Step-by-step explanation:
A/B=5/7 , B/C=6/12
Taking B=12×7=84, we get
A=12×5=60, C=7×6=42
Hence,
60:84:42. Answer
If {3,4,5} is the domain of function f:x --> 2x-1, find the range.
Answer:
Range = {5, 7, 9}
Step-by-step explanation:
Range is the set of values that are the results of respective values of x when placed in the function f(x).
[tex] \mathfrak{\blue {\underline{\implies If\: x = 3 }}} [/tex]
f(3) = 2 × 3 - 1
f(3) = 6 - 1
f(3) = 5
[tex] \mathfrak{\blue{\underline{\implies If \:x = 4 }}} [/tex]
f(4) = 2 × 4- 1
f(4) = 8 - 1
f(4) = 7
[tex] \mathfrak{\blue{\underline{\implies If\: x = 5 }}} [/tex]
f(5) = 2× 5 - 1
f(5) = 10 - 1
f(5) = 9
Therefore, the range is the set of all these values :-
Range = {5, 7, 9}
f(x) = x2 What is g(x)?
O A. g(x) = 25x2
O B. g(x) =1/5x2
O C. g(x) = 5x2
O D. g(x) = (5x)2
Answer:
C
Step-by-step explanation:
The graph is 5x^2. Hence the option C is correct
The required function g(x) is 5x² for the given graph, which is the correct option (C).
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The given function is as follows:
f(x) = x²
Substitute the value of x = 1 in the above equation,
f(1) = 1
As per the given graph, we have
g(1) = 5
Now, we can write the proportion as:
f(x)/g(x) = f(1)/g(1)
Substitute the known values in the above proportion, and solve for g(x):
x²/g(x) = 1/5
Cross-multiplying and we get:
g(x) = 5x²
Therefore, the required function g(x) is 5x².
Learn more about the functions here:
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Daniel and Saquon are each saving money. Daniel starts with $50 in his savings account and adds $8 per week. Saquon starts with $65 in his savings account and adds $5 each week.
After four weeks, who has more money in their savings account? Explain how you know.
After how many weeks will Daniel and Saquon have the same amount of money in their savings accounts?
Answer:
Sequon has more money after 4 weeks. It would take 5 weeks for their savings accounts to be equal.Step-by-step explanation:
Daniel
Daniel starts with $50 and each week he adds $8. To find out the amount he has in any given week, the following formula would work:
= 50 + 8x
The x is the number of weeks and is multiplied by 8 because the amount of money he has increase by 8 every week.
After 4 weeks he would have:
= 50 + (8 * 4)
= 50 + 32
= $82
Saquon
Applying the same formula:
= 65 + 5x
After 4 weeks:
= 65 + (5 * 4)
= 65 + 20
= $85
Saquon has more money after 4 weeks.
Number of weeks it would take for both of them to have the same amount.
To find this out, equate both formulas and solve for x.
50 + 8x = 65 + 5x
8x - 5x = 65 - 50
3x = 15
x = 15/3
x = 5 weeks
At 5 weeks they will both have:
50 + 8 * 5 = $90
65 + 5 * 5 = $90
are
equivalent to 192 ounces?
How many pounds
24
pounds.
192 ounces is equivalent to
Answer:
12 lbs
Step-by-step explanation:
There are 16 ounces in a pound
192 ounces * 1 pound / 16 ounces = 12 pounds
Step-by-step explanation:
1 pound = 16 ounces
24 pound = 16 x 24 ounces = 384 ounces
1 ounce = 1/16 pounds
192 ounces = 192/16 pounds = 12 pounds
Two numbers have a difference of 28. If the sum of the squares of the numbers is
392, what are the two numbers?
Answer:
The two numbers are 182 and 210. I hope this will help you.
Kelly is standing in a wavy water and notices the depth of the waves varies in a periodic way that can be modeled by a trigonometric function. She starts a stopwatch to time the waves. After 3.2 seconds, and then again every 3 seconds, the water just touches her knees. Between peaks, the water recedes to her ankles. Kelly's ankles are 11cm off the ocean floor, and her knees are 55 cm off the ocean floor. Find the fomula of the trigonometric function that models the depth D of the water t seconds after Kelly starts the stopwatch. Define the function using radians.
Answer:
A trig wave with average height 0 has the form f(t)=Acos(ωt+ϕ). You could also use the sin - it doesn't matter.
A trig wave with average height b has the form f(t)=b+Acos(ωt+ϕ)
The difference between the max and min heights is 2A. In your problem 2A = 55-12 = 42 so that A = 21.5.
The average wave height is b = 12 + A = 33.5
The time period of the wave is 3, so that its frequency (waves per second) is f = 1/3. Its angular frequency ω (waves per 2π) is 2πf=2π/3.
your wave is now f(t)=33.5+21.5cos(2πt/3+ϕ)
When t = 1.1 the max height is reached so that 55=33.5+21.5cos(2π(1.1)/3+ϕ). Then 1=cos(2π(1.1)/3+ϕ) which in turn means that 2π(1.1)/3+ϕ=0 and solving gives ϕ.
Key Points. One radian is the measure of the central angle of a circle such that the length of the arc is equal to the radius. of the circle. A full revolution of a circle (360∘ ) equals 2π radians 2 π r a d i a n s . This means that 1 radian=180∘π 1 radian = 180 ∘ π
Hope it helps
Graph the following inequality 6x-2y>8
Please help me and show me how to graph it.
Answer:
6x - 2y > 8
First, solve the inequality (Isolate the y-variable & put it in function format):
[tex]6x - 2y > 8\\-2y > 8 - 6x\\(-1)(-2y) > (-1)(8-6x)\\2y < 6x-8\\y < \frac{6x-8}{2} \\y < 3x - 4[/tex]
Second, graph the function y = 3x - 4 on the graph.
It should be linear.Because the inequality is < and not ≤, the values on the line aren't included in the solution, so your line should be dotted, not solid.Third, shade in the area below the line(where y-values are smaller).
Since the inequality is <, that means the solutions are smaller than the solutions of the function 3x - 4.1 point (1) Three times a number minus two times a number* Your answer
Answer:
Three times a number minus two times a number
3x-2x
=x
Please can someone help me with this question?
9514 1404 393
Answer:
C. f^-1(x) = (x +4)^2; x ≥ -4
Step-by-step explanation:
The range of the given function f(x) is -4 ≤ f(x). This will be the domain of the inverse function.
We find the inverse function by solving ...
x = f(y)
x = √y -4
x +4 = √y
(x +4)^2 = y
The inverse function is ...
f^-1(x) = (x +4)^2 . . . for x ≥ -4
Find the value of sin F rounded to the nearest hundredth if necessary
Value of sin F is 0
What is sin x?It is a trigonometric function of an angle . For right triangle, value of sin x (where x is the angle between base and hypotenuse ) will be the ratio of perpendicular to hypotenuse.
According to question ,
sin F = P/H
sin F = 12/13
sin F = 0.92
after rounding of it to nearest hundredth , we can write it as :
sin F = 0
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Ferrero Rocher chocolates are manufactured in the shape of spherical balls, which are
wrapped in foil. The Ferrero Rocher Company introduced the Ferrero collection, which
is a package of 15 chocolates, one layer deep in a 3 chocolate x 5 chocolate orientation.
A single chocolate has a diameter of 3.2 cm.
Answer:
N/A
Step-by-step explanation:
What's the question to the question?
The snack bar at your school has added sushi to its menu. The ingredients for one roll include sushi rice, seaweed sheets, cucumbers, cream cheese, and 2 oz of smoked salmon. One roll can be cut into 9 servings. Write an expression for the amount of salmon needed to make s servings of sushi. How much salmon is needed to make 18 servings? 36 servings? 90 servings? 100 servings?
Answer:
The answer si:
- 16 servings - 6 oz of salmon
- 24 servings - 9 oz of salmon
- 80 servings - 30 oz of salmon
- 100 servings - 37.5 oz of salmon
1 roll is 8 servings and it is also made of 3oz of smoked salmon. That means that 3oz of smoked salmon is needed fo 8 servings.
Now, let's made some proportions:
16 servings:
3 oz is for 8 servings, how much oz is for 16 servings:
3 : 8 = x : 16
x = 3 · 16 ÷ 8 = 6 oz
24 servings:
3 oz is for 8 servings, how much oz is for 24 servings:
3 : 8 = x : 24
x = 3 · 24 ÷ 8 = 9 oz
80 servings:
3 oz is for 8 servings, how much oz is for 80 servings:
3 : 8 = x : 80
x = 3 · 80 ÷ 8 = 30 oz
100 servings:
3 oz is for 8 servings, how much oz is for 100 servings:
3 : 8 = x : 100
x = 3 · 100 ÷ 8 = 37.5 oz
is this righ or not please say me
Answer:
Step-by-step explanation:
It's right
Whats the best definition
of slope
Answer:
The slope of a line is a number that defines the direction + steepness of a linear function. It can be found using the formula rise/run.
Step-by-step explanation:
Not sure how to explain this otherwise but that is what the slope is. ^
Answer:
The slope is the steepness of a line sometimes referred to as "rise over run".
Slope is defined as the ratio of the vertical change between two points.
slope= rise/run
OAmalOHopeO
Given a polynomial f(x), if (x − 6) is a factor, what else must be true?
f(0) = −6
f(0) = 6
f(−6) = 0
f(6) = 0
Answer:
below.
Step-by-step explanation:
f(6) = 0 because (x - 6) ---> (6 - 6) = 0
Solve for b. Round your answer to the nearest whole degree.
5.1
bº
3.6
100
Answer:
b =44
Step-by-step explanation:
We need to use the law of sines to determine b
sin b sin 100
---------------- = ----------------
3.6 5.1
Using cross products
5.1 sin b = 3.6 sin 100
sin b = 3.6 sin 100 / 5.1
Taking the inverse sin of each side
b = arcsin ( 3.6 sin 100 / 5.1)
b = 44.03984209
To the nearest degree
n = 44
Solve log6 + log6 (x-1) = 1
Answer:
[tex]\boxed{\sf x = 7 }[/tex]
Step-by-step explanation:
We are here given a logarithmic equation and we need to solve it out and then find the value of x. The given equation is ,
[tex]\sf\longrightarrow log_6 + log_6 ( x -1) = 1 [/tex]
Here I am assuming that the base of the logarithm is 6 . The equation can be written as ,
[tex]\sf\longrightarrow log_6 1+ log_6 ( x -1) = 1 [/tex]
Recall the property of log as , [tex]\sf log_x a + log_x b = log_x(ab) [/tex] , on using this property we have ,
[tex]\sf\longrightarrow log_6 \{ 1 ( x -1)\} = 1 [/tex]
Simplify ,
[tex]\sf\longrightarrow log_6 ( x -1) = 1 [/tex]
We know that , if [tex]\sf log_a b = c [/tex] then in expotential form it can be expressed as [tex]\sf a^c = b [/tex] . Using this we have ,
[tex]\sf\longrightarrow 6^1 = x - 1[/tex]
Simplify ,
[tex]\sf\longrightarrow 6 = x - 1[/tex]
Add 1 both sides ,
[tex]\sf\longrightarrow x = 6 + 1[/tex]
Therefore ,
[tex]\sf\longrightarrow \boxed{\blue{\sf \quad x = 7\quad }} [/tex]
Hence the value of x is 7 .
Answer:
x=7
Step-by-step explanation:
log6(1) + log6 (x-1) = 1
We know that log (a) * log (b) = log (ab)
log6 (1*(x-1)) = 1
log6 (x-1) = 1
Raising each side to the base of 6
6 ^log6 (x-1) = 6^1
x-1 = 6
Add 1 to each sdie
x-1+1 = 6+1
x=7
If you car was going 60mph and you increased your speed by 5mph every minute for seven consecutive minutes how fast would you be going at the end
Ming drew the model below to represent the equation 24 + 12 = blank x (8 + 4). A model with 3 rows of 8 and 3 rows of 4. What is the missing value in Ming's equation?
Given:
The equation is:
[tex]24+12=\_\_\times (8+4)[/tex]
A model with 3 rows of 8 and 3 rows of 4.
To find:
The missing value in Ming's equation.
Solution:
We have,
[tex]24+12=\_\_\times (8+4)[/tex] ...(i)
A model with 3 rows of 8 and 3 rows of 4. Using this information, we get
[tex]24+12=3\times 8+3\times 4[/tex]
Taking out the common factor 3, we get
[tex]24+12=3\times (8+4)[/tex] ...(ii)
On comparing (i) and (ii), we get the missing value is 3.
Therefore, the missing value in Ming's equation is 3.
Answer:
The answer is A: 3
Step-by-step explanation:
please help in the math
[tex] \frac{x + y}{x - y} + \frac{x - y}{x + y} - \frac{2( {x}^{2} - {y}^{2}) }{ {x}^{2} - {y}^{2} } [/tex]
Answer:
[tex] \rm \displaystyle \frac{x + y}{x - y} + \frac{x - y}{x + y} - \frac{2( {x}^{2} - {y}^{2}) }{ {x}^{2} - {y}^{2} } = \boxed{ \displaystyle \frac{4y ^2}{(x - y)(x + y)} }[/tex]
Step-by-step explanation:
we want to simplify the following
[tex] \rm \displaystyle \frac{x + y}{x - y} + \frac{x - y}{x + y} - \frac{2( {x}^{2} - {y}^{2}) }{ {x}^{2} - {y}^{2} }[/tex]
notice that we can reduce the fraction thus do so:
[tex] \rm \displaystyle \frac{x + y}{x - y} + \frac{x - y}{x + y} - \frac{2 \cancel{( {x}^{2} - {y}^{2}) }}{ \cancel{{x}^{2} - {y}^{2} }}[/tex]
[tex] \rm \displaystyle \frac{x + y}{x - y} + \frac{x - y}{x + y} - 2 [/tex]
in order to simplify the addition of the algebraic fraction the first step is to figure out the LCM of the denominator and that is (x-y)(x+y) now divide the LCM by the denominator of very fraction and multiply the result by the numerator which yields:
[tex] \rm \displaystyle \frac{x + y}{x - y} + \frac{x - y}{x + y} - 2 \\ \\ \displaystyle \frac{(x + y)^2 + (x - y)^2 - 2(x + y)(x - y)}{(x - y)(x + y)} [/tex]
factor using (a-b)²=a²+b²-2ab
[tex] \rm \displaystyle \frac{(x + y-(x - y) )^2}{(x - y)(x + y)} [/tex]
remove parentheses
[tex] \rm \displaystyle \frac{(x + y-x + y) )^2}{(x - y)(x + y)} [/tex]
simplify:
[tex] \rm \displaystyle \frac{4y ^2}{(x - y)(x + y)} [/tex]
9514 1404 393
Answer:
4y²/(x² -y²)
Step-by-step explanation:
The expression simplifies as follows:
[tex]\dfrac{x+y}{x-y}+\dfrac{x-y}{x+y}-\dfrac{2(x^2-y^2)}{x^2-y^2}\\\\=\dfrac{(x+y)(x+y)+(x-y)(x-y)-2(x^2-y^2)}{(x-y)(x+y)}\\\\=\dfrac{(x+y)^2+(x-y)^2-2(x^2-y^2)}{x^2-y^2}\\\\=\dfrac{(x^2+2xy+y^2)+(x^2-2xy+y^2)-2(x^2-y^2)}{x^2-y^2}\\\\=\dfrac{2(x^2+y^2-(x^2-y^2))}{x^2-y^2}=\boxed{\dfrac{4y^2}{x^2-y^2}}[/tex]
Find the width of a rectangular strip of land with length 25 m and area 12 square meters?
Answer:
5/4
Step-by-step explanation:
The area of a rectangle is given by
A = l*w
1/2 = 2/5 * w
Multiply each side by 5/2
5/2 * 1/2 = 2/5 *w * 5/2
5/4 = w
Formula we use,
→ A = l × w
Then the width of the rectangle,
→ A = I × w
→ 1/2 = 2/5 × w
Now multiply each side by 5/2,
→ 1/2 × 5/2 = 2/5 × w × 5/2
→ w = 5/4
Hence, the width is 5/4.
it’s my final exam and i’m so confused. please help
Find x.
Round to the nearest tenth:
29° 500 ft
y
х
x = [ ? ]ft
Enter
Answer:
437.31 ft
Step-by-step explanation:
Need help on this!!!
Answer:
7.8391
Step-by-step explanation:
Answer:
Step-by-step explanation:
The key to solving this equation is knowing how to "undo" a natural log. Just like square roots are "undone" by squaring, and cubing "undoes" a cubed root, raising a natural log to the base of e, Euler's number, undoes a natural log. Because this is an equation you have to raise both sides of it to the base of e:
[tex]e^{ln(x+3)}=e^5[/tex]
That leaves us on the left with simply
x + 3
On the right we have a constant. e is not a variable, it is a number. You can find its value on your calculator. Solving for x:
[tex]x=e^5-3[/tex] and
[tex]e^5=148.4131591[/tex], so
x = 148.4131591 - 3 and
x = 145.4132, the first choice listed.
Can someone help me with this math homework please!
Answer:
2+4/6=1
y-2/x-6=1
y-2=x-6
y=x-4
or y+4=x
Answer:
3rd option
y + 4 = x
Step-by-step explanation:
look,
point A (0, -4) forms the y intercept
(remember the condition for y intercept? the coordinates for which value of x is 0)
so in the equation
[tex]\boxed{ y= mx+c}[/tex]
c being the y intercept is equal to (-4)
finding the slope :-
[tex]m = \frac{ 2 + 4 }{6 - 0} \\ = \frac{6}{6} = 1[/tex]
plugging all these values into the equation
y = 1x - 4
y= x - 4
taking 4 to the other side
y+ 4 = x
Triangle SKY with vertices S(-7, 2), K(-1,8), and Y(-2,1) undegoes a reflection with new corrdinates S'(-7,-2), K'(-1, -8), and Y'(-2,-1). Name the line of reflection.
Step-by-step explanation:
reflection under
x-axis
hope this will help you
The line of reflection is given as x-axis.
How to transform a graph of the function?The graph of a function can be transformed by either shifting it in the right, left, up or down.
When the transformation is rightwards, the function becomes as f(x - a).
For left shifting it is f(x + a).
The coordinates of the triangle SKY before and after reflection are given as below,
S(-7, 2) → S'(-7, -2)
K(-1, 8) → K'(-1, -8)
Y(-2, 1) → Y'(-2, -1)
It is clear from the transformed coordinates that the x coordinates are the same but y-coordinate changes.
Thus, the reflection is about x-axis.
Hence, the line of reflection is x-axis.
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Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
Answer:
c
Step-by-step explanation:
First, we can transform this into a matrix. The x coefficients will be the first ones for each row, the y coefficients the second column, etc.
[tex]\left[\begin{array}{cccc}1&-2&3&-2\\6&2&2&-48\\1&4&3&-38\end{array}\right][/tex]
Next, we can define a reduced row echelon form matrix as follows:
With the leading entry being the first non zero number in the first row, the leading entry in each row must be 1. Next, there must only be 0s above and below the leading entry. After that, the leading entry of a row must be to the left of the leading entry of the next row. Finally, rows with all zeros should be at the bottom of the matrix.
Because there are 3 rows and we want to solve for 3 variables, making the desired matrix of form
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex] for the first three rows and columns. This would make the equation translate to
x= something
y= something
z = something, making it easy to solve for x, y, and z.
Going back to our matrix,
[tex]\left[\begin{array}{cccc}1&-2&3&-2\\6&2&2&-48\\1&4&3&-38\end{array}\right][/tex] ,
we can start by removing the nonzero values from the first column for rows 2 and 3 to reach the first column of the desired matrix. We can do this by multiplying the first row by -6 and adding it to the second row, as well as multiplying the first row by -1 and adding it to the third row. This results in
[tex]\left[\begin{array}{cccc}1&-2&3&-2\\0&14&-16&-36\\0&6&0&-36\end{array}\right][/tex]
as our matrix. * Next, we can reach the second column of our desired matrix by first multiplying the second row by (2/14) and adding it to the first row as well as multiplying the second row by (-6/14) and adding it to the third row. This eliminates the nonzero values from all rows in the second column except for the second row. This results in
[tex]\left[\begin{array}{cccc}1&0&10/14&-100/14\\0&14&-16&-36\\0&0&96/14&-288/14\end{array}\right][/tex]
After that, to reach the desired second column, we can divide the second row by 14, resulting in
[tex]\left[\begin{array}{cccc}1&0&10/14&-100/14\\0&1&-16/14&-36/14\\0&0&96/14&-288/14\end{array}\right][/tex]
Finally, to remove the zeros from all rows in the third column outside of the third row, we can multiply the third row by (16/96) and adding it to the second row as well as multiplying the third row by (-10/96) and adding it to the first row. This results in
[tex]\left[\begin{array}{cccc}1&0&0&-5\\0&1&0&-6\\0&0&96/14&-288/14\end{array}\right][/tex]
We can then divide the third row by -96/14 to reach the desired third column, making the reduced row echelon form of the matrix
[tex]\left[\begin{array}{cccc}1&0&0&-5\\0&1&0&-6\\0&0&1&-3\end{array}\right][/tex]
Therefore,
x=-5
y=-6
z=-3
* we could also switch the second and third rows here to make the process a little simpler
Answer:
C
Step-by-step explanation:
EDGE BOY (or girl)
Please help!!! I'll give 25 points plus brainliest.
The half-life of Palladium-100 is 4 days. In an experiment, there are 10 milligrams of Palladium-100 sample to start with.
Write the exponential function for this situation. (3 points)
Use your answer in part a to find the amount of Palladium-100 two weeks after the experiment starts. (4 points)
How long will it take for the amount of Palladium to drop below 1 mg?
Show your work or attach a sketch/screenshot if you used technology. (4 points)
Answer:
(b) 26.6 days
Step-by-step explanation:
Half life, T = 4 days
initial amount, No = 100 mg
(a) The exponential function is given by
[tex]N = No e^{-\lambda t}\\\\N = No e^{\frac{-0.693t}{T}}\\\\N = No e^{\frac{-0.693t}{4}}\\\\N = No e^{\frac{-0.17325t}{T}}\\\\[/tex]
where, N is the amount left.
(b) N = 1 mg
[tex]N = No e^{\frac{-0.17325t}{4}}\\\\1 = 100 e^{\frac{-0.17325t}{4}}\\\\4.605 = 0.17325 t \\\\t=26.6 days[/tex]
PLs help T^T im to dum.b to understand this equation
A chocolate factory uses 1/6 of a bag of cocoa butter in each packet of chocolate. The factory used 1/3 of a bag of cocoa butter today. How many packets of chocolates did the factory make?
Answer:
2 packets of chocolates
Step-by-step explanation:
Find how many packets of chocolates they made by dividing 1/3 by 1/6:
1/3 / 1/6
= 1/3 x 6
= 2
So, the factory made 2 packets of chocolates
how u do the sum pls
Answer:
[tex]{ \tt{x + 36 \degree + 48 \degree = 360 \degree}} \\ { \tt{x = (360 - 48 - 36) \degree}} \\ { \tt{x = 276 \degree}}[/tex]
