The value of f(8) is 3.
What is logarithm?
The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b. For instance, since 1000 = 103, log10 of 1000 is 3, or [tex]log_1_0=3[/tex].
Let, [tex]f(x) = log_2(x)[/tex]
We have to find the value of f(8).
Plug x = 8 in the above equation.
[tex]f(8) =log_2(8)[/tex]
Here 8 = 2 x 2 x 2 = 2^3
So, replace 8 with 2^3 in the above equation.
[tex]f(8) = log_2(2^3)[/tex]
Using the log rule: [tex]log_a(a^b) = b[/tex]
Here a = 2, b = 3
So, [tex]log_2(2^3) = 3[/tex]
Hence, f(8) = 3.
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Which system of equations is represented by the graph ?
A. y=x^2+2x+1
2x+y=2
B. y=x^2-2x+1
2x+y=2
C. y=x^2+2x+1
2x+y=2
D. y=x^2-2x+1
2x-y=2
option D, y=x^2-2x+1 , 2x-y=2 represents system of equations .
Given:
points (1,0) and (3,4)
line equation is y - y1 = m(x-x1)
y - 0 = 4-0/3-1(x - 1)
y = 2(x-1)
y = 2x - 2
2x - y =2.
The vertex of the given upward parabola is in the first quadrant so the coefficient of [tex]x^{2}[/tex] must have positive values.
so y = [tex]x^{2} -2x+1[/tex]
Therefore option D y=x^2-2x+1 , 2x-y=2 is correct.
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PLEASE HELP QUICK (no links pls)
The total length of the sari Divya make is 6 yards, so option A is correct.
What is rectangle?Four sides, four corners, and four right angles (90°) make up the enclosed 2-D shape known as a rectangle. A rectangle has opposite sides that are parallel and equal. A rectangle has length and width because it is a two-dimensional form. The length of a rectangle is its longer side; its breadth is its shorter side.
Given:
The length of saris Divya can make = 6 yards,
As the graph is showing, to make a sari Divya required 6 yards of fabric,
Therefore, the total length of the sari Divya make is 6 yards.
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a school is organizing a weekend trip to a nature preserve. for each student, there is a $60 charge, which covers food and lodging. there is also a $40 charge per student for the bus. the school must also pay a $30 cleaning fee for the bus. if the total cost of the weekend is $4,030, how many students will be going on the trip?
Using the concept of linear equation in one variable, it is concluded that the total number of students who will go on the trip are 40.
What is a linear equation in one variable?An equation that contains only one variable and has its degree one is called a linear equation in one variable. The general form of linear equation in one variable is ax + b = 0, where a and b are real numbers and a ≠ 0.
Given that food and lodging charge per student = $ 60
Charge per student for bus = $ 40
And the amount paid for the cleaning fee for the bus = $ 30
Let the total number of students who are going on the trip = x
Now, the Total charge for food and lodging = $60x
The total charge for bus fare = $ 40x
Given that total cost paid = $ 4030
Hence, $60x + $40x + $30 = $4030
$100X = $4030 - $30
$100X = $4000
x = 40
Hence, the total number of students who will go on a trip is 40.
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Simplify these pls I’ll brainlist.
1) 3b (b+4) - 4 (b-5)
2) 12(3y + 6)
Final answer: 3[tex]b^{2}[/tex] + 8b + 2
12(3y + 6) = 12 x 3(y + 2) // Factor out 12 = 36(y + 2) // Simplify the multiplication Final answer: 36(y + 2)
What is equation?An equation is a statement that two mathematical expressions are equal. It consists of two expressions separated by an equal sign (=), where one expression is on the left side and the other expression is on the right side of the equal sign. An equation represents a balance or equivalence between the two expressions, and it can be solved for the unknown variable(s) by applying mathematical operations to both sides of the equation.
Given by the question.
3b (b+4) - 4 (b-5)
= 3[tex]b^{2}[/tex] + 12b - 4b + 20 // Distribute the terms.
= 3[tex]b^{2}[/tex] + 8b + 20 // Simplify the like terms.
Final answer: 3[tex]b^{2}[/tex]+ 8b + 20
12(3y + 6)
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line that passes through the point (8,−3) and has a slope of 1/4
The equation of line having a slope of 1/4 which passes through point (8,-3) is y = (1/4)x - 5.
What is the equation of line with the given point and slope?The equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (8, -3 )
x = 8y = -3Slope m = 1/4Determine the y-intercept 'b'.
Substitute the point and slope into the equation of line formula and solve for b.
y = mx + b
-3 = (1/4)(8) + b
-3 = 8/4 + b
-3 = 2 + b
b = -3 - 2
b = -5
Now, substitute slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = (1/4)x + (-5)
y = (1/4)x - 5
Therefore, the equation of the line is y = (1/4)x - 5.
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Ibram got a job selling bags of peanuts at the local fairground. He is paid a fixed amount of $340 per week plus $0.84 per item sold. This is represented by the equation P = 0.84 + 340 where P is the amount he is paid for the week and n is the number of bags of peanuts he sold. How much will Ibram be paid if he sells 380 bags of peanuts? If Ibram sells 380 bags of peanuts, he will earn S How many bags of peanuts did Ibram sell if he earned $1,087.60? for the week. If Ibram has earned $1,087.60, he sold bags of peanuts.
Answer:
Assuming the bags sold were for 1 week period.
1. $659.20 for 1 week and 380 bags of peanuts
2. 890 bags
Step-by-step explanation:
The equation is missing the variable, n (the number of bags sold). I'll take the liberty to add it after the $0.84/bag term, where it belongs:
P = 0.84n + 340
The 340 is $340/week. n must be in units of "bags/week."
1. How much will Ibram be paid if he sells 380 bags of peanuts?
P = $0.84n + $340
n = 380 bags (we will assume in 1 week).
P = $0.84n + $340
P = $0.84(380) + $340
P = $659.20
2. How many bags of peanuts did Ibram sell if he earned $1,087.60?
P = $0.84n + $340
P = $1087.60
$1087.60 = $0.84n + $340
$1087.60 - $340 = $0.84n
$0.84n = $1087.60 - $340
$0.84n = $747.60
n = 890 bags ( ! - I'm impressed)
Write the equation for the following relation. P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}
The equation of the relation x and y is y = 4x - 4
How to represent linear equation?The relation follows a linear pattern. Therefore, the relationship is linear.
A linear relationship can be represented in different form such as slope intercept form and point slope form.
Let's represent the equation in slope intercept form.
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = 4 - 0 / 2 - 1
m = 4 / 1
m = 4
Therefore, let's find the y-intercept using (1, 0)
y = 4x + b
0 = 4(1) + b
b = -4
Therefore, the equation is y = 4x - 4
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What type of angles are labeled and what is the value of m? Show your work.
Answer:
see explanation
Step-by-step explanation:
m + 20 and 100 are vertically opposite angles and are congruent , then
m + 20 = 100 ( subtract 20 from both sides )
m = 80
The angles are vertically opposite angles and value of m is 80°
What is vertically opposite angles?Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Given two angles which are Vertically opposite to each others,
We know Vertically opposite angles are equal to each other, so,
m + 20° = 100°
m = 100° - 20°
m = 80°
Hence, the value of m is 80°
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Select all equations that are equivalent to
(6x + 2)
3
-=2(3x +14)
(Select all that apply.)
(6x + 2)
3
(6x + 2) = 2 (3x+14)
2x+3=2-(3x +14)
=-3x-12
6x + 2 = -9x-36
(6x + 2)
3
= -3x+16
Using simplification, the equations that are equivalent to [tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex] are [tex]\frac{(6x+2)}{3 } = -3x-12[/tex] and 6x + 2 = -9x - 36
What are equivalent equation?Two systems of equations are equivalent if they have the same solution(s)
In a simpler term, two equations are equivalent if they have the same solution.
Therefore, let's simplify the equation to find the equivalent solutions.
[tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex]
let's open the brackets of the right side of the equation.
[tex]\frac{(6x+2)}{3}=2-(3x+14)[/tex]
[tex]\frac{(6x+2)}{3} = 2-3x-14[/tex]
[tex]\frac{(6x+2)}{3 } = -3x-12[/tex]
Therefore, let's cross multiply
6x + 2 = 3(-3x - 12)
6x + 2 = -9x - 36
Therefore, the equivalent equation are as follows:
[tex]\frac{(6x+2)}{3 } = -3x-12[/tex]6x + 2 = -9x - 36learn more on equivalent equation here: https://brainly.com/question/10522819
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Calculate the distance around a triangle whose sides are :
The distance around the triangle is equivalent to 13x/12.
What is triangle?
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given are the sides of triangle as x/2, x/3, x/4
The distance around the triangle is equivalent to perimeter of triangle. We can write perimeter as -
P = x/2 + x/3 + x/4
P = (6x + 4x + 3x)/12
P = 13x/12
Therefore, the distance around the triangle is equivalent to 13x/12.
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Help me on this math problem pls
The quadratic inequality that will represent the parabola will be
y ≤ 2[tex]x^{2}[/tex] - 8x + 3
The given graph is a parabola where the mouth is open upwards. So from here we can clearly say that the coefficient of [tex]x^{2}[/tex] will be positive.
The vertex of the parabola is given as (2 , -5) in the graph.
So let us put value of x in the inequations given to us.
first option is
y ≤ 2[tex]x^{2}[/tex] - 8x + 3
y ≤ 2*[tex]2^{2}[/tex] - 8*2 + 3
y ≤ 8 - 16 + 3
y ≤ -5
Therefore the quadratic inequality that will represent the parabola will be
y ≤ 2[tex]x^{2}[/tex] - 8x + 3
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6. Find the distance between each pair of points. Then order each line segment from longest to shortest.
a. A(−6, 1), B(−1, 6)
c. E(2,7), F(4, -2)
e. J(−4, −2), K(1, −5)
b
C(-5, 8), D(5,8)
d. G(7,3), H(7,−1)
f. L(3, -8), M(7, −5)
Using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.
What is the distance Formula?The formula for the distance(d) , between two points whose coordinates are (x₁ ,y₁) and (x₂, y₂) is:Distance Formula: d = √[(x₂ - x₁)² - (y₂ - y₁)²]
Now, calculate the distance using the distance formula as follows:
(A) The distance between A and B is:
d = √(-1-(-6))²+(1-6)²)d = √5² + 5²d = √50(B) The distance between C and D is:
d = √[(5 -(-5))²+ (8-(8))²]d = √10² + 0d = 10(C) The distance between E and F is:
d = √[(4-2)²+ ((-2)-7)²]d = √2² + 9²d = √85(D) The distance between G and H is 2.
(E) The distance between J and K is:
d = √ [(1-(-4))² + (-5-(-2))²]d = √5² + 3²d = √34(F) The distance between L and M is:
d = √[(7-3)²= (-5-(-8))²]d = √4² + 3²d = 5Hence, the distance using the distance formula is:
(A) The distance between A and B is √50.(B) The distance between C and D is 10.(C) The distance between E and F is √85.(D) The distance between G and H is 2.(E) The distance between J and K is √34.(F) The distance between L and M is 5.Therefore, using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.
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if the population were not approximately normal, would the confidence interval constructed in part (a) be valid?
No, to construct a confidence interval, the population should be is approximately normal.
The information about distribution of population is important in order to find out the sampling distribution. When we want to construct confidence interval, the accuracy of results depend on three conditions.
1. The data needs to be randomly selected.
2. The sampling distribution needs to be normally distributed
3. The observations must be independent.
So one of the conditions is to ensure that the population is normally distributed.
We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10
np ≥ 10
n(1 - p) ≥ 10
When the population follows normal distribution then a small number of samples will be adequate, on the other hand, if the population is skewed then we need a greater sample size to ensure normal sampling distribution.
Therefore, the population is approximately normal before constructing a confidence interval.
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Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he
has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.
a. What will the new principal be when he begins making loan payments?
b. How much interest will he pay over the life of the loan?
a) The new principal (principal + capitalized interest) when Rich begins making loan payments will be $9,425.10.
b) The total interest that Rich will pay over the life of the loan is $4,914.20.
How is interest on student loans determined?The interest on student loans is based on simple interest.
The only interest capitalized is the interest during the non-payment period if the student does not pay the interest.
Some students elect to pay the interest during the non-payment period to reduce the capitalized interest and principal during the payment period.
Capitalization refers to the addition of interest to the principal amount.
Period of student loan = 10 years
The amount of the federal unsubsidized student loan = $7,900
Interest rate = 4.29%
Capitalized interest during the non-payment time = $1,525.10 ($7,900 x 4.29% x 4.5)
New principal when Rich begins making loan payments = $9,425.10 ($7,900 + $1,525.10)
Total interest for loan = $4,914.20 ($7,900 x 4.29% x 14.5)
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PLEASE ANSWER
What are the coordinates of the point that is one half the distance between A(−1, −2) and B(6, 12)?
( , )
please help!!!!! math functions
Answer:
A and C
Step-by-step explanation:
For every x value, there should be at most 1 y value.
B and D violate that constraint.
AWNSER PLSS !How can a negative number be written in scientific notation?
Use remainder theorem for x^3+8x^2+11x-20 by (x+4)
Answer:
x^3 + 64 + 11x - 20bxy - 80by
(if I am wrong, apologies)
Answer:
x^2+4x-5
Step-by-step explanation:
x^3+8x^2+11x-20/x+4=x^2+4x-5
Given the relation {(3,4),(-2,1),(0,6),
(5,-3)), what is the domain of the
relation?
Answer:
Domain: {-2, 0, 3, 5}
Step-by-step explanation:
The domain is the list of possible inputs
Evaluate the expression and enter your answer in the box below.
|34|
Answer:
34
Step-by-step explanation:
Absolute value means the distance from 0. So the absolute value of 34 is just 34.
Which angles are congruent to <5
Answer:
1, 3, 7 (<5 is also congruent to <5, but this is not a choice.)
Step-by-step explanation:
The angles congruent to <5 are:
<1 by corresponding angles.
<3 by alternate interior angles.
<7 by vertical angles.
<5 by the theorem: congruence of angles is reflexive.
simplify each expression x = 2x + 48
(please its for today
Write a letter to your friend wishing him success
Answer:
Hello _____,
You are a pig, a fatty, a dunce, and a monkey. Also, you smell like a diseased pustule on the butt of a wildebeest.
Cordially,
_____
Step-by-step explanation:
Solve the following equation for y. 3y - 7(y + 5) = y - 35 Also Show your work Describe and show each step taken.
A. y = 0
B. y = 1
C. y = 2
D. All real values for y are correct solutions.
Answer:
a) y = 0
Step-by-step explanation:
Given equation,
→ 3y - 7(y + 5) = y - 35
Now the value of y will be,
→ 3y - 7(y + 5) = y - 35
→ 3y - 7y - 35 = y - 35
→ -4y - y = -35 + 35
→ -5y = 0
→ y = 0/-5
→ [ y = 0 ]
Hence, the value of y is 0.
NEED HELP PLEASE AS FAST AS YOU CAN
Answer:
3.87
Step-by-step explanation:
b =
[tex] \sqrt{8 ^{2} -7 ^{2}} [/tex]
-13-7=
+
?
Write as addition.
Answer:
As addition: -13+(-7)=-20
A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The
function f(x)=100/x-5 represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function f(x)=1/x
transformed to create the graph of the function f(x)=100/x-5?
Answer:
The parent graph has been dilated by a scale factor of 100 and has been moved to the right by 5 units
Step-by-step explanation:
The change made to f(x) = 1/x to f(x) = 100/x is a dilation by a scale factor of 100(the function has been multiplied by 100) .
The transformation of function f(x) = 100/x to f(x) = 100/x-5 is moving o the right 5 units (whenever a constant, let's call it "c", is being subtracted from the x when graphing, it means the graph has moved "c" units to the right, and vice versa--if "c" was added to x, then the graph would be moved "c" units to the left.).
TL;DR: f(x-c) means c units to the right, f(x+c) means c units to the left. f(x)*c means a dilation of c units.
Figure E is dilated from point D, the center of dilation
The figure that is a dilation of figure E is the figure F
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the dilated figure?The graph represents the given parameter
From the figure, we have the original shape to be figure E
The center point of figure E is the origin
This means that a line drawn from the origin that passes through point E must pass through the same point on the shape
From the figure, the line passes through the same point on figure E and F
Hence, figure F is a dilation of figure
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the width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm. (a) what is the probability that a randomly chosen bolt has a width between 942 and 959 mm? (round your answer to four decimal places.) (b)
The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.
Define probability.The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.
Given,
The width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm.
Z = X - 951/10 ≈ N(0.1)
P(942 ≤ X ≤ 959)
P(942 - 951/10 ≤ X - 951/10 ≤ 959- 951/10)
P( -0.9 ≤ Z ≤ 0.8)
P(Z ≤ 0.8) - P(Z ≤ -0.9)
∅(0.8) - (1 - ∅(0.9))
∅(0.8) + ∅(0.9) - 1
0.788 + 0.859 - 1
0.647
The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.
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Mr. fitzpatrick is taking his math class to see a pearl jam concert because they have worked so hard this week in class. he purchases 22 tickets for a total of $265. tickets cost $10 for students and $15 for adults. some students must pay adult prices because they are over 18 years of age. what are the number of student tickets purchased and the number of adult tickets purchased
Mr. Fitzpatrick bought 9 adult tickets and 13 children's tickets.
It is given that Mr. Fitzpatrick bought 22 tickets
The tickets collectively cost him $265
The student tickets cost $10 while adult tickets cost $15
Let the no. of adult tickets sold be x
Let the no. of children's tickets sold be y
Therefore we get the equations
x + y = 22 [1]
15x + 10y = 265 [2]
or, 5x + 10x + 10y = 265
or, 5x + 10(x + y) = 265
from equation [1] we get
5x + 220 = 265
or, 5x = 265 - 220
or, 5x = 45
or, x = 9
Therefore,
y = 22 - 9
= 13
Therefore he bought 9 adult tickets and 13 children tickets.
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