Which criterion can be used to prove ABC and ADC are congruent? select the correct answer

Answer:

Diameter = 3.1831 cm  (aprox)

Step-by-step explanation:

Diameter = circle / π

π ≈ 3.1414

Then:

Diameter = 10 / 3.1418

Diameter = 3.1831 cm

Equation of the given data y = 1750x -20,000 and graph of the equation is attached.

As given in the question,

Data of the table :

Year :               1                 2                   3              4                5

Investment : $20,000      $21,750      $23,500    $25,250      $27,000

(x₁, y₁) = ( 1, 20,000)

(x₂, y₂) = ( 2, 21,750)

Equation of the given graph is :

( y - 20,000)/ (x -1) = (21,750 - 20,000)/ (2 -1)

⇒ ( y - 20,000)/ (x -1) = 1750

⇒ y = 1,750x -18,250

Graph of the equation  y = 1,750x -18,250 s represented by the graph.

Graph is attached.

Therefore, equation of the given data y = 1750x -20,000 and graph of the equation is attached.

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From the given figure, m∠AEB = (3x + 54)° and m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.

As given in the question,

For the given figure,

Two lines AC and BD intersect each other at point E.

Measure of angles in the form of x is given as :

m∠AEB = (3x + 54)°

m∠DEC = (7x -30)°

∠AEB and  ∠DEC are vertically opposite angles.

⇒m∠AEB = m∠DEC

⇒ (3x + 54)°= (7x -30)°

⇒ 7x - 3x = ( 54 + 30 )°

⇒ 4x = 84°

⇒ x = 21°

Hence,

m∠AEB = (3x + 54)°

⇒m∠AEB = (3(21) + 54)°

⇒m∠AEB = 117°

Therefore, from the given figure m∠AEB = (3x + 54)° and

m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.

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We see BC is in the middle of the lines AB and BD, therefore mABC + mCBD = mABD.

We're given mABD = 75, mABC = 40.

Therefore, mCBD = mABD - mABC = 75 - 40 = 35.

Answer:

∠CBD = 35°

Step-by-step explanation:

We are told in the question that m∠ABD = 75° and m∠ABC = 40°. We are then asked what the value of m∠CBD is.

As we can see from the diagram, ∠ABD is made up of the angles ABC and CBD. Therefore:

∠ABD = ∠ABC + ∠CBD

⇒ 75° = 40° + ∠CBD

⇒ 75° - 40° = 40° + ∠CBD - 40°       [

⇒ 35° = ∠CBD

∴ ∠CBD = 35°

Answer:

a) 1

b) 0.5

c)0

The quadratic expression can be factorized to:

x*(x - 6)

Here we have the expression:

x^2 - 6x

To factorize this, first, we need to find the roots, which are the solutions of:

x^2 - 6x = 0

Notice that one of the solutions is trivial, and it is x = 0.

If now we assume that x ≠ 0 and divide both sides by x, we get:

x - 6 = 0

x = 6

That is the other solution.

Now, for a square polynomial with the roots a and b, the factorized form is:

(x - a)*(x - b)

In this case, the roots are 0 and 6, then:

x^2 - 6x = (x - 0)*(x - 6) = x*(x - 6)

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Answer:

x = 41.5

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

2x + 9 + x + 13 + x - 8 = 180 , that is

4x + 14 = 180 ( subtract 14 from both sides )

4x = 166 ( divide both sides by 4 )

x = 41.5

⇒The sum of the interior angles of a triangle is 180°

⇒Meaning (2x+9)°+(x-8)°+(x+13)°=180°

⇒Simplify the above equation to find the value of x.

⇒[tex]2x+x+x+9-8+13=180\\4x+14=180\\4x=180-14\\4x=166\\\frac{4x}{4} =\frac{166}{4} \\x=41.5[/tex]

∴ x=41.5

Applying the knowledge of congruent triangles, the measures are solved as:

6. X = 14; AC = 11; T = 14; WZ = 16; WY = 60; AB = 60; m∠A = 64°; m∠Y = 64°; m∠W = 50°

7. X = 7; YZ = 28; T = 9; WZ = 10; WY = 11; AB = 28; m∠A = 31°; m∠C = m∠W = 99°

To solve for the missing measures of triangles that are congruent to each other, recall that triangles that are congruent will have corresponding sides that are equal and also corresponding angles that are equal.

6. Triangles ABC and YWZ are congruent, therefore:

m∠A = m∠Y; m∠B = m∠W; m∠C = m∠Z

AB = WY; AC = YZ; BC = WZ

Therefore:

5X - 4 = 66

Solve for X

5X = 66 + 4

5X = 70

X = 14

AC = YZ = 11

AB = WY

5T - 10 = 4T + 4

5T - 4T = 10 + 4

T = 14

BC = WZ = 16

WZ = 16

WY = 4T + 4 = 4(14) + 4

WY = 60

AB = WY = 60

AB = 60

m∠A = m∠Y

m∠A = 180 - 50 - 66

m∠A = 64°

m∠Y = 64°

m∠B = m∠W = 50°

m∠W = 50°

7. Triangles ABC and ZYW are congruent, therefore:

m∠A = m∠Z; m∠B = m∠Y; m∠C = m∠W

AB = YZ; AC = WZ; BC = WY

Therefore:

5X - 4 = 3X + 10

Solve for x

5X - 3X = 4 + 10

2X = 14

X = 7

AB = YZ

2T + 10 = 4T - 8

2T - 4T = -10 - 8

-2T = -18

T = 9

YZ = 4T - 8 = 4(9) - 8

YZ = 28

AC = WZ = 10

WZ = 10

WY = 11

AB = YZ = 28

AB = 28

m∠A = m∠Z = 3X + 10 = 3(7) + 10

m∠A = 31°

m∠C = m∠W = 180 - 31 - 50 = 99°

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The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k

The given function is f(x)=7x^2.

The given vertex = (3,5)

The equation of the parabola with the vertex of (h,k) is

y=a(x-h)^2+k

On comparing we get; a=7, h=3, k=5

Now putting the value

f(x)=7(x-3)^2+5

Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

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Answer:

5x+10y

Step-by-step explanation:

to expand we distribute each term with 5

5(x)+5(2y)

5x+10y

Hopes this helps please mark brainliest

Answer: 5x + 10y

Step-by-step explanation:

Re-order terms so constants are on the left

(x+2y)x5

5(x+2y)

Distribute

5(x+2y)

5x+10y

Answer:

∠T

Step-by-step explanation:

∠T is the common angle found in both triangles.

In ΔPTS, ∠PTS represents ∠T.

In ΔQTR, ∠T is represented by ∠QTR.

Answer:

The angle T is common side.

Step-by-step explanation:

Given triangles,

→ ∆PTS & ∆QTR

Now we have to,

→ fInd common angle of both triangles.

The common angle is,

→ <T (angle T)

→ As it is present in both triangles.

Hence, the common part is angle T.

The probability that you select a black card and a red card is 26/51 as per the condition mentioned "choosing two cards (without replacement )".

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

Since we have not mentioned the order,

so it can black-red or red-black,

=26/52*26/51+26/52*26/51

=2*26/52*26/51

=26/51

Assuming you choose two cards (without replacement), there is a 26/51 chance that you will choose a black card and a red card.

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Answer:

Step-by-step explanation:

Arithmetic Sequence

Answer:

  (a)  Arithmetic Sequence

Step-by-step explanation:

You want to know if the graph of a straight line represent an arithmetic, geometric, or neither sequence.

An arithmetic sequence is characterized by a common difference between terms that are 1 unit apart. A graph of an arithmetic sequence is points that lie on a straight line.

The graph shows an Arithmetic Sequence.

__

Additional comment

A graph of a geometric sequence would show points that lie on an exponential curve.

Answer:

[tex]\sf s =\dfrac{-q}{pr}[/tex]

Step-by-step explanation:

               q = -spr

            -spr = q

     Isolate 's' by dividing both sides by (-pr).

           [tex]\sf \dfrac{-spr}{-pr}=\dfrac{q}{-pr}\\\\\\ s = \dfrac{-q}{pr}[/tex]

Answer:

Step-by-step explanation:

Yahweh’s

Using remainder theorem, Quotient = x-9 and Remainder = x² - x.

P(x) = −x³ – 2x² −9

P(-1) = −(-1)³ – (-1)x² −9

P(-1) = −(-1) – 2(1) −9

= 1 -2 -9

= -10

Remainder of  P(-1) = −(-1)³ – (-1)x² −9 is -10.

Remainder of P(x+1)

= −x³ – 2x² −9 / x+1

Quotient = x-9 and Remainder = x² - x

Hence, using remainder theorem, Quotient = x-9 and Remainder = x² - x.

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The number of cans that are recycled is approximately 1 billion cans in 1 week.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Given that  51.9 billion aluminum cans were recycled.

Therefore, the rate of recycled the can is;

51.9 billion / 1 year

We know that 1 year has 52 weeks

Then

51.9 billion / 1 year  x  1 year / 52 weeks

= 51.9 (1) billion / 1 (52 ) weeks

= 51.9 billion/ 52 weeks

= 1 billion/ 1 week

Hence, the number of cans that are recycled is approximately 1 billion cans in 1 week.

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Answer: g= 61/5 or 12.2

Step-by-step explanation:

The exponential equation represents an exponential growth because the rate of decay is 1.02 which is greater than 1.

y = 90(1.02)^x

The general form equation is:

y(x)= a(1+r)^x such that r is the decay percent.

on comparing,

1 + r = 1.02

r = 1.02 - 1

r = 0.02

converting into percent

r = 0.02 * 100

r = 2%.

Hence the exponential growth is 2%.

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Answer:

2 minutes for a whole song.

Step-by-step explanation:

Given that,

→ (1/6) song = (1/3) minutes

Parts of whole song is,

→ (1/6) × 6 = 1

Then the required minutes taken to play whole song will be,

→ x/6 = 1/3

→ x = (1/3) × 6

→ x = 6/3

→ [ x = 2 min ]

Hence, 2 minutes for a whole song.

Most researcher fix level of significance at 5% i.e. they conclude a significant relationship when nothing is going on in 5% of cases. Hence,

Option A is correct which is 1.5%

Given that,

The majority of social scientists are willing to claim that a link is statistically significant if the likelihood of observing the relationship in the sample when nothing is happening in the population is greater than a certain threshold.

To find:

Less than what percentage of the population truly experiences nothing at all (i.e., random chance)

The majority of researchers set the level of significance at 5%, which means they draw conclusions about a meaningful association even when nothing is happening in 5% of cases.

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The line that has a slope of -2 and a y-intercept of -1 is shown in the graph below.

An equation of a line in slope-intercept form that is expressed as y = mx + b, can be graphed if we know the value of the slope (m), and the value of the y-intercept (b).

We are given the following:

To write the equation of the line in slope-intercept form, substitute m = -2 and b = -1 into y = mx + b:

y = -2x - 1

This means that the rise/run of the line, which is the slope, to be graphed would be equal to -2 while the line will intercept the y-axis at point -1, because the y-intercept given is -1.

The line with the stated features are shown in the graph below.

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Answer:

15 coaches

Step-by-step explanation:

750 people go on a coach trip each coach can hold 50 people How many coaches are needed?

750/50 = 15 coaches

Answer:

750÷50 = 15

The answer is 15.

Because 750 people are going in a coach trip and each coaches can hold 50 people.

Answer:

Step-by-step explanation:

volume of a sphere = ⁴/3 π r³. r = D/2. V = 4/3 × π × (D/2)³. V = 4/3 × π × D³/8. V = ⅓ × π × D³/2. V = ⅓× π × (24mm)³/2.

The measure of ∠ YXR is 55 degrees.

Given that:-

m∠ XOY = 110 degrees

XR is a tangent to circle O at X.

We have to find the measure of ∠ YXR.

Draw the radii XO and OY to form the isosceles triangle XOY.

We know that the radius of the circle is perpendicular to the tangent.

Hence,  ∠OXR = 90 degrees.

Consider the triangle XOR, we know that XO and OY are the radii of the triangle and hence equal.

Let, ∠ OXY = OYX = x

Hence,

110 + x + x = 180 degrees

2x = 70 degrees

x = 35 degrees

Now, we know that,

∠ OXR = ∠ OXY + ∠ YXR

90 = 35 + ∠ YXR

∠ YXR = 90 - 35 = 55 degrees.

∠ YXR = 55 degrees.

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Each text will cost Hassan $0.09

A rate is a special ratio in which the two terms are in different units. It can also be defined as the amount of money that is charged for goods or services. For example, if a 12 malt can of costs 69¢, the rate is 69¢ for 12 malt. Then 1 malt will cost ¢69/12.

Similarly $5.31 is the cost of 59 text messages

Therefore a text message will cost $5.31/12=$0.09

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The function g(X) will be of the form g(x) = |x/6| ,when stretched by a factor of 6.

The function is f(x)=|x| .

We know that for transformation of a function of the form horizontal stretch by a factor of 'a' is given by the g(x)= f(x/a)

So in this given function the horizontal stretch is by a factor of 6.

Therefore g(x) = f(x/6)

or, g(x) = |x/6|

In the graph attached the green represents the function f(x) while the red represents the function g(x).

A function transformation either "moves," "resizes," or "reflects" the graph of anything similar to the parent function. The following are the three main types of function transformations:

Dilation is the only one of these changes that modifies the size of the original shape; the other two just change its location.

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The amount a container would take to spray 1 entire lawn is 7 litres.

Given that a container with 3½ liters of weed killer can spray 1/2 of a lawn.

We want to find the amount of liters to take a spray 1 entire lawn.

3½ liters of weed killer can spray 1/2,

liters take to spray 1 lawn is 3½/1/2=7 liters

Hence, the amount of liters it would take to spray 1 entire lawn when a container with 3½ liters of weed killer can spray of a lawn is 7 liters.

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