Use the given graph to determine the limit, if it exists. A
Find limit as x approaches three from the left of f of x..
Answers
Related Questions
A basket contains 11 pieces of fruit: 4 apples, 5 oranges, and 2 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple?
Answers
The probability that Jonas will get an orange and Beth will get an apple is 20/121.
Explanation:To find the probability that Jonas will get an orange and Beth will get an apple, we need to find the probability of Jonas getting an orange and then multiply it by the probability of Beth getting an apple.
The probability of Jonas getting an orange is the number of oranges in the basket (5) divided by the total number of fruits (11):
P(orange for Jonas) = 5/11
The probability of Beth getting an apple is the number of apples in the basket (4) divided by the total number of fruits (11):
P(apple for Beth) = 4/11
To find the combined probability, we multiply these two probabilities together:
P(orange and apple) = P(orange for Jonas) * P(apple for Beth) = (5/11) * (4/11) = 20/121
A) side-side-side triangle similarity postulate
B) angle-angle triangle similarity postulate
C) angle-side-angle triangle similarity postulate
D) hypotenuse-lag triangle similarity postulate
Answers
For similarity you only have to know that 2 corresponding angles are equal.
Solve the equation ,and check the solution.
r - 3 r
____ = __
10 13 Check:
Answers
I'm assuming the equation should be (r-3)/10 = r/13.
Use parenthesis to indicate what is being divided. In this case all of "r-3" is over 10.
If my assumption above holds up, then we can solve for r like so
(r-3)/10 = r/13
13(r-3) = 10r ... cross multiply
13r-39 = 10r
13r-39-13r = 10r-13r ... subtract 13r from both sides
-39 = -3r
-3r = -39
-3r/(-3) = -39/(-3) ... divide both sides by -3
r = 13
The value of r is r = 13
-----------------------
Check:
Replace every copy of "r" with "13" to get
(r-3)/10 = r/13
(13-3)/10 = 13/13
10/10 = 13/13
1 = 1 ... equation is true; answer has been confirmed
To solve the equation, we cross multiply to eliminate the fractions and solve for r. The solution is r = 13. We can check the solution by substituting it back into the original equation.
Explanation:To solve the equation (r - 3) / 10 = r / 13, we can cross multiply to eliminate the fractions. This gives us 13(r - 3) = 10r. Distributing, we get 13r - 39 = 10r. We can then solve for r by subtracting 10r from both sides and adding 39 to both sides. This gives us 3r = 39. Dividing both sides by 3, we find that r = 13.
To check the solution, we substitute r = 13 back into the original equation. The left side becomes (13 - 3) / 10 = 10 / 10 = 1, and the right side becomes 13 / 13 = 1. Since both sides are equal to 1, we can confirm that the solution r = 13 is correct.
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Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.
Part A: Find (f + g)(x). Show your work. (3 points)
Part B: Find (f ⋅ g)(x). Show your work. (3 points)
Part C: Find f[g(x)]. Show your work. (4 points)
Answers
(f+g)(x)=f(x)+g(x)
(f+g)(x)=4x-5+3x+9
(f+g)(x)=7x+4
B:
(f•g)(x)=f(x)•g(x)
(f•g)(x)=(4x-5)(3x+9)
(f•g)(x)=12x^2-15x+36x-45
(f•g)(x)=12x^2+21x-45
C:
(f○g)(x)=f(g(x))
(f○g)(x)=4(3x+9)-5
(f○g)(x)=12x+36-5
(f○g)(x)=12x+31
what is the period of the sinusoid given by y=-4sin( [tex] \frac{2π}{3} [/tex] x) ?
Answers
[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ [/tex]
[tex]\bf \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]
with that template in mind, let's see
[tex]\bf \begin{array}{llll} y=&-4sin(&\frac{2\pi }{3}x)\\ &A&B \end{array}\qquad period\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{2\pi }{3}}\implies \cfrac{\frac{2\pi }{1}}{\frac{2\pi }{3}} \\\\\\ \cfrac{2\pi }{1}\cdot \cfrac{3}{2\pi }\implies 3[/tex]
Answer:
The answer is 3 for A P E X
Step-by-step explanation:
(25 Points)Enter numbers to write 4.23×10^3 in standard notation.
Answers
So the answer will be 4230
A rectangular garden has length twice as great as its width. A second rectangular garden has the same width as the first garden and length that is 4 meters greater than the length of the first garden. The second garden has area of 70 square meters. What is the width of the two gardens?
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Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption, the volume of the flask is ____ cubic inches. If both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be _____ times the original volume.
options for the first blank are: 20.22, 35.08, 50.07, or 100.11
options for the second blank are: 2, 4, 6 or 8
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The total volume of the flask will be 50.06 [tex]\rm inches ^3[/tex] and if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.
Given :
Flask can be modeled as a combination of a sphere and a cylinder.
The volume of Sphere is given by the:
[tex]V_s = \dfrac{4}{3}\pi r^3[/tex]
Given - diameter of sphere = 4.5 inches. Therefore, radius is 2.25 inches.
Now, the volume of sphere of radius 2.25 inches will be:
[tex]V_s = \dfrac{4}{3}\times \pi\times (2.25)^3[/tex]
[tex]\rm V_s = 47.71\; inches^3[/tex]
The volume of Cylinder is given by the:
[tex]V_c = \pi r^2h[/tex]
Given - diameter of cylinder = 1 inches then radius is 0.5 inches and height is 3 inches.
Now, the volume of cylinder of radius 0.5 inches and height 3 inches will be:
[tex]V_c = \pi\times (0.5)^2 \times 3[/tex]
[tex]\rm V_c = 2.35\; inches^3[/tex]
Therefore the total volume of the flask will be = 47.71 + 2.35 = 50.06 [tex]\rm inches ^3[/tex].
Now, if both the sphere and the cylinder are dilated by a scale factor of 2 than:
Radius of sphere = [tex]2.25\times 2[/tex] = 4.5 inches
Radius of cylinder = [tex]0.5\times 2[/tex] = 1 inch
Height of cylinder = [tex]3\times 2[/tex] = 6 inches
Now, the volume of sphere when radius is 4.5 inches will be:
[tex]V_s' = \dfrac{4}{3}\times \pi \times (4.5)^3[/tex]
[tex]\rm V_s' = 381.70\; inches ^3[/tex]
And the volume of cylinder when radius is 1 inch and height is 6 inches will be:
[tex]V_c' = \pi \times (1)^2\times 6[/tex]
[tex]\rm V_c'=18.85\;inches^3[/tex]
Therefore the total volume of the flask after dilation by a scale factor of 2 will be = 381.70 + 18.85 = 400.55 [tex]\rm inches ^3[/tex].
Now, divide volume with dilation by theorginal volume of the flask.
[tex]\dfrac{400.55}{50.06}=8[/tex]
Therefore, if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.
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SOMEBODY HELP ME WITH THESE PLEASE! I really need the help like NOW PLS!
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[tex]f(n) = 2n^2 - 5n[/tex]
then [tex]g(n) +f(n) = (n-4) + (2n^2 - 5n)[/tex]
[tex]= n - 4 + 2n^2 - 5n[/tex]
[tex]= 2n^2 -5n + n - 4[/tex]
[tex]= 2n^2 - 4n -4[/tex]
95. [tex]f(n) = -n+3[/tex]
[tex]g(n) = n^3 + 3n[/tex]
Then [tex]f(n) . g(n) = (-n+3) . (n^3 + 3n)[/tex]
[tex]= -n^4 + 3n^3 - 3n^2 + 9n [/tex]
97. [tex]f(x) = 3x+1[/tex]
[tex]g(x) = 2x[/tex]
For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).
[tex]f(g(x)) = 3*(2x) + 1[/tex]
[tex]= 6x + 1[/tex]
99. [tex]f(n) = n - 3[/tex]
[tex]g(n) = 2n^2 - 3n[/tex]
[tex]g(-7) = 2*(-7)^2 - 3 * (-7) = 2* 49 + 21 = 98 + 21 = 119[/tex]
[tex]f(g(-7)) = 119 - 3 = 116[/tex]
Answer:
97.
For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).
99.
Step-by-step explanation:
(02.02 MC)
Line segment RS is shown on a coordinate grid:
The line segment is rotated 270 degrees counterclockwise about the origin to form R'S'. Which statement describes R'S'?
R'S' is parallel to RS.
R'S' is half the length of RS
. R'S' is twice the length of RS.
R'S' is equal in length to RS.
Answers
length doesnt change, it was just rotated.
What are the roots of the function y = 4x2 + 2x – 30? To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of .
Next, factor the trinomial completely. The equation becomes .
Use the zero product property and set each factor equal to zero and solve. The roots of the function are .
Answers
factor out the GCF:
2(2x² + x - 15) = 0
factor the trinomial completely:
2x² + x - 15 = 0
2x² + 6x - 5x - 15 = 0
2x(x + 3) - 5(x + 3) = 0
(2x - 5)(x + 3) = 0
use the zero product property and set each factor equal to zero and solve:
2x - 5 = 0 or x + 3 = 0
2x = 5 x = -3
x = 2.5
The roots of the function are x=-3, x=2.5
The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2
Roots of a quadratic equationThe given quadratic equation is:
[tex]y=4x^2+2x-30[/tex]
Set y = 0
[tex]4x^2+2x-30=0[/tex]
Factor the trinomial completely
[tex]4x^2-10x+12x-30=0\\\\2x(2x-5)+6(2x-5)=0\\\\(2x-5)(2x+6)=0[/tex]
Set each factor to zero and solve
2x - 5 = 0
2x = 5
x = 5/2
2x + 6 = 0
2x = -6
x = -6/2
x = -3
The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2
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traveling at 65 miles per hour how many minutes rounded to the nearest whole number does it takes to drive 125 miles from san digit to malibu
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divide total miles by speed
125/65 = 1.923 hours
there are 60 minutes per hour
multiply 1.923*60 = 115.384 minutes
rounded off to nearest whole number = 115 minutes
The transformation from f to g represents a __________ stretch. f(x) = Square root of x. and g(x) = 6Square root of x.
Answers
The transformation from f to g represents a Vertical stretch.
Step-by-step explanation:We are given a parent function f(x) as:
[tex]f(x)=\sqrt{x}[/tex]
and the transformed function g(x) as:
[tex]g(x)=6\sqrt{x}[/tex]
We know that any function transformation of the type:
f(x) → a f(x)
represents either a vertical stretch stretch or compression depending on the value of a.
If 0<a<1 then the transformation is a vertical compression and if a>1 then the transformation is a vertical stretch.
Here we have a=6>1
Hence, the transformation is a VERTICAL STRETCH.
1. is acute. 2. is isosceles. 3. is right. Which two statements contradict each other?
Answers
Answer:
the answer is 2 and 3
Step-by-step explanation:
I took the test
Use complete sentences to describe the range of the sine function.
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Given the sine function f(x)=sinx,
This function is the function which calculates the sine of the values of x.
According to the definition of the sine of an angle x in the unit circle,
[tex]-1 \leq sinx \leq 1[/tex],
so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.
This means that the values that the sine function takes are any values between -1 and 1, inclusive.
This determines the Range of the sine function.
So the Range of the sine function is [-1, 1]
Two 6-sided dice are rolled. what is the probability the sum of the two numbers on the die will be 4?
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3/6 or 1/2 if only addition
5-1=4. 6-2=4.
2/6 or 1/3 if only subtraction
if both 5/6
Answer:
[tex]\frac{1}{12}[/tex].
Step-by-step explanation:
Given : Two 6-sided dice are rolled.
To find : what is the probability the sum of the two numbers on the die will be 4.
Solution : We have given
Two 6-sided dice are rolled.
Dice have number { 1,2,3,4,5,6} { 1,2,3,4,5,6} .
[tex]Probability =\frac{outcome\ happn}{total\ outcome}[/tex].
sum of the two numbers on the die will be 4.
Case (1) : first dice rolled 3 and second dice rolled 1.
{3,1}
3 +1 = 4 .
Case (2) : first dice rolled 1 and second dice rolled 3 .
{1,3}
1 + 3 = 4 .
Case (3) : first dice rolled 2 and second dice rolled 2.
{2,2}
2 + 2 = 4.
Then there are 3 possible outcomes where the sum of the two dice is equal to 4.
The number of total possible outcomes = 36.
[tex]Probability =\frac{3}{36}[/tex].
[tex]Probability =\frac{1}{12}[/tex].
Probability of getting sum of two dice is [tex]\frac{1}{12}[/tex].
Therefore, [tex]\frac{1}{12}[/tex].
(07.05 MC)
An equation is shown below:
4x + 2(x – 3) = 4x + 2x – 11
Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)
Part B: Name one property you used to solve this equation. (4 points
Answers
4x + 2x - 6 = 4x + 2x - 11
6x - 6 = 6x - 11
6x - 6x = -11 + 6
0 = -5...incorrect......this has no solution...0 solutions
one property used was the distributive property :2(x - 3) = 2x - 6
Answer:
-6 = -11
Distributive Property
Step-by-step explanation:
A.
4x + 2(x – 3) = 4x + 2x – 11
4x + 2x - 6 = 4x + 2x - 11
6x - 6 = 6x - 11
-6 = -11
since -6 is not equal to -11, so there's no solution
B. Distributive property
How could the relationship of the data be classified?
scatter plot with points loosely scattered going down to the right
A positive correlation
A causation
A negative correlation
No correlation
Answers
Answer: A negative correlation
Step-by-step explanation:
If the points in the scatter plot scattered going down to the right, it shows that there are inverse relationship between the quantities.
With the increase of one quantity or variable there is decrease in the other quantity or variable.
Therefore, if in the scatter plot with points loosely scattered going down to the right , then the relationship of the data be classified as a negative correlation.
Find the total area of the prism in ( _+_√_ )
Answers
a^2 + b^2 = c^2
4^2 + 6^2 = c^2
16 + 36 = c^2
52 = c^2
2√13 = c
Triangle bases:
A = (1/2) * b * h * 2
A = (1/2) * 4 * 6 * 2
A = 24 ft^2
Front Rectangle: Left side Rectangle Back Side Rectangle
A = 8 * 2√13 = 16√13 ft^2 A = 4 * 4 = 32 ft^2 A = 6 * 8 = 48 ft^2
24 + 32 + 48 + 16√13 = Total area = 104 + 16√13 ft^2
A rectangular prism with a square base has a lateral area of 192 square yards and a surface area of 264 square yards. What is the length of a base edge?
Answers
TSA = LSA + 2s²
Since the base is said to be the square, its area is equal to s² where s is the base edge. Because there are 2 bases, that's why it's 2s².
264 = 192 + 2s²
s² = (264-192)/2
s = √36
s = 6 yards
If measure of angle p=(10x-2),measure of angle o=(3x+9) , and measure of angle q=(3x-3) , list the lengths of the sides of triangle OPQ from longest to shortest.
Answers
So we can find the value of x...
10x-2+3x+9+3x-3=180
16x+4=180
16x=176
x=11
So the angles are 108°, 42°, 30°
Now using the Law of Sines we can solve for all sides.
(sina/A=sinb/B=sinc/C)
a/sin30=b/sin42=c/sin108
However, we would need to know at least one side length to solve for sides a,b, and c numerically, otherwise it can be any multiple of an arbitrary choice for the smallest side. Let a=1 for example:
b=sin42/sin30, c=sin108/sin30
b≈1.34, c≈1.90
a=1, b=1.34, c=1.9
Anyway...
If you are given any side length:
a/sin30=b/sin42=c/sin108 still holds true and you can solve for the other side lengths...
Answer:
OQ > PQ > OP
Step-by-step explanation:
In this question measure of all angles in a triangle has been given.
m∠ p = (10x - 2)
m∠ q = (3x - 3)
m∠ o = (3x + 9)
Since total of all angles is 180°, so we will equate the total of all angles to 180°
∠p + ∠q + ∠o = 180°
(10x - 2) + (3x - 3) + (3x + 9) = 180°
(10x + 3x + 3x) -2 - 3 + 9 = 180
16x - (2 + 3 - 9) = 180°
16x + 4 = 180
16x = 180 - 4
16x = 176
x = [tex]\frac{176}{16}=11[/tex]
Now we will find the measure of each angle.
∠p = (10x - 2) = 10×11 - 2 = (110 - 2) = 108°
∠q = (3x - 3) = 3×11 - 3 = (33 - 3) = 30°
∠o = (3x + 9) = 3×11 + 9 = (33 + 9) = 42°
As we know in a triangle, angle opposite to the largest side is largest and angle opposite side is the smallest.
Since ∠p > ∠o > ∠q
Therefore, in Δ OPQ opposite sides to these angles will be in the same ratio.
OQ > PQ > OP
Write an equation for the line that is parallel to the given line and that passes through the given point.
y = 1/2 – 8; (–6, –17)
A.) y = 2x – 14
B.) y = 1/5x + 5/2
C.) y = -2x + 14
D.) y = 1/2x – 14
Answers
The sum of four consecutive whole numbers is 54, what are the four numbers
Answers
The sum of the four numbers is 54, therefore
x + (x+1) + (x+2) + (x+3) = 54
4x + 6 = 54
4x = 54 - 6 = 48
x = 12
Answer:
The four numbers are 12, 13, 14, and 15
A rectangle is 42 square feet. what percent of the area of the rectangle is a square with side lengths of 6 feet?
Answers
area = L x w
42 = 6 x w
w=42/6 = 7
rectangle is 6 x 7
square would be 6 x 6 = 36 square feet
36/42 = 0.857 = 85.7% ( Round answer if needed)
(Solve for r) 0.5r − 3.8 = 5.66
Answers
0.5r = 5.66 + 3.8
0.5r = 9.46...divide both sides by 0.5
r = 9.46 / 0.5
r = 18.92 <==
0.5r = 9.46
r = 9.46 ÷ 0.5
r = 18.92
r = 18/23/25
What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y=1/2x+4?
Answers
both equal y so
2x-5=-x+1
3x-5=1
3x=6
x=2
sub back
y=2x-5
y=2(2)-5
y=4-5
y=-1
intersection is (2,-1)
paralell to a line is having same slope
y=mx+b, m is slope
given
y=1/2x+4
slope is 1/2
so
y=1/2x+b
find b
given the point (2,-1) that it must pass through
(x,y) so x=2 and y=-1
-1=1/2(2)+b
-1=1+b
-2=b
the equation is y=1/2x-2
y = -x + 1
2x - 5 = -x + 1
2x + x = 1 + 5
3x = 6
x = 6/3
x = 2
y = -x + 1
y = -2 + 1
y = -1
solution is (2,-1)...point of intersection between the 2 lines given.
y = 1/2x + 4....slope here is 1/2. A parallel line will have the same slope.
y = mx + b
slope(m) = 1/2
(2,-1)...x = 2 and y = -1
sub and find b
-1 = 1/2(2) + b
-1 = 1 + b
-1 -1 = b
-2 = b
so ur parallel equation is : y = 1/2x - 2 <==
let n be the first 3 of consecutive even integers. what is the sum of those integers?
Answers
even integers are 2 apart
so the 3 integers are n,n+2,n+4
the sum is n+n+2+n+4=3n+6
the sum is 3n+6
Line BC has an equation of a line y = 2x + 3, and line EF has an equation of a line y = negative one over 2 x + 4. These two equations represent
Answers
Answer:
Perpendicular lines.
Step-by-step explanation:
We have been given that line BC has an equation of a line [tex]y=2x+3[/tex] and line EF has an equation of a line [tex]y=-\frac{1}{2}x+4[/tex]. We are asked to determine what these both equations represent.
We know that slope of two perpendicular lines is negative reciprocal of each other. This means the product of slope of both lines is equal to [tex]-1[/tex].
Let us find the product of slopes of both lines.
[tex]2\times \frac{-1}{2}[/tex]
Upon cancelling 2 with 2 we will get,
[tex]=-1[/tex]
Therefore, the given two equations represent equations of two perpendicular lines.
Evaluate S5 for 400 + 200 + 100 + … and select the correct answer below.
25
775
1,125
500
Answers
The sum of first five terms for the geometric series is 775. The correct answer is (B).
What is a geometric sequence?In a geometric sequence, the ratio of two consecutive terms are always equal.
The general expression for the nth term is given as aₙ = a₁ × rⁿ⁻¹ .
The sum of n terms for this sequence is given as Sₙ = (rⁿ - 1)/(r - 1)
The given series is 400 + 200 + 100 + …
It is a geometric series.
Its first term is a₁ = 400.
And, common ratio is r = 200/400 = 0.5.
Now, the expression for the sum of n terms is given as below,
Sₙ = a(1 - rⁿ)/(1 - r)
Then, substitute the value of a₁, a₅ and n = 5 to obtain,
S₅ = 400(1 - 0.5⁵)/(1 - 0.5)
⇒ S₅ = 775.
Hence, the sum of first five terms of the given series is 775.
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I don't get it I got a different answer then these
Answers
So you multiply the first fraction of both numerator and denominator by 3, and the second by 2:
3(g-2) / 18 - 2(g+3) / 18 = (3g - 6 - 2g - 6) / 18 = (g-12)/18
= ---------------------
18
3g - 6 -2g - 6
= ---------------------
18
g - 12
= -----------
18
this is what i got