How many solutions does the following system of equations have?

The attached image represents the foci of the hyperbola

The equation of the hyperbola is given as:

[tex]\frac{x^2}{625} - \frac{y^2}{3600} = 1[/tex]

Rewrite as:

[tex]\frac{x^2}{25^2} - \frac{y^2}{60^2} = 1[/tex]

A hyperbola is represented as:

[tex]\frac{(x - h)^2}{b^2} - \frac{(y - k)^2}{a^2} = 1[/tex]

This means that:

h = 0

k = 0

b = 25

a = 60

Next, calculate c the distance from the center to the focus using:

[tex]c = \sqrt{a^2 -b^2}[/tex]

This gives

[tex]c = \sqrt{60^2 -25^2}[/tex]

Evaluate

[tex]c = \pm \sqrt{2975}[/tex]

This means that:

Foci = (0, -√2975) and (0, √2975)

See attachment for the hyperbola and the foci

Read more about hyperbola at:

https://brainly.com/question/16735067

#SPJ1

Answer:

x+5 (under assumption you meant to do -3x

Step-by-step explanation:

you can use long division.

Take the leading coefficient x^4 and divide it by x^3. This results in x which is going to be the first part of you quotient. Now take that x and multiply it by the divisor (x^3 - 3). This gives you x(x^3 - 3) = x^4 - 3x. Now subtract that x^4 - 3x from the original polynomial and repeat this until you can't divide anymore

[tex]x^4+5x^3-3x-15 - (x^4-3x) = 5x^3-15\\x^3/5x^3=5\\5(x^3-3) = 5x^3-15\\5x^3-15-(5x^3-15) = 0\\\\x+5[/tex]

Answer: Add the equations to eliminate k

Step-by-step explanation:

Adding the equations together, we get 2b=18.

First blank: Side-Angle-Side similarity postulate

Second blank: proportional

The area of the swimming pool on the scale drawing will be 300 sq. centimeters.

A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.

For the given scale drawing 1 centimeter represents 2 meters, therefore, the length of 40 meters in one scale drawing will be equal to,

40 meters = 40/2 centimeters = 20 centimeters

The width of 30 meters one scale drawing will be equal to,

30 meters = 30/2 centimeters = 15 centimeters

Now, the area of the swimming pool on the scale drawing will be,

Area= 20 centimeters × 15 centimeters = 300 sq. centimeters

Hence, the area of the swimming pool on the scale drawing will be 300 sq. centimeters.

The complete question is:

A rectangular swimming pool measures 40 meters in length and 30 meters in width. in the scale drawing of the pool, 1 centimeter represents 2 meters. then what is the area of the swimming pool on the scale drawing?

Learn more about Scale ratio:

https://brainly.com/question/13770371

#SPJ1

cos N = 14/20 = 0.70

Answer:

b.) Subtracting 5 then dividing both sides by -2

Step-by-step explanation:

Given expression:

⇒ -2x + 5 = 9

To solve this equation, first we need to remove the 5 on the left side. Then divide both sides by -2.

When done so:

⇒ -2x = 9 - 5

⇒ -2x = 4

⇒ -2x/-2 = 4/-2

⇒ x = -2

Answer:

f(x)=f(6)= 6^2 - 2*6=36-12=  24

Step-by-step explanation:

This is a function, so we replace x with 6. When we do this, we use it to replace x in the above equation, so instead of having x^2-2x, we have 6^2 -2x. Then we just solve the equation, leaving us with the final solution of 24.

Step-by-step explanation:

please mark me as brainlest

The coordinates of point N are (3, 5).2 the answer is 2/1 but just write 2.

We have given that,

Polygon MNOPQ is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image M′N′O′P′Q′.

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

The coordinates of point M are (2, 4), and the coordinates of point N are (3, 5)

Therefore we get,

2 the answer is 2/1 but just write 2.

To learn more about the co-ordinate visit:

brainly.com/question/17206319

#SPJ1

Answer:

[tex]4^{-5}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then

[tex]\frac{4^{3} }{4^{8} }[/tex] = [tex]4^{(3-8)}[/tex] = [tex]4^{-5}[/tex]

Answer:

The surface area of the triangular prism is [tex]624cm^{2}[/tex]

Step-by-step explanation:

First find the area of the triangle.

The formula of the area of triangle is: [tex]\frac{1}{2} * h*b[/tex]

h=height

b=base or width.

[tex]\frac{1}{2}*16*12[/tex]

But, since we have two triangles we can skip the [tex]\frac{1}{2}[/tex] because [tex]2*\frac{1}{2} =1[/tex].

[tex]16*12=192[/tex], that is the area of the two triangles combined.

Now let's find the area of the rectangles. I'll start with the diagonal one.

The formula of the area of the rectangle is: [tex]h*b[/tex].

[tex]20*9=180[/tex].

The next rectangle.

[tex]9*16=144[/tex]

The final rectangle.

[tex]12*9=108[/tex]

Now combine all the areas to find the surface area of the triangular prism.

[tex]192+180+144+108=624[/tex]

The surface area of the triangular prism is [tex]624cm^{2}[/tex]

Hope this helps!

If not, I am sorry.

It is called the y-coordinate

The point itself is called a coordinate, vertically, the vertical component of the coordinate is called the y-coordinate, while horizontally, the horizontal component of the coordinate is called the x-coordinate.

Hope that helps!

#LearnwithBrainly

1. The value of x is 40

m ∠2x + 10 = 90

m ∠3x = 120

m ∠2x +5 = 85

m ∠2x -15 = 65

2. The value of x is 15

m ∠5x = 75

From the question, we are to determine the value of x and the given angles

Since sum of angles is 360°

3x + 2x + 10 + 2x + 5 + 2x -15 = 360°

Collect like terms

3x + 2x + 2x + 2x  = 360° - 10° - 5° + 15°

9x = 360

x = 360 / 9

x = 40

∴ x = 40

Then,

m ∠2x + 10 = 2(40) + 10

m ∠2x + 10 = 80 + 10

m ∠2x + 10 = 90

m ∠3x = 3(40)

m ∠3x = 120

m ∠2x +5 = 2(40) + 5

m ∠2x +5 = 80 + 5

m ∠2x +5 = 85

m ∠2x -15 = 2(40) - 15

m ∠2x -15 = 80 - 15

m ∠2x -15 = 65

Hence, the measure of angle 2x-15 is 65

2.

Since sum of angles is 180°

Then,

5x° + x° + 90° = 180°

6x° = 180° - 90°

6x° = 90°

x = 90/6

x = 15

m ∠5x = 5(15)

m ∠5x = 75

Hence, the measure of angle 5x is 75

Learn more on Calculating angles here: https://brainly.com/question/15820650

#SPJ1

[tex]\tan(90^{\circ}-A)\\ \\ =\frac{\sin(90^{\circ}-A)}{\cos(90^{\circ}-A)}\\ \\ =\frac{\cos A}{\sin A}\\\\=\boxed{\frac{1}{\tan A}}[/tex]

The value of the variable is 4√5. Then the correct option is C.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The similar triangles are shown in the diagram.

16 / x = x / 5

    x² = 16 × 5

      x = 4 √5

Then the value of the variable is 4√5.

Then the correct option is C.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

Answer:

See below

Step-by-step explanation:

Period = 1 day      

Periodic interest = .045 / 365       (since there are 365 days in a year)

V(t) = 6000 *  ( 1 + .045/365)^t      where t is in days

V(t) = 6000 * (1+.045/365)^(t * 365)       where t is in years

Answer:

Length = 30

Width = 17

Step-by-step explanation:

Let L = length of rectangle and W = Width

The first sentence gives the equation

W = L/2 + 2 ==>

2W = L +4 ==>

L = 2W - 4 ....  (1)

The perimeter of the rectangle is 2(L+W) = 2L +2W

Second sentence gives us the equation

4L = 2L + 2W + 26 ===>
2L = 2W + 26 ......   (2)

(2) - (1) ==> L = 30   (2W cancels out)

From (1), W = 30/2 + 2 = 15 + 2 = 17

Check:
Using these values and substituting in equation 2 gives us
2 * 30 = 2* 17 + 26
60 = 34 + 26
which matches

Answer:

D

Step-by-step explanation:

definitely

Answer: Add the equations to eliminate k

Step-by-step explanation:

Adding the equations, you get 2b=18, which you can solve for b. Afterward, you can substitute this value of b back into either equation to solve for k.

Answer:

Como faltar a la escuela. Por favor, ¿cuál es el significado?

Values are given below as pairs (x,y) where x coordinate is x values in box and y coordinate is y values on box

Graph attached

The area of triangle ABC from the given vertices is gotten as; 7.5

We are given the vertices of the triangle as;

A(1, 2)

B(4, 0)

C(1,-4)

The formula for area of a triangle with 3 vertices is;

Area = ¹/₂[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

Thus;

Area = ¹/₂[1(0 + 4) + 4(-4 - 1) + 1(1 - 0)]

Area = ¹/₂(4 - 20 + 1)

Area = -7.5

Read more about area of triangle at; https://brainly.com/question/17335144

#SPJ1

The graphed that represents the new function with the same slope and y-intercept is: graph Y.

Slope = rise/run along a line.

Y-intercept is the y-value of the point on the y-axis that the line intercepts.

Slope of the function given = rise/run = 2/1 = 2

2 multiplied by 1/2 = 2/2 = 1.

Y-intercept of the given function is: 1

1 increased by 3 units is: 1 + 3 = 4

The slope of graph Y = rise/run = 2/2/ = 1

The y-intercept is also 4

Therefore, the answer is: Graph Y

Learn more about the slope and y-intercept on:

https://brainly.com/question/25722412

#SPJ1

The value obtained by doing the operation are ,a=0.11,b=11,c=(111/250)d=44,e=(1/8),f=(83/500),h=0.375,i=37.5%,j=(111/125),k=0.888,i=(777/1000),m=77%,n=0.2,o=20%,p=(777/1000),q=66.6%.

The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.

The procedure of changing the basis of a number is known as number conversion. A binary number is made up of only two numbers: 1 and 0. A decimal number is made up of ten digits ranging from 0 to 9.

The values obtained from the table the decimal and the percentage form are solved as;

[tex]\frac{1}{9} \\\\ 0.3111 \\\\\ 0.1111 \times 100 \\\\ 11.11 \%[/tex]

The other missing values are;

a=0.11

b=11

c=(111/250)

d=44

e=(1/8)

f=(83/500)

h=0.375

i=37.5%

j=(111/125)

k=0.888

i=(777/1000)

m=77%

n=0.2

o=20%

p=(777/1000)

q=66.6%

Hence all the missing values are given above.

To learn more about percentages, refer to:

https://brainly.com/question/13450942

#SPJ1

horizontal transformation 1 unit left.

vertical translation 2 units down.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given:

f(x) = [tex]4^{x}[/tex]

g(x) = [tex]4^{x+1} -2[/tex]

As, we can see that g(x) is shifted left side by 1 unit

So, horizontal transformation 1 unit left.

Now, as 2 is subtracted

So, vertical translation 2 units down.

Learn more about this concept here:

https://brainly.com/question/10269163

#SPJ1

The angle measurements the carpenter needs to cut the carpet to make it fit in his room are 144°, 144°, 144°, 144°, 144°, 90°, and 90°

From the question, we are to determine the angle measurements that the carpenter needs to cut the carpet to make it fit in his room

The diagram shows a heptagon with two of its angles, a right-angle each, and the remaining angles have equal values, x.

First, we will calculate the sum of angles in a heptagon

The sum of angles in a polygon is given by the formula

Sum of angles in a polygon = (n-2)180°

Where n is the number of sides

For a heptagon, n = 7

∴ Sum of angles in a heptagon = (7-2)180°

= 5×180°

= 900°

Now, considering the given diagram, we can write that

x + x + x + x + x + 90° + 90° = 900°

5x + 180° = 900°

5x = 900° - 180°

5x = 720°

x = 720°/5

x = 144°

Hence, the angle measurements the carpenter needs to cut the carpet to make it fit in his room are 144°, 144°, 144°, 144°, 144°, 90°, and 90°

Learn more on Angles in a polygon here: https://brainly.com/question/13263876

#SJP 1

Answer:

5 + 10^5 = 100005 (I think its this one you are looking for

(5 + 10)^5 = 759275

Step-by-step explanation:

Answer:

100,005

Step-by-step explanation:
Original: 10 * 1 = 10

First, you need to do 10 * 10 which = 100.
Next, you need to do 100 * 10 which = 1,000.
Next, you need to do 1000 * 10 which = 10,000.
Next, you need to do 10000 * 100 which = 100,000.
Lastly, you need to add 5 to 100,000 and you get 100,005.


I Hope This Helped :D