4. In the diagram below, ABC is shown with AC extended through point D. If mzBCD = 6x + 2,
m/BAC = 3x + 15, and mLABC = 2x - 1, what is the value of x?

Answer:

h = 3

Step-by-step explanation:

y-6 = 4/7 (x-(-4)

y - 6 = 4/7 (x+4)

y - 6 = 4/7 x + 16/7

y = 4/7 x + 16/7 + 6

y = 4/7 x + (16+42)/7

y = 4/7 x + 58/7

10 = 4/7 x + 58/7

4/7 x = 10 - 58/7

4/7 x = (70-58)/7

4/7 x = 12/7

7/4 * 4/7 x = 12/7 * 7/4

x = 3

Using linear approximation, the function y = √33 is approximated as 5.744

The concept behind the linear approximation formula is the equation of a tangent line. We know that the slope of the tangent that is drawn to a curve y = f(x) at x = a is its derivative at that point. i.e., the slope of the tangent line is f'(a). Thus, the linear approximation formula is an application of derivatives. Let us learn more about this formula in the upcoming sections.

In equation y = √33

We can apply linear approximation to this

y = √33 = 5.744

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f(-1) = -11 and f(3) = -3 . these functions are true .

What does a math function mean?

given function  f(x) = 2x - 9

   f(-1) = -11 ⇒ x = -1 put in function

                       f( -1 ) = 2 * -1 - 9  ⇒ - 11

    f(2) = 5   ⇒ x = 2 put in function

                    f( 2 ) = 2 * 5 - 9 = 1

    f(3) = -3  ⇒  x = 3 put in function

                     f ( 3 ) = 2 * 3 - 9 = -3

       f(-3) = 15   ⇒  x =  -3 put in function

                     f( -3) = 2 * -3 - 9 = - 15

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Answer: what picture

Step-by-step explanation:

The solution of the inequality z + 1 ≥ 29 for z , is z ≥ 28  .

Inequality can be defined as a relationship between two expressions or values that are not equal to each other.

For Example : x > 3.

In the question ,

it is given that

the inequality is " z + 1 is greater than it equal to 29 ",

we have to solve this inequality for z ,

So inequality can be rewritten as

z + 1 ≥ 29

Subtracting 1 from both sides of the inequality , we get

z + 1 -1 ≥ 29 - 1

z ≥ 29 - 1

z ≥ 28 .

Therefore , The solution for z + 1 ≥ 29 , is z ≥ 28  .

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Answer:1/4 ×256/1= 64 women that left party

256-64= 192 women who remained

192+198=390 men and women at the party

Step-by-step explanation:

Answer: A. 5/99

Step-by-step explanation: This is bc it is repeating and 5 is an odd number.

The solution is y = -5

What is Quadratic Equation?

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 solution may be real or complex.

Given data ,

Let the function be f ( x ) = y

And , y = x² + 2x - 8

So , f ( x ) = x² + 2x - 8

Substituting the value for x in the equation , we get

When x = -3

f ( -3 ) = ( -3 )² + 2( -3 ) - 8

         = 9 - 6 - 8

         = 9 - 14

f ( -3 ) = -5

When x = 1

f ( 1 ) = ( 1 )² + 2( 1 ) - 8

       = 1 + 2 - 8

       = 3 - 8

f ( 1 ) = -5

Hence , the value of y = -5

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The probability that five tails will show is 1/32.

Given that the 5 coins are tossed. The probability of getting the head or the tails is 1/2 for each toss.

This means, total number of observations  = 2⁵  = 32.

Required outcome is → 5 Heads {H,H,H,H,H}

This can occur only ONCE! when all the coins show the heads.

Thus, required outcome  = 1

so, the Probability (5 Heads)  = 1/32.

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Answer:

y-y=x2-14x+14x+1-17

x2-16=0

x2=16

x=4

The relative maxima and relative minima for  f(x) = x⁵ - 4x³ + 3x² - 8x - 6 is   is -1.871 and  1.518

The given  function is  f(x) = x⁵ - 4x³ + 3x² - 8x - 6  ,now  differentiation function with respect to x we get  

=5x⁴ - 12x² + 6x - 8

Now solving the given  equation for the critical values are:

x₁ = 0.176 + 0.73i

x₂ = 0.176 - 0.73i

x₃ = 1.518

x₄ = -1.871

Now, taking derivative of the 5x⁴ - 12x² + 6x - 8  , with respect to x we get

= 20x³ - 24x + 6

now replacing the value of  x by   1.58, we get

20 * 1.58³ - 24 * 1.58 + 6

= 46.966, which is positive so it is the  minima

Again  replacing the value of  x by   -1.871, we get

=>20 * -1.871³ - 24 * -1.871 + 6

=> -169.9, which is negative so it is the maxima

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Answer: The answer should be 1.24.

Step-by-step explanation:

1.24209 rounded to the nearest hunredth is 1.24.

Answer:

1.24

Step-by-step explanation:

there are 33.814 fluid ounces in one liter. But she mixes 24 + 18 = 42 fluid ounces which is 1.24209 liters rounded to the nearest hundredth is 1.24

Answer: I think it (7,4.1)

Step-by-step explanation:

Answer:

7.3.0

Step-by-step explanation:

Answer: x = 14

Step-by-step explanation: Because these are vertical angles we know they are equal.

5x-10 = 60

Add 10 on both sides

5x = 70

Divide by 5 on both sides

x = 14

Mrs. Rowan's  , percent error is  40% .

In the question ,

it is given that ,

the time allotted by Mrs. Rowan to complete the exam = 30 minutes

the time that the last student took to complete the exam = 42 minutes

the percent error can be calculated using the formula

percent error = (time student take - time allotted) / (time allotted) × 100

Substituting the values of allotted time and time taken by the student from above , we get

percent error = (42 - 30)/30 × 100

= 12/30 × 100

= 0.4 × 100

= 40%

Therefore , Mrs. Rowan's percent error is  40% .

The given question is incomplete , the complete question is

Mrs. Rowan allotted 30 minutes at the beginning of class for her students to complete an exam. The last student took 42 minutes to complete the exam. What is Mrs. Rowan's percent error ?

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The total 12 people answered the survey in total when in a survey, 7 people said that their favorite card game was patience.

Given that,

In a survey, 7 people said that their favorite card game was patience.

We have to find how may people answered the survey in total.

Pie charts can be used to show percentages of a whole group and show percentages at a particular moment. In contrast to bar graphs and line graphs, pie charts do not show changes over time. The pages that follow provide a description of a pie chart's many elements.

We divide the patience by 7

210/7

30

So, For each person in patience we have 30°.

The total is

60°+30°+60°+210°

2+1+2+7

12

Therefore, The total 12 people answered the survey in total when in a survey, 7 people said that their favorite card game was patience.

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Using the scale of 7 millimeters : 3 meters as used by Rick the actual parking lot is 39 meters wide

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

solving for the width of the actual parking

7 millimeters = 0.007 meters

91 millimeters = 0.091 meters

0.007 = 3

0.091 = ?

cross multiplying

0.007 * ? = 3 * 0.091

? = 0.273/0.007

? = 39 meters

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The solution to the equation by linear combination is (b)  The solution is (4, 0).

From the question, we have the following system of equations

2x + y = 8

x – y = 4

By linear combination, we start by eliminating one of the variables

This is done by adding the equations

So, we have

2x + x - y + y = 8 + 4

Evaluate the like terms

3x = 12

Divide both sides

x = 4

Substitute x = 4 in x – y = 4

4 – y = 4

So, we have

y = 4 - 4

Divide

y = 0

Hence, the solution is (b) (4, 0)

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11 times the product of 19 and a number g?

11*(19g)

= 209g

70 Cos 20° rounded up to 1d.p is 65.8 and as a fraction is 658/10.

What is a fraction?

This refers to the value that is part of a whole number. It has a numerator (upper part) and a denominator (lower part) eg.1/2.

What is Decimal point?

This refers to a dot that is used to demarcate a whole number from the fractional part of a number. eg. 12.6.

The number of points/ values after the decimal point is called the decimal place. Example: 3.7  ( 1 decimal place), 4.26 ( 2 decimal places).

From the question:

Calculate 70cos 20° rounded to 1 d.p.

=70 * 0.9397

=65.78

rounded to 1 d.p.

=65.8

As fraction:

65.8 =65.8/10

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Answer:f(-10)= -60

Step-by-step explanation:

Answer:

f(- 10) = - 300

Step-by-step explanation:

substitute x = - 10 into f(x) , that is

f(- 10) = - 3(- 10)² = - 3(100) = - 300

Answer: Wat is dat green unlined as

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the prime factors of each number:

The greatest common factor of the three numbers is:

The equation of the linear function is  f(x) = 3x + 6

Given,

In the question:

The values are given as:

f(0)=6 and f(7)=27

To write a linear function.

Now, According to the question:

Write the equation of linear function:

y = mx + b

Substitute (0,6) and (7, 27) into y = mx + b:

6 = m x 0 + b

27 = m x 7 + b

Solve the equation:

6 = b

27 = 7m + b

Swap the sides :

b = 6

27 =7m +b

Substitute into one equation:

27 = 7m + 6

7m = 27 - 6

7m = 21

m = 3

Substitute b = 6 , m = 3 into y = mx +b

f(x) = 3x + 6

Hence, The equation of the linear function is  f(x) = 3x + 6

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The percent of decrease is 63.16%

How to calculate the percentage of decrease?

First, we calculate the amount of decrease

= $3,800 - $1,400

= $2,400

Next we dividing the amount of decrease by original price (old price)

= $2,400 ÷ $3,800

= 0.6316

And then convert the result into a percentage by multiplying by 100%

= 0.6316 × 100%

= 63.16%

Thus, the percent of decrease is 63.16%

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Answer:

None

Explanation:

A unique triangle can be defined as a triangle that can be formed in one way.

The various conditions that a triangle must satisfy so that it is unique :

a) A triangle where the length of the three sides is known or given is a unique triangle.

b) A triangle where two side lengths and their included angle is given is a unique triangle.

c) A triangle where two angles and their included side is given is a unique triangle.

d) A triangle where two angles and a non - included side length is known is a unique triangle.

In the above question, we are given angles 40°, 40° and 100 degrees

3 angles are known, no side length is given. The angles above can form a triangle called the obtuse triangle because their sum = 180° and one of the angles is great we than 90°

However, this does not satisfy the criteria that makes a triangle unique.

Therefore, no unique triangle(s) can be drawn with interior angles measuring 40°, 40°, and 100°.

Answer:

Step-by-step explanation:

Effective interest rate, r = [tex](1+\frac{i}{n} )^{n}-1[/tex]
Here,
r = effective annual rate
i = nominal rate
n = number of periods

r = [tex](1+\frac{0.0489}{12} )^{12}-1[/tex]

 = 0.05001099558

 = 5.001099558 %