The mode is the most common value in a set of data and is typically used for categorical data such as eye color.
Why is the Mode used and not the Mean or Median?The mean and median, on the other hand, are measures of central tendency used for numerical data.
Since eye color is a categorical variable, the mode would be the appropriate measure to use to determine the most common eye color in Andrew's survey.
It can be seen that the mean, median, and mode are the most common measures of central tendency for a set of data, and typically, you use the mode with categorical, ordinal, and discrete data and this is the appropriate data collection that Andrew should use to find the most common eye color and not mean or median.
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2+2=4 right…………………………….
Answer: yes, it is
Step-by-step explanation:
Answer:4
Step-by-step explanation:
Leah walks to soccer practice on Saturday. She leaves her home and walks 6 blocks north. Leah then turns east and walks 4 more blocks to the soccer field. How far is the soccer field from leah’s home ? Round your answer to the nearest tenth.
Answer: The soccer field is about 8.6 blocks away from Leah's home.
Step-by-step explanation:
The soccer field is about 8.6 blocks away from Leah's home.
Leah walks 6 blocks north and 4 blocks east. To find the total distance she walked, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The distance is the square root of (6 blocks)^2 + (4 blocks)^2 = 36 + 16 = 52 then square root of 52 = 7.21
The distance of the soccer field from Leah’s home is 7.21 blocks, but it can be rounded to nearest tenth which is 8.6
Which of the following is the correct solution set?
{ } or empty set
{infinite set of points on the line}
{point in Quadrant 1}
The solution set for the given graph is a null set or empty set.
What is set?Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form.
Given is a graph of parallel lines, as we know in the system of linear equations, equations having parallel lines yields no solutions, therefore, for this also, there is no solution,
Therefore, the set will be null set or empty set.
Hence, the solution set for the given graph is a null set or empty set.
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What is the terminal point of the vector a=⟨4,3⟩ based at P=(5,2)?
Answer:
Step-by-step explanation:
The terminal point of the vector a=⟨4,3⟩ based at P=(5,2) is the point (9,5). This can be calculated by adding the components of the vector to the corresponding components of the base point:
Terminal point = (x,y) = (Px + ax, Py + ay)
= (5 + 4, 2 + 3)
= (9,5)
Answer:
Step-by-step explanation:
✔️For determining terminal point of vector a=(4,3) whose base is at the point P=(5,2).
✔️ Add to point P and that
✔️Point that the vector is pointing at to find the terminal point....
➖So we can say That
✔️Since the tail of the vector a=(4,1) a=(4,1) is a point P(2,3) then the tip of the vector, the terminal point woll be :-
(5,2)+(4,3)=(9,6)
your welcome !
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Answer:
2nd option
Step-by-step explanation:
[4 -7] * [a b] * = [1 0]
[-1 2] [c d] [0 1]
4 * a + (-7) * c = 1
4 * b + (-7) * d = 0
-1 * a + 2 * c = 0
-1 * b + 2 * d = 1
4a - 7c = 1 ==> equation 1
4b - 7d = 0 ==> equation 2
-a + 2c = 0 ==> equation 3
-b + 2d = 1 ==> equation 4
(-b + 2d = 1) * 4 ==> make -b into -4b
-4b + 8d = 4
+ (4b - 7d = 0)
-4b+4b + 8d-7d = 4+0 ==> add equations 2 and 4 to cancel the variable b
8d-7d = 4 ==> -4b+4b=0 and adding anything by 0 will result in itself: 0+3=3
d = 4
-b + 2d = 1
-b + 2(4) = 1 ==> substitute 4 for d
-b + 8 = 1 ==> simplify
-b = -7 ==> subtract 8 on both sides
b = 7 ==> simplify
Since we got the values of b and d, the matrix now looks like this:
[4 -7] * [a 7] * = [1 0]
[-1 2] [c 4] [0 1]
Now solve for a and c using equations 1 and 3:
4a - 7c = 1 ==> equation 1
-a + 2c = 0 ==> equation 3
(-a + 2c = 0) * 4 ==> make -a into -4a
-4a + 8c = 0
+ (4a - 7c = 1)
-4a+4a + 8c-7c = 0+1 ==> add equations 1 and 3 to cancel the variable b
8c-7c = 1 ==> -4a+4a=0 and adding anything by 0 will result in itself: 0+3=3
c = 1
-a + 2c = 0
-a + 2(1) = 0 ==> substitute 1 for c
-a + 2 = 0 ==> simplify
-a = -2 ==> subtract 2 on both sides
a = 2 ==> simplify
Since we got the values of a and c, the matrix now looks like this:
[4 -7] * [2 7] * = [1 0]
[-1 2] [1 4] [0 1]
Hence, the answer is the 2nd option.
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 16 gallons of fuel, the
airplane weighs 1988 pounds. When carrying 50 gallons of fuel, it weighs 2175 pounds. How much does the airplane weigh if it is carrying 64 gallons of fuel?
The plane weights 1988 pounds when it has 16 gallons of fuel on board. It is 2175 pounds heavier when carrying 50 gallons of fuel. w= 2500 .
How much does the airplane weigh if it is carrying ?The following correlation is true if the relationship between weight and fuel consumption is linear:
[tex]$\frac{2175 \text { pounds }-1988 \text { pounds }}{50 \text { gallons-16gallons }}=\frac{W-1988 \text { pounds }}{64 \text { gallons-16galons }}$[/tex]
We resolve this equation:
w = 2500.
Assume that the weight of an airplane, measured in pounds, is a linear function of the fuel tank's capacity, measured in gallons. The aircraft weighs 2030 pounds while carrying 20 gallons of fuel. It weighs 2225 pounds while carrying 50 gallons of fuel. It weighs 2338 pounds while carrying 52 gallons of fuel. Weight (in pounds) of an airplane fuel consumption (in gallons) Per gallon, Jet-A Prist is 6.75 pounds. A 100LL gallon weighs 6.0 pounds. 6.0 pounds per gallon for extras.
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The slope of a line can be used when building a ramp. Gordon is helping to build a wheelchair ramp for a neighbor's house. For every 12 inches of horizontal distance, the height of the ramp increases 1 inch.
Question 1
Part A
The height of the ramp when it connects to the house is 9 inches. What is the length of the ramp in yards?
Part B
Explain how you determined the length.
Enter the correct answers in the boxes.
The ramp is 9 inches tall, so the length of the ramp is 9×
=
inches, which is equal to
feet, and that is equal to
yards.
Answer:
Part A:
To find the length of the ramp in yards, we need to first determine the horizontal distance covered by the ramp. The slope of the ramp is 1/12, meaning that for every 12 inches of horizontal distance, the height of the ramp increases by 1 inch. Since the height of the ramp when it connects to the house is 9 inches, we can use this information to determine the horizontal distance covered by the ramp.
9 inches / (1/12) = 108 inches
To convert inches to yards, we divide by 36, so
108 inches / 36 inches/yard = 3 yards
Part B:
To determine the length of the ramp, I used the information provided about the slope of the ramp and the height of the ramp when it connects to the house. I used the slope of the ramp (1/12) to calculate the horizontal distance covered by the ramp. Then I converted the horizontal distance from inches to yards by dividing by 36. Finally, I obtained 3 yards as the length of the ramp.
Answer:
Part A = 3 yards
Part B = 9 x 12 = 108 inches = 9 feet = 3 yards
Step-by-step explanation:
Part A
1 inch height - 12 inches length
9 inches height - 9 x 12 = 108 inches length
36 inches = 1 yard
108 inches = 108/36 = 3 yards
Part B
Shown above
The ramp is 9 inches tall, so the length of the ramp is 9 x 12 = 108 inches.
1 feet = 12 inches
108 inches = 108/12 feet = 9 feet
1 yard = 3 feet
9 feet = 3 yards.
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Date Page A merchant bought a quintal of potatoes for Rs 4000. He sold all potatoes at Rs 390 per kg.
Find his profit or loss.
Answer: The merchant made a profit of Rs 35,000 by selling the potatoes.
Step-by-step explanation:
To find the profit or loss of the merchant, we first need to calculate the revenue he earned from selling the potatoes.
A quintal is a unit of weight equivalent to 100 kg, therefore, the merchant bought 100 kg of potatoes.
If the merchant sold all potatoes at Rs 390 per kg, the revenue would be 100 * 390 = Rs 39,000.
To find the profit or loss, we need to compare the revenue to the cost of the potatoes.
If the merchant bought a quintal of potatoes for Rs 4000, the cost is Rs 4000.
To calculate the profit or loss, we can use the following formula:
Profit or loss = Revenue - Cost
Using this formula, we can calculate the profit or loss as:
Profit or loss = 39,000 - 4,000 = Rs 35,000
So, the merchant made a profit of Rs 35,000 by selling the potatoes.
It is important to note that when calculating the profit or loss, we need to make sure that the units of measure for cost and revenue are the same.
When given a set of cards laying face down that spell P, E, R, C, E, N, T, S, determine the probability of randomly drawing a vowel.
A. two eighths
B. six eighths
C. two sevenths
D. six sevenths
Probability is a metric used to express the possibility or chance that a particular event will occur. Two eighths of a vowel will be drawn at random. Option A is correct.
What is probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The formula for calculating probability is expressed as:
Probability = expected/total outcome
If the given a set of cards laying face down that spell P, E, R, C, E, N, T, S, then the total outcome is:
n(S) =8
If a vowel is selected randomly, hence the expected outcome is;
E = {E, E}
n(E) = 2
P(vowel) = 2/8
Hence the probability of randomly drawing a vowel is two eighths
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Answer: A: 2/8 (Two Eighths)
Step-by-step explanation:
Danny takes a rectangular piece of fabric and cuts from one corner to the opposite corner. If
the piece of fabric is 9 centimeters long and 12 centimeters wide, how long is the diagonal
cut that Danny made?
Answer: To find the length of the diagonal cut, we can use the Pythagorean theorem.
The diagonal cut is the hypotenuse of a right triangle, with legs of length 9 and 12.
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. So, the length of the diagonal cut is the square root of (9^2 + 12^2)
So, the length of the diagonal cut is √(9^2 + 12^2) = √(81 + 144) = √225 = 15cm
Therefore, the diagonal cut that Danny made is 15 centimeters long.
Step-by-step explanation:
The stopping distance , D, of a car after the brakes are applied varies directly as the square of the speed , S, of the car. If a car traveling at a speed of 36 miles per hour can stop in 53 feet, what is the stopping distance of a car traveling at 70 miles per hour? Round your answer to the nearest foot.
Answer: There is no way 200 is the answer. it should be 103.055
Step-by-step explanation: See, 36 miles can stop in 53 feet. We want to know how many feet are there when 70 miles fast. We can write that as 36/53 = 70/x. 36 corresponds to 70 and 53 corresponds to x. Do it and you get 103.055
Problem No. 5 A 55-seater bus was 40% full of its capacity on leaving the depot. At the first stop only my friend and I boarded the bus. At the second stop one third of the passengers alighted and 9 passengers boarded. At the third stop I, together with 10 other passengers, got off the bus and 5 boarded. How many passengers were on the bus as it pulled away from the stop?
Answer: 12 passengers.
Step-by-step explanation:
55 x 0.40 = 22
22 + 2 = 24
24 ÷ 3 = 8
8 + 9 = 17
17 - 12 = 5
5 + 5 = 10
Please help me find answer
What is the slope of the line that passes through the points (3,8) and (-2,13)?
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{13}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{13}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{3}}} \implies \cfrac{ 5 }{ -5 } \implies - 1[/tex]
Answer:
[tex]\boxed{\bf Slope(m):-1}[/tex]
Step-by-step explanation:
We can use the slope formula to find the slope of a line given the coordinates of two points on the line:- (3,8) and (-2,13).
The coordinates of the first point represent x_1 and y_1. The coordinates of the second points are x_2, y_2.
[tex]\sf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\bf \left(x_1,\:y_1\right):\left(3,\:8\right)[/tex]
[tex]\bf \left(x_2,\:y_2\right):\left(-2,\:13\right)[/tex]
[tex]\bf m=\cfrac{13-8}{-2-3}[/tex]
[tex]\bf m=-\cfrac{5}{5}[/tex]
[tex]\bf m=-1[/tex]
Therefore, the slope is -1.
__________________
Hope this helps!
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Function A a line which passes through the points (2 , 3) and (-1 , -3) Function B Y= 1/2X +2 The rate of change of function A is the rate of change of function B.
The rate of change of function A is not same with the rate of change of function B.
What is rate of change of linear function?The slope of a linear function is another name for its rate of change.
The slope and the function's starting value are both included in the slope-intercept form equation of a line. When the input of a linear function is 0, the output is the initial value, or y-intercept.
Function b is in slope intercept form as Y= 1/2X + 2 and here the slope is 1/2
calculation of slope pf function A
The slope, m of the linear function is calculated using the points (2 , 3) and (-1 , -3)
m = (y₀ - y₁) / (x₀ - x₁)
m = (3 + 3) / (2 + 1)
m = (6) / (3)
m = 2
The slopes are not the same
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Hey guys does anyone have any idea how to solve for the smiley face? I am really struggling and could use some help.
The smiley face is solved to get a value of 72
How to solve to get the value of the smiley faceThe solution to the value of the smiley face is solved by forming some equations
Using the third row that have only squares
8 square - 6 square + 3 square = 60
2 square + 3 square = 60
5 square = 60
dividing through by 5
square = 60 / 5 = 12
hence a square is 12
Using the second row
12 square + 5 star = 234
substituting a square = 12
12 * 12 + 5 star = 234
144 + 5 star = 234
5 star = 234 - 144
5 star = 90
dividing through by 5
star = 90 / 5 = 18
hence a star is 18
using the first row
square + 3 triangle + star = 57
substituting square = 12 and star = 18
12 + 3 triangle + 18 = 57
3 triangle + 30 = 57
3 triangle = 57 - 30
3 triangle = 27
dividing through by 3
triangle = 27 / 3 = 9
hence triangle = 9
solving for the smiley face
substituting the values of the figures
18 (9 + 18 - 12) + 12 (18 + 9 + 9) = smiley face
solving the parenthesis
smiley face = 18 (15) + 12 (36)
smiley face = 18 * 15 + 12 * 36
smiley face = 702
hence the smiley face is 702
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Select the correct answer. What is the equation of the directrix of the parabola given by the equation (y − 3)2 = 8(x − 5)? A. y = 3 B. x = 3 C. x = 5 D. y = -5
Answer:
Choice B: x = 3
Step-by-step explanation:
The standard equation of a parabola is
[tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex]
where
(h, k) is the vertex and |p| is the focal length
The given equation is
[tex](y - 3)^2 = 8(x - 5)[/tex]
Convert this to standard form and compare with general equation
Switch the sides of the equationAnswer: Choice B: x = 3
O
During a gift exchange, ten different gifts
are labeled 1-10 and placed in a pile.
Each person takes a turn selecting a gift
without replacing it. What is the
probability that the first gift chosen is gift
#3 and the second is gift #9?
Using the given conditions in the question,the probability that the first gift chosen is gift #3 and the second is gift #9 is (1/10) * (1/9) = 1/90.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. Events with a probability of 0.5 or greater are considered likely, while those with a probability less than 0.5 are considered unlikely. The probability of all possible events in a given situation must add up to 1. In mathematical terms, probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.
How can you measure the chance of something happening?The chance of something happening can be measured by probability. It's a number between 0 and 1, where 0 means it's impossible for the event to happen and 1 means it's certain to happen. The closer the number is to 1, the more likely the event is to happen.
The probability that the first gift chosen is gift #3 and the second is gift #9 is (1/10) * (1/9) = 1/90. This is because the probability of choosing any specific gift on the first turn is 1/10, and the probability of choosing any specific gift on the second turn, given that there are now 9 gifts left in the pile, is 1/9. Multiplying these probabilities together gives the overall probability of the first gift being #3 and the second gift being #9.
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Jemma has a colletion of 240 coins. Of these coins, 20% are dated before 1910, 15% are dated between 1910 and 1950 and the remainder are dated after 1950. How many coins are dated after 1950?
So on solving provided question we can say that the probability 20% of these coins are pre-1910, 15% are between 1910 and 1950, and the remaining 75% are post-1950.
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
Emma has a collation of 240 coins.
Of these coins, 20% are dated before 1910, 15% are dated between 1910 and 1950 and the remainder are dated after 1950.
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write an equation of a line that passes through (1,0) and is parallel to 2x+y=-4
The equation of the line that passes through (1, 0) and is parallel to the line 2x + y = -4 is: y = -2x + 2.
How to Write the Equation of Parallel Lines?The equation of a line, in slope-intercept form is y = mx + b, if two lines are parallel to each other, then the value of the slope, m, would be the same for both of them.
Given the equation, 2x + y = -4, rewrite the equation in slope-intercept form to determine the slope (m):
2x + y = -4
y = -2x - 4
The slope (m) is -2.
This means the line that passes through (1, 0) will also have a slope of -2. Substitute m = -2 and (x, y) = (1, 0) into y = mx + b, to find the y-intercept (b) of the line:
0 = -2(1) + b
0 = -2 + b
2 = b
b = 2
To write the equation of the parallel line, substitute m = -2 and b = 2 into y = mx + b:
y = -2x + 2.
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Find general solution. Show steps of derivation. Check your answer by substitution.
y´=sec^2(y)
So on solving the provided question we cans ay that trigonometry y =sec^2(y); y = 1/[tex]\sqrt{2}[/tex]
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
y´=sec^2(y)
here, y = 90
y = sec^2(90)
y = 1/[tex]\sqrt{2}[/tex]
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Consider parallelogram QRST below.
Use the information given in the figure to find mLR, mLRQS, and x.
R
Q
4x
8
36°
83°
S
T
The value of [tex]m \angle R Q S[/tex] is 40.
What is parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles. A quadrilateral with two sets of parallel sides is referred to as a parallelogram. The sides of these figurines are parallel to one another and the same hue. a form having four equally long sides.The opposite angles of a parallelogram are equal, therefore:
[tex]m \angle R=m \angle T \\[/tex]
so
[tex]m \angle R=75[/tex]
Opposite sides of a parallelogram are parallel and equal so:
[tex]Q T & =R S \\[/tex]
[tex]4 x & =12 \\[/tex]
[tex]x & =\frac{12}{4} \\[/tex]
[tex]x & =3[/tex]
[tex]$$$\angle \mathrm{TSQ}$[/tex] and [tex]$\angle \mathrm{RQS}$[/tex] are alternate interior angles, therefore:
[tex]m \angle R Q S=m \angle T S Q \\[/tex]
[tex]80: \\[/tex]
[tex]m \angle R Q S=40[/tex]
The complete question is,
Consider parallelogram QRST below. Use the information given in the figure to find m ZR, x, and m ZROS.
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please answer the following four questions.
i have left a table of the hybrid car if that helps at all.
i need help with this asap so if anyone can get back to me sooner than later i would really appreacite it.
The analysis of the distance to the Grand Canyon, and the distance traveled on an amount of gas are as follows;
1 a. The distance from the middle school to the Grand Canyon = 80 miles
2 a. The graph showing the correlation between the distance traveled to the number of gallons used, created with MS Excel is attached
b. The table of values based on the data used to create the graph, presented in a tabular form using MS Word is attached
c. The equation is; d = 10·g
d. The advantages are;
The graphical presentation is a pictorial representation of the distance
The table enables further analysis
The equation can be used to predict the distance the Hybrid can travel on an amount of gas
What is a correlation between variables?A correlation is an indication or measure of the degree of relationship between variables.
1 a. The data for the Camper and the SUV that both use only gas, and the Hybrid car are as follows;
[tex]{}[/tex] Camper SUV Hybrid Car
Average Miles per Gallon [tex]{}[/tex] 4 8 10
Gallons of gas consumed [tex]{}[/tex] 20 10 8
Distance traveled = Number of gallons used × Miles traveled per gallon
The distance between the middle school and the Grand Canyon, using the data for the Camper, is therefore;
d = 20 gallons × 4 miles/gallon = 80 miles
The distance is 80 miles from the middle school to the Grand Canyon2. Amount of gas in gallons = g
Distance car drives in miles = d
The model used = The Hybrid car
Miles traveled per gallon = 10 miles/gallon
Therefore, d/g for the Hybrid car = 10 miles/gallon
d = 10·g
a. Please find attached the graph of the driven distance to the amount of gas used, created with MS Excel
b. The table based on the distance covered using different amount of gas can be created using the data used for creating the graph as follows;
Amount of gas; 0 1 [tex]{}[/tex] 2 3 4 5 6 7 8 9 10 11
Distance; 0 10 20 30 40 50 60 70 80 90 100 110
c. The equation that represents the distance traveled in miles, d, with the Hybrid when a specified amount of gasoline is used, g, is presented as follows;
d = 10·gd. The advantage of each representation are as follows;
The advantage of the graphical presentation is that the fuel consumption can be visualised to help better plan the tripThe advantage of presenting the data as a table allows the exact value of the distance traveled using an indicated amount of fuel, such that the cost of the journey can be more easily calculatedThe presentation of the relationship as an equation, allows for the relationship to be treated as a continuous function and to predict the amount of gas to be used or the distance the Hybrid car can drive
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Raoul has 72 wristbands and 96 movie passes to put in gift bags. The greatest common factor for the number of wristbands and the number of movie passes is qual to the number of gift bags. Raoul needs to make. Then find how many wristbands and how many movie passes raoul can put in each gift bag if he evenly distributes the items.
Please help I am stuck I am doing work nonstop on all weekends if I don’t get this right and done please help and will give brainlesst for the correct answer
Answer:
Step-by-step explanation:
I do know give me brainliest first
Answer:
24 gift bags
Step-by-step explanation:
Well first the question says to find the GCF and you find that by finding prime factors in each number. Then you would want to subtract 96-72 and get the answer of 24 so you would be able to make 24 gift bags. Hope this helps!!
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Can someone help me with this math problem? The answer is 7/2, but does anyone know how to get that answer?
The value of 3x₁ + x₂ is 7/2
How to find the value of 3x₁ + x₂?
A quadratic equation is an equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.
5/x - 2/x² = 2
The LCM of x and x² is x². So we have:
(5x - 2)/x² = 2
Cross multiply:
5x - 2 = 2x²
2x² - 5x + 2 = 0
Factorize:
(2x - 1)(x - 2) = 0
2x - 1 = 0 or x - 2 = 0
2x = 1 or x = 2
x = 1/2 or x = 2
Thus, x₁ = 1/2 and x₂ = 2
Therefore, the value of 3x₁ + x₂ will be:
3x₁ + x₂ = 3×(1/2) + 2 = 3/2 + 2 = 7/2
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for each pair expalin why they are equivelent 5:6 15:18
The two ratios are equivalent because if we multiply both of the numbers by 3, we will get the other ratio.
Why are the two ratios equivalent?Here we want to explain why the two ratios:
5:6 and 15:18
Are equivalent, where equivalent means that these two ratios mean the same thing.
Now, if we take any ratio
a:b
and we multiply both numbers by the same real number k (except for zero) we will get the equivalent ratio.
k*a: k*b
Now, let's look to our ratios:
5:6
If we multiply these 2 numbers by 3, we will get.
3*5: 3:6
15: 18
So yes, these are equivalent.
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riley needs to make punch for a party. One batch of punch has the ingredients shown.
cranberry juice 4 cups, lemon lime soda 1 cup, orange juice 2 cups, pineapple juice 2 cups. Write and interpret a ration that compares the cups of orange juice to the total cups in one batch of punch. Then find the cups of orange juice needed to make enough punch to fill a punch bowl that holds 27 cups
If riley needs to make punch for a party. One batch of punch has the ingredients shown. The cups of orange juice needed to make enough punch to fill a punch bowl that holds 27 cups is 6 cups.
How to find the cups of orange juice?Total cup of juice for one batch:
Total cup of juice for one batch = 4+ 1 +2 +2
Total cup of juice for one batch = 9
Since 2 cup of the 9 cups are orange juice so 2/9 of each batch will be orange and since the bowl can hold 27 cups now let find the cups of orange juice.
Cups of orange juice = 2/9 ×27
Cups of orange juice =6 cups
Therefore we can conclude that the cups of orange juice is 6 cups.
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4. The thickness of a textbook is b mm. Write the expression for each of the following:
The thickness of 5 stacked textbooks?
The thickness of each page, if the pages are numbered to 225?
When the thickness of a textbook is b mm the expressions for:
thickness of 5 stacked textbooks = 5b mm
thickness of each page, if the pages are numbered to 225 = b / 225
How to write the expressions for each conditionThe thickness for each of the condition is written as follows
For the thickness of 5 stacked textbooks
= b + b + b + b + b
= 5b
For thickness of each page, if the pages are numbered to 225
In this case division is used to ascertain the thickness of each page in the book. this is done by dividing the total thickness by the number of pages in the book
= b / 225
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find the value of x
transversals
Answer:
x = 9
Step-by-step explanation:
[tex] - 1 + 14x = 12x + 17 \\ 2x = 18 \\ x = 9[/tex]
Change the fraction 7/12 to a decimal. Round to the nearest thousandth.
The answer to this question is 0.583
