The coordinates of G(4, 4) , H (0, 2), J(8, 0)
In order to construct the three sets of relationships between the coordinates of each triangle's three sides' ends and the shared midpoint, we must first set up the three sets of relationships.
G(x(G), y(G))
K(2, 3) (2, 3)
M(6, 2) (6, 2)
H(x(H) and y(H))L (4, 1)
J(x(J), y(J))
K(2, 3) at the midway of side GH
According to the x-component:
x(H) = x(G - x(H))/2
x(G)-[x(H)-x(G)] = 2*x(H)
x(H) + x(G) = 4
x(H) = 4 - x(G) (G)
According to the y-component:
y(H) plus [y(G) - y(H)]/2 = 3.
2*y(H) plus [y(G-y(H)] = 6
y(H) + y(G) = 6
y(H) = 6 - y(G) (G)
Midpoint L(4) and side JH(1):
According to the x-component:
(x(H) + [x(J) - x(H)]/2) equals four.
2*x(H) plus [x(J)-x(H)] = 8
x(H) + x(J) = 8
x(H) = 8 - x(J) (J)
According to the y-component:
y(H) = y(J - y(H)]/2 + y(J) = 1
y(J) - y(H) = 2*y(H)
y(H) + y(J) = 2
y(H) = 2
Side GJ with M(6, 2) as the midpoint:
For the x - component, the formula is: x(J) = [x(G) - x(J)]/2 = 6 2*x(J) = [x(G)- x(J)] = 12 x(J) = 12 - x (G)
y(J) + [y(G) - y(J)]/2 = 2 2*y(J) + [y(G)- y(J)] for the y-component. = 4 y(J) = 4 - y + y(G) = 4 y(J) (G)
The x and y coordinates may now be easily separated, and we can use algebra to isolate each one and determine its location.
x(H) = 4 - x(G), 8 - x(J), and 12 - x(J) (G)
Because x(H) = x (H)
4 - x(G) = 8 - x(J) (J)
8 - x(J) - 8 - x(G) - 4 = -x(J) x(J) x(J) = 4 + x (G)
Using 1.c above and this relationship now x(J) = x(J), so:
-2 * x(G) = -8 x(G) =, 4 12 - x(G) = 4 + x(G) 12 - x(G) - x(G) - 12 = 4 + x(G) - x(G) - 12
Given that x(J) = 4 + x(G) above, x(J) = 4 + 4 = 8 and x(H) = 4 - x(G) = 4 - 4 = 0 respectively.
Let's now perform the identical procedure using the y-coordinates.
y(H) = 6 - y(G), y(H) = 2 - y(J), y(J) = 4 - y(G),
and since y(H) = y(H), 6 - y(G) = 2 - y(J), -y(G) = 2 - y(J) - 6 = -y(J) - 4 y(G) = y(J) + 4 Now that y(J) = 4 - y,
we may substitute (G).
y(H) = y(G) - 2 and y(H) + 4 - y(G) = 2
and y(H) + 4 - y(G) = 2 - 4 and y(G)
Since y(H) = 6 - y(G)
according to 1. above, y(H) = y(G) - 2 + 6 - y(G) 2 * y(H) = 4 y(H) = 2 y(H) = 2 - y(J) 2 = 2 - y(J) y(J) = 4 - y(G) 0 = 4 - y(G) y(G)
H(x(H), y(H)), G(x(G), y(G)), and J(x(J), y(J)) are the results.
To determine the coordinates of the angles or triangle's tips, we used the midpoints of each side.
The coordinates are: H (0, 2) G(4, 4) J(8, 0)
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The area of the rectangle shown is 44 m².
Work out the missing length x.
Answer:
x = 12 m
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × width
here A = 44 , then
x × 3 [tex]\frac{3}{4}[/tex] = 44 ( change mixed number to improper fraction )
x × [tex]\frac{11}{3}[/tex] = 44 ( multiply both sides by 3 to clear the fraction )
11x = 132 ( divide both sides by 11 )
x = 12 m
Solve for the Value of R
Answer:
whats the question
#3 a. Complete the table for f(x) = 2x
#3b Use the coordinate points from the table to graph f(x) = 2^x
The complete table of values of the function is
x | f(x)
0 | 1
1 | 2
2 | 4
3 | 8
The ordered pairs are (x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)
How to make a table of values for the following equation?The equation of the function is given as
f(x) = 2ˣ
On the incomplete table of values, we have the following x values
x = 0, 1, 2, 3
Next, we substitute x = 0, 1, 2, 3 in the equation f(x) = 2ˣ
So, we have:
f(0) = 2⁰ = 1
f(1) = 2¹ = 2
f(2) = 2² = 4
f(2) = 2³ = 8
So, the complete table is
x | f(x)
0 | 1
1 | 2
2 | 4
3 | 8
When represented as ordered pairs, we have
(x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)
See attachment for the graph
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[tex]-2 1\frac{1}{3} w +6=15[/tex]
help me pls
The solution for the variable w according to the given equation; -21 ⅓ w + 6 = 15 as required in the task content is; w = -27/64.
What is the value of variable w?It follows from the task content that the value of variable w is time determined according to the given equation as in the task content.
Given the equation; -21 ⅓ w + 6 = 15.
First, the mixed number must be converted to a fraction so that we have;
-21 ⅓ = -64/3.
Hence, the equation becomes;
-64w/3 + 6 = 15
Multiply both sides of the equation by 3 so that we have;
-64w + 18 = 45
-64w = 45 - 18
-64w = 27
w = -27/64.
Ultimately, the solution for variable w according to the equation as given in the task content is; w = -27/64.
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Part (a) and part (b).
The time spent exercising for a student who spends 6 hours texting is 6 hours.
The scatter plot is given in the question,
As per the given scatter plot, we take the two points (9, 1) and (3,7).
The equation of the line of best fit:
Let the approximate equation would be as:
y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 9, y₁ = 1
x₂ =3, y₂ = 7
y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
y - 1 = (7 - 1)/(3 - 9)](x - 9)
y - 1 = (- 6/6)(x - 9)
y - 1 = -1(x - 9)
y = -x + 9+ 1
y = -x + 10 ...(i)
The time spent exercising by a student who spends 4 hours texting
This means that x = 4.
Substitute the value x =4 in the equation (i), and solve for y
y = -4 + 10
y = 6
Hence, the time spent exercising for a student who spends 6 hours texting is 6 hours.
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I need help! could someone help me with this? is from Imagine Math
Answer:
1st: One solution
2nd: Infinite many solutions
3rd: No solution
4th: No Solution
5th: One Solution
Step-by-step explanation:
1st:
The solution is (6,9)
x = 6 if a vertical line going though (6,0)
y = 9 is a horizontal line going through (0,9)
The two lines with intersect at (6,9)
2nd:
3y = 15x + 6 If you divide all the way through by 3, you get
y = 5x + 2
This is identical to the first equation given. Since it is the same line, the answer is infinite many solutions.
3rd:
3y = x + 2 Divide all the way through by 3
y = 1/3 x + 2/3
9y = 3x + 7 Divide all the way through by 9
y = 1/3 x + 7/9
Since the slopes are the same in both equations (1/3), these line are parallel and will never intersect.
4th:
Since the slopes are both the same (2), the lines are parallel and they will never intersect, so the answer is no solution.
5th:
2y = 3x Divide both sides by 2
y = 3/2
-5y = -10 Divide both sides by -5
y = 2x
These equations are proportional so they go through the origin. They both have a y intercept of zero, so they intersect at (0,0). The answer is one solution.
Find the distance between the points (8,–2) and (8,7)
Answer:
9 units
Step-by-step explanation:
We see that on the x-axis, everything is equal.
On the y-axis, there are -2 and 7.
So we are finding the distance between -2 and 7
|-2|+|7|=9
So the distance between the points is 9 units.
What is the area of a circle with a diameter of 5 feet? Round to the nearest thousandth.
(7x-7)
63°
(3x +45)
(9-4)
Find x and y
Answer:
x+7=4/3x-1/3 One solution was found : x = 22 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : ... 3x-9/4x-12: correct answer right here
Step-by-step explanation:
The radioactive substance cesium-137 has a half-life of 30 years. The amount At (in grams) of a sample of cesium-137 remaining after t years is given by the following exponential function.
=At26612t30
Find the initial amount in the sample and the amount remaining after 80 years.
Round your answers to the nearest gram as necessary.
Sanjay and his paving crew laid 40 yards of new pavement. Jack and his crew just took over, and they can lay 15 yards of new pavement per hour.
Write an equation that shows the relationship between the number of hours Jack's crew works, x, and the total number of yards of pavement laid, y.
The equation that shows the relationship between the number of hours Jack's crew works, x, and the total number of yards of pavement laid, y will be;
⇒ y = 40 + 15x
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Sanjay and his paving crew laid 40 yards of new pavement.
And, They can lay 15 yards of new pavement per hour.
Now,
Let the number of hours Jack's crew works = x
And, The total number of yards of pavement laid = y
Hence, We can formulate;
An equation that shows the relationship between x and y will be;
y = 15x + 40
Thus, The equation that shows the relationship between the number of hours Jack's crew works, x, and the total number of yards of pavement laid, y will be;
⇒ y = 40 + 15x
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A pack of cards is shuffled and a card is chosen at random.
What is the probability of getting a black card?
Answer:
[tex]\dfrac{1}{2}[/tex]
Step-by-step explanation:
Probability:Number of cards = 52
Number of black cards = 13 (club) + 13 (spade)
= 26
[tex]\sf P(\text{getting a black card})=\dfrac{26}{52}[/tex]
[tex]\sf =\dfrac{1}{2}[/tex]
Differentiate the function with respect to x.
The differentiation of the given function is [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex].
In the given question we have to differentiate the given function with respect to x.
The given function is f(x)= [tex]tan(x^4)\cdot(3x^3+2)[/tex].
We have to differentiate the given function so we differentiate using the Product Rule.
The Product Rule of Differentiation is
d/dx[h(x)g(x)]=h(x) d/dx g(x)+g(x) d/dx h(x)
In the given function the value of
h(x) = [tex]tan(x^4)[/tex] and g(x) = [tex](3x^3+2)[/tex]
So;
f'(x)= [tex]tan(x^4)[/tex]d/dx [tex](3x^3+2)[/tex] + [tex](3x^3+2)[/tex] d/dx [tex]tan(x^4)[/tex]............(1)
We firstly find the value of d/dx [tex](3x^3+2)[/tex] and d/dx [tex]tan(x^4)[/tex].
We firstly find the value of d/dx [tex](3x^3+2)[/tex]
As we know that d/dx of x^n =nx^(n-1) and d/dx a=0
So;
d/dx [tex](3x^3+2)[/tex]= 3 d/dx [tex]x^3[/tex]+d/dx 2
d/dx [tex](3x^3+2)[/tex]=3(3[tex]x^2[/tex])+0
d/dx [tex](3x^3+2)[/tex]=9[tex]x^2[/tex]
Now finding the value of d/dx tan([tex]x^4[/tex])
d/dx [tex]tan(x^4)[/tex] = d/dx [tex]tan(x^4)[/tex] d/dx [tex]x^4[/tex]
d/dx [tex]tan(x^4)[/tex]= [tex]sec^2(x^4)\cdot(4x^3)[/tex]
d/dx [tex]tan(x^4)[/tex]= [tex]4x^3sec^2(x^4)[/tex]
Now putting the values of differentiation in equation 1
f'(x)= [tex]tan(x^4)\cdot9x^2[/tex] + [tex](3x^3+2)\cdot4x^3sec^2(x^4)[/tex]
f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]3x^3\cdot4x^3sec^2(x^4)+2\cdot4x^3sec^2(x^4)[/tex]
Simplifying
f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{3+3}sec^2(x^4)+8x^3sec^2(x^4)[/tex]
f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex]
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3. Plumbers deal with measurements in inches and common fractions of an inch, while surveyors use feet and decimal
fractions of a foot. Often one trade needs to interpret the measurements of the other.
(a) A drain has a run of 52 ft at a grade of 1/8 in./in. The high end of the drain has an elevation of 126.30 ft. What is the elevation at the low end?
(b) The elevation at one end of a lot is 84.12 ft, and the elevation at the other end is 94.67 ft. Express the difference in elevation in feet and inches and rounded to the nearest 1/8 in
The elevation at the lower end of a drain is 119.8 feet. For the second drain difference in feet will be 10.55 feet and in inches will be 126.6 inch.
What is elevation?The height above or below a fixed reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. A vertical surface is depicted in an elevation when viewed from a point perpendicular to the viewer's picture plane. You are looking at the front elevation, for instance, if you are standing directly in front of a building and viewing its front. The height between a point and a horizontal surface is known as HEIGHT. The height of a point above (or below) sea level is known as its ELEVATION.
Here,
a. The length of drain= 52 feet
the gradual decrease=0.125 ft
elevation at high end=126.30 feet
elevation at low end,
=126.3-(52*0.125)
=126.3-6.5
=119.8 feet
b. The elevation at one end=94.67 feet
The elevation at other end=84.12 feet
The difference in elevation,
=94.67-84.12
=10.55 feet
=10.55*12
=126.6 inches
The elevation of a drain's lower end is 119.8 feet. The second drain will differ by 10.55 feet in feet and 126.6 inches in inches.
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Identify the property that justifies each step asked about in the answer area below.
Answer:
Commutative Property of Addition2. Distributive propertyStep-by-step explanation:Given[tex]Line 1: 4(8+9x)
SOMEONE HELP GEOMETRY THXX
The lines p and q are parallel.
What are alternate exterior angles?Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines, but on opposite sides of the transversal.
Given a figure,
Since, ∠ 1 ≅ ∠ 5 and they are alternate exterior angles, then we can conclude that p║q by alternate exterior angles theorem.
Hence, The lines p and q are parallel.
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Find the unit rate
Rahul travelled 348 miles in 6 hours
Answer:
Step-by-step explanation: 348 miles and 6 hours
how to interpret data from a frequency distribution
Answer:
The first column is usually for the categories of the data set and the second or third column is usually for the frequency of each category.
The number written on the right of each category is its frequency
Step-by-step explanation:
A baseball team has three different pitchers. Randy allowed
2
22 runs and pitched
3
33 innings. Felix allowed
4
44 runs and pitched
5
55 innings. Johan allowed
5
55 runs and pitched
7
77 innings.
Which pitcher has the lowest number of runs allowed per inning?
The pitcher that has the lowest number of runs allowed per inning is Randy.
Which pitcher has the lowest number of runs per inning?In order to determine the pitcher that has the lowest number of runs per innings, divide the number of runs of each player by the number of innings of that player.
Division is the mathematical operation that is used to calculate the quotient of two or more numbers. It entails grouping a number into equal parts using another number.
Number of runs per innings = number of runs / number of innings
Number of runs per innings for Randy : (2 / 3) = 0.667
Number of runs per innings for Felix : (4 / 5) = 0.80
Number of runs per innings for Johan: (5 / 7) = 0.714
Here is the complete question:
A baseball team has three different pitchers. Randy pitched 3 innings and allowed 2 runs, Felix pitched 5 innings and allowed 4 runs, and Johan pitched 7 innings and allowed 5 runs.
Which pitcher has the lowest number of runs allowed per inning?
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A client is to receive 1,800 mL of fluid during a 24-hour period. The client is to receive 3/4 of the fluid between 7 AM and 10 PM. Calculate how many mL the client will drink during that time
Answer:
1350 ml
Step-by-step explanation:
(1800 : 4) * 3
450 * 3
1350 ml
Name the image of R(1, 2) after a 270 rotation about (0, - 2)
The image after a 270 rotation is (4, -3)
How to determine the image after rotation about a point?
If the point of rotation is not the origin, the steps are as follows:
1. Subtract the point of rotation off each vertex point of
the shape
2. Rotate as you would around the origin
3. Add the point of rotation back to each vertex point of
the shape
Given: R(1, 2) after a 270 rotation about (0, - 2)
step1: (1-0, 2-(-2)) = (1, 4)
step 2: For rotation about the origin through 270°, the image is (y, -x). Thus, (1, 4) => (4, -1)
step 3: (4, -1) => (4+0, -1+(-2) ) = (4, -3)
Therefore, the image of R(1, 2) after a 270 rotation about (0, - 2) is (4, -3)
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A car can travel
198 miles on 9
gallons of
gasoline. How
much gasoline will
it need to go 462
miles?
Answer:
21 gallons
Step-by-step explanation:
[tex]\frac{9}{198} \times 462 \\ \\ =\frac{462}{22} \\ \\ =21[/tex]
Suppose a large shipment of stereos contained 18% defectives. If a sample of size 306 is selected, what is the probability that the sample proportion will differ from the population proportion by more than 6%? Round your answer to four decimal places.
The probability that the sample proportion of a large shipment of stereos will differ from the population proportion by more than 6% is 0.0063
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 18% = 0.18
sample size, n = 306
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.18(1 - 0.18)) / 306}
= √{(0.18 * 0.82) / 306}
= 0.02196
The probability
differ from the population proportion by less than 3%
|X - 0.18| > 0.06
X < 0.12 OR X > 0.24
P(z < 0.12) + P(z > 0.24 )
z score for z < 0.06
z = (0.12 - 0.18) / 0.02196
= -2.7322
p value for z < -2.7322 = 0.003146
z score for z > 0.06
z = (0.24 - 0.18) / 0.02196
= 2.7322
p value for z > 2.7322 = 1 - 0.99685 = 0.003146
The probability required = 0.003146 + 0.003146 = 0.006292 = 0.63%
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Solve for x X/11=2
x=?
Answer:
x = 22
Step-by-step explanation:
Solve for x:
x/11 = 2
multiply both sides by 11:
11(x/11) = 11(2)
x = 22
Answer:
x = 22
Step-by-step explanation:
[tex] \sf \frac{x}{11} = 2[/tex]
Use cross multiplication.
[tex] \frac{x}{11} = \frac{2}{1} \\ \\ \sf x = 2 \times 11 \\ \\ \sf \: x = 22[/tex]
What is the product of the complex numbers below? 7-i / 3+i
Answer: 2-i
Step-by-step explanation:
multiply the fraction by 3-i/3-i
r=6%
t=6years
I=480,00
p=?
Answer:
I=PRT/100
I100=PRT dbs by Rt
l100/RT = P
48000*100/6*6
P=
A car traveled 120 miles in 2.5 hours the line represents that relationship between the distance travels and the time it took. The point 1,48 is on the line.
PLEASE NEED HELP FOR THIS ONE THANKS
The average rate of change of f(x) on the interval 30 ≤ x ≤ 60 is r = 1/5.
How to get the average rate of change?For a function f(x), we define the average rate of change over an interval:
a ≤x ≤b is given by:
( f(b) - f(a))/(b - a)
In this case we have the function defined by the table and the interval:
30 ≤ x ≤ 60
On the table we can see:
f(60) = 19
f(30) = 13
Then the average rate of change is:
r = (19 - 13)/(60 - 30) = 6/30 = 1/5
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Pls help me, giving brainliest 50 POINTS!
Pls show your work and not only your answers pls
If you can’t answer it then don’t answer but if you can thank you
You will be reported if you put links
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex] \textsf{1. Numbers are : 36, 3, 12 } [/tex]
[tex] \textsf{36 = 2 × 2 × 2 × 2 × 2 × 1} [/tex][tex] \textsf{3 = 3 × 1 } [/tex][tex] \textsf{12 = 2 × 2 × 3 } [/tex][tex] \textsf{HCF = product of total common factors of} [/tex][tex] \textsf{all three numbers, i.e : 2 } [/tex]
[tex] \textsf{LCM = product of highest power of each factor } [/tex][tex] \textsf{present in any three of them,} [/tex][tex] \textsf{i.e : 2⁵ × 3 = 32 × 3 = 96} [/tex]
Similarly,
[tex] \textsf{2. Numbers are : 6, 54, 12} [/tex]
[tex] \textsf{6 = 2 × 3 } [/tex][tex] \textsf{54 = 2 × 3 × 3 × 3 } [/tex][tex] \textsf{12 = 2 × 2 × 3 } [/tex][tex] \textsf{GCD = 2 × 3 = 6 } [/tex]
[tex] \textsf{[ 2 and 3 are the only ones common} [/tex] [tex] \textsf{among all three ]} [/tex]
[tex] \textsf{LCM = 2² × 3³ = 4 × 27 = 108} [/tex]
[tex] \textsf{3. Numbers are : 16, 8, 12 } [/tex]
[tex] \textsf{16 = 2 × 2 × 2 × 2} [/tex][tex] \textsf{8 = 2 × 2 × 2 } [/tex][tex] \textsf{12 = 2 × 2 × 3 } [/tex][tex] \textsf{GCD = 2 × 2 = 4 } [/tex]
[tex] \textsf{LCM = 2⁴ × 3 = 16 × 3 = 48} [/tex]
Answer:
Numbers are : 36, 3, 12
36 = 2 × 2 × 2 × 2 × 2 × 1
3 = 3 × 1
12 = 2 × 2 × 3
HCF = product of total common factors of all three numbers, i.e : 2
LCM = product of highest power of each factor present in any three of them, i.e : 2⁵ × 3 = 32 × 3 = 96
Similarly,
2. Numbers are : 6, 54, 12
6 = 2 × 3
54 = 2 × 3 × 3 × 3
12 = 2 × 2 × 3
GCD = 2 × 3 = 6
[ 2 and 3 are the only ones common among all three ]
LCM = 2² × 3³ = 4 × 27 = 108
3. Numbers are : 16, 8, 12
16 = 2 × 2 × 2 × 2
8 = 2 × 2 × 2
12 = 2 × 2 × 3
GCD = 2 × 2 = 4
LCM = 2⁴ × 3 = 16 × 3 = 48
solve the system of equations by the addition method
x-y= -2
x+y=4
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is }. (Type an ordered pair.)
B. There are infinitely many solutions. The solution set is {(x,y)}.
(Type an equation.)
C. There is no solution. The solution set is Ø.
Answer:
(x, y) = (1, 3)
Step-by-step explanation:
You want to solve the system of equations x-y= -2; x+y=4 by the addition method.
Addition methodThe addition method seeks to eliminate one of the variables by adding the equations with appropriate multipliers so that one of the coefficients becomes zero.
Here, we observe that the coefficient of y in one equation is the opposite of that in the other equation. This means adding the two equations will cancel the y-terms:
(x -y) +(x +y) = (-2) +(4)
2x = 2 . . . . . . . . . . . . . . . . simplify; y-term is eliminated
x = 1 . . . . . . divide by 2
1 +y = 4 . . . . . . . substitute for x in the second equation
y = 3 . . . . . . . . . subtract 1
The solution is (x, y) = (1, 3).