What fraction of 1meter is 45centimetres

In similar triangles the ratio between corresponding sides is the same in each pair of correspondig sides.

Then, if triangles ABC, ACD and BCD are similars:

If the ratio between correpondig legs and hypotenuses is equal you can use the pytagorean theorem to prove similarity.

Ratio of corresponding sides in triangles ABC and BCD:

Correspondig sides:

Hypotenuses: c (hypotenuse of triangle ABC) and a (hypotenuse of triangle BCD)

Leg: a (In trinagle ABC) and c-x (in trianlge BCD)

Solve a squared:

Ratio of corresponding sides in triangles ABC and ACD:

Correspondig sides:

leg: b (in ABC) and x(in ACD)

Hypotenuse: c (in ABC) and b (in ACD)

Solve b squared:

Pythagorean theorem,In a right triangle the sum of legs squared is equal to the hypotenuse squared

The graph of the given function is attached.

Given is a function for the rainfall in 5 months in inches.

We need to display the data,

So, as we can see that the data is not showing any proportion or pattern,

So, it can be displayed as a line chart.

Hence the chart is attached for the function.

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Answer:Rules for rotating points about the origin

1. The point (a,b) rotated 90° counterclockwise about the origin

becomes (-b,a).

A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)

A (a,b)-----------------A′ (-b,a)=(-1, 3)----------->A( 3,1)

B (a,b)-----------------B′ (-b,a)=(-2, 2)----------->B( 2,2)

C (a,b)-----------------C′ (-b,a)=(-2, 1)----------->C( 1,2)

D (a,b)-----------------D′ (-b,a)=(-1, 1)----------->D( 1,1)

Step-by-step explanation:

Answer:

$11,480

Step-by-step explanation:

Given that for every hundred pages a thickness of 1/4 inch is added to the book, then the equation is:  y = 1/2 + 1/4*x

Considering that the book's front and back covers each have a thickness of 1/4 inch, adding them together results in a thickness of 1/2 inch for the book, regardless of how many pages it has.

Given that a book's thickness increases by a quarter of an inch for every hundred pages, the equation is:

y = 1/2 + 1/4*x

where y denotes the book's width and x is the number of bond paper pages printed every 100 pages. Y has a length of inches.

Equations that have the same roots or solutions are said to be equivalent.

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Answer:

21

Step-by-step explanation:

Answer:

y=mx+b. slopes.

Fiona's equation is y=-3x+30. She will have no money after buying 10 of her favorite drink. She starts with $30 and loses $3 each time. She loses at a slower rate than Chester.

Chester's equation is y=-5x+20. He will have no money after buying 4 of his favorite drink. He starts with $20 and loses $5 each time. He loses at a faster rate than Fiona.

Answer:

hi,

Step-by-step explanation:

A consistent system of equations has at least one solution, and an inconsistent system has no solution.

Here the system has one solution.

Answer: 18(a)-89=217

Step-by-step explanation:

If a = 17 then you substitute/replace the a with the 17. Making 18(a) into 18(17). 18(17)= 306 - 89 = 217.

Hope this helped.

Answer:217

Step-by-step explanation:

putting the value of a in the equation.

18×17-89= 217

Answer:40

Step-by-step explanation:

21+8=29

29+11=40

Answer:

\(\huge\boxed{\tt{x = 24, y = 17}}\)

Step-by-step explanation:

Let the greater number be x and the smaller number be y.

So,

Condition # 1:

x - y = 7 --------------(1)

Condition # 2:

3x = 72 --------------(2)

Taking Eq. (2)

3x = 72

Divide both sides by 3

x = 72 / 3

x = 24

Now, Put x = 24 in Eq. (1)

24 - y = 7

Subtract 24 to both sides

-y = 7 - 24

-y = -17

y = 17

\(\rule[225]{225}{2}\)

Hope this helped!

The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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a. Let \(d\) be the number of daytime calls Eshwa makes, and \(e\) the number of evening calls. Then the cost \(C\) (in pence) of making \(d+e\) calls is

\(C = \boxed{50d + 40e}\)

b. £1 = 100p, so the cost \(C'\) (in £) is 1/100 of the cost found in part (a),

\(C' = \dfrac{50d + 40e}{100} = \boxed{\dfrac d2 + \dfrac{2e}5}\)

c. If Eshwa makes 30 of each type of call in a month, then the total cost (in £) is

\(C' = \dfrac{30}2 + \dfrac{2\cdot30}5 = \boxed{27}\)

c2. If Eshwa makes 20 daytime calls and 50 evening calls, then the total cost (in £) is

\(C' = \dfrac{20}2 + \dfrac{2\cdot50}5 = \boxed{30}\)

d. Let \(e=40\) and \(C'=42\). Solve for \(d\).

\(42 = \dfrac d2 + \dfrac{2\cdot40}5\)

\(42 = \dfrac d2 + 16\)

\(\dfrac d2 = 26\)

\(d = \boxed{52}\)

The zeros of the function y = -4(x-3)² + 8 are -1 and 7 and the intercept is 13

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

when y = 0

-4(x-3)² +8 = 0

expanding the equation

-4( x²-6x +9)+8 = 0

-4x² +24x -36 +8 = 0

-4x²+24x -28 = 0

divide through by 4

-x²+6x-7 = 0

-x²+7x -x -7 = 0

(-x²+7x)(-x-7) = 0

-x( x-7) 1(x-7)

1-x = 0 or (x-7 )= 0

x = -1 or 7

therefore the zeros are -1 and 7

to find the intercept:

x= 0

y = -4(0-3)²+8

y =-4+9+8

y = 13

therefore the intercept is 13

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Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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The expression can be completed as 4 × (4 + 3)

A mathematical expression is a combination of numbers, symbols, and operations that represent a mathematical relationship or calculation.

Mathematical expressions can be used to represent a wide range of concepts, including algebraic equations, geometric formulas, and statistical models.

Looking at the pages:

On page 2, we have 4 stickers per row while on page 3 we have 3 stickers per row. Also, both page 2 and page 3 have 4 rows each. Thus, we can complete the expression as follows:

4 × (4 + 3)

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Using the simple interest formula it is seen that Mrs Jo saves an amount of $180 when she chooses option B over option A.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

To determine which option is better, we need to compare the total amount of interest paid for each option.

Option A -

The principal amount is $900 and the interest rate is 8%. The term is 5 years.

Using the formula for simple interest -

Interest = Principal × Rate × Time

Interest = $900 × 0.08 × 5

Interest = $360

Total amount paid = Principal + Interest

Total amount paid = $900 + $360

Total amount paid = $1260

Option B -

The principal amount is $900 and the interest rate is 10%. The term is 2 years.

Using the formula for simple interest -

Interest = Principal × Rate × Time

Interest = $900 × 0.10 × 2 = $180

Total amount paid = Principal + Interest

Total amount paid = $900 + $180

Total amount paid = $1080

Therefore, option B is the better option because it has a lower total amount paid by choosing option B.

Mrs. Jo will save -

$1260 - $1080 = $180

Therefore, Mrs. Jo will save $180 by choosing option B instead of option A.

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The option that is most appropriate method for analyzing the results is a two-sample z-test for a difference in population proportions.

A Two-Sample Z-test is defined as a kind of test that is often employed so that it can make a comparison of the means of two samples to know and show if it is feasible that the product of the same population.

It is used to determine the difference between the two populations which is not statistically significant.

Finally, When a two-sample z-test is employed in the data, one can know and show the various difference that can be seen in population proportions.

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The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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(1) The integral of the function is (1/10)x⁵ - (1/8)x⁴ + (1/6)x³ + C.

(2) The integral is (1/4)(sec x)⁴ + eˣ(sec x) + (1/2)(sec x)² + C.

(3) The integral of cot²x dx is -1/sin(x) - sin(x) + C.

(4)The integral of the function  \(\frac{3}{8} x^{\frac{8}{3} } - \frac{6}{13} x^{\frac{13}{3} } + 21x^{\frac{2}{3}} + C.\)

(5) The shaded area under the curve is 7.22 sq units.

(1) The integral of (x⁶ - 2x⁵ + x⁴) / 2x² is determined as follows;

(x⁶ - 2x⁵ + x⁴) / 2x² = (x⁴(x² - 2x + 1)) / 2x²

= (x⁴(x - 1)²) / 2x²

= (x²(x - 1)²) / 2

∫(x²(x - 1)²) / 2 dx

= (1/2) ∫x²(x - 1)² dx

= (1/2) ∫x²(x² - 2x + 1) dx

= (1/2) ∫(x⁴ - 2x³ + x²) dx

= (1/2)(1/5)x⁵ - (1/2)(1/4)x⁴ + (1/2) (1/3)x³ + C

Simplifying further:

= (1/10)x⁵ - (1/8)x⁴ + (1/6)x³ + C

(2) The integral of (sec³x + eˣsecˣ + 1) / (sec x) dx, is calculated as follows;

(sec³x + eˣsecˣ + 1) / (sec x) = (sec³x + eˣsecˣ + 1)(sec x / sec x)

= (sec⁴x + eˣsec²x + sec x) / sec x

Note; sec x as 1/cos x

= sec⁴x/cos x + eˣsec²x/cos x + sec x/cos x

= sec³x/cos x + eˣsec x + sec x/cos x

Integrate by substitution method.

u = sec x

du = sec x tan x dx.

∫(sec³x + eˣsec x + sec x/cos x) dx

= ∫(u³ + eˣu + u) du

= (1/4)u⁴ + eˣu + (1/2)u² + C

Substitute u back in terms of sec x;

= (1/4)(sec x)⁴ + eˣ(sec x) + (1/2)(sec x)² + C

(3) The integral of cot²x dx;

cot²(x) = (cos²(x))/(sin²(x))

Let u = sin(x)

du = cos(x) dx

= ∫(1-u²)/u² du

= ∫(1/u²) - 1 du

= ∫u⁻² - 1 du

= -1/u - u + C

= -1/sin(x) - sin(x) + C

(4) The integral of the function is;

∫(x² - 2x³ + 7)/∛x dx =  ∫x²/∛x dx - ∫2x³/∛x dx + ∫7/∛x dx

= \(\frac{3}{8} x^{\frac{8}{3} } - \frac{6}{13} x^{\frac{13}{3} } + 21x^{\frac{2}{3}} + C.\)

(5) The shaded area under the curve is calculated as follows;

the given function;

\(y = x^{1/2} - x^{2} + 2x\)

∫y = A =  \(\frac{2}{3} x^{3/2} - \frac{1}{3} x^3 \ + x^2\)

the limits = 2 and 0

A = \(\frac{2}{3} (2)^{3/2} - \frac{1}{3} (2) ^3 \ + (2)^2\)

A = 1.89 - 2.67 + 8

A = 7.22 sq units

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Answer:

the answer is Y=5

hope this helps☺

Therefore, the measure of angle ∠Y to the nearest tenth of a degree is approximately 103.2 degrees.

To find the measure of angle ∠Y, we need to use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of its angles.

The formula for the law of cosines is:

\(c^2 = a^2 + b^2 - 2ab cos(C)\)

Where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite to side c.

In our case, we know the lengths of the sides w, x, and y, and we want to find the angle ∠Y, which is opposite to side y. So, we can use the formula as follows:

\(y^2 = w^2 + x^2 - 2wx cos(Y)\)

Substituting the values, we have:

\(630^2 = 170^2 + 590^2 - 2(170)(590) cos(Y)\)

Simplifying and solving for cos(Y):

\(cos(Y) = (170^2 + 590^2 - 630^2) / (2170590)\)

cos(Y) ≈ -0.236

Note that the cosine of an angle is negative if the angle is between 90 and 180 degrees, which is the case for angle ∠Y in this triangle. Therefore, we need to use the inverse cosine function to find the measure of angle ∠Y:

Y ≈ 103.2 degrees

Rounding to the nearest tenth of a degree, we get:

Y ≈ 103.2°

Therefore, the measure of angle ∠Y to the nearest tenth of a degree is approximately 103.2 degrees.

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The means score was calculated by adding the results of the tests and dividing it by the number of tests:

→ Σxi represents the sum of the scores of the tests

→ n represents the number of tests

For the average value 79. the scores of 6 tests were added:

From this expression, calculate the sum of the scores of the 6 tests:

Next, you have to calculate the score of a seventh test, so that the average score is equal to 81.

The sum of the scores of the test will be equal to the sum of the previous 6 tests plus the score of the seventh test. Let "x" represent the score on the seventh test, then Σxi=474+x will represent the sum of the scores of all tests.

This time the average has to be calculated over 7 tests, so you have to use n=7

The goal average is 81, then you can calculate the score needed as follows:

Multiply both sides by 7

Subtract 474

Ruben has to score a 93 in the next test to raise his average to 81.

The type of transformation modeled in the graph is Reflection across y-axis.

The three different kinds of coordinate transformation are listed below. The motor's three-phase current and voltage are transformed by the Clark transformation from their original natural coordinates to two-phase static coordinates determined with reference to the stator.

Because the domain or range values of the function f(x) have changed, rules of transformations assist in changing f(x) to a new function f'(x). With the use of these transformational rules, the function can be stretched or compressed as well as transformed vertically or horizontally.

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A. inequality that compares the temperatures of the two cities is: -2 > -6. B. inequality means city R, represented by -2 on the number line greater than the temperature of city S, represented by -6 on the number line. C.  city R is warmer than city S.

In mathematics, an inequality is a statement that compares two values or expressions and indicates that one is greater than, less than, or equal to the other. Inequalities are used to describe relationships between values that are not necessarily equal, and they are written using special symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

For example, the inequality 3x + 2 < 10 means that the expression 3x + 2 is less than 10. This inequality can be solved for x by subtracting 2 from both sides and then dividing by 3, yielding x < 2. This means that any value of x that is less than 2 will satisfy the inequality.

The inequality that compares the temperatures of the two cities is: -2 > -6

This inequality means that the temperature of city R, represented by -2 on the number line, is greater than the temperature of city S, represented by -6 on the number line. In other words, city R is warmer than city S.

On the number line, the further to the right a number is, the greater it is. Since -2 is to the right of -6, this indicates that -2 is greater than -6, which represents the fact that city R is warmer than city S.

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