The endpoints of WX are W(2,-7) and X(5,-4). What is the length of WX?
Answers
Answer:
WX = 3√2 unitsStep-by-step explanation:
Using the formula for calculating the distance between two points to calculate the length of WX.
D = √(y₂-y₁)²+(x₂-x₁)²
Given the endpoints W(2,-7) and X(5,-4), x₁ = 2, y₁ = -7, x₂ = 5 and y₂ = -4
Substituting this values into the formula to get the length of WX will give;
WX = √(-4-(-7))²+(5-2)²
WX = √(-4+7)²+3²
WX = √3²+3²
WX = √18
WX = √2*9
WX = 3√2 units
Hence the length of WX is 3√2 units.
Answer:
3[tex]\sqrt{2}[/tex]
Hope this helps!
Step-by-step explanation:
Related Questions
[PLEASE HELPP] write an equation that represents the area Bruce covered (y) in terms of the number of tiles he used, x?
Answers
Answer:
y=(x/6)
Step-by-step explanation
divide every input by 6 to get the output
less than 0 but greater than (−5)
Answers
Answer:
-5 < x < 0
Step-by-step explanation:
Six identical coins are tossed. How many possible arrangements of the coins include three heads and three tails?
Answers
Answer:
The possible arrangement= 18 ways
Step-by-step explanation:
Six identical coin are tossed.
Coin has only a tail and a head.
In how many possible ways can the arrangement be 3 head and 3 tail.
The possible arrangement= (3! * 3!)/2
The reason for dividing by two because coin has two face.
The possible arrangement= (3! * 3!)/2
The possible arrangement=( 6*6)/2
The possible arrangement= 36/2
The possible arrangement= 18 ways
√9m^2n^2 + 2√m^2n^2 - 3mn
Answers
Answer:
I think it is
Step-by-step explanation:
Answer:
5n√2m^ - 3mn
Step-by-step explanation:
write the statement for 4p = 8
Answers
Answer:
See below
Step-by-step explanation:
The statement that can be written for 4p = 8 is:
=> Four times a certain number equals eight.
A parallelogram has coordinates A(1, 1), B(5, 4), C(7, 1), and D(3, -2). What are the coordinates of parallelogram A′B′C′D′ after a 180° rotation about the origin and a translation 5 units to the right and 1 unit down? I need Help
Answers
Hey there! I'm happy to help!
First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).
Let's convert this below
A: (1,1)⇒(-1,-1)
B: (5,4)⇒(-5,-4)
C: (7,1)⇒(-7,-1)
D: (3,-2)⇒(-3,2)
Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.
A: (-1,-1)⇒(4,-2)
B: (-5,-4)⇒(0,-5)
C: (-7,-1)⇒(-2,-2)
D: (-3,2)⇒(2,1)
Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)
Now you know how to find the coordinates of translated figures! Have a wonderful day! :D
What is the equation perpendicular to -x+y= 7 and passes through (-1,1)
Answers
Answer:
Step-by-step explanation:
First , let us rewrite the given equation into y= mx+b format
.y= -x +7
Slope is -1
Slope of the line perpendicular to the given equation is -(-1) ie., 1
Let us find the y-intercept by plugging in the values of x,y and slope into the equation y= Mx +b
1 = -1 +b
2 = b
Equation of the line perpendicular to the given equation and passing through (-1,1) is
y=x +2
According to genetic theory, there is a very close to even chance that both children in a two child family will be of the same gender. Here are two possibilities.
(i). 24 couples have two children. In 16 or more of these families, it will turn out that both children are of the same gender.
(ii). 12 couples have two children. In 8 or more of these families, it will turn out that both children are of the same gender. Which possibility is more likely and why?
Answers
Answer:
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Step-by-step explanation:
(i) probability with 16 success out of 24 = 16/24 = 2/3
(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3
Since the two experiments have the same probability, the observed probabilities are the same.
HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.
Using the binomial distribution,
(i)
p = 1/2
N = 24
x = 16 (number of successes)
P(16,24) = C(24,16) p^16* (1-p)^8
= 735471* (1/65536)*(1/256)
= 0.0438
(ii)
p = 1/2
N = 12
x = 8 (number of successes)
P(8,12) = C(12,8) p^8* (1-p)^4
= 495*1/256*1/16
= 0.1208
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Note: It would help to mention the topic you're on so answers will correspond to what is expected. Here we cover probability and binomial distribution.
Please answer soon. Include Statement and Reason if possible.
Given: ΔABC, AC = BC, AB = 3
CD ⊥ AB, CD = √3
Find: AC
Answers
====================================================
Explanation:
Triangle CDA is congruent to triangle CDB. We can use the HL (hypotenuse leg) congruence theorem to prove this. This only works because we have two right triangles.
Since CDA and CDB are congruent, this means their corresponding pieces are the same length. Specifically AD = DB, so
AD+DB = AB
AD+AD = 3
2*AD = 3
AD = 3/2 = 1.5
For triangle CDA, we have AD = 3/2 = 1.5 and CD = sqrt(3). We can use the pythagorean theorem to find the missing side AC
a^2 + b^2 = c^2
(AD)^2 + (CD)^2 = (AC)^2
(3/2)^2 + (sqrt(3))^2 = (AC)^2
9/4 + 3 = (AC)^2
(AC)^2 = 9/4 + 3
(AC)^2 = 9/4 + 12/4
(AC)^2 = 21/4
AC = sqrt(21/4)
AC = sqrt(21)/sqrt(4)
AC = sqrt(21)/2
This is the same as writing (1/2)*sqrt(21) or 0.5*sqrt(21)
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x3 + 3x2 − 72x
Answers
Answer:
x = -6 and x = 4
Step-by-step explanation:
In math, the critical points of a function are the points where the derivative equals zero.
So, first we will find the derivative of the function. The derivative is:
[tex]f'(x)=3x^2 +6x-72[/tex]
Now, we are going to make the derivative equal zero and find the answers of the equation.
[tex]3x^2 +6x-72=0\\3(x^2 +2x-24)=0\\3(x+6)(x-4)=0\\[/tex]
So we have that the critical points are the answers to this equation:
[tex]x+6= 0 \\x= - 6[/tex]
and
[tex]x-4=0\\x=4[/tex]
Thus, the critical points are x=-6 and x=4
Using it's concept, it is found that the critical numbers of the function are:
x = -6 and x = 4.
The critical numbers of a function f(x) are the values of x for which it's derivative is zero, that is:
[tex]f^{\prime}(x) = 0[/tex]
In this problem, the function is:
[tex]f(x) = x^3 + 3x^2 - 72x[/tex]
The derivative is:
[tex]f^{\prime}(x) = 3x^2 + 6x - 72[/tex]
[tex]f^{\prime}(x) = 3(x^2 + 2x - 24)[/tex]
Then:
[tex]f^{\prime}(x) = 0[/tex]
[tex]3(x^2 + 2x - 24) = 0[/tex]
[tex]x^2 + 2x - 24 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 1, b = 2, c = -24[/tex], which we have to solve.
[tex]\Delta = 2^2 - 4(1)(-24) = 100[/tex]
[tex]x_{1} = \frac{-2 + \sqrt{100}}{2} = 4[/tex]
[tex]x_{2} = \frac{-2 - \sqrt{100}}{2} = -6[/tex]
The critical numbers of the function are x = 4 and x = -6.
A similar problem is given at https://brainly.com/question/16944025
f(x) = x + 2
g(x) = x - 4
(fg)(x) =
Answers
Answer:
Step-by-step explanation:pleased to help u....
4. Simplify the following.
3
a. 2-X5-:11
3
x5
5
6
7
Answers
Answer:
[tex]1 \frac{1}{4} [/tex]Step-by-step explanation:
[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]
To divide by a fraction, multiply the reciprocal of that fraction
[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]
Reduce the number with the G.C.F 7
[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]
Reduce the numbers with the G.C.F 17
[tex] \frac{5}{6} \times \frac{3}{2} [/tex]
Reduce the numbers with the G.C.F 3
[tex] \frac{5}{2} \times \frac{1}{2} [/tex]
Multiply the fraction
[tex] \frac{5}{4} [/tex]
In mixed fraction:
[tex]1 \frac{1}{4} [/tex]
Hope this helps..
Good luck on your assignment...
Line B passes through the points (5, 10) and (0, 0). What is the slope of the line perpendicular to line B?
Answers
Answer:
The line that is perpendicular to B has a slope of -1/2
Step-by-step explanation:
First find the slope of line B
m = ( y2-y1)/(x2-x1)
= (10-0)/(5-0)
= 10/5
= 2
Lines that are perpendicular have slopes that multiply to -1
m * 2 = -1
m = -1/2
The line that is perpendicular to B has a slope of -1/2
Answer:
-1/2x
Step-by-step explanation:
Hey there! :)
Well to find the slope of line B we'll use the following formula.
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
We'll use the points (0,0) and (5,10),
10 - 0 = 10
5 - 0 = 5
Slope = 2x
The slopes of 2 perpendicular lines are reciprocals of each other,
meaning if the slope of line B is 2x then its perpendicular lines slope is -1/2x.
Hope this helps :)
68. A hexagon has two sides each of length 3x inches. It has three sides each of length 2x inches. The sixth side has a length of 15 inches. If the perimeter of the hexagon is 135 inches, what is the value of x?
E.4
F.5
G. l0
H. 15
Answers
Answer:
G 10
Step-by-step explanation:
2*3x+3*2x+15=135 inches
6x+6x=120 inches
12x=120 inches
x= 10 inches
2. The half life of uranium-232 is 68.9 years. a) If you have a 100 gram sample, how much would be left after 250 years? b) If you have a 100 gram sample, how long would it take for there to be 12.5 grams remaining?
Answers
Step-by-step explanation:
The amount left is:
A = A₀ (½)^(t/T)
where A₀ is the initial amount,
t is the amount of time,
and T is the half life.
a) A = 100 g (½)^(250 yr / 68.9 yr)
A = 8.09 g
b) 12.5 g = 100 g (½)^(t / 68.9 yr)
0.125 = (½)^(t / 68.9 yr)
3 = t / 68.9 yr
t = 206.7 yr
Integrate the following: ∫[tex]5x^4dx[/tex]
A. [tex]x^5+C[/tex]
B. [tex]x^5[/tex]
C. [tex]5x^5+C[/tex]
D. [tex]5x^5[/tex]
Answers
Answer:
A. [tex]x^5+C[/tex]
Step-by-step explanation:
This is a great question! The first thing we want to do here is to take the constant out of the expression, in this case 5. Doing so we would receive the following expression -
[tex]5\cdot \int \:x^4dx[/tex]
We can then apply the power rule " [tex]\int x^adx=\frac{x^{a+1}}{a+1}[/tex] ", where a = exponent ( in this case 4 ),
[tex]5\cdot \frac{x^{4+1}}{4+1}[/tex]
From now onward just simplify the expression as one would normally, and afterward add a constant ( C ) to the solution -
[tex]5\cdot \frac{x^{4+1}}{4+1}\\[/tex] - Add the exponents,
[tex]5\cdot \frac{x^{5}}{5}[/tex] - 5 & 5 cancel each other out,
[tex]x^5[/tex] - And now adding the constant we see that our solution is option a!
Answer:
Answer A
Step-by-step explanation:
Use the property of integrals. You now have [tex]5 x\int\limits\,x^{4}dx[/tex] where the first x next to the 5 stands for multiplication. Let's evaluate it. We get [tex]5 (\frac{x^{5} }{5})[/tex]. From here, we can simplify this into [tex]x^{5}[/tex]. Add the constant of integration, which will give you the answer of [tex]x^{5} + C[/tex].
In the diagram AB=AD and
Answers
Answer:
AC ≅ AE
Step-by-step explanation:
According to the SAS congruence theorem, if two triangles have 2 corresponding sides that are equal, and also have one included corresponding angle that are equal to each other in both triangles, both triangles are regarded as congruent.
Given ∆ABC and ∆ADC in the question above, we are told that segment AB ≅ AD, and also <BAC ≅ <DAC, the additional information that is necessary to prove that ∆ABC and ∆ADC are congruent, according to the SAS theorem, is segment AC ≅ segment AE.
This will satisfy the requirements of the SAS theorem for considering 2 triangles to be equal or congruent.
need some help thxx ;)
Answers
Answer:
DEA
Step-by-step explanation:
rectangular field has a total perimeter of 128 feet. The width is
A
24 feet less than the length. What are the dimensions of the field?
Answers
Answer:
The length is 44 feetThe width is 20 feetStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where
l is the length
w is the width
Perimeter = 128 feet
The width is 24 feet less than the length is written as
w = l - 24
128 = 2l + 2( l - 24)
128 = 2l + 2l - 48
Group like terms
4l = 176
Divide both sides by 4
l = 44
The length is 44 feet
Substitute l = 44 into w = l - 24
w = 44 - 24
w = 20
The width is 20 feet
Hope this helps you
Classify the triangle with angles measuring 1130, 47°, and 20°.
A. Straight
B. Right
C. Acute
D. Obtuse
Answers
Answer:
D. Obtuse
Step-by-step explanation:
Answer:
You typed that incorrectly. That first angle should be 113 degrees.
It would be an obtuse triangle.
Step-by-step explanation:
what is the surface area of a cylinder height is 4 cm and diameter is 5 cm
Answers
Answer:
20cm it's is the answers
Step-by-step explanation:
5*4=20
6th grade math , help me please :)
Answers
Answer:B
Step-by-step explanation:
Please tell me if I'm right or wrong! No work needed! Brainliest will be given!
Answers
Answer:
The first one is correct
The second one is also correct
The third is also correct
Congrats!
Answer:
1) [tex]\boxed{Option \ B}[/tex]
2) [tex]\boxed{Option \ B}[/tex]
3) [tex]\boxed{Option \ B}[/tex]
You're totally correct, Man! :)
Step-by-step explanation:
Question 1:
[tex](6b^2-4b+3)-(9b^2-3b+6)\\Resolving \ the\ brackets\\6b^2-4b+3-9b^2+3b-6\\Combining \ like \ terms\\6b^2-9b^2-4b+3b+3-6\\-3b^3-b-3[/tex]
Question 2:
[tex](b+6)(b-3)\\Using \ FOIL\\b^2-3b+6b-18\\b^2+3b-18[/tex]
Question 3:
[tex](4x-3)(6x-1)\\Using \ FOIL\\24x^2-4x-18x+3\\24x^2-22x+3[/tex]
NEED HELP ASAP!!
What is the equation of the line that is parallel to the
given line and has an x-intercept of -3?
O y = x + 3
O y = ?X + 2
Oy=-3x + 3
y=-3x+2
Answers
Answer:
B
Step-by-step explanation:
The equation of the line that is parallel to the given line and has an x-intercept of -3 is y= 2/3x + 2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have a graph.
So, slope of line in graph is
= (-1-1)/ (0.-3)
= -2/ (-3)
= 2/3
and, we know that two parallel line have same slope.
so, the slope of parallel line is 2/3 and the x intercept is -3.
So, the Equation line is y= 2/3 x + b
0 = 2/3 (-3) +b
b= 2
Thus, the required equation is y= 2/3x + 2.
Learn more about Slope here:
https://brainly.com/question/2863474
#SPJ5
A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 11 students, he found the average time was 4.52 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.1 level of significance. Assume normality. (can you please show how to do this without a calculator or excel i just dont want answer but want to know how to do it).
a) What are the appropriate null and alternative hypotheses?
A) H0: μ = 5 versus Ha: μ < 5
B) H0: μ = 5 versus Ha: μ ≠ 5
C) H0: x = 5 versus Ha: x ≠ 5
D) H0: μ = 5 versus Ha: μ > 5
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
A) Fail to reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
B) Reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
C) Reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.
D) Fail to reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.
Answers
Answer:
A) Null Hypothesis;H0: μ = 5
Alternative Hypothesis;Ha: μ ≠ 5
B) test statistic = -2.1226
C) p-value = 0.0598
D) Option A is correct
Step-by-step explanation:
We are given;
x = 4.52 minutes
s = 0.75 minutes
μ = 5 minutes
n = 11
degree of freedom = n - 1 = 11 - 1 = 10
A) The hypotheses are;
Null Hypothesis;H0: μ = 5
Alternative Hypothesis;Ha: μ ≠ 5
B) t-statistic = (x - μ)/(s/√n)
(4.52 - 5)/(0.75/√11) = -2.1226
C) From the t-score calculator results attached, the p-value is approximately 0.0598.
D) The P-value of 0.0598 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant. So option A is correct.
The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles.
Answers
Answer:
We have the measure of both angles as 55 degrees and 35 degrees
Step-by-step explanation:
We know that there are three angles in a right-angled triangle. One of which is 90. FOr now, the other two are unknown, so we would designate them to be x and y.
We now set up an equation using the information we are given about the problem.
From this statement "The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle." we can set up the following equation:
x =2y -15 -------- equation 1
similarly, we know that the sum of angles in a triangle = 180 degrees. Hence, we can use this to set up another equation as follows:
x + y + 90 = 180
x+ y = 90 ------------- equation 2
we can now solve the two equations simultaneously as
x -2y =-15
x+ y = 90
from this, we have that
x = 55 and y = 35
We have the measure of both angles as 55 degrees and 35 degrees
A cylinder has a volume of 200 mm3 and a height of 17 mm.
a) The volume formula for a cylinder is v = pie r squareℎ. Isolate for the variable r in this formula.
b) Using the equation where you isolated for r in part a, find the radius of the cylinder. Round your answer to the nearest hundredth. (1 mark)
Answers
Answer:
The radius of the cylinder is 1.93mm.
Step-by-step explanation:
1) Formula to find the missing radius : V= pi r^2 (h)
( V= volume, pi=3.14 r=radius, h= height)
2) Plug all the give variables into the formula: 200=pi r^2 (17)
3) Multiply pi with 17 and then round it to the nearest hundredth which you get 53.401707511 -> 53.41, now your equation is: 200= 53.41 r^2
4) Next you want to isolate the r^2 by dividing both sides by 53.41
200/53.41= 53.41r^2/53.41 ( 3.74461711 round to the nearest hundredth --> 3.74) ---> 3.74=r^2
5) Now you have to square both sides to get rid of that exponent : squared 3.74 = squared r^2
6) Your equation would be 1.933907961 = r, round that whole decimal to the nearest hundredth and you will get 1.93 ( 19.3 = r)
7) So the radius of the cylinder given the volume is 200 mm^3 and a height of 17 mm is 1.93 mm.
45% of 80.374 is a number between
Answers
Answer:
36.1683
Step-by-step explanation:
45*80.374/100=
what is the slope of the line with the equation y= -2x - 1? A -2 B -1 C 2 D 1
Answers
Answer:
The answer is "A'' -2 because anything next to the letter x is the slope
Step-by-step explanation:
The equation to slops is y=mx+b
m= slope
b= y intercept
Slope = -2
Y intercept = ( 0 , -1)
Step-by-step explanation:
Hope this helps. Your answer would be A
The area of the region under the curve of the function f(x)=5x+7 on the interval [1,b] is 88 square units, where b>1. What is the value of b.
Answers
Answer:
[tex]\displaystyle b = 5[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^b_1 {5x + 7} \, dx = 88[/tex]
Step 2: Solve
[Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^b_1 {5x} \, dx + \int\limits^b_1 {7} \, dx = 88[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 5 \int\limits^b_1 {x} \, dx + 7 \int\limits^b_1 {} \, dx = 88[/tex][Integrals] Integration Rule [Reverse Power Rule]: [tex]\displaystyle 5 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^b_1 + 7(x) \bigg| \limits^b_1 = 88[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle 5 \bigg( \frac{b^2}{2} - \frac{1}{2} \bigg) + 7(b - 1) = 88[/tex]Simplify: [tex]\displaystyle \frac{5b^2}{2} - \frac{5}{2} + 7b - 7 = 88[/tex]Isolate: [tex]\displaystyle \frac{5b^2}{2} + 7b = \frac{195}{2}[/tex]Solve: [tex]\displaystyle b = \frac{-39}{5} ,\ 5[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer:5
Step-by-step explanation:
got it right