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Bogdan [553]
2 years ago
14

Solve for x ~

3 \: (14 - 5x) =16 - 12x" alt="3 \: (14 - 5x) =16 - 12x" align="absmiddle" class="latex-formula">

thankyou ~​
Mathematics
2 answers:
lesya692 [45]2 years ago
6 0

3(14 - 5x) = 16 - 12x

Distribute 3 throught the parentheses

42 - 15x = 16-12x

Move the variable to the left-hand side and change its sign

42 - 15x + 12x = 16

Move the constant to the right-hand side and change its sign

- 15x+12x=16 - 42

Collect like terms

- 3x =  - 26

Divide both sides of the equation by -3

\boxed{x =  \frac{26}{3} }

Andrews [41]2 years ago
3 0

  • \sf \: 3(14 - 5x) = 16 - 12x

  • \sf \: 42 - 15x = 16 - 12x

  • \sf \:  - 15x + 12x = 16 - 42

  • \sf \:  - 3x =  - 26

  • \sf x =  \frac{ \cancel -26}{  \cancel- 3}

  • \large   \boxed{\sf \underline{ \color{green}x =  \frac{26}{ 3} }}

<h3>Hope Helps~</h3>
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Answer:

Option B

Step-by-step explanation:

Let the point O is the origin.

Then the coordinates of the vertices A,B and C will be,

A → (-12, -8)

B → (-8, 0)

C → (-6, -4)

Rule for the dilation of a point (x, y) by scale factor 'k' about the origin is,

(x, y) → (kx, ky)

By this rule, coordinates of the vertices of the image triangle will be,

If k = \frac{1}{2},

A(-12, -8) → A'(-6, -4)  

B(-8, 0) → B'(-4, 0)

C(-6, -4) → C'(-3, -2)

From the given options,

Option B is the answer.

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2 years ago
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Nataliya [291]

Answer:

hope this helps :)

Step-by-step explanation:

7 0
3 years ago
A retired math teacher takes his niece shopping. He tells his niece that they can spend x dollars and x minus 49.5 equals 15. Wh
kakasveta [241]
X - 49.5 = 15
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3 years ago
Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B
Tems11 [23]

Answer:

0.75

Step-by-step explanation:

Given,

P(A) = 0.6, P(B) = 0.4, P(C) = 0.2,

P(A ∩ B) = 0.3, P(A ∩ C) = 0.12, P(B ∩ C) = 0.1 and P(A ∩ B ∩ C) = 0.07,

Where,

A = event that the selected student has a Visa card,  

B = event that the selected student has a MasterCard,  

C = event that the selected student has an American Express card,

We know that,

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

= 0.6 + 0.4 + 0.2 - 0.3 - 0.12 - 0.1 + 0.07

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5 0
2 years ago

zhuklara [117]

Step-by-step answer:

Given:

A triangle

Perimeter  = 60 cm

longest side = 4* shortest side (x)

Solution:

longest side = 4x

shortest side = x

third (intermediate side = 60 -x -4x = 60-5x

The triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle.  Hence

x + y > 4x

x + 60-5x > 4x

60 - 4x > 4x

8x < 60

x < 60/8 = 7.5, or

x < 7.5

Therefore to form a triangle, x (shortest side) must be less than 7.5 cm.

Examine the options: both 7 and 5 are both less than 7.5 cm.

40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.

Now also examine cases where 4x is NOT the longest side, in which case we need

4x>=y

or

4x >= 60-5x

9x >=60

x >= 6.67

so x=5 will not qualify, because 4x will no longer be the longest side.

The only valid option is x=7 cm

The side lengths for x=7 and x=5 are, respectively,

(7, 25, 28)

5, 20, 35  (in which case, the longest side is no longer 4x=20, so eliminated)

7 0
3 years ago
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