It is 6 kilometers from Linda's house to the nearest mailbox. How far is it in meters?

∠2 and ∠4 are vertical opposite angles and they are congruent.

Vertically opposite angles are congruent.

Therefore, let proof ∠2 and ∠4 are vertical angles

Hence,

m∠2 + m∠3 = 180

∠2 and ∠3  are linear pair.

m∠3 + m∠4 = 180

∠3 and ∠4  are linear pair.

∠2 and ∠4 are vertical angles

m∠2 + m∠3 = m∠3 + m∠4

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Answer: View picture below!

Step-by-step explanation: Just did it!

Answer: y = -3/2x + 6, y intercept is (0, 6)

Step-by-step explanation: You are dividing 2 from both -3x and 12. -3/2x cannot be simplified any further unless it's a decimal, so we leave it as -3/2x. But, since the equation was y = -3x+12 originally, we divide 12 from 2 as well and not just from 3x, and we get 6.

Hope this helped.

Answer:

x = +1

x = -1

Step-by-step explanation:

x^4-1=0​

x^4=+1​

fourth root of x^4= fourth root of +1​

x = +1

x = -1

Answer: 31 cm.

explanation:

Given, Radius = 5 cm (near to)

this means the radius is near 5 cm. It can be 4.9, 4.99, 4.999.....or 5.01,5.001,5.001...... and so on.

So, the circumference of the circle is given by:-

Circumference = 2× [tex]\pi[/tex] × r

⇒ 2 × 22/7 × 5    (for the smallest value, we'll consider r as 5 and then round off the circumference to the smallest value)

⇒ 220/7 ≈ 31.43 cm

rounding off to the smallest integer, we have

Circumference = 31 cm.

The smallest value that the circumference could have is 10 [tex]\pi[/tex]cm

Using Formula,

Circumference = 2 [tex]\pi \\[/tex] r

Radius = 5 cm

So, C = 2 [tex]\pi[/tex] 5

C = 10 [tex]\pi[/tex]cm

Therefore circumference is 10 [tex]\pi[/tex]cm.

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The solutions to the quadratic equation 50 - x² = 0 are x = ±5√2.

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The solution(s) to the quadratic equation 50 - x² = 0 can be found by setting the equation equal to zero and solving for x.

50 - x² = 0

To solve this equation, we can rearrange it as follows:

x² = 50

Taking the square root of both sides, we have:

x = ±√50

Simplifying the square root of 50, we get:

x = ±√(25 × 2)

x = ±√25 × √2

x = ±5√2

Therefore, the solutions to the quadratic equation 50 - x² = 0 are x = ±5√2.

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Answer:

6/x2

Step-by-step explanation:

Answer:

[tex]\mathsf {\frac{6}{x^{2}}}[/tex]

Step-by-step explanation:

[tex]\mathsf {\frac{2}{x^{2}} + \frac{4}{x^{2}} }[/tex]

[tex]\mathsf {\frac{2+4}{x^{2}}}[/tex]

[tex]\mathsf {\frac{6}{x^{2}}}[/tex]

Answer:

x=12

Step-by-step explanation:

Given that there is only one expression given in each triangle, if we only use the information in a single triangle, there is no way to set up an equation that we could solve to find the expression.  (For this situation, at best we could use the triangle sum theorem to say that the three angles in one triangle added to 180°, but since we don't know the other two angles, that's 3 unknowns with only 1 equation... that's not solvable)

The only way to solve this problem is to make a relationship of some sort between the two triangles.

Proving a relationship between triangles - option 1

You may have a theorem about the Third angles of two triangles... "Given two arbitrary triangles, [tex]\triangle ABC[/tex] and [tex]\triangle D E F[/tex], if [tex]\angle A \cong \angle D[/tex] and [tex]\angle B \cong \angle E[/tex],  then [tex]\angle C \cong \angle F[/tex] "

If you have this, then the third angles are congruent.

In a more general situation of a similar problem (one in which you don't know two of the angles to begin with), it might be easier to prove triangle congruence, or triangle similarity.

Other Relationships between triangles

There are two main relationships between triangles: similarity and congruence.

Most people learn about congruence first.

In the situation for this problem, the two triangles happen to be congruent (we'll prove it shortly), which implies that all corresponding angles between shapes are congruent (and all corresponding sides between shapes are congruent).

For the purpose of solving for things related to angles, proving that the two triangles are similar is enough to know that angles between triangles are congruent (sides wouldn't necessarily be equal, but would be proportional, and since we're not solving for anything related to side lengths, proving that the triangles are similar would be enough).

Proving a relationship between triangles - option 2 - congruence

Notice that the triangle on top has two angles with markings (a single mark, and a double mark), and one side with a marking (a single tick).  These three pieces are in a configuration of ASA (the side is between the two angles).

Looking at the bottom triangle, it also has angles and sides with corresponding markings, and they are also in an ASA configuration.

Thus, by ASA congruence, these triangles are congruent triangles.

Knowing the triangles are congruent (even though we only used 3 parts), the rest of the corresponding parts (including the third angles) are also congruent.

Proving a relationship between triangles - option 3 - Similarity

For similarity, the process is similar to proving congruence, however the theorems we have for proving similarity are different.

SSS, SAS, or AA similarity.

Since the triangles in our problem do have two angles that are congruent, by AA similarity, the triangles are "similar".

Knowing the triangles are similar (even though we only used 2 parts), the last set of corresponding angles are also congruent.

Building our equation

Since the third angle of each triangle is congruent, by definition of congruent angles, the measures of each of those two angles are equal, and so we can build an equation knowing that the two expressions are equal to each other:

[tex]3x-7=2x+5[/tex]

Solving for x

From there, we need some algebraic properties equality to solve for x.

Subtract 2x from both sides...

[tex](3x-7)-2x=(2x+5)-2x\\x-7=5[/tex]

add 7 to both sides...

[tex](x-7)+7=(5)+7\\x=12[/tex]

Extension

Knowing the value for x, we could solve for the measure of the angles, if that had been requested.  Simply substitute 12 back into the expressions for the angle measure (the results should be the same for both angles, since they were congruent angles)

[tex]3(12)-7\\36-7\\29[/tex]         [tex]2(12)+5\\24+5\\29[/tex]

So, if we had been asked, the measure of the angle is 29°

The slope of the given line is -2, and since perpendicular lines have negative reciprocal slopes, the slope of the line we want to find is 1/2.

Substituting into point-slope form,

[tex]y+4=\frac{1}{2}(x-8)\\\\y+4=\frac{1}{2}x-4\\\\\boxed{y=\frac{1}{2}x-8}[/tex]

Answer:

Equation of line perpendicular to y= -2x-9 is y=x/2-8 .

Step-by-step explanation:

The slope of a line gives the measure of its steepness and direction. The slope of a curve at a point is equal to the slope of the straight line that is tangent to the curve at that point.

The general equation of a line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry.

The product of slopes of two perpendicular lines gives (-1).

m1m2=(-1)

(-2)m2=(-1)

m2=1/2

y=m2x+c

Point (8,-4) satisfies the given equation :

(-4)=1/2 x 8 + c

c = (-8)

Line perpendicular to y= -2x-9 will be -

y=x/2-8

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Answer:  [tex]\textsf{3955cm}[/tex]

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Given: [tex]\textsf{Tree = 4m and 25cm, Pole = 70cm shorter}[/tex]

Find: [tex]\textsf{The height of the pole}[/tex]

Solution: The first step that we must take is to convert the tree height to centimeters and after doing so we would just subtract 70 cm from that to get the pole height.

Convert to cm

Combine

Subtract 70 from the tree height

Using the information from the problem the height of the pole would be 3955cm.

Answer:

For section A, the average rate of change is 12. For section B, the average rate of change is 300. The average rate of change in Section B is greater than Section A by 25. The rate of change keeps on increasing because the slope of the function is increasing.

Step-by-step explanation:

Concept: For a function f(x), the rate of change is given by [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]. Given function is h(x) = 3(5∧x).

For x = 0 to x = 1, the value of function would be f(0) = 3 to f(1) = 15.

The rate of change would be (15-3) / (1-0) = 12.

For x = 2 to x = 3, the value of function would be f(2) = 75 to f(3) = 375.

The rate of change would be (375-75) / (3-2) = 300.

The average rate of change in Section B is greater than Section A by

300 / 12 = 25.

Looking at the function, that is h(x) = 3(5∧x), we see that this function is an increasing function. The slope of an increasing function keeps on increasing with the value of x. The rate of increase is also a slope. That is why the rate keeps on increasing.

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Answer:

1780

Step-by-step explanation:

multiply the length value by 1760

and then divide the length value by 3

Answer:

3

Step-by-step explanation:

Slope of a line between any two points (x1,y1) and (x2,y2) is given by the equation:
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

let's take (x1,y1) as (4,4) and (x2,y2) as (5,7)

So slope = [tex]\frac{7-4}{5-4}[/tex] = 3

Answer:

y = 3x - 8

Step-by-step explanation:

y = Mx + c

m = 3 / 1

4 = 3(4) + c

4 - 12 = c

Answer:

all real numbers

Step-by-step explanation:

the answer is all real numbers.

we know this since if you plug in any value for x we will get a real number.

hope this helps

The domain of gof(x) is {x ∈ ℝ| x ≠ −2, 1} .

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

given function:

f(x) = x² + x -3

g(x) = 1/x+1

Now, solving the equation

gof = g(f(x))

=g( x² + x -3)

=1/(x² + x -3)+1

=1/ x² + x -2

= 1/ x² +2x - x -2

= 1/ x( x+ 2) - (x +2)

=1/ (x+2)(x-1)

Hence, the domain of gof(x) is {x ∈ ℝ| x ≠ −2, 1} .

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Answer:

[tex]\frac{1}{18}[/tex]

Step-by-step explanation:

The best way to solve this problem is to simplify each factorial one by one!

Starting at the numerator, the factorial for 2! is just 2, while the factorial for 5 is 120.

At the denominator, the factorial of 6! is 720, while the factorial for 3 is 6.

To write this out, we're given: [tex]\frac{(2) (120)}{(720) (6)}[/tex]

Just simply multiply and then divide, and we are given 1/18

The value of x will be 3

From given diagram, triangle ABC and EDC meet at a common vertex C.

So, triangle ABC and EDC both are congruent to each other.

Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.

Therefore,

[tex]\frac{AB}{ED} = \frac{AC}{EC} = \frac{BC}{CD}[/tex]

[tex]\frac{AC}{EC} = \frac{BC}{CD}[/tex]

Simplifying the expression,

We get

(18-x)/x = 25/5

(18-x)/x = 5

18-x = 5x

18-x-5x = 0

18 - 6x = 0

- 6x = -18

x = 3

Hence, the value of x is 3.

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Question 1

We want to choose a white marble, then a black marble.

Multiplying these probabilities, we get (9/24)(8/24) = 1/8.

Question 2

Thus, the probability is 5/10 = 1/2.

Question 3

Multiplying these probabilities, we get (7/24)(9/23) = 21/184.

Answer:

True

Step-by-step explanation:

-77 is less than -76. Since the symbol refers to less than or equal to, this statement will be true.

Answer: The answer is x < 5/2 and x > -5.

Step-by-step explanation:

First you need to separate the inequality and keep x on one side to maintain consistency. For instance the problem-

[tex]\frac{5-2x}{3} > 0\\\frac{5-2x}{3} < 5\\[/tex]

Now solve as normal.

*Note: When dividing a side or multiplying a side by a negative number, the sign of the inequality switches (this will be shown when I do the equation if it doesn't make since how I word it).

[tex]5-2x > 0*3\\5-2x < 5*3[/tex]

[tex]-2x > 0-5\\-2x < 15-5[/tex]

[tex]x < \frac{-5}{-2} =x < \frac{5}{2} \\x > \frac{10}{-2} =x > -5[/tex]

So, x < 5/2 and x > -5.

If anything is confusing about the procedure just leave a comment, and I'll try to explain further.

The equation of the line with points (2,10) and (0,0) is: y = 5x.

The line given has two points which are stated as:

(2,10) and (0,0).

Find the slope(m):

Slope (m) = change in y / change in x = (10 - 0)/(2 - 0)

Slope (m) = 10/2

Slope (m) = 5

The y-intercept (b) = 0

Substitute m = 5 and b = 0 into y = mx + b

y = 5x + 0

y = 5x

The equation of the line is: y = 5x.

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Answer:

-300

Step-by-step explanation:

113-413=-300

The correct answer is the last choice .

The parent quadratic function is f(x) = x² it's just like the image above .

if you look at the graph horizontal translation has happened two units to right , it means we have -2 inside a bracket next to x , then vertical translation has happened 4 units to up it means we have +4 outside the bracket and after x

there's also a reflection on the graph which means there's a negative before the bracket .

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Answer:

  145 square inches

Step-by-step explanation:

The surface area of a square pyramid can be found using the formula ...

  A = s(s +2h) . . . . . where s is the base side length, and h is the slant height

__

Using this formula with s=5 inches and h=12 inches, we find the area to be ...

  A = (5 in)(5 in +2(12 in)) = (5 in)(29 in) = 145 in²

The area of the pyramid is 145 square inches.

_____

Additional comment

This formula comes from the sum of the areas of the square base (s²) and the four triangular faces (4 × 1/2sh). That sum is ...

  A = s² +2sh = s(s +2h)

Answer:

A. 15

Step-by-step explanation:

9 12 15 is a

3 4 5 right triangle

Pythagorean Theorem

9^2+12^2=c^2

81+144=c^2

225

√225=√c^2

15=c