Use the parallelogram to find m
m

There are 28 ways of choosing three points from the grid below, so that they form an isosceles right triangle.

A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.

The grid figure is given in the attached image.

The given image displays seven triangles (counting the original 2).

There can be 7 x 4 = 28 isosceles right triangles,

since each has degree 4 rotational symmetry around the figure's center.

The complete figure is given in the image.

Therefore, there are 28 ways of choosing three points from the grid below.

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Similarity is the mathematical property of triangles. Two triangles are called similar if they fulfil wither of the properties: Angle Angle, wherein two angles should be congruent; Side Angle Side, wherein two sides are similar to each other and the angles congruent to each other; and Side Side Side, wherein three sides are similar to each other in ratio.

The triangle ABC and triangle EDF are similar.

The first property is angle,

∠BAC = ∠EDF = 65°

The second property is also angle.

∠ABC = ∠DEF = 48° (∠DEF = 180 - 65 - 67)

Thus, the three angles are same or congruent.

The AA property of similarity makes the two triangles ABC and DEF similar. The option 1 is correct.

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The obvious conclusion from this question is that. C. if you are not a baby, then you are not despised.

Logic can be defined as the study of rational thinking. It contains both formal and informal logic. Deductively sound inferences or logical truths are studied in formal logic. It is a formal science that examines the topic-neutral ways in which conclusions flow from premises. As opposed to informal logic, which is connected to argumentation theory, critical thinking, and informal fallacies, formal logic is a branch of logic.

Philosophy, mathematics, computer science, and linguistics are just a few of the disciplines where logic is crucial. A set of premises and a conclusion make up an argument, which is the subject of logic. Arguments can be proven right or wrong. If the premises of an argument support the conclusion, then it is valid.

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The mental math for the fraction is shown below.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Model: 1 1/4 + 2 1/3 + 3 2/3 + 4 1/2 + 5 1/2 + 6 3/4

Now, if we use mental math then we can add the whole number first.

1 + 2 + 3 + 4 + 5 + 6 = 21

Now, add the fraction with same denominator

1/3 + 2/3 = 3/3 = 1

1/2 + 1/2 = 1

1/4 + 3/4 = 4/4 = 1

Finally add all of them

21 + 1+ 1 +1= 24.

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Answer:

In order to find when the two trains will meet up, we can use the concept of relative speed. The relative speed of two trains is the sum of their individual speeds.

In this case, the relative speed is 30 + 50 = 80km/h

Since we know that the distance between London and Bristol is 100km, we can divide the distance by the relative speed to find the time it takes for the two trains to meet up:

100km / 80km/h = 1.25 hours

So, the two trains will meet up in 1.25 hours

Answer:

1 hour 15 minutes

Step-by-step explanation:

Relative Speed

If the two objects are moving in the opposite direction at different speeds, relative speed is the sum of their two speeds:

Using the formula:

[tex]\boxed{\sf Time=\dfrac{Distance}{Speed}}[/tex]

Therefore:

[tex]t=\dfrac{d}{v_1+v_2}[/tex]

where:

Given:

Substitute the given values into the formula to find the time at which the two trains meet:

[tex]\implies t=\dfrac{100}{30+50}=\dfrac{100}{80}=1.25\; \sf hours=1\; hour\;15\;mins[/tex]

Therefore, the two trains meet at 1 hour 15 minutes.

Considering the context of the question and the percentage analysis, it is concluded that a 38.64% charge has been hiked in the price of the ticket and if the extra $50 is charged for the baggage fee the hike is 61.36%.

A percentage is a number or ratio indicated as a fraction of 100. To get the percentage of any number, such number will be divided by the number of the whole and multiplied by 100. Hence, the percentage means, a part per hundred

In this case, Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $220. Now the cost is $305

Hike in price = 305 - 220 = 85

Hike % = 85/220 * 100% = 38.64%

When the extra charge is $50 for extra baggage, the total price = is $355

Hike in price = 355 - 220 = 135

Hike % = 135/220 *100% = 61.36%

Hence, in this case, it is concluded that a 38.64% charge has been hiked in the price of the ticket and if the extra $50 is charged for the baggage fee the hike is 61.36%

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= 4a + 4b

Answer:

[tex] \sf \: 4a + 4b [/tex]

Step-by-step explanation:

Given expression,

→ 4(a + b)

Let's simplify the expression,

→ 4(a + b)

→ 4(a) + 4(b)

→ (4 × a) + (4 × b)

→ 4a + 4b

Hence, the answer is 4a + 4b.

Answer: An equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:

y = -4x + 20

Step-by-step explanation:

The given equation is in slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line is 2, which means the line has a slope of 2 and is inclined at an angle of tan^-1(2).

To find an equation of a line that is perpendicular to this line, we need to find the negative reciprocal of the slope, which is -1/2. This means the slope of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is -1/2.

Now we can use the point-slope form of a linear equation to find the equation of the line passing through point P(-6, 4) and having a slope of -1/2. The point-slope form of a linear equation is:

y - y1 = m(x - x1)

Where (x1, y1) is the given point, and m is the slope of the line. So by substituting the values we get:

y - 4 = -1/2(x + 6)

Which can be written as:

y = -1/2x + 4

So the equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:

y = -1/2x + 4

Graphing the equations can confirm that the lines are perpendicular as the slope of the first line is 2 and the slope of the second line is -1/2, the product of these slopes is -1 which means they are perpendicular to each other.

Answer: Your answer is 1/3(b-21), aka the first answer slot

Step-by-step explanation: If we factor 1/3b-7, the common factor is 1/3. by this knowledge, we put 1/3(b-7/1/3), and 7/1/3 = 7x3 which is 21. So we simplify and get the answer
1/3(b-21)

Using the given information, the value of the number is 12

From the question, we are to determine the value of the number.

From the given information, we have that
"7 more than twice a number is 5 less than three times the same number"

Let the number be x

7 more than twice a number means

2x + 7

5 less than three times the number is

3x - 5

Thus,

The equation becomes

2x + 7 = 3x - 5

Now, solve for x

2x + 7 = 3x - 5

7 + 5 = 3x - 2x

12 = x

x = 12

Hence, the value of the number is 12

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Answer:

2

Step-by-step explanation:

To find the approximate annual growth rate of the stock, we can use the formula for compound annual growth rate (CAGR):

CAGR = (Ending value / Beginning value)^(1/n) - 1

Where n is the number of years.

In this case, the beginning value is $2545.30, the ending value is $4152.57 and the number of years is 6.

So, CAGR = (4152.57 / 2545.30)^(1/6) - 1

The CAGR is approximately 26.8% which is the answer 2.

Answer:

[tex]tan(A)=\frac{5}{12}[/tex]

[tex]\frac{5}{12}[/tex]

Step-by-step explanation:

The TAN function can be expressed as [tex]tan(x)=\frac{Opp}{Adj}[/tex].

The side opposite to angle A is 15

The side adjacent to angle A is 36.

Therefore

[tex]tan(A)=\frac{15}{36}[/tex]

We can simplify the fraction.

Factor 3 out of 15.

[tex]\frac{3(5)}{36}[/tex]

Factor 3 out of 36.

[tex]\frac{3(5)}{3(12)}[/tex]

Cancel the common factor of 3.

[tex]\frac{5}{12}[/tex]

Answer:

tan(A)=\frac{5}{12}tan(A)=

12

5

\frac{5}{12}

12

5

Step-by-step explanation:

The TAN function can be expressed as tan(x)=\frac{Opp}{Adj}tan(x)=

Adj

Opp

.

The side opposite to angle A is 15

The side adjacent to angle A is 36.

Therefore

tan(A)=\frac{15}{36}tan(A)=

36

15

We can simplify the fraction.

Factor 3 out of 15.

\frac{3(5)}{36}

36

3(5)

Factor 3 out of 36.

\frac{3(5)}{3(12)}

3(12)

3(5)

Cancel the common factor of 3.

\frac{5}{12}

12

5

Answer:

To find out how many batches of cookies the factory made, we need to divide the total amount of flour used (7 1/2 bags) by the amount of flour used per batch (3 3/4 bags).

We can start by converting 7 1/2 bags of flour to a mixed number: 7 1/2 bags = 7 + 1/2 = 7.5 bags

Next, we can convert 3 3/4 bags of flour to a mixed number: 3 3/4 = 3 + 3/4 = 3.75 bags

Then, we can divide the total amount of flour used by the amount of flour used per batch:

7.5 bags / 3.75 bags/batch = 2 batches

Therefore, the factory made 2 batches of cookies yesterday

Answer:

89.102 dollar

Step-by-step explanation:

let x be the total amount of bill

77.48 ×15% =11.622

11.622 is the additional tip

x=original cost +additional tip

=77.48+11.622

=89.102 dollar

Answer:

The third option.

Step-by-step explanation:

Lets write the length as L and the width as W.

Given, L = W - 4

or L - W = - 4

Perimeter of a rectangle = 2( L + W)

44 = 2 (L + W)

L + W = 22

L - W = -4

2L = 18 (adding the two equations)

L = 9

W = 13

So, the answer is the third option.

Cheers

The perimeter of the figure, is represented by the expression, 14x + 16.

The perimeter of a figure is the total length of the outer boundaries of the figure. It is the sum of all the sides of the figure.

The perimeter is used to determine the size of a figure and can be calculated by adding the lengths of all the sides together.

Therefore:

Perimeter of the figure = 4(2x - 1) + 2(3x + 10)

To simplify the expression 4(2x - 1) + 2(3x + 10), we can distribute the constants (4 and 2) to the expressions inside the parentheses.

First, we'll simplify 4(2x - 1) using the distributive property:

4(2x - 1) = 4(2x) + 4(-1) = 8x - 4

Next, we'll simplify 2(3x + 10) using the distributive property:

2(3x + 10) = 2(3x) + 2(10) = 6x + 20

Now we can add the two simplified expressions together:

8x - 4 + 6x + 20 = 14x + 16

So, the simplified form of 4(2x - 1) + 2(3x + 10) is 14x + 16.

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Therefore , as a result, the answer to the given function problem is that the  f(x) = y  = - |x-4 | represents the given points.

Mathematics encompasses a wide range of topics, including the study of numbers and their variations, equations and related structures, as well as the limits and potential uses of geometry. A "useful" is the connection between several inputs that together produce a particular output. A functional is an output-input relationship where each input yields a single, easily recognisable output. Every technique has both a territory, often known as a domain, and a city .

Here,

Given : (6,1)  and (-6,-5)

We need to choose which of the four potential functions corresponds to the graph; we have such a graph & four possible functions.

From putting the points in the below function f(x) , we get it represents the given points.

As a result, the essential task would be:

=>  y  = - |x-4 |

=> f(x) = y  = - |x-4 |

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The study of choices people make to fulfill their unlimited needs and want even though there are limited resources is called Economics. Thus option A is correct.

Resources can be defined as the means through which the material is provided to people. This will be to know that the resources are properly allocated.

An economy is a region where products and services are produced, distributed, traded, and consumed. a social domain that places an emphasis on production-related practices, discourses, and material expressions. The factors that affect production, such as land, cash, labor, and natural facilities, are governed by economic structures.

Therefore, option A is the correct option.

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The result of the expression 3(x + 2)² - 4 is equivalent to 44.

        [tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]

Given is the equation as -

(x + 2) = 4

We have to find the result of -

3(x + 2)² = 4

It is given that -

(x + 2) = 4

So, we can write -

3 x 4 x 4 = 4

48 - 4

44

Therefore, the result of the expression 3(x + 2)² - 4 is equivalent to 44.

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{Question in english -

If (x+2)=4 what is the result of 3(x+2)^2=4}

The probability of a measure less than 78 pounds is given as follows:

0.9452 = 94.52%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 70, \sigma = 5[/tex]

The probability of a weight less than 78 pounds is the p-value of Z when X = 70, hence:

Z = (78 - 70)/5

Z = 1.6

Z = 1.6 has a p-value of 0.9452.

The mean and the standard deviation of the distribution are given as follows:

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Answer: Cannot be determined from graph

Step-by-step explanation:

The number of three digit number formed are-

Repetition allowed = 125

Repetition not allowed = 60

A combination is an algebraic technique for determining the number of distinct arrangements in a set of items in which the sequence of the selection is irrelevant.

here, we have,

You can choose the items in either order in combinations. Permutations and combinations are often confused.

For the given question;

The three digit number is to be formed.

The digits are given as-  1,2,6,7,8

Case 1: Repetition allowed

The number of combination will be;

= 5×5×5

= 125

Thus, the number of three digit number formed with repetition is 125.

Case 2: Repetition not allowed

The number of combination will be;

= 5×4×3

= 60

Thus, the number of three digit number formed with without repetition is 125.

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Answer:

cos X = 3/5

Step-by-step explanation:

Cosine is a ratio. The side (leg) adjacent to Angle X is the side (leg) next to the angle. The hypotenuse is the longest side.

Cosine is the ratio of the Adjacent side /Hypotenuse.

In this image,

cos X = adj/hyp

cos X = 15/25

cos X = 3/5

cos X = 3/5

(Like the weird wording in the question:

3 fifths)

Answer:

Step-by-step explanation:

Let x be the amount invested in the 6% account.

Since he invested twice as much in the lower-yielding account, the amount invested in the 10% account is 2x.

We know that the annual interest is $3080 dollars, and the interest is calculated on the invested amount at each rate.

The interest in the 6% account is (6/100) * x = 3/50 * x

The interest in the 10% account is (10/100) * 2x = 1/10 * 2x

The total annual interest is 3/50x + 1/102x = 3/50x + 1/5x = (3+1)/5x = 4/5x

Therefore, we can write the equation:

4/5*x = 3080

To find x, we can divide both sides by 4/5:

x = 3080*5/4

x = $2310

So, the man invested $2310 in the 6% account and $2310*2 = $4620 in the 10% account.

Answer:

it is 4

Step-by-step explanation:

the slope is always the number before x and so since 4 is before x then 4 is the answer

Answer: -4/5

Step-by-step explanation:

(0,2) and (4,-3) are two coordinates here.

Using the slope formula, i.e, m = (y₂ - y₁)/(x₂ - x₁) = 4/-5 = -4/5

The equation of a line is 3y+2x+59.

When we have given one point and slope we can write the equation as

y-y1=m(x-x1)

here x1=-11,y1=-13,m=-2/3

y+11=-2/3(x+13)

=3y+2x+59

The equation becomes =3y+2x+59.

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Answer: 485.14 cm^2 (rounded)

Step-by-step explanation: Pi * Diameter = 78.06 -> 78.06/ 3.14 or Pi = radius or 12.429. That squared is 154.5. Then multiply it by Pi to get the answer.

Grayson can spend a maximum of 3 hours, h, watching television on the weekend, and is shown in the number line.

Numbers on a straight line are represented graphically as a number line. For comparing and sorting numbers, it serves as a reference. Including all whole numbers and natural numbers, it can be used to represent any real number.

Just to refresh your memory, the natural number is the collection of all counting numbers, i.e. 1, 2, 3, 4, 5, 6, while the whole number is a set of numbers that includes both zero (0) and all counting numbers.

Compare numbers more easily by writing them on a number line. The integers in the above figure are smaller on the left than they are on the right, as can be seen.

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Grayson is only permitted to watch television for a total of three hours on the weekends. 8-10. 5-5, 5-6 7.5-6

[Time = Distance Speed] is the formula for calculating time. The time formula can be changed to [Distance = Speed Time] to compute distance. Find the vertex of the parabola given a generalised quadratic function. Find a, b, and c. By changing a and b into h=-b2a, you can determine h, the vertex's x-coordinate. By evaluating k=f(h)=f(b2a), you may determine k, the vertex's y-coordinate.

In order to get the vertex (h, k) of the given quadratic y = ax2 + bx + c, one must first compute h= b 2 a h=2ab 2a, and then one must evaluate y at h in order to determine k. The speed equation is speed=distance*time. According to the currently accepted definition of the kilogramme, it reads as follows: "The kilogramme is defined by considering the fixed numerical value of h to be 6.62607015 unit Js,"

The fact is [tex]$3 \geqslant h \geqslant 0$[/tex]

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Answer:The most general form of a polynomial function of degree n that has real coefficients is:

f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0

where a_n, a_{n-1}, ..., a_1, a_0 are real numbers, and a_n is not equal to zero.

The number of distinct roots of a polynomial function of degree n can be determined using the fundamental theorem of algebra, which states that a polynomial function of degree n has exactly n roots, counting multiplicities. This means that a polynomial function of degree n can have n distinct roots, n-1 distinct roots, or any integer value in between, depending on the multiplicities of the roots.

Using the factor theorem, it is possible to determine the number of distinct roots of a polynomial function by factoring it into its irreducible factors. If the polynomial function is fully factored, the number of distinct roots is equal to the number of irreducible factors.

However, the nature of the roots (real or complex) and constraints imposed by the discriminant are also important to consider. The discriminant of a polynomial function is the value of the expression b^2-4ac, where a, b, and c are the coefficients of the polynomial function in the form f(x) = ax^2+bx+c. The discriminant determines the nature of the roots of the polynomial function. If the discriminant is positive, the roots are real and distinct. If the discriminant is zero, the roots are real and repeated. If the discriminant is negative, the roots are complex and non-real.

So, the most general form of a polynomial function of degree n that has real coefficients, can be determined by the form of the polynomial, the number of distinct roots by the fundamental theorem of algebra, by factoring the polynomial into its irreducible factors and the nature of the roots is determined by the discriminant.

Step-by-step explanation: