write the equation for a parabola with a focus at (-3,-5) and a directix at x=-7

Answer:

answer is in the attachment.

Answer:

[tex]a = 2[/tex]

[tex]b = 2^{1/6}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{x^{10}} = a^3 * \sqrt b[/tex]

[tex]x = -2[/tex]

Required

Find a and b

We have:

[tex]\sqrt[3]{x^{10}} = a^3 * \sqrt b[/tex]

Substitute -2 for x

[tex]\sqrt[3]{(-2)^{10}} = a^3 * \sqrt b[/tex]

[tex]\sqrt[3]{1024} = a^3 * \sqrt b[/tex]

Expand

[tex]\sqrt[3]{2^9 * 2} = a^3 * \sqrt b[/tex]

Split the exponents

[tex]2^{(9/3)} * 2^{(1/3)} = a^3 * \sqrt b[/tex]

[tex]2^{3} * 2^{1/3} = a^3 * \sqrt b[/tex]

By comparison:

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

So;

[tex]a = 2[/tex]

and

[tex]\sqrt b = 2^{1/3}[/tex]

Take square roots of both sides

[tex]b = 2^{1/6}[/tex]

Answer: -8, -2

Step-by-step explanation: (the previous answers are ) 1. D 2. C 3. -8,-2 (for reference of order :))

Answer:

5%

Step-by-step explanation:

First, find the amount of tax:

5250 - 5000

= 250

Divide this by the original price of $5000 to find the percent of import tax:

250/5000

= 0.05

So, the percent of import tax is 5%

Answer:

158.33 minutes = 2.63 hours

Step-by-step explanation:

Answer:

54 or 57 (read explanation below)

Step-by-step explanation:

There is a mistake in the problem.

The bottom base has length 10 not 11.

Using the correct length of 10, the area is:

A = (1/2)h(b1 + b2)

A = (1/2)(6)(10 + 8)

A = 3(18)

A = 58

Using the incorrect length of 11, the area is:

A = (1/2)h(b1 + b2)

A = (1/2)(6)(11 + 8)

A = 3(19)

A = 57

Answer:

$17

Step-by-step explanation:

You reverse the operation, and you do 85 divided by 5, which is 17. Have an amazing day!!

Answer:

6

Step-by-step explanation

Answer:

6

Step-by-step explanation:

plug in the 3

4(3-3)+5(3)-3^2

4(0)+15-9

0+15-9

15-9

6

Answer:

Independent means that one has no effect on the other. Exclusive means one cannot happen alongside the other. In simpler terms, independent events can be thought of as the chance it'll rain and how many people are flossing their teeth in the morning. Both happen, but neither one impacts the other.

Exclusive, on the other hand, means only one can happen. Lets say at nine in the evening your favorite show is on. However, you have an early morning and should be asleep by nine. You cannot both be asleep and watching your favorite show, and so these events are exclusive.

Answer:

It's C

X = -3

Step-by-step explanation:

Edge 2022

The equation represents the directrix is x=-3.

the correct option is (C).

A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix . The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.

given: y²=12x

y²=4*3*x

Here a=3

So, x+a=0

x+3=0

x=-3.

Hence, the directrix of parabola is: x=-3

Learn more about directrix here:

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Answer:

I would say D is your answer

Step-by-step explanation:

Answer:

the fourth one

use mathaway its like my best friend for math!!!

Step-by-step explanation:

Complete question is;

Mr. Matthew is testing the online popularity of his custom made belts and wallets that were marketed differently. Some items were sold prior to the online launch date.

The equation below represents the number of belts sold, s, x days after its online launch. S = 3^(x)

The equation below represents the number of wallets sold, s, x days after its online launch. S = 4x + 15

Using graphing technology, complete the statements. After ___ days, the total number of belts sold will be the same as the total number of wallets sold. The number of belts and the number of wallets Mr. Matthew sold after this many days is ___

Answer:

Number of days = 3 days

Total belts and wallets after 3 days = 54

Step-by-step explanation:

We are told that the number of belts sold, s, x days after its online launch. S = 3^(x)

Also, we are told that the number of wallets sold, s, x days after its online launch. S = 4x + 15

Now, we want to find the Number of days that total number of belts sold will be the same as the total number of wallets sold using graphing technology.

The number of days will simply be the value of x where the two graphs meet.

I have drawn the graph of both equations.

From the attached graph, we can see that the x-value at where the both graph lines meet is approximately 3. I didn't take the negative solution because number of days cannot be negative.

Thus, x = 3

Putting x = 3 in;

S = 3^(x)

S = 3^(3)

S = 27

Similarly, Putting x = 3 in;

S = 4x + 15

We have;

S = 4(3) + 15

S = 12 + 15

S = 27

Thus,total number of belts and wallets sold after 3 days = 27 + 27 = 54

Answer:

9/16

Step-by-step explanation:

3/8 ÷ 2/3

Copy dot flip

3/8 * 3/2

Multiply the numerators

3*3=9

Multiply the denominators

8*2 = 16

Numerator over denominator

9/16

Answer:

option 3

Step-by-step explanation:

[tex](4 + 3) \sqrt[5]{x {}^{2}y } = 7 \sqrt[5]{ {x}^{2}y } [/tex]

Answer:

Step-by-step explanation:

[tex]4( \sqrt[5]{ {x}^{2}y } ) + 3( \sqrt[5]{ {x}^{2} y} )[/tex]

[tex](taking \: \sqrt[5]{ {x}^{2}y } \: as \: common \: then)[/tex]

[tex] = \sqrt[5]{ {x}^{2} y} (4 + 3)[/tex]

[tex] = \sqrt[5]{ {x}^{2} y} \times 7[/tex]

[tex] = 7 (\sqrt[5]{ {x}^{2}y } )(ans)[/tex]

Answer:

cos A = 7/25

Step-by-step explanation:

Since we are given a right triangle, we can use trig functions

cos A = adj side/ hypotenuse

cos A = 7/25

Answer:

[tex]\boxed{\sf cos\ A =\frac{7}{25}}[/tex]

Step-by-step explanation:

We need to find out the value of cos A using the given triangle . Here we can see that the sides of the triangle are 7 , 25 and 24 .

We know that the ratio of sine is base to hypontenuse .

[tex]\sf\longrightarrow cos\theta =\dfrac{ base}{hypontenuse}[/tex]

Here we can see that the side along the angle A is 7 , therefore the base of the triangle is 7. And the side opposite to 90° angle is 25 . So it's the hypontenuse . On using the ratio of sine ,

[tex]\sf\longrightarrow cos \ A =\dfrac{ b}{h}=\dfrac{AB}{AC}[/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow \boxed{\blue{\sf cos \ A =\dfrac{7}{25}}}[/tex]

Hence the required answer is 7/25.

Answer:

B

Step-by-step explanation:

We are given a quadratic function f(x) whose zeros are at x = -2 and x = 6.

And we want to determine its axis of symmetry.

Recall that a parabola is symmetric about its axis of symmetry.

Therefore, the axis of symmetry is directly in the middle of the two roots.

Find the average of the roots:

[tex]\displaystyle x=\frac{(-2)+(6)}{2}=\frac{4}{2}=2[/tex]

Hence, the axis of symmetry is x = 2.

Our answer is B.

In general, if we are given the two zeros p and q of a quadratic and we want to find the axis of symmetry x, it is given by:

[tex]\displaystyle x = \frac{p+q}{2}[/tex]

The far left of the chart is the minimum(low) value of the box plot.

Answered by Gauthmath must click thanks and mark brainliest

Graph exists as an illustration of any object or a physical format by dots, lines, etc.

The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could also describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists in a particular case of the graph of an equation.

A function is defined as a connection between a set of inputs containing one output each. In simple words, a function exists as an association between inputs where each input is connected to exactly one output. Every function includes a domain and codomain or range. A function exists generally represented by f(x) where x is the input.

From the given figure,

Graph 1 exists a function.

Graph 2 exists a function.

Graph 3 doesn't exist as a function.

Graph 4 exists a function.

Graph 5 doesn't exist as a function.

Graph 6 doesn't exist as a function.

Hence, Graph exists as a representative of any object or a physical design by dots, lines, etc.

To learn more about graph refer to:

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Answer:

890 beads can be fitted in the triangular prism.

Step-by-step explanation:

If we can fill the spherical beads completely in the triangular prism,

Volume of the triangular prism = Volume of the spherical beads

Volume of triangular prism = Area of the triangular base × Height

From the picture attached,

Area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                             = [tex]\frac{1}{2}(AB)(BC)[/tex]

By applying Pythagoras theorem in the given triangle,

AC² = AB² + BC²

(13)² = 5² + BC²

169 = 25 + BC²

BC² = 144

BC = 12

Area of the triangular base = [tex]\frac{1}{2}(5)(12)[/tex]

                                             = 30 cm²

Height of the triangular prism = 18 cm

Volume of the triangular prism = 30 × 18

                                                   = 540 cm³

Volume of one spherical bead = [tex]\frac{4}{3}\pi r^{3}[/tex]

                                                   = [tex]\frac{4}{3}\pi (0.525)^{3}[/tex]

                                                   = 0.606 cm³

Let there are 'n' beads in the triangular prism,

Volume of 'n' beads = Volume of the prism

540 = 0.606n

n = 890.90

n ≈ 890

Therefore, 890 beads can be fitted in the triangular prism.

Each of the first 3 letters can be chosen from the 23 letters, {A, B, C, …, U, V, W}, so there are 23³ possible choices.

The first 2 digits can be any number from {0, 1, 2, …, 9}, so there are 10² choices.

The last digit cannot be 0 or 9, so you can select from {1, 2, 3, …, 8} which gives 8 choices.

Then the total number of PINs that you can make is

23³ × 10² × 8 = 9,733,600

Answer:

G is the midpoint of the side [tex]\overline {AB}[/tex] of triangle ΔOAB

Step-by-step explanation:

The vertices of the triangle ΔOAB are A(-15, 0), B(0, 8), and C(0, 0)

The coordinates of the point G =  (-7.5, 4)

The length from the point A to the point G, [tex]\overline {AG}[/tex] is given as follows;

[tex]\overline {AG} =\sqrt{(-7.5 - (-15))^2 + (4 - 0)^2} = \sqrt{7.5^2 + 4^2} = 8.5[/tex]

The length from the point A to the point B, [tex]\overline {AB}[/tex] is given as follows;

[tex]\overline {AB} =\sqrt{(-15 - 0)^2 + (8 - 0)^2} = \sqrt{15^2 + 8^2} = 17[/tex]

Therefore, the point G is the half way mark of [tex]\overline {AB}[/tex] = The midpoint of the side  [tex]\overline {AB}[/tex]

Answer:

[tex] {f}^{ - 1}(0) = 6[/tex]

Step-by-step explanation:

When trying to solve for inverses, we are given a y value in place of an x value. Thus we are solving for the x value which the given y value corresponds to.

Answer:

yes

Step-by-step explanation:

....

Answer:

k = 3.

Step-by-step explanation:

At the given point x = -1 an f(x) = 1/2, so we have the equation:

1/2 = (2 - k)/(5(-1) + k)

(2 - k)/(k - 5) = 1/2

Cross multiplying:

2(2 - k) = k - 5

4 - 2k = k - 5

-2k - k = -5 -4

-3k = -9

k = 3.

Answer: B. 74 cm

Step-by-step explanation:

Concept:

Here, we need to know the idea of unit conversion and perimeter.

When there are multiple units in a question, then we should convert all units into one through converting factors.

Perimeter is the distance around a two-dimensional figure.

P = 2 (w + l)

1 cm = 10 mm

Solve:

140 mm = 14 cm

230 mm = 23 cm

P = 2 (w + l) ⇒ Given

P = 2 (14 + 23) ⇒ Substitute

P = 2 (37) ⇒ Addition

P = 74 cm ⇒ Simplify through muliplication

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x=24

Step-by-step explanation:

Answer:

BC = 24

Step-by-step explanation:

Since ∠ B and ∠ C are congruent the the triangle is isosceles with

AC = AB , that is

3x - 15 = x + 33 ( subtract x from both sides )

2x - 15 = 33 ( add 15 to both sides )

2x = 48 ( divide both sides by 2 )

x = 24

Then

BC = x = 24

9514 1404 393

Answer:

  (x, y, z) = (5, 11, 6)

Step-by-step explanation:

To solve this problem, you need to understand "row operations". The ones we're concerned with are multiplying a row by a scalar, and adding rows together.

You also need to understand what the solution looks like, and the usual way that is achieved. The solution will have the 3×3 matrix left of the vertical line be a diagonal of 1s (the identity matrix). Then the numbers to the right of the vertical line represent the solution.

__

In the following, we will use the notation [a]+b[c]⇒[d] to mean that row 'a' is added to the product of row 'c' and the scalar 'b' and that sum replaces row [d]. Multiplying a row by a scalar multiplies each element in the row by that scalar.

The first several operations look like this. Notice we have made the upper left 2×2 matrix an identity matrix. Steps will continue to take care of the 3rd column.

  [tex]\left[\begin{array}{ccc|c}1&1&1&22\\6&1&8&89\\-6&4&4&38\end{array}\right] \qquad\text{given}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&-5&2&-43\\0&5&12&127\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ 6[1]+[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ $-\frac{1}{5}$[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[1]-[2]$\rightarrow$[1]}[/tex]

Now, we normalize the third column.

  [tex]\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&1&6\end{array}\right] \qquad\text{$\frac{1}{14}$[3]$\rightarrow$[3]}\\\\\left[\begin{array}{ccc|c}1&0&0&5\\0&1&0&11\\0&0&1&6\end{array}\right] \qquad\text{$-\frac{7}{5}$[3]+1$\rightarrow$[1];\ $\frac{2}{5}$[3]+[2]$\rightarrow$[2]}[/tex]

This is the target of our row operations. It tells us the solution to the system of equations is ...

  (x, y, z) = (5, 11, 6)

_____

A number of online calculators and phone or tablet apps are available for putting a coefficient matrix into this "reduced row-echelon form." Many graphing calculators will do this, too.

In the end, this is not terribly different from ad hoc solution using "elimination" methods. That is precisely what we did when we created the zeros in the first two columns of row 3.

Answer:

angle c is 63

Step-by-step explanation:

Angles in a triangle add up to 180 therefore

70+47+x=180

x=180-117

=63°

I hope this helps