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Work Shown:
[tex]A = (x_1,y_1) = (-2,4) \text{ and } B = (x_2, y_2) = (1,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-1)^2 + (4-0)^2}\\\\d = \sqrt{(-3)^2 + (4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
I used the distance formula.
A slight alternative is to plot the points to form a right triangle. The hypotenuse is the segment from A to B. Then use the pythagorean theorem to find the hypotenuse. Take note how a 3-4-5 right triangle forms.
HELPP I AM STUCK IN THIS PROBLEM AND NEED IT BY TMR!!
Answer: 100 scores
Step-by-step explanation:
Let the number of points on your fifth test be x
Hence,
[tex]\displaystyle\\\frac{59+80+65+96+x}{5}=80\\[/tex]
Multiply both parts of the equation by 5:
300+x=80*5
300+x-300=400-300
x=100
At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151. There are 6 fewer male teachers than there are female teachers. The number of female teachers is 1/16 the number of girls. How many boys are there at the school? boys
Using a system of equations, it is found that there are 204 boys at the school.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable x: number of boys in the school.Variable y: number of girls in the school.Variable z: number of male teachers in the school.Variable w: number of female teachers in the school.The average of the number of boys, girls, male teachers, and female teachers is 117, hence:
(x + y + z + w)/4 = 117
x + y + z + w = 468.
The average of the number of boys, girls, and male teachers is 151, hence:
(x + y + z)/3 = 151
x + y + z = 453.
Then:
x + y + z + w = 468.
453 + w = 468
w = 15.
There are 6 fewer male teachers than there are female teachers, hence:
z = w - 6 = 15 - 6 = 9.
So:
x + y + z = 453.
x + y = 444.
The number of female teachers is 1/16 the number of girls, hence:
y = 16w = 16 x 15 = 240.x = 444 - y = 444 - 240 = 204.There are 204 boys at the school.
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Simplify the quantity 12 minus three fifths times the square root of 25 end quantity squared plus the quantity 2 minus 4 end quantity squared.
1,804
814
85
18
The value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85
How to evaluate the expression?The expression is given as
(12 - 3/5√25)^2 + (2 - 4)^2
Evaluate the square root of 25
So, we have
(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3/5 * 5)^2 + (2 - 4)^2
Evaluate the product
So, we have
(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3)^2 + (2 - 4)^2
Evaluate the difference
So, we have
(12 - 3/5√25)^2 + (2 - 4)^2 = 9^2 + (2 - 4)^2
Evaluate the exponent and the sum
So, we have
(12 - 3/5√25)^2 + (2 - 4)^2 = 85
Hence, the value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85
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Which number rounds to 3,000 if you round it to the nearest thousand, AND to 2,500 if you round it to the nearest hundred?
Answer:
2,739 and 2,489
Step-by-step explanation:
There are many solutions to both problems:
(Rules)
If the number is 5 or higher round (up)
If the number is 4 or lower round (down)
2,739⇒3,000
↑↑↑
Higher than 500 so round up to get 3,000
2,489⇒2,500
↑↑
Higher than 50 so round up to get 2500
2,739 and 2500 are both possible solutions.
f(9)=-4(9)^2-4(9)+18=
The heights of young women are approximately normal with mean 64.5 inches and standard deviation 2.5 inches. what are the deciles of this distribution?
Deciles are 61.3 and 67.7
What are deciles?
Deciles are measures of position calculated on a set of data. The deciles are the values that separate a distribution into ten equal parts, where each part contains the same number of observations). The decile is a member of the wider family of quantiles.
Given:
Normal distribution =64.5 inches
Standard deviation=σ =2.5 inches
So, here the z- score for left decile= -1.28
and for right decile= +1.28
we know,
z= x-[tex]\mu[/tex]/σ
x= zσ + [tex]\mu[/tex]
x=-1.28*2.5 + 64.5
x= 61.3 and,
x= 1.28*2.5 + 64.5
x=67.7
hence, the deciles are 61.3 and 67.7
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Which of the following is an equivalent expression of 15x2 +12x + 8?
Answer:
15 (x + 2\/5)^2 + 28\/5
Step-by-step explanation:
What is the slope of the line that passes through the points (4, -6) and (-2, 3)?
Write your answer in simplest form.
Answer:
-3/2
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (3 - (-6))/(-2 - 4)
slope = (3 + 6)/(-6) = 9/(-6)
slope = -3/2
Answer:
Step-by-step explanation: 3/-2
Write the equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form.
The equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y = -2/3x + 1
Equation of a lineThe equation of a line is expressed as;
y = mx + b
m is the slope
b is the y-intercept
Given the equation -3x + 2y = 12
2y = 3x + 12
y = 3/2x + 6
From the equation, the slope that is perpendicular to the slope is -2/3
Determine the equation
y-(-5) = -2/3(x-3)
y+5 = -2/3x + 6
y = -2/3x + 6 - 5
y = -2/3x + 1
Hence the equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y = -2/3x + 1
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Which of the following options are examples of how you can name the angle? Select all that apply.
Answer:thr lerrkmaf
Step-by-step explanation:
and we are so cool DEA
How many ounces of a 12% alcohol solution must be mixed with 9 ounces of a 20% alcohol solution to make a 16% alcohol solution?
Answer:
9 ounces
Step-by-step explanation:
Let x = number of ounces of 12% solution.
0.12x + 0.2 × 9 = 0.16(x + 9)
0.12x + 1.8 = 0.16x + 1.44
-0.04x = -0.36
x = 9
Answer: 9 ounces
find the area of the shaded region.
round to the nearest tenth.
The area of the shaded region is 294.4 square meters
How to find the area of the shaded region?The given parameters are represented on the figure
By this;
The area of the shaded region is the sum of the area of the major sector and the area of the triangle
The area of the major sector is
A1= ∅/360 * πr²
The area of the triangle is
A2 = 0.5r²sin(x)
So, the total area is
Total = ∅/360 * πr² + 0.5r²sin(x)
This gives
Total = (360 - 130)/360 * 3.14 * 11.1^2 + 0.5 * 11.1^2 * sin(130 deg)
Evaluate
Total = 294.4
Hence, the area of the shaded region is 294.4 square meters
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Three angles are shown, ZHRM, ZHRD, and ZDRM.
D
M
H
If m/HRM = 54°, m/HRD =
m/DRM =
(²7*+11) ².
4
R
(1/22 +22), ar
x
and
what is the value of x?
Answer:
28
Step-by-step explanation:
By the angle addition postulate,
[tex]54=\frac{1}{2}x+22+\frac{1}{4}x+11 \\ \\ 54=\frac{3}{4}x+33 \\ \\ 21=\frac{3}{4}x \\ \\ x=28[/tex]
what is the fraction form of 10.0833333... repeating
What is 10.0833333 as a fraction?
To write 10.0833333 as a fraction you have to write 10.0833333 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
10.0833333 = 10.0833333/1 = 100.833333/10 = 1008.33333/100 = 10083.3333/1000 = 100833.333/10000 = 1008333.33/100000 = 10083333.3/1000000 = 100833333/10000000
And finally we have:
10.0833333 as a fraction equals 100833333/10000000
Please help this is due tomorrow
Answer: 150, 4/2, 0.5/2
Step-by-step explanation:
The endpoints of AB are A(-8,-6) and B(-3,-1). Point C lies on Ab and is 3/5 of the way from A to B. What are the coordinates of point C?
Answer: C(-6.125,-4.125)
Step-by-step explanation:
[tex]\displaystyle\\A(-8,-6)\ \ \ \ B(-3,-1)\\Let\ \frac{3}{5}=\lambda \\Hence,\\\boxed {x_C=\frac{x_1+x_2\lambda}{1+\lambda} }\ \ \ \ \ \ \boxed {y_C=\frac{y_1+y_2\lambda}{1+\lambda} }\\\\x_1=-8\ \ \ \ x_2=-3\\\lambda=\frac{3}{5} \\\\\lambda=\frac{0.6*5}{5}\\\\\lambda=0.6\\\\x_C=\frac{-8+(-3)*0.6}{1+0.6} \\\\x_C=\frac{-8-1.8}{1.6} \\\\x_C=\frac{-9.8}{1.6} \\\\x_C=-\frac{9.8*10}{1.6*10} \\\\x_C=-\frac{98}{16} \\\\x_C=-6.125\\\\\\[/tex]
[tex]\displaystyle\\y_1=-6\ \ \ \ y_2=-1\ \ \ \ \lambda=0.6\\\\y_C=\frac{-6+(-1)*0.6}{1+0.6} \\\\y_C=\frac{-6-0.6}{1.6}\\\\y_C=\frac{-6.6}{1.6} \\\\y_C=-\frac{6.6*10}{1.6*10} \\\\y_C=-\frac{66}{16} \\\\y_C=-4.125[/tex]
[tex]Thus,\ C(-6.125,-4.125)[/tex]
Which relation is also a function? 25pts!!!!!!!!
determine a skier's velocity in km/h, if it takes her 1.7 min to ski down a 1.67 km slope
Answer:58.8km/h
Step-by-step explanation: V= 1.67/1.7= 0.98 km/min
0.98*60min=58.8
If you roll a standard 6 sided die and you get paid $1 for every spot it lands on (so if you roll a 5 that would mean $5), what's the average payout for one roll?
Answer:
20
Step-by-step explanation:
pls help with this question ASAP
What equations do u insert in between these numbers to get the answer
a.5 8 3 9 =50
b.12 6 2 10=14
c.4 5 6 10=24
d.7 4 6 9 7= 16
e.4 9 6 2 =52
f.45 5 9 3 7=102
hduodoydiyd9ydiydoyeykdoyx95eeykyei6djj
Step-by-step explanation:
a) 5
One pipe can fill a tank in 8 minutes, a second can fill it in 12 minutes and a third can fill it
in 24 minutes. If the tank is empty how long will it take the three pipes, operating together,
to fill it?
1) 6х - 4 = 5х - 11 ; ??
2) 0,3( х -2) = 0,6 + 0,2(х+4) ; ??
[tex] \bf\longrightarrow \: 6x - 4 = 5x - 11 \\ \bf\longrightarrow \: 6x - 5x = - 11 + 4 \\ \bf\longrightarrow \: x = - 7[/tex]
2) 0.3(x-2) = 0.6 + 0.2(x+4) ↓[tex] \bf\longrightarrow \: 0.3(x - 2) = 0.6 + 0.2(x + 4) \\ \bf\longrightarrow \: 0.3x - 0.6 = 0.2x + 1.4 \\ \bf\longrightarrow \: 0.3x - 0.2x = 1.4 + 0.6 \\ \bf\longrightarrow \: 0.1x = 2 \\ \bf\longrightarrow \: x = \frac{ \cancel2}{ \cancel0.1} \\ \bf \longrightarrow \: x = 20[/tex]
what is the perimeter of the vertices (1,4),(-1,-2),(2,0),(4,0) to the nearest hundredth
The Perimeter of the quadrilateral = 16.93 units
How to Find the Perimeter of a Quadrilateral?The perimeter of the quadrilateral with the given vertices is the sum of the distance between every vertices.
Calculate the distance between the vertices using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Name the vertices as shown below:
A(1,4)
B(-1,-2)
C(2,0)
D(4,0)
Distance between A and B:
AB = √[(−1−1)² + (−2−4)²]
AB = √(4 +36)
AB = 6.32 units
Distance between B and C:
BC = √[(−1−2)² + (−2−0)²]
BC = 3.61 units
Distance between C and D:
CD = √[(4−2)² + (0−0)²]
CD = 2 units
Distance between A and D:
AD = √[(4−1)² + (0−4)²]
AD = 5 units.
Perimeter of the quadrilateral = AB + BC + CD + AD = 6.32 + 3.61 + 2 + 5
Perimeter of the quadrilateral = 16.93 units
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I need help with this ASAP please
Answer:
c between 30 and 40 mins
Step-by-step explanation:
if you look at the graph that's the only line going down.
What is this expression in simplified form?
Any help?
Answer Im thinking 7 but i don't know for sure
Step-by-step explanation:
A 2-cup bottle of glass cleaner costs $6.56. What is the price per fluid ounce?
Answer:
82 cents per ounce
Step-by-step explanation:
There are 8 oz in a cup so two cups = 16 ounces
$6 .56 / 8 oz = $ .82 / oz
The first term of arithmetic sequence is 2 and 10th term is 39 find the 30th term
47.
48.
3m-4+2
m+5
j³-64
j-4
49.
-5p+4p² +4
p-2
50. (4p + 3p²-1) ÷ (p + 4)
51. (20x² 13x + 2) = (5x - 2)
52. (12x² - 6x³ - 3-9x) ÷ (3x − 3)
53. (8x² - 2x - 3) + (2x + 1)
54.(-3x² + 6x³ - 4 - x) ÷ (2x + 1)
-
Please solve this
Answer:
29282829939999999 and yea
In a track meet, Team A won 3 more medals than two times the medals won by Team B. Team A won 9 more medals than Team B, Find the number of medals for each team. Show all set-up, work, and write a complete sentence for your answer.
The number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.
How to solve Algebra Word Problems?
Team A won 3 more medals than two times the medals won by Team B.
If the number of medals won by team B is x, than;
Number of medals won by team A = 3 + 2x
Number of medals won by team B = x
Also, we are told that Team A won 9 more medals than Team B.
Thus;
(3 + 2x) = x + 9
2x - x = 9 - 3
x = 6
3 + 2x = 3 + 2(6) = 15 medals
Thus, we conclude that the number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.
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Z is a standard normal random variable. what is the value of z if the area to the right of z is 0.0122?
The value of z = 2.25
Given that z is a standard normal random variable.
Now the area under a standard normal curve between two z -values gives the probability of z lying between these two z-values.
Given that the area to the right of z = 0.0122
That is probability that the standard normal random variable lies after z = 0.0122
Total probability = 1
Therefore half the area under the standard normal curve = 0.5
Therefore, 0.5 - 0.0122 = 0.4878
We will find the corresponding z-value for this probability value from the normal tables. This is because normal tables gives area between two standard normal variables.
The table value corresponding to 0.4878 = 2.25
Therefore, z -value = 2.25
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