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3 years ago

Find the value of c such that the line with equation y= 2x + c is a tangent to the parabola y = x squared + 3x

Mathematics

1 answer:

natita [175]3 years ago

6 0

Answer:

c=-1/4

Step-by-step explanation:

Y=2x+c=2(x+c/2), so m=2.

To be tangent we need to check y’ of parabola: y’=2x+3.

So for some x it must be 2x+3=2 (cause m=2). We have x=-1/2.

Now we use x=-1/2 to find y from 2nd equation (equation of parabole): we got y=1/4-3/2=-5/4.

So tangent has point (-1/2,-5/4).

Put that point in firts equation (equation of line): -5/4=-1+c,

so we have c=-1/4.

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PLEASE PLEASE HELP! Find the measure of APB^.

Whitepunk [10]

Answer:

65°

Step-by-step explanation:

Radii CA and CB are perpendicular to tangent lines AT and BT, so

$\angle CAT=\angle CBT=90^{\circ}$

Since angle BAT is equal to 65°, angle CAB has measure

$\angle CAB=90^{\circ}-65^{\circ}=25^{\circ}.$

Consider triangle ACB. This triangle is isosceles, because CA=CB as radii of the circle. Two angles adjacent to the base are congruent, thus

$\angle CBA=\angle CAB=25^{\circ}$

The sum of the measures of all interior angles in triangle is always 180°, so

$\angle CAB+\angle CBA+\angle ACB=180^{\circ}\\ \\25^{\circ}+25^{\circ}+\angle ACB=180^{\circ}\\ \\\angle ACB=130^{\circ}$

Angle ACB is central angle subtended on the minor arc AB, angle APB is inscribed angle subtended on the same minor arc AB. The measure of inscribed angle is half the measure of central angle subtended on the same arc, so

$x=\angle APB=\dfrac{1}{2}\cdot 130^{\circ}=65^{\circ}$

8 0

3 years ago

Brad needs to rent scaffolding to paint a 2-story room. Handy Rentals charges $15 plus $12.50 per hour. The EZ Rental Company ch

mrs_skeptik [129]

Answer:

6 hours

Step-by-step explanation:

lmk if you want an explanation

6 0

2 years ago

What is f(5) if f(1) = 3.2 and f(x + 1) = (f(x))?

scoray [572]

Answer:

The value of f(5) is 3.2.

Step-by-step explanation:

It is given that f(1) = 3.2 and

$f(x+1)=f(x)$

Substitute x=1 in the above equation.

$f(1+1)=f(1)$

$f(2)=3.2$

Substitute x=2 in the given equation.

$f(2+1)=f(2)$

$f(3)=3.2$

Substitute x=3 in the given equation.

$f(3+1)=f(3)$

$f(4)=3.2$

Substitute x=4 in the given equation.

$f(4+1)=f(4)$

$f(5)=3.2$

Therefore the value of f(5) is 3.2.

5 0

3 years ago

Read 2 more answers

A crew will arrive in one week and begin filming a city for a movie. The mayor is desperate to clean the city streets before fil

Tatiana [17]

Answer:

I think you would add the numbers then divide by 2

Step-by-step explanation:

8 0

3 years ago

What is the measure of an interior angle of a regular 12-gon?

gavmur [86]

Answer:

The measure of an interior angle of a regular 12-gon is 150°.

Hence, option 'C' is correct.

Step-by-step explanation:

We need to determine the measure of an interior angle of a regular 12-gon.

We know that the number of sides in a regular 12-gon = n = 12

Thus,

Using the formula to determine the measure of an interior angle of a regular 12-gon is given by

(n - 2) × 180° = n × interior angle

substitute n = 12

(12 - 2) × 180 = 12 × interior angle

10 × 180 = 12 × interior angle

Interior angle = (10 × 180) / 12

= 1800 / 12

= 150°

Therefore, the measure of an interior angle of a regular 12-gon is 150°.

Hence, option 'C' is correct.

4 0

3 years ago