i will give brainliest if you wanttt!

Answer:

C.

Step-by-step explanation:

i took the test

The standard form of the equation of the parabola that has a vertex of (-4,-3) and a directrix of x = 2 is (x+3)² = -24(y+4), the correct option is D.

If a quadratic equation is written in the form

y=a(x-h)^2 + k

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

First of all, i used this vertex formula thing since it is visible that there are quadratic functions. Otherwise, you had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.

This point (h,k) is called the vertex of the parabola that quadratic equation represents.

We are given that;

The vertex of parabola=(-4,-3)

Directrix of x is 2

Now,

The distance from a point (x,y) to the directrix x = 2 is the horizontal distance between the point and the line, which is |x - 2|. The distance from a point (x,y) to the focus (-4,f) is the distance between the point and the vertex plus the distance between the vertex and the focus, which is |y - (-3)| + |-4 - 2| = |y + 3| + 6.

|y + 3| + 6 = |x - 2|

To eliminate the absolute value, we can square both sides of the equation:

(y + 3)² + 12(y + 3) + 36 = (x - 2)²

(x - 2)² = (y + 3)² + 12(y + 3) + 36

x² - 4x + 4 = y² + 6y + 9 + 12y + 36

x² - 4x = y² + 18y + 45

x² - 4x + 4 = y² + 18y + 49

(x - 2)² = (y + 9)²

This is the standard form of the equation of the parabola, which has a vertex of (-4,-3) and a directrix of x = 2. Comparing this equation with the standard form of the equation of a parabola, we can see that the parabola opens horizontally to the left, and its focus is the point (-6,-3).

(x-2)² = -24(y+9)

Therefore, the equation will be (x+3)² = -24(y+4).

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Answer:

(y+8)(y+2)

Step-by-step explanation:

y^2 + 10y + 16

What two numbers multiply to 16 and add to 10

8*2 = 16

8+2 =10

(y+8)(y+2)

Answer:

Step-by-step explanation:

The point A has coordinates (5, 1) so the image of A which is A' has

coordinates (5 - 2,  1+3)

= (3, 4).

B', C' and D' are calculated in the same way.

So B' is (4, 1),

C' = (3, 2) and

D' = (2, 1)

Answer:

49

Step-by-step explanation:

(3m + 58) + (8m + 155) = 180

11m + 213 =180

11m = -33

m = -3

PCM = 3m + 58 = -9 + 58 = 49

Answer:

(f • g)(x) = log (-x + 1)

Step-by-step explanation:

Here is a composite function

What we simply have to do here is to make a substitution

the substitution we are going to make is that we will substitute the value of x in f(x) with the entirety of g(x)

This simply mean that we replace every x we find in f(x) with the entire equation of g(x)

we have this as;

f(g(x)) = log (-x + 1)

Answer:

linear positive association is the answer

Answer:

A

Step-by-step explanation:

Answer:

the answer is plane try I'm pretty sure it's that.

Answer:

Let the first integer be 'n.' Then n(n+2)+38=(n+2)^2. Solve using the quadratic equation: n=17. The two odd integers are 17 and 19.

Step-by-step explanation:

The integers are -39 and -38.

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of [tex]\dfrac{a}{b}[/tex] where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

Given;

The product of two consecutive positive odd integers is 38 less than the square of the greater integer

Now, let the numbers be x and x+

So, the equations will be

x(x+1)-38=(x+1)^2

x^2+x-38=x^2+1+2x

x=-39

x+1=-38

Therefore, the integer numbers will be -39 and -38.

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Answer:

I think the answer should be A

Answer:

So your answer would be A

Step-by-step explanation:

It is not B since a negative correlation, the only time it will be a negative correlation is if its going the other way or down

It is also not C since there is a correlation, (positive correlation) there would be no dots.

I dont think its D since the speed is increasing but the cost is not decreasing, this would represent a negative correlation.

So your answer would be A since the line is linear, it is mild (the points are not to close but not to far) and its positive since it is going right and up.

Hope this helped :D

Hope this help!!!

Have a nice day!!!

Explanation:

The first term has its exponents add to 1+2 = 3

The second term has its exponents add to 1+1 = 2

The third term can be written as -2x^0y^0, and those exponents add to 0

The sums count down: 3, 2, 0

So standard form means we write the terms with the largest degree sums first, then second largest and so on.

Answer:

should be 3/7 I think that's right

Answer:

8

Step-by-step explanation:

The bottom angles are equal, so the sides are equal

2x = 5x-12

Subtract 5x from each side

2x-5x= 5x-12-5x

-3x = -12

Divide by -3

x = 4

YZ = 5x-12 = 5(4) -12 = 20-12 =8

Answer:

no

Step-by-step explanation:

Example:

Answer:

factorise form of

x²+2x = x(x+2)

Answer:

[tex]S' = (-5,-5)[/tex]

[tex]Q"=(-5,-5)[/tex]

Step-by-step explanation:

Given

[tex]S = (5,-5)[/tex]

[tex]Q= (5,5)[/tex]

Solving (a): Reflect S across y-axis

The rule to reflect across y-axis is:

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

So, we have:

[tex]S(5,-5) \to S'(-5,-5)[/tex]

Hence:

[tex]S' = (-5,-5)[/tex]

Solving (b): Reflect Q across x and y-axis

The rule to reflect across x-axis is:

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

So:

[tex]Q(5,5) \to Q'(5,-5)[/tex]

The rule to reflect across y-axis is:

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

So:

[tex]Q'(5,-5) \to Q"(-5,-5)[/tex]

Hence:

[tex]Q"=(-5,-5)[/tex]

i dont get it either

Step-by-step explanation:

Answer:

10 boxes

Step-by-step explanation:

Take the number of fossils and divide by the number per box to determine the number of boxes

60/6 = 10

She needs 10 boxes

Answer:

10 boxes

Step-by-step explanation:

60 fossils are evenly distirbutd into x number of boxes so that there are 6 fossils in each box.

The equation will look like:

[tex]6x=60\\x= 10[/tex]

Hope this helped!

Complete the square:

x ^2 - 2x + y ^2 + 4y + 1 = 0

(x - 1)^2 + (y + 2)^2 + 1 = 1 + 4

(x - 1)^2 + (y + 2)^2 = 4 = 2^2

Hence the center is (1, -2) and the radius is 2. (D)

Answer:

Step-by-step explanation:

Let's FOIL this out and get it into standard quadratic format:

[tex]h(t)=-4.9t^2+490[/tex]. The lack of a linear term in the middle means therewas no upwards velocity, consistent with the object being dropped straight down as opposed to thrown up in the air tand then falling in a parabolic path. The -4.9t² represents the acceleration due to gravity, and the 490 represents the height from which the object was dropped. The constant in a quadratic that is modeling parabolic motion always represents the height from which the object was dropped (or launched). That's how you know.

The requried initial height of the object is 490 meters.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

The object is dropped from a height of 49 meters.

We know this because the initial height is given by the first term of the expression in the parentheses, which is 49. When the object is dropped from the helicopter, t is equal to zero. Substituting t=0 into the equation for h gives:

h(0) = (49 + 4.9(0))(10 - 0) = 49(10) = 490

Therefore, the initial height of the object is 490 meters.

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Answer:

6n-1

Step-by-step explanation:

The Equivalent polynomial is 6n-1.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

We have,

To divide (18n² - 9n+ 1) by (3n-1).

Now, performing the division we get

                   3n-1   |  18n² - 9n+ 1  | 6n -1

                                18n² - 6n

                              _________

                                         -3n + 1

                                          -3n +1

                                          _______

                                                  0

Thus, the quotient is 6n -1.

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Answer:

What help you need from us?????

Answer:

I think the answer is 6

Step-by-step explanation:

but it could also be 5 since its the lowest number. But if its goin based of the amount of data it should be 6

Answer:

See below

Step-by-step explanation:

[tex]x+7\leq2[/tex] or [tex]\frac{x+14}{4}\geq3[/tex]

[tex]x\leq -5[/tex] or [tex]x\geq-2[/tex]

Therefore, on the number line, you would have a closed dot at x=-5 with an arrow going to the left, and then you would have a closed dot at x=-2 with another arrow going to the right.

Answer: x=6

Step-by-step explanation:

Let's solve your equation step-by-step.

4+3(2x−4)=28

Step 1: Simplify both sides of the equation.

4+3(2x−4)=28

4+(3)(2x)+(3)(−4)=28(Distribute)

4+6x+−12=28

(6x)+(4+−12)=28(Combine Like Terms)

6x+−8=28

6x−8=28

Step 2: Add 8 to both sides.

6x−8+8=28+8

6x=36

Step 3: Divide both sides by 6.

6x

6

=

36

6

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

[tex]4+3 (2x-4)=28[/tex]

Distribute 3 to the parenthesis:

[tex]4+6x-12=28[/tex]

Add 12 to both sides:

[tex]4+6x-12=28[/tex]

          +12      +12

[tex]4+6x=40[/tex]

Subtract 4 from both sides:

[tex]4+6x=40[/tex]

-4            -4

[tex]6x=36[/tex]

Divide both sides by 6

[tex]6x=36[/tex]

/6      /6

[tex]x=6[/tex]

Hope this helps!

Answer:

[tex] \frac{15 \sqrt{209} }{209} [/tex]

Step-by-step explanation:

Objective: Understand and work with trig identies.

Recall multiple trig identies and manipulate them to get from cosecant to secant.

Given

[tex] \csc(a) = \frac{60}{16} [/tex]

Apply reciprocal identity csc a = 1/sin a.

[tex] \sin(a) = \frac{16}{60} [/tex]

Apply pythagorean identity to find cos a.

[tex]( \frac{16}{60}) {}^{2} + \cos(x) {}^{2} = 1[/tex]

[tex] \frac{256}{3600} + \cos(x) {}^{2} = 1[/tex]

[tex] \cos(x) {}^{2} = \frac{3600}{3600} - \frac{256}{3600} [/tex]

We can simplify both expression

[tex] \cos(x) {}^{2} = \frac{225}{225} - \frac{16}{225} [/tex]

[tex] \cos(x) = \frac{ \sqrt{209} }{15} [/tex]

Cosine is positve on quadrant 1 so that cos(a)

Apply reciprocal identity sec a= 1/ cos a.

The answer is

[tex] \sec(a) = \frac{15}{ \sqrt{209} } [/tex]

Rationalize the denominator.

[tex] \frac{15}{ \sqrt{209} } \times \frac{ \sqrt{209} }{ \sqrt{209} } = \frac{15 \sqrt{209} }{209} [/tex]

Answer:

if the solutsion are r1,r2 then the factored form is

y=a(x-r1)(x-r2) where a is a constant

so

r1=-1/3

r2=4

y=a(x-(-1/3))(x-4)

y=a(x+1/3)(x-4)

so it will be

y=a(x+1/3)(x-4)

a is a constant

Step-by-step explanation: