What additional information would you need to prove that ΔABC ≅ ΔDEF by SAS?​

Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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The rate of change of the function h(x) = 2x on the interval 2 ≤ x ≤ 4 is 6.

Answer:

Step-by-step explanation:

Let's start by using the formula for the perimeter of a rectangle:

P = 2L + 2W

where P is the perimeter, L is the length, and W is the width.

We are given that the perimeter is 70 cm, so we can substitute this in the formula:

70 = 2L + 2W

Dividing both sides by 2, we get:

35 = L + W

We are also given that the length is six times the width, so we can write:

L = 6W

Substituting this in the equation we just derived, we get:

35 = 6W + W

Simplifying, we get:

35 = 7W

Dividing both sides by 7, we get:

W = 5

So the width of the rectangle is 5 cm.

Using the equation L = 6W, we can find the length:

L = 6 x 5 = 30

So the length of the rectangle is 30 cm.

Therefore, the length of the rectangle is 30 cm and the width is 5 cm.

Answer: 200 texts

Step-by-step explanation:

          If they paid the same amount, we can set the equations equal to each other and solve for x using inverse operations.

    Given:

0.1x + 10 = 0.15x

    Subtract 10 and 0.15x from both sides of the equation:

-0.05x = -10

    Divide both sides of the equation by -0.05:

x = 200

I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.

II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.

III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.

IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.

I. Gaussian Elimination Method:

To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:

| 6 2 -1 | 4 |

| 1 5 1 | 3 |

| 2 1 4 |27 |

We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.

After performing the necessary row operations, we obtain the following reduced row-echelon form:

| 6 2 -1 | 4 |

| 0 4 2 | -1 |

| 0 0 3 | 6 |

From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.

II. LU-Decomposition Method:

LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.

III. Gauss-Jacobi Method:

The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.

IV. Gauss-Seidel Method:

Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.

Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.

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Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Answer:

He should drive his car at a speed of 81.25 kilometers per hour.

Step-by-step explanation:

With a velocity of 65 kilometers per hour, he reaches home in 50 minutes. What speed he needs to reach home 10 minutes earlier, that is, in 50 - 10 = 40 minutes?

To solve this, we use the relation between inverse proportion variables(as the velocity increases, time needed decreases), that is, a rule of three with line multiplication, instead of cross. So

65 kilometers per hour - 50 minutes

x kilometers per hour - 40 minutes

So

\(40x = 65*50\)

\(x = \frac{65*50}{40}\)

\(x = 81.25\)

He should drive his car at a speed of 81.25 kilometers per hour.

Answer:

a. <B = 53°

b. BC = 14

c. x = 14

Step-by-step explanation:

a. <B = ?

Use Sine.

Sine(<B) = 12 /15

<B = Sin^-1(12/15)

<B = 53.13

<B = 53°

b. BC = ?

Either use Sine(<A) = BC/16 or Cosine(<C) = BC/16

Will be using Cosine.

Cosine(<C) = BC/16

Cosine(30°) = BC/16

BC = 16 * Cos(30°)

BC = 13.856...

BC = 14

c. x = ?

Looking at the triangle. The triangle is isosceles which mean two side angle or side length are the same.

x = 14

Answer:

A: 53.13

B:13.86

C: 14

Step-by-step explanation:

A can be found by using the trigonometric ratio Sin.

Sin=

\( \frac{opp}{hyp} \)

And we have our opposite side and hypotenuse. so insert it:

Sin=12/15

Therefore use sin inverse and input that fraction

\(sin { }^{ - 1} ( \frac{12}{15} )\)

=53.13010235

Rounded off to two decimals

=53. 13

B can be found using sin again. Since we know that Sin is opp/hyp and we have the hyp, we are now looking for the opp.

So use Sin(60)=BC/16

Multiply 16 on both sides to get: 16Sin(30)=BC

13.85640646=BC

rounded off to two decimals:

13.86

C can be found using Tan. Tan is opp/adjacent

We have the adjacent and we are looking for the opposite.

So use:

tan(45)=X/14

Multiply 14 on both sides

14tan(45)=X

14=X

Hope that helps!

Answer:

A

Step-by-step explanation:

(x-4)^2 = x^2 -4x -4x + (-4)*(-4)

= x^2-8x+16 as required

Probability = # of desired options / # of total options

Our desired option is blue and there are 9 blue marbles in the bag.

There are 32 total marbles (options) in the bag.

P(blue) = 9 / 32 = 0.28125 = 28.125%

Hope this helps!

Answer:G=1/4 or the same as g=0.25

Step-by-step explanation:

Answer:

1/4 is the answer.

Step-by-step explanation:

So first, you subtract the g-9g. You get -2 = -8g, correct?

Next, you divide -2 by -8, you then get -2/-8

This simplifies to 1/4.

Hope this helped. :)

Answer:

21

Step-by-step explanation:

The number of bears that the researcher should be expected to see in the larger central Pennsylvania forest with about 1,000 total animals is given as follows:

95 bears.

To obtain the number of bears in the larger forest, first we must obtain the proportion in the smaller forest.

The proportion is given by the number of bears divided by the total number of animals, both of these amounts given by the bar graph presented at the end of the answer.

The number of bears is given as follows:

20.

The total number of animals is given as follows:

20 + 70 + 30 + 90 = 210.

Meaning that the proportion of bears is of:

20/210.

Hence, out of 1000 animals, the expected number of bears is of>

20/210 x 1000 = 20000/210 = 95 bears.

The bar graph is given by the image presented at the end of the answer.

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Answer:

830.53 in²

Step-by-step explanation:

Find the area of the full circle and divide it by 2:Use the circle area formula, A = r²Plug in 3.14 as pi, and plug in the radius:A = r²A = 3.14(23²)A = 1661.06Divide this by 2:1661.06 / 2= 830.53So, the area of one semicircle is 830.53 in²

Answer: The area of one semicircle is approximately 830.53 square inches.

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr²

where A is the area of the circle and r is its radius.

The radius of the circle cut out of the piece of wood is about 23 inches. Therefore, its area is:

A = πr²

A = π(23)²

A = π(529)

A ≈ 1661.06 square inches

The carpenter cuts the circle into two semicircles. Therefore, the area of one semicircle is:

A/2 ≈ 830.53 square inches

Therefore, the area of one semicircle is approximately 830.53 square inches.

I hope this helps! Let me know if you have any other questions.

Answer:

∠ B ≅ ∠ E

Step-by-step explanation:

Since the triangles are congruent then corresponding angles are congruent

ABC ≅ DEF

The corresponding angles are B and E

Answer:

The answer is \(\angle B\cong \angle E\)

Step-by-step explanation:

Given that

\(\Delta ABC \cong \Delta DE\)\(F\)

Hence corresponding angles are congruent

\(\angle B\cong \angle E\)

The solution to the equation 2(x+1) = -8 is x = -5.

Given information:

The equation is 2(x+1)=-8.

In order to solve the equation 2(x+1)=-8, follow the process given below.

1. Distribute the 2 to the parentheses:

2x + 2 = -8

2. Subtract 2 from both sides to isolate the x term:

2x = -10

3. Divide both sides by 2 to solve for x:

x = -5

Therefore, the solution is x = -5.

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Answer:

i think it is :

5×5×5=125

2×2×2=8

Answer:

The exponential function is

\(y = {2}^{x} \)

Answer:

$2400

Step-by-step explanation:

60 tonnes = $1800

80 tonnes = $?

= 1800 × 80/60

= $2400

Step-by-step explanation:

$2400 to Carry 80tonnes of weight

Answer:

\(\boldsymbol{\boxed{\dfrac{6}{11} }}\)

Step-by-step explanation:

According to the classical definition of probability:

\(P(A) = \dfrac{m}{n}\)

A - event

m - number of favorable outcomes

n - number of adverse outcomes

According to the task:

A - choose a student

m - 6 students

n - 11 students

\(\boldsymbol{\boxed{P(A) = \dfrac{6}{11} }}\)

the probability of getting to 5s is 2/12, or 1/6

Given:

h is composition of two functions f and g.

\(h(x)=(f\circ g)(x)\)

One of the function is 8x-9.

\(h(x)=(8x-9)^2\)

To find:

The functions f(x) and g(x).

Solution:

We know that,

\(h(x)=(f\circ g)(x)=f[g(x)]\)

We have,

\(h(x)=(8x-9)^2\)

Here, first function is 8x-9 and the second is square of it.

In \((f\circ g)(x)=f[g(x)]\), first function which is applied is g(x) and the second function is f(x).

Let \(g(x)=8x-9\) and \(f(x)=x^2\).

\(h(x)=f[8x-9]\)

\(h(x)=(8x-9)^2\)

So, our assumption is correct.

Therefore, the required functions are \(g(x)=8x-9\) and \(f(x)=x^2\).

Answer:

False

Step-by-step explanation:

I know what I talking about and I'm right

This statement is false because December is not the only month when it is winter. January February and March are also in winter.

Answer:

b. y+10=-(x-3)

Step-by-step explanation:

The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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The number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.

The number of different routes possible for the delivery driver can be calculated using combinatorics. Specifically, we need to determine the number of ways to choose 7 locations out of the remaining 8 locations. This can be found using the combination formula.

The combination formula, also known as "n choose k," is given by the expression C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from and k is the number of items to choose.

In this case, there are 8 locations remaining and the driver needs to choose 7 of them. Applying the combination formula, we have C(8, 7) = 8! / (7! * (8-7)!) = 8! / (7! * 1!) = 8.

Therefore, there are 8 possible different routes for the delivery driver to make deliveries at the remaining 8 locations, given that the driver has time to make deliveries at 7 of them.

To simplify the answer, we can state that there are 8 possible different routes for the driver.

In summary, the number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.

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