * s) (x) = t (x) * s (x) = (4x ^ 2-x + 3) * (x-7) =[/tex]
We must apply distributive property that states that:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
So:
[tex](4x ^ 2-x + 3) * (x-7) = 4x ^ 3-28x ^ 2-x ^ 2 + 7x + 3x-21 = 4x ^ 3-29x ^ 2 + 10x-21[/tex]
Answer:
[tex]4x^3-29x^2+10x-21[/tex]
Solve the equation. 9x^2+4=0
Answer:
x=2i/3
All you have to do is just to find the square root.
Answer:
x = ±(2/3)i
Step-by-step explanation:
Subtract 4, divide by 9, and take the square root.
9x^2 = -4
x^2 = -4/9
x = ±√(-4/9) = ±(2/3)i . . . . . . the solutions are imaginary numbers
Rewrite the parametric equations by eliminating the parameter. Select ONE.
X = 2t + 3 and Y = t - 2
Answer Choices:
Y = 3x + 1
Y = x - 7 / 2
Y = x + 5
Y = x - 5 / 2
Answer:
[tex]Y=(X-7)/2[/tex]
Step-by-step explanation:
we have
[tex]X=2t+3[/tex] -----> equation A
[tex]Y=t-2[/tex] -----> [tex]t=Y+2[/tex] -----> equation B
Substitute equation B in equation A
[tex]X=2(Y+2)+3[/tex]
[tex]X=2Y+4+3[/tex]
[tex]X=2Y+7[/tex]
solve for Y
[tex]2Y=X-7[/tex]
[tex]Y=(X-7)/2[/tex]