There are two numbers. The sum of 4 times the first number and 3 times the second number is 34 the difference between 2 times the first number and 3 times the second number is 12 . Find the two numbers​

Answer:

y = 3(x-1)^2 -3

Step-by-step explanation:

y = 3(x+5)^2 - 2

vertex: (-5, -2)

1 unit down :

-2 - 1 = -3

6 units to the right:

3(x+5-6)^2 -2

3(x-1)^2 - 2

make what's in the parenthesis equal to 0:

(x-1)^2 = 0

x = 1

or

-5 + 6 = 1

new vertex : (1, -3)

equation : y = 3(x-1)^2 -3

Translation involves shifting of points from one position to another. The equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]

Given that:

[tex]y = 3(x + 5)^2 - 2[/tex]

[tex](h,k) = (-5,-2)[/tex] --- vertex

The general equation of a parabola is:

[tex]y = a(x - h)^2 + k[/tex]

By comparison:

[tex]a = 3\\ h = -5 \\ k= -2[/tex]

When the vertex is shifted 1 unit down, the rule is:

[tex](x,y) \to (x,y-1)[/tex]

So, we have:

[tex](x,y) \to (-5,-2-1)[/tex]

[tex](x,y) \to (-5,-3)[/tex]

When the vertex is shifted 6 unit right, the rule is:

[tex](x,y) \to (x + 6,y)[/tex]

So, we have:

[tex](h,k) \to (-5 + 6,-3)[/tex]

[tex](h,k) \to (1,-3)[/tex]

This means that:

[tex]h = 1\\ k =-3[/tex]

Recall that:

[tex]a =3[/tex]

Substitute these values in:

[tex]y = a(x - h)^2 + k[/tex]

[tex]y = 3(x - 1)^2 - 3[/tex]

Hence, the equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]

Read more about translations at:

https://brainly.com/question/12463306

Answer:

y = 6

I hope this helps you out!

Answer:

150

Step-by-step explanation:

Increase = New Number - Original Number.

divide the increase by the original number and multiply the answer by 100.

Let x(t) denote the amount of salt (in kg) in the tank at time t. The tank starts with 18 kg of salt, so x (0) = 18.

The solution is drained from the tank at a rate of 90 L/min, so that the amount of salt in the tank changes according to the differential equation

dx(t)/dt = - (x(t) kg)/(9000 L) × (90 L/min) = -1/100 x(t) kg/min

or, more succintly,

x' = -1/100 x

This equation is separable as

dx/x = -1/100 dt

Integrating both sides gives

∫ dx/x = -1/100 ∫ dt

ln|x| = -1/100 t + C

x = exp(-1/100 t + C )

x = C exp(-t/100)

(a) Using the initial condition x (0) = 18, we find

18 = C exp(0)   ==>   C = 18

so that

x(t) = 18 exp(-t/100)

(b) After 20 minutes, we have

x (20) = 18 exp(-20/100) = 18 exp(-1/5) ≈ 14.74

so the tank contains approximately 14.74 kg of salt after this time.

Answer:

C) 82/2

Step-by-step explanation:

The area of a square is calculated by multiplying a side by itself

so one side of the square is 9 in

the area of a triangle is calculated by multiplying height and base and that divided by 2

since E is the midpoint, if we draw a line show the height from there

the height would be 9

9*9/2 = 82/2

Answer:

y-3 = 2(x-1)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-3 = 2(x-1)

Answer:

3=2x+1

Step-by-step explanation:

Use the equation y=mx+b

where y is the y component, x is the variable and b is the x intercept

Answer:

(2,-1)

Step-by-step explanation:

Solved using math.

Answer:

The solution is (2, -1) to show this by graphing do y = -1 by making a straight horizontal line at (0,-1) . And then for the other equation make a line where it starts at (0,4) and passes point (2,-1). Just plot those two points and connect them and you'll have made the line.

Step-by-step explanation:

The equation of the circle is  [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] . The option C is the correct option.

Given that the centre of the circle is (2,3) and circle has radius 4.

To find the equation of the circle, use the general equation of the circle as:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h, k) is the centre of the circle and r is the radius of the circle.

Since, h = 2, k = 3 and radius r = 4.

Therefore, the equation of the circle:

[tex](x-h)^2+(y-k)^2=r^2\\(x-2)^2+(y-3)^2=4^2\\(x-2)^2+(y-3)^2=16[/tex]

The equation of the circle cantered at (2,3) and has a radius of 4 is  [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .

Therefore, The equation of the circle cantered at (2,3) and has a radius of 4 is  [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .

Learn more about Diameter here:

https://brainly.com/question/32968193

#SPJ2

please mark this answer as brainlist

Answer: 45° and speed of light in prism 2×10⁸m/s

Step-by-step explanation:

The minimum deviation of the equilateral glass prism will form 60° angle.

So angle of incidence = 3/4×60

= 3 ×15

= 45°

Minimum deviation = δmin

= 30

After finding the value of μ using prism law

μ = 1.41

Speed of light will be 2×10⁸m/s

Must click thanks and mark brainliest

Answer:

The parabola x²=8y has,

vertex: (0,0)

focus: (0,2)

directrix: y=-2

so that option is the answer,

btw, the parabola opens up to the top and axis of symmetry is x=0

Answer:

It's A!

Step-by-step explanation:

Got it correct on my test! :)

Answer:

x2  1-

Step-by-step explanation:

Answer:

x ≥ 0

Step-by-step explanation:

Domain of a function is the x values of a function

The graph extends from 0 to positive infinity.

Since the point at x=0 is closed, the graph includes 0

Answer:

(x,y) -> (-y,x), second option.

Step-by-step explanation:

Rotation of 90 degrees about the origin:

The rule for a rotation of a point (x,y) 90 degrees about the origin is given by:

(x,y) -> (-y,x)

This is that the question asks, and so, this is the answer, which is the second option.

Answer:

0.0005m^3

Step-by-step explanation:

V=1/3hπr²

h=6m

d=12m

r=12÷2=6m

V=1/3×6×(3.14)×36

V=1/2034.72

V=0.0005m^3

Answer:

h.

[tex] \frac{9 {x}^{10}(y. {x}^{3}) {}^{2} }{y.x(3 {x}^{3}) {}^{3} } \\ \\ = \frac{9 {x}^{10}(y {}^{2} )( {x}^{6} ) }{3y. {x}^{10} } \\ \\ = \frac{ {3}^{2} {x}^{16} {y}^{2} }{3y {x}^{10} } \\ \\ = 3y {x}^{6} [/tex]

j.

[tex] \frac{(3x. {y}^{7} ) {}^{2}. {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{3 {x}^{2} . {y}^{14} . {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{ {3x}^{7} {y}^{14} }{3 {x}^{7} {y}^{4} } \\ \\ = {y}^{10} [/tex]

Answer:

y-3 = -4(x+2)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y-3 = -4(x --2)

y-3 = -4(x+2)

Answer:

0.05547

Step-by-step explanation:

Given :

_____Peter __ Alan __ Sui__total

Before 1838 __ 418 ___1475 _3731

After _ 1420 __ 329 ___1140_2889

Total _3258 __ 747 __ 2615 _6620

The expected frequency = (Row total * column total) / N

N = grand total = 6620

Using calculator :

Expected values are :

1836.19 __ 421.006 __ 1473.8

1421.81 ___325.994__ 1141.2

χ² = Σ(Observed - Expected)² / Expected

χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)

χ² = 0.05547

Answer:

4

Step-by-step explanation:

twice her age:

10*2 = 20

24-20 = 4

Answer:

4 i believe that's the answer

Answer:

B

Step-by-step explanation:

Recall that if two functions, f and g, are inverses, then by definition:

[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]

Hence, the graph of f(g(x)) should be simply y = x.

Therefore, our answer is B, as both coordinates are equivalent for all three points.

Answer:

Is answer 22 units sqaure ?

Answer:

31.5

Step-by-step explanation:

Angle Z+ Angle X+ Angle Y=180

As the triangle is isosceles, Z=X, hence Z=63/2=31.5

Answer:

the slope -3, slope meaning rate of change and y intercept is 1.

hope that answers your question

(used desmos to graph, good stuff!!!)

Answer:

C.

Step-by-step explanation:

Science questions are T/F. That's .5 or [tex]\frac{1}{2}[/tex] chance to get it right.

7 questions. Each with a [tex]\frac{1}{2}[/tex].

That's [tex](\frac{1}{2})^{7}[/tex]  

[tex](\frac{1}{2})^{7}[/tex] = [tex]\frac{1}{128}[/tex] = .0078 = .008 rounded

English questions are multiple choice. 4 choices. That's .25 or [tex]\frac{1}{4}[/tex]

3 questions. Each [tex]\frac{1}{4}[/tex]

That's [tex](\frac{1}{4})^{3}[/tex]

[tex](\frac{1}{4})^{3}[/tex] = [tex]\frac{1}{64}[/tex] = .0156 = .016 rounded

The probability of getting all questions correct is 0.004 which is lower than for science (0.016).

Science questions are said to have a 6 out of 6 correct answer range and a 0.5 chance of being answered properly.

So, P(6) = 0.5⁶

P(6) = 0.016

We are informed that there are 4 out of 4 correct answers for English, with a 0.25 chance of getting it right.

Thus; P(4) = 0.25⁴ = 0.004

Thus, we conclude that they will have to study English.

Learn more about Probability here:

brainly.com/question/251701

#SPJ7

Answer:

Hello,

This sequence is geometric with a ratio of -3

the first term is 6

Step-by-step explanation:

[tex]u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_{n+1}=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _{i=1}u_i = \lim_{n \to \infty} \sum\limits^n _{i=1}u_1*(-3)^{i-1}\\=6*\lim_{n \to \infty} \sum\limits^\infty _{i=1}(-3)^{i-1}\\=6*\frac{1-(-3)^n}{1-(-3)} \\=\dfrac{3}{2} *({1-(-3)^n)\\[/tex]

serie does not converge.

Step-by-step explanation:

36 pages in 3 days, 36/3=12 pages per day.

45 pages in 5 days, 45/5=9 pages per day.

Difference is 3 pages per day

Answer:

Deon read 3 more  pages per day than Emily.

Answer:

21.9 ft

Step-by-step explanation:

Answer:

Part A)

About 74.2°.

Part B)

About 21 feet.

Step-by-step explanation:

A 22 feet ladder is leaning against a building, where the base of the ladder is six feet from the base of the building.

This is shown in the diagram below (not to scale).

Part A)

We want to determine the angle of elevation of the ladder. That is, we want to find the value of θ.

Since we know the values adjacent to θ and the hypotenuse, we can use the cosine ratio. Recall that:

[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

The adjacent is 6 and the hypotenuse is 22. Thus:

[tex]\displaystyle \cos \theta = \frac{6}{22} = \frac{3}{11}[/tex]

Take the inverse cosine of both sides:

[tex]\displaystyle \theta = \cos^{-1}\frac{3}{11}[/tex]

Use a calculator. Hence:

[tex]\displaystyle \theta = 74.1733...\approx 74.2^\circ[/tex]

The angle of elevation is approximately 74.2°

Part B)

We want to find how high up the ladder reaches on the building. In other words, we want to find x.

Since x is opposite to θ and we know the adjacent side, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

The opposite side is x and the adjacent side is 6. The angle θ is cos⁻¹(3/11) (we use the exact form to prevent rounding errors). Thus:

[tex]\displaystyle \tan \left(\cos^{-1}\frac{3}{11}\right) = \frac{x}{6}[/tex]

Solve for x:

[tex]\displaystyle x = 6 \tan \left(\cos^{-1}\frac{3}{11}\right)[/tex]

Use a calculator. Hence:

[tex]x = 21.1660... \approx 21\text{ feet}[/tex]

The ladder reaches about 21 feet up the building.

Answer:

f(3) = 6

Step-by-step explanation:

If f(1)=10, then f(1+1)=f(1)-2

f (2) = 10 - 2 = 8

Therefore f(3) = f(2) - 2 = 8 - 2 = 6