Two supplementary angles are in the ratio 2:7. Find the measure of the Acute angle.

The fraction 3/4 can be rewritten as 6/8 when the denominator is 8.

To rewrite 3/4 with a denominator of 8, we need to find an equivalent fraction where the denominator is 8.

To do this, we observe that multiplying both the numerator and denominator of a fraction by the same non-zero number does not change its value. In this case, we can multiply 3/4 by 2/2 to get an equivalent fraction with a denominator of 8.

So, we have:

(3/4) * (2/2) = (3 * 2) / (4 * 2) = 6/8

Therefore, the fraction 3/4 can be rewritten as 6/8 when the denominator is 8.

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Answer: 12

Step-by-step explanation:

Answer:

\( \sf \: x = 12\)

Step-by-step explanation:

Given equation,

→ x - 9 = 3

Now the value of x will be,

→ x - 9 = 3

→ x = 3 + 9

→ [ x = 12 ]

Hence, the value of x is 12.

The ability for Nike to manufacture its own shoes and then build stores for distribution is an example of Forward Integration.

What is forward integration ?

In order to lower manufacturing costs and increase efficiency, a sort of vertical integration known as "forward integration" moves up the supply chain.

An operational competency is what?

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The integral of the two terms as shown below:\(∫(1 - x²)^(1/2)dx = 1/2(θ + 1/2sin(2θ)\) + C)where C is the constant of integration.

To integrate (1-x²)^(1/2) using substitution method, we use the following steps:

Step 1: We let x

= sin(θ)dx = cos(θ)dθ1-x²

= cos²(θ)

Step 2: We substitute the expression derived from Step 1 into the original function to obtain∫(1 - x²)^(1/2)dx=∫cos²(θ)dθ

Step 3: We then apply the double angle formula to obtain:cos²(θ) = (1 + cos(2θ))/2Step 4: We substitute this expression back into the integral to obtain:

∫(1 - x²)^(1/2)dx = ∫(1 + cos(2θ))/2dθ∫(1 - x²)^(1/2)dx

= 1/2 ∫(1 + cos(2θ))dθ

Step 5: Evaluate the integral of the two terms as shown below:∫(1 - x²)^(1/2)dx = 1/2(θ + 1/2sin(2θ) + C)where C is the constant of integration.

Finally, we substitute x = sin(θ) back into the expression above to obtain the final solution.

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Answer:

∠ B = 130°

Step-by-step explanation:

given ∠ B = 3 ∠ A - 20

supplementary angles sum to 180°

sum A and B and equate to 180

∠ A + 3 ∠ A - 20 = 180

4 ∠ A - 20 = 180 ( add 20 to both sides )

4 ∠ A = 200 ( divide both sides by 4 )

∠ A = 50

that is ∠ A = 50° and

∠ B = 3 ∠ A - 20 = 3 × 50 - 20 =  150 - 20 = 130°

The uncertainty in the best estimate for the length of the side of the block is approximately 0.0447 mm.

To determine the uncertainty in the best estimate for the length of the block side, we can consider the range of values obtained from the measurements. Since the uncertainty represents the possible deviation from the true value, the range of measurements can be used to estimate the uncertainty in the best estimate

To find the standard deviation represents the average amount of variation or spread among the measurements , we use the formula σ = Δb / √n, where σ is the standard deviation, Δb is the uncertainty in each measurement, and n is the number of measurements.

In this case, Δb = 0.1 mm and n = 5. Plugging these values into the formula, we get σ = 0.1 / √5 ≈ 0.0447 mm.

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Answer:

30 degrees ; 150 degrees

Step-by-step explanation:

1) rememeber that two supplementary angles have their sum equals to 180 degrees

2) write an equation with the given information

x + 5x = 180

2) solve the equation

- added up the terms with x

6x = 180

- divide the two members by 6

x = 30

- find the second angle by multiplying 30 by 5

150

The wholesale cost $423

The merchant increases the wholesale cost by 35%

The washer sells it for $571.05

The wholesale cost can be calculated as follows

y + 35/100= 571.05

y + 0.35= 571.05

1.35y= 571.05

y= 571.05/1.35

y= 423

Hence the wholesale cost is $423

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Answer:

C = 7.72 ~ 7.7

Step-by-step explanation:

So when you solve this equetion you must 1st find x then c

we can find x by using cos(60)

cos(60) = x/14

x = cos(60) × 14

x = 1/2 ×14

x = 7

so after we find x we are going to solve c by using cos (25)

cos (25) = X/C = 7/c

cos(25) × C = 7

C = 7/cos (25)

C = 7.72 ~ 7.7

so the solution is 7.7

Converting the percentage to degree in the pie chart, angle PQ and UPT are 162° and 25.2° respectively

This is a statistical tool used to represent data in a chart. It is often represented using angles or percentage.

To find the value of the respectively angles, we have to convert the values from percentage to degree.

The formula to do this is given as

Percentage = angle * (100 / 360)

A)

Angle PQ = ?

Substituting the values;

45 = angle * (100 / 360)

45 = angle * (5/18)

angle = 45 / (5/18)

angle = 162°

B) Angle UPT = ?

7 = angle * (5/18)

angle = 7 / (5/18)

angle = 25.2

The angle PQ is 162 degrees, the angle UPT is 25.2 degrees

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Answer:

14

step by step explanation

-7×(-2)

14

In this updated version, the indirection operator * has been replaced with square bracket notation []. The loop iterates over the indices from 0 to 299 (inclusive) and prints the elements of the array using square brackets to access each element by index.

Here's the rewritten loop using square bracket notation:

for (int x = 0; x < 300; x++)

cout << array[x];

In the above code, the indirection operator "*" has been replaced with square bracket notation "[]". Now, the loop iterates from 0 to 299 (inclusive) and outputs the elements of the "array" using square bracket notation to access each element by index.

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The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

WOAH!!!!

Step-by-step explanation:

Thx for sharing that!

Mark as brainlist plssss.

Answer:

Wow

Step-by-step explanation:

To solve the given third-order linear homogeneous differential equation, we can use the method of finding the characteristic equation and its roots. Let's denote y(x) as the solution to the equation.  Answer :  1,7,-31

The characteristic equation is obtained by substituting y(x) = e^(rx) into the differential equation, where r is an unknown constant. Plugging this into the equation, we get:

r^3 - 3r^2 - r + 3 = 0

To solve this equation, we can use various methods, such as factoring, synthetic division, or numerical methods. By applying these methods, we find that the roots of the characteristic equation are r = -1, r = 1, and r = 3.

Since we have distinct real roots, the general solution for y(x) can be expressed as a linear combination of exponential functions:

y(x) = C1e^(-x) + C2e^x + C3e^(3x)

To find the specific solution for the given initial conditions, we can substitute the values of x = 0, y(0) = 1, y'(0) = 7, and y''(0) = -31 into the equation and solve for the unknown coefficients C1, C2, and C3.

Using the initial condition y(0) = 1, we get:

C1 + C2 + C3 = 1

Using the initial condition y'(0) = 7, we get:

-C1 + C2 + 3C3 = 7

Using the initial condition y''(0) = -31, we get:

C1 + C2 + 9C3 = -31

Solving this system of linear equations, we can find the values of C1, C2, and C3. Substituting these values back into the general solution, we obtain the specific solution for y(x).

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1. Write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. Show all your work, including the points used to determine the slope and how the equation was determined.

Here it seems like you would use your two points - (62,63) and (70,72) to find the equation of the best fit line. Use the slope formula and once finding the slope plug that and one point into the y=mx+b formula to find b.

2. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?

The slope of the line would represent the average change in armspan with respect to height. The y intercept represents the predicted armspan if a person was 0 inches tall.

3. Test the residuals of two other points to determine how well the line of best fit models the data.

To do this you would take two other points on the graph and find the difference between the predicted y and the actual y. For example, if another point was (66,65), you would plug 66 into your best fit equation solve and then subtract the actual value (65) from your best fit value. A high residual indicates that the best fit line does not do a good job of modeling the data.

4. Use the line of best fit to help you to describe the data correlation.

If the line of best fit is positive, you may say that the data has a positive correlation. If the line of best fit has a slope of around one, you may say that a change in height yields an approximately equal change in armspan.

5.Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?

Use your line of best fit - plug in 66 as y

6. According to your line of best fit, what is the arm span of a 74-inch-tall person?

Use your line of best fit - plug in 74 as y

Answer:

Step-by-step explanation:

what grade is this ...

this look hard

Using the intermediate value theorem to determine whether the function f(x) = x^3 + 7x- 9 has a root or not between x = 1 and x = 2. The correct answer is: A) Yes, the given function has a root between [1, 2] and the root is 1.30301.

By the Intermediate Value Theorem, if a continuous function changes sign over an interval, then it must have at least one root in that interval.

Here, f(x) = x^3 + 7x - 9 is a polynomial function and is continuous on the closed interval [1, 2]. We can evaluate f(1) and f(2) to see if the signs are different:

f(1) = 1^3 + 7(1) - 9 = -1

f(2) = 2^3 + 7(2) - 9 = 15

Since f(1) is negative and f(2) is positive, the function must change sign on the interval [1, 2]. Therefore, by the Intermediate Value Theorem, there exists at least one root of f(x) between x = 1 and x = 2.

To find the root to five decimal places, we can use numerical methods such as the bisection method or Newton's method.

Using the bisection method with an initial interval of [1, 2], we can find that the root is approximately 1.30301.

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Answer:

7 crates of tomatoes

Step-by-step explanation:

588÷84=7

Answer:

Step-by-step explanation:

This is a simple division problem. To find out the number of crates, we need to divide 588 by 84.

588/84 = 7

Answer:

20% of students picked the vanilla cake.

Step-by-step explanation:

Total number of students: 16 + 64 = 80

Proportion that chose vanilla cake: 16/80 (simplify by dividing by 16) = 1/5 = 0.2 * 100 = 20%

Answer: 105

Expination: i used a calculater

Part (a)  K is a normal extension of E, but not of F.

Part (b) L is a normal extension of F, but L' is not.

Part (a)

Let E = KG(K,F). Since E is a field extension of F and K is a finite extension of F, then K is a normal extension of E. This is because F[K] is a finite separable extension and hence normal.

However, K is not a normal extension of any field F ⊆ E. This is because K is not a normal extension of F by assumption.

Part (b)

(a) L is a normal extension of F. This is because K is a normal extension of F (by assumption) and L is a splitting field of a polynomial over F, and so is a finite extension of K. Hence, L is a normal extension of F.

(b) Let L be any field such that K ⊆ L and L ≠ L'. Then L is not a normal extension of F. This is because K is a normal extension of F, and if L were a normal extension of F, then L' would also be a normal extension of F by transitivity. Because  L ≠ L', L is not a typical extension of F.

Complete Question:

Suppose that the characteristic of F is 0, and that K is a finite, but not normal, extension of F. (a) Let E = KG(K,F). Show that K s a normal extension of E, but not of any field F ES E. Solution. Proof (b) Suppose K -F(a) for some aE K. Let L be the splitting field of the minimal polynomial of a over F, with K C L. Prove that: (a) L is a normal extension of F Solution. Put your answer here... (b) For any field L, such that K L, Ç L, L' is not a normal extension of F. (L is called the normal closure of F in K.) Solution. Put your answer here...

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We can use the formula for the sum of an arithmetic series to find the value of U infinity i = 1 Ai for each given set Ai:

(a) Ai = {i, i + 1, i + 2,...}

The sum of this arithmetic series is:

U infinity i = i + (i + 1) + (i + 2) + ...

            = i + (i + 1) + (i + 2) + ... + (i + n) - (1 + 2 + 3 + ... + n)

 where n is any positive integer.

The sum of the first n positive integers is given by the formula:

1 + 2 + 3 + ... + n = n(n+1)/2

Substituting this into the expression for U infinity i, we get:

U infinity i = i + (i + 1) + (i + 2) + ... + (i + n) - n(n+1)/2

Simplifying, we get:

U infinity i = (n+1)i + n(n+1)/2 - n(n+1)/2

            = (n+1)i

Taking the limit as n approaches infinity, we get:

U infinity i = lim (n approaches infinity) (n+1)i = infinity

Therefore, U infinity i = 1 Ai for the set Ai = {i, i + 1, i + 2,...} is infinity.

(b) Ai = {0, i}

The sum of this arithmetic series is:

U infinity i = 0 + 1 + 2 + ... + i-1 + i

Using the formula for the sum of an arithmetic series, we get:

U infinity i = [i(i+1)]/2

Taking the limit as i approaches infinity, we get:

U infinity i = lim (i approaches infinity) [i(i+1)]/2 = infinity

Therefore, U infinity i = 1 Ai for the set Ai = {0, i} is infinity.

(c) Ai = (0, i)

The sum of this set is:

U infinity i = integral from 0 to i dx

Evaluating the integral, we get:

U infinity i = [x] from 0 to i = i

Therefore, U infinity i = 1 Ai for the set Ai = (0, i) is i.

(d) Ai = (i, infinity)

The sum of this set is:

U infinity i = integral from i to infinity dx

Taking the limit as the upper limit of integration approaches infinity, we get:

U infinity i = lim (b approaches infinity) integral from i to b dx

            = lim (b approaches infinity) (b - i)

            = infinity

Therefore, U infinity i = 1 Ai for the set Ai = (i, infinity) is infinity.

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Answer:

x> y-300/12

Step-by-step explanation

1. Subtract 300 from both sides

2.  Divide both sides by -12

3. Switch the sides

The scale factor is 10:3

And the value of X=30

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can increase a rectangle with sides of 2 cm and 4 cm by multiplying each side by an integer, say 2.

Scale factor = new form dimension The basic formula for calculating the scale factor is the dimension of the former shape. The formula for scaling up the original figure is Scale factor = Larger figure dimensions. Figure dimensions are reduced.

From the figure,

Scale factor of AB:AB'

=40:12

=10:3

Therefore, BB':X≅10:3

100/X=10/3

X=(3×100)/10

X=30

Therefore, the scale factor is 10:3

And the value of X=30

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Answer:

-7

Step-by-step explanation:

The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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The assumption that Q can be written as a countable union of open subsets is false, and we conclude that Q cannot be written as Q = nn=1 Un where ( un : n N ) is a sequence of open subsets in R.

According to the Baire Category Theorem, a complete metric space cannot be written as a countable union of nowhere dense sets. The set Q of rational numbers is a dense subset of the complete metric space R, and therefore it cannot be written as a countable union of nowhere dense sets.

To prove this, assume that Q = nn=1 Un, where each Un is an open subset of R. Since Q is dense in R, each Un must also be dense in R. However, this contradicts the Baire Category Theorem, which states that a complete metric space cannot be written as a countable union of nowhere dense sets. Therefore, the assumption that Q can be written as a countable union of open subsets is false, and we conclude that Q cannot be written as Q = nn=1 Un where ( un : n N ) is a sequence of open subsets in R.

In summary, the set Q of rational numbers cannot be written as a countable union of open subsets in R due to the Baire Category Theorem and the fact that Q is a dense subset of the complete metric space R.

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