Find x if et = 3x+2 and em = 5x
Answer:
x = 6
Step-by-step explanation:
The centroid (T) always splits the lines so one side is 2/3 and the second is 1/3 of the entire median line. This can also be written as 2x + x. That being said, ET isn't equal to EM, it's only equal to 2/3 of EM so that's what you have to write.
3x + 2 = 2/3 * 5x
3x + 2 = 10/3 x
*3 (3x+2) = *3(10/3x)
9x+6 = 10x
-9x -9x
x = 6
The value of x is 6.
TrianglesThe polygon has three sides. the sum of all the internal angles is 180 degrees.
Given
ET = 3x+2
EM = 5x
To findThe value of x.
How to find the value of x?We know that the centroid of triangles divides it into 2:3.
Then
[tex]\begin{aligned} \dfrac{ET}{EM} &= \dfrac{2}{3} \\\\ \dfrac{3x+2}{5x} &= \dfrac{2}{3} \\\\ 3x+2 &= \dfrac{2}{3} * 5x \\\\ 3x+2 &= \dfrac{10x}{3} \\\\ 3x - \dfrac{10x}{3} &=-2\\\\ \dfrac{-x}{3} &= -2 \\\\ x &= 6\end{aligned}[/tex]
Hence the value of x is 6.
Thus the value of x is 6.
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Which two segments are a base and its associated altitude of parallelogram QRST?
A. Segment T S is the base, and segment S R is the altitude.
B. Segment Q R is the base, and segment T U is the altitude.
C. Segment T S is the base, and segment T Q is the altitude.
D. Segment Q T is the base, and segment T U is the altitude.
Answer :- Option B is the right answer "Segment QR is the base, and segment TU is the altitude".
Explanation:-
The altitude or height of a parallelogram is the perpendicular line segment from the base to the opposite side (which may have to be extended) of the parallelogram. In the given figure, we can see that the altitude is TU=18 inches which is perpendicular to the base QR=20 inches.
Thus , option B is the correct answer. Segment QR is the base, and segment TU is the altitude.
The starting salaries of individuals with an mba degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. refer to exhibit 6-4. what is the probability that a randomly selected individual with an mba degree will get a starting salary of at least $30,000
The probability that a randomly selected individual with an MBA degree will receive a starting salary of at least $30,000, considering the mean salary is $40,000, and standard deviation is $5,000, is approximately 97.72%.
Explanation:The question pertains to the use of the normal distribution in probability, particularly in determining the probability of a randomly selected individual with an MBA degree getting a starting salary of at least $30,000. Given that the mean starting salary is $40,000 and the standard deviation is $5,000, we first need to standardize the salary amount to a z-score using the formula z = (X - μ) / σ. In this context, X refers to the salary amount in question, μ is the mean salary, and σ is the standard deviation.
So, z = (30,000 - 40,000) / 5000 = -2. This means the $30,000 salary is 2 standard deviations below the mean. When we look at the standard z-table, we find that the area to the left of z = -2 is approximately 0.0228. However, because we are looking for the probability of a salary being at least $30,000, we need to consider the area to the right, which is 1 - 0.0228 = 0.9772. So, the probability that a randomly selected MBA graduate will have a starting salary of at least $30,000 is approximately 97.72%.
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The mean weight of a litter of kittens is 3.1 pounds, with a standard deviation of 0.9 pound. Lawrence wants to know the weight of the kitten he is buying, but the seller only has the z-score of 1.22. How much does the kitten weigh?
The weight of kitten is 4.198 pounds
What is z-score?A z-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units.
Given that, the mean weight of a litter of kittens is 3.1 pounds, with a standard deviation of 0.9 pound, Lawrence wants to know the weight of the kitten he is buying, but the seller only has the z-score of 1.22.
Let x be the weight of the kitten
We know that,
z = (x- mean)/σ
Therefore,
1.22 = (x-3.1)/0.9
(1.22)(0.9) = x -3.1
x = 4.198
Hence, the weight of kitten is 4.198 pounds
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The sum of 6 times petra's age and 8 times kathy's age is 162. kathy is 1 year more than twice as old as petra is. find each of their ages.
What is the y-intercept of the line represented by the equation
Y=-3x+7
If the cost of a pound of nails increased from $2.29 to $2.48. what is the percent of the increase to the whole number percent?
The answer is provided in the image attached.
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parallel lines intersect? true or false
If in one year a city recorded a total of 97 rainy, how many of the days did it not rain?
1 year = 365 days
365 -97 = 268
it did not rain 268 days
The sum of two numbers is 67. the smaller number is 3 less than the larger number. what are the two numbers?
What is the domain and range of f(x) = |x + 6|?
domain: (negative infinite,infinite); range: f(x) (greater than or equal to) 0
domain: x (less then or equal to)-6; range: (negative infinite,infinite)
domain: x(greater than or equal to)-6 ; range: (negative infinite,infinite)
domain:(negative infinite,infinite) ; range: f(x) (less than or equal to) 0
Answer:
domain: (negative infinite,infinite); range: f(x) (greater than or equal to [tex]0[/tex]
Step-by-step explanation:
we have
[tex]f\left(x\right)=\left|x+6\right|[/tex]
The vertex of the function is the point [tex](-6,0)[/tex]
The domain is the interval--------> (-∞,∞)
The domain is all real numbers
The range is the interval ------> [0,∞)
[tex]f(x)\geq 0[/tex]
The range is all real numbers greater than or equal to zero
To better understand the problem see the attached figure
Write (7 + 3i) + (6 − i) as a complex number in standard form.
13 + 2i is (7 + 3i) + (6 − i) in standard form.
What are mathematical operations?
The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
To add two complex numbers in standard form, we simply add the real parts and the imaginary parts separately.
(7 + 3i) + (6 − i) = (7 + 6) + (3i − i) = 13 + 2i
Therefore, (7 + 3i) + (6 − i) in standard form is 13 + 2i.
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A 3-ounce serving of tuna provides 21 g of protein use equivalent ratios to find how many grams of protein are in 9 ounces of tuna! Explain
Answer: 63 grams of protein in 9 ounces of tuna
Step-by-step explanation: To find how many grams of protein are in 9 ounces of tuna, we can use equivalent ratios.
We know that a 3-ounce serving of tuna provides 21 grams of protein.
Let's set up a ratio:
3 ounces of tuna: 21 grams of protein
To find out how many grams of protein are in 9 ounces of tuna, we can set up a proportion:
3 ounces of tuna / 21 grams of protein = 9 ounces of tuna / x grams of protein
To solve for x, we can cross-multiply:
(3 ounces of tuna)(x grams of protein) = (9 ounces of tuna)(21 grams of protein)
3x = 189
Dividing both sides of the equation by 3:
x = 63
Therefore, there are 63 grams of protein in 9 ounces of tuna.
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secured debts must have?
they must have a collateral
Jeremy ate p pieces of pizza. Brandon ate 5 less pieces than Jeremy. Write an expression to represent the total amount of pizza eaten by both boys.
Monica ramirez works at the hospital as a nursing assistant. she works 15 hours per week and earns $8.50 per hour. what is monica's straight-time pay for each week?
Answer:
$127.50
Step-by-step explanation:
Given: Monica ramirez works at the hospital as a nursing assistant. She works 15 hours per week and earns $8.50 per hour.
To find: Monica's straight-time pay for each week.
Solution:
Monica earns $8.50 per hour.
Monica works for 15 hours per week.
To find the straight-time pay for each week, we need to multiply the per hour cost with the total number of hours she had worked in a week.
So, the straight-time pay for each week can be calculated as:
[tex]=15\times8.50=127.50[/tex].
Therefore, the straight-time pay for each week is $127.50
What is the solution to the system of equations below? 2x - 5y = 11 and -2x + 3y = -9
The saginaw bay tides vary between 2 feet and 8 feet. the tide is at its lowest point when time (t) is 0 and completes a full cycle in 16 hours. what is the amplitude, period, and midline of a function that would model this periodic phenomenon? amplitude = 3 feet; period = 16 hours; midline: y = 5 amplitude = 3 feet; period = 8 hours; midline: y = 3 amplitude = 6 feet; period = 16 hours; midline: y = 5 amplitude = 6 feet; period = 8 hours; midline: y = 3
Answer:
Option A
amplitude = 3 feet; period = 16 hours; midline: y = 5 amplitude = 3 feet;
Step-by-step explanation:
Given that The saginaw bay tides vary between 2 feet and 8 feet.
When we correspond these to sine curve we can say minimum 2 ft max 8 ft middle value being 5 ft
Period = 16 hours (since it completes one full cycle in 16 hours_
Amplitude = maximum - middle value or middle value-minimum
=[tex]8-5 = 5-2 = 3 ft[/tex]
Thus the equation would be as[tex]y = 3sin \frac{8}{\pi}+5[/tex]
Thus we find that minimum =2, max =8 middle line y=5
Amplitude = 3 ft and period = 16
Hence option A is right.
In a certain county, the number of charter schools is 10 less than twice the number of alternative schools. We know that there are 46 charter schools in the county. How many alternative schools are in the county?
Plz Answer ASAP
1.) Danielle pays a car insurance of $126 every three months. Danielle pays her teenage daughter's $342 car insurance twice a year.
How much should Danielle include for car insurance in her monthly budget?
A. $70
B. $88
C. $99
D. $105
2.) Which of the following is a variable expense?
A. Car insurance
B. rent
C. Retirement contribution
D. Home repair
Randy and Susie Moser are newlyweds. Randy drives their car to his job, twenty-seven miles away from home, each day. If Randy and Susie are both twenty, what premiums would they pay for bodily injury and property damage insurance in the amount of 50/100/10?
Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation. What is the scale factor of the dilation?
Answer: Its option C. (4)
Step-by-step explanation: You're welcome you dirty cheaters.
The initial volume of a gas cylinder is 750.0 ml. if the pressure of a gas inside the cylinder changes from 840.0 mm hg to 360.0 mm hg, what is the final volume the gas occupies?
Answer:
[tex]V_2=1.75L[/tex]
Step-by-step explanation:
Use the Boyle's law which states that the pressure of a gas in a closed container is inversely proportional to the volume of the container, when the temperature is constant. Mathematically this is:
[tex]P_1*V_1=P_2*V_2[/tex] (1)
Where:
[tex]P_1=Initial\hspace{3}pressure\\P_2=Final\hspace{3}pressure\\V_1=Initial\hspace{3}volume\\V_2=Final\hspace{3}volume[/tex]
Before attempting to solve the problem, let's do the pertinent conversions:
[tex]840mmHg*\frac{1torr}{1mmHg} *\frac{1Pa}{133.32torr} =6.3Pa[/tex]
[tex]360mmHg*\frac{1torr}{1mmHg} *\frac{1Pa}{133.32torr} =2.7Pa[/tex]
[tex]750ml*\frac{1L}{1000ml}=0.75L[/tex]
So, we got:
[tex]P_1=6.3Pa\\P_2=2.7Pa\\V_1=0.75L[/tex]
Now, let's isolate [tex]V_2[/tex] from (1) in order to find the final volume:
[tex]V_2=\frac{P_1*V_1}{P_2} \\\\V_2=\frac{6.3*0.75}{2.7} = 1.75L[/tex]
All sides are congruent, opposite sides are parallel, and opposite angles are congruent (but not 90) describes which shape
Consider the following conditional statement. If a + 1 = b, then b > a. A. Create a pair of values for a and b in which the numerical relationship shown in the given conditional statement is true. In your final answer, include the values of the variables and proof of truth. B. Is it possible to create a pair of values for a and b in which the numerical relationship shown in the given conditional statement is false? Use complete sentences to explain your answer.
In mathematics, creating values for a and b satisfying a given conditional statement involves fulfilling the logical relationships between the variables. It is impossible to violate the logical connection established by the initial condition of the statement.
A: Let's choose a=2 and b=3. If a+1=b, then 2+1=3, which is true. So, a=2 and b=3 satisfy the given conditional statement.
B: It is not possible to create a pair of values for a and b where the numerical relationship shown in the given conditional statement is false. This is because the statement is a logical consequence of the initial condition a+1=b.
There are 10 red marbles and 8 green marbles in a jar. if you take three marbles from the jar (without replacement), the probability that they are all red is:
There are 10 red marbles and 8 green marbles in a jar. So, the probability that all three marbles taken from the jar are red is 0.147.
Given :
Number of red marbles = 10
Number of green marbles = 8
Probability is the department of mathematics concerning numerical depictions of how likely the event is to happen or how likely it is that suggestion is genuine. The probability of an event could be number between 0 and 1 , where o shows difficulty of the event and 1 shows certainty.
Total number of marbles in a jar = 10 + 8 = 18
Total number of red marbles in a jar = 10
So, the probability that all three marbles taken from the jar are red is:
[tex]= \dfrac{10}{18}\times\dfrac{9}{17}\times\dfrac{8}{16}[/tex]
[tex]= 0.147[/tex]
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Joanna, Dana and Tracy shared some trail mix. Joanna ate 0.125 pound of trail mix, Dana ate 0.1 pound and Tracy ate 0.12 pound of trail mix. List the friends in order from least to greatest amount of trail mix eaten
We are given the following values:
0.125 pound
0.1 pound
0.12 pound
All values start with the same number which is 0.1, therefore the 0.1 is the smallest.
Next the two values are followed by 0.12, so 0.12 is the next smaller number.
So the largest number is 0.125.
Arranging from least to greatest amount of trail mix eaten:
Dana, Tracy, Joanna
A group of n students is assigned seats for each of two classes in the same classroom. how many ways can these seats be assigned if no student is assigned the same seat for both classes?
The number of ways the seats can be assigned is equal to n factorial (n!).
Explanation:The number of ways the seats can be assigned is given by the permutation formula. Since there are n students and 2 classes, each student can be assigned a seat in the first class in n ways. After that, there are (n-1) seats left and (n-1) students remaining to be assigned seats in the second class. Therefore, the total number of ways to assign seats is n * (n-1) * (n-2) * ... * 1, which is equal to n factorial (n!).
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At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]
Answer:
21
Step-by-step explanation:
Seventeen members of Troy's family are going to an amusement park during the week of their family reunion. Adult tickets cost $39.50 each and child tickets cost $31 each. If the total cost for admission to the part is $578, how many adults went to the park?