The function is not invertible if you think of it as
[tex]f:\mathbb{R}\to\mathbb{R}[/tex]
because it is not injective: [tex]f(x)=f(-x)[/tex]
So, if we restrict the domain to the positive numbers only:
[tex]f:\mathbb{R^+}\to\mathbb{R}[/tex]
Note that the range is actually [tex][9,\infty)[/tex], so we can be more precise and write
[tex]f:\mathbb{R^+}\to[9,\infty)[/tex]
To find the inverse, we solve the expression for x:
[tex]y=x^2+9 \iff y-9=x^2 \iff x=\pm\sqrt{y-9}[/tex]
But since we restricted to positive values of x, the inverse is
[tex]x=\sqrt{y-9}[/tex]
To find the inverse of the function f(x) = x² + 9, swap x and y and solve for y. The inverse function is f^(-1)(x) = ± √(x-9), with a domain restricted to x ≥ 9.
To find the inverse of the function f(x) = x^²+ 9, we need to switch the roles of x and y and solve for y. The given function is y = x² + 9. Swap x and y to get x = y² + 9. Rearrange this equation to solve for y in terms of x: y² = x - 9. Taking the square root of both sides gives us y = ± √(x-9). Therefore, the inverse function is f^(-1)(x) = ± √(x-9), and the domain is restricted to x ≥ 9.
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Find the amount of interest owed for a $1,895 loan for 4 years at a 7.9% interest rate.
Answer: The amount of interest owed is $598.82.
Step-by-step explanation: 7.9% of $1,895 is 149.705. So, 149.705 x 4 years would be $598.82 for 4 years.
Final answer:
The total interest owed on a $1,895 loan at a 7.9% interest rate over 4 years is calculated using the formula for simple interest, resulting in a total interest amount of $598.43.
Explanation:
To find the amount of interest owed on a $1,895 loan for 4 years at a 7.9% interest rate, you can use the formula for calculating simple interest, which is Interest = Principal × Rate × Time. The principal (P) is $1,895, the rate (r) is 7.9% or 0.079 when expressed as a decimal, and the time (t) is 4 years.
So the calculation would be:
Interest = $1,895 × 0.079 × 4
Let's perform the calculation:
Interest = $1,895 × 0.079 × 4 = $598.43
The total interest owed on the loan after 4 years would be $598.43.
solve for r
r/16 ≥8
a)r≥2
b)r≤128
c)r≤2
d)r≥128
The solution to the inequality [tex]\frac{r}{16}\geq 8[/tex] is r≥128.
Step-by-step explanation:
Given inequality is;
[tex]\frac{r}{16}\geq 8[/tex]
We will solve the inequality for r.
Therefore;
Multiplying both sides by 16
[tex]\frac{r}{16}*16\geq 8*16\\x\geq 128[/tex]
Therefore;
The solution to the inequality [tex]\frac{r}{16}\geq 8[/tex] is r≥128.
Rory has 3 pounds of ground beef to make meatballs. He uses 3/8 pound per meatball to make 7 meatballs. How many 1/8-pound meatballs can rory make with the remaining beef
Rory can make 3 additional 1/8-pound meatballs with the remaining 3/8 pounds of beef after making 7 meatballs that use 3/8 pound each.
Explanation:Rory has initially 3 pounds of ground beef. Since he uses 3/8 pound per meatball to make 7 meatballs, we first need to calculate the total beef used for 7 meatballs by multiplying 7 (the number of meatballs) by 3/8 pound (the amount of beef per meatball).
7 meatballs × 3/8 pound/meatball = 21/8 pounds
Now, to find out the remaining beef, subtract the beef used from the total beef available:
3 pounds - 21/8 pounds = 24/8 pounds - 21/8 pounds = 3/8 pounds remaining.
With the remaining 3/8 pounds of beef, Rory wishes to make 1/8-pound meatballs. To find out how many 1/8-pound meatballs he can make, we divide the remaining beef by 1/8 pound:
3/8 pounds ÷ 1/8 pound/meatball = 3 meatballs.
Rory can make 3 additional meatballs, each weighing 1/8 pound, with the remaining beef.
Which type of graph would be best used for showing the percentage of students in each grade level at a middle school
Answer:
A pie graph would be a good graph to use
Analyze the diagram below and complete the instructions that follow.
Find cos (0)
Please select the best answer from the choices provided
A. DF/DF
B. DF/EF
C. EF/DF
D. DE/DF
The value of the trigonometric equation is cos θ = EF/DF
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔDEF
Now , the sides of the triangle are
The hypotenuse of triangle is DF
where the measure of ∠DEF = 90°
Now , from the trigonometric relations , we get
cos θ = adjacent / hypotenuse
cos θ = EF/DF
Hence , the trigonometric relation is cos θ = EF/DF
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Solve the system using elimination.
3x + 16y = 3
3x - 16y = 3
The solution is a
(Type an ordered pair.)
The solution is (1,0)
Explanation:
The two equations are [tex]3x+16y=3[/tex] and [tex]3x-16y=3[/tex]
We need to solve the equation using elimination method.
Adding the two equations, we get,
[tex]3x+16y=3\\3x-16y=3\\-------\\6x=6[/tex]
[tex]x=1[/tex]
Thus, the value of x is 1
Substituting [tex]x=1[/tex] in the equation [tex]3x+16y=3[/tex] , we get,
[tex]3(1)+16y=3[/tex]
Simplifying, we get,
[tex]16y=3-3[/tex]
[tex]16y=0[/tex]
[tex]y=0[/tex]
Thus, the value of y is 0.
The solution is (1,0)
Round to the nearest hundredth.
27.8 = 1.55y
y≈0.06
y≈17.94
y=26.25
y=29.35
The correct answer is y = 17.94.
To solve the equation 27.8 = 1.55y for y, we first divide both sides of the equation by 1.55 to isolate y:
[tex]\[ y = \frac{27.8}{1.55} \][/tex]
Now, we perform the division:
[tex]\[ y \approx 17.935483871 \][/tex]
When rounding to the nearest hundredth, we look at the third decimal place. If it is 5 or more, we round up. If it is less than 5, we round down. In this case, the third decimal place is 5, so we round up:
[tex]\[ y \approx 17.94 \][/tex]
Therefore, the solution to the equation, rounded to the nearest hundredth, is y = 17.94.
Find the approximate volume of the cylinder shown in the diagram.
Answer: D
Step-by-step explanation:
trust me
The approximate volume of the cylinder shown is [tex]3017 cm^3[/tex] and the correct answer is option A.
Let's find the approximate volume of the cylinder shown in the diagram through the following Step-by-step process.
Identify the formula for the volume of a cylinder:The volume of a cylinder can be calculated using the formula [tex]V=\pi r^2h[/tex], where r is the radius of the base and h is the height of the cylinder.
Measure the radius and height from the diagram:From the diagram, estimate that the radius is [tex]r=\frac{17}{2} cm[/tex] (since the diameter is 17 cm) and the height is [tex]h=19 cm[/tex].
Substitute the values into the formula:[tex]V=\pi\times r^2h\\\\=\pi\frac{17}{2} ^2\times19\\\\\approx \frac{5491}{4} \pi[/tex]
Round the answer to the nearest integer:[tex]V=3017 cm^3[/tex] (rounded to the nearest integer).
Thus the approximate volume of the cylinder is [tex]3017 cm^3[/tex] corresponding to option A
Note: Since we used an approximation for the radius, the final answer is also an approximation.
What is the geometric mean of 5 and 18?
Answer:
[tex]\sqrt{90} =9.48683298051[/tex]
Step-by-step explanation:
First, mulitply the numbers
[tex]5*18=90[/tex]
Square root the last result
[tex]\sqrt{90} = 9.48683298051[/tex]
write the repeating decimal as a mixed number; 4.1111...
Answer:
Step-by-step explanation:
jalen jogged 10 miles due north, then turned due west and jogged 5 more miles. How msny miles is jalen from his starting point?
Answer:
Jalen is 11.18 miles from his starting point.
Step-by-step explanation:
Given:
Jalen jogged 10 miles due north, then turned due west and jogged 5 more miles.
Now, to find miles Jalen jogged from his starting point.
So, below is the figure attached to describe the scene.
Now, to get the distance of Jalen jogged from his starting point we use pythagoras theorem:
[tex]AB^2+BC^2=AC^2\\\\10^2+5^2=AC^2\\\\100+25=AC^2\\\\125=AC^2[/tex]
Using square root on both sides we get:
[tex]11.18=AC\\\\AC=11.18\ miles.[/tex]
Therefore, Jalen is 11.18 miles from his starting point.
Answer:
11.18 miles
Step-by-step explanation:
Carl claims that for some centers of dilation of a line, the line will remain
unchanged. He is tasked to prove his claim using the line y = 5x - 10 and a dilation
with a scale factor of 2. Which center of dilation could be used to support Carl's
claim?
A. (0,0)
B. (-5, 35)
C. (1, -5)
D. (2, 20)
Answer:
Option C.
Step-by-step explanation:
Dilation of a line:
If center of dilation lies on the line, then the line remains same.
If center of dilation does not lies on the line, then the dilated line is parallel to the original time.
The given equation of line is
[tex]y=5x-10[/tex]
The line will remain same if center of dilation lies on this line.
For x=0,
[tex]y=5(0)-10=-10\neq 10[/tex]
It means (0,0) does not lies on given line.
For x=-5,
[tex]y=5(-5)-10=-35\neq 35[/tex]
It means (-5,35) does not lies on given line.
For x=1,
[tex]y=5(1)-10=-5[/tex]
It means (1,-5) lies on given line.
For x=2,
[tex]y=5(2)-10=0\neq 20[/tex]
It means (2,20) does not lies on given line.
Center of dilation (1,-5) could be used to support Carl's claim.
Therefore, the correct option is C.
An employee’s new salary is $26.355 after getting a 5% raise. What was the salary before the increase pay?
Answer:
$25.03725
Step-by-step explanation:
Step 1: Multiply both sides by %5 to get the raise
26.355 * %5 is same as 26.355 * 0.05
$1.31775 is the raise
Step 2: Subtract the raise from the new salary
26.355 - 1.31775
25.03725
Answer: $25.03725
how to subtract and add polynomials
Answer:
To subtract, first reverse the sign of each term we are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual.
To add here is an example not sure if entirely right but here it is.
Start with:2x2 + 6x + 5 + 3x2 − 2x − 1.
Place like terms together:2x2+3x2 + 6x−2x + 5−1.
Which is:(2+3)x2 + (6−2)x + (5−1)
Add the like terms:5x2 + 4x + 4
Final answer:
To add or subtract polynomials, align like terms, add or subtract their coefficients accordingly, and ensure to distribute the negative sign across a polynomial when subtracting. Treat polynomial addition and subtraction like usual arithmetic, applying rules for positive, negative, and opposite signs.
Explanation:
Adding and subtracting polynomials is a straightforward process that involves combining like terms. Here is a step-by-step guide:
When adding polynomials, align terms with the same variable and exponent (like terms) vertically.
Next, add or subtract the coefficients of these like terms while keeping the variable part the same.
When you encounter subtraction, it's helpful to distribute the negative sign across the polynomial that is being subtracted, effectively changing the sign of each term in that polynomial.
After changing signs where necessary, proceed with addition as described above.
Remember that addition and subtraction of polynomials adhere to the usual arithmetic rules:
Adding two positive numbers gives a result with a positive sign.
Adding two negative numbers yields a result with a negative sign.
When adding numbers with opposite signs, subtract the smaller absolute value from the larger one, and the result takes the sign of the larger number.
For subtraction, change the sign of the subtracted number and then add as outlined.
Similar methods apply to vector addition and subtraction, scalar operations, and polynomial graphing. Keep these principles in mind while working through your math problems.
Stephanie is taking out a loan in the amount of $15,000. Her choices for the loan are a 4-year loan at
3% simple interest and a 5-year loan at 5% simple interest. What is the difference in the amount of interest
Stephanie would have to pay for each of these two loans?
$1,950
$3,750
$4,550
$1,800
Answer:
$1950
Step-by-step explanation:
Simple interest amount payable is given by
A=P(1+rt) where p is principal amount, A is final amount paid, t is time and r is rate of interest. For the first case
A=15000(1+0.03*4)=$16800
For second case
A=15000(1+0.05*5)=$18750
Difference will be 18750-16800=$1950
Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made 86 chocolate chip cookies and 42 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
What is the greatest number of identical packages that Shaquira can make?
To solve this question, first you would add 86 to 42 which gets you 128. Then, you should divide 128 by 2 which gets you to 64, which is the greatest number of packages you can sell.
Answer:
the REAL answer would be 2
Step-by-step explanation:
Find the value of x. The angle measures of a right triangle are
30°
2x°
3x°
Answer:
30
Step-by-step explanation:
Exterior angle equals sum of opposite interior angles
3x = 2x + 30
3x - 2x = 30
x = 30
Answer:
x=30
Step-by-step explanation:
all interior angles in a triangle must equal 180 degrees
2x+30+90=180
2x+120=180
2x=60
x=30
you can check by substituting 30:
2(30)+30+90
60+30+90=180
another way to do this:
3x is an exterior angle
however it is a supplementary one as well
that means tht
3x+90=180
3x=90
x=30
you get the same answer either way
HOPE THIS HELPS!
6K2 - 10k + 50
How to factor
Answer:
there are no real solutions
Step-by-step explanation:
The discriminant is (-10)² - 4*6*50 is below zero, hence there are no solutions.
Is 7/8x proportional or non proportional
Answer: it is proportional
Step-by-step explanation:
This is my answer because 7/8x can be written in the form y=mx+b. What does this mean?
Well, y=mx+b is slope intercept form, where m is the slope and b is the y intercept , or where the line first crosses the y axis. you can write 7/8x in slope intercept form as:
y= 7/8x+0
Also, you can see that the y intercept is 0, which means the line passes through the origin, or the point 0,0 on the coordinate plane. Therefore it must be proportional because every line that passes through 0,0 (the "origin") is proportional.
I think the other person is wrong..he/she didnt explain their reasoning..
What are two different ways of
factoring -5x - 15? Select all
that apply.
Two possible factorizations for the given sum are:
-5x - 15 = 1*(5x + 15)
-5x - 15 = 5*(-x - 3)
How to factorize an expression?
For a given sum like the one we have:
a + b
A factorization is something like:
a + b = k*(j + l), where k is a common factor between a and b.
In this case, our sum is: -5x - 15
One possible factorization is if we take the negative sign as the common factor we get:
-5x - 15 = 1*(5x + 15)
Another possible factorization is if we take 5 as the common factor:
-5x - 15 = 5*(-x - 3)
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Write two expressions where the solution is 30
Answer:
(15+0)2
Step-by-step explanation:
Here is a diagram and its corresponding equation. Find the solution to the equation.
Answer: The answer would be x=5/3
Step-by-step explanation:
First you would subtract 11 from both sides, cancelling out the 11 on the left while making 21-11=10. Your equation at this point would be 6x=10. Now you would divide by 6 on both sides making the answer x=5/3.
The value of x is 5/3.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is an equation, 6x+11 = 21
Solving for x,
6x+11 = 21
6x = 10
x = 5/3
Hence, the value of x is 5/3.
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what is the value for x
someone please help :)
Yo sup??
in the given figure
9y-3=69
9y=72
y=8
now by angle sum property
9y-3+69+5x+2=180
5x=40
x=8
Hope this helps
Answer: [tex]x=8[/tex]
Step-by-step explanation:
So seeing the equation
[tex](9y -3)[/tex] [tex]y=8[/tex] [tex](9(8)-3) =69[/tex]
therefore, 69 +69 =138
and then that only means the secound equation has to equal 42 because all angles has to equal to 180 degrees, therefore:...
[tex](5x +2)=x=8[/tex] [tex](5(8)+2)=42[/tex]
Hope this helps please give brainliest!
An ipad is worth R1200, excluding 15% VAT. What is the selling price of the ipad including VAT
Answer:
R1,380
Step-by-step explanation:
The price of the iPad without VAT is R1200
We calculate 15% to get;
[tex] = \frac{15}{100} \times 1200[/tex]
[tex] = 180[/tex]
Now the selling price of the iPad including VAT
[tex]1200 + 180[/tex]
[tex] = 1380[/tex]
Therefore, the selling price of the ipad including VAT is R1380
To find the selling price of the iPad including 15% VAT, calculate 15% of R1200, which is R180, and add it to the base price, leading to a total of R1380.
The selling price of an iPad including VAT can be calculated by first determining what 15% of the base price is, and then adding it to the base price. The base price is R1200.
To calculate 15% VAT:
Convert 15% to a decimal by dividing by 100: 15% / 100 = 0.15.
Multiply the base price by this decimal to get the VAT amount: R1200 imes 0.15 = R180.
Add the VAT to the base price to find the total selling price: R1200 + R180 = R1380.
Therefore, including 15% VAT, the selling price of the iPad is R1380.
Directions: Consider a 2-kg bowling ball sits on top of a building that is 40 meters tall. It falls to the ground. Think about the amounts of potential and kinetic energy the bowling ball has:
What is the kinetic energy of the ball as it is half way through the fall?
Answer:
392 Joules
Step-by-step explanation:
8x-4y=16 8x+4y=16 What does x= what does y=
Answer:
x = 2 y=0
Step-by-step explanation:
We can solve using elimination method
8x - 4y = 16 __________(1)
8x + 4y =16 ___________(2)
Subtract equation (2) from equation (1)
-8y = 0
Divide both-side of the equation by -8
-8y/-8 = 0/-8
y = 0
Substitute y=0 into equation (1)
8x - 4y = 16
8x - 4(0) = 16
8x = 16
Divide both-side of the equation by 8
8x/8 = 16/8
(On the left-hand side of the equation, 8 at the numerator will cancel-out 8 at the denominator leaving us with just x while on the right-hand side of the equation 16 will be divided by 8)
x = 16/8
x = 2
Therefore x = 2 and y=0
Zoe visits a departmental store to pick a can of salted mixed nuts. A 15.25 oz can of
mixed nuts is priced at $7.93 and the offer on a 25 oz can is $11.75. Assist Zoe pick up
the better deal.
Answer:15.25oz can
Step-by-step explanation:
Question 40 and it about adding and subtracting polynomials
Answer:
39x-7
Step-by-step explanation:
The perimeter is all the sides added together so
9x + 8x - 2 + 5x + 1 + 17x - 6
Since you can't solve it you just want to simplify the equation, add the like terms together
9x+8x+5x+17x = 39x
-2+1-6 = -7
Your equation is 39x-7
A cone ___ has a square base
never
always
sometimes
Answer:
Never
Step-by-step explanation:
Cuz cone has a round base
Answer:
never - a cone has a circular base
Step-by-step explanation:
Earn $23
Spend $2.46 and $$7.96
Save $10
Share ?
Answer:
12.58
Step-by-step explanation:
Answer:
3.42
Step-by-step explanation:
OWN
23-20.42=3.42
GET RID OF
2.46+7.96=10.42
+10(save)
20.42