The quadratic equation whose roots are 3 and -3 is x² - 9 = 0.
What is the quadratic equation whose roots are 3 and -3 and whose leading coefficient is 1?Given the roots of the quadratic equation;
x = 3 and x = -3
The two real distinct solutions for the quadratic equation are x = 3 and x = -3.
Which means x - 3 and x + 3 are the factors of the equation.
Hence;
( x - 3 )( x + 3 ) = 0
Now, expand using FOIL method
x( x + 3 ) - 3( x + 3 ) = 0
x² + 3x - 3x - 9 = 0
x² - 9 = 0
Therefore, the equation is x² - 9 = 0.
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FULL ANSWERS ONLY AND SHOW WORK
For each of the three expressions, rationalize the denominator and simplify. Show all steps needed to get the answer.
1)
5/4- srt3
a) What is the conjugate of the denominator?
b) Use the conjugate to rationalize the denominator. What is the simplified answer after rationalizing? Use ‘sqrt’ for square root as needed.
2.
a) What is the conjugate of the denominator?
b) Use the conjugate to rationalize the denominator. What is the simplified answer after rationalizing? Use ‘sqrt’ for square root as needed.
3.
a) What is the conjugate of the denominator?
b) Use the conjugate to rationalize the denominator. What is the simplified answer after rationalizing? Use ‘sqrt’ for square root as needed.
Answer:
Step-by-step explanation:
The simplified expression after rationalizing the denominator are:
1) (17 + √3)/13.
2) -3(2+√5)/5.
What is rationalizing the denominator?
To rationalize the denominator with two terms, find the conjugate of the denominator. Then multiply and divide the fraction by the conjugate of the denominator.
1).
a) The conjugate of the denominator is 4 + √3.
b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:
(5/4 - √3) * (4 + √3) / (4 + √3) * (4 - √3)
Simplifying the numerator:
5(4) + 5(√3) - 4(√3) - 3 / 13
= (17 + √3)/13
Therefore, the simplified expression after rationalizing the denominator is (17 + √3)/13.
2).
a) The conjugate of the denominator is 1 - √2.
b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:
2 / (1 - √2) * (1 + √2) / (1 + 2)
Simplifying the numerator:
2(1 + √2) / (-1 + 2)
= -2(1 + √2)
Therefore, the simplified expression after rationalizing the denominator is -2(1 + √2).
a) The conjugate of the denominator is 2 + √5.
b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:
3 / (2 - √5) * (2 + √5) / (2 + √5)
Simplifying the numerator:
3(2 + √5) / (-5)
= -3(2+√5)/5.
Therefore, the simplified expression after rationalizing the denominator is -3(2+√5)/5.
Hence, the simplified expression after rationalizing the denominator are:
1) (17 + √3)/13.
2) -3(2+√5)/5.
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What is the weight of a 35. 99-carat diamond in grams and ounces? (1 carat=0. 2 g)
The 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).
We can use the conversion factor of 1 carat = 0.2 g to convert carats to grams.
Diamond weight in grams: 35.99 carats x 0.2 g/carat = 7.198 g (rounded to three decimal places)
We can use the conversion factor of 1 ounce = 28.3495 g to convert the weight in grams to ounces.
Diamond weight in ounces: 7.198 g / 28.3495 g/o z = 0.254 o z (rounded to three decimal places)
Carats are now commonly used to measure the weight of gemstones, including diamonds, and are abbreviated as "ct." A 1-carat diamond, for example, weighs 0.2 grams while a 2-carat diamond weighs 0.4 grams.
As a result, the 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).
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1. What is the area of triangle ABC? * 12 60° 60° A A. 6/3 square units B. 18 V3 square units A B C. 36 /3 square units D. 72 /3 square units
Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice
What is a formula of area of triangle?
To calculate the area of a triangle, use the formula area = 1/2 * base * height.
To find the area of triangle ABC, we can use the formula:
Area = (1/2) * base * height
where the base and height are the dimensions of the triangle that form a right angle.
In this case, we don't have the dimensions of the triangle that form a right angle, but we know that the triangle has two angles that are 60 degrees each. This tells us that the triangle is an equilateral triangle, and all three sides are equal.
Let's call the length of each side "s". Then, we can use the formula for the area of an equilateral triangle:
[tex]Area = (\sqrt(3)/4) * s^2[/tex]
Plugging in the given value of 12 for s, we get:
[tex]Area = (\sqrt{(3)/4) * 12^2}\\\\ Area \ = (\sqrt{(3)/4) * 144} \\\\Area = 36\sqrt{(3)}[/tex]
Therefore, the area of triangle ABC is [tex]36\sqrt(3)[/tex] square units.
Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice.
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What conclusion can be drawn about the number of trials and the probability of the coin landing on heads or tails? (1 point)
• a
• b
The experimental probability is closer to the theoretical probability for group Y than group X.
The experimental probability and the theoretical probability for group X is the same.
• с
• d
The experimental probability and the theoretical probability for group Y is the same.
The experimental probability is closer to the theoretical probability for group X than group Y.
The correct statement regarding the probabilities is given as follows:
d. The experimental probability is closer to the theoretical probability for group X than group Y.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
For the theoretical probability, a coin is equally as likely to be heads or tails, hence for each group they are given as follows:
p = 1/2 = 0.5 = 50%.
The experimental probabilities for obtaining heads in each group are given as follows:
Group X: 33/86 = 0.384. -> closer to theoretical.Group Y: 17/64 = 0.265.More can be learned about probability at https://brainly.com/question/24756209
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car rental company a charges an $80 service fee plus $22 per day. car rental company b does not have a service fee and charges $32 per day. which equation will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b? responses 32d
Equation that will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b is [tex]\frac{80+22d}{d} = 32d[/tex]
For finding the equation we will first form separate equations of both company a and company b and then we will equate the formed equation to find the number of days.
Let the number of days be d.
For company a, we will first add the service charges and per day charge multiplied with number of days, and then divide the sum with number of days.
= [tex]\frac{80+22d}{d}[/tex]
For company b, we will multiply the per day charges with the number of days.
= [tex]32d[/tex]
Now, we will equate both the formed equation
[tex]\frac{80+22d}{d} = 32d[/tex]
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Four children take part in a swimming relay race.
The table shows their times in the race.
Name Time taken
(seconds)
Manjit: 92.4
Pierre: 86.7
Safia: 85.1
Chen: 91.8
Work out the total time taken by the team in minutes and seconds.
.................minutes ...............seconds
Answer:
5 Minutes and 56 Seconds
Step-by-step explanation:
Manjit= 1 Minute and 32.4 Seconds
Pierre = 1 Minute and 26.7 Seconds
Safia = 1 Minute and 25.1 Seconds
Chen = 1 Minute and 31.8 Seconds
4 X 1 Minute = 4 Minutes
32.4 + 26.7 +25.1 +31.8 = 116 or 1 Minute and 56 Seconds
Therefore, the answer is 5 Minutes and 56 Seconds
out of the 10,000 people who took their driving test for the first time, it was found that 6500 passed the test on the first attempt. estimate the probability that a randomly selected person would pass the driving test on the first attempt.
To estimate the probability that a randomly selected person would pass the driving test on the first attempt, we can divide the number of people who passed on the first attempt (6500) by the total number of people who took the test (10,000).
Probability = Number of favorable outcomes / Total number of possible outcomes.In this case, the favorable outcome is passing the test on the first attempt, and the possible outcomes are all the people who took the test.
Probability = 6500 / 10000= 0.65
Therefore, the estimated probability that a randomly selected person would pass the driving test on the first attempt is 0.65 or 65%. This means that there is a 65% chance that a randomly selected person from the group of 10,000 would pass the driving test on their first try.
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the soup shack usually makes tomato soup with 9 99 tomatoes for every 12 1212 bowls of soup. today, they used 6 66 tomatoes to make 8 88 bowls of soup. how does the tomato taste in today's soup compared to the usual recipe?
The taste of the tomato in today's soup compared to the usual recipe is same .
We find the tomato to soup ratio for each day to compare the taste of tomato in today's soup with the usual recipe,
For the usual recipe, the soup shack uses 9 tomatoes for every 12 bowls of soup, which can be simplified to a ratio of 9:12 ⇒ 3:4 .
This means that for every 3 parts of tomato, there are 4 parts of soup.
For today's soup, the soup shack used 6 tomatoes to make 8 bowls of soup, which can be simplified to a ratio of 6:8 ⇒ 3:4.
This means that for every 3 parts of tomato, there are 4 parts of soup, which is the same as the usual recipe.
Therefore, based on the tomato to soup ratio, the taste of tomato in today's soup is same as the usual recipe.
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The given question is incomplete , the complete question is
The soup shack usually makes tomato soup with 9 tomatoes for every 12 bowls of soup. today, they used 6 tomatoes to make 8 bowls of soup.
How does the tomato taste in today's soup compared to the usual recipe ?
Dr. Drew consumes 16 ounces of a caffeinated beverage first thing in the morning. Caffeine wears off at a rate of approximately 10.9% an hour. If you were to construct an exponential model to calculate the amount of caffeine left in Dr. Drew’s system after any number of hours, what would the initial value be?
On solving the provided question, we can say that in a day, the expression will be 16*24 of 10.9% = 384 od 10.9% = 41.856
What is expression?In mathematics, it is pοssible to multiply, divide, add, or remove. The construction of an expression is as follows: Expressiοn, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expressiοn (such as addition, subtraction, multiplicatiοn or division etc.) Expressions and phrases can be cοntrasted.
Any mathematical statement with variables, numbers, and an arithmetic οperation between them is called an expression or an algebraic expression. Fοr instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expressiοn, all of which are separated by the arithmetic sign +.
Dr. Drew cοnsumes 16 ounces of a caffeinated beverage first thing in the mοrning
Caffeine wears off at a rate of apprοximately 10.9% an hour.
in a day, the expression will be 16*24 of 10.9% = 384 od 10.9% = 41.856
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What is 2 thirds of 42
Answer:
Step-by-step explanation:
42*2/3=84/3=28
the file utility contains the following data about the cost of electricity during july of a recent year for a random sample of 50 one- bedroom apartments in a large city: 96 171 202 178 147 102 153 197 127 82 157 185 90 116 172 111 148 213 130 165 141 149 206 175 123 128 144 168 109 167 95 163 150 154 130 143 187 166 139 149 108 119 183 151 114 135 191 137 129 158 a. construct a histogram and a percentage polygon. b. construct a cumulative percentage polygon. c. around what amount does the monthly electricity cost seem to be concentrated?
a) The histogram for the data is illustrated below.
b) The cumulative percentage polygon is define in the histogram
c) The amount does the monthly electricity cost seem to be concentrated is 128 - 152
A histogram is a graphical representation of a frequency distribution. It consists of a set of bars that represent the frequency of data within certain intervals, also known as bins. The height of each bar represents the frequency or count of data points that fall within that bin.
To create a histogram for the electricity cost data, we need to first decide on the number and size of the bins. One common rule is to choose the number of bins as the square root of the sample size. In this case, we have 50 data points, so we can choose about 7 bins. The size of the bins can be determined by dividing the range of the data by the number of bins.
Once we have determined the number and size of the bins, we can create the histogram by drawing a set of bars with heights proportional to the number of data points that fall within each bin. The histogram can be further enhanced by adding labels for the x and y-axes, a title, and a legend.
As per the histogram, the amount does the monthly electricity cost seem to be concentrated is 128-152
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Aubrey is making bead kits. Each one contains 20 red beads and 15 gold beads.
Part A
Drag numbers to complete the table to show how many red beads and gold beads are in different numbers of bead kits.
Numbers may be used once, more than once, or not at all.
75 added to
75803515401003060
Kits Red Beads Gold Beads
1 20
15
2
40
30
3
60
45
4
80
60
5
100
75
Part B
Use the drop-down menus to complete the rule for each bead color.
Red: Add
20
.
Gold: Add
15
.
Part C
Choose all the ordered pairs that represent the number of red beads and gold beads in kits.
A.
(
20
,
15
)
B.
(
20
,
40
)
C.
(
30
,
45
)
D.
(
80
,
60
)
E.
(
100
,
75
)
Part D
Which of the following graphs shows the relationship between the number of red beads and gold beads in kits?
A.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (0, 0), (15, 20), (30, 40) and (45, 60).
B.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (0, 0), (30, 20), (45, 30), (60, 40), (75, 50) and (90, 60).
C.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (10, 0), (20, 10), (40, 30) and (60, 50).
D.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (0, 0), (20, 15), (40, 30), (60, 45) and (80, 60).
Part E
What would the ordered pair
(
60
,
45
)
represent? Use the drop-down menus to show your answer.
When there are 60
red
beads in kits, there will be 45
gold
beads.
1 / 7
The ordered pair that represent the number of red beads and gold beads is A. D, and E.
What is ratio and proportion?Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
From the table we observe that the number of red beads and the gold beads are in the proportion x : y = 4 : 3.
Using the proportion we see that:
A: (20, 15) = 20 : 15 = 4 : 3
D: (80,60) = 4: 3
E = (100, 25)= 4:3
Hence, the ordered pair that represent the number of red beads and gold beads is A. D, and E.
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Please help with triangles
The value of x is given as follows:
x = 131º.
How to obtain the value of x?An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.
Hence the measure of the top angle of the bottom triangle is given as follows:
a = 180 - 98
a = 82.
The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence, considering that the sum of the measures of the internal angles of a triangle is of 180º, their measures are given as follows:
2b + 82 = 180
2b = 98
b = 49.
Considering the vertical angles, the base angles of the top triangle are given as follows:
b = 49.
Hence the value of x is given as follows:
x = 180 - 49
x = 131º.
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write an expression for a triangle where side 1 is an unknown length . side 2 is twice side 1 and side 3 is 4 centimeters longer than side 1 .
Answer:
Let's call the length of side 1 "x". Then, the length of side 2 is 2x, and the length of side 3 is x + 4. So, the expression for the three sides of the triangle can be represented as:
x + 2x + (x + 4) = 3x + 4
This expression represents the sum of the lengths of all three sides of the triangle.
Step-by-step explanation:
Answer: x+2x+(4+x)
Step-by-step explanation:
since side one is unknown, we can substitute it with variable x, and side two is twice as much as side one so we do 2x, and side three is four cm longer than side one so we do 4+x at the end
8-12
find the missing measures if they are all parallelograms
Answer: Parallelogram angles add up to 360, so use angle properties and known measures.
Step-by-step explanation:
how many people have to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least assume that all possible monthly outcomes are equally likely.
The people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.
X = No of people having same month birth day
We need, P(X 2) ≥ 1/2
= 1-P(X ≤1) ≥ 1/2
1-P(No one having same month birth day) ≥ 1/2
P(No one having same month birth day)≤ 1/2..........................(1)
Now, k = Minimum no of people required to satisfy (1)
P(No one having same month birth day) =
[tex]\frac{11*10*9......*(12-k+1)}{12*12*12......*12}[/tex]
for k= 4
P(No one having same month birth day) =
[tex]\frac{11.10.9}{12.12.12} = 0.572 \geq 0.5[/tex]
for k= 5
P(No one having same month birth day) =
[tex]\frac{11.10.9.8}{12.12.12.12} = 0.38 \leq 0.5[/tex]
Therefore , the people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.
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r = 14 ft, 0= 39°; find s
The S = 37.2^0
Full answer:Below has been attached a diagram with the meaning of this problem. So we have a right triangle whose Opposite side (s) measures 18.9 and whose Adjacent side (r) measures 24.9. So, these two sides are related in the following form:
[tex]tan(S)=\frac{\text{Opposite side}}{\text{Adjacent side}} =\frac{s}{r} \\\\tan(S)=\frac{18.9}{24.9} \\\\tan(S)=0.76\\\\S=arctan(0.76)\\\\S=37.23^o\\\\\text{Roundding off:}\\\\\boxed{S=37.2^o}[/tex]
Therefore, the S = 37.2^0
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Use the following data sets to answer the question.
Set A: {20, 22, 24, 3, 28, 26, 30} Set B: (19, 47, 24, 17, 32, 51, 34}
Which statement about the data sets is true?
The data in Set A are skewed left. because the mean is less than the median. The data in Set B are symmetrical, because the mean is equal to the median.
The data in Set A are skewed right, because the mean is greater than the median. The data in set B are symmetrical, because the mean is equal to the median.
The data in Set A are symmetrical. because the mean is equal to the median. The data in Set B are skewed right, because the mean is greater than the median.
Answer:
The data in Set A are skewed left, because the mean is less than the median. The data in set B are symmetrical, because the mean is equal to the median.
Step-by-step explanation:
For prim people, this is the answer I got it right.
Solve this equation for m
Please help ASAP I need the correct answers please
The equation solved for m is written as:
(y - b)/x = m
How to solve the equation for m?
Here we have a general linear equation:
y = m*x + b
And we want to solve the equation for m, this means that we need to isolate the variable m in that equation.
We will get:
y = m*x + b
y - b = m*x
(y - b)/x = m
That is the equation solved for m.
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pls help me
pls homework
I need help in both questions
The complete question:
A carpet is laid on a rectangular floor of length 12m and breadth 8m. This leaves a margin of width 1m round the carpet. What is the area of the carpet?
Solution:
The area of the carpet laid on a rectangular floor of length 12m and breadth 8m is, 56 meter²
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
The area of the carpet can be calculated by subtracting the area of the margin from the total area of the rectangular floor.
The total area of the floor is:
= 12m x 8m
= 96 square meters.
The area of the margin is:
= 2 x (12m + 8m) x 1m
= 40m.
Therefore, the area of the carpet is:
= 96m² - 40m²
= 56 meter²
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in a sequence the first term is 4 and the common difference is 3
Answer:a=3, d=common difference=3, a2=7, a3=9
Step-by-step explanation:
firstly we have given a,d (using the arithmetic progression formula)
( an=a+(n-1) )
so we have made a sequence a2=a+d=7
a3=a+2d=9
If the water evaporates at the rate in a, for 12 hours, how many inches will evaporate?
On solving the provided question, we cans ay that inches will evaporate, the equation will be = 12x = 1/2y + 7.43
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
he water evaporates at the rate in a, for 12 hours.
inches will evaporate,
the equation will be = 12x = 1/2y + 7.43
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a license plate consists of 2 letters followed by 4 digits. (1) how many license plates are possible? (2) how many license plates are possible if the digits must be different? (3) how many license plates are there that begin with a and don't have a 7?
26 possible letters for each of the first two positions and 10 possible digits for each of the last 4 positions gives a total of 676,000,000 license plates.
(1) 26 possible letters for each of the first two positions and 10 possible digits for each of the last 4 positions gives a total of
26 x 26 x 10 x 10 x 10 x 10 = 676,000,000 license plates.
(2) The number of possible license plates where the digits must be different is the number of permutations of 10 items taken 4 at a time, or 10P4 = 5040. Multiplying by 26 x 26 gives a total of
5040 x 26 x 26 = 3,636,160 possible license plates.
(3) To find the number of license plates that begin with "A" and don't have a 7, we first find the number of license plates that start with "A" and don't have any restriction on the last 4 digits. This is
26 x 10 x 10 x 10 x 10 = 676,000
Then, we find the number of license plates that have a 7, which is
9 x 26 x 10 x 10 = 23,760
Subtracting this from the total number of license plates that start with "A" gives us
676,000 - 23,760 = 652,240 possible license plates.
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Randal’s dad is installing a new pool in their backyard. The pool is a square and has an area of 144 ft .
Randal’s dad will then build a 7 ft wide deck to surround the pool. What is the outside perimeter of the deck?
Answer: Let's call the side length of the square pool "s". We know that the area of a square is equal to the length of one side squared, so we can set up an equation:
s^2 = 144
We can solve for s by taking the square root of both sides:
s = sqrt(144) = 12
So the side length of the pool is 12 feet.
The outside perimeter of the deck is equal to the perimeter of the square pool plus the width of the deck on each side (7 feet). So the outside perimeter is:
12 + 7 + 7 + 12 + 7 + 7 = 52 feet
So the outside perimeter of the deck is 52 feet.
Step-by-step explanation:
Answer: 52 feet
Step-by-step explanation:
First, we know this is a square. So, if the area is 144, square root of 144 is 12 (12 * 12 = 144)
Adding a width of 7 feet to each side means that we can add 12+12+7+7+7+7.
52 feet!
(っ◔◡◔)っ ♥
Hope this helps.
MM4343
In a family the oldest child is 7 years older than the youngest child what is a equation to represent this situation
The equation to represent the situation where the oldest child is 7 years older than the youngest child, using x for the age of the youngest child and y for the age of the oldest child, is y = x + 7.
If we let x represent the age of the youngest child in a family, then we can say that the oldest child is 7 years older than the youngest child. We can represent the age of the oldest child using the expression "x + 7", because if we add 7 to the age of the youngest child, we get the age of the oldest child.
Therefore, we can write an equation to represent this situation by equating the age of the oldest child to the age of the youngest child plus 7. This can be written as:
x + 7 = Oldest child's age
where x is the age of the youngest child, and "Oldest child's age" represents the age of the oldest child in the family. This equation tells us that if we know the age of the youngest child, we can find the age of the oldest child by adding 7 to it.
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What is an equation of the line that passes through the points (-1,6) and (4,-4)
The linear equation that passes through the two given points is:
y = -2x + 4
How to write the equation of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Particularly, if a line passes through the points (x₁, y₁) and (x₂, y₂) then the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, 6) and (4, -4), then the slope is:
a = (-4 - 6)/(4 + 1) = -2
y = -2x + b
To find the value of b, we can replace the values of any of the points in the equation, if we use (-1, 6) we will get:
6 = -2*-1 + b
6 = 2 + b
6 - 2 = b = 4
The linear equation is y = -2x + 4
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Frodo ran 2 4/5 in 7/12 of an hour. How many miles can Frodo run in one hour?
Answer:
In 1 hour run:
4 4/5 miles
Step-by-step explanation:
2 4/5 = 2 + 4/5 = 10/5 + 4/5 = (10+4)/5 = 14/5
Proportions:
14/5 miles ⇒ 7/12 hour
A miles ⇒ 1 hour
A = (14/5 miles)(1hour) / (7/12 hour)
A = (14/5)/(7/12)
A = (14*12) / (5*7)
A = 168 / 35
A = 140/35 + 28/35
A = 4 + 28/35
A = 4 + 4/5
A = 4 4/5 Miles
m varies directly as n, and m=14 when n=7
a) write an equation that relates m and n
b) find m when n = 16
c) find n when m = 30
Answer:
see explanation
Step-by-step explanation:
(a)
given m varies directly as n then the equation relating them is
m = kn ← k is the constant of variation
to find k use the condition m = 14 when n = 7
14 = 7k ( divide both sides by 7 )
2 = k
m = 2n ← equation of variation
(b)
when n = 16 , then
m = 2 × 16 = 32
(c)
when m = 30 , then
30 = 2n ( divide both sides by 2 )
15 = n
The table shows how many hours Sara spent at several activities one Saturday.
Activity Hours
Soccer practice 222
Birthday party 333
Science project 111
What is the ratio of hours spent at soccer practice to hours spent at a birthday party?
The ratio of hours spent at soccer practice to hours spent at a birthday party are 2 for every 3.
What is a ratio?
A ratio is produced by comparing or condensing two related pieces of data. Looking at the reciprocity of the relationship allows us to calculate the number of times one quantity is equal to another. To put it simply, a ratio is a number that can be used to represent one thing as a proportion of another.
We are given that for soccer practice, Sara spends 2 hours and for birthday party, she spends 3 hours.
So, the ratio of hours spent at soccer practice to hours spent at a birthday party is 2 for every 3.
Hence, the ratio is 2 for every 3.
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Question: The table shows how many hours Sara spent at several activities one Saturday.
Activity "Hours
Soccer practice 2
Birthday party 3
Science project 1
What is the ratio of hours spent at soccer practice to hours spent at a birthday party?
Choose 1 answer:
1 for every 2
2 for every 1
2 for every 3
3 for every 2
Two numbers are co-prime if they do not have any prime factors in common. List all
possible numbers that are co-primes with the following numbers that are < 50:
(a) 390
(b) 210
(c) 49335
All possible numbers that are co-primes with the following numbers are mentioned below in detail. The possible co-primes of 390 are 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.
What are co-prime numbers?Co-prime numbers are pairs of numbers that only share the factor 1 in common. They are additionally referred to as reasonably prime numbers.
In the given question,
(a) 390
The prime factors of 390 are 2, 3, 5, and 13. All of the numbers that are co-prime with 390 are those that do not share any of these prime factors. This includes the numbers 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.
(b) 210
The prime factors of 210 are 2, 3, 5, and 7. All of the numbers that are co-prime with 210 are those that do not share any of these prime factors. This includes the numbers 1, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, and 49.
(c) 49335
The prime factors of 49335 are 5, 7, 11, and 13. All of the numbers that are co-prime with 49335 are those that do not share any of these prime factors. This includes the numbers 1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, and 49.
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