A conjecture and the paragraph proof used to prove the conjecture are shown. Given: angle 2 is congruent to angle 3. Prove: angle 1 and angle 3 are supplementary. A horizontal line. Two rays extend from upper region of the line diagonally down to the left and right and intersect the line forming interior angles labeled as 2 and 3 and an exterior angle labeled as 1. Drag an expression or statement to each box to complete the proof. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. ∠1 and ​∠2​ form a linear pair, so ∠1 and ∠2 are supplementary by the Response area. Therefore, m∠1+ Response area = 180° by the definition of supplementary. It is given that ∠2≅ Response area, so m∠2=m∠3 by the Response area. By substitution, m∠1+m∠3=180°, so ∠1 and ∠3 are supplementary by the definition of supplementary. angle congruence postulatelinear pair postulatem∠2m∠3∠3∠2

Answer:

Below.

Step-by-step explanation:

x^2 + 4x  = 18

x^2 + 4x + (2)^2 = 15 + 2^2

x^2 + 4x + 4 = 18 + 4

(x + 2)^2 = 22

x  + 2 = +/- √22

x = -2 + √22 and x =  -2 + √22

x = 2.7  and -6.7  to nearest tenth.

Answer:

[tex]m_{1} =1/2\\m_{2} =5[/tex]

Step-by-step explanation:

[tex]2m^{2} -11m+5=0[/tex]

[tex](2m-1)(m-5)=0[/tex]

[tex]2m-1=0\\2m=1\\m_{1} =1/2[/tex]

[tex]m-5=0\\m_{2} =5[/tex]

Hope this helps

The solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.

A fraction represents a part of a whole or, more generally, any number of equal parts.

A fraction  can also be described as how many parts of a certain size there are, in a given whole.

The fraction given can be written as follows;

-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16)

-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y - 4)(y+4)

-8/(2y - 8)  = [5(y - 4) - (7y + 8)] /(y-4)(y + 4)

-8/(2y - 8)  = (5y - 20 + 7y + 8)/(y-4)(y + 4)

-8/(2y - 8)  = (12y - 12)/(y-4)(y + 4)

cross and multiply both sides of the equation;

-8((y-4)(y + 4)) = (12y - 12)(2y - 8)

-8(y² - 16) = 24y² - 96y - 24y + 96

-8y² + 128 =  24y² - 120y + 96

0 = 32y² - 120y - 32

solve the quadratic equation using formula method;

a = 32, b = -120, c = - 32

y = 4 or -0.25

Thus, the solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.

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y=6

for the eqution

[tex]\frac{-8}{2y-8} =\frac{5}{y+4} -\frac{7y+8}{y^{2}-16 } \\[/tex]

Answer:

C.) [tex]x^{\frac{3}{2} } y^{\frac{19}{2} }[/tex]

Step-by-step explanation:

To simplify the expression, you need to:

1.) Rewrite [tex]\sqrt{xy^{3} }[/tex]

    -----> [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]

2.) Distribute the exponents

    -----> When an exponent is raised to another exponent, they should be multiplied

3.) Create common denominators

4.) Combine the variables

    -----> When two variables with exponents are being multiplied, the exponents should be added

To make x² + 6x = 7 a perfect square, we add 16 to the equation.

In the question, we are asked for the term that must be added to the equation x² + 6x = 7, to make it into a perfect square.

The given equation can be shown as:

x² + 6x = 7,

or, x² + 6x - 7 = 0.

To make it a perfect square, we need to find the b² term as per the 2ab term for the formula, (a + b)² = a² + 2ab + b², where a is x.

This can be shown as:

x² + 6x - 7 = 0,

or, x² + 2(x)(3) - 7 = 0, where we get b = 3.

Thus, b² = 3² = 9, can be obtained by adding 16 to the equation, as -7 + 16 = 9.

Thus, we add 16 to both sides of the equation, to get:

x² + 2(x)(3) - 7 + 16 = 16,

or, x² + 2(x)(3) + 9 = 16,

or, (x + 3)² = 16, which gives us the required perfect square.

Thus, to make x² + 6x = 7 a perfect square, we add 16 to the equation.

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Answer:

I think glide reflection

Step-by-step explanation:

a certain video on yt had explained the examples of similar look alike this picture

Answer: Read the explanation

Step-by-step explanation:

If the points of a figure are all moved the same, they are congruent.

Point A is moved 9 points right, and 7 points down.

Point B is moved 9 points right, and 7 points down.

Point C is moved 9 points right, and 7 points down.

So, they are congruent.

The simplified form of the expression is x-4 + 2/x-2

Given the following fraction below

f(x) = x^2 + 2x - 6/x-2

Using the long division as shown below;

        x + 4

x-2 |  x^2 + 2x - 6

        x^2 - 2x

_________________

                4x   - 6

                 4x   - 8

___________________

                         2

Hence the simplified form of the expression is x-4 + 2/x-2

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Using the given property, we conclude that:

f(4) = 8

We know that our function has the property:

5*f(x) = f(5*x)

Now, we also know that:

f(20) = 40

Notice that we can rewrite:

f(20) = f(5*4)

Using the above property, we know that:

f(20) = f(5*4) = 5*f(4) = 40

Using the last part:

5*f(4) = 40

f(4) = 40/5 = 8

f(4) = 8

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Answer:

See below

Step-by-step explanation:

The larger is  

7-6 = 1 unit bigger than the smaller....and this unit = 24 gallons

   each unit is 24 gallons

larger barrel holds   24 * 7 = 168 gal

smaller barrel holds  24 * 6 = 144 gal

Answer:

Small barrel=144 large barrel=168

Step-by-step explanation:

The ratio is 6 to 7 so lets assign x as a factor.

6x=Small barrel (S)

7x=Large barrel (L)

7x-6x=x

x is the difference so x is 24

x=24

6*24=144=S

7*24=168=L

Answer:

Step-by-step explanation:

Step-by-step explanation:

15 r blue marbles

20- 5 = 15

Answer:

1000xm

Step-by-step explanation:

1 meter = 3.2808 feet, hence. 9.8424 x 10^8 feet in 1 second. 1 foot in x seconds. hence it takes 1 / (9.8424 x 10^8) = 0.10168 x 10^(-8) seconds. ➡️1km = 1000xm⬅️

It will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

To find out how long it will take light to travel one meter, we need to convert the given distance of 10,000 km to meters and the time of 3.0 x 10² seconds to seconds.

Given:

Distance traveled by light = 10,000 km

Time taken by light = 3.0 x 10² seconds

To convert km to meters, we know that 1 km = 1 x 10³ m, so:

10,000 km = 10,000 x 1 x 10³ m = 1 x 10⁷ m

Now, we can find the time taken to travel one meter by dividing the total time by the total distance:

Time taken to travel one meter = Total time / Total distance

Time taken to travel one meter = (3.0 x 10² seconds) / (1 x 10⁷ m)

To simplify the expression, we can cancel out one factor of 10 from the numerator and denominator:

Time taken to travel one meter = (3.0 x 10) / (1 x 10⁶ m)

Now, we get the final answer:

Time taken to travel one meter = 3.0 x 10⁻⁵ seconds

So, it will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

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Answer:

A' (-15, -5)

B' (10, -10)

C' (-5, -20)

Answer:

A ' (-15, -5)

B ' (10, -10)

C ' (-5, -20)

Step-by-step explanation:

The scale factor is [tex]K=5[/tex]. This tells us to multiply each coordinate, of each point, by the scale factor (5) to get the dilated points.

Point A is at [tex](-3,-1)[/tex] and moves to [tex]A ' (-15, -5)[/tex] after multiplying the x and y coordinates by 5. The same applies to points B and C as well.

Point B moves from [tex](2,-2)[/tex] to [tex]B' (10,-10)[/tex] because [tex]2*5=10[/tex] and [tex]-2*5=-10[/tex]. This also means that Point C moves from [tex](-1,-4)[/tex] to [tex]C' (-5,-20)[/tex] because  [tex]-1*5=-5[/tex] and [tex]-4*5=-20[/tex].

The dilation rule can be written as [tex](x, y)[/tex] → [tex](5x, 5y)[/tex]

As a result of the dilation, triangle A'B'C' has sides that are 5 times longer compared to the corresponding sides of triangle ABC.

Answer:

C. 7

Step-by-step explanation:

The answer is 7. Use the power of a power property. To use it you have to multiply the power inside the parenthesis to the one outside of the parenthesis. 1/5 * 5 = 1. Since the power is 1, you do not need to write the power.

Hope this helps!

Step-by-step explanation:

[tex] \frac{y2 - y1 }{x2 - x1} = \frac{3 - - 2}{5 - 0} = \frac{5}{5} = 1[/tex]

The attached graph is the graph of the function f(x) = -2sin(x)

The function is given as:

f(x) = -2sin(x)

The above function is a sine function that has an amplitude of 2

Next, we plot the graph of the sine function f(x) = -2sin(x) using a graphing calculator

See attachment for the graph of f(x) = -2sin(x)

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The correct statements are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Inequality are expressions not separated by an equal sign. Given the inequality expression:

–3(2x – 5) < 5(2 – x)

Expand

-6x +15 < 10 - 5x

Collect the like terms

-6x+5x < 10 - 15

-x <-5

x > 5

Hence the correct statements are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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Answer:

x = 2/5

y = 3/5

Step-by-step explanation:

**Disclaimer** Hi there! I assumed the question to be a system of equations. The following answer is a method for solving a system of equations. Thus, if it is not, please let me know and I will modify my answer.

Given information:

[tex]\frac{x}{2}+y=\frac{4}{5}[/tex]

[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]

Eliminate fractions by multiplying 10 on both sides of the first equation:

[tex]10*\frac{x}{2}+10*y=10*\frac{4}{5}[/tex]

[tex]5x+10y=8[/tex]

Eliminate fractions by multiplying 10 on both sides of the second equation:

[tex]10*x+10*\frac{y}{2} =10*\frac{7}{10}[/tex]

[tex]10x+5y=7[/tex]

Current system:

[tex]5x+10y=8[/tex]

[tex]10x+5y=7[/tex]

Multiply the second equation by 2:

[tex]5x+10y=8[/tex]

[tex]20x+10y=14[/tex]

Subtract the first equation from the second equation:

[tex](20x+10y)-(5x+10y)=14-8[/tex]

[tex]20x+10y-5x-10y=6[/tex]

[tex](10y-10y)+20x-5x=6[/tex]

[tex]0+15x=6[/tex]

[tex]\boxed{x=\frac{2}{5} }[/tex]

Substitute the x value back to one of the equations to get the y value:

[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]

[tex](\frac{2}{5}) +\frac{y}{2} =\frac{7}{10}[/tex]

[tex](\frac{2}{5}) +\frac{y}{2}-\frac{2}{5} =\frac{7}{10}-\frac{2}{5}[/tex]

[tex]\frac{y}{2} =\frac{3}{10}[/tex]

[tex]\frac{y}{2}*2 =\frac{3}{10}*2[/tex]

[tex]\boxed{y=\frac{3}{5} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is x = 2/5, y = 3/5 or (2/5, 3/5)

First, in order to avoid fractional values during calculation, multiply both equations by 10 to simplify.

Multiply the 1st equation by 10 and 2nd equation by 5.

    3. 10 (5x +  10y) = 10 (8) ⇒ 50x + 100y = 80

    4. 5 (10x + 5y) = 5 (7) ⇒ 50x + 25y = 35

Subtract : 3rd equation - 4th equation

Now, substitute for x in the 1st equation to find y.

Multiplying both sides of an inequality by a negative number reverses the inequality symbol.

The table of values is given as:

A: (-16 > -4) (-16 < -4) (-16 = -4)

B: (40 > 8) (40 < 8) (40 = 8

C: (-45 > 15) (-45 < 15) (-45 =15)

D: (35 > -20) (35 < -20) (35 = -20)

In the above list of inequalities, the true inequalities are

-16 < -4 --- because -16 is less than -4

40 > 8 --- because 40 is greater than 8

-45 < 15 --- because -45 is less than 15

35 > -20 --- because 35 is greater than -20

Lastly, when an inequality is multiplied or divided by a negative number, the inequality sign changes

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Answer:

-16 < -4

40 > 8

-45 < 15

35 > -20

Reverses

Step-by-step explanation:

hope this helps

The first table is a quadratic function while the second table is a linear function.

1) For the first table, we have;

x y

0 5

1 0

2 -3

3 -4

4 -3

x = 2  and x = 4 have same value of y = -3  and as such it will be a Quadratic Function.

y = x²  - 6x + 5

2) For the second table, we have;

x y

2 5

5 14

6 17

8 23

10 29

This table is a Linear function because  slope is same and equal to 3 all through. Thus, the equation is y = 3x - 1  

3) For the third table, we have;

x y

-3 8

-2 4

-1 2

0 1

1 0.5

This is an exponential function because equation can be modelled by;

y = 2⁻ˣ

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Answer:

5.373 cm

Step-by-step explanation:

Divide the volume by the length to find the area of the equilateral triangle

100/8 = 12.5

Area of equilateral triangle = sqrt(3) / 4  *  s^2   = 12.5

   s^2 = 12.5 *4  / sqrt3

    s = 5.373 cm

The volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. This can be obtained by finding the area of the square using the length of the diagonal.

Given that, diagonals that run from the parabola y = - 2√x to the parabola   y = 2√x

D = 2√x - (-2√x)

D = 4√x

D² = s² +  s², where s is the side of the square

(4√x)² = 2s²

16x = 2s²

s² = 8x

s² is the area

Thus,

V = [tex]\int\limits^{15}_0 {8x} \, dx[/tex]

V =  [tex]8\int\limits^{15}_0 {x} \, dx[/tex]

V = 4 (15² - 0)

V = 4×225

⇒ V = 900 cubic unit

Hence the volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 19. The cross sections perpendicular to the x-axis on the interval         0 ≤x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. Find the volume of the solid.

The new price after the price increase of Nu 40 will be Nu 840.

The price of a pant after n Nu 40 price increases will be:

= 800 + 40

= 840

The expected weekly sales as a function of the number of price increases will be:

= n - 1) × 800

= (30 - 1) × 800

= 29 × 800

= 23200

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Answer:

[tex]x = 1 + \sqrt5, x = 1 - \sqrt5[/tex]

Step-by-step explanation:

Hello!

We can solve the quadratic by using the quadratic formula.

Standard form of a quadratic: [tex]ax^2 + bx + c = 0[/tex]

Quadratic Formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]

Given our Equation: [tex]g(x) = x^2 - 2x - 4[/tex]

Plug the values into the equation and solve.

Answer: [tex]\frac{\sqrt{6}}{2}[/tex]

Step-by-step explanation:

By the Pythagorean theorem,

[tex]2^2 + (MN)^2 = (\sqrt{10})^2\\\\4+(MN)^2 = 10\\\\(MN)^2 = 6\\\\MN=\sqrt{6}\\\\\implies \tan L=\frac{\sqrt{6}}{2}[/tex]

The equation of the function is −3<x<1. See the explanation below.

Given the graph of function f is a parabola,

Thus, equation of parabola  is y=(x+3)(x+1)

⇒y=x² +4x+3

⇒y−3+2²

= x²+2× x ×2+2²

⇒y+1=(x+2)²

We can rewrite this as

 (x+2)² =4× (1/4) ×(y+1)

Comparing the above equation to the equation of a parabola, (x−h)² =4a(y−k), where (h,k) is the coordinates of vertex of parabola, we have,

(h,k)≡(−2,−1)

Hence, the x coordinate of the vertex is −2 which lies in the interval −3<x<1

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Answer:

Step-by-step explanation: