16−4[3+2÷(9−7)]=?????

The value of x of the quadrilateral using the concept of similar quadrilaterals is; x = 1.5

Two quadrilaterals are referred to as similar quadrilaterals when the three corresponding angles are the same and as a result the fourth angles automatically become the same due to the fact that the interior angles of a quadrilateral sum up to 360 degrees and two adjacent sides have equal ratios.

Thus, we can say by the concept of similar quadrilaterals that;

AB/LM = BC/MN

Thus;

14/(x + 9) = 10/(x + 6)

14(x + 6) = 10(x + 9)

14x + 84 = 10x + 90

14x - 10x = 90 - 84

4x = 6

x = 1.5

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Answer:

Here is the answer to your question it is in this picture

The longest path that Amy can walk in Matrix Metro is equal to min(m,n)*2-1.

To see why, imagine that Amy starts at any building in the city. Without loss of generality, let's assume she starts at the bottom left corner of the city.

From this point, she has two options: continue walking to the right or turn up. If she continues walking to the right, she will eventually reach the rightmost column of the city and will have to turn up.

Since Amy cannot visit the same building twice, she can visit at most min(m,n) buildings in each row or column. If she visits all min(m,n) buildings in each row or column, she will visit a total of 2*min(m,n) - 1 buildings.

Therefore, the length of the longest path that Amy can walk in Matrix Metro is min(m,n)*2-1, and this is the maximum because Amy cannot visit any more buildings without visiting the same building twice.

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The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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The inequality that describes the domain is 0 ≤ x ≤ 5

The given parameters are

Size of tank = 3 gallons

Rate = 0.6 gallons per hour

The highest number of time is calculated as

Time = Size of tank/Rate

Substitute the known values in the above equation

So, we have the following equation

Time = 3/0.6

Evaluate

Time = 5

The domain is then represented as

0  ≤ x ≤ Time

This gives

0 ≤ x ≤ 5

Hence, the domain of the situation is 0  ≤ x ≤ 5

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The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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Answer:

D

Step-by-step explanation:

Answer:

x > -7 hope this helps

Step-by-step explanation:

The statements to complete the steps required to solve for the area of a regular hexagon (comprising of six equilateral triangles) that has side length of 12 cm are as follows;

An equilateral triangle is a triangle in which all three sides are congruent and the interior angles are also congruent and each interior angle is equal to 60°.

(1) There are six equilateral triangles

(2) The measure of each angle in an equilateral triangle is; 60°

(3) The special right triangle created by cutting an equilateral triangle down the middle is a 30°-60°-90° right triangle

(4) The vocabulary word for the segment a is the apothem

(5) The length of the short side of the 30-60-90 triangle is half the length of the side of the hexagon, which is 12 cm ÷ 2 = 6 cm

(6) The length of the hypotenuse of one of the 30-60-90 triangles, obtained from the equilateral triangle is the length of a side of the hexagon, which is 12 cm

(7) The properties of 30-60-90 triangles indicate that when the length of the short side is x, the hypotenuse is 2·x, and the long side is x·√3

The length of the sort side is; x = 6 cm, therefore, the length of the long leg is; 6·√3 cm

The height of one of the equilateral triangle is the length of the long leg which is 6·√3

(9) The area of a triangle is; A = Half base length × Height

There are six equilateral triangles in the hexagon

The base length of each equilateral triangle = 12

The height of each equilateral triangle, a = The length of the long leg = 6·√3

The area of one equilateral triangle, A = (1/2) × 12 cm × 6·√3 cm = 36·√3 cm²

(10) The number of equilateral triangles in the hexagon = 6

The area of the hexagon = 6 × The area of one equilateral triangle

Therefore;

Area of the hexagon = 6 × 36·√3 cm² = 216·√3 cm²

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Answer:

The tablecloth overhang is the amount of tablecloth that hangs over the edges of the table.

The area of the square table is 1.3m * 1.3m = 1.69m^2.

The area of the round tablecloth is pi * (diameter/2)^2 = pi * (2/2)^2 = pi * 1^2 = pi * 1 = pi m^2.

The overhang is the difference between the area of the round tablecloth and the square table.

Overhang = pi m^2 - 1.69m^2 = pi - 1.69

To find the percentage of the tablecloth that overhangs the table, we can divide the overhang by the area of the tablecloth and multiply by 100.

Overhang % = (pi - 1.69) / pi * 100 = (pi - 1.69) / pi * 100 = (3.14 - 1.69) / 3.14 * 100 = 1.45 / 3.14 * 100 = 46.14%.

So, the percentage of the tablecloth that overhangs the table is 46.14%.

The equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7) is; y = ³/₂x - 16

We want to find the equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7).

Now, the slope that is perpendicular to that line is;

m = -1/(-²/₃) = 3/2

Thus;

Equation of the new line is;

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

y + 7 = 3x/2 - 9

y = ³/₂x - 16

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Answer:

20.50 + 10m

Step-by-step explanation:

Basic expression:
8.50 + 12 + 6.25m + 3.75m

First, let's add the base payments which are 8.50 and 12.
8.50 + 12 = 20.50.
Now we have 20.50 + 6.25m + 3.75m

Next we have to add the monthly payments.
Assuming she's paying these all at the same time, 6.25m + 3.75m = 10m

Our finalized expression is:
20.50 + 10m = Club costs

Answer:

A. Yes

B. Yes

C. No

Here's what it would look like:

Answer:

(

t

+

w

)

4

=

t

4

+

4

t

3

w

1

+

6

t

2

w

2

+

4

t

1

w

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+

w

4

Explanation:

First, you should get to know Pascal's triangle. Here's a small portion of it up to 6 lines. Basically you're just adding the numbers that are beside each other, then writing the sum below them. (For example,  

1

+

2

in the third line equals to  

3

in the fourth line.) If you want a better explanation for that, feel free to do some more research on it.

Expansion of ( 4- 2z)³ using binomial expansion is equals to

64 - 96z + 48z² - 8z³.

" Binomial theorem is a way of expanding a binomial expression with exponent n, where n is any positive integer."

Formula used

Binomial Expansion

(a - b) ⁿ = ⁿC₀ aⁿb⁰+  ⁿC₁ aⁿ⁻¹ (-b)¹ +  ⁿC₂ aⁿ⁻² + ....... + (-1)ⁿ ⁿCₙ a° bⁿ

According to the question,

Given,

(4 -2z)³

a = 4

b = 2z

Substitute the value in the formula of binomial expansion we have,

= ³C₀ (4)³ (-2z)⁰ +³C₁ (4)² (-2z)¹ +³C₂ (4)¹ (-2z)² + ³C₃ (4)⁰ (-2z)³

=  (4)³ - 3 (4)² (2z) + 3 (4) (2z)² -(2z)³

= 64 -96z +48z² -8z³

Hence, expansion of ( 4- 2z)³ using binomial expansion is equals to

64 - 96z + 48z² - 8z³.

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Answer:

Diameter : 22.568 cm

Step-by-step explanation:

Hope this Helps!

Answer:

b=4

Step-by-step explanation:

So, we have the function \(f(x)=1/x\). We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

\(\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8\)

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

\(\frac{.5b-1}{2b-b^2} =\frac{-1}{8}\)

Now, cross multiply.

\(4b-8=b^2-2b\)

\(b^2-6b+8=0\)

Solve for b. Factor using the numbers -4 and -2.

\(=(b-4)(b-2)=0\)

Thus, b=4 or b=2.

However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.

We want to find an interval such that the given equation, f(x) = 1/x, has an average rate of change of -1/8 in that interval.

We will see that the interval is [2, 4]

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

For a function f(x), the average rate of change in the interval [a, b] is given by:

\(r = \frac{f(b) - f(a)}{b - a}\)

Here we have:

\(f(x) = 1/x\)

And the interval is [2, b] such that r in that interval is -1/8, so we need to solve:

\(r = -1/8 = \frac{f(b) - f(2)}{b - 2} = \frac{1/b - 1/2}{b - 2}\)

We can rewrite it to:

\(-1/8 *(b - 2)= 1/b - 1/2\\\\-1/8 *(b - 2)= 2/2b - b/2b = (2 - b)/2b = -(b - 2)/2b\)

Now we can remove the term (b - 2) because it appears on both sides, so we get:

\(-1/8 = -1/2b\\1/8 = 1/2b\\2/8 = 1/b\\1/4 = 1/b\\b = 4\)

Then we found that b must be equal to 4, so the interval is [2, 4]

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There are 27,720 different arrangements of red and yellow roses.

The total number of roses is 8 + 4 = 12. To find the number of different arrangements, we can use the formula for permutations, which is:

n! / (n - r)!

where n is the total number of objects and r is the number of objects we want to arrange.

In this case, we want to arrange all 12 roses, so n = 12. The number of red roses is 8, so r = 8. Therefore, the number of different arrangements of the roses is:

12! / (12 - 8)! = 12! / 4! = 27,720

So there are 27,720 different arrangements of the 8 red roses and 4 yellow roses.

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Answer:

$20

Step-by-step explanation:

he first buys the goat for $60, puts $10 of his own money into it to buy it for $80, but then at last sold it for $90

that's $20 in profits

XD I was so confused

Answer:

x = 5

y = 3

Step-by-step explanation:

x + 4y = 17

2x + 5y = 25

We multiply the first equation by -2

-2x - 8y = -34

2x + 5y = 25

-3y = -9

y = 3

Now we put 3 in for y and solve for x

x + 4(3) = 17

x + 12 = 17

x = 5

Let's Check the answer

5 + 4(3) = 17

5 + 12 = 17

17 = 17

So, x = 17 and y = 3 is the correct answer.

Answer:

Here's the answer hope it helps!!

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.

Starting with the given inequality:

y + 7 ≤ -1

We can begin by subtracting 7 from both sides of the inequality:

y + 7 - 7 ≤ -1 - 7

y ≤ -8

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.

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The following question may be like this:

What is a solution of the inequality shown below? y+7≤-1

Answer: Commutative Property of Multiplication/Addition

Step-by-step explanation:

The commutative property is simple

x + y = y + x

or for multiplication

x * y = y * x

Answer:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Step-by-step explanation:

Interval Notation:

(−∞, ∞)

Set-Builder Notation:

{x|x∈R}

Use the kinematic formula

\({v_2}^2 - {v_1}^2 = 2a\Delta x\)

where \(v_1,v_2\) are initial/final velocities, \(a\) is acceleration, and \(\Delta x\) is displacement. We're given \(a=-5.00\frac{\rm m}{\rm s^2}\) and \(\Delta x=15.0\,\rm m\), and the car comes to a stop so \(v_2=0\). Solve for \(v_1\).

\(-{v_1}^2 = 2\left(-5.00\dfrac{\rm m}{\rm s^2}\right) (15.0\,\mathrm m) \\\\ ~~~~ \implies {v_1}^2 = 150.\dfrac{\rm m^2}{\rm s^2} \\\\ ~~~~ \implies v_1 = \sqrt{150.\dfrac{\rm m^2}{\rm s^2}} \approx \boxed{12.2 \dfrac{\rm m}{\rm s}}\)

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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