(Lesson 1.3) Use properties to find the sum or product. (3,5,7,9,11 only)

Answer:

  y = 1/4x +1/8

Step-by-step explanation:

You want to know the equation of the table showing a linear function and points (0, 1/8), (1, 3/8).

The y-intercept of the line described by this table is the y-value when x=0. That value is 1/8.

The slope of the line described by the table is the difference in y-values for a difference in x-values of 1. The difference between x=1 and x=0 is ...

  ∆y = 3/8 -1/8 = 2/8 = 1/4

The slope-intercept equation for the table is then ...

  y = mx +b . . . . . . . line with slope m and y-intercept b

  y = 1/4x +1/8 . . . . . line with slope 1/4 and y-intercept 1/8

The equation of the table is ...

  y = 1/4x +1/8

Table A represents a function, but Table B does not represent a function.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.

As, each element of X is associated with unique element of Y, so this is a function.

Table A    

           X               Y

           3                 1

            2                 0

            1                  0

As, each element of X is associated with a unique element of Y, so this is a function.

Table B

X            Y

3           -2

5              1

5              2

Hence, Table A represents a function, but Table B does not represent a function.

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Answer:

Step-by-step explanation:

The total money earned after working the given number of hours is $18.60.

When using the cross-multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa.

Given that to pick green peppers:

15 minutes = $3.20

45 minutes = x

Using cross multiplication solve the above equation:

[tex]x = \frac{(3.20)(45)}{15} \\\\x = 9.60\\[/tex]

For picking carrots:

20 minutes = $3. 00

1 hour = 60 minutes = x

Using cross multiplication solve the above equation:

[tex]x = \frac{(3)(60)}{20}\\ \\x=9[/tex]

The total amount made after all the work is:

A = 9.60 + 9

A = 18.60.

Hence, the total amount of money she earned after all the work is $18.60.

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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 = 25[/tex]

The probability of 45 minutes of less is the p-value of Z when X = 45, hence:

Z = (45 - 70)/25

Z = -1

Z = -1 has a p-value of 0.16 (rounding).

As for the probability of an exact time, such as 95 minutes, is of 0%, as the normal distribution is continuous.

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The time interval that saw Dylan maintain the fastest average speed was B. between hour 1 and hour 2.

Dylan maintained the fastest speed at the interval that saw him cover more distance in a shorter amount of time. You can find the speed at these intervals by using the speed formula of distance divided by time.

Speed between hour 0 and 1 :
= 25 miles / 1 hour

= 25 miles per hour

Speed between hour 1 and 2 :

= ( 75 - 25 ) / 1

= 50 miles per hour

Speed between hour 3 and 5 :

= ( 125 - 75 ) / 2

= 25 miles per hour

The fastest speed was therefore between hour 1 and 2.

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Options for this question are:

Answer:

I believe the answer is 180°

The scatter plot for the given data (See full and correct details attached) is appended accordingly.

A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables).

Scatter plots aid in the visual representation of correlations between economic factors such as employment and production, inflation and retail sales, and taxes and economic growth.

As you can see there is a slight positive correlation between the number of hours meditated and the numberr of hours slept.

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The price of a sweater bought by Rahul before the discount is Rs. 80.

Let us assume the price of the sweater before the discount to be x.

Given that,

The money saved by Rahul will be equal to the discount given for the sweater.

Therefore, we can say that Rs. 20 will be equal to 25% of the price of the sweater before the discount.

The equation we would obtain from the language above would be,

25% of x = 20

Solving this equation further, we can see that,

=> 25% of x = 20

=> 25* 1/100 * x = 20

=> x/4 = 20

=> x = 80

As we assumed x to be the price of the sweater before the discount,

So, the price of a sweater bought by Rahul before the discount is Rs. 80.

Complete question: Rahul bought a sweater and saved Rs. 20 when a discount of 25% was given. What was the price of the sweater before the discount?

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When nine is divided by 60 , the quotient would be 0. 15 .

The quotient when nine is divided by 390 is 0. 023 or 3 / 130 .

The quotient refers to the result when a number is divided by another number as is the case with nine being divided by 60 .

The quotient is therefore :

= 9 ÷ 60

= 9 / 60

= 0. 15

The quotient for the division of nine by 390 is :

= 9 ÷ 390

= 9 / 390

= 0. 023

Another way to do this is to find the greatest common factor of nine and 390 which is 3 . Then use it to take the numbers to their simplest form. The quotient would then be :

= ( 9 / 3 ) / ( 390 / 3 )

= 3 / 130

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Answer:

1/15

Step-by-step explanation:

dividend=1/3

divisor=5

since

Dividend ÷ Divisor = Quotient.

1/3 ÷5 = 1/15

Therefore, quotient = 1/15

The expression that is 0.5 times as large as 342 + 156 is (342 + 156) x 0.5

This is because 0.5 is a factor that multiplies the entire sum of 342 + 156.

So the correct answer is (Choice A) (342 + 156) x 0.5

Answer: The correct answer is (A) (342 + 156) × 0.5. This is because in mathematics, multiplication and division should be done before addition and subtraction. Therefore, the parenthesis is solved first, which results in 342 + 156 = 498. Then, 0.5 is multiplied to the result, 498 × 0.5 = 249.

Step-by-step explanation:

The measure of each interior angle of the polygon is 156°.

In a regular polygon, all interior angles are equal. The interior angle of a polygon = sum of interior angles and the number of sides is the formula for determining the size of an interior angle. A polygon's exterior angles add up to 360°.

Given that the number of sides of the polygon is 15. The sum of the interior angles of the polygon is calculated by the formula:-

Sum = ( n - 2 ) x 180

Sum = ( 15 - 2 ) x 180

Sum = 2340

The measure of each angle is calculated as:-

Angle = 2340 / 15

Angle = 156°

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-3x=4y+8 is a continuous and linear equation and it can be written as y=-3/4x-2

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given equation is -3x=4y+8

This equation can written in y=mx+b form

-3x=4y+8

Add 3x on both sides

0=4y+3x+8

Subtract 4y on both sides

-4y=3x+8

Multiply with minus

4y=-3x-8

y=-3/4x-2

The line is continuous and linear

Hence, -3x=4y+8 is a continuous and linear equation and it can be written as y=-3/4x-2

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The speed of spin of carousel is 0.286 miles/minutes. The The speed at which something moves in a specific direction is known as its velocity. as the speed of a car driving north on a highway or the speed at which a rocket takes off.

based on the distance traveled in a given amount of time. These cars can travel at speeds of more than 150 kilometers per hour (km/h). Meters per second (m/s) is the fundamental unit of speed in the metric system.

Given,

distance spinned=2 miles

time taken=7min

speed=distance/time

speed=2/7=0.286 miles/minute

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When a figure is dilated using a scale factor of 1, the resulting figure is the same as the original figure.

This is because a scale factor of 1 means that the dimensions of the original figure are not changed in any way.

Mathematically, this is represented by the equation:

Original Length x Scale Factor = Resulting Length

For a scale factor of 1, the equation simplifies to:

Original Length x 1 = Resulting Length

Therefore, the resulting length is equal to the original length.

For example, if a line had a length of 5 units before dilating, the resulting length would be 5 units after dilating.

5 units x 1 = 5 units

This is because the scale factor of 1 does not change the length of the line in any way.

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We can find the value of n in exponents through various rules based on the given equation.

If x is any real number and n is a positive integer, then [tex]x^n[/tex] is equivalent to repeated multiplication.

We can also write [tex]x^n[/tex] in the following way:

[tex]x^n[/tex] = x * x * x * x * x *...... * x (n times)

This can be referred to as "n raised to the power of x," "n to the power of n," or just "n." In this case, n is the exponent or power, and x is the base.

We may infer a few fundamental guidelines for exponentiation from this concept. There are various methods of finding the exponent based on various rules, namely,

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To find the value of n in exponents, you can use the property that a^n * a^m = a^(n+m)

For example, if you have the expression (2^3)^n, you can use the property above to find the value of n by dividing both sides by 2^3, so (2^3)^n / 2^3 = 1^n. Now you can see that n = 1.

Another way to find the value of n in exponents is to use logarithms. The logarithm base "a" of a^n is n. Therefore, if you know the value of a^n, you can find the value of n by taking the logarithm base "a" of a^n.

For example, if a^n = 8 and a=2, then n = log2(8) = 3.

In summary, there are a couple of ways to find the value of n in exponents, but the most common way is to use the property of exponents or logarithms.

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Answer:

Step-by-step explanation:

To find f(-6), we need to substitute -6 for x in the function f(x) = -4x² + 4x - 1.

f(-6) = -4(-6)² + 4(-6) - 1

f(-6) = -4(36) + (-24) - 1

f(-6) = -144 + (-24) - 1

f(-6) = -167

Therefore, f(-6) = -167

1 . y'=0 is the derivative of the function y = 14.

2. y' =  9[tex]x^8[/tex]+3[tex]sec^2x[/tex]  is the derivative of the function y= [tex]x^9[/tex]+3tanx

3. y' = [tex]\frac{-4}{x^5}[/tex] + 4sinx is the derivative of the function y = [tex]\frac{1}{x^4}[/tex] - 4cos x

1 . The derivative of a constant is always zero.

A constant function is a function whose value does not depend on the input value.

So y = 4 is a constant function, its derivative is always zero.

So the derivative of y=4 is 0

2. The differentiation of [tex]x^9[/tex]+3tanx is 9[tex]x^8[/tex]+3[tex]sec^2x[/tex]

The power rule states that the derivative of x^n (where n is a constant) is nx^(n-1). So the derivative of x^9 is 9x^8.

The derivative of tanx is [tex]sec^2x[/tex].

And the derivative of 3tanx is 3[tex]sec^2x[/tex]

So, [tex]x^9[/tex]+3tanx  is differentiated as9[tex]x^8[/tex]+3[tex]sec^2x[/tex]

3. The derivative of y = [tex]\frac{1}{x^4}[/tex] - 4cos x can be found using the power rule and the chain rule.

The power rule states that the derivative of x^n (where n is a constant) is nx^(n-1). In this case, [tex]\frac{1}{x^4}[/tex] can be rewritten as [tex]\frac{1}{x^4}[/tex] and the derivative would be -4 [tex]\frac{1}{x^5}[/tex]

The chain rule states that the derivative of (f(g(x)) is f'(g(x))*g'(x). In this case, the inner function is -4cos x, the derivative of cos x is -sin x and the outer function is , [tex]\frac{1}{x^4}[/tex] the derivative of that is -4 [tex]\frac{1}{x^5}[/tex]. So the derivative of -4cos x is -4(-sin x)

So the final derivative of y = [tex]\frac{1}{x^4}[/tex]  - 4cos x is [tex]\frac{-4}{x^5}[/tex] + 4sinx

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Answer:

[tex]\boxed{384}[/tex]

Step-by-step explanation:

The image of A After a reflection in y=x followed by a reflection in x=−3. is (0. 7).

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

A = (7, -6)

Reflection rules over y = x.

(x, y) → (y, x)

So,

(7, -6) = (-6, 7)

Now,

Reflection in x = -3

Reflection rules over the y-axis.

(x, y) → (-x, y)

So,

x = -3

There are 3 units between -3 and -6.

So,

3 + 3 = 6 units will be added during reflection over y = -3

i.e

3 units on the left side of y = -3

3 units on the right side of y = -3

So,

(-6, 7) = (-6 + 6, 7) = (0, 7)

Thus,

The image of A is (0. 7).

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The reflection of image of point in y = x is (-6, 7),

and  reflection in x = −3 is (-13, -6).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

Given a point  A(7, −6)

A. a reflection in y = x

Flipping is the term for reflection. A reflection is the shape's mirror image. The line of reflection is the path taken by an image when it reflects.

reflection in y = x

x changed to y and y changed to x

x = -6 and y = 7

coordinates are A'(-6, 7)

B. a reflection in x = −3.

let the coordinates be (a, b)

reflection in x = k

image coordinates will be A" (2k - a, b)

here a = 7, k = -3, and b = -6

2k - a = 2(-3) - 7

2k - a = -13

image coordinates will be A"(-13, -6)

Hence the coordinates are A'(-6, 7),

and reflection in x = -3,

coordinates aere A"(-13, -6).

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The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4).

What is an orthocenter of a triangle?

In geometry, an orthocenter is a point in a triangle that is the intersection of the three lines containing the altitudes of the triangle. An altitude of a triangle is a line segment from a vertex of the triangle to the line containing the opposite side, and is perpendicular to that side. The orthocenter of a triangle is the point where all the altitudes of a triangle meet.

To find the orthocenter of a triangle, the first step is to find the equation of the altitudes from each vertex. Then, we can find the point of intersection of these three lines.

Given the triangle ABC with vertices A (2,6), B (8,6), and C(6,2),

The equation of altitude from vertex A is (x-2) = -2(y-6)

The equation of altitude from vertex B is (x-8) = -2(y-6)

The equation of altitude from vertex C is (x-6) = 2(y-2)

By solving the system of these three equations, we can find the coordinates of the orthocenter.

Hence, The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4)

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The value of the constant k in the equation of the division of g(x) by (x + 1); [tex]\frac{g(x)}{x + 1} = 2\cdot x - 3 + \frac{k}{x + 1}[/tex] obtained by the long division of g(x) = 2·x² - x by (x + 1) is 3.

The method or algorithm of finding the long division of a polynomial, p(x) known as the dividend, by a divisor, g(x) makes use of the equation;

p(x) = q(x) × g(x) + r(x)

Where;

q(x) = The quotient

r(x) = The remainder from the division;

The specified equation; [tex]\frac{g(x)}{x + 1} = 2\cdot x - 3+\frac{k}{x+1}[/tex], indicates that the remainder, r(x) = k.

The value of k in the specified equation, can be found by dividing the function g(x) = 2·x² - x, by (x + 1) as follows;

The expression obtained when g(x) is divided by (x + 1) using long division, is presented as follows;

 [tex]{}[/tex]        2·x - 3

(x + 1) |2·x² - x

[tex]{}[/tex]           2·x² + 2·x

[tex]{}[/tex]                    -3·x

     [tex]{}[/tex]            [tex]{}[/tex]  -3·x - 3

[tex]{}[/tex]                       [tex]{}[/tex]     3

The remainder obtained from the long division of 2·x² - x by (x + 1) is; 3

The result of the long division of 2·x² - x by (x + 1) is therefore;

[tex]\frac{g(x)}{x+1} =2\cdot x - 3 + \frac{3}{x + 1}[/tex]

Comparison of the equation; g(x)/(x + 1) = 2·x - 3 + k/(x + 1) and the equation; g(x)/(x + 1) = 2·x - 3 + 3/(x + 1), indicates that the value of k is 3

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Yes, x³ is an exponential function. An exponential function is a function in which the variable (x) is in the exponent.

The general form of an exponential function is f(x) = a^x, where a is the base and x is the exponent. In the case of x³, the variable (x) is in the exponent. x³ represents x raised to the power of 3, where x is the base and 3 is the exponent.

Exponential functions are often used to model growth and decay in a variety of natural phenomena, such as population growth, radioactive decay, and compound interest. Understanding exponential functions is important for solving mathematical problems, especially in algebra, calculus, and applied fields such as physics and engineering.

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x = 19 and x = 25 make the inequality true.

What is inequality?

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

To use substitution to determine which value of x makes the inequality true, we can substitute each value from the set {8, 19, 25} into the inequality and see if it makes the inequality true or false.

For example, if the inequality is x < 10, we can substitute 8, 19 and 25 into the inequality to see which one makes it true:

8 < 10 is true

19 < 10 is false

25 < 10 is false

So, we can see that only 8 makes the inequality true. Therefore, x = 8 makes the inequality true.

If the inequality is x > 10, we can substitute 8, 19 and 25 into the inequality to see which one makes it true:

8 > 10 is false

19 > 10 is true

25 > 10 is true

Hence, x = 19 and x = 25 make the inequality true.

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The commutative property of addition states that the order of the numbers being added does not affect the result. For example, the sum of 2 + 3 is the same as the sum of 3 + 2, which is 5.

The commutative property of addition does not work for subtraction because subtraction is not commutative. In subtraction, the order of the numbers being subtracted does affect the result. For example, the difference of 3 - 2 is 1, but the difference of 2 - 3 is -1.

The reason for this is that subtraction is the inverse operation of addition and the inverse operation of a commutative operation is not always commutative. In addition, subtraction is not commutative because when we subtract the smaller number from the larger number, we get a positive result but when we subtract the larger number from the smaller number we get a negative result.

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Answer:

a

Step-by-step explanation:

The bar represent 120 bars The histogram shows information about 480 cars.

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The answer accurate to the nearest hundredth is 38.5

How to find the nearest hundredth?

To find the nearest hundredth of a number, you can round it to the nearest hundredth. To do this, you need to look at the third digit after the decimal point.

Regarding the rectangles, since the two rectangles are similar, we know that the ratio of their corresponding sides are equal.

W1/W2 = P1/P2 = k (where k is the proportionality constant)

So, P2 = (P1 * W2)/W1 = (34 * 14)/12 = 38.5

Hence, The answer accurate to the nearest hundredth is 38.5

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The total length of the reel of thread is 5 meters, which is equal to 500 centimeters. Since Lahon used 300 centimeters of thread, he has 200 centimeters of thread left.

Lahon recently purchased a reel of thread that was 5 meters long. This is equivalent to 500 centimeters. He then used 300 centimeters of the thread for sewing. This leaves him with 200 centimeters of thread remaining. This can be expressed as 2 meters. Thus, Lahon has 2 meters of thread left from the reel of thread that he originally bought. This leftover thread can be used for other sewing projects or kept for future use. It is important to keep track of how much thread has been used and how much is left to ensure that an adequate amount of thread is available for future projects. The total length of the reel of thread is 5 meters, which is equal to 500 centimeters. Since Lahon used 300 centimeters of thread, he has 200 centimeters of thread left.

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