In ΔGHI, g = 240 cm, m m∠H=157° and m m∠I=17°. Find the length of h, to the nearest 10th of a centimeter.

The Standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.

To write an expression in standard form, we need to arrange the terms in descending order of degree and combine like terms.

The given expression is:

48 + 24x3 - x + 10x4 - 5x2

First, we arrange the terms in descending order of degree:

10x4 + 24x3 - 5x2 - x + 48

Next, we combine the like terms:

10x4 + 24x3 - 5x2 - x + 48 = 10x^4 + 24x^3 - 5x^2 - x + 48

Therefore, the standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.

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The critical point in the solution of the equation -5x + 7y > 2 and 2x - 5y < -7 using graph is

(3.5, 2.8)

The solution of the inequality equation s given as

A) -5x + 7y > 2

B) 2x - 5y < -7

would be solved by graphical method

Using the graph the point of the intersection of the two lines is the critical points of the solution. The critical point from the graph is (3.5, 2.8)

The solution also entails the areas or points covered in the areas where the two shades superimpose.

The graph showing the solution is attached

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The derivative of [tex]f(x) = \sinh{(7e^x + 2)}[/tex] is given as follows:

B. [tex]7e^x\cosh{(7e^x + 2)}[/tex]

The function in this problem is given as follows:

[tex]f(x) = \sinh{(7e^x + 2)}[/tex]

This function is a composite function, hence we use the chain rule for derivatives, which state that:

If f(x) = f(g(x)) then f'(x) = g'(x)f'(g(x)).

The inner and outer functions are given as follows:

The derivative of the hyperbolic sine is given as follows:

cosh(x).

(derivative of the outer function).

The derivative of the exponential is given as follows:

[tex](7e^x + 2)^{\prime} = 7e^x[/tex]

(derivative of the inner function).

Hence the derivative of the function is given as follows:

[tex]7e^x\cosh{(7e^x + 2)}[/tex]

(application of the chain rule).

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Answer: A = 470 in²

Step-by-step explanation:

          If the given prism is a rectangular prism, we can use the given formula to solve for the surface area of a rectangular prism.

A = 2((8 in)(15 in) + (5 in)(15 in) + (5 in)(8 in))

A = 2(120 in² + 75 in² + 40 in²)

A = 2(235 in²)

A = 470 in²

Answer:

This quadratic function has no roots.

There are no roots of the quadratic function shown in the graph

We we consider the quadratic equation given be of the form ax^2 + bx + c = 0, then

The quantity b^2 - 4ac is known its discriminant.

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

Therefore, it has to be two roots of a quadratic equation always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solutions if roots are distinct, and have 1 solution when both roots are the same.

Hence, we can conclude that there are no roots. so option D is correct.

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Answer:

Step-by-step explanation:

[tex]\frac{n}{n-1}+\frac{2}{n+1} = 2\\\frac{n^2+n + 2n-2}{n^2-1} = 2\\ n^2+3n-2 = 2n^2-2\\n^2=3n\\n^2-3n= 0\\n(n-3) = 0\\n = 0 \\or\\ n = 3[/tex]

A) The present value of the lease payments can be computed as $255,294.44, using the lease period, borrowing rate, and the monthly lease payments in the online finance calculator as parameters.

B) The journal entry for the lease on September 1, 2024 is as follows:

September 1, 2024:

Debit Lease Expense $8,000

Credit Lease Payable $8,000

(To record the lease liability, payable on September 30, 2024.)

The present value of the lease payments can be computed using an online finance calculator as follows:

N (# of periods) = 36 months (3 years x 12)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $8,000

FV (Future Value) = $0

Results:

Present Value (PV) = $255,294.44

Sum of all periodic payments = $288,000.00

Total Interest = $32,705.56

September 1, 2024:

Lease Expense $8,000 Lease Payable $8,000

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6E6 is a number written in scientific notation, which means that it represents 6 times 10 raised to the power of 6. To write this number in standard form, we need to evaluate the exponent and write the number in expanded form.

6E6 = 6 x 10^6

Evaluating the exponent 6 means multiplying 6 by 10 six times:

6 x 10^6 = 6 x 10 x 10 x 10 x 10 x 10 x 10

Simplifying the expression, we get:

6 x 10^6 = 6,000,000

Therefore, 6E6 in standard form is 6,000,000.

Answer: The correct answer is 42

Step-by-step explanation:

Answer:

8/21

Step-by-step explanation:

4 2/3=8/3, times 1/7 (or divide by 7) equals 8/21.

Answer:

150°

Step-by-step explanation:

Measure of and interior angle of 12-gon:

  [tex]\sf \boxed{\text{\bf Sum of all angles of n-polygon = (n -2) * 180}}[/tex]

n is the number of sides.

  Sum of all angles of 12-gon     = (12 - 2) * 180

                                                     = 10 *180

                                                     = 1800°

In a regular 12-gon, all the interior angles will be equal.

    [tex]\text{\bf Measure of each interior angle = $\bf \dfrac{Sum \ of \ all \ the \ angles}{number \ of \ sides}$}[/tex]

                                                            [tex]\sf = \dfrac{1800}{12}\\\\=150^\circ[/tex]

Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

Answer:

B) strong

Step-by-step explanation:

The correlation coefficient is close to 1, meaning it is both a strong correlation and a positive correlation.

Answer:

All you have to do is to find the area of a circle to know the area it will contain.

Step-by-step explanation:

3. d=150cm= 150/100m=1.5m

r= 1.5/2= 0.75m

since a drum is circular under it will take a circular area

Area of a circle=πr^2

=π×(0.75)^2

=0.5625π = 1.77m^2

4. r=48dm=48/10=4.8m

since the clock is circular it will contact a circular area

Area of a circle= πr^2

=π(4.8)^2

=23.04π= 72.38m^2

5. since it's circular

C=75cm=75/100m=0.75m

Circumference of a circle=2πr

0.75=2πr

r=0.75/2π

r=0.119m

Area of a circle= πr^2

=π×(0.119)^2

=0.045m^2

I hope it helps.

The pH level of the pool is determined as 8.6.

The pH of a solution is a measure of its acidity or basicity. The pH scale ranges from 0 to 14, with a pH of 7 being neutral, less than 7 is acidic and above 7 is alkaline.

The pH of a solution can be calculated using the formula;

pH = -log[H₃O⁺]

where;

Using the measured [H₃O⁺] concentration of 2.40 x 10⁻⁹ moles/liter, we can calculate the pH of the swimming pool as follows;

pH = -log(2.40 x 10⁻⁹)

pH = 8.62

Therefore, the pH of the swimming pool is 8.6, rounded to the nearest tenth.

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The sum of the exterior angles of the heptagon in the given diagram is 51.43 degrees.

To find the sum of the exterior angles of a heptagon, we can use the formula:

Sum of exterior angles = 360 degrees

Since a heptagon has 7 sides, it also has 7 exterior angles.

Therefore, each exterior angle of a heptagon is equal to:

= 360 degrees / 7

= 51.43 degrees (rounded to two decimal places)

Hence, the sum of the exterior angles of the heptagon in the given diagram is 51.43 degrees.

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An exponential function would best fit the data because as x increases, the y values change multiplicatively. The rate of change of the function is of approximately 0.8275.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant, which is the rate of change of the exponential function.

The rate of change for this problem is approximated as follows:

Hence the rate can be rounded to 0.8275.

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Answer:

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

Divide the total amount by the cost per piece:

Since the carpenter can only buy whole pieces of wood, they can buy 30 pieces.

Answer:

5/2

Step-by-step explanation:

The Parallelogram area is 96 square meters.

We have,

The area of a parallelogram is given by the formula A = bh, where b is the length of the base and h is the height.

In this case,

The base of the parallelogram is the length of one of its parallel sides, which is 12 m.

The height of the parallelogram is given as 8 m.

Therefore, the area of the parallelogram is:

A = bh

A = 12 m x 8 m

A = 96 square meters

Thus,

The Parallelogram area is 96 square meters.

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The axis of symmetry of the given quadratic function f(x) = -(x - 2)(x + 4) is x = -1.

Given the function in the question:

f(x) = -(x - 2)(x + 4)

To find the axis of symmetry, first expand  quadratic function f(x) = -(x - 2)(x + 4).

f(x) = -(x - 2)(x + 4)

f(x) = (-x + 2)(x + 4)

f(x) = -x(x + 4) + 2( x + 4 )

f(x) = -x² - 4x + 2x + 8

Collect and add like terms

f(x) = -x² - 2x + 8

To find the axis of symmetry, we can use the formula:

x = -b/2a

Where a = -1 and b = -2.

Substituting these values, we get:

x = -(-2) / 2(-1)

Simplify

x = 2 / -2

x = -1

Therefore, the the axis of symmetry is x = -1.

Option D) x = -1 is the correct answer.

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The coordinates of the image after the rotation are given as follows:

The five more known rotation rules are given as follows:

The coordinates of the original image are given as follows:

The rotation is a 90º counterclockwise about the origin, hence the rule is given as follows:

(x,y) -> (-y, x).

Meaning that the coordinates of the rotated image are given as follows:

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The measures of each of the arcs are: 16. m(MN) = 72°; 17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 193°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°; 24. m(PRN) = 265°; 25. m(MQN) = 288°.

Recall that in a circle, the measure of an intercepted arc is always the same or equal to the measure of the central angle it subtends.

Therefore, we have:

16. m(MN) = 72° (based on the vertical angles and inscribed angle theorems).

17. arc NQR is an half circle, therefore:

m(NQR) = 180°

18. m(NQ) = 180 - 72 = 108°

19. m(MRP) = 180 + (180 - 72 - 95)

m(MRP) = 193°

20. m(QR) = 72°

21. m(MR) = 180 - 72 = 108°

22. m(QMR) = 360 - 72

m(QMR) = 288°

23. m(PQ) = 180 - 72 - 95

m(PQ) = 13°

24. m(PRN) = 360 - 95

m(PRN) = 265°

25. m(MQN) = 360 - 72

m(MQN) = 288°

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Step-by-step explanation:

[tex]f'(x)=[(3x^2-4x+1)^4]'=4(3x^2-4x+1)^3*(3x^2-4x+1)'=4(3x^2-4x+1)^3*(6x-4)=8(3x^2-4x+1)^3(3x-2);[/tex]

The required derivative of f(x) = (3x² - 4x + 1)⁴ is f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)

We can use the chain rule and power rule of differentiation to find the derivative of f(x).

Let u = 3x² - 4x + 1, then we have:

f(x) = u⁴

Using the chain rule, we get:

f'(x) = 4u³ * u'

To find u', we can differentiate u with respect to x using the power rule:

u' = d/dx (3x² - 4x + 1) = 6x - 4

Substituting u' and u into f'(x), we get:

f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)

Therefore, the derivative of f(x) = (3x² - 4x + 1)⁴ is f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)

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A(5,0), B(3,2), C(0,5), and D(-6,1) are all located in the first quadrant. D(-6,1) is located within the second quadrant.

A coordinate system within geometry is a way to use one or more integers, or coordinates, to determine the exact placement of points and other geometrical objects over a manifold, such Euclidean space. The order of the coordinates is crucial, and they are frequently identified by their position within an arranged tuple or through a letter, such as "the x-coordinate."  Within the first quadrant is A(5,0). The first quadrant is occupied by B(3,2), followed by C(0,5) with the first quadrant, D(-6,1) with the second quadrant, E(-4,4) from the second quadrant, and F(2,-3) with the fourth quadrant.

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The values of all the solutions are,

16) m QT = 142 deg

17) m ∠STR = 23 deg

18) m ∠RSQ = 19 deg

Given that;

A circle is shown.

Now, We can formulate;

16|) The value of m QT is,

m QT = 2 ∠QST

         = 2 × 71

         = 142 degree

17) The value of m ∠STR is,

m ∠STR = 1/2 m ∠SXR

             = 1/2 × 46

             = 23 deg

17) Since,  ∠ RST = 90°

Then, We get;

m ∠RSQ = 90 - ∠QST

              = 90 - 71

              = 19 degree

Thus, The values of all the solutions are,

16) m QT = 142 deg

17) m ∠STR = 23 deg

18) m ∠RSQ = 19 deg

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The surface area of the rectangular pyramid is approximately 387.6 square yards.

To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of the four triangular faces.

The area of the base is:

Area of base = length x width

Area of base = 14 yards x 14 yards

Area of base = 196 square yards

To find the area of the four triangular faces, we need to first find the height of each triangle using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs (the two shorter sides) is equal to the square of the hypotenuse (the longest side).

In this case, the hypotenuse is the slant height of the pyramid, which is 12 yards. The legs are half the length and width of the base, which are both 7 yards.

So we have:

h² + 7² = 12²

h² + 49 = 144

h² = 95

h = √95

Now we can find the area of each triangular face using the formula:

Area of triangle = 1/2 x base x height

The base of each triangle is 14 yards, and the height is √95 yards. So we have:

Area of triangle = 1/2 x 14 yards x √95 yards

Area of triangle = 7√95 square yards

There are four triangular faces, so the total area of the four triangular faces is:

Total area of triangular faces = 4 x 7√95 square yards

Total area of triangular faces = 28√95 square yards

Finally, we can find the total surface area by adding the area of the base and the area of the four triangular faces:

Total surface area = Area of base + Total area of triangular faces

Total surface area = 196 square yards + 28√95 square yards

Total surface area ≈ 387.6 square yards (rounded to one decimal place)

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The distance d between A and B is √(68), and the square of the distance in the y direction is 64.

To find the distance d between points A and B, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values of A and B, we get:
d = sqrt((4 - 2)^2 + (5 - (-3))^2)
d = sqrt(2^2 + 8^2)
d = sqrt(4 + 64)
d = sqrt(68)
Next, to calculate the square of the distance in the y direction, we need to find the difference between the y-coordinates of A and B and square it. So:
(y2 - y1)^2 = (5 - (-3))^2 = 8^2 = 64
Therefore, the square of the distance in the y direction is 64.
I'm here to help you with your question. To find the distance d between two points A(x1, y1) and B(x2, y2), we can use the distance formula:
d = √((x2-x1)² + (y2-y1)²)
Given the points A(2, -3) and B(4, 5), let's plug in the values:
d = √((4-2)² + (5-(-3))²)
Now, calculate the difference for each coordinate:
d = √((2)² + (8)²)
Next, square the differences:
d = √(4 + 64)
Finally, calculate the square root:
d = √(68)
ow, let's find the square of the distance in the y direction, which is (y2-y1)²:
(y2-y1)² = (5-(-3))²
Calculate the difference:
(y2-y1)² = (8)²
Square the difference:
(y2-y1)² = 64
So, the distance d between A and B is √(68), and the square of the distance in the y direction is 64.

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The probability that either event will occur is given as follows:

P(A or B) = 0.82 = 82%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of events in this problem is given as follows:

23 + 18 + 9 = 50.

The events are given as follows:

Hence the number of desired outcomes is given as follows:

23 + 18 = 41.

And the probability is of:

p = 41/50 = 0.82 = 82%.

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To solve the inequality 2x < 12, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides by 2:

2x < 12

x < 6

Therefore, the solution to the inequality is x < 6. This means that all values of x that are less than 6 satisfy the inequality. We can represent this graphically on a number line:

<=======()------6-------------->

The open circle () indicates that x cannot be equal to 6, but can be any value less than 6. The arrow indicates that the inequality is true for all values of x to the left of the open circle.

In summary, the solution to the inequality 2x < 12 is x < 6.

I'm 15 BTW