linear pair theorem
ZADCZBDC
given
2m BDC=180°
definition of supplementary
mzADC-mzBDC
definition of
congruence
m *ADC +
m BDC=180°
ADC is complementary
to BDC
substitution property of
equality
m BDC=180°
ADC is supplementary
to BDC
⠀⠀
m BDC=90°
division property of
equality

Answer:

Step-by-step explanation:

This looks like it is intended to represent two equations. They can be solved as a system in any of the usual ways.

The two equations seem to be ...

Adding 4y to the second equation gives ...

  x -4y +4y = -3y +4y

  x = y . . . . . . . . simplify

Substituting for y in the first equation gives ...

  4x -x = 3

  3x = 3 . . . . simplify

  x = 1 . . . . . divide by 3

  y = 1 . . . . . same as x

The variables x and y both have a value of 1.

__

The attachment shows a graphical solution to these equations.

A graph which represents a reciprocal relationship to the given graph would slope downward, which is in an opposite direction.

A reciprocal function can be defined as a type of function which comprises an algebraic expression in its denominator and a constant on its numerator such as: f(x) = 2/x.

In Mathematics, a reciprocal function is used when describing relationships that are inversely proportional to one other such as:

As a general rule in Geometry, we can infer and logically deduce that a graph which represents a reciprocal relationship to the given graph would slope downward, which is in an opposite direction.

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The order of steps to solve the equation are;

x^2 − 15 = 2x

(x − 5)(x + 3) = 0

x − 5 = 0 or x + 3 = 0

Potential solutions are −3 and 5

Logarithm expressions are inverse of an exponential function. Given the logarithm expression shown below:

log(x^2 − 15) = log(2x)

Cancel the log on both sides

x^2-15 = 2x

Equate to zero

x^2-2x-15 = 0

Factorize

x^2 -5x + 3x -15 = 0

x(x-5)+3(x-5) = 0

(x-5)(x+3) = 0

Find the solution

x - 5 = 0 or x + 3 = 0

Potential solution are 5 and -3

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Answer:

D

Step-by-step explanation:

quadratic formula

Answer:

I hope this is helpful. I had done my calculations and got the answer. The last part in orange is the answer. Your going to have to simplify.

The length of one of the legs says line AC is 58.31.

A figure can be placed in a coordinate plane on the graph by determining the coordinate of the vertices.

For the given isosceles triangle with:

The coordinate of the vertices are:

The length of one leg is calculated as follows:

[tex]\mathbf{AC= \sqrt{(50-0)^2+(30-0)^2}}}[/tex]

AC = [tex]\mathbf{\sqrt{2500+900}}[/tex]

AC = [tex]\mathbf{\sqrt{3400}}[/tex]

AC = 58.31

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This distance can be expressed as 3.84× [tex]10^{8}[/tex] m.

What is distance with example?

Given the distance between the earth and the moon is 384000km

Representing in exponential notation,

=384000×1000m  [∵1km=1000m]

=384× [tex]10^{6}[/tex] m

=3.84× [tex]10^{8}[/tex] m

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The correct question is -

The distance between the Earth and the moon is approximately 384000 km.  this distance can be expressed as ____m.

The difference between the retail and wholesale unit price is $ 0.99.

The retail price is the price that the item is sold for to the customer.

Here,

Coordinates extracted from the graph;

(4, 1)     (12, 3)

Equation of straight line (Whole sale price)

(y - y₁) = m(x - x₁)                  

where, m = (y₂-y₁)/(x₂-x₁)

then, m = (3-1) / (12-4)

            = 2/8

           = 1/4

Now,   (y - 1) = 1/4 (x - 4)

           4y - 4 = x - 4

            x = 4y

            x - 4y = 0

Now, whole sale price for 24 boxes; x = 24

           24 - 4y = 0

            4y = 24

             y = 24/4

             y = 6

The wholesale price = $ 6

The retail price = $ 6.99

The difference between retail and wholesale = Retail - Wholesale

                                                                            = 6.99 - 6

                                                                            = $ 0.99

Thus, the difference between the retail and wholesale unit price is $ 0.99.

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To calculate the area of a circle, we use the formula : [tex]\pi r^{2}[/tex], where r is radius.

We replace the numebrs : 144[tex]\pi[/tex] = 452,389342.... = 452 (rounded)

So, the area of this circle is 452 (and whatever units)

Answer:

Area of circle = 452 units²

Step-by-step explanation:

We can use the following formula to calculate the area of a circle:

Area = π r²

where r = radius of circle (12 units)

Substituting into the formula:
Area = π × (12)²

        = π × 144

        = 452.39

        = 452 units²       (rounded to the nearest whole number)

These are the expected numbers of spins that is P(N=n)=n−1/n!

According to the statement

Let N is the number of spins AND

Let S is the sums of spins until the sum is greater than one.

we know that the For N=1, P(S) = 0.

The value of expected random variables are

E(X)=μ=∑xP(x).

Put all the integers values in it and integrate.

According to statement condition the expected number of variables become

P(N=n)=P(Sn−1<1≤Sn)

P(N=n)= P(Sn−1 < 1) - P(Sn <1)

P(N=n)=1/(n−1)!−1/n!

P(N=n)=n−1/n!

So, these are the expected numbers of spins that is P(N=n)=n−1/n!

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Answer:

C

Step-by-step explanation:

The exact point should be (0, 4) if you're looking for the Y intercept. I'm assuming that each square represents one unit. Hope I could help.

Answer:

c)4

Step-by-step explanation:

Hope it helps!!!

y= 4

x= 0

Answer: [tex]g(x)=(x-5)^2[/tex]

Step-by-step explanation:

The graph of g is the graph of f translated 2 units to the right, so its equation is [tex]g(x)=(x-5)^2[/tex]

The volume of the box is 216 ft cube.

He filled a box with 4 layers of cubes that measured one foot on each side

The bottom of the box fit 6 cubes,

1 cube length = 1 ft.

Therefore,

volume of the box = 6³

Therefore,

volume of the box = 216 ft³

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The true statements about the function are:

The complete question is in the image

From the table, the function values do not exceed 0 at the interval 0 to 2.

This means that f(x) ≤ 0 over the interval [0, 2].

Also from the table, the function values exceeds 0 at the intervals greater than -2 but less than 0

This means that f(x)>0 over the interval (-2,0)

Also from the table, the function values are at least 0 at the intervals greater than 2

This means that f(x) ≥ 0 over the interval [2,∞)

Hence, the true statements are (b), (d) and (e)

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x = -2.5 is a vertical line. The vertical graph of the equation is shown in the image attached below.

The slope of a vertical line is undefined, therefore, the equation of a vertical line is expressed as x = a, where a is the x-intercept.

Given x = -2.5, the equation suggests it is a vertical line, where the line intercepts the x-axis at -2.5, which is the x-intercepts.

Thus, the graph for x = 2.5 is shown in the diagram below.

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Answer:

$0.70 per letter, $1.50 flat fee

Step-by-step explanation:

Let x be the flat fee.

Let y be the cost of sending 1 letter.

Lets create 2 equations from those 2 instances.

First Instance: x + 35y = 26 - Equation 1

Second Instance: x + 18y = 14.1 - Equation 2

To find x and y , we can use elimination method in solving simultaneous equations.

Equation 1 - Equation 2

x - x + 35y - 18y = 26 - 14.1

17y = 11.9

y = [tex]\frac{11.9}{17} \\[/tex]

= $0.70

Now we substitute y into equation 1.

x + 35(0.70) = 26

x + 24.50 = 26

x = 26 - 24.50

= $1.50

From the above we know the post charges $0.70 per letter sent and charges $1.50 flat fee.

The percentage of unemployed women from the total percentage of unemployed is 60%

Percentage of the unemployed women from the total unemployed = 15% / 25% × 100

= 0.60 × 100

= 60%

Therefore, the percentage of unemployed women from the total percentage of unemployed is 60%

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Answer: 94

Step-by-step explanation:

The area of each of the top and bottom face is [tex](4)(6)-(2)(2)=20[/tex].

The area of each of the side faces is 12.

The area of each of the faces facing out is 6.

The area of each of the 3 'inner' faces is also 6.

Adding these together,

[tex]20(2)+12(2)+6(2)+6(3)=94[/tex]

The probability that both sides of the card is red is 0.33

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that both sides of the card is red = total number of cards in which both sides are red / total number of cards

2/6 = 1/3 = 0.33

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Answer:

C. 6.9

Step-by-step explanation:

Pretend this is a 2-d diagram and use the Pythagorean theorem.

Pythagorean theorem: a^2 + b^2 = c^2

a = 6 mm

b = 7/2 = 3.5 mm

c = x

6^2 + 3.5^2 = x^2

36 + 12.25 = x^2

48.25 = x^2

[tex]\sqrt{48.25} = \sqrt{x^2}[/tex]

x = 6.9

The preference is that ✓5 should be left in radical form as an irrational number.

It should be noted that a radical form is illustrated when n is a positive integer that is greater than 1.

Here, a rational number is a number that can be represented in the form of p/q where p and q are integers. In this case, ✓5 will nvwe give a perfect number in decimal form. Hence, it's better to leave it radical form.

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Answer:

  C.  The point where the perpendicular bisectors of the three sides of the triangle intersect.

Step-by-step explanation:

A number of centers of a triangle are defined. The circumcenter is the center of the circumscribing circle. The incenter is the center of an inscribed circle. The centroid is the center of balance of a triangle of uniform mass density.

The centers defined by descriptions A through D are ...

  A. centroid -- coincident point of medians

  B. incenter -- coincident point of angle bisectors

  C. circumcenter -- coincident point of side perpendicular bisectors

  D. orthocenter -- coincident point of altitudes

The intermediate step of x² - 4x = 45 is (x- 2)² = 49

The equation is given as:

x² - 4x = 45

Take the coefficient of x

k = -4

Divide by 2

k/2 = -2

Square both sides

(k/2)^2 = 4

Add 4 to both sides of x² - 4x = 45

x² - 4x + 4= 45 + 4

This gives

x² - 4x + 4= 49

Express as perfect square

(x- 2)² = 49

Hence, the intermediate step of x² - 4x = 45 is (x- 2)² = 49

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The correct answer is  f, g, and h only.

What is variable ?

Given,

          expression f + 2g + h/4 - 7

So, in this expression g, f and h are variables.

We can see that in our given expression g, f and h are unknown, therefore, these are variables for our given expression.

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The correct question is -

What are the variables in this expression?

f + 2g + h/4 - 7

A) f and g only

B) g and h only

C) f, g, and -7 only

D) f, g, and h only

The required inequality is 3x + 2y > 390 and two possibilities is given by (100,45) and (80,75).

Student Council is selling t-shirts and hats for $21 and $14, respectively. The club needs to raise at least $2730.

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.

Let x for the number of t-shirts and y for the number of hats.

Now,
equation for to raise at least $2730.
21x + 14y > 2730
3x + 2y > 390

Two possibility can be caroled out from the graph i,e.  (100,45) and (80,75).

Thus, the required inequality is 3x + 2y > 390 and two possibilities is given by (100,45) and (80,75).  

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Answer:

4Hz

Step-by-step explanation:

Standard form of a sine or cosine function,

y = acos(b(x+c))

where a is the amplitude, b is the value to find the period. and c is the phase shift.

Period = \frac{2\pi}{b}

From the equation given in the question,

[tex]y = 3cos(8\pi \: t + \frac{\pi}{2} ) \\ y = 3cos(8\pi(t + \frac{1}{16} )) \: \: (factorising \: 8\pi \: out)[/tex]

We can see:

Amplitude = 3,

Period = \frac{2\pi}{8\pi} = 1 / 4

Phase Shift = 1 / 16

Now we want to find the frequency.

Frequency = 1 / Period

= 1 / (1/4)

= 4Hz

Answer:

[tex]\displaystyle 4[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Acos(Bx - C) + D[/tex]

When working with a trigonometric equation like this, always remember the information below:

[tex]\displaystyle Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A|[/tex]

So, the first procedure is to find the period of this graph, and when calculated, you should arrive at this:

[tex]\displaystyle \boxed{\frac{1}{4}} = \frac{2}{8\pi}\pi[/tex]

You will then plug this into the frequency formula, [tex]\displaystyle T^{-1} = F.[/tex] Look below:

[tex]\displaystyle \frac{1}{4}^{-1} = F \\ \\ \boxed{4 = F}[/tex]

Therefore, the frequency of motion is four hertz.

I am delighted to assist you at any time.

We can solve this graphically, we will see that f(x) = g(x) when x = -2, so the solution is x = -2.

We want to solve the system:

f(x) = g(x)

Where:

[tex]f(x) = 2x + 24\\\\g(x) = 5*(0.5)^x[/tex]

Replacing the functions, we get:

[tex]2x + 24 = 5*(0.5)^x[/tex]

Notice that on the left side x is a coefficient, while on the right side, it is an exponent, so this is really hard to solve with algebra.

But what we can do, is graph both functions, and see for which value of x the graphs do intersect.

Below you can see the graphs, the green one is f(x), the blue one is g(x).

There you can see that the graphs intersect at x = -2

This means that f(x) = g(x) only for x = -2.

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Multiplication is the process of multiplying. The length of the 10 fence panels is 18 meters.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given the length of three fence panels is 5.4 meters.

The lenght of each length panel = 5.4m/3 = 1.8 meter

The length of 10 fence panel = 1.8 meter×10 = 18 meter

Hence, the length of the 10 fence panels is 18 meters.

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The complete statements for the angles as in the task content are:

It follows from the task content that the arrangement involves two parallel lines q and s which are cut by transversal line r.

On this note, according to the description in the task content, the angles formed at the intersections are related as follows;

Angles 1 and 5 are congruent because they are

corresponding angles.

Angles 4 and 6 are congruent because they are alternate angles.

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Answer:

The y-intercept is 25000 . The intercept is the fixed cost of the doughnut selling company.

Step-by-step explanation:

In the question, it is given that the fixed cost is $25000 and the expense to produce each doughnut is $0.25.

It is required to find and identify the y intercept.

To do so, use the equation derived in previous part of the exercise to interpret the slope. Compare the equation with standard equation of the line.

Step 1 of 1

The total cost of the company is the sum of fixed cost and the expenses for the doughnut, C=0.25x+25000.

Compare the equation with general linear equation y=mx+c.

The y-intercept is 25000 .

The intercept is the fixed cost of the doughnut selling company.