choose the abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent. given: ∠c, ∠f are rt. ∠'s; ∠b

The solution to the equation 2(t - 5) = 48 is t = 29.

To solve the equation 2(t - 5) = 48, we can use the following steps:

Distribute the 2 to the terms inside the parentheses:

2t - 10 = 48

Add 10 to both sides of the equation to isolate the variable term:

2t = 58

Divide both sides of the equation by 2 to solve for t:

t = 29

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A function assigns the value of each element of one set to the other specific element of another set. The zeroes of the functions are -2, 1, and 3.

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x) = (x - 1)(x + 2)(x − 3), therefore, the zeroes of the functions are -2, 1, and 3. The end behavior of the function is that if x approaches ∞ then f(x) approaches ∞, while if x approaches -∞ then f(x) approaches -∞, as can be observed from the given graph.

Hence, the zeroes of the functions are -2, 1, and 3.

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Answer:

−1, 2, −3; continues downward to the left and upward to the right

Step-by-step explanation:

A 95% confidence interval for percent of american adults who believe in aliens:  (0.6578, 0.7822)

In this question we have been given that in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens

We need to find the 95% confidence interval for percent of american adults who believe in aliens.

95% confidence interval = (p ± z√[p(1 - p)/n])

Here, n = 200

p = 72%

p = 0.72

And the z-score for 95% confidence interval is 1.960

The upper limit of interval would be,

(p + z√[p(1 - p)/n])

= 0.72 + 1.960 √[0.72(1 - 0.72)/200]

= 0.72 + 1.960 √[(0.72 * 0.28)/200]

= 0.72 + 1.960 √0.001008

= 0.72 + 0.0622

= 0.7822

The lower limit of interval would be,

(p - z√[p(1 - p)/n])

= 0.72 - 1.960 √[0.72(1 - 0.72)/200]

= 0.72 - 1.960 √[(0.72 * 0.28)/200]

= 0.72 - 1.960 √0.001008

= 0.72 - 0.0622

= 0.6578

Therefore, a 95% confidence interval = (0.6578, 0.7822)

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The first term of the arithmetic progression is 5

An arithmetic sequence can simply be defined as a sequence of numbers or terms in which the differences between successive or consecutive terms are always equal.

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + (n-1)d

Where;

Given that the first term of the sequence is a, the 43rd term is 26 and the common difference is 1/2

Substitute the values into the formula

26 = a + (43 -1)1/2

expand the bracket

26 = a + (42)1/2

Multiply through

26 = a + 21

collect like terms

a = 26 - 21

a = 5

Thus, the value is 5

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Answer:

8/3 or 2 2/3

Step-by-step explanation:

Answer:

area of whole pizza = 200.96 in²

area of slice of pizza = 25.12 in²

Step-by-step explanation:

16"/2 = 8" radius

area = πr² = (3.14)(8²) = 200.96 in²

200.96 in²/8 = 25.12 in²

Answer:

6 thousand 438 divided by 6 equals 1 thousand 73

953 divided by 7 equals 136 R 1

Step-by-step explanation:

Calculation for the equations that are correct

The equations that are correct are:

6 thousand 438 divided by 6 equals 1 thousand 73 which is written as 6,438/6=1073 will be calculated using this formula

Numerator/Denominator

Where,

Numerator=6,438

Denominator=6

Let plug in the formula

6,438/6

=1,083

953 divided by 7 equals 136 R 1 which is written as 953/7= 136.1 is calculated using this formula

Numerator/Denominator

Where,

Numerator=953

Denominator=7

Let plug in the formula

953/7

=136.1

Therefore the equations that are correct are :

6 thousand 438 divided by 6 equals 1 thousand 73 and 953 divided by 7 equals 136 R 1

1) x = 5y - 30  

2) x = - 1.6y + 3.3

im assuming these are 2 different questions

Start with the equation:

x - 5y= -30

add 5y to both sides:

x = 5y - 30

Your answer is x = 5y - 30  

Start with the equation:

3x+5y=10

subtract 5y from both sides:

3x = -5y + 10

divide by 3 to get x singular

x = - 1.6y + 3.3

Your answer is x = - 1.6y + 3.3

Hope this helps :)

Answer: 5.5 hours

Step-by-step explanation: You do 198/36 and you'll get 5.5

Answer:

We can use the formula:

time = distance / speed

where distance is the distance traveled and speed is the constant rate at which the driver is traveling.

Plugging in the values we know, we get:

time = 198 miles / 36 miles per hour

Simplifying, we get:

time = 5.5 hours

Therefore, it would take the driver 5.5 hours to drive 198 miles at a constant rate of 36 miles per hour

When the  sum of two numbers is 27. The difference between the two numbers is 5. The two numbers are

Let's call the two numbers x and y.

From the problem, we know that:

The sum of the two numbers is 27

x + y = 27

The difference between the two numbers is 5

x - y = 5

The problem is a simultaneous equation and can be solved by elimination method as follows

We can start by adding the two equations together:

x + y + |x - y| = 27 + 5

x + y + (x - y) = 32

So we can simplify the equation:

2x = 32

x = 16

substitute x = 16 into x + y = 27

16 + y = 27

y = 11

So the two numbers are x = 16 and y = 11.

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Answer:

It is not an identity.

Step-by-step explanation:

Answer:

x = 59/7, y = -15/7

Step-by-step explanation:

4x= 2y + 38;

2 - 3y=x

We can substitute for x  in the first equation since the second equation is solved for x

4(2-3y) = 2y+38

Distribute

8 - 12y = 2y+38

Add 12y to each side

8-12y+12y = 2y+12y+38

8 = 14y+38

Subtract 38 from each side

-30 = 14y

Divide by 14

-30/14 = y

-15/7 = y

Now solve for x

2 - 3y = x

2 - 3*-15/7 = x

2 +45/7 = x

14/7 + 45/7 = x

59/7 =x

The improper integral ∫(6 to ∞) dx / (x^2 - 25) is convergent. The value of the integral is equal to π/10.

To evaluate the integral, we can use the method of partial fractions. First, we factor the denominator as (x - 5)(x + 5). We can then express the integrand as A / (x - 5) + B / (x + 5), where A and B are constants.

Next, we find the values of A and B by equating the numerators of the fractions. After solving the equations, we get A = 1/10 and B = -1/10.

Using the partial fraction decomposition, the integral becomes ∫(6 to ∞) (1/10) [(1 / (x - 5)) - (1 / (x + 5))] dx.

We can then integrate each term separately. The antiderivative of 1 / (x - 5) is ln|x - 5|, and the antiderivative of 1 / (x + 5) is ln|x + 5|.

Evaluating the integral, we have [1/10 * ln|x - 5| - 1/10 * ln|x + 5|] evaluated from 6 to ∞. As x approaches infinity, ln|x - 5| and ln|x + 5| both approach positive infinity. Therefore, the integral converges to a finite value

The final result is [1/10 * ln|x - 5| - 1/10 * ln|x + 5|] evaluated at ∞ minus [1/10 * ln(6 - 5) - 1/10 * ln(6 + 5)] = [1/10 * ln∞ - 1/10 * ln6] = π/10. Thus, the value of the improper integral is π/10, indicating convergence.

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Answer:

x=4

Step-by-step explanation:

Answer:

B) x=4

Step-by-step explanation:

Answer:

  y = -6x +3

Step-by-step explanation:

You want the slope-intercept equation matching the given graph.

The line on the graph crosses the y-axis at the marked point (0, 3). Another point is marked at (1, -3), which is 1 unit right and 6 units down.

The first point tells you the y-intercept (b) is +3.

The second point tells you the slope (m) is rise/run = -6/1 = -6.

Then the point-slope equation is ...

  y = mx + b

  y = -6x +3

<95141404393>

Answer:

$9.60

Explanation:

4 divided by 5= 0.8

0.8 times 12= 9.6

Answer:

Multiply

Step-by-step explanation:

You need to multiply the number by 10 or 100 or 1000 according to the number. but after multiplying it should become a whole digit. And you also need to multiply 10 or 100 or 1000 in the dividend.

Hope this has helped you.

Answer:

H(1 , 0.5)

F(3 , 2,5)

G(5 , 0.5)

Step-by-step explanation:

First step is to get the coordinates of the points.

H(2,1)

F(6,5)

G(10,1)

To find the vertices after a dilation, we multiply the coordinates by the scale factor of the dilation. Since the scale factor is 0.5, its the same as dividing by two.

The new points are

H(1 , 0.5)

F(3 , 2,5)

G(5 , 0.5)

Answer:

4/6

Step-by-step explanation:

Answer:

9.9

i dont know how to explain this lol i just know

Answer:

y=4x+23

Step-by-step explanation:

sorry  cant choose answer choice ..i ant tell which is which...bu i think you should by now....

i hope this stilled helped

9514 1404 393

Answer:

  80

Step-by-step explanation:

If N is the total number of coins, then the number of quarters is ...

  36 = 0.45×N

 36/0.45 = N = 80

You have 80 coins you your collection.

- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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To find the sum and product of the roots of the equation x² - 2x + 3 = 0, we can apply Vieta's formulas.

Vieta's formulas state that for a quadratic equation of the form ax² + bx + c = 0, the sum of the roots is equal to the negation of the coefficient of the linear term (b) divided by the coefficient of the quadratic term (a), and the product of the roots is equal to the constant term (c) divided by the coefficient of the quadratic term (a).

In this case, the quadratic equation is x² - 2x + 3 = 0. The coefficient of the quadratic term (a) is 1, the coefficient of the linear term (b) is -2, and the constant term (c) is 3. According to Vieta's formulas, the sum of the roots is (-b/a) = -(-2)/1 = 2, and the product of the roots is (c/a) = 3/1 = 3. Therefore, the sum of the roots is 2 and the product of the roots is 3.

Vieta's formulas provide a relationship between the coefficients of a quadratic equation and the roots of the equation. For a quadratic equation of the form ax² + bx + c = 0, where a, b, and c are real numbers, the sum of the roots is given by the negative ratio of the coefficient of the linear term (b) to the coefficient of the quadratic term (a), while the product of the roots is given by the ratio of the constant term (c) to the coefficient of the quadratic term (a).

In the given equation x² - 2x + 3 = 0, the coefficient of the quadratic term is 1, the coefficient of the linear term is -2, and the constant term is 3. Applying Vieta's formulas, we find that the sum of the roots is 2 and the product of the roots is 3. This means that if we were to factorize the equation, the roots of the equation would satisfy the equation (x - root1)(x - root2) = 0, where root1 and root2 are the two roots of the equation.

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Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

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Answer:

first find constant term

y=kx

32=k(4)

32/4=4k/4

k=8

find value of y when x=5

y=kx

y=8×5

y=40

Answer:

g^3 - 7

Step-by-step explanation:

write

(2g^2+3g-8)-(5g+1)

(5g^3-8)-(5g+1)

and then you get g^3 - 7

sorry if it is not write but it should be

Answer:

\(8x^2+19x+3\)

Step-by-step explanation:

\(3x^2+7x+3+5x^2+12x=\\3x^2+5x^2+7x+12x+3=\\8x^2+7x+12x+3=\\8x^2+19x+3\)

Answer:

i did it

Step-by-step explanation: