[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{-2 -1}{1 +0} \implies \cfrac{ -3 }{ 1 }\implies -3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-3}(x-\stackrel{x_1}{0}) \\\\\\ y-1=-3x\implies y=-3x+1[/tex]
What is the location of the image of P(−8, 1) after a counterclockwise rotation of 90° about (−2, 6) ?
Answer:
(3, 0)
Step-by-step explanation:
Given:
Image: P = (-8, 1)Center of rotation: (-2, 6)Rotation rule for -90°: (x, y) → (y, -x)
As the center of rotation is not the origin, we cannot simply apply the above rule.
To rotate an image around a point other than the origin:
1. Subtract each point of the image from the point of rotation:
⇒ Point of rotation - point of image
⇒ (-2, 6) - P = (-2, 6) - (-8, 1)
= (6, 5)
2. Rotate this about the origin by applying the rotation rule:
⇒ (x, y) → (y, -x)
⇒ (6, 5) → (5, -6)
Add the point of rotation to each rotated point of the image:
⇒ (5, -6) + (-2, 6) = (3, 0)
Therefore, the location of the image of P (-8, 1) after a counterclockwise rotation of 90° about (-2, 6) is (3, 0).
Elaina Kicks A Soccer Ball With An Initial Velocity Of 28 feet per second at an angle of 58 to the horizon
Answer:
Hi,
Answer B
Step-by-step explanation:
after 1.484 s the ball hit the ground à 22.019 feet
yes the ball will be at a height of 2.93506334 feet when time is 1.348 s and height is 20 feet
no the max height happens at 11.0 has no thing to do with hitting the grat 2.937 s the ball is at -68.2754 feet
ound
How many gallons of
35
% alcohol solution and
50
% alcohol solution must be mixed to get
6
gallons of
40
% alcohol solution?
Answer:
Hi,
Step-by-step explanation:
I suppose you want an integer solution.
Let's say
a the number of gallons of 35% alcohol
b the number of gallons of 50% alcohol
[tex]\dfrac{35}{100}*a+\dfrac{50}{100}*b=\dfrac{40}{100}*6\\\\35*a+50*b=240\\\\7a+10b=48\\\\b=\dfrac{48-7a}{10}\\\\a=4+10*n\\\\b=\dfrac{48-7*(4+10*n)}{10}=2-7*n\\\\As\ b\ must\ be\ a\ positive\ number \ n=0\\\\so\ b=2\ and\ a= 4[/tex]
The endpoints of one diagonal of a rhombus are (-7, -2) and (-1, -4). If the coordinates of the 3rd vertex are (-6, -9), what are the coordinates of the 4th vertex? (-8, 13) (-2, 3) (-6, 13) (7, -8)
The coordinates of the 4th vertex of the rhombus are (-2,3)
How to determine the coordinates of the 4th vertex?The diagonals are given as:
(-7, -2) and (-1, -4)
The 3rd vertex is given as: (-6,-9)
Calculate the distance between the vertices of the diagonals and the 3rd vertex using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]
So, we have:
[tex]d_1 = \sqrt{(-7 + 6)^2 + (-2 + 9)^2} =\sqrt{50[/tex]
[tex]d_2 = \sqrt{(-1 + 6)^2 + (-4 + 9)^2} =\sqrt{50[/tex]
Let the 4th vertex be (x,y)
So, we have:
[tex]d_3 = \sqrt{(-7 - x)^2 + (-2 - y)^2} =\sqrt{50[/tex]
[tex]d_4 = \sqrt{(-1 - x)^2 + (-4 - y)^2} =\sqrt{50[/tex]
Equate d3 and d4
[tex]\sqrt{(-1 - x)^2 + (-4 - y)^2} = \sqrt{(-7 - x)^2 + (-2 - y)^2}[/tex]
Take the square of both sides
[tex](-1 - x)^2 + (-4 - y)^2 = (-7 - x)^2 + (-2 - y)^2[/tex]
Expand
[tex]1 + 2x + x^2 + 16 + 8y + y^2 = 49 + 14x + x^2 + 4 + 4y + y^2[/tex]
Evaluate the like terms
1 + 2x + 16 + 8y = 49 + 14x + 4 + 4y
Collect like terms
14x - 2x + 4y - 8y = 1 + 16 - 49 - 4
12x - 4y = -36
Divide through by 4
3x - y = -9
Next, we test the options in the above equation
Point (-8,13) means x = -8 and y = 13
So, we have:
3x - y = -9
3(-8) - 13 = -9
-37 = -9 --- this is false
Point (-2, 3) means x = -2 and y = 3
So, we have:
3x - y = -9
3(-2) - 3 = -9
-9 = -9 --- this is true.
Hence, the coordinates of the 4th vertex are (-2,3)
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Each student in Ms. Garai's class is either a junior or a senior. Ms. Garai has 30 students in her class, 24 of whom are juniors. Recently, she took some of the students from her class on a field trip. Of the 24 juniors in the class, 2/3 went on the trip.
Use this information to answer the questions below.
If not enough information is given to answer a question, click on "Not enough information."
(a) How many seniors are in the class?
(b) How many seniors from the class went on the field trip?
(c) How many juniors from the class went on the field trip?
Seniors in the class = total number of students - total number of juniors
30 - 24 = 6
Juniors that went on the field trip = 2/3 x 24 = 16 students
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A school has 100 windows. On a cool day, 95 of the windows were closed. Which decimal represents how many of the windows were open? *
Answer: 0.05
Step-by-step explanation:
Since 95 out of 100 were closed, the closed window is 95% = 0.95.
5 open windows = 5% = 0.05
If 12 photovoltaic cells at 0.5 V each produce a total of 6 V of potential energy and carry a 1A current to your phone, what is the power output of these cells and the resistance inside your phone? P = VI and R = V/I (Show calculations and units)
Answer:
The power output is 6 W. The resistance is 6 Ω.
Step-by-step explanation:
Power output= 6V * 1 A= 6W
Resistance= 6V/1A= 6 Ω
Can somebody help me out? Also please provide an explanation.
Answer:
38%
Step-by-step explanation:
Total: 93
Find percentage
Rain: 24
Snow: 11
24 + 11 = 35
Find what percentage of 90 35 is.
35 of 90 can be written as:
35
----
90
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
35 100
---- × ----
90 100
= ( 35 * 100/90) * 1/100 = 38.89/100
Therefore, the answer is 38.89%
A bacteria population has been doubling each day for the past 5 days. It is currently
100000. What was the population 5 days ago?
Give a non-zero counterexample to the following statement:
Every multiple of 10 is also a multiple of 30.
Answer:
20 or 40 or 50
(there are many others)
Step-by-step explanation:
A counterexample is an example that shows the statement is not true. The statement in this question is that if a number is a multiple of 10 (10, 20, 30, 40, 50, 60...) then it is a multiple of 30. Some numbers are, like 60 and 90, but not all numbers. So for example (counterexample) 20 is a multiple of 10 but NOT a multiple of 30.
40 is a multiple of 10, but NOT a multople of 30.
50 is a multiple of 10, but NOT a multiple of 30.
Seven more than a number is 15.
The equation is (Type an equation using x as the variable.)
Answer:
x + 7 = 15
Step-by-step explanation:
I hope the answer above was correct :)
Answer:
x + 7 = 15
Step-by-step explanation:
7 more is adding 7 to "a number" which is x. The sum is 15 so it shouldnt be that hard to put it all together
5b 2 −6b−2 is prime TURE OR FALSE!! 100 POINTS PLEASE HELP!!!!
The given quadratic expression; 5b² -6b -2 is prime because the discriminant is not a perfect square.
What is the discriminant of the expression?According to the task content; it is required to identify if the expression is prime.
On this note, it follows that the discriminant of the expression can be evaluated as follows;
= 36 -(4× 5 × -2)
= 76.
Hence, the expression is prime since 76 is not a perfect square.
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Keiko bought 13 pounds of sugar for $6. How many dollars did she pay per pound of sugar?
Step-by-step explanation:
13 pounds of sugar for $6.
for a single pound of sugar we need to divide everything by 13 to keep the same ratio (relationship).
1 pound cost then 6/13 = 0.461538462... ≈ $0.46
Which expression represents the perimeter of the triangle?
8x + 2
18x
8x
Answer:
8x
Step-by-step explanation:
(3x+1)+(3x-1), the 1's cross out, so it is 3x+3x=6x. 6x+2x=8x.
Answer:
8x
Step-by-step explanation:
got it right!!!
what is its first derivative
Answer:
2ax + b + C
where C is a constant.
Which of the following statements is true of all rotations?
Answer:
21.25 m/s
Explanation:
AVERAGE SPEED=
= \frac{s1 t1+ s2t2 + s3t3}{t1 + t2 + t3}=
t1+t2+t3
s1t1+s2t2+s3t3
= \frac{20 \times 10 + 30 \times 5 + 15 \times 5}{10 + 5 + 5}=
10+5+5
20×10+30×5+15×5
= \frac{200 + 150 + 75}{20}=
20
200+150+75
= \frac{425}{20}=
20
425
= 21.25 ms=21.25ms
can Someone helps me
Answer:
10.63
Step-by-step explanation:
To find the Hypotenuse we need to use Pythagorean Thereom. So plugging in the formula the square root of A squared plus B squared you get 10.63
Answer:
Step-by-step explanation:
To solve the triangle means to find ALL unknown elements of Δ ( sides and angles )
JH² = 8² + 7² = 113
JH = √113 ≈ 10.63 m
m∠H = β
[tex]\frac{8}{7}[/tex] = tan β ; β = arctan [tex]\frac{8}{7}[/tex] = [tex]tan^{-1}[/tex] [tex]\frac{8}{7}[/tex] ≈ 48.814°
m∠H ≈ 49 °
m∠J = 90° - 49° = 41 °
AB BG, AC GC, ZABC LGBC ZBACZBGC
A
B
#
C
G
1. What rigid transformation will take triangle GBC onto triangle ABC?
2. Explain why G' will coincide with A
3. Is triangle GBC congruent to triangle ABC? Explain your reasoning, and be sure to list any sides/angles you compared.
CAN SOMEONE HELP ME PLS, YOU’LL EARN FREE EASY POINTS IF IT’S THE RIGHT ANSWER, NO RANDOM ANSWERS BC YA’LL BE GIVING ME THE WRONG ANSWER SOMETIMES :(
Answer:
Step-by-step explanation:
1) Reflection over [tex]\overline{BC}[/tex]
2) The triangles are congruent by SAS, so when [tex]\triangle GBC[/tex] is mapped onto [tex]\triangle ABC[/tex], because points [tex]G[/tex] and [tex]A[/tex] are corresponding, [tex]G'[/tex] will correspond with [tex]A[/tex].
3) Yes, because [tex]\overline{BG} \cong \overline{AB}, \overline{GC} \cong \overline{AC}, \angle BAC \cong \angle BGC[/tex], so the triangles are congruent by SAS.
solve this algebra Sentence
1) A number is added to five is equal to twelve. write an algebra sentence then solve the number
Answer
Let x be that number We know x + 5 = 12 ( the number plus five equals to 12)=> x = 5-12 = 7 so, that number is 7.
explanation:
Hope this helps:)
:3
have a good day or a beautiful day:3
in a Table
Which statements comparing the functions are true?
Check all that apply.
f(x) and h(x) have x-intercepts.
Of(x), g(x), and h(x) have y-intercepts.
The domain of g(x) includes more values than the
domains of f(x) and h(x).
The range of g(x) includes more values than the
ranges of f(x) and h(x).
Og(x) has the greatest maximum.
h(x) has the lowest minimum.
The true statement about the functions is (d) the range of g(x) includes more values than the ranges of f(x) and h(x).
How to compare the three functions?The attached image represents the missing part of the question
From the attached image, we have the following properties:
All three functions have the same domain values (-4 to 1)The function g(x) includes more range values than othersh(x) has the greatest maximum of 2g(x) has the lowest minimum of -19The property 2 above is calculated as follows:
Range of g(x) =|-4 + 19| = 15
Range of f(x) =|1 + 2| = 3
Range of h(x) =|2 + 8| = 10
Hence, the true statement about the functions is (d) the range of g(x) includes more values than the ranges of f(x) and h(x).
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A survey of 25 randomly selected customers found the ages shown (in years). The mean is 32.64 years and the standard deviation is 9.39 years.
a) Construct a 80% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the interval have been met.
b) How large is the margin of error?
a) What is the confidence interval?
b) What is the margin of error?
The margin of error is
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A
Assuming that conditions have been met for the interval, we use the formula [tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex] where [tex]\bar{x}[/tex] represents the sample mean, [tex]t[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] is the sample size.
The critical value of [tex]t[/tex] for an 80% confidence level with degrees of freedom [tex]df=n-1=25-1=24[/tex] is equivalent to [tex]t=1.317836[/tex]
Thus, we can compute the confidence interval:
[tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}\\\\CI=32.64\pm1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\\\\CI\approx\{30.17,35.11\}[/tex]
Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.
Part B
The margin of error is [tex]\displaystyle t\frac{s}{\sqrt{n}}=1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\approx2.47[/tex]
The radius of a semicircle is 3 kilometres. What is the semicircle's perimeter?
Answer:
In terms of Pi: [tex]3\pi + 6[/tex] km
Exact value (rounded): 15.42477 km
Approximated (3.14): 15.42 km
Step-by-step explanation:
Hello!
A semicircle's perimeter can be found using the formula: [tex]P = \pi r + 2r[/tex]
We can plug in the values to solve for the perimeter.
Solve[tex]P = \pi r + 2r[/tex][tex]P = \pi(3)+ 2(3)[/tex][tex]P = 3\pi + 6[/tex]In terms of Pi, it is [tex]3\pi + 6[/tex],
Exact value of Pi, it is 15.42477
Approximation of Pi (3.14), it is = 15.42
qualities?
x + 4y > 12
3y > x + 6
The solution to the given system of inequality is (-12, 6).
System of equationsThese are equations that contains unknown variables.
Given the equations
x + 4y > 12
3y > x + 6
__________
x + 4y > 12
3y - x > 6
Subtract
4y - 3y > 12 - 6
y > 6
Substitute y = 6 into the equation
x + 4y >12
x + 4(6) > 12
x > -12
Hence the solution to the given system of inequality is (-12, 6)
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I need help asap !! I will mark Brainly!
Answer: x-axis
Explanation:
x-axis: it is the horizonzontal axisx-coordinates: it is the x-value of a point in reference to the x-axisy-axis: it is the vertical axisy-coordinates: it is the y-value of a point in reference to the y-axisHope that helps!
Write the equation of the line that passes through the points (4, -3) and (-5, 4).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.
Answer:
y₁ - y₂ = (-7/9)(x₁ - x₂)
Step-by-step explanation:
The general structure for an equation in point-slope form is:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope and the "x" and "y" values come from each point. To find "m", plug the values of each point into the equation.
Point 1: (4, -3) Point 2: (-5,4)
y₁ - y₂ = m(x₁ - x₂) <---- Original equation
-3 - 4 = m(4 - (-5)) <---- Plug values in for "x" and "y"
-7 = m(4 - (-5)) <---- Simplify left side
-7 = m(9) <---- Simplify within parentheses
-7/9 = m <---- Divide both sides by 9
I don't exactly understand what "fully simplified point-slope form" means because if all of the variables are plugged in, you wouldn't be left with an equation. It may just be asking for the slope, which in this case would make the equation look like this:
y₁ - y₂ = (-7/9)(x₁ - x₂)
It may want you to find the equation in slope-intercept form (y = mx + b), and you would have to find "b". Sorry I don't quite understand what exactly you are looking for.
Which statement about the point (-1,0) is true?
Answer:
Yes
Step-by-step explanation:
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A problem says an object's displacement is
88.8 m in a 123º direction. Which one of these
tables includes that information correctly?
The table that includes that information correctly when the problem says an object's displacement is 88.8 m is table B.
What is displacement?It should be noted that a displacement simply means the vector quantity that illustrates how far a particular place is.
In this case, the table that includes that information correctly when the problem says an object's displacement is 88.8 m is table B.
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Answer:A dude if you already know it say it to make it easier for people don't be lazy
Step-by-step explanation:
Given that 24w = 14ten .Find the unknown base
Answer:
w = 5
Step-by-step explanation:
24w = (14)10
2w + 4 = 10 + 4
2w = 10
w = 5
150pounds = what in kilograms
this is your answer.
Answer: 68.0389
Answer:
68.04 is the correct answer
I looked it up
r
2 cm
x = [?] cm
3 cm
Enter a decimal rounded to the nearest tenth.
Enter
Done
Answer:
x = 3.6
Step-by-step explanation:
By the property of intersecting chords, we have:5*x = 6*3-> 5x = 18-> x = 18/5-> x = 3.6