All categories

2 years ago

Pretty hard question

Mathematics

1 answer:

marishachu [46]2 years ago

6 0

Answer:

Step-by-step explanation:

Take x = 1.

Now substitute in the function.

f(1) = 3 + √1

f(1) = 3 + 1

f(1) = 4

Now, we know the line of the function passes through 2 points : (0, 3) and (1, 4). Graph D shows these features.

You might be interested in

The equation of a circle is (x + 6)^2 + (y - 4)^2 = 16. The point (-6, 8) is on the circle.

pantera1 [17]

Answer:

y = 8 is the equation of tangent.

Step-by-step explanation:

The equation of the tangent to the circle at (-6,8) is of the form:

y = mx + c

where m is the slope of the tangent and c is the y-intercept.

The point (-6,8) lies on the circle and the tangent line as well.

Hence (-6,8) satisfies the line equation:

8 = m(-6) + c ⇒ c-6m = 8 -------------1

We know that slope of two perpendicular lines are related as:

$m_{1}\times m_{2}=-1$

At any point on the circle, the normal line at a point is always perpendicular to the tangent line at that point.

Hence :

$m_{normal} \times m_{tangent}=-1$

We can find the slope of the normal at point (-6,8) as it passes through the centre of the circle (-6,4) by using the two-points formula for slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{8-4}{-6+6}$

= ∞

Slope of the normal is infinity and hence slope of tangent is -1/∞ = 0

Hence m=0

Putting m=0 in equation 1 we get:

c = 8

The equation of tangent line at (-6,8) is:

y = 8

6 0

3 years ago

Factor the quadratic equation below to reveal the solutions. X^2+4x-21=-9

a_sh-v [17]

Answer:

x = 3 and x = -7

Step-by-step explanation:

The given quadratic equation is $x^2+4x-21=0$ . We need to find the solution of this equation.

If the equation is in the form of $ax^2+bx+c=0$ , then its solutions are given by :

$x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$

Here, a = 1, b = 4 and c = -21

Plugging all the values in the value of x, such that :

$x=\dfrac{-b+ \sqrt{b^2-4ac} }{2a},\dfrac{-b- \sqrt{b^2-4ac} }{2a}\\\\x=\dfrac{-4+ \sqrt{(4)^2-4\times 1\times (-21)} }{2(1)},\dfrac{-4- \sqrt{(4)^2-4\times 1\times (-21)} }{2(1)}\\\\x=3, -7$

So, the solutions of the quadratic equation are 3 and -7.

6 0

3 years ago

Find the perimeter of a rectangle with a length of 6x+3 and a width of -2x-5.

blsea [12.9K]

The simple way of calculating a perimeter is to add all of the sides.
For a rectangle this would equal 2 x length + 2 x width
P = 2(6x + 3) + 2(-2x - 5)
= 12x + 6 - 4x - 10
= 8x - 4

At a higher level both the length and width must be greater than zero (= zero is a trivial rectangle)
6x + 3 > 0
6x > -3
x > -0.5

-2x - 5 > 0
2x + 5 < 0 (multiplying by -1 reverses the inequality)
2x < -5
x < -2.5

This rectangle cannot exist as x cannot be < -2.5 and > -0.5 at the same time!

8 0

3 years ago

Read 2 more answers

A circular garden has a circumference of 113 yards. Lars is digging a straight line along a diameter of the garden at a rate of

natima [27]

Answer:3hrs 59min

Step-by-step explanation:

πd=perimeter

(113÷3.14)

=35.99

9yards=1hr

35.99yards=?

35.99÷9=3hrs 59min

7 0

3 years ago

D'Quans grandmother made a quilt for his bed.the quilt is 2.44 meters long and 1.83 meters wide.what is the area of the quilt in

Ede4ka [16]

The best way to do this is to first change each of the measurements into feet and then calculate the area:

2.44m = 8.01ft
1.83m = 6.00ft

When multiplied together (to give the area) we get:

8.01*6.00 = 48.1ft²

5 0

4 years ago

Read 2 more answers