Answer: 156.7
Step-by-step explanation:
1.35x84= 113.4
270-113.4=156.60
Answer:
B
Step-by-step explanation:
1.35 x 84 = $113.40
270 - 113.40 = $156. 60
156.60 / 1.35 = 116 boxes
solve the given equation and check the solution 7/2x - 5/2 = 23/2
Answer:
The X, should be 4
Step-by-step explanation:
7/2x - 5/2 = 23/2
7/2x = 23/2 + 5/2
7/2 = 14
x = 14 . 2/7
x= 4
The solution to the equation [tex]\frac{7}{2}x - \frac{5}{2} = \frac{23}{2}[/tex] is x = 4. By substituting x = 4 back into the equation, we confirm that it satisfies the original equation, proving that the solution is correct.
Let’s solve the equation [tex]\frac{7}{2}x - \frac{5}{2} = \frac{23}{2}[/tex] step-by-step as shown below-
Let's isolate the x-term by adding [tex]\frac{5}{2}[/tex] to both sides of the equation
[tex]\frac{7}{2}x - \frac{5}{2} + \frac{5}{2} = \frac{23}{2} + \frac{5}{2}[/tex]This simplifies to:
[tex]\frac{7}{2}x = \frac{28}{2}[/tex]Next, simplify the right-hand side:
[tex]\frac{7}{2}x = 14[/tex]Now, multiply both sides by [tex]\frac{7}{2}[/tex] to solve for x:
[tex]x = \frac{(14 \times 2)}{7}[/tex][tex]x = \frac{28}{7}[/tex]And the final solution is:
[tex]x = 4[/tex]To check the solution, substitute x = 4 back into the original equation:
[tex]\frac{7}{2} \times 4 - \frac{5}{2} = \frac{23}{2}[/tex]This becomes:
[tex]14 - \frac{5}{2} = \frac{23}{2}[/tex]The left side simplifies to:
[tex]\frac{28}{2} - \frac{5}{2} = \frac{23}{2}[/tex]Which confirms:
[tex]\frac{23}{2} = \frac{23}{2}[/tex]Thus, the solution x = 4 is correct.
a. Draw the image of ΔDEF after a rotation of 90° clockwise about the point (1,0). Label the image ΔD’E’F’.
b. Draw the image of ΔD’E’F’ after a reflection across the line x = 1. Label the image ΔD”E”F”.
Please help!!
Answer:
see the attachment
Step-by-step explanation:
(a) Clockwise rotation moves a point from (x, y) to (y, -x).
__
(b) Reflection across x=1 moves a point from (x, y) to (2-x, y).
Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A’s has 60% fewer booklets than each box of Team B’s. Which of the following could be the total number of booklets distributed by the two groups?
A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900
Answer:
C. 4,100
Step-by-step explanation:
"60% more" is represented by a multiplier of 1 + 0.60 = 1.60.
"60% fewer" is represented by a multiplier of 1 - 0.60 = 0.40.
__
Let b represent the number of booklets distributed by Team B. Then the number distributed by Team A is ...
1.60 × (0.40b) . . . . 60% more boxes, each with 60% fewer booklets
= 0.64b
Then the total distributed by both teams is ...
b + 0.64b = 1.64b = (164/100)b = (41/25)b
The only answer choice that is a multiple of 41 is ...
4,100 . . . choice C
__
For 4100 to be the number of booklets distributed by both teams, Team B will have distributed 2500 booklets, and Team A will have distributed 1600 booklets. Team A might have distributed 160 boxes of 100 booklets, while Team B might have distributed 100 boxes of 250 booklets.
HELP FASTTTTT PLEASE Assume that the following figures are drawn to scale. Use your understanding of congruence to explain why square ABCD and rhombus GHIJ are not congruent.
Answer:
see the explanation
Step-by-step explanation:
we know that
If two figures are congruent, then the corresponding sides and the corresponding angles are congruent
In this problem, the corresponding sides are congruent, but the corresponding angles are not congruent
therefore
The square ABCD and the rhombus GHIJ are not congruent
Two Geometrical Shape are Congruent, only when
1. Corresponding sides are equal
2. Corresponding Interior as well as Exterior Angles are equal.
3. Areas are equal.
⇒Square ABCD and Rhombus GHIJ, have length of their Corresponding side equal , but their interior angles are not equal.
So,⇒ Square ABCD NOT≅ to Rhombus GHIJ
-81 ÷(-9)
A:729
B:-729
C:-9
D:9
Answer:
9
Step-by-step explanation:
a negative divided by a negative is a positive.
Determine all the roots given function (solve for the unknown variable)?
Answer:
The roots are:
a) z1 = 0
b) z2 = -2
c) z3 = ∛2 or 1.26
Step-by-step explanation:
First we factor z from the original equation
z⁷ + 6z⁴ - 16 z = z ( z⁶ + 6z³ -16)
z ((z³)² + 6z³ -16) express z⁶ as a power
z (z³ + 8)(z³ -2) factor
Now, equal to zero each term
z1 = 0 first answer
z³ + 8 = 0 z³ = -8 z2 = -2 second answer
z³ -2 = 0 z³ = 2 z3 = ∛2 or 1.26 third answer
When determining the roots of a function, you set the function equal to zero and solve for the variable. For example, the roots of the function f(x) = x² - 5x + 6 would be x = 2 and x = 3.
Explanation:Though the specific function is not provided in the question, the general process to determine all the roots of a function lies in setting the function equal to zero and solving for the unknown variable. The roots of the function are the values of the unknown variable that make the equation true. For example, if you have a function f(x) = x² - 5x + 6, by setting it to zero and following the method you obtain the roots as x = 2 and x = 3.
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The M&M jar has a square base with a length and width of 7 cm and a height of 6.5 cm. What would be the most reasonable lower limit for the number of M&M`s in the jar of the choices below?
A.10
B.100
C.1,000
D.10,000
Answer: I believe the answer would be 100 because there are or should be more than 100 M&M's in the jar.
Step-by-step explanation:
Joe has $4.52 in dimes, nickels, and pennies. If he has one more dime than three times the number of nickels and 10 more pennies than nickels, how many of each type of coin does he have?
Answer:
12 nickels, 37 dimes and 22 pennies
Step-by-step explanation:
Let
x ----> the number of nickels
y ----> the number of dimes
z ----> the number of pennies
we know that
1 nickel=$0.05
1 dime=$0.10
1 pennies=$0.01
so
0.05x+0.10y+0.01z=4.52 -----> equation A
y=3x+1 ----> equation B
z=x+10 ----> equation C
substitute equation B and equation C in equation A and solve for x
[tex]0.05x+0.10(3x+1)+0.01(x+10)=4.52 0.05x+0.30x+0.10+0.01x+0.10=4.52\\0.36x+0.20=4.52\\ 0.36x=4.52-0.20\\x=4.32/0.36\\x=12\ nickels[/tex]
Find the value of y
[tex]y=3(12)+1=37\ dimes[/tex]
Find the value of z
[tex]z=12+10=22\ pennies[/tex]
1.) what is the domain of the following set? (-2,4), (0,3), (1,6), (-1,2)
a. (-2,-1,0,1)
b. (1,-2,1,6,3)
c. (-2,-1,0,1,2,3,6)
d. (4,3,6,-1,2)
e. (4,3,6,-1,-2)
Answer:
A. (-2,-1,0,1) .......
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Allie needs at least 50 hours of community service for social studies class. She already has 20. How many more hours does she need? Write an inequality to model this situation.
A)
x + 20 ≤ 50
B)
x + 20 ≥ 50
C)
x - 20 ≥ 50
D)
x + 50 ≥ 20
Answer
B) x + 20 ≥ 50
Step-by-step explanation:
Answer:
B) x + 20 ≥ 50
Step-by-step explanation:
Given,
The hours she already has for social studies = 20,
After getting x more hours,
The total hours she has now = x + 20,
According to the question,
Total hours ≥ 50
[tex]\implies x + 20\geq 50[/tex]
Which is the required inequality to model give situation,
Hence, OPTION B is correct.
math question: (!!please answer right away!!)
1.) "A diver dives 47 ft below the surface of the water and then rises 12 ft. Use addition to find the divers depth."
2.) "The temperature at 6 AM is -6°F. The temperature rises 13 degrees Fahrenheit by noon. Use addition to find the temperature at noon."
For the first problem, the diver's depth after diving 47 feet and then rising 12 feet is -35 feet or 35 feet below the surface. In the second problem, the temperature rose from -6°F to 7°F by noon.
Explanation:Let's answer your mathematics problems one by one.
Problem 1:
A diver dives 47 ft below the surface of the water and then rises 12 ft. We can use addition by understanding that direction matters. A depth of 47 ft below the surface is represented as -47, while rising 12 ft means +12. So, the final depth could be represented mathematically as -47 + 12, which equals to -35 ft. It means the diver is 35 feet below the surface of the water.
Problem 2:
The temperature at 6 AM is -6°F. The temperature rises 13 degrees Fahrenheit by noon. The situation can be mathematically represented as -6 + 13. So, the temperature at noon would be 7°F.
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Solve for y. −140=18+4(5y−2) Enter your answer in the box. y =
Answer:
y = - 7.5
Step-by-step explanation:
Given
- 140 = 18 + 4(5y - 2) ← distribute and simolify right side
- 140 = 18 + 20y - 8
- 140 = 10 + 20y ( subtract 10 from both sides )
- 150 = 20y ( divide both sides by 20 )
- 7.5 = y
Sean plan to join a streaming music service. One plan is $20 down plus monthly payments of $10 a month. The second plan is $40 down and $8 a month. How many month with the total amount paid be the same for both companies? What would the amount be?
Answer:
10 months
Step-by-step explanation:
Let X represent the number of months
The cost equation for the first plan = $20 + 10x
The cost equation for the second plan =$ 40+8x
The number of months at which the cost for the two plans will be equal can be worked out by equating the costs for the two plans and then calculate the value of x.
Thus,
$20+10x = $40 +8x
10x -8x =$40-$20
2x = $ 20
x= 20/2
x= 10
Substituting X in each equation,
$20 +$10(10) = $40 + $8(10)
$ 20 +$100 =$40 +$80
$120 =$120
Thus, the amount after ten months = $120
A regression model is used to forecast sales based on advertising dollars spent. The regression line is y=500+35x and the coefficient of determination is .90. Which is the best statement about this forecasting model?a. For every $35 spent on advertising, sales increase by $1.
b. Even if no money is spent on advertising, the company realizes $35 of sales.
c. The correlation between sales and advertising is positive.
d. The coefficient of correlation between sales and advertising is 0.81.
Answer:
The correlation between sales and advertising is positive.
Step-by-step explanation:
For every $35 spent on advertising, sales increase by $1
Is FALSE, since y = 500 + 35 x $35, sales increase more than $1
Even if no money is spent on advertising, the company realizes $35 of sales
Is FALSE, if no money is spent, the sales amount to $ 500 (when X = 0)
The coefficient of correlation between sales and advertising is 0.81
Is FALSE, since R² = 0.9. The coefficient of correlation = R = 0.94, not 0.81
3:5, 3 to 5, and 5/3 all represent the same ratio. true or false
Answer:
False.
Step-by-step explanation:
The first two (3:5) & (3 to 5), represents the same ratio.
However, 5/3 does not equal to the others, for it's form would be:
5:3
5 to 3
~
Answer:
false
Step-by-step explanation:
i hope i helped :)
The population of the United States is about 3.2x10^8 the population of the United States is about 80 times the population of Oregon write the population of Oregon in scientific notation
Answer:
The answer to your question is: 4 x 10 ⁶ = population of Oregon
Step-by-step explanation:
Data
Population of the USA = 3.2 x 10⁸
Population of the USA = 80 population of Oregon
Process
3.2 x 10⁸ = 80 population of Oregon
3.2 x 10⁸ / 80 = population of Oregon
4 000 000 = population of Oregon
4 x 10 ⁶ = population of Oregon
The population of Oregon will be 4 x 10⁶.
What is Division method?
Division method is used to distributing a group of things into equal parts.
Given that;
The population of the United States = 3.2 x 10⁸
And, The population of the United States is about 80 times the population of Oregon.
Let population of Oregon = x
Then, We can formulate;
3.2 x 10⁸ = 80 × x
Solve for x as;
3.2 x 10⁸ = 80 × x
x = 3.2 x 10⁸ / 80
x = 0.04 x 10⁸
x = 4 x 10⁻² x 10⁸
x = 4 x 10⁶
Thus, The population of Oregon will be 4 x 10⁶.
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A jogger can jog 3 miles in 15 minutes and 18 miles in 1 1/2 hours. If the number of miles and the time are in a proportional linear relationship, at what rate is the jogger jogging per hour?
Answer: He jogs 12 miles per hour
Step-by-step explanation: Every 15 minutes he jogs 3 miles, there are 60 minutes in an hour, 60/15 = 4, 4 x 3 = 12
This function f(x) has a domain of x = {-a, -b, a, b}.
In order, the x values are -a, -b, b, a.
In order, the f(x) values are 3c + 1, 2d - 5, 4d + 3, 6 - 2c.
Which values of c and d make this an even function?
a. c = -7 and d = 1/3
b. c = 5 and d = 1/3
c. c = -5 and d = -4
d. c = 1 and d = -4
e. c = -7 and d = -4
Answer:
d. c = 1 and d = -4
Step-by-step explanation:
If a function is even, then f(-x) = f(x). Graphically, this means it's symmetrical about the y-axis.
f(-a) = f(a)
3c + 1 = 6 − 2c
5c = 5
c = 1
f(-b) = f(b)
2d − 5 = 4d + 3
-2d = 8
d = -4
Therefore, c = 1 and d = -4.
Sam and Amanda are brother and sister. Sam has twice as many brothers as sisters, and Amanda has five times as many brothers as sisters. How many boys and girls are there in this family?
Answer:Boys=5,girls =2
Step-by-step explanation:
Let b be the no of boys and g be the no of girls
Therefore
Sam has twice as many brothers as sisters
2g=b-1
b-2g=1--------------1
Amanda has five times as many brothers as sisters
5(g-1)=b
5g-b=5----------------2
using (1) & (2) we get
g=2
b=5
There are 5 boys and 2 girls in Sam and Amanda's family. We determined this by setting up equations based on the clues provided and solving for the number of brothers and sisters.
To solve the riddle of how many boys and girls are in Sam and Amanda's family, we must first establish two equations based on the information provided:
Sam has twice as many brothers as sisters. Let the number of brothers be 'b' and the number of sisters be 's'. Sam is a brother, so we do not count him. Thus, we have the equation b - 1 = 2s.Amanda has five times as many brothers as sisters. Since Amanda is a sister, we do not count her. So, we have the equation b = 5(s - 1).Now we solve these two equations.
From the second equation, b = 5s - 5. Substituting this into the first equation:
(5s - 5) - 1 = 2s
Simplifying, we get:
5s - 6 = 2s
Now we solve for 's':
5s - 2s = 6
3s = 6
s = 2
There are 2 sisters. Substituting 's = 2' into b = 5(s - 1), we get:
b = 5(2 - 1)
b = 5
There are 5 brothers. But since we are including Sam in the total, there are 4 boys excluding Sam.
In conclusion, the family consists of 5 boys and 2 girls.
Solve the Quadratics:
1) k^2-8k=0
2) a^2+5a=0
3) 6n^2+5n-25=0
4) 2x^2-11x-21=0
5) 2n^2+13n+19=4
Bonus Word Problem:
The larger leg of a right triangle is 7cm longer than its smaller leg. The hypotenuse is 8cm longer than the small leg. How many centimeters long is the smaller leg?
Answer:
Step-by-step explanation:
1 ) k²-8k = 0
k(k-8)=0
k = 0 or k=8
2) a²+5a=0
a(a+5) = 0
a=0 or a = - 5
3 ) 6n²+5n-25=0
delta = b²-4ac b =5 and a = 6 and c= - 25
delta = 5²-4(6)(-25) = 625 = 25²
n 1 = (-5+25)/12 = 20/12 = 5/3
n 2 = (-5-25)/12 = - 30/12 = -5/2
same method for 4) and 5)
What do I fill in the boxes?
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{4x+1}{x^2-4x-12}[/tex] ← factorise the denominator
x² - 4x - 12 = (x - 6)(x + 2)
The fraction can now be expressed as
= [tex]\frac{4x+1}{(x-6)(x+2)}[/tex]
Split the numerator into its 2 parts, that is
= [tex]\frac{4x}{(x-6)(x+2)}[/tex] + [tex]\frac{1}{(x-6)(x+2)}[/tex]
x is -4
f(x)= 5x^8-3x
The ^8 is the exponent for 5x!!!
Answer:
327692
Step-by-step explanation:
[tex]65536 = (-4)^{8} \\ \\ 65536 \times 5 = 327680 \\ \\ 327680 - 3(-4) = 327680 + 12 = 327692[/tex]
According to the Order of Operations [GEMS(A)\BOMDAS\PEMDAS etc.], in this case, you evaluate the exponent BEFORE multiplying. This is a common mistake people make.
I am joyous to assist you anytime.
A women's hospital reported 212 deliveries during June. Two sets of twins were born. There were 215 obstetrical discharges; 214 births; four women had first-time C-sections; and three women had a repeat C-section. The C-section rate for September is 3.30 percent. True or false?
Answer:
Impossible to know. Numbers provided on the statement are for June, though question is made for september. If, by any chance, question is not correctly stated, answer will be True
Step-by-step explanation:
According to the problem, there were 214 births. Seven of those 214 births were via C-section. Then: 100%*(7/214)=3.3%
It does not matter which births were natural, or C sectioned, as they are considered in the same group.
Planes X and Y and points J, K, L, M, and N are shown. Vertical plane X intersects horizontal plane Y. Point L is on the left half of plane Y. Point N is on the bottom half of plane X. Point M is on the right half of plane Y. Point K is on the top half of plane X. Point J is above and to the left of the planes. Exactly how many planes contain points J, K, and N? 0 1 2 3
Answer:
1
Step-by-step explanation:
Three points define 1 plane.
Answer:
The answer is plane 1
Step-by-step explanation:
Planes X and Y and points J, K, L, M, and N are shown.
I need some help with this problem
Answer:
1. No
2.Yes
3.Yes
4.Yes
5.No
Step-by-step explanation:
Plug in the numbers
1. 3+3 = 9+9 / 6 = 18 / NO
2. 20-0 = 20+0 / 20 = 20 / Yes
3. 3+0/3-0 / 3/3 = 1 / Yes
4. 4+3 = 16-9 / 7 = 7 / Yes
5. 0+1 = 1-0/0 / 1 = 1/0 / No
Rate as Brainliest plz
Answer: No Yes Yes Yes No
Step-by-step explanation: brain power
A right triangle whose base is 30 units is divided into two parts by a line drawn parallel to the base. It is given that the resulting right trapezoid has an area larger by 7,0 (which is sexagesimal) = 420 than the upper triangle, and that the difference between the height y of the upper triangle and the height z of the trapezoid is 20. if x is the length fo the upper base of the trapezoid, these statement lead to the relations 1/2z (x+30) = 1/2xy + 420, y - z = 20. The problem calls for finding the values of the unknown quantities x, y, and z. [Hint: By properties of similar triangles, y/(y+z) = x/30.]
Answer:
[tex]x=18[/tex]
[tex]y=60[/tex]
[tex]z=40[/tex]
Step-by-step explanation:
From the relations stablished in the problem we have the following equation system:
[tex]y-z=20[/tex] (equation 1)
[tex]\frac{1}{2} xy+420=\frac{1}{2}z(x+30)[/tex] (equation 2)
[tex]\frac{y}{y+z} =\frac{x}{30}[/tex] (equation 3)
From equation 1 we can find an expression of [tex]y[/tex] in terms of [tex]z[/tex] which we're going to call equation 4
[tex]y-z=20[/tex]
[tex]y=z+20[/tex] (equation 4)
We can then replace the equation 4 in the equation 2 in order to find an expression of [tex]x[/tex] in terms of [tex]z[/tex]
[tex]\frac{1}{2} xy+420=\frac{1}{2}z(x+30)[/tex]
[tex]\frac{1}{2} (xy+840)=\frac{1}{2}z(x+30)[/tex]
[tex]xy+840=z(x+30)[/tex]
[tex]x(z+20)+840=z(x+30)[/tex] (here we replaced the eq.4)
[tex]xz+20x+840=xz+30x[/tex]
[tex]xz+20x-xz=30z-840[/tex]
[tex]20x=30z-840[/tex]
[tex]10(2x)=10(3z-84)[/tex]
[tex]x=\frac{1}{2} (3z-84)[/tex] (equation 5)
Now, we can replace equations 4 & 5 inside the equation 3 so we can find the value of [tex]z[/tex]
[tex]\frac{y}{y+z} =\frac{x}{30}[/tex]
[tex]\frac{z+20}{z+20+z} =\frac{1}{30}*\frac{1}{2} (3z-84)[/tex]
[tex]\frac{z+20}{2z+20} =\frac{1}{30}*\frac{1}{2} (3z-84)[/tex]
[tex]\frac{z+20}{2(z+10)} =\frac{1}{2}*\frac{1}{30} (3z-84)[/tex]
[tex]\frac{1}{2}*\frac{z+20}{z+10} =\frac{1}{2}*\frac{1}{30} (3z-84)[/tex]
[tex]\frac{z+20}{z+10} =\frac{1}{10} (\frac{3z}{3}-\frac{84}{3})[/tex]
[tex]\frac{z+20}{z+10} =\frac{1}{10} (z-28)[/tex]
[tex]z+20 =\frac{1}{10} (z-28)*(z+10)[/tex]
[tex]10(z+20) =z^{2}+10z-28z-280[/tex]
[tex]10z+200 =z^{2}-18z-280[/tex]
[tex]z^{2}-28z-480=0[/tex]
This is a quadratic equation which has the form [tex]a*z^{2} +b*z+c=0[/tex]
where
[tex]a=1[/tex]
[tex]b=-28[/tex]
[tex]c=-480[/tex]
Then, we can find the solutions to this quadratic equation using the well-know quadatric formula which says that
[tex]z=\frac{-b}{2a}[/tex]±[tex]\frac{\sqrt{b^{2}-4ac} }{2a}[/tex]
then, replacing the values of a, b and c we find the values of z
[tex]z_{1}=\frac{-(-28)+\sqrt{(-28)^{2}-4(1)(-480)} }{2(1)}[/tex]
[tex]z_{1}=40[/tex]
[tex]z_{2}=\frac{-(-28)-\sqrt{(-28)^{2}-4(1)(-480)} }{2(1)}[/tex]
[tex]z_{2}=-12[/tex]
We have two possible values of z, but because we're trying to find the measure of trapezoid's height the result shouldn't be negative, so we keep only the positive value of z, then
[tex]z=40[/tex]
Now we may replace this value of z in the equations 4 & 5 in order to find the values of x & y.
[tex]y=z+20[/tex] (equation 4)
[tex]y=40+20[/tex]
[tex]y=60[/tex]
[tex]x=\frac{1}{2} (3z-84)[/tex] (equation 5)
[tex]x=\frac{1}{2} (3(40)-84)[/tex]
[tex]x=18[/tex]
So we've found the values of x, y, and z.
[tex]x=18[/tex]
[tex]y=60[/tex]
[tex]z=40[/tex]
Joseph says that in the number 9,999,999 all the digits have the same value. I'd Joseph correct? Explain Part B Describe the relationship between the value of the digits in the number
Answer:
Joseph is not correct
Each digit from the leftmost digit is ten times the digit before it
Step-by-step explanation:
* Lets explain how to solve the problem
- Any number formed from some digits, each digit has a place value
- Ex: 2,345 this number formed from 4 digits
The place value of 5 is ones ⇒ 5
The place value of 4 is tens ⇒ 40
The place value of 3 is hundreds ⇒ 300
The place value of 2 is thousands ⇒ 2,000
2,345 = 2,000 + 300 + 40 + 5
* Lets check our problem
∵ The number is 9,999,999
- The number formed from 7 digits, the digits have different places value
∴ They couldn't have the same value
∴ Joseph is not correct
∵ The number formed from 7 digits
- The place value of the leftmost digit is millions
- The place value of the digit before the million is hundred thousands
- The place value of the digit before the hundred thousands is
ten thousands
- The place value of the digit ten thousands is thousands
- The place value of the digit before thousands is hundreds
- The place value of the digit before hundreds is tens
- The place value of the digit before tens is ones
∴ 9,999,999 = 9,000,000 + 900,000 + 90,000 + 9,000 + 900
+ 90 + 9
∴ Each digit from the leftmost digit is ten times the digit before it
1 When an aero plane took off, it was noted that for every 100 m rise in altitude, the temperature dropped by 1 1/2 C. The plane reached an altitude 25 times the distance of 100 m, by how much the temperature would have dropped if the Ground temperature was 27 1/2 C
Answer:
37 1/2 C
Step-by-step explanation:
25 × 1 1/2 C = 37 1/2 C
The temperature would have dropped 37 1/2 C.
_____
The ground temperature is irrelevant to the question.
The manager of a restaurant found that the cost to produce 300 cups of coffee is $30.43, while the cost to produce 500 cups is $49.83. Assume the cost C(x) is a linear function of x, the number of cups produced.
a) Find the formula for C(x)
b) What is the fixed (initial cost)
c) Find the total cost of producing 1200 cups
Answer:
a) C(x) = 1.33 + 0.097x
b) Fixed Initial cost = $1.33
c) C(1200) = $ 117.73
Step-by-step explanation:
a) Let's first define our x variable and y variable as:
x: Number of cups of coffee produced
y: Cost of producing
y is a function of x that in this problem is called C(x) so y = C(x).
No we are told that C(x) is a linear function. All linear functions follow the rule:
C(x) = mx+b
where m is the slope of the line and b is the intercept in the y - axis or the value of the function when x=0 . To find a formula for C(x) we can use the information given because these are two points of the line where
Point 1
x1= 300 and y1 = 30.43
Point 2
x2= 500 and y2 = 49.83
With these two points we can find the slope with the formula
m= y2-y1/x2-x1 = (49.83-30.43)/(500-300) = 19.42/200 = 0.097
so we have that;
C(x) = mx+b = 0.097x+b.
Now we have to know b the intercept in y.For this problem this is equivalent to the cost that we would have to pay if we did not produced any cup so b is our fixed initial cost. Because we have a point, we can replace it in the equation and solve for b. It doesnt matter which point we use.
C(x) = 0.097x + b
b = C(x) - 0.097x
With Point 2 = x = 500 and C(x) = 49.83
b = C(x) - 0.097x
b = 49.83 - (0.097 * 500) = 49.83 -48.5 = 1.33
So the final formula for C(x) is
C(x) = 0.097x + 1.33
b) As I said before, the initial cost or fixed cost is the cost incurred if we would not produce anything or mathematically when x = 0
C(x) = 0.097x + 1.33
C(0) = 0.097*0 + 1.33 = 0+1.33 = 1.33
The fixed cost is $ 1.33 that is the same as b parameter.
c) Now that we have an equation for C(x) we only need to replace for the point x = 1200
C(x) = 0.097x + 1.33
C(1200) = (0.097*1200) + 1.33 = 116.4 +1.33 = $ 117.73
The formula for the cost function C(x) is C(x) = $0.097x + $1.33, where $1.33 represents the fixed cost. Using this formula, the total cost of producing 1200 cups of coffee is $117.73.
Find the Cost Function C(x)
To find the cost function C(x), we need two points to determine a linear function: (300, $30.43) and (500, $49.83). First, find the slope (m) of the cost function using the formula m = (y2 - y1) / (x2 - x1), which in our case is m = ($49.83 - $30.43) / (500 - 300), so m = $19.40 / 200 = $0.097 per cup. The slope represents the variable cost per cup of coffee.
With the slope, we can use one of the points to find the y-intercept (b), the fixed or initial cost. Plug in the values into y = mx + b, so $30.43 = $0.097*300 + b, which gives us b = $30.43 - $29.10 = $1.33. Therefore, the formula for C(x) is C(x) = $0.097x + $1.33.
To find the total cost of producing 1200 cups, plug x = 1200 into the cost function: C(1200) = $0.097*1200 + $1.33, which calculates to C(1200) = $116.40 + $1.33 = $117.73.
Hence, the total cost of producing 1200 cups of coffee is $117.73
An algebra tile configuration where the 2 largest tiles are labeled plus x squared, there are 4 tiles labeled negative x, where each tile is half the size of the largest tiles, and 6 tiles labeled minus that are each one-quarter the size of the largest tile. Which polynomial is represented by the algebra tiles? 2x2 – 4x – 6 2x2 + 4x + 6 –2x2 – 4x – 6 –2x2 + 4x + 6
The algebra tile configuration described represents the polynomial 2x^2 - 4x - 6.
Explanation:The algebra tile configuration you have described is representing the polynomial 2x2 - 4x - 6. This is deciphered as follows:
The 2 largest tiles labeled 'plus x squared' represent 2x2. For each of these tiles, the value is 'x squared' so two of them equals '2x squared'Four tiles half the size of the largest tiles are labeled 'negative x', thus representing -4x. If one large x tile represents 'x', then a half-size x tile represents '0.5x'. Since there are four such negative tiles, we get '4 * (-0.5x)' equals '-4x'.Six smallest tiles representing 'minus' account for the constant term of -6 since each of them is a quarter of the size of the largest tiles.In conclusion, the three parts together give us the polynomial: 2x2 - 4x - 6.
Learn more about Polynomial Representation here:https://brainly.com/question/35170067
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The polynomial represented by the algebra tiles is [tex]\(2x^2 - 4x - 6\).[/tex]Therefore, the correct option is [tex]\(2x^2 - 4x - 6\).[/tex]
To determine which polynomial is represented by the given algebra tile configuration, we need to understand the values assigned to each type of tile.
Step 1:
Interpret the tiles.
The largest tiles represent [tex]\(x^2\),[/tex] the tiles labeled negative x represent [tex]\(-x\),[/tex] and the tiles labeled minus represent [tex]\(-1\).[/tex]
Step 2:
Assign values to the tiles.
Each largest tile represents [tex]\(x^2\),[/tex] so we have [tex]\(2x^2\).[/tex]
There are 4 tiles labeled negative x, each representing [tex]\(-x\),[/tex] so we have [tex]\(-4x\).[/tex]
There are 6 tiles labeled "minus," each representing [tex]\(-1\),[/tex] so we have [tex]\(-6\).[/tex]
Step 3:
Combine the terms.
Combining the terms, we get [tex]\(2x^2 - 4x - 6\).[/tex]
So, the polynomial represented by the algebra tiles is [tex]\(2x^2 - 4x - 6\).[/tex]Therefore, the correct option is[tex]\(2x^2 - 4x - 6\).[/tex]