Answer:
5 and - 1
Step-by-step explanation:
2x^2-8x-10=0
a=2,b=-8,c=-10
x1=(-b+sqrt(b^2-4ac))/2a
x1 =(-(-8)+sqrt ((-8)^2-4*2*(-10))/2*2
x1=(8+sqrt (64+80))/4
x1 =(8+sqrt (144))/4
x1=(8+12)/4
x1=20/4
x1 =5
x2=(-b-sqrt(b ^2-4ac)) /2 *a
x2=(8-12)/4
x2=-4/4
x2=-1
What ratio is equivalent to 2/8
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{2}{8}=\dfrac{2\div2}{8\div2}=\boxed{\bf{\dfrac{1}{4}}}}}[/tex]
[tex]\mathsf{Rewrite\ \dfrac{1}{4}\ as\ ratio\ and\ that\ will\ be\ your\ answer!}[/tex]
[tex]\mathsf{\dfrac{1}{4}=\bf{1:4}}[/tex]
[tex]\boxed{\boxed{\bf{Your\ answer: \boxed{\huge\text{\bf{1:4}}}}}}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
What is the value of x in the equation 3x-47=65, when y=4?
0
x=134
0
x=21
0
x=23
0
x=27
Two farmers bought a truck. The first farmer paid 4/5 of the price, and the second paid the rest. The first farmer's share was
$9,600. What was the total price of the truck?
A $10,000
B
$12,000
C
$20,000
D
$25,000
Next >>
C) $12,000
Step-by-step explanation:4/5 = 9600
÷4
1/5 = 2400
4/5 + 1/5 = 5/5 = the whole price
9600 + 2400 = 12000
=$12,000
This graph shows the temperature in Diego's house between noon and midnight one day.
temperature (degrees F)
R
3
TO
1
2
3 4 5 6 7 8 9
time (hours after noon)
10
11
12
Which of the statements below are true statements? Correct the statements that are false to make them
true.
Example:
The highest temperature happened at 9:00. This statement is false. The correct statement is: The
highest temperature happened at 4:00.
A. Time is a function of temperature.
B. The lowest temperature occurred between 4:00 and 5:00.
C. The temperature was increasing between 9:00 and 10:00
D. The temperature was 74 degrees twice, during the 12-hour period.
E. There was a four-hour period during which the temperature did not change.
REMEMBER TO CORRECT WRONG STATEMENTS. YOU GET 1 POINT FOR EACH LETTER, 1 FOR
CORRECT, 1 FOR CORRECTING FALSE STATEMENTS.
The first three statements are false because they are opposite from the data shown in the graph, while the two last statements are true.
To determine whether a statement is true or false, you need to:
Carefully analyze the information of the graph.Read and understand the statement.Compare the information of the statement to the one of the graph.Now, let's analyze each statement:Time is a function of temperature:This statement is false, this is because time does not change with temperature, and therefore time is an independent variable. The corrected statement would be Temperature is a function of time.
The lowest temperature occurred between 4:00 and 5:00:In the graph, you can see the lowest temperature was 67° and this occurred between 11 and 12 p.m. Therefore, the lowest temperature occurred between 11:00 and 12:00.
The temperature was increasing between 9:00 and 10:00:Based on the graph from 9 to 10 p-m the temperature went from 70° to almost 65°. Therefore the temperature was decreasing between 9:00 and 10:00.
The temperature was 74 degrees twice, during the 12-hour period:This statement is true, this temperature occurred at 3:00 and 4:00.
There was a four-hour period during which the temperature did not change:This statement is true, the temperature is the same between 5:00 and 9:00.
Note: This question is incomplete because the graph is missing, here is the graph.
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Doris is going to take a 3-hour-6-minute flight from New York, New York, to
Houston, Texas, that leaves at 10:05 a.m. New York time. If New York is in the
eastern time zone and Houston is in the central time zone, what will be the
local time in Houston when the flight arrives?
Use the following to help you answer the question.
12:00 p.m. eastern time = 11:00 a.m. central time = 10:00 a.m. mountain
time = 9:00 a.m. Pacific time.
O
A. 1:11 p.m.
OB. 2:11 p.m.
O C. 11:11 a.m.
O
D. 12:11 p.m
Answer:
D. 12:11pm
(10:05am + 3hrs 6mins = 1:11pm - 1hr = 12:11pm)
Final answer:
After accounting for the flight duration of 3 hours and 6 minutes and the one-hour time difference due to the Central Standard Time Zone, Doris will arrive in Houston at 12:11 p.m. local time.
Explanation:
Doris is taking a flight from New York to Houston, and we need to calculate the local time of her arrival in Houston after a 3-hour-6-minute flight. To find the answer, we must account for the time zone difference and the duration of her flight. New York is in the Eastern Standard Time Zone, while Houston is in the Central Standard Time Zone, which is one hour behind New York.
Starting from a departure time of 10:05 a.m. in New York, we first add the flight duration which is 3 hours and 6 minutes. This gets us to 1:11 p.m. New York time. Since Houston is one hour behind New York, we subtract one hour from this time to get the local time in Houston, which will be 12:11 p.m.
The correct answer is D. 12:11 p.m. This is the time Doris will arrive in Houston, local time.
URGENT!!!!!!!!
I need the answer to both parts in this screenshot.
Answer:
a) $10
b) 0.1 hours
Step-by-step explanation:
The total amount earned by Cary,E after working h hours is calculated using:
[tex]E=10h[/tex]
The dollars Cary earns per hour is the unit rate, which is $10
If Cary earns $10 per hour, then she earns
$1 in
[tex] \frac{1}{10} hours = 6mins[/tex]
Carry has to work for 0.1 hours to earn $1
what is the equation for this line
The equation of the line is [tex]y=\frac{-1}{5} x-\frac{21}{5}[/tex].
Solution:
The points on the line are (–6, –3) and (4, –5).
[tex]x_{1}=-6, y_{1}=-3, x_{2}=4, y_{2}=-5[/tex]
Slope of the line:
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]$m=\frac{-5-(-3)}{4-(-6)}[/tex]
[tex]$m=\frac{-5+3}{4+6}[/tex]
[tex]$m=\frac{-2}{10}[/tex]
[tex]$m=\frac{-1}{5}[/tex]
Point-slope formula:
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]$y-(-3)=\frac{-1}{5}(x-(-6))[/tex]
[tex]$y+3=\frac{-1}{5}(x+6)[/tex]
[tex]$y+3=\frac{-1}{5} x-\frac{6}{5}[/tex]
Subtract 3 from both sides of the equation.
[tex]$y=\frac{-1}{5} x-\frac{21}{5}[/tex]
The equation of the line is [tex]y=\frac{-1}{5} x-\frac{21}{5}[/tex].
Jared made 12 3/4 cups of snack mix for a party.His guests eat 2/3 of the mix.How manysnack mix did his guest eat?
Answer:
The number of snacks did Jared's guest eat is [tex]12\frac{1}{12}[/tex]Step-by-step explanation:
Given that Jared made [tex]12\frac{3}{4}[/tex] cups of snack mix for a party.
Let x be the cups of snacks mix made by Jared.
Therefore [tex]x=12\frac{3}{4}[/tex]
His guests eat [tex]\frac{2}{3}[/tex] of the mix.
Let y be the guest eated snacks mix
Therefore [tex]y=\frac{2}{3}[/tex]
To find how many snack mix did his guest eat :Let z be the number of snacks did Jared's guest eat
Therefore z=x-y
[tex]z=12\frac{3}{4}-\frac{2}{3}[/tex]
[tex]=\frac{51}{4}-\frac{2}{3}[/tex]
[tex]=\frac{51(3)-2(4)}{4\times 3}[/tex]
[tex]=\frac{153-8}{12}[/tex]
[tex]=\frac{145}{12}[/tex]
[tex]=12\frac{1}{12}[/tex]
Therefore [tex]z=12\frac{1}{12}[/tex]
Therefore the number of snacks did Jared's guest eat is [tex]12\frac{1}{12}[/tex]_ ©K i2f0I2T0J vKwuRtmaU VS^o]fDtNwoaErneH fL`LnCp.H C oAllqla lrriGgQh`t[si hrae`sUeCrevYeKdA.
Volume of Prisms & Pyramids Practice
Find the volume of each figure. Be sure to include the units, and circle or box your answers.
1)
4 in
2)
12 m
10 m
2 in
2 in
2 in
2 in
3)
4 ft
4)
10 yd
8 yd
6 yd
8m
6m
9 yd
5 ft
12 ft
5)
11 m
6)
4 ft
12 ft
12 ft
4 ft
2 ft
10 m
4m
©C `2T0p2t0D RKQuMtzaZ zSZoDfOtbwGabrueq DLPLXCb.M z CA_l_lf yrHiYg]hWtysq prxeEsKeHra-v1ke-pdS.o \ eMjagdJeh swsimtxhR bIXnYfeiAnuiktYeV EGoefoYmreltsrxyW.
Worksheet by Kuta Software LLC
7)
7 ft
8)
8 m
3m
4m
9)
12 in
9 in
9 in
10)
11 mi
8 ft
6 ft
5m
10 ft
12 in
12 in
11)
12)
6 mi 6 mi
8 mi
8 mi
10 in
10 in
3 in
7 in
5 mi
6 mi
3 in
©e A2z0Y2O0G \KGuEtGaO rS^ocfCtgwAaLraeo fLFLwCE._ \ UA[lulh vrNiOgzhUtdsr yrMe[sdeGrhvce-Y2d-E.g b gMta[d\eb awoiHtdhf wILnhfjiUneiptme_ GGRebo^mtedtYrSyM.
6 mi
Worksheet by Kuta Software LLC
Help, give me the answers for 1 through 14... (100 points)
Answer:
can you reupload the photo? so I can help.
Step-by-step explanation:
Answer:
Note that for graph, Y = mx + c, where m = slope of graph and c = y-intersect
1) equation of line: y = [tex]-\frac{3}{4} x[/tex] + 4 ∴ m = -3/4 , c = 4
2) equation of line: y = [tex]\frac{3}{2} x[/tex] + 3 m = 3/2 , c = 3
3) equation of line: y = [tex]-\frac{2}{5} x[/tex] - 2 m = -2/5 , c = -2
4) equation of line: y = [tex]\frac{1}{2} x[/tex] + 3 m = 1/2 , c = 3
5) equation of line: y = -x + 2 m = -1 , c = 2
6) equation of line: y = [tex]-\frac{5}{2} x[/tex] - 1 m = -5/2 , c = -1
Step-by-step explanation:
For each of the line equations, "m" is the slope which is also dy/dx. Also the intersect "c" is on the y axis(Vertical line).
For each equation, assume a number for 'x' then solve for y.... you will be able to get coordinates (x,y) for each graph.
Using 1) as example:
1) equation of line: y = [tex]-\frac{3}{4} x[/tex] + 4 ∴ m = -3/4 , c = 4
at intersection 'c', y = 4, when x = 0
∴ y = -3/4 (1) + 4 = [tex]3\frac{1}{4}[/tex]
repeat for x = 2, 3, 4, 5, 6
Do same for equation line 2, 3, 4, 5, 6 to get coordinates to plot each graph
Select the correct answer. Amelia lost her credit card one day while on vacation. She reported the loss to the credit card company the next day. However, someone had used her card to make purchases worth $1,600 at different shopping outlets. What is the maximum amount that Amelia may have to pay back for the fraudulent charges of $1,600 made on her card? A. $0 B. $50 C. $800 D. $1,600
Answer:a
Step-by-step explanation:
The maximum amount that Amelia may have to pay back for the fraudulent charges of $1,600 made on her card is $50.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
According to the Fair Credit Billing Act (FCBA) in the United States, a consumer's liability for unauthorized charges on a credit card is limited to $50.
Amelia will be responsible for paying the first $50 of the fraudulent charges, but she will not be held responsible for any charges above that amount.
However, most credit card companies have a zero liability policy, which means that the consumer will not be responsible for any unauthorized charges made on their credit card.
Hence, the maximum amount that Amelia may have to pay back for the fraudulent charges of $1,600 made on her card is $50.
To learn more on Equation:
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In a club there is 13 women and 8 men. A committee of 9 women and 4 men is to be chosen. How many different ways are there to select the committee?
A. 50,050 ways
B. 3,744 ways
C. 273 ways
D. 34 ways
Final answer:
To find the number of ways to form a committee of 9 women and 4 men from a group of 13 women and 8 men, calculate the combinations separately for women and men, and multiply them together. The answer is 50,050 ways. So the correct option is A.
Explanation:
The question involves calculating the number of ways to choose a committee consisting of 9 women from a group of 13 women, and 4 men from a group of 8 men. This is a problem that requires knowledge of combinations, a concept in probability and statistics.
Step-by-step solution:
Calculate the number of ways to choose 9 women out of 13, which is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial. For the women, C(13, 9) must be calculated.Calculate the number of ways to choose 4 men out of 8, using the same formula. This will be C(8, 4).Multiply the two results to get the total number of ways to form the committee, since the selections of women and men are independent events.Now, using the combination formula:
C(13, 9) = 13! / (9! × (13-9)!) = 13! / (9! × 4!)C(8, 4) = 8! / (4! × (8-4)!) = 8! / (4! × 4!)Therefore, the total number of ways to select the committee = C(13, 9) × C(8, 4).After calculating, we find that the number of ways to form the committee is 50,050, which corresponds to option (A).
The temperature at 6:00 a.m. was ‐3.5°C. From 6:00 to 7:00, the temperature increased 2.5°C. From 7:00 to 8:00, it decreased by 0.25°C, and from 8:00 to 11:00, the temperature dropped 3.25°C. Which expression shows the temperature in °C at 11:00 a.m.?
The expression that shows the temperature in °C is [tex]-3.5+2.5+(-0.25)+(-3.25)[/tex].
Step-by-step explanation:
Step 1:
The initial temperature at 6.00 am was [tex]-3.5[/tex] °C.
Step 2:
From 6.00 to 7.00 am, the temperature increased by another 2.5°C, so the temperature at 7.00 am was [tex](-3.5 + 2.5)[/tex] °C.
Step 3:
From 7.00 to 8.00 a.m, the temperature decreased by another 0.25°C, so the temperature at 8.00 am was [tex](-3.5+2.5+(-0.25))[/tex] °C.
Step 4:
From 8.00 to 11.00 a.m, the temperature dropped by another 3.25 °C, so the temperature at 11.00 am was [tex](-3.5+2.5+(-0.25)+-(3.25))[/tex] °C which is represented by the fourth option.
Answer:
A i did did question on think through math think it is the answer
Step-by-step explanation:
Which statement is true regarding the functions on the
graph?
Of(-3) = g(4)
Of(-4) = 9(-3)
f(-3) = g(-3)
Of 4) = g(4)
Answer:
f(-3) = g(-3)
Step-by-step explanation:
Remember points on the graph get their location from the x-axis (horizontal) and y-axis (vertical).
In function notation, "f(x)" means when "x" is the value in the brackets, what the value of "y" will be.
First option for example: f(-3) = g(4)
Value of "y" for f(x) when x = -3:
On the blue line, when x = -3, y = -4.
Value of "y" for g(x) when x = 4:
On the red line, when x = 4, y = -3.
Therefore:
f(-3) = g(4)
-4 = -3 <= This is false.
In the third option: f(-3) = g(-3)
On f(x) blue, when x = -3: y = -4
On g(x) red, when x = -3: y = -4
Therefore:
f(-3) = g(-3)
-4 = -4 <= This is true.
Answer:C
Step-by-step explanation:
A coin is flipped 3 times If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?
Answer:
12.50
Step-by-step explanation:
The expected amount is $12.50.
What is the probability?The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
There are 8 possibilities, if coin is flipped three times.
HHH, HHT, HTH, TTH, HTT, THT and TTH,
where H is possibility of head and T is tail.
Now the probabilities,
0 tails: 1 way out of 8 total: P(0) = 1/8
1 tails: 3 ways out of 8 total: P(1) = 3/8
2 tails: 3 ways out of 8 total: P(2) = 3/8
3 tails: 1 way out of 8 total: P(3) = 1/8
The expected amount;
(1/8)X 0 + (3/8)X 5 +(3/8)X15 +(1/8)X40
= 15/8 + 45/8 + 40/8
= 100/8
= 12.50
Therefore, the expected amount is $12.50.
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Last month, the Nunez family spent $218.85 for 1,214 kilowatt hours of electricity. What is the unit rate per kilowatt hour?
Answer:
$.18 per kilowatt hour
Step-by-step explanation:
To find the rate per kilowatt hour
Take the price and divide by the kilowatt hours
218.85/1214
.180271829
Since this is money,we round to the nearest cent
$.18 per kilowatt hour
Find the missing sides
Answer:
90-30=60
Step-by-step explanation:
Was
Answer:
hypotenuse is 6 square root of 3 and short leg is 3 square root of 3
Step-by-step explanation:
A bake sale earns 80$ from selling 50 brownies. Each brownie cost the same amount. How much was 1 brownie?
Answer:
cost of one brownie is $1.60
Step-by-step explanation:
Cost of one brownie$80 from selling 50 brownies
we can create a ratio
80 : 50
x : 1
we can use cross multiplication to solve this:
80 = 50x
80/50 = x
x = $1.60
cost of one brownie is $1.60Which is the equation of the function?
f(x) = 3|x| + 1
f(x) = 3|x – 1|
f(x) = |x| + 1
f(x) = |x – 1|
Answer:
the answer is d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
During halftime of a football game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 4 feet with an initial upward velocity of 80 feet per second. The T-shirt is caught 35 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
It takes 2 seconds to reach a maximum height of 69 feet, and the range is [5, 69].
The equation is of the form
h(t) = -16t² + v₀t + h₀, where -16 is the gravitational constant, v₀ is the initial velocity, and h₀ is the initial height. Using the values from our problem, we have:
h(t) = -16t² + 64t + 5
To find the maximum height, we find the vertex. The first step in this is to find the axis of symmetry, which is given by -b/2a:
-64/2(-16) = -64/-32 = 2
This is our value for t, so it takes 2 seconds to reach the maximum. Substituting this into our function, we have
h(2) = -16(2²) + 64(2) + 5 = -64 + 128 + 5 = 64 + 5 = 69
This is the maximum height.
The range of heights goes from 5 to 69, inclusive, or [5, 69].
The T-Shirt reaches its maximum height of 104 feet at 2.5 seconds. The range of the height over time is from 4 feet to 104 feet.
To analyze the projectile motion of the T-Shirt, we'll use the kinematic equations. The height h(t) at any time t can be modeled by the equation:
h(t) = -16t2 + v0t + h0
where:
h(t) is the height at time tv0 is the initial velocity (80 ft/s)h0 is the initial height (4 ft)1. Time to reach maximum height:
To find the time to reach maximum height, we use the formula for the time at which the velocity becomes zero:
t = v0 / g
t = 80 ft/s / 32 ft/s2 = 2.5 s
2. Maximum height:
Now, substituting t = 2.5 s into the height equation, we get:
h(2.5) = -16(2.5)2 + 80(2.5) + 4
h(2.5) = -100 + 200 + 4 = 104 feet
3. Range of the height function:
The T-Shirt starts at 4 feet, reaches a maximum of 104 feet, and is caught at 35 feet. Hence, the range of the height function is [4, 104] feet.
$300 invested at 12% compounded monthly after a period of 1.5 years
Answer: $358.8 to the nearest tenth
Step-by-step explanation:
Compound interest is calculated by Where: A = P(1 + r)t
Where P= 300, r= 12% = 0.12, t= 1.5 years
Slot in the figures
300 (1 + 0.12) 1.5
300 (1.12) 1.5
300x 1.12
336e1.12
A = $ 358.84
Tickets for the school play cost $4 for students and $7 for adults. For one performance, 146 tickets were sold for $779. How many tickets were for adults and how many were for students?
a 65 students and 81 adults
b 80 students and 66 adults
c 70 students and 77 adults
d 81 students and 65 adults
Answer: D
Step-by-step explanation:
Total tickets sold is $779
Calculate the options to get the right answer.
Option D is correct at
81 students at $4 = 324
65 adults at $7= 455
Total is $ 779
PAGE 11
3) Solve for x: 1/2(4x+6)=-5x+24.7
A x=3.1
B x=3
C x=7
D x=-7.23
Answer:
A x=3.1
Step-by-step explanation:
1/2(4x+6)=-5x+24.7
Multiply each side by 2 to get rid of the fraction
2*1/2(4x+6)=2(-5x+24.7)
4x+6 = -10x +49.4
Add 10x to each side
4x+6+10x=-10x+10x+49.4
14x +6 = 49.4
Subtract 6 from each side
14x+6-6 = 49.4-6
14x = 43.4
Divide each side by 14
14x/14 = 43.4/14
x = 3.1
Find the value of x to the nearest tenth! Help ASAP
The value of x is 10.
Solution:
Given triangle is a right triangle.
θ = 50°, adjacent side = 6, hypotenuse = x
The value of cos 50° = 0.6
Using trigonometric ratio formulas,
[tex]$\cos \theta=\frac{\text { Adjacent side of } \theta}{\text { Hypotenuse }}[/tex]
[tex]$\cos50^\circ=\frac{6}{x}[/tex]
[tex]$0.6=\frac{6}{x}[/tex]
Do cross multiplication, we get
[tex]x\times 0.6=6[/tex]
Divide by 0.6 on both sides, we get
[tex]$\frac{x\times 0.6}{0.6}=\frac{6}{0.6}[/tex]
x = 10
The value of x is 10.
Which expressions are equivalent to 7⋅7⋅7⋅7⋅7⋅7
SELECT 2 Answers
It's FROM KHAN academy
Answer:
7^6
and
7⋅7⋅7⋅7⋅7⋅7/1
Step-by-step explanation:
Hope this helps! It would be better for me to see the selections though.
Answer:
A - 7^8/7^2
C - (7^2)^3
Step-by-step explanation:
So there's a question exactly like this on khan, so here's the khan answer
Don't worry I tested it
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
1. -2, -1, -i
2. 4, -√5, -5
Answer:
y=(x^2 -1)(x^2 +1)(x^2 -4)(x^2 -5)(x +5)(x -4)
sry, but i didn't want to multiply it out. T-T
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 1/2
Step-by-step explanation:
9/4 = 2.50 = 2 1/2
Answer:
D. 2¼
Step-by-step explanation:
9/4
(8+1)/4
8/4 + 1/4
2¼
explanation needed tip by using chain rule
Answer:
1/(810pi) cm/s
Step-by-step explanation:
V = pi×r²×h = pi×90²×h = 8100pi×h
dh/dt = dh/dV × dV/dt
dV/dh = 8100pi
dV/dt = 10
dh/dt = (1/8100pi) × 10
= 1/(810pi) cm/s
Quadrilateral ERGF is inscribed in a circle Find the measure of angle E (Remember to show formulas equations and numbers in those formulasequations receive creditAlso, make sure to include units on your answer ) R - 2 + 6x G EK 7x - 13
The measure of angle E is 75°.
Solution:
Given data:
∠E = 5x, ∠F = 7x – 13 and ∠R = –2 + 6x
A quadrilateral inscribed in a circle is called cyclic quadrilateral.
∠R and ∠G are opposite angles in a cyclic quadrilateral.
In cyclic quadrilateral, opposite angles are supplementary.
⇒ m∠R + m∠F = 180
⇒ –2 + 6x + 7x – 13 = 180
⇒ 13x – 15 = 180
Add 15 from both sides of the equation, we get
⇒ 13x = 195
Divide by 13 from both sides of the equation, we get
⇒ x = 15
To find the measure of angle E:
m∠E = 5x
m∠E = 5(15)
m∠E = 75
The measure of angle E is 75°.
The Highly Improbable Foods Company makes vegetarian versions of burgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of one burger, three hot dogs, and $5$ chicken wings, which costs $\$16.$ Platter B consists of two burgers, one hot dog, and $8$ chicken wings, which costs $\$20.$
A picnic organizer requires $80$ hamburgers, $95$ hot dogs, and $380$ chicken wings. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?
Answer:
$1020
Step-by-step explanation:
Let x and y represent the numbers of Platter A and Platter B the organizer needs to purchase, respectively. The given conditions can be summarized as ...
x + 2y ≥ 80 . . . . . . 80 or more hamburgers are required
3x + y ≥ 95 . . . . . . 95 or more hot dogs are required
5x +8y ≥ 380 . . . . 380 or more chicken wings are required
16x +20y = c . . . . . c must be minimized
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It is useful to graph these inequalities, and look for the vertex of the feasible region that is closest to the origin. That vertex is (x, y) = (20, 35). The other vertex that is close to the origin is (60, 10). The cost of that order would be $1310.
The value of an order of 20 Platter A and 35 Platter B is ...
20×$16 +35×$20 = $320 +700 = $1020
The minimum cost of the picnic food is $1020.