Given:
Endpoints of a line segment AB are A(2,3) and B(8,11).
To find:
(1) Slope of AB.
(2) Length of AB.
(3) Midpoint of AB.
(4) Slope of a line perpendicular to AB.
Solution:
We have, endpoints of line segment AB, A(2,3) and B(8,11).
(1)
Slope of AB is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{11-3}{8-2}[/tex]
[tex]m=\dfrac{8}{6}[/tex]
[tex]m=\dfrac{4}{3}[/tex]
Therefore, the slope of AB is [tex]\dfrac{4}{3}[/tex].
(2)
Length of AB is
[tex]AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]AB=\sqrt{(8-2)^2+(11-3)^2}[/tex]
[tex]AB=\sqrt{(6)^2+(8)^2}[/tex]
[tex]AB=\sqrt{36+64}[/tex]
[tex]AB=\sqrt{100}[/tex]
[tex]AB=10[/tex]
Therefore, the length of AB is 10 units.
(3) Midpoint of AB is
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{2+8}{2},\dfrac{3+11}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{10}{2},\dfrac{14}{2}\right)[/tex]
[tex]Midpoint=\left(5,7\right)[/tex]
Therefore, the midpoint of AB is (5,7).
(4)
Product of slopes of two perpendicular lines is -1.
Let the slope of line perpendicular to AB be m₁.
[tex]m_1\times \dfrac{4}{3}=-1[/tex]
[tex]m_1=-\dfrac{3}{4}[/tex]
So, slope of line perpendicular to AB is [tex]-\dfrac{3}{4}[/tex].
Three machines are used to produce nails. the table displays the total number of nails produced by the three machines over different lengths of time
Answer:
Step-by-step explanation
they answer would be a whole number because you are multiplying by one thousand
Using the principle of proportionality, the number of nails that will be produced by 1 machine in 1 hour is [tex] 21 \frac{3}{5} \: thousand [/tex]
Let :
Number of machines = mNumber of nails produced = nTime taken = tUsing Principle of variation :
Number of machines α nails produced α 1/time[tex] m = \frac{kn}{t} [/tex] ; where k = constant of proportionalityUsing a row from the table :
t = 15 ; n = 81/5
3 = (81/5)k / 15
Cross multiply :
3 × 15 = (81/5)k
45 = (81/5)k
Divide both sides by (81/5) to isolate k
(45 ÷ 81/5) = k
k = (45 × 5/81) = 25/9 = 2.7777
Substituting the value of k into the expression:
[tex] m = \frac{\frac{25}{9}n}{t} [/tex]
We can use the expression to obtain, the value of n ; when m = 1 and t = (1 hour = 60 minutes)
[tex] 1 = \frac{\frac{25}{9}n}{60} [/tex]
[tex] 60 = \frac{{25}{9}}{n}[/tex]
Divide both sides by 25/9 to isolate n
[tex] 60 \times \frac{9}{25} = n [/tex]
[tex] n = \frac{540}{25} = 21 \frac{3}{5} \: thousand \: nails [/tex]
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The monthly electric bills in a certain community are normally distributed, with a mean of $245 and a standard distribution of $55. If there are 461 households in the community, about how many of them have electric bills less than $200?
A. 45
B. 21
C. 95
D. 81
95 households have electricity bills of less than $200. Option C is correct.
Given that,
The monthly electric bills in a certain community are normally distributed, with a mean of $245 and a standard distribution of $55. There are 461 households in the community, how many of them have electric bills less than $200 is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
probability for the number of households has electric bills less than $200.
x = 200 , μ = 245 ; σ = 55
Now,
Probability,
z (p < 200) = [tex]\frac{X -\mu}{\sigma}[/tex]
z (p < 200) = (200 - 245)/55
= --45/5
= -0.818181
p < 200 = 0.206 (from z table)
Now, the number of households that has electricity bill less than $200,
= 461 * 0.206
= 94.966
≈ 95
Thus, 95 number of household have electricity bills of less than $200. Option C is correct.
Learn more about probability here:
brainly.com/question/14290572
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$40 game; 30% off; 5% tax
is -3/7 a rational or irrational number?
Answer:
rational
Step-by-step explanation:
it can express as a ratio of two numbers, therefore it is rational. it wouldn't be rational if it was for example 0.333333 that goes on forever.
The number 63 is how many times the number 21?
Answer:
3
Step-by-step explanation:
cause 63 divided by 21 is 3.
Answer:
21 * 3 = 63
Step-by-step explanation:
One person is chosen from a class of students here are some possible outcome
a) The person is over to 14 years old.
B)the person is less than 12 years old
C)The person is a female
D)the person is a male
For Each of these statements decide whether it’s true ‘ false ‘ or you can’t tell
A and B are mutually exclusive
A and C are mutually exclusive
C and D are mutually exclusive
The ratio of blue chairs to red chairs in Ms. Vickers' class is 2 to 5. Which of the following cannot represent the total number of chairs in Ms. Vickers' class? A 14 C 28 B 20 D 35
Answer:
I would say B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
which function represents the relationship between x and y when y=16/5 and x=20
Answer:
y = (4/25)x
Step-by-step explanation:
We are given;
y = 16/5 and x = 20
Now if y varies directly with x, then we can say;
y = mx
Where m is constant of proportionality
This means that;
16/5 = 20m
Divide both sides by 20 to get;
(16/5) × 1/20 = m
16/100 = m
m = 4/25
Thus,the equation is:
y = (4/25)x
I have a box of crackers that weighs 5.25 oz. if one serving of crackers is .15 ounces. How many servings are in the box?
Answer:
0.15÷5.25 should give u the answer
The surface area of a cone is determined by the equation
Answer:
This question is incomplete
Step-by-step explanation:
help possible branliest
Answer:
1.81
2.2^7
3. 4^5
4. 2^9
5. 1
6. 4^5
7. 6
8. 3^8
9. 15^0
10. 2^3
11. 3^2
12. 216
13. 5^3
14. 225
15. 343
16. 11^2
17. 625
18. 5^4
19. 169
20. 10^4
Step-by-step explanation:
Two planes take off from the same airport at approximately the same time. Plane A has an airspeed of 600 mph
and travels in the direction S 20° W. Plane B has an airspeed of 450 mph and travels in the direction N 35° E.
Which diagram represents the distance, x, between the planes?
Answer:
B
Step-by-step explanation:
edge 2020
Answer: option B
Step-by-step explanation:
edge 2023
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Answer:
39% , 0.39 , 39/100
Step-by-step explanation:
I thought your randomness of letters was your question lol. Hope this helps though!
please help!! :)
find the area of this parallelogram. Be sure to include the correct unit in your answer.
Answer:
7x12x13=1092
Step-by-step explanation:
Assume that last year in a particular state with 700000 children there were 1205 children out of 32600 in a random sample who were diagnosed with Autism Spectrum Disorder. Nationally, 1 out of 88 children are diagnosed with ASD. Is there sufficient data to show that the incident rate of ASD is higher in that state than nationally
Answer:
We accept Hₐ there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally
Step-by-step explanation:
The population follows a binomial distribution, and the fact that
p₀ = 1205/32600 = 0,03696 and then q₀ = 1-0,03696 = 0,9630
And both
p₀*n = 0,03696*32600 = 1205 > 10
q₀*n = 31395 > 10
The binomial distribution can be approximate to a Normal Distribution, then we need to develop a one tail test ( to the right) to evaluate if the claim " There is sufficient data to show that the incident rate is higher in the mentioned state than the national one.
Therefore:
Hypothesis Test H₀ ⇒ p₀ = p
Alternative Hypothesis Hₐ ⇒ p₀ > p
p is the population proportion mean
p = 1/88 = 0,011
We must test having a very wide Confidence Interval since the matter we are trying is public health then we choose CI = 95 %
CI = 95 % α = 5 % α = 0,05
Critical value for 0,05 is from z-table z(c) = 1,64
We compute z(s)
z(s) =( p₀ - p )/ √ p₀*q₀/n
z(s) = 0,03696 - 0,011 / √ (0,03696*0,9630)/ 32600
z(s) = 0,02596* 180,55/ √ 0,0356
z(s) = 4,687 / 0,189
z(s) = 24,9
Comparing z(s) and z(c) 24,9 > 1, 64
z(s) is out of the acceptance region and we have to reject H₀
We accept Hₐ there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally
What are 1/2 and 2/4 as a decimal?
Answer:
0.50 or 0.5
Step-by-step explanation:
Answer:
1/2= 0.5 2/4=0.5
The reason for this is because both questions are half a fraction, so both of them would be half a decimal
Step-by-step explanation:
If xy =1 show that dy/dx=-1/x²
If xy = 1, then differentiating both sides with respect to x gives
x dy/dx + y = 0
(use the product rule)
Solve for dy/dx :
dy/dx = -y/x
Solve the starting equation for y and substitute that into the derivative.
xy = 1 → y = 1/x
→ dy/dx = -(1/x)/x = -1/x²
Triangle ABC is transformed to triangle A' B'C', as shown below:
B
-4 CA-2-10
26
3 4
A
Which equation shows the correct relationship between the measures of the angles of the two triangles? (1 point)
mZCAB = mZC'B'A'
mZBCA = MZA'B'C'
OmZCAB = mZC'A'B'
OmZBCA = mZC'A'B'
Can someone help me with this question please and thank you
Answer:
The complete table will be:
x y
1 5
0.8 4
0.4 2
Step-by-step explanation:
Given rule is:
y = 5x
In the given rule, x is multiplied by 5 to get the values of y. The same rule can be manipulated to find the value of x in terms of y.
[tex]\frac{y}{5} = \frac{5x}{5}\\x = \frac{y}{5}[/tex]
Putting y = 5
[tex]x = \frac{y}{5}\\x = \frac{5}{5}\\x = 1[/tex]
Putting y = 4
[tex]x = \frac{y}{5}\\x = \frac{4}{5}\\x = 0.8[/tex]
Putting y = 2
[tex]x = \frac{2}{5}\\x = 0.4[/tex]
Hence,
The complete table will be:
x y
1 5
0.8 4
0.4 2
Given the points a ( -2,4 ) and b(7,-2) find the coordinates of the point p on the directed like segment ab that partitions ab in the ratio 1:2
9514 1404 393
Answer:
p = (1, 2)
Step-by-step explanation:
We want ...
(p -a)/(b -p) = 1/2
2(p -a) = b -p . . . . . cross multiply
3p = b +2a . . . .. . . rearrange
p = (b +2a)/3
p = ((7, -2) +2(-2, 4))/3 = (7 -4, -2 +8)/3 = (3, 6)/3
p = (1, 2)
Identify the vertex of
y = 2x2 − 4x − 2
vertex at
(
−
1
,
−
4
)
Explanation:
Given:
y
=
2
x
2
+
4
x
−
2
Convert the given form into "vertex form"
y
=
m
(
x
−
a
)
2
+
b
with vertex at
(
a
,
b
)
XXX
y
=
2
(
x
2
+
2
x
)
−
2
complete the square
XXX
y
=
2
(
x
2
+
2
x
+
1
)
−
2
−
2
XXX
y
=
2
(
x
+
1
)
2
−
4
XXX
y
=
2
(
x
−
(
−
1
)
)
2
+
(
−
4
)
which is the vertex form with vertex at
(
−
1
,
−
4
)
graph{2x^2+4x-2 [-5.455, 7.034, -5.54, 0
Identify the radius of the circle.
Help ASAP pls!!!
*its hw*!
if a store is selling 3 bottles of water for $3.24. how much would 8 bottles of water cost
Answer:
$8.64
Step-by-step explanation:
Divide 3.24 by three to get the codt of one bottle,$1.08. multiply $1.08 by 8 and we get $8.64.
Please help, I only have 30 minutes left...
Answer:
(2,-1)
Step-by-step explanation:
hope i helped <3
Answer:
(2,-1)
Step-by-step explanation:
That is the answer becasue the x-axis is 2 and the y-axis is -1
I need help again
I am
Sorry
Answer:
x = 171.16 - 5.8
x = 165.36
please give me brainlist
Step-by-step explanation:
Answer:
165.36 is Pete's height
Step-by-step explanation
You have to subtract 5.8 by 171.16 and that will be Pete's height.
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There are 2 answers for this
(Please use a comma to separate them)
Emma got 90% of the questions on her history test correct if she answered 27 questions correctly, how many questions did Emma get wrong?
There were (A) questions on the test so she got (B) questions wrong
Answer:
There were 30 questions on the test so she got 3 questions wrong.
Step-by-step explanation:
Given that:
Correct answers by Emma = 27
Percentage of correct answers = 90%
Let,
x be the total number of questions on test
90% of x = 27
[tex]\frac{90}{100}x=27[/tex]
[tex]0.9x=27[/tex]
Dividing both sides by 0.9
[tex]\frac{0.9x}{0.9}=\frac{27}{0.9}\\x=30[/tex]
There were 30 questions on the test.
Wrong answers = Total questions - Correct answers
Wrong answers = 30-27 = 3
Hence,
There were 30 questions on the test so she got 3 questions wrong.
4(5 – w) = –2(2w – 3)
Simplify the following expression where b = -2 and z = 6
4(−2−7)+3
There is a typo here. We cannot evaluate the given expression if there is no b and z to replace with the given values. Get it?
THESE ARENT MY PHOTOS but my answers are the exact same. pls help with the rest plsplspslpslpslpslplsp
Answer:
Can u add pictures of the rest?
Step-by-step explanation: