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Answer:

right angle triangle

Step-by-step explanation:

by applying Pythagoras theorem

\( RHS ={9}^{2} + 12 ^{2} = 81 + 144 = 225=√225 =15=LHS\)

hence proved

Answer:

hope it helped you:)

have a great day

Answer:

\(\boxed {\tt 3x^2+36x+81}\)

Step-by-step explanation:

Multiply the binomials using FOIL: First, Outside, Inside, Last.

Multiply the first terms, then the outside terms, then the inside terms, and finally, the last terms.

(x+9)(3x+9)

First

Outside

Inside

Last

3x²+9x+27x+81

Combine the terms.

3x²+(9x+27x)+81

3x²+36+81

The trinomial is: 3x²+36x+81

Answer:

m∠A = 25° and m∠C = 25°

Step-by-step explanation:

The sum of all three angles in a triangle must add up to 180°.  Since the measure of angle B is 130°, the sum of the other two angles have to be 50°.  

Also, the triangle is isosceles, meaning two of the sides are equal in length.  For those sides, their corresponding angles must also be equivalent.  In this case, it's the two smaller angles.  Since we have 50° between the two angles, A and C, divide 50 by 2 to get 25° for both angle measurements.  

The statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°

From the question, we are to determine which of the statements must be true

From the given information,

m ∠B = 130°

Since the triangle is an isosceles triangle, the base angles must be equal

That is,

m ∠A = m ∠C

But, angles in a triangle sum up to 180°

Then,

∠A + ∠B + ∠C = 180°

This becomes

2 × ∠A + 130° = 180°

2 × ∠A = 180° - 130°

2 × ∠A = 50°

∠A = 50° ÷ 2

∠A = 25°

Since ∠A = ∠C

Therefore,

∠C = 25°

Hence, the statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°

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The value of x that maximizes the area of the figure is 1.5 inches, and the maximum area is 3.375 square inches.

A rectangle is a two-dimensional form that has four full sides and four right angles. Because the opposing sides are parallel and congruent, it is a unique kind of parallelogram.

To find the maximum area of the figure, we need to determine the value of x that will maximize the area.

The area of the figure can be calculated as:

A = (1.5x)(x) + (1/2)(1.5x)(6-2x)

Simplifying the expression:

\(A = 1.5x^2 + 4.5x - 3x^2\)

\(A = -1.5x^2 + 4.5x\)

To find the value of x that maximizes the area, we need to take the derivative of A with respect to x and set it equal to zero:

dA/dx = -3x + 4.5 = 0

Solving for x:

3x = 4.5

x = 1.5 inches

Now that we know x=1.5 inches maximizes the area, we can substitute it back into the area equation to find the maximum area:

\(A = -1.5(1.5)^2 + 4.5(1.5)\)

A = 3.375 square inches

Therefore, the value of x that maximizes the area of the figure is 1.5 inches and the maximum area is 3.375 square inches.

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Step-by-step explanation:

a) Find the angular speed of the blade in radians per minute:

The formula for angular speed is given by:

ω = 2 * π * f

where f is the frequency of rotation in revolutions per minute, and π is approximately equal to 3.14159.

Plugging in the values, we get:

ω = 2 * 3.14159 * 4300 revolutions per minute

ω = 26,957.1 radians per minute

Rounding to three decimal places, the answer is:

ω = 26,957.1 radians per minute = 26,957.1 radians/minute

b) Find the linear speed of the saw teeth (in inches per minute) as they contact the wood being cut:

The formula for linear speed (v) is given by:

v = ω * r

where ω is the angular speed in radians per minute, and r is the radius of the blade (half of the diameter).

Plugging in the values, we get:

v = 26,957.1 radians/minute * 4.125 inches

v = 111,542.7 inches per minute

Rounding to one decimal place, the answer is:

v = 111,542.7 inches per minute = 111,543 inches/minute

Answer:

D

Step-by-step explanation:

Step-by-step explanation:

33 1/3 = (3×33 + 1)/3 = 100/3

51 = 100/3 × x

153 = 100x

x = 153/100 = 1.53

1.53 × 33 1/3 = 51

so, "that" number is 1.53.

Answer:

Step-by-step explanation:

variable is the first one
evaluate is the second one
algebraic expression is the third one
substitute is the fourth one

Answer:

The answer is 1/5

Step-by-step explanation: Turn 4 in to a fraction (4/1) and take 4/5 then flip the the 4/1 fraction (1/4) and multiply it by 4/5. 4/5*1/4=4/20 simplify it 1/5. Hope this helped!

GIVEN:

We are given a function that models the shoulder height of an African Elephant as shown below;

T is the age of the Elephant in years.

Required:

To estimate the height of an Elephant that is 10 years old.

Step-by-step solution;

To solve this problem, we have the age of the Elephant as t in the function. Where the age is now given as 10 years, we will simply substitute for t equals 10 into the function.

We now have;

We can now approximate this to the nearest whole number and we'll have;

Therefore,

ANSWER:

For a 10 year old Elephant, the height is 210 cm.

The last option is the correct answer.

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Answer:

hold yo ablo espanol

Step-by-step explanation:

If you want to save ₹117,000 to buy your first self-driving magic carpet and deposit ₹90,000 in a bank account paying an interest of 6% compounded annually, you will wait for 4.5 years (period) before you can buy your item.

The period that you will wait to earn a future value of ₹117,000 after depositing ₹90,000 at 6% compounded annually can be determined using an online finance calculator as follows:

I/Y (Interest per year) = 6%

PV (Present Value) = ₹90,000

PMT (Periodic Payment) = ₹0

FV (Future Value) = ₹117,000

Results:

N = 4.503 years

Total Interest = $27,000.00

Thus, with the present investment of ₹90,000 today, you will have a future value of ₹117,000 in 4.5 years at 6% compounded interest.

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The correct sequence of transformations that proves AMNO and APQR are congruent is: OAMNO was dilated by a factor of 3 about the origin, then reflected across the y-axis to form APQR.

The correct sequence of transformations that proves AMNO and APQR are congruent is:

OAMNO was dilated by a factor of 3 about the origin, then reflected across the y-axis to form APQR.

To see why, let's examine the properties of the two triangles:

Triangle MNO has vertices at (-2,-1), (-2,4), and (3,1).

Triangle PQR has vertices at (-6,-3), (-6,12), and (9,3).

If we dilate triangle MNO by a factor of 3 about the origin, we get a new triangle with vertices at (-6,-3), (-6,12), and (9,3). This is because each coordinate of MNO is multiplied by 3:

(-2,-1) -> (-6,-3)

(-2,4) -> (-6,12)

(3,1) -> (9,3)

If we reflect this new triangle across the y-axis, we get a new triangle with vertices at (6,-3), (6,12), and (-9,3). This is because the x-coordinates of each point are negated:

(-6,-3) -> (6,-3)

(-6,12) -> (6,12)

(9,3) -> (-9,3)

This final triangle, with vertices at (6,-3), (6,12), and (-9,3), is congruent to triangle PQR. Therefore, we have shown that AMNO and APQR are congruent.

This theorem relates to theorems previously studied in the sense that it involves transformations of geometric shapes, which is a fundamental concept in geometry. In real-world applications, these transformations can be used in computer graphics, architecture, and engineering, among other fields, to manipulate and analyze shapes and structures.

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The missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

The equation of the function is given as:

y = 5^x

And the x value is given as

x = 2

To determine the missing value, we start by substituting 2 for x in the function y = 5^x

So, we have:

y = 5^2

Evaluate the exponent

y = 25

So, the complete coordinate is (2, 25)

Hence, the missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

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Answer:

28.52

Step-by-step explanation:

105.87 - 77.35 = 28.52

Answer:

20%

Step-by-step explanation:

Think about it. 100 divided by 25 is four so just multiply 5 times 4 and you got 20. giving you the probability of 20%. Your Welcome! And I'm not a genius it's just simple math.

Answer:

90%

Explanation: 27/30 ÷ 3 = 9/10

9/10 ⇒ 9 x 10 = 90%

The maximum value of the function f (x) = -1.8x² + 7x - 11 to the nearest hundredth is,  - 4.19.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ f (x) = -1.8x² + 7x - 11

Now, We can differentiate with respect to x as;

⇒ f ' (x) = - 1.8 × 2x + 7 × 1 - 0

⇒ f ' (x) = - 3.6x + 7

Put f ' (x) = 0

⇒ - 3.6x + 7 = 0

⇒ 3.6x = 7

⇒ x = 1.94

Now, Again differentiate with respect to x as;

⇒ f ' (x) = - 3.6x + 7

⇒ f '' (x) = - 3.6 × 1 + 0

⇒ f '' (x) = - 3.6 < 0

Hence, Substitute x = 1.94 in function to get maximum value,

⇒ f (x) = -1.8x² + 7x - 11

⇒ f (x) = -1.8 (1.94)² + 7 × 1.94 - 11

⇒f (x) = - 6.77 + 13.58 - 11

⇒ f (x) = - 4.19

Thus, The maximum value = - 4.19

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Answer:

500 times

Step-by-step explanation:

Divide the thickness of a cat hair by the thickness of a human hair.

4.0 × 10^-1 / 8.0 × 10^-4 =

= 0.5 × 10^3

= 500

500 times

Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Answer:

0

Step-by-step explanation:

forgotten sorry

Answer: 20

Step-by-step explanation:

because if he earned 12 dollars and it equals 32 dollars he would have 20

Ken had $40 then spent $20 on a game he now has $20 left then he earns $12 mowing lawn and now has $32.

Ken had $40 before he bought the game

Answer:

170°

Step-by-step explanation:

180 - 10 = 170

Answer:

Step-by-step explanation:

You want the center, radius, and equations in standard form and general form for the circle shown in the graph.

The center is the point marked. Its coordinates are ...

  (x, y) = (2, -1)

The radius is the distance from the center to any point on the circle. It is usually convenient to read the radius on a graph by considering points on the same horizontal or vertical line as the center of the circle.

Here, the circle passes through point (6, -1), so the radius is 6 -2 = 4.

The radius is 4 units.

The standard form equation for a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

For center (2, -1) and radius 4, this is ...

  (x -2)² +(y +1)² = 16 . . . . standard form equation

The general form of a polynomial equation is f(x, y) = 0, with the terms listed in lexicographical order by decreasing degree. This is found from the standard form by expanding it, combining terms, and arranging them in the required order:

  (x -2)² +(y +1)² = 16 . . . . . standard form

  x² -4x +4 +y² +2y +1 -16 = 0 . . . . . eliminate parentheses, subtract 16

  x² +y² -4x +2y -11 = 0 . . . . general form equation

Answer:

(-3,3)

Step-by-step explanation:

because it's where the graphs intersect, meaning the point is contained in both solutions

Answer:

  x -5y = -6

Step-by-step explanation:

A plot of the given points shows the hypotenuse is QR, and the vertex through which the altitude line goes is point P. We want a line through P that is perpendicular to QR.

__

The equation for a line perpendicular to the one through (x1, y1) and (x2, y2) can be written in the general form ...

  (x2 -x1)(x -h) +(y2 -y1)(y -k) = 0

where (x, y) = (h, k) is a point on the line.

Using points Q(3, 5) and R(5, -5) for the two points, and (h, k) = P(-1, 1), we have ...

  (5 -3)(x -(-1)) +(-5-5)(y -1) = 0

  2x +2 -10y +10 = 0 . . . . . . . . . eliminate parentheses

The standard-form equation will have mutually-prime coefficients and the constant on the right. Dividing by 2 and subtracting 6 gives ...

  x -5y = -6