can someone please explain 10 3/4 - 6 4/4 ??

The question is incomplete and the figure is missing. Here is the complete question with the figure attached below.

In the figure, sin ∠MQP = ______.

A. Cos N and Sin R

B. Sin R and Sin N

C. Cos N and Sin M

D. Cos R and Sin N

Answer:

D. Cos R and Sin N

Step-by-step explanation:

Given:

∠MQP = 56°

sin (∠MQP) = sin (56°)

Consider the triangle NMR,

m ∠N = 56°, m ∠R = 34°

sin (∠N) = sin (56°)

So, sin (∠MQP) = sin (∠N) = sin (56°) ---------- (1)

Now, we know that, [tex]\sin x=\cos(90-x)[/tex]

Therefore, sin (∠N) = sin (56°) = cos (90°-56°) = cos (34°)

Now, from the same triangle NMR,

[tex]\cos (\angle R)=\cos (34\°)[/tex]

Therefore, sin (∠N) = cos (∠R)  ------------- (2)

Hence, from equations (1) and (2), we have

sin (∠MQP) = sin (∠N) = cos (∠R)

So, option D is correct.

Answer:

The greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Step-by-step explanation:

Given:

A group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week.

The sales tax on each rental is 16%.

The group has $2,500 available to spend on ski and snowboard rentals.

If the ratio of pairs of skis to snowboards is 7:3.

Now, to find the greatest number of pairs of skis and snowboards rentals.

So, the rent of 7 pairs of skis = [tex]7\times 45.50=\$318.50.[/tex]

And the rent of 3 pairs of snowboards = [tex]3\times 110=\$330.[/tex]

So, total rental amount of 7 pairs of skis and 3 pairs of snowboards:

[tex]318.50 + 330 = 648.50.[/tex]

Now, to get the rental amount after sales tax:

648.50 + 16% of $648.50.

[tex]=648.50 +\frac{16}{100}\times 648.50.[/tex]

[tex]=648.50+103.76[/tex]

[tex]=\$752.26.[/tex]

The total rental amount after sales tax = $752.26.

As the group has available $2,500.

So, the sets according to the given ratio:

[tex]2500\div 752.26 = 3.32.[/tex]

[tex]=3\ sets.[/tex]

Thus, there are 3 sets of the ratio 7:3.

So, the rental price according to sets are:

The rent of Skis:

[tex]7\times 3 = 21[/tex] 

[tex]21\times 45.50= 955.50[/tex]

The rent of snowboards:

[tex]3\times 3 = 9[/tex]

[tex]9\times 110 = 990[/tex]

So. the total rental amount of skis and snowboards according to sets are:

[tex]955.50 + 990 = 1,945.50[/tex]

Now, the amount of rent after sales tax:

$1945.50 + 16% of $1945.50.

[tex]=1945.50+\frac{16}{100}\times 1945.50[/tex]

[tex]=1945.50+311.28=\$2256.78.[/tex]

Thus, the total cost = $2256.78.

Now, to get the greatest number of pairs of skis to snowboards that can be rent:

[tex]2,500 - 2,256.78 = 243.22[/tex]

The cost of 21 pair of skis and 9 pairs of snowboards is $2256.78 and the group has available only $2500 to spend.

Thus, they can rent only 21 pairs of skis and 9 pairs of snowboards.

Therefore, the greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Answer:

Option C is true.

Step-by-step explanation:

See the attached diagram.

Since MN is a diameter of the circle at P, so it will always make a right angle at a point on the circumference of the circle.

Therefore, ∠ MLN = 90° as L is a point on the circumference.

Now, given that LM = 2x and LN = 3x, then we have to find MN.

So, applying Pythagoras Theorem, MN² = LM² + LN²

⇒ MN² = 4x² + 9x² = 13x²

⇒ MN = x√13

Therefore, option C is true. (Answer)

Answer:

Therefore the required Equations are

[tex]y =2(x+3)\ \textrm{is the required expression for First condition.}\\y = 3x-2\ \textrm{is the required expression for Second condition.}[/tex]

Step-by-step explanation:

Given:

'y' represents the larger number and

'x' represents the smaller number

Then, a larger number is double the sum of 3 and a smaller number will be

Larger no = double of ( 3 and smaller number)

∴ [tex]y=2(x+3)\ \textrm{is the required expression for First condition.}[/tex]

Now,

The larger number is 2 less than 3 times the smaller number.

Larger number = 3 times smaller number and 2 less

∴ [tex]y=3x-2\ \textrm{is the required expression for Second condition.}[/tex]

Therefore the required Equations are

[tex]y =2(x+3)\ \textrm{is the required expression for First condition.}\\y = 3x-2\ \textrm{is the required expression for Second condition.}[/tex]

Final answer:

The correct equations that model the situation are y = 3x - 2 and y = 2(x + 3), as they reflect the two conditions given in the problem description.

Explanation:

To determine which equations model the situation described, we should translate the worded statements into algebraic equations. The first statement tells us that a larger number 'y' is double the sum of 3 and a smaller number 'x'. This can be written as y = 2(x + 3). The second statement tells us that the larger number is 2 less than 3 times the smaller number, which can be written as y = 3x - 2.

Now, we need to verify the provided choices against these two derived equations:

y = 3x - 2 (Correct, it matches the second statement we translated from the problem description.)

3x - y = 3 (Incorrect, because rearranging this gives y = 3x - 3, which does not match either of our derived equations.)

3x - y = -2 (Incorrect, because rearranging this gives y = 3x + 2, which does not match either of our derived equations.)

y = 2 - 3x (Incorrect, this does not match the format of either derived equation.)

y=2(x + 3) (Correct, it matches the first statement we translated from the problem description.)

Answer:

4/9.

Step-by-step explanation:

There are a total of 18 people.

Prob( A Sculptor is chosen) = 3/18 = 1/6.

Prob( a photographer) = 5/18

The required probability is the sum of these 2, so

it is 3/18 + 5/18

= 8/18

= 4/9.

Answer:

[tex]\frac{8}{17}[/tex]

Step-by-step explanation:

Answer: 3.82 miles

Step-by-step explanation:

According to the shown figure, we can imagine the scene as a right triangle, where the tower is located at the right angle, and the fireman and the forest fire located at each of the other two vertices.

So, since we are dealing with a right triangle we can use the Pithagorean Theorem, in order to find the distance from the fireman to the fire [tex]d[/tex], which is also the hypotenuse.

[tex]d^{2}= (2.1 miles)^{2} +(3.2 miles)^{2}[/tex]

[tex]d=\sqrt{(2.1 miles)^{2} +(3.2 miles)^{2}}[/tex]

Finally:

[tex]d=3.82 miles[/tex]

The distance from the fireman and the fire is 3.83 miles.

Using the values given, we can calculate the distance using pythagoras ;

Inputting the values into the formula ;

distance = √2.1² + 3.2²

distance = √14.65

distance = 3.8275318418

Therefore, the distance between the fireman and the fire is 3.83 miles.

Answer:

A) [tex]y=\frac{1}{2}x+3[/tex] - Linear

B) [tex]y=4x+2[/tex] - Linear      

C) [tex]xy=12[/tex] - Nonlinear

Step-by-step explanation:

To determine whether a function is linear or nonlinear.

The function of a straight line is given as :

[tex]y=mx+b[/tex]

where [tex]m[/tex] represents slope of line and [tex]b[/tex] represents the y-intercept.

Any function that can be represented as a function of straight line is called a linear function otherwise it is nonlinear.

We will check the equations given for linear or nonlinear.

A) [tex]y=\frac{1}{2}x+3[/tex]

The function is in the form [tex]y=mx+b[/tex] and hence it is a linear function with slope [tex]m=\frac{1}{2}[/tex] and y-intercept [tex]b=3[/tex].

B) [tex]y=4x+2[/tex]

The function is in the form [tex]y=mx+b[/tex] and hence it is a linear function with slope [tex]m=4[/tex] and y-intercept [tex]b=2[/tex].

C) [tex]xy=12[/tex]

On solving for [tex]y[/tex]

Dividing both sides by  [tex]x[/tex]

[tex]\frac{xy}{x}=\frac{12}{x}[/tex]

[tex]y=\frac{12}{x}[/tex]

This function cannot be represented in the form [tex]y=mx+b[/tex], hence it is a nonlinear function.

                                   Question #15

Step-by-step explanation:

A notation such as [tex]T_{(-1, 1)}oR_{y-axis}[/tex] is read as:

"a translation of (x, y) → (x - 1, y + 1) after a reflection across y-axis.

The rule of reflection of point (x, y) across y-axis brings (x, y) → (-x, y), meaning that y-coordinate remains the same, but x-coordinate changes its sign.

As ΔABC with coordinates A(1, 3), B(4, 5) and C(5, 2). Here is the coordinates of ΔA'B'C' after the glide reflection described by [tex]T_{(-1, 1)}oR_{y-axis}[/tex].

                                            [tex]R_{y-axis}[/tex]                                   [tex]T_{(-1, 1)}[/tex]  

A(1, 3)              →                A'(-1, 3)               →                    A"'(-2, 4)

B(4, 5)             →                B'(-4, 5)               →                    B"'(-5, 6)

C(5, 2)             →                C'(-5, 2)               →                    C"'(-6, 3)

                                        Question #16

Step-by-step explanation:

A glide reflection is said to be a transformation that involves a  translation followed by a reflection in which every  point P is mapped to a point P ″ by the following steps.

As ΔABC with coordinates A(-4, -2), B(-2, 6) and C(4, 4).

Translation : (x, y)  → (x + 2, y + 4)

Reflection : in the x-axis

The rule of reflection of point (x, y) across x-axis brings (x, y) → (x, -y), meaning that x-coordinate remains the same, but y-coordinate changes its sign.

Hence,

ΔABC with coordinates A(-4, -2), B(-2, 6), C(4, 4) after (x, y)  → (x + 2, y + 4) and reflection in the x-axis.

A(-4, -2)         →     A'(-2, 2)     →     A''(-2, -2)    

B(-2, 6)          →    B'(0, 10)       →     B''(0, -10)

C(4, 4)            →    C(6, 8)         →      C''(6, -8)

Keywords: reflection, glide reflection, translation

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Answer: Each cup has 4 blueberries and 5 raspberries.

Step-by-step explanation:

Since we have given that

Number of blueberries = 36

Number of raspberries = 45

We need to find the number of each type if she wants to put an equal number of blueberries and an equal number of raspberries into each cup.

So, H.C.F. of 36 and 45 = 9

So, Number of blueberries would be

[tex]\dfrac{36}{9}=4[/tex]

Number of raspberries would be

[tex]\dfrac{45}[9}=5[/tex]

Hence, each cup has 4 blueberries and 5 raspberries.

Answer:

8 years

Step-by-step explanation:

Use formula

[tex]I=P\cdot r\cdot t,[/tex]

where

I = interest

P = principal

r = rate (as decimal)

t = time

In your case,

I = $175.84

P = $314

r = 0.07, then

[tex]175.84=314\cdot 0.07\cdot t\\ \\175.84=21.98t\\ \\t=\dfrac{175.84}{21.98}\\ \\t=8[/tex]

The question asks for the duration of an investment. We use the formula for simple interest to solve this. By plugging the known values into the rearranged formula for time, we can find the duration of the investment.

The question asks for how long the principle was invested if you received $175.84 on $314 invested at a rate of 7%. The calculation is based on the formula for simple interest, which is I = PRT (Interest = Principal x Rate x Time). From the question, we know that the Interest (I) is $175.84, the Principal (P) is $314, and the Rate (R) is 7% or 0.07 when expressed as a decimal.

We need to find the Time (T), which can be rearranged from the formula as T = I / (P x R). By plugging the values into this formula, we get T = 175.84 / (314 x 0.07). Solving for T will give the time period the money was invested for.

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Answer:

[tex] - {x}^{2} + x + 24[/tex]

Step-by-step explanation:

Subtract the functions:

[tex]f - g = (36 - {x}^{2} ) - (8 - x)[/tex]

Simplify:

[tex](36 - {x}^{2} ) - (8 - x) \\ 36 - {x}^{2} - 8 + x \\ - {x}^{2} + x + 24[/tex]

Answer:

The width of the Iphone 11 pro max is 3.36 in.

Step-by-step explanation:

since both iPhones are proportional, you will need to find the ratio of what their proportion is to one another. the length of one iphone is 5.2, and the length of the other iphone is 6.24. Therefore, the ratio of proportion to each other would be 5.2/ 6.24. to find the width of the iphone 11 pro max, you will need to use the following equation: 5.2/6.24 x 2.8/? (unknown side)      

this gives you the equation 6.24 x 2.8 = 5.2 x ?  (unknown side)

(the question mark is the unknown side of the iphone 11 pro max)

6.24 x 2.8 / 5.2 = ? (unknown side)

therefore the unknown side of the iphone 11 pro max is 3.36 in.

By using the concept of proportions, the width of the iPhone 11 Pro Max, when it's proportional to iPhone 11 Pro, is approximately 3.36 inches.

The given problem involves finding a proportional measurement. The iPhone 11 pro has dimensions 5.2 inches (length) and 2.8 inches (width). If the iPhone 11 Pro Max is proportional in size and has a length of 6.24 inches, we can find its width using the ratio between the length and the width of the iPhone 11 pro.

We will set up a proportion like this:

[tex]5.2/2.8 = 6.24/x[/tex]

Where x is the width of the iPhone 11 Pro Max. Solving for x will give us the width:

[tex]2.8 * 6.24 = 5.2 * x\\x = (2.8 * 6.24) / 5.2[/tex]

After solving this equation, we find that the width of the iPhone 11 Pro Max is approximately 3.36 inches.

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Answer:

1 / (1 + x²)

Step-by-step explanation:

Derivative of a function by first principle is:

[tex]f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

Here, f(x) = tan⁻¹ x.

[tex]f'(x)= \lim_{h \to 0} \frac{tan^{-1}(x+h)-tan^{-1}x}{h}[/tex]

Use the difference of arctangents formula:

[tex]tan^{-1}a-tan^{-1}b=tan^{-1}(\frac{a-b}{1+ab})[/tex]

[tex]f'(x)= \lim_{h \to 0} \frac{tan^{-1}(\frac{x+h-x}{1+(x+h)x} )}{h}\\f'(x)= \lim_{h \to 0} \frac{tan^{-1}(\frac{h}{1+(x+h)x} )}{h}[/tex]

Next, we're going to use a trick by multiplying and dividing by 1+(x+h)x.

[tex]f'(x)= \lim_{h \to 0} \frac{tan^{-1}(\frac{h}{1+(x+h)x} )}{h}\frac{1+(x+h)x}{1+(x+h)x} \\f'(x)= \lim_{h \to 0} \frac{1}{1+(x+h)x} \frac{tan^{-1}(\frac{h}{1+(x+h)x} )}{\frac{h}{1+(x+h)x}}[/tex]

We can now evaluate the limit.  We'll need to use the identity:

[tex]\lim_{x \to 0} \frac{tan^{-1}x}{x} =1[/tex]

This can be shown using squeeze theorem.

The result is:

[tex]f'(x)= \lim_{h \to 0} \frac{1}{1+(x+h)x}\\\frac{1}{1+x^2}[/tex]

The width of rectangle is 8 units.

Step-by-step explanation:

Given,

Area of rectangle = 40 units

Width = w

Length = w-3

Area = Length * Width

[tex]40=(w-3)*w\\40=w^2-3w\\w^2-3w=40\\w^2-3w-40=0[/tex]

Factorizing the equation

[tex]w^2-8w+5w-40=0\\w(w-8)+5(w-8)=0\\(w-8)(w+5)=0[/tex]

Either,

w-8=0         => w=8

Or,

w+5=0        =>w= -5

As width cannot be negative, therefore

Width of rectangle = 8 units

The width of rectangle is 8 units.

Keywords: area, rectangle

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Final answer:

To find the width of a rectangle with an area of 40 units and a length expressed as the width minus 3 units, we set up and solve a quadratic equation, yielding the width of the rectangle as 8 units.

Explanation:

The question asks to find the width of a rectangle when the length is the width minus 3 units and the area is 40 units. To solve this, let's denote the width as w, then the length will be w - 3. The area of a rectangle is calculated by multiplying the length by the width, so we will set up an equation: area = length × width, or 40 = w × (w - 3).

This is a quadratic equation: w² - 3w - 40 = 0. To solve it we can factor the quadratic or use the quadratic formula. Factoring gives us (w - 8)(w + 5) = 0, which means w could be 8 or -5. Since a width cannot be negative, the width of the rectangle is 8 units.

Answer:

Cotton Gin

Explanation:

A cotton gin – meaning "cotton engine" – is a machine that quickly and easily separates cotton fibers from their seeds, enabling much greater productivity than manual cotton separation.[1] The fibers are then processed into various cotton goods such as linens, while any undamaged cotton is used largely for textiles like clothing. The separated seeds may be used to grow more cotton or to produce cottonseed oil.

Handheld roller gins had been used in the Indian subcontinent since at earliest AD 500 and then in other regions.[2] The Indian worm-gear roller gin, invented sometime around the 16th century,[3] has, according to Lakwete, remained virtually unchanged up to the present time. A modern mechanical cotton gin was created by American inventor Eli Whitney in 1793 and patented in 1794. Whitney's gin used a combination of a wire screen and small wire hooks to pull the cotton through, while brushes continuously removed the loose cotton lint to prevent jams. It revolutionized the cotton industry in the United States, but also led to the growth of slavery in the American South as the demand for cotton workers rapidly increased. The invention has thus been identified as an inadvertent contributing factor to the outbreak of the American Civil War.[4] Modern automated cotton gins use multiple powered cleaning cylinders and saws, and offer far higher productivity than their hand-powered precursors.[5]

Eli Whitney invented his cotton gin in 1793. He began to work on this project after moving to Georgia in search of work. Given that farmers were desperately searching for a way to make cotton farming profitable, a woman named Catharine Greene provided Whitney with funding to create the first cotton gin. Whitney created two cotton gins: a small one that could be hand-cranked and a large one that could be driven by a horse or water power.

The invention from the late 1700s is Cotton Gin. It was invented by Eli Whitney in 1793.

A cotton gin means “cotton engine”. It is a machine that quickly and easily sorts cotton fibers from their seeds, enabling much larger productivity than manual cotton separation.

Eli Whitney began to work on this project after moving to Georgia in search of work. At that time, farmers were desperately searching for a way to make cotton farming profitable.

The fibers of cotton are then processed into various cotton goods such as linens, while undamaged cotton is used largely for textiles like clothing. The separated seeds may be used to grow more cotton or to produce cottonseed oil.

Therefore, Cotton Gin is an invention from the late 1700s.

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Answer:

Area of parallelogram is equal to the product of base and height, the area is the product of [tex]\pi r[/tex] and r, or [tex]\pi r^{2}[/tex].

Step-by-step explanation:

We are finding the area of a circle by an alternative method.

What we do is split the circle into multiple sectors and then arrange them in the form of a parallelogram and find the area of this parallelogram.

Area of parallelogram = base[tex]\times height[/tex]

Hence area is the product of base and height.

Base = [tex]\pi r[/tex]

Height = r

Area is the product of [tex]\pi r[/tex] and r = [tex]\pi r^{2}[/tex]

Answer:

about 11 years

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=?\ years\\ P=\$4,000\\ A=\$8,000\\r=9\%=9/100=0.09[/tex]

substitute in the formula above

[tex]8,000=4,000(1+0.09t)[/tex]

solve for r

[tex]2=(1+0.09t)[/tex]

[tex]0.09t=2-1[/tex]

[tex]0.09t=1[/tex]

[tex]t=11.1\ years[/tex]

Answer:

The answer is 305. Step 1 is wrong in the given answer.

Kevin's mistake is that his step 1 in the answer is  wrong.

Step-by-step explanation:

Given expression is [tex]\frac{2440}{8}[/tex]

Now to simplify the given expression:

Given expression can be written as below

Step 1: [tex]\frac{2440}{8}=\frac{2400+40}{8}[/tex]

Step 2:  [tex]\frac{2440}{8}=\frac{2400}{8}+\frac{40}{8}[/tex]

Step 3: [tex]\frac{2400}{8}+\frac{40}{8}=300+5[/tex]  (the sum of the numerators are dividing with their corresponding terms)

Step 4: [tex]\frac{2440}{8}=305[/tex]  (adding the terms)

Step 5: Therefore [tex]\frac{2440}{8}=305[/tex]

Therefore the answer is 305 and from the problem step 1 is wrong.

Kevin's mistake is that his answer is correct and the step 1 is  wrong.

The answer is 305. Step 1 is wrong in the given answer.

Answer:

Step-by-step explanation:

4x = 38

x= 38/ 4

x = 9 1/2

Answer:

D.) 7:3

Step-by-step explanation:

First, find the LCM of the numbers, which is 8.

Then divide each number by 8

56÷8=7 24÷8= 3

Then, put them in a ratio

7:3

Answer:

A

Step-by-step explanation:

Right now, our ratio of male to female is 24:56. We need to reduce this, kind of like how you would reduce a fraction. 24÷8=3 and 56÷8=7, so our new ratio is 3:7.

Answer: 6

Step-by-step explanation: First rewrite 10 as 10/1 and 1 and 2/3 as 5/3.

Mixed numbers can be changed to improper fractions by multiplying the denominator by the whole number and then adding the numerator. We then put out numerator over our old denominator.

So we have 10/1 ÷ 5/3 or 10/1 × 3/5.

It's important to understand that dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division to multiplication and flip the second fraction.

Now multiplying across the numerators and across the denominators, we have 30/5. Notice however that 30/5 is not in lowest terms so we divide the numerator and the denominator by the greatest common factor of 30 and 5 which is 6 and we end up with 6.

Therefore, 10 ÷ 1 and 2/3 = 6.

Final answer:

To find 10 divided by 1 2/3, convert the mixed number to an improper fraction (5/3), multiply by the reciprocal (3/5), and simplify the result to get 6.

Explanation:

To divide 10 by 1 2/3, first, we need to convert the mixed number 1 2/3 into an improper fraction. The mixed number 1 2/3 can be written as 5/3 because 1 (which is 3/3) plus 2/3 equals 5/3.

Next, we apply the rule for dividing fractions: we multiply by the reciprocal of the divisor. So, we take 10 (which is the same as 10/1) and multiply it by the reciprocal of 5/3, which is 3/5.

The multiplication looks like this: 10/1 × 3/5 = 30/5.

The result of 30/5 can be simplified to 6, which is the answer in simplest form. Therefore, 10 divided by 1 2/3 equals 6.

Jayden ran [tex]\frac{6}{25}[/tex] of a kilometers in one minute

Solution:

Given that Angel and Jayden were at track practice

The track is two-fifth kilometers around

[tex]\text{ track length } = \frac{2}{5} \text{ kilometers}[/tex]

Angel ran 1 lap in 2 minutes

Jayden ran 3 laps in 5 minutes

To find: distance ran by Jayden in 1 minute

3 laps were run by Jayden in 5 minutes

3 laps = 5 minutes

"x" laps = 1 minute

Therefore laps run by Jayden in one minute is:

On cross multiplication we get,

5x = 3

[tex]x = \frac{3}{5}[/tex]

Therefore Jayden ran [tex]\frac{3}{5}[/tex] laps in 1 minute

Distance covered is:

Total track length = [tex]\frac{2}{5} \text{ km}[/tex]

Distance ran in 1 minute = [tex]\frac{3}{5} \times \frac{2}{5} = \frac{6}{25}[/tex]

Thus Jayden ran [tex]\frac{6}{25}[/tex] of a kilometers in one minute

Answer:

x = -2

y = 3

Step-by-step explanation:

Since y = 3x +9, substitute this value in the first eq.

4x + 5(3x+9) = 7 ===> 4x + 15x + 45 = 7 ===> 19x = 7-45 ==> 19x = -38 ===>

===> x -38/19 ===> x = -2

Replace this value in the second eq.

y = 3(-2) + 9 ===> y = -6 + 9 ===> y = 3

Answer:

[tex]\large\boxed{if\ x\neq-3\ \wedge\ y\neq0\ \wedge\ x\neq y\ \wedge\ x\neq -y}[/tex]

second

[tex]\large\boxed{y\neq0\ \wedge\ x\neq-y\ (y\neq-x)}[/tex]

Step-by-step explanation:

We know that dividing by 0 is impossible.

Therefore, the denominator of the expression must be different from 0.

[tex]\text{For}\\\\\dfrac{(x-y)^2}{2xy+6y}\times\dfrac{4x+12}{x^2-y^2}\\\\\\2xy+6y\neq0\qquad(1)\\\\x^2-y^2\neq0\qquad(2)[/tex]

[tex](1)\\2xy+6y\neq0\qquad\text{distribute}\\\\2y(x+3)\neq0\iff2y\neq0\ \wedge\ x+3\neq0\\\\2y\neq0\qquad\text{divide both sides by 2}\\\boxed{y\neq0}\\\\x+3\neq0\qquad\text{subtract 3 from both sides}\\\boxed{x\neq-3}\\==========================\\(2)\\x^2-y^2\neq0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\(x-y)(x+y)\neq0\iff x-y\neq0\ \wedge\ x+y\neq0\\\boxed{x\neq y}\ \wedge\ \boxed{x\neq-y}[/tex]

[tex]\text{For}\\\\\dfrac{2(x-y)}{y(x+y)}\\\\y(x+y)\neq0\iff y\neq0 \wedge\ x+y\neq0\\\\ \boxed{y\neq0}\ \wedge\ \boxed{x\neq-y}[/tex]

Answer:

Length of the envelope = 14

Width of the envelope = 5.6

Step-by-step explanation:

Let the width of the rectangle be  x

Then the length of the rectangle will be [tex]2\frac{1}{2} \times x[/tex]

Also the length of the plastic band to cover the  front and back of the envolpe =  [tex]39\frac{3}{8}[/tex]

To cover one side th band required is

=>[tex]\frac{39\frac{3}{8}}{2}[/tex]

=>[tex]\frac{\frac{315}{8}}{2}[/tex]

=>[tex]\frac{\frac{315}{8}}{2}[/tex]

=>[tex]{\frac{315}{16}[/tex]

=>39.4

We know that the perimeter of the rectangle is

=> 2( L + B) = [tex]{\frac{39.4}{2}[/tex]

=> 2( [tex]2\frac{1}{2} \times x + x[/tex]) = 19.7

=> 2( [tex]\frac{7}{2}x) = 19.7 [/tex]

=>  [tex]3.5x = 19.7 [/tex]

=> [tex] x = \frac{19.7}{3.5} [/tex]

=>  [tex]x = 5.6[/tex]

Now length of the envelope =

=>  [tex]2\frac{1}{2} \times x [/tex]

=>  [tex] 2.5 \times 5.6 [/tex]

=> 14

The problem involves setting up a relationship equation using the width and length of a rectangle and solving the equation to find the width and length. The length of the plastic band is given, which helps in creating the equation.

In this problem, the rectangular envelope has its length, which is 2 1/2 times the width. There is a plastic band that wraps around the envelope and it is given that the total length of this plastic band is 39 3/8 inches. Thus, the length of the plastic band is equal to twice the length of the envelope plus twice the width of the envelope.

Let us denote the width of the envelope by w. Therefore, the length of the envelope is 2.5w. Setting up an equation using this information, we have: 2*(2.5w) + 2w = 39 3/8. Simplifying this equation, we get: 5w + 2w = 39 3/8, 7w = 39 3/8. To find the width, we can divide both sides of the equation by 7, yielding w = 39 3/8 / 7.

Having calculated the width, the length is simply 2.5 times this value. Therefore, we have found both the width and length of the rectangle envelope.

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The cost of swimming lesson in winters is $60.

Step-by-step explanation:

Given,

Cost of lessons in summer = $50 per month

Raise in winter = 20%

Amount of raise = 20% of summer's cost

Amount of raise = [tex]\frac{20}{100}*50[/tex]

Amount of raise = [tex]\frac{1000}{100}=\$10[/tex]

Cost of lesson in winter = Cost in summer + Amount of raise

Cost of lesson in winter = 50+10 = $60

The cost of swimming lesson in winters is $60.

Keywords: percentage, addition

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Answer:

Area of the field is 540 m².

Step-by-step explanation:

ABCD is the given quadrilateral in which diagonal BD is 36 m.

Now, AL ⊥ BD and CM ⊥ BD. Also, AL = 19 m and CM = 11 m.

Now, we have to calculate the area of quadrilateral shaped field ABCD.

At first, we will find the area of ΔABD and ΔBCD and then we will add the area of both the triangles to get the area of the quadrilateral shaped field.

Now, ΔABD and ΔBCD are both right angled triangles.

So,

[tex]area\; of \; triangle \; ABD = \frac{1}{2} \times base\times height[/tex]

[tex]=\frac{1}{2}\times BD\times AL=\frac{1}{2}\times36\times19=342\; m^{2}[/tex]

[tex]area \; of \; triangle\; BCD = \frac{1}{2}\times BD\times CM=\frac{1}{2}\times36\times 11 = 198\; m^{2}[/tex]

So, area of field ABCD = area of ΔABD + area of ΔCBD

= 342 + 198

= 540 m²

So, the area of quadrilateral shaped field is 540 m².

Answer:

The numbers are 23,27

Step-by-step explanation:

Let one number be x

Other number = 50 - x

50 - x - x = 4

50 - 2x = 4

-2x = 4 - 50

-2x = - 46

x = -46/-2

x = 23

Other number = 50 - x = 50 -23 = 27