In questions 6 – 9, state the solutions for the quadratic equation depicted in the graph.

Mathematics

1 answer:

Mariana [72]1 year ago

3 0

Step-by-step explanation:

It is just where it crosses the x axis

6) -3, -4

7) 1, -6

8) -5, -6

9) 3, -2.5

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Beth is 5 years younger than Celeste. Next year, their ages will have a sum equal to 57. How old ech now?

RSB [31]

Celeste is 30 and Beth is 25

let x be Celeste's age now then Beth is x - 5

next year they will be 1 year older

Celeste's age will be x + 1 and Beth will be x - 5 + 1 = x - 4

the sum of their ages is therefore

x + 1 + x - 4 = 57

2x - 3 = 57 ( add 3 to both sides )

2x = 60 ( divide both sides by 2 )

x = 30

Celeste is 30 and Beth is 30 - 5 = 25

8 0

2 years ago

What are two different ways you could find the value of a? Explain these methods.

Ulleksa [173]

See the attached figure to better understand the problem

we know that

1) First way to find the value of a
in the triangle ABC
<span>applying the Pythagorean theorem
AC</span>²=AB²+BC²--------> BC²=AC²-AB²-----> BC²=25²-15²-----> BC²=625-225
BC²=400--------> BC=20 units
a=BC
a=20 units

2) Second way to find the value of a

in the triangle ABD

AB²=AD²+BD²--------> BD²=AB²-AD²-----> BD²=15²-9²---> BD²=144
BD=12 units

in the triangle BDC
a=BC
BC²=BD²+DC²-----> 12²+16²----> 144+256------> BC²=400
BC=20 units
a=20 units