Answer:
y = 2x + 4 and 2y - x = 8 represent a system of linear equations.
In this system, the variable x represents an unknown value, while the variable y represents a value that can be determined from the equation. The coefficient 2 in the first equation is an example of a math vocabulary term, indicating that the slope of the line is 2. The term "slope" is a mathematical term that describes the steepness of a line.
The term "system" is an academic vocabulary term that refers to a group of related equations or inequalities. In this case, we have a system of two linear equations that are related to each other.
The second math vocabulary term is "solution", which refers to the set of values of the variables that satisfies both equations in the system. In this case, the solution is the unique point (3, 10), where x = 3 and y = 10.
Finally, the academic vocabulary term "consistent" is used to describe a system of equations that has at least one solution. In this case, the system is consistent because it has exactly one solution, which means the two equations intersect at a single point.
Step-by-step explanation:
Find the length in each isosceles right triangle.
a. Find the leg if the hypotenuse is 102√
Leg =
b. Find the hypotenuse if the leg is 92√
Hypotenuse =
(33 points)
The answer of the given question based on the length in each isosceles right triangle is given below,
What is Isosceles right triangle?An isosceles right triangle is right triangle in which two legs have the same length, making it isosceles triangle, and one of angles is right angle, making it right triangle. an isosceles right triangle, two acute angles are congruent, each measuring 45 degrees, and hypotenuse is equal in length to legs multiplied by √2.
The isosceles right triangle is special case of 45-45-90 triangle, where angles measure 45 degrees, 45 degrees, and 90 degrees, respectively. In 45-45-90 triangle, the hypotenuse is equal in length to legs multiplied by √2.
a. If the hypotenuse is 102√, then each leg is the same length as the hypotenuse divided by √2. Therefore:
Leg = 102√/√2 = 102
b. If one leg is 92√, then the hypotenuse is the length of that leg multiplied by √2. Therefore:
Hypotenuse = 92√ * √2 = 92 * 2 = 184.
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find area of isosceles triangle when the heights are both 13cm and the base is 10cm.
How many minutes are there in 2 years?
Answer:1,051,200 minutes.
Step-by-step explanation:
To analyze how many minutes there are in a year will allow us to multiply that number by two to get how many minutes there are in two years.
GIVENThere are 365 days in a year.
There are 24 hours in a day.
There are 60 minutes in an hour.
SOLUTION365 days x 24 hours x 60 minutes
= 525, 600 minutes in one year
525, 600 minutes x 2 (year)
= 1, 051, 200 minutes
ANSWERThere are 1, 051, 200 minutes in 2 years.
Hello! 5/6 2/5 in simplest form
Answer:
Step-by-step explanation:
5/6 - 2/5 = 25/30 - 12/30 = 13/30
Answer:
Step-by-step explanation:
To subtract two fractions, we need a common denominator. The smallest number that 6 and 5 both divide into is 30.
Converting the fractions to have 30 as the denominator, we get:
5/6 = 25/30
2/5 = 12/30
Now we can subtract:
25/30 - 12/30 = 13/30
Therefore, 5/6 - 2/5 = 13/30 in simplest form.
In rectangle ABCD
triangle ABE is equilateral
triangle CDE is isosceles, with CE = DE
Work out the size of angle x.
Your final answer must say, x =
The value of x in the given arrangement of equilateral triangle and isosceles triangle is 88°
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Given that,
A arrangement which contains,
one equilateral triangle ABE &
one isosceles triangle CDE
It is known that sum of all the angles in each direction is 180°.
ΔAEB is equilateral triangle,
so angle will be of 60°
∠AEB = 60°
And in isosceles triangle,
∠EDC = ∠ECD
∠ADC = 90°
∠ADC = ∠ADE + ∠EDC
90° = 62° + ∠EDC
∠EDC = 28° = ∠ECD
It is known that sum of all the interior angles of the triangle is 180°.
∠EDC + ∠ECD + ∠DEC = 180°
28° + 28° + ∠DEC = 180°
∠DEC = 124°
Now sum of all the angles around point E is 360°
∠AED + ∠DEC + ∠BEC + ∠AEB = 360°
x + 124° + x + 60° = 360°
2x = 176°
x = 88°
Hence, the value of x is 88°
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Q.10. Jack sells toy cars on a website. The web site fee is $30. Jack sells toy cars for $4 each.
Which inequality Jack should use to determine how many toy cars, c, he must sell to make
a profit of at least $50?
A 34c ≤50
B 34c ≥ 50
C 4c-30 ≥ 50
D 4c+30 ≥ 50
Answer:
Let's break down the cost and revenue for Jack's toy car sales:
The cost to Jack is the website fee of $30.
The revenue for Jack is the number of toy cars he sells (c) multiplied by the selling price of each toy car, which is $4 per toy car.
To make a profit of at least $50, Jack's revenue must be at least $80 ($30 website fee + $50 profit). Therefore, we can set up the following inequality:
4c - 30 ≥ 50
Solving for c, we get:
4c ≥ 80
c ≥ 20
So, Jack must sell at least 20 toy cars to make a profit of at least $50. The correct answer is option B: 34c ≥ 50.
Answer:
B
Step-by-step explanation:
34c < 50 = 136 (136 is greater than 50 wrong sign) x
B 34c > 50 = 136 (136 is greater than right sign)
C 4c-30 > 50 = -14 > 50 (wrong)
D 4c + 30 > 50 = 46 > 50 ( 46 is not greater than 50)
y = -9x +14
y=x-6
solve each system of equations by substitution .
Answer:
Step-by-step explanation:
To solve this system of equations by substitution, we need to solve one of the equations for one of the variables, and then substitute that expression into the other equation. Here's how we can do that:
y = x - 6 (equation 1)
We can solve equation 1 for y by adding 9x to both sides:
9x + y = x - 6 + 9x
y = -8x - 6 (equation 2)
Now we can substitute equation 2 into equation 3 and solve for x:
-8x - 6 = -9x + 14
Adding 8x to both sides, we get:
y = -x + 8
Subtracting 14 from both sides, we get:
-x = -6
Dividing both sides by -1, we get:
x = 6
Now that we have found the value of x, we can substitute it back into equation 1 or equation 2 to find the value of y. Let's use equation 2:
y = -8(6) - 6
y = -54
Therefore, the solution to the system of equations is:
x = 6, y = -54
We can check this by substituting these values into the original equations:
-9(6) + 14 = -54
6 - 6 = 0
So the values of x and y satisfy both equations, and therefore they are the solution to the system.
please help i need help !!!!!! is this promotional or not please help me
Answer:
I would say "not proportional" only because it's graphed on a dotted line.
If I were you, I would wait on a second opinion.
how to find the length of a pond 85 feet across; 1 inch = 4 feet
Answer:
21.25 inches.
Step-by-step explanation:
I'm guessing that you want to find how many inches a pond is if 1 in. = 4 ft.
To do this, we have to take our feet 85.
Then, we divide by how many feet equals one inch.
85/4 = 21.25 inches.
Please help me answer the question in the file link
Answer:
x=65
Step-by-step explanation:
So how I would think the equation would be would be 108 + x = 173. So how I would solve this is subtracting 108 from both sides to get x = 65. There is most likely a different way to set this up but thats what comes to mind with me.
Copy out the Venn diagram twice. On one copy shade and label the region which represents An B. On the other copy shade and label the region which represents AUB.
AnB and AUB have been labelled in the attached image.
What is Venn diagram ?Venn diagrams are the diagrams used to visually describe sets, relationships between sets, and operations carried out on them. John Venn (1834–1883) invented the Venn diagram, which makes use of circles (overlapping, intersecting, and non–intersecting) to show the relationship between sets. A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it.
A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example. The Venn diagram can demonstrate the relationship between the sets of whole numbers, integers, and natural numbers.
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5. If 3 km 500 m is subtracted from 10 km, then the result is
Answer:
The result of subtracting 3 km 500 m from 10 km is 6500 m (Or expressed in kilometers: 6.5 km).
Step-by-step explanation:
Hi,
We need to convert both measurements to the same unit (either km or meters) and then subtract:
Reminder:
1 km = 1000 m
=> 10 km = 10 * 1000 = 10000 m
=> 3 km 500 m = 3 * 1000 + 500 = 3500 m
Now we can subtract:
10000 m - 3500 m = 6500 m
The result of subtracting 3 km 500 m from 10 km is 6500 m (Or expressed in kilometers: 6.5 km).
Good luck!
Help me, please thank you
y= X b X y C
find the y- intercept and write the slope equation to match slope intercept
The slope of the equation is -2/3 and the y-intercept is 14/3.
What is y-intercept?A y-intercept is the place where a line or curve crosses, or touches, the y-axis the vertical, often darkened line in the center of a graph.
Since, the equation is not clear, let us consider the equation, 2x+3y = 14
The slope intercept form of a line is given by =
y = mx+c, where m is the slope and the c is the y-intercept.
Converting the assumed equation into slope intercept form,
2x+3y = 14
3y = -2x+14
y = -2x/3+14/3
Here we get the slope = -2/3 and y-intercept = 14/3
Hence, the slope of the equation is -2/3 and the y-intercept is 14/3.
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Levi wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Levi has 400 feet of fencing, what dimensions would maximize the area of the pen? (a) Let w be the length of the pen perpendicular to the barn. Write an equation to model the area of the pen in terms of w
Answer:
Step-by-step explanation:
Let's call the length of the pen perpendicular to the barn "w", and the length parallel to the barn "l".
The total amount of fencing available is 400 feet. The side against the barn will be of length l, and the other two sides will each be of length w. Therefore, the total length of fencing required is:
l + 2w
This length of fencing must equal 400 feet:
l + 2w = 400
We want to maximize the area of the pen. The area of a rectangle is given by:
A = lw
We can use the equation l + 2w = 400 to solve for l:
l = 400 - 2w
Substituting this expression for l into the equation for the area, we get:
A = w(400 - 2w)
Simplifying:
A = 400w - 2w^2
So the equation to model the area of the pen in terms of w is:
A = 400w - 2w^2
8 ft
4 ft
8 ft
Find area
Answer:
Step-by-step explanation:
HI:
Area of rectangle: 8*8= 64
Area of triangle: 4*8=32/2= 16
64+16= 80
Answer: 80ft^2
[tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex]
The equation [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex] is an example of the square root property. The square root property states that for any real number a, b, and c, if and only if a + b = c. This property can be used to simplify and solve equations involving square roots.
What does square root mean?
The square root of a number is the number that, when multiplied by itself, produces the original number. For instance, the square root of 16 is 4, because 4 multiplied by itself (4 x 4) equals 16.
The equation [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex] is true because it satisfies the square root property. To see this, note that [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex] implies that x+8=x+8, which is true. Therefore, the equation is true.
To solve for x, we will use the square root property. We know that [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex], so we can rewrite the equation as [tex]\sqrt{x} +\sqrt{8}-\sqrt{x+8}=0[/tex]. We can then use the square root property to simplify the equation to [tex]\sqrt{x} -\sqrt{x}=0[/tex], which implies that x=0. Therefore, the solution to the equation [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex] is x=0.
In conclusion, the equation [tex]\sqrt{x} +\sqrt{8}-\sqrt{x+8}=0[/tex] is an example of the square root property, and the solution to the equation is x=0.
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Please help me anyone with this?!!!
Answer:
B
subtract 20
80,60,40.....
Step-by-step explanation:
it's the arithmetic sequence having difference of 20
Jeff claims that a number and its opposite will always have the same aboslute value. Is Jeff correct? Yes or no
Answer:
Step-by-step explanation:
yes
Yes, Jeff is correct.
Bob ran 4/5 of a mile his sister ran one-half of a mile how much further did Bob run than his sister
30% or 3/10
Bob is 4/5
His sister is 1/2
convert to percents so 80% and 50%
he ran 30% more of a mile (3/10)
the parallelogram below has an area of 54 units²
The height of the parallelogram is 5.4 units.
What is area ?
In mathematics, the area is the measure of the size of a two-dimensional surface or region, usually expressed in square units, such as square inches or square meters. The area of a flat shape or planar figure is the amount of space inside its boundary, or the surface of the object, that is covered by a two-dimensional geometric shape.
One way to find the height is to draw a perpendicular line from point B to line segment AD, forming a right triangle. Let's call the length of this perpendicular line h.
Now we can see that the base of the parallelogram is 10 units (from A to D), and the height is h units (from B to the perpendicular line we drew). The area of the parallelogram is given as 54 units², so we can set up the following equation:
Area = base x height
54 = 10h
Solving for h, we get:
h = 54/10 = 5.4
Therefore, the height of the parallelogram is 5.4 units.
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Step-by-step explanation:
he should have multiplied
The number of passes completed by Brett Favre, quarterback for the Green Bay
Packers, was recorded for each of the 16 regular season games in the fall of 2006
(www.espn.com).
15 31 25 22 22 19 17 28
24 5 22 24 22 20 26 21
a. Draw a stem and leaf plot to describe the data.
b. Calculate the mean and standard deviation for Brett Favre’s per game pass
completions.
c. What proportion of the measurements lie within two standard deviations of
the mean?
2
EASY MATH POINTS!
Answer from the screenshot below :)
For the mapping diagram 1, we have that the domain and the range are given as follows:
The domain is: {10}.The range is: {-8, 2, 1.1}.It does not represent a function, as the input of 10 is mapped to different outputs.
For the mapping diagram 2, we have that the domain and the range are given as follows:
The domain is: {-8, 2, 1.1}.The range is: {10}.It represents a function, as each value of the input is mapped to a single output.
How to obtain the domain and the range of the diagram?The concepts for the domain and the range of the diagram are defined as follows:
Domain: all input values from which an arrow is departing.Range: all output values to which an arrow arrives.The mapping diagram will represent a function if each value of the input is mapped to a single output.
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Rotation: 180° about the origin
Answer: Move it to the the left
Step-by-step explanation: 180 degrees is the left straight line
3.
At the average minimum monthly
temperatures for San Francisco,
California, have been recorded
in the table, shown at the right.
The data have been correctly
represented by both graphs A
and B.
a. Which graph would be best to
help convince others that the
average minimum temperature
in San Francisco is much colder
in January than in August?
Explain your reason for making
this selection.
b. Why might people who thought
that there was little difference
between the average minimum
temperature in January and
August consider the graph you
chose to be misleading?
Graph A
MONTH
January
February
March
April
May
June
July
August
Average Min Tamp
Graph B
60.0
Average Min Temp
5000
40.0
January
48.9
53.0
49.8
52.9
February
510
53.6
54.5
Junway
March
February
March
Marth
June
July
June
Ant
COKE CIT 10010 TOU
va
Graph B is the one which can best convince others that the average minimum temperature in San Francisco is much colder in January than in August.
What did Graph B show about temperature level?Basically, a temperature refers to measurement of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. The level of temperature falls between the maximum and minimum temperatures or between the highest and lowest mean temperatures during a specified time interval.
The Graph A in this context, shows that there is a linear temperature level from January to August, but the Graph B, is different because it shows that the temperature level is at lowest (coldest) in January and rises as the year proceeds. Therefore, the Graph B must be used to convince others that the average minimum temperature in San Francisco is much colder in January than in August.
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Mary cart worth purchased a four piece lugar set for 750 she made a down payment of 15% and was charged 6% interest find the total installment price and the monthly payments if she payed it off in 8 months
Mary's monthly payments will be approximately $117.50.
What is the instalment price?The total instalment price is the price of the furniture plus the interest charged. Since Mary made a down payment of 15%, the amount that is subject to interest is 85% of the total price. Therefore:
Total price = (100% / 85%) * $750 = $882.35
The interest charged is 6% of the total price over the 8-month payment period. Therefore:
Interest charged = 6% * $882.35 * (8 / 12) = $35.29
The total installment price is the sum of the total price and the interest charged:
Total installment price = $882.35 + $35.29 = $917.64
To find the monthly payments, we can use the formula for the present value of an annuity:
Payment = [tex]\mathrm{PV \times (r / (1 - (1 + r)^{(-n)}))}[/tex]
where PV is the present value (total installment price), r is the interest rate per month (6% / 12 = 0.005), and n is the number of payments (8).
Substituting the values:
Payment = $917.64 × (0.005 / [tex](1 - (1 + 0.005)^{(-8)}[/tex] ≈ $117.50
Therefore, Mary's monthly payments will be approximately $117.50.
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The function, A,B and C represent the amount owed (in dollars)for a loan A,B and C respectively: the input for the functionalist t,the number of years without payment.
1. For each loan, find the average rate of change per year between:
a. the start of the loan and the end of the second year
IM
15.4: Comparing Average Rates of Change
The functions a, b, and e represent the amount owed (in dollars) for Loans A, B, and C
respectively: the input for the functions is t, the number of years without payments.
b. the end of the tenth year and the end of the twelfth year
Illustrative
Mathematics
2. How do the average rates of change for the three loans compare in each of the
two-year intervals?
a. Find (A(2)-A(0))/2, (B(2)-B(0))/2, and (C(2)-C(0))/2.
b. Find (A(12)-A(10))/2, (B(12)-B(10))/2, and (C(12)-C(10))/2. Compare the rates of change between the three loans for each interval.
a. To find the average rate of change per year between the start of the loan and the end of the second year, we need to calculate the difference in the amount owed after two years and the amount owed at the start of the loan, and then divide by two.
For loan A:
Average rate of change = (A(2) - A(0))/2
For loan B:
Average rate of change = (B(2) - B(0))/2
For loan C:
Average rate of change = (C(2) - C(0))/2
b. To find the average rate of change per year between the end of the tenth year and the end of the twelfth year, we need to calculate the difference in the amount owed at the end of the twelfth year and the amount owed at the end of the tenth year, and then divide by two.
For loan A:
Average rate of change = (A(12) - A(10))/2
For loan B:
Average rate of change = (B(12) - B(10))/2
For loan C:
Average rate of change = (C(12) - C(10))/2
2. We can compare the average rates of change for the three loans in each of the two-year intervals by comparing their values. If the average rate of change is positive, it means the amount owed is increasing, while if it is negative, it means the amount owed is decreasing. We can compare the rates to see which loan is increasing or decreasing at a faster rate in each interval.
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I need help with this review
The slope of f(x) = x² - x + 2 at x = 3 is 6.
How to calculate the slopeThe limit definition of a derivative is given by:
f'(x) = lim(h->0) [f(x+h) - f(x)] / h
To find the slope of f(x) = x² - x + 2 at x = 3, we need to evaluate this expression at x = 3.
f'(3) = lim(h->0) [f(3+h) - f(3)] / h
f'(3) = lim(h->0) [(3+h)² - (3+h) + 2 - (3² - 3 + 2)] / h
f'(3) = lim(h->0) [(9 + 6h + h² - 3 - h + 2 - 9 + 3 - 2)] / h
f'(3) = lim(h->0) (6h + h²) / h
f'(3) = lim(h->0) (h(6 + h)) / h
f'(3) = lim(h->0) (6 + h)
Now we can evaluate the limit by plugging in h = 0:
f'(3) = 6 + 0 = 6
Therefore, the slope of f(x) = x² - x + 2 at x = 3 is 6.
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A circle has a radius of 4 ft.
What is the area of the sector formed by a central angle measuring 270°?
Use 3.14 for pi and round the decimal to the nearest tenth.
42.8 ft²
37.7ft²
12 ft²
9.4 ft²
Cοnsequently, a 270° center angle's sectοr has an area οf 37.7 feet². A: 37.7 feet².
What is circle?A circle is a clοsed, twο-dimensiοnal οbject that can be described as the cοllectiοn οf all pοints in a plane that are equally spaced frοm the circle's center. The diameter οf a circle is equal tο the distance traveling thrοugh its center, while the radius is the distance frοm the center tο any lοcatiοn οn the circle. A circle's area is the rοοm it enclοses, while its circumference is the distance it spans.
given
We must apply the fοllοwing algοrithm tο determine the sectοr's area:
Sectοr area is equal tο (angle at center/360°) * radius * 2
Radius is 4 feet, and the center angle is 270 degrees. By replacing these numbers, we οbtain:
Sectοr area equals (270/360) * * 42.
Sectοr area equals (0.75) * 3.14 * 16
Sectοr size: 37.7 square feet (rοunded tο the nearest tenth)
Cοnsequently, a 270° center angle's sectοr has an area οf 37.7 feet². A: 37.7 feet².
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