The adjacent sides of a right angle triangle are 5cm and 12cm respectively . calculate the smallest angle of the triangle. How to solve it.​

The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

y=12t

Step-by-step explanation:

We must the tangent line at x = 3 of the function:

The tangent line is given by:

Where:

• m is the slope of the tangent line of f(x) at x = h,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

2) By evaluating the result of f'(x) at x = h = 3, we get:

3) The value of k is:

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

Plotting the function f(x) and the tangent line we verify that our result is correct:

The equation of the tangent line to f(x) and x = 3 is:

Answer:

Step-by-step explanation:

To find the probability of drawing a purple and yellow marble without replacement, we need to determine the number of favorable outcomes (purple and yellow marbles) and the total number of possible outcomes.

Step 1: Determine the number of purple marbles:

The given information states that there are 6 purple marbles.

Step 2: Determine the number of yellow marbles:

The given information states that there are 3 yellow marbles.

Step 3: Determine the total number of marbles:

The given information states that there are 25 marbles in total.

Step 4: Calculate the probability of drawing a purple and yellow marble:

When drawing without replacement, the probability of two events occurring is the product of their individual probabilities.

The probability of drawing a purple marble is: 6 purple marbles / 25 total marbles = 6/25.

After drawing a purple marble, the total number of marbles remaining is 24 (since one purple marble is already drawn).

The probability of drawing a yellow marble from the remaining marbles is: 3 yellow marbles / 24 remaining marbles = 3/24.

To find the probability of both events occurring (drawing a purple and yellow marble), we multiply their individual probabilities:

Probability of drawing a purple and yellow marble = (6/25) * (3/24) = 18/600 = 3/100.

Therefore, the probability of drawing a purple and yellow marble without replacement is 3/100.

Answer:

243

Step-by-step explanation:

Going in times 3 so 81 x 3 = 243

Answer:

y = 3x + 5 option A

Step-by-step explanation:

For 2 lines that are parallel with slopes m1 and m2, the slopes are equal. Hence

m1 = m2

Given the line y = 3x - 5 Comparing with the general equation of a line

y = mx + c where m is the slope of the line

m = 3

hence m1 = m2 = m = 3

For the line that passes through the given point (2,11) Using

y - y1 = m (x - x1)

y - 11 = 3(x - 2)

y - 11 = 3x - 6

Add 11 to both sides

y = 3x - 6 + 11

y = 3x + 5

Answer:

x=5

Step-by-step explanation:

im so bad at explaining things but i hope this helped

Answer:

\(\sqrt{9}\) is rational and \(\sqrt{10}\) is irrational

Step-by-step explanation:

The square root of 9 is 3 and the square root of 10 is a decimal that never stops.

The square root of 9 (√9) is rational because it results in an integer, which can be expressed as a fraction (3/1). However, the square root of 10 (√10), yields an approximate decimal that cannot be precisely expressed as a fraction, hence is an irrational number. Thus the statement √9 is rational and √10 is irrational is true.

In Mathematics, a rational number is a number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. Irrational numbers are numbers that cannot be expressed as fractions.

The square root of 9 is √9, which equals 3. This can be expressed as a fraction (3/1), so √9 is rational.

However, the square root of 10 is √10, which equals to approximately 3.16227766017. This cannot be accurately expressed as a fraction, so √10 is irrational.

Therefore, the true statement among the options provided is: √9 is rational and √10 is irrational.

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:A=1/2

Step-by-step explanation:

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

Answer:

The larger of the two is 44.67

Step-by-step explanation:

let the first number=x

let the second number=y

We can derive a system of equations using the mathematical statements

Their sum is 33:

x+y=33( call this equation 1)

Sum of first number and four times the second is -2:

x+4y=-2(call this equation 2)

Since the integer coefficients of x in both equations are the same we can quickly subtract one from the other to eliminate it

For this explanation, I choose to subtract equation 1 from 2

(x+4y=-2)-(x+y=33)=3y=-35

y=-35/3

Now plug in the value of y into any equation for that of x. Say we plug into equation 1

x+(-35/3)=33

x-35/3=33( multiply through by 3)

3x-35=99

3x=99+35

3x=134

x=134/3

Therefore,x=134/3 or 44.67 and y=-35/3 or -11.67

The area of the triangle is 47.91 units²

When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.

Heron’s formula is:

Area =√s(s−a)(s−b)(s−c)

where,

a, b, c are the side length of the triangle

s is the semi-perimeter. s = (a+b+c)/2

In this case:

Using the knowledge of the radius of a circle. We can say:

a = BC = 3 + 9 = 12 units

b = AC = 5 + 3 = 8 units

c = AB = 5 + 9 = 14 units

s = (a+b+c)/2

s = (12+8+14)/2

s = 34/2

s = 17 units

Area = √s(s−a)(s−b)(s−c)

Area = √17(17−12)(17−8)(17−14)

Area = √17(5)(9)(3)

Area = √2295

Area = 47.91 units²

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Answer:

10

Step-by-step explanation:

Since we are dealing with area, we need to multiply 16 1/4 by 11 3/4.

If we do that, we get 190 15/16

So, if we divide 190 15/16 by 20:

\(190 \frac{15}{16} / 20 = 9.5\)

You cannot have half a bag however. You will need to round the number to 10.

The fraction that shows the number of ounces of filling camilo uses in each empanadas is,

↪32 ounces

☆...hope this helps...☆

_♡_mashi_♡_

\( \bold{ \underline{SOLUTION }}\)

Required Answer

Camilo uses ounce = 32

he put emandas = 0

each tray = 3

find how many ounce of filling camilo uses in each empandas

0 × 3 = 0

{and any number is cant divided by zero.}

Thus ,,

32 empanadas fill on each ounce

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Answer: D. 94

Step-by-step explanation:

Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.

Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.

The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.

Now we have \(x1\)=2    \(x2\)=-11

then quadratic function will be

(x+2) (x+11)

\(x^2+2x+11x+22\)

\(x^2+13x +22\)

this is our required quadratic equation.

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Complete question is: Write a quadratic function f whose zeros are 2 and -13.

Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.

Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.

The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.

Now we have x¹ = 2    x² = -11

then quadratic function will be

(x+2) (x+11)

x² + 2x + 11x + 22

x² + 13x + 22

This is our required quadratic equation.

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The complete question is-

Write a quadratic function f whose zeros are 2 and -13.

Answer:

48$ is the answer to your question my dear watson..

Step-by-step explanation:

Good Job! I cracked the case!!

Answer:

45,000 is standard form.

4.5 is the coefficient.

4 of 10⁴ is the exponent.

7.6 × 10⁻⁴ is scientific notation.

10 of 10⁻⁴ is the base.

Step-by-step explanation:

Scientific notation is a way of writing very large or very small numbers in a compact and convenient form. It consists of two parts:

The base of scientific notation is always 10, which means that the number is written in terms of powers of 10.

For example, the number 4,000,000 can be written in scientific notation as 4 x 10⁶. In this case, the coefficient is 4, and the exponent is 6.

The standard form of a number is simply the usual way of writing it, without using scientific notation. For example, the standard form of 4 x 10⁶ is just 4,000,000.

Therefore, for the given problem:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Using polar/cylindrical coordinates, we take

x = r cos(t )

y = r sin(t )

z = z

so that

dV = dx dy dz = r dr dt dz

The solid is given by the set

D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}

or in cylindrical coordinates,

D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}

Then the volume of the solid is

\(\displaystyle \iiint_D \mathrm dV = \iiint_Dr\,\mathrm dr\,\mathrm dt\,\mathrm dz \\\\ = \int_0^{2\pi} \int_0^1 \int_0^{4-2r\cos(t)-r\sin(t)} r\,\mathrm dz\,\mathrm dr\,\mathrm d t \\\\ = \int_0^{2\pi}\int_0^1 (4r-2r^2\cos(t)-r^2\sin(t))\,\mathrm dr\,\mathrm dt \\\\ = \int_0^{2\pi} \left(2 - \frac23 \cos(t) - \frac13 \sin(t)\right) \,\mathrm dt \\\\ = \boxed{4\pi}\)

The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.

The volume of the solid in polar coordinates can be calculated by the double integral in polar coordinates.

\(V = \iint_R f(x,y) \,dA.\\\)

Similarly, by polar coordinates,

x = r cost

y = r sint

z = z

we get, dV = dx dy dz = r dr dt dz

The solid is given

D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}

or in polar coordinates,

D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}

The volume of the solid is

\(\rm \int \int\int\ dV = \int \int\int\ rdr dt dz\\ \rm = \int\limits^{2\pi}_0\int\limits^1_0 \int\limits^{4-2rcost-rsint}_0 rdr dt dz\\\rm =\int\limits^{2\pi}_0\int\limits^1_0 {4r-2r^{2} cost-r^{2} sint} dr dt\\\rm =\int\limits^{2\pi}_0( 2-2/3cost-1/3sint) dt\\\rm =4\pi\)

Hence, The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.

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Answer:

True

Step-by-step explanation:

Hope this helps you

Answer:

d

Step-by-step explanation:

Answer:

B. h(x)=(x+1) (10x-1)

Step-by-step explanation:

B. h(x) = (x+1) (10x-1)

h(x)=10x^2+10x-x-1

h(x)=10x^2+9x-1

Anna's total profit was $6000 + $16000 - $4000 = $14000.

How did Anna earn profit

Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.

Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.

Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.

Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.

Answer: Okay! Let's simplify step-by-step.

f(7)−f(−4)

=7f+4f

Combine Like Terms:

=7f+4f

=(7f+4f)

=11f

Step-by-step explanation:i hope this helped in any way :D best of luck!

Answer:

240cm

Step-by-step explanation:

6cm*14cm= 84cm

6*6=36

84+36=120*2=240

Answer:

7cm x 8cm

Step-by-step explanation:

The 14cm x 12cm box (top 'box 1') intersects with the 14cm x 12cm box (bottom 'box 2').

Half the values of each side are subtracted from one another, so

horizontal length: 14/2 = 7cm

vertical length: 12/2 = 6cm

Box 2 horizontal length (total) = 14cm devided by half the length of box 1 (7cm)

14 - 7 = 7cm

Box 2 vertical length (total) = 12cm devided by half the length of box 1 (6cm)

12 - 6 = 6cm

The total area is calculated by multiplying the horizontal and vertical lengths

7x6 = 42

the answer is 42

The average weight of a male Florida panther rounded to the nearest whole number is 53 kg

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Average weight = 52.6 kg

52.6

The number after decimal point is 6 which is more than 5.

So add  1 to the 52, we get 53

Thus, the average weight of a male Florida panther rounded to the nearest whole number is 53 kg

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So, 7,000 is the number in which the value of the digit 7 is 10 times that of the digit 7 in the number 4,275.

What is significant figures ?

The relevant digits in a number that show the precision or accuracy of a measurement or calculation are known as significant figures, sometimes known as significant digits. The following guidelines can be used to determine a number's number of significant figures: Each significant digit that is not zero.

The number 123.45, for instance, includes five significant digits. Zeros in between digits that are not zero are important. Zeros at the start of a number have no real meaning. The number 0.0023, for instance, has two significant figures.

To solve this problem, we need to identify the value of the digit 7 in the number 4,275 and then discover the number in which the digit 7 represents 10 times this value.

The digit 7 is in the hundreds place in the number 4,275, hence its value is 7 x 100 = 700.

As a digit in the ones place only has its face value, we must discover a number that contains the digit 7 in the thousands, hundreds, or tens places in order to determine the number in which the digit 7 represents 10 times this value.

Consider the number 7,000. The digit 7 is one position to the left of the digit 7 in 4,275, in the thousands place.

When we multiply 7 in 4,275 by 10, we get 10 x 700, which is 7,000. Hence, the value of the digit 7 in the number 7,000 is 10 times more than that of the digit 7 in the number 4,275.

So, 7,000 is the number in which the value of the digit 7 is 10 times that of the digit 7 in the number 4,275.

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In which number does the digit 7 represent 10 times the value of the digit 7 in the number 4,275?