Answer:
y = 3x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x - y + 12 = 0 ( subtract 3x + 12 from both sides )
- y = - 3x - 12 ( multiply through by - 1 )
y = 3x + 12 ← in slope- intercept form
with slope m = 3
Parallel lines have equal slopes , thus
y = 3x + c ← is the partial equation
To find c substitute (2, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = 3x - 1 ← equation of parallel line
PLEASE HELP!!!
Rectangle EFGH is reflected across the origin and then rotated 90° clockwise about the origin, forming rectangle E″F″G″H″. What are the coordinates of rectangle E″F″G″H″?
(A.) E″ (1, –5), F″ (1, –1), G″ (4, –1), H″ (4, –5)
(B.) E″ (–1, –5), F″ (–1, –1), G″ (–4, –1), H″ (–4, –5)
(C.) E″ (–1, 5), F″ (–1, 1), G″ (–4, 1), H″ (–4, 5)
(D). E″ (5, 1), F″ (1, 1), G″ (1, 4),
H″ (5, 4)
Answer:
c.
Step-by-step explanation:
90 degrees clockwise is (x,y)-(y,-x)
Answer:
The answer is A
Step-by-step explanation:
Took the test
please help. evaluate 5!.
Answer:
120
Step-by-step explanation:
! means to multiply it by every number less than itself.
Not counting 1, this means 5*4*3*2.
20*3*2
60*2
120
The answer is 120.
Answer:
120
Step-by-step explanation:
Example 2
A black die and a white die are thrown at the same
time. Display all the possible outcomes. Find the
probability of obtaining:
a) a total of 5
b) a total of 11
c) a 'two' on the black die and a six' on the white die.
It is convenient to display all the possible outcomes
on a grid. This is called a possibility diagram
It’s example 2 please help:)
Answer:
Total possible outcomes = 6×6 = 36
a) P(5) = 1/9
b) P(11) = 1/18
c) P(two and six) = 1/36
Step-by-step explanation:
A black die and a white die are thrown at the same time.
Each die has six sides so total possible outcomes are
Total possible outcomes = 6×6 = 36
The possible outcomes are given below:
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
a) Find the probability of obtaining a total of 5
Number of ways to get a total of 5 = (1, 4) (2, 3) (3, 2) (4, 1)
Number of ways to get a total of 5 = 4
The probability is given by
P = Number of desired outcomes/total number of outcomes
P(5) = 4/36
P(5) = 1/9
b) Find the probability of obtaining a total of 11
Number of ways to get a total of 11 = (5, 6) (6, 5)
Number of ways to get a total of 11 = 2
The probability is given by
P(11) = 2/36
P(11) = 1/18
c) a 'two' on the black die and a six' on the white die.
There is only one way to get a two on the black die.
Probability of obtaining a two on the black die = 1/6
There is only one way to get a six on the white die.
Probability of obtaining a six on the white die = 1/6
P(two and six) = 1/6×1/6
P(two and six) = 1/36
A forestry study found that the diameter of the trees in a forest is normally distributed with mean 34 cm with a standard deviation of 8 cm. A group of 4 trees will be used as timber if the average of the 4 trees diameter is not too thick or thin. Specifically it is desired for the mean diameter to be between 30 and 40 cm in diameter. Find the probability that a randomly chosen group of 4 trees can be used as timber
Answer:
The probability that a randomly selected group of four trees can be used as timber is 4.5 × 10⁻⁵
Step-by-step explanation:
The given parameters are;
Mean = 34 cm
The standard deviation = 8 cm
The mean
The Z score is [tex]Z=\dfrac{x-\mu }{\sigma }[/tex], which gives;
For x = 30 we have;
[tex]Z=\dfrac{30-34 }{8 } = -0.5[/tex]
P(x>30) = 1 - 0.30854 = 0.69146
For x = 40, we have
[tex]Z=\dfrac{40-34 }{8 } = 0.75[/tex]
P(x < 40) = 0.77337
Therefore, the probability that the mean of four trees is between 30 and 40 is given as follows;
P(30 < x < 40) = 0.77337 - 0.69146 = 0.08191
The probability that a randomly selected group of four trees can be used as timber is given as follows;
Binomial distribution
[tex]P(X = 4) = \dbinom{4}{4} \left (0.08191\right )^{4}\left (1-0.08191 \right )^{0} = 4.5 \times 10^{-5}[/tex]
Write each of the following expressions without using absolute value. 7m–56|, if m<8
Answer:
[tex]|7m- 56| = 56 - 7m[/tex]
Step-by-step explanation:
Given
[tex]|7m- 56|[/tex]
[tex]m < 8[/tex]
Required
Rewrite the expression without absolute values
The first step is to check if the expression in |...| is positive or negative;
The question says m < 8,
This means the value of m could be 7, 6 ...
Let's assume m is 7
[tex]7m - 56 = 7 * 7 - 56 = 49 - 56 = -7[/tex]
This means that the expression [tex]|7m- 56|[/tex] will give a negative value if [tex]m < 8[/tex]
So,
[tex]|7m- 56| = -(7m - 56)[/tex]
Open bracket
[tex]|7m- 56| = -7m + 56[/tex]
Rearrange
[tex]|7m- 56| = 56 - 7m[/tex]
The expression can't be further simplified
Which equation is perpendicular to y= 3/4x + 4 and passes through the point (0,2)
A. Y= 3/4x + 2
B. Y= -3/4x + 2
C. Y= -4/3x + 2
D. Y= 4/3x + 2
The first three steps in determining the solution set of the system of equations algebraically are shown.
y = x2 − x − 3
y = −3x + 5
What are the solutions of this system of equations?
(−2, −1) and (4, 17)
(−2, 11) and (4, −7)
(2, −1) and (−4, 17)
(2, 11) and (−4, −7)
Answer:
(2, −1) and (−4, 17)
Step-by-step explanation:
I used a graphing tool to graph the systems of equations. The parabola and line pass at points (2, -1) and (-4, 17).
Answer:(2, −1) and (−4, 17) Its C on Edge 2023
Step-by-step explanation: Its (C) after an extensive research
values of r and h, what do you notice about the proportions of the cylinders?
Answer:
Below
Step-by-step explanation:
r us the radius of the base and h is the heigth of the cylinder.
The volume of a cylinder is given by the formula:
V = Pi*r^2*h
V/Pi*r^2 = h
We can write a function that relates h and r
Answer:
One of the cylinders is short and wide, while the other is tall and thin.
Step-by-step explanation:
sample answer given on edmentum
A circle has a radius of 10. An arc in this circle has a central angle of 72 degrees. What is the length of the arc? btw, the arc is aligned with the radius
Answer:
4 Pi
Explanation:
72/360 = 1/5 so the length of the arc is (1/5) the circumference or
(1/5) ( 2 Pi * 10) => C = 2 Pi r
(20/5) Pi =
4 Pi
Petroleum motor oil does a combination of natural oil and synthetic oil. It contains 5 L of natural oil for every 3 L of synthetic oil. In order to make 768 L of petroleum oil how many liters of natural oil are needed
Answer:
480 liters of natural oil
Step by step Explanation:
ratio of natural to synthetic oil
= 5:3
If 440 liters have to be made then,
Add 5 + 3 = 8
So, 5/8 of 768 liters will be = 480 liters of natural oil
and, 3/8 of 768 liters will be = 288liters of synthetic oil
Therefore, 480 liters of natural oil will be needed
PLEASE HELP ME ASPA What is the equation of the line that has a slope of -4 and passes through the point (2, 3)? y = -4x + 5 y = -4x – 5 y = -4x + 11 None of these choices are correct.
Answer:
Third option is the right choice.
Step-by-step explanation:
y = -4x + 11 (Slope = m = -4)
3 = -4(2) + 11
3 = -8 + 11
3 = 3
True.
Please answer it now in two minutes
Answer:
y = 4
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
y × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 4
Answer:
y=4
Step-by-step explanation:
If we have a triangle with angles A, B, and C. The law of sines says that the proportion between the sin of angle A and its opposite side is equal to the proportion between the sin of angle B and its opposite side and it is equal to the proportion between the sin of angle C and its opposite side.
So, by the law of sines we can say that:
[tex]\frac{sen(60)}{4\sqrt{3} } =\frac{sen(30)}{y}[/tex]
Solving for y, we get:
[tex]sin(60)*y=4\sqrt{3}*sin(30)\\\frac{\sqrt{3} }{2}y=4\sqrt{3}*0.5\\ \frac{1}{2} y=4*0.5\\y = 4[/tex]
If the blue radius below is perpendicular to the green chord and the segment
AB is 8.5 units long, what is the length of the chord?
A
A. 8.5 units
8.5
B
O B. 17 units
O C. 34 units
O D. 4.25 units
Answer:
O B. 17 units
Step-by-step explanation:
The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:
[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]
The length of the chord is 17 units.
Answer:
The answer is 17 units :D
Step-by-step explanation:
5.
Which of the following equations has the sum of its roots as 3?
(A) 2x² – 3x + 6 = 0
(B) - x²+ 3x - 3 = 0
(C)√2x²-3/√2x+1
(D) 3x² – 3x + 3 = 0
Answer:
B
Step-by-step explanation:
Given a quadratic equation in standard form, ax² + bx + c = 0 ( a ≠ 0 )
Then the sum of the roots = - [tex]\frac{b}{a}[/tex]
A 2x² - 3x + 6 = 0
with a = 2 and b = - 3
sum of roots = - [tex]\frac{-3}{2}[/tex] = [tex]\frac{3}{2}[/tex] ≠ 3
B - x² + 3x - 3 = 0
with a = - 1 and b = 3
sum of roots = - [tex]\frac{3}{-1}[/tex] = 3 ← True
C [tex]\sqrt{2}[/tex] x² - [tex]\frac{3}{\sqrt{2} }[/tex] x + 1
with a = [tex]\sqrt{2}[/tex] and b = - [tex]\frac{3}{\sqrt{2} }[/tex]
sum of roots = - [tex]\frac{-\frac{3}{\sqrt{2} } }{\sqrt{2} }[/tex] = [tex]\frac{3}{2}[/tex] ≠ 3
D 3x² - 3x + 3 = 0
with a = 3 and b = - 3
sum of roots = - [tex]\frac{3}{-3}[/tex] = 1 ≠ 3
Thus the equation with sum of roots as 3 is B
(1/16)^(x+3) = (1/4)^(x+1)
Answer:
x=-5
Step-by-step explanation:
The answer is x = -5. The explanation and answer is in the image below.
Please answer this question now
Answer:
d = 8.5
Step-by-step explanation:
The following data were obtained from the question:
Angle D = 100°
Opposite D = d
Opposite E = e = 6
Opposite F = f = 5
Thus, we can obtain the value of d by using the cosine rule as shown below:
d² = e² + f² – 2ef Cos D
d² = 6² + 5² – 2 × 6 × 5 × Cos 100°
d² = 36 + 25 – 60 × Cos 100°
d² = 61 – – 10.419
d² = 61 + 10.419
d² = 71.419
Take the square root of both side.
d = √71.419
d = 8.5
Therefore, the value of d is 8.5
A set of numbers is shown below: {0, 0.4, 1, 2, 3} Which of the following shows all the numbers from the set that make the inequality 4x + 1 ≥ 5 true? {2, 3} {1, 2, 3} {0, 0.4, 1} {0.4, 1}
Answer:
{1,2,3}
Step-by-step explanation:
The others will not show all the numbers from the set to make the inequality true
Answer:
1,2,3
Step-by-step explanation:
-3 raised to 2 + -3 raised to 2 =
Answer:
Step-by-step explanation:
(-3)² + (-3)² = (-3)*(-3) + (-3)*(-3)
= 9 + 9
= 18
Answer:
18
Step-by-step explanation:
A tissue sample is three cells thick. Each cell has a thickness of 0.000004m. What is the thickness of the tissue sample in mm. Give your answer in standard form. PLZ SHOW WORKING NOT IN NANO METERS. IN STANDARD FORM
Answer:
0.012 millimeters
Step-by-step explanation:
First, we solve for 0.000004 m to mm = 0.004 mm x 3 = 0.012 millimeters
49 students choose to attend one of three after school activities: football, tennis or running.
There are 18 boys.
11 students choose football, of which 1 are girls.
29 students choose tennis.
7 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
The probability that student chose running is 9/49 .
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Consider the information as that 49 students choose to attend one of three after-school activities: football, tennis, or running.
11 students choose football, 29 students choose tennis.
The students choose running = 49 - 11 - 29 = 9.
The students choose running = 0
This means out of 49 students 9 choose running.
P(E) = 9/49
Hence, the probability that student chose running is 9/49 .
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ2
Find the measure of c. A. 136 B. 144 C. 123 D. 149
Answer:
Option (D)
Step-by-step explanation:
Given quadrilateral in the circle is a cyclic quadrilateral.
By using the property of cyclic quadrilateral,
"Sum of each pair of opposite angles is 180°".
In the given cyclic quadrilateral,
d + 57° = 180°
d = 180 - 57
d = 123°
Similarly, c + 31° = 180°
c = 180° - 31°
c = 149°
Therefore, Option (D) will be the answer.
What is the translation from quadrilateral EFGH to
quadrilateral E'F’G’H
Answer:
The translation from quadrilateral EFGH to quadrilateral E'F'G'H' is [tex]T_{(2, -4)}[/tex], which is two units to the right (x direction) and 4 units down (negative y direction)
Step-by-step explanation:
The coordinates of quadrilateral EFGH are;
Point E has coordinates (-1, 1)
Point F has coordinates (0, 4)
Point G has coordinates (3, 1)
Point H has coordinates (3, 0)
The coordinates of the translation are;
Point E' has coordinates (0, -3)
Point F' has coordinates (1, 0)
Point G' has coordinates (4, -3)
Point H' has coordinates (4, -4)
The change in the y-coordinate values (y values) are;
From point E to point E', we have;
(-3 - 1) = -4 which is four units down
The change in the x-coordinate values (x values) are;
From point E to point E', we have;
(0 - (-1)) = 2 which is two units to the right
The total change in translation is [tex]T_{(2, -4)}[/tex].
A mega-pack of markers contains red markers, black markers, and blue markers. There are 24 red markers in the pack. The probability of randomly choosing a red marker is 1 in 3. If the probability of randomly choosing a blue marker is 1 in 8, how many blue markers are in the pack?
Will mark brainlist
Answer:
Number of blue markers = 9
Step-by-step explanation:
Given that there are 24 red markers.
Probability of randomly choosing a red marker is 1 in 3.
Probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
That means the ratio of red markers to total markers is 1:3.
Here number of favorable cases are 24 i.e. the number of red markers
and Total number of cases are equal to total number of markers.
Let T be the total number of markers.
As per definition of probability:
[tex]\dfrac{1}{3}=\dfrac{24}{T}\\\Rightarrow \bold{T = 72}[/tex]
Also, given that the probability of choosing a blue marker is 1 in 8.
Let the number of blue markers be B.
As per definition of probability:
[tex]\dfrac{1}{8}=\dfrac{B}{72}\\\Rightarrow \bold{B = 9}[/tex]
Hence, the answer is:
Number of blue markers = 9
What is the point-slope form of a line with slope 4/5 that contains the point
(-2, 1)?
Answer:
Y-1=4/5(x-(-2))
Step-by-step explanation:
Point slope form is written as y-y1=M(x-X1)
M is the slope
so replace the variables for the given value
Y-1=4/5(x-(-2))
Answer: y - 1 = 4/5 (x + 2)
Step-by-step explanation:
Carter bought a bear and paid for a football uniform. The total cost was $38.50. Write and solve an equation to find the cost, x, of buying a bear.
Answer:
Equation:- [tex]x + y = 38.50[/tex]
Solution of x:- [tex]x = 38.50 - y[/tex]
Step-by-step explanation:
Given
Total Purchase = $38.50
Required
Determine the equation for finding the cost of a bear
From the question; we understand that the cost of 1 bear is represented with x
Solving further; by representing the cost of 1 football uniform with y
So;
[tex]1\ bear + 1\ uniform = 38.50[/tex]
Substitute x for 1 bear and y for 1 uniform to give us an equation
[tex]x + y = 38.50[/tex]
Solving for x (Subtract y from both sides)
[tex]x +y - y = 38.50 - y[/tex]
[tex]x = 38.50 - y[/tex]
The equation can't be solved further
Please answer this in two minutes
Answer:
R = 21.8° to the nearest tenth
Step-by-step explanation:
To find Angle R we use tan
tan ∅ = opposite / adjacent
From the question
The opposite is 2
The adjacent is 5
So we have
tan R = 2/5
R = tan-¹ 2/5
R = 21.8° to the nearest tenthHope this helps you
Can someone help me with this question (:
I’d appreciate it!
brainliest to the correct answer/explanation) ♀️
Answer:
bet whats the question
Step-by-step explanation:
In how many ways can the letters of the word ``COPYRIGHT'' be arranged?
Answer:
362,880 ways
Step-by-step explanation:
There are 9 letters so 9!
And none of them are repeated so 9!/0!
9! = 362,880
I hope this helps, and plz mark me brainliest!!
Please helpppppppppppp
Answer:
678 ft²
Step-by-step explanation:
The opposite sides of the cuboid are congruent, thus surface area is
2(11 × 9) ← front and back + 2(11 × 12) ← top and base + 2(12 × 9) ← sides
= 2(99) + 2(132) + 2(108)
= 198 + 264 + 216
= 678 ft²
The function, f(x) = –2x2 + x + 5, is in standard form. The quadratic equation is 0 = –2x2 + x + 5, where a = –2, b = 1, and c = 5. The discriminate b2 – 4ac is 41. Now, complete step 5 to solve for the zeros of the quadratic function. 5. Solve using the quadratic formula. x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction What are the zeros of the function f(x) = x + 5 – 2x2? x = StartFraction negative 1 plus or minus StartRoot 41 EndRoot Over negative 4 EndFraction x = StartFraction 1 plus or minus StartRoot 41 EndRoot Over negative 4 EndFraction x = StartFraction negative 1 plus or minus StartRoot 39 EndRoot Over negative 4 EndFraction x = StartFraction 1 plus or minus StartRoot 39 EndRoot Over negative 4 EndFraction
Answer:
To solve for the zeros of the function equate f(x) = 0
That's
- 2x² + x + 5 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a = - 2 b = 1 c = 5
And from the question
b² - 4ac = 41
So we have
[tex]x = \frac{ - 1± \sqrt{41} }{2( - 2)} = \frac{ - 1± \sqrt{41} }{ - 4} [/tex]
[tex]x = \frac{1± \sqrt{41} }{4} [/tex]
We have the final answer as
[tex]x = \frac{1 + \sqrt{41} }{4} \: \: \: \: or \: \: \: \: x = \frac{1 - \sqrt{41} }{4} [/tex]
Hope this helps you
Answer:
The CORRECT answer is A.
Step-by-step explanation:
just did it.