Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.(14+3)(2 x 6)B▸ Math symbols▸ Relations▸ Geometry▸ Groups▸ TrigonometryStatistics▸ Greek

The theorem that justifies why triangle ABC is congruent to triangle CDA is the: SAS.

The SAS theorem states that if we can show that two triangles have a pair of corresponding congruent included angles, and two pairs of corresponding sides that are also congruent to each other, then we can prove that both triangles are congruent to each other.

The triangles, ABC and CDA have:

Two pair of corresponding sides that are congruent to each other, which are AB ≅ BC, and AC ≅ CA.

A pair of corresponding included angles, which is angle 1 ≅ angle 2.

Based on the above known information, we can conclude that triangle ABC is congruent to triangle CDA by SAS theorem.

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The area is 25π square inches

Given a radius, r = 5 in.

The area of a circle is given by the formula:

Substituting the value of r, we have:

The area is 25π square inches

First let's see how many hours are in a year:

We found that 1 year has 8769 hours, then if we lived 1,000,000 hours, we have to divide it by 8760 to know the number of years lived:

therefore, you would have lived 114.15 years

Answer:

the answer is c actully

Step-by-step explanation:

iv'e took that test b4 so you welcome

Given data:

The given figure is shown.

The area of the given figure is,

Thus, the area of the composite figure is 978 sq-inches.

First, we need to know the ratio of boys to girls in Mrs. Navarro's class. There are 16 boys and 20 girls. The ratio would be 16:20.

From this given, we can choose from the options which rations are equivalent to our given ratio.

8 to 10 is a ratio that is equivalent from our given. If we scale are ratio by 2, we can get 8:10.

5:4, 8:18, and 5 to 9, however, are NOT equivalent to 16:20.

4:5 is equivalent. We just need to scale 16:20 by 4, and we will get 4:5.

10:8 is another ratio that is NOT equivalent to 16:20.

*Scaling ratios are similar to finding the lowest terms of fractions.

Answer:

Substitute x = -8 into f(x).

f(-8) = 3(-8)² - 5(-8) + 20

= 3(64) + 40 + 20

= 192 + 60

= 252

1) Gathering the data

E (5,1.5) Circumcenter

H (4.3,2.3) incenter

I (3.6, 2.6) is the centroid.

2) Examining the figure we can see point C and B as the vertices of the

triangle, to find the radius let's use the distance formula between point E and C

E(5, 1.5) and C(3,5)

Since the radius is a line segment from the origin to the circumference then the distance BC = radius of the circumscribed triangle

Radius = 2.28

Mean Value Theorem

Supposing that f(x) is a continuous function that satisfies the conditions below:

0. f(x) ,is continuous in [a,b]

1. f(x) ,is differentiable in (a,b)

Then there exists a number c, s.t. a < c < b and

However, there is a special case called Rolle's theorem which states that any real-valued differentiable function that attains equal values at two distinct points, meaning f(a) = f(b), then there exists at least one c within a < c < b such that f'(c) = 0.

As in our case there is no R(t) that repeats or is equal to other R(t), then there is no time in which R'(t) = 0 between 0 < t < 8 based on the information given.

Answer: No because of the Mean Value Theorem and Rolle's Theorem (that is not met).

To answer this question we will use the following property of sets:

(a) Since Ash has 153 cards in his collection (without any duplicates), Brock has 207 cards in his collection (also without any duplicates) and they have 91 cards in common, then:

Simplifying the above result we get:

(b) Expressing the above result using set notations:

Answer:

(a) There are 269 unique cards in between them.

(b)

we have the points

(9,7) and (8,7)

Note that: The y-coordinates of both points are equal

that means

we have a horizontal line

therefore

Answer:

25/18 - 20

155/36 - 62

25/8 - 45

Step-by-step explanation:

Using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.

So, a number of adults and children who purchased the tickets:

Now, the equation can be:

Now, the second equation will be:

43.85a + 15.95c = 338.85

Now, substitute a = 9 - c in equation (2) as follows:

Hence:

Then:

Therefore, using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.

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Yesterday Ali had n Baseball cards.

Today he gave away 6 cards.

We are asked to write an expression for the number of cards Ali has left.

Ali had a total of n cards and he gave away 6 from them.

So, we have to simply subtract 6 cards from the total n cards.

Therefore, the expression is n - 6 represents the number of cards Ali has left.

As given by the question

There are given that function

Now,

To find the value of r(a^2), put x = a^2 into the function

Then,

Hence, the function is shown below:

Solve;

Therefore, x = -1

Step 1: Concept

You are going to apply the slope formula to find the slope of the line through each coordinate.

Step 2: Slope formula

The function is given as,

It is asked to find the value of the expression,

This can be obtained by replacing 'x' by 7 in the given expression of the function,

Resolve the parenthesis,

Simplify the terms further,

Thus, the value of the expression f(7) is obtained as,

we have that

K is the center of circle

J -----> point of tangency

segment IK is a radius

segment JL is a chord

segment GI is a secant

segment JI is a diameter

segment GJ is a tangent

arc JIL is a major arc

arc JL is a minor arc

arc JLI is a half circle (180 degrees)

Part 2

we have that

arc ST

Remember that

arc ST+87+72=180 degrees ------> by half circle

so

arc ST=180-159

arc WV

we have

arc WV+arc UV=180 degrees -----> by half circle

arc UV=72 degrees

so

arc WV=180-72

arc VUT

arc VUT=arc VU+arc UT

substitute given values

arc VUT=72+87

Answer:

I believe the answer is g(x)=x+10

Step-by-step explanation:

it moves 4 units to the right making it positive, adding to the previous 6 units, making it move 10 units to the right

In mathematical logic, the Law of Detachment says that if the following two statements are true:

( 1 ) If p, then q.

( 2 ) p

Then we can derive a third true statement:

( 3 ) q.

In our question, we have

( 1 ) If 0º< A <90º, then A is an acute angle.

( 2 ) The measure of A is 58º.

Then, from the first statement, we can affirm

( 3 ) A is an acute angle.

The minimum number of goals scored is 0 and maximum number of goals scored is 7. The range is equal to difference between maximum number of goals and minimum number of goals.

Determine the range for the goals scored.

So answer is 7.

By definition, a perfect square trinomial is a trinomial that can be written as the square of a binomial. It is in the form:

The simple trinomial is in the form:

Not all the simple trinomials can be written as the square of a binomial, then we need to check if the trinomial follows the structure of the perfect square trinomial. If it doesn't, then the factors won't be the same, and this is the main difference.

a. The given trinomial is:

If it is a perfect square trinomial then:

b. The given trinomial is:

Let's check if it is a perfect square trinomial:

Answer:

Step-by-step explanation:

I would recommend looking up the magic trig hexagon, it has all of these identities and more within it.

1 - this corresponds with C as sin^2(x)+cos^2(x)=1

1-cos^2(x) - this corresponds with A, using the identity from number 1, we can rewrite it in the form sin^2(x)=1-cos^2(x)

cot(x) - for this it is important to know that cotangent is the inverse of tangent. Since tan(x)=sin(x)/cos(x), cot=cos(x)/sin(x) which is B.

sec^2(x) - much like the cos and sin pythagorean identity, sec and tan are related. sec^2(x)=tan^2(x)+1 which is answer choice E.

tan(x) - this is sin(x)/cos(x), choice D.

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

Given,

The points which the line passes, (x₁, y₁) = (7, 6)

Slope of the line, m = 0

We have to find the equation of the line:

We know that,

y - y₁ = m(x - x₁)

So,

y - 6 = 0(x - 7)

y - 6 = 0

y = 6

That is,

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

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We were told that the distance from the Old North Church in Boston to Charlestown is approximately 1,410 meters.

Given that the speed of light is approximately 3 x 10 to the power of 8 meters per second and

speed = distance/time

It means that the number of seconds it took for the light to be visible in Charlestown is also the time it took the light to travel through 1410 meters

Therefore,

time = distance/speed

time = 1410/3 * 10 ^8 = 0.0000047 seconds

time = 4.7 * 10^-6 seconds

Without dividing, we can tell that 30:6 has smaller quotient between 30:5 and 30:6.

According to the question,

We have the following two expressions:

30:5 and 30:6

Now, we can easily find which expression has a smaller quotient when the dividend is the same. We need to look at the divisor. If the dividend is the same then the quotient will be smaller for the one with the greater divisor.

In this case, 30:6 has a greater divisor than 30:5 (6 is larger than 5). So, it will have smaller quotient.

Now, we can prove this by dividing both the expressions.

30/6 = 5

(So, it has smaller quotient.)

30/5 = 6

Hence, 30:6 has smaller quotient than 30:5.

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The first three terms of the sequence defined by the formula; Un=5n-2n³ as in the task content are; 3, -6 and -39 respectively.

It follows from the task content that the first three terms of the sequence defined by the formula be determined.

On this note, it follows that the first three terms are at; n = 1, n = 2 and n = 3 respectively.

Hence we have;

Hence, the first three terms are; 3, -6 and -39.

The first three terms of the sequence are as listed above.

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Solution

Using the Slope formula written above;

Therefore, the missing co-ordinate r is 5.

We have to solve the equation.

We have 2 unknowns and one equation, so we can only express one in function of the other.

We already have x in function of y, so we will now express y in function of x:

Answer:

y = -x/8 + 9/8