Answer:
The inequality to set up is [tex]t+16 \ge 31[/tex]
It solves to [tex]t \ge 15[/tex]
Bill needs to run at least 15 more miles.
================================================
Explanation:
He has run 16 miles so far. Add on another t miles to get 16+t or t+16 to represent the total amount he runs. This expression must be 31 or larger
Either t+16 > 31 or t+16 = 31
Those two items condense to [tex]t+16 \ge 31[/tex]
To solve for t, we subtract 16 from both sides to undo the +16.
[tex]t+16 \ge 31\\\\t+16-16 \ge 31-16\\\\t \ge 15\\\\[/tex]
Bill needs to run at least 15 more miles.
Meaning that t = 15, t = 16, t = 17, etc.
Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. You order a pizza. The kind of pizza you order is recorded by entering the appropriate number on an order form. The numbers used are given below. 1) Pepperoni 2) Mushroom 3) Black Olive Are these data qualitative or quantitative? -Qualitative -Quantitative Are these data discrete or continuous? -Discrete -Continuous -Neither What is the highest level of measurement the data possesses? -Nominal -Ordinal -Interval
- Ratio
The data is qualitative, discrete, and at the nominal level of measurement.
How to classify data?The data is qualitative, as it describes the type of pizza ordered, which cannot be measured numerically.
The data is discrete, because there are only a finite number of possible values that the variable can take on, which in this case is one of the three types of pizza: Pepperoni, "Mushroom, or Black Olive.
The highest level of measurement for this data is nominal, because the numbers used to record the type of pizza do not imply any order or ranking between the categories. The numbers are simply a code to identify which type of pizza was ordered, and do not have any intrinsic numerical value or relationship between them. Therefore, the data falls into the nominal level of measurement, which is the lowest level of measurement that data can have.
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identify the numerator and the denominator of the fraction and identify the fraction as proper or improper. 4/7
The numerator is 4 and the denominator is 7. It is a proper fraction.
What is fraction?A fraction represents the part of a set of objects. It has two parts separated by a dividing line, generally written
a/b
Where
a is numeratorb is denominatorThere are 3 types of fraction. They are
1. Proper fraction
A proper fraction is a fraction whose numerator is less than the denominator. It makes the value is less than 1.
Example: 3/4, 2/5.
2. Improper fraction
An improper fraction is a fraction whose numerator is more than the denominator. The value is more than 1.
Example: 9/8, 7/5.
3. Mixed fraction
A mixed fraction is a combination of a whole number and a proper fraction. It is the quotient and the remainder of improper fraction.
Example:
9/5 = 1 4/511/2 = 5 1/2From the explanation above, the fraction of 4/7 has the numerator of 4 and the denominator of 7. The numerator 4 is less than the denominator 7, so the fraction is a proper fraction.
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A floor plan was drawn using the following scale:
1 inch: 2 1/2 feet
One wall of the house was represented by a line 6 1/2
inches long on the floor plan. Which proportion could be used to find the length of the actual wall, in feet? pls help me hurry than k u
a. 2/5=13/2x
b. 2/5=13x/2
c. 5/2=13/2x
d. 5/2=13x/2
The proportion that could be used is (a) 2/5=13/2x
How to determine the proportion that could be usedFrom the question, we have the following parameters that can be used in our computation:
Scale = 1 inch: 2 1/2 feet
The proportion that can be used is:
actual length / length on the floor plan = scale factor
So, we can set up the proportion as follows:
actual length / 6 1/2 inches = 2 1/2 feet / 1 inch
Solving for actual length (x), we get:
x/(13/2) = 5/2
So, we have
2x/13 = 5/2
Rewrite as
13/2x = 2/5
Hence, the proporton is (a) 2/5=13/2x
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how does the phase of matter affect its properties
The process by which the various phase of matter affect its properties is mentioned below.
What is a state of matter?In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life : solid, liquid, gas, and plasma.Given is to find how does the phase of matter affect its properties.
A solid holds its shape and the volume of a solid is fixed by the shape of the solid. In the liquid phase the molecular forces are weaker than in a solid. A liquid will take the shape of its container with a free surface in a gravitational field. In microgravity, a liquid forms a ball inside a free surface.Matter in the gaseous state has both variable volume and shape, adapting both to fit its container. Its particles are neither close together nor fixed in place.Therefore, the process by which the various phase of matter affect its properties is mentioned above.
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armen and rosanna are two employees in an electronics store. the store manager has put an emphasis on increasing the number of applications for the store credit card. the manager randomly selected 24 weeks for each employee and recorded the number of completed applications for each week, which is provided in the samples below. each employee completed 21 applications in one of the weeks selected. based on the z-scores you calculated above, would carmen or rosanna be more likely to complete 21 applications in one week? select the correct answer below: A. carmen is more likely to complete 21 applications in one week, because the absolute value of the z-score for rosanna is less than for carmen. B. carmen is more likely to complete 21 applications in one week, because the absolute value of the z-score for carmen is less than for rosanna. C. rosanna is more likely to complete 21 applications in one week, because the absolute value of the z-score for carmen is less than for rosanna.
D. rosanna is more likely to complete 21 applications in one week, because the absolute value of the z-score for rosanna is greater than for carmen .
The correct answer is A. Carmen is more likely to complete 21 applications in one week, because the absolute value of the z-score for Rosanna is less than for Carmen.
Based on the calculated z-scores, we can determine which employee is more likely to complete 21 applications in one week.
The z-score for Carmen is -1.56, which indicates that her performance is slightly below average, but still within one standard deviation of the mean. On the other hand, the z-score for Rosanna is -2.83, which is more than two standard deviations below the mean and indicates that her performance is much lower than average.
Therefore, it is more likely for Carmen to complete 21 applications in one week compared to Rosanna, as Carmen's performance is closer to the mean and within one standard deviation of it. Hence, the correct answer is A. Carmen is more likely to complete 21 applications in one week, because the absolute value of the z-score for Rosanna is less than for Carmen.
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Any help would be great
Answer:
50+6.3= 56.3
Step-by-step explanation:
The boxplots shown below summarize two data sets, I and II. Based on the boxplots, which of the following statements about these two data sets CANNOT be justified? a) The median of data set I is equal to the median of data set II b) o The interquartile range of data set l is equal to the interquartile range of data set 1. c) The range of data set I is greater than the range of data set II d) Data set I and data set II have the same number of data points. Review Later
The boxplots below summarize two data sets, I and II so Data set I and data set II have the same number of data points. so potion D.
The distribution of data is shown using a boxplot, which is a standardised method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum"). It can reveal information about your outliers' values. Boxplots can also show you how tightly your data is grouped, whether or not your data is skewed, and whether or not your data is symmetrical.
A box plot is a graph that displays information from a five-number summary that includes one of the central tendency measures. It does not clearly depict the distribution as a stem and leaf plot or histogram does. However it is mostly used to show whether a distribution is skewed or not and whether there are any potential outliers—unusual observations—in the data collection. When comparing or involving numerous data sets, boxplots are also highly helpful.
We can't make the conclusion from the given boxplots whether Data set I and Data set II have the same number of data points or not.
Hence,
Option D is correct.
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Complete question:
The boxplots shown below summarize two data sets, I and II. Based on the boxplots, which of the following statements about these two data sets CANNOT be justified? a) The median of data set I is equal to the median of data set II b) o The interquartile range of data set l is equal to the interquartile range of data set 1. c) The range of data set I is greater than the range of data set II d) Data set I and data set II have the same number of data points.
if one person from this study is randomly selected, find the probability, rounded to four decimal places, that their class / academic rank is that of a junior and they usually drink bottled water.
The probability of selecting a junior who usually drinks bottled water is 0.0156. This is calculated by finding the probability of each separate event (being a junior and drinking bottled water) and multiplying them together.
To find the probability of selecting a junior who usually drinks bottled water, first calculate the probability of being a junior. There are 12 juniors out of a total of 30 students, so the probability of being a junior is 0.4. Then, calculate the probability of usually drinking bottled water. There are 10 students who usually drink bottled water out of a total of 30, so the probability of usually drinking bottled water is 0.3333. Finally, multiply the probabilities together to get the overall probability of 0.0156. This can be rounded to four decimal places to get the final answer of 0.0156.
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Theorem: The difference between any odd integer and any even integer is odd. In an attempted proof of this statement a student wrote the following lines: Suppose n is any odd integer, and m is any even integer. By definition of odd, n = 2k + 1 where k is an integer. By definition of even, m = 2k where k is an integer. Then n m = (2k + 1) – 2k = 1 and 1 is odd. Therefore, the difference between any odd integer and any even integer is odd. Which one of the following best describes the reason the proof is not correct? a. The proof assumes m and n are consecutive integers.
b. It does not prove that 1 is odd. c. The proof violates the parity property. d. The proof violates the zero product property.
The best describes reason the proof is not correct is c. The proof violates the parity property.
The reason the attempted proof of the statement "The difference between any odd integer and any even integer is odd" is not correct is "The proof violates the parity property."
The student incorrectly subtracted an even integer from an odd integer and concluded that the result is odd. However, the difference between an odd integer and an even integer is always odd, which can be proven directly as follows:
Let n be any odd integer and m be any even integer. Then, by definition, n = 2k + 1 and m = 2j for some integers k and j. The difference between n and m is:
n - m = (2k + 1) - 2j
= 2k - 2j + 1
= 2(k - j) + 1
Since k and j are integers, k - j is also an integer. Therefore, the difference between any odd integer and any even integer is of the form 2x + 1, where x is an integer, which is an odd integer.
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HELP ASAP!!
The sum of two integers is three the sum of the squares 185 find the integers.
Answer:
the two integers are 11 and -8
Step-by-step explanation:
Let's call the two integers we're trying to find "x" and "y".
From the problem statement, we know two things:
x + y = 3 (the sum of the two integers is three)
x^2 + y^2 = 185 (the sum of the squares is 185)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for "y" in terms of "x" by subtracting "x" from both sides:
y = 3 - x
Now we can substitute this expression for "y" into the second equation:
x^2 + (3 - x)^2 = 185
Expanding the square on the left-hand side, we get:
x^2 + 9 - 6x + x^2 = 185
Combining like terms, we get:
2x^2 - 6x - 176 = 0
We can simplify this equation by dividing both sides by 2:
x^2 - 3x - 88 = 0
Now we can solve for "x" using the quadratic formula:
x = (3 ± sqrt(3^2 - 4(1)(-88))) / 2(1)
Simplifying, we get:
x = (3 ± sqrt(361)) / 2
We can ignore the negative root, since it would give us a negative value for "y". So, taking the positive root, we get:
x = (3 + 19) / 2 = 11
Now we can use the first equation to solve for "y":
y = 3 - x = 3 - 11 = -8
Suppose the speeds that people drive down the Pat Bay Highway are normally distributed with a mean of 90 km/hr and a standard deviation of 7 km/hr. Answer each of the following.
(a) What proportion of drivers are travelling between 80 and 120 km/hr? To answer this question, convert the probability question that is being asked to a probability question regarding Z
How do you get 2.57 for Z2
Answer:
92.3%
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
Mean μ = 90Standard deviation σ = 7Therefore, if the speeds that people drive down the Pat Bay Highway are normally distributed:
[tex]\boxed{X \sim\text{N}(90,7^2)}[/tex]
where X is the speed in km/h.
f we want to find what proportion of drivers travel between 80 and 120 km/h, we need to find P(80 ≤ X ≤ 120).
[tex]\implies \sf P(80 \leq X \leq 120)=P(X \leq 120)-P(X \leq 80)[/tex]
Converting to the Z distribution:
[tex]\boxed{\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \dfrac{X-\mu}{\sigma}=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)}[/tex]
Transform X to Z:
[tex]\sf P(X \leq 120)=P\left(Z \leq \dfrac{120-90}{7}\right)=P\left(Z \leq \dfrac{30}{7}\right)[/tex]
[tex]\sf P(X \leq 80)=P\left(Z \leq \dfrac{80-90}{7}\right)=P\left(Z \leq -\dfrac{10}{7}\right)[/tex]
Therefore:
[tex]\begin{aligned}\implies \sf P(80 \leq X \leq 120)&=\sf P\left( -\dfrac{10}{7} \leq Z \leq \dfrac{30}{7}\right)\\\\&=\sf P\left(Z \leq \dfrac{30}{7}\right)-P\left(Z \leq -\dfrac{10}{7}\right)\\\\&=\sf 0.999990892...-0.0765637255...\\\\&= \sf 0.9234271...\\\\&=\sf 92.34271...\%\end{aligned}[/tex]
Therefore, the proportion of drivers travelling between 80 and 120 km/h is 92.3% (nearest tenth).
Just solve number 2 please. Thanks
The probability of digits 0 to 9 represent the medicine being not effective.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
As the digit 9 is not effective
So the number of not effective is 2+1+2+2+1+3
=11
The probability=effective numbers/all numbers
=30-11/30
=19/30
Hence, the probability of digits 0 to 9 represent the medicine being not effective.
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On many cell phones with GPS, an approximate location can be given before the GPS signal is received. This is done by a process called triangulation, which works by using the distance from two known points. Suppose there are two cell phone towers within range of you, located 3000 feet apart along a straight highway that runs east to west, and you know you are north of the highway. Based on the signal delay, it can be determined you are 2050 feet from the first tower, and 1420 feet from the second. Determine the angle, , between your line of sight to the first tower and the highway to the nearest tenth of a degree. (A calculator is needed for this question)
Find the result if 24,312 is increased by 22,211.
Answer:
Step-by-step explanation:
To find the result of increasing 24,312 by 22,211, you would simply add the two numbers:
24,312 + 22,211 = 46,523
So, the result of increasing 24,312 by 22,211 is 46,523.
Answer: 46,523
Step-by-step explanation:
Line up the two numbers by their number places (making sure to put the larger number on top). The add the digits that are on top of each other until you get your answer.
Do the ratios and
4/8 and 1/7 form a proportion
The given two ratios are not form a proportion.
What is ratio and proportion?
Ratio is defined as the comparison of two quantities of the same kind by the method of division.
Proportion is an equation it is formed when two ratios are equivalent to each other.
The given two ratios are 4/8 and 1/7.
i.e., 4:8 and 1:7
By simplifying this ratio 4:8 we get 1:2
That is these two ratios are not equal.
proportion is formed only when the two ratios are equal.
Hence, the given two ratios are not form a proportion.
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a football is thrown horizontally at 56ft/s parallel to the sideline. a tv camera is 92ft/s from the path of the football. find theta/dt the rate at whicht the camera must turn to foloow the ball when theta
The camera must turn at a rate of about 53.67 degrees/s to follow the ball at an angle of 15 degrees.
In this issue, we are given the underlying speed of the football and the distance of the television camera from the way of the football. We really want to find the rate at which the camera should go to follow the ball at a specific point theta=15 degrees. We can utilize geometry to take care of this issue. The point between the way of the ball and the line associating the camera and the ball is given by 90 - 15 = 75 degrees. Utilizing the cosine capability, we can find the part of the speed of the football opposite to the camera, which is 56*cos(15) = 53.17 ft/s. Presently, utilizing the digression capability, we can find the rate at which the camera should go to follow the ball, which is (53.17/92)*tan(75) = 0.937 radians/s or roughly 53.67 degrees/s. In this manner, the camera should turn at a pace of around 53.67 degrees/s to follow the ball at a point of 15 degrees.
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The complete question is:
A football is thrown horizontally (very little arc) at 56 ft./s parallel to the sideline. A TV camera is 92 ft. from the path of the football. Find de/dt, the rate at which the camera must turn to follow the ball when θ = 15°. football TV camerao 92 ft.
Given x>0 and a natural number n, show that there exists a unique positive real number r such that x=r^n. Usually r is denoted by x^(1/n).
For any given positive real number x and natural number n, there exists a unique positive real number r such that [tex]x = r^n[/tex].
Let x be a positive real number and n be a natural number. We want to show that there exists a unique positive real number r such that [tex]x = r^n[/tex]. This can be expressed mathematically as [tex]x^(1/n) = r[/tex], where r is the unique positive real number we are looking for.
To solve for r, we can take the nth root of both sides of the equation. This gives us [tex]r = x^(1/n)[/tex]. Since x is a positive real number and n is a natural number, it follows that r is also a positive real number.
Furthermore, since x is a fixed value and n is a fixed value, we can conclude that the positive real number r is unique. In other words, for any given x and n, there is only one r that satisfies the equation [tex]x = r^n[/tex].
Therefore, for any given positive real number x and natural number n, there exists a unique positive real number r such that [tex]x = r^n[/tex].
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Mrs. Taylor, the librarian, has the following puzzle on a shelf: 3 puzzle with 1,000 pieces 8 puzzle with 500 4 puzzle with 100 pieces 3 puzzle with 50 pieces. Lola will randomly choose 1 puzzle to put together. What is the probability that lola will choose a puzzle with 1,000 pieces?
Answer:
Step-by-step explanation:
Which graphs represent functions?
HELPPPPPPPPP
A . c and d
B. d only
C. b and d
D. a only
Answer:
A
Step-by-step explanation:
There probably is a good explanation but I don't have it.
find the measure of such angle whose supplementary angle is 35 degree more than twice of its complementary angle
The required angle is 35 degrees whose supplementary angle is 35 degrees more than twice its complementary angle.
What is the supplementary angle?The definition of a supplementary angle is that it adds up to 180 degrees.
Let's represent the required angle as "x".
We know that the supplementary angle to "x" is 180 - "x".
Similarly, the definition of a complementary angle is that it adds up to 90 degrees, so we know that the complementary angle to "x" is 90 - "x".
Given that the supplementary angle to "x" is 35 degrees more than twice its complementary angle, so we can write this as an equation:
180 - x = 2(90 - x) + 35
Simplifying this equation, we get:
180 - x = 180 - 2x + 35
Adding x to both sides, we get:
x = 35
Therefore, the required angle is 35 degrees.
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Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of several mice takes with a noise as stimulus. What are the null hypothesis H0 and alternative hypothesis Ha?
The null hypothesis H0 to for mice to complete the maze is equal to 18 seconds and alternative hypothesis Ha for mice to complete the maze is less than 18 seconds.
The null hypothesis is the default assumption that there is no effect of the noise stimulus on the time it takes for mice to complete the maze. The alternative hypothesis is the hypothesis that the noise stimulus does have an effect and causes the mice to complete the maze faster. The researcher will conduct a statistical test to determine if there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.
The researcher is hypothesizing that the true population mean time taken by mice to complete the maze with a loud noise stimulus is less than 18 seconds, Ha< 18seconds. The mean time for mice to complete the maze with the noise stimulus is equal to 18 seconds. Ha: 18 seconds
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suppose you have another picture that is 10 inches by 5 inches, and are now using a fancy paper that is 8.5 inches by 4 inches to frame the picture. again, the frame is to be uniform in thickness all the way around. no fancy framing paper is to be wasted!
The thickness of the framing paper used to frame the picture with uniform thickness will be 1.13 inches.
First, we have to find the perimeter of the picture. We know that the perimeter of a rectangle is 2(length + breadth). So, The perimeter of the picture will be :
⇒ 2(10 + 5)
⇒30 inches
Now, finding the area of the framing paper :
⇒ length x breadth
⇒ 8.5 x 4
⇒ 34 inch²
Now, we know that thickness x perimeter = area
∴ Thickness = area / perimeter
⇒ 34 / 30
⇒ 1.13 inch
Therefore, the thickness needed to frame the picture with uniform thickness using the fancy paper without wasting any paper is 1.13 inch.
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The complete question will be :
suppose you have another picture that is 10 inches by 5 inches, and are now using a fancy paper that is 8.5 inches by 4 inches to frame the picture. again, the frame is to be uniform in thickness all the way around. no fancy framing paper is to be wasted! Find out how thick the frame should be.
square root of 88 simplifying radicals
Answer:
[tex]2\sqrt{22}[/tex]
Step-by-step explanation:
Simplify (6x4y2 − 3xy3 − 4xy) + (4x4y2 − xy3 + 4xy).
10x4y2 − 2xy3
10x4y2 − 4xy3
10x4y2 − 4xy3 − xy
10x4y2 − 4xy3 + 2xy
An equation is a part of every formula. A formula is not always an equation. In order to be solved for a variable, equations must be given. Evaluation of formulas
What is meant by equation?An equation is a mathematical statement made up of two expressions connected together by the equal sign. An example of an equation is 3x - 5 = 16. By resolving this equation, we can establish that the variable x has a value of 7.In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal."A mathematical expression called an equation has two equal sides and an equal sign in the middle. For example, 4 + 6 = 10 is an equation.Given,
[tex]$\left(6 x^4 y^2-3 x y^3-4 x y\right)+\left(4 x^4 y^2-x y^3+4 x y\right)[/tex]
[tex]$=6 x^4 y^2-3 x y^3-4 x y+4 x^4 y^2-x y^3+4 x y[/tex]
Group like terms
[tex]$=6 x^4 y^2+4 x^4 y^2-3 x y^3-x y^3-4 x y+4 x y[/tex]
Simplifying the above equation,
[tex]$=10 x^4 y^2-3 x y^3-x y^3-4 x y+4 x y[/tex]
Simplify,
[tex]$=10 x^4 y^2-4 x y^3-4 x y+4 x y[/tex]
Then we get,
[tex]$=10 x^4 y^2-4 x y^3[/tex]
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The cafeteria manager took a poll of 150 students to find the most popular lunch. The circle graph below displays the data
How many more students chose spaghetti and pizza than corn dogs , tacos, and cheeseburgers, as their favorite lunch
There are 60 students who chose spaghetti and pizza over corn dogs, tacos, and cheeseburgers, as their favorite lunch.
What is a circular graph?
A circular graph is also known as a pie chart. It is used to display a set of data. The data can be in percentages or degrees or radians.
The given data are as follows:
Pizza: 45%
Corn dogs: 10%
Cheeseburger: 8%
Tacos: 12%
Spaghetti: 25%
The total number of students is 150.
The total percentage of students who eat spaghetti and pizza is (25%+45%), that is, 70%.
The total percentage of students who eat corn dogs, tacos, and cheeseburgers is (10%+12%+8%), that is, 30%.
The percentage difference is (70%-30%), that is, 40%.
Now, calculate 40% of the total students, that is, 150.
150×40% = 150×40/100
= 60
Therefore, the obtained answer is 60.
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The complete question is given in the following chart.
65 mi/hr = ? meters per min
Answer:
1743.46[tex]\frac{meters}{min}[/tex]
Step-by-step explanation:
Two unit multipliers will be used here:
1 mile (mi) = 1,609.344 meters
1 hour (hr) = 60 minutes (min)
65 [tex]\frac{mi}{hr}[/tex] = (65[tex]\frac{mil}{hr}[/tex])×([tex]\frac{1609.344 meters}{1 mile}[/tex])×([tex]\frac{1 hour}{60 minutes}[/tex])
The miles unit in the numerator and denominator will cannel each other out completely. In addition, the hour unit in the numerator and denominator will also cancel each other out completely:
= 1743.46 [tex]\frac{meters}{min}[/tex]
Determine whether the table represents an exponential growth function, an exponential
decay function, or neither.
The function is an exponential decay function. Then the correct option is B.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as,
y = a(b)ˣ
At (-1, 50), then the equation is given as,
50 = a / b ...1
At (1, 2), then the equation is given as,
2 = ab ....2
From equations 1 and 2, then we have
2 = 50b · b
b² = 1/25
b = 1/5
Then the value of 'a' is given as,
2 = a x 1/5
a = 10
The value of the variable 'b' is less than one that is 1/5. Then the function is an exponential decay function. Then the correct option is B.
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find the value of x. SIMPLEST RADICAL FORM
For given triangle, x is 4√5 using Pythagorean theorem.
What is Pythagorean Theorem?
Pythagoras Theorem (also known as Pythagorean Theorem) is a mathematical concept that explains the relationship between the sides of a right-angled triangle. The sides of a right triangle are also referred to as Pythagorean triples. This theorem's formula and proof are discussed with examples here.
The Pythagorean theorem is used to calculate the length of an unknown side and the angle of a triangle. We can deduce the base, perpendicular, and hypotenuse formulae from this theorem.
The Pythagoras Theorem formula is presented in the definition as:
Perpendicular² + Base² = Hypotenuse²
c² = a² + b²
Now,
Given that perpendicular =19
Hypotenuse=21
then Base²=21²-19² using Pythagoras theorem
Base=√441-361
=√80
=4√5
Hence,
x is 4√5
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Write an expression that is equivalent to -5+6a+(-8)+(-3a)
Answer:
-5+6a-8-3a
=6a-3a-5-8
=3a-13
What is the product of 3a +5 and 2a² + 4a - 2?
O 6a³ +22a²+14a-10
O 6a³+22a²+26a-10
O 18a³+10a²+14a-10
O 28a³+14a-10
Answer:
(a) 6a³ +22a² +14a -10
Step-by-step explanation:
You want the product of (3a +5) and (2a² +4a -2).
Distributive propertyThe distributive property is used to eliminate the parentheses when simplifying the product.
(3a +5)(2a² +4a -2) = 3a(2a² +4a -2) +5(2a² +4a -2)
= 6a³ +12a² -6a +10a² +20a -10
= 6a³ +(12+10)a² +(-6+20)a -10
= 6a³ +22a² +14a -10
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Additional comment
The leading coefficient of the product is the product of the leading coefficients: 3·2 = 6. This eliminates the last two answer choices.
The first two answer choices differ only in the "a" term, so you only need to find that one. It will be the sum of terms (3a)(-2) and (5)(4a), so is -6a+20a = 14a.
You can also "guess" that the "a" term will be 14a, because that appears the most often among the answer choices.
The first answer choice is the correct one.