Answers
Answer:
The length x is 16 m==============
Imagine the height of the triangle is h, which is perpendicular to 15 m side.
The area is:
A = bh/2Use this formula and given values and find the value of h:
60 = 15h/2h = 60*2/15h = 8 mSince h is opposite to 30° angle and x is the hypotenuse of the formed right triangle, we'll use the property of 30°x60°x90° triangle.
Hypotenuse is twice the length of the side opposite to 30° angle.In our case h is opposite to 30° angle, therefore we have:
x = 2h = 2*8 = 16 mAnswer:
x = 16
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] absinC
where a, b are 2 sides of the triangle and C the angle between them
here a = 15, b = x, C = 30° and A = 60 , then
[tex]\frac{1}{2}[/tex] × 15 × x × sin30° = 60
7.5x × [tex]\frac{1}{2}[/tex] = 60 ( multiply both sides by 2 to clear the fraction )
7.5x = 120 ( divide both sides by 7.5 )
x = 16
Related Questions
A piece of land is shaped like a right triangle. Two people start at the right angle of the triangle at the same time and walk at the same speed along different legs of the triangle. If the area formed by the positions of the two people and their starting point (the right angle) is changing at 2 sq. meter per seconds, then how fast are the people moving when they are 5 meters from the right angle? (Round your answer to two decimal places.)
Answers
definetly not a
Step-by-step explanation:
because it is an incompetent answer
Given the function h of x equals negative 5 times the square root of x, which statement is true about h(x)?
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (–∞, 0).
The function is decreasing on the interval (0, ∞).
The function is increasing on the interval (0, ∞).
Answers
Answer:
The function is decreasing on the interval ( 0,∞)The function h(x) = -5√x is decreasing on the interval (–∞, 0) is true, Option A is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function h of x equals negative 5 times the square root of x.
h(x) = -5√x
The value of h(x) decreases as the value of x increases.
The function h(x) is a decreasing function over the interval (–∞, 0) because it is a negative function over the interval.
Hence, the function is decreasing on the interval (–∞, 0) is true.
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x varies directly as y. Find x when y=12 and k=6
Answers
72
x varies directly as y
hence x=k y
k=6
y=12
x=6×12
x=72
AB is a common external tangent to circles D and C. The points of tangency are at A and B. DC = 13, BC = 2 and AD = 7.
Find AB.
Answers
Based on the calculations, the length of side AB is equal to 13.93 units.
How to find the length of AB?Since the points of tangency are at A and B, we would determine the side length of the point lying between side A and D as follows:
AM = AD - BC
AM = 7 - 2
AM = 5 units.
Now, we can determine the length of side AB by applying Pythagorean's Theorem:
AB² = BM² + AM²
AB² = 13² + 5²
AB² = 169 + 25
AB = √194
AB = 13.93 units.
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2y + 9 = 4 pls aswer the question pls pls
Answers
Step-by-step explanation:
2y+9= 4
2y=-5
y=-5/2
y= -2and 1/2
Find the constant of proportionality
(
r
)
(r)left parenthesis, r, right parenthesis in the equation
y
=
r
x
y=rxy, equals, r, x.
Answers
The constant of proportionality is 0.1
Complete questionFind the constant of proportionality (r)in the equation y=rx.
r =
x y
14 1.4
16 1.6
21 2.1
How to determine the constant of proportionality?The equation is given as:
y = rx
When x = 14 and y = 1.4, we have:
1.4 = r * 14
Divide both sides by 14
r = 0.1
Hence, the constant of proportionality is 0.1
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!!!! PLEASE HELP !!!!
The senior classes at High School A and High School B planned separate trips to
New York City. The senior class at High School A rented and filled 4 vans and 3
buses with 133 students. High School B rented and filled 9 vans and 1 bus with 167
students. Each van and each bus carried the same number of students. How
many students can a van carry? How many students can a bus carry
A) Van: 23, Bus: 16
C) Van: 6, Bus: 34
B) Van: 25, Bus: 36
D) Van: 16, Bus: 23
Answers
How do you write an equation in function form?
Answers
Answer: Writing an equation in function form. You want to remove the x term from the side y is on and move it to the other side of the equal sign. To do this either add or subtract the x term from both sides. Next divide by the coefficient of the y term. Now your equation is in function form.
explanation: like 57 * Y =142500
what is the number for Y if u don't know u could divided 142500 by 57 and it equals? 2500;) hope I helped
Need help (pic included)
Answers
Answer:
r = 5
Step-by-step explanation:
The zeroes ( where the function intersects the x - axis) are equi-distant from the vertex line of symmetry
vertex 2,4 to get to -1 , 0 you have to go three units in the negative x direction ..... the other zero is on the OTHER side of the vertex 3 units which would be 5,0 so r = 5
Here is a graph to look at:
A company ordered $6,000 worth of chairs. Some of the chairs ordered cost $20 each and the others cost $40 each. If twice as many $20 chairs as $40 chairs were ordered, how many chairs were ordered altogether
Answers
In total 180 chairs are ordered for the cost $6000.
The total cost of chairs=$6,000.
What are simultaneous equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Let x be the chairs ordered each at $20 and y be the chairs ordered each at $40.
Then equation will be 20x+40y=6000-------(1)
Given that, twice as many $20 chairs as $40 chairs were ordered.
That is 2x=y⇒2x-y=0--------(2)
Multiply equation (2) by 40.
That is 80x-40y=0--------(3)
By adding equation (2) and (3) we get
20x+40y+80x-40y=6000
⇒100x=6000
⇒x=60
Substitute x=60 in equation (2)
That is, 2x=y
⇒y=120
Total number of chairs=x+y=60+120=180 chairs.
Hence, in total 180 chairs are ordered for the cost $6000.
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Match each box plot to the data set it represents.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
{20,18,8,18,10,8,4}
{12,14,16,20,4,8,10}
{12,16,4,20,8,6,8}
Answers
An expression can either be an equation or an inequality.
The correct classification of the terms are:
Expression; 4x+20
Inequality: 4x+20>40
Equation: 4x+20=40
We have given that,
{20,18,8,18,10,8,4}
{12,14,16,20,4,8,10}
{12,16,4,20,8,6,8}
How to determine the correct classification?To determine the correct classification, we make use of the following highlights
When an expression has the =, then the expression is an equation.
When an expression has any of the following signs>, <, >=, <= or != , then the expression is an inequality.
When the expression is neither an equation nor an inequality, then it is just an expression.
Hence, the correct classifications are:
Expression; 4x+20
Inequality: 4x+20>40
Equation: 4x+20=40
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What is the range of the relation in the table below?
Answers
Range is the set of all values which the given function can output. The correct option is A.
What is domain and range of a function?Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.Since y is the output for the given function, and the only outputs that can be seen for the function are 0, 2, and 4. Therefore, the range of the function is {0,2,4}.
Hence, the correct option is A.
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y = 7x (6/7,-1/4) ….
Answers
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given: y = 7x (6/7, -1/4)
we can plug in the point (6/7, -1/4)
-1/4 = 7(6/7)
-1/4 = 6
-1/4 does not equal 6 so this point is not on the line
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A box contains x apples.
5 are green and the rest are red.
Write an expression for P(red).
Answers
The expression for P(red) is (x - 5)/x
How to determine the expression?The given parameters are:
Apple = x
Green = 5
The number of red apples is:
Red = Apple - Green
This gives
Red = x - 5
The expression for P(red) is then calculated as:
P(Red) = Red/Apple
This gives
P(Red) = (x - 5)/x
Hence, the expression for P(red) is (x - 5)/x
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answers
Answer:
m∠5 + m∠6 =180°m∠2 + m∠3 = m∠6m∠2 + m∠3 + m∠5 = 180°Step-by-step explanation:
m∠5 + m∠6 = 180° - This is true because the exterior angle and interior angle form a linear pair, and are thus supplementary.
m∠2 + m∠3 = m∠6 - This is true by the exterior angle theorem.
m∠2 + m∠3 + m∠5 = 180° - This is true because the interior angles of a triangle add to 180 degrees.
The three right options are:
m∠5 ₊ m∠6 = 180° which represents a linear pair.
∠2 ₊ ∠3 = ∠6 showing the exterior angle property of triangle.
m∠2 m∠3 m∠5 = 180° as the sum-triangle
sum-triangleproperty.
Given,
the interior angles of the triangle are 2,3,5
the exterior angle at ∠2 is ∠1.
the exterior angle at ∠3 is ∠4.
the exterior angle at ∠5 is ∠6.
Now, take into account a triangle with external angles as ∠1 , ∠4 and ∠6.
Apply the exterior angle property of a triangle.
The sum of the opposing internal angles determines the outer angle of a triangle.
For exterior ∠1 we get
∠1 = ∠5 ₊ ∠3
Similarly, for exterior ∠4 we get
∠4 = ∠5 ₊ ∠2
Then for exterior ∠6 we get
∠6 = ∠2 ₊ ∠3
∴ through the exterior angle property we get the correct option as
m∠6 = m∠2 ₊ m∠3
Now we know the sum-triangle property that sum of the angles in triangle is equal to 180°
∴ m∠2 ₊ m∠3 ₊ m∠5 = 180°
We know the linear pair property i.e, If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.,
∴ m∠5 ₊ m∠6 = 180°
Hence we get the statements which match the diagram are:
m∠5 ₊ m∠6 = 180°
m∠2 ₊ m∠3 ₊ m∠5 = 180°
m∠6 = m∠2 ₊ m∠3
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I need help with a question
Answers
Solution :-
Here we have been given with two equations :
x + 5y = 0 (Equation No.1)3y + 2x = -21 (Equation No.2)¤ From Equation No.1 :
>> x = -5y
¤ In Equation No.2 :
Substituting the value of x which we got above as -5y here.
>> 3y + 2(-5y) = -21
>> 3y + 2 × (-5y) = -21
>> 3y - 10y = -21
>> -7y = -21
>> 7y = 21
>> y = 21 / 7
>> y = 3
¤ Finding out value of x :
>> x = -5y
>> x = -5(3)
>> x = -15
Step-by-Step Explanation:
=> x + 5y = 0 (Eq. 1)
=> 2x + 3y = -21 (Eq. 2)
From Eq. 1 :-
x = 0 - 5y
=> x = -5y (Eq. 3)
Substitute value of ‘x’ from Eq. 3 in 2 :-
2x + 3y = -21
2(-5y) + 3y = -21
-10y + 3y = -21
-7y = -21
7y = 21
y = 21/7
=> y = 3
Therefore, y = 3
Substitute value of ‘y’ in Eq. 3 :-
x = -5y
x = -5(3)
x = -5 * 3
=> x = -15
Therefore, x = -15
Hence, x = -15, y = 3 (-15, 3)
The time it takes me to wash the dishes is uniformly distributed between 7 minutes and 15 minutes.
What is the probability that washing dishes tonight will take me between 13 and 14 minutes?
Give your answer accurate to two decimal places.
Answers
. Mathematically speaking, there are nine different times your dish-washing could take you. It could take you 7, 8, 9, 10, 11, 12, 13, 14 or 15 minutes.
And the probability for it to take you, say, 10 minutes, is equal to every other probability. This is, therefore, a situation of equiprobability.
100 / 9 = about 11,11111…
Meaning that each of the different outcome (be it for it to take 7, 8, 9, 10, 11, 12, 13, 14 or 15 minutes) has a 11,1111… probability to occur.
However, we are interested in two specific outcomes if our situation: we are interested in the dish-washing taking us 13 or 14 minutes.
2 x 11,1111 = roughly 22, 22 % probability, or 0,22 of probability.
I hope this helps! Have a nice day :)
Kayla has just subscribed to a music streaming service. For a one-time fee of $12.99, she can download songs for $0.65 each, for an entire month. Kayla's budget will allow her to spend no more than a total of $27 on the streaming service this month. What is the maximum number of songs she can download while still remaining within her budget?
a) x <= 22
b) <= 41
c) x <= 21
d) X <= 42
Answers
The maximum number of songs she can download while still remaining within her budget is x <= 21
How to determine the maximum number of songs?The given parameters are:
One-time fee = $12.99
Rate = $0.65 per song
Budget = $27
The inequality is then represented as:
One-time fee + Rate * x <= Budget
So, we have:
12.99 + 0.65x <= 27
Subtract 12.99 from both sides
0.65x <= 14.01
Divide both sides by 0.65
x <= 21.55
Round down
x <= 21
Hence, the maximum number of songs she can download while still remaining within her budget is x <= 21
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Please help with this
Answers
Answer:
(a) Horizontal line test
Step-by-step explanation:
A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.
Inverse relationThe inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.
Inverse functionIf the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to pass.
A function will have an inverse function if it passes the Horizontal Line Test.
__
Additional comment
The attached graph shows a function (red curve) that does not pass the horizontal line test. Its inverse relation is the green curve, which you can see is not a function. It does not pass the vertical line test.
The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.
Find the missing length A. 80
B. 15
C. 64
D. 60
Answers
Answer:
the answer is C.64
Step-by-step explanation:
Answer:
the answer is C
Step-by-step explanation:
because the
Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. find the missing term. the roots of x2 − ( ) 34 are 5 ± 3i.
Answers
The missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have the roots of a quadratic equation:
5 ± 3i
To find the quadratic equation:
(x - (5+3i))(x - (5-3i))
[tex]\rm =x^2+x\left(-\left(5-3i\right)\right)-\left(5+3i\right)x-\left(5+3i\right)\left(-\left(5-3i\right)\right)[/tex]
= x² -10x + 34
The missing value is 10x
The quadratic equation is:
= x² -10x + 34
Thus, the missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.
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Mr. avanzado has an underground in his house. what unit of measure will he use to find its value
Answers
Answer: Volume
Step-by-step explanation:
(-3 +6 i )(-3 - 6 i )
Answers
Answer:
45
Step-by-step explanation:
What would be the cost for 5 of the gift cards?
Answers
Answer:
$100
Step-by-step explanation:
It appears that each gift card costs $20, so 5 of them would be $20 * 5 gift cards = $100
Answer:
$100
Step-by-step explanation:
From the graph we see that each card costs $20.
A survey was given to ask a group of adults if they liked chocolate or vanilla ice cream more. The table shows the survey results of three age groups.
(see attachment for table)
A person is selected at random. Determine the probability of each described event. Round your answers to two decimal places.
P(20s | Chocolate) = ________
P(Chocolate | 30s) * P(Vanilla | 30s) = ________
Answers
P(20s | Chocolate) = 33 / 127 = 0.26 (2dp)
There are 122 people in their 30s 53 liking chocolate and 69 vanilla
P(chocolate | 30s) x P(vanilla | 30s) = 53/122 x 69/122 = 0.25 (2dp)
The probability of P(20s | Chocolate) and P(chocolate | 30s) x P(vanilla | 30s) will be 0.26 and 0.25, respectively.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
Adults were polled to determine whether they preferred vanilla or chocolate ice cream. The survey findings for three age groups are displayed in the table.
There are 127 people who enjoy chocolate, and 33 of them are in their 20s is given as,
P(20s | Chocolate) = 33 / 127 = 0.26
There are 122 persons in their 30s, and 53 of them prefer chocolate 69 others prefer vanilla is given as,
P(chocolate | 30s) x P(vanilla | 30s) = 53/122 x 69/122 = 0.25
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Which of the following statements must be true about parallelogram ABCD? A) angle B+ angle D=180^ B) angle ABC cong angle CDA C) overline AC || overline BD D) overline BC cong overline CD
Answers
Detailed Explanation:
In a Parallelogram, Opposite Angles are Equal. Therefore, in this Figure ∠ABC = ∠CDA and ∠BAD = ∠BCD.
Therefore, Option B is True about the Parallelogram ABCD.
x y 1 -1 2 -3 3 -5 4 -7
A. y = 1 − 2x B. y = -x − 1 C. y = x − 2 D. y = 2x − 1
Answers
Answer:
A) y = 1 - 2x
Step-by-step explanation:
Substitute the points given into all of the equations
Let's take point (1, -1)
A) y = 1 - 2x
-1 = 1 - 2(1)
-1 = 1 - 2
-1 = -1 ✓
B) y = -x - 1
-1 = -1 - 1
-1 = -2 ✘
C) y = x - 2
-1 = 1 - 2
-1 = -1 ✓
D) y = 2x - 1
-1 = 2(1) - 1
-1 = 2 - 1
-1 = 1 ✘
So far, lines A and C can be possible solutions. Let's try point (2, -3)
A) y = 1 - 2x
-3 = 1 - 2(2)
-3 = 1 - 4
-3 = -3 ✓
C) y = x - 2
-3 = 2 - 2
-3 = 0 ✘
Thus, line A is the correct answer
PLEASE HELP!!!
Part A: Solve the equation 4(x + 5) = 9x + 4x − 34, and show your work. (5 points)
Part B: Use this list of properties to justify each step of your math work. Justifications may be used more than once if needed. (5 points)
Distributive Property
Subtraction Property of Equality
Combine Like Terms
Multiplication Property of Equality
Division Property of Equality
Given
Addition Property of Equality
Answers
Answer:
See below
Step-by-step explanation:
4(x + 5) = 9x + 4x − 34
4x + 20 = 9x + 4x − 34 [Distributive]
4x + 20 = 13x − 34 {Combine Like Terms]
4x - 13x + 20 = 13x - 13x − 34 [Subtractive: -13x both sides]
-5x + 20 = - 34 [Combine Like Terms]
-5x + 20 - 20 = -34 - 20 [Subtractive: - 20 both sides]
-5x = -54 [Combine Like Terms]
x = -54/-5 [Division Property: divide both sides by -5]
x = - 10 4/5
Find the area of the smaller sector.
Round to the nearest tenth.
50°
7.13 ft
Area = [?]ft²
Answers
Answer:
A ≈ 22.2 ft²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{50}{360}[/tex]
= π × 7.13² × [tex]\frac{5}{36}[/tex]
= 50.8369π × [tex]\frac{5}{36}[/tex]
≈ 22.2 ft² ( to the nearest tenth )
Step-by-Step Solution:
Radius (r) = 7.13 ft
Angle (θ) = 50°
Area of a Sector = θ/360 * πr^2
Therefore,
= θ/360 * πr^2
= θ/360 * π * r * r
= 50/360 * 3.14 * 7.13 * 7.13
= 50/360 * 3.14 * 50.8369
= 5/36 * 159.63
= 798.15/36
= 22.17
=> 22.2
Area of the Sector = 22.2 ft^2
A gas tank consists of a cylinder with a hemisphere on top. It is made of metal that is 1 cm
thick. It has an overall height of 90 cm and an external diameter of 20 cm. Calculate:
a the surface area of the tank
b the internal volume of the tank.
(Give answers correct to two significant figures)
Answers
The surface area of the cylinder is 5969.03 cm²
The internal volume is 23156.68 cm³
Given:
A gas tank consists of a cylinder with a hemisphere on top.
The thickness of the metal is 1 cm
The overall height is 90 cm
The external diameter is 20 cm
To Find
a) the surface area of the tank
We will add the area of the bottom circle of radius 10 cm (counting the 1 cm thickness in), the external surface area of cylinder of height (90 - 10) cm =80 cm and radius 10 cm, and the surface area of the hemisphere of radius 10 cm.
So, the surface area of the cylinder is
[tex]\pi\times(10)^2+2\times\pi\times 10\times 80+ 2\times \pi \times (10)^2[/tex]
= π×(100+1600+200)
= π×(1900)
= 5969.03 cm²
b) To find the internal volume of the tank we find the internal volume of the hemisphere with an internal radius (10-1)=9 cm,
the internal volume of the cylinder of radius 9 cm and height (80-1) cm
= [tex]\frac{4}{3}\times \pi \times 9^3[/tex]+[tex]\pi\times 9^2\times 79[/tex]
= 23156.68 cm³
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