Divide and round to the nearest tenth 3.5 divided by 2.29

Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$ Pls help.

nirvana33 [79]

Answer:

-56/9

Step-by-step explanation:

By Vieta's formulas,

$r + s = -\frac{4}{3}$ and $rs = \frac{12}{3} = 4.$ Squaring the equation $r + s = -\frac{4}{3},$ we get

$r^2 + 2rs + s^2 = \frac{16}{9}.$ Therefore,

$r^2 + s^2 = \frac{16}{9} - 2rs = \frac{16}{9} - 2 \cdot 4 = -\frac{56}{9}}$

5 0

2 years ago

M∠a=(48−x)°m∠b=(9x−38)°m∠c=90°

Pachacha [2.7K]

The question does not specify the condition that must satisfy the given angles. We assume they are the internal angles of a triangle.

Answer:

x = 10

Step-by-step explanation:

Internal Angles of a Triangle

The measure of the angles of a triangle are given as 48-x, 9x-38, and 90. Since the sum of the internal angles of a triangle is 180°:

48 - x + 9x - 38 + 90 = 180

Simplifying:

100 + 8x = 180

Subtracting 100:

8x = 180 - 100 = 80

x = 80/8

x = 10

7 0

2 years ago

Please help with geometry. 20 points, and another question worth 98 on my profile!

vovikov84 [41]

Answer:

Part 1) m∠1 =(1/2)[arc SP+arc QR]

Part 2) $PR^{2} =PS*PT$

Part 3) PQ=PR

Part 4) m∠QPT=(1/2)[arc QT-arc QS]

Step-by-step explanation:

Part 1)

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

we have

m∠1 -----> is the inner angle

The arcs that comprise it and its opposite are arc SP and arc QR

so

m∠1 =(1/2)[arc SP+arc QR]

Part 2)

we know that

The Intersecting Secant-Tangent Theorem, states that the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

so

In this problem we have that

$PR^{2} =PS*PT$

Part 3)

we know that

The Tangent-Tangent Theorem states that if from one external point, two tangents are drawn to a circle then they have equal tangent segments

so

In this problem

PQ=PR

Part 4)

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

In this problem

m∠QPT -----> is the outer angle

The arcs that it encompasses are arc QT and arc QS

therefore

m∠QPT=(1/2)[arc QT-arc QS]

4 0

2 years ago

Jenn went shopping and spent $112. She bought a book for $24 and CD's that cost $8 each. What equation would you use to find out

slavikrds [6]

I would use the equation
24 + 8x = 112

let x = the amount of CDs she bought.

Hope this helps!!

3 0

2 years ago

The millers drove 150 miles in 3 hours at what rate how long will it take them to drive 400 miles

valentina_108 [34]

Rate = (150 miles)/(3 hrs) = 50 mph

so . . .

(50 mph)*(time) = 400 miles

*divide both sides by 50 mph

time = (400 miles)/(50 mph) = 8 hrs

time = 8 hrs

8 0

3 years ago

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