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The substitution property states that if two expressions are equal, then they remain equal when the same values are substituted into them.

This is usually expressed as:

The substitution property states that if two expressions are equal, then they remain equal when the same values are substituted into them. This means that if one expression is equal to another, then the same value can be swapped in for any of the variables within them and the equality will still hold.

For example, if we have the equation 4x + 7 = 11, then we can swap in any value for x and the equation will still be true. This is because the substitution property allows us to make a substitution for any of the variables and the equation will remain true.

This property is useful in solving equations and is a key part of algebra.

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Answer:

  ∠MAR = 28

Step-by-step explanation:

Given angle MAR bisected by ray AT to form angle MAT = (6x-4) and RAT = (2x+8), you want to know the measure of MAR.

An angle bisector divides an angle into two congruent parts:

  ∠MAT = ∠RAT

  6x -4 = 2x +8

  4x = 12 . . . . . . . . add 4-2x

  x = 3 . . . . . . . divide by 4

Then the measure of one of the halves is ...

  ∠RAT = 2x +8 = 2·3 +8 = 14

So, the measure of the whole is ...

  ∠MAR = 2·14

  ∠MAR = 28

Answer: 37-12=25

25 divided by 5 = 5 so you can figure it out

Answer:

Image 1 answer → not a polygon

Image 2 answer → n = 49 degrees

Image 3 answer → Square

Step-by-step explanation:

Image 1 explanation: Circles and ovals aren't polygons because their area and perimeter are calculated differently. So the answer is not a polygon.

Image 2 explanation: All complementary angles add up to 90 degrees, so 131 and 139 are incorrect. 41 and 49 add up to 90 degrees, which makes 49 degrees your answer.

Image 3 explanation: All options listed are quadrilaterals, but a square is the only shape that has 4 congruent sides and angles. Therefore, a square is a shape that possesses all the characteristics listed.

Have a great day! :)

The domain of the modulus function is the set of all real numbers. The range of the modulus function is the set of non-negative real numbers.

The modulus function, also known as the absolute value function, is a function that takes any real number as input and returns its distance from zero on the number line.

In mathematical notation, the modulus function can be represented as |x|, where x is the input.

For example, if x = -3, then |x| = 3, and if x = 5, then |x| = 5.

In class 11, the domain of the modulus function is all real numbers, which is represented by (-∞, +∞) and the range is non-negative real numbers represented by [0, +∞)

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Answer:

No

Step-by-step explanation:

For the passenger to be correct, the two ratios should equal each other.

[tex]\frac{156}{34}[/tex] = [tex]\frac{39}{9}[/tex]  Multiply both sides by 34 and 9

[tex]\frac{(34)(9)}{1}[/tex] x [tex]\frac{156}{34}[/tex] = [tex]\frac{(34)(9)}{1}[/tex] x [tex]\frac{39}{9}[/tex]  On the left side of the equation, the 34's cancel each other out.  On the right side of the equation, the 9's cancel out.  That leaves us with:

(9)(156) = (340)(39)

1404 = 13260

These numbers do not equal each other so the ratios are not equal.

The expression 70x-40x^4 if  factor is:-10x (4x^3-7).

Expressions  can be defined as equation that has both number that are known as well as numbers that are not known .

Example of expression is the sum of 9 and 1  will gives us 10  which is calculated as (9+1 =10).

Given data:

Expression: 70x-40x^4

Now let factor the expression using the given expression

70x-40x^4

Rearrange the expression

-40x^4 +70x

Common factor

-10(4x^4 -7x)

So the expression is:

-10x (4x^3-7)

Therefore we can conclude that the expression is -10x (4x^3-7).

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Dante deposited $5,000 into an account with an annual interest rate of

3.5%. He plans to deposit an additional $200 each year, just after the

interest is compounded. His balance will be $9,838.44 after 16 years.

It displays the actual percentage rate of interest owed on any outstanding debts, including credit card debt and loans.

Because it takes compounding effects into account, the effective annual interest rate is the real interest rate on an investment or loan. The rate increases as the compounding periods get more frequent. Advertisements for loans or savings accounts may include both the nominal interest rate and the effective yearly interest rate. The rate that should be used to compare loan and investment rates of return is the effective annual interest rate.

We can substitute the known values into the formula and calculate the final balance:

A = $5,000 (1 + 0.035)¹⁶

We can calculate the final balance by using a calculator, or we can use the formula of compound interest:

A = P(1 + r/n)ˣ

where, A= Amount

P= Principle($5,000 )

x= Time(16 years)

n= Rate(3.5%)

A = $5,000 (1 + 0.035/1)¹⁶

Now we can add the $200 deposit each year for 16 years:

A = $5,000 (1 + 0.035)¹⁶ + $200 × 16

A = $9,838.44

Dante's balance will be $9,838

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Answer: To find out which loan option will have the least interest, you need to calculate the interest amount for each option. You can do this by using the formula:

Interest = Principal x Interest Rate x Time (in years)

For option A, the interest amount would be:

Interest = $12,000 x 0.05 x (48/12) = $2,400

For option B, the interest amount would be:

Interest = $12,000 x 0.045 x (60/12) = $3,000

For option C, the interest amount would be:

Interest = $12,000 x 0.0375 x (66/12) = $2,970

For option D, the interest amount would be:

Interest = $12,000 x 0.04 x (72/12) = $3,840

As we can see the lowest interest amount is option C which is $2,970. Thus Ciara will pay the least interest if she chooses option C.

Step-by-step explanation:

The distance flown by the plane East of the starting point is (60 minutes * 500 km/h * cos(120°))/60 minutes/hour = 250 * cos(120°) km.

What is the Pythagorean theorem in plain English?

Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The distance flown by the plane South of the starting point is (60 minutes * 500 km/h * sin(120°))/60 minutes/hour = 250 * sin(120°) km.

To find the distance of the plane from the starting point, we need to use the Pythagorean theorem.

The distance would be √((250 * cos(120°))^2 + (250 * sin(120°))^2) = √(62,500 + 62,500) = √125,000 = approximately 111.8 km

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Using trigonometric ratios,  tree is leaning 106.1°-90° = 16.1° away from the vertical.

Pythagorean identities, reciprocal identities, sum and difference identities, double angle and half-angle identities are the main trigonometric identities. We must apply the sine rule and the cosine rule to the non-right-angled triangles.

6² = 3.5²+4² -2(3.5) (4) cos θ

36 = 12.2.5+16 - 28 cos θ

36 = 28.25 - 28 cos θ

7.75 = -28cos θ

7.75 / 28 = cos θ

Cos⁻¹ (7.75/28) = θ

106.1°=θ

So, the tree is leaning 106.1°-90° = 16.1° away from the vertical

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Although there are other factors to take into account, a model is worth your attention if its R-Squared is more than 0.6: R-squared values lower than 0.5 are normal for any science that tries to predict human behavior, such as psychology.

There are multiple phases involved in the actual R-squared computation. Finding the line of best fit, frequently from a regression model, entails taking the data points (observations) of dependent and independent variables.

Predicted values would then be calculated, actual values would be subtracted, and the results would be squared.

You would deduct the average actual value from each of the actual values, square the findings, and add them to determine the overall variance.

The R-squared is obtained by dividing the first sum of mistakes (unexplained variance) by the second sum (total variance) and deducting the result from one.

Hence, Although there are other factors to take into account, a model is worth your attention if its R-Squared is more than 0.6: R-squared values lower than 0.5 are normal for any science that tries to predict human behavior, such as psychology.

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The line TU is parallel to QR and SQR is dilated version of STU by a scale factor of 4.

What is midpoint theorem?

The line segment of a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.

Through the diagram it can be seen that T and U are midpoints of SQ and SR respectively.

And it can also be seen that TU is parallel to QR.

It is given that ST = 2, TQ = 6, SU = 3 and UR = 9

The length of side SQ -

SQ = ST + TQ

SQ = 2+6

SQ = 8

The length of side SR -

SR = SU + UR

SR = 3+9

SR = 12

The measurement of QR = SQ as seen in the diagram.

According to midpoint theorem the mid points line segment TU measures half of its parallel third side of triangle QR.

Now, to find the scale factor -

= QR - TU

= 8 - 4

= 4

Therefore, the scale factor is 2.

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It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 2 and 3

2 + 3 < 7

5 > 7

Now we add 2 and 7

2 + 7 > 3

9 > 3

Now we add 3 and 7

7 + 3 > 2

10 > 2

It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

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The Mixed number is -6 1/6, an integer is -6.16, proper fraction is -13/6

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Answer:

cubic polynomial

The average rate of change of f(x) over -6≤x-4 is -70.

The average rate of change of g(x) over -6≤x-4 is -140.

The average rate of change of g(x) is 2 times that of f(x)

The average rate of change of an equation can be determine by using the formula below:

average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]

From the given information, f(x) = 7x², g(x) = 7x² and  x₁ = -6, x₂ = -4

For f(x) = 7x²:

average rate of change =  ([7(-4)²] - [7(-6)²]) / (-4-(-6))

                                       = (112-252)/2

                                      = -70

For g(x) = 14x²:

average rate of change =  ([14(-4)²] - [14(-6)²]) / (-4-(-6))

                                       = (224-504)/2

                                      = -140

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0.5  is the best estimate of the correlation coefficient for the variables in the scatter plot.

What is the short definition of a scatter plot?

A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they can display the degree of connection, if any, between values of observable quantities or events (called variables).

What is the purpose of a scatter plot?

To illustrate how much one variable affects another, scatter plots are used to exhibit data points on a horizontal and vertical axis.

                       A marker is used to represent each row in the data table, and the position of the marker depends on the values of the columns that are set up on the X and Y axes.

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Answer: 23

Step-by-step explanation: Both triangles are the same in measurements so whatever number - 4 that equals 19 is the answer. 23-4=19

Yes, the given equation y = 10x is a direct variation.

Direct variation is a type of proportionality in which one quantity directly varies with respect to a change in another quantity. This means that if one quantity increases then the other quantity will also experience a proportionate increase.

Similarly, if there is a decrease in one quantity then the other quantity also decreases. Direct variation is a linear connection hence, the graph will be a straight line. Further, if the two entities are in a direct variation relationship then one will be a constant multiple of the other.

A direct variation equation has the form

y = kx  

Here, k is the constant of variation

Now, y = 10x is in this form, thus it is a direct variation.

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On solving the provided question, we can say that by trigonometry so sin 90 = p/h => y = 19

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures

here,

it is a right angled triangle

by trigonometry

so sin 90 = p/h

1 = 19/y

y = 19

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Water fills the cone to a capacity of 75%. 0.75 is the decimal equivalent of 75%.

Find the whole amount of what you're looking for to get a percentage of.

To calculate the percentage, divide the number.

Add 100 to the value.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, 35% is equal to the fraction 0.35 or the decimal 0.35.

The value of the number out of 100 is the proportion of the number. For instance, there are 26 females and 24 boys in a class. As a result, 52 out of 100 students in the class are females, or 52% of the class.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Percentages.

According to our question-

volume of water  =  (3/4) * (1/3)(a)(h)

volume of water  =  (3/4) * volume of cone

volume of water  =  75% of the volume of cone

75% of the cone's volume is filled with water.

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The number of aerobics classes that will cost the same for members and non-members is 5 classes.

The linear equation that represents the amount paid by members is:

membership fee + (amount per class x number of classes)

= $10 + ($3 x m)

= $10 + $3m

The linear equation that represents the amount paid by no-members is: (amount per class x number of classes)

$5 x m

= $5m

When the two costs are the same, the two equations would be equal:

$5m = $10 + $3m

$5 - $3m = $10

$2m = $10

m = $10 / $2

m = 5

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The vertex of the function is at (5, 10) .For the function, the domain exists on all real numbers while the range exist for the value f(x) ≥ 10

Vertex, domain and range of a function

The vertex of a quadratic or linear function is in the form

y =  a(x – h)^2 + k

where;

(h, k) is the vertex of the function

Given the function expressed as;

f(x) = |x-5| + 10

On comparison, you can see that h = 5 and k =10, hence the vertex of the function is at (5, 10)

For the domain and range

Domain are the dependent variable for which a function exist while the range is the independent variable for which a function exist.

For the function, the domain exists on all real numbers while the range exist for the value f(x) ≥ 10

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The center point formula,  (x h) 2 + (y k) 2 is r, must be converted into standard form in order to get the center and radius. 2 (x-h)2 + (y-k)2 is r2 (x-h)2 + (y-k)2 =is r2).

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The compound inequality given is "and" inequality.

Compound inequalities are inequalities which consist of more than two expressions connected with two or more inequality signs.

Compound inequality can be divided into two or more simple inequalities.

"And" inequalities are those compound inequalities where both the inequalities need to be true for the statement to be true.

"Or" inequality needs only any one of them true.

Given inequality is,

6 > x + 1 > 3

Subtracting 1 throughout,

5 > x > 2

Here x lies between 2 and 5 where x > 2 and x < 5.

Hence this inequality is "and" inequality.

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Answer: false

Step-by-step explanation:

False

Answer:

See below

Step-by-step explanation:

Since lines n and p intersect, they must have different slopes.  Lets say they have slopes 2 and 4, as an example.  They will intersect.  Lines m and l are perpendicular to n and p, so their slopes will be the negative inverse of 2 and 4.  That gives them slopes of -(1/2) and -(1/4).  These slopes are different, so they will intersect.

The attached graph illustrates this intersection with lines having the above slopes.  Lines m and l intersect at (-1,1) in this example.  Lines m and l also intersect, off the graph at the top left.

It defines conclusions or rounding a number to the nearest decimal place or to the nearest ones, tens, hundreds, and so on.

Estimation refers to obtaining a result that is close to the correct or actual result. It involves conclusions or rounding a number to the nearest decimal place or to the nearest ones, tens, hundreds, and so on.

There are various reasons, the estimate is especially useful when there is not enough information to calculate an exact value. Accountants use estimates when they want to calculate transaction amounts.

To estimate the quotient, we round the dividend to the nearest tens, hundreds, or thousands.

There are two methods for estimating the quotient:

let us consider an example:

for 371 nearest value is 400 because in the tens place it is equal to 400.

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Answer:

Step-by-step explanation: