To complete squares on the quadratic equation we need to add 16 in both sides.
How to complete squares?Here we want to complete squares on the quadratic equation:
x^2 - 8x = 9
Remember the perfect square trinomial:
(a + b)^2 = a^2 + 2ab + b^2
We can rewrite the give expression as:
x^2 - 2*4*x = 9
Then we need toa add (-4)^2 = 16 in both sides, then we will get:
x^2 - 2*4*x + 16 = 9 + 16
(x - 4)^2 = 25
So we need to add 16 in both sides.
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What is the difference between 5,198 and 8,250
Answer: 3052
Step-by-step explanation: 8250 - 5198 = 3052
Please answer 2,4,6,8,10,12,14,16,18,20,22 and 24
The answers are given below.
What is the BODMAS rule?According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.
Given:
2) -23×0×43=0
4) 9× -8× -3=216
6) (-56)/-8=7
8) 144/-6=-24
10) 124/-4 = -31
12) -(-4)×3=12
14)-(-6)=6
16) -36×3 / -6 =18
18) 7×(-5)×8=280
20) 8×9/-3=-24
22) -12×6×3 /-8=27
24)17×-4×-1/ -2/-1=34
Hence, The answers are given above.
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a relation where every input has exactly one output
Function is a relation where each input has exactly one output.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, co domain, and domain. The usual way to refer to a function is as f(x), where x is the input.
The link between INPUT and OUTPUT is demonstrated by the relation. A function, on the other hand, is a relation that yields one OUTPUT for each given INPUT.
Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co domain, respectively.
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WHICH EQUATION BEST USES COMPAITABLE NUMBERS TO ESTIMATE 318/38
318/38=9.
What are compatible numbers?
The term "compatible numbers" refers to those that are simple or complimentary. It indicates that the numbers are compatible if they are simple to add, subtract, multiply, or divide. It is also simpler to estimate the answer and solve difficulties because these numbers are near to the real numbers in value.
Step by step explaination:
318/38=8.3
to round of 8.3 to 9
The equation to the compatible number 318/38 is 9
(318/38=9).
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A bug is crawling down a tree at a rate of -7 millimeters per second . The bug passes a big beach which we will call position 0 which equation reprints the bugs positions 8 seconds after it passes the branch
Answer: The equation representing the position of the bug 8 seconds after passing the branch is given by:
x = -7t + 8, where x is the position in millimeters and t is the time in seconds.
Step-by-step explanation:
Tamara likes to run on the treadmill. If she runs at a speed of 5.75 miles per hour for 0.92 hours, how many miles does she run? Recall distance = speed x time. Estimate to check your answer.
PLEASE BE ACCURATE!!! Thank you!!!:)
In order to finish a marathon in 4 hours, your average pace needs to be 9 min, 9.62 sec per mile, or 9:9.62 minutes per mile.
What is meant by marathon?
The marathon is a long-distance foot race that takes place over a distance of 42.195 km (26 mi 385 yards), though it can also be done on trail routes.You can run the marathon or use a run/walk method to finish it. There are several categories for wheelchairs.There are more than 800 marathons organized annually throughout the world, and while larger marathons can draw tens of thousands of competitors, the vast majority of those running them are recreational athletes.In 1896, the marathon was one of the first modern Olympic competitions. Before 1921, the distance was not standardized. The 1983-starting World Athletics Championships also feature the distance.To learn more about marathon refer to
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What is the equation for the graph given below?
The equation for the graph given below is option B. x² + (y + 4)² = 4 because, axis y is a plus 4.
What is an equation?An equation is a mathematical statement that states that two expressions are equal. It is usually written using an equals sign, with the expressions on either side of the equals sign separated by operators such as plus and minus signs or multiplication and division symbols.
Therefore, the mathematical expression that indicates or expresses the graph attached if option B.
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The distance between two points can be determined by the
of the real number values of the two points.
Answer: The absolute value of the difference
Step-by-step explanation:
Hope this helps
a fair die is cast until a 6 appears what is the probability that it must be cast more than 5 times times
The probability that the fair die must be cast more than 5 times is 0.4315 or 43.15%.
The probability that it must be cast more than five times is the complement of the probability that it will be cast five or less times.
The probability of getting a 6 on the first roll is 1/6, the probability of not getting a 6 on the first roll is 5/6. The probability of getting a 6 on the second roll, given that it was not obtained on the first roll, is 1/6. The probability of getting a 6 on the third roll, given that it was not obtained on the first and second rolls is 1/6 and so on.
The probability of not getting a 6 in five rolls is (5/6)⁵. The probability of getting a 6 on the fifth roll is 1/6. The probability of getting a 6 on the fifth roll or not getting it on the first five rolls is (5/6)⁵ + 1/6.
So the probability of getting a 6 in five rolls or less is (5/6)⁵ + 1/6.
Therefore, the probability of getting a 6 in more than five rolls is 1 - ((5/6)⁵ + 1/6) = 0.4315
So the probability of having to cast the die more than five times to get a 6 is 0.4315 or 43.15%.
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Milos is an avid maker of tinctures, which are concentrated liquid forms of natural herbs. One common herb that is formed into a tincture is the vanilla bean, which is sold in stores under the moniker Vanilla Extract. One means by which to create a tincture is by soaking the herb in grain alcohol for several weeks. It is possible to purchase grain alcohol called Everclear, which is 97% alcohol; However, vanilla requires a 60% alcohol solution (97% is too strong). To adjust for alcohol that is too strong, the solution can be diluted with water (0% alcohol) to achieve the desired concentration. Suppose Milos is planning on making a 12-ounce vanilla extract. How much water and alcohol should he use?
The alcohol required to make 12 ounce vanilla extract is 7.42 ounces.
In the given question, we have to find how much water and alcohol he should use.
Given that vanilla extract requires a 60% alcohol solution and that Given that the pure alcohol content in 12 ounces of vanilla extract is 97%.
Let x denote the alcohol required in ounces.
Let y represent the needed water in ounces.
Then, we must find x and y such that
x + y = 12
Given the desired strength, the volume needed, and the pure alcohol percentage, the following formula can be used to determine the pure alcohol:
Required Pure Alcohol = Desired strength × Volume required Pure alcohol content
x = 60 × 12
97x = 7.42
Therefore the alcohol required to make 12 ounce vanilla extract is 7.42 ounces.
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#4 PLS HELP 8.03 Reflections
The requried coordinates of the image of the given triangle is A'(-2, 3), B'(-5, 6), and C' (-6, 0).
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
Here,
Coordinate of the given triangle before reflection across the y-axis,
A = (2, 3)
B = (5, 6)
C = (6, 0)
Since reflection is to be performed across the y-axis,
So the equation of the trasformation is given as,
Triangle A'B'C' ⇒ (-x,y)
So the coordinate of the image formed is given as,
A'(-2, 3), B'(-5, 6), and C' (-6, 0).
Thus, the requried coordinates of the image of the given triangle is A'(-2, 3), B'(-5, 6), and C' (-6, 0).
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Write a polynomial of least degree with roots 0 and 8.
Write your answer using the variable x and in standard form with a leading coefficient of 1
Answer:
x² - 8x
Step-by-step explanation:
The least degree polynomial with two roots has to be a quadratic polynomial.
Since the roots are 0 and 8, the factors are, (x - 0)(x - 8) = x² - 8x
Cheers
Answer:
The polynomial of least degree with roots 0 and 8 is x(x-8)=0. This can be written in standard form as x2 - 8x = 0.
Please help!! urgent!! 25 points
Answer:
33 15/16
Step-by-step explanation:
which expression gives the closest estimate of 327+171
The expression that gives the closest estimate of 327+171 is 325+175.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Here, we have
Given: 327+171
We have to find the closest estimate of the given expression.
We concluded that the closest estimate of the given expression is 325+175.
327 is close to 325.
175 is close to 325.
Hence, The expression that gives the closest estimate of 327+171 is 325+175.
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suppose you have 5 blue marbles and 5 red marbles in a bag. you pull out one marble, which may be blue or red and do not replace it. what is the probability that the second marble will be red?
Therefore , the solution of the given problem of probability comes out to be probability that the second marble will be red = 0.5.
What exactly does the probability process entail?Calculating the likelihood that a statement is true or that an event will occur is the focus of the branch of mathematics known as probability theory. Any number from 0 to 1, where 1 represents certainty and 0 normally represents possibility, may be used to represent chance. The likelihood that a particular event will occur is depicted in a probability diagram. Probabilities can be represented by the numbers 0 and 1, percentages with a range of 0% to 100%, and a small number of extra characters. the proportion of incidents that occurred among a set of equally likely possibilities out of all potential outcomes
Here,
(p = 5/10) First Blue
Blue II (p = 4/9)
Red 2 (p = 5/9)
Primary Red (p = 5/10)
Blue II (p = 5/9)
Fourth Red (p = 4/9)
Interestingly, if you observe the first marble and then put it back in, the outcome will remain the same (sampling with replacement). The second draw doesn't depend on the first.
=> Pr(B, R) = Pr(B)*Pr(R)
=> (5/10), (5/10), (1/2), (1/2), and 1/4.
and
=>Pr(R, R) = Pr(R)*Pr(R)
=> (5/10), (5/10), and (1/2).
(1/2) = 1/4
Pr
R, R, or (B, R) = (1/4) + (1/4) = 1/2
Therefore , the solution of the given problem of probability comes out to be probability that the second marble will be red = 0.5.
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a store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. how many ways are there to choose:
The number of ways to choose 32 candies is 58,905 ways.
How many combinations of r items are there from n different items?A combination is a way of choosing items from a collection in which the order of selection does not matter.
The number of combinations of n items taken r at a time is determined by the following formula:
[tex]^{(n+r-1)} C_{(r-1)}[/tex]
where:
n represents the total number of items; and
r represents the number of items being chosen at a time.
In this case, a store is selling 5 types of candies, which means the number of types of items or r = 5. And being questioned the number of ways to choose 32 candies, which means the number of items or n = 32.
So, n = 5 and r = 32. Now, substitute both values into the formula:
= [tex]^{(n+r-1)} C_{(r-1)}[/tex]
= [tex]^{(32+5-1)} C_{(5-1)}[/tex]
= [tex]^{36} C_{4}[/tex]
= [tex]\frac{36!}{4!(36-4)!}[/tex]
= 58,905
Hence, the number of ways to select 32 candies is 58,905.
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Although part of your question is missing, you might be referring to this full question: A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. How many ways are there to choose 32 candies?
Compute the mean cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete
your choice, please help and explain
The Mean is 391.75, the Median is 441, and no mode.
What is a mean median and mode?
The mean is the average of a set of numbers, calculated by adding all the numbers together and dividing by the number of items in the set. The median is the middle value in a set of numbers, or the average of the two middle values if the set has an even number of items. The mode is the most frequently occurring value in a set of numbers.
Data: $436, $403, $479, and $249.
Mean = SUm of all observation / total no. of observations.
Mean = 436 + 403 + 479 + 249 / 4.
Mean = 391.75
No. of terms n = 4(even)
Median = (n/2+(n/2 + 1)) / 2
Median = 403 + 479 / 2
Median = 441.
Mode is the value repeating the more no. of times
So, there is no mode.
Hence, the Mean is 391.75, the Median is 441, and no mode.
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a gas occupies 7.3 liters at 320k. if the volume is allowed to change to 7.4 liters at constant pressure, what will be the new temperature? provide your answer with one decimal place.
The new temperature of a gas will be 324.38k .
The Ideal Gas Equation defines the four gas variables and one constant for a better understanding. The four gas variables are pressure (P), volume (V), number of moles of gas (n), and temperature (T). Lastly, the constant in the equation shown below is R, known as the gas constant.
PV=RT
at constant pressure
V∝T
[tex]\frac{V_{1} }{V_{2} } = \frac{T_{1} }{T_{2} }[/tex]
According to the question,
[tex]V_{1} = 7.3 litres[/tex] , [tex]V_{2} = 7.4 litres, T_{1} = 320k[/tex]
⇒ [tex]\frac{7.3}{7.4} = \frac{320}{T_{2} }[/tex] (substitute the values)
⇒ [tex]T_{2} =\frac{320 * 7.4}{7.3}[/tex]
⇒ [tex]T_{2} =324.38[/tex]
Hence, the new temperature will be 324.38k.
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Point D is located at (-6,-5) on the coordinate plane. Point D is reflected over the x-axis to create point D' . What ordered pair describes the location of D'
The ordered pair which describes the location of D' include the following: (-6, 5).
What is a reflection?In Geometry, a reflection over the x-axis is given by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the x-axis to the coordinates of this triangle the image coordinates include the following:
(x, y) → (x, -y)
Ordered pair D = (-6, -5) → Ordered pair D' = (-6, -(-5)) = (-6, 5).
In conclusion, we can logically deduce that the location of D' after a reflection over the x-axis is (-6, 5).
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Please help !!!!meeeeee
Answer: 3
Step-by-step explanation:
Answer:
No. Divide the group of 12 small blue squares by small groups of 4 small blue squares, and you get 3, not 0.03.
Step-by-step explanation:
6.
The large square is divided into small squares. There are 10 small squares on each side of the large square. Since 10 × 10 = 100, the large square is divided into 100 small squares.
The large square is 1 unit.
Since the large square, 1 unit, is divided into 100 small squares, then each small square represents 1/100 of a unit, or 0.01 unit as a decimal.
There are 12 small squares shaded blued.
Each small square is 0.01 unit, so 12 squares represent 12 × 0.01 = 0.12.
The group of 12 small squares is divided into 3 smaller groups of 4 small squares each. Each group of 4 small squares represents 4 × 0.01, or 0.04.
Now we are asked what 0.12 ÷ 0.04 equals.
Look at the figure. The 0.12 of the entire blue shading makes up 3 groups of 0.04 size, so 0.12 ÷ 0.04 = 3.
The division 0.12 ÷ 0.04 is the same as asking how many groups of 4 small squares can you fit in the group of 12 small squares? The answer is 3.
0.12 ÷ 0.04 = 3
The answer 0.12 ÷ 0.04 = 0.03 is incorrect.
Answer: No. Divide the group of 12 small blue squares by small groups of 4 small blue squares, and you get 3, not 0.03.
How is no solution described?
No solution can be described as a situation in which there is no solution or outcome that meets the needs of all parties involved.
When no solution is present, it is often because the problem is too complex or the parties involved have conflicting interests.
This can lead to a stalemate between parties, leaving no one satisfied with the outcome.
No solution can also be the result of a lack of resources or other constraints. It is important to recognize when no solution is present in order to move forward and find a suitable alternative.
No solution can be defined as a problem or situation without a clear answer or resolution. It can be a complex issue that is difficult to solve or a situation with no path forward.
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twice the length decreased by 5. (grade 7)
Answer: 2x-5
Step-by-step explanation: twice=2 the lenght=x We don't know the length, and decreased= subtract sign
2x-5
Triangle ABC has vertices A = (1, 5), B = (3, 2), and C = (4, 7). Triangle A'B'C' is formed when triangle ABC is shifted using the rule (x, y) --> (x-3 , y-1). What are the coordinates of triangle A'B'C' ?
I need help understanding how to find the outer perimeter.
Answer:
im doing the same thinggg okay so to find the outer perimeter you have to divide that shape up so start with the triangle with the right angle.
Step-by-step explanation:
i would just go on yt and watch a vid on how
The Washington monument is one of the tallest structures in the United States. It is about 555 feet tall. How many yards is this?
Answer: 185 yards
Divide it by 3 to convert to yards
State the minimum monthly income and hourly wage per worker needed to cover monthly expenses for the family in the photo. Then, explain how to calculate the hourly wage based on the monthly income and state the hourly wage. Assume that each full-time worker works four 40 hour work weeks per month and each part-time worker works four 40 hour weeks per month.
Full-time worker minimum monthly income = US$ 7,846.40
Part-time worker minimum monthly income = US$ 7,846.40
Full-time worker hourly wage = US$ 49.04
Part-time worker hourly wage = US$ 98.08
Explanation:1.Review the information
Monthly costs of a 2-adult and 3-children family in the Modesto metro area = US$ 5841
Full-time worker = 4 weeks of 40-hour per month
Part-time worker = 2 weeks of 40-hour per month
2. Let's calculate the minimum monthly income and hourly wage per worker
Full-time worker hourly wage = Monthly costs/160
Part-time worker hourly wage = Monthly costs/80
Full-time worker hourly wage = 5841/160
Part-time worker hourly wage = 5841/80
Full-time worker hourly wage = US$ 36.5
Part-time worker hourly wage = US$ 73
Full-time worker minimum monthly income = Hourly wage * 160
Part-time worker minimum monthly income = Hourly wage * 80
Full-time worker minimum monthly income = US$ 5840
Part-time worker minimum monthly income = US$ 5840
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what's the height of the prism? h, 6 square inches, volume=42 cubic inches
Answer:64
Step-by-step explanation: i did the test
Arnold is testing a new train locomotive on circular rail track with a radius of 0. 9 kilometers. How many times around the track does Arnold need to run the train to cover a distance of at least 50 kilometers?
So, Arnold needs to run the train 9 times around the track to cover a distance of at least 50 kilometers.
We know that the radius of the circular rail track is 0.9 kilometers, so the circumference of the track can be found using the formula C = 2πr, where C is the circumference and r is the radius of the circle.
C = 2 * 3.14 * 0.9 = 5.652 km
To find out how many times Arnold needs to run the train around the track to cover a distance of at least 50 kilometers, we need to divide 50 by the circumference of the track.
50 km / 5.652 km = 8.9
Arnold needs to run the train around the track approximately 8.9 times to cover a distance of at least 50 kilometers.
To be more precise, we can round up the result, so Arnold needs to run the train 9 times around the track to cover a distance of at least 50 kilometers.
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How do you round 15 to the nearest 10?
The Round-off of 15 nearest to the 10th is 20. This process is called rounding off the numbers.
The process is used to simplify the numbers so that the number can easily be calculated, this is called round-off. The Round-off process can take place to the nearest 10, 100,1000, and so on.
In round-off, the numbers 0,1,2,3,4 are considered as nearest to the "0" and the numbers 5,6,7,8,9,10 are considered as nearest to the "10". Just like that, 15 is considered as nearest to the "20".
It can also be used for numbers as well as decimal numbers so that we can write the decimal number in simplified form.
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Subtract the two polynomials:
(3x^5-2x^4-5)-(2x^4-10)
Answer:
3x5−4x4−x2+5
Simplify the expression.