Find the distance between the points (2, −3) and (−4, −7).

Answer:

SSS theorem

Step-by-step explanation:

It is indicated in the image that 2 sides of the triangles are congruent, and the third side is shared, which makes the third side automatically congruent as well. Therefore, we can use the side-side-side theorem to prove that the triangles are congruent.

You'll first Cross multiply: 5× 3x

that'll give you 15x.

15x=12(12 is a numerical constant).

Divide both sides by the the coefficient of X .That is 15x/15= 12/15

Therefore the answer is 12/15= x

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathsf{5 = 1 \dfrac{2}{3}x}[/tex]

[tex]\mathsf{1 \dfrac{2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{1\times3 + 2}{3}x= 5}[/tex]

[tex]\mathsf{\dfrac{3 + 2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{5}{3}x = 5}[/tex]

[tex]\large\text{MULTIPLY }\rm{\dfrac{3}{5}}\large\text{ to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{3}{5}\times\dfrac{5}{3}x = \dfrac{3}{5}\times5}[/tex]

[tex]\large\text{SIMPLIFY IT!}[/tex]

[tex]\mathsf{x = \dfrac{3}{5}\times5}[/tex]

[tex]\mathsf{x = \dfrac{3}{5}\times\dfrac{5}{1}}[/tex]

[tex]\mathsf{x = \dfrac{3\times5}{5\times1}}[/tex]

[tex]\mathsf{x = \dfrac{15}{5}}[/tex]

[tex]\mathsf{x = \dfrac{15\div5}{5\div5}}[/tex]

[tex]\mathsf{x = \dfrac{3}{1}}[/tex]

[tex]\mathsf{x = 3\div1}[/tex]

[tex]\mathsf{x = 3}[/tex]

[tex]\huge\text{Therefore, your answer: \boxed{\mathsf{x = 3}}}\huge\checkmark[/tex]

Answer:

  f(x) = 2(x -3)² +5   or   f(x) = 2x² -12x +23

Step-by-step explanation:

The equation of a quadratic is easily written in vertex form when the coordinates of the vertex are given. Here, the point one horizontal unit from the vertex is 2 vertical units higher, indicating the vertical scale factor is +2.

__

The vertex form equation for a parabola is ...

  f(x) = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'

For vertex (h, k) = (3, 5) and vertical scale factor a=2, the vertex form equation of the parabola is ...

  f(x) = 2(x -3)² +5 . . . . . vertex form equation

Expanded to standard form, this is ...

  f(x) = 2(x² -6x +9) +5

  f(x) = 2x² -12x +23 . . . . . standard form equation

The domain of the function [tex]y=\sqrt{(x+6)}-7[/tex] is given by (B) that is [tex]x \geq-6[/tex]

Domain of a function refers to the values or range of input values of a function for which the function exists in real.

In this problem the given function is

[tex]y=\sqrt{(x+6)}-7[/tex]

Now the above function exists if the expression under square root is greater or equal to 0, since negative number cannot be square rooted in real, that gives imaginary number.

So, for existence of function it is must to

[tex]x+6\geq0[/tex]

[tex]x\geq-6[/tex]

Hence the domain of the given function is given by [tex]x\geq-6[/tex]

Hence the correct option is (B).

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The value of a is 1 , b = 3 , c = 4 , Option B is the correct answer.

The correct question is

Which values of a, b, and c represent the answer in simplest form?

7/9 divided by 4/9 = [tex]\rm a\dfrac{b}{c}[/tex]

1: a = 1, b = 4, c = 3

2: a = 1, b = 3, c = 4

3: a = 1, b = 63, c = 36

4: a = 1, b = 36, c = 63

Reducing to simplest form means to reduce to an extent where the numerator and denominator have nothing in common to be cancelled out.

It is given in the question that

(7/9) / (4/9) =  [tex]\rm a\dfrac{b}{c}[/tex]

It can also be written as

(7*9)/(4*9) =  [tex]\rm a\dfrac{b}{c}[/tex]

7/4 = [tex]\rm a\dfrac{b}{c}[/tex]

[tex]\rm 1 \dfrac{3}{4} = a\dfrac{b}{c}[/tex]

Therefore the value of a is 1 , b = 3 , c = 4 , Option B is the correct answer.

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Answer:

By using opposite angles of two intersecting straight lines are congruent we proved that x = 28°

Step-by-step explanation:

Opposite angles of two intersecting straight lines are congruent

Therefore ∠DLE = ∠GLH

Here ∠DLE = 2x = ∠GLH

Sum of all angles on a straight line is 180°

Therefore ∠ELG + ∠GLH = 180°

Given that ∠ELG = 124°

124° + ∠GLH = 180°

124° + 2x  = 180°

2x = 180° -  124°

2x = 56°

x = 28°

hence proved that x = 28°

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Answer:

D)

Step-by-step explanation:

47 is the right answer! Have an cool day!

The area of the piece of red paper after the hole for the photograph has been cut is,

⇒ 47 square units.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Now, First, find the area of the two squares:

The photograph have vertices:

(-3, -2), (-2, 2), (2, 1), and (1, -3).

Since, The square is diagonally aligned, so we need to find the length between two points in order to find the area.

For (1, -3) and (2, 1).

There is a 1 unit length and a 4 unit height.

We can use the Pythagorean theorem to find the hypotenuse of the triangle, which is the length of the square's side:

1² + 4² = x²

1 + 16 = x²

x = √17

The side length for the square of the photograph is the square root of 17,

so the area of the photograph is 17 units²

Now, The red paper has side lengths of 8. The distance between (-4, 4) and (4, 4) is 8 units wide, so we do not need to use the Pythagorean theorem.

Now , we know the area of the red paper and photograph, you can subtract the area to find the red paper with the hole:

64 - 17 = 47 square units.

Thus, The area of the piece of red paper after the hole for the photograph has been cut is,

⇒ 47 square units.

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Answer: C

Step-by-step explanation:

[tex]50 < 5x-10\\\\60 < 5x\\\\x < 12[/tex]

However, the angle has to have positive measure, so:

[tex]5x-10 > 0\\ \\ 5x > 10\\\\x > 2\\\\\therefore \boxed{2 < x < 12}[/tex]

Answer:

[tex] \frac{ {3x}^{2} }{x + 5} + \frac{15x}{x + 5} [/tex]

[tex] \frac{3 {x}^{2} + 15x}{x + 5 } [/tex]

3x ( x + 5) /( x + 5).

Answer:

[tex]\large{\boxed{35_{10} = \sf 23_{16}}}[/tex]

Explanation:

[tex]\sf Given : 35_{10}[/tex]

Compute:

35 ÷ 16 = 2.1875 = 2R3

2 ÷ 16 = 0.125 = 0R2

Jot down the remainders:

======

[tex]\sf Answer : \ 35_{10} = 23_{16}[/tex]

[tex]\hrulefill[/tex]

Let's look at another example:  [tex]\sf 325_{10} = [?]_{16}[/tex]

Compute:

325 ÷ 16 = 20.3125 = 20R5

20 ÷ 16 = 1.25 = 1R4

1 ÷ 16 = 0.0625 = 0R1

Jot down remainders:

=====

[tex]\sf 325_{10} = [145]_{16}[/tex]

[tex]\hrulefill[/tex]

Another example: [tex]\sf 500_{10} = [?]_{15}[/tex]

Compute:

500 ÷ 15 = 33.33... = 33R5

33 ÷ 15 = 2.2 = 2R3

2 ÷ 15 = 0.13... = 0R2

Jot down remainders:

=====

[tex]\sf 500_{10} = [235]_{15}[/tex]

This is general conversation of decimal integer to hexadecimal integer

Let's check

This is in decimal form

We know the ways to convert decimal into other forms like

For third way

(2)_16 is one part

Next

3 is not divisible by 16

i.e

Hence

other part is (3)_16

Add (not general addition)

The final answer is

Answer:

78

Step-by-step explanation:

even numbers are numbers that end in 0, 2, 4, 6, or 8. these numbers can be considered even because they would evenly split between a group of 2

the "sum" of a group of numbers is the numbers added together

So, the numbers between 23 and 29:

23, 24, 25, 26, 27, 28, 29

(even numbers are in bold)

    if we add these numbers together,

 {1}                                  {carry the 1 from the 18 in the one's place}

  24

  26

+ 28

______

  78

So the sum of all the even numbers between 23 and 29 is 78.

hope this helps!!

Answer:

[tex]m > 5[/tex]

Step-by-step explanation:

[tex] \frac{m + 4}{3} > 3 \\ \frac{m + 4}{3} \times 3 > 3 \times 3 \\ m + 4 > 9 \\ m + 4 - 4 > 9 - 4 \\ m > 5[/tex]

Answer:

29

Step-by-step explanation:

if you calculate the mathimatical equipment to the $2,000 it'll be better

Step-by-step explanation:

each term in the sequence is half of the value of the previous term, and in the opposite sign.

therfore, the quotient between terms is (-2)

so, to get one term from the previous term, we multiply by 1/(-2), so:

d(n) = d(n-1) × 1/(-2)

the first term is 56 so d(1)=56

Answer:

56 and -1/2

Step-by-step explanation:

khan

Answer:

10

Step-by-step explanation:

Answer: 1.25

Step-by-step explanation:

The explicit formula for the sequence is [tex]a_{n}=10(0.5)^{n-1}[/tex]

Substituting in n=4,

[tex]a_{4}=10(0.5)^{4-1}=\boxed{1.25}[/tex]

Answer:

  x = y = 4

Step-by-step explanation:

A 2-variable linear programming problem is nicely solved by graphing. The solution will be one of the vertices of the solution set. The attached graph shows that means it is one of (x, y) = [(0, 0), (0, 6), (4, 4), (6, 2), (7, 0)}.

__

Evaluating the objective function at each of these vertices will show you the solution that maximizes it.

(0, 0) -- P = 40·0 +50·0 = 0

(0, 6) -- P = 40·0 +50·6 = 300

(4, 4) -- P = 40·4 +50·4 = 360

(6, 2) -- P = 40·6 +50·2 = 340

(7, 0) -- P = 40·7 +50·0 = 280

_____

Additional comment

The solution set would ordinarily be the area that is covered by the shading that signifies the solution set of each of the 5 inequalities. 5 different overlapping shadings can make the graph quite messy, so we have elected to shade the areas that are NOT part of the solution set. In doing so, we have made the boundary lines dashed when they are part of the solution set

The possible solutions are the vertices of the white space on the graph.

The black line on the graph is the line corresponding to the maximum value of the objective function. To maximize the objective function, we want that line as far from the origin as possible. It is shown intersecting the vertex of the solution space that meets that condition.

Answer:

256

80÷100×320=256

80÷100=0.8

0.8×320=256

Hii!

[tex]\leadsto\parallel\boldsymbol{Answer.}\parallel\gets[/tex]

_________________________________________________________

3v+4w-1

__________________________________________________________

[tex]\leadsto\parallel\boldsymbol{Explanation.}\parallel\gets[/tex]

We use the distributive property to "distribute" the minus sign.

[tex]\sf -(-3v-4w+1)=-1\cdot(-3v)+(-1)\cdot(-4w)+(-1)\cdot1}[/tex].

Simplify!

[tex]\sf 3v+4w-1}[/tex]. Which is our final answer.

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]

[tex]\boldsymbol{-Greetings!-}[/tex]

_________________________________________________________

Answer:

11.65

Step-by-step explanation:

3x+99x=102x

1188/102=11.65

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3x + 99x = 1,188}[/tex]

[tex]\large\textbf{COMBINE the LIKE TERMS}[/tex]

[tex]\mathsf{(3x + 99x) = 1,188}\\\mathsf{3x + 99x = 1,188}\\\mathsf{\bold{102x} = 1,188}[/tex]

[tex]\large\textbf{DIVIDE 102 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{102x}{102} = \dfrac{1,188}{102}}[/tex]

[tex]\large\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{x = \dfrac{1,188}{102}}[/tex]

[tex]\mathsf{x = 11.64705882}[/tex]

[tex]\large\textbf{AND IF YOU'RE ROUNDING}[/tex]

[tex]\mathsf{x \approx 12}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x \approx 12}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

4

Step-by-step explanation:

Area of a triangle = bh/2

B = 2h

16 = 2h × 2/2

h×2 = 16

2h = 16

* put a square root on both sides then u will get the answer which is

Height of the triangle = 4

Answer:

The square root of -1 is i

Step-by-step explanation:
"i" is the imaginary unit and represents the value of sqrt -1

The pounds of corn in the second month is 390

We have:

First month, a = 300

Rate, r = 35%

The pounds of corn in the second month is calculated using:

Pound = a * (1 + r)

So, we have:

Pound = 300 * (1 + 30%)

Evaluate the sum

Pound = 300 * 1.3

Evaluate the product

Pound = 390

Hence, the pounds of corn in the second month is 390

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 The binomial expansion of (2+3x)^5 - (2 - 3x)^5 is 480x + 2160x^3 + 486x^5

Concept: Binomial expansion is to expand and write the terms which are equal to the natural number exponent of the sum or difference of two terms.

For two terms x and y the binomial expansion to the power of n is (x + y)n = nC0 0 xn y0 + nC1 1 xn - 1 y1 + nC2 2 xn-2 y2 + nC3.

Binomial expansion of (2+3x)^5 =32+240x+720x^2+1080x^3+810x^4+243x^5

Binomial expansion of (2-3x)^5 = 32-240x+720x^2-1080x^3+810x^4-243x^5

Combining both the expansions,=32+240x+720x^2+1080x^3+810x^4+243x^5 - (32-240x+720x^2-1080x^3+810x^4-243x^5)

= 32+240x+720x^2+1080x^3+810x^4+243x^5 - 32+ 240x - 720x^2 +1080x^3 -810x^4 +243x^5

=480x + 2160x^3 + 486x^5

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Answer:

The standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.

Step-by-step explanation:

Standard deviation: It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

The given parameters are:

Proportion, p = 10%

Sample size, n = 1000

The standard deviation is calculated as:

σ=[tex]\sqrt{np(1-p}[/tex]

So, we have:

σ=[tex]\sqrt{1000*10%*(1-10%)}[/tex]*(1-10%)

Evaluate:

σ= 9.49

Hence, the standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.

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Answer:

- x + y - 4

Step-by-step explanation:

Given polynomial:

[tex] \rm \: x+2y+1-(2x+y+5)[/tex]

Solution:

Removing parentheses,we obtain

Collecting and combining like terms,we obtain

Done!

Answer:

Triangular Prism

Step-by-step explanation:

A plane of symmetry divides a three dimensional shape into two congruent halves that are mirror images of each other. An isosceles triangular based prism has 2 planes of symmetry. An isosceles triangular based prism has 2 planes of symmetry. An isosceles triangular based prism has 2 planes of symmetry.

Answer:

t = - 6

Step-by-step explanation:

8t + 3(t + 4) = 6(t - 3) ← distribute parenthesis on both sides )

8t + 3t + 12 = 6t - 18 , that is

11t + 12 = 6t - 18 ( subtract 6t from both sides )

5t + 12 = - 18 ( subtract 12 from both sides )

5t = - 30 ( divide both sides by 5 )

t = - 6