1) The equation of the parallel line in Slope Intercept Form is; y = -x - 1
2) The equation of the perpendicular line in Slope Intercept Form is;
y = ³/₂x - 4
How to write equation in Slope Intercept Form?1) When two lines are parallel, it means their slopes are the same.
Formula for equation in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, slope of y = -x + 1 is m = -1.
Equation of parallel line is;
(y - (-5))/(x - 4) = -1
y + 5 = -x + 4
y = -x - 1
2) When two lines are perpendicular, it means their slopes are the negative inverse of each other. Thus;
Slope of line = -2/3 and so slope of perpendicular line = 3/2. Thus, equation of new line is;
(y + 1)/(x - 2) = 3/2
2y + 2 = 3x - 6
2y = 3x - 8
y = ³/₂x - 4
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In analyzing hits by certain bombs in a war, an area was partitioned into regions, each with an area of km2. A total of bombs hit the combined area of regions. Assume that we want to find the probability that a randomly selected region had exactly 3 hits.
x is 3 that is the number of hits
e = 2.71828 is the Euler number
μ is the mean in the given interval = 0.967
There is 5.72% probability that a randomly selected region had exactly three hits.
Let X be the random variable denoting the number of bombs hitting the selected sample.
The following formula determines the likelihood that x in a Poisson distribution corresponds to the number of successes of a random variable.
P(X = x) = e^₋μ × μˣ / (x)!
Here, X is the random variable denoting the number of bombs hitting the selected sample.
μ is the mean number of hits per region.
e is the constant value.
Since 535 bombs struck a total of 553 regions, the ratio of strikes per region to the total number of regions is 535 to 553.
μ = 535 / 553
μ = 0.967
Assume that we want to find the probability that a randomly selected region had exactly 3 hits.
which means, P(X = 3)
P(X = x) = e^₋μ × μˣ / (x)!
P(X = 3) = e^₋0.967 × (0.967)³/ (3)!
= 0.057
There is approximately 5.72% probability that a randomly selected region had exactly three hits.
Your question was incomplete. Please find the missing content here.
In analyzing hits by certain bombs in a war, an area was partitioned into 553 regions, each with an area of 0.95 km². A total of 535 bombs hit the combined area of regions. Assume that we want to find the probability that a randomly selected region had exactly 3 hits.In applying the Poisson probability distribution formula, P(X) = e^₋μ × μˣ / (x)!, identify the values of μ, x and e. Also , briefly describe what each of those symbols represent.
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will give brainliest
Answer:
f(x) = x^(1/2) + 3
Step-by-step explanation:
Translating to the right 3 units would change these:
0^(1/2) = 0 /// 3 units to the right would be (0,3)
1^(1/2) = 1 //// 3 units to the right would be (1,4)
4^(1/2) = 2 //// 3 units to the right would be (4,5) etc
In the figure, two poles are 25 m and 30 m high. A cable 16 m long joins the tops of the poles. Find the distance between the poles. HELP PLEASE.
Answer:
The distance between the poles is approximately 15.2 m.
Step-by-step explanation:
GivenTwo poles of 25 m and 30 m height,Distance between tops of the poles is 16 m.To findThe distance between the polesSolutionThe distance between the poles is the segment d which connects the top of the shorter pole with the point at 5 m from the top of the longer pole, which is the difference of lengths of poles.
The three points form a right triangle, with hypotenuse of 16 m, and legs 5 m and d.
Use Pythagorean to find the value of d:
[tex]d=\sqrt{16^2-5^2} =\sqrt{256-25} =\sqrt{231} =15.2[/tex] m (rounded)find the volume, show solution pls
The volume of the square prism shown is 1568 cubic meters
Volume of square prismThe formula for calculating the volume of square prism is expressed as;
V = Base area * height/3
Determine the base are
B = 14 * 14
B = 196 square meters
Determine the height
h = √25² - 7²
h = √625 - 49
h = 24m
Substitute
Volume = 196. * 24/3
Volume = 196 * 8
Volume = 1568 cubic meters
Hence the volume of the square prism shown is 1568 cubic meters
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Simplify each expression by combining like terms
-5(n-5)+3(n+1)
Answer:
-2n + 28
Step-by-step explanation:
-5(n-5) + 3(n+1)
Let's distribute!
-5n + 25 + 3n + 3
Now we can add the like terms (n's with n's and numbers with numbers)
-2n + 28
Answer: -2n+28
Step-by-step explanation:
We can use the distributive property to solve this problem.
-5n+25+3n+3
-2n+28
[19. Solve the given radical equation: √3x +31= x+7.
Step-by-step explanation:
√3x+31=x+7
√3x=+7-31
DBS by√3
√3x/√3=7-31/√3
x=−12.12435565298
x=12.1
If $1 in U.S. Dollars is equivalent to 0.1273 Chinese yuan, convert 13,000 to yuan.
Answer:
1654.9
Step-by-step explanation
1/0.1273 = 13000/x
x=1654.9
a) 11 pounds, 8 pounds
O Like terms
11 pounds - 8 pounds =
O Not like terms
Answer:
Like terms
Step-by-step explanation:
Both terms have the same unit, which is pounds.
HELP ASAP
What is the perimeter of rectangle MNOP, rounded to the nearest tenth of a meter?
M
60°
N
O
O
28 m
79.2 m
67.6 m
88.1 m
76.5 m
30°
Answer: 76.5 meters
Step-by-step explanation:
To find the side lengths you use trig ratios for 30,60,90 triangles. The ratio is n (attached to the opposite side of the 30-degree angle, or the smallest leg), n[tex]\sqrt{3}[/tex] (attached to the opposite side of the 60-degree angle, or the longest leg), 2n (attached to the hypotenuse). Using the inner triangle you can use 2n=28 to find the side opposite the 30-degree angle, 14. Then you plug 14 into every n and add the sides. the full answer is 76.4974226 but this problem said to round making your final answer 76.5 meters. always remember to give proper units.
Daniel wrote the following two-column proof for the given information.
The information given about the proof does that Daniel made an error on line 2.
How to illustrate the information?Given:
1. AB = 3x +2; BC = 4x + 8; AC = 38
2. AB + BC = AC incorrect (not an angle angle addition postulate)
3. 3x+2 + 4x + 8 = 38 correct
4. 7x + 10 = 38 correct
5. 7x = 28 correct
6. x = 4
Daniel made an error on line 2.
Here is the complete question:
Daniel wrote the following two-column proof for the given information. Given: AB = 3x + 2; BC = 4x + 8; AC = 38 Prove: x = 4 Statements Reason 1. AB = 3x + 2; BC = 4x + 8; AC = 38 1. Given 2. AB + BC = AC 2. Angle Addition Postulate 3. 3x + 2 + 4x + 8 = 38 3. Substitution Property of Equality 4. 7x + 10 = 38 4. Combining Like Terms 5. 7x = 28 5. Subtraction Property of Equality 6. x = 4 6. Division Property of Equality On which line, did Daniel make his error? line 2 line 3 line 4 line 5
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1/2oz 3x day for 7 days how many doses will a patient use
The amount of dose is 10.5oz
How to determine the dose?The dosage is given as:
1/2oz 3x day for 7 days
This means that:
The patient will use 1/2 oz 3 times daily for 7 days
So, the dose is
Dose = 1/2 oz * 3 * 7
Evaluate the product
Dose = 10.5oz
Hence, the amount of dose is 10.5oz
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A manufacturer knows that their items have a normally distributed length, with a mean of 14.2 inches, and standard deviation of 1.9 inches. If one item is chosen at random, what is the probability that it is less than 11.9 inches long? Round your answer to 4 decimal places.
The probability that it is less than 11.9 inches long will be 0.11304.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
A manufacturer knows that their items have a normally distributed length, with a mean of 14.2 inches, and standard deviation of 1.9 inches.
If one item is chosen at random.
Then the probability that it is less than 11.9 inches long will be
Then the z-score will be
z = (11.9 – 14.2) / 1.9
z = –1.21
Then the probability will be
P(x < 11.9) = P(z < –1.21)
P(x < 11.9) = 0.11304
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Solve for x 3x – 2(3x – 2) = 2(4 – x) + 3
Answer:
x = -7Step-by-step explanation:
First, lets open up the parentheses.
3x - 6x + 4 = 8 - 2x + 3
Combine like terms.
-3x + 4 = 11 - 2x
Add 2x to both sides
-x + 4 = 11
Subtract 4 from both sides
-x + 4 -4 = 11 -4
Simplify
-x = 7
Divide both sides by -1
x = -7
Hope this helps! (:
Answer:
x = -7
Step-by-step explanation:
3x – 2(3x – 2) = 2(4 – x) + 3
The first step is to distribute when solving for x
3x – 6x +4 = 8 – 2x + 3
Then combine like terms
-3x+4=-2x+11
Add 3x to each side
-3x+3x+4=-2x+3x+11
4 = x+11
Subtract 11 from each side
4-11 = x+11-11
-7 = x
(-a, 0)
(0, b)
(0,0)
(0,-b)
What is the perimeter of the polygon in the diagram?
(a,0)
Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary. show work
f(x) = - 0.5x + 2
g(x) = x^3 - 5x^2 + 3
The points of intersection for the two functions and round to the nearest tenth are (0.5, 1.4) and (4.85, -0.3)
System of equationsGiven the following function
f(x) = - 0.5x + 2
g(x) = x^3 - 5x^2 + 3
The point of intersection is the point where f(x) = g(x)
x^3 - 5x^2 + 3 = - 0.5x + 2
x^3 - 5x^2 + 3 + 0.5x - 2 = 0
x^3 - 5x^2 + 0.5x + 1 = 0
Factorize and determine the value of x
x = 0.53 and 4.85
If x = 0.53
f(0.53) = -0.5(0.53) + 2
f(0.53) = -0.265 + 2
f(0.53) = 1.375
If x = 4.85
f(4.85) = -0.5(4.85) + 2
f(4.85) = -2.425 + 2
f(4.85) = -0.245
Hence the points of intersection for the two functions and round to the nearest tenth are (0.5, 1.4) and (4.85, -0.3)
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Really confused don’t understand please help me
Answer:
62cm²Step-by-step explanation:
Surface Area Formula
SA = 2lw + 2lh + 2hw
2 * 2 * 5 + 2 * 2 * 3 + 2 * 3 * 5 =
62cm²
1) (b + a) = 4; use a = 1 and b = 3
2) c(b + b); use b = 1 and c = 5
3) 4+ pm; use m = 4 and p =3
4) 5+ pm; use m = 4 and p = 2
5) m(p + 2); use m = 5 and p = 2
6) h+j²; use h = 1 and j = 4
7) y-(x - 5); use x = 5 and y = 6
8) 4xy; use x = 5 and y = 2
9) n(p + 3); use n = 2 and p = 2
10) y +x+x; use x = 3 and y=5
11) 6+ a-b; use a = 4 and b = 4
The equations will be solved by putting the values of the variables in the bracket.
How to calculate the values?1. (b + a) = 4; use a = 1 and b = 3
( 1 + 3) = 4
2) c(b + b); use b = 1 and c = 5
5(1 + 1)
= 5 × 2 = 10
3) 4+ pm; use m = 4 and p =3
= 4 + (4 × 3)
= 4 + 12
= 16
4) 5+ pm; use m = 4 and p = 2
= 5 + (2 × 4)
= 5 + 8
= 13
5) m(p + 2); use m = 5 and p = 2
= 5(2 + 2)
= 5 × 4
= 20
6) h+j²; use h = 1 and j = 4
= 1 + 4²
= 17
7) y-(x - 5); use x = 5 and y = 6
= 6 - (5 - 5)
= 6 - 0
= 6
8) 4xy; use x = 5 and y = 2
= 4 × 5 × 2
= 40
9) n(p + 3); use n = 2 and p = 2
= 2(2 + 3)
= 10
10) y +x+x; use x = 3 and y=5
= 5 + 3 + 3
= 11
11) 6+ a-b; use a = 4 and b = 4
= 6 + 4 - 4
= 6
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Please can you help me
Answer:
92.16Step-by-step explanation:
(-41.8 + 32.2)² =
(-9.6)² =
92.16
Answer:
92.16
Step-by-step explanation:
solving the brackets first, -41..8 + 32..2 equals -9.6 in total. The bracket has a square around it so our answer would be the square of wat ever we get in the bracket meaning (-9.6)^2 which gives us 92.16
0.3(8-2x) - 1.2(2-3x) < -21
Answer:
x=-7
Step-by-step explanation:
0.3(8-2x) - 1.2(2-3x) < -21
2.4 - 0.6x - 2.4 + 3.6x < -21
3x < -21
x < -7
What is the range of these weights?
79 g
88 g
116 g
109 g
93 g
Answer:
[tex]\huge\boxed{\sf 37 }[/tex]
Step-by-step explanation:
Highest weight = 116 g
Lowest weight = 79 g
Range:= Highest weight - lowest weight= 116 g - 79 g
= 37
[tex]\rule[225]{225}{2}[/tex]
Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are
common catches. The mean length of a bluefish is 267 millimeters with a standard deviation of
39 mm. For pompano, the mean is 155 mm with a standard deviation of 28 mm.
Using the normal distribution, it is found that due to the greater z-score, Stewart caught the longer fish relative to the same specie.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.To find who caught the longer fish relative to the same specie, we need to find out who had the higher z-score.
Stewart caught a bluefish with a length of 322 mm, hence the parameters are as follows:
[tex]X = 322, \mu = 267, \sigma = 39[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{322 - 267}{39}[/tex]
Z = 1.41
Gina caught a pompano with a length of 176 mm, hence the parameters are as follows:
[tex]X = 176, \mu = 155, \sigma = 28[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{176 - 155}{28}[/tex]
Z = 0.75.
Hence Stewart caught the longer fish relative to the same specie.
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A desk is on sale for $123.20, which is 72% less than the regular price.
What is the regular price?
Answer:
170.833
Step-by-step explanation:
we have to find real value which has to be find.
let take it as x,
in the question they said reduction percentage is equal to $123
then x*72/100=$123
x=$123*100/72
x=12300/72
x=170.8333
Answer:
I believe it's 211.90$.
Ethel is in town for the day making several purchases on her credit card. She spends $154.18 on groceries and $122.79 on tops at a sale at the local dress shop. Then she goes by to pay the utility bill, which is $219.54. How much did she charge to the nearest dollar?
Answer:
$497
Step-by-step explanation:
Added all three purchases (154.18 + 122.79 + 219.54) will give you $496.51. Rounded to the nearest dollar, you get $497.
Evaluate the expression for s = -15. -S=
Answer:
-S = 15
Step-by-step explanation:
You are asked to find the opposite of the given value.
OppositeThe opposite of an integer value is obtained by changing its sign.
S = -15
-S = -(-15) = 15
__
Additional comment
Equivalently, you are multiplying by -1. The product of an even number of minus signs is a plus sign. We usually don't write the plus sign for a numerical value.
Which list shows all the factors of 24?
A. 1, 2, 3, 4, 6, 8, 12, 24
B. 1, 2, 3, 4, 6, 12, 24
C. 1, 2, 4, 5, 6, 12, 24
D. 1, 2, 4, 6, 12, 24
Answer:
A. 1, 2, 3, 4, 6, 8, 12, 24
Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.Calculate, to four decimal places, the first ten terms of the sequence. an = 1 +(−4/9)^n
The first ten terms of the sequence [tex]a_n=1 + (-\frac{4}{9} )^n[/tex] is 0.5556, 1.1975, 0.9122, 1.039, 0.9827, 1.0077, 0.9966, 1.0015, 0.9993 and 1.0003
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given that:
[tex]a_n=1 + (-\frac{4}{9} )^n\\\\When\ n=1:a_1=1 + (-\frac{4}{9} )^1=0.5556\\\\When\ n=2:a_2=1 + (-\frac{4}{9} )^2=1.1975\\\\When\ n=3:a_3=1 + (-\frac{4}{9} )^3=0.9122\\\\When\ n=4:a_4=1 + (-\frac{4}{9} )^4=1.039\\\\When\ n=5:a_5=1 + (-\frac{4}{9} )^5=0.9827\\\\When\ n=6:a_6=1 + (-\frac{4}{9} )^6=1.0077\\\\When\ n=7:a_7=1 + (-\frac{4}{9} )^7=0.9966\\\\When\ n=8:a_8=1 + (-\frac{4}{9} )^8=1.0015\\\\When\ n=9:a_9=1 + (-\frac{4}{9} )^9=0.9993\\\\[/tex]
[tex]When\ n=10:a_{10}=1 + (-\frac{4}{9} )^{10}=1.0003\\[/tex]
The first ten terms of the sequence [tex]a_n=1 + (-\frac{4}{9} )^n[/tex] is 0.5556, 1.1975, 0.9122, 1.039, 0.9827, 1.0077, 0.9966, 1.0015, 0.9993 and 1.0003
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What are the solutions to the equation? 5x² + 20x = 9 Complete the square to solve. 2145 5 -2 √145 5 0-2± 0-4± -4 29 5 145 5
Answer: [tex]x=-2 \pm \sqrt{29/5}[/tex]
Step-by-step explanation:
[tex]5x^2 + 20x=9\\\\5(x^2 + 4x)=9\\\\5\left((x+2)^2 -4 \right)=9\\\\5(x+2)^2 - 20=9\\\\5(x+2)^2 = 29\\\\(x+2)^2 = \frac{29}{5}\\\\x+2 =\pm \sqrt{29/5}\\\\x=-2 \pm \sqrt{29/5}[/tex]
Wxyz is a dilation image of wxyz. Wich is the correct description of the dilation?
Solve 2w2 + 12w + 10 = 0 by completing the square
A)
w = –15, w = 5
B)
w = –5, w = –1
C)
w = –5, w = 1
D)
w = 5, w = 1
The value of w is -1 and -5.
The correct option is (B)
What is equation?
A mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
Given:
2w² + 12w + 10 = 0
First, divide through by 2
2w²/2 + 12w /2 + 10/2 =0/2
w² + 6w + 5 = 0
now, Take half of the w term and add - subtract the square of it
w² + 6w + 5 + 3² - 3² = 0
w² + 2*3w + 3² + 5 - 9 = 0
(w+3)² = 4
w+3 = ±2
w = +2 - 3, -2-2
w= -1 and -5.
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Hay 20% mas duendes que magos en el club de magia. Hay 120 duendes en el club de magia.
¿Cuántos magos hay en el club de magia?
Answer:
Hay 600 en el club de magia.