Answers
Answer:
[tex]x \to f(x)[/tex]
[tex]0.25 \to -1[/tex]
[tex]0.5 \to -0.5[/tex]
[tex]1 \to 0[/tex]
[tex]2 \to 0.5[/tex]
[tex]4 \to 1[/tex]
[tex]8 \to 1.5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = log_4(x)[/tex]
[tex]x = 0.5[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(0.5) = log_4(0.5)[/tex]
Apply law of logarithm
[tex]f(0.5) = \frac{log(0.5)}{log(4)}[/tex]
Using a calculator, we have:
[tex]f(0.5) = -0.5[/tex]
[tex]x = 1[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(1) = log_4(1)[/tex]
Express 1 as 4^0
[tex]f(1) = log_4(4^0)[/tex]
Apply law of logarithm
[tex]f(1) = 0*log_4(4)[/tex]
[tex]f(1) = 0[/tex]
[tex]x = 2[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(2) = log_4(2)[/tex]
Apply law of logarithm
[tex]f(2) = \frac{log(2)}{log(4)}[/tex]
Using a calculator, we have:
[tex]f(2) = 0.5[/tex]
[tex]x = 4[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(4) = log_4(4)[/tex]
[tex]log_a(a) = 1[/tex]
So:
[tex]f(4) = 1[/tex]
[tex]x = 8[/tex]
[tex]f(x) = log_4(x)[/tex]
[tex]f(8) = log_4(8)[/tex]
Apply law of logarithm
[tex]f(8) = \frac{log(8)}{log(4)}[/tex]
Using a calculator, we have:
[tex]f(8) = 1.5[/tex]
So, the complete table is:
[tex]x \to f(x)[/tex]
[tex]0.25 \to -1[/tex]
[tex]0.5 \to -0.5[/tex]
[tex]1 \to 0[/tex]
[tex]2 \to 0.5[/tex]
[tex]4 \to 1[/tex]
[tex]8 \to 1.5[/tex]
Related Questions
Please help me with this questions
Answers
SOMEONE PLEASE HELP :(
Answers
Answer:
[tex](x-3)^{2} = 10[/tex]
Step-by-step explanation:
[tex]\\Question 1\\\\-2xc = -6x\\2xc = 6x\\c = \frac{6}{2} \\c = 3\\x^{2} - 6x + cx^{2} = 1 + c^{2} \\x^{2} - 6x + 3^{2} = 1 + 3^{2}\\x^{2} - 6x + 9 = 1 + 9\\x^{2} - 6x + 9 = 10\\(x - 3)^{2} = 10\\REWRITINGx^{2} - 6x = 1 is equal (x -3)^{2} = 10\\[/tex]
I hope this help!
I don't know the second one ^-^
The angle of elevation to the top of a Building in Seattle is found to be 5 degrees from the ground at a
distance of 1 mile from the base of the building. Using this information, find the height of the building.
Answers
Answer:
Height = 125 tan 6°
I need help asap again pls help me io needd help plzzzzzzzzzzzzzz
Answers
Answer: isosceles
equilateral is all sides are the same
scalene is all sides dif
isosceles is at least two sides the same
If anyone could help I would be so happy!
Answers
Answer: well i cant help... so dont be happy! :)
4
Acellus
Find the lateral area of this cone.
Leave your answer in terms of pie
4ft
3ft
LA = [ ? ] pie ft2
Hint: Lateral Area of a Cone = mre
Where l = slant height
Enter
Answers
Answer:12
Step-by-step explanation: I multiplied 3 times 4
The Lateral Surface Area of cone is 12 π ft³
what is Lateral Surface area of Cone?The lateral area of a cone is defined as the area covered by the curved surface of the cone. It is also called lateral surface area (LSA) or curved surface area (CSA) of a cone. A cone is a 3-D object which tapers smoothly from the flat circular base to a point. In other words, it is a shape formed by a set of line segments coming from the base that connects to a common point
example:
Find the lateral area of a cone having base radius of 21 units and height of 20 units. (Use π = 22/7)
Solution: Given that r = 21 units and h = 20 units
Thus, slant height of the cone, l = √(r2 + h2) = √(212 + 202) = √(441 + 400) = √841 = 29 units
We know, the lateral area of the cone = πrL
Lateral area of a cone = (22/7) × 21 × 29
= 22 × 3 × 29
= 1914 units2
Answer: The lateral surface area of the given cone is 1914 units2
Given:
l= 4 ft
r= 3 ft
Lateral area = πrl
Lateral area = π * 3 * 4
Lateral area = 12 π ft³
Learn more about this concept here:
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(6x-5)+(-7x+2)
and
(6x-5)-(-7x+2)
Need work
Answers
Answer:(6x-5)+(-7x+2)
1 Remove parentheses.
6x-5-7x+2
2 Collect like terms.
(6x-7x)+(-5+2)
3 Simplify.
-x-3
_____________________________
1 Remove parentheses.
6x-5+7x-2
6x−5+7x−2
2 Collect like terms.
(6x+7x)+(-5-2)
3 Simplify.
13x-7
Hope this helps
-Tobie the dog <3
6x - 5 + (-7x + 2) = ...
= 6x - 5 - 7x + 2
= (6x - 7x) + (-5 - 2)
= -x - 7
[tex]\:[/tex]
B)6x - 5 - (-7x + 2) = ...
= 6x - 5 + 7x + 2
= (6x + 7x) + (-5 + 2)
= 13x - 3
What is 9X plus 2Y equals -14 in slope intercept form
Answers
Answer:
y = -9/2x-7
Step-by-step explanation:
9x+2y = -14
-9x -9x
2y= -9x-14
/2 /2
y= -9/2x-7
What is 32 divided by 4 to the second power plus 35-20 divided by 5
Answers
College Math!!! I did the first half of the question, I just need the bottom half of it.
Answers
Answer:
-49
Step-by-step explanation:
[tex]\int _{-5}^{-2}\:\left(8\:w\left(r\right)-3\right)dr[/tex] = [tex]\int _{-5}^{-2}\:8\:w\left(r\right)dr[/tex] -3 (-2 -(-5)) = [tex]8 \int _{-5}^{-2}\:\:w\left(r\right)dr[/tex] -9 =8(-5) -9 = -49
Help plssss!!! I would really appreciate it!
Answers
Answer:
The table represents a linear function.
Step-by-step explanation:
Graphed, the points go in a straight line, and you are able to draw a line through it. The equation for the line is y = 4x + 4.
What is the median?
2, 2, 1, 3, 5, 10, 2, 5
Answers
Answer:
The Miriam is 1,2,2,2,3,5,5,10
Step-by-step explanation:
Answer:
2.5
Step-by-step explanation:
arrange the numbers in assending order.
Please help me with this i need a real answer not tjose file things
Answers
Answer:
c
Step-by-step explanation:
4^2•2^-3 =
2
1/2
-128
Answers
2^-3 = 0.125
16 • 0.125 = 2
The answer is 2.
Sets A and I are defined as follows.
A={-5, -2,0,2,5}
I={-5, -1,1,5,8}
Find the union of A and I.
Answers
Answer:
AUI = { -5 , -2 , -1 , 0 , 1 , 2 , 5 , 8 }
If you shift the linear parent function, f(x) = x, down 6 units, what is the
equation of the new function?
Answers
Answer:
f(x) = x - 6
Step-by-step explanation:
The original function would go through (0,0) since you shift the function down 6 units, it will go through (0,-6)
so, the equation of the line would be f(x) = x - 6
Anyone know how to do this ?
Answers
Answer:
( 3 / 4) * λ = - 1 - - > λ = - ( 4 / 3)
y = - ( 4 / 3) * x + 6
Answer:
Y= -4/3 X + 6
Step-by-step explanation:
I've explained this answer in attachment.
The sum of 3 consecutive even numbers is 78.
What is the second number in this sequence?
Answers
Answer: 10
Step-by-step explanation: 8+10+60=78
Plz help this is due today AND NO LINKS OR GROSS PICTURES OR I REPORT.
Answers
Answer:
b- If two sides are perpendicular, then it is a right triangle. It can be isosceles or scalene. It cannot be equilateral because all the angles in an equilateral triangle are acute.
Step-by-step explanation:
An equilateral triangle has 3 equal sides and 3 congruent angles, each with an acute measure of 60 deg.
If two sides are perpendicular, they form a right angle, w/ measure of 90 deg. Therefore, cannot be equilateral.
30-60-90 triangles are quite common and useful in geometry... they are scalene and have 2 perpendicular sides.
45-45-90 triangles are isosceles and have 2 perpendicular sides.
Both are types of right triangles.
Question 1 of 10
Using the graph below, select all statements that are true.
.
+10
O A. (5.1) = 5
OB. This graph is one-to-one.
C. f(0.6) = 0
D. This is the graph of the greatest integer function,
E. (-3.2) = -3
SUBMIT
Answers
Answer:
the answer is going to be b
Box Plot for Problem #12
Answers
For a certain brand of tomato seeds, the seed package claims that it takes 87 days after planting for the tomato plants to produce fruit. Sarah, a botanist, wanted to know whether the mean number of days for the plants to produce fruit where she lives is different from 87 days. She planted 40 seeds and recorded the number of days for each plant to produce fruit. With all conditions for inference met, the hypothesis test was conducted at the significance level a = 0.05, and the test resulted in a p-value of 0.0752. ?
Which of the following is a correct conclusion?
A. Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is greater than 87 days.
B. Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
C. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is greater than 87 days.
D. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
E. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is equal to 87 days.
Answers
Answer:
D. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
Step-by-step explanation:
The population mean, μ is given as 87
This population value is used to state the Null hypothesis ;
H0 : μ = 87
The alternative hypothesis is the opposite of the Null ; and hence, claims that the mean is different from the population mean, μ ≠ 87
H1: μ ≠ 87
The Decison level :
When Pvalue < α ; We reject the Null otherwise we fail to reject the null
The given p and α value :
P-value = 0.0752
α = 0.05
0.075 > 0.05 ; Hence ;
Pvalue > α ; We fail to reject the Null
We can thus conclude that there is not enough evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
Find the Laplace Transform for 102
Answers
Answer:
d'f(t) = 6cos 2t(2)+5sin 2t(2)
= 12cos 2t + 10sin 2t
Step-by-step explanation:
perimeter and area of a rectangular figure has a perimeter of 34cm its length is 9cm
Answers
Answer:
Perimeter of rectangle = 32
Step-by-step explanation:
32 = 2(L+B)
L+B=16
B=16-L
B=16–9
B=7
AREA = L*B
AREA = 63sq.cm
1
3
16
Which expression is equivalent to 3/64a6b7c9?
O zabo (V4a?b°c)
4a²b2c (VD
Baºbc* (V50
Ba?b%cº (PD)
Answers
Answer:
Step-by-step explanation:
The equivalent expression is,
⇒ 4a²b²c³ ∛b
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ ∛64a⁶b⁷c⁹
Now, We can simplify the expression as;
⇒ ∛64a⁶b⁷c⁹
⇒ ∛64a⁶b⁷c⁹
⇒ ∛4³ (a²)³ (b²)³ (b) (c³)³
⇒ 4a²b²c³ ∛b
Thus, The equivalent expression is,
⇒ 4a²b²c³ ∛b
Learn more about the mathematical expression visit:
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PLEASE HURRY WILL MARK BRAINLEST
If the odds of being born on each day of
the week is equal, what is the probability
of two separate babies both being born
on a school day? (Monday through
Friday)
Answers
Answer:
1/25
Step-by-step explanation:
days in a week is 7
odds of being born on each 7 days is equal
x born = 7 days
pr(one separate baby) = 1 ÷ 5
pr(second separate baby) = 1 ÷ 5
pr(both being born on a school day) = 1/5 × 1/5
= 1/25
Which of the following points are solutions to the equation 3x - 4y - 8 = 12?
Select all that apply.
(0-5)
(82)
(-16-17)
(-1,-8)
(-40,-34)
Answers
Sorry I did it wrong.
Answer:
(0, -5) and (-16, -17)
Step-by-step explanation:
You can plug in the points into the function to test them.
(0, -5)
3(0) - 4(-5) - 8 = 12
20 - 8 = 12
12 = 12
(8, 2)
3(8) - 4(2) - 8 = 12
24 - 8 - 8 = 12
8 ≠ 12
(-16, -17)
3(-16) - 4(-17) - 8 = 12
-48 + 68 - 8 = 12
12 = 12
3(-1) - 4(-8) - 8 = 12
-3 + 32 - 8 = 12
21 ≠ 12
3(-40) - 4(-34) - 8 = 12
-120 + 136 - 8 = 12
8 ≠ 12
Evan is thinking of a number that contains the digit 2 The digit 2 in Evan's number has 10 times the value of the
digit 2 in the number 328,907.
Which number could be the number that Evan is thinking of?
127,905
145,298
290,837
352,987
Answers
Answer:
C, 290,837
Step-by-step explanation:
The 2 in his number is 10x the 2 in the number 328,907
This means you need to move the number to the left once, hence it being in the hundred thousands.
290,837 is the final answer.
(PLSSSS HELP, MY FATE IS IN YOUR HANDS) Determine which three out of the six points shown below are a solution to the equation x-3y=22 Plot the three points that are in the solution set, draw a line through the three points and then answer the questions below.
Answers
Answer:
The required points are -
(-2,8), (7,5), (1,7)
A certain television is advertised as a 90- inch Tv ( the diagonal length).
Answers
Answer:
The width is 64.3 inches
Step-by-step explanation:
Given
[tex]d = 90[/tex] --- diagonal
[tex]h = 63[/tex] --- height
Required
Determine the width (w) of the TV
To do this, we make use of Pythagoras theorem which is illustrated as:
[tex]d^2 = h^2 + w^2[/tex]
So, we have:
[tex]90^2 = 63^2 + w^2[/tex]
Evaluate all squares
[tex]8100 = 3969 + w^2[/tex]
Collect like terms
[tex]w^2 = 8100 - 3969[/tex]
[tex]w^2 = 4131[/tex]
Take positive square roots of both sides
[tex]w = \sqrt{4131[/tex]
[tex]w = 64.3[/tex] -- approximated