Answer:
[tex]f(8) = - 42[/tex]
Step-by-step explanation:
Hi there!
You have to substitute x = 8 into:
[tex]f(x) = 6(1 - x)[/tex]
It then becomes:
[tex]f(8) = 6(1 - 8)[/tex]
Calculate the above
[tex]f(8) = - 42[/tex]
I hope this helps
Solve each equation. Check your answers.
log 2 x=-1
log (2x) = -1 => x = 0.05, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: log (2x) = -1
Raising both sides to 10, in order to remove the logarithm:
=> [tex]10^{log_{10}(2x)} = 10^{-1}[/tex]
=> 2x = [tex]\frac{1}{10}[/tex] ( as [tex]a^{log_a(x)} = x[/tex])
=> x = [tex]\frac{1}{20} =[/tex] 0.05
Hence, log (2x) = -1 => x = 0.05, by properties of logarithm.
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Find the new given amount given the original amount and the percent of change
$7; 20% increase
The new amount is $ __
Answer:
8.4
Step-by-step explanation:
7 x .2 is the increase 1.4
Add 1.4 to 7 to get 8.4
A periodic function goes through 5 complete cycles in 4 min . What is the period of the function?
(A) (1/5) min (B) (1/4) min (C) 48 s (D) 75 s
The period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
A periodic function goes through 5 complete cycles in 4 min
From the question:
f = 5/4 cycles per minutes
f = 5/240 cycles per seconds [1 minutes = 60 seconds]
f = 1/48
Period = 1/f
Period = 48 minutes
Thus, the period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.
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The period of the given periodic function is 48 sec.
What is periodic function?
A periodic function is a function which returns same values at regular intervals. Let f be a periodic function then
f( x +P ) = f(x) , for every x in the domain of f and P is some non zero constant
P is the regular interval or period after which a periodic function returns same values.
P=[tex]\frac{1}{f}[/tex]
where [tex]f[/tex] is the frequency of the periodic function
or [tex]f[/tex] = no of cycles per unit time
Given that a periodic function goes through 5 cycles in 4 min
therefore frequency for this periodic function , f is given by
[tex]f=\frac{5}{4}[/tex] cycles per min
or
[tex]f=\frac{5}{4*60} \\f=\frac{5}{240} \\[/tex]
[tex]f=\frac{1}{48}[/tex] cycles per sec
Thus,
Period of the given periodic function , P =[tex]\frac{1}{f}=1/\frac{1}{48}=48[/tex] sec
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thunder from a bold of lightning travels 1/10 mile 1/2 second. At this rate how many miles can it travel
in one second
Thunder from a bolt of lightning can travel 1/5 miles in one second.
Given, distance = 1/10 mile and
time = 1/2 second .
we need to find distance travelled in one second.
The distance travelled by thunder bolt from lightning in one second can be calculated using unitary method. So, to calculate we will relate the known distance with given time. Further, we will compare it at with desired time.
So, distance travelled in 1/2 second = 1/10 mile
Hence, distance travelled in 1 second = 1/10 ₊ 1/10
Shifting 2 to the numerator and 10 to the denominator. The new fraction will be -
Distance travelled in 1 second = 2/10 = 1/5
Distance travelled in 1 second = 1/5 mile
Hence, thunder from a bolt of lightning can travel 1/5 miles in one second.
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someone help me with thisss
The equation of the line that is perpendicular to the given line and that passes through the given points is x + 3y = 6
From the question, we are to determine the equation of the described line.
First,
We will determine the slope of the line that the equation was given.
The equation of the line is
y = 3x - 9
Comparing the equation to the general form of the equation of a straight line
y = mx + b
Where m is the slope
and b is the y-intercept
Thus,
By comparison,
m = 3
That is, the slope of the given line is 3
NOTE: Two lines are perpendicular if the product of their slope is -1.
That is,
m₁ × m₂ = -1
3 × m₂ = -1
m₂ = -1/3
The slope of the line that is perpendicular to the given line is -1/3.
We have that the line passes through the point (3, 1).
Then,
Using the point-slope form of the equation of a line
y - y₁ = m(x - x₁)
m = -1/3
x₁ = 3
y₁ = 1
Then,
y - 1 = -1/3(x - 3)
Multiply through by 3
3(y -1) = -1(x - 3)
3y - 3 = -x + 3
3y + x = 3 + 3
x + 3y = 6
Hence, the equation of the line that is perpendicular to the given line and that passes through the given point is x + 3y = 6
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If C=24, what values of A and B complete Ax+By=C for each graph? Write the standard form for each equation.If C24, what values of A and B complete for each graph? Write the standard form for each equation.
The standard form for the equation of this line is equal to 3A - 4B = 12.
What is a linear equation?A linear equation can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
In Mathematics, the standard form of a linear equation is given by the following:
Ax + By = C.
When C = 24, the line passes through point (4, 0) and we have;
Ax + By = C.
4A + B(0) = 24.
4A = 24
A = 24/4
A = 6
When C = 24, the line passes through point (0, -3) and we have;
A(0) + B(-3) = 24
-3B = 24
B = -24/3
B = -8
Therefore, the standard form for the equation of this line is given by:
6A - 8B = 24
Dividing all through by 2, we have:
3A - 4B = 12
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Please help!!!! w+ 5w + 4 = 3 (2w - 1) Show your work!!!!
Answer:
No solution
Step-by-step explanation:
Given equation:
[tex]w+5w+4=3(2w-1)[/tex]
Distribute the parentheses:
[tex]\implies w+5w+4=3 \cdot 2w- 3 \cdot 1[/tex]
[tex]\implies w+5w+4=6w- 3[/tex]
Combine like terms:
[tex]\implies 6w+4=6w-3[/tex]
Add 3 to both sides:
[tex]\implies 6w+4+3=6w-3+3[/tex]
[tex]\implies 6w+7=6w[/tex]
Subtract 6w from both sides:
[tex]\implies 6w+7-6w=6w-6w[/tex]
[tex]\implies 7=0[/tex]
As 7 ≠ 0 there is no solution.
Paula walked on the treadmill for 11 minutes. The machine told her she had a total of 759 strides. What was her rate in strides per minute?
A.
69 strides per minute
B.
70 strides per minute
C.
67 strides per minute
D.
68 strides per minute
Answer:
A. 69 strides per minute
Step-by-step explanation:
In order to find the strides per minute divide 759 by 11
➟ 759/11
➟ 69
∴ Her rate was 69 strides per minute
btw Zarahs office is 2cm wide and 4 cm long
The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office
Given data
Zarah's office is 2 cm wide and 4 cm long
Another office is 8 cm long and 4 cm wide
How to solve for the size of the officesArea of an office = length * width = long * wide
Area of Zarah's office = 4 cm * 2 cm = 8 cm2
Area of another office = 8 cm * 4 cm = 32 cm2
comparing the two areas
say by how much is 32 cm2 greater than 8 cm2
32 cm2 / 8 cm2 = 4
The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office.
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Maddie is buying flour to make cookies for a bake sale. At the store a 3 pound bag costs $3.69. She needs 25 pounds of flour to make enough cookies for a bake sale. How much will it cost for the flour?
Cost of 25 pound flour is $30.75.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Price of 3 pound flour = $3.69
She needs 25 pounds of flour to make enough cookies for a bake sale.
Now, Price of 3 pound flour = $3.69
Hence, Cost of 1 pound flour = $3.69 ÷ 3 = $1.23
So, Cost of 25 pound flour = 25 x $1.23
= $30.75
Therefore, Cost of 25 pound flour is $30.75.
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At a sale, dresses were sold for $56 each. If the dresses originally cost $200 each, what percentage of its original price was a dress sold for?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The percentage at which the dress was sold from its original price is 28%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The selling price of the dress = $56
The original price of the dress = $200
The percentage at which the dress was sold from its original price.
= 56/200 x 100
= 56/2
= 28 %
Thus,
The percentage at which the dress was sold from its original price is 28%.
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X² - x -12 ÷ x-4
3x-9. 12
The result of division of (x² - x - 12) by (x - 4) is (x + 3).
What is termed as factorization?The breaking or dissolution of an entity (for example, a number, a matrix, or even a polynomial) into such a product of some other entity, or factors, that when multiplied together give the previous figure or matrix, etc.It is simply dividing an integer or linear function into factors that, when multiplied together, result in the original or initial integer or polynomial. We use the factorisation method to simplify any algebraic as well as quadratic equation by representing it as the product of factors rather than expanding the brackets.The given equation is;
(x² - x - 12) / (x - 4)
where, (x² - x - 12) is the numerator and (x - 4) is the denominator.
Find the factors of the numerator.
= (x - 4)(x + 3)/(x - 4)
Cancel the values (x - 4) from the numerator an denominator part.
= (x + 3)
Thus, the solution of the factorization is found as (x + 3).
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If a recipe serve six people and requires one 1/2 cups of flour, how much flour do you need if you are serving 15 people? Write your answer as a decimal rounded to the nearest hundredth.
Answer:
Step-by-step explanation:
1 1/2 cups = 1.05
Use a table to solve each equation. Round to the nearest hundredth.
6²x=10
[tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: [tex]6^{2x} = 10[/tex]
Taking logarithm on both sides:
=> log ([tex]6^{2x}[/tex]) = log 10
=> 2x (log 6) = log 10 ( as [tex]log_b(a)^m = m (log_b(a))[/tex])
=> 2x = [tex]\frac{log10}{log6}[/tex]
=> 2x = [tex]\frac{1}{0.778}[/tex]
=> 2x = 1.285
=> x = 0.642
Hence, [tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.
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Which of the following could represent the cost of 5 t-shirts and a $7 tax?
Answer:
y = 5x + 7
Step-by-step explanation:
I am guessing, but you are leaving something out.
y = the total cost.
x = the number of shirts.
Answer:
The total cost for the 7 shirts including tax is 7n + 6
Step-by-step explanation:
We want to find the Cost of 7 t-shirts and $6 tax.
Now, the let the cost of the 7 shirts be n. Thus, we can now say that cost of 7 shirts is 7n.
Now, since there is an additional cost of $6 for tax, we can now say that the total cost for the 7 shirts including tax is expressed as;
7n + 6
Thus, we conclude that the total cost for the 7 shirts including tax is 7n + 6
The sum of two numbers is 37. One of the numbers is 15 more than the other number. What are the two numbers?
Answer: 11 and 26
Step-by-step explanation:
(help quick please) Solve
Can someone please describe the domain and range in these sets?
Answer:
a.
D=[-6,4)
R=(-3,4]
b.
D=[-6,7)
R=[-1,6)
Step-by-step explanation:
[,] <-- used for when the point is included in the answer (closed circle or greater than/less than or equal to sign)
(,) <-- used for when the answer does not include point (open circle or greater than/less than sign not equal to)
Plug in the points where shown on each line.
Hey again! Just answered your last domain and range question so I hope I helped again!
What is the difference between −125 and 18?
Identify each function or situation as an example of exponential growth or decay. What is the y -intercept?
b. y=11(0.75x)
The given function is exponential growth and the y-intercept is y=11.
Given that the given function is y=11(0.75)ˣ.
Exponential growth or decay describes the process of reducing or growing an amount by a consistent percentage rate over a period of time and it is represented by the function y=a(1-b)ˣ where, y is the final amount, a is the original amount and b is the growth or decay factor and x is the amount of time passed.
If a is positive and b is greater than 1 then it is exponential growth.
If a is positive and b is less than 1 but greater than 0 then it exponential decay.
The graph of the given function y=11(0.75)ˣ is shown in attached image.
From the graph, it is visible that the given function is an exponential growth because a is 11 and it is positive and it is greater than 1.
Now, we will find the y-intercept by substituting x=0, we get
y=11(0.75)⁰
y=11(1)
y=1
Hence, the given function or situation y=11(0.75)ˣ as an example of exponential growth and the y-intercept is 11.
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Simplify each expression.
3¹/₄+27¹/₄
The expression has to be written in it's prime factor form. 27 = 3x3x3 = 3^3 in index form. 3=3^1 . By power rule (a^m)^n = a^mn.
(3^1)^1/4+(3^3)^1/4
3^1/4 + (3^2x3^1)^1/4
3^1/4+3^2/4x3^1/4
3^1/4(1+3^1/2)
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Under her cell phone plan, Jaya pays a flat cost of $60.50 per month and $5 per gigabyte. She wants to keep her bill under $75 per month. Which inequality can be used to determine xx, the maximum number of gigabytes Jaya can use while staying within her budget?
The inequality used to determine Jaya's maximum number of Gigabytes available for use, within her budget is 60.50 + 5x ≤ 75.
What is inequality?
The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
Jaya pays a flat cost of $60.50 per month and $5 per gigabyte and keep her bill under $75 per month.
According to given question we have
Let the cost of gigabyte be x
flat cost =$60.50 per month
Budget= $75 per month
i.e
60.50 + 5x ≤ 75
Therefore, the inequality used to determine Jaya's maximum number of Gigabytes available for use, within her budget is 60.50 + 5x ≤ 75.
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I keep getting the answer of 28.89° but that’s wrong and I don’t know how to get to the right answer.
Answer:
for (a) i got 15
Step-by-step explanation:
AE=17, AB=16 which makes AM=8
so from there u do pythagorean theorem
17^2 - 8^2 = 225
√255= 15
Answer:
26.565⁰
Step-by-step explanation:
Triangles AEM and BEM are congruent since
AE = BE
m∠AME = m∠BME=90°
and EM is the common side
So AM = BM = AB/2 = 16/2 = 8
Triangle EAM is a right triangle with hypotenuse AE = 17 and AM = 8
So EM² = (17² - 8²) by the Pythagorean theorem
EM² = 289 - 64 = 225
EM = √225 = 15 cm
To find m∠ECM, note that triangle ECM is a right triangle with m∠EMC = 90° and the side opposite ∠EMC = EC, the side opposite ∠ECM is EM
By the law of sines
EC/sin90 = EM/sin(∠ECM)
So,
sin(∠ECM) = EM/EC since sin 90 = 1
So we have to compute EC
Again note that the triangle MCB with sides BM, MC and BC is a right triangle with m∠CBM = 90°
The hypotenuse is MC
So MC ² = MB² + BC² = 15² + 30² = 1125
MC = √1125 = 33.54 cm
Therefore
sin(∠ECM) = EM/MC = 15/33.54 = 0.4472
m∠ECM = sin⁻¹ (0.4472)
= 26.565⁰
To be honest I am not 100% sure of this answer, please check and see if this works. Thanks
A survey of 62 customers was taken at a bookstore regarding the types of books purchased. The survey found that 38 customers
purchased mysteries, 31 purchased science fiction, 21 purchased romance novels, 18 purchased mysteries and science fiction, 12
purchased mysteries and romance novels, 9 purchased science fiction and romance novels, and 5 purchased all three types of
books.
a) How many of the customers surveyed purchased only science fiction?
b) How many purchased mysteries and science fiction, but not romance novels?
c) How many purchased mysteries or science fiction?
d) How many purchased mysteries or science fiction, but not romance novels?
e) How many purchased exactly two types of books?
a) There were customers who purchased only science fiction.
(Simplify your answer.)
For given survey of 62 customers was taken at a bookstore regarding the types of books purchased,
a) The number of customers surveyed who purchased only science fiction = 9
b) The number of customers surveyed who purchased mysteries and science fiction, but not romance novels = 13
c) The number of customers surveyed who purchased mysteries or science fiction = 51
d) The number of customers surveyed who purchased mysteries or science fiction, but not romance novels = 46
e) The number of customers surveyed who purchased exactly two types of books = 2
In this question,
we have been given a survey of 62 customers was taken at a bookstore regarding the types of books purchased.
38 customers purchased mysteries,
31 purchased science fiction,
21 purchased romance novels,
18 purchased mysteries and science fiction,
12 purchased mysteries and romance novels,
9 purchased science fiction and romance novels,
and 5 purchased all three types of books.
Let S represents the set of customers who purchased science fiction books,
R represents the set of customers who purchased romance novels books and
M represents the set of customers who purchased mysteries books.
From given information,
n(S) = 31
n(R) = 21
n(M) = 38
n(M ∩ S) = 18
n(M ∩ R) = 12
n(S ∩ R) = 9
n(M ∩ R ∩ S) = 5
a) we need to find the number of customers surveyed who purchased only science fiction.
= n(S) - n(M ∩ S) - n(S ∩ R) - n(M ∩ R ∩ S)
= 31 - (18 - 5) - (9 - 5) - 5
= 31 - 13 - 4 - 5
= 9
b) we need to find the number of customers surveyed who purchased mysteries and science fiction, but not romance novels
= n(M ∩ S) - n(M ∩ R ∩ S)
= 18 - 5
= 13
c) we need to find the number of customers surveyed who purchased mysteries or science fiction
n(M ∪ S) = n(M) + n(S) - n(M ∩ S)
= 38 + 31 - 18
= 51
d) we need to find the number of customers surveyed who purchased mysteries or science fiction, but not romance novels
= n(M ∪ S) - n(M ∩ R ∩ S)
= 51 - 5
= 46
e) we need to find the number of customers surveyed who purchased exactly two types of books
= n(M ∩ S) - n(S ∩ R) - n(M ∩ R)
= (18 - 5) - (9 - 5) - (12 - 5)
= 13 - 4 - 7
= 2
Therefore, for given survey of 62 customers was taken at a bookstore regarding the types of books purchased,
a) The number of customers surveyed who purchased only science fiction = 9
b) The number of customers surveyed who purchased mysteries and science fiction, but not romance novels = 13
c) The number of customers surveyed who purchased mysteries or science fiction = 51
d) The number of customers surveyed who purchased mysteries or science fiction, but not romance novels = 46
e) The number of customers surveyed who purchased exactly two types of books = 2
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If point A is located at (5,-7), and there are 8 points between A and B , what could be the possible coordinates for points B ?
Possible coordinates for points B (-3, 13)
Given that
point A (5 , -7)
and there are 8 points between A and B.
The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.
The equation of a circle centerd in the point (x0, y0) is:
(x - x0)² + (y - y0)² = r²
where r = radius of the circle
So we can draw a circle of 8 units around A, and get:
(X - 5)² + (Y - (-7))² = 8²
So from this equation we can find all the possible values of B.
Y = √(8² - (X- 5)²) - 7
So for a given value of X, you can find the value of Y. where (8² - (X-5)²) can not be a negative number, so
8² ≥ (X - 5)²
So X = -3 (because (-3 - 5)² = 8²)
to X = 13 (because (13 - 5)² = 8²)
So X is in the range (-3, 13)
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HALP I NEED HALP AND I DONT GOT A LOT POINTS LEFT PLS I NEED THIS.
Its just vector sums pls help
3x{12-[2x(12-3-2x3)]+4
Answer:
30
Step-by-step explanation:
Quadratic Formula
Simplify
6-√√25
4
DONE
11
Answer:
1/4, alternate forms are .25 and 2^-2
Step-by-step explanation:
Square Root of 25 is 5
6-5 =1
1/4
36x² - 65x + 25 = 0
Work out the value of x.
Let’s solve this step-by-step
First factor the equation,
(9x - 5) (4x - 5) = 0
Then set each factor equal to zero,
9x - 5 = 0 and 4x - 5 = 0
Both x = 5 / 9 or x = 5 / 4 are correct
What’s APY? can someone please simplify the definition.
APR, or effective annual rate, can also be called an effective annual rate or EAR when "r" is the annual interest rate and "n" is the number of compounding periods to be completed each year. :D