Triangle A has a height of 2.5cm and a base of 1.6cm. The height and base of triangle B are proportional to the height and base of triangle A. Which of the following could be the height and base of triangle B?

Answer:

  (x, y) = (-6, -10)

Step-by-step explanation:

Pick a variable whose coefficient you want to be zero in the sum. Note the two coefficients of that variable in the two equations. Write the second coefficient in the first box, and the opposite of the first coefficient in the second box.

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If you want to eliminate x-terms, the x-coefficients are -2 and -3. Write -3 in the first box and +2 in the second box.

  -3(-2x +2y = -8)   ⇒   6x -6y = 24

  +2(-3x +y = 8)      ⇒   -6x +2y = 16

Added together, the resulting equation is ...

  0x -4y = 40

  y = -10 . . . . . . . divide by -4

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If you want to eliminate y-terms, the y-coefficients are 2 and 1. Write 1 in the first box, and -2 in the second box.

  1(-2x +2y = -8)   ⇒   -2x +2y = -8

  -2(-3x +y = 8)    ⇒   6x -2y = -16

Added together, the resulting equation is ...

  4x +0y = -24

  x = -6 . . . . . . . . divide by 4

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Now, you know the solution is (x, y) = (-6, -10).

_____

Additional comment

It does not matter which is the first equation. You can swap the two equations and still achieve the desired results. Also, if the coefficients have a common factor, you can divide that out. As you may have noticed, the arithmetic is a little easier if one of the chosen coefficients is 1 or -1.

If you're combining the equations using addition, as we have done here, then one of the coefficient multipliers must be negated, as we have described. If you're combining the equations using subtraction, then you can preserve the original signs of the coefficients (or change them both).

Answer:

  CD = 3 -√3

Step-by-step explanation:

The ratio of leg lengths in a 30°-60°-90° triangle is ...

  1 : √3 : 2

The longest leg of ΔABD is 2√3, so we must multiply all of these ratio values by √3 to see the actual lengths of the triangle sides.

  AB : BD : AD = 1 : √3 : 2 = √3 : 3 : 2√3

That is ...

  AB = √3

  BD = 3

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The lengths of the legs in isosceles right triangle ABC are the same, so ...

  BC = AB = √3

Then the length of interest is ...

  CD = BD -BC

  CD = 3 -√3 . . . . . . . a=3, b=-1

Answer:

42 ft minimum.

Step-by-step explanation:

you need to place the ladder 12ft from the house and it is 30 ft above the ground.

Answer:

IVE BEEN LOCKED OUT OF MY HOUSE BEFORE.

Step-by-step explanation:

42 ft

Answer:

60

Step-by-step explanation:

5water=1/2punch multiply by 12 to get 6 cups of punch so 5 x 12=60 and 1/2 x 12=6

Answer:

15h+40f

15(7)+40(9)

105+360

465

465 fixtures

Step-by-step explanation:

Answer: 465 fixtures

Step-by-step explanation:15h+40f15(7)+

40(9)105+
360465= 465 fixtures

Answer:

2 x 2 x 3 x 2 x 2

2 x 2 x 89

2 x 2 x 2 x 5 x 31

Step-by-step explanation:

factor tree

Answer:

86 - 3x

Step-by-step explanation:

1- Calculate

Answer:

x=97°

Step-by-step explanation:

(n-2)180°

(5-2)180°

3×180°=540°

total angle=540°

136+127+108+72+x=540°

Answer:

y = −x + 1

y = −3/5x + 3

Answer:

the length of inch is 20

Step-by-step explanation:

because 21 inch -20=1

Answer:

b=3.5

Step-by-step explanation:

Answer:

3.5x-1

Step-by-step explanation:

Solving:

4bx = 14

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Divide each side by '4x'.

b = 3.5x-1

Simplifying

b = 3.5x-1

Answer:

3(x-1) 2 if x=4,99

3(499-1)2

3(4,98)2

14.94 + 2 =16.94

Step-by-step explanation:

Answer:

I think standard form would be best because it is simplest.

Step-by-step explanation:

hope this helps

Answer: Intercept Form

Step-by-step explanation:

There are three methods for determining the minimum value of a quadratic equation. Each of them can be useful in determining the minimum. The first way is by using a graph. You can find the minimum value visually by graphing the equation and finding the minimum point on the graph. The y-value of the vertex of the graph will be the minimum. This is especially easy when you have a graphing calculator that can do most of the work  for you.

Answer:

y = -5/2x - 4

Step-by-step explanation:

When given a point and a slope, we use slope-intercept formula:

y - y1 = m (x - x1)

m = slope  point: (-2,1)

y - y1 = m (x - x1)

y - 1 = -5/2 (x - (-2))

y -1 = -5/2x - 5

 + 1          + 1

y = -5/2x - 4

To check our answer, I attached the graph.

Hope this helps!

Step-by-step explanation:

the general point-slope form is

y - y1 = m(x - x1)

with (x1, y1) being a point on the line, and m being the slope (the incline of the line).

we have the point. we can pick one from the 2 choices, I typical go for the one with smaller values. so, I will use (-3, 1).

now we need to calculate the slope.

the slope is the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.

so, for our 2 points we see

x changes by +1 (from -4 to -3).

y changes by +2 (from -1 to +1).

and the slope is +2/+1 = 2

therefore our equation is

y - 1 = 2(x - -3)

or simplified

y - 1 = 2(x + 3)

Answer:

First one
2x²+x-1

Step-by-step explanation:

3x²-x²=2x²

x

8-9=-1

2x²+x-1

Answer:

49x²+126x+81

Step-by-step explanation:

Area of any square is length²

If the length given is 7x+9, we can square this to find out what represents the area:

[tex](7x+9)^{2}[/tex]

[tex](7x+9)(7x+9)[/tex]

[tex]49x^{2} +63x+63x+81[/tex]

[tex]49x^{2} +126x+81[/tex]

Answer:

49x² + 126x + 81

Step-by-step explanation:

A = a²

Since a = 7x + 9

=> A = (7x+9)²

= 49x² + 126x + 81

Note: (a+b)² = a² + 2ab + b²

Answer:

Compound interest

$34633.25

Step-by-step explanation:

Everything starts of at 100% and the rate of interest is 9.5% so we add them on=109.5%

Now we want this percentage as a decimal so we divide by 100 = 1.095 this our multiplier

Then get the original amount that you borrowed = 6000 times by the multipler=1.095 to the power of number of years so

6000 multipled by 1.095 to the power of 5

Giving me $34633.25

Answer:

Step-by-step explanation:

Tangent is the ratio of perpendicular to the base. The distance between the base of the tree and the swing set is 18 feet.

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

Base is the adjacent smaller side of the angle θ.

As it is given that the height of the tree is 11 feet, while the angle of depression is 31.43°, therefore, the tangent can be written as,

[tex]\rm{Tangent(31.43^o) = \dfrac{AB}{BC}[/tex]

Where BC is the length between the base of the tree and the AB is the height of the tree.

[tex]\rm Tangent(31.43^o) = \dfrac{11}{BC}\\\\BC = 17.999 \approx 18[/tex]

Hence, the distance between the base of the tree and the swing set is 18 feet.

Learn more about Tangent (Tanθ):

https://brainly.com/question/10623976

Interval, 1 a.m. to 12 noon has the greater rate of snowfall, in inches per hour.

First step

1am - 12 noon will gives us 11 hours

6am - 3pm will gives us 9 hours

Second step

Inches per hour for 11 hours

=33-1/11

=32/11

=2.91 inches per hour

Inches per hour for 9 hours

=36-11/9

=25/11
=2.27 inches per hour

Therefore based on the above analysis Interval, 1 a.m. to 12 noon has the greater rate of snowfall, in inches per hour.

Learn more about interval here:https://brainly.com/question/479532

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Answer:

I think the answer is 3

Step-by-step explanation

16 x 3 = 48

Answer:

4) k = 3

5) h = 35

6) y = 3.5

Step-by-step explanation:

Hope it Helps

Answer:

20$ is the answer of your question

Answer

Its already in order: 1/7 4/14 2/3

Step-by-step explanation:

Because the common denominator for all three is 42, which turns the fractions to 6/42, 12/42, and 28/42 making it easier to place in order

ANSWER:

1/7,4/14,2/3.......................

Answer:

x ≥ 48

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

because you add 3 to -1 and get 2 and you subtract - 4 to 4

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

solution;

here,

=(2p+3q)(P-q)

=(2*4+3*2)(4-2)

=(8+6)(2)

=13*2

=26

3) 60

Step-by-step explanation:

718 ÷ 9 = 79.78

So, if you round to the nearest whole number its about 80, the closest answer from your options is 60 so I think the best estimate is number three: 60.