Answer:
Use a TI84 calculator.
Step-by-step explanation:
There is no way to solve this by hand on paper as the answer is an indefinite number.
Where is the function f(x)=3x^2-6x-45/x^2-5x discontinuous, and what types of discontinuities does it have?
Answer:
Below.
Step-by-step explanation:
f(x)=3x^2-6x-45/x^2-5x
= 3x^2-6x-45 / (x(x - 5))
The denominator is zero when x - 0 and x = 5.
So there will be a vertical asymptote at x = 0 and a hole at x = 5.
If we do the division we get f(x) = 3 remainder 9x - 45
so there will also be a horizontal asymptote where x = 3.
Answer:
Hole at (3, 4.8)
Asymptotes at x = 0 and y = 3
Step-by-step explanation:
[tex]f(x)=\dfrac{3x^2-6x-45}{x^2-5x}[/tex]
Factor the numerator:
[tex]\implies 3x^2-6x-45[/tex]
[tex]\implies 3(x^2-2x-15)[/tex]
[tex]\implies 3(x^2+3x-5x-15)[/tex]
[tex]\implies 3(x(x+3)-5(x+3))[/tex]
[tex]\implies 3(x-5)(x+3)[/tex]
Factor the denominator:
[tex]\implies x^2-5x[/tex]
[tex]\implies x(x-5)[/tex]
Factored form of function:
[tex]\implies f(x)=\dfrac{3(x-5)(x+3)}{x(x-5)}[/tex]
Discontinuity: a point at which the function is not continuous.
Holes
After factoring the rational function, if there is a common factor in both the numerator and denominator, there will be a hole at that point (x-value):
[tex]\implies (x-5)=0 \implies x=5[/tex]
Factor out the common factor from the function and input the found value of x into the new function to find the y-value of the hole:
[tex]\implies f(x)=\dfrac{3(x+3)}{x}[/tex]
[tex]\implies f(5)=\dfrac{3(5+3)}{5}=4.8[/tex]
Therefore, there is a hole at (5, 4.8)
Asymptotes
To find the vertical asymptotes, set the denominator of the new (factored) function to zero and solve:
⇒ Vertical Asymptote at x = 0
As the degrees of the leading terms of the numerator and denominator are equal (both x²), the horizontal asymptote is equal to the ratio of the leading coefficients.
⇒ Horizontal Asymptote at y = 3
5. Sarah made 17 out of 25 free throws during practice. What percentage of free throws did she NOT make? A. 68% B. 58% C. 32% D. 36%
Answer:
C. 32%
Step-by-step explanation:
The percent 17 is of 25.
17 of 25 can be written as:
17/25
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
17/25 * 100/100
= (17 * 100/25) * 1/100 = 68/100
Therefore, the answer is 68%
If Sara made 68% of her free shows, that means she didn't make 32% of her free throws (100 - 68 = 32).
Solve the system of linear equations
x+y=4
-3x-y+-8
Answer:
y=3x+8
Step-by-step explanation:
Formula is L(x)=f(a)+f(a)(x-a)
This is for linearization
WHICH ONE?? NEED HELP ASAP
Answer:
DD
Step-by-step explanation:
If you distribute the 2 you get 12.2x + 14 so D
The function C (t) = StartFraction 4 t Over t squared + 2 EndFraction models the cost per student of a field trip when x students go on the trip. How is the parent function On a coordinate plane, 3 curves are shown. One curve opens up and to the right in quadrant 1 and goes through (2, 4) and (4, 1). Another curve approaches x = negative 2 in quadrant 2, changes direction at (0, 0), and then decreases in quadrant 4 and approaches y = 2. The third curve opens down and to the left in quadrant 3 and goes through (negative 4, negative 1) and (negative 2, negative 4). transformed to create the function On a coordinate plane, 2 curves are shown. One curve opens up and to the left in quadrant 2 and goes through (negative 4, 8) and (negative 6, 6). Another curve opens down and to the right and goes through (negative 1, negative 3), (0, 0), and (6, 3).?
Answer:
It is vertically stretched by a factor of 200 and shifted 10 units up.
Step-by-step explanation:
cool like that
It is vertically stretched by a factor of 200 and shifted 10 units up.
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
How do you write a function?You write functions with the function name followed by the dependent variable.
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difference of 2.4 − 1.8 = ________ by rounding each number to the nearest whole number.
On a coordinate plane, the pre-image is shifted 2 units to the right and 1 unit up. It is rotated 90 degrees counterclockwise.
Which sequence of transformations produced the image?
Answer:B.
Step-by-step explanation:
B.a translation 2 units to the right and 1 unit up followed by a counter-clockwise rotation 90° about the origin
Which one of the following statements is not true.
A. Soil is the second layer of Earth's crust.
B. Metals can be extracted from minerals.
C. Oil is made from dead plants and animals.
D. Chemical weathering can break down rocks into fragments.
Answer:
I think c sorry if wrong
Step-by-step explanation:
have a good day
<~~• ¥ Pls HELP me!! ¥ • ~~>
Answer:
18
Step-by-step explanation:
Area of a triangle: 0.5 x base x height
In this case: 0.5 x 9 x 4
hope this helps
have a good day
Answer:
Area = 18
Step-by-step explanation:
Formula
b*h /2
so
9 *4 /2
= 18
a 2-quart cartoon od chocolate milk costs 1.52 what is the price per cup
Answer:
The price per cup is $0.19
Step-by-step explanation:
In a quart there are 4 cups.
1.52÷4=0.38
But because there are 2 quarts you have to divide it by 2.
Which is 0.19
Thats the answer
Pls give Brainliest
Im desperate...
A correlation coefficient of -0.85 means:
As one variable increases in value the other variable decreases in value
No relationship between the variables
As one variable increases in value the other variable also increase in value
Answer:
do you got an answer key
Step-by-step explanation:
Lines c and d are perpendicular. The slope of line c is −1/3. What is the slope of line d?
Answer:
1/3
Step-by-step explanation:
When two lines are perpendicular, it means the lines intersect at a right angle and have opposite reciprocal slopes.The slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 degrees.
To figure out d we need to use the formula:
- 1 / m
Plug in:
- 1 / - 1/3
Solve:
1/3
[tex]~~~~~~m_c \times m_d = -1\\\\\implies -\dfrac 13 \times m_d=-1\\\\\implies m_d = 3\\\\\text{The slope of line d is 3.}[/tex]
A car who travels 225km in 15 hours, what is the average speed?
Answer:
= 15km/hour
Step-by-step explanation:
Distance = 225km
Time = 15 hours
We will divide distance over time and then we will get the average speed so the average speed will be = 15 km\hour.
Answer:
Below in bold.
Step-by-step explanation:
Speed = distance / time
= 225/15
= 15 km/hour.
Which function results after applying the sequence of transformations, in this order, to f(x) = x^5
• stretch vertically by 3
• translate up 1 unit
• translate left 2 units
Answer:
C. f(x) = 3(x+2)^5 + 1
Step-by-step explanation:
The basic equation take the form a(x-h)+k
We can plug in the values of 3 for a, 1 for k, and 2 for h, and get the equation f(x) = 3(x+2)^5 + 1
Here is a 15-by-8 rectangle divided into triangles.
8
9
6
Is the shaded triangle a right triangle?
no
The sides of the shaded triangle do not form a Pythagorean triple, therefore, it is not a right triangle.
What is a Right Triangle?A triangle is a right triangle if the square of its longest side equals the sum of the square of the other two smaller sides, based on the Pythagorean Theorem.
Using the Pythagorean Theorem, find the lengths of the legs of the shaded triangle, and find out the sum of their squares equals the length of the longest side.
First leg of the shaded triangle = √(8² + 6²) = 10
Second leg of the shaded triangle = √(8² + 9²) = 12
The third side (longest side) of the shaded triangle is 9 + 6 = 15.
15² = 10² + 12²
225 = 244 (not true)
Therefore, the shaded triangle is not a right triangle.
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Given: sin = 4/5 and cos x = -5/13 ; evaluate the following expression.
cos( ∅ - x )
Answer:
[tex]\cos(\theta - x)=\dfrac{33}{65}[/tex]
Step-by-step explanation:
Given:
[tex]\sin\theta=\dfrac{4}{5}\implies \cos \theta=\dfrac{3}{5}[/tex]
[tex]\cos x=-\dfrac{5}{13}\implies \sin x=\dfrac{12}{13}[/tex]
Using the trig identity:
[tex]\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B[/tex]
[tex]\begin{aligned}\implies \cos(\theta - x) &=\cos \theta \cos x + \sin \theta \sin x\\\\&=\dfrac{3}{5} \cdot -\dfrac{5}{13} + \dfrac{4}{5} \cdot \dfrac{12}{13}\\\\&=-\dfrac{15}{65} + \dfrac{48}{65}\\\\&=\dfrac{33}{65}\end{aligned}[/tex]
sinø=4/5
so
cosø=3/5And
cosx=-5/13
so
sinx=12/13cos(ø-x)
sinøsinx+cosøcosx(4/5)(12/13)+(3/5)(-5/13)(48/65)-(15/65)48-15/6533/65Answer the following.
Calculate the cost of carpet for the following room.
The room is 15 feet x 12 feet. The cost of the carpet is $2.99 per square foot and the cost of
the pad is $.50 per square foot. Installation costs are $.50 per square foot.
Answer:
I think the total is 628.20$
Step-by-step explanation:
15*12=180
180*2.99=538.2
180*.5=90
90+538.2=628.2
Hope this helped :)
y(z + y): use y = 2, and z = 4
Which problem can be solved with 16 divided by one-eighth?
The value of the 16 divided by one-eighth is 48 after simplification of the fraction.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that are +, -, ×, and ÷.
We have:
16 divided by one-eighth.
Here the option is not given, but we can solve the above expression.
= 16 ÷ (1/8)
= 16×8 (after simplification)
= 48
Thus, the value of the 16 divided by one-eighth is 48 after simplification of the fraction.
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PLEASE HELP ASAP A can has a radius of 1.3
inches and a height of 3.8 inches. What is the
volume of the can? (The volume of a cylinder
is V = Tr? where 7 ~ 3.14, r is the radius,
and / is the height.)
Answer:
V=20.17
Step-by-step explanation:
V=πr²h
=π1.3²×3.8
=20.17
PLS HELP
Find the value of x and y
Answer: 'X' = 24 degrees
Step-by-step explanation:
5 times 'X' = 120 degrees (because the formula is base times height divided by 2).
120 divided by 5 = 'X'
= 24
'X' = 24 degrees
Triangle congruence by SSS/SAS
State if the two triangles are congruent. If they are, state how you know.
Answer:
if all three side equal to another traingle than we can say SSS congruent criteria
if two side and one angle equal than we can say SAS criteria
Step-by-step explanation:
I hope it's helpful for youWhich expression does (cos 3x)(cos x) − (sin 3x)(sin x) simplify to?
cos 4x
sin 2x
cos 2x
sin 4x
The result for the expression (cos 3x)(cos x) − (sin 3x)(sin x) is cos 4x.
Trigonometric Identities What is trigonometric identities ?Equations involving trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
The addition/sum formula in trigonometry:In terms of functions of A and B, angle addition formulae express trigonometric functions of sums of angles A[tex]\frac{+}{_}[/tex]B.
Sum formula or cos:cos (A+B) = cosA.cosB + sinA.sinB
Application of sum formula of cos:The give equation is as follows,
(cos 3x)(cos x) − (sin 3x)(sin x)
Applying the sum formula,
= (cos 3x)(cos x) − (sin 3x)(sin x)
= cos(3x + x)
= cos 4x
Therefore, the result of the given equation is cos 4x.
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Amna multiplies 38 by 4.
Should her answer be greater than or less than 4?
It should be greater not lesser
Please answer as soon as possible, thankyou.
The coordinates of point A when it is rotated about 180 degrees will be (7,-4).
What is coordinate geometry?A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Given that:-
Point A is shifted by an angle of 180 degrees about an origin.As it is turned 180 degrees from its initial position ( -7,4) just opposite side of the origin so the new coordinates of the point will be (4,-7).
Therefore the coordinates of point A when it is rotated about 180 degrees will be (7,-4).
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PLEASE HELP ME WITH THIS!!!
Answer:
B. 1
Step-by-step explanation:
imagining where 10 would be on the graph you can see that the line will cross with 1 missed shot
So i can not figure out the answer to this question if anyone could help that would be awesome
Answer:
MN is correct
Step-by-step explanation:
A segment bisector passes through the midpoint of the segment and divides it in half. Since MN does both of these, it is the segment bisector.
Answer:
MN: 32
Step-by-step explanation:
Where is the circumcenter of a right triangle located?
on the hypotenuse
on one of the legs
outside the triangle
inside the triangle
Answer:
on the hypotenuse
Step-by-step explanation:
Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle.
what is 17+6-6+6 divided by 6 + 17.
only 99.9 percent of people could solve. ill give brainiest to first to answer.
Answer:
[tex]\boxed{\bold{1}}[/tex]
Using Pedmas rule:
[tex]\dashrightarrow \sf \dfrac{17+6-6+6}{6+17}[/tex]
subtract: 6-6 = 0
[tex]\dashrightarrow \sf \dfrac{17+6}{23}[/tex]
simplify the following
[tex]\dashrightarrow \sf \dfrac{23}{23}[/tex]
the numerator and denominator cancels out
[tex]\dashrightarrow \sf 1[/tex]
Given statement:
17 + 6 - 6 + 6 divided by 6 + 17The phrase "divided by" means division. Therefore,
⇒ (17 + 6 - 6 + 6) ÷ (6 + 17)
⇒ (17 + 6) ÷ (6 + 17)
Recall: A number divided by itself is 1
⇒ 1
Therefore, 1 is the solution to the expression.
WILL MARK BRAINLIEST
Answer:
cot(t) = 56/33
Step-by-step explanation:
cot(t) = 56/33, because cot = adj/opp simple as that..
