Mathematics, 29.06.2019 15:10 randallmatthew5665

Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola.
equation 1: (x – 3)2 = y – 4
equation 2: y = -x + b
in order for this solution to be reasonable, which qualifications must be met?
b must equal 7 and a second solution to the system must be located at the point (2, 5).
b must equal 1 and a second solution to the system must be located at the point (4, 5).
b must equal 7 and a second solution to the system must be located at the point (1, 8).
b must equal 1 and a second solution to the system must be located at the point (3, 4).

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Answer from: skateyo2553

Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)

Step-by-step explanation:

step 1

Find the vertex of the quadratic equation

The general equation of a vertical parabola in vertex form is where (h, k) is the vertex we have so , the vertex is the point (3,4)

step 2

Find out the value of b in the linear equation we know that if the vertex is a solution of the system of equations, then the vertex must satisfy both equations substitute the value of x and the value of y of the vertex in the linear equation for x=3, y=4.

step 3

Find out the second solution of the system of equations we have

> equation A

> equation B

Solve the system of equations by graphing . Remember that the solutions are the intersection points both graphs . The second solution of the system of equations is (2,5)

Therefore , b must equal 7 and a second solution to the system must be located at the point (2, 5)

Answer from: Quest

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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Tom determines the system of equations below has two solutions, one of which is located at the verte...