Answer:
32
Step-by-step explanation:
3(8(3)-5(2))-2((3)+(2))
3(24-10) -2(5)
3(14) -10
42-10
32
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{3(8a - 5b) - 2(a + b)}\\\\\huge\textsf{= 3(8(3) - 5(2)) - 2(3 + 2)}\\\\\huge\textsf{= 3(24 - 10) - 2(3 + 2)}\\\\\huge\textsf{= (3)(14) - 2(3 + 2)}\\\\\huge\textsf{= 42 - 2(3 + 2)}\\\\\huge\textsf{= 42 - 2(5)}\\\\\huge\textsf{= 42 - 10}\\\\\huge\textsf{= 32}}[/tex]
[tex]\huge\boxed{\textsf{Answer: 32}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
help with 5 please( question tuped below too).
Prove that y=x+2 is a tangent to the locous P(2t²,4t).
find the point of contact of this tangent to this locous and hence find the equation of normal at the point.
thanks
9514 1404 393
Answer:
tangent point: (2, 4)normal: y = -x +6Step-by-step explanation:
The derivative of P with respect to t is ...
P' = (x', y') = (4t, 4)
so the slope of the curve for some value of t is ...
dy/dx = y'/x' = 4/(4t) = 1/t
The line we want to be a tangent is y = x +2, which has a slope of 1. The curve will have a slope of 1 where ...
1/t = 1 ⇒ t = 1
At t=1, the point P is (2·1², 4·1) = (2, 4). For x=2, the point on the desired tangent is y = x +2 = 2 +2 = 4, or (x, y) = (2, 4).
The curve and the given line both have a slope of 1 at the point (2, 4), so that is the tangent point.
__
The normal to the curve at (2, 4) will have a slope that is the opposite reciprocal of the slope of the tangent: -1/1 = -1. Then point-slope form of the equation of the normal line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -4 = -1(x -2) . . . . . . line with slope -1 through point (2, 4)
y = -x +6 . . . . . . . . equation of the normal line in slope-intercept form
Find the reflection of the point (x,y) in the line y=mx+c
Answer:
[tex]\displaystyle \left(\frac{-(m^{2}-1)\, x + 2\, m\, y - 2\, m \, c}{m^{2} + 1},\, \frac{(m^{2} - 1)\, y + 2\, m \, x + 2\, c}{m^{2} + 1}\right)[/tex].
Step-by-step explanation:
Consider the line that is perpendicular to [tex]y = m\, x + c[/tex] and goes through [tex](x,\, y)[/tex].
Both [tex](x,\, y)[/tex] and the reflection would be on this new line. Besides, the two points would be equidistant from the intersection of this new line and line [tex]y = m\, x + c[/tex].
Hence, if the vector between [tex](x,\, y)[/tex] and that intersection could be found, adding twice that vector to [tex](x,\, y)\![/tex] would yield the coordinates of the reflection.
Since this new line is perpendicular to line [tex]y = m\, x + c[/tex], the slope of this new line would be [tex](-1/m)[/tex].
Hence, [tex]\langle 1,\, -1/m\rangle[/tex] would be a direction vector of this new line.
[tex]\langle m,\, -1\rangle[/tex] (a constant multiple of [tex]\langle 1,\, -1/m\rangle[/tex] would also be a direction vector of this new line.)
Both [tex](x,\, y)[/tex] and the aforementioned intersection are on this new line. Hence, their position vectors would differ only by a constant multiple of a direction vector of this new line.
In other words, for some constant [tex]\lambda[/tex], [tex]\langle x,\, y \rangle + \lambda\, \langle m,\, -1 \rangle = \langle x + \lambda \, m,\, y - \lambda \rangle[/tex] would be the position vector of the reflection of [tex](x,\, y)[/tex] (the position vector of [tex](x,\, y)\![/tex] is [tex]\langle x,\, y \rangle[/tex].)
[tex]( x + \lambda \, m,\, y - \lambda )[/tex] would be the coordinates of the intersection between the new line and [tex]y = m\, x + c[/tex]. [tex]\lambda\, \langle m,\, -1 \rangle[/tex] would be the vector between [tex](x,\, y)[/tex] and that intersection.
Since that intersection is on the line [tex]y = m\, x + c[/tex], its coordinates should satisfy:
[tex]y - \lambda = m\, (x + \lambda \, m) + c[/tex].
Solve for [tex]\lambda[/tex]:
[tex]y - \lambda = m\, x + m^{2}\, \lambda + c[/tex].
[tex]\displaystyle \lambda = \frac{y - m\, x - c}{m^{2} + 1}[/tex].
Hence, the vector between the position of [tex](x,\, y)[/tex] and that of the intersection would be:
[tex]\begin{aligned} & \lambda\, \langle m,\, -1 \rangle \\= \; & \left\langle \frac{m\, (y - m\, x - c)}{m^{2} + 1},\, \frac{(-1)\, (y - m\, x - c)}{m^{2} + 1}\right\rangle \\ =\; &\left\langle \frac{-m^{2}\, x + m\, y - m\, c }{m^{2} + 1},\, \frac{-y + m\, x + c}{m^{2} + 1}\right\rangle \end{aligned}[/tex].
Add twice the amount of this vector to position of [tex](x,\, y)[/tex] to find the position of the reflection, [tex]\langle x,\, y \rangle + 2\, \lambda \,\langle m,\, -1 \rangle[/tex].
[tex]x[/tex]-coordinate of the reflection:
[tex]\begin{aligned} & x + 2\, \lambda\, m \\ = \; & x + \frac{-2\, m^{2}\, x + 2\, m \, y - 2\, m \, c}{m^{2} + 1} \\ =\; & \frac{-(m^{2} - 1) \, x + 2\, m \, y - 2\, m \, c}{m^{2} + 1}\end{aligned}[/tex].
[tex]y[/tex]-coordinate of the reflection:
[tex]\begin{aligned} & y + (-2\, \lambda)\\ = \; & y + \frac{- 2\, y + 2\, m\, x + 2\, c}{m^{2} + 1} \\ =\; & \frac{(m^{2} - 1) \, y + 2\, m \, x + 2\, m \, c}{m^{2} + 1}\end{aligned}[/tex].
Which best describes the relationship between the line that passes through the points (-6,5) and (-
2,7) and the line that passes through the points (4, 2) and (6, 6)?
Answer:
Slope passes through (-6, 5) and (-2, 7)
[tex]m_1=\frac{y_2-y_1}{x_2-x_1} =m_1=\frac{7-5}{-2+6}[/tex]
[tex]m_1=\frac{2}{4} =\frac{1}{2}[/tex]
Slope passes through (4, 2) and (6, 6)
[tex]m_2=\frac{6-2}{6-4}[/tex]
[tex]\frac{4}{2} =2[/tex]
[tex]m_1\times m_2 \neq -1[/tex] [tex]m_1\neq m_2[/tex]
Answer:- A) neither perpendicular nor parallel.
OAmalOHopeO
Ugh I’m going insane trying to do this. Please help.
Answer:
y(x)=6^(x)-3
Step-by-step explanation:
Let the exponential function be y(x) = ab^(x) but since the graph is translated 3 units down, y(x) = ab^(x)-3. Now, y(0)=-2=a*b^(0)-3. a=1. The equation is nearly complete but we need b, we can find it by using the point y(1)=3. y(x)=b^(x) - 3. y(1)=3=b-3, b=6. The equation of the function is y(x)=6^(x)-3
Answer:
I agree with the first one
Cho A=( căn x -4x /1-4x -1) : (1+2x/1-4x -2căn x/ 2căn x -1 -1)
Answer:
0.85714285714286 x 100 = 85.7143%.
Step-by-step explanation:
A 7% acid solution will be mixed with a 15% acid solution. 20 L of a 12% acid solution needs to be made.
Identify the two variables in the problem by completing the following statements: * Let r represent: Let y represent:
Answer:
Let r = amount of the 7% solution
y represent the amount of the 15 percent solution
r =7.5 L
y = 12.5 L
Step-by-step explanation:
Let r = amount of the 7% solution
y represent the amount of the 15 percent solution
.07r + .15 y = (r+y) .12
r+y = 20
y = 20-r
.07r + .15 (20-r) = (20) .12
0.07r+0.15(20-r)=2.4
.07r+ 3 - .15r = 2.4
-.08r = 2.4-3
-.08r = -.6
Divide by-.08
r =7.5
y = 20-7.5
y = 12.5
Analyze the key features of the graph of the quadratic function f(x) = –x^2 + 4x – 3.
1. Does the parabola open up or down?
2. Is the vertex a minimum or a maximum?
3. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
9514 1404 393
Answer:
downmaximumx=2; (2, 1), -3Step-by-step explanation:
1. The negative leading coefficient (-2) tells you the parabola opens downward.
__
2. The fact that the parabola opens downward tells you the vertex is a maximum.
__
3. For quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For this parabola, that is x = -4/(2(-1)) = 2. The y-value of the vertex is f(2) = -2^2+4(2)-3 = -4+8-3 = 1. The y-intercept is the constant, c = -3.
axis of symmetry: x = 2vertex: (2, 1)y-intercept: (0, -3)first off thanks to the ppl who answered before 2nd off i need help again
Answer:
This number line show the inequality x > 2
solve for x! please help (show work)
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
Solving for [tex]x[/tex], we get:
[tex]16=2(3x-6)+x[/tex]
[tex]16=2*3x+2(-6)+x[/tex] (Distributive Property of Multiplication)
[tex]16=6x-12+x[/tex] (Multiply distributed terms)
[tex]16=7x-12[/tex] (Combine like terms)
[tex]16+12=7x-12+12[/tex] (Add [tex]12[/tex] to both sides of the equation to isolate [tex]x[/tex])
[tex]28=7x[/tex] (Combine like terms / Simplify)
[tex]\frac{28}{7}=\frac{7x}{7}[/tex] (Divide both sides of the equation by [tex]7[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]\bf x=4[/tex] (Simplify / Symmetric Property of Equality)
Hope this helps!
Step-by-step explanation:
[tex]16 = 2(3x - 6) + x \\ 16 = 6x - 12 + x \\ - 6x - x = - 12 - 16 \\ - 7x = - 12 - 16 \\ 7x = 12 + 16 \\ 7x = 28 \\ x = \frac{28}{7} \\ x = 4[/tex]
6 x ____ = 9
6 times what number equals 9
Answer:
3/2
Step-by-step explanation:
6 * _x___ = 9
Divide each side by 6
6 x __x__ = 9
x = 9/6
Simplify
x = 3/2
Answer:
1.5
Step-by-step explanation:
Well, in this form you'd multiply 1 and .5 by 6 separately and then add them together. This makes 1*6 = 6 and 0.5*6=3, add them together and you get 9.
Select the expression that represents the following statement: 3 times one fourth the difference of 26 and 10.
one fourth x (26 + 10) x 3
one fourth x (26 − 10) x 3
3 x one fourth x 26 − 10
3 x one fourth x 26 x 10
PLEASEE HEPPP
Answer:
the second option #2
one fourth x (26-10) x 3
Step-by-step explanation:
Two of the options (#1 and #4) can be ruled out immediately since they don't involve the difference of 26 and 10.
#3 can be ruled out because the difference needs to be multiplied by one fourth, but this option gives the wrong answer since the multiplication is done before subtraction (BODMAS)
Answer:
c
Step-by-step explanation:
I got it correct on a quiz
Milo receives a commission of 4% on all sales. If his commission on a sale was $51.00 , find the cost of the item he sold.
Answer:
1275
Step-by-step explanation:
51.00 = x*.04
51/.04 = 1275
Answer:
Step-by-step explanation:
4% x = 51
4/100 * x = 51 Multiply both sides by 100
100 * 4/100 * x = 5100
4x = 5100 Divide by 4
x = 5100/4
x = 1275
I didn't believe it was that large. Give the other answerer the Brainlest.
Sequence of transformation that take the graph y=x^2 to y=-2(x-5)^2+4
Answer:
(x-5) so translated 5 units to the right
Multiplied with 2, p vertically compressed
+4 means translated 4 units up
Draw the perpendicular bisector of the given line segment a.9.4 cm b. 8.6cm c. 10 cm
Answer:
Please do it by your shelf because if we measure it and send you may not be able to do by online .So, please do it by by yourself using your scale .
what number should be added to -5/8 to get -3/2
Answer:
-7/8
Step-by-step explanation:
-5/8+x=-3/2
x= -3/2+5/8=-12/8+5/8= -7/8
Use the numbers 6 2 9 5 2 3
to make 36.
Answer:
6+2+9+5+2+3+6+3 = 36
Step-by-step explanation:
If you like my answer than please mark me brainliest
An object is moving at a speed of 5 kilometers every 4.5 hours. Express this speed in miles per minute
Answer:
Step-by-step explanation:
1 km = 0.621 mi
1 hr = 60 min
(5 km)/(4.5 hr) × (0.621 mi)/km × (1 hr)/(60 min) = (0.0115 mi)/min
can somone heelp me
m
Answer:
b
Step-by-step explanation:
Suggest that you and your boss schedule regular check-ins at lunchtime and at the end of the day
Keep smiling and have a nice day :)
The graph below represents which of the following functions?
Answer:
D
Step-by-step explanation:
The correct answer is D, try graphing them on desmos.
solve for x. Solve for x solve for x solve for x
Answer:
x=29
Does the answer help you?
Answer:
x=29
Step-by-step explanation:
What is the area in square units of trapezoid ABCD shown Below ?
Answer: Choice B) 50 square units
Work Shown:
A = h*(b1+b2)/2
A = 5*(12+8)/2
A = 5*(20)/2
A = 100/2
A = 50 square units (choice B)
Notice how the b1 and b2 are the parallel bases, while the height h = 5 is perpendicular to both of these bases.
The area of Trapezium ABCD is 50 square unit.
what is area of Trapezium?
The formula to calculate the area of trapezium is:
Area = ½ x Sum of parallel sides x Distance between the parallel sides
Given:
base 1= 8 , base 2 = 12 unit
height= 5 unit
so, the area of Trapezium
= 1/2 ( base 1 + base 2) /2
= 1/2 (8 + 12) x5
= 1/2 x 20 x 5
= 10 x 5
= 50 square unit.
Learn more about area of Trapezium here:
https://brainly.com/question/16687907
#SPJ2
The graph of y=x√ is translated 5 units to the left and 7 units up. What is the equation of the graph that results from this translation?
Answer:
[tex]y = \sqrt{x - 5} + 7[/tex]
Help due today
No links
Answer:
-6
Step-by-step explanation:
Answer:
[tex]24 + x = 13 \\ x = 13 - 24 \\ x = - 11 \\ thank \: you[/tex]
14. Solve for p. Assume that none of the denominators are equal to 0
Plz help me
Answer:
Step-by-step explanation:
Divide by y
kl/y = f/(p + n) + r/u Subtract r/u from both sides
kl/y - r/u = f/(p + n) Multiply both sides by (p + n)
(kl/y - r/u ) (p + n) = f Divide by (kl/y - r/u)
p + n = f / (kl/y - r/u) Subtract n from both sides
p = f / (kl/y - r/u) - n
I think I'd leave this as the answer. I don't think you are expected to make it a 2 tier fraction.
How do u do this I don’t understand pls and thanks
Answer: Look it up on internet
Step-by-step explanation: INTERNET
Solve for X
(Ignore the math I did on top)
5 A machine puts tar on a road at the rate of 4 metres in 5 minutes.
a) How long does it take to cover 1 km of road
b) How many metres of road does it cover in 8 hours?
Answer:
5 a) Total = 20.83 hrs = 20 hrs and 50 mins (1250mins total)
5 b) Total = 96 meters. = 0.096km in 8 hrs.
Step-by-step explanation:
1km = 1000 meters
5 mins = 4 meters
1000/4 = 250 multiplier
250 x 5mins = 1250 minutes
1250/60 = 20hrs + 50 minutes
50 / 60 = 0.83 = 20.83hrs
b) 8 hrs = 8 x 60 = 480 minutes
480/5 = 24 multiplier of 4 meters
24 x 4 = 96 meters
What would the equation be if I multiplied each side by 12
Answer:
It's option a. 36 + 6x^2 = 28x
Step-by-step explanation:
Evaluate [x + 1/y]^m × [x-1/y]^n /[y+1/x]^m [y-1/x]^n
9514 1404 393
Answer:
(x/y)^(m+n)
Step-by-step explanation:
[tex]\displaystyle\frac{\left(x+\frac{1}{y}\right)^m\left(x-\frac{1}{y}\right)^n}{\left(y+\frac{1}{x}\right)^m\left(y-\frac{1}{x}\right)^n}=\left(\frac{x}{y}\right)^m\left(\frac{x}{y}\right)^n\\\\=\boxed{\left(\frac{x}{y}\right)^{m+n}}[/tex]
Find the value of x.
A. 86
B. 172
C. 94
D. 188
Answer:
188
Step-by-step explanation:
Tangent Chord Angle = 1/2Intercepted Arc
94 = 1/2 x
Multiply by 2
2*94 =x
188 =x
