The solution is Option C.
The equation of line is given by y = -2x + 58
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 2 , 54 )
Let the second point be Q ( 5 , 48 )
The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 54 - 48 ) / ( 2 - 5 )
On simplifying the equation , we get
Slope m = 6 / -3
Slope m = -2
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 54 = -2 ( x - 2 )
On simplifying the equation , we get
y - 54 = 2x + 4
Adding 54 on both sides of the equation , we get
y = -2x + 58
Therefore , the graph is plotted through the points ( 0 , 58 ) , ( 1 , 56 )
Hence , the equation of line is y = -2x + 58
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Help asap please!!!! 15 points for the person to answer correctly!!!
line segment xy has endpoints at (1, -3) and (5, -4). the segment reflects over the x-axis. then it undergoes a translation of 3 units to the right . what are the coordinates of the endpoints? does the transformation affect the length of the line?
a) (4,3) and (8,4); no, the length of the line segment is not affected
b) (-4,3) and (8,4); yes the transformation increases the length of the line
c) (3,4) and (8, -1); no the length of the line segment is not affected
d) (4,1) and (7, -6); yes, the transformation shortens the length of the line segment
Coordinates of the given endpoints of the line segments ( 1, -3) and (5,-4) after translation of 3 units to the right and reflected over x-axis is given by :
a. Coordinates ( 4,3) and (8,4) , length of the given line segment does not get affected.
As given in the question,
Line segment of xy with endpoints (1, -3) and ( 5,-4).
Distance between endpoints are:
√( 5 -1)² + ( -4 + 3)²
= √17
Conditions given:
Line segment reflected over x-axis.
After reflection y-coordinates become positive.
Endpoints become : ( 1, 3 ) and ( 5, 4)
Translation of 3 units to the right.
New coordinates after translation:
(1 +3, 3) and ( 5+3 , 4)
= ( 4,3) and (8,4)
Distance between new endpoints are:
√( 8 -4)² + ( 4 - 3)²
= √17
Therefore, for the given endpoints of the line segment after reflection and translation as per given condition new coordinates are given by:
Option a. Coordinates ( 4,3) and (8,4) , length of the given line segment does not get affected.
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tudents were surveyed on the number of siblings they have. the following probability model was created from the results. a 2-column table with 5 rows. column 1 is labeled number of siblings with entries 0, 1, 2, 3, 4 or more. column 2 is labeled probability with entries 0.223, 0.532, 0.121, 0.085, 0.039. what is the probability that a randomly selected student has at least 2 siblings? enter your answer as a decimal rounded to the thousandths place. p(at least 2 siblings)
The probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.
The probability of a randomly selected student having at least two siblings can be calculated by adding the probabilities of having two and three or more siblings.
Using the given probabilities, the calculation is as follows:
P(at least 2 siblings) = P(2 siblings) + P(3 or more siblings)
= 0.121 + 0.039
= 0.160
Therefore, the probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.
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6. A cafeteria is trying to scale a small pancake recipe up in order to feed a group of tourists. The recipe feeds
6 people and the cafeteria is trying to feed 75. The recipe calls for 4 cups of flour and 14 cups of milk and
% cup of sugar (as well as some other minor ingredients such as baking powder).
(c) If there are 4 cups in a quart and 4 quarts in a
gallon, will we need more or less than a gallon
of milk for this recipe?
(b) If one 10 pound bag of flour contains 38 cups
of flour, how many pounds of flour will be
needed for this recipe? Round to the nearest
tenth of a pound.
(d) The cafeteria has a 1.5 kilogram bag of sugar.
If a cup of sugar weighs 0.5 pounds and there
are 2.2 pounds per kilogram, does the cafeteria
have enough sugar to make this recipe?
Answer:
c) To feed 75 people, the cafeteria would need 14*75/6 = 21 cups of milk. Since 4 cups are in a quart and 4 quarts are in a gallon, the cafeteria would need 21/16 = 1.3125 gallons of milk, which is more than 1 gallon.
b) For the recipe to feed 75 people, the cafeteria needs 475/6 = 6 cups of flour. A 10 pound bag of flour contains 38 cups, so 6/38 = 0.158 of a 10 pound bag is needed. So the cafeteria needs 0.15810 = 1.58 pounds of flour, rounded to the nearest tenth of a pound.
d) The cafeteria has 1.52.2 = 3.3 pounds of sugar in the 1.5 kilogram bag. A cup of sugar weighs 0.5 pounds, so the cafeteria needs 140.5 = 7 pounds of sugar. The cafeteria has enough sugar as 3.3 pounds is more than 7 pounds.
a corner of a tiled floor is shown. if the entire floor is tiled in this way and each of the four corners looks like this one, then what fraction of the tiled floor is made of darker tiles?
The fraction of the tiled floor is made of darker tiles is = [tex]\frac{4}{9}[/tex]
Now, According to the question:
Let's know:
What is a fraction in math?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
The given data is;
A corner of a tiled floor is shown.
If the entire floor is tiled in this way and each of the four corners looks like this one.
To find fraction of the tiled floor is made of darker tiles.
Take the total darker portion is 16
All is = 6 x 6 = 36
The fraction of the tiled floor is made of darker tiles will be:
[tex]\frac{16}{36}=\frac{4}{9}[/tex]
The answer is:
= [tex]\frac{4}{9}[/tex]
Hence, The fraction of the tiled floor is made of darker tiles is = [tex]\frac{4}{9}[/tex]
to use a binomial distribution to approximate the count of successes in an srs, why do we check that the population size be at least 10 times the sample size?
As per the binomial distribution, the population size be at least 10 times the sample size is N
The term binomial distribution in math is defined as a probability distribution used in statistics that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions
Here we have given that we have to use a binomial distribution to approximate the count of successes in an SRS.
Here we know that if the 10 % condition is met, then a binomial distribution can be used to approximate the number of successes in a simple random sample.
Here we have also know that the 10% condition requires that the sample represents less than 10% of the population.
On the other hand the fact that the sample size is far too tiny in comparison to the population, then here it is reasonable to infer that the trials of occurrences are independent.
Therefore, the given situation suggests that the sample size n must be smaller than 10% of the population size N in this situation.
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Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 21 pipes has a standard deviation of 14.6 inches. Show each step.
The 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)
given that
95% confidence interval for the standard deviation of the lengths of pipes
a sample of 21 pipes
standard deviation of 14.6 inches
chi-squared(1 - a/2) < or = (n-1)s^2/(std. dev.)^2 < or = chi-squared(a/2)
in the above
a is alpha
std is standard deviation
a = (1-95/100) = 1 - 0.95 = 0.05
then, degree of freedom = 21 - 1 = 20
chi-squared(0.975) = 20.5
chi-squared(0.025) = 3.25
chi-squared for 20.5 = (21-1)×[tex](14.6)^{2}[/tex] / 20.5 = 103.98
chi - squared for 3.25 = (21-1)×[tex](14.6)^{2}[/tex] / 3.25 = 655.8
we need to square-root of the above values
chi-squared for 20.5 = [tex]\sqrt{103.98}[/tex] = 10.2
chi - squared for 3.25 = [tex]\sqrt{655.8}[/tex] = 25.6
the 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)
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If point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x). True OR
False
The statement that when a point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x) is true. This can be calculated using the formula (x cos θ – y sin θ, x sin θ + y cos θ), where θ is the angle of rotation.
When point (x, y) is rotated 270 degrees about the origin, the coordinates of the resulting point can be calculated using the following formula: (x cos 270° – y sin 270°, x sin 270° + y cos 270°).
Plugging in the values, we get (y, -x). Therefore, the statement is true.
When rotating a point (x, y) around the origin, the coordinates of the resulting point can be calculated using the following formula: (x cos θ – y sin θ, x sin θ + y cos θ). Here, θ is the angle of rotation. In this case, when the point is rotated 270 degrees about the origin, the resulting point is (y, -x).
The statement that when a point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x) is true. This can be calculated using the formula (x cos θ – y sin θ, x sin θ + y cos θ), where θ is the angle of rotation.
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14. money a pancake breakfast fundraiser served 400 people and charged $5
for adults and $3.50 for children. use x to represent the number of adults
served and write an expression to show how much money was raised. then
simplify the expression.
A = 1.5x + 1400 is the equation for how much money was raised.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation.
The "=" sign and terms on both sides must always be present when writing an equation. both parties.
According to our question-
Let's stand in for
Adults = x, number of them
children = y is the number.
The total amount raised equals A
In the query, it is stated that:
400 people were fed during a pancake breakfast fundraiser that cost $5 for adults and $3.50 for kids.
Consequently, x + y = 400. Formula 1: y = 400 - x
Hence:
A is equal to $5 x and $3.50 y.
Where A = 5x + 3.50 and y = 400 - x (400 - x)
A = 5x + 1400 - 3.50x A = 1.5x + 1400
The formula for calculating how much money was raised is as follows:
A = 1.5x + 1400
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A monument casts a shadow 28.7 feet long. a man who is 6 feet tall casts a shadow 8.2 feet long. the triangle drawn with the monument and its shadow is similar to the triangle drawn with the man and his shadow. how tall is the monument? *complete the statement by providing the correct answer in number form.
The information presented states that perhaps the sculpture is 21 feet in height.
What exactly is a triangle?A closed, two-dimensional triangle has three sides, three angles, and three vertices. A polygon also includes a triangle. Triangle ABC is shown in the image above. A triangle through one obtuse angle (more than 90°) and several acute angles is known as an obtuse trio (or obtuse-angled triangle). No Riemann triangle can contain more than one obscure angle because in Euclidean geometry, a rectangle angles must add up to 180°.
AB/DE = BC/EF
f/6 = 28.7/8.2
=> f/6 = 3.5
=> f = 3.5 *6 = 21 ft
Consequently, the memorial is 21 feet tall.
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The complete question is-
A monument casts a shadow 28. 7 feet long. A man who is 6 feet tall casts a shadow 8. 2 feet long. The triangle drawn with the monument and its shadow is similar to the triangle drawn with the man and his shadow. How tall is the monument? Complete the statement by providing the correct answer in number form.
At the same time, Min’s little brother throws a baseball from a height of 4 feet with an initial vertical velocity of 20 feet per second. What polynomial models the height of this ball, in feet?
The polynomial models the height of this ball will be D = (x² - 400) / 19.6 feet.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
At the same time, Min’s little brother throws a baseball from a height of 4 feet with an initial vertical velocity of 20 feet per second.
Let the final speed be 'x'. Then the equation is given as,
x² - (20)² = 2(9.8) · D
19.6D = x² - 400
D = (x² - 400) / 19.6
The polynomial models the height of this ball will be D = (x² - 400) / 19.6 feet.
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a student is randomly eelected from mr.willets class and that studenr is also in ap satts what is the probability that they are as senior?
If m < 1 equals (6x + 3) and m < 2 equals 117 what is the value of x
The value of x is 19.
What is the slope intercept?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.
We can start by using the information given in the problem to set up an equation. We know that:
m < 1 = 6x + 3
m < 2 = 117
We are also given that m < 1 and m < 2 represent different values.
Now we can substitute the second equation into the first equation:
6x + 3 = 117
To solve for x, we can subtract 3 from both sides:
6x = 114
Finally, we can divide both sides by 6:
x = 19
Hence, the value of x is 19.
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Eliud was running 125 miles per week. Now, he’s running 20% more miles per week.
b) How many miles is Eliud running per week? Write and solve an equation to determine how many miles Eliud is now running per week, r.
Answer:
125 miles per week
Step-by-step explanation:
He is running: 100 x (100 + 20)% = 100 x 120% = 100 x 6/5 = 125 miles
He is running 125 miles per week
=> r = 125 miles
a cylinder has a diameter of 8 cm and a height of 6 cm. what is the volume of the cylinder? use 3.14 for pi, and round your answer to the nearest hundredth. 75.36 cm3 150.72 cm3 301.44 cm3 1,205.76 cm3
The volume of the cylinder is 301.44 cm³. We use the radius that is half of diameter length in the formula for the volume of a cylinder.
What is the volume of a cylinder?The formula for the volume of a cylinder is
V = πr²h
Where
V = volumer = radius of cylinderh = height of cylinderA cylinder has
Diameter, d = 8 cmHeight, h = 6 cmUsing π = 3.14, find the volume of the cylinder!
We find the radius of the cylinder.
r = ½d
r = ½(8) cm
r = 4 cm
The volume of the cylinder would be
V = πr²h
V = (3.14)(4)²(6)
V = 18.84 (16)
V = 301.44 cm³
Hence, the volume of a cylinder with the diameter of 8 cm and height of 6 cm is 301.44 cm³.
The correct option is (c).
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Answer:
301.44
Step-by-step explanation:
v=3.14 times radius squared times height
Diameter is the radius times 2
8 the diameter divided by 2 is 4
replace those
v=(3.14)4^2(6)
final answer is 301.44
an ordinary deck of cards is randomly divided into four equal piles (each pile has 13 cards). what is the probability that one pile contains all the face cards?
The probability that one pile contains all the face cards is 0.047%.
A standard deck of cards has 52 cards, with 12 face cards (4 Kings, 4 Queens, and 4 Jacks). When the deck is randomly divided into four equal piles, each pile will have 13 cards.
To calculate the probability that one pile contains all the face cards, we need to consider the total number of ways that the 52 cards can be divided into four piles of 13 cards, and the number of ways that the 12 face cards can be in one of those piles.
The total number of ways to divide 52 cards into four piles of 13 cards is:
52! / (13! * 13! * 13! * 13!) = 22, 948, 036, 544
The number of ways to put 12 face cards in one pile and the other 40 cards in the remaining piles is:
(12! * 40!) / (12! * 13! * 13! * 13!) = 1, 077, 744
So the probability that one pile contains all the face cards is:
1,077,744 / 22,948,036,544 = 4.7*10^-5 or 0.00047 or 0.047%
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Jennifer makes cupcakes to sell at the local farmers market along with her own cookbook which she recently finished creating. On a recent Saturday, Jennifer sold all 473 cupcakes she made at a cost of $2.50 each. The cost of all ingredients used to make the cupcakes was $97.82. Jennifer only sold 27 cookbooks for $18 each, with the costs of production and licensing costing her $2,200. The Farmers market charged her $200 for use of the booth for the entire day.
From the given data, we said that this business is not profitable. This can be solved using addition method.
What is addition?Mathematically, addition is the process of merging several numbers together. The numbers that are being added are known as addends, and the outcome of the addition process, or the answer we ultimately obtain, is known as the sum. It is a fundamental mathematical operation that we employ on a daily basis. We add numbers in many different contexts. In arithmetic sums, the plus sign (+) is used to indicate addition.
The combination of at least two integers constitutes basic addition. Once a student has mastered counting, they may begin to study basic addition. By locating the addend at the top of the chart and tracing down to the row of the second addend, they may utilize an addition chart as a learning tool.
Given that,
Jennifer makes cupcakes to sell at the local farmers market along with her own cookbook which she recently finished creating.
On a recent Saturday, Jennifer sold all 473 cupcakes she made at a cost of $2.50 each, so total amount = 473 × $2.50 = $1182.5
Now, the cost of all ingredients:
= $97.82 + (27 × $18) + $2,200 + $200
= $2983.82
Now, we said that this business is not profitable.
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0) A half-marathon is roughly 13.1 miles long. Which equation could be used to determine the time, t it takes to run a marathon as a function of the average speed, s, of the runner where t is in hours and s is in miles per hour?A) t = 13.sB) t = 13.1/sC) t= 13.1 - 13.1sD) t= 13.1s - S/13.1
The formula distance = speed x time must be used to calculate the duration of a marathon as a function of the runner's average speed.
1: List the known data. For example, a marathon is 13.1 miles long, and an average runner moves at s miles per hour.
2 :Rearrange the equation to solve for time in Step 2: Time = Speed/Distance
3: Enter the known numbers for distance and speed into the equation: time = 13.1 miles per second.
4: If necessary, simplify the equation. The units of miles will cancel out because the time is measured in hours and the speed in miles per hour, therefore the ultimate unit of time will be hours.
The final answer is t = 13.1/s, which expresses the duration of a marathon (in hours) as a function of the runner's average speed (in miles per hour).
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For a set population, does a parameter ever change? A. always B. unknown C. sometimes D. never
Answer:
Step-by-step explanation:
D. never
A parameter is a fixed value that represents a characteristic of a set population, such as the population mean or population proportion. It is a fixed value that is true for the entire population, it is calculated using all the data of the population. For example, the mean of the height of all adults in a country is a parameter. Since it is based on all the data, it is not an estimation, it is the true value of the population. Therefore, a parameter does not change, it is a fixed value for a set population.
I can't remember how to solve for inequalities or graph them, can someone help me? (This is a repost with a picture instead)
Answer:
see below
Step-by-step explanation:
1. -2/3x [tex]\geq[/tex] 7
first, we need to divide -2/3 from x and 7 to get x alone, we also need to flip the inequality sign since we are dividing by a negative
x [tex]\leq[/tex] 21/2
or x [tex]\leq[/tex] 10 1/2
2. 32 > 23 - x
first, rearrange the inequality
32 + x > 23
subtract 32 from both sides
x > -9
3. 2 (x + 6) < 10
divide both sides by 2
x + 6 < 5
subtract 6 from both sides
x < -1
4. 15 - 4x [tex]\leq[/tex] 3x - 6
rearrange the equation
-4x + 3x [tex]\leq[/tex] - 15 - 6
-7x [tex]\leq[/tex] - 21
multiply both sides by -1 and reverse the inequality sign
7x [tex]\geq[/tex] 21
divide both by 7
x [tex]\geq[/tex] 3
im super sorry but im not sure how to help you with the graphing :(
two friends are playing with water balloons. they each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. joy walked 12 steps forward, and shaunte walked 8 steps backwards. which expression correctly represents the distance between the friends?
The correct expression that represents the distance between the friends is 4 steps.
To calculate this
Joy walked 12 steps forward and Shaunte walked 8 steps backward. To find the distance between the two friends, we can add the number of steps they each took, so the expression would be:
12 + (-8) = 12 - 8 = 4
So the correct expression that represents the distance between the friends is 4 steps.
Note that the negative sign in front of Shaunte's steps indicates that she walked backward, and the positive sign in front of Joy's steps indicates that she walked forwards.
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Your family drives 52.2 miles in one hour. How far does your family drive in 1.5 hours?
Answer:
78.3 miles
Step-by-step explanation:
Your family drives 52.2 miles in one hour. How far does your family drive in 1.5 hours?
52.2 : 1 = x : 1.5
x = 52.2 × 1.5 : 1
78.3 miles
Create a linear function which gives the radius of the circle in inches after t minutes
Make a linear function that, after t minutes, returns the circle's radius in inches. The circle's radius will have increased by inches, hence the radius increases by inches [3 points]. Create a linear function that returns the circle's radius.
What exactly is an equation for a linear function?The slope-intercept form of a linear function equation. As a result, it is written as f(x) = mx + b, where m is the slope & b is the y-intercept of a line.
Therefore, the distance to the safe zone is 24 * 4 + 70, which is 166.
The formula should be D=166-24t. She needs to go 166 meters, and since she is approaching the safe place at 24 meters per second, her distance to the safe zone is decreasing by 24 meters per second, making the calculation -24 meters per second rather than 24 meters per second.
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1000 kg of limestone is subjected to intense heat and high pressure to form marble. all but one of the statements applies to the formation of the marble.
a) marble is a metamorphic rock.
b) about 1000 kg of marble is produced.
c) marble is formed by recrystalization.
d) marble is formed close to earth's surface.
1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.
When limestone is subjected to the heat and pressure of metamorphism, marble is created as a metamorphic rock. Calcite (CaCO3) makes up the majority of its composition, but it also frequently includes other minerals such clay, mica, quartz, pyrite, iron oxides, and graphite.
When limestone undergoes a process known as metamorphism, which involves heat and tremendous pressure, marble is created. The marble's interconnecting calcite crystals are created when the calcite limestone recrystallizes after metamorphism.
Hence, 1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.
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What is the area, in square feet, of an isosceles triangle whose vertex angle is $120^{\circ}$ and whose base is $20$ feet long
The area of the given isosceles triangle is 480 square units.
Isosceles triangle:
An isosceles triangle is a triangle with two sides of equal length. Let's do a little activity to understand this better. Take a square piece of paper and fold it in half. Draw a line from the folded top corner to the bottom edge (see image below). Open the sheet and you will see a triangle. Mark the triangle vertices as O, D, C. Then measure OD and OC. Repeat this activity at different scales and observe patterns. We can see that OD and OC are always the same. A triangle with two equal sides is called an isosceles triangle.
Given,
base (b) = 20 units and
height (h) = 120 units.
The formula to calculate the area is 1/2 × b × h square units.
By substituting the values, we get
⇒ Area = 1/2 × 20 × 120
= 480 unit Squares
Therefore, the area of the given isosceles triangle is 96 square units.
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Pleaseeee help this is due today
Answer:
Its 24ft
Step-by-step explanation:
(w2x−3)÷10⋅z when w=−6, x = 1.2, and z=−67
Answer:
see below : -0.0492
Step-by-step explanation:
-6*-6-3/10*-67=-33/670 = -0.0492
Choose the letter of the expression listed on the right that completes each step to show how to use the power and product properties of logarithms to prove that the quotient property is true for logb x y . logb x y = = = =
By using the logarithmic properties we can probe that,
(a) [tex]$\log _b \frac{x}{y}=\log _b x+\log _b y^{-1}$[/tex]
(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]
What is a logarithm?The logarithm is exponentiation's opposite function In mathematics. This means that the exponent which [tex]$b$[/tex] must be realized To produce a number [tex]$x$[/tex] is the logarithm of [tex]$x$[/tex] the base [tex]$b$[/tex]. For Instance, because[tex]$1000=10^{\wedge} 3$, Its logarlthm In base 10 is 3 , or $\log 10=3$.[/tex]
Given: [tex]$\log _b \frac{x}{y}$[/tex]
We have to prove,
(a) [tex]$\log _b \frac{x}{y}=\log _b x+\log _b y^{-1}$[/tex]
(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]
(a) Consider, [tex]$\log _b \frac{x}{y}=\log _a x+\log _b y^{-1}$[/tex]
L. H. S [tex]$=\log _b \frac{x}{y}$[/tex]
Using the Identity: [tex]$\frac{1}{\nu}=y^{-1}$[/tex]
L.H.S [tex]$=\log _b x y^{-1}$[/tex]
Using Identity: [tex]$\log _b m n=\log _b m+\log _b n$[/tex]
[tex]$$\Rightarrow \text { L.H.S }=\log _b x+\log _b y^{-1}$$[/tex]
Hence, L.H.S = R.H.S
(b) Consider [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]
L.H.S [tex]$=\log _b \frac{x}{y}$[/tex]
Using the Identity
[tex]$$\begin{aligned}& \log _b \frac{m}{n}=\log _b m-\log _b n \\& \Rightarrow \text { L.H.S }=\log _b x-\log _b y \\& \text { L.H.S = R.H.S }\end{aligned}$$[/tex]
Hence, proved.
Hence, by using the logarithmic properties we can probe that,
(a) [tex]$\log _b \frac{x}{y}=\log _h x+\log _b y^{-1}$[/tex]
(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]
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Answer:
=C
=A
=D
=B
Step-by-step explanation:
Correct on Edge
Help asap Brainlyest and 30 points
Answer: A, [tex]\frac{-6}{17}[/tex]
Step-by-step explanation:
g(3) = 2([tex]3^{2}[/tex]) - 3(3) + 1 = 18 - 9 + 1 =10
f(10) = [tex]\frac{4-10}{7+10}[/tex] = [tex]\frac{-6}{17}[/tex]
There is 5 mg in 2.5 mL how many milligrams are in 7 mL
Answer: 14 mg
Step-by-step explanation:
5 mg/2.5 mL = 2 mg per mL
2 mg * 7 mL = 14 mg
Answer:
there are 14 milligrams in 7 mL.
Step-by-step explanation:
to find the number of milligrams in 7 mL, you can use the proportion:
(5 mg) / (2.5 mL) = (x mg) / (7 mL)
Where x is the number of milligrams in 7 mL. To solve for x, you can cross-multiply and divide:
(5 mg) * (7 mL) = (2.5 mL) * (x mg)
x = (5 mg) * (7 mL) / (2.5 mL)
x = 14 mg
Volume: 655
4. a square pyramid has a base that
measures 8 inches on each side. the height
of the pyramid is 11.5 inches. determine the
volume of the pyramid.
y
