Multiply and simplify. 4√16 x⁸ . 4√x¹⁴

The slope intercept form of the equation become y = (-1/3)x - 1/3.

According to the statement

We have to find that the slope intercept equation.

So, For this purpose, we know that the

Slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

From the given information:

y - 3x = 8

y = 3x + 8  

Slope = 3

And

Perpendicular lines have slopes that are negative reciprocals of each other. So, the new line will have a slope of = -1/3.

P(-4,1)

y - 1 = (-1/3)(x +4)

y - 1 = (-1/3)x - 4/3

y = (-1/3)x - 1/3.

So, The slope intercept form of the equation become y = (-1/3)x - 1/3.

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694 divided by 41 goes into 16 times with remainder 38.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Now, We can use long division in finding the remainder.

Place the divisor which is 41, outside the long division sign, and 694 under the long division sign as;

41 ) 694 ( 16

   - 41

  ---------

    284

 -  246

  ----------

      38

Hence, 694 divided by 41 goes into 16 times with remainder 38.

Since, 10 + 3 + 2 + 1 = 16

Therefore, 694 divided by 41 is 16 with remainder 38.

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Answer:

64

Step-by-step explanation:

10^3 is 1000

64000/1000=64

Answer: The sum is always a rational number.

Step-by-step explanation:

Step-by-step explanation:

Given, sum of two rational numbers is always a rational number

We have to determine if the given statement is true or false

Consider two rational numbers 2/3 and 4/5

Sum of two numbers = 2/3 + 4/5

= [2(5) + 4(3)]/3(5)

= (10 + 12)/15

= 22/15

22/15 is a rational number.

Consider two rational numbers 2/3 and 1/3

Here, the denominators are same

Sum of two numbers = 2/3 + 1/3

= (2 + 1)/3

= 3/3

= 1/1

1/1 is also a rational number

Therefore, the given statement is true.

Answer:-2/1

Step-by-step explanation:

rise is -2 and 1 is run

The length of hJ is 17.

Given, the line HJ has a length

HJ = ?

HI = 14

IJ = 3

Since line HJ = HI + IJ

                       = 14+3

                        =17

Therefore the length of HJ will be 17.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of a body is called length.

In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.

Types of Line Segment

Parallel Line. Two lines in the same plane either meeting each other or not.

Intersecting Lines.

Concurrent Lines.

Collinear Points.

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The probability that 3 randomly selected points from A, B, C, and D are collinear is; 3/4

Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear.

Now, from the given image, there are 4 points but only three of them namely A, B and C are collinear. Thus, the 4 possible points picked could be; ABC, ABD, ACD, BCD

Thus, there are only three that can be collinear and so the probability is; 3/4

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The solution of factorization of x ³ + 64 is ( x + 4 )( x ² - 4 x + 16 ) [ Option C ].

The question asks to factorize the given polynomial, that is, x ³ + 64.

The question clearly states that we need to use the sum of cubes formula to factor the given polynomial x ³ + 64.

Sum of cube formula is given as

a ³ + b ³  = ( a + b ) ( a ² - a b + b ² ).

Substitute the values of variable a and b from the given polynomial x ³ + 64

x³ + 64 can be written as x ³ + 4 ³

=> a = x and b = 4

=> x ³ + 4 ³ = ( x + 4 ) ( x ² - 4 x + 4 ² )

=>  x ³  + 4 ³ = ( x + 4 ) ( x ² - 4 x + 16 )

This matches with the option c among the multiple choices for this question.

Therefore, we get the solution of factorization of x ³ + 64 as ( x + 4 )( x ² - 4 x + 16 ).

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Answer:if A= [2 6] prove that (A')' = A

3 7

4 9​

Step-by-step explanation:

Answer:

36°C

Step-by-step explanation:

[tex]|-6(6)|=36[/tex]

The exponential function to model the height of the ball is

                  h = 72*[tex](1/2)^{n}[/tex]

According to the question we have been given that

         at first bounce the height of the ball is = 36 inches

and    at the second bounce the ball is at the height = 18 inches

The exponential model is given as

                             h = a.[tex]b^{n}[/tex]      (1)

 where h = height of the ball

            n = number of bounces

Putting the different values of h and n in equation (1) and getting the value of a and b, we get

 when h = 36 and n=1

                     36 = a.[tex]b^{1}[/tex]

                     36 = a.b   (2)

 when h = 18 and n =2

                     18 = a.[tex]b^{2}[/tex]

                     18 = a.b.b

                     18 = 36.b

                     b = 1/2

substituting the value of b in equation (2) we get

                    a = 72

Hence putting the value of a and b in equation (1),  the exponential function to model the height of the ball is

                   h = 72*[tex](1/2)^{n}[/tex]

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Answer:

g(x) = | x + 2 | + 1

Step-by-step explanation:

the parent function f(x) = | x | has its vertex at the origin

the translated function has the form

g(x) = | x - h | + k

where (h, k ) are the coordinate of the vertex

the vertex of g(x) is at (- 2, 1 ) , then

g(x) = | x - (- 2) | + 1 , that is

g(x) = | x + 2 | + 1

we get the graph of the quadratic function by plotting the points on the graph paper.

We are given the quadratic function as:

f (x) = x²

We need to graph the function and find the values of the function for some given points of x.

For x = - 2, we get that:

f (x) = x²

f (- 2) = (- 2)²

f (- 2) = 4

For x = - 1, we get that:

f (x) = x²

f (- 1) = (- 1)²

f (- 1) = 1

For x = 0, we get that:

f (x) = x²

f (0) = (0)²

f (0) = 0

For x = 1, we get that:

f (x) = x²

f (1) = (1)²

f (1) = 1

For x = 2, we get that:

f (x) = x²

f (2) = (2)²

f (2) = 4

Plotting these points on the graph, we obtain the graph of the quadratic function.

Therefore, we get the graph of the quadratic function by plotting the points on the graph paper.

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Answer:

Super = 20 + 10x

Fance = 60 + 2x

Step-by-step explanation:

→ Start with the set fee for both

Super = 20 +

Fancy = 60 +

→ Assign a new variable to denote hours

x

→ Complete

Super = 20 + 10x

Fance = 60 + 2x

Answer: 110%

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad C(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +3}{2}~~~ ,~~~ \cfrac{ y +8}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE B}}{(11~~,~~20)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +3}{2}=11\implies x+3=22\implies \boxed{x=19} \\\\\\ \cfrac{ y +8}{2}=20\implies y+8=40\implies \boxed{y=32}[/tex]

The most appropriate choice of density will be given by

Total volume is 3.3 [tex]m^{3}[/tex]

What is density?

Ans : Density is mass per unit volume of a substance.

The density of Oats is [tex]410[/tex]  [tex]kg/m^{3}[/tex]

volume of 1025 kg of oats = [tex]\frac{1025}{410}[/tex] [tex]m^{3}[/tex]

                                            = 2.5 [tex]m^{3}[/tex]

Density of wheat is 770 [tex]kg/m^{3}[/tex]

volume of 616 kg of wheat =  [tex]\frac{616}{770}[/tex] [tex]m^{3}[/tex]

                                             = 0.8 [tex]m^{3}[/tex]

Total volume = (2.5 + 0.8) [tex]m^{3}[/tex]

                      = 3.3 [tex]m^{3}[/tex]

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Answer:

36

Step-by-step explanation:

[tex]3^{2}[/tex] = 9 (3x3)

[tex]3^{3}[/tex] = 27 (3x3x3)

9 + 27 = 36

Answer: Therefore, it is proven that any number or expression raised to the power of zero is always equal to 1. In other words, if the exponent is zero then the result is 1.

Step-by-step explanation: have a good day!

Answer:

7x+2

Step-by-step explanation:

-9x+8+2x-6

8-6

-9x+2+2x

combine like terms

-9x+2+2x

-9+2

7x+2

Applying proportions, the decimal value is given by:

B. 32.064.

Santo got the wrong answer because he counted 6 and 4 as the tenths and hundredths digits, instead of hundredths and thousandths.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for digit values in a number.

For this problem, we just have to apply the digit values of the number to find the decimal value, adding the factors, hence:

Hence:

30 + 2 + 0.06 + 0.004 = 32.064.

The decimal value is given by:

B. 32.064.

Santo got the wrong answer because he counted 6 and 4 as the tenths and hundredths digits, instead of hundredths and thousandths.

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In the given diagram the value of x is  is 140° and 25° respectively

In the diagram a, when you have 2 parallel lines cut by a transversal, the corresponding angles are equal and the value of x is equal to the corresponding angle as they are vertical angles, vertical opposite angles are equal.

In the diagram b, angle x is equal to the angle that is supplementary to 155° (Sum of supplementary angles is equal to 180°)

180-155=25°

In the given diagram the value of x is 140° in the diagram a and 25° for the diagram b respectively

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Your question is incomplete as the diagram is missing but the above answer might help you out.

The solving of fraction shows that there are 4 cups of lemonade use the table.

A fraction seems to be a part of a whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by that of the denominator. Both are integers in a simple fraction. A complex fraction has a fraction in both the numerator and the denominator.

Fractions help children know the nature of numbers but instead their interactions (e.g., the meaning of division) (e.g., the meaning of division). If a child does not grasp how fractions work, he will struggle to understand algebra later in life.

Based on the given conditions, formulate:

= [tex]16 \times \frac{1}{2} \div\left(\frac{1}{2}+1 \frac{1}{2}\right)[/tex]

Convert the expression into a fraction:

= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{1}{1}+\frac{1}{2}\right)\right)}[/tex]

Expand the fraction to get the least common denominator:

= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{2}{1 \times 2}+\frac{1}{2}\right)\right)}[/tex]

Calculate the product or quotient:

= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{2}{2}+\frac{1}{2}\right)\right)}[/tex]

Write the numerators over common denominator:

= [tex]\frac{16}{2 \times \frac{1+2+1}{2}}[/tex]

Write the numerators over common denominator:

= [tex]\frac{16}{2 \times \frac{3+1}{2}}[/tex]

Calculate the sum or difference:

= [tex]\frac{16}{2 \times \frac{4}{2}}[/tex]

Calculate the sum or difference:

= 16 /2

Cross out the common factor:

= 4

This shows that there are 4 cups of lemonade use the table.

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1) The vertical angle will be

∠RPQ= ∠TPU

Vertical angles are angles opposite each other where two lines cross.

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other. Real-life settings where vertical angles are used include; railroad crossing sign, letter “X'', open scissors pliers etc.

2) angle ∠QPR and angle ∠TPS are supplementary to ∠RPS

Supplementary angles are two angles whose measures add up to 180° . The two angles of a linear pair

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly,

3) complementary angle will be

∠QPR and ∠RPS

When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.

4) The adjacent angle will be ∠TPS

The two angles are said to be adjacent angles when they share the common vertex and side. The endpoint of the rays, forming the sides of an angle, is called the vertex of an angle. Adjacent angles can be a complementary angle or supplementary angle when they share the common vertex and side.

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Answer:

z score

Step-by-step explanation:

So, this distribution is positively skewed.

 A positively skewed distribution, also known as a right-skewed distribution, is a type of distribution in statistics in which most values are centered around the left tail and the right tail is longer. The direction of outliers is revealed by skewness. A distribution curve's tail is longer on the right side when there is a positive skew. As a result, the distribution curve's outliers are more extreme to the right and closer to the mean to the left.

Given Data

6 10 02 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Mean = [tex]\frac{6 + 10+2+4+6+8+10+12+14+16+18+20+22+24+26+28+30}{17}[/tex]

Mean = [tex]\frac{256}{17}[/tex]

Mean = 15.05

The distribution is said to be negatively skewed if the mean is lower than the mode. Positive skewness occurs when the mean exceeds the median in the distribution. The distribution is said to be negatively skewed if the mean is lower than the median.

So, this distribution is positively skewed.

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