What is the directrix of the parabola defined by 1/4(y 3)=(x-2)^2?

Answer:

x=-4

Step-by-step explanation:

Given:

2x^2+8x=x2-16

2x^2-x^2+8x+16=0

x^2+8x+16=0

As per the formula (a+b)^2= a^2 +2ab +b^2

x^2+2(4)x+(4)^2=0

(x+4)^2=0

x+4=0

x=-4!

Answer:

x=-4

Step-by-step explanation:

Hello,

thanks for leaving your query here in brainly. I think I can help you with this

[tex]2x^{2} +8x=x^{2} -16\\organizing\ the\ terms\\2x^{2} +8x-x^{2}+16=0\\x^{2}+8x+16=0\\[/tex]

this can be factorized as

[tex]x^{2}+8x+16\\a^{2}  +2ab+b^{2}=(a+b)^{2}\\ x^{2}+8x+16=(x+4)^{2}[/tex]

hence

[tex](x+4)^{2}=0\\now, isolate\ x\\\\\sqrt[]{(x+4)^{2}} =\sqrt{0}\\ x+4=0\\x=-4\\[/tex]

I hope it helps, Have a nice day.

Answer:

DH and HF correspond.

Step-by-step explanation:

The order matters in a congruence statement.

You are given Figure GHF=Figure EHD.

I say the order matters in a congruence statement because it tells you the parts that correspond.

Angles G and E correspond because they are both first.

Angles H and H correspond because they are both second.

Angles F and D correspond because they are both third.

The same thing works with the segments.

Segments GH and EH correspond because it goes first to second for both.

Segments HF and HD correspond because it goes second to third for both.

Segments FG and DE correspond because it goes third back to first for both.

I have named all the correspond parts for you congruence statement:

Figure GHF=Figure EHD.

So let's look at the choices.

DH and HF correspond.

Answer:

DH and HF correspond.

Step-by-step explanation:

Answer:

reflected

Step-by-step explanation:

ΔXYZ was dilated, then reflected, to create ΔQAG.

Answer:

The correct options are A and B.

Step-by-step explanation:

Given information: ΔABC≅DEF

Corresponding parts of congruent triangle are congruent (CPCTC).

The corresponding angles of both triangles are congruent.

[tex]\angle A\cong \angle D[/tex]

[tex]\angle B\cong \angle E[/tex]

[tex]\angle C\cong \angle F[/tex]

The corresponding side of both triangles are congruent.

[tex]\angle AB\cong \angle DE[/tex]

[tex]\angle BC\cong \angle EF[/tex]

[tex]\angle AC\cong \angle DF[/tex]

Therefore the correct options are A and B.

The congruencies that are true are;

A. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DE}[/tex], and B. ∠C ≅ ∠F

The reason the selected options are correct is given as follows;

Known parameter;

ΔABC ≅ ΔDEF (Change of ~ to ≅ based on complete question accompanying screen grab as posted online)

CPCTC is the acronym for Congruent Parts of Congruent Triangles are Congruent

Required: To select the congruences that are true

Solution:

By observation, the height of ΔABC is equal to the height of ΔDEF, therefore;

∠C and ∠F are angles located in corresponding parts of both triangles

While the other options; ∠E and ∠C, ∠A and ∠E, [tex]\overline{AB}[/tex] and [tex]\overline{DF}[/tex], and [tex]\overline{AC}[/tex] and [tex]\overline{DE}[/tex] are not corresponding parts and they are therefore not congruent

The congruencies that are true are; A. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DE}[/tex], and B. ∠C ≅ ∠F

Learn more about CPCTC here:

https://brainly.com/question/1805755

Answer:

[tex]\large\boxed{(3x^2-2x)(2x^2+3x-1)==6x^4+5x^3-8x^2+2x}[/tex]

Step-by-step explanation:

Use the distributive property and [tex](a^n)(a^m=)=a^{n+m}[/tex]

[tex](3x^2-2x)(2x^2+3x-1)\\\\=(3x^2)(2x^2)+(3x^2)(3x)+(3x^2)(-1)+(-2x)(2x^2)+(-2x)(3x)+(-2x)(-1)\\\\=6x^4+9x^3-3x^2-4x^3-6x^2+2x\qquad\text{combine like terms}\\\\=6x^4+(9x^3-4x^3)+(-3x^2-5x^2)+2x\\\\=6x^4+5x^3-8x^2+2x[/tex]

multiplication of  (3x^2-2x)(2x^2+3x-1)​ is 6X⁴+5X³-9x²+2X

CALCULATION:-

⇒(3X²-2X)(2X²+3X-1)

⇒6X⁴+9X³-3X²-4X³-6X²+2X

⇒ 6X⁴+5X³-9x²+2X  (answer)

Learn more about polynomials here:-https://brainly.com/question/2833285

#SPJ2

Answer:

Step-by-step explanation:

The formal definition of a common difference is d = a_(n + 1) - a_n)

so

d = ?

a_(n+1) = a_2 = 14

a_n      = a_1 = 24

d = 14 - 24

d = - 10

-10

In the question, it is asking you to find the common difference between the numbers 24, 14, 4,...

In order to find the common difference between the numbers, we would nee to find the change between them.

In other words, we need to find out how much it's changing by between each number.

When you look at the sequence 24, 14, 4, you would know that it is decreasing each time. This means that the common difference would be a negative number.

Now, we need to figure out how much it is decreasing by.

When you subtract 24 and 14, [tex]24-14=10[/tex], you would get 10. When you subtract 24 by 10, you would get 14. So we know that the difference would be -10.

We can also check the next number. When you subtract 14 by 4, [tex]14-4=10[/tex], you would get 10. Then, when you subtract 14 by 10, you would get 4.

This means that the common difference of the sequence is -10

Answer:

2304

Step-by-step explanation:

The volume of the sphere is 2304π cubic units or 7238.229 cubic units if the radius is 12 units.

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]

We have a radius of the sphere R = 12 units

Volume:

[tex]\rm V = \dfrac{4}{3} \pi (12)^3[/tex]

V = 2304π cubic units or

V = 7238.229 cubic units

Thus, the volume of the sphere is 2304π cubic units or 7238.229 cubic units if the radius is 12 units.

Learn more about the sphere here:

brainly.com/question/11374994

#SPJ2

Answer: [tex]\sqrt[3]{-62}[/tex]

Step-by-step explanation:

It is important to remember the following:

[tex]a^{(\frac{1}{n})=\sqrt[n]{a}[/tex]

In this case we have:

[tex]-62^{\frac{1}{3}[/tex]

Then, in order to simplify it, we need to rewrite it in radical form, where the index of the root will be 3 and the radicand will be -62.

Therefore, the simplified form is this:

[tex]-62^{\frac{1}{3}}=\sqrt[3]{-62}[/tex]

Answer: -4

Step-by-step explanation: I put it in Desmos calc.

Answer:

x > 17

Step-by-step explanation:

Given

x + 1 > 18 ( isolate x on the left by subtracting 1 from both sides )

x > 17

Answer:

x > 17​

Step-by-step explanation:

x +1 > 18​

Subtract 1 from each side

x +1 -1> 18-1

x > 17​

Answer:

i) sin(2x) = [tex]-\frac{\sqrt{3}}{2}[/tex]

ii) cot(x+360) = [tex]-\frac{\sqrt{3}}{3}[/tex]

iii) sin(x-180) = [tex]\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

sec(x) = 2

Since cos(x) is reciprocal of sec(x), this means:

cos(x) = [tex]\frac{1}{2}[/tex]

cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.

Part i)

sin(2x) can be simplified as:

sin(2x) = 2 sin(x) cos(x)

First we need to find the value of sin(x). According to Pythagorean identity:

[tex]sin^{2}(x)=1-cos^{2}(x)\\\\ sin(x)=\pm \sqrt{1-cos^{2}(x)}[/tex]

Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:

[tex]sin(x)=- \sqrt{1-cos^{2}(x)}\\\\ sin(x)=-\sqrt{1-(\frac{1}{2})^{2}}\\\\ sin(x)=-\frac{\sqrt{3}}{2}[/tex]

So,

[tex]sin(2x)=2 \times -\frac{\sqrt{3} }{2} \times \frac{1}{2}\\\\ sin(2x)=-\frac{\sqrt{3}}{2}[/tex]

Part ii)

We have to find cot(x + 360)

An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.

cot(x + 360) = cot(x)

[tex]cot(x) = \frac{cos(x)}{sin(x)}\\[/tex]

Using the values, we get:

[tex]cot(x)=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2} }\\\\ cot(x)=-\frac{\sqrt{3}}{3}[/tex]

Part iii)

We need to find the value of sin(x - 180)

sin(x - 180) = - sin(x)

Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.

So,

sin(x - 180) = [tex]-(-\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}[/tex]

Answer:

The correct answer is option C.

Step-by-step explanation:

Weight of George = 14 pounds

Weight of Igor = 6 pounds

Difference between weight of cats :

= 14 pounds - 6 pounds = 8 pounds

This means that George is 8 pounds more in weight than Igor.

Answer:

10

-------------

3x^2

Step-by-step explanation:

First lets simplify what is inside the square root

300x8

---------------

27x12

3 * 100 x^8

------------------

3 *9 x^12

The 3's cancel  and we know a^b/ a^c = a^(b-c)

100/9 x^ (8-12)

100/9 x^-4

sqrt( 100/9 x^-4)

Put the negative exponent in the denominator and make it positive

sqrt( 100 / (9x^4) )

We know that sqrt( a / b) = sqrt(a) / sqrt( b)

sqrt(100)

----------------

sqrt( 9x^4)

10

-------------

3x^2

Answer:

2160°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 14, hence

sum = 180° × 12 = 2160°

Answer:

G

Step-by-step explanation:

Answer:

You can divide the numerator by the denomintor, then you move the decimal two places to the right.

Step-by-step explanation:

For example, say you want to turn 1/2 into a percent. You do 1 divided by 2. Which would give you 0.5. Next, you move the decimal two spaces to the right. All you have to do next is to add the percent sign. 50%

Natasha could have 9 red apples and 4 green apples, or 10 red apples and 3 green apples.

To determine the number of red and green apples Natasha could have, we need to consider the given information. Natasha has a total of 13 apples, and she has more red apples than green apples.

Let's assume that Natasha has r red apples and g green apples. We know that r + g = 13, since she has a total of 13 apples.

Given that she has more red apples than green apples, we can say that r > g.

Now, we need to find the possible values of r and g that satisfy these conditions. We can use trial and error to find the values that work:

Based on our analysis, Natasha could have either 9 red apples and 4 green apples, or 10 red apples and 3 green apples.

ANSWER

Commutative property of addition.

EXPLANATION

Let a,b be real numbers. The commutative property of addition states that,

[tex]a + b = b + a[/tex]

If we let a=-10 and b=6, then

[tex]-10+6=6+(-10)[/tex]

Therefore the given expression demonstrates the commutative property of addition.

The commutative property of addition tells us that, the order in which we add two real numbers does not affect the result.

Answer:0.035

Step-by-step explanation:

I used a calculator and put in 15 / 4 and got 0.035

Charlie should divide the 15 cents into four bags with 1 cent, 2 cents, 4 cents, and 7 cents respectively. Using combinations of these bags, he can pay any amount between 1 cent and 15 cents without opening them.

The question asks us to figure out how Charlie can divide 15 cents among four small bags so he can use these bags to pay any amount between 1 cent and 15 cents without opening them.

To solve this, we need to think about the binary representation of numbers, because each bag can either be used or not used in each transaction, similar to how a binary '1' or '0' can represent 'on' or 'off'.

Therefore, he should put the amounts that correspond to the powers of 2 in three of the bags: 1 cent, 2 cents, and 4 cents, and in the last bag, we put the sum of these three, which is 7 cents.

This way, he can make any amount up to 15 cents:

Answer:

A. (1.55, 2)

Step-by-step explanation:

The formula to apply when finding the midpoint of a segment where the coordinates of the end points are given is;

[tex]midpoint=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

where (x₁,y₁) and (x₂,y₂) are the coordinates of the end points

Given;

x₁= -0.4 ,y₁=2.5,  x₂=3.5, y₂=1.5 then applying the formula for midpoint

[tex]=(\frac{-0.4+3.5}{2} ,\frac{2.5+1.5}{2} )\\\\\\=(\frac{3.1}{2} ,\frac{4.0}{2} )\\\\\\=(1.55,2.0)[/tex]

Answer:

-2

Step-by-step explanation:

The rate of change is

roc = f(x2) - f(x1)

        ---------------

         x2 -x1

x2 is the last point or 15

x1 is the first point or 10

f(15) = 10 from the graph

f(10) = 20 from the graph

roc = f(15) - f(10)

        ---------------

         15-10

roc = 10 - 20

        ---------------

         15-10

roc = -10

        --------

            5

roc = -2

Answer:

The correct answer option is B. Point X.

Step-by-step explanation:

We are given a graph where two triangles, a fixed point X and an arc is shown and we are to determine the center of rotation in it.

Center of rotation is basically a fixed point on a plane or a graph about which and figure rotates. It acts like a pivot in a door.

So here. we can see that point X is the center of rotation about which the vertex of a triangle is rotated 90° counterclockwise, forming an arc.

Slope intercept form is [tex]y=mx+b \to y=-3x+4[/tex]

Answer:

y=-3x+4

Step-by-step explanation:

Slope-intercept form is y=mx+b

where m is the slope and b is the y-intercept.

m=-3 because -3 is the slope.

b=4 because 4 is the y-intercept.

Let's plug that into y=mx+b giving us y=-3x+4.

Answer:

The answer is 3x^2+7x+2

Step-by-step explanation:

Multiply each term of the second bracket with the first bracket.

We can write:

(x+2)(3x+1)= 3x(x+2)+1(x+2)

By multiplying the terms we get:

=3x^2+6x+x+2

Now simplify by combining like terms:

=3x^2+7x+2

Thus the answer is 3x^2+7x+2....

Answer:

3x² + 7x + 2

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x(3x + 1) + 2(3x + 1) ← distribute both parenthesis

= 3x² + x + 6x + 2 ← collect like terms

= 3x² + 7x + 2

Answer:

There is no clear correlation between apple eaten per week and the times sick per year.

Step-by-step explanation:

The person who ate 7 apples got sick the same amount as the person who ate 0 apples did. When you graph the points, there's no clear correlation between the apples and the sick times

russin agree with other peson

Answer:

x= 0   x=2

Step-by-step explanation:

x^2 − 2x = 0

Factor out an x

x(x-2) =0

Using the zero product property

x =0  x-2 =0

x= 0   x=2

bearing in mind that a diagonal line from the center of a square will give us an isosceles triangle, Check the picture below.

Answer:

The area of this polygon is 98.1 yd²

Step-by-step explanation:

Check the image below.

The diagonal line from the corner of a square to the center of this one will shape an isosceles triangle.

The Pythagoras theorem give us the following formula:

A² + A² = H²

Both "A" are the sides and H is the hypotenuse, seeing the figure, the diagonal coincide with the hypotenuse and the measure is 7 yd.

A² + A² = 72  

2A² = 49

A²= 49/2

A²= 24. 5

A=√24.5

A= 4.95 yd

Knowing that the diagonal ends up in the center of the square, we assume that the side of the triangle (“A” side) is the half of the side of the square, then this last one is 2A. Bearing in mind that square have all of the sides with the same measure, the four sides have a 2A size.

2A = 2(4.95) =9.9 yd

Each side of the square measures 9.9 yd

The area of a square is  

Side²= (2A)2²

(9.9)²= 98.1 yd²

The area of this polygon is 98.1 yd²

Answer:

The volume is 36 inches cubed.

Step-by-step explanation:

The volume of a rectangular prism is W*L*H.

You are given the H=3i, W=2 in, and L=6 in.

So now we plug into our formula for the volume of a rectangular prism which will result in 2*6*3=12*3=36.

The volume is 36 inches cubed.

Answer: [tex]36\ in^3[/tex]

Step-by-step explanation:

The volume of a rectangular prism can be calculated with this formula:

[tex]V=lwh[/tex]

Where "l" is the lenght, "w" is the width and "h" is the height.

In this case we know that this rectangular solid is 3 inches high, 6 inches long and 2 inches wide. Then:

[tex]h=3\ in\\l=6\ in\\w=2\ in[/tex]

Then, substituting these values into the formula, we get that its volume is:

[tex]V=(6\ in)(2\ in)(3\ in)\\\\V=36\ in^3[/tex]

Answer:

h(x) = 6x² - 10x - 4

Step-by-step explanation:

f(x)g(x) = (2x - 4)(3x + 1)

Each term in the second factor is multiplied by each term in the first factor

2x(3x + 1) - 4(3x + 1) ← distribute both parenthesis

= 6x² + 2x - 12x - 4 ← collect like terms

= 6x² - 10x - 4

To find h(x), which is the product of f(x) and g(x), one must perform a binomial multiplication. The resulting function after simplification is h(x) = 6x² - 10x - 4.

The student is asking for the product of two functions, f(x) and g(x), defined as F(x)=2x-4 and G(x)=3x+1 respectively. To find the new function h(x), which is the result of multiplying f(x) and g(x) together, we use the following process:

h(x) = f(x) × g(x)

This translates into h(x) = (2x - 4)(3x + 1). We need to perform a binomial multiplication (also known as FOIL - First, Outside, Inside, Last) to combine these two expressions.

Applying binomial multiplication, we get:

Combining these terms, we get the final expression for h(x):

h(x) = 6x² + 2x - 12x - 4

Simplifying further:

h(x) = 6x² - 10x - 4

Answer:

Step-by-step explanation:

The domain is (-5, infinity).  There's no graph for x ≤ -5.

The range is [2, infinity).

Answer:

C. The domain is [-k, ∞), and the range is [C, ∞).

Step-by-step explanation:

To be able to answer this question we first need to understand what exactly are the domain and range of a function. Domain and Range can be defined as the following,

Domain: are all the possible input values a function can recieve, displayed as the x-coordinates on a graph.

Range: are all the possible output values that a function can spit out, displayed as the y-coordinates on a graph.

With this understood, we can look at the graph and easily point out the domain and range as the following values.

Domain being [-5,∞) ..... closed bracket because the value is included

Range being [2, ∞) ..... infinity values always take an open parenthesis

Based on this information we can safely assume the answer is C. The domain is [-k, ∞), and the range is [C, ∞).

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.