I need help I’m not sure I did this right and need help on the graphing!! And table next to it please :( !
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The solution for the given system of equations, y = [tex]\frac{-1}{2}[/tex]x + 5 and y = 3x - 2 is (2,4) and the graph is attached below
What is the system of equations?The system of equations is a set of equations consist the same variables. If the given equation are all linear then, it is the system of linear equation.
To solve such system, it is required to figure out the variable values that can solve all the equations involved in the system.
For the given system of equation the variable value is x.
So, [tex]\frac{-1}{2}[/tex]x + 5 = 3x - 2
2 + 5 = 3x + [tex]\frac{x}{2}[/tex]
7 = x ([tex]\frac{6+1}{2}[/tex]) = [tex]\frac{7x}{2}[/tex]
x = 2
Now apply the obtained value of x in either of the equations:
y = 3x - 2
y = 6 - 2
y = 4
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Related Questions
Please explain and help me get the correct answer. Thank you. Practice work that is not graded.
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First, from the formula given we solve the equation for D:
[tex]\begin{gathered} 4PD=D^2LN\pi, \\ \frac{4PD}{LN\pi}=D^2, \\ \sqrt{\frac{4PD}{LN\pi}}=D^{}. \end{gathered}[/tex]Now, substituting the given data:
(a) PD=405 cu in, L=4.7 in, and N=7,
in the above equation we get:
[tex]D=\sqrt[]{\frac{4\times405}{4.7\times7\times\pi}}in=\sqrt[]{15.6736175}in\approx3.96\text{ in}[/tex](b) PD=399.4 cu in, L=2 in, and N=6,
in the above equation we get:
[tex]D=\sqrt[]{\frac{4\times399.4}{2\times6\times\pi}}in=\sqrt[]{42.37765618}in\approx6.51\text{ in}[/tex]Answer:
(a) 3.96 in.
(b) 6.51 in.
Write and equation for each of the following problems and solve. (40 points each)3. The length of a rectangle is 5 cm more than three times the width. If the width is 12, what is thelength of the rectangle?
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It is given that,
The length of a rectangle is 5 cm more than three times the width.
That is, l=3w+5
Put width, w=12.
Therefore, the length becomes,
l=3(12)+5
l=36+5
l=41 cm.
Hence, the length of the rectangle is 41 cm.
A crate of medicine with a density of 2,200 kilograms per cubic meter will be shipped from England to the U.S. What is the crate's density in pounds per cubic foot?
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The crate's density in pounds per cubic foot = 137.28 lb/ft³
What is density?Density is defined as the quantity that shows the relationship between the mass and volume of an object which is measured in kilograms per cubic meter or in pounds per cubic foot.
The density of the given crate of medicine = 2,200 kg / m³
To convert to pounds per cubic foot;
1 kg/m³ = 0.0624 lb/ft³
2,200 kg/m³ = X
Make X the subject of formula;
X = 2,200 × 0.0624/1
X = 137.28 lb/ft³
Therefore, when converter to pounds per cubic foot the density of the crate of the medicine= 137.28 lb/ft³.
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PLEASEEE HELPP
Megan is in a musical production. She was at practice for 2 hours yesterday and 3 hours today. Altogether she spent of her practice hours dancing. How many total hours did Megan spend dancing yesterday and today?
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Answer:
2.0833
Step-by-step explanation:
2 3/4 + 3 1/2 =6.25
6.25(1/3)=2.0833
Elijah and his brother ran a race. Elijah reached the finish line in 60.26 seconds and his brother reached the finish line 6 seconds later. How long did it take Elijah's brother to run the race?
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Solve for X picture include
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The sum of angles of a triangle is equal to 180 degree.
Determine the value of x, by using angle sum for the triangle.
[tex]\begin{gathered} 2x-4+3x-4+3x-4=180 \\ 8x=180+12 \\ x=\frac{192}{8} \\ =24 \end{gathered}[/tex]The value of x is 24
In 5 minutes, a conveyor belt moves 100 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans thesame distance in 9 minutes. If both belts are used, find how long it takes to move the cans to the storage area.The conveyor belts can move the 100 pounds of recyclable aluminum from the delivery truck to a storage area in minutes.(Simplify your answer. Type an integer, fraction, or a mixed number.)
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we know that
a greater conveyor belt moves 100 pounds ------------> 5 minutes
so
Applying proportion
1-minute ---------> move 100/5=20 pounds
a smaller conveyor belt moves 100 pounds ------> 9 minutes
so
Applying proportion
1-minute --------> move 100/9 pounds
therefore
If both belts are used
then
1-minute --------> move 20+(100/9)=(180+100)/9=280/9 pounds
Applying proportion
Find out how long it takes to move 100 pounds
[tex]\begin{gathered} \frac{1}{\frac{280}{9}}=\frac{x}{100} \\ \\ solve\text{ for x} \\ x=\frac{100}{\frac{280}{9}}=\frac{900}{280} \end{gathered}[/tex]Simplify the fraction
45/14
Convert to a mixed number
45/14=42/14+3/14=3 3/14 minutes
The answer is 3 3/14 minutesThe figure shows a circle inscribed into a regular pentagon.Cis the center of the circle and the regular pentagon.G and H are on the edge of both the circle and the regular pentagon.The radius of the circle is 3 inches.GHCPart A. Find the area of the dark shaded region. Show your work.Part B. Find the area of the light shaded region. Show your work.
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Solution
Part A: The area of the dark shaded region = S1,
where
The radius of the circle is 3 inches.
[tex]\begin{gathered} S_1=\frac{4}{5}\pi r^2 \\ =\frac{4}{5}\pi.3^2 \\ S_1=\frac{36}{5}\pi in^2 \end{gathered}[/tex]Part B: The area of the light shaded region = S,
[tex]\begin{gathered} S=S_2-S_1 \\ S=5\times\frac{1}{2}r.rtan36 \\ S=\frac{45}{2}\sqrt{5-2\sqrt{5}} \\ S=\frac{45}{2}\sqrt{5-2\sqrt{5}}-\frac{36}{5}\pi in^2 \end{gathered}[/tex]I NEED HELP ON TRIG PROOFS, SOMEONE PLEASE HELP!!!! URGENT!!!!
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Step-by-step explanation:
:)))))))))))))))))))))
Bill Jensen deposits $8500 with Bank of America in an investment paying 5% compounded semiannually. Find the compound amount in 6 years
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Given:
Initial deposit = $8500
rate of interest = 5% compounded annuallly
time (t) = 6 years
If Ao is invested at an annual interest rate r and compounded semiannually, the amount At after t years is given by the formula:
[tex]A_t\text{ = }A_0(1\text{ + }\frac{r}{2})^{2t}[/tex]The compound amount in 6 years:
[tex]A_t\text{ = 8500 }\times\text{ (1 + }\frac{0.05}{2})^{2\times6}[/tex]Simplifying we have:
[tex]\begin{gathered} A_t\text{ = 8500 }\times1.025^{12} \\ =\text{ 11431.56} \end{gathered}[/tex]Answer:
$11431.56
Oscar drew a scale drawing of a house. The garage, which is 8 meters long in real life, is 4centimeters long in the drawing. What is the drawing's scale factor?Simplify your answer and write it as a fraction.
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Answer:
1/200
Explanation:
Length of the garage in the drawing = 4 centimeters
Length of the garage in real life = 8 meters
The ratio of the lengths = 4 cm : 8m
Divide both sides by 4
[tex]\begin{gathered} \frac{4\operatorname{cm}}{4}\colon\frac{8m}{4} \\ 1\operatorname{cm}\colon2m \end{gathered}[/tex]1 m =100cm
2m= 2 x 100 =200cm
Converting both to the same unit, we have:
[tex]\begin{gathered} 1\operatorname{cm}\colon200\operatorname{cm} \\ =\frac{1}{200} \end{gathered}[/tex]The drawing's scale factor in fraction form is 1/200.
IS THIS A FUNCTION YES OR NO?? (ALGEBRA 1)
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Answer: Yes
Step-by-step explanation:
Yes, the numbers in the table are a function. The equation for the equation would be
y = 2x
ABC is shown . D is a point on AB,AC =7, AD=6, and , BC=18.
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ok
AC = 7
AD = 6
BC = 18
It must be 12, because the sum of two sides of a triangle is higher than the other side.
And 6 + 5 = 11
AB + AC = 11 + 7 = 18
What is the magnitude (size) of -7.5?_______________________________O A. -7.5, because |-7.5| = 7.5O B. 7.5, because |-7.5 = 7.5O C. 7/5, because |-7.5| = 7/5O D. 7.5, because | -7.5| = - 7.5
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it is given that the expression is -7.5
the magnitude of -7.5 is,
I-7.5I = 7.5
thus, the answer is option A
After 12 weeks, how much more will he made in sales of buttered popcorn than the sales of caramel popcorn
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We have two functions for the sales of popcorn:
[tex]\begin{gathered} B(w)=8w+9 \\ C(w)=6w-1 \end{gathered}[/tex]being B(w) the number of buttered popcorn sold over "w" weeks and C(w) the number of caramel popcorn sold over "w" weeks.
We now have to calculate how much more he would have made after 12 weeks in sales of buttered popcorn than the sales of caramel popcorn.
We can calculate this as the difference of sales of buttered popcorn and the sales of caramel popcorn for w = 12.
Each sale will be the product of the cost per unit (in this case, is $11 for both types) and the number of units sold (B(w) or C(w), depending on the ytpe of popcorn).
Then, we can calculate the difference in sales as:
[tex]\begin{gathered} D=11\cdot B(12)-11\cdot C(12) \\ D=11\cdot(8\cdot12+9)-11\cdot(6\cdot12-1) \\ D=11\cdot(96+9)-11\cdot(72-1) \\ D=11\cdot105-11\cdot71 \\ D=1155-781 \\ D=374 \end{gathered}[/tex]Answer: he would have made $374 more in sales from buttered popcorn than from caramel popcorn.
Convert compressions to simplified faction or integer. If it’s not a real number, enter None
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Given an expression:
[tex](-81)^{\frac{1}{4}}[/tex]We have to simplify the expression, if it does not result in a real number then the answer is NONE.
Let:
[tex]x=(-81)^{\frac{1}{4}}[/tex]Then,
[tex]\begin{gathered} x=(-81)^{\frac{1}{4}} \\ \Rightarrow x^4=((-81)^{\frac{1}{4}})^4 \\ \Rightarrow x^4=-81 \end{gathered}[/tex]There is no real number whose power 4 is a negative number.
Thus, the answer is not a real number. The answer is NONE.
micrometers, T is measured in seconds, and D accounts for the weakening of the earthquake due to the distance from the epicenter.
If an earthquake occurred for 4 seconds and D = 2, which graph would model the correct amount on the Richter scale?
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The graph that can be used to model the correct amount on the Richter scale is r = log(a/4) + 2.
How to illustrate the information?It should be noted that the magnitude of an earthquake is gotten by using the equation:
r = log(a / t) + d.
where
r = magnitude of an earthquake
a = amplitude
t = time
d = distance.
In this case, the earthquake occurred for 4 seconds and D = 2. We'll substitute the value into the equation and this will be r = log(a/4) + 2.
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Find the solution of the system of equations.6x – 3y = -303x – 6y = 12
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6x - 3y = -30 -------------------------------(1)
3x - 6y = 12 ---------------------------------(2)
Multiply through equation(1) by 3 and then multiply through equation (2) by 6
18x - 9y = - 90 ---------------------------------(3)
18x - 36y = 72 ----------------------------------(4)
subtract equation (4) from equation (3)
This figure shows a circle with a radius of 3.
A circle with its radius labeled as 3.
What is the circumference of the circle?
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The circumference of the circle has a value of 18.86 units
How to determine the circumference of the circle?From the question, we have the following parameters:
Radius, r = 3 units
The circumference of the circle can be calculated using the following circumference formula
C = 2πr
Where
π = 22/7 (a constant)
r = 3
Substitute the known values in the above equation
So, we have the following equation
C = 2 * 22/7 * 3
Evaluate the products
So, we have the following equation
C = 18.86
Hence, the circumference is 18.86 units
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A combined total of 598 hamburgers and cheeseburgers were sold. There were 52 fewer cheeseburgers sold in hamburgers. How many hamburgers were sold
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explanation:
598-52 = 546
Evaluate. 43⋅(100÷25)−50 Enter your answer in the box.
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Answer:
122
Step-by-step explanation:
43 * (100/25) - 50
43 * 4 - 50
172 - 50
122
Hope this helps! :)
A sequence is defined recursively using the formula f(n+1) =-0.5f(n) . If the first term of the sequence is 120, what is f(5)?
−15
−7.5
7.5
15
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Suppose we have the recursive formula of sequence, [tex]\displaystyle{f(n+1)=0.5f(n)}[/tex]. From this formula, we know that:
[tex]\displaystyle{f(2)=0.5f(1)}\\\\\displaystyle{f(3)=0.5f(2)}\\\\\displaystyle{f(4)=0.5f(3)}\\\\\displaystyle{f(5)=0.5f(4)}[/tex]
Since the first term of sequence is 120. Therefore, [tex]\displaystyle{f(1)=120}[/tex]. Since [tex]\displaystyle{f(4)=0.5f(3)}[/tex] then substitute in [tex]\displaystyle f(5)[/tex]:
[tex]\displaystyle{f(5)=0.5\cdot 0.5f(3)}[/tex]
Then substitute f(3) down to f(1):
[tex]\displaystyle{f(5)=0.5\cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 120}\\\\\displaystyle{f(5)=(0.5)^4\cdot 120}\\\\\displaystyle{f(5)=7.5}[/tex]
Therefore, f(5) = 7.5
A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is not yellow
P(not yellow)
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The probability that it is not yellow candies will be 119/139.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
A bag contains;
Number of red candies = 42
Number of green candies = 45
Number of yellow candies = 20
Number of purple candies = 32
Now,
Total number of candies in a bag = 42 + 45 + 20 + 32
= 139
And, The number of candies in a bag not contain yellow candy
= 139 - 20
= 119
Thus, The probability that it is not yellow candies will be;
Probability = Number of not yellow candies / Total candies
= 109 / 139
Therefore, The probability that it is not yellow candies will be 119/139.
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Help solve this problem it's 8th grade math identifying coordinates on a graph
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Answer:
C -9, -4
E -8, 4
G-4, 0
I-6, -8
B0, 0
D-16, 4
F-2, 9
H0, 7
J9,-2
Quadrilatral ABCD has the following vertices
A(-6,-2)
B(-4,4)
C(8,1)
D(6,-6)
Angle a is right angle
is ABCD a rectangle
pls help i will give brainliest
Answers
From the calculations below, we can tell that quadrilateral ABCD is not a rectangle because AB is not parallel to CD
How to Identify a rectangle?
We are given that the quadrilateral is ABCD with the vertices as;
A(-6,-2)
B(-4,4)
C(8,1)
D(6,-6)
We are further told that Angle A is a right angle. Thus;
AB must be perpendicular to AD.
Secondly, for ABCD to be a rectangle, AB must be parallel to CD. Thus;
By slope formula, for AB and CD are gotten from the formula;
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope of CD = (-6 - 1)/(6 - 8)
Slope of CD = -7/-2 = 7/2
Slope of AB = (4 - (-2))/(-4 - (-6))
Slope of AB = 6/2
Slope of AB = 3
Since Slope of AB and AC are not equal then ABCD is not a rectangle.
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Write two expressions that represent the volume of the cube, one with exponents and one without. The side of the cube is the fraction 3/5.
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(3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5.
1.) For the first expression with exponents:
(3/5)to the power of 3 can be written as , where the number 3/5 is called the base, and 3 is the power or exponent of the expression. So (3/5) times 3 .
Where, Side of the cube (a) = 3/5
⇒ (3/5)^3
⇒ 0.216 cube.units
2.) For the second expression without exponents:
The formula of volume of the cube is given by volume(side) =a*a*a, where a is the length of its sides or edges.
Cube ⇒ ( 3/5 × 3/5 × 3/5)
Cube ⇒ 0.216 cube.units
Cube of having side (3/5) = 0.216 cube.units
Hence, (3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5 .
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The quotient of 1 and the square of a number. Write it as an expression
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Answer:
1 ÷ [tex]\sqrt{n\\}[/tex] = x
Step-by-step explanation:
For the given, "the quotient of 1 and the square of a number", the expression is 1+√n
What is a mathematical expression?
A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, Mathematicians have the ability to multiply, divide, add, and subtract. A mathematical operator, a number or variable, and an expression make up an expression.
The phrase "The quotient of 1 and the square of an integer" is presented.
The dividend and the amount being divided by the divisor are, respectively, referred to as the dividend and the amount being divided by it. The quotient is created by dividing the result.
If n is the number the expression can be written as,
=1+√n
Thus, for the given expression the expression is 1+√n.
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Drop down options for 1 2 and 4 are Forest A or Forest B
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Given :
[tex]A(t)=107(1.015)^t[/tex][tex]B(t)=88(1.025)^t[/tex]1)
Set t=1 we get
[tex]A(t)=107(1.015)^t[/tex]in the figure shown Line O is parallel to line P and line M is Parallel to linea N
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we have that
In this problem angle x and angle of 62 degrees are supplementary angles
that means
x+62=180
solve for x
x=180-62
x=118 degrees8. Tabitha made 12 out of 23 free throw attempts in the first half of practice and 20 out
of 27 attempts in the second half of practice. What is her free throw average for the
whole practice, written as a decimal?
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Answer: 0.64 ...........