Answer:
[tex]\large\boxed{7\sqrt2}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (-3, 2) and (4, -5). Substitute:
[tex]d=\sqrt{(4-(-3))^2+(-5-2)^2}=\sqrt{7^2+(-7)^2}=\sqrt{49+49}=\sqrt{(49)(2)}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{49}\cdot\sqrt2=7\sqrt2[/tex]
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:
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.
Kerry donated 1/10 of her $500 savings to a charity. How much money did she donate?
Answer:
Kerry donated $50 to a charity.
Step-by-step explanation:
500/10=50
Answer:
$50
Step-by-step explanation:
1/10 of $500 =
= 1/10 * $500
= $500/10
= $50
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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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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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.
Find the quadratic function that fits curve below. Select the correct answer.
The answer is:
The quadratic function that fits the given picture is:
[tex]y=-3x^{2}+13x-5[/tex]
Why?We can solve the problem and find the correct function that fits the curve below by finding which function intercepts the y-axis at -5 (we can see it from the picture), also, we need to look for a function that represents a parabola opening upwards. We need to remember that when a parabola is opening upwards, its quadratic term coefficient is negative.
So, we can see that from the given functions, the only function that represents a parabola opening upwards and its y-intercept is located at y equal to -5 is the second option:
[tex]y=-3x^{2}+13x-5[/tex]
We have that :
[tex]a=-3(negative)\\b=13\\c=-5(y-intercept)[/tex]
We can see that the quadratic term (a) is negative, and the quadratic function intercepts the y-axis at y equal to -5.
Hence, the answer is:
The quadratic function that fits the given picture is:
[tex]y=-3x^{2}+13x-5[/tex]
Have a nice day!
Note: I have attached a picture for better understanding.
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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if tan θ= -3/8 which expression is equivalent to cot θ?
Answer:
-8
If cot Ф = ------
3
Step-by-step explanation:
Justine, when you're given answer choices, please share them. Thank you.
-3
If tan Ф = ------
8
then:
-8
If cot Ф = ------
3
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.
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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.
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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
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
convert y=-1.4x+9.6 to standard form
Answer:
14x-10y=-96
Step-by-step explanation:
we know that
The equation of the line in standard form is equal to
Ax+By=C
where
A is a positive integer
B and C are integers
so
we have
y=1.4x+9.6
Multiply by 10 both sides
10y=14x+96
isolate the variable x and y (Remember that A must be positive)
14x-10y=-96 -----> standard form
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
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.
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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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]
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].
I am joyous to assist you anytime.
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]
Y=8x-3/-4x-10 has a vertical asymptote with equation(enter equation of the vertical asymptote
Answer:
x=-2.5 if the function is [tex]f(x)=\frac{8x-3}{-4x-10}[/tex]
Step-by-step explanation:
[tex]y=\frac{8x-3}{-4x-10}[/tex] has discontinuities when the denominator is 0.
You will either have a hole or a vertical asymptote depending on what happens to the numerator after you find when the bottom is 0.
That is whatever you found that makes the bottom 0, if it makes the top also 0 then you will have a hole at x=the number that made the bottom 0.
If it makes the top anything other than 0, then it is a vertical asymptote at x=the number you found that made the bottom 0.
Let's do this now.
When is -4x-10 equal to 0?
We have to solve the equation:
-4x-10=0
Add 10 on both sides:
-4x=10
Divide both sides by -4:
x=10/-4
Reduce by dividing top and bottom by 2:
x=5/-2
x=-5/2
or
x=-2.5 (if you want decimal form)
Now does it make the top 0? This is the deciding factor on whether you have a hole at x=-2.5 or a vertical asymptote at x=-2.5.
Let's see.
8(-2.5)-3=-23
Since the top is not 0 at x=-2.5 then you have a vertical asymptote at x=-2.5.
If the top were 0, then you would have had a hole at x=-2.5.
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.
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
Give the equation of the line passing through the point (20,2)that is perpendicular to y=−4x.
Answer:
y-2 = 1/4(x-20) point slope form
y = 1/4x -3 slope intercept form
Step-by-step explanation:
y = -4x
The slope is -4
The slope that is perpendicular is the negative reciprocal
- (1/-4) = 1/4
The slope of our new line is 1/4
We have a point and the slope, so we can use point slope form
y-y1 = m(x-x1)
y-2 = 1/4(x-20)
If we want the line in slope intercept form, distribute
y-2 = 1/4x -5
Add 2 to each side
y-2+2 = 1/4x -5+2
y = 1/4x -3
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]
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
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.
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.
i don't understand the problem
Check the picture below.
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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