What’s 3 and two tenths minus 1 and 4 tenths

The only possible solution is x = 2. Therefore, the three consecutive integers that form the sides of the right triangle are 2, 3, and 4.

Since they are consecutive integers, let's assume that the hypotenuse, which is the longest side of the right triangle, is x+2, as it is three units longer than the shortest side.

In a right triangle, the hypotenuse's square is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. We can thus write:

\((x+2)^2 = x^2 + (x+1)^2\)

Expanding the squares, we get:

\(x^2 + 4x + 4 = x^2 + x^2 + 2x + 1\)

Simplifying and rearranging terms, we get:

\(2x^2 - 2x - 3 = 0\)

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± \(\sqrt{b^2 - 4ac}\)) / 2a

where a = 2, b = -2, and c = -3.

Plugging in these values, we get:

x = (-(-2) ± \(\sqrt{((-2)^2 - 4(2)(-3)))\) / 2(2)

x = (2 ± \(\sqrt{(4 + 24))\) / 4

x = (2 ± \(\sqrt28}\) / 4

x = (2 ± \(2\sqrt{7}\)) / 4

x = 1/2 ± \(\sqrt{7}\)/2

The only option is x = 2, since x must be an integer. As a result, the numbers 2, 3, and 4 are the three consecutive integers that make up the sides of the right triangle.

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Answer:

  3

Step-by-step explanation:

Those wearing a shirt of another color are ...

  1 - 5/8 -1/4 = 8/8 -5/8 -2/8 = 1/8

of the total number of students in the classroom

  (1/8)×(24 students) = 3 students . . . . wearing another color

_____

Alternate solution

With the given information, you know ...

  (5/8)(24) = 15 . . . students wear blue

  (1/4)(24) = 6 . . . . students wear white

  24 -15 -6 = 3 . . . students wear another color

Step-by-step explanation:

\(x = 125.9 - 2 \\ x = 1259 - 2 \div 100\)

100 as u are removing the decimal

mate I framed it as easy I can

and I know now u can solve it

enjoy your day

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Answer:

x=12.95

Step-by-step explanation:

first you should divide both sides by 2 it should look like this:2x/2=25.9/2

then you should divide and you should get: x=25.9/2

then you divide and you should get 12.95

Answer:

Step-by-step explanation:

first you have to find the area of the small triangle ⇒

1/2×10×24=120

find the area of the big triangle ⇒

1/2×18×24=216

∴the area of this shape=120+216=336 square units

Answer:

1

Step-by-step explanation:

it has to be the same slope and only slope that is right is 1.

Answer:

(4,5)

Step-by-step explanation:

Use the midpoint formula

(( x1 + x2)/2, (y1 + y2)/2 )

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

When you add a negative number, you're basically subtracting it.

7 - 3 = 4

Hope this helps! Good luck :)

SOLUTIONS

Yes, all rectangles are parallelograms because a rectangle has two sets of parallel sides and two pairs of opposite sides that are equal. Therefore, it abides by all the properties of a parallelogram

No, a parallelogram is not always a rectangle. In a rectangle, all angles must be equal to 90°. But for a parallelogram, no angles need to be equal to 90°

The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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take 35:45 and just multiply both sides by the same number to find an equivalent ratio.

ex:/// 35 x 2 (70)    45 x 2 (90)

whichever number comes first in the original ratio, the product is going to be the first in the next ratio.

ex:/// 70:90

\(x7 - 2 \: or \: x \leqslant - 3\)

Step-by-step explanation:

On a polar plane, the shape will be a line that goes through the pi/2- pi quadrant , and 3pi/2- 2pi quadrant

On a Cartesian or rectangular plane, the shape will be a line as well passing through 2nd and 4th quadrant

Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

If y = -0.025x^2 + 4x, then

y' = -0.05x + 4

Set y' = 2:

2 = -0.05x + 4

-2 = -0.05x

40 = x

Go back to y to find the point:

y = -0.025(40)^2 + 4(40) = 120

So the point (40, 120) on y = -0.025x^2 + 4x will have tangent line with a slope of 2.

Answer:

$298.125 = $298.13

Step-by-step explanation:

Original Cost: $375

Cost with discount: 375*0.75 = $281.25

Cost with 6% tax: 281.25*1.06 = $298.125 = $298.13

Based on equations, Angus worked 6 hours on Saturday and 10 hours at his after-school job last week earning a total of $127.80.

The hourly rate at Angus' Saturday job = $8.80

The hourly rate at Angus' after-school job = $7.50

The total earnings last week = $127.80

Let the hours Angus worked at Saturday job = x

Let the hours Angus worked after-school = 4 + x

The total hours worked = x + x + 4

2x + 4

The total earnings last week 127.80 = 8.8x + 7.5x + 4 (7.5)

127.80 = 8.8x + 7.5x + 30

127.8 - 30 = 16.3x

x = 6 hours

x + 4 = 10 hours

2x + 4 = 16 (12 + 4)

Check:

Earnings at Saturday job = $52.80 ($8.80 x 6)

Earnings at after-school job = $75.00 ($7.50 x 10)

Total earnings = $127.80

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The Area of Square is 81 cm².

let the side of the square which is length for both rectangles be a.

let the width of rectangle be x and y.

So, x+ y= a

sum of perimeters= 54

2 (a +x ) + 2 (a+ y) = 54

2a+ 2x + 2a+ 2y = 54

2a + 2a + 2(x+ y) = 54

4a + 2 (a) = 54

4a + 2a = 54

6a = 54

a= 54/6

a= 9

So, area of square

= 9 x 9

= 81 cm²

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Answer:

1 gallon

Step-by-step explanation:

unit rate is 23 mi/gal.

Multiply this by 1 gallon to get to 23 miles

23 mi/ gal * 1 gallon = 23 miles

1 gallon

Answer:

it takes 1 gallon to travel 23 mil

AAnswer:

Las Letras A B C , en matematicas el valor puede variar ; ya que ya depende del valor que se le otorge o ya si es una operacion , pues el valor que se obtiene , es decir las letras en matematicas no tiene o poseen un valor fijo

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the the track is circular

Circumference of a circle = πd

where

d is the diameter

π = 3.14

From the question

diameter = 150 feet

Circumference = 150π

= 150(3.14)

We have the final answer as

Hope this helps you

Answer:

471.23 ft

Step-by-step explanation:

The circumference of this space is C = πd = (150 ft)π, or approximately

471.23 ft

There are two ways to confirm the identity.

Method 1

\(\tan(x)\cot(x) = 1\\\\\tan(x)\frac{1}{\tan(x)} = 1\\\\\frac{\tan(x)}{\tan(x)} = 1\\\\1 = 1 \ \ \checkmark\\\\\)

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

Method 2

\(\tan(x)\cot(x) = 1\\\\\left(\frac{\sin(x)}{\cos(x)}\right)\left(\frac{\cos(x)}{\sin(x)}\right) = 1\\\\\frac{\sin(x)\cos(x)}{\cos(x)\sin(x)} = 1\\\\\frac{\sin(x)}{\sin(x)} = 1\\\\1 = 1 \ \ \checkmark\\\\\)

The rectangular coordinates of the polar coordinates (3√5, -π/8) are approximately (3.35, -0.77).

To convert polar coordinates (r, θ) to rectangular coordinates (x, y), we use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

In this case, the given polar coordinates are (3√5, -π/8).

Applying the formulas, we have:

x = (3√5) * cos(-π/8)

y = (3√5) * sin(-π/8)

Evaluating the trigonometric functions using a calculator or trigonometric tables, we find:

x ≈ 3.35

y ≈ -0.77

Rounding these values to the nearest hundredth, the rectangular coordinates of the polar coordinates (3√5, -π/8) are approximately (3.35, -0.77).

Please note that the angle -π/8 represents a counterclockwise rotation of π/8 radians from the positive x-axis in the Cartesian coordinate system.

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The statement that are true are:

a) (Vx) (x+xzx). (R)

c) (3x) (3*=x²). (R)

d) (3) (3x). (R)

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R)

a) (Vx) (x+xzx). (R) - This statement is true. It is a vacuously true statement, meaning it is true because the predicate (x+xzx) is never satisfied for any element x in the universe (R).

b) (3x) (2x+3=6x+7). (N) - This statement is false. There is no value of x in the universe (N) that satisfies the equation 2x+3=6x+7.

c) (3x) (3*=x²). (R) - This statement is true. For every value of x in the universe (R), 3 times x is equal to x squared.

d) (3) (3x). (R) - This statement is true. For any value of x in the universe (R), multiplying x by 3 will always result in a real number, which means 3x is also in the universe (R).

e) (3x) (3(2-x)=5+8(1-x)). (R) - This statement is false. There is no value of x in the universe (R) that satisfies the equation 3(2-x)=5+8(1-x).

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R) - This statement is true. For any two elements x and y in the universe (R) where x<y, 3x is always less than 3y, so the implication (3x<3y) is true. Since this is true for all x and y, the universal quantifiers (Vx)(Vy) make the statement true.

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Answer:

I dont understand what you mean by this I questions, but that is the Order of Operations. You use "PEMDAS" to memorize all 4 Order of Operations..

Step-by-step explanation:

Answer:

sin(r) = 15/17

cos(r) = 8/17

tan(r) = 15/8

sin(s) = 8/17

cos(s) = 15/17

tan(s) = 8/17

Step-by-step explanation:

⭐What are trigonometric functions?

To find out what sin, cos, or tan of each angle is, we need to identify what type of side lengths the given side lengths are (opposite, adjacent, or hypotenuse).

I have labeled it in the picture attached to this response.

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Answer: approximately 3.14

Step-by-step explanation: In decimal form, the value of pi is approximately 3.14. But pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666...). (To only 18 decimal places, pi is 3.141592653589793238.)