The linear function f(x) passes through the points (1,2) and (3,0).
A few values from the exponential function g(x) are shown in the table
What is the positive difference in the y-intercept of f(x) and g(x)?)
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Related Questions
Find the x-intercept of the tangent line to the graph of f at the point P(0,f(0)) when f(x)= e^-x(5cosx+2sinx)
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f ` ( x ) = - e^(-x) * ( 5 cos x + 2 sin x ) + e^(-x) * ( - 5 sin x + 2 cos x ) =
( using the chain rule )
= e^(-x) * ( - 5 cos x - 2 sin x - 5 sin x + 2 cos x ) =
= e^(-x) * ( - 3 cos x - 7 sin x )
f ` ( x ) = 1 * ( - 3 - 0 ) = - 3
The equation of the tangent line:
y - f ( 0 ) = f ` ( 0 ) * ( x - 0 )
y - 5 = - 3 x
y = - 3 x + 5
The x - intercept of the tangent line:
0 = - 3 x + 5
3 x = 5
x = 5 / 3
or ( 5/3, 0 )
X^2-5=-4x^2 3x in standard form
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this is the answer i guess if -4X^2 times 3X
Convert to proper fraction or mixed number (do not reduce to lowest terms)
5.27 ...?
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5.27 can be converted to a mixed number 5 27/100, where 5 is the whole number and 27/100 is the decimal part expressed as a fraction, without reducing to lowest terms.
Explanation:To convert the decimal number 5.27 to a proper fraction or a mixed number, we first recognize that .27 is the decimal part of 5.27. We can write .27 as a fraction by considering it as 27 hundredths, which is 27/100. Therefore, we have the whole number 5 and the fraction 27/100. Combining these, we get the mixed number 5 27/100. Since we are instructed not to reduce to lowest terms, the mixed number remains as is.
Paul has 2/3 as many postcards as shawn . the number of postcards shawn has is 3/5 of the number of postcards tim has. if the three boys have 280 postcards altogether,how many more postcards does tim have than paul ?
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s = ( 3 / 5 )t ;
p + s + t = 280 ;
Then, p =( 2 / 3 )( 3 / 5 )t ;
p = ( 2 / 5 )t;
We solve the equation : ( 2 / 5 )t + ( 3 / 5 )t + t = 280 ;
( 2 / 5 )t + ( 3 / 5 )t + ( 5 / 5 )t = ( 1400 / 5 )t;
10t = 1400 ;
t = 1400 ÷ 10 ;
t = 140 postcards has Tim;
p = ( 2 / 5 ) × 140 = 56 postcards has Paul;
s = ( 3 / 5 ) × 140 = 84 postcards has Shawn ;
What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x minus 2
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Answer: The simplified form will be
[tex]\frac{1}{(x+3)(x+4)}[/tex]
Step-by-step explanation:
Since we have given that
[tex]\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}[/tex]
We need to simplify the above expression, we get that
[tex]\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}\\\\=\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}\\[/tex]
Now, we first factorize the quadratic equation:
[tex]x^2+x-6\\\\=x^2+3x-2x-6\\\\=x(x+3)-2(x-3)\\\\=(x+3)(x-2)[/tex]
Similarly,
[tex]x^2+5x+4\\\\=x^2+4x+x+4\\\\=x(x+4)+1(x+4)\\\\=(x+4)(x+1)[/tex]
So, it will become
[tex]\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}\\\\=\frac{x+1}{(x+3)(x-2)}\times \frac{x-2}{(x+4)(x+1)}\\\\=\frac{1}{(x+3)(x+4)}[/tex]
Hence, the simplified form will be
[tex]\frac{1}{(x+3)(x+4)}[/tex]
The wheeler's bill at a restaurant is $63.00 how much money should mr. wheeler leaves as a tip if he plans to tip 15%?
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63/100x15=9.45
when you want to figure out a tip, you take your total bill and multiply it by the percentage you would like to tip them and put a decimal in front of the percentage. So the problem would look like 63x .15 =9.45
answer that for me please i am very confused
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Use the linear approximation (1+x)^kapprox 1+kx to find an approximation for the function f(x) for values of x near zero.
a.) f(x)=(1-x)^(8) approx
b.) f(x)=-8/(1-x) = approx
c.) f(x)= 1/(sqrt(1+x)) = approx
d.) f(x)=sqrt(4+x^2) approx =
e.) f(x)=(6+3x)^(1/3) approx =
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To approximate functions near zero using the linear approximation (1+x)^k ≈ 1 + kx, we find an approximation for each given function.
Explanation:To approximate the function f(x) for values of x near zero using the linear approximation (1+x)^k ≈ 1 + kx, we need to find an approximation for each given function:
a.) f(x) = (1-x)^8 ≈ 1 - 8x
b.) f(x) = -8/(1-x) ≈ -8x
c.) f(x) = 1/(sqrt(1+x)) ≈ 1 - 0.5x
d.) f(x) = sqrt(4+x^2) ≈ 2 + x^2/4
e.) f(x) = (6+3x)^(1/3) ≈ 2 + x/3
consider the function f(x)=2x^2-8x+5.
a)express f(x) in the form of a(x-p)^2+q,where a,p,q are Z?
b)find the minimum value of f(x)? ...?
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f(x) = 2x^2 - 8x + 5
f(x) = 2(x^2 - 4x) + 5
f(x) = 2[(x-2)^2 - 4] + 5
f(x) = 2(x-2)^2 - 8 + 5
f(x) = 2(x-2)^2 - 3
f(x) is at a minimum when (x-2) = 0, therefore x = 2
f(2) = 2(2-2)^2 - 3
f(2) = -3
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solve for x. round your answer to two decimal places. show your work for full credit. a right triangle is shown with the hypotenuse labeled x. one angle has a measure of thirty degrees, and the opposite leg has a length of ten.
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The value of x is 20 when right triangle is with the hypotenuse labeled x , one angle has a measure of thirty degrees, and the opposite leg has a length of ten.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Right ∆ with Hypotenuse is x, Opposite is 10
Reference angle = 30°.
We need to find the value of x
Since we are given a reference angle with opposite length, and we are to find the hypotenuse length, x, apply the following trigonometric ratios formula:
sin(theta)=opposite side/hypotenuse
Plug in the values into the equation
sin 30 = 10/x
1/2=10/x
Apply cross multiplication
x=20
Hence, the value of x is 20 when right triangle is with the hypotenuse labeled x , one angle has a measure of thirty degrees, and the opposite leg has a length of ten.
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How do you write 6 19/25 as a decimal?
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[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{6 \dfrac{19}{25}}[/tex]
[tex]\mathsf{= \dfrac{6\times25 + 19}{25}}[/tex]
[tex]\mathsf{= \dfrac{150 + 19}{25}}[/tex]
[tex]\mathsf{= \dfrac{169}{25}}[/tex]
[tex]\mathsf{= 169 \div 25}[/tex]
[tex]\mathsf{= 6.76}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{6.76}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
You have $6,500 to deposit. If you deposit the money in a savings account at your local bank, you will earn 1.45% annual interest and will be able to make ATM withdrawals at your bank's ATMs. If you deposit the money in an online savings account, you will earn 2.25% interest, but you will be charged $4 every time you make an ATM withdrawal. Assuming that your ATM withdrawals do not reduce the amount of interest you earn, how many ATM withdrawals must you make in a year for the local savings account to be a better deal than the online savings account?
a.
5
b.
12
c.
14
d.
10
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Amount from local account = 6,500(1.0145)ⁿ
Amount from online account = 6,500(1.0225)ⁿ - 4x
Where n is the number of years and x is the number of ATM withdrawals.
6,500(1.0145)ⁿ > 6,500(1.0225)ⁿ - 4x
4x > 6,500[(1.0225)ⁿ - (1.0145)ⁿ]; n = 1
x > 13
The number of withdrawals must exceed 13.
The answer is C.
Answer:
C. 14
Step-by-step explanation:
I just answered it correct
Multiply.
Express your answer as a simple fraction or improper fraction.
7 · 3/4 = n
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Find the integral of sqrt(4x-x^2)dx.
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= 2[(4x - x²)^(3/2)] / 3(4 - 2x)
The value of integral is 2 * arc sin((x - 2) / 2) + (x - 2) * √(4 - (x - 2)²) / 2 + C.
To solve the integral ∫ √(4x - x²) dx, follow these steps:
Complete the Square: Rewrite the quadratic expression under the square root. Start with: 4x - x²
Rearrange it to the standard quadratic form: -x² + 4x. To complete the square, factor out the negative sign: (x² - 4x)
Next, complete the square inside the parentheses:
x² - 4x = (x - 2)² - 4
So, we get:
(x² - 4x) = - [(x - 2)² - 4] = 4 - (x - 2)²
Therefore:
√(4x - x²) = √(4 - (x - 2)²)
Substitute Variables: Let u = x - 2. Then, du = dx, and the integral becomes:
∫ √(4 - u²) du
Apply the Trigonometric Substitution: Use the trigonometric substitution u = 2 sin θ. Then du = 2 cos θ dθ. Substitute these into the integral:
∫ √(4 - (2 sin θ)²) * 2 cos θ dθ
= ∫ √(4 - 4 sin² θ) * 2 cos θ dθ
= ∫ √(4 (1 - sin² θ)) * 2 cos θ dθ
= ∫ 2 cos θ * 2 cos θ dθ
= ∫ 4 cos² θ dθ
Use Trigonometric Identity: Apply the double-angle identity cos² θ = (1 + cos 2θ) / 2:
∫ 4 cos² θ dθ
= ∫ 4 * (1 + cos 2θ) / 2 dθ
= ∫ (4 + 4 cos 2θ) / 2 dθ
= ∫ (2 + 2 cos 2θ) dθ
Integrate each term:
∫ 2 dθ + ∫ 2 cos 2θ dθ = 2θ + sin 2θ + C
Back-substitute: Replace θ with the original variable x. Recall u = 2 sin θ, so θ = arcsin(u / 2). Since u = x - 2, substitute back:
θ = arcsin((x - 2) / 2)
Therefore:
2 * arcsin((x - 2) / 2) + sin(2 * arcsin((x - 2) / 2)) + C
Using the identity sin(2θ) = 2 sin θ cos θ:
sin(2 * arcsin((x - 2) / 2))
= 2 * (x - 2) / 2 * √(1 - ((x - 2) / 2)²)
= (x - 2) * √(4 - (x - 2)²) / 2
Assume a 30-month cd purchased for $3000 pays simple interest at an annual rate of 5.5%. how much total interest does it earn? what is the balance at maturity?
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? x 2.5 years = total interest earned.
4000 + interest earned = balance at maturity.
The total simple interest earned on a $3000 CD over 30 months with an annual interest rate of 5.5% is $412.50 and the balance at maturity is $3412.50.
Explanation:To calculate the total amount of simple interest earned on a certificate of deposit (CD) we use the formula I = Prt, where I is interest, P is the principal amount (initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years. For the given 30-month CD purchased for $3000 with an annual simple interest rate of 5.5%, we first convert 30 months to years by dividing by 12 (30 / 12 = 2.5 years).
Using the formula: I = $3000 × 0.055 × 2.5 = $412.50. Therefore, the total interest earned is $412.50.
To calculate the balance at maturity, we add the total interest to the principal: Balance = Principal + Interest = $3000 + $412.50 = $3412.50.
is 48/72 and 6/9 Proportional or Nonproportional
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The fractions (48/72) and (6/9) are proportional as, (8/8)(6/9) is equal to (48/72).
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, A fraction 48/72.
Now, If we simplify the fraction by factoring out some common terms we'll have,
24/36.
= 12/18.
= 6/9.
So, They are proportional.
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Match Term Definition
Line Segment A) a series of points that extend in two directions without end
Plane B) two lines that intersect at 90° angles
Perpendicular Lines C) lines that lie in the same plane and do not intersect
Line D) a flat surface that extends infinitely and has no thickness
Parallel Lines E) part of a line that has two endpoints
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Answer:
Line segment: E
Plane: D
Perpendicular lines: B
Line: A
Parallel lines: C
Step-by-step explanation:
This middle school mathematics question asks for matches between geometric terms and their definitions. Line segments have two endpoints, planes extend infinitely without thickness, perpendicular lines intersect at 90 degrees, lines extend indefinitely in two directions, and parallel lines never intersect.
Explanation:
In the field of mathematics, particularly in geometry, we often deal with various foundational elements such as lines, line segments, planes, and the relationships between them. To understand these concepts, it is essential to know their definitions and how they relate to each other.
A line segment is best described as a part of a line that has two distinct endpoints. This means a line segment is contained and does not extend infinitely in any direction. An example of this is the edge of a ruler, which begins and ends at specific points. The correct match for a line segment in the provided list is E) part of a line that has two endpoints.
A plane in geometry is a flat, two-dimensional surface that extends infinitely in all directions. It's similar to a vast sheet of paper with no edges. It is defined by at least three noncollinear points and is often represented in drawings as a four-sided figure, but it continues without end. The correct definition for a plane is D) a flat surface that extends infinitely and has no thickness.
Perpendicular lines are two lines that intersect at an angle of 90 degrees. The point where they cross forms right angles, and the two lines are always at the same distance from each other at this point. The definition of perpendicular lines is B) two lines that intersect at 90° angles.
Regarding a line, it is an undefined term in geometry that represents a straight path that extends infinitely in both directions with no thickness. It is comprised of an infinite number of points. A simple description of a line is A) a series of points that extend in two directions without end.
Lastly, parallel lines are lines in the same plane that do not intersect, no matter how far they are extended on either side. This is because they are always the same distance apart, maintaining a consistent separation across their entire length. The correct match for parallel lines is C) lines that lie in the same plane and do not intersect.
Find the value of cos θ for the angle shown
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Factor out the greatest common factor
-5x^2 - 5x^3 - 15x^4
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Our greatest common factor, or GCF, is [tex] -5x^{2} [/tex], so when we factor is out, our divide each term by [tex] -5x^{2} [/tex], we get our answer. To check this, we can multiply the [tex] -5x^{2} [/tex] back across the parenthesis and see if we get the same result as our initial question.
Hope this helped! :))
You are expecting a call from a friend anytime between 3:00 P.M. and 5:00 P.M. At 3:20 P.M, you discover that someone accidentally left the phone off the hook. What is the probability that you missed your friend’s call?
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Difference between 3:00 and 5:00 = 120 mins or 2 hours.
There is a possibility of 20/120 that you missed your friends call.
Hope this helped. If you need more explaining, let me know in the comments.
The probability that you missed your friend’s call is 1/6
How to determine the probability?The range is given as:
Range = 3:00 P.M. and 5:00 P.M.
The number of minutes in the range is:
Total = 120 minutes
At 3:20 that you notice the phone is off the hook, the number of minutes missed is:
Time missed = 20 minutes
The probability is then calculated as:
P = 20/120
Evaluate
P = 1/6
Hence, the probability that you missed your friend’s call is 1/6
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true or false Volume can be measured in liters or cubic meters.
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What is greater four liters or one gallon
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so, 4 L = 1.05 gal, which is greater than 1 gal
So, 4 L will be Greater!
Hope this helps!
Answer:
One Gallon
Step-by-step explanation:
One Imperial gallon is 4.54 litres so in that case the gallon is greater but one US gallon is only 3.79 litres so in that case the litres is bigger. ... or 1 gallon =1/. 22 =4.545 liters. so one gallon is greater than 4 liters.
The product of two numbers is 48, and one of the numbers is 12. find the other number. which equation can be used to solve this problem?
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Solve for the equation. u + 3.5 = 5
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Question 4 Rachel, Greg, and Trey sent a total of 71 text messages over their cell phones during the weekend. Trey sent 3 times as many messages as Greg. Greg sent 9 more messages than Rachel. How many messages did they each send?
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16x3=48
7+16=23
23+48=71
7+16+48=71
What substitution should be used to rewrite 4x12 – 5x6 – 14 = 0 as a quadratic equation?
u = x2
u = x3
u = x6
u = x12
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4x12 – 5x6 – 14 = 0
this equation is equivalent to 4(x^6)² – 5(x^6) – 14 = 0
so if u=x^6
we have 4(u)² – 5(u) – 14 = 0, and it is a quadratic equation
so the answer is u = x6
What fraction is.85 of an inch?
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Step 2: Simplify 85/100 = 17/20
hope this helps you
is y=-3x-8 perpendicular, parallel, or neither?
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Thus, it is neither.
If one line is parallel to another line, then they will both have the same slope (the coefficient next to the x).
For instance, y=5x+8 is parallel to y=5x-4.
If one line is perpendicular to another line, then the slopes must be negative reciprocals of one another (reciprocals multiply together and yield one, like 1/3 and 3.)
A parallel line to y=-3x-8 would be y=-3x
A perpendicular line to y=-3x-8 would be y=1/3x
Since the line we are comparing y=-3x-8 to, which is y=3x+8, meets neither of the constraints for being parallel or perpendicular, the correct answer is neither.
What is the total interest on a ten-year. 6.1% loan with a principal of $32,000?
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Final answer:
The total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.
Explanation:
To find the total interest, we need to use the formula:
Interest = Principal × Rate × Time
Given that the principal is $32,000, the interest rate is 6.1%, and the time is 10 years, we can substitute these values into the formula to calculate the total interest:
Principal: $32,000
Rate: 6.1%
Time: 10 years
Interest = $32,000 × 0.061 × 10 = $19,520
Therefore, the total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.
Ted and Robin each gave a basket of green apples to their friend Lily. Ted’s basket contains 5 apples, each weighing ounces. Robin’s basket contains 6 apples, each weighing ounces. Whose basket is heavier and by how much?
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Robin's basket is heavier than Ted's basket by 2 ounces.
Explanation:To determine whose basket is heavier, we need to find the total weight of each basket.
Ted's basket contains 5 apples, each weighing 8 ounces. Therefore, the total weight of Ted's basket is 5 * 8 = 40 ounces.
Robin's basket contains 6 apples, each weighing 7 ounces. Therefore, the total weight of Robin's basket is 6 * 7 = 42 ounces.
Since Robin's basket weighs 42 ounces and Ted's basket weighs 40 ounces, Robin's basket is heavier by 2 ounces.