Answer: 17,147
Step-by-step explanation:
Find an equation for the perpendicular bisector of the line segment whose endpoints
(5, -3) and (-7, -7).
are
Answer:
[tex]y=-3x-8[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Midpoint: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] where the endpoints are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, 3/4 and -4/3, etc.)1) Determine the midpoint of the line segment
When two lines bisect each other, they intersect at the middle of each line, or the midpoint.
[tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
Plug in the endpoints (5, -3) and (-7, -7)
[tex](\frac{5+(-7)}{2} ,\frac{-3+(-7)}{2} )\\(\frac{-2}{2} ,\frac{-10}{2} )\\(-1,-5)[/tex]
Therefore, the midpoint of the line segment is (-1,-5).
2) Determine the slope of the line segment
Recall that the slopes of perpendicular lines are negative reciprocals. Doing this will help us determine the slope of the perpendicular bisector.
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the endpoints (5, -3) and (-7, -7)
[tex]\frac{-7-(-3)}{-7-5}\\\frac{-7+3}{-7-5}\\\frac{-4}{-12}\\\frac{1}{3}[/tex]
Therefore, the slope of the line segment is [tex]\frac{1}{3}[/tex]. The negative reciprocal of [tex]\frac{1}{3}[/tex] is -3, so the slope of the perpendicular is -3. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-3x+b[/tex]
3) Determine the y-intercept of the perpendicular bisector (b)
[tex]y=-3x+b[/tex]
Recall that the midpoint of the line segment is is (-1,-5), and that the perpendicular bisector passes through this point. Plug this point into [tex]y=-3x+b[/tex] and solve for b:
[tex]-5=-3(-1)+b\\-5=3+b[/tex]
Subtract 3 from both sides
[tex]-5-3=3+b-3\\-8=b[/tex]
Therefore, the y-intercept of the line is -8. Plug this back into [tex]y=-3x+b[/tex]:
[tex]y=-3x-8[/tex]
I hope this helps!
I need the answer. Please help.
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Work Shown:
Use the tangent ratio
tan(angle) = opposite/adjacent
tan(B) = AC/AB
tan(61) = AC/1
tan(61) = AC
AC = tan(61)
AC = 1.80404775527142
AC = 1.8
The river is about 1.8 miles wide between points A and C.
Make sure your calculator is in degree mode. One way to check is to type in tan(45) and you should get 1.
Select the correct answer from each drop-down menu.
A quadrilateral has vertices A{11, -7), 89,-4), (111, -1), and D13,-4).
Quadrilateral ABCD is a
If the vertex c (11, -1) were shifted to the point c(11,1) quadrilateral Abcd would be a
Answer:
A non-equilateral rhombus.
Step-by-step explanation:
We can solve this graphically.
We start with square:
ABCD
with:
A = (11, - 7)
B = (9, - 4)
C = (11, - 1)
D = (13, - 4)
Only with the vertices, we can see that ABCD is equilateral, as the length of each side is:
AB = √( (11 - 9)^2 + (-7 -(-4))^2) = √( (2)^2 + (3)^2) = √(4 + 9) = √13
BC = √( (11 - 9)^2 + (-1 -(-4))^2) = √13
CD = √( (11 - 13)^2 + (-1 -(-4))^2) = √13
DA = √( (11 - 13)^2 + (-7 -(-4))^2) = √13
And we change C by C' = (11, 1)
In the image you can see the 5 points and the figure that they make:
The figure ABCD is a rhombus, and ABC'D is also a rhombus, the only difference between the figures is that ABCD is equilateral while ABC'D is not equilateral.
A manufacturer claims that the mean amount of juice in its bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The hypotheses are:
Answer:
The null hypothesis is [tex]H_0: \mu = 16.1[/tex].
The alternate hypothesis is [tex]H_1: \mu < 16.1[/tex]
Step-by-step explanation:
A manufacturer claims that the mean amount of juice in its bottles is 16.1 ounces.
This means that at the null hypothesis, we test if the mean amount of juice is of 16.1, as claimed, that is:
[tex]H_0: \mu = 16.1[/tex]
A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.
This means that at the alternate hypothesis, we test if the mean amount of juice is less than the claimed mean of 16.1 ounces. So:
[tex]H_1: \mu < 16.1[/tex]
i have a lot of work but anyone know the answer to this one pls
Answer:
0.24
Step-by-step explanation:
Convert [tex]\frac{6}{25}[/tex] into decimal
which will give 0.24
CitiBank recorded the number of customers to use a downtown ATM during the noon hour on 32 consecutive workdays. 39 41 25 17 48 29 31 17 24 36 17 24 40 38 42 11 43 47 27 25 17 23 43 20 32 48 26 26 9 46 44 44 Click here for the Excel Data File (a) Find the mean, midrange, geometric mean, and 24 percent trimmed mean. (Round your answers to 2 decimal places.)
Answer:
Mean = 31.22
Midrange = 28.50
Geometric mean = 28.74
Trimmed mean = 31.56
Step-by-step explanation:
Given the data :
39 41 25 17 48 29 31 17 24 36 17 24 40 38 42 11 43 47 27 25 17 23 43 20 32 48 26 26 9 46 44 44
Ordered data :
9, 11, 17, 17, 17, 17, 20, 23, 24, 24, 25, 25, 26, 26, 27, 29, 31, 32, 36, 38, 39, 40, 41, 42, 43, 43, 44, 44, 46, 47, 48, 48
The mean, xbar :
Xbar = Σx / n = 999 / 32 = 31.22
The midrange : (maximum - minimum) / 2
Midrange = (48 + 9) / 2 = 57 / 2 = 28.5
Geometric mean :
(x1*x2*.. xn)^1/n
Geometric mean = (x1*x2*.. xn)^1/32 = 28.74
24% trimmed mean :
24% of 32 = 0.24 * 32 = 7.68 ; this mean cutting off 8 values from the top and bottom and calculating the mean of the remaining values.
Data left :
24, 24, 25, 25, 26, 26, 27, 29, 31, 32, 36, 38, 39, 40, 41, 42
Σx / n = 505 / 16 = 31.5625
Trimmed mean = 31.56
what are prime factors i cant understand
Carlos is making a model pyramid for a history project. A net of his pyramid is
shown. What is the lateral surface area of the pyramid?
9514 1404 393
Answer:
60 cm²
Step-by-step explanation:
The lateral surface area is the area of the four blue triangles. Each one has an area of ...
A = 1/2bh
A = 1/2(6 cm)(5 cm) = 15 cm²
The lateral surface area is 4 times the area of one triangle, so is ...
LA = 4(15 cm²) = 60 cm²
Solving the following system using any method.
−3x+y=5
−2y=−6x+10
Answer:
No solution
Step-by-step explanation:
see the steps below:)
Solve
8 (d+2) – 36 = 2 + 6(1 – d)
Answer:
d=2
Step-by-step explanation:
8(d+2)-36=2+6(1-d)
Expand the equation
8d+16-36=2+6-6d
Put like terms together
8d+6d = 2+6-16+36
14d= 28
Divide 14 on both sides to get the value of d
[tex] \frac{14d}{14} = \frac{28}{14} [/tex]
d=2
a water tank is filled with 10 gallons of water in 2 minutes. what is the volume of the water, in gallons, that is in the tank in 1 minute?
Answer:
5 gallons of water in 1 minute
please help asap!!!!
Answer:
Hello! answer: 585
Step-by-step explanation:
This polygon can be split into 6 triangles so all you have to do is find the area of 1 then multiply by 6 to get the whole things area so...
15 × 13 = 195 195 ÷ 2 = 97.5 97.5 × 6 = 585 therefore the area is 585 hope that helps you!
jucinta has two blue marbles 4 red marbles and five green marbles in the bag of the marbles are the same size she will select one marble from the bag without looking what is the probability that Justina will select green marble write your answer as a fraction
Answer:
2+4+5 = 11. since there are 5 green marbles the answer is 5/11
Find the value of x in the figure.
A. 18
B. 33
C. 35
D. 41
Answer:
D 41
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180 degrees.
so, we have already 35 for one angle, that leaves 145 for the other two.
x + 2 + 2x + 20 = 145
3x + 22 = 145
3x = 123
x = 41
Please Only jack2k can answer
Answer:
Larger number is 7, and the smaller number is 3. This is because 7 + 3 = 10, and 7 - 3 = 4.
Step-by-step explanation:
Prodigy perhaps???
Please help and if you can explain it please
Answer:
1) 1/3 2a)2/5 2b)1/2 2c)9/20
Step-by-step explanation:
1) A fair die has 6 sides (1,2,3,4,5,6) so there are 2 sides that are greater than 4. Probability is chance of occurance/total chances so 2/6 which simplifies to 1/3
2) The set is (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19, 20) The prime numbers in that set are (2,3,5,7,11,13,17,19)
a)So the probability that a prime number is picked is 8/20 which simplifies to 2/5
b) The odd numbers are (1,3,5,7,9,11,13,15,17,19) so probability of odd is 10/20 which simplifies to 1/2
c) The single digit numbers are (1,2,3,4,5,6,7,8,9) so the probability is 9/20
Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .9370? a. .8264 b. – 1.53 c. 1.50 d. 1.96
Answer:
z₁(s) = - 1.53
Step-by-step explanation:
a) Value of z or z₁(s) area to the right is .9370
1 - 0.9370 = 0.063
Then if area to the left is 0.063 z₁(s) = - 1.53
GUYS HELP PLS
You have 100ml of a solution that has a strength of 10mg/50ml.
This is diluted with a further 100ml of water.
How strong is the solution now per 50ml?
okay so a circle has half a line of 11 in. , what's the circumference and area?? i'm not good at math and so confused
Answer:
C = 69.12 in.
A = 380.13 in.²
Step-by-step explanation:
Circumference of a circle is the length around the circle.
Circumference, C = 2πr
where,
Radius (r) = 11 in. (Given)
To find the circumference, substitute r = 11 into the circumference formula
C = 2*π*11
Input this into your calculator, you would get:
C = 69.1150384
C = 69.12 in. (Approximated to nearest hundredth)
Area = πr²
Plug in the value of r
A = π*11²
A = 380.132711
A = 380.13 in.² (to nearest hundredth)
Park View Apartments has 2 buildings Each building has 3 floors Each floor has
16 windows What is the total number of windows in the Park View Apartment
buildings?
Answer:
96
Step-by-step explanation:
24% of what is 25? Round to the nearest tenth.
math Question Help to solve Multiple Choice
Answer:
B. 49
Step-by-step explanation:
f(7) = 7² = 49
_______
Select the correct difference.
-3z^7- (-5z^7)
Every 10th student was chosen from the cafeteria line to answer a question about pets. This is an example of:
A)Simple Random Sample
b)Convenience Sample
C)Systematic Random Sample
D)Voluntary Response Sample
Answer:
C)Systematic Random Sample
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this case:
Every kth element(in this exercise 10th) is systematic sample. So the answer is given by option c.
PLEASEEEEE HELPPPPP IM BEGGINGGGG. SOMEONE PLEASEEEEEEE
9514 1404 393
Answer:
3. (x, y) = (-1, -2)
4. (x, y) = (-8, 6)
Step-by-step explanation:
The equations are graphed in the attachments.
3. The equations of problem 3 are easily graphed using the slope and intercept. The second equation is ...
y = 2x
when solved for y.
__
4. The equations of problem 4 may be more easily graphed using the x- and y-intercepts. These are found by dividing the constant by the coefficients of x and y, respectively. Once the intercepts are plotted, a line can be drawn through them to make the graph of the equation.
In ΔWXY, the measure of ∠Y=90°, YX = 40, XW = 41, and WY = 9. What ratio represents the cosine of ∠W?
Answer:
Step-by-step explanation:
cosine W=9/41
Answer:
cos W = [tex]\frac{9}{41}[/tex]
Step-by-step explanation:
cos W = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{WY}{XW}[/tex] = [tex]\frac{9}{41}[/tex]
During a school event Mario is selling pizza at a stand for $ 2.50 per slice. How many slices of pizza would Mario have to sell to earn $195? Explain your reasoning.
Answer:
78 slices
Step-by-step explanation:
195/2.5=78
Answer:
78
Step-by-step explanation:
195/2.5=78
he will need to sell 78 pizzas in order to get $195
Find the Z-scores that separate the middle 22% of the distribution from the area in the tails of the standard normal distribution.
The Z scores are _____?
Find the value of z a The value of α = 0.27
The value of z 0.27 is _____
Find the Z-score such that the area under the standard normal curve to the left is 0.33
_____ is the z - score such that the area under the curve to the left is 0.33.
Answer:
0.279
0.613
-0.44
Step-by-step explanation:
The Zscore that seperates the middle 22% of the distribution ; could be obtained thus. The midpoint is the mean and the probability to either the right or left could be obtained.
To obtain the Zscore that seperates the middle 22% is equivalent to :
The probability to the left of the distribution :
P(x < (0.5 + 0.22/2) = p(x < 0.61)
Using the Z probability calculator :
P(x < 0.61) is equivalent to a Zscore of 0.279
α = 0.27
Z(1 - α) = Z(1 - 0.27) = Z0.73 = p(Z < 0.73) = 0.613
P(x < 0.33) = - 0.44 (Z probability calculator)
PLS ANSWER ASAP!!person with correct answer will be marked brainliest
Answer:
114
Step-by-step explanation:
angle one is vertical opposite angle and also angle on a straight line
if you were to roll a dice one time what is the odds of rolling a number less than three?
Answer:
1/3
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome. On a fair die, the number are 1 to 6 while 1 and 2 are the only numbers less than 3.
Hence the odds of getting a number is the ratio of 6 to 6 while the odds of getting a number lower than 3 will be
= 2/6
= 1/3 (in the lowest term)
This is because the odd of getting 1 is 1/6 and the odd of hetting 2 is 1/6 9 recall that both numbers appear once on a die). Hence the odd of getting 1 or 2 will be
= 1/6 + 1/6
= 2/6
=1/3