Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft. from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.
will give 5 stars and mark brainliest.
Answers
Answer:
6.67 feet
Step-by-step explanation:
The situation is as shown in the figure.
ON is the normal to the mirror at the point of incidence O
⇒ ∠BON = ∠DON = 90°
By the laws of reflection: angle of incidence = angle of reflection :
∠AON = ∠CON
⇒ ∠AOB = ∠COD
⇒tan(∠AOB) = tan(∠COD)
⇒[tex]\frac{AB}{OB}[/tex] = [tex]\frac{CD}{OD}[/tex]
⇒[tex]\frac{6}{4}[/tex] = [tex]\frac{10}{x}[/tex]
⇒x = [tex]\frac{40}{6}[/tex] = [tex]\frac{20}{3}[/tex] = 6.67 ft
∴ Distance of the mirror from basketball goal is 6.67 ft
Final answer:
Using the principles of similar triangles, we determine that the mirror is 6 feet from the basketball goal by setting up a proportion between the heights and distances of the triangles formed by the goal and Mumford's line of sight. The mirror is 6 feet from the basketball goal.
Explanation:
To determine how far the mirror is from the basketball goal, we can use the principles of similar triangles. Basketball star Mumford is a six-foot-tall senior forward, meaning he is 6 feet above the ground. The basketball goal is 10 feet tall. If he walks backward four feet, and then he is able to see the top of the basketball goal, we can set up a proportion because the angles of incidence and reflection are equal.
Let's let x be the distance from the base of the basketball goal to the mirror. We then have two similar triangles to work with:
The large triangle with the height of the goal (10 feet) and the base x + 4 feet (distance from the goal to Mumford's eyes).
The smaller triangle with the height from Mumford's eyes to the ground (which is 6 feet because he's a six-foot-tall person) and the base x (distance from the goal to the mirror).
The proportion we set up is:
(Height of basketball goal) / (Distance from goal to Mumford's eyes) = (Height of Mumford's eyes from the ground) / (Distance from goal to the mirror)
10 / (x + 4) = 6 / x
Solving for x gives us the distance from the mirror to the basketball goal:
10x = 6(x + 4)
10x = 6x + 24
4x =24
x = 6
Therefore, the mirror is 6 feet from the basketball goal.
Related Questions
6x - 11y = 29
-5x + 22 y = 40
Answers
Answer:
x=14, y=5. (14, 5).
Step-by-step explanation:
6x-11y=29
-5x+22y=40
--------------------
5(6x-11y)=5(29)
6(-5x+22y)=6(40)
-------------------------
30x-55y=145
-30x+132y=240
---------------------------
77y=385
y=385/77=5
6x-11(5)=29
6x-55=29
6x=29+55
6x=84
x=84/6=14
x=14, y=5.
A fuzzy sticker costs $.50 and an oily sticker costs $.75.
How much would k fuzzy stickers and m oily stickers cost?
Answers
Answer:
Total = 0.5k + 0.75m
Step-by-step explanation:
A saleswoman earns 9% commission on all merchandise that she sells. Last month she sold $9000 worth of merchandise. How much commission (in dollars) did she earn last month
Answers
Answer:
$810
Step-by-step explanation:
you have to turn your commission into a decimal and then multiply it by the total amount and then you will get your answer
The saleswoman earned $810 in commission last month.
Explanation:To find the commission earned by the saleswoman, we need to calculate 9% of the total merchandise sold.
9% of $9000 = $9000 * 0.09 = $810.
Therefore, the saleswoman earned $810 in commission last month.
This set of ordered pairs defines a function. {(-49,7), (-56,8), (-63,9), (-70,10)} Which table represents the inverse of the function defined by the ordered pairs? A. x 7 8 9 10 y -49 -56 -63 -70 B. y -70 -63 -56 -49 x -10 -9 -8 -7 C. y 49 56 63 70 x -7 -8 -9 -10 D. x 7 8 9 10 y 49 56 63 70
Answers
Option A. x 7 8 9 10 y -49 -56 -63 -70 is the right answer.
Step-by-step explanation:
The inverse of a function means that the input becomes the output of the function and the output becomes input. When the function is given in the form of ordered pairs, the fiirst element of each ordered pair represents input and second element represents the output.
So, for given function: {(-49,7), (-56,8), (-63,9), (-70,10)}
The inverse will be:
{(7, -49), (8,-56), (9,-63), (10, -70)}
Hence,
Option A. x 7 8 9 10 y -49 -56 -63 -70 is the right answer.
Keywords: Function, Inverse
Learn more about functions at:
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Correct Answer:
X= 7, 8, 9, 10
Y= -49, -56, -63, -70
Which of the following equations matches the proportional relationship?
(A) A cell phone rate plan costs 6 cents per minute.
y= 0.06x
(B) A bag of 10 apples costs $6.
y= 60x
(C) A car is driving at an average speed of 60 miles per hour.
y= 0.60x
(D) A person burns 6 calories per minute using a rowing machine.
y= 60x
Answers
Answer:
Option (A) will be the correct match.
Step-by-step explanation:
We are asked to find which of the given equations matches the proportional relationship.
The only option (A) matches,
It is given that a cell phone rates plan costs 6 cents per minute.
Now, 6 cents is equivalent to $0.06.
Therefore, for a call of duration x minutes the cost of the call y, in dollars, will be given by
y = 0.06x
So, option (A) will be the correct match. (Answer)
Corbin’s parents want to save $50,000 for his college education and already have $25,000. About how long would it take them to double their current savings if they can earn an 8% interest rate?
Answers
Answer:
about 9 years
Explanation:
To solve this problem we will use what is known as 'The Rule Of 72.' This particular rule is what the Mathematical World considers a 'short cut.' That's because it is an efficient way to calculate how long it takes money to double, base solely on the interest rate. However, it is important to remember that this rule only provides an estimate, and not an exact amount of years.
The Rule Of 72 is as follows:
[tex]\displaystyle\frac{72}{[interest][rate]}[/tex] = time it takes for investment to double
*please note that I separated the word 'interest' and 'rate' using brackets. however, please ignore them. as I only used the brackets to separate the words since the equation option does not allow space between letters.
Now that you understand the Rule Of 72, let's use it to solve the given problem.
Corbin’s parents want to save $50,000 for his college education and already have $25,000. About how long would it take them to double their current savings if they can earn an 8% interest rate?
Although the first sentence in the problem gives us information of the parents goal and their current amount saved, this information will not be useful to us. As the Rule Of 72 goes, we only need to know the interest rate to solve.
Looking at the second sentence it states the interest rate is: 8%
Now substitute the interest rate in the Rule Of 72.
[tex]\displaystyle\frac{72}{[interest][rate]}[/tex] ⟶ [tex]\displaystyle\frac{72}{8}[/tex]
The last step is to simplify (or divide).
[tex]\displaystyle\frac{72}{8} = 9[/tex]
So, according the Rule Of 72, it will only take about 9 years to double their current savings.
Answer:
9 years
Step-by-step explanation:
i did that and i got it right
Which of the following represents the equation of the inverse of y=5x-20
Answers
The equation of the inverse of y = 5x - 20 is y = (x + 20)/5.
Explanation:To find the equation of the inverse of y = 5x - 20, we need to switch the x and y variables and solve for y. So the inverse equation will be x = 5y - 20. Now, let's isolate y by adding 20 to both sides: x + 20 = 5y. Next, divide both sides by 5: (x + 20)/5 = y. Therefore, the equation of the inverse is y = (x + 20)/5.
What is the value of p?
LaTeX: (21+9)-(8-4)=p( 21 + 9 ) − ( 8 − 4 ) = p
Group of answer choices
A. 42
B. 26
C. 18
D. 8
Answers
Answer: B. 26
Step-by-step explanation:
(21+9)-(8-4)=p
30-4=p
26=p
44. Melissa helps her grandfather at his store. Each mornin
ther at his store. Each morning before the store opens, she places a
total of $100 into the cash register so that change can be made for purchase
must include the following:
change can be made for purchases. The total amount
• $20 in five-dollar bills and $30 in one-dollar bills
• At least one roll each of quarters, dimes, nickels, and pennies
i ne partially completed chart below shows the dollar value for each kind of money that Melissa
must put into the cash register. Complete the chart to show one way Melissa could make a tota
must put into the
of $100.
Money to be placed in the Cash Register
Kind of Money
Dollar Amount
of Each Kind
of Money
Number of Each
Kind of Money
to be placed in
Cash Register
Total Amount of
Each Kind of
Money
$20.00
$30.00
30
$5 bill
$1 bill
Rolls of Quarters
Rolls of Dimes
Rolls of Nickels
Rolls of Pennies
$5.00
$1.00
$10.00
$5.00
$2.00
$0.50
$100.00
Answers
HOW TO: SOLVE AN APPLICATION
Step 1. Identify what you are asked to find and choose a variable to represent it.
Step 2. Write a sentence that gives the information to find it.
Step 3. Translate the sentence into an equation.
Step 4. Solve the equation using good algebra techniques.
Step 5. Check the answer in the problem and make sure it makes sense.
Step 6. Write a complete sentence that answers the question.
Remember that whatever the application, once we write the sentence with the given information (Step 2), we can translate it to a percent equation and then solve it.
Do you pay a tax when you shop in your city or state? In many parts of the United States, sales tax is added to the purchase price of an item. See Figure 6.7. The sales tax is determined by computing a percent of the purchase price.
To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost—this is what the customer pays.
Which postulate proves these two triangles are congruent?
Answers
Answer:
the ASA which is B. proves that the two triangles are congrugent
which of the following is important to remember when writing a job object? select all that apply
Answers
Answer:
i believe it is a and b
Step-by-step explanation:
Answer:
make it general to include a career goal and qualifying skills.
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
which of the following is important to remember when writing a job objective select all that apply :
make it general to include a career goal and qualifying skills. make it as detailed as possible. write to the highest job level your qualified for. write to the lowest job level your qualified for. Included only jobs that are located where you live. Included only jobs that are located where you want to live.My answer:
We need to understand what is a career objective?
It is a short introduction about your resume or CV to prove recruiters why they should hire you. It should be short and attractive with no more than five lines. Declaration career goals should be realistic and specific roles (SMART goal) In this case, a joint statement with career goals and skills your eligibility can serve as a good job goals
Only the first choice is the best answer for this question.
Hope it will find you well.
Two different ways to show 38
Answers
Answer:
Two ways to show 38 is 12 x 3 = 38 and 1 x 38 = 38.
Step-by-step explanation:
Hope it helps! :)
There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Find the numbers.
Answers
There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Then the numbers are 45 and 19
Solution:Given that, There are two numbers whose sum is 64.
Let the number be a and b in which a is bigger.
Then, a + b = 64 ------ eqn (1)
The larger number subtracted from 4 times the smaller number gives 31.
4 x b – a = 31
4b – a = 31 ----- eqn (2)
We have to find the numbers.
So, from eqn (2)
a = 4b – 31
Subatitute a in (1)
4b – 31 + b = 64
On solving we get
5b = 64 + 31
5b = 95
b = 19
So, b = 19, then eqn 1
a + 19 = 64
On simplification,
a = 64 – 19
a = 45
Hence, the two numbers are 45 and 19
what answer list all the common factors of 18 and 32
Answers
Answer:
Common factors of 18 & 32: 1, 2
Step-by-step explanation:
1 x 18 = 18
1 x 32 = 32
2 x 9 = 18
2 x 16 = 32
~
Which CANNOT be used in a proof?
A) Theorems
B) Postulates
C) Properties
D) Undefined terms
Answers
find the measure of the complement and supplement of 3y
Answers
Answer:
Step-by-step explanation:
x + y = 180
x = 3y + 8
3y+8 + y = 180
4y = 172
y = 43 degrees
x = 180-43 = 137 degrees
3/4(8p+12)+3/8(16p-8)
Answers
6 • (2p + 1) Is the correct answer.
*^<Please Help>^*
Suppose x is an odd number. Write an expression to represent each of the following:
a. The odd number immediately following x. _________
b. The odd number immediately preceding x. _________
Thank You!! =^)
Answers
Answer:
a. The odd number immediately following x = ( x+ 2)
b. The odd number immediately preceding x = ( x- 2)
Step-by-step explanation:
Odd Numbers : The number which DO NOT have 2 as their common factor are called odd numbers.
Hence, odd number IS NOT divisible by 2.
Some examples are : 1,3,5,7,9,..........
So, by the given examples, we can see that the difference between any TWO consecutive odd number is ALWAYS 2.
Here, given x : odd number
So, using the above argument :
a. The odd number immediately following x = ( x+ 2)
b. The odd number immediately preceding x = ( x- 2)
Final answer:
a. The expression for the odd number immediately following an odd number x is x + 2.
b. The odd number immediately preceding x is x - 2.
Explanation:
a. If x is an odd number, the next consecutive number is an even number, which is obtained by adding 1 to x. Since odd numbers are two units apart, adding 2 to an odd number x would result in the next odd number. Therefore, the expression to represent the odd number immediately following x would be x + 2.
b. Similarly, the odd number immediately preceding an odd number x can be found by subtracting 2, because the prior odd number is two units less than x. The expression for the odd number immediately preceding x is x - 2.
The population of Australia is approximately 19,500,000. Approximately 195,000 are of the ethnic group called
Aborigines. The Aborigines population is about what percent of the total population?
Answers
Answer:
1% of the whole australian population is Aborigines.
Step-by-step explanation:
Do [tex]\frac{part}{whole}[/tex] which is [tex]\frac{195000}{19500000}[/tex] and you get the answer 0.01 which (as a percent) can also be recognized as 1%.
Final answer:
The Aboriginal population forms about 1% of the total population of Australia when using the provided figures of a total population of 19,500,000 and an Aboriginal population of 195,000.
Explanation:
To calculate the percentage of the Aboriginal population in Australia relative to the total population, we can use the following formula:
Percentage = (Part / Whole) × 100
Here the 'Part' is the Aboriginal population and the 'Whole' is the total population of Australia. Plugging in the values provided:
Total Population (Whole) = 19,500,000Aboriginal Population (Part) = 195,000Percentage of Aboriginal population = (195,000 / 19,500,000) × 100
Perform the division:
Percentage = 0.01 × 100
Finally, we multiply by 100 to convert the decimal to a percentage:
Percentage = 1%
Therefore, the Aboriginal population forms about 1% of the total population of Australia. Note that this number might be an underrepresentation since recent estimates indicate that the Aboriginal population is about 450,000, which would be a larger percentage.
the school office users r reams or white paper and 3 reams of blue paper every day use distributive property to write and simplify an expression for how much paper the school office uses in one day
Answers
Answer:
(500r + 1500) sheets per day.
Step-by-step explanation:
The school office uses r reams of white paper and 3 reams of blue paper every day.
Now, the total number of reams of paper that the school office uses every day will be (r + 3) reams.
Now, we know that 1 ream of paper is equivalent to 500 sheets of paper.
So, the school office uses a total 500(r + 3) sheets of paper every day.
Now, using the distributive property the total number of sheets will be = (500r + 1500) (Answer)
Answer:(500+1500)
Step-by-step explanation:
find the distance between (20, -2) and (19, 5)
any help would be appreciated thx! ❤❤❤
Answers
Answer: 5 root 2
Step-by-step explanation:
using pyth. theorem
x^2= 1^2 +7^2
x^2 = 50
x = 5 root 2
Answer:
Square root of 50 approx. 7.07
Step-by-step explanation:
Do the distance formula, Which is d= sqrt of (xsub2-xsub1)squared + (ysub2-xsub1)Squared.
It would be d= sqrt of (19-20)^2 +(5-(-2))^2 = sqrt of 50
What is the sum of a number and 5
Answers
Answer:
x+5
Step-by-step explanation:
x+5
Please answer these 3 questions
Answers
1. 64 - 7c
2. 4x-3
3. p< -28
Step-by-step explanation:
6. -6 -7(c+10)
[tex]-6-7c+70\\-7c+64\\64-7c[/tex]
64 - 7c
7. 3x+4(x-6)-3(x-7)
[tex]3x+4x-24-3x+21\\4x-3[/tex]
4x-3
8. p+4 < -24
Subtracting 4 from both sides
[tex]p+4-4<-24-4\\p<-28[/tex]
p< -28
Keywords: linear equations, subtraction
Learn more about linear equations at:
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if anna had 50 apples and jack had 75 green apples how much is all together
Answers
Answer: 125 apples
Step-by-step explanation:
If Johnny has 22 biscuits and Lucy has 5 how many biscuits does Ruby have?
Answers
Answer:
Ummmmm none I guess
Step-by-step explanation:
rawr
Answer: 27
Step-by-step explanation: bc thats what some random persons teacher said.
please answer me ,,,,,
Answers
Answer:
3/10
Step-by-step explanation:
Okay so we know that a whole pizza = 1
First of all let's convert all the denominators
1 = 10/10
1/2 = 5/10
1/5 = 2/10
5/10 + 2/10 = 7/10
10/10 - 7/10 = 3/10
Leonard wants to save $100 in the next 2 months. He knows that in the
second month, he will be able to save $20 more than the first month.
How much should he save each month?
Answers
Answer:
$40,$60
Step-by-step explanation:
Let the money in the first month be x.
2x+20=100
x=40
-5/7 is greater than -4/5
Answers
Answer:
Yes.
Step-by-step explanation:
Forget about the negative sign for now.
Just compare 5/7 and 4/5 first.
Find the common denominator so it's easy to determine which one is bigger/larger.
5/7=25/35 and 4/5=28/35
From here, you can tell which one is bigger/larger, right?
Definitely, 25/35<28/35.
5/7<4/5, but don't forget the negative sign.
It's -5/7 compared to -4/5, so the answer is yes, -5/7>-4/5.
Because it is..................
What is the area of a circle with a diameter of 4x - 24? Specifically what steps would you take?
Answers
Answer:
12.56x^2+452.16
Step-by-step explanation:
A=pie r^2
(4x-24)/2= 2x-12 which is your radius
(2x-12)^2=4x^2+144
Pie=3.14ish
3.14(4x^2+144)
12.56x^2+452.16
Answer:
Step-by-step explanation:
The formula for the area of a circle is
A = πr². We need the radius, r, to calculate the circle.
If the diameter of the circle is 4x - 24, then the radius is half that, or
2x - 12.
Then the area of the circle in question is A = πr², or
A = π(2x -12)²
If desired, this could be expanded:
A = π(4)(x - 6)² = 4π(x^2 -12x + 36)
Simplify this equation 6√40 -2√90 +3√160
Answers
Answer:
BRAINLIEST PLZZZ
Step-by-step explanation:
Pull terms out from under the radical, assuming positive real numbers.
Exact Form:
18 √ 10
Decimal Form:
56.92099788
…