Answer:
4 × 4000 = 16000cm or 160 meters
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°
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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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, ∞).
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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Please help with this
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.
2y + 9 = 4 pls aswer the question pls pls
Step-by-step explanation:
2y+9= 4
2y=-5
y=-5/2
y= -2and 1/2
Simplify the following expressions
if someone could do all and or tell me how to do it that would be great if someone dose them all they'll get brainliest
Answer:
See below.
Step-by-Step Explanation:
5) 8x+9-6x-7
8x + 2 - 6x (Subtract the numbers)
2x + 2 (Combine like terms)
2 (x + 1) (Common factor - Factor by grouping twice)
6) 2y-6+5y+9
2y + 3 + 5y (Add the numbers)
7y + 3 (Combine like terms)
7) 3x+8+4x-9
3x - 1 + 4x (Subtract the numbers)
7x - 1 (Combine like terms)
8) 9y+16-12y+24
9y + 40 - 12y (Add the numbers)
-3y + 40 (Combine like terms)
9) 7g-5-8g+12
7g + 7 - 8g (Add the numbers)
-g + 7 (Combine like terms)
10) 11c-8+5c-8
11c - 16 + 5c (Subtract the numbers)
16c - 16 (Combine like terms)
16 (c - 1) (Common factor - Factor by grouping twice)
11) 5(2x + 3) (This one was a bit blurry, I am assuming that's a addition sign.)
10x + 15 (Distribute)
12) 5(-2x+3)
-10x + 15 (Distribute)
Hope this helps!
Answer: those are the answers its a long time.
Question 5 Answer: 2(x+1)
8x+9−6x−7
Multiply and combine like terms.
2x+2
Factor out 2.
2(x+1)
Questio 6 Answer : 7y + 3
2y−6+5y+9
Combine 2y and 5y to get 7y.
7y−6+9
Add −6 and 9 to get 3.
7y+3
Question 7 Answer: 3x+8+4x−9
Combine 3x and 4x to get 7x.
7x+8−9
Subtract 9 from 8 to get −1.
7x−1
Question 8 Answer: - 3y + 40
9y+16−12y+24
Combine 9y and −12y to get −3y.
−3y+16+24
Add 16 and 24 to get 40.
−3y+40
Question 9 Answer: -g + 7
7g−5−8g+12
Combine 7g and −8g to get −g.
−g−5+12
Add −5 and 12 to get 7.
−g + 7
Question 10 Answer: 16 ( c - 1 )
11c−8+5c−8
Combine 11c and 5c to get 16c.
16c−8−8
Subtract 8 from −8 to get −16.
16c - 16
Question 11 Answer: 10x +15
5(2x+3)
Use the distributive property to multiply 5 by 2x+3.
10x+15
Question 12 Answer: 15 - 10x
5(−2x+3)
Use the distributive property to multiply 5 by −2x+3.
−10x+15
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.
Find the constant of proportionality
(
r
)
(r)left parenthesis, r, right parenthesis in the equation
y
=
r
x
y=rxy, equals, r, x.
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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A box contains x apples.
5 are green and the rest are red.
Write an expression for P(red).
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 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)
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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(c) Find the number of sets where all three cards are the same for exactly $0$ attributes. (d) Find the number of sets where all three cards are the same for exactly $1$ attribute.
C. For the first card, there are three ways to choose the number of card.
For the another, there two options, and likewise there's only 1 choice of card. So there are 3 × 2 × 1 = 6 ways that the calculation can be chosen.
Doing this for the other attributes, we get 6 × 6 × 24 × 6 ways. But the order of cards does not count in a set of card, so we divide by 3! 6 * 6 * 24 × 6 ÷ 3! = 864. It means there are 864 sets for part.
D. The cards may have the same number, color, shapess, orshading.
However, also there are 6 × 24 × 6 × 3! = 144 sets of cards, If all the colors are thesame. How ever, also there are 144 sets of cards.
If all the calculation are the same. We get the same number for shape and shadings, so there are 4 × 144 = 576 sets of cards.
what is Probability?
Probability is branches of mathematics concerning numerical descriptions of how to the likely an event is to occurs, or how to the likely it is that a proposition is true. The probability of an event is a numbers between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the events and 1 indicates certain of cards.
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Need help (pic included)
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:
x varies directly as y. Find x when y=12 and k=6
72
x varies directly as y
hence x=k y
k=6
y=12
x=6×12
x=72
If f(x) is a linear function, which statement must be true?
O f(x) has no constant term.
O f(x) has no x²-term.
Of(x) has no terms with a coefficient other than 1.
Of(x) has no x-term.
Answer:
has no x^2 term
Step-by-step explanation:
Has no x^2 term <====== that would make it an exponential function, not linear
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) = ________
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
Find the missing length A. 80
B. 15
C. 64
D. 60
Answer:
the answer is C.64
Step-by-step explanation:
Answer:
the answer is C
Step-by-step explanation:
because the
Which of the following are solutions to the equation below?
Check all that apply.
4x²-12x+9 = 5
□ A. x = -√5 + ³/2
B. x= √√4-3
C. X= -√√4-3
D. x = √5 + 1/2
3
N|W
□ E. x= -√5 +3
2
□ F. X=
√√5+3
2
The solutions of the given equation are x= (√5+3)/2 & x= (-√5+3)/2
What is sridharacharya formula ?
If ax²+bx+c = 0 is a quadratic equation ,where a,b,c are real numbers, Then the solution is x = (-b±√(b²-4ac))/2a , where a≠0
Which are the solutions of the equation ?The given equation is, 4x²-12x+9 = 5
So, 4x²-12x+9 = 5
⇒ 4x²-12x+9-5 = 0
⇒ 4x²-12x+4 = 0
Comparing this equation with ax²+bx+c = 0 we get,
a = 4, b = -12, c = 4
Applying sridharacharya formula we get,
x = (-(-12)±√((-12)²-4×4×4))/(2×4)
= (12±√(144-64)/8
= (12±√80)/8
= (3±√5)/2
The values of x are (√5+3)/2 & (-√5+3)/2
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What is the measurement of m? 24 6
The value of n is 12. and m is 6root5
We have given the diagram,
The measurement of m,
n = 12
According to the altitude theorem
What is the altitude theorem?
The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse.
24/n = n/6
The Cross multiply
24 * 6 = n²
144 = n²
n² = 144
n = √144
n = 12
[tex]m^2=6^2+n^2[/tex]
[tex]m^2=6^2+12^2\\m^2=36+144\\m^2=180[/tex]
[tex]m=\sqrt{180} \\m=2\cdot \:3\sqrt{5}\\m=6\sqrt{5}[/tex]
Hence the value of n is 12.
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Answer:
12
Step-by-step explanation:
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.
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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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.)
definetly not a
Step-by-step explanation:
because it is an incompetent answer
Find the area of the smaller sector.
Round to the nearest tenth.
50°
7.13 ft
Area = [?]ft²
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 )
This is a Math question.
Please explain how you can graph points on a coordinate plane to create
geometric figures such as squares, triangles, rectangles, and
parallelograms.
A figure can be graphed on a coordinate plane as a set of points located on specific places, specified by their coordinates.
How to draw graph on cartesian coordinate plane?The cartesian coordinate plane is an infinite 2 dimensional plane and each point of a cartesian plane is tracked by a location.
Now, the perpendicular distance of point from the horizontal axis and vertical axis are respectively usually named x-axis and y-axis. The location is then written as (a,b) where;
a is that point's shortest distance from the y-axis and called x-coordinate of that point.
b is that point's shortest distance from the x-axis, and called y-coordinate of that point.
Thus, those given geometric figures can be graphed on a coordinate plane as a set of points located on specific places, specified by their coordinates.
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[tex]3x^{2} +8x- 10[/tex]
Answer:
07698+96965#5_(-&)!:86539'6";
The solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
The given equation will be solved as:-
= 3x² + 8x - 10
Using the formula of factors:-
x = [tex]\dfrac{-b\pm\sqrt{b^-4ac}}{2a}[/tex]
x = [tex]\dfrac{-8\pm\sqrt{64-(-120)}}{2\times 3}[/tex]
x = [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].
Therefore the solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].
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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}
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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simplify (3+√5)(3+√2)
When we simplify (3 + √5)(3 + √2), the result obtained is:
9 + 3√2 + 3√5 + √10
Surd operationa√b × c√d = (a × c)√(b × d)
How to simplify (3 + √5)(3 + √2)(3 + √5)(3 + √2)
Expand by clearing the bracket
3(3 + √2) + √5(3 + √2)
9 + 3√2 + 3√5 + √10
Thus,
(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10
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(-3 +6 i )(-3 - 6 i )
Answer:
45
Step-by-step explanation:
what is the measure of this angle
Answer:
135
Step-by-step explanation:
Depending on where you start, the protractor can read in different ways. Since the measure of this angle started from the left, you read the numbers at the top. If the measure would have started from the right, you read the numbers below.
A good rule of thumb is that if the angle appears to be greater than 90 degrees, or an obtuse angle, you would choose the only answer choice that is above 90 degrees.
Hope this helps!
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
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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Which of the following is equivalent to
(16 3/2)^1/2 ?
O 6
O 8
O 12
O 64
Step-by-step explanation:
[tex] = { ({16}^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]
[tex] = { ({( {2}^{4}) }^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]
[tex] = {2}^{4 \times \frac{3}{2} \times \frac{1}{2} } [/tex]
[tex] = {2}^{ \frac{12}{4} } [/tex]
[tex] = {2}^{3} [/tex]
[tex] = 2 \times 2 \times 2[/tex]
[tex] = 8[/tex]
The answer is B.
What is the y-intercept of the line shown?
-1
0
1
Answer:
-1
Step-by-step explanation:
The y-intercept is where the line crosses the y-axis.
Answer:
[tex]\huge\boxed{\sf y-intercept = -1}[/tex]
Step-by-step explanation:
Y-intercept is the point of the line of the equation where:x = 0the line of the equation passes through the y-axis.Here,
y-intercept = -1Since, this is the point where x = 0 and where the line passes through the y-axis.
[tex]\rule[225]{225}{2}[/tex]
