which is the axis of symmetry of a parabola with equation x^2=-4y?

Answer:

[tex]\frac{13-7\sqrt{3}}{2}[/tex]

Step-by-step explanation:

We need to rationalize the denominator of [tex]= \frac{5-\sqrt{3}}{4+2\sqrt{3}}[/tex]. For rationalizing we multiply the equation by [tex]\frac{4-2\sqrt{3}}{4-2\sqrt{3}}[/tex]

So, solving

[tex]= \frac{5-\sqrt{3}}{4+2\sqrt{3}}*\frac{4-2\sqrt{3}}{4-2\sqrt{3}} \\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{4+2\sqrt{3}*4-2\sqrt{3}}\\=\frac{(5-\sqrt{3})(4-2\sqrt{3})}{(4)^2-(2\sqrt{3})^2}\\= \frac{5(4-2\sqrt{3})-\sqrt{3}(4-2\sqrt{3})}{16-(4*3)}\\=\frac{20-10\sqrt{3}-4\sqrt{3}+2*3}{16-12}\\=\frac{20+6-14\sqrt{3}}{4}\\=\frac{26-14\sqrt{3}}{4}\\= \frac{2(13-7\sqrt{3})}{4}\\=\frac{13-7\sqrt{3}}{2}[/tex]

Answer:

0.25

Step-by-step explanation:

Answer: Option C

The equation is:

[tex](x+8)^2 +(y+3)^2=9[/tex]

Step-by-step explanation:

First we must calculate the midpoint between the two given points.

Then the midpoint will be the radius of the circumference

The midpoint between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is:

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

In this case the points are:

(-5 -3) and (-11 -3)

The the center is:

[tex](\frac{-5-11}{2}, \frac{-3-3}{2})[/tex]

[tex](-8,\ -3)[/tex]

Then the equation is:

[tex](x+8)^2 +(y+3)^2=r^2[/tex]

To find r we substitute one of the points in the equation and solve for r

[tex](-5+8)^2 +(-3+3)^2=r^2[/tex]

[tex](3)^2 +0=r^2[/tex]

[tex]r^2 =3^2[/tex]

[tex]r =3[/tex]

Finally the equation is:

[tex](x+8)^2 +(y+3)^2=9[/tex]

Answer:

Option C

Step-by-step explanation:

The standard form of equation of circle is:

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

As we only know two points on the circle which are the ends of diameter.

As we know

Radius=Diameter/2

We have to find the length of diameter using the distance formula first to calculate radius. So,

Diameter= √((-11-(+5))^2+(-3-(-3)^2 )

= √((-11+5)^2+(-3+3)^2 )

=√((-6)^2+(0)^2 )

= √36

=6

Now,  

Radius=6/2

=3

As the diameter passes through centre, so the mid-point of diameter will be centre of the circle:

Mid-point=((x_1+x_2)/2,(y_1+y_2)/2)

=((-5-11)/2,(-3-3)/2)

=((-16)/2,(-6)/2)

=(-8,-3)

Putting the values of radius and centre in standard form

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

(x-(-8))^2+ (y-(-3))^2=3^2

(x+8)^2+ (y+3)^2=9

So the correct answer is option C ..

Answer:

Annie has 95 apples now

Answer:

Annie has 95 Apples

Step-by-step explanation:

7 Apples - 5 Apples = 2

2 + 3 more apples = 5 Apples

5 Apples - 2 Apples = 3 Apples

3 Apples + 9 more apples = 12 Apples

12 - 6 = 6 Apples

6 Apples + 89 more apples = 95 Apples

Answer:

252 hours

Step-by-step explanation:

1 day = 24 hours

1 week = 7 days

= 24 * 7

= 168 hours

3 days = 24 * 3

= 72 hours

1/2 day = 24 / 2 = 12 hours

Add up all values/hours:

168 hours + 72 hours + 12 hours = 252 hours

Answer:

1 week- 168 hours

3 days-72 hours

1/2 day-12 hours

Step-by-step explanation:

1 week- 24x7=168

3 days- 24x3=72

1/2 day- 24x.5=12

Answer:

lower your mortgage interest rate

Step-by-step explanation:

The higher your credit score, the __lower your mortgage interest rate__.

Because the higher your credit score, the less risk you represent for a lender, so it will most likely grant you a lowest rate for your mortgage/loan.

The "lower your savings interest rate " is not the answer because savings interest rates are not related to the credit score...

"higher your car loan rate " and "higher risk you are to a creditor " are consequences of a low credit score.

For this case we must find the value of "c" of the following expression:

[tex]\frac {c} {3} = \frac {30} {5}[/tex]

We solve the right side of the equation:

[tex]\frac {30} {5} = 6[/tex]

Rewriting:

[tex]\frac {c} {3} = 6[/tex]

We multiply both sides of the equation by "3":

[tex]c = 6 * 3\\c = 18[/tex]

Answer:

[tex]c = 18[/tex]

Answer:

the last one

Step-by-step explanation:

Answer:

the answer is indeed the last one

Step-by-step explanation:

7x-3x is the only one that meets the requirements for this statement

7-3x would be the difference between seven and three times a number

7x-3 would be the difference between seven times a number and three

have an absolutely fantastic day my friend!

Answer: OCTOBER 16th

Step-by-step explanation: The teams will meet again on October 16th

Answer: Angle 10 and Angle 2

ANSWER

5 units up

EXPLANATION

The given function is

[tex]y = 2 {x}^{2} [/tex]

The new graph is

[tex]y = 2 {x}^{2} + 5[/tex]

The new function is obtained by adding 5 to the original function.

This will shift the graph up by 5 units.

The translation is a vertical shift up by 5 units.

Answer:

The translation is 5 units up

Step-by-step explanation:

+5 on the outside means up by 5

Answer:

9 units

Step-by-step explanation:

Because you start at -3 and go up so you do not add the -9 its just 9

It's 9 units because there's no such thing as -9 units!

Answer:

$18.99

Step-by-step explanation:

Step 1: Take the per topping amount ($1.25) and multiply it by the amount of toppings (4). $1.25x4=$5

Step 2: Add your toppings total ($5) to the base pizza cost ($13.99). $13.99+$5=$18.99

Answer:

18.99

work:

13.99 + (1.25 x 4 )

13.99 + 5

18.99

trust me, 18.99 + (1.25 x 4) will work and the work showing also

Answer: Option G

[tex]a_6 = -2048[/tex]

Step-by-step explanation:

The geometric series have the following form:

[tex]a_n = a_1 (r) ^ {n-1}[/tex]

Where [tex]a_1[/tex] is the first term of the sequence and r is the common radius.

In this case we know that

[tex]a_1 = -2\\\\r = 4[/tex]

So:

[tex]a_n = -2(4) ^ {n-1}[/tex]

To find the sixth term [tex]a_6[/tex], substitute [tex]n = 6[/tex] in the equation.

[tex]a_6 = -2 (4) ^ {6-1}\\\\a_6 = -2 (4) ^ 5\\\\a_6 = -2048[/tex]

I think 9 should be added to both sides.

cofficient of x = 6

half of it = 6/2 = 3

square the 3

to give 3 squared = 3*3 9

Answer:

9

Step-by-step explanation:

To make it a Perfect Square Trinomial, you can square root 9 and multiply it to get 6, therefore 9 is correct

Answer: 72

Step-by-step explanation:

722 —> 720

9 —> 10

72 divided by 1 is 72

Answer:

The correct answer is option "C"

"The interquartile range increases"

The value of the (RIC) will increase from 4 to 5.75, that is, 44%

Step-by-step explanation:

The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin

The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.

Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%

Answer:

Step-by-step explanation:

[tex]|x-4|<9\iff x-4<9\ \wedge\ x-4>-9\qquad\text{add 4 to both sides}\\\\x<13\ \wedge\ x>-5\to-5<x<13[/tex]

Essentially this question is asking, If we made circle O as big as circle O1, how could we move it to the same spot. Therefore, I would expect the Answer to be D.

Answer:

The measure of the major arc MBD is 270°

Step-by-step explanation:

we know that

The measure of major arc MBD is equal to the sum of the measure of the arc MB plus the measure of the arc BD

BD is a diameter-----> divide the circle into two equal parts

so

arc BD=180°

arc MB is a quarter of circle

so

arc MB=90°

therefore

arc MBD=180°+90°=270°

Answer:

[tex]\boxed{x^{2} + 2x - 8}[/tex]

Step-by-step explanation:

6. Practice

The dimensions of the current park are x long and x wide.

The new park will be 4 longer and 2 thinner.

Its new dimensions will be x + 4 long and x – 2 wide.

Its new area will be

A = width × length = (x – 2)(x + 4)

Find the product

[tex]\begin{array}{lll}\textbf{Steps} & \textbf{Problem: }(x - 2)(x + 4) & \\\textbf{1. List variables} & a = x - 2 & \\ & b = x & \\ & c = 4 &\\\textbf{2. Distribute (x - 2)} & (x -2)(x + 4)\\ & = (x - 2)(x) + (x - 2)(4)\\\textbf{3. Distribute x and 4} & x^{2} -2x + 4x - 8\\\textbf{4. Combine like terms}& x^{2} + 2x - 8\\\end{array}\\\text{The area of the updated skatepark will be }\boxed{\mathbf{ x^{2} + 2x - 8}}[/tex]

Corresponding angles are congruent

From concept of base angle of parallel line, Option(D) Corresponding angles are congruent.

Given that ∠1 ≅ ∠2 .

In the diagram given aside, line a and b are parallel where the ∠4 and ∠2 are base angle subtended by the parallel lines.

From the traversal property of congruency, we know that the base angles of a parallel lines always subtend equal and congruent angles when it is intercepted by a common traversal.

Thus, from concept of base angle of parallel line, Option(D) Corresponding angles are congruent.

To learn more about base angle of parallel lines, refer -

https://brainly.com/question/13352230

#SPJ2

Answer:

Mean because it is the average of all of them combined = best representation of all grades.

84% & Mean

Step-by-step explanation:

88 + 73 + 97 + 76 + 90 + 80 = 504

**divide by how many grades there are** (6 of them)

504 / 6 = 84

Meaning the best center representation would be 84%

Answer: The Mean

The mean is when you add up all of those grades and divide by the amount of exams.

Answer:

9.2 ft

Step-by-step explanation:

The length of the ladder is 15 ft

The ladder makes an angle of 52° with the ground

The distance (x) from the base of the house to the foot of the ladder is given by;

[tex]\frac{x}{15}[/tex] = cos 52°

x = 15 × cos 52° = 9.23492213 ft

Which equals to 9.2 ft (rounded off to tenth of a foot)

The distance between the base of the building and the bottom of the ladder is 11.72 feet.

It is given that

Length of the ladder = 15 feet

The angle of inclination = 52°

Let us say the distance between the base of the building and the bottom of the ladder is x.

The tangent of an angle is the ratio of the opposite side(to that angle) to the base of the triangle.

Tan 52° = length of the ladder / distance between base of building and bottom of the ladder.

Tan 52 = 15/x

x= 15/Tan 52

x = 11.72 feet.

Therefore, The distance between the base of the building and the bottom of the ladder is 11.72 feet.

To get more about Trigonometric ratios visit:

https://brainly.com/question/24349828

Answer:

the length of major semiaxes a = 8.45 cm  and minor semiaxes b= 5.63 cm.

Step-by-step explanation:

Area of ellipse = π*a*b

Let major semiaxes = a and minor semiaxes = b

then a:b = 3:2

a/b = 3/2

=> a = 3/2 b

Putting in the value of formula

150 = π * (3/2)b * b

150 = 3.14 * 1.5b * b

150= 4.71 b^2

150/4.71 = b^2

=> b^2 = 31.8

b= 5.63

a = 3/2 * b

a = 1.5 * 5.63

a = 8.45

So, the length of major semiaxes a = 8.45 cm  and minor semiaxes b= 5.63 cm.

Answer:

Major: 8.5 cm

Minor: 5.6 cm

Step-by-step explanation:

The answer is B i had this problem.

Answer: OPTION B

Step-by-step explanation:

Multiply both denominators to find the Least Common Denominator:

[tex]LCD=(3y-4)(y^2)[/tex]

Now, divide each original denominator by the LCD and multiply the result by each numerator. Then:

[tex]=\frac{(6y^2+2y)(y^2)-(9y-7)(3y-4)}{(3y-4)(y^2)}[/tex]

Applying Distributive property, you get:

[tex]=\frac{6y^4+2y^3-(27y^2-36y-21y+28)}{3y^3-4y^2}\\\\=\frac{6y^4+2y^3-27y^2+36y+21y-28}{3y^3-4y^2}[/tex]

Add the like terms in the numerator:

[tex]=\frac{6y^4+2y^3-27y^2+57y-28}{3y^3-4y^2}[/tex]

M refers to midpoint.

[tex]

A(9, 8) \\

B(-1, -2) \\

M(\frac{x_1-x_2}{2}, \frac{y_1-y_2}{2}) \\

M(\frac{9-(-1)}{2}, \frac{8-(-2)}{2}) \\

M(\frac{10}{2}, \frac{10}{2})\Longrightarrow\boxed{M(5, 5)}

[/tex]

Hope this helps.

r3t40

Answer:

x = 100°

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 = 7, hence

sum = 180° × 5 = 900°

Sum the given interior angles and equate to 900

x + 155 + 116 + 135 + 135 + 116 + 143 = 900

x + 800 = 900 ( subtract 800 from both sides )

x = 100°

Answer:

248.39

Step-by-step explanation:

421 × .59 =248.39

Answer:

Hey No worries. Its very easy.

Step-by-step explanation:

Look,

Volume= 84 in.cube

Length=6 in.

Breadth=2 in.

therefore, Height= Volume/(Length*Breadth)

=84/(6*2)

=84/12

=7

Answer:

h = 7 in

Step-by-step explanation:

The volume (V) of a cuboid is calculated using the formula

V = lbh ( l is length, b is breadth and h is height )

Given V = 84 in³, then

lbh = 84 ← substitute l = 6 and b = 2

6 × 2 × h = 84

12h = 84 ( divide both sides by 12 )

h = 7

Answer:

x = -94/17, y = -6, z = -48/17

Step-by-step explanation:

If solving this system of equations is what you want, here's the answer.