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damaskus [11]
2 years ago
10

The sum of three numbers is 11 . The sum of twice the first​ number, 5 times the second​ number, and 6 times the third number is

44. The difference between 4 times the first number and the second number is 10. Find the three numbers.
Mathematics
1 answer:
Assoli18 [71]2 years ago
4 0

Answer:

4, 6, 1

Step-by-step explanation:

We can solve this problem using a system of equations:

1) a + b + c = 11

2) 2a + 5b + 6c = 44

3) 4a - b = 10

First, we can substitute the value of b from equation #3 into equation #1:

b = 4a - 10

a + (4a - 10) + c = 11

5a - 10 + c = 11

5a + c = 21

c = 21 - 5a

Now, we can plug the values of b and c into equation #2, as b and c are represented in terms of a:

2a + 5(4a - 10) + 6(21 - 5a) = 44

2a + 20a - 50 + 126 - 30a = 44

-8a + 76 = 44

-8a = -32

a = 4

b = 4a - 10 = 4(4) - 10 = 6

c = 21 - 5a = 21 - 5(4) = 1

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A building makes a 90° angle with the ground. A ladder leans against the building, making a 110° exterior angle with the ground.
liberstina [14]

<u>Answer:</u>

A building makes a 90^{\circ} angle with the ground .The two interior angles are 70^{\circ} and 20^{\circ}

<u>Solution: </u>

Given, a ladder which is against the building wall makes an exterior angle of 110^{\circ}

And building makes a  90^{\circ} angle with the ground.

So, altogether it makes a right angle triangle with ladder as hypotenuse and ground as base leg and building as another leg.  

Now, we know that, sum of exterior angles and interior angles equals to 180^{\circ}

Here, in the case of ground and ladder, exterior angle is 110^{\circ} and interior angle is unknown.

Exterior angle + interior angle = 180

110 + interior angle = 180

Interior angle = 180 – 110

Interior angle = 70^{\circ}

We have found one of the two interior angles of right angle triangle.

We know that, sum of angles in a triangle is 180 degree

Known Interior angle + unknown interior angle + right angle = 180

70 + unknown interior angle + 90 = 180

Unknown interior angle + 160 = 180

Unknown interior angle = 180 - 160

Unknown interior angle = 20^{\circ}

Hence the two interior angles are  70^{\circ} and 20^{\circ}

7 0
3 years ago
5x(2x-y) -3y(2+3x) expand and simplify​
OleMash [197]

Answer:

10x² - 14xy -6y

Step-by-step explanation:

5x(2x-y)-3y(2+3x)

10x²-5xy-6y-9xy

10x² - 14xy - 6y

5 0
3 years ago
15 points and crown <br> solve by factoring (x+6)(2x-5)=0<br> I am confused
Reika [66]
Remember, in order for this equation to be true either one of the polynomials has to equal 0
So:

-> x+6 = 0

x=-6


-> 2x-5 = 0

2x= 5

x= 5/2


So the answer is x=-6 and x= 5/2.


Hope this helps!
7 0
3 years ago
$3000 is invested at 3% annual interest for 3 years.<br> a. Simple Interest b. Compound Interest
stich3 [128]

Answer:

a. $270

b. $3,278.18

Step-by-step explanation:

Given that

The principal amount is $3,000

Annual rate of interest is 3%

And, the time period is  3 years

We need to find out the simple interest & compound interest

The following formulas should be used

a. For simple interest

= Principal × rate of interest × time period

= $3,000 × 3% × 3 years

= $270

b. For compound interest

= Principal × (1 + rate of interest)^time period

= $3,000 × (1 + 0.03)3

= $3,000 × 1.03^3

= $3,278.18

8 0
3 years ago
Select the ordered pairs that are solutions to the inequality 2x-3y greater than or equal to 12
Dima020 [189]
Just rank every pair of numbers for example:
The first one is: 1,-3.
2•1-3•-3>12
2+9>12
11>12
That's Incorrect. The first pair of numbers doesn't match the inequality.
Now do the same thing to all the other pairs of numbers.
3 0
3 years ago
Read 2 more answers
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