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Answer: 75 square units

Given:

sin(C) = 1/2

Area of Triangle:

= 1/2 × a × b × sin(C)

= 1/2 × 13 × 23 × 1/2

= 74.75

≈ 75 square units

Answer:

31

Step-by-step explanation:

x + 149 = 180

x = 180 - 149

x = 31

Answer: 31

Answer:

31°

Step-by-step explanation:

x + 149° = 180°

reason : because they are supplementary angle...

x = 180° - 149°

x = 31°

[tex]...[/tex]

The value of the expression 21x + 30y is -9

The equation is given as:

7x+10y=−3

Multiply both sides by 3

3 * 7x + 3 * 10y=−3 * 3

Evaluate the product

21x + 30y = -9

Hence, the value of the expression 21x + 30y is -9

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Answer:

Option (1)

Step-by-step explanation:

Angles 2 and 5 are supplementary by the same-side interior angles theorem.

Answer:

a. t = 3 + √15  or  t = 3 - √15

b. t =  6.87  or  t = -0.87

Step-by-step explanation:

a.

Given : t² = 6t + 6

t² = 6t + 6 ⇔ t² - 6t + 6 = 0

USING THE QUADRATIC FORMULA:

[tex]t=\frac{6\pm \sqrt{\left( -6\right)^{2} -4\left( 1\right)(-6) } }{2}[/tex]

Then

[tex]t=\frac{6\pm \sqrt{36 +24 } }{2}[/tex]

Then

[tex]t=\frac{6\pm \sqrt{60 } }{2}[/tex]

Then

[tex]t=\frac{6\pm 2\sqrt{15 } }{2}[/tex]

Then

t = 3 ± √15

Then

t = 3 + √15  or  t = 3 - √15

…………………………………………………

b.

t = 3 + √15 = 6.872983346207 ≈ 6.87

or  t = 3 - √15 = -0.872983346207 ≈ -0.87

Step-by-step explanation:

so, in other words, the price is

43.85 + 2.7 + 2.7 - 1.1 - 1.1 - 4.45 =

= 43.85 + 5.4 - 2.2 - 4.45 = 43.85 + 3.2 - 4.45 =

= 43.85 - 1.25 = 42.60

Answer:

A and C

Step-by-step explanation:

solving the equations

A

x² - 4 = 0 ( add 4 to both sides )

x² = 4 ( take square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2 ← required solution

B

x² = - 4 ← has no real solutions

C

4x² = 16 ( divide both sides by 4 )

x² = 4 ( take square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2 ← required solution

D

2(x - 2)² = 0 , then

x- 2 = 0 ( add 2 to both sides )

x = 2 ← not the required solution

Answer:

Answer A and C

Step-by-step explanation:

Let us solve the equations one by one and let us check whether the answers are matching with the answers given in the questions.

A) x² - 4 = 0

   ( x² - 2² ) = 0

   ( x -2 ) ( x + 2 ) = 0

   ∴ x - 2 = 0                   or           x + 2 = 0

      x = 2                                       x = -2               ( Matched )

B) x² = -4

  x = ±√-4  ← no real solutions                    (Not matched )

B)   3x² + 12 = 0

      3 ( x² + 4 ) = 0

      3 ( x² + 2² ) = 0 ← no real solutions      (Not matched)

C) 4x² = 16

Divide both sides by 4.

 x² = 4

 x = ±√4

 ∴ x = 2         or        x = -2       (Matched)

 D) 2 ( x - 2 )² = 0    

      (2x - 4)² = 0

      4x² - 16x + 16 = 0

Divide the whole equation by 4.

   x² - 4x + 4 = 0

 x² - 2x - 2x + 4 = 0

x ( x - 2 ) - 2 ( x - 2 ) = 0

( x - 2 ) ( x - 2) =

∴ x - 2 = 0          or        x - 2 = 0

  x = 2                            x = 2                 ( Not matched )

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope. The correct option is C.

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Since the given parallel line has equation y = 2x + 2 , thus its slope is 2 and thus, the slope of the needed line is 2 too.

The next step that Gerald should take is Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.

Hence, the correct option is C.

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Step-by-step explanation:

The translations of the typical functions are

[tex]y = a(bx + c) + d[/tex]

Where a is the vertical translation,

If a is greater than 1 or less than -1, we have a vertical stretch

If a is between -1 and 1 , we have a vertical compressions or shrink.

If a is negative, we have a negative reflection across the x axis.

If b is greater than 1 or less than -1, we have a horizontal compression or shrink

If b is between -1 and 1, we have a horizontal stretch

If b is negative, we have a reflection about the y axis,

If c is negative, we have a translation to the right c units

If c is positive, we have a translation to the left c units

If d is positive, we have a translation upward d units

If d is negative, we have a translation downward d units.

Here in this problem, our parent function is x^3.

So I would do the following transformations.

Answer:

10

Step-by-step explanation:

BX=2/3 (BP)

2/3 of 15 = 10

Using the t-distribution, the 95% confidence interval of the population mean rating for Miami is (4.97, 6.51).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 5.74, s = 2.7, n = 50[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Hence the bounds of the interval are given as follows:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 5.74 - 2.0096\frac{2.7}{\sqrt{50}} = 4.97[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 5.74 + 2.0096\frac{2.7}{\sqrt{50}} = 6.51[/tex]

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Answer:

Step-by-step explanation:

cost of 25 kg =262.50x25

                      =6562.5

In the case above, there will be about 6084 different codes and thus would  tree diagram would not be practical in this case because option C.  No, since there are too many choices.

Since there are 26 letters in an alphabet and only  9 digits in the third place is to be used.

Therefore, multiply the total number of alphabet cases is formed using letters in the first two characters and the digit in the third place and thus it will be:

26 × 26 × 9 = 6084

If a person is to show these 6084 cases using a tree diagram, it will be very complex and thus In the case above, there will be about 6084 different codes and thus would  tree diagram would not be practical in this case because option C.  No, since there are too many choices.

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Answer:

The translation is [tex]X+0[/tex]

Step-by-step explanation:

A translation means the transformation that moves every point in a figure at the same distance in the same direction.

The translation can be described using words like moved up 3 and over 5 to the left or with the notation.

As for the given, there can be no rule described. so the translation is [tex]X+0[/tex]

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The translation is [tex]X+0[/tex]

A translation means the transformation that moves every point in a figure at the same distance in the same direction.

The translation can be described using words like moved up 3 and over 5 to the left or with the notation.

As for the given, there can be no rule described. so the translation is[tex]X+0[/tex]

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Answer:

[tex]\boxed {D) -\frac{2y}{x}}[/tex]

Step-by-step explanation:

Solving :

[tex]\implies \mathsf {\frac{(-2xy^{2})^{3}}{4x^{4}y^{5}}}[/tex]

[tex]\implies \mathsf {\frac{-8x^{3}y^{6}}{4x^{4}y^{5}}}[/tex]

[tex]\implies \mathsf {\frac{-2y}{x}}[/tex]

Answer:

  6/x²

Step-by-step explanation:

Rational expressions are added the same way numerical fractions are added. Their sum is the quotient of the sum of numerators, and the common denominator.

__

The given fractions already have the same denominator, so we simply add their numerators.

  [tex]\dfrac{2}{x^2}+\dfrac{4}{x^2}=\dfrac{2+4}{x^2}=\boxed{\dfrac{6}{x^2}}[/tex]

At x = -1 , 0 ,1 ,2 , the y value = 0, 1, 2, 3, Option C is the correct answer.

A function is a law that relates a dependent variable to an independent variable.

The points of line are

(- 1, 0), (0, 1),(1, 2).

The equation of the line formed will be

y = mx +c

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

m = 1

y = x +c

at x = 0 , y =1

c = 1

The equation is

y = x+1

The option 1 is

x = - 1, 0, 1, 2.

y1 = 0, 4, 6, 8.

y2= 0, 2, 4, 6

y3 =0, 1, 2, 3.

From the equation

at x = -1 , 0 ,1 ,2

the y value = 0, 1, 2, 3

Therefore Option C is the correct answer.

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Step-by-step explanation:

x | y

-2.| 13

-1. | 15

0. | 17

1. | 19

2. | 21

just start with the y-intercept and then add 2 or subtract two depending on whether your increasing x or decreasing x. as x increases 1 y increases 2.

Answer:

C

Step-by-step explanation:

A quadratic has to have an exponent of 2 somewhere. The only one of these functions that does is C

The quadratic parent function is f ( x ) = x²

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.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

f ( x ) = x²

The graph of the function f(x) = x² is a parabola that opens upward, symmetric with respect to the y-axis, and its vertex is at the origin (0, 0)

Now , the value of y is the square of x

Hence , the parent function is f ( x ) = x² and graph is plotted

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I assume you meant r(x) = |x-2| -1.

Answer:

The horizontal asymptote is y=1 and

The vertical asymptote is x=5

Answer:

(3y+z)/20

Step-by-step explanation:

Begin by moving 3y to the right side of your equation:

20x=3y+z

Then divide both sides by 20 isolating x on one side of your equation:

x=(3y+z)/20

The required solution of the following equation 20x - 3y = z is

x=(3y+z)/20

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The following equation is

20x - 3y = z

According to given question we have

The equation is

20x - 3y = z

By simplifying we have to solve in terms of x

By move 3y to the right side of your equation:

20x=3y+z

Then divide both sides by 20 isolating x on one side of your equation:

x=(3y+z)/20

Therefore, the required solution of the following equation 20x - 3y = z is

x=(3y+z)/20

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Answer:

b is your answer

Step-by-step explanation:

Answer:

y = 2x - 1

Step-by-step explanation:

Given equation: 2x - y = 1

We're being asked to solve for y. This is also known as the Slope-Intercept Form. It is represented by the following formula:

y = mx + b

where:

Steps:

1. Subtract 2x from both sides:

[tex]\sf 2x-2x - y = 1-2x\\\\\implies-y=-2x+1[/tex]

2. Divide both sides by -1:

[tex]\sf \dfrac{-y}{-1}=\dfrac{-2x+1}{-1}\\\\\implies y=2x-1[/tex]

This equation has a slope of 2, and a y-intercept of -1.

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Answer: True: The graph of y=3x²-3 opens up

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (0,−3)(0,-3)

Focus: (0,−35/12)

Axis of Symmetry: x=0

Directrix: y=−37/12

X={-2, -1, 0, 1, 2}

Y={9, 0, -3, 0, 9

Step-by-step explanation:

Answer:

The y-coordinates do not change under a horizontal stretch. The x-coordinates do not change under a vertical stretch.

Step-by-step explanation:

Answer:

jackson sold 27 pounds of bananas and 12 pounds of grapes :D

Step-by-step explanation:

Taking into account the definition of a system of linear equations, the number of pounds of bananas and grapes sold are 36 and 16 respectively.

A set of two or more first-degree equations with two or more connected unknowns is referred to as a system of linear equations.

Finding the value of each unknown in order to satisfy all of the system's equations constitutes the process of solving an system of equations. To put it another way, it is necessary to find the values of the unknowns, as they must be replaced with values that, when used to solve the equations, is the process of solving a system of equations

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x +y= 52

x + 2.25y= 72

There are several methods to solve a system of equations, it is decided to solve it using the graphical method. The system's equations are graphically represented by graphs in the graphical method. The solution of the system is the point of intersection between the graphs, since the coordinates of said point satisfy both equations.

Graphically, it can be seen that the intersection point is (36; 16). That is, the value of x is 36 and the value of y is 16.

Finally, the number of pounds of bananas sold are 36 and the number of pounds of grapes sold are 16.

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There are 5 students who are 65 inches or taller. Option C is correct.

Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.

The term "height" is frequently used to describe someone's or something's height.

The height of the student in the Spanish class in the data set;

65, 63, 67, 59, 73, 60, 68, 61, 64, 60, 69

Student's heights are 65 inches or taller from the data set are;

65,67,73,68,69

There are 5 students who are 65 inches or taller.

Hence, option C is correct.

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Answer:

The responses for the seniors are reversed.

Hope this helped!