Answer:
y = 8x + 6
Step-by-step explanation:
The slope intercept form is: y = mx + c
where m ⇒ slope
c ⇒ y-intercept
(x,y) is a point on the graph the satisfy the equation representing that graph. x is the x-coordinate of a point on the line and y is the y-coordinate of a point on the line.
m = 8
Y-intercept = 6
y = mx + c ⇒ y = 8x + 6
For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 of the amount he invested the first year.
During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than 3/2 times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year.
If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ ???, and the amount Sally invested the last year is $ ???
Answer:
The first year Sam invested $2,000. The third year sally invested $1,900.
Step-by-step explanation:
Let $x be the amount of money Sam invested the first year. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year, then the second year he invested
[tex]\$\left(\dfrac{5}{2}x-2,000\right).[/tex]
The third year, he invested $1,000 more than 1/5 of the amount he invested the first year, then the third year he invested
[tex]\$\left(\dfrac{1}{5}x+1,000\right).[/tex]
During three years Sam invested
[tex]\$\left(x+\dfrac{5}{2}x-2,000+\dfrac{1}{5}x+1,000\right)=\$\left(\dfrac{37}{10}x-1,000\right).[/tex]
The first year, Sally invested $1,000 less than 3/2 times the amount Sam invested the first year, then the first year she invested
[tex]\$\left(\dfrac{3}{2}x-1,000\right).[/tex]
The second year, she invested $1,500 less than 2 times the amount Sam invested the first year, then the second year she invested
[tex]\$(2x-1,500).[/tex]
The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year, then the third year she invested
[tex]\$\left(\dfrac{1}{4}x+1,400\right).[/tex]
During three years Sally invested
[tex]\$\left(\dfrac{3}{2}x-1,000+2x-1,500+\dfrac{1}{4}x+1,400\right)=\$\left(\dfrac{15}{4}x-1,100\right).[/tex]
If Sam and Sally invested the same total amount at the end of three years, then
[tex]\dfrac{37}{10}x-1,000=\dfrac{15}{4}x-1,100,\\ \\\dfrac{37}{10}x-\dfrac{15}{4}x=1,000-1,100,\\ \\-\dfrac{1}{20}x=-100,\\ \\x=\$2,000.[/tex]
Thus,
[tex]\$\left(\dfrac{1}{4}\cdot 2,000+1,400\right)=\$1,900.[/tex]
If f(x)=(-x) cubed, then f(-3)?
Answer:
f(-3) = 27
Step-by-step explanation:
f(x) = (-x)^3
We want the value when x =-3
Substitute this in
f(-3) = (--3)^3
f(-3) = 3^3
f(-3) = 27
The difference between two numbers is 15. The greater number is two less than twice the lesser number.
Find the numbers.
Answer:
x=32, y=17
Step-by-step explanation:
Difference between two numbers is 15:
x-y=15
Greater number (x) is two less than twice the lesser number:
x=2y-2
-----
x-y=15,
x=2y-2.
x-y-x=15-2y+2
-y=15-2y+2
y=15+2
y=17
-----
x-y=15
x-17=15
x=17+15
x=32
To solve the word problem, we transcribe the information into algebraic equations. We then isolate one variable to solve for it first, and then substitute that variable's value into the second equation. The solution we find is that the two numbers are 17 and 32.
Explanation:To solve the problem, we must translate the word problem into algebraic equations. We're trying to find two numbers based on the information that's given to us: their difference is 15, and the larger number is two less than twice the smaller number.
First, let's define the numbers as follows: x = smaller number and y = larger number. Now we can set up our two equations based on the problem:
y - x = 15 (because the difference between two numbers is 15) y = 2x - 2 (because the larger number is two less than twice the smaller number)
Now we can substitute equation (2) into equation (1) which gives us: 2x -2 - x = 15. Simplify the equation, we get x = 17 and substitute x = 17 into equation (2), we get y = 32.
So, the two numbers are 17 and 32.
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Would a horizontal line, a straight slanted line, a curve, or a jagged curve best represent the calories you burn during the day?
Answer:
A jagged curve
Step-by-step explanation:
Your always going to burn calories but the rate will always change and how many based on what you do will always change so it is never a constant slope.
Answer:
a jagged curve
Step-by-step explanation:
The number of calories you burn varies throughout the day, increasing and decreasing. A jagged curve represents increases and decreases over time.
To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 6x + 5y = 2 4x + 2y = 8
Answer:
Multiply each equation by the coefficient of y in the other one.
Step-by-step explanation:
(1) 6x + 5y = 2
(2) 4x + 2y = 8
Multiply each equation by the coefficient of y in the other one.
Multiply (1) by 2 and (2) by 5.
(3) 12x + 10y = 4
(4) 20 x + 10y = 40 Subtract (3) from (2)
8x = 36 Solve for x
x = 9/2
Answer:
Subtract 5 times the first equation from 2 times the second equation
Step-by-step explanation:
2(6x + 5y = 2)
5(4x + 2y = 8)
12x + 10y = 4
20x + 10y = 40
Subtracting the second equation from first gives:
−8x = −36
x =
−36
−8
x =
9
2
Can soneone help me with these basic vector math problems?!
Given an initial point (5,3) and a terminal point (10,-8), find the component form for vector v.
A. (2, 18)
B. (15, -5) <-- My choice
C. (5, -11)
D. (13, 13)
2. Is vector v with an initial point of (0,0) and a terminal point of (50, 120), equal to vector u with an initial point of (50, 120) and a terminal point of (0,0)?
A. No, the two vectors have different directions.
B. No, the two vectors have different initial points. <-- I think it's this one
C. Yes, the two vectors have the same magnitude.
D. Yes, the two vectors have the same slope.
The solution to the basic vector problems are given as,
1) (5, -11), option C is correct.
2) . No, the two vectors have different initial points, option B is correct.
Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.
Here,
1)
initial point (5,3) and a terminal point (10,-8),
Vector = 10i -8j - 5i - 3j
Vector = 5i - 11j or [5, -11]
2)
Vector v with an initial point of (0,0) and a terminal point of (50, 120), is not equal to vector u with an initial point of (50, 120) and a terminal point of (0,0).
Thus, the solution to the basic vector problems are given as,
1) (5, -11), option C is correct.
2) . No, the two vectors have different initial points, option B is correct.
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Final answer:
To find the component form for vector v, subtract the initial point from the terminal point. The answer is option C. The vectors in the second question have different initial points, so they are not equal.
Explanation:
To find the component form for vector v, we need to subtract the initial point from the terminal point. Subtracting the x-coordinates and y-coordinates separately, we get (10 - 5, -8 - 3), which simplifies to (5, -11). Therefore, the component form for vector v is option C, (5, -11).
For the second question, the vectors have the same initial points but different terminal points, so they cannot be equal. Therefore, the correct choice is option B, No, the two vectors have different initial points.
Simplify the expression below: − 4 − 5 y + 12 + 15 ( 7 + y )
We must first open the parenthesis. We get 15*7+15y, or 105+15y. We can now add 12 to 105 which would be 117. Now we have -4-5y+117+15y. With this we can move the -4 to 117 which is 113 and the -5y to 15y which is 10y. So we got 113+10y as our answer.
Hope this helps. <3
if y=6x+8 and y=-4x-2,what is the value of x+y when the two equations are equal?
Answer:
x + y = 1
Step-by-step explanation:
If the two equations are the same, then it can be shown by this:
6x + 8 = -4x - 2
We need to isolate the x values, so we need to move the -4x over to the other side making it a +4x:
6x + 4x + 8 = -2
Next, move the +8 over to the other side making it a -8:
6x + 4x = -2 - 8
10x = -10
x = -1
So now we can plug this value into the first equation:
6(-1) + 8 = y
-6 + 8 = y
y = 2
x + y = -1 + 2 = 1
So x + y = 1
I need help with this PLEASE SHOW WORK
Answer:
RM ≈ 6.08 ( to 2 dec. places )
Step-by-step explanation:
to calculate the distance use the distance formula
• d = √(x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = R(- 2, 3) and (x₂, y₂ ) = M(4, 2)
d = [tex]\sqrt{(4+2)^2+(2-3)^2}[/tex] = [tex]\sqrt{36+1}[/tex] = [tex]\sqrt{37}[/tex] ≈ 6.08
Write the equation in logarithmic form. N^4/3=m. Please show all your steps!!
Answer:
[tex]log_n(m)= \frac{4}{3}[/tex]
Step-by-step explanation:
N^4/3=m
[tex]n^{4/3}=m[/tex]
We need to write the equation in logarithmic form
we take log on both sides
[tex]log(n^{4/3})=log(m)[/tex]
We apply log property to remove the exponent 4/3
As per log property we can move exponent before log
log(a^m) = m log (a)
So our equation becomes
[tex]\frac{4}{3}log(n)=log(m)[/tex]
Now we divide both sides by log(n)
[tex]\frac{4}{3} =\frac{log(m)}{log(n)}[/tex]
Now we apply change of base formula
log(a)/ log(b)= log_b(a)
[tex]\frac{4}{3} =log_n(m)[/tex]
So log form is
[tex]log_n(m)= \frac{4}{3}[/tex]
To convert [tex]N^{4/3}[/tex] = m to logarithmic form, identify the base (N), the exponent (4/3), and the result (m). The logarithmic form is [tex]log_N(m)[/tex] = 4/3.
To convert the given equation [tex]N^{4/3}[/tex] = m into logarithmic form, we'll follow these steps:
Identify the base, which is N in this case.The exponent in the equation is 4/3.The result is m.The general logarithmic form of the equation aᵇ = c is [tex]log_a(c)[/tex] = b.
Applying this to our equation:
The base a is N.The result c is m.The exponent b is 4/3.Hence, the logarithmic form of the equation [tex]N^{4/3}[/tex] = m is:
[tex]log_N(m)[/tex] = 4/3Given m(x)=3x-2 and p(x)=-4+2, what is (m-p)(x)?
Final answer:
(m-p)(x) represents the subtraction of function p(x) from m(x). Assuming p(x) is -4x + 2, (m-p)(x) simplifies to 7x - 4.
Explanation:
To calculate (m-p)(x), we need to subtract the function p(x) from the function m(x).
Given m(x) = 3x - 2 and noting there seems to be an error in p(x), as it should likely be a function of x, let's assume the student meant p(x) = -4x + 2 based on the pattern of the provided information.
The subtraction of these two functions is performed as follows:
m(x) - p(x) = (3x - 2) - (-4x + 2)
Simplify by distributing the negative sign through the second polynomial:
(3x - 2) + 4x - 2 = 3x + 4x - 2 - 2
Combine like terms:
7x - 4
So, (m-p)(x) = 7x - 4.
Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k. k = ______ Graph of two lines. f of x equals 1 over 3 x plus 2 and g of x equals 1 over 3 x plus 5
Solution:
As given , g(x)= f(x) + k --------(1)
As also given : f(x) = [tex]\frac{1}{3}[/tex](x+2)
g(x) = [tex]\frac{1}{3}[/tex](x+5)
Putting the value of f(x) and g(x) in equation (1).
→ [tex]\frac{1}{3}[/tex](x+5) = [tex]\frac{1}{3}[/tex](x+2) + k
→ [tex]\frac{1}{3}[x+5-x-2][/tex]= k
→ k = [tex]\frac{1}{3} \times 3=1[/tex]
So , the value of k is 1.
Answer:
K=5
Step-by-step explanation:
there you go
a man purchased 100 oranges at 800$ and sold each of them at 10$. What is his percentage profit
Answer:25%
Step-by-step explanation:
fomula => percantange profit = Profit/buying price x 100% we find profit by taking money sold for each orange multiplied by total numbers of orangessubtracted my inital buying price of oranges(10 x 100) - 800= 200
200/800 x 100
percantage profit= 25%
Answer:
80%
Step-by-step explanation:
800 ÷ 100 = 8$ → purchased each
8$ to 10$ = 80%
What is the value of f(3) when f(x) =4x+1
Answer: 13
Step-by-step explanation:
f(x) = 4x + 1
f(3) = 4(3) + 1
= 12 + 1
= 13
solve this equation 11/20 +x= 9/10
11/20 + x = 9/10
x = 9/10 - 11/20
x = 18/20 - 11/20
x = 7/20
Answer:
x = 7/20
Step-by-step explanation:
11/20 +x= 9/10
Subtract 11/20 from each side
11/20-11/20 +x= 9/10-11/20
x = 9/10-11/20
We need a common denominator of 20
x = 9/10 *2/2 - 11/20
x =18/20 -11/20
x = 7/20
Need help quickly! Must be correct. Thanks!
Because AC lies opposite the angle of the smaller measure than the angle opposite FH. The sides at these angles have the same length.
Find the value of y when x = 4 in the equation y - x = 1/3(x + 14) Show your work help
Write the ratio of the area of a circle with radius r to the circumference of the same circle
Answer:
[tex]\frac{r}{2\pi r} =\frac{1}{2\pi }[/tex]
Step-by-step explanation:
A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.
To write a ratio, we count the number of each quantity we are comparing or use the variable for that quantity. We write radius:circumference. Recall, the circumference of a circle can be found using [tex]\pi d[/tex] or [tex]2\pi r[/tex].
We write r: [tex]\pi d[/tex] or r:[tex]2\pi r[/tex].
We can also write in fraction form:
[tex]\frac{r}{\pi d}[/tex] or [tex]\frac{r}{2\pi r} =\frac{1}{2\pi }[/tex]
You can use the fact that ratio of one quantity to other is fraction involving one quantity over another quantity.
The specified ratio is given as
[tex]r:2\\\\or\\\\\dfrac{r}{2}[/tex]
What is the ratio of a to b ?The ratio of a to b is [tex]\dfrac{a}{b}[/tex]
It is sometimes written as [tex]a:b[/tex]
We can remove common factors of a and b to simplify them.
Thus, if
[tex]a = c \times x\\b = d \times x\\[/tex]
then
[tex]\dfrac{a}{b} = \dfrac{c \times x}{d \times x} = \dfrac{c}{d}[/tex]
What is the area of a circle and circumference of a circle with radius r units?The area of a circle with radius r units is
[tex]Area = \pi r^2[/tex]
The circumference of a circle with radius r units is
[tex]Circumference = 2 \pi r[/tex]
( Remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2 \times x = 2x[/tex] )
Their ratio is
[tex]\dfrac{Area_r}{Circumference_r} = \dfrac{\pi r^2}{2\pi r} = \dfrac{r}{2}[/tex]
Thus,
The specified ratio is given as
[tex]r:2\\\\or\\\\\dfrac{r}{2}[/tex]
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In geometry vertical angles are congruent, meaning they have the same degree measure. You see these when two straight lines form and X shape. Angles that are opposite one another are called vertical angles. If two of these congruent angles have the same degree measure and angle 1 is (3x+10) degrees and angle 2 is (5x-4) degrees, set the expressions equal to one another and find the degree measure. Hint: Don't just solve for the variable X, you have to solve for degree measure by substitution. Do so in both expressions as a way to check your work. The degree measures should be the same if you solved for the variable correctly
Answer:
The two angles are each 31 degrees.
Step-by-step explanation:
Find x
3x + 10 = 5x - 4 Add 4 to both sides3x + 10 + 4 = 5x - 4 + 43x + 14 = 5x Subtract 3x from both sides.3x - 3x + 14 = 5x -3x14 = 2x Divide by 214/2 = 2x/2 7 = x Switch x = 73x + 10
3*7 + 1021 + 10 315x - 4
5(7) - 4 35 - 431By setting 3x+10 equal to 5x-4, we find x=7. Substituting this value back into the expressions for both angles 1 and 2, we find that both angles measure 31 degrees, confirming that our solution is correct.
Explanation:The question asks you to solve for the degree measure of both angles 1 and 2, which are represented by the expressions (3x+10)° and (5x-4)° respectively. Because these angles are vertical, we know that they are congruent, or equal in measure.
Therefore, we can form an equation by setting the two expressions equal to each other and then solving for x:
(3x+10) = (5x-4)
Subtracting 3x from both sides yields:
10 = 2x - 4
Then, adding 4 to both sides, we get 14 = 2x. Dividing both sides by 2, we find x = 7.
To check our work, we substitute x = 7 into the original equations for both angle 1 and angle 2:
Angle 1: 3(7) + 10 = 31°
Angle 2: 5(7) - 4 = 31°
As you can see, the degree measures are the same, which verifies that we solved for the variable correctly.
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if you borrow $421 for nine years at an interest rate of 4% how much interest will you pay
Answer:
the answer is $151.56
Step-by-step explanation:
our formula of interest is I = PxRxT
P (principal) = 421
R (rate) = 4% (we have to turn it into a decimal which is 0.04)
T (time) = 9 years
so :
I = 421 x 0.04 x 9
I = 151.56
The total interest paid will be $151.56.
To find out how much interest you will pay on a loan of $421 over nine years at an annual interest rate of 4%, we can use the formula for simple interest:
Simple Interest = Principal × Rate × Time
Where the Principal amount is $421, the Rate is 4% (or 0.04 when converted to a decimal), and the Time is 9 years.
Let's plug the values into the formula:Write the following equation in the general form Ax + By + C = 0. 2x + y = 6
Ginger you has a principal of $900 in her savings account. It earns 6% interest compounded quarterly. What is the amount in the account at the end of the third quarter?
A: $935.67
B: $941.11
C: $945.22
D: $987.33
Answer:
B.$941.11
Hope this helped
Step-by-step explanation:
Given two random points, A and B, let's find the locus of point P, such that PA=PB.
If PA = PB ,then P is located on perpendicular bisector of AB.
Look at the picture.
I need help with this one if you answer it right I will follow you promise but first help me
write each fraction as a decimal. Use bar notation if necessary.
1. 5/8
Answer:
5/8=0.625
Step-by-step explanation:
[tex]50 + (40 - 15) \div 6[/tex]
Answer:
12.5
Step-by-step explanation:
first you do the one in the 40-15 then you add 50 the you divide by 6
Answer: [tex]54\frac{1}{6}[/tex]
Step-by-step explanation:
Order of Operations (PEMDAS) states that we need to do the parenthesis first then division and then addition.
50 + (40 - 15) ÷ 6
parenthesis: 50 + 25 ÷ 6
division: 50 + [tex]4\frac{1}{6}[/tex]
addition: [tex]54\frac{1}{6}[/tex]
in one hour a seamstress can sew 52 yards of material. How many yards can she sew in 45 minutes?
Answer:
39 yards
hope it helps
Step-by-step explanation:
52 ÷ 4 = 13 per quarter of an hour
we are gonna divide by four because there are 4 quarters in a hour and in 3 quarters there is 45 minutes
13 x 3 = 39
The seamstress can sew 39 yards of material in 45 minutes.
Explanation:To find out how many yards the seamstress can sew in 45 minutes, we need to convert 45 minutes into hours. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours.
Next, we can use the given information that the seamstress can sew 52 yards of material in one hour. Multiply the yards per hour by the fraction of an hour to find out how many yards can be sewn in 45 minutes:
Yards in 45 minutes = 52 yards/hour × 0.75 hours = 39 yards.
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what is the unit rate of 90 miles in 1.7
Answer:
52.94 miles per unit
Step-by-step explanation:
The unit rate is found by dividing miles per time
90 miles /1.7 unit
52.94117647 miles per unit
Y=
Pls help solve for
Answer:
[tex]y=39\degree[/tex]
Step-by-step explanation:
The given triangle is a right angle triangle .
The known sides of the triangle that is opposite to angle y is 8 units while the side adjacent is 10 units.
The value of y can be calculated using the tangent ratio.
[tex] \tan(y)=\frac{8}{10}[/tex]
We solve for y to get,
[tex]y=arctan(\frac{4}{5})[/tex]
We evaluate to obtain,
[tex]y=38.66[/tex]
[tex]y=39\degree[/tex] to the nearest degree
solve the system by the elimination method
Answer:
x=2, y=2
(2,2)
Step-by-step explanation:
To solve by elimination, we need to have on variable an its coefficient be the opposite of the other
I will multiply the second equation by 2 to make 2x become 4x to eliminate the x variable
2(2x+4y) = 12*2
4x+8y = 24
Now add the first equation with the modified second equation
-4x - 2y = -12
4x +8y =24
-------------------
6y = 12
Divide each side by 6
6y/6 = 12/6
y =2
Now we need to find x
2x+4y = 12
Substitute in y=2
2*x + 4*2 = 12
2x+8 = 12
Subtract 8 from each side
2x +8-8 = 12-8
2x=4
Divide each side by 2
2x/2 =4/2
x=2
What is the value of the fifth term?
Answer:
a(5) = 7
Step-by-step explanation:
Look at 5 on the n line, the horizontal line look up to the dot on that line. Whats it value on the vertical line a(n)? 7 so a(5) = 7