a. Rewrite the equation in exponential form.b. Create a table of coordinates, using the exponential form from part (a). Begin by selecting -2, -1, 0, 1, and 2 for y.c. Using the coordinates from part (b), graph the logarithmic function.y = log 3xa. Rewrite the equation in exponential form. x =b. For each given value of y, find the value of x to complete the ordered pair.x = 3Yy(x,y)x = 3-2-2X = 3-1-1x = 300X = 3¹x = 3²12.-2)].0)(0.2)
Answers
We have the equation:
\(y=\log_3x.\)a) To express x in terms of y, we take into account the following property of logarithms:
\(y=\log_ax\Rightarrow x=a^y.\)Choosing a = 3, we have:
\(x=3^y.\)b) Now, we evaluate this function for the values y = -2, -1, 0, 1 and 2. To do that, we simply replace the value of y in the last equation, then we simplify the result:
1) y = -2
Replacing y = -2 in the equation of x, we have:
\(x=3^{-2}.\)Now, the negative power of a number can be written as the positive power but in the denominator:
\(x=\frac{1}{3^2}.\)The 3 square is equal to 3*3 = 9, so we have:
\(x=\frac{1}{9}.\)So the point for y = -2 is:
\((x,y)=(\frac{1}{9},-2).\)2) y = -1
\(y=-1\operatorname{\Rightarrow}x=3^{-1}=\frac{1}{3^1}=\frac{1}{3}\Rightarrow(x,y)=(\frac{1}{3},-1).\)3) y = 0
\(y=0\operatorname{\Rightarrow}x=3^0=1\Rightarrow(x,y)=(1,0).\)4) y = 1
\(y=1\operatorname{\Rightarrow}x=3^1=3\Rightarrow(x,y)=(3,1).\)5) y = 2
\(y=2\Rightarrow x=3^2=9\Rightarrow(x,y)=(9,2).\)Answera) The exponential form is: x = 3^y
b) The values of x for the table are:
• y = -2 ⇒ (,1/9,, -2)
,• y = -1 ⇒ (,1/3,, -1)
,• y = 0 ⇒ (,1,, 0)
,• y = 1 ⇒ (,3,, 1)
• y = 2 ⇒ (,9,, 2)
Related Questions
PLEASE ANSWER - PLEASE ANSWER
The diagram shows triangle ABC. ABC and BED are straight lines. AB = 12.2cm, CD = 5.8cm, BE:ED = 3:1, Angle ADB = 90°, Angle ABD = 38°.
Work out the size of angle DCE, correct to 1 decimal place. SHOW ALL WORKING IN TEXT FORM, NO IMAGES.
Answers
The measure of angle DCE in this problem is given as follows:
m < DCE = 22.5º.
How to obtain the measure of angle DCE?The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.
The three trigonometric ratios are given as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:
cos(38º) = DB/12.2
DB = 12.2 x cosine of 38 degrees
DB = 9.6 cm.
BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:
DE = 1/4 x 9.6
DE = 2.4 cm.
Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:
tan(x) = 2.4/5.8
x = arctan(2.4/5.8)
x = 22.5º
m < DCE = 22.5º.
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Answer:
x = 22.5°
Step-by-step explanation:
BD = cos(38)*12.2 = 9.61DE = 9.61*¼ = 2.4∠DCE = tan(2.4/5.8) = 22.5°Franklin has three coins, two fair coins (head on one side and tail on the other side) and one two-headed coin.
1) He randomly picks one, flips it and gets a head. What is the probability that the coin is a fair one?
2) He randomly picks one, flips it twice. Compute the probability that he gets two tails.
3) He randomly picks one and flips it twice. Suppose B stands for the event that the first result is head, and C represents the event that the second result is also head. Are B and C independent? Are B and C independent, conditioned on the event that the two-headed coin was picked?
Answers
Answer:
1. 0.445 or 0.5
2. 0.167 or 0.2
3. Yes and No
Step-by-step explanation:
2 coins are fair and the 3rd is two-headed
So there are 2 tails and 4 heads altogether.
(A) He randomly picks one, flips it and gets a head. What is the probability that the coin is a fair one?
The probability that the coin is a fair one is: Probability of a fair coin x Probability of obtaining a head
= 2/3 x 4/6 = 0.445 to 3 decimal places
(B) He randomly picks one and flips it twice. Compute the probability that he gets 2 tails
This is = [the sum of the probability that each coin produces a tail 2 times when flipped twice] divided by 3.
For Coin 1, 0.5 is the probability of getting tails. For two consecutive tails, the probability would be 0.5 x 0.5 = 0.25
Same goes for Coin 2 which is the second fair coin.
For Coin 3, the probability of getting a tail at all is 0.
So [0.25 + 0.25 + 0] / 3 = 0.167 to 3 d.p.
(C) Suppose B = the event that the first result is head
Suppose C = the event that the second result is also head
- Are B and C independent (if the two-headed coin wasn't picked)?
YES
- Are B and C independent (if the two-headed coin was picked)?
NO
Given that Franklin has three coins, two fair coins (head on one side and tail on the other side) and one two-headed coin, to determine 1) if he randomly picks one, flips it and gets a head, what is the probability that the coin is a fair one; 2) if he randomly picks one, and flips it twice, what is the probability that he gets two tails; and 3) if he randomly picks one and flips it twice, supposing B stands for the event that the first result is head, and C represents the event that the second result is also head, if B and C are independent, the following calculations must be made:
1)
Total heads = 4fair heads = 22/4 = 0.5The probability that the coin is a fair one is 50%.
2)
2/6 x 2/6 = X0.333 x 0.333 = X0.1111 = XThe probability that he gets two tails is 11.11%.
3)
B and C will be independent as long as it is a fair coin.
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The data set below shows a relationship between the number of hours tara works and her paycheck:{ 1, 25), (2, 40), (3, 55), (4, 70), (5, 85), (6, 100) what is Tara's hourly pay rate?
Answers
Step-by-step explanation:
Need to find out total hours and total pay and simplify the answer.
Total Hours = 1+2+3+4+5+6 = 21
Total Pay = 25+40+55+70+85+100 = 375
Pay ÷ Hours = 375 ÷ 21 = 17.86
Not convinced with this answer tbh but it's what I got.
Seven years ago, Grogg's dad was 6 times as old as Grogg, and 3 years ago, his dad was 4 times as old as Grogg. How old is Grogg's dad currently?
Answers
Answer:
Grogg's dad is 22
Step-by-step explanation:
Let D = dad's current age
Let g = Grogg's current age
6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g
4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g
Set the two equations equal to each other and solve for d
6d - 35 = 4d - 9 Subtract 4d from both sides
2d -35 = -9 Add 35 to both sides
2d = 44 Divide both sides by 2
d = 22
Helping in the name of Jesus.
Answer:
Step-by-step explanation:
d = current dad age
g = current grogg age
d-7 = 6(g-7)
d-3 = 4(g-3)
Let's solve the first equation first:
Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35
Substitude d = 6g - 35 for d in d - 3 = 4g - 12
(6g-35)-3 = 4g-12 = 6g-38 = 4g-12
Subtract 4g from both sides: 2g - 38 = -12
Add 38 to both sides: 2g = 26
Easy: g = 13
And now substitude g in for any equations.
d-3 = 52-12
d = 43
Find the Measure of each angle.
Answers
Answer:
x = 10
Step-by-step explanation:
to find the measure of angles we first need to find the value of x
The sum of interior angles in a triangle is equal to 180
9x + 7x + 2x = 180 add like terms
18x = 180 divide both sides by 18
x = 10 to find angle measures replace x with 10 in each representative like:
m<L = 9x and 9*10 = 90 and so on
What's the first term of the expansion of (x+y)9?
Answers
Select the correct answer from each drop-down menu.
The total area of the three triangles is
square units.
The area of the figure is
square units.
Answers
The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
From the figure, the area of triangles can be calculated using the:
Area = (1/2)height×base length
Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)
Area of three triangle = 1/2(24×3) = 36 square units
Area of the figure = area of three triangle + area of the rectangle
= 36 + 6×4
= 60 square units
Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
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Total population was 6,013 in 2018 and 5,175 in 2019.
What was the percent of change in population from 2018 to 2019?
Answers
Answer: : it is 4 over 8 and *
Step-by-step explanation:
Best represents the population
Answers
The equation that best represents the population of the town, which increases exponentially at the rate of 6% every year, after x years is C. y = 158,260(1.06)ˣ.
What is exponential growth?Exponential growth refers to a constant percentage or rate of growth per period.
The opposite of exponential growth is exponential decay and refers to the constant rate of decay in value per period.
The town's initial population = 158,260
Growth rate per year = 6%
Let x = the number of years of growth
Let y = the population after x years
Equation:y = 158,260(1 + 0.06)^x
Thus, the correct equation representing population growth after x years is Option C.
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Select the correct answer from each drop-down menu.
The area of the shaded square is
square inches. The length of the unshaded rectangle is
inches.
The estimated value of the length of the shaded square is
inches. The estimated value of the area of the unshaded rectangle is
square inches.
Answers
The completed statement with regards to the area of the square and the rectangle are;
The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.
What is the area of a square?The area of a square is the product of the side lengths which are congruent, therefore;
Area of a square = Side length, s × Side length, s = s²
The possible figure in the question includes;
A shaded square that is 125 square inches
An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches
Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.
Therefore;
The side length of the square = √(125) inches = 5·√5 inches
The estimated value of the side length of the square is; 5·√5 inches
The area of a rectangle = Length × Width
The length of the rectangle = 7·√5 inches
The width of the rectangle = 5·√5 inches
Therefore;
The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175
The estimated area of the unshaded rectangle is 175 square inches
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find the area A and round three decimal places
Answers
Answer:
24.740
Step-by-step explanation:
35/360 × 3.142 × 9² = 24.740
Answer:
A = 35/360 x pi x 9^2
A= 24.740m^2
Answer is 24.740m^2
Hope this helps!
Please check all that apply
Answers
The symbols which correctly relates the two numbers are :
>≥≠We could relate the two given numbers 100 and 20 on the basis of magnitude and equality.
100 is greater than 20, 100> 20
100 is greater than or equal to 20 , 100 ≥ 20
100 is not equal to 20 , 100≠20
Therefore, the symbols which relates the numbers are :
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What is the sum of the series?
Answers
(3x^3)^2 write without exponent
Answers
Answer:
9*x*x*x*x*x*x.
Step-by-step explanation:
(3x^3)^2
= 3^2 * x^(3*2)
= 3^2 * x^6
= 9*x*x*x*x*x*x
how many times does 12 go into 72
Answers
Answer:
Step-by-step explanation:
6
Perform the operation and write the result in standard form.
(4 − 3i)2
Answers
Answer:
8-6i
Step-by-step explanation:
Multiply each part of the equation inside the parenthesis by 2. So you have 8 - 6i
help with math please it means the world to me!!
Answers
Answer:
10 units^2
Step-by-step explanation:
Part 1: 12% annual interest on 132000 for 8 days
Part 2: 12% annual interest on 106,750 for 20 days.
If it helps, it's a 5 year note. Assuming 365 days in a year.
Answers
The interest for Part 1 is approximately $385.10.
The interest for Part 2 is approximately $709.31.
To calculate the interest for Part 1 and Part 2The formula is as follows:
Interest is calculated as follows: Principal * Rate * Time
Where
Principal represents the starting sumThe interest rate is rateTime measures length in years.Part 1:
$132,000 is the principal.
(Decimal) Rate = 12% = 0.12
Time = 8 days/365 days.
How much interest is there in Part 1?
Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10
Therefore, the interest for Part 1 is approximately $385.10.
Part 2:
$106,750 as the principal
(Decimal) Rate = 12% = 0.12
Time = 20 days / 365 days.
How much interest will there be in Part 2
Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31
Therefore, the interest for Part 2 is approximately $709.31.
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Help me plssssssssss
Answers
Answer:
The answers are as follows:
5. \(12+3 = 3+12\)
7. \((6+4)+8 = 6+(4+8)\)
9. \((10*5)*7 = 10*(5*7)\)
Step-by-step explanation:
5. 12 and 3
Commutative property of addition states that the order of two numbers in addition doesn't matter; the result will be the same. If a and b are two numbers then the property will be:
a+b = b+a
For the given question, the commutative property will be:
\(12+3 = 3+12\)
Associative property deals with three numbers or variables. It states that when 3 numbers are being added or multiplied their order doesn't affect the result.
It can be stated as:
(a+b)+c = a+(b+c)
7. 6,4 and 8
The associative property will be:
\((6+4)+8 = 6+(4+8)\)
9. 10,5 and 7
\((10*5)*7 = 10*(5*7)\)
Hence,
The answers are as follows:
5. \(12+3 = 3+12\)
7. \((6+4)+8 = 6+(4+8)\)
9. \((10*5)*7 = 10*(5*7)\)
Round off 1,296,717 to 3 significant figures
Answers
Answer:6 1296720 1.29672 × 106
5 1296700 1.2967 × 106
4 1297000 1.297 × 106
3 1300000 1.30 × 106
2 1300000 1.3 × 106
1 1000000 1 × 106
Step-by-step explanation:
The word isometric can be broken into two parts. The prefix "iso-” means "of the same,” and "-metric” means "measure.” How does the meaning of the word isometric relate to determining if an isometric transformation occurred? Include the defining characteristics of angle measure and line segments in your response.
Answers
The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.
When we speak about geometric figures, the concept of shape, size, and orientation come into play.The defining characteristics of angle measure and line segments play a critical role in determining whether an isometric transformation has occurred. In geometry, angle measures are the measurements of angles in a geometric figure. An angle is formed by two line segments that share a common endpoint. It is a unit used to calculate the measure of a plane figure's interior or exterior, such as a polygon. In other words, the size of the angle doesn't change during an isometric transformation.Line segments are the building blocks of geometric figures. They are used to construct geometric figures such as polygons, triangles, and rectangles, among others. In an isometric transformation, the length of the line segments remains constant because the shape and size of the original figure and its transformed equivalent remain the same.In conclusion, the word "isometric" implies that the transformation has the same measurements of the original figure. It is a transformation that retains the original geometric figures' shape, size, and orientation. The defining characteristics of angle measure and line segments remain unchanged during the isometric transformation. This means that if an isometric transformation occurs, the original and transformed figures have the same measurements of angles and line segments.For such more question on isometric
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what is -8m + 3x - 2m + 7x and please explain why.
Answers
Answer:-10m+10x
Step-by-step explanation: add -8m plus -2m which gives you -10m and then add 3x plus 7x which gives you 10x so the final answer is -10m+10x.
If the base area of a cylinder is 176.625
square centimeters and the height is 3.5
centimeters, determine the volume of the
cylinder
Answers
Answer:
618.1875 cm^3
Step-by-step explanation:
Volume = base area x height, so 176.625 x 3.5 = 618.1875
Twenty -six students are going on a field trip and 18 students are staying at school. What is the ratio of the number of students who are going on the field trip to the number of students who are staying at school?
Answers
Answer:
26 to 18
26 cause that's the number of kids goin g to the field trip to 18 cause that's all the kids staying
help plz!!!! 30 points!!!!!!!!!! i will mark brainliest for who answers first! anveer bought 0.7 pounds of sliced ham at his local deli. If the deli charged $6.79 per pound, how much did Tanveer pay? A. $2.04 B. $4.75 C. $7.49 D. $9.70
Answers
Answer:
B
Step-by-step explanation:
\(6.79 \times 0.7\)
\(=4.753\)
Answer:
The correct answer would be $4.75
Step-by-step explanation:
6.79 × 0.7
=$4.75
Hope that was helpful.Thank you!!!
Expressed as a single fraction, 3/4x - 2/5x is equal to
Answers
The single fraction is 7x/20
What is a fraction?A fraction can be defined as the part of a whole variable, number or element.
The different types of fractions are;
Simple fractionsMixed fractionsProper fractionsComplex fractionsImproper fractionsWhat are algebraic expressions?Algebraic expressions are mathematical expressions consisting of terms, coefficients, variables, factors and constants.
They are made of operations such as multiplication, addition, subtraction, division, etc
Given the expression;
3/4x - 2/5x
Find the LCM
15x - 8x/20
7x/20
Thus, the value is 7x/20
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ALGEBRA please put a very small explanation to the awnser
Answers
Certainly! The problem can be solved using the Pythagorean theorem,
which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.
The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.
By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.
Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.
We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.
Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.
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1. Samuel paid #34.20 for a blanket. If the marked price of the blanket is #41.78. What is the discount?
2. A mother buys a dress for her daughter at a discount of 18%. If the price of the dress is #35.00. How does she actually pay for the dress?
Answers
Answer:
1. The discount is 10%
2. 250
please help thank you !!
Answers
Answer:
80 gallons
Step-by-step explanation:
First to find this, we must divide 10 by 4, and yes I know this will give us a decimal, but it must be done. This division will give us 2.5, we must then multiply 2.5 by 32, as we are given 32 gallons for 4 loads of dishes, and if 2.5 times 4 loads is 10 loads, then we must multiply 32 by 2.5 as well, giving us the answer, 80 gallons
Answer:
80 gallons
Step-by-step explanation:
The answer is 80 gallons when using the distributive, and communitive property of multiplication and division.
Feel free to give brainliest. I hope everyone has an excellent day!
If anyone is willing to try and answer this go ahead
Answers
Answer:
X intercept: x = 4 or in point form (4,0)
Zero for the function at (4, 0)
Y intercept : y = 160 or in point form (0,160)
slope = -40 mph
Step-by-step explanation:
The y-intercept, x-intercept are directly obtained from the graph by noticing the points on the axes where the line crosses them.
The slope is calculated using the points (0, 160) and (4, 0) and the formula for the slope of the segment that joins them:
slope = (y2 - y1)/(x2 - x1) = (160 - 0) / (0 - 4) = -160/4 = -40
and the units of the slope are miles over hour (that is miles per hour or mph)