The area of the triangle is 6√3 units.
How to the area of the triangle, in square units?given that the altitude to the hypotenuse of a triangle with angles of 30 and 60 degrees is 3 units.
The hypotenuse of a triangle with angles of 30°, 60°, and 90° is always twice as long as the side opposite the 30° angle, and it is almost three times as long as the side opposite the 60° angle.
so, let the shorter side of triangle is x.
the longer side of triangle is x√3.
the hypotenuse of the triangle is 2x.
now find the value of side of triangle
[tex]x \sqrt{3} = 3 \\ \frac{x \sqrt{3} }{ \sqrt{3} } = \frac{3}{ \sqrt{3} } \\ x = \frac{3 \sqrt{3} }{3} \\ x = \sqrt{3} [/tex]
so, the length of shorter side is √3 units.
now, find the value of hypotenuse of triangle
2x = 2√3
so, the length of hypotenuse of the triangle is 2√3 units.
now, find the base of the triangle
base = a√3 = (2√3) (√3) = 2(3) = 6
base = 6 units.
now, find the area of triangle
formula 1/2 (base)(height)
A = 1/2 (6) (2√3)
A = 6√3
Hence,the area of the triangle is 6√3 units.
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işlemleriyle çözer misiniz?
Question 11(multiple choice worth 2 points) (order of operations mc) joshua purchased a game card for the arcade for a total of $18. he played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each. how much did he have left on the game card? $4.50 $6.50 $13.00 $13.50
The total balance remaining on Joshua's game card is $4.5. So, the correct option is (A).
In the Question, It is given that Joshua purchase a game card for $18 which makes the Balance Bal = $18 on his card.
Now, He played 2 rounds of Basketball hoop and each costs $3.25 which makes total for Basketball B = 2*3.25 => B = $6.25
And, He played 4 rounds of Air Hockey each game cost $1.75 which makes the total for Air Hockey A = 4*1.75 => A = $7
To calculate the remaining balance on his card we need to subtract these games' costs from the balance on his card :
=> T = Bal - B - A, Where T = Total, Bal = Balance on card, B = Basketball, A = Air Hockey
=> T = 18 - 6.25 - 7 => T = $4.5
Hence, the Total balance remaining on his card T = $4.5
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Mr. Johns is using a high-clearance sprayer with two 30-foot booms. It will spray a 60-foot-wide strip. He sprayed a
960-foot-wide wheat field for weeds.
a. How many feet from the edge should he start?
b. How many round trips are needed to cover the field?
a) He will start 900 feet from the edge
b) 16 Round trips are needed to cover the field.
Because Mr. Johns intends to check a wheat field 960 feet wide for weeds so he will distribute a 60-foot wide strip using a high clearance sprayer that has two 30-foot booms.
a) 960 foot - 60 foot = 900 foot
Therefore, he should start 900 feet from the edge.
b) 960 foot / 60 foot = 16 Trips.
Therefore, 16 round trips are needed to cover the field.
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1. Construction workers build 54 feet of a bridge each day for 9 days. To determine whether the bridge is at least 490 feet long, can you use an estimate, or is an exact answer required? Explain.
The total length of the bridge built is less than the total length of the bridge.
How to Estimate Lengths?
We are given;
Length of bridge to be built per day = 54 feet
Number of days they built the bridge = 9 days
Thus, to find the total length that the bridge will span, we multiply the length built each day by the number of days. Thus;
Total Length of bridge = (54 * 9)
Total Length of bridge = 486 ft
Since we want to find if the bridge is at least 490 feet long. Thus, the total length of the bridge built is less than the total length of the bridge.
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The oldest zoo in the United
States is the Central Park Zoo
in New York City. The zoo
opened in 1864.
1. How many years had the
Central Park Zoo been open
in 19642
2. How many years had it been
open in the year 2000?
The square of T varies directly with the cube of a and inversely with the square of d; T = 2 when a = 2 and d = 4
The general formula that describes the variation is T² = 18a³/d²
Direct variation: When a variable x changes directly with another variable y, it is written in this form;x ∝ y.
This can then be written as;
x = ky
Where;
k = constant rate of change.
Inverse: When one variable x changes in the opposite direction to another variable y, it is written in this form; x ∝ 1 / y This can then be written as; x = k (1/y) Where; k = constant rate or variationCombined variation: When a variable x varies directly with variable y and inversely with variable z, we write it in this form;x ∝ (y/z)
This can then be written as;
x = k (y/z)
Where;
k = constant rate or variation
The square of T varies directly with the cube of a and inversely with the square of d.
Note that
square of T = T²
cube of a = a³
square of d = d²
Therefore, we can write;
T² ∝ a³/d²
T² = k (a³/d²)
Since;
T = 4 when a = 2 and d = 3
We can find the constant of proportionality k, by substituting the values of T=4, a = 2 and d = 3 into equation (i) and solve as follows;
(4)² = k (2³/3²)
16 = k (8/9)
8k = 16 x 9
8k = 144
k = 144/8
k = 18
Therefore, The overall formula for describing the variation is
T² = 18 a³/d²
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nb 3 all parts pls pls very important pls and thank you!!
Step-by-step explanation:
(a)
First:
Get AE using Pythagoras
[tex] {ae}^{2} = {6}^{2} + {8}^{2} [/tex]
[tex] {ae}^{2} = 100[/tex]
AE =10
Connect OM to form Traingle AOM.
AM=5cm (AE is 10 and AM=ME meaning that they are divided into two equal parts)
AM^2=OM^2+AO^2
5^2=OM^2+4^2
OM^2=5^2-4^2
OM=3
(B) OM is parallel to BE because of midpoint theorem
The Theorem states that The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
(C) AOM is a right angled triangle at O because angle AOM is 90°. Because OM is a perpendicular Line that bisects the chord of AB
I need help, please IT CAN NOT WAIT
Answer:
D and E
Step-by-step explanation:
In order for the equations to have infinite amount of solutions, they have to be equal to each other.
A: 3x-1 doesn't equal 3x+1
B: 2x-1 is not equal to 1-2x since they negate each other.
C: 3x-2 doesn't equal 2x-3
D: 3(x-1)=3x-1*3=3x-3 ==> D is an answer.
E: 2(x+1)=2x+1*2=2x+2 ==> E is an answer
F: 3(x-2)=3x-6. However, 2(x-3)=2x-6. 3x-6 doesn't equal 2x-6.
Hence, 3(x-2) doesn't equal 2(x-3).
There are three number a,b and c, where a>b and b>c. Describe the positions of numbers on a number line
Answer:
the numbers lie on the number line from left to right: c, b, a
Step-by-step explanation:
a > b > c
bigger numbers are to the right on the number line
does someone mind helping me with this? Thank you!
Answer:
196m²
Step-by-step explanation:
area is w multiplied by h so 14x14
Answer:
196 [tex]m^{2}[/tex]
Step-by-step explanation:
The area of a rectangle is length times width. A square is a type of rectangle that has four equal sides, so if we know one side we know all four.
A = l x w
A = 14m x 14m
A = 196[tex]m^{2}[/tex]
In a 36% sale, the price of a phone reduced by $135.
Find the original price of the phone.
Answer:
$210.94
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
Answer:
The original price was $375.
Step-by-step explanation:
The original price of the phone is x.
36% of x is $135.
0.36x = 135
x = 135/0.36
x = 375
Answer: The original price was $375.
solve and show your work.
3(2x+3) -4x = -3
A TV show had 3.6 x 10^4 viewers in the first week and 4.1 x 10^4 viewers in the second week. Determine the average number of viewers over the two weeks and write the final answer in scientific notation.
really need help pls pls
Find m∠ABC and m∠CBD
5. m∠ABC = 64°
m∠CBD = 26°
6. Using the linear pair postulate,
m∠ABC = 97°
m∠CBD = 83°
7. Using the linear pair postulate,
m∠ABC = 112.5°
m∠CBD = 67.5°
How to Apply the Linear Angles Postulate?Two angles on a straight line form a linear pair which have a sum of 180 degrees based on the linear pair postulate.
5. (11x - 2) + (5x - 4) = 90 [complementary angles]
11x - 2 + 5x - 4 = 90
16x - 6 = 90
16x = 90 + 6
16x = 96
x = 6
m∠ABC = 11x - 2 = 11(6) - 2 = 64°
m∠CBD = 5x - 4 = 5(6) - 4 = 26°
6. 8x + 9 + 6x + 17 = 180 [linear pair postulate]
14x + 26 = 180
14x = 180 - 26
14x = 154
x = 11
m∠ABC = 8x + 9 = 8(11) + 9 = 97°
m∠CBD = 6x + 17 = 6(11) + 17 = 83°
7. 14x - 6.5 + 7x + 8 = 180 [linear pair postulate]
21x + 1.5 = 180
21x = 180 - 1.5
21x = 178.5
x = 8.5
m∠ABC = 14x - 6.5 = 14(8.5) - 6.5 = 112.5°
m∠CBD = 7x + 8 = 7(8.5) + 8 = 67.5°
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(b) by how much could the smallest sample observation, currently 8.1, be increased without affecting the value of the sample median?
The smallest sample observation that can increase 8.1 without changing the sample median's value is 4.4.
By sample median, what do you mean?The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set. Simply expressed, the sample median is the middle value after sorting the observations in ascending order if the sample size is odd. The sample median is the average of the two middle values if the sample size is equal. The data set's median value is the value that falls in the middle, ordered by magnitude. The sample median is the average of the two middle terms when the number of samples in the data set is even. When the data set is symmetrically distributed, the sample mean serves as a reliable indicator of the central tendency.
The median can be calculated as (12.5+12.6)/2=12.55.
The incremented least observed value is 12.5-8.1=4.4, and the difference is that.
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solve for a in terms of b and c
b = 3a + 5ac
pls help me it’s due today!!
By checking the piecewise function and evaluating it at x = 1, the result of the piecewise function is equal to - 4.
How to evaluate a piecewise function at a given point of the real set
Piecewise functions are functions formed by several expressions constrained by intervals in the real set. In this case we find a piecewise functions consisting in two expressions constrained by two intervals in the real set. The piecewise function is defined by these expressions:
f(x) = (x + 2)² - 5 for x ≠ 1, that is x < 1 and x > 1.f(x) = - 4 for x = 1.Then, we need to evaluate the piecewise function at x = 1. By direct inspection, we conclude that the value according to the piecewise function evaluated at x = 1 is equal to - 4.
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Which numbers are irrational?
√100 √21 √36 √47
Which numbers are irrational? Select all that apply.
A. √21
B. √ 100
C. √47
D. √36
What expressions are equivalent to 4d+6+2d4d+6+2d4, d, plus, 6, plus, 2, d ?
The hexagon is made from a rectangle and two identical triangles
Answer:
108cm^2
Step-by-step explanation:
Find the areas of the rectangle and the two triangles. Then add all three areas together. See image.
A teacher has $230 in a bank account to spend on school supplies and wins an additional $50 to put toward the school supplies. The teacher spends $120 on binders for students and wants to buy the classroom a new $180 tablet.
Answer:
-20
Step-by-step explanation:
3 to the power of -2 is equivalent to _____.
i need help ASAP (i will give brainliest)
Answer:
1/9
Step-by-step explanation:
3^-2 = 1/3^2
which is 1/9
Step-by-step explanation:
Evaluating 3^-2
3^-2
= 1/3²
= 1/ 3 × 3
= 1/9
Or
if you're talking about 3^-2 in decimal then...
3^-2 = 0.111111111 (in decimal)
Hope this helps
Ace that testGood luck ✅Find the sum. 69,348 + 76,290
Answer:
The answer you will be looking for is 145638!
If you need help how to i will explain!
Identify each as an expression, equation, or inequality
Answer:
Equations
expression
inequality
equation
expression
equation
Step-by-step explanation:
An expression does not have an equal sign.
An equation does have an equal sign
Inequality has a > or< symbols
Find the midpoint of line segment AB, given:
A(-7, 4) and B((3,-4)
Answer:
I believe the answer is not solvable I don’t know I might be wrong
Step-by-step explanation:
What’s the distance between (2,-3) and (4,-3)
12. A colony of rabbits in the wild found that the colony doubles in population
every year. At first there were 10 rabbits. After how many years will there
be more than 160 rabbits?
Answer:
5
Step-by-step explanation:
In the question it states that in each year the number of rabbits increase by (2) of which is represented by the word (doubled) and so this will solve this question horizontally
note that (Y) represents year
First Year =10 rabbits
Second Year=20
Third Year =40
Fourth Year =80
Fifth Year =160
Pls pls help whoever gets it right gets a crown
Answer:
8/45m² + 2/35m
Step-by-step explanation:
...........................
candace works at a chocolate factory that makes 2,850 chocolates in 30 minutes. what is the constant of proportionality that relates the number of chocolates, y, to the minutes, x?
A bag contains 3 blue balls and x yellow balls. Write down the total number of balls in the bag
The answer to the question is 3+x
and the probability of blue balls is 3/3+x
We are required to find out the total number of balls that is the sum of blue and yellow balls
so the total number of balls in the bag is 3+x
The concept here used is probability.
Probability is the quantitative relation of rangethe amount|the quantity} of outcomes in thorough set of equally possible outcomes that manufacture a given event to the whole number of doable outcomes
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
probability of blue balls=blue balls/total balls
=3/3+x
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Hey your question is incomplete, the complete question is
A bag contains 3 blue balls and x yellow balls.Write down the total number of balls in the bag.If a ball is drawn from the bag, write down the probability that it is blue.