the correct option is:
"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."
Which of the following statements can be used to construct an algebraic proof the point A lies on circle P?
A circle is defined as the set of equidistant points to a given point which is the center of the circle.
That distance to the center is called the radius.
Here, the center is at the point (0, 0), also called the origin, so if the distance between the point A and the origin, then point A lies on top of the circle P.
From that, we conclude that the correct option is:
"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."
That is the only proof that we can (and should) use to prove that a point lies on a circle.
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Answer:
The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."
Step-by-step explanation:
I did the test
4(6)^x 864 for x answer for x
Answer:
x = 3
Step-by-step explanation:
Maybe you want the value of x such that ...
4(6^x) = 864
SolutionDividing by 4 gives ...
6^x = 216
You may know that 216 = 6^3. Using that, we can equate exponents:
6^x = 6^3
x = 3
Alternatively, we can use logarithms to find x. Taking logs gives ...
x·log(6) = log(216)
x = log(216)/log(6) = 3
A drink bottle is 3/8 full. It contains 240 millilitres of water. How much water does the bottle contain when it is half-full?
Answer: 320 mL
Step-by-step explanation:
Given information
The bottle is currently 3/8 full
Current Volume = 240 mL
Concept:
Imagine the water in the bottle being separated into 8 parts
Currently, 3 parts are being occupied
Determine the volume for 1 part
3 parts = 240 mL
1 part = 240 / 3 = 80 mL
Determine the volume for half-full (4 parts)
1 part = 80 mL
4 parts = 80 × 4 = [tex]\Large\boxed{320~mL}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A teacher wants to split 6 decks of cards between 8 students equally. How many decks of cards will each student get?
6 decks of cards = 60 cards
---> 60/8 = 15/2 = 7.5
7.5 cards = 0.75 decks of cards
Therefore, each student will get 0.75 decks of cards.
Answer:
1
Step-by-step explanation:
Everyone gets 1 and there's 2 left over
7. stano. (2pt) Find the centers, foci, vertices and asymptotes of the hyperbola with equation given by: 16y²-x² - 6x - 32y = 57 And also sketch the hyperbola. (2pts)
The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.
According to the statement
we have to find the centers, foci, vertices and asymptotes of the hyperbola from the given equations.
So, For this purpose,
Hyperbola is a a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant.
So, The given equation is:
16y²-x² - 6x - 32y = 57
So, rearrange it then
-x² - 6x - 32y + 16y² = 57
-(x² + 6x) + (16y² - 32y ) = 57
-(x² + 6x) + 16(y² - 2y ) = 57
-(x² + 6x + 9) + 16(y² - 2y +1 ) = 57 +1(16) + 9(-1)
-(x+ 3)² + 16 (y-1)² = 64
-(x+ 3)² + 16 (y-1)² = 64
divide whole equation by 64 then
[tex]\frac{-(x+ 3)^{2}}{64} + \frac{16 (y-1)^{2}}{64} =\frac{64}{64}[/tex]
then equation become
[tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex]
This become the equation of hyperbola.
So,
here coordinates of center is (0,0)
And asymptote is become 16.
So, The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.
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Solve the inequality 2x>30+5/4x
Answer:
Step-by-step explanation:
[tex]2x > 30+\frac{5}{4x} \\2x-\frac{5}{4x} > 30\\\frac{8x^2-5}{4x} > 30\\case~1\\if~x > 0\\8x^2-5 > 120x\\8x^2-120x > 5\\x^2-15x > \frac{5}{8} \\adding~(-\frac{15}{2} )^2~to~both~sides\\(x-\frac{15}{2} )^2 > \frac{5}{8}+\frac{225}{4} \\(x-\frac{15}{2} )^2 > \frac{455}{8} \\x-\frac{15}{2} < -\sqrt{\frac{455}{8} } \\x < \frac{15}{2}-\sqrt{\frac{455}{8} } \\or~x < 0\\rejected~as~x > 0[/tex]
[tex]x-\frac{15}{2} > \sqrt{\frac{455}{8} } \\x > \frac{15}{2} +\sqrt{\frac{455}{8} }[/tex]
case~2
[tex]if~x < 0\\8x^2-5 < 120x\\8x^2-120x < 5\\x^2-15x < \frac{5}{8} \\adding~(-\frac{15}{2} )^2\\(x-\frac{15}{2} )^2 < \frac{5}{8} +(-\frac{15}{2} )^2\\|x-\frac{15}{2} | < \frac{5+450}{8} \\-\sqrt{\frac{455}{8} } < x-\frac{15}{2} < \sqrt{\frac{455}{8} } \\\frac{15}{2} -\sqrt{\frac{455}{8} } < x < \frac{15}{2} +\sqrt{\frac{455}{8} } \\but~x < 0\\7.5-\sqrt{\frac{455}{8} } < x < 0[/tex]
Alok started a business investing Rs 90, 000. After three
months Prabir joined him with capital of Rs 1,20000
If at the end of 2 years, the total profit made
by them was
Rs 96,000 what will the difference
between Alok and Prabir's share in it?
The difference between Alok and Prabir share exists 8000.
What will the difference between Alok and Prabir share?Given: Invested by Alok = Rs 90, 000
Invested by Prabir = Rs 1,20000
The time period of Alok = 3 months
The time period of Prabir = 2 years
They earn a profit = Rs 96,000.
Profit exists directly proportional to the product of the amount invested and the time period of investment.
8000 = 90000 [tex]*[/tex] 24/120000 [tex]*[/tex] 21
= 5/7
5x + 7x = 96000
x = 8000
first = 40000
second = 48000
so the difference exists at 8000.
The difference between Alok and Prabir share exists 8000.
Therefore, the correct answer is 8000.
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Find the magnitude of −1−5i
The magnitude of -1-5i is √26.
What is the magnitude of -1-5i ?
Given the complex expression; -1 - 5i
To find the magnitude, we use the formula;
| a+bi | = √[ a² + b² ]
a = -1b = -5| a+bi | = √[ a² + b² ]
| -1-5i | = √[ (-1)² + (-5)² ]
| -1-5i | = √[ 1 + 25 ]
| -1-5i | = √26
Therefore, the magnitude of -1-5i is √26.
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what is 4,928 will rounded to the nearest hundred
Answer:
4.93
See the discussion below if the number is 4928.
Step-by-step explanation:
Comment
Do you really mean hundred? If you do, the nearest hundred is 0 when the actual value is 4.928
If you mean the nearest hundredth that means that 2 is the value of the hundredth now. Rounded, the answer is 4.93
If the given value is 4928, the hundred's place is the 9. Look at the 10s place (2). Since the 2 is less than 5, the 9 is not changed. 2 zeros are at the end of 49 since the hundreds place is rounded.
4900 is the answer
Hi there,
please see below for solution steps :
__________
Let us revise the rounding rules :
1) if the number you’re rounding to is followed by a number from 0 to 4, you drop that number
2) if the number you’re rounding to is followed by a number equal to 5 or more, you add 1 to that number
________
Now,
Nearest Hundredth => 3 digits after the decimal point
Thus,
4.928 => 4.93
Hope the Answer - and steps - made sense to you,
Happy Studying !!
Frozen Melody
if a and b are consecutive even integers, where aa) 2a+1
b)2a^2+2b
c)3a^2+3b^2
d)2a+3b^2
e)2a+3b
The formula that can be used to illustrate consecutive even numbers is a + 2.
How to illustrate the information?It should be noted that the information is incomplete. Therefore, an overview will be given.
It should be noted that consecutive even numbers we the numbers that follow each other and have a difference of 2.
Examples of such numbers include 2, 4, 6,8, 10, etc.
In this case, the formula that can be used to illustrate consecutive even numbers is a + 2.
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If 2 angles have the same angle measure they are said to be what
2 angles that have the same angle measure are congruent.
Given that the two angles have the same angle measure.
Congruence is a term reserved for geometry. Two metrics are congruent when you can perfectly map to each other by mirroring, rotating, and translating without distortion.
We know that two shapes or objects are congruent if they have the same shape and the same size. For two angles to be congruent, they must coincide when they are overlapped. This is only possible if the two angles are equal.
Therefore, if two angles have the same measure, then they are said to be congruent.
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Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. The equation y=60x+30
y=60x+30 represents what Health Club B charges. Health Club A charges a $50 sign-up fee and $27 per month.
Answer:
y = (constant variable x time) + independent variable
y = 60x + 30 ← Health Club B
y = 27x + 50 ← Health Club A
Step-by-step explanation:
I can't see the question at the bottom due to the covering but if you comment I can edit this and give a proper answer. Otherwise this is all I can give you.
A company's sales equal $60,000 and cost of goods sold equals $20,000. Its beginning inventory was $1,600 and its ending inventory is $2,400. The company's inventory turnover ratio equals:
The company's inventory turnover ratio, based on the financial data, equals 10 times.
What is the inventory turnover ratio?The inventory turnover ratio measures the number of times the company sells and replaces its inventory over a given period.
The formula for calculating the Inventory Turnover Ratio is the Cost of Goods Sold divided by the Average Inventory.
The Average Inventory is the mean of the beginning and ending inventories.
Data and Calculations:Sales revenue = $60,000
Cost of goods sold = $20,000
Beginning inventory = $1,600
Ending inventory = $2,400
Average inventory = $2,000 ($1,600 + $2,400)/2
Inventory turnover ratio = 10x ($20,000/$2,000)
Thus, the company sells and replaces its inventory over a period of 10 times.
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What is the value of the expression shown below?
8 + (7 + 1)2 + 4
07
9
021
24
Answer: 28
Step-by-step explanation:
[tex]8+(7+1)2+4\\\\8+(8)2+4\\\\8+16+4\\\\24+4\\\\28[/tex]
Mike and Tim are looking to earn a little extra money. The beach committee offers them the opportunity of picking up plastic bottles, paying them $0.20 per bottle. Mike realizes as they pick up it will get harder and harder to find more bottles. So as an incentive to keep looking he suggests a different form of payment. He suggests $0.10 for the first bottle and increase the pay by 2% for each bottle after that. Tim thinks Mike is crazy to propose an increase of just 2% per piece. He plans to ask for a one cent increase for every piece, starting at 15 cents for the first bottle
The first five terms of the sequence representing each bottle scheme for Mike is illustrated below.
How to calculate the sequence?From the information given, Mike and Tim are looking to earn a little extra money and the beach committee offers them the opportunity of picking up plastic bottles, paying them $0.20 per bottle.
For Mike, the price for the first bottle is $0.10.
The price for the second bottle will be:
= 0.10 × 1.02 = 0.102
The price for the third bottle will be:
= 0.10 × 1.02² = 0.10404
The price for the forth bottle will be:
= 0.10 × 1.02³ = 0.10612
The price for the fifth bottle will be:
= 0.10 × 1.02⁴ = 0.10824
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Complete question:
Mike and Tim are looking to earn a little extra money. The beach committee offers them the opportunity of picking up plastic bottles, paying them $0.20 per bottle. Mike realizes as they pick up it will get harder and harder to find more bottles. So as an incentive to keep looking he suggests a different form of payment. He suggests $0.10 for the first bottle and increase the pay by 2% for each bottle after that. Tim thinks Mike is crazy to propose an increase of just 2% per piece. He plans to ask for a one cent increase for every piece, starting at 15 cents for the first bottle. Write the first five terms of the. sequence representing each bottle scheme for Mike.
A large bakery buys flour in 20-pound bags. The bakery uses an average of 1050 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $15 per order. Annual Carrying costs are $ 55 per bag. a) Determine the economic order quantity? b) What is the average number of bags on-hand? c) How many orders per year will there be? d) Compute the total cost of ordering and carrying flour? e) If holding costs were to increase by $5 per year, how much would the minimum total annual cost?
Given the following:
Demand = 1050Ordering cost = 15Holding cost = 55The economic order quantity is 24.
What is the economic order Quantity?Eoq = √2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 55)
EOQ = 24
What is the average number of bags on-hand?The Average inventory = EOQ / 2
= 24 / 2
= 12
How many orders per year will there be?Expected number of orders = demand / EOQ
= 1050 / 24
= 44
What is the total cost of ordering and carrying flour?Annual holding cost (AHC) = (EOQ / 2) * Holding cost
= (24 / 2) * 55
= 660
Annual ordering cost (AOC) = (demand / EOQ) * ordering cost
= (1050 / 24) * 15
= 656
Thus,
Total cost of managing = AHC + AOC
= 660 + 656
TCM = 1,316
If holding costs were to increase by $5 per year, how much would the minimum total annual cost?5. For holding cost of 60
EOQ= √(2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 60)
= 23
Annual holding cost = (EOQ / 2) * holding cost
this gives us
= (23 / 2) * 60
= 690
Annual ordering cost = (demand / EOQ) * ordering cost
= (1050 / 23) * 15
= 685
Total cost of managing = AHC+ AOC
= 690 + 685
= 1375
Change in total annual cost = new - old
= 1375 - 1316
= 59
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Evaluate 3x² - 4xy + 2y² - 1 for x = - 3 and y = 5
Answer:
[tex]3x^{2} - 4xy + 2y { }^{2} - 1 \\ 3 \times ( - 3) { }^{2} - 4 \times ( - 3) \times 5 + 2 \times 5 {}^{2} - 1 \\ (3 \times 9) - ( - 60) + 50 - 1 \\ 27 + 60 + 50 - 1 \\ 165 [/tex]
Answer: 136
Substitute -3 for x and 5 for y.
[tex]3x^2 - 4xy + 2y^2 - 1[/tex]
[tex]3(-3)^2-4(-3)(5)+2(5)^2-1[/tex]
[tex]3(9)-4(-15)+2(25)-1[/tex]
[tex]27+60+50-1[/tex]
[tex]87+50-1[/tex]
[tex]137-1[/tex]
[tex]136[/tex]
hope this helped!
How do I this please
(i) The expanded form of (1 / 2 - 2 · x)⁵ in ascending form is 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵.
(ii) The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.
What is the value of a coefficient of the power of a binomial
In this problem we must apply the concept of Pascal's triangle to expand the power of a binomial of the form (x + y)ⁿ and further algebra properties.
(i) First, we proceed to expand the power binomial (1 / 2 - 2 · x)⁵ in ascending order:
(1 / 2 - 2 · x)⁵ = (1 / 2)⁵ + 5 · (1 / 2)⁴ · (- 2 · x) + 10 · (1 / 2)³ · (- 2 · x)² + 10 · (1 / 2)² · (- 2 · x)³ + 5 · (1 / 2) · (- 2 · x)⁴ + (- 2 · x)⁵
( 1 / 2 - 2 · x)⁵ = 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵
(ii) Second, we proceed to expand the following product of polynomials by algebra properties:
(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = (1 + a · x + 3 · x²) · [1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵]
(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = 1 / 32 + (a / 32 - 5 / 8) · x + (- 5 · a / 8 + 163 / 32) · x² + (- 175 / 8 + 5 · a) · x³ + (65 - 20 · a) · x⁴ + (- 92 + 40 · a) · x⁵ + (120 - 32 · a) · x⁶ - 96 · x⁷
In accordance with the statement, we find that:
- 5 · a / 8 + 163 / 32 = 13 / 2
- 5 · a / 8 = 45 / 32
a = - 9 / 4
Thus, the coefficient of x³ is:
C = - 175 / 8 + 5 · (- 9 / 4)
C = - 265 / 8
The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.
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The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).
How to simplify the addition between two rational equations
In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:
(n + 5) / (n² + 3 · n - 10) + 5 / (3 · n²) Given(n + 5) / [(n + 5) · (n - 2)] + 5 / (3 · n²) x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)1 / (n - 2) + 5 / (3 · n²) Associative and modulative property / Existence of the multiplicative inverse[3 · n² + 5 · (n - 2)] / [3 · n² · (n - 2)] Addition of fractions with different denominator(3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²) Distributive property / Power properties / ResultTo learn more on rational equations: https://brainly.com/question/20850120
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PLEASE I NEED THIS FAST there are 3 denominations of bills in a wallet: $1, $5, and $10. there are 5 fewer $5-bills than $1-bills there are half as many $10-bills if there is $115 altogether, find the number of each type of bill in the wallet
The count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.
In the question, we are given that there are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills.
We are asked to find the count of each denomination, given there was altogether $115 in the bag.
We assume the number of $1-bills in the bag to be x.
Total amount in x bills of $1 = x * $1 = $x.
Given that there are 5 fewer $5-bills than $1-bills in the bag, number of $5-bills in the bag = x - 5.
Total amount in (x - 5) bills of $5 = (x - 5) * $5 = $5(x - 5).
Given that there are half as many $10-bills as $5-bills in the bag, number of $10-bills in the bag = (x - 5)/2.
Total amount in (x - 5)/2 bills of $10 = (x - 5)/2 * $10 = $5(x - 5).
Thus, the total amount in the bag = $x + $5(x - 5) + $5(x - 5).
But, the total amount in the bag = $115.
Thus, we get an equation:
$x + $5(x - 5) + $5(x - 5) = $115,
or, x + 5x - 25 + 5x - 25 = 115,
or, 11x = 115 + 50,
or, 11x = 165,
or, x = 165/11,
or, x = 15.
Thus, number of $1-bills = x = 15.
The number of $5-bills = x - 5 = 15 - 5 = 10.
The number of $10-bills = (x - 5)/2 = (15 - 5)/2 = 10/2 = 5.
Thus, the count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.
The provided question is incomplete. The complete question is:
There are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills. If there is $115 altogether, find the number of each type of bill in the wallet."
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Which number line best shows how to solve –4 – (–8)? A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 4. Another arrow points from negative 4 to 8. A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 4. Another arrow points from negative 4 to 4. A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 4. Another arrow points from negative 4 to negative 8. A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 4.
The second number line best shows how to solve –4 – (–8). This can be obtained by finding the value of –4 – (–8) and checking which number line has the required arrow mark.
Which number line best shows how to solve –4 – (–8)?The value of –4 – (–8) is obtained.
–4 – (–8) = –4 + 8
–4 – (–8) = 4
The arrow should move from zero to - 4 and the second arrow should move from - 4 to 4.
From the question given the number lines,
First number line,The first arrow is moving from zero to - 4.
First condition is satisfied.
The second arrow is moving from - 4 to 8.
Second condition is not satisfied.
Second number line,The first arrow is moving from zero to - 4.
First condition is satisfied.
The second arrow is moving from - 4 to 4.
Second condition is satisfied.
Hence the second number line best shows how to solve –4 – (–8).
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George cuts a rectangular piece of glass down one of the diagonals as shown below. What is the length of the diagonal that he cut to the nearest whole inch? Enter only the number. An image shows a rectangle with length = 18 inches and width = 36 inches. A red dotted line crosses the rectangle from the upper left corner to the lower right corner.
The length of the diagonal that he cut to the nearest whole inch is 36 inches
TriangleA rectangle with length = 18 inchesWidth = 36 inchesA red dotted line crosses the rectangle from the upper left corner to the lower right corner to form a triangle.
Length of the diagonal of a rectangle;
Hypotenuse² = adjacent² + opposite²
= 18² + 36²
= 324 + 1296
hyp² = 1620
Take the square root of both sideshyp = √1620
hyp = 35.4964786985976
Approximately,
hypotenuse = 36 inches
Therefore, the length of the diagonal that he cut to the nearest whole inch is 36 inches.
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Directions: Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
Answer:
1) 13m, 2) 10ft, 3) 11.4ft, 4) 12.7m
Step-by-step explanation:
Since all of these triangles are right triangles, we can use the Pythagorean Theorem: a^2+b^2 = c^2
1) 5^2+12^2 = c^2 = 25+144 = c^2 = 169 = c^2 = 13 = c
2) 6^2+8^2 = c^2 = 36+64 = c^2 = 100 = c^2 = 10 = c
3) 5^2+10.3^2 = c^2 = 25+106.09 = c^2 = 131.09 = c^2 = 11.4494541 = 11.4 = c
4) 8.6^2+9.4^2 = c^2 = 73.96+88.36 = c^2 = 162.32 = c^2 = 12.7404866 = 12.7 = c
Let f(x)=x²+kx+4 and g(x)=x³+x²+kx+2k, where k is a real constant.
Find the values of k such that the graph of f and the graph of g only intersect once.
The value of k such that the graph of f and the graph of g only intersect one is equal to 2.
The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.
How to find the value of the constant k of a system of two polynomic equations
Herein we have a system formed by two nonlinear equations, a quadratic equation and a cubic equation. Given the constraint that both function must only intersect once, we have the following expression:
f(x) - x² - k · x = 4 (1)
g(x) - x² - k · x = x³ + 2 · k (2)
x³ + 2 · k = 4
x³ + 2 · (k - 2) = 0
If f and g must intersect once, then the roots must of the form:
(x - r)³ = x³ + 2 · (k - 2)
x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)
Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:
2 · (k - 2) = 0
k - 2 = 0
k = 2
Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.
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if g(x)=-2f(x), whats the right graphing
Answer:
IT HAS A SLOPE OF -2
Y INTERCEPT IS 0,0
Step-by-step explanation:
NEED HELP QUICKLY! 75 POINTS!!!!
Only 2 questions
1. Given the functions f(x) = log2(5x) and g(x) = [tex]5^{x}[/tex] – 2, which of the following statements is true?
a. Both f(x) and g(x) decrease on the interval of (–∞, 1).
b. Both f(x) and g(x) have the same domain of (0, ∞).
c. Both f(x) and g(x) have a common range on the interval (–2, ∞).
d. Both f(x) and g(x) have the same x-intercept of (1, 0).
2. What is the solution to 3y2 + 5y > –2?
a. x < –1 or x is greater than negative two thirds
b. x is greater than or equal to negative two thirds or x < 1
c. negative two thirds is less than or equal to x is less than or equal to 1
d. negative two thirds is greater than x is greater than negative 1
1. Given the functions f(x) = log₂(5x) and g(x) = 5ˣ - 2 only statement c is true
2. The solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds
1. How to find which statements are true.Statement a
Since f(x) = log₂(5x) which is a logarithm function is undefined for (-∞, 0) and defined for (0, +∞) and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).
Also, since f(x) is decreasing on the interval (0, 1/5) while g(x) decreases on the interval (-∞, 0). So, they have do not have a common interval on (0, 1).
So, statement a. Both f(x) and g(x) decrease on the interval of (–∞, 1).
is false
Statement b
Since f(x) = log₂(5x) which is a logarithm function is defined for (0, +∞) and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).
So, the statement b Both f(x) and g(x) have the same domain of (0, ∞) is false
Statement c
Since f(x) = log₂(5x) which is a logarithm function has a range of (0, +∞). and g(x) = 5ˣ - 2 which is an exponential function is has a range of (-2, +∞).
So, they have a common interval of (0, +∞).
So, the statement c. Both f(x) and g(x) have a common range on the interval (–2, ∞) is true
Statement d
To find the x-intercept of f(x), we equate f(x) to zero.
So, f(x) = log₂(5x)
0 = log₂(5x)
2⁰ = 5x
1 = 5x
x = 1/5
To find the x-intercept of g(x), we equate g(x) to zero.
g(x) = 5ˣ - 2
0 = 5ˣ - 2
2 = 5ˣ
x = ㏒₅2
Since the x-intercept of f(x) = 1/5 and the x- intercept of g(x) = ㏒₅2. So, they do not have a common x - intercept.
So, the statement d. Both f(x) and g(x) have the same x-intercept of (1, 0) is false.
So, only statement c is true
2. How to find the solution of 3y² + 5y > -2?3y² + 5y > -2
3y² + 5y + 2 > 0
3y² + 3y + 2y + 2 > 0
3y(y + 1) + 2(y + 1) > 0
(3y + 2)(y + 1) > 0
So, the boundary values are at
(3y + 2)(y + 1) = 0
(3y + 2) = 0 or (y + 1) = 0
y = -2/3 or y = -1
So, we require (3y + 2)(y + 1) > 0
For y < -1 say -2, (3y + 2)(y + 1) = (3(-2) + 2)((-2) + 1)
= (-6 + 2)(-2 + 1)
= -4(-1)
= 4 > 0
For -1 < y < -2/3 say -1/3, (3y + 2)(y + 1) = (3(-1/3) + 2)((-1/3) + 1)
= (-1 + 2)(-1 +3)/2
= 1(-2/2)
= -1 < 0
For y > -2/3 say 0, (3y + 2)(y + 1) = (3(0) + 2)((0) + 1)
= (0 + 2)(0 + 1)
= 2(1)
= 2 > 0
So, for (3y + 2)(y + 1) > 0, y < -1 or y > -2/3
So, the solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds
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Answer:
1. D. Both f(x) and g(x) have the same x-intercept of (1, 0).
2. A. x < –1 or x is greater than negative two thirds
Step-by-step explanation:
I took the exam
Need done!! Please helpp
Answer:
e
Step-by-step explanation:
[tex]volume~of~cone=\frac{1}{3}volume ~of~cylinder\\volume~of~cylinder=3 \times volume ~of~cone=3 \times15=45 \\volume ~of~two~cylinders=2 \times45=90[/tex]
40 points
The table shows the heights of students in a group.
Student Height (in inches)
A 45
B 48
C 49
D 40
E 53
What is the mean height of the students in the group?
47 inches
49 inches
51 inches
53 inches
Answer:
Step-by-step explanation:
answer: 47
add the heights then divide by 5
For a standard normal distribution, find:
P(-1.64 < z < 0.2)
For a standard normal distribution, the probability of the 2 - scores P(-1.64 < z < 0.2) is 0.52876
How to find the p-value from 2 z-scores?
We want to find the p-value between 2 z-scores expressed as;
P(-1.64 < z < 0.2)
To solve this, we will solve it as;
P(-1.64 < z < 0.2) = 1 - [P(z < -1.64) + P(z > 0.2)]
From normal distribution table, we have that;
P(x < -1.64) = 0.050503
P(x > 0.2) = 0.42074
Thus;
P(-1.64 < z < 0.2) = 1 - (0.050503 + 0.42074)
P(-1.64 < z < 0.2) = 0.52876
Thus, For a standard normal distribution, the probability of the 2 - scores P(-1.64 < z < 0.2) is 0.52876
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Cual es el valor de x+6=15
Answer: 9
Step-by-step explanation: it is what it is
15-6=9 omg i never knew
Which statement is true?
1-31 = 3 and -1-4| = -4
1-31 = 3 and 1-4| = -4
-131 = 3 and 14| = 4
1-31 = 3 and -14| = 4
Answer:
|-3| = 3 and -|-4| = -4
Step-by-step explanation:
The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.
|-3| = 3 (true) and -|-4| = -4 (true) ⇒ this statement is true
|-3| = 3 (true) and |-4| = -4 (false) ⇒ this statement is false
-|3| = 3 (false) and |4| = 4 (true) ⇒ this statement is false
|-3| = 3 (true) and -|4| = 4 (false) ⇒ this statement is false
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Additional comment
A compound "and" statement is only true if all of the parts of it are true.