The diagram shows a isosceles right triangle, follow the steps to explore relationships between Saint triangles, measure the length of each leg and hypotenuse

The equation of the line that passes through the points (-2,6) and (4,0) is

y = -x + 4

The slope, m of the linear function is calculated using the points (-2, 6) and (4, 0)

m = (y₀ - y₁) / (x₀ - x₁)

m = (6 - 0) / (-2 - 4)

m = (6) / (-6)

m = -1

equation passing through point (4,0) using point slope formula given by

(y - y₁) = m'  (x - x₁)

y - 0= -1(x - 4)

y = -x + 4

the equation of the line is y = -x + 4

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It should be noted that two cups : 2/3 have a unit rate of three. This is true.

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). This simply indicates that you're dividing the variable A by B.

In this case, two cups : 2/3 have a unit rate of three. This can be Illustrated as:

= 2 ÷ 2/3

= 2 × 3/2

= 3

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Answer:

Step-by-step explanation:

no

There will be two x-intercept for the quadratic function

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution.

The value of y in the quadratic equation ax²+bx+c=0 is y ≤ 2. This means that the maximum value is 2.

With this that the parabola will be downward and and the maximum value will be 2.

With this there will be two intercepts on the x axis.

Therefore for a range of y≤2 there will be two x-intercept.

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By percentage method the total recommended daily amount, in milligrams, of sodium is calculated to be 2370 mg.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Amount of sodium in chicken salad - 640 mg

Percentage 640 mg is of recommended amount - 27%

Let x be the total recommended daily amount (in mg) of the sodium.

According to the question -

27% of x = 640

x = (640 × 100)/27

x = 2370.37 ≈ 2370

Therefore, the recommended amount is 2370 mg.

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Answer:

11 : 16

Step-by-step explanation:

There are 11 girls and 5 boys taking taekwondo lessons. This means that in total there are 16 people taking lessons, we can turn this into a ratio that equals 11 : 16

The square meters of land that were palnted with fruit-bearing trees is 399 m².

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The measurement of the piece of land is 950 square meters

Then we were told to find the 42% of it with fruit-bearing trees which is the 42% of the land.

Then this can be written as :

42/100 * 950 = 399 m²

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The equation that can be used to solve for the length, y , is y²-5y = 750

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Area is measured in squared unit.

The area of a rectangle is given by the expression:

A = l × w

where l is the length and w is the width of the rectangle.

The width of the rectangle is 5 feet less than that of the length. The length is represented by y. this means that w = y-5

Area = length × width

area = 750

therefore 750 = y ×( y-5)

opening the parentheses,

750 = y² - 5y

therefore the equation that can be used to solve for the length of the rectangle is

y²-5y = 750

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Answer:

5/3

Step-by-step explanation:

The first step in finding the reciprocal of 1 2/3 is to make 1 2/3 into a fraction, which would be 5/3. The reciprocal of a given fraction is simply that fraction flipped over. The reciprocal of 5/3 would be 3/5.

Answer:

1/123

Step-by-step explanation:

reciprocal is just   1/ 123

The numeric value of ∠MJK is 135°

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

Some measurements of angles of JKLM and PQRS are given. m∠MJK = (12x+15)°, m∠SPQ = (14x-5)°, m∠JKL = 115°,

m∠JML = (8y + 12)°, m∠PSR = = (13y-18)°.

And we know the quadrilaterals are similar.

Two quadrilaterals are similar, so their corresponding angles are equal.

JKLM and PQRS are shown, where JKLM is similar to PQRS.

So,

m∠MJK= (12x+15)° = m∠SPQ = (14x-5)°

12x + 15 = 14x - 5

2x = 20

x = 10

So,

m∠MJK= (12(10)+15)°

m∠MJK = (135)°.

Therefore, 135° is the measure of ∠MJK

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Answer:

m = - 14

Step-by-step explanation:

[tex]\frac{6}{7}[/tex] m - 3 = [tex]\frac{5}{7}[/tex] m - 5

multiply through by 7 to clear the fractions

6m - 21 = 5m - 35 ( subtract 5m from both sides )

m - 21 = - 35 ( add 21 to both sides )

m = - 14

Answer:

Step-by-step explanation:

6/7m - 3 = 5/7m - 5

(as you can see, there are simple numbers and some with m besides them, you have to group the "m" together and the simple ones on the other side of the "=" which means that you have to take away numbers that are "on the wrong side")

(first with -3, you add 3 on both sides)

6/7m - 3 + 3 = 5/7m - 5 + 3

6/7m + 0 = 5/7m - 2

(then with 5/7m)

6/7m - 5/7m =  5/7m - 5/7m - 2

1/7m = 0m - 2

(good job ! now, since we only want "m", we take away 1/7 by dividing both sides by 1/7 since it's a multiplication)

1/7m /1/7 = - 2 / 1/7

m =  - 2 * 7 (because dividing a fraction is multiplying it by the inverse )

m = - 14

verify if it's correct , and you can finish :)

The data set's mean absolute deviation (MAD) is 5.6.

The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection.

It is a statistical summary of statistical variability or dispersion.

We know that:
Dakota County high school cheerleading coaches' yearly salaries.

Data:
41, 38, 36, 57, 43

Mean = (41 + 38 + 36 + 57 + 43)/5

= 215/5

= 43

mean absolute deviation (MAD)   = (1/5) ∑ | Mean - xi |      i = 1 to 5

| 43 - 41| = 2

| 43 - 38 | = 5

| 43 - 36| = 7

| 43 - 57} = 14

| 43 - 43 | =0

mean absolute deviation (MAD)   = (1/5) (2 + 5 + 7 + 14 + 0)

=28/5

= 5.6

Therefore, the data set's mean absolute deviation (MAD) is 5.6.

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The values of angles are ∠A =  61°, ∠B = 107°, ∠C = 12°.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol △ and consists of three connected vertices. Triangles can be divided into several categories according to their sides and angles.

Given

∠A = 3x + 28°

∠B =5x + 52°

∠C = 2x - 10°

sum of angles of triangle is 180°

∠A + ∠B  + ∠C  = 180°

3x + 28° + 5x + 52° + 2x - 10° = 180

10x + 80 - 10 = 180

10x = 180 - 70

10x = 110

x = 11

∠A = 3x + 28° = 3(11) + 28

∠A =  61°

∠B =5x + 52° = 5(11) + 52

∠B = 107°

∠C = 2x - 10° = 2(11) -10

∠C = 12°

Hence measure of angles is ∠A =  61°, ∠B = 107°, ∠C = 12°.

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The area of the model boat sail, given the shape of the sail being a triangle, is :

The area of a triangle can be found by the formula :

= 1 / 2 x base x height

In the model boat given, the sail has the base of 6 inches and has a height of 12 inches.

This means that the area of the triangle is :

= 1 / 2 x ( 6 x 12 ).

= 1 / 2 x 72

= 36  inch ²

The reason the units are squared is that the units for area is squared.

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The mean stays at 83.5°,Every value increases in mean and median by the same constant if a constant is added to each value.

Every value increases in mean and median by the same constant if a constant is added to each value. Take a set of scores, for instance, that have a mean of 5 and a median of 6. Every score will increase by 10, changing the median and mean to 15 and 16, respectively.

When we multiply the values in the data set by 2, we get the mean, median, mode, range, and IQR multiplied by 2.

Explanation:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57 the set multiplide by 2

The mean stays at 83.5°.

The mean stays at 83.5°,Every value increases in mean and median by the same constant if a constant is added to each value.

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Answer: stays at 83.5

Step-by-step explanation:

The quarter tossed by Moriano fall a distance of 22 feet

The given parameters in the question are

Location of the quarter after the fall = -22 feet.

Top of the well = 0 feet

The required distance can be calculated using the following equation

Distance = Top of the well - Location of the quarter after the fall

Next, we substitute the given values in the above equation

When this is done, the equation becomes

Distance = 0 + 22

Evaluate the sum

Distance = 22

Hence, the value of the distance is 22 feet

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Answer:

  See attached

Step-by-step explanation:

You want the slopes of the various graphs, and a description of how you got it.

As you know from your real-world experience a steep slope has more vertical change in the same horizontal distance than one that is less steep. When the height increases over a horizontal distance, we say the slope is positive. When the height decreases, the slope is negative.

In the real world, a downhill (negative) slope turns into a positive (uphill) slope if you just turn around and go the other direction.

On an x-y (Cartesian) coordinate plane, we define the direction as positive to the right. So, a line or curve with positive slope goes up to the right. A line or curve with negative slope goes down to the right. (The slope of a horizontal line is zero. The slope of a vertical line is "undefined.")

Slope can be described different ways. The natural slope of a pile of loose material (sand, gravel, rock, salt, coal, and the like) can be described by its angle of repose. Dry sand may have an angle of repose of as much as 34°. When it is filled with water, it may slump to 15° or so.

The slope, or grade, of a roadway or other path is often described as a percentage (feet of rise or drop per 100 horizontal feet). Many places a 10% grade (about 5.7°) would be considered a pretty steep slope. The steepest hills in San Francisco have a 31.5% grade. A "black diamond" ski run is one with a slope of 40% (about 22°) or more.

In Algebra, we usually give a slope a numerical value. Its units will be the ratio of the units of the vertical measure on a graph to the units of the horizontal measure on the graph. For a graph with no particular units, or where the horizontal and vertical units are the same, the slope is simply a "pure number" that has no units.

Slope is defined as the ratio of vertical change to the corresponding horizontal change. On a graph, the vertical change between two points is the difference of their vertical (y) coordinates. The horizontal change is the difference of the horizontal (x) coordinates taken in the same order.

The formula for the slope between two points (x₁, y₁) and (x₂, y₂) is ...

  [tex]\text{slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The points can be designated as "point 1" and "point 2" in any order, but the chosen designation needs to be used consistently in the calculation.

If the denominator is zero, the slope is "undefined."

The graphs show the coordinates of the points you are to use to calculate the slope. In the attachment, we use the point on the right as "point 2" and the point on the left as "point 1". That makes the difference of x-coordinates positive, so the sign of the slope will be the sign of the difference of corresponding y-coordinates. (The slope is positive in all cases here.)

The "procedure" is simply a description of what you did to find the slope. It is described above, and also in the attachment. You know what you did, so all you need to do is write that down.

The answer to question 3 is the same as the answer to any of the parts of question 1, except you're using different symbols for the coordinates of the point. Considering graph A, you're using "u" and "v" instead of "4" and "9". The letters go in the same places the numbers do in the equation for slope.

The attachment has the answers to the questions.

Answer:

the populate the same it increst then decrest the same amont

Step-by-step explanation:

The best interpretation of the probability that the number landing face up will be less than 3 is [tex]\frac{1}{3}[/tex].

For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is [tex]\frac{1}{3}[/tex].

As per the given question a fair die with its faces numbered from 1 to 6 will be rolled.

Here we have to calculate the probability that the number landing face up will be less than 3.

The event of the number landing face up will be less than 3 is exhaustive, mutually exclusive, and independent face of a die = 6

(1, 2, 3, 4, 5, 6)

Favorable number of faces of a die = 2

(1, 2)

Since the number landing faces up will be less than 3.

Therefore the probability that the number landing face up will be less than 3

[tex]=\frac{\text { Favourable Number }}{\text { Total Number }}$[/tex]

[tex]& =\frac{2}{6} \\[/tex]

[tex]& =\frac{1}{3}[/tex]

Therefore the best interpretation of the probability that the number landing face up will be less than 3 is [tex]\frac{1}{3}[/tex]

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The long-run relative frequency of a number less than 3 landing face up is 2/3.

The best interpretation of the probability that the number landing face up will be less than 3 is that for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3. This can be expressed mathematically as P(x<3) = 2/3, where P(x) is the probability of the number landing face up being less than 3.

For a single roll of the die, the probability of a number less than 3 landing face up is 1/2. This is because there are three numbers (1,2,3) which are less than 3, and 6 possible outcomes. Therefore, the probability of any one of those three numbers landing face up is 3/6, or 1/2.

For multiple rolls of the die, the probability of a number less than 3 landing face up is the sum of the probabilities of each of those three numbers landing face up. This can be expressed mathematically as P(x<3) = (1/2) + (1/2) + (1/2), or 2/3.

Therefore, for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3.

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Answer:

107

Step-by-step explanation:

By the converse of the corresponding angles theorem, [tex]x=107[/tex].

The question that can be represented by the equation ? * 1/8 = 3 is (1). How many 1/8's are in 3?

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

? * 1/8 = 3

Represent the expression ? with x

So, we have

x * 1/8 = 3

Divide both sides of the equation by 1/8

This gives

x = 3/(1/8)

This means that how much 1/8 can be gotten from 3

Hence, the question is (1)

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 60}}{\left( \cfrac{10}{100} \right)60}\implies 6~minutes[/tex]

Answer:

Step-by-step explanation:

The monthly payment for car at rate of 2.9% is $358.57.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Given the cost of car = $19,999

rate per annum = 2.9% = 0.029

interest compounded monthly,

n = 12

time 5 years

compound interest  formula for amount P =[tex]\frac{Cr/12}{[(1+r/12){12t} - 1]}}[/tex]

P = 19999*{(0.029/12)/[(1+0.029/12)^12*5 - 1}

p =  $358.47

Hence the monthly payment is $358.47.

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the answer to your question is mathematics was invented not created.

Answer: Sophie can use 225

Step-by-step explanation: