The correct option is angles are complementary if their sum is 90º.
What are complementary angles?When the sum of two angles is 90°, then they are complements of each other and hence called complementary angles.
Given is a statement, If the sum of two angles is 90º, then the angles are complementary.
Rewriting the sentence to check the hypothesis, in it.
It should be this:
The two angles are complementary if the sum of the two angles are 90 degrees.
A.) There are two angles.
While this is a true statement, it's a little too vague to understand. We can eliminate this answer choice.
B.) The sum of two angles is 90 degrees.
This is also a true statement, but it doesn't describe what type of angles sum to 90 degrees, so we can eliminate this as well.
C.) The angles are complementary.
This is similar to answer choice A. It's a little too vague for specific understanding. We can eliminate this answer choice.
D.) Angles are complementary if their sum is 90 degrees.
This is an accurate statement, and provides details to support its claim, also rewriting the original sentences into one properly.
Hence, the correct option is option D.
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13. Identify the table that does not represent a function.
The four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e : ( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).
What is Function?
Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.
There are many types of functions in mathematics such as :
Linear Function → f(x) = ax + b
Quadratic Function → f(x) = ax² + bx + c
Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
Logarithmic function → f(x) = ln x
Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...
If function f : x → y , then inverse function f⁻¹ : y → x
Let us now tackle the problem!
According to the definition above, it can be concluded that a function cannot have the same x value.
Of the four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e :
( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).
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Find the Missing Side Lengths
Instructions: Use the ratio of a 45-45-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.
x=____
y=_____
The value of x is 13 units and the value of y is 13 units
The given triangle is right triangle
The ratio of the given triangle angles = 45-45-90 degrees
To find the length of the sides we have to use the trigonometric functions
sin θ = Opposite side / hypotenuse
cos θ = Adjacent side / hypotenuse
tan θ = Opposite side / adjacent side
Find the value of x
sin 45 = Opposite side / 13[tex]\sqrt{2}[/tex]
Opposite side = 13[tex]\sqrt{2}[/tex] × sin 45
= 13 units
Similarly
cos 45 = Adjacent side / 13[tex]\sqrt{2}[/tex]
Adjacent side = 13[tex]\sqrt{2}[/tex] × cos 45
= 13 units
Therefore, the length of the side x and y is 13 units
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Solve the following rational equation. Be sure to list the NPV’s and verify your solution(s).
[tex]\frac{2}{2x-6}-\frac{x}{x^2-9} =\frac{3}{x-3}[/tex]
Answer:
NPV: ±3x = -2Step-by-step explanation:
You want the solutions to the rational equation ...
[tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}=\dfrac{3}{x-3}[/tex]
RewriteWe choose to rewrite the equation in the form f(x) = 0. We can start by subtracting the term on the right side (from both sides).
[tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}-\dfrac{3}{x-3}=0\\\\\dfrac{2}{2(x-3)}-\dfrac{x}{(x-3)(x+3)}-\dfrac{3}{x-3}=0\\\\\\\dfrac{(x+3)-x-3(x+3)}{(x-3)(x+3)}=0\qquad\text{cancel 2 in first term; common denominator}\\\\\\\dfrac{-3x-6}{(x-3)(x+3)}=0\qquad\text{collect terms}[/tex]
SolutionThe "not-possible values" will be values of x that make the denominator zero: x = ±3. The solution is ...
[tex]-3(x+2)=0\qquad\text{numerator must be zero}\\\\\boxed{x=-2}\qquad\text{divide by -3, subtract 2}[/tex]
CheckIn the original equation, we have ...
[tex]\dfrac{2}{2(-2)-6}-\dfrac{-2}{(-2)^2-9}=\dfrac{3}{(-2)-3}\\\\\dfrac{2}{-10}-\dfrac{-2}{-5}=\dfrac{3}{-5}\\\\-\dfrac{1}{5}-\dfrac{2}{5}=-\dfrac{3}{5}\qquad\text{TRUE}[/tex]
__
Additional comment
We like to write the equation as a single fraction compared to zero so that any common factors can be cancelled from numerator and denominator. This helps prevent extraneous solutions. Here, there are none.
f(x) = 5x-10 and g(x) = -x+4
Calculate f(-3)
The value of f(-3) if f(x) = 5x - 10 and g(x) = -x + 4 is -25.
What is the equation?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
Given:
f(x) = 5x - 10 and g(x) = -x+4
Calculate the f(-3) by putting the value of x = -3 as shown below,
f(x) = 5(-3) - 10
f(x) = - 15 - 10
f(x) = -25
Therefore, the value of f(-3) if f(x) = 5x-10 and g(x) = -x+4 is -25.
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In ADEF, FDFE. Name two congruent angles.
E
D
F
D-0
Step-by-step explanation:
It is not possible to determine the congruent angles in the given statement, as it is incomplete and does not provide enough information. In order to determine congruent angles, we need to know the shape and the specific angles being compared. For example, if the statement was "In a triangle ABC, angles A and C are congruent," then we would know that angles A and C are congruent.
the function f(x) = x(x+2)^3 has the first derivative f'(x) = (4x+2)(x+2)^2 and second derivative f"(x) = 12(x+1)(x+2).
A) Find the intervals where f(x) is increasing or decreasing.
B) Find the values of x where f(x) has local maximum and local minimum values (if there are any).
C) Find the intervals of concavity and the (x,y) coordinates of inflection points (if there are any).
D) Use the info from parts a - c to sketch the graph.
Answer:
A) Increasing: (-0.5, ∞)
Decreasing: (-∞, -2) ∪ (-2, -0.5)
B) x = -¹/₂
C) Concave up: (-∞, -2) ∪ (-1, ∞)
Concave down: (-2, -1)
Points of inflection: (-2, 0) and (-1, -1)
D) See attachments.
Step-by-step explanation:
Given function and derivatives:
[tex]f(x) = x(x+2)^3[/tex]
[tex]f'(x) = (4x+2)(x+2)^2[/tex]
[tex]f''(x) = 12(x+1)(x+2)[/tex]
Part A[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}}\implies f'(x) > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies f'(x) < 0[/tex]
Increasing function
[tex]\begin{aligned}f'(x) & > 0\\(4x+2)(x+2)^2 & > 0\\2(2x+1)(x+2)^2 & > 0\\(2x+1)(x+2)^2 & > 0\end{aligned}[/tex]
Therefore, the function is increasing on the Interval:
[tex]\left(-\dfrac{1}{2}, \infty \right)[/tex]
Decreasing function
[tex]\begin{aligned}f'(x) & < 0\\(4x+2)(x+2)^2 & < 0\\2(2x+1)(x+2)^2 & < 0\\(2x+1)(x+2)^2 & < 0\end{aligned}[/tex]
Therefore, the function is decreasing on the Interval:
[tex](- \infty, -2) \cup \left(-2,-\dfrac{1}{2} \right)[/tex]
Part BLocal minimum/maximum points occur when f'(x) = 0.
[tex]\begin{aligned}f'(x) &= 0\\(4x+2)(x+2)^2 & = 0\\2(2x+1)(x+2)^2 & = 0\\(2x+1)(x+2)^2 &= 0\\\\2x+1&=0 \implies x=-\dfrac{1}{2}\\(x+2)^2&=0 \implies x=-2\end{aligned}[/tex]
[tex]f''\left(-\dfrac{1}{2}\right) = 12\left(-\dfrac{1}{2}+1 \right)\left(-\dfrac{1}{2}+2 \right)=9 > 0\implies \textsf{minimum}[/tex]
[tex]f''\left(-2\right) = 12\left(-2+1 \right)\left(-2+2 \right)=0\implies \textsf{point of inflection}[/tex]
Therefore, the value of x where f(x) has a local minimum is x = -¹/₂.
Part CAt a point of inflection, f''(x) = 0.
[tex]\begin{aligned}f''(x) &=0\\12(x+1)(x+2)&=0\\(x+1)(x+2)&=0\\\\x+1&=0 \implies x=-1\\x+2&=0 \implies x=-2\end{aligned}[/tex]
Substitute the found values of x into the original function to the find the y-coordinates of the points of inflection:
[tex]\implies f(-1) = -1(-1+2)^3=-1[/tex]
[tex]\implies f(-2) = -2(-2+2)^3=0[/tex]
Therefore, the inflection points are:
(-2, 0) and (-1, -1)A curve y = f(x) is concave up if f''(x) > 0 for all values of x.
A curve y = f(x) is concave down if f''(x) < 0 for all values of x.
Concave up
[tex]\implies f''(x) > 0[/tex]
[tex]\implies 12(x+1)(x+2) > 0[/tex]
[tex]\implies (x+1)(x+2) > 0[/tex]
Therefore, the function is concave up at:
[tex]\left(-\infty,-2\right) \cup \left(-1,\infty \right)[/tex]
Concave down
[tex]\implies f''(x) < 0[/tex]
[tex]\implies 12(x+1)(x+2) < 0[/tex]
[tex]\implies (x+1)(x+2) < 0[/tex]
Therefore, the function is concave down at:
[tex](-2,-1)[/tex]
Part DSee attachment 1 for how to sketch the graph using the information from parts A-C.
See attachment 2 for the final sketch of the graph.
Find the inverse of the following function pairs
Answer:
B
Step-by-step explanation:
This is the only pair of functions where [tex]f(g(x))=g(f(x))=x[/tex].
There are 121 males and 104 females participating in a marathon. To the nearest percent, what percent of the participants are female?
Answer:
54% are females
Step-by-step explanation:
In total there would be 225 participants -
104 + 121 = 225
Next, Divide 121 and 225. After, multiply by 100.
225/121(100)=53.78
53.78 rounded to the nearest percent is 54.
I hope this helped your question!
A rectangular vegetable garden will have a width that is feet 2 less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation: x(x-2)=48
What is the length, x, of the garden?
The length is blank feet. I ended up getting x=8 and x=-6
Answer:
Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
We must create equations from the provided data and relationships in order to determine the length of the rectangular flower garden. The area and the relationship between the width and length are the measurements that are provided. We create the necessary equations from these. What we do is:
Area = Length x Width
where length = x ft
width = x - 3 ft
area = [tex]54 ft^2[/tex]
[tex]54 ft^2 = x ft (x -3) ft\\\54 ft^2 = x^2 - 3x ft^2[/tex]
When we solve for x, we will get two answers, one of which is x = -6 ft (NOTE: This number cannot be the solution because the length cannot have a negative value).
Which means the correct answer is:
length(x)=9ft
(Hope this helped you
Helppppp!!!!!!! Please
Then translons the resulting image units to the right is y=0 5 units.
What is line?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that are inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
Reflect [tex]$\triangle P Q R$[/tex] across the line [tex]$y=0$[/tex]. we can get [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex]. then translate [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex] 5 units to the right. we can get s STU. So the answer is A. y=0 5 units.
A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
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What value of P makes this equation true
2p=-3p-6/4
Answer:
The answer is p = -6/3. This is the value of p that makes the original equation true.
Step-by-step explanation:
To solve this equation, we must first isolate the variable p on one side of the equation. To do this, we can use the properties of equality to add or subtract the same value from both sides of the equation.
First, we can subtract 2p from both sides of the equation to get rid of the 2p term on the left side. This gives us 0 = -3p - 6/4.
Next, we can add 6/4 to both sides of the equation to get rid of the constant term on the right side. This gives us 6/4 = -3p.
Finally, we can multiply both sides of the equation by -4/3 to get rid of the coefficient -3 on the right side. This gives us -6/3 = p.
Therefore, the value of p that makes the equation true is p = -6/3.
Please. Help quickly
Answer: it is a
Step-by-step explanation:
1. Each month, Billy earns $2000 for working the night shift at Amazon, before taxes and
retirement are taken out. If 8% of his paycheck goes to income taxes, and 10%
automatically goes into retirement, what is Billy's net pay each month?
The net pay of Billy after 8% taxes and 10% retirement policy is $1600.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, From Billy's salary of $2000 8% of his paycheck goes to income taxes, and 10% automatically goes into retirement.
So, To obtain a net salary of Billy we'll subtract the percentage amount of 8% and 10% from the base of $2000.
Therefore, Net pay of Billy is {2000 - (8/100)×2000 - (10/100)×2000}.
= {2000 - 160 - 200}.
= (2000 - 360).
= $1640
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What is the sum when you add seven-and-five-twelfths and three-and-seven-twelfths together? Make sure to show the answer in simplest terms
Answer:
11
Step-by-step explanation:
y=-2x+4y=−2x+4y, equals, minus, 2, x, plus, 4 Complete the missing value in the solution to the equation. ((left parenthesis ,-2),−2)
After solving the equation for x, the resultant answer is (3, -2).
What are equations?The definition of an equation in algebra is a mathematical statement that shows the equivalence of two mathematical expressions.
For example, the equation 3x + 5 = 14 comprises the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, we have the equation:
y = -2x +4
Now, get value of x for y = -2 as follows:
Fill in the equation with the value of y and find x:
-2 = -2x +4 . . . . use -2 for y
-6 = -2x . . . . . . . subtract 4
3 = x . . . . . . . . . .divide by -2
Therefore, after solving the equation for x, the resultant answer is (3, -2).
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Complete question:
y=−2x+4y, equals, minus, 2, x, plus, 4
Complete the missing value in the solution to the equation.
3. Lucas and Tucker each have a baseball card collection.
The number of cards in Lucas's collection can be represented by c.
The number of cards in Tucker's collection is 4 times the number in Lucas's collection.
The total number of cards in both collections is 205.
What is c, the number of baseball cards in Lucas's collection?
41 cards
51 cards
820 cards
164 cards
.
●
Which is an equation of the line with a slope of 1/4 and a y intercept of -2
use y = mx + b
this is slope and y intercept
m is slope b is y intercept
y = 1/4x -2
can someone help me with this
The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.
The given functions are c(x)=2x, b(x)=x+5 and r(x)=0.75x.
What is the composite function?When the result of one function is used as the input for another, this is known as a composite function.
The most common kind of critical hit simply deals additional damage, most commonly dealing double the normal damage that would have been dealt, but many other formulas exist as well (such as ignoring defense of the target or always awarding the maximum possible damage).
A critical hit has the base damage x multiplied, next the damage reduction is applied to the critical hit. Bonus damage is not subject to damage reduction or critical hits, so this is applied last.
Here, Critical hit × Bonus × Damage reduction
That is, (c·r·b)(x) or (r·c·b)(x)
The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.
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I don't need help but I am giving the answer to everyone :) hope it helps
The number of cannonballs in illustration is 506.
What is illustration?Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.
The number of cannonballs in the first layer = 1² = 1
Number of cannonballs in the second layer = 2² = 4
Number of cannonballs in the third layer = 3² = 9
So, the generalized formula to count the balls is given as
= n(n + 1) (2n + 1)/ 6
Here, n= the total number of layers
Put n =11
11(11 + 1)(2(11) + 1) / 6
= 11(12)(23)/6
= 3036/6
= 506
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28+16x^4 i need it factored completely
Answer:
[tex]4(x^4+7)[/tex]
Step-by-step explanation:
Taking out the greatest common factor,[tex]16x^4+28=4(x^4+7)[/tex].
Which ordered pairs lie on the graph of the exponential function f(x) = 3(2)2x ?
Select each correct answer.
Responses
(0,1)
, , begin ordered pair 0 comma 1 end ordered pair, ,
(3,192)
, (3,192) ,
(1,12)
The ordered pair (1, 12) lies on the graph of the exponential function f(x) = 3(2)2x. which is the correct answer would be option (A).
The graph of an exponential function of the form f(x) = abˣ is a curve that passes through the point (0, a), where a is the initial value of the function.
In the given equation, the initial value is 3, so the graph of f(x) passes through the point (0, 3).
To find other points on the graph of f(x), we can plug different values of x into the equation and solve for the corresponding value of y.
For example, if we plug x = 3 into the equation, we get:
f(3) = 3(2)² × 3
= 3(16)
= 48
Therefore, point (3, 48) does not lie on the graph of f(x).
Similarly, if we plug x = 1 into the equation, we get:
f(1) = 3(2)² × 1
= 3(4)
= 12
Thus, point (1, 12) lies on the graph of f(x).
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Help pls any one pls fast
Answer:
p=106
Step-by-step explanation:
p and 106 are corresponding so they are =
What is the equation of a hyperbola with a = 7 and c = 9? Assume that the transverse axis is horizontal.
The equation of a hyperbola with a=7 and c=9 is (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.
Define Hyperbola.A hyperbola is a kind of smooth curve that appears to lie in a plane. It is made up of two connected components or branches that are mirror reflections of one another and look like two infinite bows. A hyperbola is a collection of points whose difference in distance between two foci is a fixed amount. This discrepancy is calculated by subtracting the distance from the farther focus from the distance from the closest focus.
As we know the standard equation of the hyperbola with a horizontal transverse axis is:
(x-h)²/a²-(y-k)²/b²
Now, put the given values a=7 and c=9 in the Pythagorean theorem to get the value of b.
c²=a²+b²
(9)²=(7)²+b²
81=49+b²
81-49=b²
32=b²
Now square root both sides:√
32=√b²
√32=b
Assuming that the center of a hyperbola is (0,0):
(x-0)²/a²-(y-0)²/b²=1
x²/a²-y²/b²=1
x²/(7)²-y²/(√32)²=1
x²/49-y²/32 = 1
Therefore, the equation of a hyperbola with a=7 and c=9 (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.
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in a recent year, 34.1% of all registered doctors were female. If there were 56,600 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number.
324309
doctors were registered that year.
Explanation:
The questions says, "18.1% of all registered doctors are females"
(Consider, total number of registered doctors as
x
)
that's,
18.1
%
of
x
are female.
and
18.1
%
of
x
is
58
,
700
.
Mathematically,
18.1
100
⋅
x
=
58700
x
=
58700
⋅
100
18.1
x
=
324309
doctors were registered that year.
Find the equation of a line that passes through (-7,2) and is parallel to the line 7x+2y=0
Answer:
write the given equation in a standard form of y = mx + c
7x + 2y = 0
2y = -7x
y = -7/2x
parallel lines have equal gradient
m = -7/2
y - y1 = m(x - x1)
y - 2 = -7/2(x - (-7) )
y - 2 = -7/2( x + 7 )
y - 2 = -7/2x - 49/2
y = -7/2x - 49/2 + 2
y = -7/2 - 45/2
Given NEB NE is 7.5cm and TAN of B is 4 Fill in the rest of the triangle.
Answer:
Hope the picture will help you........
Solve the area of the following shapes
Complete the chart for the given proof. GIVEN: the midpoint of AB <AX = <NY NX = BY PROVE: <X = <Y
Two-column proof
See missing statements and reasons below.
Statement Reason
N is the midpoint of AB GivenAN ≅ NB Definition of a midpointAX ≅ NY GivenBX ≅ BY GivenΔAXN ≅ ΔNYB Side-side-side congruency∠X ≅ ∠Y CPCTCProvedWhich expression is equivalent to sin
12
COS
os (72) - cos (1) sin (72)?
12
Answer:
Step-by-step explanation:
What do the following equations represent in R3?
Match the two sets of letters:
a. a vertical plane
b. a horizontal plane
c. a plane which is neither vertical nor horizontal
A. −5x+3y=−5
B. x=3
C. y=−9
D. z=−10
A. −5x+3y=−5=a vertical plane
B. x=3=a =a vertical plane
C. y=−9=a=a vertical plane
D. z=−10=b=a horizontal plane
What is a vertical plane?A plane that crosses a vertical line: a perspective plane that is parallel to both the ground plane and the image and passes through the point of sight.
What is a horizontal plane?The body is divided into superior and inferior halves by an anatomical plane called the transverse plane, also referred to as the horizontal plane, axial plane, and transaxial plane. Its angle with the coronal and sagittal planes is perpendicular.
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