Find the length represented by x for each pair of similar triangles.
18cm, 9cm, and x
30cm, 15cm, and 25cm

Answer:

8:3

16:6

Step-by-step explanation:

First, let's check if 9 and 24 have any common factor. If they do have any common ones, we must find the GCF (greatest common factor).

Factors of 9: 1, 3, 9

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The common factors both of the numbers share and 1 and 3. To find the GCF, simply compare one of the factors to the other.

1 < 3

Now that we know the GCF, we can divide the two numbers in the ratio 24 : 9 by it (3).

24:9

24/3:9/3

8:3

Now that our ratio is simplified, it's going to be much easier to find more ratios that are equivalent. 8:3 is already one equivalent ratio, but if we multiply each number in the ratio by any other number, we can get a new equivalent ratio. Let's multiply each number in the ratio by 2:

8:3

8 ⋅ 2:3 ⋅ 2

16:6

So, another equivalent ratio to 24:9 (and 8:3) is 16:6.

Answer:

A) Vertical test

B) y=x

C) x

D) domain

If the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.

Inverse functions are functions which can be reversed in to another function.

Then the function is said to be the inverse of the second function.

The test which is used to know whether an inverse is a function or not is Vertical line Test.

So, if the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.

Composition of a function and it's inverse is always x.

Let y = f(x) be a function. Then x = f⁻¹ (y)

(f⁻¹of)(x) = f⁻¹ (f(x)) = f⁻¹ (y) = x

The graph of an inverse is the reflection of the graph of the function over the line y = x.

The range values of the inverse function are the domain values of the original function.

Hence the blank terms are found.

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Answer:

[tex]s=6\sqrt{3}[/tex]

Step-by-step explanation:

In any 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.

In the given diagram, the hypotenuse is marked as 12 miles. Therefore, the side opposite to the 30 degree angle must be [tex]12 \div 2=6[/tex] miles. The final leg, [tex]s[/tex], must then represent the [tex]x\sqrt{3}[/tex] part of our ratio, hence [tex]\implies \boxed{6\sqrt{3}}[/tex]

x=35

vertical opposite angles are equal.

Answer:

hope this helps buddy, please mark the brainliest.

Step-by-step explanation:

Answer:

16 bookmarks were sold

Answer:

40

Step-by-step explanation:

They sold 9 book marks for every 2 books (9:2 ratio).

72/9 = 2/x

Cross multiply. 72 * x = 72x

9 * 2 = 18

72 divided by 18 = 40

Answer:

The measure of an arc is the size of the corresponding central angle, so angle 1 for AB,

Answer: B 30

Answer:

y = 3x+2

Step-by-step explanation:

First find the slope using the slope formula

m= (y2-y1)/(x2-x1)

   = ( -1 - -4)/(-1 - -2)

   = (-1 +4)/ (-1 +2)

   = 3/1

  = 3

The slope intercept formula is

y = mx+b where m is the slope and b is the y intercept

y = 3x+b

Using the point (-1,-1) and substituting into the equation

-1 = 3(-1)+b

-1 = -3+b

-1+3 = b

2 = b

y = 3x+2

Answer:

The slope is -4/5

The y intercept is (0,7)

Step-by-step explanation:

f(x) = 7 -4/5x

Rewriting

y = -4/5x +7

This is in slope intercept form

y = mx+b where m is the slope and x is the y intercept

The slope is -4/5

The y intercept is (0,7)

Answer:

3c^2

Step-by-step explanation:

9514 1404 393

Answer:

  ₹1537.86

Step-by-step explanation:

With the 14% tax added, the final cost is ...

  ₹1349 × (1 +14%) = ₹1349×1.14 = ₹1537.86

Answer:

Centre is,

((5+7)/2,(8+6)/2)

or, (12/2,14/2)

or, (6,7)

radius is,

[√{(5-7)²+(8-6)²}]/2

= [√(2²+2²)]/2

= [√(4+4)]/2

= [√8 ]= [2√2]/2 = √2

The center of a circle = (6, 7)

the radius of a circle = [tex]\sqrt{2}[/tex] units

"The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by  [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}[/tex]"

"The coordinates of the midpoint of the line segment having endpoints [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]m=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] "

"It is the line segment through the center and touching two points on its edge. "

For given question,

The diameter of circle has endpoints at (5, 8) and (7,6).

Let [tex](x_1,y_1)=(5,8),(x_2,y_2)=(7,6)[/tex]

First we find the length of the diameter of the circle.

Using the distance formula,

[tex]\Rightarrow d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2} \\\\\Rightarrow d=\sqrt{(7-5)^2+(6-8)^2} \\\\\Rightarrow d=\sqrt{2^2+(-2)^2}\\\\\Rightarrow d=\sqrt{4+4}\\\\\Rightarrow d=2\sqrt{2}~units[/tex]

We know that the diameter = 2 × radius

⇒ radius (r) = [tex]\frac{2\sqrt{2} }{2}[/tex]

⇒ r = [tex]\sqrt{2}[/tex] units

We know that the midpoint of the diameter is the center of the circle.

Using midpoint formula the center of the circle would be,

[tex]\Rightarrow O=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\\Rightarrow O=(\frac{5+7}{2} ,\frac{8+6}{2} )\\\\\Rightarrow O=(\frac{12}{2} ,\frac{14}{2} )\\\\\Rightarrow O=(6,7)[/tex]

Therefore, the center of the circle is (6,7)

Hence, the center of a circle = (6, 7)

the radius of a circle = [tex]\sqrt{2}[/tex]

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Answer:

3

Step-by-step explanation:

3 - 3/x

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

1 - 1/x

Multiply the top and bottom by x

x(3 - 3/x)

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

x(1 - 1/x)

3x -3

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

x-1

Factor the numerator

3(x-1)

-------

x-1

Cancel like terms

3

-----

1

3

1 dozen = 12

144 / 12 = 12 dozen

12 dozen/ 3 = 4

They need 4 times the amount of flour:

3 1/4 x 4 = 13

They need 13 cups of flour

Perimeter:

We have two straight, congruent sides from the square that are 24 cm, and two semi-circles (or one whole circle).

24 + 24 + 1/2(24pi) + 1/2(24pi)

48 + 12pi + 12pi

48 + 24pi cm

Area:

We have a semi-circle and a square that is missing a semi-circle. Let's find the area of the square minus the semi-circle, then add the additional semi-circle.

Square = 576

Missing semi-circle = 144pi / 2 = 72pi

Semi-circle = 144pi / 2 = 72pi

576 - 72pi + 72pi

576 cm^2

Hope this helps!

Answer:

Slope: 1

Y-intercept: (0,3)

Step-by-step explanation:

The y intercept is when the slope reaches the y-axis line. In this case, it is given to us. Anything that is formed like this: (0, y) is the y-intercept.

Y intercept: (0, 3)

For slope, you can use the formula rise over run. [tex]\frac{Rise}{Run}[/tex]

From the picture, I have drawn the rise over run, which is [tex]\frac{3}{3}[/tex], which is also 1.

Slope: 1

Hope this helped.

Answer: 1

Step-by-step explanation: got it right on edge

Answer:

[tex]y = -7x -13[/tex]

Step-by-step explanation:

Given

Perpendicular to

[tex]7y = x -4[/tex]

Passes through

[tex](-2,1)[/tex]

Required

The equation

First, we calculate the slope of:

[tex]7y = x -4[/tex]

Divide through by 7

[tex]y = \frac{1}{7}x - \frac{4}{7}[/tex]

A linear function is:

[tex]y=mx + c[/tex]

Where;

[tex]m \to slope[/tex]

So:

[tex]m = \frac{1}{7}[/tex]

For the perpendicular line; the slope is:

[tex]m_2 = -\frac{1}{m}[/tex]

So, we have:

[tex]m_2 = -\frac{1}{1/7}[/tex]

[tex]m_2 = -7[/tex]

The equation is:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = -7(x - -2) + 1[/tex]

[tex]y = -7(x +2) + 1[/tex]

Open bracket

[tex]y = -7x -14 + 1[/tex]

[tex]y = -7x -13[/tex]

Answer:

option D is the answer

Step-by-step explanation:

using the HH,ll,ha and la,

where h is the hypotenuse and l is the leg

Answer: A

Step-by-step explanation: x=-2, y=3, z=-3

Answer:

A. -2, 3, -3

Step-by-step explanation:

x = 7 - 2y + z

y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =

= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z

13y = 63 + 8z

y = (63 + 8z)/13

2x + 2y - 3z = 11

2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11

2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11

14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11

-2×(63 + 8z)/13 - z = -3

-2×(63 + 8z) - 13z = -39

-126 - 16z - 13z = -39

-29z = 87

z = -3

y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3

x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2

Answer:

well I don't know

Step-by-step explanation:

your speaking vietnam

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  (c)  A = 38.13 square inches; P = 23.42 inches

Step-by-step explanation:

The radius of the circle is half the diameter, so is 3 inches. This means the entire figure will fit in a rectangle 6 inches wide and 4+3 = 7 inches high. The perimeter of such a rectangle is ...

  P = 2(L+W) = 2(7+6) = 26 inches

The area of that rectangle is ...

  A = LW = (7)(6) = 42 square inches

Then area of the given figure is less than 42 square inches, and the perimeter is less than 26 inches. The only answer choice that matches these bounds is ...

  A = 38.13 square inches; P = 23.42 inches

Answer:

0.45d + 4

Step-by-step explanation:

45% of d => 0.45d

Then a number 4 more is gonna be 0.45d + 4

Answer:

-5≤x <1

Step-by-step explanation:

sqrt( x+5) / sqrt(1-x)

The numerator must be greater than zero since it is a square root

sqrt(x+5) ≥0

Square each side

x+5≥0

x≥-5

The denominator must be greater than zero (the denominator cannot be zero)

sqrt(1-x)> 0

Square each side

1-x > 0

1>x

Putting these together

-5≤x <1

Answer:

let 2 no. be x and y

x+y=31 ..... (1)

x-y=11 .........(2)

from (1)

x=31-y ..........(3)

putting (3) in (2)

31-y-y=11

-2y=11-31

-2y=-20

2y=20

y=10

Answer:

There are 21 people in the line (including Kollam himself).

Answer:

5 cm

Step-by-step explanation:

Let x = width of frame.

The width of the frame is added all around the painting, so you must add 2x to the length of the painting and 2x to the width of the painting to find the total length and width including the frame.

painting length: 30

total length: 2x + 30

painting width: 20

total width: 2x + 20

total area = LW

total area = (2x + 30)(2x + 20)

total area = 1200

(2x + 30)(2x + 20) = 1200

(x + 15)(x + 10) = 300

x^2 + 10x + 15x + 150 = 300

x^2 + 25x - 150 = 0

(x - 5)(x + 30) = 0

x - 5 = 0  or  x + 30 = 0

x = 5  or x = -30

The width of the frame cannot be a negative number, so we discard the solution x = -30.

Answer: 5 cm

Answer:

A

Step-by-step explanation:

We are given the function:

[tex]\displaystyle y = x^2 - 6x - 7[/tex]

And we want to determine its graph.

One of the most important features of a quadratic is its vertex. So, we can start by finding the vertex using the formulas:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = 1, b = -6, and c = -7.

Find the x-coordinate of the vertex:

[tex]\displaystyle x = -\frac{(-6)}{2(1)} = 3[/tex]

Substitute this back into the equation to find the y-coordinate:

[tex]\displaystyle y(3) = -16[/tex]

Therefore, our vertex is at (3, -16).

The only graph whose quadratic's vertex is at (3, -16) is Graph A. Thus, our answer is A.

Answer:

40.4502 billion dollars

51.3432 billion dollars

Step-by-step explanation:

Given :

Total amount spent in billions in pets x years after year, 2000 ;

P(x)=2.1786x + 25.2

Amount spent in 2007 ;

x = 2007 - 2000 = 7 years

Put x = 7 in the equation :

P(7)=2.1786(7) + 25.2 = 40.4502

Amount spent in 2012 :

x = 2012 - 2000 = 12 years

Put x = 12 in the equation :

P(12) = 2.1786(12) + 25.2 = 51.3432

The amount spent in billik dollars on pets in :

2007 = $404502 billion

2012 = $51.3432 billion

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)