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1 year ago

Three more than twice a number is less than negative thirteen. Solve the inequality for the unknown number.

Mathematics

1 answer:

Goshia [24]1 year ago

4 0

Answer:

Step-by-step explanation:

The number = x

Three more than the number = x + 3

twice the number = 2x

which means:

2x + 3 < -13

2x + 3 -3 < -13 -3 (subtract 3 from both sides)

2x < -16

2x/2 < -16/2 (divide 2 from both sides)

x < -8

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A circle is shown. Secants S V and T V intersect at point V outside of the circle. Secant S V intersects the circle at point W.

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<u>Given</u>:

Secants S V and T V intersect at point V outside of the circle. Secant S V intersects the circle at point W. Secant T V intersects the circle at point U.

The length of TU is (y - 2).

The length of UV is 8.

The length of SW is (y + 4)

The length of WV is 6.

We need to determine the length of line segment SV.

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The value of y can be determined using the intersecting secant theorem.

Applying, the theorem, we get;

$WV \times SV=UV \times TV$

Substituting the values, we have;

$6 \times (y+4+6)=8 \times (y-2+8)$

$6 \times (y+10)=8 \times (y+6)$

$6y+60=8y+48$

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$y=6$

Thus, the value of y is 6.

<u>Length of SV:</u>

The length of SV is given by

$SV=SW+WV$

$SV=y+4+6$

$SV=6+4+6$

$SV=16$

Thus, the length of SV is 16 units.

Hence, Option D is the correct answer.

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