By reviewing Damon's work, the true statement is, Damon used the subtraction property of equality.
what is true statement?
A statement is true if the assertion it makes is true, and it is false if the assertion it makes is untrue. For example, the statement "The trains are always late" is only accurate if the situation it describes—that is, if the trains are indeed always late—actually exists.
As given, Damon is saving for a vacation.
He estimates that he’ll need about $2,500 for the trip.
He created an equation last week to model his savings plan to determine how many more months of saving it will take to reach his goal.
In the equation Damon created, x represents the number of months since last week and y represents the total amount he’s saved for the vacation.
The statements are,
Step 1: y = 500 + 400x
Step 2: y - 500 = 500 + 400x - 500
Step 3: y - 500 = 400x
Step 4: y - 500/400 = 400x/400
Step 5: y - 500/400 = x
Step 6: 2500 - 500/400 = x
Step 7: 5 = x
Therefore, the true statement is Damon used the subtraction property of equality in step 3.
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1.) Solve the following equation for w: 3w-4(w-3) = 6
Answer: w=6
Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.
2. simplify again. 3w-4w is -w.
3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.
Write the equation of the parabola that has the same shape as f(x)=-3x² but with vertex (5,9) in the form f(x)=a(x-h)²+k
f(x)=
Which has greatest rate help please
The last function having the greatest rate of change.
What is rate of change?
The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.
Consider the first function,
From this function we get two points (2, 1) and (-2, -1).
To find rate using this points.
Rate = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-1-1}{-2-2} = \frac{-2}{-4}=\frac{2}{4} =\frac{1}{2}[/tex]
Consider the second function,
The second function is a vertical line of x = -3.
Since the rate of vertical line is undefined.
Consider the third function,
The third function is a horizontal line y = 4.
Since two points having the same y - value.
Hence, the rate is zero.
Consider, the last function,
From last function we get two points (1, 5) and (-3, -3).
So,
Rate = [tex]\frac{-3-5}{-3-1} = \frac{-8}{-4} = \frac{8}{4} = 2[/tex]
Hence, the last function having the greatest rate.
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The population of a city has increased by 24% since it was last measured. If the current population is 65,100, what was the previous population?
Answer: 49476
Step-by-step explanation:
can you help me with this question
The graph that represents the solution of the inequality is
What is a system of inequality?
An inequality is known as an expression in which two value do not have an equal sign. they have either >, <,≥,≤. And to compute the solution
We plot the inequality and find the common region between them.
We are given a system of inequalities
Which are
y > x-1 and y< -x-2
We plot the graphs of the inequalities
Now we have plotted the graph the red one represents inequality y> x-1
and blue one represents inequality y< -x-2
And the intersection of the two is known as the solution of the system of inequality
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You are a new loan officer with Alpha Mortgage, and the manager of the loan department has just presented a problem to you. He is unable to complete the APR calculation on an adjustable rate mortgage that a borrower applied for yesterday. The loan features initial payments based on a 5 percent rate of interest at loan closing. The current composite rate on the loan is 7 percent. Two discount points have been paid by the borrower. Any difference between borrower payments and the interest payment required at the composite rate will be accrued in the mortgage balance in the form of negative amortization. The mortgage amount desired by the borrower is $74,500 for a 30-year term.
Required:
Determine the APR, assuming that the ARM is made with a 2 percent annual and 5 percent over-the-life interest rate cap. (Do not round intermediate calculations.)
Answer:
Step-by-step explanation:
Apr is 248 the customer has to pay 248 dollars every month for 30 years he has to pay 7,440 dollars to the bank or he will lose the house.
What is the approximate percent decrease from 1865 to 1240?
Answer: It should be 33.5%
SOME ONE PLS HELP RNNNNNNN ! WILL GIVE BRAINLEST
Answer:
below
Step-by-step explanation:
point -1,-4
y - -4 = 3 ( x - -1)
y + 4 = 3 ( x+1) <====== I think this is a far as they want you to take it
y = 3x -1 slope - intercept form
Solve the exponential equation 31^d = 38
What is a graph theory in math?
Answer:
Graph theory is used in dealing with problems that have a reasonably natural graph/network structure.
Explanation:
For example,
road networks - nodes = towns
road junctions, arcs = roads
Communication networks - telephone systems
'Computer systems'
Foreign exchange/multinational tax planning (network of fiscal flows).
Hope it helped! :)
Graph theory is applied to problems that have a fairly natural graph/network structure.
What is graph theory?Graph theory is the study of graphs in mathematics, which are mathematical structures used to model pairwise relationships between objects. In this context, a graph is made up of vertices (also known as nodes or points) connected by edges (also called links or lines).
Graph Theory is the study of relationships. Graph theory, given a set of nodes and connections that can abstract anything from city layouts to computer data, provides a useful tool for quantifying and simplifying the many moving parts of dynamic systems.
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7 (4-x)=84
74-x)7=84/7
4-x-12
4-x-4=-12-4
-x=-16
-x/=1=-16/-1
=16
Answer Is=16 How do I Check my answer??
Answer:
x = - 8
Step-by-step explanation:
7(4 - x) = 84 ( divide both sides by 7 )
4 - x = 12 ( subtract 4 from both sides )
- x = 8 ( multiply both sides by - 1 )
x = - 8
As a check
substitute x = - 8 into the left side of the equation and if equal to the right side then it is the solution.
7(4 - (- 8) )
= 7(4 + 8)
= 7(12)
= 84 = right side
Then x = - 8 is the solution to the equation
Employees wage please help me!
3. Two of the vertices of an equilateral triangle are (0, -a)
and (0, a). The third vertex is on the x-axis to the right of
the origin. Name the coordinates of the third vertex.
The third coordinate of the equilateral triangle is [tex](\sqrt3a,0)[/tex]. Ir can be obtained by distance formula.
What is distance formula?
It gives the distance between two coordinates.
Distance formula is given by the following expression:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Consider the third cordinate is (x,0) and x is positive because it is on tight side on the x axis.
Now, since the triangle is equilateral hence, the distance of (x,0) from (0, -a) and (0, a) should be equal to distance between (0, -a) and (0, a).
Now, caculate the distance between (0,-a) and (0, a).[tex]\sqrt{(0-0)^2+(-a-a)^2}=2a[/tex]
Now, distance between (x,0) and (0, a) should be 2a.
[tex]\sqrt{(x-0)^2+(0-a)^2}=2a\\\sqrt{x^2+a^2}=2a[/tex]
Now, square on both the sides.
[tex]x^2+a^2=4a^2\\x^2=3a^2\\x=\sqrt3a[/tex]and [tex]-\sqrt3a[/tex]
But the negative value of x is not possible because the coordinate lies on the right side.
Hence, the third coordinate of equilateral triangle is [tex](\sqrt3a,0)[/tex].
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Distribute 28(x + 0.7)
28x + 19.6
28x + 28.07
28x + 0.7
(x+0.7)/28
Answer:
just multiply 28 and (28x), then 28 and 0.7 (19.6) and then put them into the correct answer (28x+19.6)
1. If the ice skates are on sale for 30% off, how much money
would you save?
Answer:
14.40 rounded, 14.3999 whole number
Step-by-step explanation:
hope this helps :)
a plant is already 11 centimeters tall, and it will grow one centimeter ever month.Let H be thed plants height(in centimeters) after M months. Write an equation realted H to M
The growth follows a linear equation, for that we need
y = mx + c
The number of months would be the x axis as that is the thing changing, and the height would be the y axis as that is the thing being measured to change.
That now gives us
H = mM + c
m is the gradient and c is the y intercept
We can figure out the gradient because after 1 month the height increases by 1 so the change in y vs the change in x is 1 so the gradient must be 1.
The y intercept in this case is the initial condition and therefore is 11cm.
The final answer being
H = M + 11
Mrs. Croaker’s class calculated that their class frog, named Fred, jumped 23 times every day, for 14 days in a row. Write an equation the students could use to find the total number of jumps Fred took. Discuss how you know this equation will solve the problem, and then solve it.
The required equation is y = 23x - 9 which represents the total number of jumps.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
Mrs. Croaker’s class calculated that their class frog, named Fred, jumped 23 times every day, for 14 days in a row.
the total number of jumps = total days × number of jumps per day
the total number of jumps = 14 × 23
the total number of jumps = 322
We can see that two points are (1, 23) and (14, 322)
y - 14 = (322-23/14-1)(x - 1)
y - 14 = 23(x - 1)
y = 23x - 23 + 14
y = 23x - 9
Therefore, the required equation is y = 23x - 9 which represents the total number of jumps.
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Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=
The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9
How to determine the equation of the parabola?The equation of the function is given as
f(x) = 3x²
Also, we have
Vertex = (5, 9)
The form of the equation is given as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
This means that
Vertex = (h, k) = (5, 9)
Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 5)² + 9
This also means that
f(x) = -3(x - 5)² + 9
The -3 is gotten from f(x) = -3x²
Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9
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How do you change a fraction to a decimal?
Group of answer choices
Divide the numerator by the denominator
Move the decimal over 2 places
Change the denominator to 100
Divide the denominator by the numerator
Answer:
it is the answer number 1
Bilquis has x dimes and y nickels. She has at least 15 coins worth no more than $1 combined. Solve this system of inequalities graphically and determine one possible solution.
One of the possible solutions to this system of linear inequation is
(10, 5).
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, Bilquis has x dimes and y nickels.
We know a nickel is 5 cents and a dime is 10 cents.
She has at least 15 coins,
∴ x + y ≥ 15...(i)
She has no more than $1 combined.
0.05x + 0.1y ≤ 1...(ii)
The possible solution of these two inequalities by the graphing method we get (10, 5)
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is going to invest $820 and leave it in an account for 19 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for John to end up with $1,830?
The rate of interest for an amount which is compounded quarterly is 4.25%
Given,
The principal amount invested by Oliver, P = $820
The time period of the investment, t = 19 years
The interest is compounded quarterly, n = 4
The amount after 19 years, A = $1830
The compound interest formula;
A = [tex]P (1+\frac{r}{n} )^{nt}[/tex]
We have to find the rate of interest;
For that;
A = [tex]P (1+\frac{r}{n} )^{nt}[/tex]
1830 = 820 [tex](1+\frac{r}{4} )^{76}[/tex]
1830/820 = [tex](1+\frac{r}{4} )^{76}[/tex]
₇₆√1830/820 = 1 + r/4
₇₆√1830/820 - 1 = r/4
r = 4 (₇₆√1830/820 - 1)
r = 0.042 x 100
r = 4.25%
That is,
The rate of interest for an amount which is compounded quarterly is 4.25%
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What theorem is used to find the side of a triangle in a right triangle?
A. midsegment theorem
B. base angle theorem
C. triangle proportionality theorem
D. Pythagorean theorem
Using the distributive property, an expression is equivalent to 20+30
Suppose you want to have $500,000 for retirement in 35 years. Your account earns 4% interest. How much would you need to deposit in the account each month?
The answer, the money needs to be deposited each month is $557.47.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The future money plan to have 500000
Retirement in 35 years.
The interest 4%.
number of time periods = 35 years * 12 months per year = 420
interest will be .4166666667% per month
The formula = [tex]p(\frac{(1+r/n)^{r/n} -1 }{\frac{r}{n} } )[/tex]
⇒500000*(.014/12) = d(3.98-1)
⇒d = 1666.7/2.98 = 557.47
Hence the money needs to be deposited each month is $557.47
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Find the equation of a line that passes through the point (2,-4) and has a gradient of -5. Leave your answer in the form y = m x + c
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 5}(x-\stackrel{x_1}{2}) \implies y +4= -5 (x -2) \\\\\\ y+4=-5x+10\implies {\Large \begin{array}{llll} y=-5x+6 \end{array}}[/tex]
Solve this system of equations by graphing. First graph the equations, and then type the
solution.
y = 5/2x - 1
y = 2x - 3
Click to select points on the graph.
The solution of the system equation is (-4,-11).
What is system equation?
One or more equations involving a number of variables make up a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
Here the given system equation is,
=> y = 5/2x-1------->1
=> t=2x-3---------->2
Put 1 into 2 then
=> 5/2x-1=2x-3
=>1/2 x=-2
=> x=-4
Put x=-4 into 2 then,
=> y=-8-3=-11.
Hence the solution of the system equation is (-4,-11).
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Work out 132% of 96 m
Give your answer as a decimal in metres (m).
Answer:
126.72m
Step-by-step explanation: 1.32 x 96 = 126.72, I struggled with that stuff too no shame
what is the slope of a line perpendicular to the line whose equation is 2x+2y=-12
Answer:
The slope of a line perpendicular to m=2 is m= 1.
Step-by-step explanation:
2x+2y=-12
2y=-2x-12
y= -x-6.
The equation is in slope-intercept form now, so it is easy to tell what the slope is.
The slope of y= -x-6 is m = -x. Technically, -x = -1x, so now make the -1 positive and find the reciprocal, which is still 1.
All you need to do to find the perpendicular slope of any line is simply to find the reciprocal of the number and make the positive/negative number the opposite. I hope this helps, have a good day/night! :)
riangle ABCis transformed with the center of dilation at the origin.
Pre-image: △ABC with vertices A(−5, −4), B(−7, 3), C(3, −2)
Image: △A′B′C′with vertices A′(−3.75, −3), B′(−5.25, 2.25), C′(2.25, −1.5)
What is the scale factor of the dilation that maps the pre-image to the image?
Which of the following tables represents the proportional relationship for 3 cups of grape juice for every one fourth cup of rainbow sherbet?
Grape Juice (cups) 0.25 1 1.5
Rainbow Sherbet (cups) 3 6 9
Grape Juice (cups) 3 6 9
Rainbow Sherbet (cups) 0.25 0.5 0.75
Rainbow Sherbet (cups) 0.25 1 1.5
Grape Juice (cups) 3 6 9
Rainbow Sherbet (cups) 3 6 9
Grape Juice (cups) 0.25 0.5 0.75
The table that represents the proportional relationship for 3 cups of grape juice for every one fourth cup of rainbow sherbet is:
Grape Juice (cups) 3 6 9
Rainbow Sherbet (cups) 0.25 0.5 0.75
What table represents the proportional relationship?The table that represents the proportional relationship would have a constant ratio of grape juice to rainbow sherbet of 3 cups to one fourth constantly.
One-fourth is equivalent to 1 / 4 when written as a fraction and 0.25 when written as a decimal.
In the second table, when 3 and 0.25, 6 and 0.5, 9 and 0.75 cups of grape juice and rainbow sherbet are expressed in it simplest form, they are all equivalent to 3 and 1/4.
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Answer:
Grape Juice (cups) 3 6 9
Rainbow Sherbet (cups) 0.25 0.5 0.75
Step-by-step explanation:
I took the exam and got it right
