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The Pythagorean theorem is also known as the Pythagoras' theorem. The height of the triangle is 12cm.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

Given a=10cm and b=13cm, therefore, the height of the triangle can be found using the Pythagoras theorem, therefore,

AB² = AD² + BD²

13² = AD² + 5²

169 = AD² + 25

AD = 12cm

Hence, the height of the triangle is 12cm.

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The given function y = 2(x² - 1) is decreasing for all values in the domain and it has a horizontal asymptote along the x-axis so options (B) and (C) will be correct.

A certain kind of relationship called a function binds inputs to essentially one output.

The nature of the relationship between the variables that makes up a function, such as y = sinx and y = x +6, defines the function.

Given the function,

y = 2(x² - 1)

If we increase the value of x to positive then the denominator x² - 1 will go to increase and thus y will decrease.

If we increase the value of x in negative then denominator x² - 1 will go to increase and thus y will decrease.

Therefore it is decreasing for all values in the domain.

Now,

Lim at x tends to ∞ of function is 2/∞ = 0 so y = 0 means there is a horizontal asymptote along the x-axis.

Hence "The given function y = 2(x² - 1) is decreasing for all values in the domain and it has a horizontal asymptote along the x-axis".

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Answer:

it is 18

Step-by-step explanation:

Based on the definition of supplementary angles, the measure of both angles are: 80° and 100°.

The sum of angles that are supplementary to each other equals 180 degrees.

Let the measure of the supplementary angle be x.

The other angle will be: x + 20.

(x + 20) + x = 180

x + 20 + x = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 160/2

x = 80°

The other angle will be x + 20 = 80 + 20 = 100°.

The measure of the angles are: 80° and 100°.

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Answer:

m = -1/3

Step-by-step explanation:

Find two points in order to calculate slope:

Slope (m) =

ΔY /ΔX= -1/ 3= -0.33333333333333

Slope intercept:

y = -0.33333333333333x + 2

Answer:

Slope = - 1/3

Step-by-step explanation:

Choose the point on the right and move upwards. How many times did you move upwards until you were at the same level as the point on the left? You moved once, which means your rise is 1.

Now from the point where you are at now, move right or left depending on where the point is. In this case, it's on the left which means our run will be negative. Now move left until you reach that point on the left. How many times did you move left? You moved three times, which means your run is 3.

Rise/Run = -1/3

Slope = Rise/Run

Slope: - 1/3

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The age of the bird skeleton is 6539.

An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Here, N =[tex]N_{0}.e^{-0.0001t}[/tex]

             = 52% N₀

[tex]e^{-0.0001t}[/tex] = 0.52

-0.0001 t = ln 0.52

t = -10000 ln 0.52

t = 6539

Thus, the age of the bird skeleton is 6539.

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Answer:

Step-by-step explanation:

Answer:

[tex]7x[/tex]

Step-by-step explanation:

[tex]\text{Let,}~~\\\\~~~~~~~y = e^{\ln 7x}\\\\\implies \ln y = \ln \left(e^{\ln 7x} \right)\\\\\implies \ln y = \ln (7x) \ln e\\\\\implies \ln y = \ln (7x)\\\\\implies y = 7x\\\\\implies e^{\ln 7x} = 7x[/tex]

The sine of ∠I is represented by the ratio 63:65

First, let's draw the triangle (see the picture below.)

We need to use it here.

-sin = opposite/hypotenuse

-cos = adjacent/hypotenuse

-tan = opposite/adjacent.

Assuming that ∠I is Ф,

we can see that its opposite side is equal to 63 and the hypotenuse is 65. Therefore,

[tex]sin(I)=\frac{63}{65} \\\\sinI=75^0[/tex]

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Answer:

0.18

Step-by-step explanation:

It’s right bc I got it correct with that answer

Answer:

d

Step-by-step explanation:

Comparing the graphs we understand :

⇒ g(x) is equal to f(x) when shifted down 2 units

===========================================================

Hence :

⇒ g(x) = f(x) - 2

⇒ g(x) = (x + 7)² - 2

Answer:

Answer:

[tex] \frac{7}{2} [/tex]

Step-by-step explanation:

[tex] \frac{3! + 0!}{2! \times1! } = \frac{(3 \times 2 \times 1) + 1}{(2 \times 1) \times 1} = \frac{6 + 1}{2} = \frac{7}{2} [/tex]

Answer:

A = 26.35 mm²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 8.5 and h = 6.2 , then

A = 0.5 × 8.5 × 6.2 = 26.35 mm²

Step-by-step explanation:

1/2 ×bh

1/2×8.5×6.2

=26.35mm

[tex]~~(2I_2)A\\\\\\=2\begin{bmatrix} 1&0\\0&1 \end{bmatrix}\begin{bmatrix} 4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix} 2&0\\0&2 \end{bmatrix}\begin{bmatrix} 4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix} 8+0&4+0\\0+6&0-6 \end{bmatrix}\\\\\\=\begin{bmatrix} 8&4\\6&-6 \end{bmatrix}[/tex]

Answer:

If the cost of 3 notebooks is 30.30, we can infer the cost of one notebook is 10.10.

Step-by-step explanation:

[tex]10.10 * 15 = x[/tex]

[tex]10.10 * 15 = 151.5[/tex]

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We are asked to find the cost of 15 notebooks, given that the cost of 3 notebooks is 30.30.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So we divide the cost of three notebooks (30.30) by 3:

[tex]\star~\large\pmb{30.30\div3}[/tex]

[tex]\star~\large\pmb{10.10}[/tex]

That's the cost of 1 notebook. Now, multiply that times 15 (we're asked to find the cost of 15 notebooks).

[tex]\star~\large\pmb{10.10\times15}[/tex]

This gives us:

[tex]\star~\large\pmb{151.5}[/tex]

That's the cost of 15 notebooks if the cost of one notebook is 10.10.

Hope it helps you out! :D

Ask in comments if any queries arise.

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Answer:

b

Step-by-step explanation:

Amount of tax you need to pay on a taxable income of $40,000 is,

= $6423.75

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

According to table, $40,000 falls in the 3rd category between $31,850 and $77,100

And, The tax is "$4,386.25 + 25% of amount over 31,850"

Hence, we have:

= $4,386.25 + 25% of (40,000 - 31,850).

= $4,386.25 + 0.25 x 8150

= $6423.75

Thus, Amount of tax you need to pay on a taxable income of $40,000 is,

= $6423.75

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Answer:

56.52

Step-by-step explanation:

The formula for circumference is C=2πr

So, C=2(3.14)(9)

C=56.52 answer

The value of x and y is -0.0434 and -4.5652.

equation, statement of equality between two expressions consisting of variables and/or numbers.

given:

x - 4.5y=20.5

x + 4.7y= -21.5

Solving above two equation we have:

20.5+4.5y=-21.5-4.7y

42= -9.2y

y= -42/9.2

y= -4.5652

x=-0.0434

Hence, the value of x and y is -0.0434 and -4.5652.

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The simplest form of the given expression (3x² + 4x - 8) - (-2x² + 4x + 2) will be  5x² - 10.

A quadratic equation is the second-order degree algebraic expression in a variable.

The standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We have been given an expression

(3x² + 4x - 8) - (-2x² + 4x + 2)

(3x² + 4x - 8 + 2x² - 4x - 2)

Solving like terms

5x² + 4x - 4x - 10

5x² - 10

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A slope is also known as the gradient of a line. The slope of the line is 1.4.

A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

Natasha drew a line on the coordinate plane that passes through the point (15,13) and has a y-intercept of -8. Since the coordinate of a point on the line is known the value of the y-intercept is known, therefore, we can write,

13 = m15 - 8

13 + 8 = 15m

21 = 15m

m = 7/5 = 1.4

Hence, the slope of the line is 1.4.

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Answer:

x=3

Step-by-step explanation:

We can use the slope formula to help complete this question

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

-1 = ( -6-0)/(x- -3)

-1 = -6/ (x+3)

Multiply each side by (x+3)

-x-3 = -6

Add 3 to each side

-x -3+3 = -6+3

-x =-3

Multiply each side by -1

x = 3

Answer:

  x = 3

Step-by-step explanation:

The given slope and point can be used to write the equation of the line using the point-slope form. To find x for a given y, we can solve that equation.

__

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

For (h, k) = (-3, 0), and m = -1, the equation is ...

  y -0 = -1(x -(-3))

  y = -x -3

We want x when y = -6, so this becomes ...

  -6 = -x -3

Adding x+6 to both sides of the equation, we get ...

  (x +6) -6 = -x -3 +(x +6)

  x = 3 . . . . . . . simplify

Let that be theta

Here perpendicular is lamp post and base is the shadow

Answer:

59.0° (nearest tenth)

Step-by-step explanation:

This can be modeled as a right triangle (see attachment).

To find the angle of elevation (marked as [tex]x[/tex] on the attached diagram), use the tan trig ratio:

Tan trigonometric ratio

[tex]\sf\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substitute the given values into the formula and solve for x:

[tex]\implies \sf\tan(\theta)=\dfrac{10}{6}[/tex]

[tex]\implies \sf\theta=\tan^{-1}\left(\dfrac{10}{6}\right)[/tex]

[tex]\implies \theta = \sf 59.03624...^{\circ}[/tex]

[tex]\implies \theta = \sf 59.0^{\circ}\:(nearest\:tenth)[/tex]

Step-by-step explanation:

you use Sin60 to find y because Sin60=

[tex] \frac{y}{8} [/tex]

The exact dimensions of the cone of largest volume that will fit inside the sphere will be 14.67 inches and 22✓2/3 inches.

From the information given, the height of the cone will be:

h = 11 + x

h = 11 + 3 2/3

h = 14 2/3 inches

The radius of the base of the cone will be:

= ✓121 - ✓121/9

= 2✓2(11)/3

= 22✓2/3

Therefore, the dimensions of the cone aren't 14.67 inches and 22✓2/3 inches.

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Step-by-step explanation:

[tex] {x}^{2} + 8x + 7 \\ [/tex]

Based on the calculations, the exact area of this rectangle is equal to 16√3 + 32 mm².

Mathematically, the area of a rectangle can be calculated by using this formula:

Area = Length × Width

Note: Radius (R) is equal to 2 mm.

Joining the center of the circles would form an equilateral triangle with side length of 2R. Also, the height of the equilateral triangle is given by:

Height = √2R² - R²

Height  = √3R

For the length and width of this rectangle, we have:

Length = R + 2R + R

Length  = 4R

Width = 2R + height of equilateral triangle

Width = 2R + √3R

Width = (2 + √3)R

Therefore, the area of a rectangle becomes:

Area = 4R × (2 + √3)R

Area = 4(2 + √3) × R²

Area = 4(2 + √3) × 2²

Area = (8 + 4√3) × 4

Area = 16√3 + 32 mm² ≡ a√3 + b

In conclusion, a = 16 and b = 32.

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Part A

Explanation:

Refer to the converse of the corresponding angles theorem. The original version is stated as part A, and the converse is marked in bold above.

Conditional statements are of the form "if this, then that". Symbolically we can use the template "If P, then Q". The P and Q are placeholders for logical statements.

The converse of "if P, then Q" is "If Q, then P". We swap the positions of P and Q. Do not negate either piece.

========================================================

Part B

Explanation:

Recall that for any triangle, the three interior or inside angles always add to 180 degrees. In short: A+B+C = 180. If C = 70, then A+B = 180-C leads to A+B = 180-70 and A+B = 110. This process can be reversed.

========================================================

Part C

Explanation:

For more information, check out the converse of the alternate interior angles theorem. The regular version of the theorem is "If two lines are parallel, then the alternate interior angles are congruent".

The converse of this theorem flips things to say: "If alternate interior angles are congruent, then the lines are parallel".

========================================================

Part D

Explanation:

Throwing coins in a fountain is one way to lose money, but there are other ways. He could drop a coin somewhere, or leave the coin somewhere he forgot.

In other words, just because he lost his money does not mean he threw a coin in the fountain.

Answer:

a

Step-by-step explanation:

I say you need to get mays age to even get lilacs age

The number of laps that Swimmer A swam was 50 laps.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Let we suppose that:

Swimmer A swam x laps

Swimmer B swam y laps.

Then, according to the given data, we have:

x    +    y   =   175   laps

y    =   25   +  2x  

(25 more than twice of laps of A is the number of laps of B).

Thus, we get a system of two equations:

x   +   25  +  2x  =   175

3x   +  25    =   175

3x   =   175  -  25  =  150

x   =   50

As x is the number of laps Swimmer A swam, thus, the number of laps that Swimmer A swam was 50 laps.

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Answer:

express as a mixed fraction 5¼×6

I need method

And answer should be 31½