[tex]\huge\text{Hey there!}[/tex]
[tex]\text{If John is currently 9 years old and we’re trying to figure out how old he will be}\\\text{in 20 years.}[/tex]
[tex]\text{Let us label your equation to:}[/tex]
[tex]\text{9 - a = 20 OR BETTER YET a - 9 = 20; your “a”-value will be labeled as}\\\text{John future age.}[/tex]
[tex]\textsf{Equation:}[/tex]
[tex]\mathsf{a - 9 = 20}[/tex]
[tex]\textsf{ADD 9 to BOTH SIDES}[/tex]
[tex]\mathsf{a - 9 + 9 = 20 + 9}[/tex]
[tex]\textsf{SIMPLIFY IT}[/tex]
[tex]\mathsf{a = 20 + 9}[/tex]
[tex]\mathsf{a = 29}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{John\ will \ be \ \boxed{\mathsf{29}} \ years \ old}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Use the order of operations to simplify the expression.
5-8
8-5
+ (7 - 2²)
Answer:
2
Step-by-step explanation:
-3/3 + (7-2^2) = _
-1+3=2
Which could be a possible value of x for the expression below to be a rational number? √9x+4
X=4
X=13
X=14
X=16
28:32 simplified
Does any one know?
it will be 7:8
Step-by-step explanation:
28/4 32/4
7 8
Suppose you want to have $600,000 for retirement in 30 years. Your account earns 6% interest. How much would you need to deposit in the account each month?
To have $600,000 for retirement in 30 years with 6% interest , we need to deposit $498.29 in the account each month.
As given in the question,
Final amount 'A'= $600,000
Time 't' = 30years
Rate of interest 'r'= 6%
Month =12
Let 'P' be the amount deposit in the account each month
[tex]A = \frac{(P(1+\frac{r}{m})^{mt}-1 )}{\frac{r}{m} }\\\\\implies 600,000 = \frac{(P(1+\frac{6}{12\times 100})^{12\times 30}-1 )}{\frac{6}{12\times 100} }\\\\\implies 600,000 \times \frac{1}{200}= P (\frac{12.06}{12})^{360}-1 \\\\\implies 3000 +1 = P(1.005)^{360} \\\\\implies P = \frac{3001}{6.02258} \\\\\implies P = \$498.29[/tex]
Therefore, to have $600,000 for retirement in 30 years with 6% interest , we need to deposit $498.29 in the account each month.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the following equation algebraically. Show your work.
17=−13−8x
Answer:
-15/4 = x
Step-by-step explanation:
17 = -13 -8x
Solving for x
Add 13 to each side
17 +13 = -13+13-8x
30 = -8x
Divide each side by -8
30/-8 = -8x/-8
Simplify by dividing the top and bottom by 2
-15/4 = x
The number of cars a salesman sold each month for a two year period are represented by the box and whisker plot below. Which of the following statements is most likely to be true?
In approximately 50% of the months he sold less than 9 cars.
In approximately 25% of the months he sold less than 12 cars.
In approximately 75% of the months he sold more than 12 cars.
In approximately 25% of the months he sold less than 9 cars.
The true statement is that (a) in approximately 50% of the months he sold less than 9 cars.
How to determine which of the statements is most likely to be true?The given parameter is the box and whisker plot
As mentioned above, the box and whisker plot is a great tool to show the five-number summary.
The five-number summaries are:
MinimumLower quartileMedianUpper quartileMaximumOn the box and whisker plot, we have the following five-number summaries:
Minimum: 0Lower quartile: 4Median: 9Upper quartile: 12Maximum: 19The difference between the quartlles is
Difference = Upper quartile - Lower quartile
So, we have
Difference = 12 - 4
Evaluate
Difference = 8
This means that in approximately 50% of the months he sold 8 cars
8 is less than 9
This means that in approximately 50% of the months he sold less than 9 cars.
Hence, the true statement is that (a) in approximately 50% of the months he sold less than 9 cars.
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Dominie practices the piano 714 minutes in 2 weeks. at what rate did she practice, in minutes per day?
The number of minutes per day that Dominie practise the piano is 51 minutes per day.
What is the rate of practice?The first step is to convert two weeks to days.
1 week = 7 days
2 weeks : 7 x 2 = 14 days
The second step is to divide the total minutes Dominie practices by the total number of days. Division is the mathematical operation that is used in grouping a number into equal parts using another number. The result of a division is known as the quotient. The sign used to represent division is ÷.
Number of minutes they practice per day : total practice / number of days in two weeks
714 / 14 = 51 minutes per day
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Calculate the area of one triangle so that you can begin building the tabletop .What is the area of each triangle in square inches
A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.
The area of each triangle is 200 square inches.
What is a right triangle?A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.
We have,
The area of a right triangle is given by:
= 1/2 x base x height
We have from the figure,
Base = 20 inches
Height = 20 inches
Area = 1/2 x 20 x 20
Area = 10 x 20
Area = 200 square inches
Thus the area of each triangle is 200 square inches.
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The complete question is:
You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches?
A. 200 square inches
B. 400 square inches
C. 570 square inches
D. 2,800 square inches
E. 5,600 square inches
Determine the relationship between the quantities on the given graph.
Wages Earned ($)
OA. The hourly rate depends on the wages earned.
B.
The time worked depends on the wages earned.
C.
The wages earned depends on the time worked.
The time worked depends on the hourly rate.
O D.
Total Wages
Time Worked (hours)
The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct
The graph given in the question shows the time worked on x axis and wages earned on y axis and a ray staring from the origin and moving upward
from the graph we can say that when time worked is zero then wages earned is zero. As the time worked is increasing the wages earned is also increasing .
Hence, it can be said that The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct
The correct question is -Determine the relationship between the quantities on the given graph.
Total Wages
Wages Earned ($)
Time Worked (hours)
OA. The hourly rate depends on the wages earned.
OB. The time worked depends on the wages earned.
OC. The wages earned depends on the time worked.
OD. The time worked depends on the hourly rate.
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The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
A. Two
B. One
C. Zero
D. Infinitely many
The two lines have only one intersection
[tex]\therefore[/tex] There are only one solution to the system of equation.
For what values of x is x^3+18x^2+92x+120=0 a true statement.
For x = -2,-6, and -10 the value of the polynomial will be satisfied.
What are the roots of an equation?Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.
Given the polynomial,
x³ + 18x² + 92x + 120 = 0
By hit trial method let's put x = -2
-8 + 72 - 184 + 120 = 0
-192 + 192 = 0
0 = 0
Now,divide x³ + 18x² + 92x + 120 = 0 by x + 2
(x + 2)(x²+ 16x + 60) = 0
(x + 2)(x + 6)(x + 10) = 0
x = -2,-6 and -10.
Hence "For x = -2,-6, and -10 the value of the polynomial will be satisfied".
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Simplify the expression −7+ −5−40 ×−8
The value of the given expression when simplified is equal to 318.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be simplified using the PEMDAS as shown below.
-7 + 5 - 40 × -8
As per the PEMDAS multiplication should be solved first,
= -7 + 5 + 320
Further, solve addition,
= -7 + 5 + 320
= -7 +325
= 318
Hence, the value of the given expression when simplified is equal to 318.
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O LINEAR EQUATIONS AND INEQUALITIES
Finding a percentage of a total amount: Real-world situations
Das
A file that is 244 megabytes is being downloaded. If the download is 18.5% complete, how many megabytes have been downloaded? Round your answer to the
nearest tenth.
megabytes
The size of the file that has been downloaded is 50 megabytes.
Given total size of the file is 244 megabytes
The percentage that completed the download till now = 18.5%
We have to determine the size of the file downloaded till now can be written as
= 18.5 % of 244
= 18.5 / 100 * 244
= 45.14 megabytes
≈ 50 megabytes
The size of the file that has been downloaded is 50 megabytes.
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Find the smallest positive integer, n,such that 168n is a square number.
Answer:
n = 42 and the square number is 7056
==============================
Prime factors of 168 are:
168 = 2*2*2*3*7In order to make 168n a square number we need to use each prime factor even number of times.
Add 2, 3 and 7 to the prime factors (as a minimum) to get:
168*2*3*7 = 168*42 = 2⁴*3²*7² = (2²*3*7)² = 84² = 70565m + n = 10 Solve for m
Answer:
[tex]m = - \frac{1}{5} n + 2[/tex]
I need help with this please
Answer: m<ABC = 45 degrees, m<DBC = 36 degrees
Step-by-step explanation:
set both equations equal to 81 because they add up to form one angle:
5x + 6 + 9x - 9 = 81
Combine like terms
14x - 3 = 81
Add three to both sides
14x = 84
Divide by 14 to find x
x = 6
To find the angles:
Measurement of angle ABC:
9(6) - 9 = 45 degrees
Take the original angle of 81 and subtract the angle you just found to find the remaining angle:
81 - 45 = 36
Therefore, the angle of DBC is 36 degrees
2x - 7y=1
4x - 14y= 22
elimination process
Answer:
No solution
Step-by-step explanation:
Let's solve your system by elimination.−2x+14y=−29;x−7y=19Multiply the second equation by 2, then add the equations together.(−2x+14y=−29)2(x−7y=19)
Becomes
−2x+14y=−292x−14y=38Add these equations to eliminate x:0=9
ASAP pls help .....
11 Points
Answer:
0.008 3repeating
Step-by-step explanation:
Line AL is a perpendicular bisector of segment CM. Which of the following are true
Triangle ABC is an isosceles right triangle.
Because of A(-8,7) B(-4,2) C(1,6)
So AB=√[-8-(-4)]²+(7-2)²
=√41
BC=√(-4-1)²+(2-6)²
=√42
AC=√(-8-1)²+(7-6)²
=√82
AB=BC
AB²+BC²=AC²
So triangle ABC is an isosceles right triangle.
What is isosceles right triangle?
An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.
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HELP PLEASE
Graph the point (-2,3) and 3 more points using a slope of -1/2
The linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2
How to graph the point (-2,3) and 3 more points using a slope of -1/2?The given parameters are
Slope, m = -1/2
Point, (x1, y1) = (-2, 3)
The linear equation is calculated as:
y = m(x - x1) + y1
Substitute the known values in the above equation
y = -1/2(x + 2) + 3
Expand
y = -1/2x - 1 + 3
Evaluate the sum
y = -1/2x + 2
This means that the linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2
See attachment for the graph of the point and the three other points
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Find the lateral area of this square based pyramid. base is 10 ft. and slant is 10 ft.
The lateral area of the square pyramid that has a base of 10ft and height of 10 ft is calculated as: 200 ft²
How to Determine the Lateral Surface Area of a Square Pyramid?A square pyramid is a solid that has a square base and four triangular lateral faces.
The lateral area of the square pyramid is therefore the total area of the four triangular lateral faces of the square pyramid.
Area of one triangular lateral face = 1/2(base)(height)
Lateral area of the square pyramid = Total area of the four triangular lateral faces = 4 × 1/2(base)(height) = 2(base)(height)
We know the following:
Base = 10 ft
Height = 10 ft
Therefore:
Lateral area of the square pyramid = 2(10)(10)
Lateral area of the square pyramid = 200 ft²
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Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends. Is she correct?
Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends. He is incorrect
How to illustrate the information?From the information, Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends.
Let's add (-3) + (-4)
It should be noted that the addition is equal to -7.
It should be noted that this doesn't corelate with what Luciana said.
Therefore, she is incorrect. It's only correct for positive numbers.
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Name three points that are collinear
Answer:
B, J, C.
Collinear points means the points are on the same straight line, which means they have the same gradient. B, J, C are the only points on the sane straight line.
Which transformation would take Figure A to Figure B?
Answer:
Reflection over y- axis
Write the number name and expanded form for the number of driver ants that could be in two colonies.
Up to 22000 000 driver ants can live in a single colony
Number name = 22 million
Expanded form = 20,000,000 + 2,000,000
How to write a number in expanded form?
To write the number name and expanded form for the number of driver ants that could be in two colonies.
Given that Up to 22,000,000 driver of ants can live in a single colony
Now, from number expressions, we know that;
1, 000, 000 = 1 million
Thus number name is;
22,000,000= 22 million
Expanded form of 22,000,000 = 20,000,000 + 2,000,000
Thus, we conclude that;
Number name = 22 million
Expanded form = 20,000,000 + 2,000,000
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If one of the points that this relationship passes through is (,)=(300,10), find the
proportionality constant for this relationship. Round your answer to 3 decimal places.
Answer:
.033
Step-by-step explanation:
When there is a proportional relationship the constant of proportionality is y/x and in this case that would be 10/300 and that would be .033 rounded to three decimal places.
The number of words in books are discrete or continuous
514 gram in kg convert into
Answer:
514 grams is equal to 0.514 kilograms
Solve the equation P(x) = 8.
Answer:
Step-by-step explanation:
ole has $1,750 to invest. His bank offers two different types of accounts to choose from. Cole will not make any additional deposits or withdrawals. Which account will earn the most interest at the end of 3 years?
At the end of 3 years second account will earn the most interest, that is $148.38
Given,
The amount Cole has with him = $1750
Two types of account bank offered:
First account has simple interest rate = 2.75% annually
Second account has compound interest rate = 2.75% compounded annually.
Number of years = 3
We have to find the account which earn the most interest at the end of 3 years.
Simple interest = PRT/100
Compound interest = A - P
A is the amount
A [tex]=P(1+\frac{R}{N} )^{NT}[/tex]
Where,
P is the principal amount
R is the rate of interest
T is the time period
N is the number of times interest compounded yearly.
Here,
P = 1750
R = 2.75%
T = 3 years
N = 1
Now,
First account:
Simple interest = PRT/100
SI = (1750 × 2.75 × 3) / 100
SI = 14437.5/100
SI = 144.375
First account offers $144.375 as interest for 3 years.
Second account:
Compound interest = A - P
A [tex]=P(1+\frac{R}{N} )^{NT}[/tex]
A = 1750 [tex](1+\frac{0.0275}{1} )^{1(3)}[/tex]
A = 1750 (1 + 0.0275)³
A = 1750 × 1.0275³
A = 1750 × 1.084789547
A = 1898.381707
A ≈ 1898.38
Compound interest = A - P
CI = 1898.38 - 1750
CI = 148.38
Second account offers $148.38 as interest for 3 years.
So, we can conclude that second account will earn the most interest at the end of 3 years.
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