Given:
A new four way intersection is being constructed in New York Hyde park through point P(-3,-15).
Equation of line of one road : [tex]y=-\dfrac{3}{4}x+7[/tex].
New road that will run perpendicular to the first road
To find:
The equation of line for the new road.
Solution:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
We have,
[tex]y=-\dfrac{3}{4}x+7[/tex]
Slope of this line is [tex]-\dfrac{3}{4}[/tex] and y-intercept is 7.
Product of slopes of two perpendicular line is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]-\dfrac{3}{4}\times m_2=-1[/tex]
[tex]m_2=\dfrac{4}{3}[/tex]
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope.
The slope of new line is [tex]\dfrac{4}{3}[/tex] and it passes through P(-3,-15). So, the equation of line of new road is
[tex]y-(-15)=\dfrac{4}{3}(x-(-3))[/tex]
[tex]y+15=\dfrac{4}{3}(x+3)[/tex]
[tex]y+15=\dfrac{4}{3}x+4[/tex]
Subtract 15 from both sides.
[tex]y=\dfrac{4}{3}x+4-15[/tex]
[tex]y=\dfrac{4}{3}x-11[/tex]
Therefore, the equation of the line representing the new road is [tex]y=\dfrac{4}{3}x-11[/tex].
What the solution for x is in 14+x=3a+ab?
Answer: a= x+14 /b+3
Step-by-step explanation:
Answer:
Step-by-step explanation:
Simplifying
14 + x = 3a + ab
Solving
14 + x = 3a + ab
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-14' to each side of the equation.
14 + -14 + x = 3a + -14 + ab
Combine like terms: 14 + -14 = 0
0 + x = 3a + -14 + ab
x = 3a + -14 + ab
Reorder the terms:
x = -14 + 3a + ab
Simplifying
x = -14 + 3a + ab
Given a 30-60-90 triangle with a hypotenuse of 11 mm solve for the other sides. (Explain)
Answer:
Need a calculator
Step-by-step explanation:
This will be hard to explain without the ability to draw an example.
The one thing you can memorize is SOH - CAH - TOA
This stands for SIN(Opposite/Hypotenuse), COS(Adjacent/Hypotenuse) and TAN(Opposite/Adjacent).
When you know the angles of a right triangle and at least one side length, you can get the length of all the sides.
So a right triangle has two legs (sides) and the hypotenuse. If you use the first angle ( 30 degrees) you can use the formulas above to calculate the side length.
Pick either the SOH or the CAH. Let's use SOH and write out the equation:
SIN(30 degrees) = Opposite Side divided by the Hypotenuse (11mm)
You can solve for the Opposite Side by multiplying both sides of the equal sign with 11mm. You end up with SIN(30 degrees) X 11m = Opposite Side.
So the side directly across from the 30 degree angle should be 5.5mm
You can do the exact same thing with the 60 degree angle.
SIN(60 degrees) = Opposite Side divided by Hypotenuse (11mm) OR
SIN(60 degrees) X 11mm = Opposite Side
This comes out to about 9.5mm
You can check the math by using the other equation CAH
Start with the 30 degree angle and solve for the adjacent side. This is the side that is touching the 30 degree angle. Equation will be
COS(30 degrees) X 11mm = Adjacent Side or about 9.5mm
The other equation will give you the side that is touching the 60 degree angle.
COS(60 degrees) X 11mm = Adjacent Side or 5.5mm
You can also use one last thing to check your math. The Pathagorean Theorem says in a right triangle [tex]A^{2}[/tex] + [tex]B^{2}[/tex] = [tex]C^{2}[/tex] where C is the hypotenuse and A and B are the two sides.
[tex]5.5^{2}[/tex] + [tex]9.5^{2}[/tex] should equal [tex]11^{2}[/tex]. Give or take a few decimal places, it's almost exactly 11 (10.977 to be exact).
Which number line shows the graph of 0.3
Answer:
im dumb im sorry but u can look it up
Step-by-step explanation:
If the perimeter of the regular pentagon is 75 cm what is the length of each side
Plz help nowww
If you wanna be crowed a brainliest:-)
Answer:
15 (mark me brainliest if you want and lmk if you need more help understanding)
Step-by-step explanation:
perimeter is (l*w)*2
if a pentagon is 5 sided, you do 75/5 which is 15.
each side has 15 cm
Give 5 reasons explaining why math is your favorite subject.
Give 5 reasons why you dont like math.
Give 5 areas that math can help you now or in the future.
Answer:Math is important
Step-by-step explanation:
It could help you get into collage and get a good job and with that you could start your life.
Answer:
1.)
I love working with numbers
I love math because of what a challenge it is
I love math because I can become a engineer
I love math because I can also become a doctor with it
I love math because it is useful
2.)
I don't like math because of the word problems
I don't like math because it sometimes gets too easy
I don't like math because I usually have to help others
I don't like math because people call me a nerd
I don't like math because it makes me explain in words
3.)
when your in the store and it helps you with knowing how much your spending
lets you know about if the discount in the store is really good or bad
helps you with becoming certain things when you grow up
it will help you with most of your jobs
Will help others if you know it, you can share your knowledge
Step-by-step explanation:
brainlist pls :>
Which best explains the relationship between the two triangles below? Triangle D C A. Angle D is 51.2 degrees and angle A is 96.5 degrees. Triangle S R T. Angle S is 32.3 degrees and angle R is 96.5 degrees. Triangle A D C is similar to triangle R T S because Angle A is congruent to angle R, Angle C is congruent to angle S, and Angle D is congruent to angle T. Triangle A D C is similar to triangle R T S because Angle A is similar to angle R, Angle C is similar to angle S, and Angle D is similar to angle T. Triangle A D C is not similar to Triangle R T S because Angle D is not congruent to Angle S. Triangle A D C is not similar to Triangle R T S because C D less than S T, D A less than T R, and C A less than S R.
Answer:
Answer is A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
i just take the test
What is the value of x? Enter only the number in the box! Help Asap
Answer:
x = 5
Step-by-step explanation:
90 - 55 = 35
8x - 5 = 35
+5 +5
8x = 40
x = 5
What is the image of (-5, 6) after a reflection over the line y = -2
Answer:
I'm pretty sure it would be (5,6)
Step-by-step explanation:
Reflecting a point over the Y-axis would change the x-coordinate, but not the y-coordinate
A math test had 26 questions. The questions were either true/false or multiple choice. The true/false questions were worth 2 points each and the multiple choice were worth 5 points each. If the test is worth 100 points, how many of each type of question are included on the test?
Answer:
True/ false type 10 questions
Multiple choice type 16 questions
Step-by-step explanation:
Using the given formation we can make equations to solve for the number of questions of either type is to be included
let the no of true/false be =x
let the number of multiple choice to be included be = y
x + y=26 .............(1)
now making the equation of points
2x + 5y = 100 .........(2)
substitute y = 26-x from first equation in the second equation
2x + 5(26 - x ) = 100
2x - 5x + 130 = 100
3x=30
x=10
y =26-10=16
what is the next 3 terms for (-6,42,-294,2058)
Answer:
es
Step-by-step explanation:
Answer:
A. 14,406. it runs by a -7 sequence, so D would be the 6th in the sequence.
Step-by-step explanation:
f(x) = 3x - 5 and g(x) = 5x + 8. Find 3g(x) - 2f(x).
Answer:
9x + 34
Step-by-step explanation:
3g(x) - 2f(x); f(x) = 3x - 5 & g(x) = 5x + 8.
3(5x + 8) + - 2(3x - 5) (Plug g(x) & f(x) into equation)
15x + 24 + - 6x + 10 (Use distributive property)
9x + 34 (Combine like terms) - This is as much as it can be simplified.
Create a one step equation using the numbers 4 and 6. One you create the
equation, solve it and find the solution.
Answer:
x=1.5
Step-by-step explanation:
4x=6
6/4=1.5
3b) Two pizzas are made to the same dimensions. The only difference is that
Pizza 1 is cut into pieces at 30° angles and Pizza 2 is cut at 45° angles. They are
sold by the slice. The slices for Pizza 1 sell for $1.45/slice and the slices for Pizza 2
sell for $1.75/slice. What is the difference in total sales between Pizza 2 and Pizza
1?
Step-by-step explanation:
$0.30 because they only sell 30 cents less/more than each other
When finding the product, what is the first step?
(-c)x(-2a)x12b
btw the x's are multiply signs.
Thanks :)
Answer:
24abc
Step-by-step explanation:
(-c)*(-2a)*12b
Multiply the numbers
-1 * -2 *12 = 24
Multiply the variables
c*a*b = abc
Put it back together
24abc
I need helpppp IDKK
Answer:
Step-by-step explanation:
Choice
Answer:
Can you award me brainest
Write sec 325° in terms of the secant of'a positive acute angle.
Answer:
sec35°
Step-by-step explanation:
sec325° = sec(360 - 325)° = sec35°
The secant of a positive acute angle of sec 325° = sec 35° = 1.22077
What are Trigonometric Ratios?
Trigonometry values are all about the study of standard angles for a given triangle with respect to trigonometric ratios.The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given data ,
The trigonometric ratio is = sec 325°
Now , to express the ratio in terms of a positive acute angle , we take the four quadrants of the graph and express the angle in the first quadrant.
And , 325° lies on the 4th Quadrant , where all cosines and secants are positive.
Therefore , sec 325° = sec ( 360° - 35° )
= sec ( 35° )
=1.22077
Hence , the secant of a positive acute angle of sec 325° = sec 35° = 1.22077
To learn more about trigonometric ratio click :
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When solving for x, the sine of 33º is used. What other angle and trigonometric function could be used to solve for x? a. cos 57º c. tan 57º b. tan 33º d. cos 33º
hurry
Answer:
The answer is A.Cos 57.
Step-by-step explanation:
Took the test..
(5.31 x 103) – (2.8 x 103)
Answer:
258.53
Step-by-step explanation:
Hope This Helps!
Plz Mark Brainliest!
Answer:
I believe it is 258.53 ,,,,
In an online practice test, Sam got 11 correct answers. However, 3.5 points were deducted for incorrect answers. If he scored 18.5 points in the test, how much did he score for each correct answer?
PLEASE HELP ASAP! (picture is attached) You real one if you do
Answer:
x is equal to 1
Step-by-step explanation:
12(4x -1/4x ) 2 + 5(4x-1/4x) - 2
solve it
HELP pleasee and ty to whoever does!!
Please help me! Two pictures!
Answer:
B. y<=-2x+1
Step-by-step explanation:
Answer:C
Step-by-step explanation:
You can graph the answer into desmos, a website which helps you graph, I graphed it and got C.
What is the value of x in the equation x*3 = 27 512 ?
You bike 11.2 miles in 1.4 hours at a steady rate. What equation represents the proportional relationship between the x hours you bike and the distance y in miles that you travel?
Answer:17
Step-by-step explanation:
Answer:
Y=8x
Hope this helped
Step-by-step explanation:
When I graph the inequality symbol > should it be a open or closed
circle on the number line?
Answer:
It should be open.
Step-by-step explanation:
Hope this helped!
school sold 2 adult tickets and 10 child tickets for a total of $56. The school took in $52 on the second
The school that Elisa goes to is selling tickets to a fall musical. On the first day of ticket sales the
second day by selling 4 adult tickets and 5 child tickets. What is the price each of one adult
ticket and one child ticket?
Answer:
x+y=4+8=12
$12 for one of each
or if you mean indivually (the wording confused me)
$4 for child, $8 for adult
Step-by-step explanation:
x=adult
y=child
2x+10y=56
4x+5y=52
iin order to be able to subtract values and find x and y im going to multiply 4x+5y=52 by two and get 8x+10y=104
8x+10y=104
-2x+10y=56
6x=48 divide each side by 6
x=8
plug 8 back into an equation to find cost of y
2(8)+10y=56
-16 -16
10y=40
y=4
im literally crying because im so stressed and i don't understand if you know the answer please help i will do anything :(
Answer: 9x + 45 = 9x + 45 Infinitely many
Step-by-step explanation: Use distributive property for the left and add like terms for the right
Answer:
9,45,9,45 and infinite
Step-by-step explanation:
ngl im probably wrong but i tried
Question 6
1 pts
If f(x) = 0.41x is a function that represents the cost to mail
x number of letters, what is a reasonable domain for f?
O all real numbers
o all real numbers greater than 0
O the set of all whole numbers
o the set of all integers
Answer:
B
Step-by-step explanation:
The domain of the function 'f' represents the set of all whole numbers.
What is a function?A function is a relation between two sets. One set is called domain of the function and the other one is called range range of the function.
Given function is: f(x) = 0.41x.
f(x) represents the cost of mail.
Here, x represents the number of letters in the mail.
It can't be real numbers because, real numbers consist of negative numbers, fractions, etc.
It can not be integers, real numbers consist of negative numbers.
Therefore, the domain of must be all whole numbers.
Learn more about a function here:
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BRAINLIEST PLEASE JELP
What is the slope of a line perpendicular to the given line?
Answer:
4
Step-by-step explanation:
The perpendicular slope means opposite reciprocal
opposite: 1/4
reciprocal: 4
Answer:
The slope is undefined
Step-by-step explanation:
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