Answer:
Step-by-step explanation:
The distance between a point (x,y) and the point (-3,4) is
d1= [tex]\sqrt{ (x+3)2+(y-4)2}[/tex] .
The distance between a point (x,y) and the point (0,0) is
d2= [tex]\sqrt{x2+y2}[/tex] .
You know what y is from the equation of the line, so substitute that, set d1=d2, and solve for x.
The coordinates of the point on the straight line y=3x+1 that is equidistant from the origin and (−3, 4) is (-33/18, 39/6)
The distance formula is expressed as:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\[/tex]
For the coordinate point (x,y) to (-3, 4), the distance is expressed as:
[tex]D_1 = \sqrt{(x+3)^2+(y-4)^2}\\[/tex]
For the coordinate point (x,y) to (0, 0), the distance is expressed as:
[tex]D_2=\sqrt{(x-0)^2+(y-0)^2}\\D_2 = \sqrt{x^2+y^2}[/tex]
Since the distance are equidistant, then D1 = D2
[tex]\sqrt{(x+3)^2+(y-4)^2} = \sqrt{x^2+y^2}\\ (x+3)^2+(y-4)^2 = x^2+y^2\\x^2+6x+9+y^2-8y+16 = x^2+y^2\\6x+9-8y+16=0\\6x-8y+25=0[/tex]
Substitute y = 3x+1 and get x
6x - 8y + 25 = 0
6x-8(3x+1) - 25 = 0
6x -24x-8-25=0
-18x-33 = 0
-18x = 33
x =-33/18
Sincey= 3x + 1
y = 3(33/18) + 1
y = 33/6 + 1
y = 39/6
Hence the required coordinates is (-33/18, 39/6)
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Find all points on the curve x=4cos(t),y=4sin(t) that have the slope of 12.
Answer:
[tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].
Step-by-step explanation:
We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.
[tex]x=4cos (t)[/tex]
[tex]\dfrac{dx}{dt}=-4sin (t)[/tex]
[tex]y=4sin (t)[/tex]
[tex]\dfrac{dy}{dt}=4cos (t)[/tex]
Now,
[tex]\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}[/tex]
[tex]\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}[/tex]
[tex]\dfrac{dy}{dx}=-\cot t[/tex]
So, slope of the curve is [tex]-\cot t[/tex].
[tex]-\cot t=\dfrac{1}{2}[/tex]
[tex]-\tan t=2[/tex]
[tex]\tan t=-2[/tex] ...(1)
Using [tex]\sec^2t=1+\tan^2t[/tex], we get
[tex]\sec^2t=1+(-2)^2[/tex]
[tex]\sec^2t=1+4[/tex]
[tex]\sec t=\pm \sqrt{5}[/tex]
[tex]\cos t=\pm \dfrac{1}{\sqrt{5}}[/tex]
Now,
[tex]\sin^2t=1-cos^2t[/tex]
[tex]\sin t=\pm \sqrt{1-\dfrac{1}{5}}[/tex]
[tex]\sin t=\pm \sqrt{\dfrac{4}{5}}[/tex]
[tex]\sin t=\pm \dfrac{2}{\sqrt{5}}[/tex]
It equation (1), tan(t) is negative. So, sin and cos have different signs.
If [tex]\sin t= \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t=- \dfrac{1}{\sqrt{5}}[/tex].
[tex]x=4cos (t)=-\dfrac{4}{\sqrt{5}}[/tex]
[tex]y=4sin (t)=\dfrac{8}{\sqrt{5}}[/tex]
If [tex]\sin t=- \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t= \dfrac{1}{\sqrt{5}}[/tex].
[tex]x=4cos (t)=\dfrac{4}{\sqrt{5}}[/tex]
[tex]y=4sin (t)=-\dfrac{8}{\sqrt{5}}[/tex]
Therefore, the two points are [tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].
Simplify 0.05x + 1.02x.
Answer:
107x-
-------
100
Step-by-step explanation:
how do u factorise 45x - 10
Answer:
-450
Step-by-step explanation:
The value of factors of the function are,
⇒ 5 (9x - 2)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The expression is,
⇒ 45x - 10
Now, We can factor the equation as;
⇒ 45x - 10
⇒ 5×9x - 5×2
⇒ 5 (9x - 2)
Thus, The value of factors of the function are,
⇒ 5 (9x - 2)
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The two rectangles in the sketch below are congruent. Which sequence exhibits their congruence? A rotation 90° clockwise about the origin followed by a reflection across the x-axis A rotation 90° counterclockwise about the origin followed by a reflection across the y-axis A rotation 90° counterclockwise about the origin followed by a reflection across the x-axis A rotation 180° counterclockwise about the origin followed by a reflection across the y-axis
Answer:
A rotation 90° counterclockwise about the origin followed by a reflection across the x-axis
Step-by-step explanation:
it's rotated about the origin counterclockwise by 90 degrees and then reflected over the X axis in order to find the shape there.
a seven sided number cube with sides numbered 1,2,3,4,5,6,7 is rolled. what is the probability that a 4 or odd number is rolled ? which fraction ? 5/7 2/7 3/7 4/49
The probablity of rolling a 4 = 1/7
There are 4 odd numbers, so the probablity of rolling an odd number = 4/7
4/7 + 1/7 = 5/7
Please emergency!!!
Please
Answer:
plane Q
Step-by-step explanation:
Please marke as a brainlist...
Is 0.7 a rational or irrational number?
0.7 is a rational number.
Explanation:Because it is a terminating decimal expansion.
Answer:
0.7 is a rational number- experssed as a fraction, it is equal to 7/10
please help me with these two questions ( show work plz )( it's ok if you only now one)
Answer:
1.8.09
2.-6
Step-by-step explanation:
1. 11b=89
b=89/11
8.09
2. 13+k/3=11
k/3=11-13
k/3=-2
k=-2*3
=-6
Answer:
Number 2 is - 6
Step-by-step explanation:
2. 13 + k/3 = 11
We can start off my subtracting 13 in both sides.
-13 + 13 + k/3 = 11 - 13
k/3 = -2. now we have to multiply 3 in both sides
3 x k/3 = -2 x 3
k = -6
Hope this helps!!
I give Brainliest to whom says this question is stupid. What is -2x-8
Answer:
No solution it IS STUPID.
Step-by-step explanation:
Answer:
that question is stupid.
Problem
3x + 5 + 2x = 12 + 4x
Answer:
x=7
Step-by-step explanation:
because u add the like terms so
3x+2x
which would be
5× so now its
5x+5=12+4x
-4. -4
x+5=12
-5. -5
x=7
Use the given endpoint Y and the midpoint M of YZ (there is a line over YZ) to find the coordinates of the other endpoint Z
The x-coordinate of our midpoint = 3
The x-coordinate of Y = 0
k = x-coordinate of Z
3 = (0 + k) / 2
Multiply both sides by 2
6 = k + 0
Simplify
6 = k
The y-coordinate of our midpoint = 3
the y-coordinate of Y = 5
w = y-coordinate of Z
3 = (w + 5) / 2
Multiply both sides by 2
6 = w + 5
Subtract 5 from both sides
1 = w
For problem #17, Z(6, 1)
Let's do problem 18 now.
The x-coordinate of our midpoint = 5
The x-coordinate of Y = -1
k = x-coordinate of Z
5 = (k + (-1)) / 2
Multiply both sides by 2
10 = k + (-1)
Simplify the right side
10 = k - 1
Add 1 to both sides
11 = k
The y-coordinate of our midpoint = 9
The y-coordinate of Y = -3
w = y-coordinate of Z
9 = (w + (-3)) / 2
Multiply both sides by 2
18 = w + (-3)
Simplify the right side
18 = w - 3
Add 3 to both sides
21 = w
For problem #18, Z(11, 21)
The price of a tv is rs3000.if the discount is rs1560,find the percent of discount.
Answer:
price of tv = 3000
discount =1560
discount % = 1560/3000 * 100% = 52%
Step-by-step explanation:
Answer:
52
Step-by-step explanation:
Formula =discount ×100÷original price
1560×100÷3000=52%
Evaluate the expression for x = -3 and y = 4
3x2 – 2xy
Answer: -36 is your answer
Step-by-step explanation:
Round 8,542,310 to the nearest million
Answer:
9,000,000
Step-by-step explanation:
Since the 5 next to the 8 is a number with a value of 5 or higher, you can round the 8 up to a 9 thus rounding to the nearest million.
6(m+2)+6m=-5(-7m-7) Solve for m.
Answer:
m = -1
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
m = -1
☽------------❀-------------☾
Hi there!
~
Let's solve your equation step-by-step.
[tex]6(m+2)+6m=-5(-7m-7)[/tex]
Step 1: Simplify both sides of the equation.
[tex]6(m+2)+6m=-5(-7m-7)[/tex]
[tex](6)^{(m)} + (6)(2)+6m= (-5)(-7m)+(-5)(-7)[/tex] (Distribute)
[tex]6m+12+6m=35m+35[/tex]
[tex](6m + 6m)+(12)=35m + 35[/tex] (Combine Like Terms)
[tex]12m + 12 = 35m + 35[/tex]
[tex]12m + 12 = 35m + 35[/tex]
Step 2: Subtract 35m from both sides.
[tex]12m + 12 - 35m = 35m + 35 - 35m[/tex]
[tex]-23m + 12 = 35[/tex]
Step 3: Subtract 12 from both sides.
[tex]-23m + 12 - 12= 35 - 12[/tex]
[tex]-23m = 23[/tex]
Step 4: Divide both sides by -23.
[tex]\frac{-23m}{-23} = \frac{23}{-23}[/tex]
[tex]m = 1[/tex]
❀Hope this helped you!❀
☽------------❀-------------☾
how does math play a role in the activities of your everyday life activities
Answer:
-Managing money $$$
-Balancing the checkbook.
-Shopping for the best price.
-Preparing food.
-Figuring out distance, time and cost for travel.
-Understanding loans for cars, trucks, homes, schooling or other purposes.
-Understanding sports (being a player and team statistics)
-Playing music.
These are things we do everyday that use Math.
Mathematics makes our life orderly and prevents chaos. Certain qualities that are nurtured by mathematics are power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability and even effective communication skills.
Please answer and give an explanation.
Answer:
h=12.5
Step-by-step explanation:
It’s a right triangle, so you can use the Pythagorean Theorem.
9.2²+8.5²=h²
84.64+72.25=h²
156.89=h²
√156.89=h
h=12.5255
h=12.5
2/7(x+4)=-6 what is the value of x?
Answer:
2/7 as decimal is 0.28
2/7(x+4)=-6
2/7x+ 1 1/4= -6
-6 - 1 1/4 = -7.25
0.28x = -7.25
x = -25.89
x -0.63 = 1.16 I couldn't find the answer can someone please help me?
Answer:
x= 1.79
Step-by-step explanation:
x-0.63=1.16 add 0.63 to both sides
x= 1.79
Answer:
x =1.79
Step-by-step explanation:
x -0.63 = 1.16
Add .63 to each side
x -0.63+.63 = 1.16+.63
x =1.79
Un volcan lanza una roca con una rapidez de 47.5 m/s con un angulo de 39.4° sobre el eje x. La roca toca el suelo a 1750 m por debajo de la altura inicial si se desprecia la resistencia del aire y considerando un valor constante de aceleracion debido a la gravedad de 9.81 m/s¨2 cual es el tiempo en completar la trayectoria
Explicación paso a paso:
El tiempo necesario para completar la trayectoria se conoce como tiempo de vuelo.
Tiempo de vuelo = dónde;
U es la velocidad inicial del cuerpo = 47,5 m / s
es el ángulo de lanzamiento = 39,4 °
g es la aceleración debida a la gravedad = 9,81 m / s²
Sustituyendo los parámetros dados en la fórmula anterior, tendremos;
[tex]T = \dfrac{2(47.5)sin39.4^0}{9.81} \\\\T = \dfrac{95sin39.4^0}{9.81} \\\\T = \dfrac{95*0.6347}{9.81} \\\\T = \dfrac{60.2994}{9.81} \\\\T =6.1467 secs[/tex]
El tiempo necesario para completar la trayectoria es de 6.1467 segundos.
Write the fraction 12/28 in the simplest form
Answer: 3/7
Step-by-step explanation:
Answer:
12/28 is 3 /7 is your answer
A. B. 3(x+2) x+2 =18 =6 1) How can we get Equation BBB from Equation AAA? Choose 1 answer: Choose 1 answer: (Choice A) A Add/subtract the same quantity to/from both sides (Choice B) B Add/subtract a quantity to/from only one side (Choice C) C Multiply/divide both sides by the same non-zero constant (Choice D, Checked) D Multiply/divide only one side by a non-zero constant
Answer:
C. Multiply/divide both sides by the same non-zero constant
A. Yes
Just Did It On Khan Academy
Step-by-step explanation:
To get equation A from equation B multiply/divide only one side by a non-zero constant option (C) Multiply/divide only one side by a non-zero constant is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
Two linear equations:
A. 3(x + 2) = 18
B. x + 2 = 18
In equation B multiply by 3 on one side:
3(x + 2) = 18
Thus, to get equation A from equation B multiply/divide only one side by a non-zero constant option (C) Multiply/divide only one side by a non-zero constant is correct.
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13.) The ratio of the weight of an object on Mars to the weight of that object on Earth is 4:10. If a rocket weighs 15 tons on earth, how many tons would it weigh on Mars? (Need help quick please)
Answer: 6 tons
Step-by-step explanation: 4:10 is also 2/5 so all we need to do is 2/5 of 15 which is 6. [15x(2/5)]
Hope this helps!
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The temperature falls from 0 degrees to -12.4 degrees in 3 hours. Which expression finds the change in temperature
per hour?
Answer: should be 4.13
Step-by-step explanation: -12.4 divided by 3 is -4.13333333333 and goes on
what is (10y+6) (8y-6) ?
Answer:
y = 3/4 or y = -3/5
Step-by-step explanation:
Solve for y:
(8 y - 6) (10 y + 6) = 0
Hint: | Find the roots of each term in the product separately.
Split into two equations:
8 y - 6 = 0 or 10 y + 6 = 0
Hint: | Look at the first equation: Factor the left hand side.
Factor constant terms from the left hand side:
2 (4 y - 3) = 0 or 10 y + 6 = 0
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides by 2:
4 y - 3 = 0 or 10 y + 6 = 0
Hint: | Isolate terms with y to the left hand side.
Add 3 to both sides:
4 y = 3 or 10 y + 6 = 0
Hint: | Solve for y.
Divide both sides by 4:
y = 3/4 or 10 y + 6 = 0
Hint: | Look at the second equation: Factor the left hand side.
Factor constant terms from the left hand side:
y = 3/4 or 2 (5 y + 3) = 0
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides by 2:
y = 3/4 or 5 y + 3 = 0
Hint: | Isolate terms with y to the left hand side.
Subtract 3 from both sides:
y = 3/4 or 5 y = -3
Hint: | Solve for y.
Divide both sides by 5:
Answer: y = 3/4 or y = -3/5
Hi can someone tell me how is the answer 113?? how do i type it in the calculator?? im confused can someone please explain ASAP!!!!!!!!
THANK YOU
You shouldn't need a calculator for this. The quadratic equation is written in standard form.
ax^2 + bx + c = 0
You substitute a, b, and c into the discriminant formula and solve as shown in the example in the picture you provided.
(-7)^2 - 4(2)(-8)
49 - 4(-16)
49 - (-64)
49 + 64
113
Best of Luck!
What type of information is being presented on this graph?
What is 28828+88+8+78282882728288+8+888+8882828888-8–88-89939x929299999299292929+839929828-0+9929299x91919192939939+929292992929999-9-9-9999299202839393=
Answer:
-8.2667628e+22
-Step-by-step explanation:
Describe the transformation.
Answer:
C. reflection across the x-axis
Answer:
C
Step-by-step explanation:
This is a reflection across the x-axis because it is the same thing but reflected.
Hope this helps.
milo runs 4.5 miles around his house he has to run 6.7 miles how many miles does he have to run left
Answer:
2.2 miles
Step-by-step explanation:
6.7 - 4.5 = 2.2
Answer:
6.7 miles
Step-by-step explanation:
The sentence about 4.5 miles is extra info. you don't need. In the question it says he needs to run 6.7 miles, then continues to ask how many miles he needs to run.
I hope this answers your question and you understand! Have a great rest of your day! :)