Answer:
x = ±11
Step-by-step explanation:
x^2 = 121
Take the square root of each side
sqrt(x^2) = sqrt(121)
x = ±11
Calculate the average rate of change of the function f(x) = 3x2 over the interval 1 ≤ x ≤ 5.
Answer:
18
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ 1, 5 ]
f(b) = f(5) = 3 × 5² = 75
f(a) = f(1) = 3 × 1² = 3, hence
average rate of change = [tex]\frac{75-3}{5-1}[/tex] = [tex]\frac{72}{4}[/tex] = 18
Answer:18
Step-by-step explanation:
here [ a, b ] = [ 1, 5 ]
f(b) = f(5) = 3 × 5² = 75
f(a) = f(1) = 3 × 1² = 3, hence
average rate of change = = = 18
What is the value of x?
x=______units
Answer:
x = 12 unitsStep-by-step explanation:
ΔQTR and ΔRTS are similar (AAA). Therefore the corresponding sides are in proportion:
[tex]\dfrac{RT}{TS}=\dfrac{TQ}{RT}[/tex]
We have
[tex]RT=x,\ TS=9,\ TQ=16[/tex]
Substitute:
[tex]\dfrac{x}{9}=\dfrac{16}{x}[/tex] cross multiply
[tex]x^2=(9)(16)\\\\x^2=144\to x=\sqrt{144}\\\\x=12[/tex]
NEED HELP ASAP, 40 POINTS THANKS
Given: Circle k(O), EPSK trapezoid,
KE = OS = 8
Find: Perimeter and the angles of EPSK
Answer:
If KE = OS then we can deduce that the trapezoid is constructed of 3 equilateral triangles and thus we can easily work out the angles.
OSK = 60
SKE = 120
KEP = 120
EPO = 60
We can also easily work out the perimeter since we can deduce that PE = SK = KE and thus the perimeter is 5 * 8 = 40
The measure of ∠S, ∠K, ∠E, and ∠P is 60°, 120°, 120°, and 60°, respectively. While the perimeter of EPSK is 40 units.
What is a Trapezoid?A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
Given KE=OS=8, but OS is the radius of the circle, therefore, it can be written as,
OS = OP = KE = OK = OE = radius of the circle = 8 units.
Since in ΔOEK all sides are equal it is an equilateral triangle therefore, the measure of the angle ∠EOK is 60°.
As the measure of the angle, ∠EOK is 60°, the measure of the angle, ∠KOS and ∠EOP will be 60° each.
Also, in ΔSOK and ΔPOE, the sides OS = OP = KE = OK = OE are equal, they are equilateral triangles as well.
Therefore, the measure of ∠KSO and ∠EPO will be 60° each.
The angles at the end of the non-parallel sides of a trapezium are supplementary. Therefore, we can write,
∠KSO + ∠SKE= 180°
∠SKE = 120°
Similarly, the measure of the ∠PEK is 120°.
Further, it is known that the measure of the sides OS=OP=PE=EK=KS = 8 units, therefore, the perimeter of the trapezium is,
Perimeter = OS + OP + PE + EK + KS = 8+8+8+8+8 = 40 units.
Hence, the measure of ∠S, ∠K, ∠E, and ∠P is 60°, 120°, 120°, and 60°, respectively. While the perimeter of EPSK is 40 units.
Learn more about Trapezoid:
https://brainly.com/question/8643562
#SPJ2
Which fraction goes in the blank to make the comparison true?
Circle the letter of the correct answer
5/8<_________. A:5/8 B:4/8 C:6/8 or D:1/8
Blake chose A as the correct answer. How did he get that answer?
C is the correct answer. Good luck!
What catapulted object hit the ground first?
Catapult A:
h(x)= -16x^2+64x+17
Catapult B:
time- 0,0.5,1.0,1.5,2.0,2.5,3.0,3.5
height- 28,48,60,64,60,48,28,0
Answers:
Object from Catapult B
They reached the ground at the same time
Object from catapult A
It went up but then never came down
Answer:
Object from Catapult B
Step-by-step explanation:
The question is on time of flight in falling objects
Given catapult A: h(x)= -16x^2+64x+17, find the height the object will reach at time 2.0
substitute value x=2 in h(x)= -16x^2+64x+17;
h(2)= -16 × (2)² +64 ×2 +17
h(2) = -16×4 + 145
h(2)= 81
However with catapult B at t=2.0 the height reached will be 60
Solution
Catapult A object will attain h=81, when t=2.0
Catapult B object will attain h=60, when t=2.0
Thus Object from Catapult B will hit the ground first because it covered a lesser distance compared to the object from catapult A
A dairy needs 204 gallons of milk containing 5% butterfat. How many gallons each of milk containing 6% butterfat and milk containing 3% butterfat must be used to obtain the desired 204 gallons?
To achieve 204 gallons of 5% butterfat milk, one would need 136 gallons of 6% butterfat milk and 68 gallons of 3% butterfat milk by solving a system of linear equations.
How to Mix Butterfat Percentages for Milk
To solve the problem of mixing two different butterfat percentages of milk to achieve a certain amount of milk with a desired fat content, we will use a system of equations.
Let x represent the gallons of 6% butterfat milk, and y represent the gallons of 3% butterfat milk.
To achieve 204 gallons of 5% butterfat milk, we have the following equations:
Equation 1: x + y = 204 (total gallons of milk)
Equation 2: 0.06x + 0.03y = 0.05(204) (total butterfat content)
Solving these equations simultaneously, we find:
From equation 1, we can express y as y = 204 - x.
Substituting this into equation 2 gives us 0.06x + 0.03(204 - x) = 10.2.
Simplifying this, we get 0.06x + 6.12 - 0.03x = 10.2, which leads to 0.03x = 4.08.
Hence, x = 136 gallons of 6% butterfat milk and y = 68 gallons of 3% butterfat milk.
the train traveled at an average speed of 48 miles per hour for the first 2 hours and at 60 miles an hour for the next hours. What was the train's average speed for the 6-hour trip? ( Average speed equals total miles divided by total time.)
Answer: 56 mph
Step-by-step explanation:
48 miles x 2 hours = 96 miles
60 miles x 4 hours = 240 miles
240 + 96 = 360 total miles
360 / 6 (hours) = 56 mph
if f(x) = x-6 and g(x)= 1/2x (x+3), find g(x) * f(x)
Answer:
Final answer is [tex]g\left(x\right)\cdot f\left(x\right)=\frac{\left(x-6\right)}{2x\left(x+3\right)}[/tex].
Step-by-step explanation:
given functions are [tex]f(x)=x-6[/tex] and [tex]g\left(x\right)=\frac{1}{2x\left(x+3\right)}[/tex].
Now we need to find about what is the value of [tex]g\left(x\right)*f\left(x\right)[/tex].
[tex]g\left(x\right)*f\left(x\right)[/tex] simply means we need to multiply the value of [tex]f(x)=x-6[/tex] and [tex]g\left(x\right)=\frac{1}{2x\left(x+3\right)}[/tex].
[tex]g\left(x\right)\cdot f\left(x\right)=\frac{1}{2x\left(x+3\right)}\cdot\left(x-6\right)[/tex]
[tex]g\left(x\right)\cdot f\left(x\right)=\frac{\left(x-6\right)}{2x\left(x+3\right)}[/tex]
Hence final answer is [tex]g\left(x\right)\cdot f\left(x\right)=\frac{\left(x-6\right)}{2x\left(x+3\right)}[/tex].
Which is the graph of y=[x]-2
the last one on the right
Please help it’s 10 points
Answer:
2 4/20, which you can simplify as 2 1/5
Hope this helps if u can (thanks and brainliest) please. Have a good day!! Ask any questions if u need to!!
26. Pete drives 150 meters in 18 seconds. What is his speed in meters per second?
a. 8 m/s
b. 8.3 m/s
c. 8.3 m/s north
d. none of the above
All you have to do is divide 150 by 18 and that will get you how many meters Pete drives per second
150 ÷ 18
8.3333333333333333333
so...
8.3 m/s (B)
Hope this helped!
~Just a girl in love with Shawn Mendes
Speed is defined as quotient of distance and time.
[tex]
s=\frac{d}{t}=\frac{150}{18}=8.33\dots
[/tex]
Speed is a scalar value therefore we cannot determine its vector. Speed with vector is known as velocity and that is where we specify its vector because velocity is a vector value.
So the answer is 8.3 m/s.
Hope this helps.
r3t40
given the parent function f(x)=x^2 describe the graph of y=(x-5)^2-2
Step-by-step explanation:
Shift to the right 5 units and down 2 units.
what does 5q + 5q equal
Answer:
10q
Step-by-step explanation:
Allison pays all her bills using her bank's online bill pay. This is considered to be what type of electronic banking service?
Answer:
Transactional service
Step-by-step explanation:
If Allison pays all her bills using her bank's online bill pay, it will be considered as transactional service which is a type of electronic banking service.
A transaction involves paying a supplier for its services provided or any goods delivered.
Here the services used will include electricity, water, internet, gas, etc for which the bills are paid. Therefore, the correct answer is transactional service.
Answer:
Transaction service
Step-by-step explanation:
kim drew the diagram below to find x, the length of the pole holding up the stop sign that is at an angle with the ground as shown.
Answer:
sin 40/x =sin 60/12
Step-by-step explanation:
The question is on law of sines
Given a triangle with sides a, b, c and angles A, B, C respectively, the sine law states that; a/sin A = b/sin B = c/sin C
In the question x=a, b=12 feet, A=40° , B=60° and C=80°
Finding value of x;
x/sin 40° = 12/sin 60°
x sin 60° =12 sin 40°
x=12 sin 40 / sin 60
x=29.33 ft
Answer:
The length of the pole is 9.90 feet.
Step-by-step explanation:
From the figure, it is given that x is the length of the pole and the pole casts a shadow when the sun is at 40 degree angle.
Thus, using the sine law, we have
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
Substituting the given values, we get
[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}=\frac{c}{sin80^{\circ}}[/tex]
Taking the first two equalities, we have
[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}[/tex]
[tex]x=\frac{12sin40^{\circ}}{sin60^{\circ}}[/tex]
[tex]x=\frac{12{\times}0.642}{0.866}[/tex]
[tex]x=8.90 feet[/tex]
Therefore, the length of the pole is 9.90 feet.
solve the equation 3/2 + b = 7/4 what's b?
For this case we must find the value of "b" of the following equation:
[tex]\frac {3} {2} + b = \frac {7} {4}[/tex]
Then, we subtract [tex]\frac {3} {2}[/tex] from both sides of the equation:
[tex]\frac {3} {2} - \frac {3} {2} + b = \frac {7} {4} - \frac {3} {2}\\b = \frac {7} {4} - \frac {3} {2}\\b = \frac {14-12} {8}\\b = \frac {2} {8}\\b=\frac{1}{4}[/tex]
Answer:
[tex]b = \frac {1} {4}[/tex]
Answer:
The answer is 1/4.
For the last 10 years, Megan has made regular semiannual payments of $1,624.13 into an account paying 1.5% interest, compounded semiannually. If, at the end of the 10 year period, Megan stops making deposits, transfers the balance to an account paying 2.3% interest compounded monthly, and withdraws a monthly salary for 5 years from the new account, determine the amount that she will receive per month. Round to the nearest cent.
a.
$616.39
b.
$615.21
c.
$39,079.25
d.
$39,154.16
Answer:
the answer is A.616.39
Step-by-step explanation:
Megan can withdraw $615.21 per month for 5 years from the new account.
Option B is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To solve this problem, we need to use the formula for the future value of an annuity:
[tex]FV = P [(1 + r/n)^{n\times t} - 1]/(r/n)[/tex]
where:
P = payment per period
r = interest rate per period
n = number of compounding periods per year
t = number of years
FV = future value of the annuity
First, we can calculate the future value of Megan's semiannual payments after 10 years:
P = $1,624.13
r = 1.5%/2 = 0.0075 (semiannual interest rate)
n = 2 (semiannual compounding periods)
t = 10 years
So,
[tex]FV = 1,624.13 \times[(1 + 0.0075/2)^{2\times10} - 1]/(0.0075/2)[/tex]
= $21,070.58
Next, we need to calculate the future value of this amount when transferred to the new account:
r = 2.3% / 12 = 0.00191667 (monthly interest rate)
n = 12 (monthly compounding periods)
t = 5 years (60 months)
FV
[tex]= $21,070.58 \times (1 + 0.00191667)^{60}[/tex]
= $24,526.41
Finally, we need to calculate the monthly payment Megan can withdraw for 5 years from this account, assuming the balance is depleted at the end of the 5 years:
P = ?
r = 2.3% / 12 = 0.00191667 (monthly interest rate)
n = 12 (monthly compounding periods)
t = 5 years (60 months)
Using the formula for the present value of an annuity:
[tex]P = FV \times (r/n) / [(1 + r/n)^{n\timest} - 1][/tex]
[tex]= $24,526.41 \times (0.00191667) / [(1 + 0.00191667)^{60} - 1][/tex]
= $615.21
Therefore,
Megan can withdraw $615.21 per month for 5 years from the new account.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ7
Which equation does the graph of the systems of equations solve?
−1/3x + 3 = x − 1
1/3x − 3 = −x + 1
−1/3x + 3 = −x − 1
1/3x + 3 = x − 1
Answer: The correct answer is 1/3x − 3 = −x + 1
Step-by-step explanation:
add 3 to both sides
simplify
add x to both sides
simplify
multiply both sides by 3
simplify
divide both sides by 2
simplify
The graph of the system of equations solves the equation -1/3x + 3 = x - 1.
Explanation:The first step in solving a system of equations is to isolate one variable in one of the equations. We can begin by rearranging the first equation -1/3x + 3 = x - 1 to isolate x. First, multiply both sides of the equation by 3 to get rid of the fraction: -x + 9 = 3x - 3. Then, add x to both sides to bring all the x terms to one side: 9 = 4x - 3. Finally, add 3 to both sides to solve for x: 12 = 4x. Dividing both sides by 4 gives us x = 3.
Substitute this value of x into either of the original equations to solve for y. Let's use the second equation: (1/3)(3) - 3 = -3 + 1. Simplifying this equation, we get 1 - 3 = -2. This tells us that y = -2.
Therefore, the solution to the system of equations is x = 3 and y = -2, and it satisfies the equation -1/3x + 3 = x - 1.
Learn more about system of equations here:https://brainly.com/question/32829907
#SPJ2
what is the slope of the line by the equations below? y-9=15 (x-5)
To find the slope, you should rearrange the equation into slope-intercept form, ie. y = mx + c, where m is the gradient.
y - 9 = 15(x - 5)
y = 15(x - 5) + 9 (Add 9 to each side)
y = 15x - 15*5 + 9 (Expand 15(x - 5))
y = 15x - 75 + 9
y = 15x - 66
Therefor, the slope of the equation is 15.
Answer:
Use the slope-intercept form
y
=
m
x
+
b
to find the slope
m
.
m
=
15
Step-by-step explanation:
Cuz i know all that
what is the number in scientific notation? 0.000013
Answer:
1.3 x 10^-5
Step-by-step explanation:
To convert 0.000013 to scientific notation, the decimal point is moved five places to the right, resulting in 1.3 × 10⁻⁵.
To express the number 0.000013 in scientific notation, follow these steps:
Identify the first non-zero digit in the number, which is 1 in this case.Move the decimal point to the right of this first non-zero digit. You need to move it 5 places to the right so the number becomes 1.3.Count the number of places the decimal was moved. Since it was moved 5 places to the right, this will be a negative exponent. So, 0.000013 becomes 1.3 × 10⁻⁵.Therefore, the scientific notation for 0.000013 is 1.3 × 10⁻⁵. This notation is particularly useful for representing very small numbers in a compact and readable form.
Which of the following are measurements for triangles that are similar to a triangle with sides measuring 6, 8, and 12? Check all that apply
A. 3, 4, and 6
B. 18, 24, and 36
C. 2, 3, and 4
D. 4.8, 6.4, 9.6
E. 14.4, 20.8, and 36
you can choose more than one answer
Answer:
A, B, D
Step-by-step explanation:
Use the LCM to help...
Can you use Pythagorean Theorem to find the missing side? Why or why not?
No. You cannot use the Pythagorean theorem to find the missing side, because you can only use The Pythagorean theorem when you are dealing with a right triangle.
Solve
-2x+8=14
3
-11
-3
11
Answer:
-3
Step-by-step explanation:
-2x+8=14
Subtract 8 from each side
-2x+8-8=14-8
-2x = 6
Divide by -2
-2x/-2 = 6/-2
x = -3
-2x + 8 = 14
Step 1: Bring 8 to the right side of the equation. To do this subtract 8 to both sides (this is the opposite of addition and will cancel 8 from the left side)
-2x + (8 - 8) = 14 - 8
-2x + 0 = 6
-2x = 6
Step 2: Isolate x by dividing -2 to both sides (division is the opposite of multiplication and will cancel -2 from the left side)
-2x/-2 = 6/-2
x = -3
Check:
Plug -3 where you see x and solve
-2(-3) + 8 = 14
6 + 8 = 14
14 = 14...............................Correct!
Hope this helped!
Please answer right away
For this case we have that by definition of trigonometric relations that, the sine of an angle is equal to the opposite leg to the angle on the hypotenuse. So:
[tex]Sin (36) = \frac {5} {x}[/tex]
Clearing x:
[tex]x = \frac {5} {sin (36)}\\x =\frac {5} {0.58778525}\\x = 8.517887564 [/tex]
Rounding off we have to:
[tex]x = 8.51[/tex]
Answer:
Option D
A surveyor starts at the southeast corner of a lot and
charts the following displacements: A = 600 m, N;
B = 400 m, W; C = 200 m, S; and D = 100 m, E.
What is the net displacement from the starting point?
Find the difference vertically( North and South) and the difference horizontally ( East and West)
Then use the Pythagorean Theorem.
600 North - 200 South = 400 m
400 West - 100 East = 300 m
Now using the Pythagorean Theorem;
400^2 + 300^2 = total displacement^2
Total displacement^2 = 160,000 + 90,000
Total displacement^2 = 250,000
Total displacement = √250,000
Total displacement = 500 m
Help! Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value. F(x)=-4(x-6)^2+3.
Answer:
maximum value of the given function is = 3
Step-by-step explanation:
Given function is [tex]F(x)=-4(x-6)^2+3[/tex].
Now we need to find about what is the maximum value of the given function [tex]F(x)=-4(x-6)^2+3[/tex] and explain the method about how did you find the maximum value.
Given function [tex]F(x)=-4(x-6)^2+3[/tex] looks similar to the quadratic function of the form [tex]f(x)=a(x-h)^2+k[/tex].
Comparing both we get: h=6, k=3
We know that maximum value occurs at the vertex where maximum value is given by "k"
Hence maximum value of the given function is = 3
Marie is riding her bike at 15 miles per hour. What is her rate of speed in feet per second?
5.9
1.5
88
22
Answer:
22
Step-by-step explanation:
We know that 1 miles = 5280 ft and 1 hour = 3600 seconds
15 miles 5280 ft 1 hour
--------------- * ------------- * -------------- =
1 hour 1 mile 3600 second
The units cancel leaving us ft/s
22 ft/s
Working alone, Pablo can put up a tent in 12 minutes. His mom can put it up by herself in 4 minutes. How many minutes would they take to put up the tent working together?
Answer:
3 minutes
Step-by-step explanation:
we know that
Pablo can put up a tent in 12 minutes
so
100% of the work Pablo can do in -------> 12 minutes
In one minute Pablo can do (100/12)%
His mom can put it up by herself in 4 minutes
so
100% of the work his Mon can do in -------> 4 minutes
In one minute his Mon can do (100/4)%
therefore
Pablo and his Mon together in one minute can do
(100/12)%+(100/4)%=(400/12)%
By proportion find how many minutes would they take to put up the tent working together
1/(400/12)%=x/100%
x=12*100/400=3 minutes
The table of values represents the function g(x) and the graph shows the function f(x).
The statements about the functions that are true include:
A. f(x) and g(x) intersect at exactly two points.
B. The x-intercepts of f(x) are common to g(x).
In Mathematics and Geometry, the x-intercept of any function is the point at which the graph of a function crosses or touches the x-axis and the y-value or value of "y" is equal to zero (0).
By critically observing the table of values and graph shown in the image attached above, we can reasonably and logically deduce the following x-intercepts for both f(x) and g(x):
x-intercepts of f(x) = (-1, 0) and (1, 0).
x-intercepts of g(x) = (-1, 0) and (1, 0).
Therefore, the x-intercepts of f(x) are common to g(x), which means they intersect at exactly two points.
For the minimum value of f(x) and g(x), we have;
Minimum value of f(x) = -1
Minimum value of g(x) = -3
Therefore, the minimum value of f(x) is greater than the minimum value of g(x).
For the y-intercept of f(x) and g(x), we have;
y-intercept of f(x) = (0, -1).
x-intercepts of g(x) = (0, 1).
In conclusion, we can logically deduce that f(x) and g(x) have different y-intercept.
What is the vertex of y=2x^2
Use the vertex form, y=a(x−h)2+k y = a ( x - h ) 2 + k , to determine the values of a a , h h , and k k . Since the value of a a is positive, the parabola opens up. Find p p , the distance from the vertex to the focus. Find the distance from the vertex to a focus of the parabola by using the following formula.
I really hope this answer helps you out! It makes my day helping people like you and giving back to the community that has helped me through school! If you could do me a favor, if this helped you and this is the very best answer and you understand that all of my answers are legit and top notch. Please mark as brainliest! Thanks and have a awesome day!
Answer:
Step-by-step explanation:
It is a first cousin to y=x^2. The only difference is the 2 in front of the x^2 which narrows x^2.
The vertex is at (0,0)