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natali 33 [55]
3 years ago
8

Seven times a number plus three times another number equals -1 the sum of two numbers is -3 what are the numbers? 25 points!!

Mathematics
1 answer:
Reptile [31]3 years ago
5 0
7x+3y=-1
x+y=-3

8x+4y=-4
2x+y=-1
y=-1-2x

x+y=-3
x-1-2x=-3
-x=-2
x=2
y=-1-2*2=-1-4=-5
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Write the given trinomial if possible as a square of a binomial or as an expression opposite to a square of a binomial: 15ab-9a^
MrMuchimi

Answer:

- \bigg(3a -  \frac{5}{2} b) \bigg)^{2}

Step-by-step explanation:

15ab-9a^2-6  \frac{1}{4} b^2 \\  \\  = 15ab-(3a)^2-\frac{6 \times 4 + 1}{4} b^2 \\  \\ = 15ab-(3a)^2-\frac{24+ 1}{4} b^2 \\  \\ = 15ab-(3a)^2-\frac{25}{4} b^2 \\  \\   = 15ab- (3a)^2- \bigg(\frac{5}{2} b \bigg)^2  \\  \\ =  -  \{ - 15ab + (3a)^2 +  \bigg(\frac{5}{2} b \bigg)^2  \} \\  \\ =  -  \{ (3a)^2 +  \bigg(\frac{5}{2} b \bigg)^2 - 15ab  \} \\  \\  =   - \bigg(3a -  \frac{5}{2} b \bigg)^{2}

3 0
2 years ago
Investments historically have doubled every 9 years. if you start with 2,000 investment, how much money would you have after 45
77julia77 [94]

Answer: 64,000

Equation: 2,000*2^(45/9)

4 0
3 years ago
Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(2, −5, 6), C(4, −2, −1), D(3, 4, −4
almond37 [142]

Answer:

Area = 71.3 sq unit

Step-by-step explanation:

a) We will use properties of parallelogram to verify the given vertices.

Property: Have a pair of parallel opposite sides

Hence, vectors AB AD BD BC CD AC. A pair should be parallel:

vectors

AB = A - B = (1, 1 , 3) - ( 2 , -5 , 6 ) = (-1 , 6 , -3)

AD = A - D = (1, 1 , 3) - (3, 4 , -4) = (-2 , -3 , 7)

BC = B - C = (2 , -5 , 6) - (4, -2 , -1) = (-2 ,-3 , 7)

CD = C - D = (4, -2 , -1) - (3, 4 , -4) = (1 , -6 , 3)

Hence we can see  that AB //CD and AD // BC as their unit vector co-efficents are identical/scalar multiple of each other.

b)

Equation of line AB = (1,1,3) + t*(-1 , 6 , -3 )

Point E = (1-t , 1+6t , 3 -3t) ... denotes an position of point E on line AB.

Choose a point on line CD, lets suppose C = ( 4 , -2 , -1 )

Vector EC = ( 1-t , 1+6t , 3-3t ) - (4 , -2 , -1 ) = (-3 -t , 3 +6t , 4 -3t)

For EC to be perpendicular to AB then dot product of AB . EC = 0

Hence,

EC . AB = -1 * (-3-t) -2*(3+6t) -3*(4-3t) = 0

3 + t -6 -12t -12+9t = 0

-2t-3 = 0

t = -3/2

Vector EC = (-3 -t , 3 +6t , 4 -3t) = (-1.5 , -6 , 8.5)

Area = magnitude (AB) * magnitude (EC)

Area = sqrt ((-1)^2 + 6^2 + (-3)^2) * sqrt ((-1.5)^2 + 6^2 + (8.5)^2)

Area = sqrt (46) * sqrt (442) / 2

Area = 71.3 unit^2

6 0
3 years ago
Add 3/ 4 + (−2 1/2).
Marat540 [252]
Exact form-13/4

decimal form-3.25

mixed number form- 3 1/4

hope I helped :)
7 0
3 years ago
Increase £248 by 30%
AfilCa [17]
p\%=\frac{p}{100}\\\\30\%=\frac{30}{100}=\frac{3}{10}=0.3\\\\30\%\ of\ \£248=0.3\cdot\£248=\£74.40\\\\increase\to\£248+\£74.40=\boxed{\£322.40}\leftarrow answer
5 0
3 years ago
Read 2 more answers
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