Solution:
Given system of equations are:
[tex]\frac{1}{4}x + \frac{1}{8}y =2 ---------- eqn\ 1\\\\\frac{1}{3}x + \frac{1}{2}y = 4 -------------- eqn\ 2[/tex]
We have to find value of y
From eqn 1,
[tex]\frac{1}{4}x + \frac{1}{8}y =2 \\\\2x + y = 2 \times 8\\\\2x + y = 16 ---- eqn\ 3[/tex]
From eqn 2,
[tex]\frac{1}{3}x + \frac{1}{2}y = 4\\\\2x + 3y = 4 \times 6\\\\2x + 3y = 24 ------ eqn\ 4[/tex]
Subtract eqn 3 from eqn 4
2x + 3y = 24
2x + y = 16
( - ) -----------------
2y = 8
y = 4
Thus value of y is 4
How much work is done lifting a 5 kg ball from a height of 2 m to a height of 6 m? (Use 10 m/s for the acceleration
of gravity)
19
In physics, work is defined force that causes displacement. So this can be expressed by the following equation:
[tex]W=Fs[/tex]
Where:
[tex]F:Force \\ \\ s:Displacement[/tex]
The force can be found as:
[tex]F=ma \\ \\ F=5(10)=50N[/tex]
And for the displacement:
[tex]s=6-2=4m[/tex]
The force (weight) is down and the displacement is up, then the work must be negative. So:
[tex]W=-(50)(4) \\ \\ \boxed{W=-200J}[/tex]
What is the justification for step 1 in the solution process?
8x + 15 = 11x + 2
Step 1: 8x = 11x − 13
A.
the division property of equality
B.
the addition property of equality
C.
the subtraction property of equality
D.
the multiplication property of equality
HURRY PLEASE U GET 15 POINT PLEASE HURRY THO
Step 1 used C) the subtraction property of equality to subtract 15 from both sides of the initial equation.
Explanation:In step 1 of the solution process to the equation 8x + 15 = 11x + 2, the C) subtraction property of equality is used.
This property states that if you subtract the same number from both sides of an equation, the equation remains balanced. In this case, 15 was subtracted from both sides to get 8x = 11x - 13.Learn more about Subtraction Property of Equality here:https://brainly.com/question/33218308
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To find the height of the Eiffel Tower, Antoine placed a mirror of 500 meters away from the tower. He then positions himself so the top of the tower is visible in the mirror. He is standing 2.75 meters from the mirror and his eyes are 1.8 meters off the ground. How y’all is the tower?
984′, 1,063′ to tip.
the ' is feet
The required height of the Eiffel Tower is given as 327.27 meters.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Let the height of the Eiffel tower be x,
According to the question,
The ratio of the height to the base of the Eiffel tower is equal to the ratio of height to the
base of men,
x / 500 = 1.8 / 2.75
x = 327.27 meters
Thus, the required height of the Eiffel Tower is given as 327.27 meters.
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The box plots show the average gas mileage, in miles per gallon, of the cars sold at a dealership in June and in December.
Gas Mileage of Cars Sold in June
2 box plots. The number line goes from 14 to 34. For cars sold in June, the whiskers range from 21 to 33, and the box ranges from 22 to 29. A line divides the box at 24. For Cars sold in December, the whiskers range from 14 to 26, and the box ranges from 18 to 21. A line divides the box at 19.
Gas Mileage of Cars Sold in December
Which inference can be made about the cars?
The type of cars sold in June typically gets better gas mileage.
The type of cars sold in December typically gets better gas mileage.
The types of cars sold in the two months typically get about the same gas mileage.
The types of cars sold in the two months typically get better gas mileage than those sold in other months.
PLS HELP! THANKS
Since both have the same interquartile range, the inference made would be: types of cars sold in the two months typically get about the same gas mileage.
What is the Interquartile Range?The interquartile range is a measure of variability, which can be used in comparing two data distribution.
Interquartile range = Q3 - Q1.
Interquartile range for gas mileage of cars sold in June = 33 - 21 = 12.
Interquartile range for gas mileage of cars sold in December = 26 - 14 = 12.
Therefore, since both have the same interquartile range, the inference made would be: types of cars sold in the two months typically get about the same gas mileage.
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Answer: Its C.
Step-by-step explanation:
Edge 2022
1,5947 + 2001 find the answer
Answer:
2002.5947
Step-by-step explanation:
I did the calculations :)
Norma has 9 pies to divide among 4 friends. How many pies will each friend receive if all of the pies must be used and can be divided into smaller parts? A. 2/9 pie B. 4/9 pie C. 1 1/4 pies D. 2 1/4 pies
Answer:
D. 2 1/4
Step-by-step explanation:
Answer: D: 2 1/4
Step-by-step explanation:
Mark me 5 star pls
Is 11.250 greater or less or equal to 11.25
Answer:
Equal, 250 and 25 are both 1/4
Step-by-step explanation:
Answer: 11.250 is equal to 11.25
Step-by-step explanation:
The value of 0 behind is insignificant
What is the median house price?
$750,000
$764,000
$880,000
$1,200,000
Submit
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OEM W
Answer: $822,000
Step-by-step explanation:
Median of even numbers is the average of two middle most numbers
From the question, median
= $764,000 + $880000 ÷ 2
= $1,644,000÷2
$822,000
The graph of a linear function h contains the points given in the table below.
Find hl.
Answer:
21
Step-by-step explanation:
find the value of b
b-12=46
Answer:
b=58
Step-by-step explanation:
b-12=46
b=46+12
b=58
y = -2x + 8x – 5
quadratic equation
Answer:
x=5/6 or x=.83
Step-by-step explanation:
Answer; y= 6x-5
Step-by-step explanation:
Write the linear equation given two points (-6, 8) and (3, -7). *
[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-6)}}}\implies \cfrac{-15}{3+6}\implies \cfrac{-15}{9}\implies -\cfrac{5}{3}[/tex]
[tex]\bf \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}{8}=\stackrel{m}{-\cfrac{5}{3}}[x-\stackrel{x_1}{(-6)}]\implies y-8=-\cfrac{5}{3}(x+6) \\\\\\ y-8=-\cfrac{5}{3}x-10\implies y = -\cfrac{5}{3}x-2[/tex]
Answer:
[tex]m=\frac{-5}{3}[/tex]
Step-by-step explanation:
Step 1: Let's find the slope between your two points.
[tex](-6,8); (3,-7)\\\\(x_{1} ,y_{1} )=(-6,8)\\\\(x_{2} ,y_{2} )=(3,-7)[/tex]
Step 2: Use the slope formula
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }\\\\=\frac{(-7) - 8}{3- (-6)} \\\\=\frac{-15}{9}\\\\= \frac{-5}{3}[/tex]
Therefore, the equation is [tex]\frac{-5}{3}[/tex]
Convert the angle 0= 9pi/5 radians to degrees
[tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .
Step-by-step explanation:
Degrees are a unit of angle measure. A full circle is divided into 360 degrees. For example, a right angle is 90 degrees. A degree has the symbol ° and so ninety degrees would written 90°. Another unit of angle measure is the radian.
The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.
We know that 1 radian = 180°/[tex]\pi[/tex] . So [tex]\frac{9\pi }{5}[/tex] radians is equal to :
⇒ [tex]\frac{9\pi }{5}(\frac{180}{\pi } )[/tex]
⇒ [tex]\frac{9(180) }{5}[/tex]
⇒ [tex]9(36)[/tex]
⇒ [tex]324[/tex]°
Therefore , [tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .
To convert 9pi/5 radians to degrees, multiply by the conversion factor of 180°/π, resulting in 324 degrees.
Explanation:To convert the angle 0 = 9pi/5 radians to degrees, we need to use the relationship between radians and degrees. Recall that 360° = 2π radians. Consequently, to convert radians to degrees, we can multiply by a conversion factor of 180°/π. Using this conversion factor, the computed angle in degrees is:
9π/5 radians × (180°/π) = 9/5 × 180° = 9 × 36° = 324°
Therefore, the angle of 9π/5 radians is equivalent to 324 degrees.
5x + 2y=7
- 2x + 6y=9
Answer:
x = [tex]\frac{12}{17}[/tex] or 0.706
[tex]y = \frac{59}{34}[/tex] or 1.735
Step-by-step explanation:
5x + 2y=7 ----->(eq 1)
- 2x + 6y=9 ----->(eq 2)
Multiply (eq 1) with 3
3×(5x + 2y) = 3×7
15x + 6y = 21 ----->(eq 3)
substract (eq 3) from (eq 2)
- 2x + 6y - (15x + 6y) = 9-21
- 2x + 6y - 15x - 6y = 9-21
- 2x - 15x + 6y - 6y = 9-21
-17x = -12
x = -12 ÷ -17
x = [tex]\frac{12}{17}[/tex]
put x = [tex]\frac{12}{17}[/tex] in (eq 1)
[tex]5*\frac{12}{17} + 2y = 7[/tex]
[tex]2y = 7- 5*\frac{12}{17}[/tex]
[tex]2y = \frac{7*17 - 60}{17}[/tex]
[tex]2y = \frac{119- 60}{17}[/tex]
[tex]2y = \frac{59}{17}[/tex]
[tex]y = \frac{59}{17*2}[/tex]
[tex]y = \frac{59}{34}[/tex]
What is the length of EF in the triangle? Show your work. HELP!
The length of EF in the given triangle is 8.80 m.
Step-by-step explanation:
Step 1:
In the given triangle, the opposite side's length is 16.2 m, the adjacent side's length is x m while the triangle's hypotenuse measures 16.2 m units.
The angle given is 90°, this makes the triangle a right-angled triangle.
So first we calculate the angle of E and use that to find x.
Step 2:
As we have the values of the length of the opposite side and the hypotenuse, we can calculate the sine of the angle to determine the value of the angle of E.
[tex]sinE = \frac{oppositeside}{hypotenuse} =\frac{13.6}{16.2} = 0.8395.[/tex]
[tex]E = sin^{-1} (0.8395), E = 57.087.[/tex]
So the angle E of the triangle DEF is 57.087°.
Step 3:
As we have the values of the angle and the hypotenuse, we can calculate the cos of the angle to determine x.
[tex]cos E = \frac{adjacentside}{hypotenuse} = \frac{x}{16.2} .[/tex]
[tex]cos(57.087) = 0.5433, x = 16.2 (0.5433) = 8.8014.[/tex]
Rounding this off to the nearest hundredth, we get x = 8.80 m.
Midge arranges her Collection of 762 seashells and two trays with eight shells in each tray Find the number of trays she needs
The number of trays she needs is 94 trays.
Step-by-step explanation:
Total seashells = 762.Number of trays she already has = 2 trays.Number of seashells in each tray = 8 seashells.Number of trays she needs :
Number of seashells already arranged = 2[tex]\times[/tex]8 = 16 seashells.Remaining seashells = 762 - 16 = 746 seashells.Number of trays needed = Remaining seashells / 8
⇒ 746/8
⇒ 93 trays and remaining 2 seashells is arranged in another tray
⇒ 93+1 = 94 trays.
What is the measure of arc ECF in circle G? 52° 98° 158° 177
Answer:
B. 98
Step-by-step explanation:
Have a nice day!
Based on the inscribed angle theorem, the measure of arc ECF in circle (G) is equal to: B. 98 degrees.
What is the inscribed angle theorem?The inscribed angle theorem states that the measure of an inscribed angle whose vertex lies on a circle is half of the intercepted arc subtended at a point on the circle.
Given the following data:
Inscribed angle = 79°Intercepted arc = ∡DFBy using the inscribed angle theorem, we would find the intercepted arc as follows:
∠DEF = ∡DF/2
79 = ∡DF/2
∡DF = 2 × 79
∡DF = 158 degrees.
Now, we can determine measure of arc ECF:
∡ECF + ∡DF + ∡DE = 360
∡ECF + 158 + 104 = 360
∡ECF + 262 = 360
∡ECF = 360 - 262
∡ECF = 98 degrees.
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Please hurry it’s urgent
Answer:5
Step-by-step explanation:
What is the solution of x2-1/x2+5x+4 less than or equal to 0?
Answer:
Fourth answer choice.
Step-by-step explanation:
Start by factoring the numerator and the denominator:
(x - 1)(x + 1)
-----------------
(x + 1)(x + 4)
Note that x can be neither -1 nor -4, since either results in an undefined quotient. These two x-values are critical values because of this. If we cancel the (x + 1) terms, we obtain the result
(x - 1)
--------- for x ≠ -1 and x ≠ - 4
(x + 4)
The next step is to evaluate the given quotient on the three intervals defined by {-4, -1}: (-∞, -4), (-4, -1), (-1, ∞ ). We choose an x-value from within each interval and evaluate the given function at each. Suitable test values include {-10, -3, 0}:
At x = -10, the reduced given quotient (x - 1) / (x + 4) takes on the value (-10 - 1) / (-10 + 4) = -11/(-6), which is positive. Reject this interval, as we want and expect the quotient value to be 0 or less.
At x = -3, we get (-3 - 1) / (-3 + 4), which is negative. The given inequality is true on the interval (-4, -1) (or -4 < x < -1).
At x = 0, we get (0 - 1) / (0 + 4), which is negative, so the inequality is true on (-1, ∞ ).
So the fourth answer choice is the correct one.
Answer:
Answer D
Step-by-step explanation:
Multiply 4.2 • (-1.3).
Answer:
-5.46
Step-by-step explanation:
Hope this helps!
Answer:
-5.46
Step-by-step explanation:
Represent 4.2 as 42/10 and -1.3 as -13/10
Multiply 42 by -13 and then divide by 100.
A credit card customer owes $523.85 they are only able to make a payment of $184.50 how much money does the customer still owe?
Answer:
339.35
Step-by-step explanation:
The amount of money the credit card customer still owes to pay is $339.35.
We are given that,
The amount the credit card customer owes = $523.85.
The amount the credit card customer paid = $184.50.
We have to find the amount of money the credit card customer still owes to pay.
The amount of money the credit card customer still owes to pay :
= The amount the credit card customer owes - The amount the credit card customer paid
= $523.85 - $184.50
= $339.35
Thus, the amount of money the credit card customer still owes to pay after paying $184.50 is $339.35.
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It takes Jill 2 hours to run 14.5 miles at this rate how far could she run in 3 hours
Answer:
21.75
Step-by-step explanation:
i hoped this helped. 14.50 divide-by 2 = 7.25 so 14.50 + 7.25= 21.75
A table has a square top. The area of the table top measures 18 square feet. Find
the length of one side of the table top
Answer:
the answer is about 4.243
Step-by-step explanation:
Squares mean all sides would have the same length. So you just need to find the square root of the area (18) which is about 4.243 and just to check multiply 4.243 by itself and you would get 18.
Final answer:
The length of one side of the table top with an area of 18 square feet is approximately 4.24 feet, as calculated by taking the square root of the area.
Explanation:
To find the length of one side of a table top with an area of 18 square feet, we should understand that a square has all sides of equal length. Therefore, to find the side length of a square, we take the square root of the area. In this case, we have an area of 18 square feet, so the calculation would be √18, which is approximately 4.24 feet. Thus, the length of one side of the table top is approximately 4.24 feet.
I need help with this ASAP
From the options , [tex]4x + 28[/tex] is equivalent to only [tex]4(x+7)[/tex] & [tex]4.x+ 7.4[/tex] and [tex]14+16y-3-y[/tex] is equivalent to only [tex]15y+11[/tex] & [tex]11+15y[/tex] .
Step-by-step explanation:
We have 2 expressions for which we need to check which expression can be further simplified or is equivalent to the same. Lets consider :
Question 1:
[tex]4x + 28[/tex] is given equation, Now we will simply this as :
⇒[tex]4x+28[/tex]
⇒[tex]4(x+7)[/tex]
⇒[tex]4.x+ 7.4[/tex]
From the options , [tex]4x + 28[/tex] is equivalent to only [tex]4(x+7)[/tex] & [tex]4.x+ 7.4[/tex] .
Question 2:
[tex]14+16y-3-y[/tex] is given equation, Now we will simply this as :
⇒[tex]14+16y-3-y[/tex]
⇒[tex]15y+11[/tex]
⇒ [tex]11+15y[/tex]
From the options , [tex]14+16y-3-y[/tex] is equivalent to only [tex]15y+11[/tex] & [tex]11+15y[/tex] .
Use the distributive property to write the following expression in expanded form. 2(b+c)
Answer:
2b + 2c
Step-by-step explanation:
If you distribute the 2 in b and c you will get to separate terms that will be added together. Since they are not like terms they cannot be combined.
The distributive property means you just multiply the outside number by the terms in the parenthesis. So 2 * b and 2 * c
[tex]2(b + c)\\2(b + 2c)[/tex]
Answer:
2b+2c
Step-by-step explanation:
We need to expand this term by multiplying a term and an expression.
The following product distributive property will be used:
A(B+C)=AB+AC
In our example, the resulting expression will consist of 2 terms:
the first term is a product of 2 and b.
the second term is a product of 2 and c.
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Jose and Jayden go to the movie theater and purchase refreshments for their friends. Jose spends a total of $43.25 on 5 bags of popcorn and 4 drinks. Jayden spends a total of $24.25 on 3 bags of popcorn and 2 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer: The equations are as follows;
5p + 4d = 43.25 ————(1) and
3p + 2d = 24.25 ————(2)
Also a bag of popcorn costs $5.25
Step-by-step explanation: We start by assigning letters to the unknown variables. Let a bag of popcorn be p and let one drink be d. The clues given in the question include the cost of buying five bags of popcorn and four drinks which is a total of $43.25. This can be expressed as
5p + 4d = 43.25 ————(1)
Another clue is that three bags of popcorn and two drinks cost $24.25. This also can be expressed as
3p + 2d = 24.25 ————(2)
Now we have a pair of simultaneous equations as follows
5p + 4d = 43.25 ————(1)
3p + 2d = 24.25 ————(2)
We shall use the elimination method since all the unknowns have coefficients greater than 1. Multiply equation one by 3, and multiply equation two by 5 (so as to eliminate ‘p’)
5p + 4d = 43.25 ——— x3
3p + 2d = 24.25 ——— x5
15p + 12d = 129.75 ———(3)
15p + 10d = 121.25 ———(4)
Subtract equation (4) from equation (3) and we have
2d = 8.5
Divide both sides of the equation by 2
d = 4.25.
That means each drink costs $4.25
We can now substitute for the value of d into equation (2)
3p + 2d = 24.25
When d = 4.25
3p + 2(4.25) = 24.25
3p + 8.5 = 24.25
Subtract 8.5 from both sides of the equation
3p = 15.75
Divide both sides of the equation by 3
p = 5.25. This means a bag of popcorn costs $5.25
What is the slope of (4,12) and (-8,2)
Answer:
Slope = [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Slope = [tex]\frac{2 - 12}{-8 - 4}[/tex]
Slope = [tex]\frac{-10}{-12}[/tex]
Slope = [tex]\frac{5}{6}[/tex]
Answer: Slope = [tex]\frac{5}{6}[/tex]
Ally has 4 times as many pencils as Anna Claire. They have 30 pencils in all. How many pencils does Ally have?
T = 30
A = 4c
A + c = T
Anna Claire has 6 pencils. Times 4 makes Ally's pencil count. 4 * 6 = 24
24 + 6 = 30. So, you answer is: Ally has 24 pencils.
Please help with this algebra!! I’m
Answer:
(-4, -1)
Step-by-step explanation:
x = 4y
-4x - y = 17
Plug in 4y for x in the second equation:
-4(4y) - y = 17
Simplify. Remember to follow PEMDAS. Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.
First, multiply 4y with -4:
-4(4y) = -16y
-16y - y = 17
Simplify. Combine like terms:
-16y - y = 17
-17y = 17
Isolate the variable, y. Divide -17 from both sides:
(-17y)/-17 = (17)/-17
y = 17/-17
y = -1
Plug in -1 for y in the first equation:
x = 4y
x = 4(-1)
x = -4
x = -4, y = -1
Answer: (-4, -1)
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I need help with my homework can anyone help me please?
Answer:
For 14 from left to right should be 11 10 10 9 8 6. For 15 is wrong because 4 people jumped 3 feet and 3 people jumped 4 feet