Using the elimination method, the solution to the system of equations is as follows:
x = 19 / 13 and y = - 74 / 13
How to solve system of equation?System of equations can be solved using different methods such as the elimination method, substitution method, and graphical method.
Let's use the elimination method to solve the system of equations as follows:
The elimination method is the process of eliminating one of the variables in the system of equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.
Therefore,
4x - 7y = 10
3x + 2y = -7
multiply equation(ii) by 3.5
4x - 7y = 10
10.5x - 7y = 24.5
subtract equation(i) from equation(ii)
6.5x = 14.5
x = 14.5 / 6.5
x = 145 / 65
x = 19 / 13
Let's find y
3(19 / 13) + 2y = -7
57 / 13 + 2y = -7
2y = - 7 - 57 / 13
2y = -91 - 57 / 13
2y = - 148 / 13
cross multiply
26y = - 148
y = - 148 / 26
y = - 74 / 13
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#12: A train left Philadelphia at 8 AM on July 1st. It traveled
2,864 miles to Portland, Oregon, arriving at 9AM on July 4th.
What was the average rate of change of the train in miles per
hour?
Round to the nearest hundredth
Answer: 39.23 miles per hour
Step-by-step explanation:
1 day = 24 hour
3 days = 72 hours
Add one more hour for both to get to 9 AM, so it will take 73 hours to get there.
Now we find the average rate of change.
We take 2864 divided by 73 = 39.23 miles per hour
Alex has $600 in her checking account. She wants to spend a part of this money on a computer.
She wants to have at least $250 left in her checking account after buying the computer. Write an
inequality that can be used to find t, the amount of money in dollars that Alex can spend on the
computer, and solve fort.
Amount of computer can be 350 or more than 350.
What do you mean by inequality?
Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether it is less than or higher than.
Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.
It is given that Alex has $600 in her checking account and She wants to have at least $250 left in her checking account after buying the computer.
Let the amount of computer be t
According to the question , inequality become:
600 - t ≥ 250
600 - 250 ≥ t
350 ≥ t
Therefore, amount of computer can be 350 or more than 350.
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.... i need help past due
Question
A square based pyramid has a height of 6 feet and the edge length of the base is 2 feet. A second square based pyramid is 2 feet taller and the edge length of the base is 0.5 feet greater than the first pyramid. How much greater is the volume of the second pyramid than the volume of the first pyramid? Round your answer to the nearest hundredth.
please help
A pyramid is a solid shape with a specified shaped base. The required answer is 8.67 cubic feet.
A pyramid is a solid shape with a specified shaped base. While a square based pyramid is a type of pyramid which has its base to be a square.
Volume of a square based pyramid = [tex]\frac{1}{3}[/tex] x base area x height
Also, are of a square = length x length
So that,
i. For the first pyramid;
volume = [tex]\frac{1}{3}[/tex] x (2 x 2) x 6
= 8 cubic feet
The volume of the first pyramid is 8 cubic feet.
ii. For the second pyramid, we have;
height = 8 feet
base side = 2.5 feet
So that.
Volume = [tex]\frac{1}{3}[/tex] x (2.5 x 2.5) x 8
= 16.6667
Volume = 16.67 cubic meters
The volume of the second pyramid is 16.67 cubic meters.
Therefore, the volume of the second pyramid is greater than the volume of the first pyramid by;
volume of the second pyramid - volume of the first pyramid = 16.67 - 8.0
= 8.67 cubic feet
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Andrew just started a running plan where he runs 12 miles the first week and then increases the number of miles he runs by 5% each week. If he keeps up this plan for 10 weeks, how many total miles would Andrew have run, to the nearest whole number?
Answer:
18 miles.
Step-by-step explanation:
You start with 12 miles and then you first need to figure out what 5% of that is by doing the equation x/12 = 5/100 and you will then get .6. Then you multiply that number by 10 (one for each week) getting 6. Then you add the 6 to your starting total to get 18.
Will swims a total of 45.6 laps in 2.85 hours. How many laps does he swim each hour?
The number of swims that Will swims by using decimal divisions is 16 laps in each hour.
What is decimal division?
When dividing decimals, the divisor must be converted to a whole number by moving the decimal point to the right. The dividend's decimal point is then carried up to the same number of places to the right, and the resulting numbers are divided in the same manner as regular long division.
Given, Will swims a total of 45.6 laps in 2.85 hours
That is, 2.85 hours = 45.6 laps
or, 1 hour = 45.6/2.85 = 16 laps
Hence, he swims 16 laps each hour.
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Nora placed 12 cans in each box.How many boxes will she need if she has 240 cans?
Answer:
20 boxes
Step-by-step explanation:
12 cans = 1 box
240 = x
apply rule of three
(240/12) x 1 = x
20 = x
Answer:
She will need 20 boxes
Step-by-step explanation:
Take the total number of cans and divide by the number of cans per box
240/12
20
She will need 20 boxes.
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If
AD = 12 and EA = 13, solve for AC. Round your answer to the nearest tenth if
necessary.
The line AC from the diagrammatic expression of the tangent of the circle shows that line AC is 24.0
What is the tangent of a circle?A tangent of a circle is a line that intersects the circle at a single point. The site at which the tangent intersects the circle is referred to as the site of tangency.
From the given information:
Line |CD| = Diameter
Line |EA| = radius = 18
Line |DB| = 12
Then, we can infer that line EA = DE since they are both (radii of the circle.)
Line |DE| = |EA| = 18
By using the formula for Pythagoras' theorem, we can find line |EA|.
hyp² = opp² + adj²
where;
Line |BE| = hypotenuse = DB + BE = 12 + 18 = 30
Line |AB| = opposite (x) = ???
Line |EA| = adjacent = 18
Thus;
30² = x² + 18²
900 = x² + 324
-x² = -900 + 324
x = √576
x = 24.0
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solve for 2x² = 80?
Answer:
x=2√10,−2√10
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Answer:
a) 23.1 million
b) year 2013
Step-by-step explanation:
Given a population in millions is modeled by A = 23.1e^(0.0152t) for t years after 2000, you want to know the population in year 2000, and the year in which the population is 28.3 million.
a) Initial populationWhen t=0, the exponential factor is 1. The population is given by the coefficient of that factor: 23.1
The population in 2000 was 23.1 millions.
b) Year of 28.3MWe can solve for t to find the year the population is 28.3 million:
28.3 = 23.1e^(0.0152t)
28.3/23.1 = e^(0.0152t) . . . . .divide by 23.1
ln(28.3/23.1) = 0.0152t . . . . . take natural logs
t ≈ 13.36
The population will reach 28.3 million in the year 2013.
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1. Line L contains points (4, -1) and (4,9). Point P has coordinates (1,6)
The distance between the point and the line is 3 units.
Find the equation for line L
Begin by finding the slope of the line through the given points, (4,-1) and (4,9) ; its intercept:
m = (y₂ - y₁) / (x₂ - x₁)
= (9 - (-1) ) / 4 - 4
= 10 / 0
= Undefined
Because the slope is undefined, then line L is a vertical line which has an x-intercept of (4,0):
x=4
Because, line L is vertical, then the line w perpendicular to it is a horizontal line that passes through (1,6)(1,6) so its equation is y=6. Hence, L and w intersect at (4,6) which we will denote as Q.
The perpendicular distance is the distance from point P(1,6) to point Q(4,6) which is simply the absolute value of the difference of the x-coordinates:
d = | 1 - 4 |
= |-3|
= 3
Hence, The distance between the point and the line is 3 units.
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A taxi ride in a large city costs $2.75 plus 5 for each mile traveled. write an equation to represent the situation where D is the distance traveled and see is the total cost of the trip. if Brandon traveled 9.5 miles by taxi how much was the cost C of his taxi ride?
Answer: $50.25
Step-by-step explanation:
First, we will write an equation to represent this situation.
C = $2.75 + $5D
Next, we will substitute 9.5 miles into D and solve.
C = $2.75 + $5D
C = $2.75 + $5(9.5)
C = $50.25
Answer:
(a) c = 2.75 + 5d
(b) $50.25
Step-by-step explanation:
(a)
The information tells us the following:
Cost of a taxi ride = $2.75 + (5 * number of miles travelled)
We can use the variables c and d to represent the descriptions:
c = 2.75 + 5d
(b)
Substitute 9.5 into the equation as d:
c = 2.75 + 5(9.5)
Simplify:
c = 2.75 + 47.5
c = 50.25
Therefore, the cost of a 9.5 mile ride is $50.25.
For the function f(x) shown graphed below, over which of the following intervals is f(x) <0?
The function f(x) is greater than zero when the value of x lies in between -3 and 5 and this can be determined by using the given graph.
What is graph?Graph is a mathematical representation of a Networks and it's describes the relation between lines and points.
The graph of the function f(x) is given.
The following steps can be used in order to determine the interval for f(x):
Step 1 - The value of f(x) means the value of y.
Step 2 - The value of f(x) is positive when the graph of f(x) is in the first or in the second quadrant.
Step 3 - So, according to the graph function f(x) is positive when the value of x is in between -3 and 5.
Therefore, the correct option is 3).
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2) Solve: 115 − 10 = −12 − 5(2 − 6)
Answer:
False
Step-by-step explanation:
Simplify 115 − 10 : 105Subtract the numbers 115 − 10 = 105
2.Simplify 12 − 5(2 − 6) : 8
105=8
this shows that the sides are not equal so it is false
In the coordinate plane, the point X(-4,-2) is translated to the point X'(-6,-5) . Under the same translation, the points Y(0,0) and Z(-2,2) are translated to Y' and Z' , respectively. What are the coordinates of Y' and Z' ?
Under the same translation as X and X' the coordinates of Y' = (-2, -4) and Z' = (-4, -1)
What is translation of a point in coordinate system?
A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.
According to the given question:
It is given about the points X (-4, -2) and X' (-6, -5).
We see that the translation is moving -2 units horizontally to the left and -3 units vertically down.
Therefore, the point Y(0,0) is translated to Y'(0-2,-1-3) = Y'(-2,-4)
and the point Z(-2,2) is translated to Z'(-2-2,2-3) = Y'(-4,-1).
Hence, under the same translation Y' = (-2, -4) and Z' = (-4, -1)
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Graph the following features: Y intercept = -3 Slope = 4/5
The equation of line where the y intercept is -3 and slope is 4/5 is
y = ( 4/5 )x - 3
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the equation A is y = mx + b
The y intercept of the line b = -3
The value of b = -3
The slope of the line m = 4/5
The value of m = 4/5
Now , substituting the values in the equation of line , we get
y = mx + b
y = ( 4/5 )x + ( -3 )
y = ( 4/5 )x - 3
The graph of the equation y = ( 4/5 )x - 3 is given below
Therefore, the value of the equation of line A is y = ( 4/5 )x - 3
Hence , The equation of line where the y intercept is -3 and slope is 4/5 is
y = ( 4/5 )x - 3
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For the high school basketball game, it costs $12 for every 3 tickets.
Complete the table below showing the cost and the number of tickets.
Based on the unit rate of the table, the missing values that shows the cost and the number of tickets are:
$32 and 9 tickets.
How to Complete the Table Showing Cost and Number of Tickets?To calculate the missing values in the table shown in the attachment below, we have to find the unit rate, which is the cost of 1 ticket.
Given that 3 tickets will cost $12, therefore:
Unit rate = 12 / 3 = $4 per ticket.
Using this rate, find the missing values as explained below.
For 8 tickets, we will have the following cost:
8 × $4 = $32
For $36, we will have the following tickets:
$36/$4 = 9 tickets
Thus, the missing values that will complete the table will be:
$32 and 9 tickets.
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(10)
Write the equation
of the line in
Slope-Intercept
Form.
Answer: y= -3x -1
Step-by-step explanation: y=mx+b
The Y-intercept is at (0,-1), so b is -1
The slope is rise/run, and the graph is down 3, right 1, so the slope is -3/1
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You have rented a moving truck to move into your first apartment. ABC truck has interior dimensions of 168 inches times 96 inches times 77 inches. The dimensions of your storage boxes are 24 inches times 13 inches times 28 inches. Determine how many boxes can fit into the truck.
what is the answer of this question?
Step-by-step explanation:
The given mass of the Earth is 5.972 × 10²⁴
The given mass of the Jupiter is 1.898 × 10²⁷
Now,
1.898 × 10²⁷ ÷ 5.972 × 10²⁴
= 0.3178 × 10³ = 317.8
Thus, Jupiter is 317.8 heavier than Earth
Find the slope: m=
Find the y-intercept: b=
Equation: y=
Answer:
y = - [tex]\frac{5}{4}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = [tex]\frac{0-5}{4-0}[/tex] = [tex]\frac{-5}{4}[/tex] = - [tex]\frac{5}{4}[/tex]
the line crosses the y- axis at (0, 5 ) ⇒ b = 5
y = - [tex]\frac{5}{4}[/tex] x + 5 ← equation of line
A semicircle is divided into two circular sectors of which one is 4/5 of the other. The radius of the circle measures 18cm. Calculate the length of the two arcs and the area of the two circular sectors
The length of the two arcs and the area of the two circular sectors can be calculated as follows:
Since the semicircle is divided into two circular sectors, each sector has an angle of 180/2 = 90 degrees. Therefore, the smaller circular sector has an angle of 90 * (4/5) = 72 degrees, and the larger circular sector has an angle of 90 - 72 = 18 degrees.
The length of the arc of a circle is equal to the circumference of the circle multiplied by the ratio of the central angle of the arc to 360 degrees. Therefore, the length of the smaller arc is 18 * pi * (72/360) = 8pi cm, and the length of the larger arc is 18 * pi * (18/360) = 2pi cm.
The area of a circular sector is equal to the area of the circle multiplied by the ratio of the central angle of the sector to 360 degrees. Therefore, the area of the smaller circular sector is 18^2 * pi * (72/360) = 288pi cm^2, and the area of the larger circular sector is 18^2 * pi * (18/360) = 72pi cm^2.
Therefore, the length of the two arcs is 8pi cm and 2pi cm, and the area of the two circular sectors is 288pi cm^2 and 72pi cm^2.
In the following diagram, AD || BC and AB || DC.
Prove angle A is congruent to angle C
what is this in Algebra tiles (x-1) (x+3)
please help me.
The area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.
Given that, the dimensions of a rectangle (x-1) and (x+3).
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Here, the area of a rectangle
= (x+3)×(x-1)
= x²+3x-x-3
= x²+2x-3
Hence, the area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.
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"Your question is incomplete, probably the complete question/missing part is:"
Find the area of a rectangle with the dimensions (x-1) and (x+3).
solve for b in the trapezoid.
180 - 57 = 123 ( ALLIED ANGLE )
a prestigious program accepts 2 out of every 9 applicants per yer. if the program accepted 360 applicants, how many applicants were not accepted?
If a prestigious program accepts 2 out of every 9 applicants per year than the program will accept 360 applicants out of 1620.
What is ratio math example?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
What is a equation example?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
the ratio is given:
2/9 = 360/x
solving for the value of x;
x/9=360/2
x=(180)9
x=1620
this is the required value of applicants that were not accepted.
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a paddle wheel on a boat is 4 feet in diameter. the fins along the outer edge travel at a speed of 1.3 feet per second. how long does it take the paddle wheel to complete 100 full revolutions ? round to the nearest second.
_ minutes and _ seconds.
Answer: To find out how long it takes the paddle wheel to complete 100 full revolutions, we need to calculate the circumference of the paddle wheel and divide that by the speed at which the fins along the outer edge are traveling.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius of the circle.
The radius of the paddle wheel is 2 feet (the diameter of 4 feet divided by 2), so the circumference is:
C = 2π * 2 = 8π feet
To find out how long it takes the paddle wheel to complete 100 full revolutions, we divide the number of feet traveled in one revolution (the circumference of 8π feet) by the speed at which the fins are traveling (1.3 feet per second):
100 * 8π feet / 1.3 feet per second = 615.38 seconds
Rounded to the nearest second, it takes approximately 615 seconds for the paddle wheel to complete 100 full revolutions.
Find the scale factor
Please help me!
Answer:
[tex]\frac{7}{5}[/tex] or 7:5
Step-by-step explanation:
You are going from the smaller triangle to the larger.
Let x = the scale factor. Find two corresponding sides that you know both lengths.
50x = 70 Divide both sides by 50
x = [tex]\frac{70}{50}[/tex] Divide both the numerator and denominator by 10
[tex]\frac{7}{5}[/tex]
For the conditional write the converse , inverse , and contrapositive: Walking in front of a moving car is dangerous to your health .
The converse of the conditional statement is “If dangerous to your health then walking in front of a moving car”.
The inverse of the conditional statement is “If not dangerous to your health then not walking in front of a moving car”.
The contrapositive of the conditional statement is “if not walking in front of a moving car then not dangerous to your health."
What is the conditional statement?The conditional statement is defined as the two fundamental components that make up a conditional statement Hypothesis (if) and Conclusion (then).
The given conditional statement is "walking in front of a moving car is dangerous to your health."
The converse of the conditional statement is “If dangerous to your health then walking in front of a moving car”.
The inverse of the conditional statement is “If not dangerous to your health then not walking in front of a moving car”.
The contrapositive of the conditional statement is “if not walking in front of a moving car then not dangerous to your health."
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Find the three consecutive integers such that the smallest and three times the largest is 330. What is the smallest integer?
The smallest integer out of the three integers is 109
What is a number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
Three consecutive integers:
x, x+1, x+2
The sum of the integers,
x+(x+1)+(x+2) = 330
3x + 3 = 330
3x= 327
x= 327/3
x= 109
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