Identify the perimeter and area of an equilateral triangle with height 12√2cm. Give your answer in simplest radical form. PLEASE HELP ASAP!!
Answers
Answer: (D) P=24√6, A=96√3
Step-by-step explanation:
Consider ΔABC where D is the midpoint of BC. Since ABC is an equilateral triangle, then segment AD is a perpendicular bisector with length of 12√2. This creates ΔADC which is a 30°-60°-90° triangle.
Now you can use the rules for this special triangle to find the length of the hypotenuse.
30° ⇄ side length "a" base - DC on ΔADC
60° ⇄ side length "a√3" height - AD on ΔADC
90° ⇄ side length "2a" hypotenuse - AC on ΔADC
Step 1: solve for "a"
[tex]AD: a\sqrt3=12\sqrt{12}[/tex]
[tex]\dfrac{a\sqrt3}{\sqrt3}=\dfrac{12\sqrt2}{\sqrt3}[/tex]
[tex]a=\dfrac{12\sqrt2}{\sqrt3}\bigg(\dfrac{\sqrt{3}}{\sqrt{3}}\bigg)[/tex]
[tex]= \dfrac{12\sqrt6}{3}[/tex]
[tex]=4\sqrt6[/tex]
Step 2: solve for "2a"
[tex]AC: 2a =2(4\sqrt{6})[/tex]
[tex]=8\sqrt{6}[/tex]
Step 3: find the perimeter
The side length is equivalent for all 3 sides so
P = 3(AC)
[tex]=3(8\sqrt{6})[/tex]
[tex]=24\sqrt{6}[/tex]
Step 4: find the area
[tex]A=\dfrac{1}{2}b \cdot h[/tex]
[tex]=\dfrac{1}{2}(8\sqrt6)(12\sqrt2)[/tex]
[tex]=(48\sqrt{12})[/tex]
[tex]=(96\sqrt3)[/tex]
Related Questions
There are 8 brooms and 6 mops in a janitors closest. What is the ratio of the number of mops to the number of brooms
Answers
Answer:
The ratio of mops to brooms is 3:4
Step-by-step explanation:
To find this, we first need to simply plug in the numbers.
Mops:Brooms
6:8
Now we can simplify by noticing that both are divisible by 2
3:4
Answer:
IT SAID 3/7 FOR ME!
HDJKSHFNDSKLFDSFDS
Step-by-step explanation:
PLEASE SOMEONE HELP NOW 30 points!!!!!!!!!!!
Answers
The answer to this question is -6.
To solve this problem, we need to understand certain properties about exponents. To begin, let's remember that when we raise a number, the base, in this case y, to a certain power that is then raised to another power, we multiply these two exponents together when evaluating. Another important concept that is vital to understanding this problem is that negative exponents are positive exponents in the denominator of fractions. For example, y^-4 = 1/y^4.
Using this knowledge, we know that b * 4 must equal 24 (because raising a power to another power implies multiplication). Therefore, we know that the magnitude of the variable b must be six. However, we must also recognize that y^24 is in the denominator of the answer, which means that one of the exponents of the variable y must be negative. Since the exponent 4 is not negative, the exponent of b, or 6, must be.
Therefore, your answer is -6.
If you do not understand my explanation, feel free to ask me any clarifying questions.
Hope this helps!
Answer:
-6
Step-by-step explanation:
(y^b)^4 = 1/ (y^24)
We know (a^b)^c = a^(b*c)
and 1/ y^a = y ^ -a
y ^(4b) = y ^ (-24)
When we have the same bases, the exponents must be the same
4b = -24
Divide by 4
4b/4 = -24/4
b =-6
What is the equation of the line that contains the point (3,-1) and has the same slope as the the line y=1/3x+5
Answers
Answer:
y = 1/3x - 2
Step-by-step explanation:
Line y = 1/3x + 5 has slope 1/3, so the line we are looking for also has slope 1/3.
y = 1/3x + b
We know a point, so we plug in the values of x and y, and we solve for b.
y = 1/3x + b
-1 = (1/3)(3) + b
-1 = 1 + b
b = -2
Now that we know b, the equation is:
y = 1/3x - 2
plsplsplsplsplsplspls help!!!!!!!!
Answers
Answer:
1. My estamite, close to -1
2. 1.5
3. Remote interior angles
4. 84
5. 60 degrees
Step-by-step explanation:
15 Points!!!!!!!!! Mike attends basketball practice sessions every week. The coach assesses his progress at the end of each session by asking him to attempt 10 free throws. Prior to starting the sessions, Mike missed 6 out of 10 free throws. At the end of the first practice session, Mike missed 5 of his 10 free throws. At the end of the second session, he missed 4 of his 10 free throws. This constant decrease in the number of missed throws continues until Mike does not miss any of his 10 free throws at the end of a practice session. If the number of free throws Mike misses is dependent on the number of practice sessions he has attended, select the appropriate domain that describes this relationship.
A. D = [0, 10]
B. D = {0, 1, 2, 3, 4, 5, 6}
C. D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
D. D = [0, 6]
Answers
Answer:
In the case of Mike's free throws, the Domain that describes this relationship can be either B or D.
Step-by-step explanation:
In the case of a relationship that represents a 'constant' increase or decrease, we know that there will be an independent and dependent variable. The independent variable is our 'x' value and the dependent variable is our 'y' value. In this case, they tell us that the number of free throws Mike misses is dependent on the number of practices sessions he has attended. Therefor, 'x' would represent the number of practices and 'y' would represent the number of missed free throws. At the start, before practices or an 'x' value of 0, Mike, misses 6 free throws. He continues to decrease his missed throws by for each practice, until the sixth practice where he misses none. So, the 'x' values would be 0, 1, 2, 3, 4, 5, and 6. This can be shown by letter 'B', which includes all numbers, or letter 'D', which represents all numbers between, and including 0 and 6.
Answer:
I'd choose B since it includes all of the numbers.
Step-by-step explanation:
Enter numbers into the table so that the paired values are in a proportional relationship.
x 1 3 ____ 7 9
y ____ 18 30 42 54
Answers
Answer:
x- 5
y- 6
Step-by-step explanation:
A proportional relationship is a relationship for which a proportional constant y/x exists and for which it passes through (0,0) or the origin.
The proportional constant is 6.
18/3=6
42/7=7
54/9=6
Thus the filled in blanks should be x 1, 3, 5, 7, 9 and y 6, 18, 30, 42, 54.
Answer:
The missing numbers are 5 and 6.Step-by-step explanation:
From the given table, if we divide each pair as y/x, we find the ratio is 6.
[tex]\frac{18}{3}=6\\\frac{42}{7}=6\\\frac{54}{9}=6[/tex]
Therefore, the missing numbers have to be in the same ratio.
[tex]\frac{x}{1}=6\\x=6[/tex]
[tex]\frac{30}{x}=6\\ x=5[/tex]
So, the missing numbers are 5 and 6, because they are also in the same ratio of 6.
A new sports store recently opened downtown that specializes in baseball cards. Delmar has over 200 baseball cards in his collection and plans to see how much money he can get for some of his cards. After looking through Delmar's cards, the dealer tells Delmar that 15 of the cards can be sold for $23.50 each, and 27 of the cards can be sold for $32.50 each. The rest of the cards can be sold somewhere in the range of $3 to $10 each. If Delmar sells all of the cards worth $23.50 and $32.50, how much money would Delmar receive?
Answers
Answer: 15 of the cards can be sold for $23.50 each, and 27 of the cards can be sold for $32.50 each. This is all he wants to sell so the answer would be (23.5 x 15) + (27 x 32.5)
$1230
Please mark brainliest.
Step-by-step explanation:
Which additional information could be used to prove that the triangles are congruent using AAS or ASA? Check all that apply.
Answers
Consider the given triangles.
Given: [tex]\angle C \cong \angle Q[/tex]
ASA congruence criterion states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
AAS congruence criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Consider the first part:
1. In triangles ABC and QPT
If we take [tex]\angle B \cong \angle P , BC \cong PQ[/tex] along with the given condition.
Then the triangles are congruent by ASA congruence criterion.
2. If we take [tex]\angle A \cong \angle T[/tex] and [tex]AC= TQ=3.2[/tex] along with the given condition.
Then the triangles are congruent by ASA congruence criterion.
3. As,[tex]\angle C \cong \angle Q[/tex], [tex]\angle A \cong \angle T[/tex] and [tex]\angle B \cong \angle P[/tex], so the triangles can not be congruent.
4. If we take [tex]\angle A \cong \angle T[/tex] and [tex]BC \cong PQ[/tex] along with the given condition.
Then the triangles are congruent by AAS congruence criterion.
5. If we take AC=TQ=3.2 and CB=QP=3.2 along with the given condition, then the triangles are congruent but by SAS congruence criteria neither by ASA nor AAS congruence criterion.
Answer: it’s A,B, and D
Rearrange the formula V = 1 3 πr2h for h. A) h = 3V πr2 B) h = V 3πr2 C) h = 3πr2 V D) h = πr2 3V
Answers
Answer:
A) h = 3V/ πr^2
Step-by-step explanation:
V = 1/ 3 πr^2h
Multiply each side by 3
3V = 3*1/ 3 πr^2h
3V = πr^2h
Divide each side by πr^2 to isolate h
3V /πr^2 = πr^2/πr^2 h
3V /πr^2 = h
Simplify -4m + 5n - 2 - 3m + 3n + 7.
A) -7m + 8n - 9
B) -7m + 8n + 5
C) -7m2 + 8n2 - 9
D) -m + 8n - 9
Answers
-4m + 5n - 2 - 3m + 3n + 7 combine like terms
= (-4m - 3m) + (5n + 3n) + (-2 + 7)
= -7m + 8n + 5 → B)I NEED HELP NOW WHAT IS THE ANSWER PLZ HELP 40 POINTS
Answers
Answer:
B 8 n^18
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length of a square
64 n^36 = s^2
Take the square root of each side
sqrt(64 n^36 )= sqrt(s^2)
Sqrt(ab) = sqrt(a) sqrt(b)
sqrt(64) sqrt(n^36) = s
8 n^18 =s
Which equation represents a proportional situation?
y = – 3x + 4
y = 3x – 12
y = –2x + 23
y = 9x
Answers
Answer:
option D is correct.
y=9x represents a proportional situation
Step-by-step explanation:
If two quantities are said to have a proportional relationship if they vary in such a way that one of the quantities is a constant multiple of the other i.e,
y = |k|x ; where |k| is constant proportionality.
By definition :
y =9x where k =9 is constant , represents a proportional relationship.
Answer:
The correct answer option is y = 9x.
Step-by-step explanation:
From the given equations as the possible answer options, y = 9x is the correct answer which represents a proportional situation.
Two values (variables in this case) are said to be proportional if they change in a way such that there is a constant multiple multiplied to one of the values.
Here, in the equation y = 9x, y and x are the two variable and 9 is the constant multiple.
Given: f(x) = x2 + 7x + 10. From the Rational Root Theorem, we know p=10 and q=1. List all potential roots using the ratio p/q.
Answers
Answer:
There are 8 roots
1,2,5,10,-1,-2,-5,-10
Step-by-step explanation:
The rational root theorem says take all the factors of p over all the factors of q
p = 1,2,5,10
q = 1
roots ± 1,2,5,10
--------------------
1
roots ±1, ±2, ±5,±10
I have $4.85 in my pocket what fraction in simplest form represents the amount of money I have in my pocket
Answers
Answer:97/20
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER
What is the equation of the line represented by the table of values below?
A. Y = 3x - 2
B. Y = -3x + 2
C. Y = 3x + 2
D. Y = -3x - 2
Answers
Answer:
Step-by-step explanation:
A regulation soccer field has an area of 59,400 square feet. If the length is 330 feet, what is the width in feet
Answers
Answer:
The answer is 180 feet.
Step-by-step explanation:
Here's your equation. (330 x W = 59,400). If you want to find the width then divide 59,400 by 330 and you get 180 feet.
You can check by multiplying 330 and 180 which will result in 59,000.
So the correct answer is 180 feet.
Given: g(x) = √ x− 3 and ℎ(x) = 2x − 7.
a) What are the restrictions on the domain of g° ℎ? Show your work for full credit.
xx ≥ _____________
b) What is g(ℎ(13))? Simplify your answer in lowest terms. Show your work for full credit
Answers
Answer:
Restrictions on the domain: x>=5
g(h(13)) = ±4
Step-by-step explanation:
g° ℎ is the composite function
We stick the function h in for x in the function g
g(x) = sqrt(x-3)
h(x) = 2x-7)
g(h(x)) = sqrt( 2x-7 -3)
g(h(x)) = sqrt( 2x-10)
The restrictions on the domain , or the allowed values of x
sqrt (2x-10) >= 0
Square each side
2x-10 >= 0
2x>= 10
Divide by 2
x>=5
Let x=13
g(h(13)) = sqrt( 2*13-10)
sqrt(26-10)
sqrt(16)
±4
Matt has 12 balloons that he wants to give to 4 friends. He wants each friend to have the same number of balloons. Select the three statements that describe how Matt should give the balloons to his friends.
Answers
Answer:
Step-by-step explanation:
Math has 12 ballons.
If we divide 12 by 4 friends we got 3, so we can have those situations:
He can give 3 to each friend, and he will not have any.
Also, he can give 2 for each friend , and he will have 4 more.
Also, he can give 1 for each friend, and he will have 8 more.
Matt has 12 balloons that he wants to give to 4 friends.
He wants each friend to have the same number of balloons.
Select the three statements that describe how Matt should give the balloons to his friends.
Each friend gets 124 balloons.
Each friend gets 12÷4 balloons.
Each friend gets 3 of the 12 balloons.
I got this correct and I also added screen shots that I got it correct
Yuki bought a pound of confetti for \$12$12. What is the price, in dollars, per ounce of confetti? There are 1616 ounces in 11 pound.
Answers
Answer:
$0.75
Step-by-step explanation:
We have been given that Yuki bought a pound of confetti for $12.
To find the price of per ounce of confetti, we will divide the total price of 1 pound confetti by number of ounces in 1 pound.
1 pound = 16 ounces.
Let us divide 12 by 16 to find the price of confetti per ounce.
[tex]\text{Price of per ounce confetti}=\frac{12}{16}[/tex]
[tex]\text{Price of per ounce confetti}=\frac{3}{4}[/tex]
[tex]\text{Price of per ounce confetti}=0.75[/tex]
Therefore, the price of per ounce confetti is $0.75.
The function f(x)=125(0.9)x models the population of a species of fly in millions after x years.
How does the average rate of change between Years 1 and 5 compare to the average rate of change between Years 11 and 15?
The average rate of change is about 13
as fast in Years 1 to 5.
The average rate of change is about 3 times as fast in Years 1 to 5.
The average rate of change is about 12
as fast in Years 1 to 5.
The average rate of change is 2 times as fast in Years 1 to 5.
Answers
Answer: (B) 3 times as fast
Step-by-step explanation:
rate of change is the "slope" between the given interval.
f(x) = 125(.9)ˣ
f(1) = 125(.9)¹
= 112.5
f(5) = 125(.9)⁵
= 73.8
[tex]\dfrac{f(5) - f(1)}{5 - 1} = \dfrac{73.8-112.5}{5-1} = -\dfrac{38.7}{4} = -9.675[/tex]
********************
f(11) = 125(.9)¹¹
= 39.2
f(15) = 125(.9)¹⁵
= 25.7
[tex]\dfrac{f(15) - f(11)}{15 - 11} = \dfrac{39.2-25.7}{15-11} = -\dfrac{13.5}{4} = -3.375[/tex]
********************
The rate of change from years 1 to 5 is approximately 3 times the rate of change from years 11 to 15.
please help on this one?
Answers
Answer:
D
Step-by-step explanation:
The factorization of these is ...
A: F(x) = (x -3)(x +3)² . . . . 3 real roots, one with multiplicity 2.
B: F(x) = (x -3)³ . . . . 3 real roots, one with multiplicity 3.
C: F(x) = (x +3)³ . . . . 3 real roots, one with multiplicity 3.
D: F(x) = (x +3)(x² +9) . . . . 1 real root, 2 complex roots.
_____
Note
A graphing calculator is helpful in factoring these. The quadratic factor of option D was found using synthetic division, after the real root was found using the graphing calculator.
Simplify: (7+2a)·3–20 =
Answers
Final answer:
The expression (7+2a)·3−20 simplifies to 1 + 6a. You distribute the 3 to the terms inside the parentheses and then subtract 20 from 21 to combine like terms.
Explanation:
To simplify the algebraic expression (7+2a)·3−20, we start by distributing the 3 to both terms inside the parentheses.
7·3 + 2a·3 − 20 = 21 + 6a − 20
Next, we eliminate terms wherever possible by combining like terms. We subtract 20 from 21, which gives us:
21 − 20 + 6a = 1 + 6a
So, the expression simplifies to:
1 + 6a
We can check if this is reasonable by substituting a value for 'a'. If 'a' is 3, for example, then:
1 + 6×3 = 1 + 18 = 19
Which is the result we would expect after simplifying the original expression with 'a' being 3.
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
Answers
Answer:
Its the graph at the bottom right.
Step-by-step explanation:
Adding f(x) and g(x) we get
-x^2 + 3x + 5 + x^2 + 2x
= 5x + 5 = (f+ g)(x)
This has a slope of 5 and a y-intercept of 5, so its bottom right graph.
(f + g)(x) is a composite function of f(x) and g(x), and it is represented by graph (c)
The functions are given as:
[tex]\mathbf{f(x) = -x^2 + 3x + 5}[/tex]
[tex]\mathbf{g(x) = x^2 + 2x}[/tex]
To calculate (f + g)(x), we make use of the following formula
[tex]\mathbf{(f + g)(x) = f(x) + g(x)}[/tex]
So, we have:
[tex]\mathbf{(f + g)(x) = -x^2 + 3x + 5 + x^2 + 2x}[/tex]
Collect like terms
[tex]\mathbf{(f + g)(x) = x^2-x^2 + 3x+ 2x + 5 }[/tex]
Evaluate the like terms
[tex]\mathbf{(f + g)(x) = 5x + 5}[/tex]
The above function is a linear function.
A linear function is represented as:
[tex]\mathbf{y = mx + c}[/tex]
Where m represents the slope, and c represents the y-intercept
So, by comparison:
[tex]\mathbf{m = 5}[/tex]
[tex]\mathbf{c = 5}[/tex]
The graph that has a slope of 5, and a y-intercept of 5 is graph (c)
Hence, graph (c) represents (f + g)(x)
Read more about composite functions at:
https://brainly.com/question/20379727
Tracy ran a lap around the school track in 74.2 seconds.Malcom ran a lap in 65.92 seconds. Estimate the difference in the times in which the students completed the lap.
Answers
Answer:
The difference would be 8.3 second
Step-by-step explanation:
Tom and his brothers caught 100 fish on a week-long fishing trip. the total weight of the fish was 239 pounds. part 1 out of 3 enter the expression that will find the weight of one fish. assume that the weight of each fish is the same. the expression that gives the weight of one fish is ÷ .
Answers
Answer:
Expression that gives weight of 1 fish: [tex]\frac{239}{100}[/tex].
The weight of 1 fish is 2.39 pounds.
Step-by-step explanation:
We have been given that Tom and his brothers caught 100 fish on a week-long fishing trip. The total weight of the fish was 239 pounds.
Assuming that the weight of each fish is the same, we can find weight of 1 fish by dividing the total weight of fish by total number of caught fish.
[tex]\text{The weight of 1 fish}=\frac{239}{100}[/tex]
Therefore, the expression that gives the weight of 1 fish is [tex]\frac{239}{100}[/tex].
Upon dividing 239 by 100 we will get,
[tex]\text{The weight of 1 fish}=2.39[/tex]
Therefore, the weight of 1 fish is 2.39 pounds.
Anya grandfather gives her a collection of souvenir subway tokens. He gives her 9 tokens from the 1980s. She wants to make a display of each type of token. She wants all three displays to have rows with the same number of tokens in them . Are the number of tokens in each of Anya's collections prime or composite numbers? Explain your reasoning
Answers
A shoe store sends an email survey to all customers who pay with a debit card. The previous month, 34,000 people made debit card purchases. Surveys were sent to 2,000 of these people, chosen at random, and 256 people responded to the survey. Identify the population and the sample. The population is 34,000 and the sample is 2,000. The population is 2,000 and the sample is 256. The population is 256 and the sample is 34,000. The population is 2,000 and the sample is 34,000. The population is 34,000 and the sample is 256.
Answers
Answer:
"The population is 34,000 and the sample is 256."
Step-by-step explanation:
The population is the general audience you will generalize about. While the sample is the subset of people you actually study or interview or receive responses. Here the population is 34,000 and the sample is 256.
Coco's garden has 88 tomato plants, 44 pepper plants, 33 squash plants, and 66 pumpkin plants. For every 77 plants in Coco's garden, there are 22 \_\_\_\_____ plants. Choose 1 answer: Choose 1 answer: (Choice A) A Tomato (Choice B) B Pepper (Choice C) C Squash (Choice D) D Pumpkin
Answers
You have to first find out the ratio of the different plants
Tomato:Pepper:Squash: Pumpkin: Total
= 88:44:33:66:231
Divide 231 by 77 =3
This means that the original number of plant is also 3 times of 22, as the ratio and proportion of this plant out of the total number of plant will be the same.
Hence you multiply 22 with 3 to get 66, which is the original number of pumpkin plants.
MATH HELP PLEASE I WILL GIVE 82 POINTS
Answers
Angle FEG = 90 degrees based on the square marker symbol in the diagram.
Angle ABE = 90 degrees as well because BEF is 90 (supplementary to FEG) and because ABE and BEF are alternate interior angles
Angle D is 40 degrees. Why? because triangle DEG is a reflection of triangle FEG (this can be proven using SAS)
Angle EGF is 50 degrees. With any right triangle, the acute angles add to 90, so 40+50 = 90, or put another way 90-40 = 50
Which is a coordinate rule for the translation of f(x) to g(x)?
(x, y) → (x – 4, y)
(x, y) → (x, y – 4)
(x, y) → (x, y + 4)
(x, y) → (x + 4, y)
Answers
The coordinate rule for a translation tells how to move each point in f(x) to create g(x). Different rules correspond to different shifts: left, down, up, or right by 4 units.
Explanation:The coordinate rule for a translation indicates how to move each point in a graph to create a new function. For example, a rule of '(x, y) → (x – 4, y)' would indicate that every point of the function f(x) would move 4 units to the left to create the new function g(x). Similarly, the coordinate rule '(x, y) → (x, y – 4)' would move every point 4 units down, '(x, y) → (x, y + 4)' would move every point 4 units up, and '(x, y) → (x + 4, y)' moves every point 4 units to the right. Depending on which direction you want to move the function f(x) in to create g(x), any of these coordinate rules could be valid.
Learn more about coordinate translation here:https://brainly.com/question/31905085
#SPJ6
A coordinate rule for a transformation tells us how to move each point in the plane. The four provided rules indicate left, down, up, and right translations respectively. The specific translation from f(x) to g(x) would depend on their exact positions.
Explanation:The question is asking about the coordinate rule for the translation of one function to another, specifically f(x) to g(x) in a two-dimensional plane. A coordinate rule for a transformation tells us how to move each point in the plane.
For example, the rule (x, y) → (x – 4, y) means that we translate each point 4 units to the left. The rule (x, y) → (x, y – 4) moves each point 4 units down. (x, y) → (x, y + 4) moves each point 4 units up, and (x, y) → (x + 4, y) moves each point 4 units to the right.
The exact translation from f(x) to g(x) would depend on the specific position and movements of these functions on the coordinate grid, which is not provided in the question.
Learn more about Coordinate Transformation here:https://brainly.com/question/37212834
#SPJ6