The value of x is 0.636.
What is logarithms?
The opposite of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
f(x) = [tex]log_{a}x[/tex] (r) y = [tex]log_{a}x[/tex], where a > 0. It is the inverse of the exponential function a^y = x. Log functions include natural logarithm (ln) or common logarithm (log).
Given equation is
e^(5x) = 24
taking log with base e on both sides:
ln e^(5x) = ln 24
Applying the formula ln e^a = a
5x = ln 24
Divide both sides by 5:
x = 0.636
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Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y =
The solution for the system of equations is the point (3, 5), and the difference x - y gives:
x - y = -2
How to solve the system of equations?Here we have the following system of equations:
5x + 3y = 30
-5x - 2y = -25
Notice that in the two equations we have the "5x", but in one case is positive and in the other negative, then we can just add them so we get:
(5x + 3y) + (-5x - 2y) = 30 - 25
(5x - 5x) + (3y - 2y) = 5
0 + y = 5
y = 5
So we found the value of y, by evaluating the second linear equation in y = 5 we will get:
-5*x - 2*5 = - 25
-5x = -25 + 2*5
-5x = -25 + 10
-5x = -15
x = -15/-5 = 3
So y = 5 and x = 3, the difference x - y gives:
3 - 5 = -2
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1/2 of a 360
circle in degrees
Answer:
Step-by-step explanation:
180 because if you add 180 + 180 = 360
Solve each system by elimination: x+5y=4 3x-7y=-10
Answer: x= -1 y= 1
Step-by-step explanation: Times -3 to get the same x
-3x - 15y = -12
3x - 7y = -10
-22y = -22
y= 1
Then put 1 back in for letter y and you get x= - 1
1/2 - 1/7 =
3/5 - 1/2
Answer:
1/2 - 1/7 = 5/14
3/5 - 1/2 = 1/10
Step-by-step explanation:
Find the measure of angle f given the information below.
A= 122 degrees
E=48 degrees the image is below!!
Answer:
74
Step-by-step explanation:
if a is 122 b is 58
b is congruent to g to g=58
58+48=106
180-106=f
180-106=74
The rate of change is how a quantity is changing with respect to a change in another quantity.
True false question.
True
False
Answer: True
Step-by-step explanation:
The rate of change or the slope is the changes to another quantity with a constant.
Write a rule for the n th term of the sequence. Then find a_{20}
$51,48,45,42,...$
The rule for the nth term of arithmetic sequence is a + (n - 1)d.
What is the nth term of arithmetic sequence?The difference between consecutive terms in an arithmetic sequence is always the same.An arithmetic sequence's nth term is given by a = a + (n - 1)d. The number d is known as the common difference because any two consecutive terms of an arithmetic sequence differ by d, and it can be found by subtracting any two terms a and an+1.Here also,
We use the definition for the nth term of an arithmetic sequence:
an = a1 + (n - 1) d
Here first term (a1) = 51
common difference (d) = a2 - a1
= 48 - 51
= -3
We have to find 20th term,
a[20] = a1 + (20 - 1) d
= 51 + 19 x -3
= 51 - 57
= - 6
Therefore 20th term of the sequence 51,48,45,42,... is -6.
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Roger is moving 40 1/2pounds of bricks for a landscaping project. He moves 7 1/3 pounds of bricks in each load, then takes a short break. Which equation will help you solve to find out how many whole loads of bricks, b, Roger will move?
The equation to find how many loads of bricks that Roger move will be 44x=243.
What does linear equation mean?A linear polynomial over a field with zero coefficients can be used to create a linear equation. The answers to such an equation are the numbers that, when the unknowns are replaced, make the equality true.
This particular situation, in which the variable is accurately referred to as the unknown, is commonly referred to as a "linear equation."
In the case of two variables, each solution can be thought of as a point's Cartesian coordinates on the Euclidean plane. The answers to a linear equation result in a line.
Given,
Total amount of bricks load carried by Roger=40 1/2pounds
=81/2 pounds
Per each load --- 7 1/3pounds
1 load --------- 22/3 pounds
x -----81/2 pounds
(81/2)(3/22)=x
243=44x
44x=243
Therefore, the equation to find how many loads of bricks that Roger move will be 44x=243.
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9. You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula A = P(1 + r/n) ^nt to give:
a. The future value in 4 years.
b. The interest gained in 4 years.
The compound interest formula [tex]A = P(1 + r/n) ^nt[/tex] Monthly compounding is a common strategy used by interest-bearing CDs to boost returns. The annual interest rate is divided by twelve in this scenario.
How to calculate interest ?After 4 years, you should have $763 in your account.After four years of saving $4 every month, your funds may reach $762.90. This includes a $500.00 initial balance and a 2.85% yearly rate of return.
Invest $500 in a 4-year certificate of deposit (CD) earning 2.85% interest compounded monthly.utilizing the compound interest formula [tex]A = P ( 1 + r / n ) ^{nt}[/tex]
The formula for calculating simple interest is S.I. = P R T, where P stands for principal, R for the annual percentage rate of interest, and T for time, which is typically expressed as the number of years. The interest rate is expressed as a percentage, or r%, and should be represented as r/100.
Many interest-bearing CDs use monthly compounding to increase returns. This model divides the annual interest rate by twelve.
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Olivia want to have a 90 average in algebra, where tet count for 55%, quizze count for 30ge % and homework count for 15%. If he ha a 92 tet average and 100% HW average, what mut her quiz average be? Let x = the average of the
In order to score 90 average in algebra her quiz average should be 82%.
It involves calculating the result of multiplying a number of quantities by their sum, then dividing the result by the total number of quantities.
Given,
She has a test grade of 55%, a quiz grade of 30%, and a homework grade of 15%.
If she achieved a score of 92% on the test
Make x the number of tests,
x = (90 - (0.55(92) + 0.15(100)))/0.30
x = 82
To receive a 90 in math, Olivia needs to have a quiz average of 82.
One of the oldest subfields of mathematics, algebra covers number theory, geometry, and analysis. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.
Algebra covers a wide range of topics, from the study of abstractions to the solution of simple equations.
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Which equation represents how to determine the speed of an object?
The equation that the speed of an object is speed = distance/time
How to determine the equation of an objectFrom the question, we have the following parameters that can be used in our computation:
Parameter = Object
Argument = Speed
By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object
Mathematically, this can be represented as
Speed = Distance : Time
Express as fraction
Speed = Distance/Time
Hence, the equation is Speed = Distance/Time
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At a football stadium, 25% of the fans in attendance were teenagers. If there were 10 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
40 people
Step-by-step explanation:
25% = 10
50% = 20
100% = 40
A hospital is going to be built in the land of the shape of a rhomus having its
diagonals 250 m and 480 m respectively in a mountainous district of Nepal. Find
the area covered by the hospital in Ropani. (1 Ropani = 508.72 m²).
Answer:
117.94 Ropani
Step-by-step explanation:
Area Of Rhombus=½×d1×d2
=½×480×250
=60,000m²
1Ropani=508.72 {As Given}
60,000m²=(60,000÷508.72)Ropani
=117.94 Ropani
Answer:
60000 m^2
117.943 ropani
Step-by-step explanation:
the area of rhombus = 250 × 480 ÷2=60000 m^2
60000 m^2 = 117.943 ropani
what is x and what is the reason why (circle theorems)
Check the picture below.
Harmony pays $64.00 per month for a base cable package and an additional amount for on-demand programming. Last month, Harmony received a $67.36 cable bill.
$64.00 + x = $67.36
Ignoring sales tax and additional fees, how much did she spend for on-demand programming?
A) $3.36
B) $6.36
C) $70.72
D.) $131.36
Are any of these numbers linear expressions? 5x+3, 8xy, 14, or 3x^2
Answer: 5x+3 is a linear expression
Step-by-step explanation:
The linear expression is y=mx+b
5x +3 has a slope and y-intercept, so it is a linear expression!
8xy is not because it is just a variable
3x^2 is not because it has ^2
Determine the equation of the parabola with vertex (7,4) and a directrix y=10.
The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application",
What is the parabola?pa·rab·o·la pə-ˈrab-ə-lə : a curve formed by the intersection of a cone with a plane parallel to a straight line in its surface : a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. : something that is bowl-shaped.This form is called the standard form of a quadratic function. The graph of the quadratic function is a U-shaped curve is called a parabola. The graph of the equation y=x2, shown below, is a parabola.The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax. Some of the important terms below are helpful to understand the features and parts of a parabola.
The equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .
It is given to us that -
The vertex of the parabola = (-8,5)
The directrix of the parabola is y = -3
We have to find the equation of the parabola with the given vertex and directrix.
We know that any point on a given parabola represented as () is equidistant from the directrix and the focus.
So, the equation for the point can be represented as
[tex][y-(-3)]=\sqrt{([x-(-8} ]^{2} +(y-5)^{2}[/tex]
[tex](y+3)^2} =(x+8)^{2} +(y-5)^{2} \\=y^{2}+9+2*y*3=(x+8)^{2} +y^{2}+25-2*y*(-5)=6y-10y=(x+8)^{2} +16=-4y=(xx+8)^{2} +16=y=\frac{-1}{4} (x+8)^{2}+4[/tex]
Thus, the equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .[tex]=y=\frac{-1}{4} (x+8)^{2} +4[/tex]
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A shopper at a clearance sale is pleased to discover some lamps on sale for $9 each. The original price tags read $30. What percentage is the discount?
Answer: 70% of a discount
Step-by-step explanation:
Hillary is using the figure shown below to prove Pythagorean Theorem using triangle similarity: In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC. The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC. Which of these could be a step to prove that BC2 = AB2 + AC2? (6 points) By the addition property of equality, AC2 plus AD2 = AB multiplied by DC plus AD2. By the addition property of equality, AC2 plus AD2 = BC multiplied by DC plus AD2. By the addition property of equality, AC2 plus AB2 = AB multiplied by DC plus AB2. By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.
Answer: By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.
The angles of a triangle are 44 degrees, 110 degrees, and 26 degrees. Classify the triangle
The measure of angles form an scalene triangle.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
An angle requires two straight line, such that they're connected on one of their endpoints. The point of their joint is called vertex of that angle.
We are given that the angles of a triangle are 44 degrees, 110 degrees, and 26 degrees.
Since we know that angle sum property of a triangle;
44 + 110 + 26
180
Therefore, the measure of angles form an scalene triangle.
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A large pizza at palanzio pizzeria cot $6. 80 plu $. 90 for each topping. The cot of a large pizza at guido' pizza i $7. 30 plu $. 65 for eachtopping. How many topping need ti be added ti a large pizza from palanziod pizzeria and guido' pizza in order for the pizza to cot the ane not including tax
2 toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.
Let x be the number of toppings to be added to each pizza and y be the total cost of pizza.
A large pizza at Palanxio's Pizzeria cot $6. 80 plu $. 90 for each topping.
So, we get an equation,
y = 6.80 + 0.90x
The cot of a large pizza at Guido's Pizza i $7. 30 plu $. 65 for eachtopping.
So, we get an equation,
y = 7.30 + 0.65x
We need to find the number of toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.
Now let's equate the costs of both pizzas and solve for x.
6.80 + 0.90x = 7.30 + 0.65x
0.25x = 0.50
x = 2
Therefore, 2 toppings to be added to each pizza
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What is the y-intercept of this line?
Answer: b=13
Step-by-step explanation:
This equation is in point-intercept form: y = mx + b
slope = m = 4/3
y-intercept = b = 13
. if you start with 1/4, you can create an entire class of fractions equivalent to 1/4 like the one above, by multiplying 1/4 by different forms of what number?
If you start with 1/4, you can create an entire class of fractions equivalent to 1/4 by multiplying 1/4 by different forms of the number 1.
What are fractions?The connection between two numbers, known as the numerator and the denominator, is expressed mathematically as fractions. The number of pieces is represented by the numerator, while the total number of components is represented by the denominator. For instance, if a pizza is cut into 8 slices and someone eats 3 of them, the fraction corresponding to the quantity consumed would be 3/8.
Diverse mathematical ideas, including division, ratios, and proportions, can be represented using fractions. They can also be used to represent decimal and percentage values, with the decimal point placed to the right of the numerator and the number of decimal places represented by the denominator.
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for every 8chin ups Melanie can do Theresa can do 5. If Melanie did 48 chin ups, how many fewer did Theresa do
Answer: Theresa did 18 fewer chin-ups.
Step-by-step explanation:
Melanie 8,16,24,32,40,48
Theresa 5,10,15,20,25,30
48-30=18
7. What is the number?
The number is between 10 and 20.
The number is composite.
The number is odd.
Answer:
The number is 15
Answer:
15
Step-by-step explanation:
The number is between 10 and 20.
10 11 12 13 14 15 16 17 18 19 20
The number is composite or have more than 2 factors.
10 12 14 15 16 18 20
The number is odd.
15
Jimmy, Johny, and Jolly worked part-time on the weekend to earn some extra money. Three of them together earned $57. If Johny earned twice as much as Jolly did and Jimmy earned $3 less than Johny did, how much did Jimmy earn?
On solving the provided linear equation question - Jolly = $17.4, Jimmy =2x-30 =4.8 and Johnny = 2x=34.8
What is a linear equation?A linear equation has the algebraic form y=mx+b. where m is the slope and b is the y-intercept, consisting of a first-order (linear) term and a constant. If x and y are variables, the above is sometimes called a "two-variable linear equation".
Take Jolly's expenditure as x.
Jimmy would have spent twice as much as Jolly.
Johnny Equals 2x-30 if Johnny spent $30 less than Johnny.
Total amount spent: $57
Therefore,
[tex]x+ (2x-30) + 2x = 57\\ x+ 2x -30 +2x =57.\\ 5x = 57+ 30\\[/tex]
x = 87/5
x= 17.4
Now take is that - X= 17.4.
Jolly is that - x= $17.4
Jimmy is that - =4.8
Johnny is that = =34.8
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three solutions of the equation y= -2x
Answer:
three solutions of the equation:
y = -2x - 1
=>
1) (0, -1)
2) (1, -3)
3) ( -1, 1)
Step-by-step explanation:
there are 5 children on your guest list and 40 people in total. what percentage of the people are children?
Answer: 12.5%
Step-by-step explanation:
5/40
0.125 x 100
12.5%
Answer:
2 children I believe so
Step-by-step explanation:
because you take 40%×5 and u will get 2
Algebraic fractions which option is correct
Answer:
A
Step-by-step explanation:
because to solve this question the division would change into multiplication and the second fraction would be converted upside down
power 121.three consecutive prime numbers, each less than $100$, have a sum that is a multiple of $5$. what is the greatest possible sum?
The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.
We have,
To find the three consecutive prime numbers with a sum that is a multiple of 5 and each less than 100, start by listing the prime numbers less than 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Check each combination:
(2, 3, 5): Sum = 2 + 3 + 5 = 10 (which is a multiple of 5)
(3, 5, 7): Sum = 3 + 5 + 7 = 15 (which is a multiple of 5)
(5, 7, 11): Sum = 5 + 7 + 11 = 23 (not a multiple of 5)
(7, 11, 13): Sum = 7 + 11 + 13 = 31 (not a multiple of 5)
(11, 13, 17): Sum = 11 + 13 + 17 = 41 (not a multiple of 5)
(13, 17, 19): Sum = 13 + 17 + 19 = 49 (which is not a multiple of 5)
(17, 19, 23): Sum = 17 + 19 + 23 = 59 (not a multiple of 5)
(19, 23, 29): Sum = 19 + 23 + 29 = 71 (not a multiple of 5)
(23, 29, 31): Sum = 23 + 29 + 31 = 83 (not a multiple of 5)
(29, 31, 37): Sum = 29 + 31 + 37 = 97 (not a multiple of 5)
(31, 37, 41): Sum = 31 + 37 + 41 = 109 (which is not a multiple of 5)
(37, 41, 43): Sum = 37 + 41 + 43 = 121 (which is not a multiple of 5)
(41, 43, 47): Sum = 41 + 43 + 47 = 131 (not a multiple of 5)
(43, 47, 53): Sum = 43 + 47 + 53 = 143 (which is not a multiple of 5)
(47, 53, 59): Sum = 47 + 53 + 59 = 159 (which is not a multiple of 5)
(53, 59, 61): Sum = 53 + 59 + 61 = 173 (not a multiple of 5)
(59, 61, 67): Sum = 59 + 61 + 67 = 187 (not a multiple of 5)
(61, 67, 71): Sum = 61 + 67 + 71 = 199 (not a multiple of 5)
(67, 71, 73): Sum = 67 + 71 + 73 = 211 (not a multiple of 5)
(71, 73, 79): Sum = 71 + 73 + 79 = 223 (not a multiple of 5)
(73, 79, 83): Sum = 73 + 79 + 83 = 235 (which is a multiple of 5)
(79, 83, 89): Sum = 79 + 83 + 89 = 251 (not a multiple of 5)
(83, 89, 97): Sum = 83 + 89 + 97 = 269 (not a multiple of 5)
Thus,
The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.
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