Answer:
x = [tex]\frac{y-b}{a}[/tex]
Step-by-step explanation:
y = xa + b ( subtract b from both sides )
y - b = xa ( isolate x by dividing both sides by a )
[tex]\frac{y-b}{a}[/tex] = x , that is
x = [tex]\frac{y-b}{a}[/tex]
-------------------------------------
y = xa - b ( add b to both sides )
y + b = xa ( isolate x by dividing both sides by a )
[tex]\frac{y+b}{a}[/tex] = x , that is
x = [tex]\frac{y+b}{a}[/tex]
--------------------------------------------
assuming you mean
y = [tex]\frac{x+2}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
2y = x + 2 ( subtract 2 from both sides )
2y - 2 = x , that is
x = 2y - 2
What is the percent of change from 74 to 35?
Round to the nearest percent.
Answer:
Step-by-step explanation:
52%
is the line through (-4, 26, 1) and (-2, 0, -3) parallel to the line through (10, 18, 4) and (5, 3, 14)?
No, the line passing through (-4, 26) and (-2, 0) is not parallel to line passing through (10, 18) and (5, 3) because slopes of both lines are different.
Line is possible in 2-d forms so, it has only x and y-co-ordinates. Z-co-ordinates is not possible.
We know very well that to prove any two lines are parallel to each other we need to prove only whether their slopes are equal or not.
Now, talking about the slopes we know that if any line is passing from point(x₁,y₁) and again passing from other point(x₂,y₂) then slope(m) of that line is given by the formula=(y₂-y₁) / (x₂-x₁)
So, for first line we have (x₁, y₁)=(-4,26)
and (x₂, y₂)=(-2,0)
So, slope(m₁) of first line is =(0-26)/(-2 - (-4))
=>m₁ = -26/2
=>m₁ = -13 ----(eq1)
Similarly, for second line, we have (x₁, y₁)=(10,18)
and (x₂, y₂)=(5,3)
So, slope(m₂) of second line is =(3-18) / (5-10)
=>m₂ = -15/-5
=>m₂= 3 -------(eq2)
On comparing eq1 and eq2,we get
=>m₁≠m₂.
Hence, the given lines are not parallel.
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(Complete question) is:
Is the line through (-4, 26) and (-2, 0) parallel to the line through (10, 18) and (5, 3)?
what is the probability that between 10:00 and 10:30 the switchboard will receive more than 9 calls but fewer than 18 calls?
Between 10:00 and 10:30, there is a 0.333 percent chance that the switchboard will field more than 9 calls but fewer than 18 calls.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Time = 30 min (as 10:00 to 10:30)
Total calls = 9+18 =27
Probability receive more than 9 calls but fewer than 18 calls
p(9 < x > 18) = { 10, 11, 12, 13, 14, 15, 16, 17, 18} = 9 (all possibilities)
Total Probability = (likely event / total outcomes)
p(9 < x > 18) = (9/27)
p(9 < x > 18) = 1/3
p(9 < x > 18) = 0.333
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b(x) = 6x², when x = 16
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra ISubstitution
Functions
Function NotationApplicationStep 1: DefineLet's see what the problem as given us.
[tex]\displaystyle\begin{aligned}& b(x) = 6x^2 \\& x = 16\end{aligned}[/tex]
Step 2: WorkWe can easily see that we can substitute in x as 16.
[Equation] Define given:∴ our final answer to the question is b(16) = 1536.
___
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___
Topic: Algebra I
Unit: Functions
If x^8 • x^a = x^64 and (x^2) ^b = x ^ 5, what is the product of a and b?
A. 168
B. 140
C. 58
D. 24
E. 11
Work shown would be helpful please! Giving 100 brainly points!!
The product of a and b is 140. Hence option B is the correct option.
What is an exponential function?
The formula for an exponential function is f (x) = a^xx, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
Given exponential equations are
x^8 • x^a = x^64 .....(i)
(x^2) ^b = x ^ 5 .....(ii)
Solve the equation (i) to calculate the value of a:
x^8 • x^a = x^64
Applying the formula of product of two exponents with same base a^b • a^c = a^(b+c):
x^(8+a) = x^64
Now compare the exponent of the above equation:
8 + a = 64
Subtract 8 from both sides:
a = 64 - 8
a = 56
Solve the equation (ii) to calculate the value of b:
(x^2) ^b = x ^ 5
Now applying the formual (a^b)^c = a^ (bc)
x^(2b) = x^5
Now compare the power of x of the above equation:
2b = 5
divide both sides by 2
b = 5/2
The product of a and b is 56 • (5/2) = 140.
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How do you solve 14/x = 2/5 ?
Answer:just solve it
Step-by-step explanation:
it is super easy
Consider the differential equation: dy/dx=ey(3x2-6x)
a) Sketch a slope field for the given equation and include six points on the graph.
b) FInd y=f(x), the particular solution to the differential equation that passes through (1,0).
c) Write an equation for the tangent line to the graph of f at the point (1,0). Use the tangent line to approximate f(1,2).
F(x)= -ln(-x3+3x-1) is a particular solution to the differential equation that passes through (1, 0). An equation for the tangent line to the graph of f at the point (1,0) = -3.
b.[tex]\frac{dy}{e^y} = (3x^2-6x)dx\\[/tex]
∫[tex]e^{-y} dy =[/tex] ∫[tex](3x^2-6x)dx[/tex]
[tex]-1e^{-y} = x^3-3x^2+C\\e^{-y} = -x^3+3x^2+C_{2}\\ -y= ln(-x^3+3x^2+C_{2}) \\y=-ln(-x^3+3x^2+C_{2}[/tex]
Given (1,0)
[tex]0= -ln (-1+3+C)\\0=ln_{c} (2+C)\\e^{0} = 2+C\\-1=C\\so f(x)= -ln(-x^3+3x^2-1)\\[/tex]
f(1.2)=-.465 as the actual value.
c. tangent line slope at (1,0).[tex]= e^0 (3(1)^2-6(1))\\[/tex]
[tex]=-3[/tex]
Line equation: y= 3(x-1) or y= 3x + 3
with f(1,2)=-3(1.2)+3 =-.6
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1. What is the area of the rectangle? Must show all work.
(7 points)
a. What is the formula for the area of the rectangle?
b. Find the length of the base. Round to the nearest tenth if needed.
c. Find the length of the height. Round to the nearest tenth if needed.
d. Find the area of the rectangle.
Answer:
a. Area of rectangle: Length x Width or Base x height
b. The length of the base is 6
c. The height is 3
d. Area of the rectangle is 18
Step-by-step explanation:
a. Area of the rectangle formula is: L x W
b. We find the Length, which means we find the distance of the x; we see that to get from point A to point B the x change is 6, so the base is 6
c. We find the height, which means we find the distance of the y; we see that get from point B to point C, the y change by 3, so the height is 3
d. To find the area we take 6 times 3 = 18
let c(n) be a city's cost, in millions of dollars, for plowing the roads when n inches of snow have fallen. let c(n)
The cost of plowing the roads after 24 inches have fallen is increasing at a rate of $0.4 million per inch.
Evaluate this expression, we need to break this into two pieces. First, we have the value of c(15), so thankfully, we don't need to run any calculations to find it. This means that we just need to evaluate this definite integral, which is the integral of the derivative of c(n) from 15 to 24.
The Fundamental Theorem of Calculus relates a function to its antiderivative as a way to find the value of the integral of that function. Since the antiderivative of , which we have the value for at the endpoints of this integral, we can evaluate this integral as follows.
[tex]\int\limits^a_b {c'(n)} \, dn = c(24 ) - c(15) = 0.4 - 0.6 = -0.2[/tex]
We can now find the value of this entire expression as follows.
[tex]c(15) +\int\limits^a_b {c'(n)} \, dn = 0.6 + (-0.2) = 0.4[/tex]
Since this represents the derivative of C(n), the cost for plowing the roads, this tells us that the cost of plowing the roads after 24 inches have fallen is increasing at a rate of $0.4 million per inch.
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Which point would be a solution to the system of linear inequalities shown below?
y ≥ -3x-4
y > 1/2x-6
1. (-12,10)
2. (-4,7)
3. (-4,8)
4. (-10,10)
By using graphical method, it can be seen that-
(-4, 8) satisfies the system of inequality
So third option is correct
What is linear inequation?
Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤.
A one degree inequation is known as linear inequation.
The system of linear inequation is to be solved graphically
For y ≥ -3x-4
The line passes through (0, -4) and ([tex]-\frac{4}{3}, 0[/tex])
Since (0, 0) satisfies the line, shaded region is towards the origin
Now, as equality is maintained, line is a solid line
The above line is plotted by a red line
For [tex]y \geq \frac{1}{2}x-6[/tex]
The line passes through (0, -6) and (12, 0)
Since (0, 0) satisfies the line, shaded region is towards the origin
Now, as equality is not maintained, line is a dotted line
The above line is plotted by a blue line
From the intersection of two shaded regions, it can be seen that (-4, 8) satisfies the system of inequality
So third option is correct
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I NEED THIS DONE ASAP PLEASE HELP ME!!!
The equivalent of the expressions are as follows;
3(3t - 4) - (2t + 10) = 7t - 225(2t + 1) + (-7t + 28) = 3t + 33[tex](4t -\frac{8}{5} ) - (3-\frac{4}{3}t ) = \frac{16}{3}t - \frac{23}{5}[/tex][tex](-\frac{9}{2}t+4 )+(\frac{7}{4}t+33 ) = \frac{25}{4}t+ 37[/tex]How to find equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Two expressions are equivalent if:
They can both be simplified to equivalent expressions.Substituting a value into both expressions results in the same number.Hence, let's simplify the expression to find it equivalent.
Therefore,
3(3t - 4) - (2t + 10)
open the bracket
9t - 12 - 2t - 10
7t - 22
5(2t + 1) + (-7t + 28)
10t + 5 - 7t + 28
3t + 33
[tex](4t -\frac{8}{5} ) - (3-\frac{4}{3}t ) = 4t+\frac{4}{3}t - \frac{8}{5}- 3 = \frac{12t+4t}{3} +\frac{-8-15}{5} = \frac{16}{3}t - \frac{23}{5}[/tex]
[tex](-\frac{9}{2}t+4 )+(\frac{7}{4}t+33 ) = -\frac{9}{2}t+ \frac{7}{4}t + 4 + 33 = \frac{-18t+7t}{4} + 37 = \frac{25}{4}t+ 37[/tex]
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Complete the table.
Distances:
a = _pi
b = _pi
c = _pi
Heights:
d =
e =
f =
The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.
What is distance?The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.
Given:
The time, t = π / 2 sec,
Calculate the distance by using the formula given below,
[tex]Distance = r\times time[/tex]
So, for distance, a = 1 × π / 2 = π / 2
for distance, b = 1 × π = π
for distance, c = 1 × 3 π / 2 = 3 π / 2
Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.
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Find the value of Za, Z0.33 Click the icon to view a table of areas under the normal curve. Z0.33-LI (Round to two decimal places as needed.)
The value of area under the normal curve at a z-score of 0.33 with respect to the mean is 0.63 (2 dp).
What is z - score?It is a value that describes the deviation of a value from the standard deviation. Z-score is the number of standard deviations a given data point lies above or below mean.
How to find area from z-score?To find the area under the normal curve at a specific value of z we look into the normal distribution table.
At 0.33 we can see that the value is 0.6293. This value is given from the center, which is the mean of the data.
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What do the parts of the expression of 48 is represent
Therefore the part of expression of 48 represent the price per scarfs .
What is expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. (Mathematical Operator, Number or Variable, Expression) is the structure of an expression.
Here,
In the given the expression 483, represents the number 0f scarves and 48 represents the price per scarf Buyers are charged shipping fee of $4.75 for each scarf order:
Therefore, from the given we can see the 48 represents the price per scarf.
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what is the slope of the line that passes through (−2, 3) and (5, −6) ?responses −12 negative 1 half −1 negative 1 −97 negative fraction 9 over 7 i don't know.
Answer:
slope = -9/7 or (negative fraction 9 over 7)
Step-by-step explanation:
what is the slope of the line that passes through (−2, 3) and (5, −6)?
slope = change in y / change in x
slope = (3 - (-6) / (-2 - 5)
slope = 9/-7
slope = -9/7
from your options:
negative fraction 9 over 7
The two horizontal lines in the diagram are parallel.
The value of x is ___ °
The value of angle x in the triangle is 130 degrees
How to determine the value of x?From the question, we have the following parameters that can be used in our computation:
Lines = parallel lines
Shapes = Triangles
By the alternate interior angle, the third angle in the bottom triangle has the same measure as 60 degrees
This means that
x = 70 + 60 -- by the alternate exterior angle throrem
Evaluate the sum
x = 130
Hence, the value of x is 130
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Select the correct answer. What are the solutions of this quadratic equation? x2 + 10 = 0
Answer:x=-5
Step-by-step explanation:
x2+10=0
0-10=-10
x2=-10
-10/2=-5
x=-5
p,3,5,7,q,13 is a sequence of prime numbers.Find the value of p+q.
A.10
B.12
C.13
D.14
Answer: P is 1 and q is 11, making your answer 12.
Step-by-step explanation:
If the chart is displaying prime numbers in order from 1 to 13, list all of the prime numbers. We would start with '1' because '1' is a prime and the first one on the list, thus followed by 3, then 5, then 7, then 11 because the only prime number between 7 and 13 is 11.
Then, add your P and q together, 1 and 11 in this example, to get your final answer of 12.
Rectangular prism A is similar to rectangular prism B. The ratio of the surface of A to B is 4:1. If the volume of rectangular prism B is 12 cm3 , what is the volume of rectangular prism A?
The volume of rectangular prism A will be 48 cm³
How to find area of Rectangular Prism?
The volume of a rectangular prism is given by the formula:
A = lwh
Where:
l = length
w = width
h = height.
Since the surface ratio of rectangular prism A to rectangular prism B is 4:1, the ratio of the linear dimensions of A to B must also be 4:1.
This means that if one linear dimension of rectangular prism A is 4 times the size of the corresponding dimension of rectangular prism B, then all of the linear dimensions of A will be 4 times the size of the corresponding dimensions of B.
Since the volume of a rectangular prism is given by the product of its linear dimensions.
The volume of rectangular prism A will be 4 times the volume of rectangular prism B.
Therefore, if the volume of rectangular prism B is 12 cm³, the volume of rectangular prism A will be 4 * 12 cm³ = 48 cm³.
Hence, The volume of rectangular prism A will be 48 cm³.
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Find the slope of each line. Tell whether the slop is Positive, Negative, Undefined or Zero
Answer: The slope is Negative
Step-by-step explanation:
The slope is rising over run
Let's pick 2 points (-3,0) (0,-2)
The slope is -2/3
a chemist has a mixture with a temperature of 3.5 C. Then the chemist cools the mixture. The temperature changes by -- 14.2 C What is the temperature of the mixture when it cools
The temperature of the mixture when it cools is; -10.7°C
What is the change in temperature?A change in temperature is defined as the difference in the initial and final temperatures.
Now, we are told that the chemist has a mixture with a temperature of 3.5°C.
We are also told that the temperature changes by -14.2 °C
Let the initial temperature be T₁ and the final temperature be T₂ and as such, the change in temperature will be;
ΔT = T₂ - T₁
Plugging in the relevant values gives;
-14.2 = T₂ - 3.5
T₂ = -14.2 + 3.5
T₂ = - 10.7°C
This is the temperature of the mixture after it cools.
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james rode his bike 7 yards in 3 seconds. set up the table with the information you know. yards seconds 7 3 you got it! what is the missing value? solve on paper if you need to. yards seconds 7 3 120
The missing value after solving is 280 seconds .
Given :
james rode his bike 7 yards in 3 seconds. set up the table with the information you know. yards seconds 7 3 you got it!
Seconds :
The second ( s or sec ) is the International System of Units ( SI ) unit of time measurement.
Table :
yards seconds
7 3
120 x
we need to find x :
1 yard = 7/3 seconds
120 yards = 7 / 3 * 120 seconds
= 7 / 1 * 40 seconds
= 7 * 40 seconds
= 280 seconds.
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Two main categories of physical fitness are endurance-related fitness and skill-related fitness.
Please select the best answer from the choices provided.
Fitness related to endurance and fitness related to skill are the two basic types of physical fitness. Running is most likely the simplest solo sport for fostering both physical and mental fitness.
what is physical fitness ?Jogging, riding, swimming, and brisk walking are among examples. Exercises that build muscle strength are known as resistance training. Using a resistance band and lifting weights are two examples. Walking on uneven ground can be made simpler with balance exercises, which can also assist prevent falls.
Fitness related to endurance and fitness related to skill are the two basic types of physical fitness. Running is most likely the simplest solo sport for fostering both physical and mental fitness.
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Which of the following is a solution of the equation 3x-7 = 7-4x
Answer:
x = 2
Step-by-step explanation:
⭐What is the solution of an equation?
the value of the variable that makes LHS (the left-hand side) equal RHS (the right-hand side)Thus, we need to solve for x, the variable.
Given:
3x - 7 = 7 - 4x
To solve for x, we need to have all the variables on the LHS (or RHS), and all the constants on the RHS (or LHS).
To do so, first add 4x to the LHS and RHS. This "moves" -4x to the LHS:
3x +4x - 7 = 7 +4x -4x
Add like terms (terms with the same variable) to simplify:
7x - 7 = 7
Next, add 7 to the LHS and RHS. This "moves" -7 to the RHS:
7x +7 -7 = 7 +7
7x = 14
Finally, divide the LHS and RHS by 7 to isolate the variable:
[tex]\frac{7x}{7} = \frac{14}{7}[/tex]
∴ x = 2
⭐ if this response helped you, please mark it the brainliest!⭐
costheta/1-tantheta - sin^2theta/costheta-sintheta}=costheta+sintheta
Prove it with steps
Answer:
To prove the given identity, we can start by multiplying both sides of the equation by (cosθ - sinθ) to obtain:
(cosθ/1 - tanθ) (cosθ - sinθ) - sin^2θ/(cosθ - sinθ) = (cosθ + sinθ)(cosθ - sinθ)
Expanding both sides of the equation gives us:
cos^2θ - tanθcosθ - sin^2θ = -sin^2θ + cos^2θ
We can simplify this equation to:
-tanθcosθ = -sin^2θ + cos^2θ
We can simplify this further by using the identity cos^2θ + sin^2θ = 1:
-tanθcosθ = 1 - 2sin^2θ
We can rearrange this equation to solve for sin^2θ:
sin^2θ = (1 + tanθcosθ)/2
This is the desired result, so we have successfully proved the given identity.
I hope this helps! Let me know if you have any questions.
Step-by-step explanation:
SELF EXPLANATORY
as a mobile node gets farther and farther away from a base station, what are the two actions that a base station could take to ensure that the loss probability of a transmitted frame does not increase?
As per the given probability, the two action that the base station would takes are, 1) increasing the transmission power, and 2) reducing the transmission rate.
Probability:
In statistics, probability refers the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Given,
Here we need to find the two actions that a base station could take to ensure that the loss probability of a transmitted frame does not increase.
Here we have given that, a mobile node gets farther and farther away from a base station,
And the two actions that a base station could take to ensure that the loss probability of a transmitted frame does not increase will be solve by increased transmission power and then reduce the rate.
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A sponge has a blue circle printed on it. The blue circle has a radius of 5 centimeters when the sponge is dry. When wet, the sponge expands, and the area of the blue circle increases by 44%. What is the radius, in centimeters, of the blue circle when the sponge is wet?
HELP PLSSS 59 POINTS!!!!
Answer:
7.20cm I think
........
The figure below has a point marked with a large dot.
First, translate the figure 7 units down.
Then, give
the coordinates of the marked point in the original figure and the final figure.
Therefore ,The marked point will now have the updated coordinates P' (2, 7).
Define Translation of Points on a Coordinate Plane.When a figure is transferred from one area to another without altering its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.
Here,
On an X-Y coordinate plane, a figure is plotted.
When translating a figure 7 units to the down, we must provide the coordinates of the indicated point in the original figure
"(x, y)" = "(x + m, y + n)"
In response to the query, we have
The specified point's coordinates are: P (5,4).
The new coordinates of the indicated spot after this figure is translated 6 units to the right will be -
P'( 5,4- 7) = P'(5, -3) (5, -3)
As a result, the designated point's new coordinates are P' (5, -3)
The new coordinates of the marked point will be - P'(5, -3)
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A spinner contains 3 sectors of the same size. One sector is
labeled red and two sectors are labeled blue. Kathryn spins
the spinner and records the results. After conducting a
number of trials for this experiment, Kathryn concludes that
there is a flaw in her experiment. Which of the following best
demonstrates that her experiment is flawed?
Three identically sized sectors make up a spinner. Two sectors are colored blue, while one sector is labeled red. Kathryn turns the spinning while recording the outcomes. Kathryn comes to the conclusion that there is a problem with her experiment after running several trials for it.
What is the theoretical probability of spinning a 3?The object's sample space affects theoretical probability. For instance, the likelihood of rolling a 3 when using a fair die is 1/6. This is so because, when a fair die is rolled, the number 3 indicates one of the six possible results.
Divide the total number of trials by the number of times the desired result has occurred to determine the experimental probability.Every time, one fourth of the time, the spinner will land on a different color. The likelihood of rolling each number on the die in Experiment 2 is always one sixth. The results are equally likely to occur in both of these tests. Let's examine a test in which the results are not equally likely.
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Which of these expressions is equivalent to log (20 35)
Answer:
log_20(35)= 1.5372435736805
Step-by-step explanation: