Answers
The vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.
Given an equation showing profits of A Christmas vendor as
P=-0.1[tex]g^{2}[/tex]+30g-1200.
We have to find the number of gingerbread houses that the vendor needs to sell in order to earn profit of $665.60 and $1500.
To find the number of gingerbread houses we have to put P=665.60 in the equation given which shows the profit earned by vendor.
665.60=-0.1[tex]g^{2}[/tex]+30g-1200
0.1[tex]g^{2}[/tex]-30g+1200+665.60=0
0.1[tex]g^{2}[/tex]-30g+1865.60=0
Divide the above equation by 0.1.
[tex]g^{2}[/tex]-300g+18656=0
Solving for g we get,
g=[300±[tex]\sqrt{(300)^{2}-4*1*18656 }[/tex]]/2*1
g=[300±[tex]\sqrt{90000-74624}]/2[/tex]
g=[300±[tex]\sqrt{15376}[/tex]]/2
g=(300±124)/2
g=(300+124)/2 , g=(300-124)/2
g=424/2, g=176/2
g=212,88
Because 212 is much greater than 88 so vendor prefers to choose selling of 88 gingerbread houses.
Put the value of P=1500 in equation P=-0.1[tex]g^{2}[/tex]+30g-1200.
-0.1[tex]g^{2}[/tex]+30g-1200=1500
0.1[tex]g^{2}[/tex]-30g+1500+1200=0
0.1[tex]g^{2}[/tex]-30g+2700=0
Dividing equation by 0.1.
[tex]g^{2}[/tex]-300g+27000=0
Solving the equation for finding value of g.
g=[300±[tex]\sqrt{300^{2} -4*1*27000}[/tex]]/2*1
=[300±[tex]\sqrt{90000-108000}] /2[/tex]
=[300±[tex]\sqrt{-18000}[/tex]]/2
Because [tex]\sqrt{-18000}[/tex] comes out with an imaginary number so it cannot be solved for the number of gingerbread houses.
Hence the vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.
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Related Questions
On a coordinate plane, a point is at (1, 2) and (5, 2). Find the distance between (1, 2) and (5, 2). The points lie in the same quadrant . The distance is .
Answers
Answer:
The points lie in
✔ the same quadrant
The distance is
✔ 4 units
Step-by-step explanation:
the same quadrant
4 units
The distance between the two points (1, 2) and (5, 2) is 4 units. And both the points (1, 2) and (5, 2) lie in the same quadrant.
What is Distance between the two points?Distance between two points is the length of the line segment that connects two given points.
Formula for the distance between two points[tex]d = \sqrt{(x_{2}-x_{1} ^{2}) +(y_{2}-y_{1} ) ^{2} }[/tex]
According to the given question
We have
Two points
(1, 2) and (5, 2)
Let,
[tex](x_{1},y_{1}) = (1, 2)[/tex]
And, [tex](x_{2},y_{2} ) = (5,2)[/tex]
Therefore,
The distance between the points (1,2) and (5, 2)
= [tex]\sqrt{(5-1)^{2} +(2-2)^{2} }[/tex]
[tex]=\sqrt{(4)^{2}+0 }[/tex]
[tex]=4[/tex] unit.
Hence, the distance between the two points (1, 2) and (5, 2) is 4 units.
Since, the x coordinate and y coordinate of both the points (1,2) and (5, 2) are positive. Therefore, they both lie in the first quadrant. Hence, the points lie in the same quadrant.
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find the area of the figure
Answers
find the inequality of 3x-2÷4+3≥12
Answers
Answer:
x + 5 = ,3
Step-by-step explanation:
x+5-5= +3-5
x= -2
Can someone help me with these two questions plss
Answers
Answer:
c. 6
d. 3
Step-by-step explanation:
:-)
What is the solution to the equation below? √x+6 = x-6
A. x=12
B. x=3
C. x=4
D. x=10
Answers
Answer:
√x+6=x-6
squarring both side
x+6=x²-12x+36
0=x²-12x-x+36-6
x2-13x+30=0
x²-10x-3x+30=0
x(x-10)-3(x-10)=0
(x-10)(x-3)=0
either
x=10
or
x=3
Answer:
D:X=10
Explanation
Find a slope for each line (each block is one unit):
Answers
Graph a line with a slope of 1 and a y-intercept of 4.
Answers
Answer:
Step-by-step explanation:
Plot the y-intercept (0, 4). Starting at (0, 4), move your pencil point 1 space to the right, to (1, 4), and from (1, 4) up 1 space to (1, 5). Draw a straight line through (0, 4) passing through (1, 5) also.
Sunning itself on a cliff 5.8 feet above sea level. The iguana dove into the water from the cliff. When the iguana reached the deepest part of its dive, its total change in elevation was 8.3 feet. What was the iguana's position relative to sea level at the deepest part of its dive?
Answers
Answer:
deepest part of dive is 2.5 feets below sea level ;
-2.5 feets
Step-by-step explanation:
Given :
Initial Position = 5.8 feets above sea level = +5.8
Deepest part of dive = x
Change in elevation between initial position and deepest part of dive = 8.3 feets
Position relative to sea level at deepest part of dive :
x = change in elevation - Initial position
x = 8.3 feets - 5.8 feets
x = 2.5 feets
Hence, deepest part of dive is 2.5 feets below sea level
в треугольнике abc точки d и m принадежат сторонам ab и bc dm и ac параллельны докажи что треугольник bdm подобен треугольнику abc
Answers
Answer:
this is in Russian please ask in English
Step-by-step explanation:
I know what is the question but you should ask in English after translating ok
In solving quadratic equation, if the constant term is missing what is the best method to
use?
Answers
Step-by-step explanation:
If you are looking for its roots, try completing the square method, and factoring out the common terms. These two is what I usually use.What is the answer to 3/8 + 2/4
Answers
Answer:
1 1/2
Step-by-step explanation:
1.) First find the common denominator of the 2 fractions (8) 4: 4
8: 4, 8
2.) then you write a new expression with the numerator left blank and the denominator as 8 shown below in the step by step explanation. /8 + /8
3.)3/8 + 2/4 multiply by 1 both numerator and denominator for the first fraction. And multiply by 2 both numerator and denominator for the second fraction. 3/8 + 4/8.
4.) Then you add those 2 fractions which I assume you already know how by adding the numerators together, and get 12/8.
5.) You simplify 12/8 and get 1 4/8. 4/8 is equal to 1/2 so its 1 1/2.
please help me and thank you
Answers
Hope this helps
Help me plz ??? Help
Answers
Answer:
16
Step-by-step explanation:
Kyla wants to add songs to her phone to listen to while she is riding on the bus. She bought 100 songs on her account.She is planning to download an equal number of songs each week for the next 5 weeks. The number of songs left to download, y, for a certain number of weeks, c is shown in the graph.
A graph titled Song Downloading shows Number of Weeks on x-axis and Number of Songs Left to Download on y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 140 at increments of 20. A straight line joins the ordered pairs 0, 100 and 1, 80 and 2, 60 and 3, 40 and 4, 20 and 5, 0.
Part A: Determine the rate of change and the initial value (2 points) of the function show on the graph. What does each represent in the scenario (2 points)? Show/Explain the work you completed to find the rate of change and initial value (2 points).
Part B: Using the information from Part A, write the equation that would model this relationship between x and y in slope-intercept form. (4 points)
Answers
Answer:
Slope = - 20; intercept, c = 100
y = - 20x
Step-by-step explanation:
The slope (s) = Rise / Run
using the pairs : (0, 100) and (5, 0)
x1 = 0 ; y1 = 100 ; x2 = 5 ; y2 = 0
Rise = (y2 - y1) = (0 - 100) = - 100
Run = (x2 - x1) = (5 - 0) = 5
Slope = - 100 / 5
Slope = - 20
Using the slope intercept relation :
y = mx + c
m = slope ; c = intercept
y = - 20x + c
Using the point (4, 20) to find c
20 = - 20(4) + c
20 = - 80 + c
20 + 80 = c
100 = c
Hence, c = 100
Slope, m = number of songs downloaded per week
c = Total number songs at week 0
The equation expressed in slope intercept form:
General form:
y = mx + c
m = - 20 ; c = 100
y = - 20x + 100
2 1/7+1 2/5 Give your answer as a mixed number where appropriate.
Answers
Answer:
3 19/35
Step-by-step explanation:
Find the least common denominator of the two.
The LCD is 35.
Now convert the fractions to a denominator of 35.
This will be it>>>
2 5/35 + 1 14/35.
Now the answer to that will be: 3 19/35
Which pair of angles is congruent?
Answers
√26+10-15 cuanto es me ayudan ?
Answers
Step-by-step explanation:
If the whole thing is in a square root, then the answer is sqrt21.
If only sqrt26 is in the square root, then the answer is -5+sqrt26.
(esto es en español) (This is in spanish transalation)
Si todo está en una raíz cuadrada, entonces la respuesta es la raíz cuadrada 21.
Si solo la raíz cuadrada 26 está en la raíz cuadrada, entonces la respuesta es -5 + raíz cuadrada 26.
tim played 20 games of draughts he won 16 of those games.what fraction of the game did he win
b) he played 30more games he had then 68% of all his games how amny of 30 games did he win
Answers
Answers to both subparts are shown:
(A) The fraction of games Tim wins is 4/5.(B) Tim wind has 20 games when he plays 30 games.What is a fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.So, (A) fraction of the game Tim wins:
The number of games played is 20.The game won is 16.Then, the fraction will be:
16/204/5(B) Games Tim wins in 30 games.
The total number of games played is 30.The winning percentage is 68%.So, a number of games won:
30/100 × 680.30 × 6820.4Rounding off: 20Therefore, answers to both subparts are shown:
(A) The fraction of games Tim wins is 4/5.(B) Tim wind has 20 games when he plays 30 games.Know more about fractions here:
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The correct question is shown below:
(A) tim played 20 games of draughts he won 16 of those games.what fraction of the game did he win
b) he played 30 more games he had then 68% of all his games how amny of 30 games did he wi
PLEASE HELP! worth 50 points!! Please only put the right answer in I really need help trying to get my grade up..
Answers
Answer:
1) x = 41.8 deg
2) x = 64.2 deg
3) x = 51.3 deg
Step-by-step explanation:
Problem 1
For angle x, 4 is the opposite leg and 6 is the hypotenuse.
sin x = 4/6
x = sin^-1 2/3
x = 41.8 deg
Problem 2
For angle x, 14 is the adjacent leg, and 29 is the opposite leg.
tan x = 29/14
x = tan^-1 29/14
x = 64.2 deg
Problem 3
For angle xm 25 is the adjacent leg, and 40 is the hypotenuse.
cos x = 25/40
x = cos^-1 5/8
x = 51.3 deg
Which postulate proves the two
triangles are congruent
A. SAS
B. ASA
C. SSS
D. HL
Answers
Answer:
SSS
Step-by-step explanation:
1. Find the slope
>
X
18
8
10
24
0 -5
y
10
1 7
Rise =
Run =
m =
Answers
Answer:
I think the slope is y, but look for an expert opinion
Step-by-step explanation:
Please help due today
Answers
Answer:
23 = 1
46 = 2
92 = 4
138 = 6
Step-by-step explanation:
hope this helps
can anyone solve this
Answers
Answer:
Step-by-step explanation:=(1+sinA)2+cos2A/cosA(1+sinA)
=1+sin2 A+2sin A+cos2 A/cos A(1+sin A)
=1+2sin A+1/cos A(1+sin A)
=2(1+sin A)/cos A(1+ sin A)
=2sec A
Answer:
see explanation
Step-by-step explanation:
Consider the left side
[tex]\frac{1+sinA}{cosA}[/tex] + [tex]\frac{cosA}{1+sinA}[/tex] ← combine into a single fraction
= [tex]\frac{(1+sinA)^2+cos^2A}{cosA(1+sinA)}[/tex] ← expand and simplify numerator
= [tex]\frac{1+2sinA+sin^2A+cos^2A}{cosA(1+sinA)}[/tex] [ sin²A + cos²A = 1 ]
= [tex]\frac{1+2sinA+1}{cosA(1+sinA)}[/tex]
= [tex]\frac{2+2sinA}{cosA(1+sinA)}[/tex] ← factor out 2 on the numerator
= [tex]\frac{2(1+sinA)}{cosA(1+sinA)}[/tex] ← cancel (1 + sinA) on numerator/ denominator
= [tex]\frac{2}{cosA}[/tex]
= 2secA = right side, thus verified
Jonas and Marisol were the only candidates for sixth grade class president. Jonas received 60 votes and Marisol received 90 votes.
Of the 90 votes cast for Marisol, 40% were girls. How many girls voted for Marisol?
Answers
Answer:
36 girls voted for Marisol
Step-by-step explanation:
h(x) = x^3 - 2x
g(x) = 3x + 4 Find (h+g)(4)
Answers
9514 1404 393
Answer:
72
Step-by-step explanation:
h(4) = 4^3 -2·4 = 64 -8 = 56
g(4) = 3·4 +4 = 16
Then the sum is ...
(h+g)(4) = h(4) + g(4) = 56 +16
(h+g)(4) = 72
Can someone help me with this problem? 3[x(-6)]
Answers
Answer:
-18x
Step-by-step explanation:
First step: remove the parentheses.
So, you'll have -3x*6.
multiply the numbers (3 x 6 = 18)
and you'll get -18x.
hope this helps!
how do you factor: 2x + -15
Answers
Answer:
It is not factorable.
Step-by-step explanation:
It is not factorable with rational numbers.
Answer:
This expression is not factorable with rational numbers.
Step-by-step explanation:
2x+(-15)=2x-15
Please helpppp 15 points!!!
Answers
Answer:
105 students and 150 guests
Step-by-step explanation:
equation to find the answer are
1x + 5y = 855
x + y = 255
with
x + y = 255
x = 255 - y
now we replace x with (255 - y) into 1x + 5y = 855 to find y
1(255 - y) + 5y = 855
255 - y + 5y = 855
255 + 4y = 855
4y = 855 - 255
4y = 600
y = 150 (number of guests)
now we got y = 150, let's find x
x + y = 255
x + 150 = 255
x = 255 - 150
x = 105 (number of students)
(Please heart the answer if you find it helpful, it's a motivation for me to help more people)
Can someone please check my answer for this function???
Answers
Answer:
You're wrong, it's the bottom left
Step-by-step explanation:
x^2-49 is a difference of squares so it factors into (x+7)(x-7) which obviously cancels out with the denominator leaving x-7 left. This is the line you should graph, but keep in that x+7 is still in the denominator so x cannot be equal to -7 which means that this point should be be on the line which leaves the answer to be the one on the bottom left.
Find x
I need help plz :(
A. 6
B. 24
C. 12
D. 12 sqr root of 3
E. 36
Answers
Answer:
b
Step-by-step explanation:
Answer:
To determine the value of X, what you would need to do is to use a trigonometric ratio, that would make use of the value of x and the side length of 12. This can either be, sin 30 or cos 60. Both of them will enable you to solve for x.
The final value for x would be either
X = 12/Sin 30
X = 12/Cos 60
Compute these in your calculator and you will find the final value in these cases.