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3 years ago

Help geometry question

Mathematics

1 answer:

Sauron [17]3 years ago

6 0

Answer:

x=10

Step-by-step explanation:

43 and (4x+3) are vertical angles, which mean they are equal

so, 43=(4x+3)

43-3=(4x+3-3)

40=(4x)

40/4=4x/4

10=x

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Svet_ta [14]

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so i'm assuming you'd use Pythagoras:

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What number is 4 times as many as 25

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4 times as many as 25 is 100

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3 years ago

Read 2 more answers

Y = 4x - 9 complete the missing value in the solution to the equation

Zanzabum

Answer: If you substitute the x for 3, and multiply 4 times 3, you’ll get 12 and then you subtract 9 from 12 and then you’ll get 3. I’m pretty sure y=3

Step-by-step explanation:

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3 years ago

If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then is the triangle isosceles?

Ne4ueva [31]

Answer:

True

Step-by-step explanation:

The perpendicular bisector of the opposite side to the vertex bisects the angle at the vertex into two equal parts and also bisects the triangle into two equal parts.

Let A be the angle at the vertex, then assume that the angle is an isosceles triangle with base angles B.

We need to show that A = 180 - 2B for an isoceles triangle

The perpendicular bisector bisects A into two so the new angle in the vertex one half of the bisected triangle is A/2.

Since this half triangle is a right-angled triangle, the third angle in it is 90.

So, A/2 + B + 90 = 180 (Sum of angles in a triangle)

subtracting 90 from both sides, we have

A/2 + B + 90 - 90 = 180 - 90

A/2 + B = 90

subtracting B from both sides, we have

A/2 + B = 90

A/2 = 90 - B

multiplying through by 2, we have

A = 2(90 - B)

A = 180 - 2B

Since A = 180 - 2B, then our triangle is an isosceles triangle.

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3 years ago

The standard form of a quadratic equation is given as y=ax^2+bx+c and vertex form is given as y=a(x−h)^2+k. Write a formula that

Tju [1.3M]

Answers:

$h = -\frac{b}{2a}\\\\k = \frac{-b^2+4ac}{4a}\\\\$

where 'a' cannot be zero.

=========================================================

Explanation:

The vertex is (h,k)

The x coordinate of the vertex is h which is found through this formula

$x = -\frac{b}{2a}$

For example, if we had the quadratic $y = 3x^2-6x+5$ , then we'll plug in a = 3 and b = -6 to get: $h = -\frac{b}{2a} = -\frac{-6}{2*3} = 1$

------------

To find the value of k, we plug that h value into the original standard form of the quadratic and simplify.

$y = ax^2+bx+c\\\\k = ah^2+bh+c\\\\k = a\left(\frac{-b}{2a}\right)^2+b\left(\frac{-b}{2a}\right)+c\\\\k = a*\frac{b^2}{4a^2}+\frac{-b^2}{2a}+c\\\\k = \frac{b^2}{4a}+\frac{-b^2}{2a}+c\\\\$

$k = \frac{b^2}{4a}+\frac{-b^2}{2a}*\frac{2}{2}+c*\frac{4a}{4a}\\\\k = \frac{b^2}{4a}+\frac{-2b^2}{4a}+\frac{4ac}{4a}\\\\k = \frac{b^2-2b^2+4ac}{4a}\\\\k = \frac{-b^2+4ac}{4a}\\\\$

It's interesting how we end up with the numerator of $-b^2+4ac$ which is similar to $b^2-4ac$ found under the square root in the quadratic formula. There are other ways to express that formula above. We need $a \ne 0$ to avoid dividing by zero. The values of b and c are allowed to be zero.

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3 years ago