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Answers:

A = 3

B = -7

C = 3

D = -7

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Explanation:

You could use the AC method to factor, but I think the method described below is a more efficient way of factoring.

Set the given expression equal to zero and solve for x using the quadratic formula. So the goal is to find the roots for [tex]9x^2-42x+49=0[/tex]

We'll plug in a = 9, b = -42, and c = 49.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-42)\pm\sqrt{(-42)^2-4(9)(49)}}{2(9)}\\\\x = \frac{42\pm\sqrt{0}}{18}\\\\x = \frac{42+0}{18}\\\\x = \frac{42}{18}\\\\x = \frac{7}{3}\\\\[/tex]

Because the root is x = 7/3, it leads to the factor 3x-7 = 0

Note that we go from x = 7/3 to 3x = 7 after multiplying both sides by 3. Then we subtract 7 from both sides.

It turns out that we have two copies of the identical factor (3x-7) because x = 7/3 is a double root.

So in reality we have the factorization (3x-7)(3x-7) which we can shorten into (3x-7)^2 if we wanted.

Use the box method or FOIL method to expand (3x-7)(3x-7) and you should get 9x^2-21x-21x+49 which simplifies to 9x^2-42x+49. This confirms we have the correct factorization.

Therefore, A and C are both 3, while B and D are both -7.

Answer:

1.5

Step-by-step explanation:

Four goes into six once, then four goes into 20 5 times

The population model is most sufficient for 2005 because 2005 is the closest to 2000

The population function is given as:

[tex]P(x) = 10550(1.1)^x[/tex]

From the question, we understand that the population model is for years after 2000.

This means that the model cannot be used for the year 1950; because 1950 is before 2000.

The model can be used for years 2005, 2025 and 2050.

However, it is most sufficient for 2005 because 2005 is the closest to 2000, and the population model can change with time

Read more about population functions at:

https://brainly.com/question/15680851

Answer:

B!

Step-by-step explanation:

Answer:

y=-x+A

Step-by-step explanation:

Answer:

y=-4x+7

Step-by-step explanation:

1) find the slope first between the two points

m= y2-y1/x2-x1

m= -1-7/2-0

m=-8/2

m=-4

2) use the linear equation y=mx+c

using the slope we find earlier and the coordinate

to substitute into the equation which is,

y=mx+c

7=-4(0)+c

c=7

3) the answer

y=-4x+7

Answer:

SSS, SAS, ASA, AAS, HL

Step-by-step explanation:

1. SSS (side side side) says if 3 sides of one triangle are congruent to 3 sides of another triangle, then the 2 triangles are congruent.

2. SAS (side angle side) says if 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent.

3. ASA (angle side angle) says if 2 angles and the included side of a triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent.

4. AAS (angle angle side) says if 2 angles and the none included side of one triangle are congruent to the corresponding parts of another triangle, then the 2 triangles are congruent.

5 HL (hypotenuse leg) says if 2 right triangles that have a congruent hypotenuse and a corresponding congruent leg, then the 2 triangles are congruent.

Because it is a rectangle, the sides are equal, and they share the same hypotenuse.

Answer:

6 miles

Step-by-step explanation:

2 inches : 1.5 miles

8 inches : 4(2 inches)

8 inches : 4(1.5 miles)

8 inches : 6 miles

6 miles away

-Chetan K

The actual distance between the two trails is 6 miles.

Given the scale of the map is 2 inches to 1.5 miles, we can set up a proportion to find the actual distance between the two trails.

Let x represent the actual distance between the trails in miles. The proportion would be:

(2 inches / 1.5 miles) = (8 inches / x miles)

Now, solving for x:

2/1.5 = 8/x

Cross-multiplying:

2x = 1.5 × 8

2x = 12

Divide by 2:

x = 6

So, the actual distance between the two trails is 6 miles.

Learn more about proportion here:

https://brainly.com/question/1496357

#SPJ3

Answer:

y = 5x + 2

Step-by-step explanation:

Given the equation 5x + 2

Plug in 0

y = 5(0) + 2

y = 2

(0,2)

Given the equation 5x + 2

Plug in 1

y = 5(1) + 2

y = 7

(1,7)

Answer:

Outlier, clusters, and gap in your value.

Step-by-step explanation:

An OUTLIER is a data point that falls away from the rest of the points in a scatter plot. It doesn't seem to fit with the rest of the points. DATA CLUSTERS are groups of points that are all graphed close together. A GAP IN VALUE occurs when there are points clustered at two different spots on a scatter plot.

Answer:

- 5

Step-by-step explanation:

Given

3x = 21 ( divide both sides by 3 )

x = 7

Then

23 - 4x = 23 - 4(7) = 23 - 28 = - 5

4x^2 + 2x - 4

Hope this helps

Answer: 3.14159

Step-by-step explanation:

Answer:

increasing the area of their contact

Step-by-step explanation:

we have a right-angled triangle, that is "hovering" 1.61 m above the ground.

the Hypotenuse (the side opposite of the 90 degree angle) is the line of sight from the eye to the top of the skyscraper.

one leg is the height of the skyscraper (minus the 1.61 m).

the other leg is the ground distance from Jacob to the skyscraper (281 m).

we know already 2 angles : the 90° angle between the ground distance and the skyscraper height. and the 25° between the ground distance and the line of sight.

and as we know that the sum of all angles in a triangle is always 180°, we know that the third angle (between the line of sight and the skyscraper height) is

180 - 90 - 25 = 65°

now we can use the law of sines

a/sin(A) = b/sin(B) = c/sin(C)

(the ratio between a side and its opposing angle)

to get all missing side lengths.

the 25° angle is opposite of the skyscraper height, and the 65° angle is opposite of the ground distance (the only side length we know so far).

so,

height/sin(25) = 281/sin(65)

height = 281 × sin(25)/sin(65) = 131.0324519... m

to get the full height of the skyscraper, we need to add the 1.61 m that the described triangle was "hovering" above ground.

therefore, the height of the skyscraper is

131.0324519... + 1.61 = 132.6424519... ≈ 132.6 m

Answer:

8.08248

Step-by-step explanation:

Use a calculator

Answer:

y=8x+4

Step-by-step explanation:

I am assuming you are asking for an equation.

Total cost = $8*(number of people) + $4

Find g(f(x)) f(x)=3x^2+6x-4 g(x)=-3x+4. f(x)=3x2+6x−4 f ( x ) = 3 x 2 + 6 x - 4 g(x)=−3x+4 g ( x ) = - 3 x + 4. Set up the composite result function.

Answer:

2

Step-by-step explanation:

Answer: Tyson is 188 centimetres tall.

Answer:

12.0

Step-by-step explanation:

Answer:

452.4

Step-by-step explanation:

Answer:

Since both terms are perfect cubes, factor using the sum of cubes formula,

a³+b³=(a+b)(a²-ab+b²) where

a=n and b=8

(n+8)(n²-8n+64)

Answer

(n+8)(n²-8n+64)

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Carryonlearing

Answer:

Step-by-step explanation:

The only one that has a chance of being correct is D. That's because the first term is correct and you have to assume that the second one is as well.

cubrt(512) = 8

The first term is (n + 8)

The second term is (n^2 - 8*n + 8^2) = n^2 - 8n + 64

All the other answers have the wrong first term

A: it should be n + 8 not n - 8

B and C are both wrong because the cube root of 512 is 8 not 4.

Answer:

  x = 9/4

Step-by-step explanation:

Locate point G on segment DE so that DG = 1 and GE = 4. CG is parallel to AD, so ΔCGE ~ ΔABC. Corresponding sides are proportional.

  AB/BC = CG/GE

  x/1 = 9/4

  x = 9/4

_____

Additional comment

Using the given triangles, you can write the proportion statement as ...

  (9+x)/x = 5/1

We judge this to take more steps to solve, so we prefer the method shown above.

Answer:

x  =  24  +  y

Step-by-step explanation:

Move all terms that don't contain  x  to the right side and solve.

Answer:

Step-by-step explanation:

5x − 5y = 120

y= −7x + 8

Use the second equation in the first (eliminates y)

5x − 5(−7x + 8) = 120

5x (+35x -40) = 120

40x -40 = 120

40x = 160

x = 4

----

If x = 4:

y= −7x + 8

y= −7*(4) + 8

y= -28 + 8

y = -20

====

The solution is (4,-20)

Step-by-step explanation:

Given (2x + 23), (8x + 2) and (20x - 52) are three consecutive terms of an arithmetic sequence.

(8x + 2) - (2x + 23) = (20x - 52) - (8x + 2)

or, 6x - 21 = 12x - 54

or, 12x - 6x = - 21 + 54 = 33

or, 6x = 33

or, 2x = 11

∴ x = 11/2

∴2x + 23 = 2 × 11/2 + 23 = 34

8x + 2 = 8 × 11/2 + 2 = 46 and

20x - 52 = 20 × 11/2 - 52 = 110 - 52 = 58

34, 46 and 58 are three consecutive terms of an arithmetic sequence.

∴ Common difference(d) = 46 - 34 = 58 - 46 = 12, it is proved.

Hence, the common difference of the sequence is 12.

[tex]\huge \bf༆ Answer ༄[/tex]

The additional information needed to prove that the triangles are congruent is ~ A

Answer:

if it is (2x-y)8

then it is 16x - 8y

[tex]x^0[/tex]y = 1.y = y

so the co efficient of y is -8

Step-by-step explanation: