The Magnitude of earthquake that hit Texas is 5.8; With the help of the logarithmic equation so found, we can get the value of M, with which we can get the magnitude of the Texas earthquake.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given:
Magnitude of earthquake that hit Indian Ocean = 9.1 [tex]I_1[/tex] = Intensity of weaker earthquake[tex]I_2[/tex] = Intensity of greater earthquake.To find: Magnitude of earthquake that hit Texas.
Finding:
From the given, [tex]\frac{I_2}{I_1}[/tex] gives the ratio of the greater earthquake's intensity to the weaker earthquake's intensity.This ratio, when written as an exponential equation, equals [tex]30^M[/tex] where M is the increase in magnitude difference:=> [tex]\frac{I_2}{I_1}[/tex] = [tex]30^M[/tex]
For [tex]\frac{I_2}{I_1}[/tex] = 74900, the above expression becomes:
=> 74900 = [tex]30^M[/tex]
Taking logarithm on both sides, with base 10 gives:
=> log (74900) = log ([tex]30^M[/tex])
As [tex]log_b(a)^m = m(log_b(a))[/tex],
=> log (74900) = M ( log (30))
=> [tex]\frac{log(74900)}{log (30)}[/tex] = M
=> M ≈ 3.3, i.e., the increase in magnitude difference is approximately 3.3.
Thus, the magnitude of the earthquake that hit Texas = 9.1 - 3.3 = 5.8.
The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex]. By finding the solution of this equation, we get the value of M, which gives us the value of the increase in the magnitude of the earthquakes.With the help of this value so found, we can find the required value of the magnitude of earthquake in Texas, as we already know that of Indian Ocean, by basic algebra.To learn more about logarithms, refer to the link: brainly.com/question/25710806
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If ashima drove the first 348 mi off her trip in 6 hr, how long will it take her, if she drives at the same rate, to drive the remaining 145mi
The time it will take to cover another distance of 145 miles is; 2.5 hours
How to solve proportion word problems?
We are given;
First distance driven = 348 miles
Time taken for first distance = 6 hours
Formula for speed is;
Speed = Distance/Time taken
Thus;
Speed for fist distance = 348/6
Speed = 58 mph
Now, at the same speed she wants to cover another distance 0f 145 miles. Thus;
Time taken = distance/speed
Time taken = 145/58
Time taken = 2.5 hours
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what is 5/9 + (-2/9)
Answer: 1/3
Step-by-step explanation:
Answe3/9
Step-by-step explanation: You just subtract the 2 from the 5 because the denominators are the same. You subtract because there is one subtraction sign and one addition sign.
Given G is the midpoint between points R and T. R has
the coordinates of (-5, -2) and G has the coordinates
of (0, 3).
Find the coordinates of T.
Answer:
(-2.5 , 0.5)
Step-by-step explanation:
You can use the midpoint formula.
x(sub1) + x(sub2) / 2 , y(sub1) + y(sub2) / 2
For example:
-5 + 0 / 2 , -2 + 3 / 2
-5 / 2 , 1 / 2
-2.5 , 0.5
midpoint = (-2.5 , 0.5)
Tell weather the graph shows a reflection across the y -axis or neither
Step-by-step explanation:
yes, this is a reflection across the y-axis.
the points near to the mirror appear also near in the reflection. and the points far from the mirror appear also far in the reflection.
PLSS HELP :((
will mark brianlist if its the correct answer ty
By applying the Alternate Interior Angles Theorem, the measure of angle x is: C. 60 degrees.
What is the Alternate Interior Angles Theorem?The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
Since the two lines are parallel lines, angles 3 and 4 are alternate interior angles. Therefore, by applying the supplementary angle theorem, the measure of angle 3 is given by:
Q + R = 180°
85° + m<3 = 180°
Angle 3 = 180° - 85°
Angle 3 = 95°
Also, the sum of the angles formed on a straight line is supplementary and equal to 180°. Therefore, we have:
x + 25° + 95° = 180°
x + 120° = 180°
x = 180° - 120°
x = 60°
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Put these in order from the smallest to largest 1 to the power of 8 ,2 to the power of 4 ,3 to the power of three and 5 to the power of two
answer the question attached
The answer is cone -7 7=9÷7
What is the slope of the line that passes through the points (2, 8) and
(12, 20)? Write your answer in simplest form
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{12}-\underset{x_1}{2}}} \implies \cfrac{12}{10}\implies {\LARGE \begin{array}{llll} \cfrac{6}{5} \end{array}}[/tex]
A line intersects the points
(8,-10) and (9, 4).
m = 14
Write an equation in point-slope form
using the point (8, -10).
If b is the midpoint of ac find the coordinates of c if a(12,4) and b(9,11)
Answer:
good less to the worl then
Augustus looks in the mirror and decides that he is gaining weight. He is afraid that all that candy will just make it worse, so he tells his parents that it would be ok if they just give him 1 candy on the first day, 2 on the second day, continuing to double the amount each day as he completes his homework. Mr. and Mrs. Gloop like Augustus’ plan and agree to it.
how many candies will he get on day 30?
The number of candies that Augustus will spend on the 30th day will be 536870912 candies.
How to illustrate the information?It should be noted that from the information, Augustus is afraid that all that candy will just make it worse, so he tells his parents that it would be ok if they just give him 1 candy on the first day, 2 on the second day, continuing to double the amount each day as he completes his homework.
Therefore, the amount that he will get on the 30th day will be:
= 1 × 2^29
= 1 × 536870912
= 536870912
Therefore, the number of candies that Augustus will spend on the 30th day will be 536870912 candies.
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Greg is riding on a bike course that is 20 miles long. So far, he has ridden 6 miles of that course. What percentage of the course had Greg ridden so far?
(3/x+3 - 4/x+4) divided by (2x/x+3 - x/x+4)
The answer is
7x-1/8x
An angle measures 8° more than the measure of its supplementary angle. What is the measure of each angle?
86° is the measure of each angle when its supplementary angle.
What does math's supplementary angle mean?
Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complimentary angles is 90 degrees.If two angles in geometry sum up to 180 degrees, they are considered to be supplementary angles. For instance, A and B are referred to as supplementary angles if A + B = 180°.Let the larger angle be x.
Smaller angle = x - 8
As both angles are supplementary,
x + (x - 8) = 180°
2x - 8 = 180°
2x = 188°
x = 94°
Therefore, larger angle = 94°
Smaller angle = 94° - 8° = 86°
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Elina has a total of $2.60. All of her change are in nickels, quarters, and dimes. She has twice as many dimes as quarters and two less quarters than nickels. Is it possible that Elina has eight dimes, four quarters, and six nickels?
Answer:
10 Dimes, 5 quarters, and 7 Nickels
Step-by-step explanation:
10 Dimes - 1 dollars
5 Quarters - 1.25 dollars
7 Nickels - 35 cents
1 + 1.25 = 2.25
2.25 + 35 = 2.60
Chloe is making hair bows to sell at a craft show. The table shows the cost per yard of different types of ribbon.
Ribbon Cost per Yard ($)
Chiffon 5.88
Satin 1.50
Lace 3.29
Tulle 2.25
Chloe bought 5.5 yards of satin ribbon and 3.8 yards of tulle. If Chloe paid with a $20 bill, how much change will she receive?
The change received by Chloe after paying a $20 bill for ribbons is $3.2.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given is the table that represents the cost per yards of the ribbons.
From the question, we can write -
Ribbon Cost per Yard ($)
Chiffon 5.88
Satin 1.50
Lace 3.29
Tulle 2.25
Cost of one yard of satin ribbon → $1.50.
Then, the cost of 5.5 yards of satin ribbon [A1] → 5.5 x 1.50 = $8.25.
Cost of one yard of tulle ribbon → $2.25.
Then, the cost of 3.8 yards of tulle ribbon [A2] → 3.8 x 2.25 = $8.55.
Total cost of both the Ribbons → A1 + A2 = 8.25 + 8.55 = $16.8.
Money paid by Chloe → $20
Change received by Chloe → 20 - 16.8 = $3.2
Therefore, the change received by Chloe after paying a $20 bill for ribbons is $3.2.
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Principal:=$500
interest rate=5%
Time=5 years
What is the interest earned
Answer:
$125
Step-by-step explanation:
I = Prt
I = ($500)(.05)(5) = $2,500(.05) = $125
your teacher was driving on a toll road which has a speed limit of 60 mph (miles per hour). two weeks later they receive a ticket for speeding for going at least 25 mph over. your teacher is outraged and doesn’t believe that they have any way of proving they went 85 mph since there weren’t any radar guns on the road. because you are good at math the teacher turns to you and asks you to help them make a case against the toll road company. here is the information that the toll company provided your teacher as proof of their speeding. toll booth a – entrance on toll road time: 6:00 mile marker: 15 toll booth b – exit on toll road time: 7:00 mile marker: 100 is the toll road company correct to give your teacher a ticket? come up with some arguments one way or the other. include the mean value theorem where appropriate.
Yes , the toll company is correct to give the teacher a ticket.
Mean Value Theorem for a function f(x): [a,b]→ R such that f(x) is continuous and differentiable over the interval.
(i) f(x) is continuous on [a,b].
(ii) f(x) is differentiable on (a,b).
(iii) There exist a point c in (a,b) such that f'(c)=f(b)-f(a)/(b-a).
In the given question
Speed Limit = 60 mph
Time of entrance on toll road = 6:00
Time of exit from toll road = 7:00
Total time on toll road = 1 hr
Mile marker on entry in toll road = 15 mile
Mile marker on exit from toll road = 100 mile
Total distance travelled on toll road = 100-15= 85 miles
[tex]Average.Speed=\frac{total . distance}{total.time}[/tex]
Substituting the values we get .
Avg Speed = 85/1 = 85 mph
Overspeed = Avg Speed - Speed Limit
=85-60
=25 mph
The teacher over speed by 25 mph.
Since 85 mph is the average speed , it means that for some instance he was travelling below the average speed and for some instance he was travelling above the average speed.
By Mean value Theorem , it is clear that there have been at least one point where the teacher was travelling above 85 mph , which means he was over speeding .
Therefore , Yes , the toll company is correct to give the teacher a ticket.
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-6x+4y=24
3 plot points for a graph
Answer:
(1, 7.5)
(2, 9)
(3, 10.5)
Step-by-step explanation:
-6x+4y=24
first we want to put the equation in slope intercept form which is y=mx+b
-6x+4y=24
first we add 6x to both sides
4y=24+6x
now we divide everything by 4
y=6+6/4x
simplified
y=3/2x+6
now we input our x values to find the y values (x,y)
y=3/2(1)+6
y=15/2 or 7.5
y=3(2)+6
y=9
y=3/2(3)+6
y=21/2 or 10.5
with this information, our points to plot on the graph are
(1, 7.5)
(2, 9)
(3, 10.5)
i hope this helped! if you have any questions just ask!
Charles can run at a speed of 8.6 meters per second. If he runs for 65 seconds, how far does he run?
A. 559 meters
B. 755 meters
C. 86 meters
D. 16 meters
A. 559 meters Is the answer
Pre-Calc: Consider the following function.
(answer (a), (b), and (c))
Using the Factor Theorem, we have that:
a) The zeros of the function are x = 3i, x = -3i, x = 4.5.
b) The factored function is: F(x) = (x² + 9)(x - 4.5).
c) From the graph of the function given at the end of the answer, the only x-intercept is x = 4.5, which is the only real zero of the equation.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the following rule.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).
For this problem, the function is defined by the following rule:
F(x) = 2x³ - 9x² + 18x - 81.
Using a calculator, the zeros of the function are given as follows:
x = 3i, x = -3i, x = 4.5.
In factored form, the function is given by:
F(x) = (x - 3i)(x + 3i)(x - 4.5)
Considering that i² = -1, we have that:
The factored function is: F(x) = (x² + 9)(x - 4.5).
From the graph of the function given at the end of the answer, the only x-intercept is x = 4.5, which is the only real zero of the equation.
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If 8597 - x = 7429 -4358 , find x
Answer:
x=5526
Step-by-step explanation:
8597-x=7429-4358
Combine like terms
8597-x=3071
Group all constants on the right side of the equation
8597-x=3071
Subtract 8597 from both sides
(8597- x )-8597=3071-8597
Group like terms
-x+(8597-8597)=3071-8597
Simplify the arithmetic
-x=3071-8597
Simplify the arithmetic
-x=-5526
Isolate the x
-x=-5526
Multiply both sides by-1
-X x -1=-5526 x -1 the small x is for multiplication
Remove the one(s)
X=-5526 x -1
Simplify the arithmetic
x=5526
Substitute each point (-3,5) and (2,-1) into the slope-intercept form of a linear equation to write a system of equations. Then use the system to find the equation of the line containing the two points. Explain your reasoning.
The slope-intercept form of the equation of the line described is y = -6x/5 + 7/5.
Given the following data:
Points on x-axis = (-3, 2).
Points on y-axis = (5, -1).
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope, m = (-1 - 5)/2 + 3)
Slope, m = -6/5
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the intercept.At point (2, -1), we have:
-1 = -6/5(2) + c
-1 = -12/5 + c
c = 12/5 - 1
c = 7/5
In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is y = -6x/5 + 7/5.
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X+2/y-1=2 solve for x
A pharmacist dilutes 18 liters of an 8% solution with a 4.5%
solution to make a 6% solution. how many liters of the 4.5%
solution are added?
24.67 liters of the 4.5% solution are added.
As per the known fact, the relation between concentration and volume of solution is -
[tex] C_{1} V_{1} + C_{2} V_{2} = C_{final}V_{final}[/tex]
Let the [tex] V_{2}[/tex] be x. So, final volume will be (18 + x).
Keep the values in formula to find the value of volume of solution required for dilution -
8%×18 + 4.5%×x = 6%×(18 + x)
Rewriting the equation -
0.08×18 + 0.045×x = 0.06(18 + x)
Performing multiplication to find the value of x -
1.44 + 0.045x = 1.08 + 0.06x
Rewriting the equation -
1.44 - 1.08 = 0.06x - 0.045x
Performing subtraction on both sides of the equation -
0.37 = 0.015x
Shifting 0.015 to other side fo equation and performing division
x = 0.37 ÷ 0.015
x = 24.67 liters
Hence, 24.67 liters of 4.5% solution should be added to make a 6% solution.
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Elliot is paid a salary of $600 per week plus 1% commission on sales OVER $7500. His sales last week totaled $16,700.
What is is commission for the week and his total pay for the week?
Answer:
692
Step-by-step explanation:
600 + (16,700 - 7,500) x 1%
600 + 16,700 - 7,500/100
600 + 9,200/100
600 + 92 = 692
I hope this helped.
Please correct me if I am wrong.
help me with 43 pls 1.29 & 1.3 midpoint I'll mark brainliest
The midpoint of the given numbers (1.29 and 1.3) is 1.295
Calculating MidpointFrom the question, we are to calculate the midpoint of the given numbers
The given numbers are 1.29 and 1.3
To determine the midpoint of two numbers on a number line, we will add the two numbers together, and then divide value of their sum by 2
Adding up the numbers
1.29 + 1.3
= 2.59
Now, divide the result by 2
Dividing
2.59/2
= 1.295
∴ On the number line, the midpoint of the given numbers is 1.295
Hence, the midpoint of the given numbers (1.29 and 1.3) is 1.295
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The length of a rectangle is 4 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the dimensions of the rectangle.
Answer:
The dimensions are 10 inches and 24 inches.
Step-by-step explanation:
Since the quadrilateral is a rectangle, the diagonal divides the rectangle into two right triangles. That means we can use the Pythagorean Theorem, which applies only to right triangles.
On the bottom left triangle, the sides forming the right angle are the legs. They measure x and 2x + 4. The are a and b in the Pythagorean Theorem equation. The side of the triangle measuring 2x + 6 is the hypotenuse of the right triangle, the side opposite the right angle and the longest side in a right triangle. The hypotenuse is c in the Pythagorean Theorem equation.
Start with the equation of the Pythagorean theorem.
[tex] a^2 + b^2 = c^2 [/tex]
Now substitute the values we have for a, b, and c.
[tex] (x)^2 + (2x + 4)^2 = (2x + 6)^2 [/tex]
Square the two binomials. You an use the pattern:
[tex] (a + b)^2 = a^2 + 2ab + b^2 [/tex]
which I will use, or you can use FOIL and collect like terms.
[tex] x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36 [/tex]
Collect like terms, and move all terms to the left side equaling zero.
[tex] 5x^2 + 16x + 16 = 4x^2 + 24x + 36 [/tex]
[tex] x^2 - 8x - 20 = 0 [/tex]
Try to factor the left side. We need two numbers whose product is -20 and whose sum is -8. -10 and 2 work.
[tex] (x - 10)(x + 2) = 0 [/tex]
Set each factor equal to zero, and solve for x.
x - 10 = 0 or x + 2 = 0
x = 10 or x = -2
Since one side of the rectangle measures x, x = -2 cannot be a solution since you cannot have a negative side length.
x = 10 is acceptable.
2x + 4 = 2(10) + 4 = 24
Answer: The dimensions are 10 inches and 24 inches.
Show where the balance point is for the two sides .
how do you solve 2x²+4x=3+3x²