y = -2x-3
Lines that are perpendicular have slopes that are negative reciprocals of each other. Meaning, if a line has slope , then a line perpendicular to this has slope . That means the slope of our perpendicular line is
The equation of the line that is perpendicular to 8x - 2y = 4 and passes through the point (4, 3) is y = (-1/4)x + 4.
To find the equation of a line that is perpendicular to the line 8x - 2y = 4 and passes through the point (4, 3), we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope:
8x - 2y = 4
-2y = -8x + 4
Divide both sides by -2:
y = 4x - 2
The slope of the given line is 4.
The slope of a line perpendicular to this line would be the negative reciprocal of 4, which is -1/4.
Now, we have the slope (-1/4) and a point (4, 3). We can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
Substituting the values, we have:
y - 3 = (-1/4)(x - 4)
Expanding and simplifying, we get:
y - 3 = (-1/4)x + 1
Adding 3 to both sides, we have:
y = (-1/4)x + 4
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SUBJECT: Graphs and Function
Identify the range of the function shown in the graph.
Indicate in standard form the equation of the line through the given points, writing the answer in the equation box below.
K(6, 4), L(-6, 4)
9514 1404 393
Answer:
y = 4
Step-by-step explanation:
The given points are on the horizontal line ...
y = 4
This is the standard-form equation of that line.
use the ratio of a 45-45-90 triangle to solve for the variables
Answer:
1:1:√ 2
Step-by-step explanation:
Answer:
u = 14
v = 14
Step-by-step explanation:
since both angles around the 90 degree angle are the same, also the sides need to be of equal length. v = u
so, we can use Pythagoras
(14×sqrt(2))² = u² + u² = 2u²
196×2 = 2u²
196 = u²
u = 14 = v
Which of the following is a solution of y + x < -5?
(-2, -3)
(-4, -2)
(-3, -2)
(-1, -3)
The answer is (-4, -2)
-2 + -4 < -5
-6 < -5
Hope this helps!
Answer:
(- 4, - 2 )
Step-by-step explanation:
Substitute the coordinate value into the left side of the inequality and compare the value obtained to the right side
(- 2 , - 3 )
- 3 - 2 = - 5 = - 5 ← not a solution
(- 4, - 2 )
- 2 - 4 = - 6 < - 5 ← solution
(- 3, - 2 )
- 2 - 3 = - 5 ← not a solution
(- 1, - 3 )
- 3 - 1 = - 4 > - 5 ← not a solution
Amanda teaches the art of quilling to 4 students. These students each teach the art of quilling to 4 other students. This process continues through 3 more generations.
4x4=16 16x3=48 so I think the answer is 48
1. You buy rice at $0.71 a pound. One batch of fried rice requires 6.5 pounds of rice. How much does the rice for one batch cost? Round to the nearest cent.
Select one:
a. $4.60
b. $4.65
c. $4.61
d. $4.62
The cost for one batch of fried rice will be $4.62.
Since the rice is bought at $0.71 a pound and one batch of fried rice requires 6.5 pounds of rice, then the cost of one batch of rice will be:
= $0.71 × 6.5
= $4.615
= $4.62 approximately.
In conclusion, the cost for one batch of fried rice will be $4.62.
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A. Explain why the point (100,2) is on the graph.
B. What is the x-intercept of the graph? Explain how you know.
49
C. When will the graph meet the line y = 5? Explain how you know.
Answer:
the log function is the "inverse" function of an exponential function
by definition [tex]log_{a} b = c[/tex] then [tex]a^{c} = b[/tex]
in this problem you have [tex]log_{10} 100[/tex]
thus what x solves this ? [tex]10^{x} = 100[/tex] the answer is [tex]10^{2}[/tex]
thus (100,2)
B) the x intercept is when y = 0
[tex]10^{0} = 1[/tex]
x intercept at (1,0)
C) at 100, the curve will hit y = 5000
Step-by-step explanation:
A group of rowdy teenagers near a wind turbine decide to place a pair of
pink shorts on the tip of one blade. They notice that the shorts are at its
maximum height of 16 metres at t = 10 s and its minimum height of 2 metres at
t = 25 s.
a) Determine the equation of the sinusoidal function that describes
the height of the shorts in terms of time.
b) Determine the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a metre.
Answer:
a) Sinusoidal functions are y = a sin [b(x-h)] + k (or)
y = a cos [b(x-h)] + k
Where a is amplitude a= (max-min)/2=(16-2)/2=7
period p= 2π/b
b=2π/30
Horizontal transformation to 10 units right h=10
k= (max+min)/2=(16+2)/2=9
h = 7 cos [π/15(t-10)]+ 9
b) t=10min=600 sec
substitue in the above equation
h=5.5m
divide 180 in three parts 1/10: 1/15: 1/20
Answer:
83,55,41
Step-by-step explanation:
1/10 : 1/15 : 1/20
180/10 : 180/15 : 180/20
18 : 12 : 9
=> 6 : 4 : 3
Sum of the ratios = 6 + 4 + 3 = 13
1st ratio: (6/13) * 180 = 83 (approximately)
2nd ratio: (4/13) * 180 = 55 (approximately)
3rd ratio: (3/13) * 180 = 41 (approximately)
∴ Three parts of 180 in the ratio 6 : 4 : 3 is 83, 55 and 41
Number 13 I don’t get it
===========================================
Explanation:
The two equations given to us are
ab = 3ab^2 = 18Divide the second equation over the first equation and that would lead to b = 6
Notice how the 'a' terms divide to 1 and go away, i.e. cancel out.
The b terms divide to (b^2)/b = b
The right hand side values divide to 18/3 = 6
So that's how we end up with b = 6
-------------------------
Now if b = 6, then we can say,
ab = 3
a*6 = 3
a = 3/6
a = 1/2
Or we could say
ab^2 = 18
a*6^2 = 18
a*36 = 18
a = 18/36
a = 1/2
help me pls I need help its Pythagorean theorem I’m failing pls
Answer:
22.2 m.
Step-by-step explanation:
They walk in a right triangle.
First they walk 7 then 6 m = 13 m.
We calculate the distance of the diagonal using Pythagoras:
x^2 = 6^2 + 7^2 = 85
x = √85
= 9.2 m. yo nearest 1/10.
Answer is 13 + 9.2
= 22.2 m.
2x - y - 4 = 0
3x + y - 9 = 0
What is the solution set of the given system?
A. {(6, 5)}
B. {(5, 6)}
C. {(13/5, 6/5)}
D. {(6/5, 13/5)}
Step-by-step explanation:
+ Both equations
You will get : 5x=13 ; x=13/5
and put x to the first equation
2*13/5-y=4
y=6/5
(13/5;6/5)
Answer is C
O 131 If cos 23°=P, express without the use of a calculator the following in terms of p.
Cos203°
Answer:
cos203° = - p
Step-by-step explanation:
Using the addition formula for cosine
cos(a + b) = cosacosb - sinasinb
cos203°
= cos(180 + 23)
= cos180°cos23° - sin180°sin23°
= cos180°. p - 0
= - 1 . p
= - p
How do I solve this: h + 6/5 = 2
if my mine craft house was burning leaves irl and i was watering my boat on a Wednesday on a weekend in December when its summer how many fish will become orphans late nights in the middle of june?
Complete the table, and then use the drawing tools to create the graph representing the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
The complete table of the function is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
The equation missing from the question is:
[tex]y = 72 - 12x[/tex]
To complete the table, we simply calculate the y value for each x value;
When [tex]x = 0[/tex], [tex]y = 72 - 12 * 0 = 72[/tex]
When [tex]x = 1[/tex], [tex]y = 72 - 12 * 1 = 60[/tex]
When [tex]x = 2[/tex], [tex]y = 72 - 12 * 2 = 48[/tex]
When [tex]x = 3[/tex], [tex]y = 72 - 12 * 3 = 36[/tex]
When [tex]x = 4[/tex], [tex]y = 72 - 12 * 4 = 24[/tex]
When [tex]x = 5[/tex], [tex]y = 72 - 12 * 5 = 12[/tex]
When [tex]x = 6[/tex], [tex]y = 72 - 12 * 6 = 0[/tex]
So, the complete table is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
To create a graph of f(x), we simply type [tex]y = 72 - 12x[/tex] on a drawing tool and the graph will be generated.
See attachment for graph
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Answer:
Step-by-step explanation:
find the value of x in the diagram below
Answer:
70
Step-by-step explanation:
In a trapezoid lines are parallel, so corresponding angle sum = 180
X+X+40 = 180
2x + 40 = 180
2x = 180-40
2x = 140
X = 140/2
X = 70
Answered by Gauthmath
which of the following is a result of shiftinga circle with equation (×-2)+(y-3)^2= 25 to the left 2 unit ?
Answer:
x^2+(y-1)^2=25
Step-by-step explanation:
eqn of circle : (x-h)^2+(y-k)^2=r^2
center of circle = (h,k)
hence, the center of the current circle is (2,3)
moving 2 units to the left would make the center (0,1)
the radius would remain the same (5) , hence the new eqn would be
(x-0)^2+(y-1)^2=25
x^2+(y-1)^2=25
Sin theta = 9/15. Find tan theta. A. 15/12. B. 9/12 C. 12/15 D. 12/9
Answer:
B
Step-by-step explanation:
[tex]Sin \ theta = \frac{9}{15}=\frac{Opposite \ side}{hypotenuse}\\[/tex]
Pythagorean theorem,
Adjacent side ² = hypotenuse² - opposite side²
= 15² - 9²
= 225 - 81
= 144
Adjacent side = √144 = √(12*12) = 12
[tex]Tan \ theta = \frac{opposite \ side}{adjacent \ side}= \frac{9}{12}[/tex]
13. The Cyclone Coaster has 16
cars. Some of them hold 2
passengers and some hold 3
passengers. If there is room for
36 people altogether, how many
cars hold 3 passengers?
Answer:
Four cars that can hold 3 passengers
Step-by-step explanation:
The number of cars on the Cyclone Coaster = 16 cars
The number of passengers some cars hold = 2 passengers
The number of passengers the other cars hold = 3 passengers
The number of people altogether the Cyclone Coaster has room for = 36 people
Let x represent the number of cars that can hold 3 passengers, and let y represent the number of cars that can hold 2 passengers, we have;
3·x + 2·y = 36...(1)
x + y = 16...(2)
The value of x can be found by making y the subject of equation (1) and equation (2) and equating both values of y given in x as follows;
The value of y from equation (1) is, y₁ = (36 - 3·x)/2 = 18 - 3·x/2
∴ y₁ = 18 - 3·x/2
The value of y from equation (2) is, y₂ = 16 - x
Equating both y values, to find the coordinates of the common point to both equations, gives;
At the common point y₁ = y₂
By the substitution property of equality
∴ 18 - 3·x/2 = 16 - x
3·x/2 - x = 18 - 16 = 2
x/2 = 2
∴ x = 4
The number of cars that can hold 3 passengers, x = 4
(From y₂ = 16 - x, we have
y₁ = y₂ = 16 - 4 = 12
y = 1
The number of cars that can hold 2 passengers, y = 12).
Can someone help me out
Answer:
75.7
Step-by-step explanation:
Area of the sector,
17²×π×30/360
= 289π/12
= 75.7 (rounded to the nearest tenth)
Answered by GAUTHMATH
find the value of x in the triangle.
Answer:
The answer is 36°.
Hope it helps.
Step-by-step explanation:
• • •
You are making pudding for five friends. The recipe calls for 1/4 cup of sugar per serving. How much sugar do you need?
Answer:
1 1/4 cups I think..
Step-by-step explanation:
1/4 times 4 is 1, plus another 1/4 for the 5th friend is 1 1/4 cups.
Answer:
[tex]\frac{5}{4}[/tex] or [tex]1\frac{1}{4}[/tex] cups
Step-by-step explanation:
This question asks how much total sugar will be needed for 5 servings of 1/4 cup. In other words, this is asking for 1/4 cup to be added together 5 times. However, repeated addition is just multiplication, so this can become a multiplication problem. To do this make both terms a fraction by putting 5 over 1. This looks like: [tex]\frac{5}{1} *\frac{1}{4}[/tex]. Then, simply multiply the numerators together and the denominators together. This equals [tex]\frac{5}{4}[/tex]. If needed this can be put into the mixed fraction of [tex]1\frac{1}{4}[/tex] cups.
The diameter of the circle above is 18 cm. What is the circumference of the circle? (Use = 3.14.)
Answer:
56.57
Step-by-step explanation:
See attached photo for steps
EDIT: I forgot to add 3.14, I am so sorry
Answer:
56.52
Step-by-step explanation:
Given that sin 0 = 21/29, what is the value of cose, for 0° <0<90°? please help
Answer:
3rd option
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ( subtract sin²x from both sides )
cos²x = 1 - sin²x ( take the square root of both sides )
cosx = ± [tex]\sqrt{1-sin^2x}[/tex]
Given
sinθ = [tex]\frac{21}{29}[/tex] and 0 < θ < 90 , then
cosθ
= [tex]\sqrt{1-(\frac{21}{29})^2 }[/tex]
= [tex]\sqrt{1-\frac{441}{841} }[/tex]
= [tex]\sqrt{\frac{400}{841} }[/tex] = [tex]\frac{\sqrt{400} }{841}[/tex] = [tex]\frac{20}{29}[/tex]
Bob is hired by Company A and is given an annual salary of $35 000 with a 10% raise
after 1 year. Sam is hired by Company B and is paid $3842.42 per month with a 5% raise
after 1 year. Determine the difference of salary after 1 year.
Step-by-step explanation:
Bob's salary : $35000 per year plus 10% after one year
100% = 35000
1% = 100%/100 = 35000/100 = $350
10% = 10×1% = 10×350 = $3500
so in total, his salary will be $35000+$3500 = $38500 after one year.
Sam's salary : $3842.42 per month plus 5% after one year.
100% = $3842.42 per month. but to make it comparable to Bob's salary, we need to calculate the annual salary.
so, 100% 12×3842.42 = $46109.04
1% = 100%/100 = 46109.04/100 = $461.09
5% = 5×1% = 5×461.09 = $2305.45
so, in total, his salary will be $46109.04+$2305.45 = $
please help geometry!!
Answer:
A' (-5, 5)
B' (20, 0)
C' (5, -15)
Step-by-step explanation:
Multiply each coordinate by 5, and your result is given above.
Answer:
Step-by-step explanation:
cho tứ giác ABCD. Gọi M,N,P,Q là trung điểm của các cạnh AB, CD, AD, BC. Chứng minh rằng vecto MP = vecto QN, vecto MQ = vecto PN
Answer:
Step-by-step explanation:
Xét tam giác DAB có: P là trung điểm AD, M là trung điểm AB
=> MP là đường trung bình của tam giác DAB => MP//BD và MP=[tex]\frac{1}{2}[/tex]BD (1)
Xét tam giác DBC có: N là trung điểm DC, Q là trung điểm BC
=> QN là đường trung bình của tam giác DBC => QN//BD và QN=[tex]\frac{1}{2}[/tex]BD (2)
Từ (1) và (2) => vecto MP song song cùng chiều với vecto QN
và độ dài MP = độ dài QN = [tex]\frac{1}{2}[/tex]BD
=> vecto MP = vecto QN
Tương tự xét các tam giác DAC và tam giác ABC => vecto MQ = vecto PN
Find x.
A. 6√6
B. 18
C. 9√2
D. 24√3
Answer:
C
Step-by-step explanation:
4.
Which point is NOT part of the solution of the inequality y < (3x + 1?
(-4, 12)
(0,0)
(2, -9)
(3, 15)
Answer: The non solutions of the inequality are A and D.
Step-by-step explanation:
