1. Find the area of the given shape:
65m

6m

The simplified form of  (2x - 1)/(x² - 2x - 3 + 1)/(x - 3) is

(2x - 1)(x - 3)/(x - 1 - √3)(x - 1 + √3).

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, (2x - 1)/(x² - 2x - 3 + 1)/(x - 3).

=  (2x - 1)/(x² - 2x - 2)/(x - 3).

=  (2x - 1)/(x - 1 - √3)(x - 1 + √3)/(x - 3).

= (2x - 1)(x - 3)/(x - 1 - √3)(x - 1 + √3).

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Answer: [tex]\frac{5}{6}z+\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{5}{6}z+5-\frac{1}{2}-4\\\\\frac{5}{6}z+1-\frac{1}{2}\\\\\frac{5}{6}z+\frac{1}{2}[/tex]

2. The distance traveled by the remote control car each second is given as follows: C. 3 feet.

3. The equation of the linear function is given as follows: y = -2.5x + 80.

This distance is the rate of change of the output variable relative to the input variable of the linear function, hence it is the slope of the linear function.

Two points on the graph are given as follows:

(0,0) and (1,3).

Then the slope is calculated as the change in the output divided by the change in the input, as follows:

m = (3 - 0)/(1 - 0) = 3.

Meaning that option C is correct.

The linear function in this problem is defined in slope-intercept format, as follows:

y = mx + b.

In which the coefficients are given as follows:

When x = 0, y = 80, hence the intercept is given as follows:

b = 80.

When x increases by 8, y decayed by 20, hence the slope is calculated as follows:

m = -20/8 = -2.5.

This means that the equation is given as follows:

y = -2.5x + 80.

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For the given modeled of equation ý = 0.66x + 33.3 the interpretation of the residual is given option  D. 1.3 The regression line underpredicts the students class average.

As given in the question,

Equation to represents the grade of a students based on class attendance is given by :

ý = 0.66x + 33.3

Where ý is the grade of students in form of percentage.

And 'x' is the students attendance

Actual percentage = 94% when x = 90

Predicted percentage is,

ý = 0.66(90) + 33.3

  = 92.7%

Residual = Actual  - Predicted

              = 94% - 92.7%

               = 1.3

Actual > Predicted

Therefore, from the given equation the interpretation of the residual is given by Option D. 1.3 student's class average was underpredicted by the regression line.

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Answer:

DDDDDDDDDD

Step-by-step explanation:

please mark as brainliest please!!!!!!!

Answer:

45

Step-by-step explanation:

it's very easy to do if u know

For the given inequality 14 - 3f > 2 the option that comes out be correct is

f < 4 i.e option 2.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.The majority of the time, size comparisons between two numbers on the number line are made.

Here, "Less than" and "Greater than" have new meanings.

Less-than sign is the symbol for such phrase.

14 - 3f > 2

adding 3f on both sides:

14 - 3f + 3f > 2 + 3f

14 > 2 + 3f

subtracting 2 on both sides:

14 - 2 > 2 + 3f - 2

12 > 3f

dividing 3 on both sides:

(12)/3 > (3f)/3

4 > f

which means f < 4

Therefore, option 2 is correct.

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The simplification of the following expression, are;

21. 5t(2)(3) = 30t

24. 9(8n)= 72n

22. 7(a-b+5)= 7a - 7b + 35

25. 3k+ 6k-12 = 9k - 12

23. 9y+ 15y-10y = 14y

26. 2t + 5m+7t-4m = m + 9t

The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.

We are given the following expression, we need to simplify all of them;

21. 5t(2)(3)

= 30 t

24. 9(8n)

= 72n

22. 7(a-b+5)

= 7a - 7b + 35

25. 3k+ 6k-12

= 9k - 12

23. 9y+ 15y-10y

= 14y

26. 2t + 5m+7t-4m

= m + 9t

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Answer:

2

Step-by-step explanation:

The number of yellow marbles based on the given ratio will be 78.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Suppose, the number of yellow marbles is Y while purple marbles are P.

As per the given,

The ratio Y/P = 13/4

Total Y + P = 102

(13/4)P + P = 102

13P + 4P = 408

17P = 408

P = 24

And, Y = 102 - 24 = 78

Hence "The number of yellow marbles based on the given ratio will be 78".

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The subset of real numbers √3 belong to is irrational numbers

What is a subset ?

If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.

When all the components of Set A are also present in Set B, Set A is said to be a subset of Set B. Alternatively said, Set B contains Set A. Example: If set A contains X and Y and set B contains X, Y, and Z, then set A is a subset of set B because set B also contains X and Y.

As √3 is irrational number

∴it is a  subset of real numbers √3 belong to is irrational numbers

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The addition of equality states that "if you add on one side, you must add the same number to the other side."

The third term is

-2(3) +5 = -6+5 = -1

The fourth term is

-2(4) + 5 = -8+5 = -3

The fifth term is

-2(5) +5 = -10 +5 = -5

Add these 3 terms together

-1+-3+-5 = -9

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Answer:

If you divide 32.4 by 6, then you get 5.4 as an answer

Answer:

its 5

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

x^3/3-y

3^3/3-1

27/3-1

9-1

8

Hopes this helps please mark brainliest

The value for which test score is below 95% percent for the given mean and standard deviation on a college placement is equal to 696.

As given in the question,

Given :  95% of the test takers score are below z.

z-score is given  by,

z=(x-μ)/σ

Mean of the score 'μ' = 500

Standard deviation of the score ' σ' = 100

Z = 95%

  = 0.95

P(z<Z) = 1-0.95

           = 0.05

The value of z which corresponds to 0.05 in the table is equal to 1.96.

Substitute all the values we get,

z=(x-μ)/σ

⇒1.96 = ( x - 500 ) / 100

Multiply by 100 both the sides we get,

⇒ 196 = ( x - 500 )

⇒ x = 696

Therefore, the value for which test score is below 95% percent for the given mean and standard deviation is equal to 696.

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The ordered pair that describes the location of M' is (-5, -1)

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

Point M = (5, -1)

This point can be represented as

(x, y) = (5, -1)

Also, from the question, we have the transformation to be:

Point M is reflected over the y axis

Mathematically, this can be expressed as

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

So, we have

Point M' = (-5, -1)

Hence, the image is (-5, -1)

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Answer:

  $13.60

Step-by-step explanation:

You want to evaluate the rental cost function C(x) = 12.00 +0.08x for x = 20.

Put the value for x where x is in the cost function and do the arithmetic.

  C(x) = 12.00 +0.08x

  C(20) = 12.00 +0.08·20 = 12.00 +1.60

  C(20) = 13.60

The total rental cost if Josh drives 20 miles is $13.60.

The equation after the transformation is y = -5x - 1

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

Equation: 5x - y = 15

Make y the subject

So, we have

y = 5x + 15

The rule of reflection across the y-axis is

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

So, we have the following equation

y = -5x + 15

The rule of translation by (3 -1) is

(x, y) = (x + 3, y - 1)

So, we have the following equation

y = -5(x + 3) + 15 - 1

Expand

y = -5x - 15 + 15 - 1

So, we have

y = -5x - 1

Hence, the equation is y = -5x - 1

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The required transformations would carry reflection over the y-axis of the triangle in the given figure.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The figure is given in the question,

According to the given graph, the required transformations would be as:

In the above illustration, the needed transformations would convey reflection over the y-axis of the triangle.

Thus, the required transformations would carry reflection over the y-axis of the triangle in the given figure.

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When two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.

Alternate External Angles

The pairs of angles outside the two lines and on either side of a transversal that cuts two lines are referred to as the alternate external angles.

In the given diagram below, the alternate exterior angles are:

∠2 and ∠8

∠1 and ∠7

Hence, when two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.

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To graph a sequence, let a term's position number [tex]n[/tex] in the sequence be [tex]x[/tex]value.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

Starting with a number and repeatedly adding a fixed constant (d) to it is an easy technique to create a series. An arithmetic sequence is this kind of sequence.

Definition: A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.

The term [tex]a_{n}[/tex] is the corresponding y value

Plot the ordered pairs

Make a table then plot the ordered pairs ([tex]n, a_{n}[/tex])

Position, [tex]n[/tex]                                   Term, [tex]a_{n}[/tex]                                    ([tex]n, a_{n}[/tex])

     1                                                  -15                                        (1, -15)

     2                                                  0                                          (2, 0)

     3                                                  15                                         (3, 15)

     4                                                  30                                        (4, 30)

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The probability that we dealt with two queens as private cards is = 0.0046 .

In the question ,

it is given that ,

the two cards are drawn as private cards,

we have to find the probability that you are dealt with two queens .

the total number of cards in deck is = 52 ,

total number of queens in the deck is = 4 ,

So , the number of ways 2 queens can be drawn from 4 queens is = ⁴C₂ ways .

So , the total number of ways 2 cards can be drawn is = ⁵²C₂

So , the required probability is = ⁴C₂ / ⁵²C₂ .

= 6/1326

= 0.0046

Therefore , the required probability is 0.0046  .

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Step-by-step explanation:

When Mr Norman turns 58, he will be two years older than twice the age his daughter will turn in January. How old is Nicole now?

equation: 58 = 2d + 2

58 = 2d + 2

subtract 2 from both sides:

56 = 2d

divide both sides by 2:

d = 28 , so his daughter is 28 years old.

The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.

The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.

To do this, you must multiply both the ordinates and the powers of ten portions of the two numbers (the mantissas).

In mathematics and algebra, multiplying seven occurrences of a given number by themselves yields the number's seventh power.

Consequently, n7 = n n n n n n.

Let's write 7 to the power of 4.0.2 to the power of 4 is 0.0016 one step at a time.

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The value of x will be;

⇒ x = 8 1/4

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ - 1/3 (x + 1 1/2) = - 3 1/4

Now,

Since, The expression is,

⇒ - 1/3 (x + 1 1/2) = - 3 1/4

Solve for x as;

⇒ - 1/3 (x + 3/2) = - 13/4

⇒ x + 3/2 = 13/4 × 3/1

⇒ x + 3/2 = 39/4

⇒ x = 39/4 - 3/2

⇒ x = 39/4 - 6/4

⇒ x = 33/4

⇒ x = 8 1/4

Thus, The value of x will be;

⇒ x = 8 1/4

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Answer:4 tablespoons

Step-by-step explanation:

1 = 16 tablespoons

1/4 = 4 tablespoons

Take 16 divided by 4 = 4

Step-by-step explanation:

please see the attachment