Why are the two triangles congruent?

Answer:

y = 3x + 2

Step-by-step explanation:

1. Work out the gradient of the line segment: change in y/change in x: -2 - -6/ -8 - 4 = 4/-12 = -1/3

2. Work out the gradient of the perpendicular bisector: the gradient of the line segment and the perpendicular bisector should multiply to get -1. This means that we can do -1 ÷ -1/3 to work out the gradient which is 3

4. Find the midpoint of the line segment: (-8 + 4) ÷ 2 = -2, and (-2 + -6) ÷ 2 = -4, so the midpoint is (-2, -4)

3. The equation will be in the format y = 3x + c and will go through (-2, -4), so we can substitute those values into the equation to find c:

The equation of the line is y = 3x + 2

Hope this helps!

Answer:

$180

Step-by-step explanation:

20*5=100

36*5=180

Answer: the cost of the bicycle is 180$

Step-by-step explanation:

If Juanita has saved 20% of the money she needs to buy a new bicycle and she has saved $36, we can calculate the cost of the bicycle using the following formula:

(100% - 20%) x cost of bicycle = $36

To find the cost of the bicycle, we can divide both sides of the equation by 80% (100% - 20%), like this:

cost of bicycle = $36 / (100% - 20%)

We know that Juanita has saved $36 and the percentage saved is 20% , so the cost of the bicycle is $180

Mr. Karbon 1,14,05,52,000 times has his heart been beating during his life.

Adults typically have a resting heart rate between 60 and 100 beats per minute. A lower resting heart rate typically indicates improved cardiovascular fitness and more effective cardiac function. A well-trained athlete, for instance, might have a typical resting heart rate that is closer to 40 beats per minute.

Based on your age, you may calculate your maximum heart rate. Subtract your age from 220 to get a ballpark idea of your maximal age-related heart rate. For instance, the predicted maximum age-related heart rate for a 50-year-old person would be computed as 220 - 50 years = 170 beats per minute (bpm).

There are total 60 minutes in an hour,

1440 minutes in a day,

There are 365 days in a year,

and Mr. Karbon has lived for 35 years.

his heart beats on average 62 beats per minute.

His heart has beaten for 35 × 365 × 1440 × 62

1,14,05,52,000 times has his heart been beating during his life.

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The ratio 5:73 represents A. The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Number of 8th grade baseball players = 5

Total number of athletes = 73

Therefore the ratio will be:

= 5 / 73

= 5:73.

The correct option is A

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The geometric mean return of the given data set is 0.02.

The geometric mean return measures the compound rate of return over a period of time. It is calculated by taking the product of all the returns and then taking the nth root of the product, where n is the number of returns.

Formula: GMR = ((1+r1)(1+r2)…(1+rn))^1/n – 1

In this case, the data set is as follows:

r1 = 0.05

r2 = 0.03

r3 = -0.02

Using the formula above, the geometric mean return is calculated as:

GMR = ((1+0.05)(1+0.03)(1-0.02))^1/3 - 1

GMR = ((1.05)(1.03)(0.98))^1/3 - 1

GMR = (1.1394)^1/3 - 1

GMR = 0.0204

Therefore, the geometric mean return of the given data set is 0.02.

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Round to the nearest tenth , if necessary the value of x is 11.5.

What is right triangle ?

A right triangle is a type of triangle in which one angle is equal to 90 degrees. The side opposite this 90-degree angle is known as the hypotenuse, and the other two sides are known as the legs. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles.

Triangle ABC is a right angle triangle,

We can apply the Pythagorean Theorem to get,

[tex]x^{2} +8^{2} = 14^{2} \\x^{2} = 14^{2}-8^{2} \\x^{2} = 196-64\\x^{2} =132[/tex]

x ≈ 11.5

So , Round to the nearest tenth , if necessary the value of x is 11.5.

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Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.

Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

What is the uses of latitude?

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

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The value of x in the triangle is 38 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

The exterior angle theorem can be used to find the angle x in the triangle.

Hence,

x + (180 - 84) = 134

x + 96 = 134

subtract 96 from both sides of the equation

x = 134 - 96

Therefore,

x = 38 degrees

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Answer: x=38

Step-by-step explanation:

x=38

Answer:

77.3

Step-by-step explanation:

Cos = Adjacent/Hypotenuse

Adjacent = 2.25 & Hypotenuse = 10.25

So that means...

Cos = 2.25/10.25

*When you type in the calculator type Cos-1 (2.25/10.25).

The answer is 77.319....

When you round it, it would become 77.3°.

Hope it's helpful.

To find the acute angle of each angle in a triangle if the given angles are in the form of an equation follow the steps in the main answer part

To find the acute angles of a triangle given the angles in the form of an equation, you can use the following steps:

Example: Let's say you are given an equation,

A+B+C = 180°

If

A = 70°

B = 70° then

C = 40°

C is not acute, so subtract it from 180° to get C= 140°

Now you have A = 70° and C = 140° which are acute angles.

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The simplified expression of the radical is √10/3

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

the square root of 40 and then divide by 6

This statement can be mathematically represented as

√40/6

Simplify the numerator

So, we have the following representation

2√10/6

Divide 2 and 6

√10/3

Hence, the solution is √10/3

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Answer:

Product 1, because the function is exponential

Step-by-step explanation:

An exponential function, such as f(x) = 3^x, grows very quickly.

Answer: Product 1, because the function is exponential

Answer:

-8/4 or -2

Step-by-step explanation:

First of all notice the graph is negative. Meaning that this will be a negative slope.

Now we can use rise over run, counting up 8 spaces, and to the left 4.

Since the graph is negative make the rise negative. -8/4.

To simplify this fraction divide -8 by 4, and receive an answer of -2.

-Hope this helped

For what value of k = -48 the equation 3x 8y 0 and 6x Ky =- 16 represent coincident lines.

The equation 3x + 8y = 0 and 6x + Ky = -16 represent coincident lines when the two lines are identical, or when their slope and y-intercept are the same.

To find the value of k for which this is true, we can set the two equations equal to each other and solve for k.

3x + 8y = 0

6x + Ky = -16

The equation 3x + 8y = 0 represents the slope-intercept form of a line, where the slope is -3/8 and the y-intercept is 0.

The equation 6x + Ky = -16 represents the general form of a line, where the slope is -K/6 and the y-intercept is -16/K.

To find the value of k for which the two lines are identical, we need to make the slopes and y-intercepts equal.

-3/8 = -K/6

0 = -16/K

Solving for K, we get:

K = -48

So the lines are coincident when K = -48

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Scale is represented as a ratio, such as 1:100. A drawing with a scale of 1:100 indicates that the thing is 100 times smaller than it would be in real life. You may also remark that one unit in the illustration equals one hundred units in real life.

Enlarging scale indicates that the drawing is made with larger dimensions than the real dimensions of the thing. A representative proportion of 1:0.2 equals 5:1, implying that the depiction is five times larger than the actual thing. As a result, the scale is increasing in size.

On November 28, 2022, it was revised. A ratio scale is a quantitative scale with a real zero and equal gaps between nearby points. In contrast to an interval scale, a zero on a ratio scale indicates that the variable being measured is completely absent. Ratio scales include things like length, area, and population.

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Scale is represented as a ratio, such as 1:100. A drawing with a scale of 1:100 indicates that the thing is 100 times smaller than it would be in real life. You may also remark that one unit in the illustration equals one hundred units in real life.

Enlarging scale indicates that the drawing is made with larger dimensions than the real dimensions of the thing. A representative proportion of 1:0.2 equals 5:1, implying that the depiction is five times larger than the actual thing. As a result, the scale is increasing in size.

On November 28, 2022, it was revised. A ratio scale is a quantitative scale with a real zero and equal gaps between nearby points. In contrast to an interval scale, a zero on a ratio scale indicates that the variable being measured is completely absent. Ratio scales include things like length, area, and population.

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The equation of the line in slope intercept form is y = -4x + 1.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Intercept of a line is the point where the line touches with one of the axis.

The general equation of a line in slope intercept form is,

y = mx + d, where m is the slope and d is the y intercept.

y intercept point touches the y axis.

Take any two points from the line.

Let it be (0, 1) and (-1, 5).

Slope = (5 - 1) / (-1 - 0) = 4 / (-1) = -4

m = -4

We have the point (0, 1), where the line touches the Y axis.

y intercept, d = 1.

Equation of the line is,

y = -4x + 1

Hence the equation of the line is y = -4x + 1, when slope is -4 and y intercept is 1.

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The dilation transformation is determined by the scale factor and the centre of dilation. The image stretches when the scaling factor exceeds 1. When the scale factor is between 0 and 1, the image gets smaller.

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The dilation transformation is determined by the scale factor and the center of dilation. The image stretches when the scaling factor exceeds 1. When the scale factor is between 0 and 1, the image gets smaller.

Ratio of scale (Dilation) How much larger or smaller the image will be depends on the scale factor in a mathematical object's dilatation (compared to the original object). When the scaling factor's absolute value exceeds 1, an expansion takes place.

The x and y values of each point will be multiplied by 2 to enlarge the graphic by a factor of 2. To identify the new triangle, I plotted each new point. The x-value of each point will be multiplied by 2 to enlarge the image by a factor of two.

A scale factor is defined as the ratio of an original object's scale to that of a new, smaller version of the original object.

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The equation for a slope of -2/3 and an intercept of -4 is 2x+3y+12=0.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

y=mx+b

m=-2/3

b=-4

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

y=-2x/3-4

3y=-2x-12

2x+3y+12=0

The equation for slope given as -2/3 and intercept as -4 is 2x+3y+12=0.

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There are 720 people (60 percent) attended a music festival on Friday night in Dawson Christian Academy.

A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages. Additionally, you can indicate them by adding "percent" or "pct" after the number.

Given that Dawson Christian Academy have people to attend a music festival is 1200

out of these people to attend a music festival on friday is 60%

No. of people to attend a music festival on friday is 60% of 1200

⇒ (60/100)*1200

⇒ 0.60*1200

⇒ 720 people

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an appropriate follow-up quetion to ak thi tudent is the culture

M. Nichol’ cla i having a dicuion about Greek mythology.. She i the godde of the harvet a well a the cycle of life.

What is the follow-up question to be asked?

M. There are four basic theories of myth. Those theories are: the rational myth theory, functional myth theory, structural myth theory, and the psychological myth theory.. Nichol’ cla i having a dicuion about Greek mythology.

What are the 3 biggest Greek gods?

Especially the “big three”. Zeus, Poseidon, and Hades.

an appropriate follow-up quetion to ak thi tudent is the culture

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The coordinate of the point that partitions the line segment is; (-4, 15)

We are given the line DC with coordinates as;

C(-10, 6) and D(-2, 18)

Now the formula to find the coordinates of a partitioned line segment in the ratio a:b is;

(x, y) = (bx₁ + ax₂)/(a + b), (by₁ + ay₂)/(a + b)

From the ratio given to us, we can say that a = 1 and b = 3. Thus;

(x, y) = ((3*-2) + (1*-10))/(1 + 3), ((3*18) + (1*6))/(1 + 3)

(x, y) = (-16/4), (60/4)

(x, y) = (-4, 15)

This is the coordinate of the point that partitions the line segment.

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The value of x is 16 units.

we know that

If two triangles are similar, then the ratio of their corresponding sides is equal and is called the scale factor.

According to the question,

The larger right triangle of the longer leg is x units.

so,

[tex]\frac{12}{3} = \frac{x}{4}[/tex]

⇒ [tex]x = \frac{12 * 4}{3}[/tex]

∴x = 16

Therefore, the value of x is 16 units.

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The value of x in the equation 3x = 48 is 16 and for equation 4x = 64 is 16.  

What is equation ?

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

3x = 48

As it is multiplication we divide it by 3

3x / 3 = 48 / 3

x = 16

4x = 64

As it is multiplication we divide it by 4

4x / 4 = 64 / 4

x = 16

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The width of the box is 4 inches wide

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

Area = 20 square inches

Height = 5 inches

The width of the box can be calculated using the following equation

Width = Area/Height

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

Width = 20/5

Evaluate the quotient

Width = 4

Hence, the width is 4 inches

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Complete question

The side of a box has an area of 20 square inches and a height of 5 inches. How many inches is the width of the box?

An inequality in mathematics shows how two values are related in an imbalanced algebraic expression.

In mathematics, an inequality displays the connection between two values in an unbalanced algebraic statement. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

There are four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.

A comparison of any two values, known as an inequality, demonstrates whether one value is less than, larger than, or equal to the value on the opposite side of the equation. A relationship in a real-world scenario can be demonstrated by writing an inequality.

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Using the property of exponents, the value of x for the formula 3x=729 is 6.

The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 23. Keep in mind that a number raised to the power of one is itself. Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself. For example, 6 is multiplied by itself four times, yielding 6 6 6 6. This is written as 64. The exponent is 4 and the base is 6.

Here,

3ˣ=729

3ˣ=3⁶

x=6

The value of x for expression 3ˣ=729 is 6 using property of exponents.

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Answer:120 dimes, 80 nickels, and 300 quarters

Step-by-step explanation: Go step by step multiplying

It is not possible to construct a triangle with the given lengths (4,3,7).

A triangle is a polygon. It has three sides and three vertices. It is one of the famous shapes in geometry. A triangle has three vertices A, B, and C, and is denoted ΔABC.

Triangle Inequality Theorem :

The summation of the lengths of any two sides of a triangle is greater than the length of the third side.

Given three sides are 4,3,7cm

We know that the summation of two sides of a triangle is greater than the third side.

But given sides, 4+3=7 ( using addition)

Hence, it is not likely to construct a triangle with lengths of sides 4cm, 3cm, and 7cm.

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So on solving the provided question we can say  that 3x³ is a polynomial as it have exponential power

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

here,

3x³ is a polynomial

as it have exponential power

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