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3 years ago

Photo attached! 10 points! Thank you in advance!!

Mathematics

2 answers:

Fantom [35]3 years ago

6 0

$ax^2+bx+c=0\\\\x^2+7x+9=3\qquad|\text{subtract 3 from both sides}\\\\x^2+7x+9-3=3-3\\\\\boxed{x^2+7x+6=0\to A.}$

$a=1,\ b=7,\ c=6$

sleet_krkn [62]3 years ago

5 0

The answer is A because you subtract 3 from both sides to get the equation set to 0

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Barbara drives between Miami, Florida, and West Palm Beach, Florida. She drives 50 mi in clear weather and then encounters a thu

cluponka [151]

Answer:

Her speed driving in nice weather is 50 mph and in thunderstorm is 32 mph.

Step-by-step explanation:

Barbara drives 50 miles in clear weather and then encounters a thunderstorm for the last 16 miles.

Suppose, her speed in nice weather is $x$ mph.

As she drives 18 mph slower through the thunderstorm than she does in clear weather, so her speed in thunderstorm will be: $(x-18) mph$

We know that, $Time = \frac{Distance}{Speed}$

So, the time of driving in clear weather $=\frac{50}{x}$ hours

and the time of driving in thunderstorm $=\frac{16}{x-18}$ hours.

Given that, the total time for the trip is 1.5 hours. So, the equation will be......

$\frac{50}{x}+ \frac{16}{x-18}=1.5 \\ \\ \frac{50x-900+16x}{x(x-18)}=1.5\\ \\ \frac{66x-900}{x(x-18)}=1.5 \\ \\ 1.5x(x-18)=66x-900\\ \\ 1.5x^2-27x=66x-900\\ \\ 1.5x^2-93x+900=0\\ \\ 1.5(x^2 -62x+600)=0\\ \\ x^2 -62x+600=0\\ \\ (x-50)(x-12)=0$

Using zero-product property.........

$x-50=0\\ x=50\\ \\ and\\ \\ x-12=0\\ x=12$

We need to ignore $x=12$ here, otherwise the speed in thunderstorm will become negative.

So, her speed driving in nice weather is 50 mph and her speed driving in thunderstorm is (50-18) = 32 mph

3 0

3 years ago

Find the coordinates of the circumcenter of the triangle with the given vertices. X(-2, 1), Y(2, -3), Z(6, -3).

lana [24]

Answer:

C (4,3)

Step-by-step explanation:

Steps to find the circumcenter:

1) Find and Calculate the midpoint of given coordinates or midpoints.

2) Calculate the slope of the perpendicular bisector lines

3) By using the midpoint and the slope, find out the equation of the line

$( y-y_1 )= m(x-x_1)$

4) Do the same for another line

Solve the equations of two lines to get the intersection point.

The intersection point will be the circumcenter of the triangle.

Given :

X(-2,1), Y(2,-3), Z(6,-3)

Please see the attached file:

5 0

3 years ago

A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which e

maw [93]

Answer:

Ф = ------------ = 7/5 radians

Step-by-step explanation:

"e" is inappropriate format here. Use Ф or α or similiar character for central angle.

Here, (arc length) = (radius)(central angle), or s = rФ, and so:

(central angle) = Ф = (arc length) / (radius)

7 ft

Here, Ф = ------------ = 7/5 radians

5 ft

3 0

3 years ago

What is the quotient of 1060 ÷ 48

nikdorinn [45]

1060 / 48 = 22.08 = 22.1

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8 0

3 years ago

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mafiozo [28]

Answer: 21 cm is the volume

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4 0

3 years ago