Flying against the wind, an airplane travels 4720 kilometers in 8 hours. Flying with the wind, the same plane travels 4040 kilometers in 4 hours. What is the rate of the plane in still air and what is the rate of the wind?​

A number between 47 and 53 such that the prime factors are not repeated is:

3*17 = 51

Remember that any number can be written as a product of prime factors.

If we want to find a number between 47 and 53, such that there are no repeated factors, we just need to take different primes and multiply them.

For example:

2*3*5*7 = 210

There are no repeated factors, but the number is not in the desired range.

2*5*7 = 70

Still not in the range.

You can try some times until you get for example:

3*17 = 51

This a number in the desired range, such that their prime factors are not repeated.

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Therefore , the solution of the given problem of expression comes out to be probably 4 slices.

In mathematics, it is possible can multiply, division, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression. Expressions and phrases can be contrasted.

Here,

you figure if a toaster takes about 1-2 minutes to toast a piece of bread  and a toaster usually can fit 2 slices at a time i would say 4.

Preheat oven broil to high. Move oven rack to highest position.

Place sliced bread on an ungreased baking sheet. 4 slices of bread.

Broil bread for 1 minute, or until golden brown, then flip and broil for another 20-30 seconds. ...

Top with butter, jam, or any other favorite topping!

The temperature needed for the hot ambient air in a toaster, which makes the bread turn brown, is around 310°F (146°C). The heating element inside a toaster is a nickel-chromium alloy. The electrical current that runs through it heats it to make it red hot, with a temperature of 1,100°F to 1,200°F (519°C to 566°C).

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On solving the provided question, we can say that - here in the percentage obtained = 500 => so, 500/1000X100 = 50%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is = 1000

obtained = 500

so, 500/1000X100 = 50%

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The right triangles are congruent by HL theorem.

The triangles having congruent corresponding parts are called congruent triangles.

Given are two right triangles, with equal hypotenuse and one of the bases.

The question is by which theorem do they are congruent,

HL theorem :-

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Since, we know that, when two right triangles have congruent hypotenuse and one of their legs are also congruent, then both are congruent by HL theorem of congruence.

Here, both the right triangles are following the condition of the HL theorem.

Hence, the correct option is HL.

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Answer:

27:-3×9

51:-3×17

In 27 and 51 the common one is 3 and hence it is the greatest common factor.✓✓

if you want smallest or lowest common factor then you have to take the common 3 as one and multiply like this:-3×9×17=459 is the Lowest common factor.

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Rewriting the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42 is 7(5 + 6).

The process of factorization simply has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.

The common factor to both 35 and 42 is 7. This will be:

35 + 42 = 7(5 + 6)

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Complete question

How do i rewrite the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42

Answer:

sq root of 21=7

Step-by-step explanation:

we need to use Pythagoras theorem

so distance(isa-jul)^2 +distance(ele-jul)^2= distance(isa-ele)^2

now just do the square root and there you go.

The given statement “if the slope of a line is 3, then the slope of a parallel line is 4” is false because parallel lines have equal slopes

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

Slope of a line = 3

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 3

This means that the slope is 3

The slopes of parallel lines are equal

This means that the slope of the other line is 3

Hence, the statement is false

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Answer:

7.5 units

Step-by-step explanation:

5-(-2.5)=7.5

The conditions of the line to be intersecting, parallel, and coincident are explained below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The types of lines are as follows:

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Answer: 8

Step-by-step explanation:

Im guessing this is your question

Noah's family bought some fruit bars to put in the gift bags. They bought one box each of four flavors: apple, strawberry, blueberry, and peach. The boxes all had the same number of bars. Noah wanted to taste the flavors and ate one bar from each box. There were 28 bars left for the gift bags. Use the tape diagrams to determine how many fruit bars were originally in each box.

Answer:

Step-by-step explanation:

x-5

me bye u see okay later

The compound ratio of natural number ratios 2 : 3 and 5 : 4 is equal to 5 : 6.

Herein we must determine a compound ratio, that is, the product of two ratios, whose definition is shown below:

For a : b and c : d, where a, b, c, d are natural numbers, the compound ratio is equal to (a · c) / (b · d).

If we know that a : b = 2 : 3 and c : d = 5 : 4, then the compound ratio is equal to:

r = (2 · 5) : (3 · 4)

r = 10 : 12

Finally, we simplify the resulting expression:

r = 5 : 6

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Part A

Reason:

Divide the side lengths of B over A to get B/A = 3/5. The order is important. The fraction 3/5 is smaller than 1 to indicate a size reduction. There are no units involved with the scale factor.

=========================================

Part B

Reason:

The linear scale factor is 3/5. The area scale factor is (3/5)^2 = 9/25. It means if figure A had area 25, then figure B would have area 9.

Let's use that idea to set up the following:

(area of figure B)/(area of figure A) = 9/25

B/A = 9/25

x/15 = 9/25

25x = 15*9

25x = 135

x = 135/25

x = 5.4 represents the area of figure B

The minimum is the smallest value in the data set. The maximum is the largest value in the data set.

We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

A minimum or a maximum is called an extreme point. A local extreme point is the smallest or largest value in its neighborhood. If it is also the smallest or largest at the entire domain of the function, it is called a global extreme point. The local minima and maxima can be found by solving f'(x) = 0.

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Complete question is: What is the difference between Minimum or maximum value?

The total number of students in the student body is 110.

Percentage is the ratio of an amount expressed as a number out of 100. The sign that is used to represent percentage is %.

In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.

In order to determine the total number of students in the student body, divide the number of students that watch TV everyday by the given percentage.

Number of students in the student body = number of students that watch TV everyday / percentage

88 / 80%

= 88 / 0.8 = 110

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The probability that the area of the triangle is at most 20 is 5/9

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. Thus area of triangle XYZ is

1/2×12×6=36

Now if the area of the triangle is at most 20 then the required probability is = 20/36

                      =5/9

Hence, The probability that the area of the triangle is at most 20 is 5/9

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First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.

The assumption is equivalent to the following two statements:

(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]

(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]

Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].

On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].

Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.

The expression does not represent next year's population is 0.991. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the population of a city decreases by 0.9% per year. The expression for the population depreciation is,

Population = ( 100% - 0.9%)P

Population = (1 - 0.009)P

Population = 0.991P

Hence, the expression not representing the depreciation is 0.991.

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An equation which has one (1) solution include the following: D. |W| = 0.

In Mathematics, an absolute value function can be defined as a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).

Mathematically, an absolute value function can be represented by this mathematical expression:

|x| = x, x ≥ 0.

|x| = x, x < 0.

Generally speaking, an equation or absolute value function would have exactly one (1) solution when there is only one (1) value for the variable (W) that makes the equation to be true as shown below:

|W| = 0

W = ±0

W = 0

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Answer:

Ah and mc are parallel segments

The expression A' represents the statement for all of the elements which are not in set A.

A set is a collection of well defined objects.

Given that A students wants to write an expression for all of the elements which are not in set A.

The elements within set A are denoted by A.

We have to find  all of the elements which are not in set A.

U represents the universal set and A is the given set.

A'=U-A

Hence, the expression A' represents the statement for all of the elements which are not in set A.

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Answer:

look below!

Step-by-step explanation:

To get the vertex for an equation your best bet is to convert the form into vertex form,which is y=a(x−h)+k . In vertex form (h,k) is the vertex

Each nested cart add to the length of the row is 1.5 feet long.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, the store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

Each row has a starting cart that is 4 feet long, and the nested carts are next to it.  

It is measured that a row of 13 nested carts has a length of 23.5 feet.

Therefore, the original length of 13 nested carts is (23.5 - 4) = 19.5 feet.

So, each nested cart add to the length of the row 19.5/13 =1.5 feet

Again, a row of 18 nested carts to be 31 feet long.

Therefore, the actual added length of 18 nested carts is (31 - 4) = 27 feet.

So, each nested cart add to the length of the row 27/18 =1.5 feet

Therefore, each nested cart add to the length of the row is 1.5 feet long.

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"Your question is incomplete, probably the complete question/missing part is:"

A store is designing the space for rows of nested shopping carts. Each row has a starting cart that is 4 feet long, followed by the nested carts (so 0 nested carts means there's just the starting cart). The store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

How much does each nested cart add to the length of the row?

Answer:

  see below

Step-by-step explanation:

You want the ingredient quantities for several different multiples of the basic recipe.

To fill the table, consider what the column heading is as a multiple of the recipe for 12 people. Use that multiplier for the rest of the numbers in the column.

  [tex]\begin{array}{ccccc}\text{12 people}&\times2&\times3&\times\dfrac{1}{3}&\times\dfrac{1}{2\vphantom{g_g}}\\\cline{1-5}1\text{ cup}&2&3&\dfrac{1\vphantom{b^b}}{3\vphantom{g_g}}&\dfrac{1}{2}\\3\text{ cups}&6&9&1&1\dfrac{1}{2}\\2\text{ cups}&4&6&\dfrac{2}{3\vphantom{_g}}&1\\\dfrac{1}{2}\text{ cup}&1&1\dfrac{1}{2}&\dfrac{1}{6}&\dfrac{1\vphantom{^b}}{4\vphantom{_g}}\\1\dfrac{\vphantom{^b}1}{3}&2\dfrac{2}{3}&4&\dfrac{4}{9}&\dfrac{2}{3}\end{array}[/tex]

Answer:

(a)  13.9 blocks (nearest tenth)

(b)  32.9 blocks (nearest tenth)

Step-by-step explanation:

The given scenario can be modeled as a right triangle.

If Amy walks south 7 blocks, one leg of the triangle is 7.

If Amy then walks west 12 blocks, the other leg of the triangle is 12.

To calculate the number of blocks Amy walks on her way home if she walks directly from school to her home, find the length of the hypotenuse of the right triangle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Substitute a = 7 and b = 12 into Pythagoras Theorem and solve for c (hypotenuse):

[tex]\implies 7^2+12^2=c^2[/tex]

[tex]\implies 49+144=c^2[/tex]

[tex]\implies 193=c^2[/tex]

[tex]\implies c=\sqrt{193}[/tex]

[tex]\implies c=13.8924439894...[/tex]

Therefore, Amy walks 13.9 blocks (nearest tenth) on her way home.

To calculate the number of blocks Amy walks in one day for her round trip to school and back home, sum the side lengths of the right triangle:

[tex]\implies 7 + 12 + 13.9 = 32.9[/tex]

Therefore, Amy walks 32.9 blocks (nearest tenth) in one day for her round trip to school and back home.

The coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:

A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The vertices of the original polygon for this problem are given as follows:

A(-1,-1), B (0, 1), C (2, 2), and D (2, -1).

The scale factor for the dilation in this problem is given as follows:

k = 2.

Hence the coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:

A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).

(as each coordinate of each vertex was multiplied by the scale factor of 2).

The problem is incomplete, hence the coordinates of the vertices of the image after the dilation were obtained to show how the dilation works.

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The distance the treat falls before Lola catches the treat is 3.5 feet.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The distance of the treat from the ground = 5 feet.

The distance the dog jumps to catch the treat from the ground = 1.5 feet.

Now,

The distance the treat fall before Lola catches.

= 5 - 1.5

= 3.5 feet

Thus,

The treat falls for 3.5 feet.

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Answer:

x = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 6[tex]\sqrt{2}[/tex]

This is the exact value for x. It may be rounded if you wish

Answer:

[tex]x=6\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the given values into the cosine trigonometric ratio and solve for x:

[tex]\implies \cos(45^{\circ})=\dfrac{6}{x}[/tex]

[tex]\implies \dfrac{\sqrt{2}}{2}=\dfrac{6}{x}[/tex]

[tex]\implies x\sqrt{2}=6 \cdot 2[/tex]

[tex]\implies x\sqrt{2}=12[/tex]

[tex]\implies x=\dfrac{12}{\sqrt{2}}[/tex]

[tex]\implies x=\dfrac{12}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]\implies x=\dfrac{12\sqrt{2}}{2}[/tex]

[tex]\implies x=6\sqrt{2}[/tex]

Answer:

1/30 of a mile per minute.

Step-by-step explanation:

8/4 = 2 miles per hour.

2/60 = 1/30 of a mile per minute.

Answer:

−12r+32−2r 2

Step-by-step explanation:

(−8−r)(2r−4)

Apply the distributive property by multiplying each term of −8−r by each term of 2r−4.

−16r+32−2r

2

+4r

Combine −16r and 4r to get −12r.

Answer:

R-12

Step-by-step explanation:

Open the parenthesis, then solve

-8-r + 2r-4

-r+2r-8-4

r-12

Your answer will be R-12