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3 years ago

How many solutions does the system of equations have 2x = -10y + 6 and x + 5y = 3

Mathematics

1 answer:

kipiarov [429]3 years ago

3 0

Infinite

x=-5y+3 is the same as x+5y=3

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4 years ago

Diego measured the length of a pen to be 21 cm. The actual length of the pen is 23 cm. Which of these is closest to the percent

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3 years ago

If there are a hundred centimeters in a meter how many centimeters are in 1/2 meters

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3 years ago

Read 2 more answers

Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 ho

Triss [41]

Answer:

16 mph

Step-by-step explanation:

You should first form equations related to this information

Given,Tamara can go 4 mph faster than her sister, Samantha

Lets take speed to ride a bike for Samantha to be= x mph

The speed to ride a bike for Tamara will be= x+4 mph

To cover a distance of 80 miles, Samantha takes 1 hour longer than Tamara

Introduce the formula for time; time=distance/speed=D/S where D is distance in miles and S is speed in miles per hour

Here time Samantha takes to cover a distance of 80 miles is 1 hour more than that taken by Tamara, hence

Time taken by Samantha

$=\frac{80}{x}$

Time taken by Tamara

$=\frac{80}{4+x}$

Equation for difference in time

$=\frac{80}{x} -\frac{80}{4+x} =1$

Solve the equation for difference in time to get value of x which is samantha speed

$=\frac{80}{x} -\frac{80}{x+4} =1\\\\\\=80(4+x)-80(x)=x(4+x)\\\\\\=320+80x-80x=4x+x^2\\\\\\=x^2+4x-320=0$

Solve quadratic equation by the quadratic formula where a=1,b=4 and c=-320

x=(-b±√b²-4ac)÷2a

x=(-4±√4²-4×1×-320)÷2×1

$x=\frac{-4+/-\sqrt{4^2-4*1*-320} }{2} \\\\\\x=(-4+/-\sqrt{1296} )/2\\\\\\x=\frac{-4+36}{2} =\frac{32}{2} =16$

Samantha speed is 16 mph

6 0

3 years ago

Evaluate the following expression using the values given: Find 2r2 + 3s3 − r2 + 4t2 − r2 if r = −2, s = −3, and t = 5. −19 −37 2

crimeas [40]

2r² + 3s³ - r² + 4t² - r² = 3s³ + 4t²
if s = -3 and t = 5
3s³ + 4t² = 3 * (-3)³ + 4 * 5² = 3 * (-27) + 4 * 25 = -81 + 100 = 19

Answer: 19

5 0

3 years ago