Answer:
The area of the triangle is 5.875 square units.
Step-by-step explanation:
First, we need to calculate the lengths of the triangle by means of Pythagorean Theorem:
[tex]a = \|\overrightarrow {QR}\| = \sqrt{(5-4)^{2}+(7-4)^{2}+(-2+1)^{2}}[/tex]
[tex]a \approx 3.317[/tex]
[tex]b = \|\overrightarrow {RS}\| = \sqrt{(3-5)^{2}+(2-7)^{2}+(-4+2)^{2}}[/tex]
[tex]b \approx 5.745[/tex]
[tex]c = \|\overrightarrow {QS}\| = \sqrt{(3-4)^{2}+(2-4)^{2}+(-4+1)^{2}}[/tex]
[tex]c \approx 3.742[/tex]
Now, we can use the following formula to fid the area of the triangle ([tex]A[/tex]), measured in square units:
[tex]A = \sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}[/tex]
Where:
[tex]s[/tex] - Semiperimeter of the triangle, dimensionless.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Sides of the triangle, dimensionless.
The semiperimeter can be determined by this:
[tex]s = \frac{a+b+c}{2}[/tex]
If we know that [tex]a \approx 3.317[/tex], [tex]b \approx 5.745[/tex] and [tex]c \approx 3.742[/tex], the area of the triangle is:
[tex]s = \frac{3.317+5.745+3.742}{2}[/tex]
[tex]s = 6.402[/tex]
[tex]A = \sqrt{(6.402)\cdot (6.402-3.317)\cdot (6.402-5.745)\cdot (6.402-3.742)}[/tex]
[tex]A \approx 5.875[/tex]
The area of the triangle is 5.875 square units.
What is a number divided by 9
What is the relative size of (how many times as large) a circle's' circumference C to its diameter, d
Answer:
The circumference is pi times larger than the diameter of a circle.
Step-by-step explanation:
The formula of the circumference of a circle is
C = 2(pi)r = (pi)d
C = (pi)d
To find the ratio of the circumference to the diameter, divide both sides of the equation by d.
C/d = pi
The circumference is pi times larger than the diameter of a circle.
If it is an addition problem with different signs what do you do
Answer:
To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest. Subtract an integer by adding its opposite.
plz give brainlist
hope this helped
!Need help!
Solve using Substitution Method
2x + 5y = 7
x = 2 - 4y
Answer:
x = 6y = - 1Step-by-step explanation:
2x + 5y = 7 ......... Equation 1
x = 2 - 4y .......... Equation 2
Substitute x that's equation 2 into equation 1 and solve for y
That's
2( 2 - 4y ) + 5y = 7
4 - 8y + 5y = 7
- 3y + 4 = 7
- 3y = 7 - 4
- 3y = 3
Divide both sides by - 3
y = - 1
Substitute the value of y into equation 1
That's
x = 2 - 4(-1)
x = 2 + 4
x = 6
Therefore the solutions are
x = 6y = - 1Hope this helps you
Evaluate the expression and write your answer in the form a + bi. 1) (2-6i)+(4+2i)2) (6+5i)(9-2i)3) 2/(3-9i)4) (3 − 5i)(7 − 2i)
Answer:
Step-by-step explanation:
Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.
1) (2-6i)+(4+2i)
open the parenthesis
= 2-6i+4+2i
collect like terms
= 2+4-6i+2i
= 6-4i
2) (6+5i)(9-2i)
= 6(9)-6(2i)+9(5i)-5i(2i)
= 54-12i+45i-10i²
= 54+33i-10i²
In complex number i² = -1
= 54+33i-10(-1)
= 54+33i+10
= 54+10+33i
= 64+33i
3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i
= 2/3-9i*3+9i/3+9i
=2(3+9i)/(3-9i)(3+9i)
= 6+18i/9-27i+27i-81i²
= 6+18i/9-81(-1)
= 6+18i/9+81
= 6+18i/90
= 6/90 + 18i/90
= 1/15+1/5 i
4) For (3 − 5i)(7 − 2i)
open the parenthesis
= 3(7)-3(2i)-7(5i)-5i(-2i)
= 21-6i-35i+10i²
= 21-6i-35i+10(-1)
= 21-41i-10
= 11-41i
Simplified form of the given expressions will be,
1). 6 - 4i
2). 64 + 33i
3). [tex]\frac{1}{15}+\frac{1}{5}i[/tex]
4). [tex]\frac{31}{53}-\frac{31}{53}i[/tex]
1). In a complex number (a + bi),
a = Real part of the complex number
bi = Imaginary part
Expression given in the question → (2 - 6i) + (4 + 2i)
Rule to solve the given expression,
"Add real part and imaginary part of two complex numbers separately"
(2 - 6i) + (4 + 2i) = (2 + 4) + (-6i + 2i)
= 6 + (-4i)
= 6 - 4i
Therefore, simplified form of the given expression will be (6 - 4i).
2). Given expression → (6 + 5i)(9 - 2i)
Rule to solve the expression → i² = -1
(6 + 5i)(9 - 2i) = 6(9 - 2i) + 5i(9 - 2i)
= 54 - 12i + 45i - 10i²
= 54 - 12i + 45i + 10 [Since, i² = -1]
= (54 + 10) + (45i - 12i)
= 64 + 33i
Therefore, simplified form of the given expression will be (64 + 33i).
3). Given expression → [tex]\frac{2}{3-9i}[/tex]
Multiply numerator and denominator with the conjugate of (3 - 9i) to convert the expression into (a + bi).
[tex]\frac{2}{3-9i}= \frac{2(3+9i)}{(3-9i)(3+9i)}[/tex]
[tex]=\frac{2(3+9i)}{3^2-(9i)^2}[/tex]
[tex]=\frac{6+18i}{9-81(-1)}[/tex]
[tex]=\frac{6+18i}{9+81}[/tex]
[tex]=\frac{6+18i}{90}[/tex]
[tex]=\frac{6(1+3i)}{90}[/tex]
[tex]=\frac{1}{15}+\frac{1}{5}i[/tex]
Therefore, simplified form of the given expression will be [tex]\frac{1}{15}+\frac{1}{5}i[/tex]
4). Given expression → [tex]\frac{(3-5i)}{(7-2i)}[/tex]
Multiply numerator and denominator with the conjugate of the denominator.
[tex]\frac{(3-5i)}{(7-2i)}=\frac{(3-5i)(7+2i)}{(7-2i)(7+2i)}[/tex]
[tex]=\frac{3(7+2i)-5i(7+2i)}{7^2-(2i)^2}[/tex]
[tex]=\frac{21+4i-35i-10i^2}{49-4(-1)}[/tex]
[tex]=\frac{21-31i+10}{53}[/tex]
[tex]=\frac{31-31i}{53}[/tex]
[tex]=\frac{31}{53}-\frac{31}{53}i[/tex]
Therefore, simplified form of the given expression will be [tex]\frac{31}{53}-\frac{31}{53}i[/tex].
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The scale of a map is 1 in = 11.9 miles. How many inches will be drawn on the map to represent 30.9 miles?
Answer:
2.60 inches
Step-by-step explanation:
Map and actual distances are proportional. So the map distance m for 30.9 miles will be related to the actual distance in the same way the scale is:
m/30.9 = 1/11.9
m = 30.9/11.9 ≈ 2.5967
The length on the map is about 2.60 inches.
2.5 8.7 *** 9.6 4.6 *** 5.1 9.9 *** 10.0 6.0 10.3 *** 10.5 6.5 *** 6.6 11.6 8.5 12.0
Consider the sample of n = 20 scores. Notice that they are listed in order from 2.5 to 12.0,
but that some of the scores are obscured by ***. The mean, M, of these scores is 8.0. Suppose you are asked for the sample standard deviation of these scores. Since you don't have all of them, you cannot calculate it. Which of the following is the best estimate of the sample standard deviation?
a. 9.5
b. 0.5
c. 6.4
d. 2.7
Answer:
D. 2.7
Step-by-step explanation:
Given
[tex]Mean = 8.0[/tex]
[tex]n = 20[/tex]
[tex]Range = 2.5\ to\ 12.0[/tex]
Required
Estimate the standard deviation
Since, the given data has incomplete parameters, we can apply the range rule to estimate the standard deviation;
This is done as follows;
[tex]S.D = \frac{1}{4}(Max - Min)[/tex]
In this case:
[tex]Max = 12.0[/tex]
[tex]Min = 2.5[/tex]
So:
[tex]S.D = \frac{1}{4}(Max - Min)[/tex]
[tex]S.D = \frac{1}{4}(12.0 - 2.5)[/tex]
[tex]S.D = \frac{1}{4}(9.5)[/tex]
[tex]S.D = 2.375[/tex]
From the list of given option, the closest to 2.375 is 2.7;
Hence, the best estimate is 2.7
The correct option is D. 2.7
Given that,
The mean is 8.0.the n = 20.The range is from 2.5 to 12.0The calculation is as follows:The standard deviation should be
[tex]= \frac{1}{4} (12 - 2.5)\\\\ = \frac{1}{4} (9.5)[/tex]
= 2.375
= 2.7
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What is another way to name line l?
Answer:
Line UM.
Step-by-step explanation: you can name a line by naming at least two points on it.
Line l can be called line UM, line LM, and line UL because line l is contained in plane S.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
m is the ratio of the line,
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases.
It is given that:
A plane S contains a line l.
It is possible to give a name for line l in different ways.
The line l can be called:
Line UMLine LMLine ULLines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
Thus, line l can be called line UM, line LM, and line UL because line l is contained in plane S.
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MATH HELP! 22 points
Answer:
im sorry
Step-by-step explanation:
Give EG = 5x+7 EF =5x and FG=2x-7
Answer:
x = 7
42, 35, 7
Step-by-step explanation:
EG = 5x+7 EF = 5x FG = 2x-7Point F is on line segment of EG, therefore EG = EF + FG
5x + 7 = 5x + 2x - 72x = 14x = 7Then
EG = 5*7 + 7 = 42EF = 5*7 = 35FG = 2*7 - 7 = 7Need help with this question
Answer:
i cant see it
Step-by-step explanation:
umm
n = 3 (m+7); m
I’m so confused, please help
Answer:
[tex]m=\frac{n}{3} -7[/tex]
When looking at the Cov-19 data globally, it shows that 34 out of 50 (which is 68%) confirmed cases of infected people have recovered already. If that 68% holds true everywhere, answer the following: If a US state had about 56,000 confirmed cases, about how many people should have recovered?
Answer:
____________________
68% of 56000 is 38080.
I guess that'd be the amount of people that recovered.
____________________
Negotiating in trade means you are ________
A. coming to an agreement on an item's value
B. discussing how to get to market
C. calculating your total cost
D. exchanging a damaged good
Negotiating in trade means you are coming to an agreement on an item's value option (A) is correct.
What is negotiation?The goal of negotiation is to obtain an agreement on one or more contentious issues between two or more parties.
As we know,
On the other hand, trade negotiation is a procedure whereby countries come together to talk about the potential for trade with the aim of arriving at a trade agreement.
When you bargain in trade, you're settling on a price for a product.
Thus, negotiating in trade means you are coming to an agreement on an item's value option (A) is correct.
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A 6- foot roll of waxed paper costs $3.60. What is the price per inch?
Step-by-step explanation:
hope this helps
20 cent per inch
If km = 67 what is LM
Answer:
LM = 28 units
Step-by-step explanation:
Length of segment KL = (4x + 7) units
Length of segment LM = (5x - 12) units
Length of LM = 67 units
Since length of KM = length of KL + length of LM
By substituting the given values in the expression,
67 = (4x + 7) + (5x - 12)
67 = (4x + 5x) + (7 - 12)
67 = 9x - 5
9x = 67 + 5
x = [tex]\frac{72}{9}[/tex]
x = 8
Therefore,
LM = (5x - 12)
= (5×8) - 12
= 40 - 12
= 28
Length of segment KM is 28 units.
How is multiplying intergers
Similar to multiplying whole
numbers?
Answer:
Multiplying integers is very similar to multiplying whole numbers. ... A positive number times a positive number equals a positive number. A positive number times a negative number equals a negative number. A negative number times a negative number equals a positive number.
Answer:
integers are whole numbers
2. What fractional part of the quadrilateral is not shaded?
Answer:
plz show the pic so I can understand
gordon drives 220 miles from new york to boston in 4 hours. what is his car's average speed?
Answer:
55 mph
Because he drives to new york to boston in 4 hours and its 220 miles so 220 is the miles and you divide by the hours so 4 hours so he drove 55 mph
!!!URGENT!!! Read Image Below.
Answer:
[tex] x = \frac{6 \pm \sqrt{(-6)^2 - 4(3)(8)}}{2(3)} [/tex]
Step-by-step explanation:
Given the equation, [tex] 3x^2 - 6x + 8 = 0 [/tex], the quadratic formula for solving this equation is given as:
[tex] x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
Where,
a = 3
b = -6
c = 8
Plug in the above values into the quadratic formula.
[tex] x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(3)(8)}}{2(3)} [/tex]
[tex] x = \frac{6 \pm \sqrt{(-6)^2 - 4(3)(8)}}{2(3)} [/tex]
Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknownA) 1116B) 2115C) 1939D) 2223
A 24-ft chain must be cut into two pieces so that one piece is twice as long as the other. Find the length of each piece of chain.
Answer:
8ft and 16ft
Step-by-step explanation:
you guess and check till you reach the answer
1+23 5+19
2+22 6+18
3+21 7+17
4+20 8+16
What is the value of x (3x-10)° 149
Steps to solve:
(3x - 10) = 149
~Add 10 to both sides
3x = 159
~Divide 3 to both sides
x = 53
Best of Luck!
The answer is 37. Use addition multiplication and must have a fraction showing the equation
that is correct because 37/ one and 37×1
this is the correct answer
which statement correctly describes the expression
Answer:
c
Step-by-step explanation:
choice A means
[tex]11 - 2 {m}^{3} [/tex]
choice B means
[tex]2m - 11[/tex]
choice C means which is the answer
[tex] {2m}^{3} - 11[/tex]
choice D means
[tex] {(2m)}^{3} - 11[/tex]
hope it helps ❤❤❤
For any question comment me
how would you solve for 5x=13 for x
Answer:
divide by 5: x = 13/5 = 2.6
Step-by-step explanation:
Make use of the properties of the multiplicative inverse and the multiplication identity element. Multiplying both sides of the equation by the multiplicative inverse of the coefficient of x makes the result be 1x on the left side.
(1/5)(5x) = (1/5)(13)
1x = 13/5
The multiplicative identity element (1) does not change the value of what it multiplies, so this simplifies to ...
x = 13/5
_____
Effectively, we divide (both sides) by 5.
write the number 3/100 as a decimal.
Answer:
Step-by-step explanation
0.03.
Give two points with integer coordinates that have a slope of 5/7 between them.
Answer:
(2,3) and (7,10)
Step-by-step explanation:
Use the slope 5/7 to get to a new point by moving up 5 units and moving to the right 7 units.
If the coordinate point is (x, y) then the coordinate of the other point will be (x + 5, y + 7).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The slope is the ratio of the rise or fall and run.
The slope is 5/7. The rise is 5 and the run is 7.
If the coordinate point is (x, y) then the coordinate of the other point will be (x + 5, y + 7).
More about the coordinate geometry link is given below.
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which statement most accurately describes what can happen to jobs in a bad economy
Ansewern
I think you forgot the stament and please add it so i can helpyou out with it.
Step-by-step explanation:
rewrite 4x4x4x4x4 using a exponent can someone please help me
Answer:
4 to the 5th power
Step-by-step explanation:
since 4 is being multiplied by itself 5 times, then 5 becomes the exponent :)
The exponential form of the expression is [tex]4^5[/tex].
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
4 x 4 x 4 x 4 x 4
There are five 4's.
So,
= [tex]4^5[/tex]
Thus,
The exponential form is [tex]4^5[/tex].
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