Answer:
a. _ √20 , about 4.472136
b - (-3, 8)
c- Slope of 2
Step-by-step explanation:
Calculator
Answer:
a. [tex]AB=2\sqrt{5}[/tex]
b. [tex](-3,8)[/tex]
c. [tex]2[/tex]
Step-by-step explanation:
You have the points:
A(-2,10)
where i will call: [tex]x_{1}=-2[/tex] and [tex]y_{1}=10[/tex]
B(-4,6)
where i will call: [tex]x_{2}=-4[/tex] and [tex]y_{2}=6[/tex]
for our calculations we are going to need the distance in x between the points ([tex]\Delta x[/tex] )and the distance in y between the points ([tex]\Delta y[/tex]):
[tex]\Delta x =|x_{2}-x_{1}|=|-4-(-2)|=|-4+2|=|-2|=2\\\Delta y =|y_{2}-y_{1}|=|6-10|=|-4|=4[/tex]
a. To find AB (the distance between point A and point B) you need The Pythagorean Theorem:
[tex](AB)^2=(\Delta x)^2+(\Delta y)^2\\(AB)^2=(2)^2+(4)^2\\(AB)^2=4+16\\\\AB=\sqrt{20}\\ AB=2\sqrt{5}[/tex]
b. to find the coordinates of the midpoint we average the x-coordinates and the y coordinates
[tex]x_{mid}=\frac{x_{1}+x_{2}}{2} =\frac{-2-4}{2}=\frac{-6}{2} =-3\\y_{mid}=\frac{y_{1}+y_{2}}{2} =\frac{10+6}{2}=\frac{16}{2} =8\\[/tex]
so the midpoint [tex](x_{mid},y_{mid})[/tex] is at: [tex](-3,8)[/tex]
c. For the slope we use the slope formula:
[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-10}{-4-(-2)}=\frac{-4}{-2}=2[/tex]
The slope is equal to 2.
i don't understand the problem
Check the picture below.
the point (3,0) lies on the graph of P(x)=x^3-7x^2+15x-9. True or False
Answer:
True
Step-by-step explanation:
We can plug in and see.
If (3,0) is on the graph of P, then P(3) will evaluate to 0.
Let's try it:
P(3)=(3)^3-7(3)^2+15(3)-9
P(3)=27-7(9)+45-9
P(3)=27-63+45-9
P(3)=-36+45-9
P(3)=9-9
P(3)=0
Since P(3)=0, then (3,0) is an ordered pair of P.
Yes it is true that the point (3,0) lies on the graph of
P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex].
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given equation
P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex]
If (3,0) is on the graph of P, then P(3) will evaluate to 0.
Substitute x = 3 in the given equation
P(3) = [tex](3)^3-7(3)^2+15(3)-9[/tex]
P(3) = [tex]27-7(9)+45-9[/tex]
P(3) = [tex]27-63+45-9[/tex]
P(3) = 9-9
P(3) = 0
Since P(3)=0, then (3,0) is an ordered pair of P.
Yes it is true that the point (3,0) lies on the graph of
P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex].
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the volume of a cone is 36 pie in. cubed. what is the volume of a cylinder with the same base and height as the cone
Answer:
12 pi in³
Step-by-step explanation:
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What is the diameter of the circle whose center is at (6, 0) and that passes through the point (2, -3)?
A. (x+16)2+(y+30)2=1156
B. (x+16)2+(y+30)2=34
C. (x−16)2+(y−30)2=34
D. (x−16)2+(y−30)2=1156
Answer:
The diameter is 10 units.
The equation of the circle is [tex](x-6)^2+y^2=25[/tex].
Step-by-step explanation:
You ask for the diameter but the choices give you the equation of the circle?
I will do both.
So they actually tell us the radius is from (6,0) to (2,-3).
So the radius is whatever that length is. We can find the length by using the distance formula.
[tex]d=\sqrt{(6-2)^2+(0-(-3))^2}[/tex]
[tex]d=\sqrt{(4)^2+(3)^2}[/tex]
[tex]d=\sqrt{16+9}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]d=5[/tex]
So the radius is 5.
The diameter is twice the radius so the diameter is 2(5)=10.
Now the equation of our circle which doesn't match any of the choices is
[tex](x-6)^2+(y-0)^2=5^2[/tex].
You are probably wondering how I got that. I used the center-radius form for a circle which is [tex](x-h)^2+(y-k)^2=r^2[/tex].
The center is (h,k) and the radius is r.
We had the center for our circle was (6,0) and the radius was 5.
I'm going to simplifying our equation just a bit:
[tex](x-6)^2+y^2=25[/tex].
All I did was y-0 which is y and 5^2 which is 5(5) which equals 25.
Give the equation for a circle with the given center and radius.
Center at (4, 1), radius = 6
Answer:
(x-4)^2 + (y-1)^2 = 6^2
or
(x-4)^2 + (y-1)^2 = 36
Step-by-step explanation:
The equation for a circle is given by
(x-h)^2 + (y-k)^2 = r^2
where (h,k) is the center and r is the radius
(x-4)^2 + (y-1)^2 = 6^2
or
(x-4)^2 + (y-1)^2 = 36
Answer:
(x - 4)^2 + (y - 1)^2 = 6^2
Step-by-step explanation:
Adapt the standard equation of a circle with center at (h, k) and radius r:
(x-h)^2 + (y-k)^2 = r^2
Here we have:
(x - 4)^2 + (y - 1)^2 = 6^2
La suma de las edades de unos gemelos y unos trillizos es 150 años si se intercambian las edades la nueva suma es 120 años ¿ cual es la edad de los trillizos?
Answer:
The age of triplets is 42 years old
Step-by-step explanation:
The question in English is
The sum of the ages of twins and triplets is 150 years if the ages are exchanged the new sum is 120 years. What is the age of triplets?
Let
x -----> twins age
y ----> triplets age
we know that
2x+3y=150 ------> equation A
2y+3x=120 -----> equation B
Solve the system by graphing
The intersection point both graphs is the solution of the system
The solution is the point (12,42)
see the attached figure
therefore
The age of triplets is 42 years old
Expected Value (50 points)
Game: Roll two dice. Win a prize based on the sum of the dice.
Cost of playing the game: $1
Prizes:
Win $10 if your sum is odd.
Win $5 if you roll a sum of 4 or 8.
Win $50 if you roll a sum of 2 or 12.
Answer both question. Will give brainly.
Explain HOW to find the expected value of playing this game. What is the expected value of playing this game? Show your work. (30 points)
Interpret the meaning of the expected value in the context of this game. Why should someone play or not play this game. Answer in complete sentences. (20 points)
Let [tex]W[/tex] be the random variable representing the winnings you get for playing the game. Then
[tex]W=\begin{cases}9&\text{if the sum is odd}\\4&\text{if the sum is 4 or 8}\\49&\text{if the sum is 2 or 12}\\-1&\text{otherwise}\end{cases}[/tex]
First thing to do is determine the probability of each of the above events. You roll two dice, which offers 6 * 6 = 36 possible outcomes. You find the probability of the above events by dividing the number of ways those events can occur by 36.
The sum is odd if one die is even and the other is odd. This can happen 2 * 3 * 3 = 18 ways. (3 ways to roll even with the first die, 3 ways to roll odd for the die, then multiply by 2 to count odd/even rolls)The sum is 4 if you roll (1, 3), (2, 2), or (3, 1), and the sum is 8 if you roll (2, 6), (3, 5), (4, 4), (5, 3), or (6, 2). 8 ways.The sum is 2 if you roll (1, 1), and the sum is 12 if you roll (6, 6). 2 ways.There are 36 total possible rolls, from which you subtract the 18 that yield a sum that is odd and the other 10 listed above, leaving 8 ways to win nothing.So the probability mass function for this game is
[tex]P(W=w)=\begin{cases}\frac12&\text{for }w=9\\\frac29&\text{for }w=4\text{ or }w=-1\\\frac1{18}&\text{for }w=49\\0&\text{otherwise}\end{cases}[/tex]
The expected value of playing the game is then
[tex]E[W]=\displaystyle\sum_ww\,P(W=w)=\frac{71}9[/tex]
or about $7.89.
The expected value is positive, so a player can expect to earn money in the long run, and so should play the game.
The phosphate groups that are the polar of the phospholipid because they are A.charged B. Neutral C. Hydrophilic D. hydrophobic
Answer:
The phosphate groups that are the polar of the phospholipid because they are charged - A.
The phosphate groups that are the polar of the phospholipid because they are A. charged
What is phospholipid?It is group of polar lipids that consist of two fatty acids , a glycerol unit and a phosphate group .
A phosphate group has a negatively charged oxygen and a positively charged nitrogen to make this group ionic. A single phospholipid molecule has a phosphate group on one end and two chains of fatty acids . The phosphate group is negatively charged making the head polar and hydrophilic .
correct answer A) charged
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Find the center and radius of the circle (x+3)^2+(y-1)^2=81
The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2
h and k is the center point of the circle and r is the radius.
In the given equation (x+3)^2 + (y-1)^2 = 81
h = -3
k = 1
r^2 = 81
Take the square root of both sides:
r = 9
The center is (-3,1) and the radius is 9
Please help me.. What is the length of side x?
3.25
12
14.5
16
Answer:
x = 16
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{RS}{MN}[/tex] = [tex]\frac{RT}{MO}[/tex], that is
[tex]\frac{8}{x}[/tex] = [tex]\frac{6.5}{13}[/tex] ( cross- multiply )
6.5x = 104 ( divide both sides by 6.5 )
x = 16
Which of the sets of ordered pairs represents a function?
A = {(1, -2). (3.-5), (5,2), (7,5)}
B = {(4,2), (4, -2), (9,3), (9, -3)}
Answer:
The correct answer is A. Each x-value corresponds to exactly one y-value.
4 times the sun q and p
Typo is probably in "sun" being really "sum".
Just write an equation.
[tex]4(q+p)=4q+4p[/tex]
Hope this helps.
r3t40
1/8 x3-1/27y3 please help ...factor ths expression completely, then place the factors in the proper location on the grid
Answer:
factored form is: [tex](\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{1}{8}x^3 - \frac{1}{27}y^3[/tex]
The expression can be written as:
[tex](\frac{1}{2}x)^3-(\frac{1}{3}y)^3[/tex]
We know, a^3-b^3 = (a-b)(a^2+ab+b^2)
a= x/2 and b = y/3
Putting values in the formula given:
[tex](\frac{x}{2}-\frac{y}{3})((\frac{x}{2})^2+(\frac{x}{2})(\frac{y}{3})+(\frac{y}{3})^2)\\(\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]
So, factored form is: [tex](\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]
Find x to the nearest tenth.
Please answer
Using the Pythagorean theorem:
x = √(11.7^2 - 8.6^2)
x = √(136.89 - 73.96)
x = √62.93
x = 7.9
The answer is D.
The Garcia family and the Lee family each used their sprinklers last summer. The Garcia family's sprinkler was used for 40 hours. The Lee family's sprinkler was used for 20 hours. There was a combined total output of 2000L of water. What was the water output rate for each sprinkler if the sum of the two rates was 60L per hour?
Answer:
Lee= 20 L per hour.
Garcia = 40L per hour
Step-by-step explanation:
This formula is:
40x + 20y = 2000L
with if being known that x + y = 60.
In this x is the rate for Garcia and y is the rate for Lee.
You can also say that x = 60 - y, which you can fill in.
40 * (60-y) + 20y = 2000
2400 - 40y + 20y = 2000
-20y = -400
y = 20 L per hour.
So x = 60 - 20 = 40L per hour
what is an inequality? where would u use them in the real world
An inequality is comparing the relation of two equations that are not equal.
Depending on a persons cell phone plan, if they can only talk for so many minutes per month or send so many texts per month, this is an inequality written as number of minutes/ texts per month needs to be less than or equal to the allowable amount.
What is the vertex of the graph of y = 5(x + 4)2 + 3? (1 point)
Answer:
[-4, 3]
Step-by-step explanation:
That -h gives you the OPPOSITE terms of what they really are, and k gives you the EXACT terms of what they really are. So, your vertex is [-4, 3].
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Samuel has 5 bags of almonds. A full bag weighs 3 pounds. How many pounds of almonds does Samuel have? (Multiply)
A.15 Pounds
B.12 pounds
C.8 pounds
Answer:
15 pounds
Step-by-step explanation:
5 bags @ 3 pounds
5 x 3 = 15 lbs.
Samuel has 5 bags of almonds, each weighing 3 pounds. By multiplying the number of bags by the weight of each bag (5 * 3), we find that Samuel has a total of 15 pounds of almonds.
The total weight of Samuel's 5 bags of almonds is:
Multiply the weight of a full bag (3 pounds) by the number of bags (5): 3 pounds/bag x 5 bags = 15 pounds
Therefore, Samuel has 15 pounds of almonds.
What is the slope of the line in the graph?
To find the slope of a line you must do [tex]\frac{rise}{run}[/tex]
Look at the image to find the rise (in pink) and run (in green) on the graph:
In this case the rise is 3 and the run is -4 (the reason the four is negative is because it "runs" to the left, which is the negative direction of the coordinate plane) so the slope of this line is:
[tex]\frac{-3}{4}[/tex]
Hope this helped!
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Please help!!!
Estimate the value of \sqrt(14)+\sqrt(3) to the nearest hundredth.
A. 3.79
B. 5.47
C. 2.01
D. 4.12
Answer:
B.
Step-by-step explanation:
Let's figure out what two consecutive integers is 14 between.
We also need to do this for 3.
14 is between 9 and 16 which means [tex]\sqrt{14}[/tex] is between [tex]\sqrt{9}[/tex] and [tex]\sqrt{16}[/tex].
3 is between 1 and 4 which means [tex]\sqrt{3}[/tex] is between [tex]\sqrt{1}[/tex] and [tex]\sqrt{4}[/tex].
So 14 is closer to 16 which means [tex]\sqrt{14}[/tex] is closer to 4. Let's say [tex]\sqrt{14}\approx 3.7[/tex]
So 3 is closer to 4 which means [tex]\sqrt{3}[/tex] is closer to 2. Let's say [tex]\sqrt{3}\approx 1.8[/tex].
So now we do 3.7+1.8=5.5.
The answer that is closet to this is 5.47.
Now if we put [tex]\sqrt{14}+\sqrt{3}[/tex] in our calculator we get:
3.74+1.73=5.47
What is the factored form of 3x2 + 5x - 12?
Answer:
[x + 3][3x - 4]
Step-by-step explanation:
First off, we need to find two numbers that when differed to 5, they also multiply to -36 [3 × -12]. Those numbers are -4 and 9. Next, we find the Greatest Common Factor [GCF], which means the LEAST DEGREE TERM possible:
[3x² - 4x] + [9x - 12]
x[3x - 4] 3[3x - 4]
As you can see, whenever we have a leading coefficient greater than 1, we need to break up our B into our two numbers we found [in BOLD], and have to attach an x to them because it replaced Bx, according to the Quadratic Equation of y = Ax² + Bx + C. So, after we completed our factoring, you see two identical factors, which we use ONCE. The other factor comes from the terms outside the duplicates. So, you get the above answer after you completed the steps: [x + 3][3x - 4].
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37. Two years ago, Bob flew 6 x 105 miles in an airplane. This was 15 times as many
miles as he flew last year.
How many miles did Bob fly last year?
A. 4* 104 miles
B. 4 x 106 miles
C. 9 x 104 miles
D. 9 * 106 miles
Answer:
A. 4·10⁴
Step-by-step explanation:
The problem statement tells you ...
6×10⁵ miles = 15 × (last year's mileage)
Dividing by 15 gives ...
(60×10⁴ miles)/15 = (last year's mileage) = 4×10⁴ miles
_____
Further explanation
An exponent is an indication of repeated multiplication.
10⁵ = 10·10·10·10·10 = 100,000
We can use the associative property of multiplication to rewrite the number of miles:
6×10⁵ = 6·(10·10·10·10·10) = 600,000 = (6·10)·(10·10·10·10) = 60×10⁴
y varies inversely with x. When y = 3.6, x = 1.2. What is the value of k, the constant of inverse variation? Round to the nearest hundredth, if necessary.
Answer:
The constant, k, is 4.32.
Step-by-step explanation:
y varies inversely with x means y=k/x.
y varies directly with x means y=kx.
Anyways we have the first relation: y=k/x where k is a constant.
We divided by x because it said inversely.
We are given (x,y)=(1.2,3.6) is on this curve.
This gives us enough information to find the constant, k.
[tex]y=\frac{k}{x}[/tex] with [tex](x,y)=(1.2,3.6)[/tex].
[tex]3.6=\frac{k}{1.2}[/tex]
Multiply both sides by 1.2:
[tex]3.6(1.2)=k[/tex]
[tex]4.32=k[/tex]
The constant, k, is 4.32.
In a triangle, the measure of the second angle is twice the measure of the first angle. the third angel is equal to the sum of the other angels
Answer:
So the angles have measurements 30,60, and 90 degrees.
Step-by-step explanation:
We have a triangle which means the interior angles of that triangle has sum 180 degrees.
Let's call the angle measurements: A, B, and C.
A+B+C=180
B=2A (The second angle is twice the first.)
C=A+B (The third angle is the sum of the other 2.)
If C=A+B, then C=A+2A (since B=2A).
So we have this system:
A+B+C=180
B=2A
C=3A (since C=A+2A=3a).
Now I'm going to use the first equation A+B+C=180 and plug in the other equations we have below it:
A+B+C=180 with B=2A and C=3A.
A+2A+3A=180
6A=180
Divide both sides by 6:
A=180/6
A=30
If B=2A and A=30, then B=2(30)=60.
If C=3A and A=30, then C=3(30)=90.
So the angles have measurements 30,60, and 90 degrees.
What are the sides of PQR?
Answer:
Hi there!
The answer to this question is: B
Answer choice B is correct because the dash above the two letter represents a line segment or side of a triangle
-------------------------------------------------------------------------------------------
Answer choice A: incorrect
Explanation: The little carrot in front of each letter shows that it is an angle not a side
Answer C: incorrect
Explanation: It tells you points of the triangle
Answer:
B.Step-by-step explanation:
[tex]A.\ \angle P,\ \angle Q,\ and\ \angle R-\bold{angles}\\\\B.\ \overline{PQ},\ \overline{QR},\ and\ \overline{PR}-\bold{sides}\\\\C.\ P,\ Q,\ and\ R-\bold{vertexs}[/tex]
The function F(c) = 9/5 c + 32 allows you to
Answer:
convert from Celsius to Fahrenheit
Step-by-step explanation:
i work with thermometers i know
For this case we have that by definition, to convert degrees Celsius to Fahrenheit we use the following formula:
[tex]F = \frac {9} {5} C + 32[/tex]
Where:
C: Represents the degrees Celsius
So, we can write a function:
[tex]F (C) = \frac {9} {5} C + 32[/tex]
Answer:
The function allows to convert degrees Celsius to Fahrenheit
find an explicit formula for the arithmetic sequence -45,-30,-15,0...
Answer:
15(n-1)-45
Step-by-step explanation:
Increases by 15, so sequence is arithmetic, and goes to positive.
1st term is -45
so 15(n-1) gives us first term.
Reply for any questions I got you
[tex]\bf -45~~,~~\stackrel{-45+15}{-30}~~,~~\stackrel{-30+15}{-15}~~,~~\stackrel{-15+15}{0}~\hspace{7em}\stackrel{\textit{common difference}}{d=15} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=-45\\ d=15 \end{cases} \\\\\\ a_n=-45+(n-1)15\implies a_n=-45+15n-15\implies a_n=15n-60[/tex]
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Let Bikes = B and cars = c
a bike has 2 wheels and a car has 4 wheels.
Equation 1: add bikes and cars to get total students:
b + c = 80
Equation 2: multiply the number of wheels by each type and add to equal the total wheels.
2b +4c = 270
Rewrite the first equation as b = 80- c
Now substitute that for b in the second equation:
2(80-c) + 4c = 270
Simplify:
160 - 2c + 4c = 270
160 +2c = 270
Subtract 160 from both sides:
2c = 110
Divide both sides by 2
c = 110/2
c = 55
Replace c with 55 in the first equation and solve for b:
b + 55 = 80
b = 80-55
b = 25
b = 25, c = 55
If $125 is invested at an interest rate of 18% per year and is compounded continuously, how much will the investment be worth in 2 years? Use the continuous compound interest formula A=Pe^rt
Answer:
$179.17
Step-by-step explanation:
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Answer: The investment be worth $ 174.05 in 2 years .
Step-by-step explanation:
Given : The principal amount invested : A= $125
Interest rate : r = 18% =0.18 [ Percent convert into decimal if we divide it by 100]
Time : t = 2 years
The formula to find the accumulated amount if compounded continuously :-
[tex]A=Pe^rt\\\\=(125)(1+0.18)^{2}\\\\= 125 (1.18)^2\\\\ = 125 (1.3924)\\\\=174.05[/tex]
Hence, the investment be worth $ 174.05 in 2 years .
Given the triangle below, what is the length of the third side, rounded to the nearest whole number?
Answer:
Hi there!
The answer to this question is: C. 14
Step-by-step explanation:
Using the formula for sine I solved the missing side.
sin(62)= 12/x
then you need to solve for x
x= 12/ sin(62)
and you get 13.59 so round up to get 14
The length of the third side of a triangle is 16.
How to find the length of the third side of a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
Use the Law of Cosine to find the third side of the triangle.
Law of Cosine is given by
[tex]$$a^{2}=b^{2}+c^{2}-2 b c$$[/tex]
Substituting the known values, we get
[tex]$$a^{2}=12^{2}+19^{2}-2 \cdot 12 \cdot 19 \cos 56$$[/tex]
By simplifying, we get
[tex]&a^{2}=505-456 \cos 56 \\[/tex]
[tex]&a^{2}=250.008 \\[/tex]
[tex]&a=15.81[/tex]
When rounded to the nearest whole number, the length of the third side is 16.
The length of the third side of a triangle is 16.
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