Answer:
7
Step-by-step explanation:
13.07 minus 6.07 is 7
7 divided by 1 is 7
ans is 7
f f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f circle g) (x)?
hi
f°g mean apply g(x) and then use result of g(x) as "x" in f(x)
so as g(x) = x² +1 and f(x) = 3x+2
so if we call g(x) X we have
f( X) = 3 X +2
now we replace " X" for it's value
f(X) = 3 ( x² +1) +2
f(X) = 3x² +3 +2
f(X) = 3x² +5
so f°g = 3x² +5
need help with this asap
The converse, inverse and contrapositive of each conditional statement include:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.What is a conditional statement?
A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
In this scenario, we would write the converse, inverse and contrapositive of each conditional statement as follows:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.Read more on conditional statement here: brainly.com/question/16951916
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A line is parallel to the line y = x and passes
through the parabola y = x² - 3 at
(4, 13). What is the other point at which the two
functions intersect?
Answer:
Step-by-step explanation:
hello here is an solution
Match the expressions to their solutions or equivalents. -1/9 / (-1/3)
The quotient of the given expression is 1/3
Difference and division of fractionsFractions are written as a ratio of two integers
Given the expression below'
-1/9 / (-1/3)
Change the division to multiplication
-1/9 * -3/1
1/9 * 3/1
1/3
Hence the quotient of the given expression is 1/3
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The terminal side of Ø is in quadrant II and cos ø = -5/13 What is sin ø?
the value of sin ∅ is 12/ 13
Quadrants and the "cast" Rule:In the first quadrant, the values for sin, cos, and tan are positive.In the second quadrant, the values for sin are positive only.In the third quadrant, the values for tan are positive only.In the fourth quadrant, the values for cos are positive only.From the given question,
We have, cos ∅= 5/13
From the trigonometric identities, we have that
[tex]sin^2\alpha + cos^2\alpha = 1[/tex]
Then , let's substitute the value of cos ∅
[tex]sin^2\alpha +(\frac{-5}{13} )^2 = 1[/tex]
Let make sin the subject of formula and find the squares of the fraction
sin²∅ = [tex]1 - \frac{25}{169}[/tex]
Find the LCM
sin²∅ = [tex]\frac{169 - 25}{169}[/tex]
Find the difference
sin²∅ = [tex]\frac{144}{169}[/tex]
Find the square root
sin∅ = [tex]\sqrt{\frac{144}{159} }[/tex]
sin∅ = [tex]\frac{12}{13}[/tex]
In quadrant II , sin is positive, so we have
sin ∅ = 12/ 13
Thus, the value of sin ∅ is 12/ 13
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What is the most precise name for quadrilateral ABCD with vertices
A(-1,0), B(4, 0), C(5, 4), and D(0, 4)?
A. rhombus
B. rectangle
C. square
D. parallelogram
Parallelogram is the quadilateral ABCD with vertices A(-1,0), B(4, 0),
C(5, 4), and D(0, 4)
What is parallelogram?A parallelogram is a quadrilateral whose opposite sides are parallel and equal.
first, find the length of the sides of the quadilateral.
AB = [tex]\sqrt{(4-(-1))^2+0-0^2} \\[/tex]= [tex]\sqrt{5^2+0}[/tex] = [tex]\sqrt{25}[/tex] = 5
BC = [tex]\sqrt{(5-4)^2+(4-0)^2}[/tex] = [tex]\sqrt{1^2+4^2}[/tex] = [tex]\sqrt{1+16} = \sqrt{17}[/tex]
CD = [tex]\sqrt{(0-5)^2+(4-4)^2} = \sqrt{(-5)^2+0} = \sqrt{25-0} = 5[/tex]
DA = [tex]\sqrt{(-1-0)^2+(0-4)^2} = \sqrt{(-1)^2+(-4)^2} = \sqrt{1+16} = \sqrt{17}[/tex]
opposite side length is equal.
so quadilateral is parallelogram.
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The most precise name for quadrilateral ABCD with vertices
A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is parallelogram.
What is the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4)?The most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is parallelogram.The parallelogram has opposite parallel sides.A parallelogram is a flat 2d shape that has four angles.The opposite interior angles are equal.If the parallelogram has anyone of the angles is a right angle, then all the other angles will be at a right angle.Hence, the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is a parallelogram.
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find y' if x^y = y^x
The answer is [tex]\boxed {\frac{dy}{dx} = \frac{y^{x}logy-yx^{y-1}}{x^{y}logx-xy^{x-1}}}[/tex].
Apply logarithmic differentiation on each side.
LHS
u = x^ylog u = y log x1/u du/dx = y/x + log x (dy/dx)du/dx = x^y (y/x + log x dy/dx)du/dx = yx^(y - 1) + x^y logx dy/dxRHS
v = y^xlog v = x log y1/v dv/dx = x/y dy/dx + logydv/dx = y^x (x/y dy/dx + logy)dv/dx = xy^(x - 1) dy/dx + y^x logyEquating both sides
yx^(y - 1) + x^y logx dy/dx = xy^(x - 1) dy/dx + y^x logydy/dx (x^y logx - xy^(x - 1)) = y^x logy - yx^(y - 1)[tex]\boxed {\frac{dy}{dx} = \frac{y^{x}logy-yx^{y-1}}{x^{y}logx-xy^{x-1}}}[/tex]+++++
3
2
0
+++++++
1
-2
-3
Intro
Which statements are true? Check all that apply.
0-2.5=-2/2
0-1.5 -0.5
-0.5 0
-2.5 -2
11.5
Done
Step-by-step explanation:
++++5
+++++++_2
1=false
true
false
false
I NEED THE ANSWERS PLEASE ANYONE ANSWERS WILL DO
Answer:
1. x = -1 y= -2
2. infinitely many solutions
3. x = 6 y= -7
4.no solution
5. x = -3 y = -17
6. x= 3 y = 7
Step-by-step explanation:
1) y=x-1
7x+6y= -19
6y= -19 -7x
y= (-7x-19)/6
since x-1 and (-7x-19)/6 are both equal to y they are equal to each other
this is how to get x
x-1 = (-7x-19)/6
6x-6 = -7x-19
13x = -13
x = -1
now put back -1 in the equation to get y
y=x-1
y = -1 -1
y= -2
2)-10x+2y=-12
y=5x-6
2y= -12 + 10x
y= -6 + 5x
y = 5x - 6
5x-6 = 5x - 6
0 = 0
when something is
equal to itself its
infinitely many solutions
(when something is not equal to something its no solution)
((when something is equal to just one answer its one solution)
3) y= -4x+17
y=x-13
-4x+17 = x-13
30 = 5x
x = 6
y=x-13
y=6-13
y= -7
4) -3x-15y=8
x+5y=5
-3x-15y=8 -> y = -1/15(3x-8)
5y=5-x -> y= 1/5 (5-x)
-1/15(3x-8) = 1/5 (5-x)
-x-8/3 = 5-x
0 = 23/3
(when something is not equal to something its no solution)
5) -3x+6y=-3
3x-y=8
-3x+6y= -3 -> y = 1/6(3x-3)
3x-y=8 -> y = 3x-8
1/6(3x-3) = 3x-8
3x-3 = 18x-48
x-1 = 6x - 16
5x = -15
x = -3
3x-y=8
3(-3)-y=8
-9-8 = y
y = -17
6) -6x+6y=24
-3x-8y=1
-6x+6y=24 -> y = 1/6(6x+24) -> y = x+4
-3x-8y=1 -> -3x-1 = 8y -> y = 1/8 (-3x-1)
1/8 (-3x-1) = x+4
-3x-1 = 8x+32
11x = 33
x= 3
-6x+6y=24
-6(3)+6y=24
-18 + 6y = 24
6y = 24 + 18
6y = 42
y = 7
A procedure has an 81% success rate. The procedure is tried on 12 patients what is the probability that at least 8 patients show improvement
The probability that at least 8 patients show improvement is; 0.94
How to use Binomial Probability Distribution?The formula for Binomial Probability Distribution is;
P(X = r) = nCr * p^(r) * (1 - p)^(n - r)
where;
n = number of trials
r = number of specific events you wish to obtain
p is probability of success
From the question, we have;
n = 12
r = 8
p = 81% = 0.81
The probability that at least 8 patients show improvement is expressed as;
P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)
Using online binomial probability calculator gives us;
P(X ≥ 8) = 0.11954 + 0.22649 + 0.28967 + 0.22453 + 0.07977
P(X ≥ 8) = 0.94
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6x+2y=8
9x+3y=14
Skew
Neither
Perpendicular
Parallel
Someone please help with this question!
The value of angle 20 is as follows:
m∠20 = 50.9 degrees.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line l and m are parallel lines cut by the two transversal.
Hence,
m∠6 ≅ m∠20 (alternate angles)
Therefore, alternate angles are congruent
m∠20 = 2x - 4
m∠19 + m∠20 = 180 (angles on a straight line)
5x - 8 + 2x - 4 = 180
7x - 12 = 180
7x = 180 + 12
7x = 192
x = 192 / 7
x = 27.4285714286
x = 27.43
Therefore,
m∠20 = 2(27.43) - 4
m∠20 = 50.8571428571
m∠20 = 50.9 degrees.
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Rewrite 1/2 x 1/2 x 1/2 as an exponential expression with a base of 2.
The equivalent expression of 1/2 * 1/2 *1/2 is 2^-3
How to rewrite the expression?The expression is given as:
1/2 * 1/2 *1/2
Apply the product law of indices
1/2 * 1/2 *1/2 = (1/2)^3
Apply the power law of indices
1/2 * 1/2 *1/2 = (2^-1)^3
This gives
1/2 * 1/2 *1/2 = 2^-3
Hence, the equivalent expression of 1/2 * 1/2 *1/2 is 2^-3
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A farmer with 3380 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
The largest possible total area of the four pens is 285610 ft²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the length of the pen and x represent the width of the pen.
Hence:
Perimeter = x + y + x + y + x + x + x = 2y + 5x
2y + 5x = 3380
y = (3380 - 5x)/2 (2)
Area (A) = xy
A = x * (3380 - 5x)/2
A = (3380x - 5x²)/2
The maximum area is at A' = 0, hence:
A' = (1/2)(3380 - 10x)
0 = (1/2)(3380 - 10x)
10x = 3380
x = 338 ft.
2y + 5(338) = 3380
y = 845 ft.
Largest possible total area = 338 * 845 = 285610 ft²
The largest possible total area of the four pens is 285610 ft²
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I need helping solving this :)
Answer: answer is B
Step-by-step explanation:
use Pythagorean theorem to find other side. And sine is opposite side over hypotenuse.
f(x)= x+28/x-7 for inverse functions
The inverse function of the given function is [tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]
What is the inverse of a function?A function g is the inverse of a function f, if and only if the values of y= f(x), x = g(y).
From the formula given:
[tex]\mathbf{y=f(x) = \dfrac{x+28}{x-7}}[/tex]
Let's substitute x with y;
[tex]\mathbf{y= \dfrac{x+28}{x-7}}[/tex]
[tex]\mathbf{x=\dfrac{y+28}{y-7}}[/tex]
Solve for y;
[tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]
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What is the approximate length of the line segment?
Answer:
18.4 units
Step-by-step explanation:
We can use the distance formula, d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] to find the length of the line segment.
d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] = [tex]\sqrt{(5+12) ^{2} +(-10+3) ^{2}}[/tex] = [tex]\sqrt{(17) ^{2} +(7) ^{2}}[/tex]=[tex]\sqrt{338}[/tex]=18.38
What is the inverse of the function f (x) = 3(x + 5)2 – 4, such that x ≤ –5?
inverse of f of x is equal to negative 5 plus the square root of the quantity x plus 4 all over 3 end quantity
inverse of f of x is equal to negative 5 minus the square root of the quantity x plus 4 all over 3 end quantity
inverse of f of x is equal to negative 5 plus the square root of the quantity x over 3 plus 4 end quantity
inverse of f of x is equal to negative 5 minus the square root of the quantity x over 3 plus 4 end quantity
The equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse functions?The function f(x) is given as
f(x) = 3(x + 5)^2 - 4
Express f(x) as y
So, we have
y = 3(x + 5)^2 - 4
Swap the positions of x and y
So, we have
x = 3(y + 5)^2 - 4
Add 4 to both sides of the equation
So, we have
x + 4 = 3(y + 5)^2
Divide through by 3
So, we have
1/3(x + 4) = (y + 5)^2
Take the square root of both sides
So, we have
√[1/3(x + 4)] = y + 5
Subtract 5 from both sides of the equation
So, we have
y = -5 + √[1/3(x + 4)]
Rewrite as
f-1(x) = -5 + √[1/3(x + 4)]
Hence, the equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]
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Which of the following functions are discontinuous?
Answer:
D. I, II, and III
Step-by-step explanation:
A discontinuous function is a function which is not continuous.
If f(x) is not continuous at x = a, then f(x) is said to be discontinuous at this point.
To prove whether a function is discontinuous, find where it is undefined.
A rational function is undefined when the denominator is equal to zero.
Therefore, to find the values that make a rational function undefined, set the denominator to zero and solve.
Function I
Denominator: x - 2
Set to zero: x - 2 = 0
Solve: x = 2
Therefore, this function is undefined when x = 2 and so the function is discontinuous.
Function II
Denominator: 4x²
Set to zero: 4x² = 0
Solve: x = 0
Therefore, this function is undefined when x = 0 and so the function is discontinuous.
Function III
Denominator: x² + 3x + 2
Set to zero: x² + 3x + 2 = 0
Solve:
⇒ x² + 3x + 2 = 0
⇒ x² + x + 2x + 2 = 0
⇒ x(x + 1) + 2(x + 1) = 0
⇒ (x + 2)(x + 1) = 0
⇒ x = -2, x = -1
Therefore, this function is undefined when x = -2 and x = -1, and so the function is discontinuous.
Therefore, all three given functions are discontinuous.
If a boat with a value of $23, 000 depreciates at a rate of 18% per year, what is the value
after 5 years?
The value of the car after 5 years is 8527.02 dollars
How to find the value after depreciation?Depreciation is the reduction in the value of an asset over time due to elements such as wear and tear. For example a car is said to "depreciate" in value after a discovery of a faulty transmission.
The value after 5 years can be found as follows:
Rate = 18% = 18 / 100 = 0.18
Initial Value = $23,000
time = 5 years
Therefore,
y = 23000(1 + 18%)⁵
y = 23000(1 - 0.18)⁵
y = 23000(0.82)⁵
y = 23000 × 0.3707398432
y = 8527.0163936
y = 8527.02 dollars
Therefore, the value of the car after 5 years is 8527.02 dollars
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Using an exponential function, it is found that the value of the car after 5 years will be of $8,527.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.For this problem, the initial cost and the decay rate are given as follows:
A(0) = 23000, r = 0.18.
Hence the value of the boat after t years is given as follows:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 23000(1 - 0.18)^t[/tex]
[tex]A(t) = 23000(0.82)^t[/tex]
The value after 5 years will be of:
[tex]A(5) = 23000(0.82)^5 = 8527[/tex]
The value of the car after 5 years will be of $8,527.
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An animal shelter has a total of 5 * 47 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one half the number of cats, and there are 20 more cats than dogs, how many dogs are at the shelter?
The number of dogs in the animal shelter which comprise of cats, dogs, and rabbits is 84 dogs.
EquationTotal animals = 5 × 47
= 235
Number of rabbits = 1/2(d + 20) - 5Number of cats = d + 20Number of dogs = d235 = d + (d + 20) + 1/2(d + 20) - 5
235 = d + d + 20 + 1/2d + 10 - 5
235 = 2 1/2d + 25
235 - 25 = 2 1/2d
210 = 2 1/2d
d = 210 ÷ 2 1/2
d = 210 ÷ 5/2
= 210 × 2/5
= 420/5
d = 84 dogs
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Which of the following functions has an initial value of -1/2 and a rate of change of -2?
Find the eighth term of the
geometric sequence, given the
first term and common ratio.
a1=6 and r=-1/3
Answer:
7
Step-by-step explanation:
haha
for
for
haha
but
birthday
can
7 answer
Answer:
the answer is -2/729
Step-by-step explanation:
When you're given the first term and the common ratio, you just need to multiply the first term by the common ratio and then raise to the power of the nth term minus 1.
In this case, 6(-1/3)^7
What is the solution for x² + 4x > 77?
Ox<-7 or x> 11
Ox<-11 or x>7
0-7
0-11
TERENO
TOTAPE
Whilsend
BATTLES
HEYRPRIP
GTHEBEN TEN OF JESHIREMERS
EN ERTER IS BELE RE
A
BODYER an
S
THERE THE
13627
STERIS
MINER
50 POINTS!!!!!!!!!!!!!!!!!!!!!!!! SOLVE THIS QUICKLY WITH AN EXPLANATION
Answer:
x = 30 degrees
Step-by-step explanation:
angles MNO, LNM, and KNL make a straight line: 105+45+y = 180 --> y = 30 degrees
KNL = 30 degrees
angle KLN is 90 degrees, a triangle is equal to 180 degrees
2x+30+90 = 180
2x = 60
x = 30 degrees
You have a credit card that charges an interest rate of 16.15% compounded monthly. The table below shows your activity for the month of April. Date Activity Amount Balance April 1 Beginning Balance 1,000.00 April 5 Purchase 29.10 1,029.10 April 12 Payment −225.00 804.10 April 15 Purchase 97.25 901.35 April 23 Purchase 19.00 920.35 April 26 Purchase 28.40 948.75 April 30 Ending Balance 948.75 What is the average daily balance for this account? $ What is the finance charge for the month of April? $
1. The average daily balance for this credit card account is $187.74.
2. The finance charge for the month of April is $249.22.
How is the average daily balance calculated?The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.
A billing cycle for a credit card account is usually one month.
Data and Calculations:Interest rate = 16.15% compounded monthly
Date Activity Amount Balance
April 1 Beginning Balance $1,000.00
April 5 Purchase 29.10 1,029.10
April 12 Payment −225.00 804.10
April 15 Purchase 97.25 901.35
April 23 Purchase 19.00 920.35
April 26 Purchase 28.40 948.75
April 30 Ending Balance 948.75
Total $5,632.05
Average daily balance = $187.735 ($5,632.05/30 days)
Daily interest rate = 0.04425 (16.15%/365)
Finance charge = $249.22 ($187.74 x 0.04425 30 days)
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If you go out to eat with 3 friends and your meal was $72.50, there is 6.75% sales tax
and you should tip the waiter 15%. How much should each person pay?
Tax $
Total meal cost
Tip $
Total cost of meal with tip
Price for each person
After the tax and the tip are counted, we conclude that each friend must pay $30.
How much should each person pay?We know that the meal cost is $72.50.
Now, there is a 6.75% sales tax and a 15% tip on the waiter (we assume that the tip is based on the total meal cost, after the tax is applied).
Then the total meal cost is:
C = $72.50*( 1 + 6.75%/100%) = $72.50*(1 + 0.0675) = $77.39
Now we also need to add the tip, which is a 15% of that, so the total cost with the tip included is:
C' = $77.39*(1 + 15%/100%) = $88.998 = $90
(Where we rounded up).
Then, if there are 3 friends, each one must pay:
$90/3 = $30
Each friend must pay $30.
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An H0-scale model railroad engine is 9 inches long. The H0 scale is 87 feet to 1 foot. How long is a real engine?
The real engine is 65.25 feet long
How to determine the length?The scale is given as:
Scale = 87 feet to 1 foot
The scale length is given as
Scale length = 9 inches
Convert inches to feet
Scale length = 9/12 feet
The actual length is then calculated as:
Actual = 87 * 9/12 feet
Evaluate
Actual = 65.25 feet
Hence, the real engine is 65.25 feet long
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Solve the inequality by the method of intervals
The solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).
What is the solution of the given inequality problems ?The first inequality is (x² - 25)/(x + 10) ≥ 0
⇒ x² - 25 ≥ 0
⇒ x² ≥ 25
∴ x ≥ 5
Thus the domain of the given inequality from method of interval is x = [5,∝).
The second inequality is (x + 2)(x² - 64)/(x² + 45) ≤ 0
⇒ (x + 2)(x² - 64)≤ 0
Either (x + 2)≤ 0 or (x² - 64)≤ 0
Either x ≤ -2 or x ≤ 8
Thus , the combined domain of the given inequality from method of interval is x = [-2,0]∪[8,-∝) .
Therefore, the solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).
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The ratio of the weight of an object
The weighing of the man on the earth given the ratio is 174 pounds
Ratioratio of the weight of an object on the earth to the moon = 6:1Weight of a man on the moon = 29 poundsWeight of the man on Earth = xEquate the ratio
6 : 1 = x : 29
6/1 = x/29
cross product6 × 29 = 1 × x
174 = x
x = 174 pounds
Complete question:
The ratio of the weight of an object on the earth to the moon is 6:1. If a man weighs 29 pounds on the moon, calculate his weighing on the earth.
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