The value οf the median MN fοr the given trapezοid is 70.59 units.
What is the law οf sines?The law οf sines specifies hοw many sides there are in a triangle and hοw their individual sine angles are equal. The sine law, sine rule, and sine fοrmula are οther names fοr the sine law. The side οr unknοwn angle οf an οblique triangle is fοund using the law οf sine.
Any triangle that is nοt a right triangle is referred tο as an οblique triangle. At least twο angles and their cοrrespοnding side measurements shοuld be used at οnce fοr the sine law tο functiοn.
Given that, SPQR is a trapezοid with SP parallel tο QR,
Nοw, we knοw that MN is the average οf the lengths οf the bases SP and QR.
That is,
MN = (SP + QR) / 2.
Fοr the given values we have:
SP = PQ = 12, sο QR = 2MN - SP
Nοw, m∠QRS = 120 and m∠QPS = 135,
Thus,
m∠SPQ = 180 - 120 - 135 = -75.
Hοwever, angles cannοt be negative, sο we add 360 tο get 285 degrees.
Since SPQR is a trapezοid, we knοw that m∠SPQ = m∠QRN. Alsο, since MN is the median οf the trapezοid, it divides the trapezοid intο twο cοngruent triangles, sο m∠QMN = m∠RNM.
Using the law οf sines in triangle QMN tο find MN:
sin(m∠QMN) / MN = sin(m∠MQN) / QN.
Since QN = NR:
sin(m∠QMN) / MN = sin(m∠RNM) / NR.
sin(135) / MN = sin(285) / NR.
NR = sin(285) / sin(135) * MN.
2MN - SP = 2 * sin(285) / sin(135) * MN
2MN - 12 = 2.17MN
MN = 12 / 0.17 = 70.59
Hence, the value οf the median MN fοr the given trapezοid is 70.59 units.
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If these two shapes are similar, what is the measure of the missing length d?
inches
24 in
6 in
9 in
d
Answer:
d = 36
Step-by-step explanation:
9/6 = d/24
6d = (9)(24)
d = 216/6 = 36
Answer:
Step-by-step explanation:
Similar shapes have proportional sides.
Make a ratio and solve for d.
[tex]\frac{6}{9}[/tex] = [tex]\frac{24}{d}[/tex]
cross mulitply then divide
9 × 24 = 6d
216 = 6d
216/6 = 6d/6
36 = d
F(x)= 2X³-7X+4
Determine the intervals on which the function is positive on (-3;3), give the boundaries of the intervals rounded to four decimals.
Therefore , the solution of the given problem of function comes out to be the interval's edges, rounded to four decimals, are -1.3233 and 0.7838.
What does function actually mean?The math lesson includes a variety of subjects, such as math, integers, but one's subdivisions, as well as architecture, construction, and that both real but rather fictitious geographic locations. A work covers the connections between different variables that all work together to produce the same result. A utility is made up of a variety of distinctive components that cooperate to create distinctive results for each input.
Here,
First, we assess f(x) at the interval's endpoints:
=> f(-3) = 2(-3)^3 - 7(-3) + 4 = -43
=> f(3) = 2(3)^3 - 7(3) + 4 = 44
There must be at least one root in each of the gaps between (-3, r) and (r, 3), where r is the function's root, because the function changes sign at x = -3 and x = 3. To find the function's roots numerically,
we can use the bisection technique or Newton's method.
We can plot the function using a graphing calculator or computer software and see that there is one root in the range (-3, -2), one root in the range (-2, 0), and one root in the range (-3, -2). (0, 3).
Consequently, the periods where the function is positive on the range (-3, 3) are as follows:
=> (-3, -1.3233) and (0.7838, 3) (0.7838, 3)
The interval's edges, rounded to four decimals, are -1.3233 and 0.7838.
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need help on this multiple choice question asap
Answer:
C
Step-by-step explanation:
We will have to distribute because volume equals length times width times height
Match the following expression to the correct problem
Column A
1. ___ thirteen times a number squared
2. ___ a number times eleven plus thirty-three
3. ___ twelve less than a number
4. ___ The quotient of a number and twenty
Column B
A. 11n + 33
B. p ÷ 20
C. y - 12
D. 13b^2
Example: 1. ___ D: 13b^2
the cοrrect expressiοns are, 1)Thirteen times a number squared - D)
2)A number times eleven plus thirty-three - A) 11n + 33
3) Twelve less than a number - C) y - 12
4)The quοtient οf a number and twenty - B) p ÷ 20
What is expressiοn?Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. Unknοwn variables, integers, and arithmetic οperatοrs are the cοmpοnents οf an algebraic expressiοn. There are nο symbοls fοr equality οr inequality in it.
Here we need to convert given statement into expression. Then,
1)thirteen times a number squared
=> 13[tex]\times b^2[/tex] = [tex]13b^2[/tex]
2) a number times eleven plus thirty-three
=> 11 times of number+ 33
=> 11*n+33
=> 11n+33
3) twelve less than a number
=> number -12
=> y-12
4)The quotient of a number and twenty
=> p/20
=> p ÷ 20
Hence the correct expressions are,
1)Thirteen times a number squared - D) [tex]13b^2[/tex]
2)A number times eleven plus thirty-three - A) 11n + 33
3) Twelve less than a number - C) y - 12
4)The quotient of a number and twenty - B) p ÷ 20
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A bag of the same size balls contains six blue balls firebrand balls five yellow balls and four green balls what is the probability of selecting a blue or green ball on the first draw
Answer:
The probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.
Step-by-step explanation:
The probability of selecting a blue or green ball on the first draw can be calculated by adding the probability of selecting a blue ball to the probability of selecting a green ball.
The probability of selecting a blue ball on the first draw is the number of blue balls divided by the total number of balls in the bag:
P(blue ball) = 6/(6+5+4) = 6/15 = 2/5
Similarly, the probability of selecting a green ball on the first draw is:
P(green ball) = 4/(6+5+4) = 4/15
Therefore, the probability of selecting a blue or a green ball on the first draw is:
P(blue or green ball) = P(blue ball) + P(green ball)
= 2/5 + 4/15
= 2/3 = 0.67
So, the probability of selecting a blue or green ball on the first draw is 2/3 or 0.67
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1 kg of rice cost $4.10.what is the cost of 1/4 kg of a rice?
Answer: $1.03
Step-by-step explanation:
4.10 x 1/4 = 1.025
whats the range for the measures 3.8 and 9.2
Answer: It's not clear what measures 3.8 and 9.2 represent. However, if they represent angles in degrees, then the range of these measures would be:
- If there are no restrictions on the angles, the range would be [0°, 360°), meaning any angle between 0 degrees and 360 degrees (excluding 360 itself).
- If the angles are restricted to be acute angles (less than 90 degrees), then the range would be (0°, 90°), meaning any angle between 0 degrees and 90 degrees (excluding 0 and 90 themselves).
- If the angles are restricted to be obtuse angles (between 90 and 180 degrees), then the range would be (90°, 180°), meaning any angle between 90 degrees and 180 degrees (excluding 90 and 180 themselves).
- If the angles are restricted to be right angles (exactly 90 degrees), then the range would be {90°}, meaning only the angle of 90 degrees.
Step-by-step explanation:
f(x)=-x^2+4x if the domain is {-2,0,1}
The range of the function for the given domain is {-12, 0, 3}.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.
If the domain of f(x) is {-2,0,1}, we can evaluate the function for each value in the domain:
When x = -2:
f(-2) = -(-2)² + 4(-2) = -4 - 8 = -12
When x = 0:
f(0) = -(0)² + 4(0) = 0
When x = 1:
f(1) = -(1)² + 4(1) = 3
Therefore, the range of the function for the given domain is {-12, 0, 3}.
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Find the associated z score or scores that represent the following standard normal areas hint use the excel function=NORM.S.INV()
A. Middle 50 percent
B. Lowest 5 percent
C. Middle 90 percent
URGENT/High points will be rewarded
The 90% of the standard normal distribution has z-scores between -1.645 and 1.645, the lowest 5% has z-scores between -1.645 and 1.645, and the middle 50% of the standard normal distribution has z-scores between -0.6745 and 0.6745.
Define standard normal variation?The probability density function f(x) for the continuous random variable X taken into account in the system defines the normal distribution. It is a function who's integral over a range (let's say, x to x + dx), when taking into account values between x and x + dx, yields the probability of the random variable X.
The mean and variance of a typical normal distribution are both 0. An alternative term for this is a z distribution.
Yes, the z-scores for the specified standard normal areas are shown here:
Middle 50%: The middle 50% of a standard normal distribution can be found between the 25th and 75th percentiles. We can determine the z-scores associated with those percentiles using Excel's NORM.S.INV () function as follows:
The z-score for the 25th percentile is -0.6745 (percentile).
The z-score for the 75th percentile is 0.6745.
The middle 50% of the ordinary normal distribution is thus represented by z-scores that vary from -0.6745 to 0.6745.
Minimum 5%: The lower 5% of the standard normal distribution are represented by the region to the left of the 5th percentile. We can determine the z-score associated with that percentile by using Excel's NORM.S.INV () function as follows:
-1.645 is the z-score assigned to the fifth percentile.
Hence, -1.645 is the z-score that represents the bottom 5% of the standard normal distribution.
Middle 90%: The middle 90% of the standard normal distribution is the region between the 5th and 95th percentiles. We can determine the z-scores associated with those percentiles using Excel's NORM.S.INV () function as follows:
-1.645 is the z-score assigned to the fifth percentile.
The 95th percentile's corresponding z-score is 1.645.
The middle 90% of the standard normal distribution is thus represented by z-scores that vary from -1.645 to 1.645.
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I need help with this please
Answer:
2500 ml
Step-by-step explanation:
In order to convert liters to ml, we need to multiply the volume value by 1000.
[tex]2.5\times 1000=2500[/tex]
Scott Salman, a travel agent, is paid on variable commission, is married, and claims four withholding allowances. He receives 3% of the first $20,000 in sales, 4% of the next $10,000 in sales, and 6% of all sales over $30,000. This week he has sales of $45,550 and the following deductions: FICA, Medicare, federal withholding, state disability insurance, state withholding, a retirement contribution of $45, a savings bond of $50, and charitable contributions of $20. Find his net pay after subtracting all of his deductions.
Scott Salman's net pay after subtracting all his deductions is $1,185.97.
How to calculate interest ?
To calculate Scott Salman's net pay after all deductions, we need to first determine his gross pay based on his variable commission.
Sales up to $20,000 will earn him a commission of 3%, which is $600. Sales between $20,000 and $30,000 will earn him a commission of 4%, which is $400. For sales over $30,000, he will receive a commission of 6%. In this case, the sales over $30,000 are $45,550 - $30,000 = $15,550, so his commission on this amount is $933.
Adding up all three commissions, Scott's gross pay is $1,933 ($600 + $400 + $933).
Next, we need to calculate his total deductions. FICA and Medicare deductions are based on a percentage of gross pay, which is 7.65%. For Scott, this comes out to be $147.70 ($1,933 x 7.65%).
Federal and state withholdings are calculated based on his tax bracket and filing status. Assuming he is filing jointly with his spouse, we can estimate his federal withholding to be $345 and state withholding to be $120.
State disability insurance varies by state and cannot be estimated without knowing where Scott lives. Assuming a standard rate of 1%, this comes out to be $19.33 ($1,933 x 1%).
Adding up all these deductions, we get a total of $632.03 ($147.70 + $345 + $120 + $19.33).
In addition, Scott has also made contributions towards his retirement plan, savings bond, and charitable donations. His retirement contribution is $45, his savings bond is $50, and his charitable contributions are $20. Adding these up, his total additional deductions come to $115.
Subtracting his total deductions from his gross pay, we get Scott's net pay:
$1,933 - $632.03 - $115 = $1,185.97.
Therefore, Scott Salman's net pay after subtracting all his deductions is $1,185.97.
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tibor is 5.5 feet tall and casts a shadow that is 7 feet long. Tibor's sister casts a shadow that is 5.25 feet long. how many feet tall is tibors sisters ?
In linear equation, 4.125 feet tall is tibors sisters.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
If the ratio of the student to their shadow and flagpole to its shadow are equal, then you can use the proportion
5.5/7 = x/5.25 and cross multiply to find x.
5.5 × 5.25 = 7 * x
28.875 = 7x
x = 28.875/7
x = 4.125
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The spot price of silver is $0.69 per gram. Silver has a density of 10.49 g/cm³. What is the cost a silver bar that is 4 cm x 10 cm x 1 cm? Round to the nearest cent.
Answer: $289.52
Step-by-step explanation: We will solve the problem by first finding the number of cubic centimeters in the bar, then finding the number of grams, then converting that number of grams to a price.
We are given the dimensions of the silver bar. With this, we can find how many cubic centimeters are in the bar. Cubic centimeter is a three-dimensional unit and we are given the three dimensions. We simply multiply the dimensions by each other to find the # of cubic centimeters since this would be the same as (cm^1)^3. This gives a unit in cm^3. 4*10*1 is 40 or 40 cm^3.
We are also given that there are 10.49 g/cm^3 meaning in each cm^3 of silver, there are 10.49 grams. We can multiply the # of cm^3 by 10.49 to find the #of grams. 10.49*40 is 419.6 or 419.6 grams.
Finally, we are given that each gram is worth 69 cents or $.69. We simply multiply the # of grams by this value to find the total price. .69*419.6 is 289.52. This is the answer in dollars.
Hope this helps! These types of problems all just come down to unit conversion so focus on what units are being used.
If x = 52 degrees, find the measures of angles 1, 2, and 3.
Answer:
∠1 = 128°
∠2 = 52°
∠3 = 128°
Step-by-step explanation:
∠1 and ∠3 are supplementary angles of x. Therefore, the sum of either with x is 180°. 180° - 52° = 128°. So ∠1 and ∠3 = 128°. ∠2 is opposite x, meaning they are vertical angles. Vertical anges have the same measurements so x = ∠2 = 52°.
PLEASE HELP ME QUICK IM STRESSING OUT AND I NEED THIS FAST !!
Answer:In an arithmetic sequence, the difference between consecutive terms is constant. Let us denote the common difference by d.
We know that a2 = -5, which means that the second term of the sequence is -5. Using the formula for the nth term of an arithmetic sequence, we can write:
a2 = a1 + d
-5 = a1 + d
We also know that a6 = 7, which means that the sixth term of the sequence is 7:
a6 = a1 + 5d
7 = a1 + 5d
We now have two equations with two unknowns (a1 and d), which we can solve for using substitution or elimination.
Substituting -5 = a1 + d into 7 = a1 + 5d, we get:
7 = -5 + 6d
12 = 6d
d = 2
Substituting d = 2 into -5 = a1 + d, we get:
a1 = -7
So the arithmetic sequence is: -7, -5, -3, -1, 1, 3, ...
The 5th term of this sequence is -1
Step-by-step explanation:
if y= -10x+4 is translated to the right by 2 units, then reflected across the y-axis, the new equation is
Answer:
y=-10x+6
Step-by-step explanation:
4 is the y interecept which lets you know if it goes left or right and by how much. Therefore you add 2 + 4.
Prove the divisiblity of each of the following numbers 7^6+7^5-7^4 by 11
The Expression came in two parts, we started by solving the first part and getting a whole number and the second part was used to divide the first part.
The answer is 12005
Given Data
we have the expression
7^6+7^5−7^4 by 11
The dividend = 7^6+7^5−7^4
The divisor = 11
Let us express the dividend as a whole number
7^6+7^5−7^4 = 117649 + 16807 - 2401
7^6+7^5−7^4 = 132055
Hence the expression 7^6+7^5−7^4 by 11
= 132055/11
= 12005 ans
The regular price of a desk is $484.77. This week, it is on sale for $243.45 off. What is the sale price of the desk?
The sale price of the desk is $241.32 if, The regular price of a desk is $484.77. This week, it is on sale for $243.45 off.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Given that The regular price of a desk is $484.77. This week, it is on sale for $243.45 off.
To find the sale price of the desk, we need to subtract the amount of the discount from the regular price:
Sale price = Regular price - Discount
Discount = $243.45
Regular price = $484.77
So, substituting the values, we get:
Sale price = $484.77 - $243.45
Sale price = $241.32
Therefore, the sale price of the desk is $241.32.
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Use the given lengths to determine if AB || DE. 7 B 21 D 24 E 8 A type yes or no
The line DE which divides the main triangle is parallel to AB of the original triangle. This is a true statement.
What are parallel lines?A parallel line is defined as the type of line that exists between two lines on the same plane that can never never intersect or meet each other.
Line AB is said to be parallel to line DE because the line DE correctly divides both line BC and CA at a point that triangle CDE is similar to triangle CBA with a scale factor of = 4
That is = line BC/DB = AC/EA
= 28/7 = 32/8 = 4
Therefore the line DE is parallel to line AB as both will never meet till infinity.
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Evaluate the given expression and show the steps, please.
Answer:
80
Step-by-step explanation:
To do this very simply, you need to input every value of k into the equation that the sigma notation asks of you and then sum them all together. You can do this question simply by inputting k = 1,2,3,4 into the equation and adding all the values together. (the bottom sigma value k=1 is the initial value of what you start with and the final value at the top is the value you need to get to by adding 1 to k each time and putting it in the equation every time i.e. think of it as 1 through 4 values you need to input into the equation and add together)
2(3^1-1) = 2
2(3^2-1) = 6
2(3^3-1) = 18
2(3^4-1) = 54
After adding them, you get 80.
Answer:
s₄ = 80
Step-by-step explanation:
[tex]\displaystyle s_4=\sum^4_{k=1}2\left(3^{n-1}\right)[/tex]
The given sigma notation means the sum of the series with nth term 2(3ⁿ⁻¹), starting with n = 1 and ending with n = 4.
As 2(3ⁿ⁻¹) is exponential, the series is geometric.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Comparing 2(3ⁿ⁻¹) with the general form of a geometric sequence:
a = 2r = 3The formula for the sum of the first n terms of a geometric series is:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Therefore, substitute a = 2, r = 3 and n = 4 into the sum formula to find the sum of the first 4 terms of the geometric series:
[tex]\implies S_4=\dfrac{2(1-3^4)}{1-3}[/tex]
[tex]\implies S_4=\dfrac{2(1-81)}{-2}[/tex]
[tex]\implies S_4=\dfrac{2(-80)}{-2}[/tex]
[tex]\implies S_4=\dfrac{-160}{-2}[/tex]
[tex]\implies S_4=80[/tex]
Therefore, the sum of the first 4 terms of the geometric series is 80.
Write an equation to model the fish population y in a fishery that has a linear growth rate of 40 new fish each season *, and an initial population of 1250 fish.
After how many seasons will the population reach 1690 fish? Write an equation for a second fish population that grows by 60 new fish each season with an initial population of 1100 fish. After how many seasons will they have the same population?
Graph your equations in the coordinate plane.
Help please
The equation to model the fish population y in a fishery with a linear growth rate of 40 new fish each season and an initial population of 1250 fish can be written as:
y = 40x + 1250What is the equation about?The equation to model the fish population y in a fishery with a linear growth rate of 40 new fish each season and an initial population of 1250 fish can be written as:
y = 40x + 1250
where x is the number of seasons.
To find out how many seasons it will take for the population to reach 1690 fish, we can substitute y = 1690 into the equation and solve for x:
1690 = 40x + 1250
440 = 40x
x = 11
So it will take 11 seasons for the population to reach 1690 fish.
For the second fish population that grows by 60 new fish each season with an initial population of 1100 fish, the equation to model the population can be written as:
y = 60x + 1100
To find out after how many seasons they will have the same population, we can set the two equations equal to each other and solve for x:
40x + 1250 = 60x + 1100
20x = 150
x = 7.5
So it will take 7.5 seasons for the two populations to have the same population.
To graph the equations, we can plot points on the coordinate plane using values of x and y. For the first equation, we can plot the points (0, 1250) and (11, 1690). For the second equation, we can plot the points (0, 1100) and (7.5, 1500). Then we can connect the points with a straight line for each equation. The resulting graph will show how the populations of the two fish populations change over time.(Note: In the question, A season is not defined and as such, we assume it to be one year for simplicity.)
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find the total amount in Mr.hunter account, if he invests $900 for 2 years at 6% interest rate
Answer:
To find the total amount in Mr. Hunter's account, we need to use the formula:
A = P(1 + r/n)^(nt)
where:
A = the total amount
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $900, r = 0.06, n = 1 (compounded annually), and t = 2.
So, plugging in these values, we get:
A = 900(1 + 0.06/1)^(1*2)
A = 900(1.06)^2
A = 900(1.1236)
A = $1,011.24
Therefore, the total amount in Mr. Hunter's account after 2 years is $1,011.24.
You have found three investment choices for a one - year deposit:
10% APR compounded monthly,
10% APR compounded annually, and
9% APR compounded daily.
Compute the EAR for each investment choice. (Assume there are 365 days in the year)
Part A: 10% APR compounded monthly: EAR = 10.47%.
Part b: 10% APR compounded annually: EAR = 10%.
Part c: 9% APR compounded daily: EAR = 9.42%
Explain about the Effective Annual Interest Rate?The anticipated rate of return with compound interest is known as the effective annual interest rate. The yearly percentage rate of an investment will be less than its effective annual interest rate because of compounding.Part A: 10% APR compounded monthly,
Effective annual interest rate (EAR):
EAR = [tex](1 + \frac{I}{n} )^{n }[/tex] - 1
I is the annual percentage rate/nominal interest rate
n is the number of compounding periods (in a year)
For monthly compounding.
EAR = [tex](1 + \frac{0.10}{12} )^{12}[/tex] - 1
EAR = 10.47%
Part b: 10% APR compounded annually,
For annual compounding.
The effective yearly interest rate will be the same as the nominal interest rate if the interest rate gets compounded annually.
EAR = Nominal interest rate
EAR = 10%
Part c: 9% APR compounded daily.
EAR = [tex](1 + \frac{0.09}{365} )^{365}[/tex] - 1
EAR = 9.42%
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7.08 Scale factor and equations Pls I need Help ASAP!!
you can use an equation (such as x = scale factor * length of corresponding side on larger rectangle) to find the length of the corresponding side on the larger rectangle.
Sure! The scale factor refers to the ratio between the measurements of two similar figures. For example, if you have two triangles that are similar, you can find the scale factor by dividing the length of one corresponding side of the larger triangle by the length of the corresponding side on the smaller triangle.
Equations can be used to find missing measurements in similar figures using the scale factor. For example, if you know the scale factor between two similar rectangles and the length of one side on the smaller rectangle,
Hope that helps! Let me know if you have any other questions.
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Multiply and simplify if possible.
(6-√3) (4+√3)
Need to know that the function intervals are increasing or decrease
..........................................................................................................
Find one half and one quarter quarter of the following
(A)1/2 of 32. (B) 1/2 of 28. (C). 1/2 of 64 (D) 1/2 of 54
Answer:
A. 16 B. 14. C. 32 D. 27
Step-by-step explanation:
A. 1/2 × 32 = 16. 1/4 ×32 = 8
B. 1/2 × 28 = 14. 1/4 ×28 = 7
C. 1/2 × 64 = 32. 1/4 × 64 = 16
D. 1/2 × 54 = 27. 1/4 × 54 = 13.5
Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1,5,5).
To find the area of a triangle in three-dimensional space, we can use the cross product of two vectors that lie in the plane of the triangle. We can use the vectors formed by subtracting the coordinates of one vertex from the other two vertices.
Let's take A as our reference vertex. Then the vectors AB and AC can be calculated as follows:
AB = B - A = (2, 3, 5) - (1, 1, 2) = (1, 2, 3)
AC = C - A = (1, 5, 5) - (1, 1, 2) = (0, 4, 3)
To find the area of the triangle, we need to take the magnitude of the cross product of AB and AC and divide by 2:
Area = |AB x AC| / 2
where x denotes the cross product. The cross product of AB and AC can be calculated as follows:
AB x AC = (23 - 54, 50 - 13, 14 - 20) = (-7, -3, 4)
Taking the magnitude of this vector gives:
|AB x AC| = sqrt((-7)^2 + (-3)^2 + 4^2) = sqrt(74)
Therefore, the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5) is:
Area = |AB x AC| / 2 = sqrt(74) / 2
So, the area of the triangle is (1/2) sqrt(74) square units.
Select all that are a radius of circle O.
AB
PQ
OB
OC
Please answer the question in the picture, I will mark brainliest. Show all work pls!!!
Circle A has been transformed to circle B. What is the translation rule for these circles?
Answer choices are:
(x+4),(y+3)
(x-1),(y+4)
(x-2),(y+3)
(x+2),(y+3)
The translation transformation part of the rule that transforms circle A into circle B is; ((x + 2), (y + 3))
What is a translation transformation?A translation transformation is a geometric transformation that involves moving an object in a straight line, without rotating or dilating the object.
The coordinates of the centers of the circle indicates the translation rule, used to transform the circles.
The coordinate of center of circle A is; (-1, -1)
The coordinates of the center of circle B is; (1, 2)
Therefore, we get;
The difference in the x and y values of the circles are;
Difference in the x-values = 1 - (-1) = 2
Difference in the y-values = 2 - (-1) = 3
The translation transformation part of the transformation that produces circle B from circle A is; ((x + 2), (y + 3))
Learn more on translation transformation here: https://brainly.com/question/11134096
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