1+1223x8+9+6+3+126+3+78+9+66

Answer:

Explanation:

Here, we want to get the value of x

What we have is a right triangle with the hypotenuse being 10 (the hypotenuse is the longest side of a right triangle. It faces the right angle (the small box))

From the Pythagoras' theorem, the square of the hypotenuse equals the sum of the squares of the two other sides

Thus, we have it that:

Answer:

31.5/21

Step-by-step explanation:

31.5 over 21

Answer:

31.5/21

Step-by-step explanation:

31.5/21 = 1.5 and 18/12 = 1.5

Answer:

0

Step-by-step explanation:

If 4x + b = 4x, then b = ?

Let's solve!

4x + b = 4x

Minus 4x on both sides

b = 4x - 4x

b = 0

We can check, does 4x + 0 = 4x?

Yes, it works.

Hope this helps :)

Have a nice day!

A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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Answer:

x = 9/2 or 4.5

Step-by-step explanation:

5-4x=23 |-5

5-4x-5=23-5

-4x=18 |*(-1)

4x=18 | /2

2x=9 |/2

x=9/2 or 4.5

Answer:

x = 4.5

Step-by-step explanation:

Subtract 5 from BOTH sides to start with:

5-5 = 0 (5 cancels out on left side) 23-5 = 18

New Equation: -4x = 18

Divide BOTH sides by -4

4 cancels out (x is left) 18/4 = 4.5

New: x = 4.5

Answer as a fraction:  73/4

Answer in decimal form: 18.25

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

Explanation:

If alpha and beta are the roots of the quadratic ax^2+bx+c = 0, then we can say

For more information refer to Vieta's Formulas. Focus on the quadratic case.

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

Comparing 2x^2+5x-12 = 0 to ax^2+bx+c = 0, we have

Which leads us to

Or in short

Let's square both sides of the first equation to get

alpha+beta = -2.5

(alpha+beta)^2 = (-2.5)^2

alpha^2 + 2*alpha*beta + beta^2 = 6.25

alpha^2 + 2*(-6) + beta^2 = 6.25

alpha^2 - 12 + beta^2 = 6.25

alpha^2 + beta^2 = 6.25 + 12

alpha^2 + beta^2 = 18.25 = 73/4

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

Verification:

Use the quadratic formula to solve 2x^2+5x-12 = 0 to get the roots of x = -4 and x = 3/2 = 1.5

Those are the values of alpha and beta in either order.

alpha^2 + beta^2 = (-4)^2 + (1.5)^2 = 18.25 = 73/4

The answer is confirmed.

Option (D) She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1 is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Patti is using mental math to evaluate the expression (70 + 12.8 + 30) + 6.1.

The number expression is:

= (70 + 12.8 + 30) + 6.1

As we know from the commutative property

a +  b = b + a

Applying commutative property in the number expression:

= (70 + 30+ 12.8) + 6.1

She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1.

Thus, option (D) She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1 is correct.

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Answer:

Hope you can understand my handwriting though

The difference between the depths in February and July is 31 feet.

The method of measuring depth depends on what we are trying to measure the depth of. Here are some general methods for measuring different types of depth:

Depth of water: The depth of water can be measured using a sounding device such as a sonar or a simple depth gauge. A sonar uses sound waves to determine the distance from the water's surface to the bottom. A depth gauge is a simple device that measures the distance from the surface of the water to the bottom using a weight and a line.

Depth of a hole: The depth of a hole can be measured using a tape measure or a ruler. Simply insert the measuring device into the hole and measure the distance from the top of the hole to the bottom.

Depth of a trench: The depth of a trench can be measured using a measuring tape or a surveyor's level. Place the measuring device at the edge of the trench and measure the distance from the top of the trench to the bottom.

Depth of a pool: The depth of a pool can be measured using a pool depth marker or by using a measuring tape. A depth marker is usually located on the side of the pool and indicates the depth at various points. Alternatively, you can use a measuring tape to measure the distance from the surface of the water to the bottom of the pool.

Depth of a well: The depth of a well can be measured using a well sounder or a tape measure. A well sounder is a device that sends a signal down the well and measures the time it takes for the signal to bounce back. The time it takes is then used to calculate the depth of the well. Alternatively, a tape measure can be used to measure the distance from the surface of the water to the bottom.

Given, In February, it measured 6 ft deep, or |−6| and in July, it was 25 ft deep, or |−25|.

The difference between the depths in February and July is:

|−6| − |−25| = 6 − (−25) = 6 + 25 = 31

Therefore, the correct choice is B) 31 feet.

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Option B) The statement does not make sense because the sum of the probabilities of Jonas winning and not winning the race must equal = 1

Since the above question says that the probability of Jonas winning the race is = 0.6

And the question says that the probability of Jonas losing the race is = 0.5

If we sum up the probabilities of winning and losing,

Probability = 0.4 + 0.5

= 0.9

Hence, the above situation is not possible because the probability must be = 1.

According to the phenomenon of Probability,

Let us consider two probabilities that are

The winning probability is given = x

The Losing probability is given =  y

So, x + y = 1 ( must be 1 )

Therefore, Option B) The statement does not make sense because the sum of the probabilities of Jonas winning and not winning the race must equal = 1

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Decide whether the following statement makes sense (or clearly true) or does not make sense (or is clearly false). Explain your reasoning. The probability that Jonas will win the race is 0.6 and the probability that he will not win is 0.5. Choose the correct answer below.

A. The statement makes sense because it is true that the probability of Jonas not winning the race is

B. The statement does not make sense because the sum of the probabilities of Jonas winning and not winning the race must equal to 1.

C. The statement makes sense because the probability of Jonas winning the race will always be between 0 and 1.

D. The statement does not make sense because the probability of Jonas winning the race cannot be greater than the probability of him not winning the race.

The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.

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The unknown side lengths of the given right triangle ∆LJK where LJ 30° and JK 5 are LJ = 6, and JK = 4.

Triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry. A triangle has three sides and three angles, usually measured in degrees. The angles always add up to 180°. Triangles can be classified according to the lengths of their sides or the sizes of their angles. Types of triangles include right, acute, obtuse, scalene, isosceles, and equilateral. Triangles are also used to form more complex shapes in geometry, such as polygons and circles.

To find the unknown side lengths of a right triangle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that the square of the hypotenuse (the longest side of a triangle) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is JK and the other two sides are LJ and JK.

We can use the Pythagorean Theorem to find the unknown side length of JK. We know that the angle LJ is 30°, so we can use the sine rule to calculate the length of side LJ. The sine rule states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all three sides. Therefore, we can calculate the length of LJ by dividing the sine of 30° (0.5) by the length of the opposite side (JK).

We can now use the Pythagorean Theorem to calculate the length of side JK. We know that the length of LJ is 6, and the length of JK is 5. We can plug these values into the equation a2 + b2 = c2, where a is the length of LJ (6), b is the length of JK (5), and c is the hypotenuse (JK). This yields the equation 36 + b2 = c2, which simplifies to b2 = c2 - 36. Since we know that c2 = 52, we can solve for b2 by subtracting 36 from 52, which gives us 16. The square root of 16 is 4, so the length of JK is 4.

Therefore, the unknown side lengths of the given right triangle ∆LJK where LJ 30° and JK 5 are LJ = 6, and JK = 4.

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Answer:

21

Step-by-step explanation:

I believe this because when you add it all together you get 20.77

The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.

Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.

As p is a prime number, and 2 is the smallest prime number, so, p\(\geq\)2

So, the positive divisors of the integer n are: 1,p,p².

As σ(n) represents the sum of all positive divisors of the integer n.

σ(n)=1+p+p²

In order to prove that σ(n) < 2n,for all n of the form n = p².

1+p+p²<2p²

p²-p-1>0

It is know that, p\(\geq\)2.

So, p²-p-1\(\geq\)1

Thus, σ(n) < 2n holds true for all n of the form n = p².

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Answer:

Where's the graph?

Step-by-step explanation:

Answer:

  5/6 mile

Step-by-step explanation:

The formula for the area of a rectangle can be used with the given values to write an equation for the length of the farmland.

__

Here is the equation for the area of a rectangle.

  A = LW . . . . . area is the product of length and width

When we fill in the area and width, we have ...

  5/9 mi² = L(2/3 mi) . . . . . equation for the length of the farmland

Solving this equation gives ...

  L = (5/9)/(2/3) mi . . . . . . . . divide by the coefficient of L

  L = (5/9)/(6/9) mi = 5/6 mi . . . . . perform the division

The length of Sandra's farmland is 5/6 mile.

Answer:

D: KD, CJ, JF

Step-by-step explanation:

I just took the quick check and it was right.

The volume of the solid formed by the figure shown above is calculated as: 3,934 cm³.

The volume of the figure can easily be found by identifying the height or length of the prism, then find the product of the base area and the height of the prism.

This is:

Volume = base area * length/height of prism = 1/2 * base * height * length of prism.

Given the following:

base = √(31.4² - 14²) ≈ 28.1 cm [Pythagorean theorem]

height = 14 cm

Length of prism = 20 cm

Substitute:

Volume = 1/2 * 28.1 * 14 * 20

= 3,934 cm³

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Answer:

The value of n is 7.

Step-by-step explanation:

For each teen, there are only two possible outcomes. Either they buy soda at least once each week, or they do not. Since they were selected randomly, the teens are independent of each other, which means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

In the binomial distribution, we have that n is the size of the sample. In this question, seven teens are randomly selected, which means that the value of n is 7.

Answer:

3a⁴b³

Step-by-step explanation:

subtract exponents and divide numbers

Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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4 units, 6.93 units, 9.801 units, and 6.93 units are the missing lengths.

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Triangles are the focus of trigonometry, or more specifically, the connection between a right-angled triangle's angles and sides. A triangle has three sides: Hypotenuse, Adjacent, and Opposite. Trigonometric Ratio refers to the ratio between these sides based on the angle between them.

Here,

cos 60°=b/8

0.5=b/8

b=4 units

sin 60°=p/8

0.866*8=p

p=6.93 units

sin 45°=6.93/h

h=6.93/0.707

h=9.801 units

cos 45°=b/9.801

0.707*9.801=b

b=6.93 units

The missing lengths are 4 units, 6.93 units, 9.801 units and 6.93 units.

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Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

What is differentiation?

In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.

Main body:

by using product rule;

Let = u = x² + 4x + 6

⇒ du/dx = 2x + 4 .

Now y = u⁵

⇒ dy/dx = 5u⁴ .

dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)

= 5 * (x² + 4x + 6)⁴ * (2x + 4)

= 5(2x + 4) * (x² + 4x + 6)⁴

hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

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The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Step-by-step explanation:

Answer:

C=12π

Step-by-step explanation:

C=2πr

Radius is half of Diameter.

C= 2π(6)

C=12π

Answer:

Step-by-step explanation:

8 učiteľov 39 študentov

1 výbor = 2 učitelia + 4 študenti

8 učiteľov :2=4

39 študentov :4= 9,75

Takže máme 4 výbory ...viacej to nemôže byť aj keď nám zostávajú študenti pretože je daný počet učiteľov...

Answer: 2303028

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

\(\sqrt{15}\)

Step-by-step explanation:

a^2+b^2=c^2

7^2+b^2=8^2

49+b^2=64

b^2=15

b=\(\sqrt{15}\)

Answer:

(22,0)

Step-by-step explanation:

y=mx+b

y=-2/3x+44/3

0=-2x/3+44/3

x=22

(22,0)