Question 22
The sum of two numbers is 107. The difference of the two numbers is 53. What are the two
numbers.
Let z be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 107."
Write an equation that expresses the information in the sentence "The difference of the two
numbers is 53."
Solve the system you have written above.
The larger number, a is
> Next Question
The smaller number, y is

Answer:Need answer choices to answer

Step-by-step explanation:

Answer:

There are no boxes bro so how can I answer you . I gonna get better to see your boxes but I can't see i think there is a attachment you forget to take with quest .Because this quest is not looking like Mathematics it's like English Grammar.If you didn't like my answer you will say anything you want . But in my decision you my bestfriend. I help others to give answers so I am trying my best.

-Thank You By MrIshaan

The integral of 1/(2+4x²+25x²) using partial integration is (1/2) arctan(10x) + C, where C is the constant of integration.

To solve this integral, we will use the technique of partial integration. This technique is also known as integration by parts and is used to find the integral of a product of two functions. The formula for integration by parts is as follows:

∫u dv = uv - ∫v du

where u and v are functions, and du/dx is the derivative of u with respect to x, and dv/dx is the derivative of v with respect to x.

Let's apply this formula to our integral:

∫1/(2+4x²+25x²) dx

We need to choose two functions, u and dv, such that when we differentiate u, we get a simpler function, and when we integrate dv, we get a simpler function. In this case, we can choose:

u = 1, and dv = 1/(2+4x²+25x²) dx

Now, let's find du/dx and v:

du/dx = 0 (since u is a constant)

To find v, we need to integrate dv. We can use the substitution method to evaluate the integral:

Let u = 5x

du/dx = 5

dv = 1/(2+4x²+25x²) dx

Substituting u and dv:

v = ∫ dv/dx du = ∫1/(2+4u²) du

v = (1/2) arctan(2u)

v = (1/2) arctan(2(5x))

v = (1/2) arctan(10x)

Now, we can apply the formula for integration by parts:

∫1/(2+4x²+25x²) dx = uv - ∫vdu

∫1/(2+4x²+25x²) dx = (1) x (1/2) arctan(10x) - ∫(1/2) arctan(10x) x 0 dx

∫1/(2+4x²+25x²) dx = (1/2) arctan(10x) + C

where C is the constant of integration.

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The similarity ratio between the two octagons is 1:2 (Option b).

To begin, we need to know that similar figures have the same shape, but they may differ in size. For instance, we can have two octagons with different areas but the same shape. In this case, we are given that the two octagons are similar, and we are given the areas of the two octagons.

Let the similarity ratio between the two octagons be "x". For areas, we know that the ratio of the areas of two similar figures is the square of their similarity ratio. Therefore, we can set up the following equation:

x² = (Area of smaller octagon) / (Area of larger octagon)

Substituting the given areas, we get:

x² = 4 / 16    

x² = 0.25

Taking the square root of both sides, we get:

x = √0.25

x = 0.5

Therefore, the similarity ratio between the two octagons is 1:2 (Option b).

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An equation of the line in slope-intercept form include the following: y = 4x + 3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (0, 3) and a slope of 4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 4(x - 0)  

y - 3 = 4x

y = 4x + 3

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Answer:

f(x) = 0 at x = -2, 1, 3

A, B, and D are the correct choices.

There are 6 different ways can the flags be arranged in a row.

We have,

Total number of flags = 6

So, to find the number of ways to arranged n object = n!

Then, the number of ways to arrange the flag

= 6!

= 6 x 5 x 4 x 3 x 2 x 1

=120 x 6

= 720 ways

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The probability that they both select a poodle is bigger. The probability is 0.074

In the store, there are 11 puppies, and 3 of them are poodles.

If Rebeca and Aaron chose at random, then the probabilities are; for Rebbeca, there is a 3/11 probability to get a poodle ( because there are 3 poodles of eleven dogs) and the probability for Aaron is 2/10 because now there are one less poodle (and in consequence one less puppy)

now, the joint probability of these two events happening is the product of each probability, this is:

p = (3/11)*(2/10) = 6/110, that we can simplify at 3/55 if we divide both denominator and numerator by 2.

If the dog is replaced after Rebeca picked hers, then Aaron also has a 3/11 probability of picking a poodle, and in that case, the joint probability is:

q = (3/11)*/3/11) = 9/121

now, p = 3/55 = 0.055 and q = 9/121 = 0.074

Thus, this means that the probability of both of them selecting a poodle is bigger when the dog is replaced (which makes a lot of sense)

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Answer:

20 blue pens

Step-by-step explanation:

Since it is a 3 to 4 ratio (Green to Blue) and you have 15 green pens you need to multiply 5 to the 3(green pens). Since you multiplied 5 it needs to stay equal you need to multiply 5 to the blue pens which would give you 20 blue pens

Answer: 1.5283

Step-by-step explanation:

When saying something like log base 8 of 24, we know that this means 8 to the power of what is equal to 24. The answer is 1.5283. If you would like to round sine it is the approximate value, do it.

Please, say thanks, rate, and please please please, give brainlist.

Pour développer il faut appliquer la distributivité de la multiplication :

7m + 5.5(2+m) = 7m + 5.5 x 2 + 5.5m

= 7m + 11 + 5.5m

Il faut combiner les termes contenant m :

= 7m + 5.5m + 11

= (7 + 5.5)m + 11

= 12.5m + 11

The quadratic equation in the given graph can be written as:

y = -3*(x + 2)^2 + 4

We can see a quadratic equation that opens downwards and we can see that the vertex is at (-2, 4), then if the leading coefficient is a, we can write this as:

y = a*(x + 2)^2 + 4

We can also see that the parabola passes through (0, -8) replacing these values we will get:

-8= a*(0 + 2)^2 + 4

-8 - 4 = a*4

-12/4 = a

-3 = a

Then the quadratic equation is

y = -3*(x + 2)^2 + 4

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Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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The area of the face of a clock with a circumference of 14 inches is approximately 15.6 square inches. This is calculated using the formula for the area of a circle, which is πr², where r is the radius of the circle.

To find the area of the face of the clock, we need to use the formula for the area of a circle, which is

A = πr²

where A is the area of the circle, π (pi) is a constant approximately equal to 3.14, and r is the radius of the circle.

Since the circumference of the clock is 14 inches, we can use the formula for the circumference of a circle to find the radius

C = 2πr

14 = 2πr

r = 14 / (2π)

r = 2.227 in (approx)

Now that we know the radius, we can use the formula for the area of a circle

A = πr²

A = 3.14 x (2.227)²

A = 15.6 sq in (approx)

Therefore, the area of the face of the clock is approximately 15.6 square inches.

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Answer:

Cannot be drawn directly.

Step-by-step explanation:

The graph of every function w = f (x, y, z) will be a surface in R 4, though it can't be drawn directly; however, slicing horizontally by w = c produces relations c = f (x, y, z) in x, y, and z whose graphs will be surfaces in 3-space which can be drawn. Therefore, the graph of the function shown above cannot be drawn directly.

The parallel lines are

a) y = ( 4/7 )x + 6/7

b) 7y = 4x - 18

The perpendicular lines are

a) y = - ( 7/4 )x - 7/4

b) y = - ( 7/4 )x + 2

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = ( 4/7 )x - 3

where the slope of the line is m = 4/7 and y-intercept is b = -3

The parallel lines have the same slope and the perpendicular lines have the negative reciprocal slope

So , the equation of lines are

The parallel lines are

a) y = ( 4/7 )x + 6/7

b) 7y = 4x - 18

And , the perpendicular lines are

a) y = - ( 7/4 )x - 7/4

b) y = - ( 7/4 )x + 2

The lines which are neither parallel not perpendicular are y = 2/3x - 3 and y = -4/7x + 7

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Answer:

a) y = -2x + 3

b) y = -3x + 7

c) y = -1/2x + 4

d) y = 2

Step-by-step explanation:

Gradient is also known as slope

a) y = mx + b

3 = (-2)0 + b

b = 3

y = -2x + 3

b) y = mx + b

1 = (-3)(2) + b

1 = -6 + b

b = 7

y = -3x + 7

c) Slope m = (y2 - y1)/(x2 - x1)

m = (2 - 3)/(4 - 2) = -1/2

y = mx + b

3 = -1/2(2) + b

3 = -1 + b

b = 4

y = -1/2x + 4

d) The x‐axis or any line parallel to the x‐axis has a slope of 0.

y = mx + b

2 = -3(0) + b

b = 2

y = 2

Answer:

a) The equation of this line is y = -2x + 3

b) The equation of this line is y = -3x + 7

c) The equation of this line is y = -1/2x + 4 or y = -0.5x + 4

d) The equation of this line is y = 2

Step-by-step explanation:

The equation of a line can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.

a) The equation of the line with a gradient of -2 and cutting the y-axis at 3 can be found using the point-slope form of a linear equation. The point-slope form is given by y - y1 = m(x - x1), where m is the gradient and (x1, y1) is a point on the line. Substituting m = -2 and (x1, y1) = (0, 3), we get:

y - 3 = -2(x - 0)

Simplifying the right-hand side gives:

y - 3 = -2x

Adding 3 to both sides gives the final equation:

y = -2x + 3

b) The equation of the line with a gradient of -3 and passing through the point (2, 1) can be found using the point-slope form again. Substituting m = -3 and (x1, y1) = (2, 1), we get:

y - 1 = -3(x - 2)

Simplifying the right-hand side gives:

y - 1 = -3x + 6

Adding 1 to both sides gives the final equation:

y = -3x + 7

c) To find the equation of the line passing through the points (2, 3) and (4, 2), we first need to find its gradient. The gradient is given by:

m = (y2 - y1)/(x2 - x1)

Substituting the coordinates of the two points, we get:

m = (2 - 3)/(4 - 2) = -1/2 or -0.5

Now, we can use the point-slope form again, this time with (x1, y1) = (2, 3) and m = -1/2:

y - 3 = (-1/2)(x - 2)

Simplifying the right-hand side gives:

y - 3 = (-1/2)x + 1

Adding 3 to both sides gives the final equation:

y = (-1/2)x + 4 or y = -0.5x + 4

d)The line is parallel to the x-axis and passes through the point (-3 ; 2). A line parallel to the x-axis has a gradient of 0. The general equation of a line is y = mx + c, where m is the gradient and c is the y-intercept. Since the gradient is 0, the equation becomes y = c. Since the line passes through the point (-3 ; 2), we can substitute y = 2 into the equation to find that c = 2. Therefore, the equation of this line is y = 2.

The triangles are not congruent.

Given that, two triangles, EFG and HIJ are similar,

So,

Since, the triangles are similar, but according to the definition of similarity, two objects that are similar are not necessarily congruent,

so the Δ EFG is not congruent to Δ HIJ.

Cos 30° = HI / HJ

√3/2 = 3/HI

HI = 3.5

Therefore, the scale factor Δ EFG to Δ HIJ = EF / HI = 10/3.5 = 2/0.7

The ratio of perimeter of similar objects are same as the scale factor,

so, the ratio of their perimeters = 2/0.7

The ratio of the areas of the similar objects are the ratios of the squares of the scale factor.

So, the ratio of their areas = 4/0.49

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If Farmer Johnson's minimum AVC is, for example, $1.50 per dozen eggs, then any price below $1.50 would result in losses that he could not sustain in the long run.

To determine the lowest price a dozen eggs could reach before Farmer Johnson would be forced to shut down in the short run, we need to know his minimum average variable cost (AVC) of producing eggs.

The average variable cost is the variable cost per unit of output, and it includes costs that vary with the level of production, such as labour, feed, and utilities.

If the price of a dozen eggs falls below the minimum AVC, Farmer Johnson will not be able to cover his variable costs and will incur losses. In the short run, he may continue to produce as long as he can cover his variable costs, but he will eventually be forced to shut down if he cannot cover his fixed costs as well.

Without information on Farmer Johnson's specific costs, we cannot determine the exact minimum AVC or the lowest price at which he would shut down. However, we can say that the lowest price a dozen eggs could reach before he would be forced to shut down is equal to his minimum AVC.

If Farmer Johnson's minimum AVC is, for example, $1.50 per dozen eggs, then any price below $1.50 would result in losses that he could not sustain in the long run.

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The probability that a randomly selected carton has a puncture or a smashed corner is 17.5%.

Given that, a company has 8% puncture, 10% have a smashed corner, and 0.5% have both a puncture and a smashed corner cartons,

We need to find the probability that a randomly selected carton has a puncture or a smashed corner,

So,

P(A or B) = P(A) + P(B) - P(A and B)

= 0.08 + 0.10 - 0.005

= 0.175

= 17.5%

Hence, the probability that a randomly selected carton has a puncture or a smashed corner is 17.5%.

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The calculated value of the length of segment DF is 51.96 units

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

The right triangle

The length of segment DF is then calculated as

sin(60) = DE/DF

Substitute the known values in the above equation, so, we have the following representation

sin(60) = 45/DF

So, we have

DF = 45/sin(60)

Evaluate the quotient

DF = 51.96

Hence, the segment DF is 51.96 units

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Answer:

The sum of the interior angle measures of a regular hexagon is 720°.

Step-by-step explanation:

To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

In the case of a hexagon, n = 6. So, we can plug this value into the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:

Sum of interior angles of hexagon = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

Answer:

Set your calculator to degree mode.

Using the Law of Cosines:

37^2 = 23^2 + 20^2 - 2(23)(20)(sin C)

1,369 = 929 - 920sin(C)

440 = -920sin(C)

sin(C) = -11/23

C = sin^-1 (-11/23) = 151.4°

The approximate amount to be deposited each month at a guaranteed APR of 6.5% that will accrue to $15,000 in 9 years is $97.57.

In order to find out how much you should deposit each month to end up with $15,000 in 9 years, we can use the future value formula for an annuity:

FV = PMT * [(1 + r)^n - 1] / r

where:

The total number of deposits, n,  is the number of months in 9 years:

n = 9 * 12 = 108

The monthly interest rate from the annual percentage rate (APR):

r = (1 + 0.065/12) - 1 = 0.0054166667

Let's substitute the values and solve for PMT:

Therefore, you should deposit approximately $97.57 each month to end up with $15,000 in 9 years, assuming a guaranteed APR of 6.5%.

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The symbol for the stock boeing is BA.

We are given that;

Quotation 80.12 81.09 79.20 81.00

Now,

It is the first item in the quotation after the company name. The other items are the previous close price, the open price, the low and high prices of the day, the current price, the change in percentage, the volume in millions, the dividend yield and the P/E ratio.

Therefore, by the equation the answer will be BE.

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There are 3/20 pink tulips

A flower garden is composed of 1/2 tulips

3/10 of this amount are the pink tulips

Therefore the number of pink tulips can be calculated as follows

= 1/2 × 3/10

= 3/20

Hence 3/20 of the tulips in the garden are pink

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If male and female students of section B in DPS and DAV are in ratio 3 : 2 and 4:3 respectively then male students of section B are 40% more than female students of section B considering both the schools (approx).

(A) 50% (C) 36% (B) 25% (D) 40%.

Hence, the correct option is D.

Let us assume that there are 3x male students and 2x female students in section B of DPS, and there are 4y male students and 3y female students in section B of DAV. We can set up the following equations to represent the given ratios

3x : 2x = male : female in DPS section B

4y : 3y = male : female in DAV section B

By simplifying these ratios, we get

3 : 2 = x/y for DPS section B

4 : 3 = x/y for DAV section B

Solving for x and y, we get

x = 6y for DPS section B

x = 4.5y for DAV section B

Now, let us add the male and female students in section B from both schools.

Male students = 3x + 4y = 3(6y) + 4(4.5y) = 30y

Female students = 2x + 3y = 2(6y) + 3(4.5y) = 21y

So, the ratio of male to female students in section B from both schools combined is

30y : 21y = 10 : 7

Therefore, male students are (10 - 7)/7 = 3/7 = 0.4286 (approx. 43%) more than female students in section B from both schools combined.

However, the question asks for the percentage more, so we need to multiply this answer by 100 to get a percentage.

0.4286 x 100 ≈ 42.86%

Therefore, male students in section B are approximately 42.86% more than female students in section B from both schools combined. Rounding to the nearest percent that is 40%.

Hence, the correct option is D.

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Answer: The scale factor used to create the image is 0.8

Step-by-step explanation: To determine the scale factor used to create the image, we can divide the corresponding side lengths of the dilated polygon D' by the corresponding side lengths of the original polygon D.

For example, the top and bottom sides of polygon D have a length of 8, while the corresponding sides of polygon D' have a length of 6.4.

So, the scale factor used to create the image is:

6.4 / 8 = 0.8

Therefore, the scale factor used to create the image is 0.8.