[tex]\text{Let,}\\\\~~~~~~~a^x =b^y = c^z = k\\\\\text{So,}\\ \\a = k^{\dfrac 1x}\\\\b=k^{\tfrac 1y}\\\\\ c = k^{\tfrac1z}\\\\\text{Now, given that,}\\\\~~~~~~~~~b^2 = ac\\\\\implies \left( k^\tfrac 1y \right)^2 = k^{\tfrac 1x} \cdot k^{\tfrac 1z}\\\\\implies k^{\tfrac 2y} = k^{\tfrac 1x + \tfrac 1z} ~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies \dfrac 2y = \dfrac 1x + \dfrac 1z\\\\\implies \dfrac 1x + \dfrac 1z = \dfrac 2y \\\\\text{Proved.}[/tex]
Are the equations 6x-6=3x and x-1=3x equivalent?
Answer:
No, they aren't the same (equivalent).
Step-by-step explanation:
First, solve for both equations:
Equation #1: 6x-6=3x
Simplifying
6x + -6 = 3x
Reorder the terms:
-6 + 6x = 3x
Solving
-6 + 6x = 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
-6 + 6x + -3x = 3x + -3x
Combine like terms: 6x + -3x = 3x
-6 + 3x = 3x + -3x
Combine like terms: 3x + -3x = 0
-6 + 3x = 0
Add '6' to each side of the equation.
-6 + 6 + 3x = 0 + 6
Combine like terms: -6 + 6 = 0
0 + 3x = 0 + 6
3x = 0 + 6
Combine like terms: 0 + 6 = 6
3x = 6
Divide each side by '3'.
x = 2
Simplifying
x = 2Equation #2: x-1=3x
Simplifying
x + -1 = 3x
Reorder the terms:
-1 + x = 3x
Solving
-1 + x = 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
-1 + x + -3x = 3x + -3x
Combine like terms: x + -3x = -2x
-1 + -2x = 3x + -3x
Combine like terms: 3x + -3x = 0
-1 + -2x = 0
Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1
Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1
Combine like terms: 0 + 1 = 1
-2x = 1
Divide each side by '-2'.
x = -0.5
Simplifying
x = -0.5answer please image is below 35 points btw
Keith is working two jobs this summer as a lifeguard and a tutor. he earns $16 an hour as a lifeguard and $18 an hour as a tutor. he wants to earn at least $250 to put towards his car. what is one possible combination of hours he can work at each job to earn at least $250?
Answer:
He could work 10 hours as a lifeguard, and 5 hours as a tutor
Step-by-step explanation:
If he makes $16 an hour as a lifeguard
and $18 an hour as a tutor,
He could work 10 times $16, to make $160 for 10 hours.
Now we subtract this from $250, this makes $90.
We know need to find out how many times 18 goes into 90, 5 times.
So we know that he could work 10 hours as a lifeguard and 5 hours as a tutor.
I hope this is right.
I hope this helps too, have a nice day!
Pleaseeee!
I need help evaluating this:
Tan 2 theta-(1-tan^ 2 )=?
Answer:
[tex]\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]
Key:
• [tex]-\left(a-b\right)=-a+b[/tex]
Step-by-step explanation:
[tex]\tan \left(2\theta\right)-\left(1-\tan ^2\left(\theta\right)\right)[/tex]
[tex]-\left(1-\tan ^2\left(\theta\right)\right)=-1+\tan ^2\left(\theta\right)[/tex]
[tex]=\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]
a water tap fills a tank within 4 hours, at the bottom of the tank
there is a hole for empty. the tank takes one hour to be empty. If the tap and the hole
are turning on together, the tank is fully filled. how long will the tank take to be completely
empty?
(70 min, 80 min, 90 min, 100 min)
Let V be the volume of the tank. The tap fills the tank at a rate of V/(4 hours), or V/4 per hour. The hole empties the tank at a rate of V per hour. If both the tap and hole work together, the net rate of water flow is V/4 - V or -3V/4 per hour.
Starting with a full tank, the volume v of water at time t is given by the function
v(t) = V + (-3V/4) t
Solve v(t) = 0 to find the time it takes to empty:
V - 3V/4 t = 0
V = 3V/4 t
t = V / (3V/4) = 4/3
So it takes 4/3 hours = 80 minutes to empty a full tank.
The regular price of a tennis racquet is $79.99 and the sale price is $64.99. Find the percent of discount to the nearest whole percent.
Step-by-step explanation:
$79.99 - $64.99 = $15
(79.99 - 64.99)/|79.99| =15
15/79.99 =
15 ÷ 79.99 =
15 ÷ 79.99 × 100/100 =
(15 × 100 ÷ 79.99)/100 =
(1,500 ÷ 79.99)/100
≈18.752344043005/100 =
18.752344043005% ≈18.75%;
The figure below shows a line graph and two shaded triangles that are similar:
Which statement about the slope of the line is true? (1 point)
It is fraction negative 1 over 3 throughout the line.
It is −3 throughout the line.
The slope from point O to point A is one-third times the slope of the line from point A to point B.
The slope from point O to point A is three times the slope of the line from point A to point B.
Answer: A
Step-by-step explanation: took the test, got it right.
The points E(- 4, 6), F(- 6, - 2), G(2, - 4) , and H(4, 4) form quadrilateral EFGH. Plot the points then click the "Graph Quadrilateral " button.
The slope of EF, FG, GH, and HE is 4, -1/4, 4, and -1/4 respectively. And the length of sides EF, FG, GH, and HE will be √68, √68, √68, and √68 units respectively.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The points E(-4, 6), F(-6, -2), G(2, -4) , and H(4, 4) form quadrilateral EFGH.
Then the slopes are calculated below.
Slope of EF = (6 + 2)/(-4 + 6)
Slope of EF = 8/2
Slope of EF = 4
Slope of FG = (-4 + 2)/(2 + 6)
Slope of FG = -2/8
Slope of FG = -1/4
Slope of GH = (4 + 4)/(4 - 2)
Slope of GH = 8/2
Slope of GH = 4
Slope of HE = (6 - 4)/(-4 - 4)
Slope of HE = -2/8
Slope of HE = -1/4
Then the distance between the point will be
EF² = (-6 + 4)² + (-2 - 6)²
EF² = (-2)² + (-8)²
EF² = 4 + 64
EF = √68
FG² = (2 + 6)² + (-4 + 2)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
GH² = (4 - 2)² + (4 + 4)²
GH² = (2)² + (8)²
GH² = 4 + 64
GH = √68
FG² = (4 + 4)² + (4 - 6)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
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A square notepad has sides that are 10 centimeters long. What is the notepad's area?
Answer:
100cm²
Step-by-step explanation:
The notepad is square.
The area of a square = length X width.
All the sides of a square are the same length.
Therefore, the area of the notepad = 10 X 10 which equals 100.
Don't forget the units!
The units for area is cm².
The units for volume is cm³.
This is area so your answer is 100cm².
Hope this helped, have a nice day!
1
Use f(x) = ½ x and ƒ˜¹(x) = 2x to solve the problems.
f(2)=
f¹1)=[
f(f(2)) =
Answer:
f(2) = 1
(1) = 2
(f(2)) = 2
Step-by-step explanation:
f(x) = x
(x) = 2x
f(2) = (2)
f(2) = 1
(1) = 2(1)
(1) = 2
(f(2)) = 2((2))
(f(2)) = 2(1)
(f(2)) = 2
The function's solution is given as follows:
f(1) = 2
f(f(2)) = f(1) = f(1) = 1/2
What is a function?A function is a mathematical formula that illustrates the relationship between the dependent and independent variables.
The independent variable's value and the dependent variable's value both change in the function.
Mathematical expression is defined as the relationship between numerical variables and mathematical operations such as addition, subtraction, multiplication, and division.
For the given function [tex]f(x) = \dfrac{1}{2}x[/tex],
[tex]f(2) =\dfrac{1}{2} (2) = 1[/tex]
For the given function [tex]f^{-1}(x) = 2x[/tex],
[tex]f'(1) = 2(1) = 2[/tex]
Therefore, the solution for the function is [tex]f^{1}(1) = f^{-1}(1) = 2[/tex]
The composition of functions to find f(f(2)):
[tex]f(f(2)) = f(1) = \dfrac{1}{2} (1) = \dfrac{1}{2}[/tex]
Therefore, the solution for the function [tex]f(f(2)) = \dfrac{1}{2}[/tex].
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Factor: 5x2 – 15x – 20.
(a) 5(x-4)(x+1),
(b) -2(x-4)(x+5),
(c) -5(x+4)(x-1),
(d) 5(x+4)(x+1).
Answer:
[tex]a)~5(x-4)(x+1)[/tex]
Step-by-step explanation:
[tex]~~~5x^2 -15x -20\\\\=5(x^2 -3x -4)\\\\=5(x^2 -4x +x -4)\\\\=5\textbf{[}x(x-4) +(x-4)\textbf{]}\\\\=5(x-4)(x+1)[/tex]
Factor completely AND solve for the solutions of the quadratic.
please help... Identify the shape of a cross section of the cone below.
Answer:
The vertical cross-section of a cone is a triangle, and the horizontal cross-section is a circle.
Step-by-step explanation:
Find the measure of angle F if angle D = 88°
Answer:
52
Step-by-step explanation:
Two triangles are similar
m<B = m<E
m<C = m<D
m<A = m<F
now, the sum of interior angles in a triangle is equal to 180
angle B is given as 40 (so angle E is also 40) and angle D is given as 88 to find m<F:
40 + 88 + m<F = 180 add like terms
128 + m<F = 180 subtract 128 from both sides
m<F = 52
The mean of a set of 10 number is 56,
If the mean of the first nine is 55 find the 10th number
Answer:
65
Step-by-step explanation:
10*56=5609*55=495560-495=65=653.3.1. Calculate the new cost per night of the standard and family standard chalets. Round of (4) your answer to the nearest hundred. 3.3.2. Calculate the percentage increase that Pule proposes for the Luxe suite. Use the following formula: Percentage Difference Original 1 x 100% (3) 3.4. Pule decides to run a special on the Family standard chalet. He will charge: R4 000 per night but will decrease the amount by R100 per person occupying the chalet. 3.4.1. Use the information above to complete the table below: Number of 1 2 3 4 5 8 9 10 people(c) 4 000 3 900 Cost per night (R) (n) (3) 3.4.2. Write an equation that shows the relationship between the cost per night C and the number of people staying in the chalet n. (3) 3.4.3. The graph below shows the cost of renting the family standard chalet at the usual rat On the same set of axes, draw the graph that represents renting the chalet at the spe rate. (Remember to include all missing graph elements). (4)
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in math when you do not know the exact number in a calculation.
Given that:
Pules Rs 4000 per night but will decrease the amount by R100 per person occupying the chalet.
Number of People Cost per night
1 4000
2 3900
3 3800
4 3700
5 3600
6 3500
7 3400
8 3300
9 3200
10 3100
let C be cost per night and n be the number of people of staying in chalet.
equation: C= 4000-100(n-1)
for n=1: C= 4000- 0=4000
n=2, C= 4000-100(1)= 3900
The graph is attached below:
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the amount (a) that principal (p) will be worth after t years at interest rate (r) compounded annually is
a = p(1 + r)^t
suppose $6,000 is invested at 5.5% and yields a total of $7,255. how many was it invested
The number of years the money was invested with annual compounding is 3.45 years.
How many years was it invested?When an amount earn interest compounded annually, it means that both the amount invested and the interest earned increases in value once a year.
Number of years = (In FV / PV) / r
Where:
FV = future valuePV = present valuer = interest rate(In 7255 / 6000) 0.055 = 3.45 years
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Convert 5.6 times 10 to power of 4 to ordinary form
The graphs of f(x) = -2x and g(x)=()* are shown.
What are the solutions to the equation -2x = ()*?
Select each correct answer.
0-2
0 -1
02
04
-10-8-6-4
10
8
6-
72
-4
6
in
8
10+
2 4 6 8 10
The solutions to the equation -2x = 2^x are (1,2) and (2,4)
How to determine the solutions?The attached graph represents the missing part of the question
The equations are given as:
f(x) = -2x
g(x) = 2^x
The solution to -2x = 2^x is the points where the graphs of f(x) and g(x) intersect
From the attached graph, the points of intersection are:
(1,2) and (2,4)
Hence, the solutions to the equation -2x = 2^x are (1,2) and (2,4)
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help me on this question. If l || m, m7 = 2x and m2 = x, then what is the measure of angle 2?
Answer:
i dont know bc its not the complete expression
Step-by-step explanation:
Patty had four times as many quarters as nickels. She had $12.60 in all. How many nickels and
she have?
Answer:
Hi,
Step-by-step explanation:
Let say n the number of nickels
4*n the number of quaters.
Let's calculate in cents:
n*5+4*n*25=1260
5n+100n=1260
105*n=1260
n=12 (number of nickels)
4n=48 (number of quaters)
Proof: 12*5+48*25=1260
Answer is equation B
A physical therapist claims that 75% of people lose their balance if they close their eyes while standing on one foot. A gymnast feels that the rate is less than 75%. To test this, she randomly selects 100 people and finds that 80 of them lose their balance while standing on one foot. To determine if these data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%, 150 trials of a simulation are conducted. The gymnast is testing the hypotheses: H0: p = 75% and Ha: p < 75%, where p = the true proportion of people who will lose their balance while standing on one foot and closing their eyes. Based on the results of the simulation, what is the estimate of the P-value of the test? A dotplot. A number line labeled simulated sample percentage of people who lose balance goes from 64 to 88 percent. 64, 3; 66, 3; 67, 4; 68, 8; 69, 5; 70, 7; 71, 8; 72, 11; 73, 15; 74, 12; 75, 11; 76, 8; 77, 18; 78, 10; 79, 10; 80, 5; 81, 4; 82, 2; 83, 2; 84, 1; 85, 2; 87, 1. 0.1133 0.17 0.887 0.92
Answer:
75
Step-by-step explanation:
becAUSE IF YOU TEST IT THATS UR ANSWER
Anyone know the answer?
James is using cement to make a new sidewalk and new steps.
He will make a new rectangular sidewalk that is 8 feet long, 4 feet wide, and 0.25 foot thick.
What is the volume, in cubic feet, of the cement used to make the sidewalk? Show or explain all of the steps you used to determine your answer.
Enter answer, including explanation, here
The volume, in cubic feet, of the cement used to make the sidewalk is 8 cu.ft.
What is a Cuboid ?A cuboid is a three dimensional figure with six rectangular faces .
The volume of the cuboid is given by
V = length * breadth * height
It is given in the question that
a new rectangular sidewalk that is 8 feet long, 4 feet wide, and 0.25 foot thick , this will be in the shape of a cuboid
The volume of cement required = 8 * 4 * 0.25
= 8 cu.ft
The volume, in cubic feet, of the cement used to make the sidewalk is 8 cu.ft.
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HELP ME PLEASE!!!
.................................................
Answer:
Step-by-step explanation:
Find each square (x+4)^2
Answer:
[tex]x^{2} +8x+16[/tex]
Step-by-step explanation:
There are 2 ways to find the square of a binomial. You can use FOIL or use a formula. Just remember that the square of a binomial will always be a trinomial.
FOIL
Since we are squaring a binomial we can rewrite the expression as (x+4) * (x+4). FOIL stands for First, Outside, Inside, Last. This explains how to multiply out 2 binomials. This method will give you 4 different terms that can then be combined to find the answer.
First - multiply the first terms of each binomial
x * x = [tex]x^{2}[/tex]Outside - multiply the terms on the outside of both binomials
x * 4 = 4xInside - multiply the terms on the inside of both binomials
4 * x = 4xLast - multiply the last terms of each binomial
4 * 4 = 16Now we can combine these terms to create the new polynomial [tex]x^{2} +4x+4x+16[/tex]. Then, combine like terms for the final answer: [tex]x^{2} +8x+16[/tex].
Shortcut
Another way to square binomials is to use the formula [tex]a^{2} +2ab+b^{2}[/tex], where a is the first term and b is the second term. So, for this formula, the binomial would look like (a+b).
So, we can apply this formula by plugging in x for a and 4 for b.
[tex]x^2+2*4*x+4^2[/tex]Then, multiply the middle term
[tex]x^{2} +8x+4^2[/tex]Finally, square 4
[tex]x^2+8x+16[/tex]This gives us the same final answer as the method above.
Step-by-step explanation:
(x+4)^2
you can also expand it
(x+4)(x+4)
x^2+4x+4x+16
x^2+8x+16
what is an equation for the circle with center 92,40 and radius 7
Answer:
17 i think im like 30 pecent sure
Using the segment addition postulate, which is true?
The complete question is
"Using the segment addition postulate, which is true?
AB + BC = AD
AB + BC = CD
BC + CD = AD
BC + CD = BD"
Using the segment addition postulate, the true option is D; BC + CD = BD.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
We have been given the number line and four points A, B, C, and D on the line with coordinates -6, -1, 2, and 8 respectively.
(a) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = AD = 14 ≠ 8.
So, this option is incorrect.
(b) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = CD = 6 ≠ 8.
So, this option is incorrect.
(c) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = AD = 14 ≠ 9.
So, this option is incorrect.
(d) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = BD = 9.
So, this option is correct.
Hence, the correct option is (d).
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Which polynomial is equal to the sum of polynomials 1 and 2?
Polynomials 1 and 2 are represented below with tiles.
Polynomial 1
X²X²
X²
Polynomial 2
A. 2x²+2x+1
OB. 5x² + 4x+6
OC. 7x² +6x+7
OD. 7x² +6x+5
SUBMIT
Polynomial are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is C.
What is a polynomial?Polynomial are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Example:
x² + 3x + 5
As per the given tile diagram, the first polynomial is,
First polynomial = 5x² + 4x + 6
The second polynomial equal is,
Second polynomial = 2x² + 2x + 1
Now, the sum of the two polynomial can be written as,
Sum = 5x² + 4x + 6 + 2x² + 2x + 1
= 7x² + 6x + 7
Hence, the correct option is C.
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Ninety members of a gym were asked whether or not they use a treadmill when they exercise and whether or not they lift weights when they exercise.
The results of the poll are as follows:
14 members do not use a treadmill or lift weights
31 members use a treadmill but do not lift weights
28 members lift weights but do not use a treadmill
17 members use a treadmill and lift weights
Which two-way table represents the information found in the poll?
The answer is Y
Step-by-step explanation:
You have to compare the numbers with conditions both in Rows and Columns.
3.991 nearest one hundred answer
[tex]\huge\purple{hi!}[/tex]
3.991 nearest one hundred is 3.99
The answer wood be 3.99
Since 1 is closer to 0 you round down and it is 3.99