A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,240 ft Determine the​ flag's width and length if the length is 460 ft greater than the width.

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.

a. The area of the parallelogram ABCD in this problem is given as follows: 24 units squared.

b. The fraction of the area of the parallelogram that is shaded is given as follows: 1/4. (option C).

The area of a parallelogram is given by the multiplication of the length of the base by the height, as follows:

Area = base x height.

The base and the height for this problem are obtained counting the number of dots, hence:

Hence the area is given as follows:

Area = 4 x 6

Area = 24 units squared.

The shaded region is composed by a triangle with base 4 and height 3, hence:

Area shaded = 0.5 x 4 x 3 = 6 units squared.

(formula for the area of the triangle).

Meaning that the fraction is given as follows:

6/24 = 1/4.

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Answer:

Step-by-step explanation:

the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.

Answer:

it is undefined

Step-by-step explanation:

Slope of the line x=-24 is undefined. We'll compare the line x = -24, with x = h. So this line is a vertical line that is parallel to the y-axis. We know that the slope of the y-axis is undefined. Since x=-24 and y-axis are parallel, so x=-24 will have the same slope, that is undefined.

Answer:

undefined slope

Step-by-step explanation:

When you have the line x=-24, you have a vertical line, where the x-value is constant, given in the equation, but the y-value varies between negative infinity and positive infinity. If we were to plug two points into the slope formula, we would get: [tex]\frac{y_2-y_1}{-24-(-24)}\to\frac{y_2-y_1}{0}[/tex], because there is no change in x, the x values are the same. Thus it is said that the slope is undefined.

D. mz1 = 45° and mz2 = 45 are complementary angles (mz1 + mz2 = 90°), but neither angle is obtuse (greater than 90°), so the guess is wrong. This is a counter-example to show.

A supplementary angle is an angle where the sum of two angles is 90 degrees. That is, if angle A and angle B are complementary, angle A measurement + angle B measurement = 90 degrees. Supplementary angles may be adjacent (having a common vertex and edge) or non-adjacent (having no common vertex or edge), but they always complement each other.

There are various kinds of angles to study.

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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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Answer:

-3/4

Step-by-step explanation:

y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.

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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Length of fence = Circumference of the pool – width of the gate. Length of fence = 6.28x – 150 cm.

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There are 34 ways by which  pairs of potential clients can be randomly chosen from pool or eight candidates.

We can be able to talk about the combination when the order of the selection is not seen as important as in the case that we have in the question here. We have been told that the pairs are to be chosen randomly.

As such we would have the use of the formula for combination as follows;

C = n!/r!( n - r)!

C = 8!/2!(8 - 2)!

C = 8 * 7 * 6!/2! 61

C = 8 * 7/ 2 * 1

C = 28

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The values of a , b and c from the equation is ( 3 , 0 , -1 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

( 6 × 10ᵃ ) + ( 6 × 10ᵇ ) + ( 6 × 10^c ) = 6006.6   be equation (1)

Now , the number 6006.6 is written as

6000 + 6 + 0.6 = 6006.6

On simplifying the equation , we get

( 6 × 10ᵃ ) = 6000

Divide by 6 on both sides of the equation , we get

10ᵃ = 1000

So , 10ᵃ = 10³

Therefore , the value of a = 3

Now , ( 6 × 10ᵇ ) = 6

Divide by 6 on both sides of the equation , we get

10ᵇ = 1

when b = 0

10⁰ = 1

Therefore , the value of b = 0

Now , ( 6 × 10^c ) = 0.6

Divide by 6 on both sides of the equation , we get

10^c = 0.1

when c = -1

10⁻¹ = 0.1

Therefore , the value of c = -1

Hence , the value of a , b and c is 3 , 0 and -1 respectively

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Step-by-step explanation: 1 is in the ten thousand places and has a place value of 10,000. 3 is in the thousand's place and has a place value of 3,000. 5 is in the hundreds and has a place value of 500.

Answer:

Step-by-step explanation:

X+X+X+Y+Y=

you simply count equal letters and add them x+x+x is 3x and y + y = 2y.

x + x + x + y + y =

3x + 2y

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 end behavior of the function f(x) = 1/9 x¹² is

The end behavior of the function f(x) = -1/10 x¹⁸ is

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = 1/9 x¹²

The positive exponents will mean that x will always yield positive values hence f(x) is always positive

f(x) = -1/10 x¹⁸

The positive exponents will mean that x will always yield positive values however the negative constant -1/10 will make f(x) always negative hence f(x) is always negative

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Answer: 5. 2x+8  6. 5(x-9)   7. -3x+-21

Step-by-step explanation: Multiply the number outside the parenthesis by everything inside it

Answer: The equation of a line in the form y = mx + b can be written as y - mx - b = 0. So we can rewrite the equation of the line as 2y - 3x + 5 = 0. This means that the slope of the line is -3/2.

The slope of a line perpendicular to this line would be the negative reciprocal of -3/2, which is 2/3. Let's call the point M (x, y). We know that the line passing through (2, 6) has a slope of 2/3. So we can write the equation of this line as:

y - (2/3)x - b = 0

Substituting the point (2, 6) into this equation, we get:

6 - (2/3)(2) - b = 0

b = 4

So the equation of the line passing through (2, 6) is:

y - (2/3)x - 4 = 0

To find the coordinates of point M, we need to find the point where these two lines intersect. Setting the two equations equal to each other and solving for x and y, we get:

2y - 3x + 5 = y - (2/3)x - 4

5 - 2y = y - (5/3)x + 4

(5/3)x = 3 - y

x = (3 - y) * (3/5)

Substituting this expression for x into one of the original equations, we can solve for y:

2y - 3((3 - y) * (3/5)) + 5 = 0

2y - (9 - 3y)(3/5) + 5 = 0

(10/5)y - (9/5) + 5 = 0

y = (9/5) + (5/5)

y = 2

Substituting this value for y back into the expression for x, we get:

x = (3 - 2) * (3/5)

x = 1

So the coordinates of point M are (1, 2).

Step-by-step explanation:

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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The solution to the product expression 4/3 * 5/3 is 20/9

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

The product 4/3*5/3

To start with, we need to represent the statement as an expression

So, we have the following representation

4/3 * 5/3

Using a calculator, we multiply the numerator

So, we have the following representation

4/3 * 5/3 = 20/3 * 1/3

Using a calculator, we multiply the denominator

So, we have the following representation

4/3 * 5/3 = 20/9

Hence, the solution is 20/9

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Answer:

Step-by-step explanation:

the answer is 6

Answer: The ratio 18:26 simplified is 9:13.

Step-by-step explanation:

To simplify the ratio 18:26, we find the greatest common divisor of 18 and 26, and then we divide 18 and 26 by the greatest common divisor.

The greatest common divisor that you can use to simplify 18:26 is 2. Which means the answer to ratio 18:26 simplified is: 9:13

Answer:9/13

explanation: k12

Answer: y = -150x + 1800

Step-by-step explanation:

1. Find the linear slope of the line between two points.

(Change in Y)/(Change in X)

2. Write out an equation in point slope form.

(y-y1) = m(x-x1)

y-1800 = -150(x-0)

3. Simplify the equation and turn it into slope-intercept form.

y = -150x + 1800

It will take roughly 15.7 months to drop in value to less than £1200 if the current value of the bike is £2550.

You can use the following formula to calculate how many months it will take for a motorbike with a value of £2550 value to drop to under £1200:

n = (1200 - 2550) ln / ln (1 - 0.05)

Where 0.05 denotes the 5% monthly depreciation rate, ln is indeed the natural logarithm function, and n refers to the number of months.

When we enter the values, we will get:

n = (1200 - 2550 - 1 - 0.05) / ln(1 - 0.05) = about 15.7 months

The motorcycle will take approximately 15.7 months to drop in value to less than £1200.

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The relative frequency table that summarizes the data is given by the image at the end of the answer.

The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.

Given:

The percentage of people interested in waterskiing

= 90/250 x 100

= 36%.

Thus, the percentage of people that was not interested in waterskiing is

=100-36

= 64%

Now, the percentages related to paddle boarding are :

Yes: 72/250 = 28.8%.

No: 18/250 = 7.2%.

Of those not interested in waterskiing, the percentages related to paddle boarding are

Yes: 112/250 = 44.8%.

No: (120 - 72)/250 = 19.2%.

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Answer:

Step-by-step explanation:

LHS = tanθ/secθ - 1 + tanθ/secθ + 1

Cross multiplication,

tanθ(1 - secθ) - tanθ(1 + secθ)/1 + sec^2θ

= tanθ(1 - secθ - 1 - secθ)/-tan^2θ

= -2secθ/-tanθ

= 2 x 1/cosθ / sinθ/cosθ

= 2cosecθ = RHS

Hence proved.

The ratio of number of burgers without onions to the number of burgers with onions is 4:1.

The ratio of numbers implies the relationship between the numbers when expressed in its simplest fraction. The relationship can be written in form of a/ b or a:b.

Given in the question that Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. Then the ratio required can be expressed as;

ratio of number of burgers without onions to burgers with onions = (number of burgers without onions)/ (number of burgers with onions)

                = 12/ 3

                = 4/ 1

The ratio of number of burgers without onions to burgers with onions = 4:1

Therefore, the ratio of the number of burgers without onions to the number of burgers with onions is 4:1.

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