The area of the ar (APQ) = 18 cm ^ 2 for the given triangle ABC.
Define the term median of triangle?A line segment from such a vertex here to middle of the other side is what is meant by a median. When the vertex is just an angle in a right triangle and the non-congruent angle about an isoceles triangle, it also functions as an angle bisector.Given that:
AD is ABC's median, ABC will be divided into two distinct triangles by AD.We are aware that a triangle's middle separates that into two triangles with equal areas. Triangle ABC's median is AD, and ABD's median is PQ.Then, area (ΔABD) = area (ΔADC)
And, area (ΔABD) = 1/2 area (ABC) eq.....(i)
Thus, In ΔABD, PQ is the median, as PQ are the mid points on AB and AD respectively.
Then,
ar (APQ) = 1/2 ar(ΔABD)
ar (APQ) = 1/2 × [1/2 ar(ABC)] ....... (Use eq (i))
ar (APQ) = 1/4 ar(ΔABC)
ar (APQ) = 1/4 *72 cm ^ 2
ar (APQ) = 18 cm ^ 2
Thus, the area of the ar (APQ) = 18 cm ^ 2 for the given triangle ABC.
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Select all the equations that are true when x = 6.
6x = 12
17 – x = 11
x ÷ 2 = 3
19 ÷ 3 = x
5 + x = 11
12.5% as a fraction (simplified)
Answer: 12.5% is 1/8
Answer: 25/2 would be your answer, as it is already in it's simplest form. I hope this helps! :)
Step-by-step explanation:
the length of the mid segment is:
Check the picture below.
so from the picture below we can say that parallel sides or bases of the trapezoid are AB and DC, that means our midsegment is found halfway of BC and halfway of AD, let's get the midpoints for those and then get their length.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad D(\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 2 +0}{2}~~~ ,~~~ \cfrac{ 0 +3}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 3 }{2} \right)\implies (1~~,~~\frac{3}{2}) \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad C(\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 +2}{2}~~~ ,~~~ \cfrac{ 4 +5}{2} \right) \implies \left(\cfrac{ 8 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies (4~~,~~\frac{9}{2})[/tex]
let's get their distance
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{\frac{3}{2}})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{\frac{9}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(4-1)^2 + (\frac{9}{2}-\frac{3}{2})^2}\implies d=\sqrt{3^2 + 3^2}\implies {\Large \begin{array}{llll} \stackrel{midsegment}{ d=\sqrt{18}} \end{array}}[/tex]
in the diagram below of trapezoid RSUT, X is the midpoint and V is the midpoint of SU if RS=30 and XV=44, what is the length of TU
The length of TU in a trapezoid RSUT is 34 units.
How to calculate length of TU in a Trapezoid?To find the length of TU, we can use the midpoint formula. The midpoint formula states that for a line segment with endpoints (x1, y1) and (x2, y2), the midpoint is ((x1 + x2)/2, (y1 + y2)/2).
In this case, we know that X is the midpoint of line segment RS and V is the midpoint of line segment SU. So we can set up the following equation:
(RS/2) + (SU/2) = 44
Where (RS/2) = (30/2) = 15 and (SU/2) = TU/2
So we can substitute this into the equation and get:
15 + (TU/2) = 44
To find TU, we can solve this equation by multiplying both sides by 2:
TU = 2(44) - 2(15) = 64 - 30 = 34
So the length of TU is 34 units.
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i need the answer because i dont know
The functions f and have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.
What is a graph ?
Graph can be defined as the visual representation of the given data using ordered pairs.
Graph of f(x)
You can read the y-intercept on the graph. It is the value of y-coordinate when x = 0; so ti is y = 6.
The axis of simmetry is the vertical line that split the graph into two symmetrical forms. That is the same that the vertical line that passes through the vertex. You can see that it is x = 2
2) Table of values of g(x)
The y-intercept is the value of y-coordinate when x = 0, so it is y = 8.
The axis of symmetry is x = 2.
Hence, The functions f and have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.
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A measure computed from the entire population is called: Select one: a. a statistic. b. a qualitative value. c. a mean. d. a parameter.
A measure computed from the entire population is called a parameter.
The correct answer is an option (d)
We know that a parameter is nothing but a numerical value that describes a certain characteristic of the entire population. It is computed using the population values such as population mean, population variance, etc.
Whereas, a statistic is a numerical value that defines certain characteristic of a sample.
It is computed using the sample values such as the sample mean, sample variance, etc.
A qualitative value or a qualitative data are represented by a name, symbol, or a number code. This data is the data about categorical variables.
And the mean is nothing but the average of a set of values.
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adding fractions with unlike denominators worksheets
The simplification of the addition of two or more fraction with unlike denominator is:
Convert the denominator with like terms and then add the numerators.
Method of simplification of addition of fraction with unlike denominator is:
Calculate the least common multiple of all the denominator of unlike fraction.Convert the denominator of the fraction with like terms.Now add the numerator of the given fraction.Example : ( 1 / 2) + ( 3 / 5 )Least common multiple of 2 and 5 is 10.Multiply by ( 5 / 5) to ( 1/ 2) which is equal to ( 5 / 10 ).Multiply ( 2/ 2 ) to ( 3 /5 ) we get ( 6 /10).Add like fraction ( 5/10) + ( 6 /10) = ( 5+ 6 ) /10Result is 11 /10.Therefore, to simplify unlike fractions find least common multiple and add the like fractions.
The given question is incomplete, I answer the question in general according to my knowledge:
Simplification of adding fractions with unlike denominators with example?
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Using powers of 10, give a low and high estimate for the number of teachers in the U. S
0.0000732 = 7.32 x 10⁻⁵
The power of 10 will be the number of places the original decimal point was moved and it will be positive as it was moved towards the left side.145,000 = 1.45 x 10⁵
Now, According to the question:
If the number is given in the decimal notation, move the decimal point to the right side of its original position and place the decimal point after the first non zero digits. The power ten will be the number of places the original decimal point was moved and it will be negative as it was moved towards the right side.
0.0000732 = 7.32 x 10⁻⁵
If the whole number greater than 10 is to be changed into the power of 10, then move the decimal point to the left side of its original position and place the decimal point after the first digit. The power of 10 will be the number of places the original decimal point was moved and it will be positive as it was moved towards the left side.
145,000 = 1.45 x 10⁵
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What are the missing angle measures in triangle abc? 1.4° and 88.6° 18.6° and 71.4° 35.5° and 54.5° 44.4° and 45.6°
The missing angle measures in triangle ABC are 35.5° and 54.5°.
We know that,
In the right triangle ABC
∠A +∠B =90° ( by complementary angles)
We find the measure of angle B.
we know that
[tex]tanB = \frac{opposite side angle B}{adjacent side angle B}[/tex]
According to the question,
Opposite side angle B= 7 in
Adjacent side angle B = 5in
So, [tex]tanB = \frac{7}{5}[/tex]
[tex]B = arc tan(\frac{7}{5})[/tex]
B = 54.5°
Then, we find the measure of angle A
A + B = 90°
A = 90°-B
A = 90° - 54.5° ( using subtraction)
A = 35.5°
So, The angles measured in triangle ABC are 35.5° and 54.5°.
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The frequency table shows the results of a survey about favorite exhibits. Find the relative frequency that a randomly selected student's favorite exhibit was either butterflies, or trains, as a percent
Butterfly - 12
Dinosaurs - 25
Planets - 17
Trains - 6
The relative frequency as a percentage is 25.7%.
The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency. Divide each frequency by the overall sample size, in this example 20 students, to determine the relative frequencies.
The relative frequency of students who picked either butterflies or trains as their favorite exhibit is 18 (12 + 6) out of a total of 70 students.
The relative frequency as a percentage is 18/70 * 100 = 25.7%.
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calculate the sample covariance. b. calculate the sample correlation coefficient. c. describe the relationship between x and y.
The relationship between x and y can be described based on the value of the sample correlation coefficient.
Sample covariance measures the degree to which two variables are linearly related and the direction of their linear relationship. The formula for sample covariance is:
[tex]Cov(x,y) = (1/(n-1)) * \Sigma(x-\bar x)(y- \bar y)[/tex] where,
[tex]\bar x[/tex] and [tex]\bar y[/tex] are the sample means of x and y, respectivelyn is the sample size.The sample correlation coefficient, also known as Pearson's correlation coefficient, measures the degree to which two variables are linearly related and the direction of their linear relationship. It is a normalized version of the sample covariance, with a value between -1 and 1. The formula for the sample correlation coefficient is:
r = Cov(x,y) / (s1 * s2) where,
s1 and s2 are the sample standard deviations of x and y, respectively.To calculate the sample covariance and sample correlation coefficient, we need to have a sample of data containing the variables x and y. Once we have the data, we can calculate the sample means, and sample standard deviations, and then use the formulas above to calculate the sample covariance and sample correlation coefficient.
The relationship between x and y can be described based on the value of the sample correlation coefficient.
A value close to 1 indicates a strong positive linear relationshipA value close to -1 indicates a strong negative linear relationship A value close to 0 indicates no linear relationship.Learn more about covariance here:
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The complete question is:
Given a sample of data containing the variables x and y, calculate the sample covariance and the sample correlation coefficient, and describe the relationship between x and y.
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Roberto's parents open a savings account for him by depositing $250 on his birthday. The account earns simple interest at an annual rate of 5%. How much will be in Roberto's account after 5 years
To calculate the amount of money in Roberto's savings account after 5 years, you can use the formula for simple interest:
I = Prt
Where:
I = Interest earned
P = Principal (original amount of money in the account)
r = Annual interest rate (expressed as a decimal)
t = Number of years
In this case, the principal is $250, the annual interest rate is 5% (or 0.05 as a decimal), and the number of years is 5.
So, you can plug these values into the formula:
I = 250 * 0.05 * 5
To find out the total amount of money in the account after 5 years, you need to add the interest to the principal:
250 + I = 250 + (250 * 0.05 * 5) = 250 + 62.5 = $312.5
Roberto's account will have $312.5 after 5 years.
. Zachariah has 9 American stamps out of 15 stamps. Khai has 13 American stamps out of 20 stamps. Which statement is correct?
Due to the fact that 8 over 14 is more than 11 over 21, Zachariah has a higher ratio of American stamps than Khai.
What is a fraction?Due to the fact that 8 over 14 is more than 11 over 21, Zachariah has a higher ratio of American stamps than Khai.
An element of a number or any number of equal pieces is represented by a fraction.
Given that Khai and Zachariah are stamp collectors.
Zachariah also contains eight of the fourteen American stamps that are available.
Khai contains 11 American stamps out of a total of 21.
Khai equals 8/14 Zachariah equals 11/21
Zachariah has a higher proportion of American stamps than Khai does since 8 over 14 is more than 11 over 21.
After all, we would convert 11/21 and 8/14 into fractions.
Tell them that we would turn their fractional values into decimals and then into percentiles.
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what is the answer to 12+13
Answer: 25
Step-by-step explanation: 10+10=20 and 2+3=5. 20+5=2
It takes 2 h for students to plabt seeds in 3/8 of a community garden. Vanessa says it will take 4 h for the students to plant seeds for the whole garden. Is vanessa corect? Explain your reasoning
Students can plant seeds in a whole community garden in 5 1/3 h. Hence, Vanessa is not correct.
In the example question, students must plant seeds in 3/8 of a community garden in two hours.
The children will need 4 hours to plant the seeds for the entire garden, according to Vanessa.
We must confirm whether Vanessa is correct.
Within two hours, students plant seeds in 3/8 of the community garden.
Students can therefore plant seeds in 1 community garden in = 2/(3/8) h.
In one of the community gardens, students can sow seeds in = 2/3 * 8 hours.
In one of the communal gardens, students can plant seedlings in 16/3 hours.
In one of the communal gardens, students can sow seeds in 5 1/3 hours.
Students can therefore plant seeds in the entire community garden in 5 1/3 hours. Hence, Vanessa is not correct.
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A concrete beam is to rest on two concrete pillars. The beam is a cuboid with sides of length 0.5m, 3m and 0.4m. The pillars have diameter 0.4m and height 2m. Calculate the total volume of concrete needed to make the beam and the pillars. Round your answer to a sensible level of accuracy.
In a case whereby concrete beam is to rest on two concrete pillars. The beam is a cuboid with sides of length 0.5m, 3m and 0.4m with diameter 0.4m and height 2m. the total volume of concrete needed to make the beam and the pillars is 1.103m^3
How can the concrete needed to make the beam be calculated?The concept here is total volume , then we can calculate this for concrete needed to make the beam and the pillars as:
Vtd = V1 + V2
= V1= lwh
where length l = 0.5m,
width w= 3m
height h= 0.4m.
V1 + V2 = (0.5m* 3m * 0.4m) + 2(π/4 d^2. h)
where h =height 2m
Then V1 + V2 = 1.1026m^3
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To make ends meet, Ms.
Farnsby works three jobs. Her total income last year was $48,000. Her income from teaching was just $6000 more than her income from house painting. Royalties from her textbook sales were one-seventh of the total money she received from teaching and house painting. How much did she make from each source last year?
The money that a organisation earns in return for their labour or products is referred to as income.She make from each source last year $6000.
What is income?The money that a person or organisation earns in return for their labour or products is referred to as income.
Salary, rent, capital gains, company revenue, and income from other sources are a few typical sources of income. Understanding how each type of income is taxed is not always simple, and you may require an income tax calculator to do so.
Let t=teaching income, p=painting income, and b=book sales income.
t=p+6000 b=(t+p)/7 b+t+p=48000 (t+p)/7 +p+6000+p=48000 substitute (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000 multiply each side by 7 to eliminate the fraction.
substitution (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000
2p+6000+7p+42000+7p=336000
16p+48000=336000
16p=336000-48000
16p=288000 \s16p/16=288000/16
p=$18,000.
t=18000+6000
t=$24,000.
b=(24000+18000)/7
=42000/7
=$6000.
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Rectangle ABCD with vertices A(-3,0), B(1, 2),
C(2, 0), and D(-2,-2): k = 3
Determine if the ordered pair (6, 4) is a solution to the inequality y is less than three fourths times x minus 3.
No, because (6, 4) is above the line
Yes, because (6, 4) is below the line
Yes, because (6, 4) is on the line
No, because (6, 4) is on the line
The ordered pair (6, 4) is not a solution to the inequality
The graph is given below
Option A is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
Ordered pair = (6, 4)
This means,
(6, 4) = (x, y)
Now,
y < 3/4(x - 3)
Substitute (6, 4) = (x, y)
4 < 3/4(6 - 3)
4 < 3/4 x 3
4 < 4
This is not true.
From the graph,
(6, 4) is above the line.
Thus,
The graph is given below
(6, 4) is not a solution.
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4. Analyze and Persevere What is a power that
has the same value as 18? Explain.
The powers that have same value as 1^8 are 1^n, n^0 where n=real number.
What are real numbers?
Real numbers are simply the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also. At the same time, the imaginary numbers are the un-real numbers, which cannot be expressed in the number line and are commonly used to represent a complex number. Some of the examples of real numbers are 23, -12, 6.99, 5/2, π, and so on.
Now,
As we know anything raised to the power of 1 is always one and 0 raised to the power of anything is also one.
Hence, the powers that have same value as 1^8 are 1^n, n^0 where n=real number.
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Which of the following expressions are equivalent to 16a^3b^2 - 8a^5b^5 + 12a^4b? Select all that apply.
Answer:
um i don't know.... 99
Step-by-step explanation:
99 +12
15% off 84.75 pls help
Answer: If you take 15% off of 84.75, the new amount would be 71.8875. This can be calculated by multiplying 84.75 by 0.15 (15% written as a decimal), and then subtracting that result from 84.75.
Set up a system of equations for the given information by filling in the boxes with the coefficients of the variables and the constant values, where is the amount invested in stocks, is the amount invested in bonds, and is the amount invested in CD's.
If there is no visible coefficient, then enter
for the coefficient.
If a specific variable is not present in the equation, then enter
for the coefficient.
Country Day's scholarship fund receives a gift of $200000. The money is invested in stocks, bonds, and CDs. CDs pay 5% interest, bonds pay 2.9% interest, and stocks pay 10.9% interest. Country day invests $20000 more in bonds than in CDs. The total amount earned from the investments is $11165.
Total amount invested:
+ +
=
Total amount earned from investements:
+ +
=
Relation of bonds and CDs:
+ + =
Answer: Total amount invested:
= 200000
Total amount earned from investements:
0.109x + 0.029y + 0.05z = 11165
Relation of bonds and CDs:
= +20000
Step-by-step explanation:
X - 4.65 less than or equal to 0.09
it's an equation not a question
The required given expression is a equation x - 4.65 = 0.09.
What is Equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to question:In any expression variables and constants are expressed by equal sign,
Then the expression is called equaion.
So, as question says,
x - 4.65 = 0.09
x = 4.74
Thus, It is a equation of value 4.74.
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Adam, Barry and Charlie are brothers.
Here is some information about their ages
• Adam is twice as old as Barry
• Charlie is three years younger than Barry
• The sum of all their ages is 53
How old is Barry?
For the sum of ages of Adam, Barry, and Charlie is 53 , Barry is 14 years old.
Number of brothers are three.
Adam, Barry and Charlie.
Let us consider 'x' years be the age of Barry.
Adam age is equal to (2x) years.
And Charlie age is equal to ( x - 3 )years.
Sum of their ages = 53
Substitute the value of Adam, Barry and Charlie age we get,
⇒ x + 2x + x - 3 = 53
⇒ 4x = 53 + 3
⇒ 4x = 56
⇒ x = 56 / 4
⇒ x = 14 years
Barry is 14 years old.
Adam = 2(14 )
= 28 years
Charlie = 14 - 3
= 11 years
Therefore, as per the information about the ages of Adam, Barry and Charlie , the Barry is 14 years old.
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Lauren deposited $300 to start her savings account. After one year, she had $312 in
her account. If she did not deposit or withdraw any money that year, how much
interest did she earn?
N
Answer:
12 dollars
Step-by-step explanation:
she started with 300 and didn't add any money or take any away... sooo she earned $12 in interest
What is the equation of the line that passes through the point (3,-6) and has a slope of -3?
Answer:
y = -3x + 3
Step-by-step explanation:
the equation of a line in point-slope form is.
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - (-6) = -3 (x - 3)
y+6 = -3x+9
Answer:
y = -3x+3
Step-by-step explanation:
Remember that y = mx+c
The slope is m aka the gradient and we know that that's -3.
So just chuck it into the equation:
y = -3x + c
We still have to find c (which is the y intercept)
So substitute the point (3,-6) into the equation
We will have: -6 = -3(3) +c
Once you do algebra you'll get 3=c
So substitute that back into the equation (without the point (3,-6) since we only need the equation)
y = -3x + 3
the height if a triangle is 8 cm shorth than its base. if the are of the trinagle is 24cm^2 find the height of the triangle
The height of the given triangle is 4cm.
Let the base of the triangle be x cm.
It is given that the height of the triangle is 8cm shorter than the base.
∴ Height of the triangle = ( x-8 ) cm
Now,
Formula for the area of a triangle = 1/2 × Base × Height sq units.
It is given that the area of the triangle is 24 cm^2.
Area= 1/2* x(x-8) cm^2
⇒ 1/2 × x(x-8) = 24
⇒ x(x-8) = 48
⇒ [tex]x^{2}[/tex] - 8x -48=0
⇒ [tex]x^{2}[/tex] - 12x + 4x -48 = 0
⇒ x(x -12) +4(x-12) = 0
⇒ ( x-12 )( x + 4) =0
⇒ x= 12 , -4
Since, x is a length so it can not be negative value.
∴ x = 12 cm
Now, height = x-8= 4 cm
Therefore, The height of the given triangle is 4cm.
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Which of the following is a factor of 4x2 + 23x + 15
A: (4x + 5)
B: (2x + 3)
C: (4x + 3)
D: (2x + 5)
A number is doubled and the result is increased by 8. If the final result is 36. What is the number?
Answer:
14
Step-by-step explanation:
This question can be expressed as the following linear equation:
2x+8=36, where x is our unknown number.
From here,
2x+8=36
2x=28 (-8 both sides)
x=14 (/2 both sides)
Therefore the number is 14