Find (a) PQ to the nearest tenth and (b) the coordinates of the midpoint of PQ.
P(2.6), Q(-6,1)
(a) PQ=(Round to the nearest tenth as needed.)
Answers
Answer/Step-by-step explanation:
Given:
P(2, 6)
Q(-6, 1)
Required:
a. PQ
b. Coordinate of the midpoint of PQ
SOLUTION:
a. [tex] PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] P(2, 6) = (x_1, y_1) [/tex]
[tex] Q(-6, 1) = (x_2, y_2) [/tex]
[tex] PQ = \sqrt{(-6 - 2)^2 + (1 - 6)^2} [/tex]
[tex] PQ = \sqrt{(-8)^2 + (-5)^2} = \sqrt{64 + 25} [/tex]
[tex] PQ = \sqrt{89} = 3.1 [/tex] (to nearest tenth)
b. Coordinate of the midpoint of PQ
[tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex]
Let [tex] P(2, 6) = (x_1, y_1) [/tex]
[tex] Q(-6, 1) = (x_2, y_2) [/tex]
Thus:
[tex] M(\frac{2 +(-6)}{2}, \frac{6 + 1}{2}) [/tex]
[tex] M(\frac{-4}{2}, \frac{7}{2}) [/tex]
[tex] M(-2, \frac{7}{2}) [/tex]
The coordinates of the midpoint of PQ are (-2,3.5) and this can be determined by using the midpoint formula.
Given :
Coordinates -- P(2,6) and Q(-6,1)
The following steps can be used in order to determine the coordinates of the midpoint of PQ:
Step 1 - According, to the given data, the coordinates of point P(2,6) and Q(-6,1).
Step 2 - The formula of midpoint can be used in order to determine the midpoint of PQ.
Step 3 - The midpoint formula is given below:
[tex]\rm x = \dfrac{x_1+x_2}{2}[/tex]
[tex]\rm y = \dfrac{y_1+y_2}{2}[/tex]
Step 4 - Substitute the values of the coordinates in the above formula.
[tex]\rm x = \dfrac{2-6}{2} = -2[/tex]
[tex]\rm y = \dfrac{6+1}{2}=3.5[/tex]
So, the coordinates of the midpoint of PQ are (-2,3.5).
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Related Questions
Simplify the expression 5^3•5^-5
Answers
Answer:
5^8Step-by-step explanation:
[tex]5^3\times\:5^5\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times\:a^c=a^{b+c}\\5^3\times\:5^5=5^{3+5}\\\\=5^8=390625[/tex]
The solution of the expression will be 5⁻².
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 5³ x 5⁻⁵. The expression will be solved as below,
E = 5³ x 5⁻⁵
E = 5³⁻⁵
E = 5⁻²
Hence, the expression will be E = 5⁻².
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5) Determine o conjunto solução da equação: x² + 12x - 189 = 01 ponto{ - 21, 9}{ 21, -9 }{ 21 }{ - 9 }
Answers
Answer:
x = 9 or x = -21
Step-by-step explanation:
Solve for x over the real numbers:
x^2 + 12 x - 189 = 0
The left hand side factors into a product with two terms:
(x - 9) (x + 21) = 0
Split into two equations:
x - 9 = 0 or x + 21 = 0
Add 9 to both sides:
x = 9 or x + 21 = 0
Subtract 21 from both sides:
Answer: x = 9 or x = -21
The graph below represents which of the following functions?
Answers
Answer:I believe the answer is C
Step-by-step explanation:
The y-intercept is 2
Rosalia passed out fliers that say, “Vote for Rosalia!” She gave out 85 fliers on Monday, 66 fliers on Tuesday, and 99 fliers on Wednesday. What fraction of the fliers did she give out on Wednesday? Use a diagonal fraction bar in your answer. Explain how you found the answer
Answers
Answer:
0.66
Step-by-step explanation:
Rosalia passed out fliers that say, “Vote for Rosalia!” She gave out 85 fliers on Monday, 66 fliers on Tuesday, and 99 fliers on Wednesday.
Total fliers shared= 85+66+99
Total fliers shared= 250 fliers
Fraction of the fliers she gave out on Wednesday= fliers on Wednesday/total fliers
=99/150
= 33/50
= 3.3/5
= 0.66
Answer:
0.66
Step-by-step explanation:
The grade received on a certain teacher's 100-point test varies in direct proportion to the amount of time a student spends preparing for the test. If a student receives 72 points on a test for which she spent 3 hours preparing, what score would she receive on the next test if she spent 4 hours preparing?
Answers
Answer:
The teacher woll award the student 96 points for studying for 4 hours
Step-by-step explanation:
The student receives 72 point for preparing a test as long as 3 hours.
If she prepares for another test for 4 hours.
3 hours= 72 points
4 hours=( 72*4)/3
4 hours=72/3 *4
4 hours = 24*4
4 hours= 96 points
The teacher woll award the student 96 points for studying for 4 hours
Sam had 225 dollars to spend on 8 books. After buying them he had 17 dollars. How much did each book cost?
Answers
Answer:
Each book costs 26 dollars
Step-by-step explanation:
Let b be the price of each book
8*b +17 = 225
Subtract 17 from each side
8b+17-17 = 225-17
8b =208
Divide by 8
8b/8 = 208/8
b =26
Each book costs 26 dollars
Find a fundamental matrix solution for the system x 0 1 7x1 + 4x2 + 12x3, x 0 2 x1 + 2x2 + x3, x 0 3 −3x1 − 2x2 − 5x3. Then find the solution that satisfies x®(0) h 0 1 −2 i .
Answers
Here is the correct format for the question.
[tex]x'_1 = 7x_1 +4x_2+ 12x_3 , \ \ x'_2 = x_1 + 2x_2 + x_3 , \ \ x'_3 = -3x_1 -2x_2 -5x_3[/tex] . Then find the solution that satisfies [tex]x \limits ^{\to} = \left[\begin{array}{c}0\\1\\-2\end{array}\right][/tex]
Answer:
[tex]\mathbf{c_1 = -3, c_2 = 2, c_3 = 2}[/tex]
Step-by-step explanation:
From the figures given above:
the matrix can be computed as,
[tex]\left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right] x \limits ^{\to} = \left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right] = x \limits ^{\to} = \left[\begin{array}{c}x_1'\\x_2'\\x_3'\end{array}\right][/tex]
The first thing we need to carry out is to determine the eigenvalues of A,
where:
[tex]A = \left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right][/tex]
[tex]|A-rI|=0[/tex]
[tex]\begin {vmatrix} 7-r&4&12\\1&2-r&1\\-3&-2&-5-r \end {vmatrix}=0[/tex]
the eigenvalues are r = 0, 1, 3
However, the eigenvector correlated to each eigenvalue can be calculated as follows.
suppose r = 0
(A - rI) x = 0
[tex]\left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right] \left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right] = \left[\begin{array}{c}0\\0\\0\end{array}\right][/tex]
now the eigenvector is [tex]\left[\begin{array}{c}-4\\1\\2\end{array}\right][/tex]
However, for eigenvalue = 1, we have : [tex]\left[\begin{array}{c}-4\\1\\2\end{array}\right][/tex]
for eigenvalue = 3, we have:[tex]\left[\begin{array}{c}-2\\-1\\1\end{array}\right][/tex]
The solution now can be computed as :
[tex]x(t)= c_1 \left[\begin{array}{c}-4\\1\\2\end{array}\right] + c_2e^t \left[\begin{array}{c}-4\\3\\1\end{array}\right]+ c_3e^{3t} \left[\begin{array}{c}-2\\-1\\1\end{array}\right][/tex]
Similarly, the fundamental matrix solution is:
[tex]\left[\begin{array}{ccc}-4&-4e^t&-2e^{3t}\\1&3e^t&-e^{3t}\\2&e^t&e^{3t}\end{array}\right][/tex]
[tex]-4c_1 -4c_2-2c_3 =0 \\ \\ c_1 + 3c_2 -c_3 = 1\\ \\ 2c_1+c_2 +c_3 = -2[/tex]
Solving the above equation, we get:
[tex]\mathbf{c_1 = -3, c_2 = 2, c_3 = 2}[/tex]
What is the factored from of the polynomial. x^2 + 9x + 20
Answers
Answer:
Step-by-step explanation:
Hello, the sum of the roots is -9=-4-5 and the product is 20=(-4)*(-5) so we can write
[tex]x^2+9x+20=(x+4)(x+5)[/tex]
thanks
Answer:
( x + 4 ) ( x + 5 )
Step-by-step explanation:
For this polynomial, we will factor the coefficient of the x^2 term and the constant.
The coefficient of x^2 is 1, which just factors to 1.
The constant 20 factors into 2 * 2 * 5.
Note, that our middle term coefficient is 9 and thus we want a pairing of 1 with either 2, 4, or 5 to make 9. 4 + 5 = 9, so we will choose that.
Using the standard binomials, we will factor the polynomial:
( x^2 + 9x + 20 )
= ( x + 4 ) ( x + 5)
We can check by performing foil:
= ( x + 4 ) ( x + 5 )
= ( x * x + x * 5) + ( 4 * x + 4 * 5)
= ( x^2 + 5x ) + ( 4x + 20 )
= ( x^2 + 9x + 20 )
Thus, we have successfully factored our polynomial.
Cheers.
To which set of numbers does -15 belong to? Select all apply.
Answers
Answer:
Integer
Step-by-step explanation:
On every number line we have both negative and positive numbers. So negative 15 is an integer
i will GIVE THE BRAINIEST
Without simplifying, select all the expressions that represent a rational number.
Answers
Answer:
The first and the fourth one.
The ones that could be rationalized are automatically the ones you should pick.
Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) 5, 1, 4
Answers
Answer:
The direction cosines are:
[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex] and [tex]\frac{4}{\sqrt{42} }[/tex] with respect to the x, y and z axes respectively.
The direction angles are:
40°, 81° and 52° with respect to the x, y and z axes respectively.
Step-by-step explanation:
For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.
If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.
Where;
cos α = [tex]\frac{a . i}{|a| . |i|}[/tex] ---------------------(i)
cos β = [tex]\frac{a.j}{|a||j|}[/tex] ---------------------(ii)
cos γ = [tex]\frac{a.k}{|a|.|k|}[/tex] ----------------------(iii)
And from these we can get the direction angles as follows;
α = cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )
β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )
γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )
Now to the question:
Let the given vector be
a = 5i + j + 4k
a . i = (5i + j + 4k) . (i)
a . i = 5 [a.i is just the x component of the vector]
a . j = 1 [the y component of the vector]
a . k = 4 [the z component of the vector]
Also
|a|. |i| = |a|. |j| = |a|. |k| = |a| [since |i| = |j| = |k| = 1]
|a| = [tex]\sqrt{5^2 + 1^2 + 4^2}[/tex]
|a| = [tex]\sqrt{25 + 1 + 16}[/tex]
|a| = [tex]\sqrt{42}[/tex]
Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e
cos α = [tex]\frac{5}{\sqrt{42} }[/tex]
cos β = [tex]\frac{1}{\sqrt{42} }[/tex]
cos γ = [tex]\frac{4}{\sqrt{42} }[/tex]
From the value, now find the direction angles as follows;
α = cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )
α = cos⁻¹ ( [tex]\frac{5}{\sqrt{42} }[/tex] )
α = cos⁻¹ ([tex]\frac{5}{6.481}[/tex] )
α = cos⁻¹ (0.7715)
α = 39.51
α = 40°
β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )
β = cos⁻¹ ( [tex]\frac{1}{\sqrt{42} }[/tex] )
β = cos⁻¹ ( [tex]\frac{1}{6.481 }[/tex] )
β = cos⁻¹ ( 0.1543 )
β = 81.12
β = 81°
γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )
γ = cos⁻¹ ([tex]\frac{4}{\sqrt{42} }[/tex])
γ = cos⁻¹ ([tex]\frac{4}{6.481}[/tex])
γ = cos⁻¹ (0.6172)
γ = 51.89
γ = 52°
Conclusion:
The direction cosines are:
[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex] and [tex]\frac{4}{\sqrt{42} }[/tex] with respect to the x, y and z axes respectively.
The direction angles are:
40°, 81° and 52° with respect to the x, y and z axes respectively.
angel buys a 12-pack of granola bars for $9. What is the unit price?
Answers
Answer:
If 12 granola bars are nine dollars,
(12/9)
We divide the amount by the price!
Twelve divided by nine is about $1.33.
The image is rounded to the nearest thousandth
50pts.
A problem states: "There are 2 more horses than cows in a field. There are 16 animals in the field in all. How many horses are there in the field?" Let c represent the number of cows. Which equation represents the situation?
c + 2 = 16
2c−2=16
2(c+2)=16
2c + 2 = 16
Answers
Answer:
its the 3rd 1
Step-by-step explanation:
Solve for y. 7x-5y=-35
Answers
Answer:
y = 7(1 + x/5)
Step-by-step explanation:
7x - 5y = -35
-5y = -35 - 7x
5y = 35 + 7x
y = (35 + 7x) / 5
y = 7 + 7x/5
y = 7(1 + x/5)
Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $775 per week. How much did she earn last week if she sold $4,300 in electronics merchandise? Round your intermediate calculations and answer to the nearest cent.
Answers
Answer:
$1108.25
Step-by-step explanation:
Danielle's commission on $4300 in sales is ...
0.0775 × $4300 = $333.25
That, added to her base salary, gave her weekly earnings of ...
$333.25 +775 = $1108.25 . . . . Danielle's pay last week
Help me please thank you
Answers
Answer:
y = 120º
Step-by-step explanation:
180 - (33 + 87) = 60
x = 60
180 - 60 = 120
y = 120º
or y = 33 + 87, because the outer angle of one angle equals the other two inner angles.
Answer: 120°
Step-by-step explanation:
If you add up all the triangles angles, it always is 180. So, when you add 33+87, you get 120. This means that x=60 because 120+60 =180.
Then, you also know that x and y together, make a 180° also because it is a straight line. So, y is equal to 120° because 60+120 = 180°.
Hope this helps! :)
( -7v 4 - 5v ) - ( -5v 3 - 2v ) + ( -7v - 6v 4 - 4v 3 ) simplified
Answers
Answer:
-13v^4 + v^3 - 10v (if simplified)
Step-by-step explanation:
combine like terms
(-7v^4 - 5v) - (-5v^3 - 2v)+ ( - 7v - 6v^4 - 4v^3)
-7v^4 + -6v^4 = -13v^4
-5v^3 + -4v^3 = v^3 (the five becomes positive because of the negative sign infront of the parenthesis) Example: -(-5v^3) = +5v^3
-13v^4 + v^3 -5v -(-2v) -7v (now we have the -2 left alone in the parenthesis which means it becomes positive too) Example: -(-2v) = +2v
-5v +2v - 7v = -3v -7v = -10v
Answer: -13v^4 + v^3 - 10v
Solve for x.
to
118°
X°
Answers
Answer:
[tex] \boxed{ \bold{ \huge{\boxed{ \sf{62}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{x ° + 118 ° = 180 ° }[/tex]
( Sum of angle in straight line )
Move 118 to right hand side and change it's sig
⇒[tex] \sf{x ° = 180 ° - 118 °}[/tex]
Calculate
⇒[tex] \sf{x = 62 °}[/tex]
Hope I helped!
Best regards!!
Find the slope of the line that passes through each pair of points. Express as a fraction in simplest form.
(-9,-11), (6,3)
Answers
6/8 skkssbjsjdsdhdhbddbd dhhdhshshs
Answer:
14/15
Step-by-step explanation:
To find the slope
m= ( y2-y1)/(x2-x1)
= ( 3 - -11)/( 6 - -9)
= ( 3+11)/( 6+9)
= 14/15
what is the input set of a function called
Answers
Answer:
A function is a mathematical device that converts one value to another in a known way. ... The set of allowable inputs to a given function is called the domain of the function. The set of possible outputs is called the range of the function.
Step-by-step explanation:
Hopefully this was mindfull
The input set of a function is called the "Domain" of the function.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
For any function, the values which we are putting form a set of intervals called domain.
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.
Hence "The input set of a function is called the "Domain" of the function".
For more details about the range and domain of the function,
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206 MAI
ALEKS Probabilities of draws with replacement
Toples
? SAMPLE QUESTION
A fair die is rolled 6 times. What is the probability of having no 4 and no 5 among
places.
(If necessary, consult a list of formulas.)
3
Answers
Step-by-step explanation:
Two of the sides are 4 and 5. The other four sides are 1, 2, 3, and 6.
The probability of rolling a number other than 4 or 5 on any roll is 4/6, or 2/3.
The probability of rolling no 4s or 5s six times is:
P = (2/3)⁶
P ≈ 0.088
The ______ can be used to determine whether the graph a relation is a function.
Answers
Answer:
The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.
Step-by-step explanation:
Is 63 greater than 48.1 or less than
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answers
Answer:
63 is greater than 48.1 ...
63 > 48.1
Step-by-step explanation:
63 is greater than 48 remember. So you need to remove the [.1] and focus on the 63 and 48.
Hope it helps!!Please mark me as the brainliest!!!Thanks!!!!❤❣❤
:)Explanation:
63.0 > 48.1
Even though .0 < .1 but 63 > 48
So therefore, 63 > 48.1
Determine the level of measurement of the variable.Livability rankings for cities Choose the correct level of measurement.A. Ratio.B. Ordinal.C. Nominal.D. Interval.
Answers
Answer:
B. Ordinal
Step-by-step explanation:
The level of measurement used for a variable in statistical analysis determines what summary statistics and analysis are possible. In statistical analysis, we have three types of level of measurement.
Nominal , Ordinal , Interval/ Ratio
The nominal is the most basic level of measurement. It is the qualitative level of measurement such as color or number. Data in Nominal scale of measurement are stored as a word or as numerical code.
Ordinal level of measurement are variables based on ranks or hierarchy. Ordinal level of measurement posses a sequential step-wise order but the intervals between the variables are not equal. They are usually expressed in frequencies.
Therefore, the level of measurement of variable that determines the livability rankings for cities based on their ranks or hierarchy is Ordinal.
The interval/ratio level of measurement is the highest level of measurement where data are being measured and ordered in a sequential process.
here is a histogram of the yearly number of unprovoked attacks by alligators. what is the overall distributions
Answers
Answer:
Hello your question has some missing parts attached is the missing part
answer : slightly skewed to the right ( B )
Step-by-step explanation:
From the attached histogram related to the question above, it can be seen that the the right tail is longer than the left tail and this can help us draw the conclusion that the overall shape of the distribution is slightly skewed to the right
Raphael's neighborhood kid's pool is shaped like a square with an area of 120 ft2. What is the approximate side length of the pool?
Answers
Answer:
10.95 or 11 if rounded up
Step-by-step explanation:
The side length of a pool shaped like a square with an area 120ft² is
S = [tex]\sqrt{120}= 10.954[/tex]
Side of a square:Given,
Raphael's neighborhood kid's pool is shaped like a square.Area of the pool = 120 ft²Let side of the pool = S
Area of the pool = S² = 120
Hence, the side of the pool = S = [tex]\sqrt{120}= 10.954[/tex] ft
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Find an equation of a sphere if one of its diameters has endpoints (4, 1, 6) and (8, 3, 8).
Answers
Answer:
The equation of a sphere with endpoints at (4, 1, 6) and (8, 3, 8) is [tex](x-6)^{2}+(y-2)^{2}+(z-7)^{2} = 6[/tex].
Step-by-step explanation:
Given the extremes of the diameter of the sphere, its center is the midpoint, whose location is presented below:
[tex]C(x,y,z) = \left(\frac{4+8}{2},\frac{1+3}{2},\frac{6+8}{2}\right)[/tex]
[tex]C(x,y,z) = (6,2,7)[/tex]
Any sphere with a radius [tex]r[/tex] and centered at [tex](h,k,s)[/tex] is represented by the following equation:
[tex](x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}[/tex]
Let be [tex](x,y,z) = (4,1,6)[/tex] and [tex](h,k,s) = (6,2,7)[/tex], the radius of the sphere is now calculated:
[tex](4-6)^{2}+(1-2)^{2}+(6-7)^{2}=r^{2}[/tex]
[tex]r = \sqrt{6}[/tex]
The equation of a sphere with endpoints at (4, 1, 6) and (8, 3, 8) is [tex](x-6)^{2}+(y-2)^{2}+(z-7)^{2} = 6[/tex].
1. Write the ratio 2/3 to 8 as a fraction in simplest form.
Answers
Answer:
2/3 +8/3=10/3
Step-by-step explanation:
10 pts
Point K (-2,-3) is translated (x + 5, y-7). What are the coordinates K?
Answers
Answer: (3,-10)
Step-by-step explanation:
Using the translated rule that x is increase by 5 and y is decreased by 7 put it into the equation and solve for the coordinates of k.
(-2 +5 ) = 3
(-3 -7) = -10
So now the coordinates will be (3,-10)
Simplify
20/3root5 solve it
Answers
Step-by-step explanation:
hope it will help you.......