The correct answer is A. y - 3 = -6(x + 1) of the linear equation in point-slope form for the line that goes through (-1,3) and (1, -9).
To write the linear equation in point-slope form, we need to use the formula:
[tex]y - y_1 = m(x - x_1),[/tex]
where [tex](x_1, y_1)[/tex] represents one of the given points, and m represents the slope of the line.
Step 1: Find the slope (m):
[tex]m = \frac {(y_2 - y_1) }{(x_2 - x_1)}\\= \frac {(-9 - 3)} { (1 - (-1))}\=\frac {-12 } {2}= -6.[/tex]
Step 2: Choose one of the given points (-1, 3), and substitute its coordinates into the point-slope form:
[tex]y - 3 = -6(x - (-1)).[/tex]
Step 3: Simplify and rearrange the equation:
[tex]y - 3 = -6(x + 1)\\y - 3 = -6x - 6.[/tex]
Therefore, the correct equation is A. y - 3 = -6(x + 1).
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MATH!!! Volume of prisms stuff
need help fast given lim x→c f(x) = "-4" and lim x→c g(f) =1/5 what is lim x→c [g(f)/f(x)]
Work Shown:
[tex]\displaystyle \lim_{x \to c}f(x) = -4\\\\\\\lim_{x \to c}g(x) = 1/5\\\\\\L = \lim_{x \to c}\frac{g(x)}{f(x)}\\\\\\L = \frac{\displaystyle \lim_{x \to c}(g(x))}{\displaystyle \lim_{x \to c}(f(x))}\\\\\\L = \frac{1/5}{-4}\\\\\\L = (1/5)*(-1/4)\\\\\\L = -1/20\\\\[/tex]
Put simply, we divide the two given values g(x) = 1/5 over f(x) = -4 to end up with -1/20
An unusual number cube (with 6 sides) has the numbers 2, 2, 4, 4, 6, and 6 on its faces.
It is rolled once. Match the outcome to its probability.
1. P(2 or 4)
2. A(multiple of 2)
3. P(multiple of 3)
4. P(odd prime numbers)
2/3
0
1
1/3
Answer:
1. P(2 or 4) - 2/3
2. P(multiple of 2) - 1
3. P(multiple of 3) 1/3
4. P(odd prime numbers) 0
Step-by-step explanation:
Good luck lol
P(2 or 4) = 2/3
P( multiple of 2) = 1
P( multiple of 3) = 1/3
P(odd prime numbers) = 0
What is probability?Probability is the likelihood of an event happening or not.
Analysis:
possible outcome = (2,2,4,4,6,6) = 6
P(2 or 4)
n( 2) = required outcome = (2,2) = 2
P(2) = 2/6 = 1/3
n(4) = (4,4) = 2
P(4) = 2/6 = 1/3
P(2 or 4) = 1/3 + 1/3 = 2/3
n( multiple of 2) = (2,2,4,4,6,6) = 6
P( multiple of 2) = 6/6 = 1
n(multiple of 3) = (6,6) = 2
P(multiple of 3) = 2/6 = 1/3
P(odd prime numbers) = 0
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Which expression is equivalent to
(5ab)^3
30a b-7? Assume a≠0, b≠0.
1. a7b¹0/6
2. 125a¹8b21/30
3. 25a³b4/6
4. 25a9b¹0/6
The equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]\frac{(5ab)^3}{30ab^{-7}}[/tex]
Expand the numerator
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{125a^3b^3}{30ab^{-7}}[/tex]
Divide 125 and 30 by 5
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^3b^3}{6ab^{-7}}[/tex]
Apply the law of indices
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{3-1}b^{3+7}}{6}[/tex]
Evaluate the exponent
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{2}b^{10}}{6}[/tex]
Hence, the equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]
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how old is someone, who is a million minutes old?
Explanation and work out pls
Answer:
1.93 or 2 years old
Step-by-step explanation:
First divide 1,000,000 by 60 to get the hours then by 24 to get the days then by 30 to get the months then by 12 to get the years.
Answer:
2 years old(Rounded)
Keys:
YtvWhere Y is Years, m is minutes, and v is the default value for dividing minutes into years.
Step-by-step explanation:
Y = m ÷ v
m = 1,000,000
v = 525,600
m ÷ v = 1.903
Neyha has six number cards. Here are four of Neyha's cards. 8;8;8;8 The mean of all six cards is 8 The range of all six cards is 4 What are the other two cards?
After considering the given data we come to the conclusion that the two other cards are 6 and 10, under the condition that Neyha has six number cards. Here are four of Neyha's cards. 8;8;8;8.
Let us assume that the other two cards x and y.
The given mean of all six cards is 8. Then, the sum of all six cards is 48 (8×6). We have that four of the cards are 8s.
So, the summation of these four cards is 32 (8×4).
The dedicated range of all six cards is 4. Therefore, the difference between the largest and smallest card is 4.
Furthermore, we know that four of the cards are 8s, the other two cards must be different from 8.
Hence, we can consider that x and y are the smallest and largest numbers in the set.
Here we have to apply basic algebraic expression
We can perform the setting up two equations:
x + y = 48 - 32 = 16 (the summation of x and y is equivalent to the summation of all six cards minus the summation of the four 8s)
y - x = 4 (the difference considering y and x is equal to the range of all six cards)
Evaluating these equations simultaneously gives us:
y = 10
x = 6
Therefore, the other two cards are 6 and 10.
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Can a parabola have both a minimum and a maximum point? Explain.
Find a possible formula for the trigonometric function represented by the given table of values. (enter your answer in the form y = a cos(bx − c) d or y = a sin(bx − c) d. )
A function assigns the values. The function will be 8cos(2x-π)+4.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the maximum value is 12, while the minimum value is -4, therefore,
A = (Max-Min)/2 = 12-(-4)/2 = 8
D = (Max+Min)/2 = (12-4)/2 = 4
Period=π, but since x =-4 at 0 or π, therefore,
(2π/B) = π
B = 2π/π = 2
C/B = π/2, {∴At π/2 maximum}
C=π
Hence, the function will be 8cos(2x-π)+4.
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Please help is a choose al that apply
Answer:
Your answers are:
A, B and C
Step-by-step explanation:
So 12 over 3 is equal to 4 which is a Whole number. meaning Not a fraction, an Integer is a whole number (not a fractional number) that can be positive, negative, or zero. Rational numbers would include this example as well
Hope this helped have a wonderful day/night/afternoon
Can someone please help me with this? it's really important, ill give 10 points for this.
Answer:
ill answer
Step-by-step explanation:
but what is the question please make me brillianist
A bag contains 4 blue balls, 7 yellow balls and 4 white balls. Event A is defined as drawing a blue ball on the first draw and event B is defined as drawing a white ball on the second draw. If two balls are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form? A. B. C. D.
P(B|A) expressed in simplest form is 8/105.
What is the probability?Probability determines the chances that an event would happen. The chance of the event happening lies between 0 and 1.
P(B|A) = (number of blue balls / total number of balls) x (number of white balls / total number of balls - 1 )
(4/15) x 4/14 = 8/105
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PLEASE ANSWER THESE!!!!!!!!!!!!!!!!
Answer:
First one: X= 11.5
Second one: W = 3
X= 41.4°
Third one: 516.8
Step-by-step explanation:
Remember SOH CAH TOA when dealing with trigonometry and study the diagrams well
Ava earns 9.20 per hour for the first 6 hours she works each day then time and a half.
What is her pay if she works for 9 hours?
What is the length of segment XZ?
Answer:
24 is the length of segment XZ
What is the end behavior of the function f(x)=−1/4x^2?
Answer:
As x approaches infinity, f(x) approaches negative infinity
As x approaches negative infinity, f(x) approaches negative infinity
Step-by-step explanation:
Because the function goes in the downward direction on both sides, it would be negative infinity for both.
It's basically saying, as the x values go towards the positives, the y values go towards the negatives
and as the x values go towards the negatives, the y values go towards the negatives.
anyone know the answer
Answer:
y=x+4
Step-by-step explanation:
pretty sure
Which of the following choices is a reference angle to θ = 225º?
30 degrees
45 degrees
60 degrees
90 degrees
Answer:
45 degrees
Step-by-step explanation:
A reference angle can be found by identifying its terminal side and see by what angle the terminal side is close to the x-axis.
To do this, we can subtract this given angle by the nearest 90° angle.
270° is the closest.
[tex]\textsf {Solving :}[/tex]
[tex]\implies \textsf{Reference angle = 270 - 225}[/tex]
[tex]\implies \textsf {45 degrees}[/tex]
The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
As per the given angle,
θ = 225°
It is going to the third quadrant as shown below,
The reference angle is the angle from x-axis.
The angle from the negative x-axis will be as,
180° + x = 225°
x = 225° - 180° = 45°
Hence "The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°".
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how do u convert a percentages into fractions ??
Answer:
Step-by-step explanation:
To convert a percent to a fraction, we have to remove the percent sign and divide the given number by 100
ex: 11% = 11/100
There is a set of 10 jobs in the printer queue. One of the jobs in the queue is called job A. How many ways are there for the jobs to be ordered in the queue so that job A is the first to finish or the last to finish
The number of ways for the jobs to be ordered in the queue so that job A is the first to finish or the last to finish is; 2 * 9!
How to solve permutation and combination?We are told that;
There is a set of 10 jobs in the printer queue.
One of the jobs is job A. Thus, there are 9 other identified jobs.
Number of ways to order this nine jobs = 9!
Since the job A has to be ordered first or last, then;
Number of ways to order job A = 2 ways.
Thus;
Total number of ways to order the jobs in the given order = 2 * 9!
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If arc CE is 125°, what is the measure of angle CDE?
Check the picture below.
Answer:
A. 55
Step-by-step explanation:
10m−p=−n, for m
10m−p=−n, for m
10m−p=−n, for m
10m−p=−n, for m
Answer:
[tex]m=\dfrac{-n+p}{10}[/tex]
Step-by-step explanation:Solve for 'm'
To solve for 'm', we have to isolate 'm'.
First add p to both sides to cancel (-p) in the left side10m - p = -n
10m = -n + p
Now, divide the equation by the coefficient of 'm', which 10[tex]\sf\dfrac{10m}{m}=\dfrac{-n+p}{10}\\[/tex]
[tex]\sf \boxed{\bf m = \dfrac{-n+p}{10}}[/tex]
Need help checking my work for Trigonometry. Will mark brainist!
Answer:
1. 0.9925 (4 d.p.)
2. 17°
3. 67°
Step-by-step explanation:
Question 2
⇒ sin 83° = 0.9925461516...
⇒ sin 83° = 0.9925 (4 d.p.)
Question 3
[tex]\sf \implies \sin X=0.2923[/tex]
[tex]\sf \implies X=\sin^{-1}(0.2923)[/tex]
[tex]\implies \sf X=16.99570395...^{\circ}[/tex]
[tex]\implies \sf X=17^{\circ}\:\:(nearest\:degree)[/tex]
Question 4
Sine Ratio
[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuse (the side opposite the right angle)From inspection of the triangle:
[tex]\theta[/tex] = WO = OS = 24H = OW = 26Substitute the values into the formula and solve for W:
[tex]\implies \sf \sin(W)=\dfrac{24}{26}[/tex]
[tex]\implies \sf W= \sin^{-1}\left(\dfrac{24}{26}\right)[/tex]
[tex]\implies \sf W=67.38013505...^{\circ}[/tex]
[tex]\implies \sf W=67^{\circ}\:\:(nearest\:degree)[/tex]
While Al was staying overnight on vacation with his friends his only expenses were for food. Al spent $7.52 on lunch, $9.74 on dinner, and then $5.16 on breakfast the next morning. If Al had $2.68 left, how much money did he begin with?
$19.74
$25.10
$15.36
$22.42
Answer:
$25.10
Step-by-step explanation:
lunch=$7.52
dinner=$9.74
breakfast=$5.16
money left=$2.68
make total money he began with ‘x’
to find the total money he began with it will be
x-lunch+dinner+breakfast=money left
x-$7.52+$9.74+$5.16=$2.68
x-$22.42=$2.68
x=$2.68+$22.42
x=$25.10
Please Help I Don't Understand!
Answer:
5.3
Step-by-step explanation:
Since they are similar triangles, we assume the ratio between AM/AN is equal to the ratio between MB/NC.
AM/AN = 6/8 = 3/4
If MB is 4
3/4 = MB/NC = 4/NC
3/4 = 4/NC
3NC = 16
NC = 16/3
16/3 = 5.333333
Find the value of x.
Round to the nearest tenth.
B
63
142°
61
A
C
X
x = [?
X
Law of Cosines: c² = a² + b² - 2ab cos C
The value of x in the triangle using the cosine rule is 22.1 degrees.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:
c² = a² + b² - 2ab cos C
Where a, b, c are the sides and C is the angle opposite side c.
Using cosine rule:
8² = 14² + 19² - 2(14)(19) * cos(x)
cos(x) = 0.9267
x = 22.1°
The value of x in the triangle using the cosine rule is 22.1 degrees.
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Using the law of Cosines, the value of x to the nearest tenth is 77.8
Law of CosinesFrom the question, we are to determine the value of x
Using the law of Cosines
c² = a² + b² - 2ab cos C
c is the unknown side length
a and b are the given side lengths
and C is the included angle
From the given information,
a = 63
b = 62
C = 142°
Then,
x² = 63² + 61² -2×63×61 cos 142°
x² = 3969 + 3721 -7686(-0.788)
x² = 7690 + 6056.568
x² = 13746.569
x = √13746.569
x = 77.8
Hence, the value of x to the nearest tenth is 77.8
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Which three ordered pairs describe points that are 5 units away from P(-1,2)?
A. (1,5)
B. (-6,7)
C. (-1,-3)
D. (4,2)
E. (2,-2)
The ordered pair that is 5 units away is (-1, -3)
What is a line?
A line is a distance between two points.
Analysis:
see attached file.
In conclusion, the ordered pair is (-1, -3)
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6. Find the principal value of each of the following to the nearest minute:
Arccsc (1.607)
A. 38°64
B. 39°24'
C. 38°48'
D. 38°32'
E. 39°37'
F. 38°29'
The principal value of Arccsc (1.607) to the nearest minute is 38°29'
To answer the question, we need to know what arccsc is
What is arccsc?Arccsc is the inverse of the cosec of an angle.
Let x = arccsc(1.607)
So, taking the inverse, we have
csc(x) = 1.607
Since csc(x) = 1/sinx, we have
1/sinx = 1.607
sinx = 1/1.607
sinx = 0.6223
The value of x
Taking inverse, we have
x = arcsin(0.6223)
x = 38.483°
Since 60' = 1°, we have
x = 38 + 0.483° × 60'/1°
x = 38° + 28.98'
x = 38°28.98'
x ≅ 38°29'
So, the principal value of Arccsc (1.607) to the nearest minute is 38°29'
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The table shows values for a quadratic function.
What is the average rate of change for this function for the interval from x = 1
to x = 3?
The average rate of change for this function for the interval from x = 1
to x = 3 will be 8. Therefore option B is correct.
How to find the average rate of change of something?Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where when
[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]
The average rate of change can be calculated as;
From x=1 to x=3,
y = 2 and y = 18
Therefore, based on the table, when:
[tex]x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18[/tex]
Then:
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8[/tex]
Therefore option B is correct.
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On the blue prints for a house, 2 inches represents 3 feet. If the width of a room on
the plan is 6½ inches, what is the actual width of the room?
Please help!!
Answer:
The actual width would be 9.75 feet. (I think).
Step-by-step explanation:
If two inches represents three feet, then two inches also represents thirty-six inches. You would then have to set up the proportion [tex]\frac{2}{36} = \frac{6.5}{x}[/tex]. Solving that proportion would get you an answer of 117 inches, equal to 9.75 feet. I hope this helps! :)
The area of a square is 36 square feet. each side of the square measures