Using the properties of logarithm we get the value y = 100x⁻¹ in the exponential form axⁿ
The given logarithmic equation is :
log ₁₀y + log ₁₀x = 2
Now we know that: 1 = log₁₀10
∴log ₁₀y + log ₁₀x = 2× log₁₀10
or, log ₁₀y + log ₁₀x = log₁₀10² (10 raised to the power 2)
or, log ₁₀y + log ₁₀x = log₁₀100
we know that log p+ log q = log pq
or, log ₁₀xy = log₁₀100
Now we take antilog on both sides of the equation:
or, xy = 100
or, y = 100 / x
or, y = 100x⁻¹
Problems that cannot be solved using the concept of basic exponents alone can be solved with a logarithm. Simply said, a logarithm is another way to talk about exponents.
A relatively simple way to remember this is that base remains the base in both forms and base does not remain solely with exponent in log form. Be aware that "b" is the base on both the left and right sides of the implies symbol, and that when an equation is written in log form, the base b and exponent x do not necessarily stay on the same side of the equation.
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Write an equation of a line in slope-intercept form with the given slope and y-intercept.
slope: -2, y-intercept: 7
Answer: y=-2x+7
Step-by-step explanation:
we know that equation is y=mx+b
b=y intercept
x=the x coordinate
m=slope
y=y coordinate
then you can just fill it in from there . hope this helps
The straight line L passes through the points (4, -1) and (6, 4)
The straight line M is perpendicular to L and intersects the y-axis at the point (0, 8)
Find the coordinates of the point where M intersects the x-axis.
Answer:
Step-by-step explanation:
gradient of L:
4-(-1)/6-4
=5/2
Gradient of m=perpendicular gradient=m1xm2= -1
5/2m2=-1
5m2=-2
m2= 2/5
y intercept given=8
equation:
y= -2/5x+8
y will be0 when line crosses x-axis
input y as 0
0= -2/5x+8
2/5x=8
2=40x
x= 20
coordinate=(-20,0)
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Write an expression that represents the total owed for 6 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $50?
6(c) + 50
6(c + 50)
2(50) + c
50c + 6
Factorize Completely
6xb + 2xy - 9mb - 6my
Answer:
(3b + 2y)(2x - 3m)
Step-by-step explanation:
6xb + 2xy - 9mb - 6my ( factor first/second and third/fourth terms )
= 2x(3b + y) - 3m(3b + 2y) ← factor out (3b + 2y) from each term
= (3b + 2y)(2x - 3m)
Sam can paint a house in 5 hours. Gary can do it in 3 hours. How long will it take the two working together?
It takes them approximately 1.8 hours to paint the house together
Given,
Sam can paint a house in 5 hrs.
and, Gary can do it same work in 3 hrs.
To find the how long it will take the two working together?
Sam can paint a house in 5 hours. This means that Sam's unit rate of working is 1/5
Gary can paint the same house in 3 hours.
This means that Gary's unit rate of working is 1/3
If they work together, it would take them lesser time because they are working simultaneously. This means that their unit rates are additive. Combining their unit rates, it becomes
1/5 + 1/3 = 8/15
Assuming that if they work together, it will take them t hours. Therefore, Their unit rate of working will be 1/t.
Therefore,
8/15 = 1/t
8t = 15
t = 15/8 = 1.875
Hence, It takes them approximately 1.8 hours to paint the house together.
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Find the values of x and y. Write your answers in simplest form. Please show how the work so I can see and learn how to get the answer.
According to the area of triangle, the value of x is 8.6 and the value of y is 10.5
Area of triangle:
The area of the triangle is defined as the region enclosed by its perimeter or the three sides of the triangle.
Given,
Here we have the triangle with side values and height.
Now, we have to find the value of x and y in the triangle.
We know the formula of the triangle is,
A = 1/2 b x h
Here the value of b is x + 9 and the value of h = 6
So, the area of the triangle is,
=> [(x + 9) x 6]/2
=> 2 = 6x + 54
=> 6x = 52
=> x = 52/6
=> 8.6
Now, the value of y is calculated by using the Pythagoras theorem,
=> y² = (8.6)² + 6²
=> y² = 73.96 + 36
=> y² = 109.96
=> y = √109.96
=> y = 10.5
Therefore, the value of y is 10.5
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Element X is a radioactive isotope such that every 11 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 70 grams, how long would it be until the mass of the sample reached 14 grams, to the nearest tenth of a year?
The time taken for 14g of the radioactive isotope to remain is 25.70 years.
What is the time taken?We know that the half life is the time that it would take for us to have only half of the number of the original radioactive isotopes in the sample still remaining in the sample.
We have the following information;
Half life of the sample = 11 years
Amount of the sample initially present = 70 grams
Amount of the sample after time t = 14 grams
Given that;
N/No = (1/2)t/[tex]t_{\frac{1}{2} }[/tex]
N = amount of radioatve isotpe at time t
No = amount of radioactive isotope initially present
t = time taken
[tex]t_{\frac{1}{2} }[/tex] = half life
14/70 = (1/2)^t/11
0.2 = (1/2)^t/11
ln 0.2 = t/11 ln0.5
t/11 = ln 0.2/ ln0.5
t = 11 * ln 0.2/ ln0.5
t = 11 * (-1.61/-0.69)
t = 25.70 years
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Answer: 2.5
Step-by-step explanation:
got it right
I NEED A ANSWER RN PLS!!
A cylindrical jar has a radius of 6 inches and a height of 10inches. The jar is filled with marbles that have a volume of 20 in3. Use 3.14 for pi. Show work. Complete sentences.
a. What is the volume of the jar?
b. How many whole marbles can fit in the jar? *Each marble has the volume of 20 cubic inches
The volume of the jar is 1130.4 cubic inches and the number of marbles that can fit is 56.
What is a cylinder?In geometry, it is defined as a three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
It is given that:
A cylindrical jar has a radius of 6 inches and a height of 10inches.
The volume:
V = π(6)²(10)
V = (3.14)(6)²(10)
V = 1130.4 cubic inches
Number of marbles = 1130.4/20 = 56.52 = 56 marbles
Thus, the volume of the jar is 1130.4 cubic inches and the number of marbles that can fit is 56.
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Josh spends of his savings to buy 48 4 5 shares in a cech company. He has $18 left. Part A: How much does each share of the tech company cost? Show your work. Part B: How many more shares can Josh buy with the remainder of his savings? Explain.
Each share of the tech company cost is $1 and 18 more shares can Josh buy with the remainder of his savings.
Given:
Josh spends of his savings to buy 48 4/5 shares in a cech company. He has $18 left.
Let x be the total savings
4/5 x = 48
x = 48*5/4
= 240/4
= $60
= 4/5*60
= 240/5
= $48.
Part A:
The cost of each share of the tech company = 48/48
= $1
Part B :
He has 18 so he can buy =18*1
= 18 shares .
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Which of the following describes how the dotted line relates to the solid line (f(x))? reflection through the y-axis, f(x) → f(-x) reflection through the x-axis, f(x) → -f(x) reflection through the y-axis, f(x) → -f(x) reflection through the x-axis, f(x) → f(-x) | 100 POINTS|
Answer:
B) reflection through the x-axis, f(x) → -f(x)========================
We observe on the graph that:
The line is reflected across the horizontal axis, which is the x-axis,The reflection doesn't affect the x-coordinates,The reflection changes each y-coordinate to opposite sign.All the above helps us to conclude that:
This is the reflection through the x-axis, f(x) → -f(x)Answer:
Reflection through the x-axis, f(x) → -f(x).
Step-by-step explanation:
On comparison of the dotted red line with the solid blue line, it is apparent that the x-coordinates do not change, yet the y-coordinates are negatives of each other.
This suggests a reflection in the x-axis.
(Note: If the function was reflected in the y-axis, the y-coordinates would not change, yet the x-coordinates would be negatives of each other).
Mapping rule for reflection in the x-axis:
(x, y) → (x, -y)Therefore, as y → -y then f(x) → -f(x).
So the correct answer that describes how the dotted line relates to the solid line f(x) is:
Reflection through the x-axis, f(x) → -f(x).this was due the 7th i didn't even relize i had this due!!! pls help
The function for motorboat's distance from the shore is y = -4x + 50.
A function is a formula, rule, or law that specifies how one variable (the independent variable) and another variable are related. The linear equation is of the form Ax+By+C=0.
Where A and B are the coefficient and C is the constant.
After 9 minutes, boat is 14 km from the shore, so finding the rate of change,
Rate of Change [tex]=\frac{14-50}{9}\\[/tex]
[tex]=\frac{-36}{9}\\ =-4[/tex]
So, the rate of change of distance is 4 km / minutes.
Now, finding the function,
The function for the distance of motorboat from the shore will be,
y = -4x + 50
Where y will be the final distance and x is the minutes.
Therefore, the function for motorboat's distance from the shore is y = -4x + 50.
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expand by using the distributive property: (y^2 - 3y^3 x^-1) 2m^0 y^-2
The expanding the expression y^2 - 3y^3 x^-1) 2m^0 y^-2 using distributive property is 2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²
We need to expand the expression (y² - 3y³ + x⁻¹) (2m⁰ + y⁻²)
The distributive property allows to multiply a sum by multiplying each term separately and then add all of the products together.
y²(2m⁰ + y⁻²) - 3y³(2m⁰ + y⁻²) + x⁻¹(2m⁰ + y⁻²)
2(1)y² + y²⁻² - 3y³2(1) - 3y³⁻² + x⁻¹2(1) + x⁻¹y⁻²
2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²
Therefore, the expanding the expression y^2 - 3y^3 x^-1) 2m^0 y^-2 using distributive property is 2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²
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Please help me ASAP!!! Answer both questions for example: 1= C and 2= A
2. The equation is given as follows: x + 4x = 25.
3. The constrains are given as follows: 0 ≤ x ≤ 25, 0 ≤ y ≤ 75.
What is the equation in item 2?The time spent running is given by:
Running = 4x.
The time spent walking is one-fourth of the time spent walking, hence it is given by:
Walking = 4x/4 = x.
The total time is the sum of the times spent running and walking, hence the expression is presented as follows:
x + 4x = 25.
What are the constraints in item 3?The variables are given as follows:
x: number of out-of-state hires.y: number of in-state hires.You can accept at most 25 out-of-state hires, hence:
0 ≤ x ≤ 25
(as the number cannot be negative).
The company plans to have three times as many in-state hires, hence:
0 ≤ y ≤ 75.
As:
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help please
.............
Answer:
x ≈ 41.7 ° (a)
Step-by-step explanation:
b² = a² + c² - 2ac × cosβ
~~~~~~~~~~~
25² = 32² + 37² - 2(32)(37)cosx
625 = 2,393 - 2,368 cosx
cosx = [tex]\frac{-2393+625}{-2368}[/tex] ≈ 0.74662162
x ≈ 41.7 ° (a)
cybil and ronda are sisters. the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the cards. what is the probability that one letter is from each sister's name? express your answer as a common fraction.
Using the theories of probability, we got that 5/9 is the probability that one letter is from each sister's name if the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement.
We know very well that if we want to count number of ways by which r object can be chosen from n objects ,this can be done in [tex]^nC_r[/tex] ways which is equivalent to =(n!/(r!.(n-r)!)
Here are the same case, we have 10 cards, in each of the card there is letter written on it. So number of ways to choose two cards such that it contains any letter is can be done in [tex]^1^0C_2[/tex] ways which is equivalent to 45 ways.
Similarly, number of ways of choosing card which contains only Cybil`s name =[tex]^5C_2[/tex] ways=10 ways.
Similarly, number of ways of choosing card which contains only Ronda`s name =[tex]^5C_2[/tex] ways=10 ways.
So the number of ways containing one letter from each name = 45 - 10 - 10 = 25
So....the probability of choosing one of these sets = 25 / 45 = 5 / 9 =0.55
Hence, Cybil and Ronda are sisters. the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the cards. the probability that one letter is from each sister's name is = 5/9.
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(Complete question) is:
cybil and ronda are sisters. the 10 letters from their names are placed on 10 identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the 10 cards. what is the probability that one letter is from each sister's name? express your answer as a common fraction.
2. How would you explain why the equation √z= -7 does not have a solution?
Answer:
It does not have an answer because the square root of any number cannot be negative
Yes, the equation √z= -7 does not have a solution.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
given that, the equation √z= -7
now, we know, that the equation √z= -7 does not have a solution.
because, we know,
It does not have an answer because the square root of any number cannot be negative.
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1. George plays basketball in a week-long camp. On day 3, he scored 10 points. On day 6, he scored 16 points. Explain how to measure his average rate of change.
PLEASE HELP WILL GIVE BRAINLIEST
Answer:
The average rate of change is 2
Step-by-step explanation:
First set divide your data into 2 sets of separate data:
Independent Data= Day 3
Dependent Data = 10 points
Independent Data= Day 6
Dependent Data = 16 points
Then subtract your two independent data: 6-3=3
Then subtract your two dependent data: 16-10=6
Next divide: difference in dependent/ difference in independent
6/3=2
So, your rate of change is 2.
Calculate a four-day moving average for the price of the stock for the end of day 7. Day 1 - 62. 00; day 2 - 56. 00; day 3 - 50. 00; day 4 - 60. 00; day 5 - 59. 00; day 6 - 55. 00; day 7 - 59. 00; day 8 - 63. 0.
The average for the price of the stock for the end of day 7 is 57.28
Given,
The stock of 8 days;
Day 1 - 62. 00
Day 2 - 56. 00
Day 3 - 50. 00
Day 4 - 60. 00
Day 5 - 59. 00
Day 6 - 55. 00
Day 7 - 59. 00
Day 8 - 63. 00
We have to find the average for the price of the stock for the end of day 7.
Here,
Average = Total sum / Number
Then,
Average = (day 1 + day 2 + day 3 + day 4 + day 5 + day 6 + day 7) / n
= (62 + 56 + 50 + 60 + 59 + 55 + 59) / 7
= 401/7
= 57.28
Therefore,
The average for the price of the stock for the end of day 7 is 57.28
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Explain how you would find 36×3/4 mentally
Answer:
= 27
Step-by-step explanation:
36×3/4
36 × 3
--
4
(cross multiplication)9 × 3
= 27
sin60° change to fraction
Answer:
[tex]\frac{\sqrt{2} }{3}[/tex]
Step-by-step explanation:
Mrs.Galicia bakes and then sells cookies and brownies from her bakery. Her revenue for each baked good (in
dollars) is modeled by the equations, where x is the number of days since the bake goods started to sell.
Brownies: M (d) = 2x² + 8x - 4
Cookies: R(d) = 2x + 4
(a) Solve the system algebraically. After how many days is the revenue for each item the same? Show
your work and explain your answer.
(b) Graph this system to show both solutions. Label each axis appropriately.
a) After 1 day, the revenue for each item is the same.
b) Graph is shown in the attachment.
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
M(d) = 2x² + 8x - 4
R(d) = 2x + 4
a) Find x by taking y=M(d)=R(d). ( same revenue=y)
y= 2x² + 8x - 4
y= 2x + 4
This shows that right-side expressions are equal.
2x² + 8x - 4 = 2x + 4
2x² + 8x - 4 - 2x - 4=0
2x² +6x-8=0
Find the factors
2(x-1)(x+4)=0
x-1=0, x+4=0
x= 1, x=-4
consider positive value for days
So, after 1 day, the revenue for each item is the same
b) The equations:
y= 2x² + 8x - 4
y= 2x + 4
By taking some random values for x and finding the corresponding y values, we get the ordered pairs in the form of (x,y).
By plotting and joining those points, we get the graph as shown in the attachment.
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£410 is divided between Gordon, Malachy & Paul so that Gordon gets twice as much as Malachy, and Malachy gets three times as much as Paul. How much does Malachy get?
The amount of money that Malachy get is £123 .
In the question ,
it is given that ,
£410 is divided between Gordon, Malachy and Paul .
also given that Malachy gets three times as much as Paul ,
let the amount that Paul get = x .
So , the amount that Malachy get = 3x
it is given that Gordon gets twice as much as Malachy ,
that means , the amount that Gordon get = 2(3x) = 6x
given the total amount is £410 ,
So, equation representing the total amount is
x + 3x + 6x = 410
4x + 6x = 410
10x = 410
x = 410/10
x = 41
So , the amount that Paul get = £41 ,
amount that Malachy get = 3(41) = £123
amount that Gordon get = 6(41) = £246
Therefore , The amount of money that Malachy get is £123 .
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Why is the degree of the dilated function one more than the degree of the original function?
The degree of a function has no effect by the dilation of the function.
and the degree of the dilated function is same as the degree of the original function.
Dilation is defined as, when a function is multiplied by any number, the graph of the function retain a new shape, either by stretch or by compression in different directions.
Now, when a function is dilated it is either stretched or compressed in upward or downward direction.
It does not affect the degree of the function as the number of roots will be same as original function.
So, the degree of the dilated function is same as the degree of the original function.
Hence, the degree of the dilated function is same as the degree of the original function.
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PLEASEEEE HELP!!!
Directions: write the equation of the graph in slope-intercept form
Answer:
Step-by-step explanation:
y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis)
try this it works
please help!
Solve the equation.
√3x-5-3√x = 0
x = -
[?
Answer:
x = 7
x = 2
√ 3x − 5 = x − 3
or
3x − 5 = ( x − 3 ) 2
or
3x − 5 = x 2 − 6x + 9
or
x 2 − 9x + 14 = 0
or
x 2 − 7x − 2x + 14 = 0
or
x(x − 7) − 2(x − 7) = 0
or
(x − 7) ( x − 2) = 0
or
x − 7 = 0
or
x = 7
Ans
1
or
x − 2 = 0
or
x = 2
Ans
2
A triangle has two sides of length 4 and 6. What is the largest possible whole-number length for the third side?
Answer:
9
Step-by-step explanation:
given 2 sides of a triangle then the third side x lies within the limits
difference of 2 sides < x < sum of 2 sides , that is
6 - 4 < x < 6 + 4
2 < x < 10
then the largest possible length is 9
write 75 (base 10) using 2 numerals
Answer:
Step-by-step explanation:
75 = 64 + 8 + 2 + 1 = 1*2^6 + 1*2^3 + 1*2^1 + 1*2^0
There is no power 5, 4, or 2 so zeros go in those slots.
75 = 1001011 (Base 2)
Evaluate: 3y - 5/4x=
when y = 2 and x = 4
Answer:
1
Step-by-step explanation:
3(2)-5/4(4)
6-20/4
6-5
1
Please help ASAP!! It's due tomorrow at 745am
Answer:
L = 22 W = 4
Step-by-step explanation:
It says that the length is 6 more than 4 times its width, this means
4W + 6 = L
Perimeter is 52, this means
2W + 2L = 52
and Area is 88, this means
W*L = 88
2W = 52 - 2L
W = 26 - L
4(26 - L) + 6 = L
104 - 4L + 6 = L
104 + 6 = L + 4L
110 = 5L
L = 22
W = 26 - 22
W = 4
Plumbing: If a 45 gallon hot water tank holds 360 lbs of water, what weight of water will a 55 gallon tank hold?
Weight of water will a 55 gallon tank hold 440 lbs.
How to find the weight of water will a 55 gallon tank hold ?If a 45 gallon hot water tank holds 360 lbs.
45 gal⇒ 360 lb
55 gal ⇒ x lb?
Ratio
45 : 360 = 55 : x
Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.
Here,
do the relation
[tex]\frac{45}{360} = \frac{55}{x}[/tex]
solve the x
[tex]x = \frac{55 * 360}{45} \\ = 440[/tex]
Hence weight of water will a 55 gallon tank hold 440 lbs.
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