Dr. Black is standing 15 feet from a streetlamp. The lamp is making his shadow 8 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the street lamp 50 degrees. To the nearest foot, the streetlamp is about
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Related Questions
Whats 12 divided by 3 1/2
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3 1/2 = 7/2
12 / 7/2 = 12*2 =24/7 = 3 3/7
Julia spends $2.25 on gas for her lawn mower. She earns $14.00 mowing her neighbor's yard. What is Julia's profit?
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What is the value of 0 in 601,199
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10,000.
Which is the graph of a logarithmic function?
A B C or D
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Answer-
The D plot represents the logarithmic function.
Solution-
1st plot represents the rectangular hyperbola (with vertical asymptote at x=3 and horizontal asymptotes at y=0),
[tex]f(x) =\frac{1}{x-3}[/tex]
2nd plot represents the straight line (passing through origin and slope 1/5),
[tex]f(x)=\frac{x}{5}[/tex]
3rd plot represents the parabola (vertex at 3, 0),
[tex]f(x)=\frac{1}{c} (x-3)^{2}[/tex] (where c is a constant)
4th plot represents the logarithmic curve,
[tex]f(x)=c\log x[/tex] (where c is a constant)
∴ The 4th graph is a graph of a logarithmic function.
Alisa says it is easier to compare the numbers in Set A (45,760 and 1,025,680) than the numbers in Set B (492,111 and 409,867). What is one way you could construct an argument justifying whether Alisa's conjecture is true?
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How many pair of socks a person has to take out from the drawer to be sure to have at least 4 pairs of blue socks?
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Carl’s Cable Company charges $55 for monthly service plus $4 for each pay-per-view movie. Teleview Cable Company charges $110 per month with no fee for movies. For what number of movies is the cost of Carl’s Cable Company less than the cost of Teleview?
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The number of movies for which the cost of Carl's Cable Company is less than the cost of Teleview is about 13.
What is inequality?The relation between two unequal expressions is defined as inequality.
Given, Carl's Cable Company charges $55 for monthly service and $4 for each movie.
Let the number of movies be x, then the total charge for Carl's Cable Company is:
Carl's Cable = 55 + 4x
The cost of Teleview Cable Company is $110.
Therefore, the cost of Carl's Cable Company is less than the cost of Teleview if:
55 +4x < 110
4x < 110 - 55
4x < 55
x < 55/4
x < 13.75
Hence, the number of movies for which the cost of Carl's Cable Company is less than the cost of Teleview is about 13.
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Final answer:
Carl's Cable Company is cheaper than Teleview Cable Company when the number of pay-per-view movies watched is less than 14. As we can't watch a fraction of a movie, Carl's Cable is less expensive for up to 13 movies.
Explanation:
To determine for what number of movies is the cost of Carl's Cable Company less than the cost of Teleview, we set up an inequality based on the cost structures provided. Let m represent the number of pay-per-view movies.
Carl's Cable Company: $55 + $4m
Teleview Cable Company: $110
To find the number of movies where Carl's is cheaper, we want to find when:
$55 + $4m < $110
Now we solve for m:
Subtract $55 from both sides to isolate the variable term: $4m < $110 - $55
Simplify the right side: $4m < $55
Divide both sides by $4 to solve for m: m < $55 / $4
Simplify: m < 13.75
Since m must be a whole number (you can't watch a fraction of a movie), Carl's Cable is cheaper for up to 13 movies.
please help with below question
find the smallest possible constant C such that x,y,z are all integers
2x+y=C
3y+z=C
x-4z=C
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C=23
[tex]\ \left \lbrace \begin{array} {r @{ = } l} 2x+y & C \\ 3y+z & C \\ x-4z & C \end{array}\right\\\\ \ \left \lbrace \begin{array} {r @{ = }l} x & \frac{7}{23}*C \\ y & \frac{9}{23} *C \\ z & \frac{7}{23}* C \end{array}\right\\\\ [/tex]
3y + z = C [2]
x - 4z = C [3]
PART 1:
Rearrange [3] like so, to get an expression for x:
x = 4z + C
Sub' expression equivalent to x into [1] and rearrange to get an expression for C:
2(4z + C) + y = C
8z + 2C + y = C
8z + C + y = 0
C = -8z - y [4]
This equation will be useful later on so I will let it be [4]
PART 2:
We will also need this rearrangement (can be found by rearranging [4]):
8z + C = -y
We need to take out x from the left side like so:
x = 4z + C
So:
8z + C = x + 4z
And so:
-y = 4z + x
y = -4z - x [5]
This one is also essential so I will let it be [5]
PART 3:
Sub' expression for C from [4] into [2] and rearrange to get an expression for z like so:
-8z - y = 3y + z
9z = -4y
z = -4y/9 [6]
PART 4:
Sub' expression for y from [5] into [2] and simplify like so:
3(-4z - x) + z = C
-12z - 3x + z = C
-11z - 3x = C
PART 5:
Now, sub' in expression for C from [3] into the equation just above and rearrange to express in terms of z:
-11z - 3x = x - 4z
7z = -4x
z = -4/7x [7]
PART 6:
Sub' in expression for z from [6] into [7] and simplify:
-4/7x = -4/9y
-36x = -28y
-9x = -7y
9x = 7y
From the equation just above; we know 9 and 7 must both multiply by two integers to give the same number;
In order to find the two integers (x and y), we first need to find the LCM (lowest common multiple) of the two so:
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, ...
63 is a the LCM, none of the multiples of 9 are also multiples of 7;
All we have to do know is set 9x and 7y equal to 63 and solve for x and y:
9x = 63
x = 7
7y = 63
y = 9
PART 7:
Now, to get z, we just sub' y = 9 or x = 7 into equations [6] and [7] respectively;
It is good practice to double check answers when you can so I would sub' both y = 9 and x = 7 into their respective equations to see if I get the same value (you should get the same value as equations [6] and [7] are both equivalent to z) and hence confirm whether my working is correct;
So:
z = -4/9y
z = -4/9(9)
z = -4
z =-4/7x
z = -4/7(7)
z = -4
As you can, see z = -4 regardless of whether I used the x in the x equation or the y in the y equation.
So, the values of x, y and z are:
x = 7
y = 9
z = -4
And the value of C, therefore, is 23
PART 8:
You should always check your values as I mentioned before so lets do that:
For [1]:
2(7) + 9 = 23
For [2]:
3(9) - 4 = 23
For [3]:
7 - 4(-4) = 23
As you can see, the integer values of x, y and z that I have found can all be subbed in to any of the equations in their respective variables and you will get the same number, 23.
I am quite sure this is the smallest value of C you would find as I did use the lowest common multiple and so I would expect I did get the smallest possible C value.
Does this table represent a function?
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q(a+y)=67y+93 help me answer this
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Item 10 A restaurant earns $1240 on Friday and $921 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day.
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The average earning over the 3 days is [tex] \frac{1240+921+x}{3}= \frac{2161+x}{3} [/tex] dollars.
we equalize this expression to $1000:
[tex]\frac{2161+x}{3} =1000\\\\ 2161+x=3000\\\\x=3000-2161\\\\x=839[/tex] dollars
Thus the equation is : [tex]\frac{1240+921+x}{3}(\$/day)=1000(\$/day) [/tex]
What is the greatest common factor of 28, 48, and 64?
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28 = 2 x 2 x 7
48 = 2 x 2 x 2 x 2 x 3
64 = 2 x 2 x 2 x 2 x 2 x 2
The only factor which appears in all lists is 2. It appears twice in the first number, so the greatest common factor in the group is 2 x 2 = 4
Please click 'thanks' for the answer :-)
The greatest common factor of 28, 48, and 64 is, 4
We have to given that,
To find the greatest common factor of 28, 48, and 64
Now, We can find prime factor all of the numbers.
Then, collect the factors which appear in all three lists:
28 = 2 x 2 x 7
48 = 2 x 2 x 2 x 2 x 3
64 = 2 x 2 x 2 x 2 x 2 x 2
Here, The only factor which appears in all lists is 2.
It appears twice in the first number,
So, the greatest common factor of 28, 48, and 64 is 2 x 2 = 4
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wildlife protection groups buld bat houses to help sve bate one bat house holds about 300 bats larry says 12 bat houses hold about 4500 bats do you agree
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one bat hous holds about 3000 bats => 300 bats / house
So, to estimate the number of bats holded by 12 bat houses do>
300 bat / house * 12 house = 3600 bats
That is very far from the 4500 bats that Larry says.
Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.
Megan solved a similar equation below. Is Megan's solution correct? Explain why or why not.
3(2x − 4) = 5x − 1
6x − 12 = 5x − 1
11x − 12 = –1
11x = 11
x = 1
can someone do it step by step?
Answers
When you use the Distributive Property, we will find...
5x - 4 = -6x - 4
Eliminate 4 by adding it to both sides.
5x = -6x
Add 6x to both sides and we get 11x = 0.
11x = 0
Divide both sides by 11.
x=0
The only mistake Megan made was when adding 5x with Megan accidentally subtracting 5x from the other side.
For this problem:
3(2x − 4) = 5x − 1
Distribute
6x - 12 = 5x - 1
Add 1 to both sides
6x - 11 = 5x
Subtract 6x from both sides
-11 = -x
Divide both sides by -1.
x = 11.
Hope this helps! Like this answer? Give it a Brainiest reward if so.
Use the distributive property to calculate what's in the parentheses
5x - 4 = -6x - 4
Add 4 to both sides
5x = -6x
(From here you can say x = 0 but here's a few final steps if you want)
Add 6 x to both sides
11x = 0
Divide both sides by 11
X=0
---------------------------------------------
Problem 2: Megan's solution
Megan correctly distributed the parentheses in her first step
Megan errored when she ADDED 5x to the left side but SUBTRACTED 5x from the right side in her third line
From that error she correctly finished the problem, but due to her error she got the wrong answer
The correct answer is x=11
State the ratio of 700 participants to 28 judges
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Solve the trigonometric equation on the interval 0 ≤ θ < 2π. (enter your answers as a comma-separated list.) 2 sin(θ) − 2 = 0
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Final answer:
The solution to the trigonometric equation 2 sin(θ) − 2 = 0 on the interval 0 ≤ θ < 2π is θ = π/2.
Explanation:
The given trigonometric equation is 2 sin(θ) − 2 = 0. To solve this equation, we can isolate the sine function by adding 2 to both sides, resulting in 2 sin(θ) = 2. Then, dividing both sides by 2 gives us sin(θ) = 1. Since we are looking for solutions on the interval 0 ≤ θ < 2π, we know that the sine function is equal to 1 at π/2. Therefore, the solution to the equation is θ = π/2.
DIVIDING ALGEBRAIC FRACTIONS
a^2-7a-18/4a^3 divided by a^2-4a-45/2a^3-4a^2 multiplied by a^2+3a-10/a^2-4+4
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Answer:
a+2/2a
Step-by-step explanation: this is the correct answer
Currently, the area of Oak Park is represented by (9x2 + 6x + 9). The city will be expanding the park this summer. The area of the expansion is represented by 8x − 7. Which polynomial expression represents the total area of Oak Park after the expansion?
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Answer:
9x2 + 14x + 2
Step-by-step explanation:
Combine like terms
(9x2 + 6x + 9) + (8x −7)
9x2 + 14x + 2
Compute
$(\sqrt{3755}+\sqrt{3752})(-\sqrt{3755}-\sqrt{3752})(\sqrt{3755}-\sqrt{3752})(\sqrt{3752}-\sqrt{3755})$.
Thanks!
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[tex](a-b)(a+b)=a^2-b^2[/tex]
For the first and third factors there will be:
[tex](\sqrt{3755}+\sqrt{3752})(\sqrt{3755}-\sqrt{3752})=(\sqrt{3755})^2-(\sqrt{3752})^2=\\\\3755-3752=3[/tex]
and for the second and fourth:
[tex](-\sqrt{3755}-\sqrt{3752})(\sqrt{3752}-\sqrt{3755})=\\\\= (-\sqrt{3755}-\sqrt{3752})(-\sqrt{3755}+\sqrt{3752})=\\\\= (-\sqrt{3755})^2-(\sqrt{3752})^2=3755-3752=3[/tex]
So the answer is:
[tex]3\cdot 3=\boxed{9}[/tex]
In your own words explain how to round 9660 to the nearest thousand
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first, find the number in the thousands place. It is the 9. Now look to the number directly to the right of it.
** if that number is 5 or above, u round the 9 up to 10.
** if that number is 4 or below, that 9 stays the same.
that number directly to the right of 9 is 6. It is above 5, therefore, u round the 9 up to a 10.
so 9660 rounded to the nearest thousand is 10,000. Because , after all, 9660 is closer to 10,000 then it is to 9000.
Find the zeros of the function
f(x)=2x^2-4x-2.9 to the nearest hundredth
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Leon evaluated the expression (–4a – 6) + a2 for a = 8. (-4(8) - 6) + 82 (-32-6) + 82 (-38) + 82 (-38) + 16 –19 + 16 –3 Analyze Leon's work. Check all that apply. Leon should have subtracted inside the parentheses before he multiplied. The expression inside the parentheses should be simplified to –26 instead of –38. Leon multiplied 8 by 2 when he should have raised 8 to a power of 2. The multiplication of two negative values in step 4 should result in a positive value. The correct answer should be 35.
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Answer:
c,d,e
Step-by-step explanation:
Final answer:
Leon should have simplified the expression inside the parentheses before adding -38 and 64.
Explanation:
Leon evaluated the expression (–4a – 6) + a2 for a = 8.
Substituting a = 8 into the expression, we get (-4(8) - 6) + 82.
Simplifying the expression, we have (-32 - 6) + 64.
Combining like terms, we get -38 + 64.
Finally, adding -38 and 64 gives us 26.
the length of the kitchen counter of Sal's house is 9 times the length of a book. The length of a book is 8 inches. What is the length, /, of the kitchen counter? Draw a picture and write an equation to solve
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The perimeter of a trapezoid is 39 – 7. Three sides have the following
lengths: 9, 5 + 1, and 17 – 6.
What is the length of the fourth side?
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9, 6, 11 are your other sides
9 + 6 + 11 = 26
32 - 26 = the fourth side
the fourth side = 6
hope this helps
Charissa is eating out with friends, and it is her turn to pay the gratuity. The bill for the food is $26.50. If she plans to tip at 20%, what should she pay if she doesn’t want to leave pennies on the table?
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So the total she’ll pay is $31.80
A baseball player went up to bat 250 times in a season. He hit the ball 100 times. Find the rate of balls hit to times at bat. Express as a simplified fraction.
a. 2/5 b.5/2 c. 2/3 d. 3/5
Answers
250/50=5
100/50=2
5/2
Final answer:
To find the rate of balls hit to times at bat, divide 100 hits by 250 at bats, simplifying the fraction by dividing both numerator and denominator by 50, resulting in a simplified fraction of 2/5.
Explanation:
The rate of balls hit to times at bat can be found by dividing the number of hits by the number of times at bat. In this case, the baseball player hit the ball 100 times out of 250 times at bat.
To find the simplified fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 50:
100 ÷ 50 = 2 and 250 ÷ 50 = 5.
Thus, the simplified fraction of the rate of balls hit to times at bat is 2/5.
A certain brand of coffee comes in two sizes. An 11.3 -ounce package costs $2.88 . A 27.8 -ounce package costs $6.48 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
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To calculate the unit price for each coffee package, you divide the total cost by the number of ounces. The 11.3-ounce package has a unit price of about $0.255 per ounce, and the 27.8-ounce package has a unit price of about $0.233 per ounce. The 27.8-ounce package is the better buy with a lower unit price.
Explanation:To find the unit price for each size of coffee package, you divide the cost by the number of ounces.
For the 11.3-ounce package:
Unit price = Total price / Number of ouncesUnit price = $2.88 / 11.3 ouncesUnit price ≈ $0.255 cents per ounce (rounded to the nearest cent)For the 27.8-ounce package:
Unit price = Total price / Number of ouncesUnit price = $6.48 / 27.8 ouncesUnit price ≈ $0.233 cents per ounce (rounded to the nearest cent)Comparing the unit prices, the 27.8-ounce package is the better buy based on the lower unit price.
To find the unit price, divide the cost by the number of ounces. The 27.8-ounce package is the better buy based on a lower unit price.
Explanation:To find the unit price for each size of the coffee, we divide the cost by the number of ounces. The unit price of the 11.3-ounce package is $2.88 divided by 11.3, which is approximately $0.255.
The unit price of the 27.8-ounce package is $6.48 divided by 27.8, which is approximately $0.233.
Based on the unit price, the 27.8-ounce package is the better buy as it has a lower unit price than the 11.3-ounce package.
Problem Page Round 84,548 to the nearest thousand.
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hope this helps
The sum of three numbers is 104. The first number is 6 less than the second. The third number is 3 times the second. What are the numbers
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Because we already know what x and z are in terms of y, we can substitute our values for x and z into the first equation. This now looks like (y-6) + y + (3y) = 104. Now we can simplify our equation to find our value for y.
y-6 + y + 3y = 104 simplifies to 5y - 6 = 104, then 5y=110, and finally y=22.
Now that we know our value for y we can find our values for x and z by substituting our value for y into the other two equations.
The second equation x = y-6 can be simplified as x = 22 - 6 and further simplified as x = 16.
The third equation z = 3y can be written as z = 3(22) or z = 66.
Our three numbers are 16, 22, and 66. Hope this helps you!
Frederick is working on a number puzzle and discovers that the product of the two base numbers is exactly twice as large as the sum of those same base numbers.
Help on this, please?
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To solve this problem, we are going to use trial and error.
If the 2 numbers are 3 and 4 then 3 and 4 is 12 and 3 + 4 = 7
which cannot be divided equally, so this is not the answer.
3 and 5 = 15 but this is not divisible by 2.
6 and 3 = 18 and 6 + 3 = 9 which is 1/2 of 18
therefore, one set is 6 and 3.