First, let's define variables:
A = adults
C = children
Okay, now that's done, time to set up the two equations required to solve:
10a + 7c = 6549
a + c = 783
One way you can solve this is to set up the second equation to isolate a variable. For example,
a = -c + 783
Using this, we can plug it into the first equation and solve for c.
10(-c+783) + 7c = 6549
-3c = -1281
c = 427
Now, use the value of 427and plug it in either equation to solve for a.
a + 427 = 783
a = 356
356 adult tickets were sold, and 427 children tickets were sold.
Akiko wants to fence in her [tex]12[/tex] ft by [tex]10[/tex] ft vegetable garden. There will be a path [tex]x[/tex] ft wide between the garden and the fence. The area to be enclosed by the fence will be [tex]360[/tex] sq ft. Write a quadratic function that can be used to determine the value of [tex]x[/tex].
Answer:
see below
Step-by-step explanation:
The length is 12 + 2x and the width is 10 + 2x
A = l*w
360 = ( 12+2x) ( 10+2x)
FOIL
360 = 120 + 24x+20x + 4x^2
Combine like terms
360 = 4x^2 +44x+120
Subtract 360 from each side
0 = 4x^2 +44x +120-360
0 = 4x^2+ 44x -240
For fun, lets solve
0 = 4( x^2 + 11x - 60)
0 = 4( x+15) ( x-4)
Using the zero product property
x= -15 x=4
Since we cannot have negative length
x=4 ft
Answer:
[tex]x^2+11x-60=0[/tex]
Step-by-step explanation:
Refer to the drawing.
We know that the area enclosed by the fence is 360 square feet. Remember that the area for a rectangle is given by the following formula:
[tex]A=bh[/tex]
So, let's substitute 360 for A, (12+2x) for b, and (10+2x) for h. This yields:
[tex]360=(12+2x)(10+2x)[/tex]
We can simplify this. On the right, factor out a 2 from the first term and a 2 from the second. This yields:
[tex]360=2(6+x)\cdot2(5+x)[/tex]
Multiply:
[tex]360=4(x+6)(x+5)[/tex]
Divide both sides by 4:
[tex]90=(x+6)(x+5)[/tex]
Multiply on the right:
[tex]90=x^2+6x+5x+30[/tex]
Add on the right:
[tex]90=x^2+11x+30[/tex]
Subtract 90 from both sides. So, our equation is:
[tex]x^2+11x-60=0[/tex]
And we're done!
Definition: Ifa = b. then a - c= b - c. This is the what property of equality
Answer:
Subtraction property
Step-by-step explanation:
Show the work for this problem
how do I find measure of angles
Answer:
you are going to need a protractor
Step-by-step explanation:
Find the area of quadrilateral JKLM with vertices J(-2,1), K(3,1), L(3.-2), and M(-2,-2).*
Write the converse of the following conditional? If you own a Prius, then you own a car made by Toyota.
Answer:
You own a car made by Toyota if you own a Prius.
Step-by-step explanation:
If the conditional is p->q then the converse would be q->p. So basically to get the converse switch the order of the statements.
I will give away all my points if you can answer this with no sweat.
Answer:
4
Step-by-step explanation:
it would equal 2^7/2^5, which equals 2², which equals 4
10. Calculate the speed of waves in a puddle that are .15 apart and made by tapping the water
surface twice each second.
Since the waves are 0.15 apart and made by tapping the water surface twice each second the speed of waves in the puddle is 0.6 m/s
To answer the question, we need to know what a wave is
What is a wave?A wave is a disturbance in space which carries energy from one point to another
What is the speed of a wave?The speed of a wave v = fλ where
f = frequency and λ = wavelengthWavelength of waveSince the puddles are 0.15 m are and we know that this is the distance from crest to crest.
Also, the distance from crest to crest is λ/2
So, λ/2 = 0.15
λ = 2 × 0.15 m
= 0.3 m
Frequency of wave
Also, since the tapping by the water surface is done twice each second, the frequency, f = 2 times/s = 2 Hz
Speed of waves in puddleSubstituting the values of the variables into the equation, for speed, we have
v = fλ
v = 2 Hz × 0.3 m
v = 0.6 m/s
So, the speed of waves in the puddle is 0.6 m/s
Learn more about speed of wave here:
https://brainly.com/question/4054018
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Which statements about the values of 4.099 and 40.99 are true? Select all that apply. 4.099 is 110 of 40.99. 4.099 is 1100 of 40.99. 40.99 is 10 times more than 4.099. 40.99 is 100 times more than 4.099. 4.099 is 10 times more than 40.99.
Answer:
40.99 is 10 times more than 4.099
Step-by-step explanation:
Given the values :
4.099 and 40.99
4.099 is 110 of 40.99 : 110 * 40.99 = 4508.9 (false)
4.099 is 1100 of 40.99 : 1100 * 40.99 = 45089 (false)
40.99 is 10 times more than 4.099 : (10 * 4.099) = 40.99 (true)
40.99 is 100 times more than 4.099 : (100 * 4.099) = 409.9 ( false)
4.099 is 10 times more than 40.99 : (10 * 40.99) = 409.9 (false)
Answer:
the answer is c trust me
Step-by-step explanation:
8 ghosts greet each other with 'Boo!
How many times is the phrase 'Boo! being said?
Hint For three ghosts, Boo
is said 6 times For four ghosts, Boo is
said 12 times!
Answer:
im pretty sure 16 times
Step-by-step explanation:
well if you look at it there are 8 ghost's. they are going to greet each other, soo. B would say 8x7 because 8 ghost's would say boo to 7 more. soo 8x7=56
p.s
sorry if wrong
5. Arrange the following interest rates in ascending order (least to greatest):
4.72
4 1/4
4.168
4 1/5
4 1/6
4.22
17v + 3v = 20
Solve for V.
Answer:
v=1
Step-by-step explanation:
Answer:
V = 1
Hope this helped :)
The first three terms of a geometric sequence are as follows.
-7, 14, -28
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
-7, 14, -28, 00
Answer:
The next two terms of the sequence -7, 14, and -28 are 56 and - 112.
Step-by-step explanation:
-7 * -2 = 14
14 * -2 = -28
The sequence is to multiply each number by -2.
-28 * -2 = 56
56 * -2 = -112
Answer: The next two terms of the sequence -7, 14, and -28 are 56 and - 112.
Step-by-step explanation:
What is the value of x?
Answer:
31 degrees
Step-by-step explanation:
149 + 149 = 298
360 - 298 = 62
62 / 2 =31
Answer:
61 degrees
Step-by-step explanation:
you know that there is a strait line which is equal to 180. So if you subtract 149 from 180 you get 31 which is the angle included with x. therefore you subtract your total number, which is 92 by 31 and you get 61 degrees
I need help asap I'm giving the rest of my points
Answer:
a. 32. 3
Step-by-step explanation:
4x3=12
1×3=3 (3 min missing from table)
32×3=96 (32 songs miss)
solving literal equations a-bc=d solve for a
Answer:
a=d+Bc
Step-by-step explanation:
a-bc=d
+bc
a=d+bc
Can you help me please?
Answer:
61.5 in 41 mins 90 in one hour,
Step-by-step explanation:
i multiplied 1 1/2 by 41 and by 60
hope this helps i am very sorry if it is incorrect..
Jonathan and Pedro are collecting clothes for a clothing drive. Pedro collected 1/2 as many
clothes as Jonathan did. If Jonathan collected 4 bags of clothes, how many bags of clothes
did Pedro collect?
Writo your answer as a fraction or as a whole or mixed number.
Answer:
2
Step-by-step explanation:
4/2=2
Peter wants to rent an apartment for six months . What kind of lease should he look for
Answer:
A short-term lease
Step-by-step explanation:
Answer:
A 6 month lease. NOT a yearly lease.
You rode 180 miles at 60 miles per hour. Let t be the time it took. Can t be 4 hours?
Answer:
t = 3 hours, therefore it cannot be 4 hours
Step-by-step explanation:
Divide the miles traveled by the rate you traveled. This will find the time it took to travel.
180/60 = 3
You drove 3 hours to travel 180 miles, therefore t cannot equal 4.
Solve the system of equations by using substitution. Give your final answer in the form of an ordered pair.
5x - 2y = 26
y + 4 = x
What is "fifty thousand, six hundred thirty-one" in standard form?
Answer:
50,631
Step-by-step explanation:
Answer:
55,631
Hope it helps!
For the points A(-3, 2), B(-3, 7), and C(2, 7), find the equation of the line
through B perpendicular to line AC.
Answer:
The equation of the line perpendicular to AC and passing through point B is y = -x + 4
Step-by-step explanation:
We start by finding the slope and equation of line AC
The equation of a straight line can be given as;
y = mx + c
where m is the slope and c is the y-intercept
Mathematically, the slope is given as;
m = (y2-y1)/(x2-x1)
m = (7-2)/(2-(-3)) = 5/5 = 1
So the equation becomes ;
y = x + c
We only need the slope since we are trying to get another line perpendicular to this
If two lines are perpendicular, then the product of the slopes of both lines is equal to -1
This means that m1 * m2 = -1
So this means that the slope of the perpendicular line is -1/1 = -1
Thus, the equation of the line we are finding would be;
y = -x + c
since it passes through line B, we can make a substitution of the coordinates of point B
That would be;
7 = -(-3) + c
7 = 3 + c
c = 7-3
c = 4
So the equation of that line is;
y = -x + 4 or simply y = 4-x
I need help. What is m
Answer:
A
Step-by-step explanation:
(8x + 4) = (10x-6)
If you solve this you find x = 5, plug that into one and you get 44 degrees
solve.
6- X = 2x + 9
A 3-inch by 5-inch photo is enlarged proportionally such that its smaller dimension is now 1 foot 3 inches. How many inches are in the larger dimension?
Answer:
There are 25 inches in the larger dimension.
Step-by-step explanation:
∵ 1 foot = 12 inches
∵ The small dimension after enlargement is 1 foot and 3 inches
→ Change it to inches only
∴ The small dimension = 1(12) + 3 = 12 + 3
∴ The small dimension = 15 inches after enlarged
∵ The small dimension of the photo before enlarged = 3 inches
→ Divide its length after enlarged by its length before enlarged to
find the scale of the enlargement
∵ 15 ÷ 3 = 5
∴ The scale of enlarged is 5
→ To find the larger dimension after enlarged multiply its length
before enlarged by 5
∵ The larger dimension before enlarged = 5 inches
∴ The larger dimension after enlarged = 5 × 5
∴ The larger dimension after enlarged = 25 inches
∴ There are 25 inches in the larger dimension.
Use the distributive property to rewrite the following expression.
-(x - 3) - 2(-3x - 8)
Pls I need this last question
Answer:
-5x-19
Step-by-step explanation:
-(x-3) - 2(-3x-8)
-x+3 - 6x -16
-5x-19
A boat cost $16,500 and decreases in value by 13% per year how much will the boat be worth after eight years?
Answer:
$5,415.49
Step-by-step explanation:
Cost of the boat = $16,500
Decrease in value per year = 13%
Worth of the boat in 8 years = ?
Remaining value = 100% - 13%
= 87%
Worth of the boat in 8 years = cost of the boat × remaining value^8
= $16,500 × 87%^8
= $16,500 × 87/100^8
= $16,500 × 0.87^8
= $16,500 × 0.3282116715437121
= $5,415.49
The worth of the boat after 8 years = $5,415.49
Why you do not have to do any computing or math do solve 15 x 0 x (13 + 7)? Explain.
Answer:
because when you do 15*0 it =0 so anything else multiplied by 0 is 0
Step-by-step explanation:
A 7-day cruise is 15% off the regular price of $1,800. How much is the discount?
Answer:
The discount is $270
The new price would be $1,530
Step-by-step explanation:
You just multiply 1800 times 0.15 to get how much the discount would be and then if you are trying to find the new price you would subtract the discount or multiply 1800 times 0.85 because 100-15 is 85.