Answer:
y = 3/5x - 1
Step-by-step explanation:
y = mx + b
m = slope
m = 3/5
to find the y - intercept we have to make x = 0 by adding or subtracting
in this case it is +5
add five to both x and y
[tex](-5, -6) + (5, 5) = (0, -1)[/tex]
the y intercept focuses on what y is when x is 0
the y intercept in this case is -1
please help solve it
Answer:
Step-by-step explanation:
1 to find AB
in triangle ADB
here 4 and 2[tex]\sqrt{6}[/tex] are the legs of the right triangle so let them be a and b respectively.
AB is the hypotenuse (longest side ) and let it be x
using pythagoras theorem
a^2 + b^2 = c^2
4^2 + [tex](2\sqrt{6} )^2[/tex] = AB^2
16 + 4*6 = AB^2
16 + 24 = AB^2
40 = AB^2
[tex]\sqrt{40}[/tex] = AB
[tex]2\sqrt{10}[/tex] = AB
therefore AB =v[tex]2\sqrt{10}[/tex] .Hence proved .
In triangle ADC
here 6 and [tex]2\sqrt{6}[/tex] are the legs of the right angle so let them be a and b respectively. AC is the hypotenuse (longest side) so let it be c
usinfg pythagoras theorem
a^2 + b^2 = c^2
6^2 + [tex](2\sqrt{6} )^2[/tex] = AC^2
36 + 4*6 = AC^2
36 + 24 = AC^2
60 = AC^2
[tex]\sqrt{60}[/tex] = AC
[tex]2\sqrt{15}[/tex] = AC
To prove triangle ABC is a right angled triangle
AD and BD are the legs and AB is hypotenuse
according to pythagoras theorem to be the right angle triangle the sum of square of two smaller sides of a triangle must equal to the square of hypotenuse(longest side)
let two smaller sides be a and b respectively and c be hypotenuse
using pythagoras theorem
a^2 + b^2 = c^2
4^2 + [tex](2\sqrt{6} )^2[/tex] = [tex](2\sqrt{10} )^2[/tex]
16 +2^2*6 = 2^2*10
16 + 4*6 = 4*10
16 + 24 = 40
40 = 40
since both sides are equal it is proved that the triangle ABC is a right angled triangle.
Hope this helps u !!
Answer:
2 square root 10
Step-by-step explanation:
firstly you must find the hipotenus using the hipotenus formula AB is the hipotenus
(4)*2 + (2 square root 10)*2 = 40 juat press a calculator if you dont know
and then you press square root of 40 then you will get 2 square root 10 so you already prove that AB is 2 square root 10
Is (2, 3) a solution to this system of equations?
2x + 5y = 19
X + 16y = 5
yes
no
Answer:
No
Step-by-step explanation:
To check if (2,3) is a solution to the system of equations, we simply have to plug the coordinate points into the two equations and see if it is valid.
[tex]2*2+5*3=\\4+15=\\19\\\\19=19[/tex]
(2,3) belongs in the first equation.
[tex]2+16*3=\\2+48=\\50\\\\50\neq 5[/tex]
(2,3) does not belong in the second equation.
Therefore, (2,3) is not a solution to this system of equations.
I hope this helps! Let me know if you have any questions :)
Express 384kg in tones
Answer:
1000kg = 1 tone
384/1000=0.384 tone
One fourth of the sum of a number and two is three.
Answer:
x = 10
Step-by-step explanation:
(1/4(x +2) = 3
x+2 = 12
x = 10
Answer:
The number is 6.
Step-by-step explanation:
[tex]\frac{1}{4}=0.25[/tex]
0.25 × (y × 2) = 3
0.25 × 2y = 3
0.5y = 3
0.5y ÷ 0.5 = 3 ÷ 0.5
y = 6
Check:
0.25 × (y × 2) = 3
0.25 × (6 × 2) = 3
0.25 × 12 = 3
3 = 3
The thickness of eight pads designed for use in aircraft engine mounts are measured. The results, in mm, are 41.8, 40.9, 42.1, 41.2, 40.5, 41.1, 42.6, and 40.6. Assumed that the thicknesses are from a normal distribution. Can you conclude that the mean thickness is greater than 41.0 mm a) State your hypotheses. b) Test your hypotheses at .01 significance level. c) Your conclusion (in the context of this problem)
Answer:
We accept H₀ we don´t have enough evidence to support that the mean thickness is greater than 41 mm
Step-by-step explanation:
Sample Information:
Results:
41.8
40.9
42.1
41.2
40.5
41.1
42.6
40.6
From the table we get:
sample mean : x = 41.35
sample standard deviation s = 0.698
Hypothesis Test:
Null Hypothesis H₀ x = 41
Alternative Hypothesis Hₐ x > 41
The test is a one-tail test
If significance level is 0.01 and n = 8 we need to use t-student distribution
From t-table α = 0.01 and degree of freedom df = n - 1 df = 8 - 1
df = 7 t(c) = 2.998
To calculate t(s) = ( x - 41 ) / s/√n
t(s) = ( 41.35 - 41 ) / 0.698/√8
t(s) = 0.35 * 2.83/ 0.698
t(s) = 1.419
Comparing t(s) and t(c)
t(s) < t(c)
t(s) is in the acceptance region we accept H₀
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3
O y + 2 =1/3(x + 3)
O y-2=1/3(x-3)
O y + 3 = 1/3(x+ 2)
O y-3= 1/3(x-2)
Answer:
y - 2 = 1/3(x - 3)
Step-by-step explanation:
Point slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Plug in the slope:
y - y1 = m(x - x1)
y - y1 = 1/3(x - x1)
Plug in the given point:
y - y1 = 1/3(x - x1)
y - 2 = 1/3(x - 3)
So, the correct answer is y - 2 = 1/3(x - 3)
Help meeeeeeeeeeeeeeeeeeeee
Answer:
question please so I can help you
A survey related to presidential favorability was administered to members of
the same party as the president. The results of the survey showed 85%
favorability. Another national survey was administered to members of both
parties. The results of this survey showed 45% favorability. This is a classic
example of an error in which phase of inferential statistics?
A. data analysis
B. probability-based inference
C. data gathering
D. data organization
Answer:
Step-by-step explanation:
A data analysis
Please help me with this as quickly as possible!
Answer:
1:2
is your answer
Step-by-step explanation:
An expression is shown below:
f(x) = 4x2 + 8x − 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
Given function:
f(x) = 4x² + 8x - 5Part AThe x-intercepts are the points when f(x) = 0.
Set up equation and solve:
4x² + 8 x - 5 = 0x = ( - 8 ± √(8² + 4*4*5))/8x = (- 8 ± √144)/8x = ( - 8 ± 12)/8x = - 20/8 = - 2.5 and x = 4/8 = 0.5The x-intercepts are (-2.5, 0) and (0.5, 0)
Part BThe vertex form of the quadratic equation:
y = a(x - h)² + k, where (h, k) is the vertexThe vertex is minimum if the leading coefficient is positive and maximum if the leading coefficient is negative. The given equation has a = 4, hence its vertex is minimum.
Convert the given equation into vertex form:
y = 4x² + 8x - 5 y = 4x² + 8x + 4 - 4 - 5 y = 4(x² + 2x + 1) - 9 y = 4(x + 1)² - 9As per equation the vertex is (- 1, - 9)
Part CFrom the previous parts we found the two x-intercepts and vertex, also found that the vertex is the minimum, so the graph opens up.
Plot the points and connect to obtain the graph.
See below.
The altitude of a triangle is increasing at a rate of 1.5 1.5 centimeters/minute while the area of the triangle is increasing at a rate of 1.5 1.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8 8 centimeters and the area is 88 88 square centimeters
Answer:
The base reduces at 3.75cm/min
Step-by-step explanation:
Given
Let
[tex]h \to altitude[/tex]
[tex]b \to base[/tex]
[tex]A \to Area[/tex]
So:
[tex]\frac{dh}{dt} = 1.5cm/min[/tex]
[tex]\frac{dA}{dt} = 1.5^2cm/min[/tex]
The area of a triangle is:
[tex]A = \frac{1}{2}bh[/tex]
Calculate b when [tex]A =88cm^2; h =8cm[/tex]
[tex]A = \frac{1}{2}bh[/tex]
[tex]88=\frac{1}{2} * b * 8[/tex]
[tex]88 =b * 4[/tex]
Solve for b
[tex]b = 88/4[/tex]
[tex]b = 22[/tex]
We have:
[tex]A = \frac{1}{2}bh[/tex]
Differentiate with respect to time
[tex]\frac{dA}{dt} =\frac{1}{2}(h\frac{db}{dt} + b\frac{dh}{dt})[/tex]
Substitute the following values in the above equation
[tex]\frac{dh}{dt} = 1.5cm/min[/tex] [tex]\frac{dA}{dt} = 1.5^2cm/min[/tex] [tex]b = 22[/tex] [tex]h = 8[/tex]
[tex]1.5 = \frac{1}{2}(8 * \frac{db}{dt} + 22 * 1.5)[/tex]
Multiply both sides by 2
[tex]3 = 8 * \frac{db}{dt} + 22 * 1.5[/tex]
[tex]3 = 8 * \frac{db}{dt} + 33[/tex]
Collect like terms
[tex]8 * \frac{db}{dt} = 3 -33[/tex]
[tex]8 * \frac{db}{dt} = -30[/tex]
Divide both sides by 8
[tex]\frac{db}{dt} = -\frac{30}{8}[/tex]
[tex]\frac{db}{dt} = -3.75[/tex]
HELP QUICK help find the value of x and the measure of each angle
Answer:
A = 102° B = 78°
Step-by-step explanation:
(3x + 12°) + (2x + 18°) = 180°
5x = 180° - 12° - 18°
5x = 150|:5
x = 30°
Answer: x=30 A=102 B=78
Step-by-step explanation:
These are linear pairs so they add up to 180.
Your equation is: 3x+12+2x+18=180
5x+30=180
x=30
Plug x into the equations to find their values.
3(30)+12=102
2(30)+18=78
11x^2-2x^3+7 and -x^2+6x-7 as sum
Answer:
-2x³+10x²+6x
Step-by-step explanation:
-2x³+11x²+0x+7
0x³ - x²+ 6x-7
_____________
-2x³+10x²+6x+0
_____________
Ocuocktxjrxutxjxttuxudutx
Given:
The stem and leaf plot of a data set is given.
Legend:1|0 represents 10.
To find:
The original data set for the given stem and leaf plot.
Solution:
It is given that 1|0 represents 10 in the given stem and leaf plot. Using this, the original data set from the given stem and leaf plot is:
10, 11, 14, 21, 24, 24, 27, 29, 33, 35, 35, 35, 37, 38, 40, 41.
These values are in ascending order.
Therefore, the original set of data is 10, 11, 14, 21, 24, 24, 27, 29, 33, 35, 35, 35, 37, 38, 40, 41.
NO LINKS OR ELSE YOU'LL BE REPORTED!Only answer if you're very good at Math.No guessing please.
The director of health services is concerned about a possible flu outbreak at her college.She surveyed 100 randomly selected residents from the college's dormitories to see whether they had received a preventive flu shot.The results are shown below.What is the probability that a dormitory resudent chosen at random from this group had a flu shot, given that he is male?
A: 39/80
B: 13/17
C: 39/100
D: 51/100
=============================================================
Explanation:
The "given that he is male" stated at the end means we only focus on the male column. This is because we know 100% that the person selected is male. Either we're told this by someone else, or we can determine this another way.
There are 39 males that got the flu shot out of 51 males total. The probability we're after is 39/51 = (3*13)/(3*17) = 13/17
It's effectively saying: out of every 17 males, 13 of them got the flu shot.
18.96 x 2.03 correct to 2 significant figures equals what?
9514 1404 393
Answer:
38
Step-by-step explanation:
The product of the given numbers is 38.4888. Rounding this to two significant digits gets you 38.
There is a bag filled with 3
blue marbles, 7 red and 1 yellow.
Deeka picks out a marble from
the bag, notes its colour and
replaces it. She then takes
another marble out of the bag.
What is the probability of getting
exactly 1 blue?
Answer:
6/11 you could pull one of the three blues first or one of the three blues second
At least that's my best guess
Answer:
48/121
Step-by-step explanation:
In symbols:
(P blue ∩ P non blue) ∪ (P non blue ∩ P blue)
∩ = *
∪ = +
Since the marble is replaced, the total probability is always the same
(3/11 * 8/11) + (8/11 * 3/11)
24/121 + 24/121 = 48/121
what is the measure of angle D?
A.) 75
B.) 80
C.) 95
D.) 110
Answer:
D = 110
Step-by-step explanation:
MPTS is similar to CDHK
That means
angle M = C
P = D
T = H
S = K
We know P = 110 so D = 110
I need the answer plsss
Answer:
Its H
There should be one dot on 4, 2 dots on 2, 3 dots on 1, 3 dots on 0, 1 dot on 7, 1 dot on 3
Step-by-step explanation:
brainly plz!
61% of all statistics classes require a statistical calculator and 29% require the use of a computer that has statistical software of the classes that require a statistical calculator 16% also require the use of a computer if statistics course is selected at random find probability of statistical calculator
Answer:
Step-by-step explanation:
Given
61% of all statistics classes require a statistical calculator.
29% require the use of a computer that has statistical software.
of the classes that require a statistical calculator 16% also require the use of a computer.
if statistics course is selected at random find probability of statistical calculator.
Events
A = calculator
O = computer
P(A) = 0.61
P(O) = 0.29
P(A and O) = 0.16*0.61 = 0.0976
if statistics course is selected at random find probability of statistical calculator.
Answer is part of information given : P(A) = 0.61
P(calculator | computer)
= P(A & O)/P(O)
= 0.0976/0.29
= 976/2900
= 244/725
(=0.33655 approx.)
p(computer given calculator)
P(O|A) = P(A & O)/P(A)
= 0.0976/0.61
= 976/6100
= 0.16 (as per given information)
Are they mutually exclusive (they means P(calculator | computer) and p(computer given calculator) ??)
They are not mutually exclusive.
They are referring to the same thing: classes that use both, BUT using a different sample space.
are they independent
They are not independent. If they are, the conditional probabilities would be both zero.
Simplify Expressions. Which expression is
equivalent to 5x - 2 + 2x - 6
7X-8
3X-8
7x - 4
3X - 4
Answer:
7x - 8
Step-by-step explanation:
Hope this helps!
Which of the following is a point-slope equation of a line with the point (-6,2)
and a slope of ? 1/2
Answer:
Choose (D)
y-y1=m(x-x1)
y-2=1/2(x+6)
Solve for r.
-3r-9=1r+2
Answer:
[tex] - 3r - 9 = 1r + 2 \\ - 3r - r = 11 \\ - 4r = 11 \\ r = - \frac{11}{4} [/tex]
I need help ASAP please eeeee
Answer:
46
Step-by-step explanation:
2×(3×1 + 3×5 + 1×5) = 46 centimeters squared
You pick a card at random.
2 3 4 5
What is P(odd)?
Write your answer as a percentage.
Answer:
1/2-50%..?
Step-by-step explanation:
The probability of picking an odd numbered card is 50%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, the numbers on cards are 2 3 4 5.
Number of favorable outcomes = 2
Total number of outcomes = 4
Probability of getting odd numbers = 2/4
= 0.5
= 0.5 ×100
= 50%
Therefore, the probability of picking an odd numbered card is 50%.
To learn more about the probability visit:
https://brainly.com/question/11234923.
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In ΔFGH, f = 7.2 cm, g = 1.2 cm and h=6.6 cm. Find the area of ΔFGH to the nearest 10th of a square centimeter.
9514 1404 393
Answer:
3.6 cm²
Step-by-step explanation:
Heron's formula is usually used for calculating triangle area from side lengths.
The semiperimeter is ...
s = (7.2 +1.2 +6.6)/2 = 7.5
Then the area is ...
A = √(s(s -f)(s -g)(s -h)) = √(7.5(0.3)(6.3)(0.9)) = √12.7575
A ≈ 3.57176 cm²
The area of ΔFGH is about 3.6 square centimeters.
The area of a square is64. Cm
What is the length of its side
Answer:
The length is 8 cm. Since its a square, so the length of both its sides are equal.
l^2=64
where l=length of side
square root both sides
then, l=8
Answer:
8cm is the length of its side.
Step-by-step explanation:
Troy has already spent 2 minutes on the phone, and he expect to spend 3 more minutes with every phone call he routes. In all How many phone calls dose troy have to route to spend a total of 32 minutes on the phone?
2 divided by 32 is 16 so im gonna say 16
16 is ur answer
Help meeee pleasssseeee
Answer:
x = 8
Step-by-step explanation:
The side-splitter theorem states that when a line that is parallel to the third side of a triangle intersects the other two sides of the triangle, it divides the two sides proportionally.
Applying this theorem, we have the following equation:
x/52 = 2/13
Cross multiply
x*13 = 2*52
13x = 104
13x/13 = 104/13
x = 8
Nhan and Phuong both left town A for town B at 5 am . After 5 hours , Nhan and Phuong were 102 km and 52 km away from town B respectively . The ratio of Nhan's speed to Phuong's speed was 3 : 4 and their speeds remained the same the whole journey . At what time did Nhan reach town B ? Show your full work.
Answer:
Nhan reach town B at 13:24 pm
Step-by-step explanation:
Let
Speed of Nhan=3x km /hour
Speed of Phoung=4x km/hour
After 5 hours,
Distance covered by Nhan=3x(5)=15 xkm
Distance covered by Phuong=4x(5)=20x km
Total distance covered by Nhan to reach town B=15x+102 km
Total distance covered by Phuong to reach town B=20x+52 km
Distance between town A and town B for both person is same therefore,
[tex]15x+102=20x+52[/tex]
[tex]102-52=20x-15x[/tex]
[tex]50=5x[/tex]
[tex]x=10[/tex]
Speed of Nhan=3(10)=30 km/h
Speed of Phuong=4(10)=40 km/h
Total distance between town A and town B=102+15(10)=252 km
Time taken by Nhan to reach town B from town A=[tex]\frac{distance}{speed}[/tex]
Time taken by Nhan to reach town B from town A=[tex]\frac{252}{30}=8.4 hours[/tex]
[tex]8.4 hours=8+0.4\times 60[/tex]
=8 hours 24 minutes
1 hour=60 minutes
Nhan reach town B at 13:24 pm
