Answer:
x = 3/2 , y = -1
Step-by-step explanation:
I'm assuming that you are being asked to solve the system of equations for x and y.
given:
4x- 2y = 8 ---------------(1)
2x + y =2 -----------------(2)
We can solve this by elimination:
multiple (2) by 2, we get:
2(2x + y) =2(2)
4x + 2y = 4 ------------(3)
(1) + (3) , we get:
(4x- 2y) - (4x + 2y) = 8 + 4
8x = 12 (divide both sides by 8)
x = 12/8
x = 3/2 answer, substitute this into (2)
2(3/2) + y =2
3 + y = 2 (subtract 3 from both sides)
y = 2 - 3
y = -1 answer
Please solve thank you Jesus loves you
lynn had 14 grapes. she ate 8 of them. she wants to eat 6 more grapes. will lynn have enough grapes? Explain.
Yes she will be left with 0 grapes
Step-by-step explanation:
14-8=6 6-6=0
Which order pair is a solution of y=4x-3?
Answer:
4x-y=3
Step-by-step explanation:
IT'S standard form
A right triangle, DEF, is shown below.
What is sin FDE?
Answer:
sin ∠FDE is 12/13
Step-by-step explanation:
The trigonometric ratios will be used to find the value of sin∠FDE
In the given triangle, according to angle FDE
Base = DE = 5
Hypotenuse = DF = 13
Perpendicular = EF = ?
sin ∠FDE = [tex]\frac{perpendicular}{Hypotenuse} = \frac{EF}{DF}[/tex]
We have to find the length of DF first
Pythagoras theorem will be used as the given triangle is a right angled triangle
[tex](Hypotenuse)^2 = (Base)^2+(perpendicular)^2\\(DF)^2 = (DE)^2+(EF)^2\\(13)^2 = (5)^2 + EF^2\\169 = 25+EF^2\\EF^2 = 169-25\\EF^2 = 144\\\sqrt{EF^2} = \sqrt{144}\\EF = 12[/tex]
So,
sin ∠FDE = EF/DF
sin ∠FDE = 12/13
Hence,
sin ∠FDE is 12/13
Which of these could be the lengths of side of a right triangle?
Answer:
c
Step-by-step explanation:
reason:
5^2+12^2=13^2
Answer:
c
Step-by-step explanation:
1. square the two smaller numbers and add them (5^2 + 12^2 = 169)
2. Take the square root of answer ( 13 )
lillian is a business woman of manufacturing phones. she must pay a daily fixed cost to rent the building and equipment and also pays a cost per phone produced for materials and labor. let c represent the total cost in dollars of producing p phones in a given day. the table below has select values showing the linear relationship between p and c. determine fixed cost for rent and equipment?
P: 2,4,6
C: 1200, 1400, 1600
Answer:
1000 dollars
Step-by-step explanation:
Given
P: ---2 -----,4 ----,6
C: 1200, 1400, 1600
Required
Calculate the fixed cost
First, we need to determine the equation that determines the relationship between P and C
We start by selecting any two corresponding values of P and C
We have that:
[tex](P_1,C_1) = (2,1200)[/tex]
[tex](P_2,C_2) = (6,1600)[/tex]
Calculate the slope, using:
[tex]m = \frac{C_2 - C_1}{P_2 - P_1}[/tex]
[tex]m = \frac{1600 - 1200}{6 - 2}[/tex]
[tex]m = \frac{400}{4}[/tex]
[tex]m = 100[/tex]
The equation is then calculated using:
[tex]C - C_2 = m(P - P_2)[/tex]
Where
[tex]m = 100[/tex] and
[tex](P_2,C_2) = (6,1600)[/tex]
[tex]C - 1600 = 100(P - 6)[/tex]
[tex]C - 1600 = 100P - 600[/tex]
Collect Like Terms
[tex]C = 100P - 600 +1600[/tex]
[tex]C = 100P + 1000[/tex]
From the equation above,
100P represents the amount paid for P phones produced
1000 represents the fixed cost paid
C represents the total amount paid
Andy went on a hike and finished at 1:30 P.M. He hiked for 1 hour and 5 minutes. What time did he start?
Answer:
12:25
Step-by-step explanation:
Answer:
12:25 p.m
Step-by-step explanation:
1:30 - 1 hour = 12:30
12:30 - 5 minutes = 12:25
I hope this helped, please mark Brainliest, thank you!! :)
Could you help me please with the answer: 2 + 2 / 4 - 9 % 2 = ?
Answer:
-4/25
Step-by-step explanation:
(Giving branliest on this 1 !! :D)
Solve five and four tenths times two.
A) ten and four twentieths
B) ten and four tenths
C) ten and eight tenths
Answer:
I am not sure if I am correct but I think it is ten and eight tenths too not a 100% sure
Answer:
its 10 8/10 :) <3
Step-by-step explanation:
The isosceles triangle below has height AQ of length 3 and base BC of length 2. A point P may be placed anywhere along the line segment AQ. What is the minimum value of the sum of the lengths of AP, BP, and C
The question is missing parts. Here is the complete question.
The isosceles triangle below has height AQ of length 3 and base BC of length 2. A point P may be placed anywhere along the line segment AQ.
What is the minimum value of the sum of the lengths of AP, BP and CP?
Answer: The sum is 4.73.
Step-by-step explanation: Height of a triangle is a perpendicualr line linking a vertex and its opposite side.
Because triangle ABC is isosceles, point Q divides the base in 2 equal parts:
BQ = CQ = 1
Suppose QP = x
To calculate minimum value of the sum:
AP = AQ - QP
AP = 3 - x
Since triangles BQP and CQP are congruent and right triangles, use Pythagorean Theorem to figure out the value of BP and CP:
BP = CP = [tex]\sqrt{BQ^{2}+PQ^{2}}[/tex]
BP = [tex]\sqrt{1+x^{2}}[/tex]
Then, sum of AP, BP and CP is
[tex]f(x)=3-x+2\sqrt{1+x^{2}}[/tex]
The minimum value is calculated using first derivative:
[tex]f'=-1+\frac{2x}{\sqrt{x^{2}+1} }[/tex]
The value of x is limited: it can assume value of 0, when P=A and x=3, when P=Q. So, interval is [0,3].
x has value:
[tex]-1+\frac{2x}{\sqrt{x^{2}+1} }=0[/tex]
[tex]2x=\sqrt{x^{2}+1}[/tex]
[tex]4x^{2}-x^{2}-1=0[/tex]
[tex]3x^{2}=1[/tex]
x = ± [tex]\frac{1}{\sqrt{3} }[/tex]
x can't assume negative value because is not in the interval:
x = [tex]\frac{1}{\sqrt{3} }[/tex]
To find the minimum value of the sum, substitute x in the function above:
f([tex]\frac{1}{\sqrt{3} }[/tex])=[tex]3-\frac{1}{\sqrt{3} } +2\sqrt{1+(\frac{1}{\sqrt{3} })^{2} }[/tex]
[tex]f(\frac{1}{\sqrt{3}} )=3-\frac{1}{\sqrt{3}}+2(\sqrt{\frac{4}{3} } )[/tex]
[tex]f(\frac{1}{\sqrt{3}} )=3-\frac{1}{\sqrt{3}} +\frac{4}{\sqrt{3}}[/tex]
[tex]f(\frac{1}{\sqrt{3}} )=3+\frac{3}{\sqrt{3} }[/tex]
[tex]f(\frac{1}{\sqrt{3}} )=4.73[/tex]
The minimum value of the sum of AP, BP and CP is 4.73.
The minimum value of the sum of the lengths of AP, BP and CP is [tex]3 + \frac{\sqrt{3}}{3}[/tex] units.
According to this statement we must determine the sum of the line segment lengths so that a minimum is found. By Pythagorean theorem and given data we have the following expression:
[tex]y = AP + BP + CP[/tex]
[tex]y = 3-x +2\sqrt{x^{2}+1}[/tex] (1)
Now we proceed to find the critical values by performing first and second derivative tests.
FDT
[tex]-1 +\frac{2\cdot x}{\sqrt{x^{2}+1}} = 0[/tex]
[tex]2\cdot x = \sqrt{x^{2}+1}[/tex]
[tex]4\cdot x^{2}-x^{2}-1=0[/tex]
[tex]3\cdot x^{2} = 1[/tex]
[tex]x^{2} = \frac{1}{3}[/tex]
[tex]x = \frac{\sqrt{3}}{3}[/tex]
SDT
[tex]y'' = \frac{2\cdot \sqrt{x^{2}+1}-2\cdot x \cdot \left(\frac{2\cdot x}{\sqrt{x^{2}+1}} \right)}{x^{2}+1}[/tex]
[tex]y'' = \frac{2\cdot x^{2}+2-4\cdot x^{2}}{(x^{2}+1)^{3/2}}[/tex]
[tex]y'' = 2\cdot \frac{1-x^{2}}{(x^{2}+1)^{3/2}}[/tex]
[tex]y'' \approx 0.866[/tex]
A minimum exists when [tex]y'' > 0[/tex], then we conclude that [tex]x = \frac{\sqrt{3}}{3}[/tex] lead to a relative minimum. And by (1) we have the minimum sum:
[tex]y = 3-\frac{\sqrt{3}}{3}+2\sqrt{\frac{4}{3} }[/tex]
[tex]y = 3 - \frac{\sqrt{3}}{3} +\frac{4\sqrt{3}}{3}[/tex]
[tex]y = 3+\frac{\sqrt{3}}{3}[/tex]
The minimum value of the sum of the lengths of AP, BP and CP is [tex]3 + \frac{\sqrt{3}}{3}[/tex] units.
Nota - The statement reports typographical issues, the correct form is presented below:
The isosceles triangle below has height AQ of length 3 and base BC of length 2. A point P may be placed anywhere along the line segment AQ. What is the minimum value of the sum of the lengths of AP, BP and CP.
We kindly invite to check this question on maxima and minima: https://brainly.com/question/12870574
Find the value of x. Then tell whether the side lengths from a Pythagorean triple sides 20,16 find x
Answer:
x = 12
Step-by-step explanation:
Pythagorean triplet
12,16,20
So, the value of x is 12
x + 256 = 400
x = 400 - 256
x = 144
The square of 12 is 144
PLEASE HELP ME OUTTTTTTTTT
===============================================
Work Shown:
Subtract the time values
131.25 - 119.5 = 11.75
This rounds to 12 when rounding to the nearest whole number.
This means she ran about 12 minutes faster. Since she ran 12 miles, this tells us she ran about 12/12 = 1 minute faster per mile.
The more accurate amount is 11.75/12 = 0.97916666666667 and we can see this is fairly close to 1. If we round to the nearest whole number, then we would get 1.
Factor the algebraic expression 4x + 12y.
how do i give brainiest ill give it
Help me out ASAP please
Answer:
4(x+3y)
Step-by-step explanation:
factor 4 out of 4x and 12 y
help!! attachment below!
Answer:
4800
Step-by-step explanation:
In 10 seconds his wings will flap 800 times!
So in 60 seconds his wings will go 6 times more frequently.
10 /800 = 60/x
10 x = 800 * 60
10 x = 48000
x = 48000/10
x = 4800
Write down step by step the process that you use
to solve multiplying a fraction by an integer.
Answer:
you place the 1 under the integer and follow the steps keep change it flip it . SO basically you keep the integer and the 1 and you change the sign to division and you place the numerator where the denominator is and the denominator goes where the numerator is.
Step-by-step explanation:
Find the equation, in standard form, of the parabola going through (-2,4),(0,-4), and (2,4). What is a + b + c?. There is no visual. I NEED THIS ASAP
Answer:
y = 2x^2 - 4a + b + c = -2Step-by-step explanation:
Parabola is the graph of a quadratic function:
y = ax^2 + bx + cGiven points:
(-2,4), (0,-4) and (2,4)Substituting the points:
1.
4 = a(-2)^2 + b(-2) + c ⇒ 4 = 4a - 2b + c ⇒ 4a -2b + c = 42.
-4 = a*0 + b*0 + c ⇒ c = -43.
4 = a(2)^2 + b(2) + c ⇒ 4 = 4a + 2b + c ⇒ 4a + 2b + c = 4Considering c = -4 in the other equations:
4a - 2b - 4 = 4 ⇒ 4a - 2b = 8and
4a + 2b - 4 = 4 ⇒ 4a + 2b = 8Comparing the above two equations:
4a - 2b = 4a + 2b ⇒ 4b = 0 ⇒ b = 0Then finding a:
4a = 8 ⇒ a = 2So we have equation:
y = 2x^2 - 4and
a + b + c = 2 + 0 - 4 = -2
A movie theater complex gave a poll as viewers exited from two theaters showing the same film. They had a 20% response rate from the people in theater A and a 30% response rate from the people in theater B. There were 800 people in total in theaters A and B.
Part A: It was estimated that an equal number of people from each theater responded to the poll. If this was the case, how many people in total would have been in theater A?
Part B: In reality, 440 people were in theater A and 360 people were in theater B. What was the total response rate for the poll? Express your answer as a percentage.
Answer:
Let´s define the variables:
x = number of people in theater A
y = number of people in theater B
We know that a 20% (or 0.2 in decimal form) of the people in theater A answered the survey, then the number of people from theater A that answered the survey is: Na = 0.2*x
We know that a 30% (or 0.3 in decimal form) of the people in theater B answered the survey, then the number of people from theater B that answered the survey is: Nb = 0.3*y
There where 800 people in total (counting from the two theatres)
Then x + y = 800.
A) In this case we have:
Na = Nb
this means that:
0.2*x = 0.3*y
and we also have the equation:
x + y = 800
To solve this, we need to isolate one variable in one of the equations, i will isolate x in the second equation:
x = 800 - y
And now we can replace this in the other equation to get:
0.2*(800 - y) = 0.3*y
We need to solve this for y:
160 - 0.2*y = 0.3*y
160 = 0.3*y + 0.2*y = 0.5*y
160/0.5 = y = 320
Then there where 320 people in theater B, and:
x + y = 800
x + 320 = 800
x = 800 - 320 = 480
There where 480 people in theather A.
B) Now we have:
x = 440
y = 360
then:
Na = 0.2*440 = 88
In theater A, 88 people answered the survey.
Nb = 0.3*360 = 108
In theater B, 108 people answered the survey.
In total, 88 + 108 = 196 people answered the survey.
which pair of factors of 8 has a sum of 9
Answer:
jbbhhhhhhhhhhhhhhhhh,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Step-by-step explanation:
Ade is baking mini-loaves of bread. How many mini-loaves could he make with 10 cups of flour?
12.5
15
25
50
Answer
10
Step-by-step explanation:
it takes 3/4 of a cup to make a mini loaves of bread and 3/4 is about one cup so 10
The number of mini-loaves that he could make with 10 cups of flour will be 25 cups.
From the complete information, it was stated that 1 cup of flour can be used to make 2.5 loaves.
Therefore, based on the information given, in order to calculate the number of mini-loaves that he could make with 10 cups of flour, we've to multiply the values. This will be:
= 2.5 × 10 = 25
In conclusion, the correct option is 25 cups.
Read related link on:
https://brainly.com/question/15546607
(4x3 + 3x2 + 2x + 1)
(3 + 2)
Answer:
26 is the answer. am I right?
2. Last year, Springfield Middle School had 620
students. This year, it has 582 students. To the nearest
tenth, what is the percent of decrease?
A) 6.1%
B) 6.6%
C) 93.9%
D) 106.5%
Answer: A
Step-by-step explanation: In all logic its only a 40 soemthing difference and its a bigger number so my guess is 6.1
The percentage decrease in the number of students will be 6.6%. The correct option is B.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that last year, Springfield Middle School had 620 students. This year, it has 582 students.
The percentage decrease will be calculated as:-
Percentage decrease = ( 620 - 582 ) / 582
Percentage decrease = ( 38 / 582) = 0.0652
Percentage decrease = 0.0652 x 100 = 6.52% ≅ 6.6%
Therefore, the percentage decrease in the number of students will be 6.6%. The correct option is B.
To know more about percentages follow
https://brainly.com/question/24304697
#SPJ5
PLEASE EXPLAIN
Yvonne wants to rent a kayak for 7 hours. How much would this cost at each company? Which one should she choose?
Answer: IT will cost $63
Step-by-step explanation:
hope it helps.
At noon, a tank contained 20 in. of water. After several hours, it contained 16 in. of water. What is the percent decrease of water in the tank
Answer:
20 percent decrease
Step-by-step explanation:
it lost 4 inches of water (20-16) and 4 is a fifth of 20. a fifth is 20 percent so it is a 20 percent decrease
You are most likely to encounter an irrational number when you're
Answer:
working with circles (using pi for circumference, area, etc)
Your friend thinks that the equation -3.3 = 21 is a true statement. Is your friend correct? Explain.
Hope this helps!!
John left the museum and drove south at a rate of 55 mph. Sally left four hours later driving 10 mph faster than John in an effort to catch up to him. How
long did Sally have to drive to catch up with John?
28 hours
22 hours
20 hours
18 hours
Answer:
22 hours (B)
Step-by-step explanation:
John's velocity = 55mph
Sally's velocity = 65mph
John's time taken = x
Sally's time taken = x - 4
since they must cover the same distance.
and, distance = vel × time
Sally's vel × time = John's vel × time
55x = 65(x-4)
55x = 65x - 220
-10x = -220
x = 22 hours.
Therefore, Sally catches up after 22 hours
Noah bought 4 tacos and paid $6. At this rate how many tacos could he buy for 15$
PLEASE HELP!!! URGENT!
Let f(x)=x√ and g(x)=2x.
Use the composition of functions to determine if f(x) and g(x) are inverse functions.
Drag and drop the answers into the boxes to correctly complete each statement.
Answer:
1st one is "square root of 2x"
2nd one is "2 square root of x"
3rd one is "is not"
Step-by-step explanation:
1st one: you have 2x for g(x) then you plug that into the x for f(x) giving you square root of 2x
2nd one: you have square root of x for f(x) then you plug that into the x for g(x) giving you 2 square root of x
3rd one: the inverse of the square root of x is x^2
The function [tex]\rm f(g(x)) = \sqrt{2x}[/tex] and the function [tex]\rm g(f(x)) =2\sqrt{x}[/tex] and the function f(x) is not the inverse of g(x) and this can be determined by using the given data.
Given :
[tex]\rm f(x) = \sqrt{x}[/tex][tex]\rm g(x) = 2x[/tex]The following steps can be used in order to determine the f(g(x)) and g(f(x)):
Step 1 - First write the given functions.
[tex]\rm f(x) = \sqrt{x}[/tex]
[tex]\rm g(x) = 2x[/tex]
Step 2 - Now, the function f(g(x)) is given by replacing x with g(x) in the function f(x).
[tex]\rm f(g(x)) = \sqrt{g(x)}[/tex]
Step 3 - Substitute the value of g(x) in the above expression.
[tex]\rm f(g(x)) = \sqrt{2x}[/tex]
Step 4 - Now, the function g(f(x)) is given by replacing x with f(x) in the function g(x).
[tex]\rm g(f(x)) =2f(x)[/tex]
Step 5 - Substitute the value of f(x) in the above expression.
[tex]\rm g(f(x)) =2\sqrt{x}[/tex]
Step 6 - The inverse of f(x) can be determined by replacing x by f(x) and f(x) by x.
[tex]\rm \sqrt{f(x)} = x[/tex]
[tex]\rm x^2 = f(x)[/tex]
Step 7 - Now, the inverse of g(x) is given by:
[tex]\rm 2g(x) = x[/tex]
[tex]\rm g(x) = \dfrac{x}{2}[/tex]
The function [tex]\rm f(g(x)) = \sqrt{2x}[/tex] and the function [tex]\rm g(f(x)) =2\sqrt{x}[/tex] and the function f(x) is not the inverse of g(x).
For more information, refer to the link given below:
https://brainly.com/question/12431044
Let x = 6. What is the value of the expression 5x2+x−7? Enter your answer in the box.
Answer:
Well the answer would be 9.
Step-by-step explanation:
All you have to do is put 6 in the place of X. So the new equation would be 5x2+6-7, and all you do is solve that. So multiply 5 and 2 to get 10, than add 10 to 6 and get 16, 16 minus 7 to get your answer of 9.
Hope this is right, pls tell me and sorry its so late lol
In ΔXYZ, the measure of ∠Z=90°, ZY = 4, XZ = 3, and YX = 5. What ratio represents the tangent of ∠X?
Answer: 4/3
Step-by-step explanation:
you're finding the tangent of X which is at the top so you do opposite over adjacent