Find an equation of the line passing through the
point (6,5) and perpendicular to the line whose
equation is 2y + 3x = 6.
Answer:
In slope-intercept form:
[tex]\displaystyle y=\frac{2}{3}x+1[/tex]
Or, in standard form:
[tex]2x-3y=-3[/tex]
Step-by-step explanation:
We want to find the equation of the line that passes through the point (6, 5) and is perpendicular to the line whose equation is:
[tex]2y+3x=6[/tex]
Since the new line is perpendicular, its slope and the slope of the first equation will be negative reciprocals of each other.
So, find the slope of the first equation. Subtract 3x from both sides:
[tex]2y=-3x+6[/tex]
And divide both sides by two:
[tex]\displaystyle y=-\frac{3}{2}x+3[/tex]
So, the slope of the first equation is -3/2.
The slope of the new line is its negative reciprocal. So, the slope of the perpendicular line is 2/3.
Next, we also know that it passes through the piont (6, 5). We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
Substitute:
[tex]\displaystyle y-(5)=\frac{2}{3}\left(x-6\right)[/tex]
And we have our equation!
If desired, we can simplify it into slope-intercept form:
[tex]\displaystyle \begin{aligned} y-5&=\frac{2}{3}x-4\\\\y&=\frac{2}{3}x+1\end{aligned}[/tex]
Or, into standard form:
[tex]\displaystyle \begin{aligned} y&=\frac{2}{3}x+1\\\\3y&=2x+3\\\\ 2x-3y&=-3\end{aligned}[/tex]
A ladder leans against the side of a house. The angle of elevation of the ladder is 68" when the bottom of the ladder is 16 it from the side of the house. Find the
length of the ladder. Round your answer to the nearest tenth
PLZ HELP ASAP!!!
Answer:
Length = 42.7 feet
Step-by-step explanation:
By considering it as right triangle we use trigonometric ratios to find the length of the ladder.
Given angle of elevation and adjacent side. We have to find the hypotenuse.
Trigonometric ratios
[tex]sin \theta = \frac{Opposite}{hypotenuse}\\\\cos \theta = \frac{adjacent }{hypotenuse }\\\\Tan \theta = \frac{opposite}{adjacent}\\ \\[/tex] [tex][ \ where \ \theta = 68^{ \circ} \ ][/tex]
To find length of ladder ( or hypotenuse ) :
[tex]cos \theta = \frac{16}{Length \ of \ ladder}\\\\Length \ of \ ladder = \frac{16}{cos 68} = 42.711\\\\[/tex]
Therefore, length of the ladder = 42.7 feet.
Question 7
1. Calculate and write your answer as a mixed number
1 4/5 + 2 2/3 - 16/15
Answer:
3 7/15
Step-by-step explanation:
1 4/5 + 2 2/3 - 16/15
9/5 + 8/3 - 16/15
27/15 + 40/15 - 16/15
52/15 = 3 7/15
Answer:
3 2/5
Step-by-step explanation:
STEP 1: Convert all fractions into improper fractions
9/5 + 8/3 - 16/15
Step 2: pass denominators
(9x3 + 8x5 - 16) / 15
=51/15
Step it into proper mixed number
3 2/5
A right rectangular prism has a square base and a height of 4 feet. Its volume, V, is 16 cubic feet. What are the lengths of the sides of the base?
A. 2 ft.
B. 4 ft.
C. 8 ft.
D. 16 ft.
Why is the product of a rational number and an irrational number irrational?
A) because the product is always a non-terminating, non-repeating decimal
B) because the product is always a fraction
C) because the product is always a negative number
D) because the product is always a repeating or a terminating decimal
Answer:
A
Step-by-step explanation:
Answer:
✔ Because the product is always a non-terminating, non-repeating decimal.
Step-by-step explanation:
E 2021
In parallelogram HJKL if m∡KLH=125∘find m∡LHJ.
Answer:
∠ LHJ = 55°
Step-by-step explanation:
Consecutive angles in a parallelogram are supplementary, sum to 180° , so
∠ LHJ + ∠ KLH = 180° , that is
∠ LHJ + 125° = 180° ( subtract 125° from both sides )
∠ LHJ = 55°
what is the examole of equal set ?
Answer:
Two sets are equal, if they have exactly the same elements. Example: {a, c, t} = {c, a, t} = {t, a, c}, but {a, c, t} ≠ {a, c, t, o, r}. Example: {x : x is a letter in the word “book”} = {b, o, k}, but {b, o, k} ≠ {b, o, t}.
Step-by-step explanation:
For the following set of data, find the percentage of data within 2
population standard deviations of the mean, to the nearest percent.
58, 77, 31, 54, 58, 54, 56, 58, 56
Answer:
58,+77,+31,+54+,58+,54+,46+,58+,56/9
If the value of the mean is 55.78. Then the standard deviation will be 10.98.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
The data set is given below.
58, 77, 31, 54, 58, 54, 56, 58, 56.
Then the mean of the data set will be
Mean = (58 + 77 + 31 + 54 + 58 + 54 + 56 + 58 + 56) / 9
Mean = 502 / 9
Mean = 55.78
Then the standard deviation will be
[tex]\rm SD = \sqrt{\dfrac{(58 - 55.78)^2+(77-55.78)^2 + ..... + (56-55.78)^2 }{9}}\\\\SD = \sqrt { \dfrac{1085.5}{9}}\\[/tex]
On further solving we have
SD = 10.98
If the value of the mean is 55.78. Then the standard deviation will be 10.98.
More about the standard deviation link is given below.
https://brainly.com/question/12402189
#SPJ2
physics
Joseph Jogs from one end A to the other end B of a straight
300m road in 2 minutes 30 second then turns around and jogs 100 m back to point C in another minute. What are Josef's Average speeds and velocities in jogging from
a) A to B
and
b) A to C
pls give answer with explination do not send link
Answer:
a) Josef jogging from A to B;
i. speed = 2 m/s
ii. velocity = 2m/s
a) a) Josef jogging from A to C;
speed = 1.9 m/s
ii. velocity = 2.2 m/s
Step-by-step explanation:
One major difference between speed and velocity is that speed is a scalar quantity, while velocity is a vector quantity.
a) Josef jogging from A to B;
distance = 300 m
time = 2.5 seconds = 150 seconds
i. his average speed = [tex]\frac{distance}{time}[/tex]
= [tex]\frac{300}{150}[/tex]
= 2 m/s
ii. his average velocity = [tex]\frac{displacement}{time}[/tex]
= [tex]\frac{300}{150}[/tex]
= 2 m/s
b) Josef jogging from A to C,
distance = 300 + 100 = 400 m
time = 2.5 + 1 = 3.5 minutes
= 210 seconds
i. his average speed = [tex]\frac{distance}{time}[/tex]
= [tex]\frac{400}{210}[/tex]
= 1.9 m/s
ii. his average velocity = [tex]\frac{\sqrt{V_{1} ^{2} + V_{2} ^{2} } }{2}[/tex]
[tex]V_{1} ^{2}[/tex] = 4 m/s
[tex]V_{2} ^{2}[/tex] = 1.9 m/s
his average velocity = [tex]\frac{\sqrt{4^{2} + 1.9^{2} } }{2}[/tex]
= 2.2 m/s
If x = 3, then 4x - 2 = 10 True or False
Answer:
True
Step-by-step explanation:
If x = 3, then we can subtitute in 3 for x in the equation;
4x - 2 = 10
4(3) - 2 = 10
12 - 2 = 10
10 = 10
Therefore the answer is True.
Hope this helps!
Please show me 3+2 (2x - 4) and can you please show the work?
Answer:
4x -5
Step-by-step explanation:
3+2 (2x - 4)
Distribute
3 + 2*2x - 2*4
3+4x - 8
Combine like terms
4x +3-8
4x -5
Answer:
4x - 5
Step-by-step explanation:
3+ 2 (2x) + 2 (-4)
3+4x - 8
Find the H.C.F of the following expressions.
1) 16x⁴ - 4x² - 4x - 1 , 8x³ - 1
2) 9x² - 4y² - 8yz - 4z² , 4z² - 4y² - 9x² - 12xy , 9x² + 12xz + 4z² - 4y²
3) x² - 18x - 19 + 20y - y² , x² + x - y² + y , x² - y² + 2y - 1
Irrelevant / Random answers will be reported !!
Step-by-step explanation:
Hey there!
Please look your required answer in pictures.
Hope it helps!
What is the product of (a+b) (a-b)
Answer:
[tex]a^{2}+b^{2}[/tex]
Step-by-step explanation:
(a+b)(a-b)
[tex]a^{2}[/tex]-ab+ab-[tex]b^{2}[/tex]
[tex]a^{2} + b^{2}[/tex]
What is the volume of the following cylinder? Do not round your answer. (Use 3.14 for π.)
volume = ____yd3
Answer: 1962.5
Step-by-step explanation: Just did this question it's right hope this helps
PLEASE HELP I’LL GIVE BRAINLIEST
What is the slope of the line shown below?
10+
(-6, 3) 5+
(12,6)
15
-10-
o A. - 1
O B. 6
O C.-6
OD
Answer:
B
Step-by-step explanation:
B
Answer:
the most likely answer is D 1/6
Step-by-step explanation:
Im not 100% sure
but hope this help if so can you mark me brainiest
thank you
A wire is in the shape of a rectangle Pentagon of side 12 centimetres. It is rebent into the shape of a rectangle whose length is 3 divided by 2 times it's breadth. Find the length and breadth of the rectangle
Answer
Total Length of Wire = Perimter of Pentagon
= 12 × 5 = 60 cm
Perimeter of Rectangle = 2 (l + b)
Given, l = 3/2 b
Therefore,
2(3/2 b + b) = 60
2 (5b/2) = 60
5b = 60
Breadth b = 12 cm
Length l = 3/2 × 12 = 18 cm
The Naturally Made Bath and Body store pays $550 a month for rent and utilities. The average cost for its products to be manufactured is about $3.00 an item. If the average price for a product sold in the store is $5.50, what will the break-even point be?
Answer:
Break-even point is at quantity 220.
Step-by-step explanation:
Given the rent amount that is fixed cost for the store = $550
The average cost of the goods = $3
The average price of the goods = $5.50
Let the total number of break-even items = Q
Thus, total revenue = 5.50 x Q = 5.50Q
At break-even, TR = TC
5.50Q = FC + VC
5.50Q = 550 + 3Q
5.50Q - 3Q = 550
2.50Q = 550
Q = 550 / 2.50
Q = 220
Thus break-even point is at quantity 220.
Helpppppp pls
Find h.
h = [?] in
Answer:
h=rt.96=4 rt.6
Step-by-step explanation:
r=2 inches
therefore 100= root over h + 4
=>h=rt.96=4 rt.6
A car dealership has seven cars in the lot unfortunately the keys to the cars of been mixed up the manager randomly grab the key and tries to start a car salesman also randomly picks a different key and tries to start another car what is the probability that both cars start
To determine The probability of both of these occurring, you would multiply the probability of each together. So, there is a 1/7 chance of the first salesman getting the right key, and 1/6 chance of the second salesman getting the right key. 1/7 x 1/6= 1/42 chance of both occurring.
how do you find the missing angles? thank you pls answer will give brainliest
Answer:
1. 70
2. 65
3. 115
4. 65
5. 65
6. 65
7. 65
Step-by-step explanation:
All of them are correct so dont worry
Have a nice day
Tori is cutting fabric squares to make a quilt. Her squares on average are 5 in. on each side with a standard deviation of 0.1 in. If her cuts are normally distributed, what percentage of her squares would be between 4.9 and 5.1 in?
Answer:
[tex]\approx 68\%[/tex]
Step-by-step explanation:
For normal distributions only, all data falls within approximately 68% of one standard deviation, 95% of two standard deviations, and close to 100% of three standard deviations. The standard deviation is far too small to represent two or three standard deviations, hence [tex]\implies \boxed{68\%}[/tex].
*Important: This problem would be unsolvable if the question did not say her cuts were normally distributed, because the information above is only applicable to normal distributions.
Answer:
68.26%Step-by-step explanation:
Given:
Mean μ = 5 inStandard deviation σ = 0.1 inThe squares between 4.9 and 5.1 represent:
x = 5 ± 0.1Relevant z- scores are:
z = (x - μ)/σz = (5.1 - 5)/0.1 = 1z = (4.9 - 5)/0.1 = -1From the z-score table we get:
z = 1 ⇒ 84.13% markz = -1 ⇒ 15.87% markThe data between these points is:
84.13% - 15.87% = 68.26%Which dot plot shows 3 students purchased 4 books at the book fair? A dot plot titled Number of Books Purchased at Book Fair goes from 1 to 5. 1 has 3 dots, 2 has 0 dots, 3 has 3 dots, 4 has 4 dots, and 5 has 2 dots. A dot plot titled Number of Books Purchased at Book Fair goes from 1 to 5. 1 has 1 dot, 2 has 3 dots, 3 has 4 dots, 4 has 2 dots, and 5 has 2 dots. A dot plot titled Number of Books Purchased at Book Fair goes from 1 to 5. 1 has 3 dots, 2 has 2 dots, 3 has 3 dots, 4 has 3 dots, and 5 has 1 dot.
Answer:
A dot plot titled Number of Books Purchased at Book Fair goes from 1 to 5. 1 has 3 dots, 2 has 2 dots, 3 has 3 dots, 4 has 3 dots, and 5 has 1 dot.
Step-by-step explanation:
The title given to a boxplot will be the values labeled on the horizontal axis, hence since the title of the plot is the number of books purchased at a book fair, If 3 students purchased 4 books, then the Horizontal label at 4 (number of books purchased) will have 3 dots (which corresponds to the number of students who purchased 4 books).
Convert 14 into base 2
Answer: 0b1110
Step-by-step explanation:
please help me with this question. find the exact circumference of the circle using the given inscribed polygon please help me
53,38
Step-by-step explanation:
x = √15² + 8²
x = √225 + 64
x = √289
x = 17
circle's circumference = π × d
3,14 × 17 = 53,38
what is the order of the numbers from least to greatest
Answer:
-3.7, -1.9, -1/2, 1 1/3, 1.6, 2 1/3
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if this answer is wrong.
Answer:
-3.7, -1.9, -1/2, 1 1/3, 1.6, 2 1/3
Step-by-step explanation:
hope this helps! have a great day!
Find mean, median, mode, range
Answer:
Range = 30
Mode = 80
Median = 90
mean = 87
Danessa is working with consecutive even numbers. If x is her first number, which expression represents her second number?
x + 1
x – 1
x + 2
2x
Answer:
x + 2
Step-by-step explanation: I believe that can help you!
A battery with a voltage of 3 V provides a voltage of 0.56 C to some circuits. Calculate the electrical power provided by this battery
Answer:
The power is 1.68 W.
Step-by-step explanation:
Voltage, V = 3 V
charge, q = 0.56 C
time, t = 1 s
The power is given by
P = V q/t
P = 3 x 0.56 / 1
P = 1.68 W
A motorist drives at an average speed of 80 km/hr. How far does she travel in 3(1/2)
hours?
Answer: 280 km
Step-by-step explanation:
[tex]3\dfrac{1}{2} \: hours = 3.5 \: hours[/tex]
S = V × t
V = 80 km/h
t = 3.5 h
S = 80 × 3.5 = 280 km
i will give you brainliest if you help me with this
Answer:
a) 9 + 3 = 12
b) 5x = (5 x 6 = 30) 30
c) 2x (2 x 3 = 6) = 13
d) 5x (5 x 2 = 10) = 14 + x (10)
Step-by-step explanation:
I hope it is right
Answer:
a. x=9
b. x=6
c. x=3
d. x=10/4