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4 years ago

32(4x – 1) – 3x = 54 – (x + 2)

Mathematics

2 answers:

Blababa [14]4 years ago

7 0

Answer:

Step-by-step explanation:

x = 2/3= 0.667

Marizza181 [45]4 years ago

6 0

The answer is x= 2/3 but in domain form it’s x=0.6

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One triangle has side lenghts of 6,8,10. A similar triangle has a perimeter of 60. What are the lengths of the similar triangle?

mamaluj [8]

Answer:

Lengths of second triangle are 15,20,25

Step-by-step explanation:

Given:

One triangle side lengths = 6 , 8 ,10

Similar triangle perimeter =60

To Find:

Lengths of similar triangle = ?

Solution:

A similar triangle is a one in which there is a particular increase in lengths of the sides by a common ratio. This ratio is same for all the sides and by these the similar triangle is formed.

As Lengths are increased by a common ratio so the perimeter of the triangles which are similar will also increase by that

So for this problem if we find out the perimeter increase then we can find out sides

Now For 1st triangle whose sides are given

Lets its perimeter is perimeter 1

Now

Perimeter 1 =sum of length of all sides

= 6 + 8 +10

= 24

Now

Ratio = Perimeter of second triangle / Perimeter 1

= 60 / 24

= 2.5

So perimeter is increased by a factor of 2.5

We can find the length by multiplying each length of triangle 1 with this 2.5

Now Length of first side = 6*2.5

= 15

Length of second side = 8 * 2.5

=20

Length of third side = 10 * 2.5

= 25

Lengths of second triangle are 15,20,25

5 0

3 years ago

A (0, 2) and B (6,6) are points on the straight line ABCD.

elena-14-01-66 [18.8K]

Answer:

(18, 14)

Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

The distance formula states that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ , the distance is denoted by: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ . Let's find the distance between A and B:

d = $\sqrt{(6-0)^2+(6-2)^2}=\sqrt{6^2+4^2} =\sqrt{36+16} =\sqrt{52} =2\sqrt{13}$

Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:

4√13 = $\sqrt{(6-a)^2+(6-b)^2}$

Square both sides:

208 = (6 - a)² + (6 - b)²

Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

208 = (6 - a)² + (6 - b)²

208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²

208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52

0 = 13/9a² - 52/3a - 156

13a² - 156a - 1404 = 0

a² - 12a - 108 = 0

(a + 6)(a - 18) = 0

a = -6 or a = 18

We know a can't be negative so a = 18. Plug this back in to find b:

b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

8 0

4 years ago

Read 2 more answers

Krya wants to solve the equation x/10+8=5 what steps should she use on both sides of the equation

maria [59]

Multiplied by 10
x+80=50
x=-30

7 0

3 years ago

Gordon types 2,736 words in 36 minutes. Find the unit rate.

STALIN [3.7K]

Answer:

76 words each minute

Step-by-step explanation:

8 0

3 years ago

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Y=3x-2<br> Y=2x-5<br> Find X and Y using substitution

tiny-mole [99]

$y = 3x -2~~~.....(i)\\\\y = 2x-5~~~.....(ii)\\\\\text{Substitute equation (i) in equation (ii):}\\\\3x-2 = 2x -5\\\\\implies 3x -2x = -5+2\\\\\implies x = -3\\\\\text{Substitute}~ x =-3,~ \text{in equation (i):}\\\\y = 3(-3) -2 = -9 -2 = -11\\\\\text{Hence,}~ (x,y) = (-3,-11)$

4 0

3 years ago