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Ierofanga [76]
3 years ago
9

In the following system of equations, determine whether the system has a unique

Mathematics
1 answer:
Rina8888 [55]3 years ago
5 0

Answer:

the system has a unique solution

Step-by-step explanation:

Start with an equation of a line in standard form,

ax + by = c

Solve it for y to put it into the slope-intercept form:

by = -ax + c

y = -\dfrac{a}{b}x + \dfrac{c}{b}

The slope is -a/b.

Now look at your system of equations. The slope of the first equation is -a/b = -2/3. The slope of the second equation is -a/b = -6/5.

You have a system of two linear equations with two lines with different slopes, so the lines must intersect at a single point.

Answer: the system has a unique solution

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Trey is taking out a loan for $85000. It is a 20-year loan with an APR of 5.85% what will his monthly payment be?
ololo11 [35]

Answer:

$768.54 (Approximate)

Step-by-step explanation:

Trey is taking out a loan for $85000. It is a 20-year loan with an APR of 5.85%.

Therefore, if we consider the interest rate is simple interest, then using the simple interest formula, the sum will become after 20 years

85000(1 + \frac{5.85 \times 20}{100}) = 184450 dollars.

Therefore, the monthly payment for the loan will be \frac{184450}{20 \times 12} = 768.54 dollars. (Answer)

8 0
3 years ago
Question 28 of 42
lina2011 [118]

Answer with explanation:

Properties of Rectangle

1. Opposite sides are equal and parallel.

2. Diagonals are equal and bisect each other.

3. Adjacent Sides are Perpendicular to each other.

→If two lines are parallel their slopes are equal and if two Lines are perpendicular, their product of slopes is -1.

→A Rectangle is a Quadrilateral also.

→Adjacent sides are perpendicular ,so , their slopes can't be equal.Product of their slopes should be equal to ,-1.

⇒Slope of AB × Slope of BC = -1

⇒Also, Slope of AB × Slope of BC = -1

Slope of AB × Slope of AD = -1

⇒ Slope of AD × Slope of CD = -1

Slope of CB × Slope of CD = -1

Option B And Option C

are statement which proves that polygon ABCD is not a rectangle.

5 0
3 years ago
There are red, blue, and white buttons in a box. The ratio of the
vampirchik [111]

Answer:

680

Step-by-step explanation:

Ratio of red to white 4 : 7

Number of white = 280

White + red buttons = x

7x / 11 = 280

7x = 280 * 11

7x = 3080

x = 3080 / 7

x = 440

Number of red buttons 440 - 280 = 160

Number of red bottons ;

Blue + red buttons = x

3 : 2 ; blue : red

3 + 2 = 5 ;

2x / 5 = 160

2x = 160 * 5

2x = 800

x = 800 / 2

x = 400

Number of Blue buttons :

400 - 160 = 240

Total :

White + red + blue

280 + 160 + 240 = 680 buttons

5 0
3 years ago
Given the triangle that has a base of five less than triple the height. The height is 2x+6.
Deffense [45]

Answer:

<h3>          A = 0.5(2x+6)(6x+13) = 6x² + 49x + 78</h3>

Step-by-step explanation:

H = 2x+6          - the hight

3H = 3(2x+6)      - triple the hight

3H-5 = 3(2x+6) - 5    -  five less than triple the height

Area of triangle:  A = 0.5BH

B = 3(2x+6)-5 = 6x + 18 - 5 = 6x + 13

H = 2x+6

So:

    A = 0.5(2x+6)(6x+13) = (x+6)(6x+13) = 6x² + 13x + 36x + 78

    A = 6x² + 49x + 78

5 0
3 years ago
Two minor league baseball players got a total of 214 hits. Washington had 20 more hits than Sanchez.find the number of hits for
Lelu [443]

Answer:

Sanchez-97

Washington-117

Step-by-step explanation:

3 0
2 years ago
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