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3 years ago

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Can you help me please

1 answer:

notka56 [123]3 years ago

7 0

the answer is 5/10 units

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Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does the line with equatio

lina2011 [118]

Answer:

The point of intersection is:

$\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)$

Step-by-step explanation:

We want to find the point in QI at which the line with the equation:

$y=0.5x+5$

Intersect a circle with a radius of 3 and a center of (0, 5).

First, write the equation of a circle. The equation for a circle is given by:

$(x-h)^2+(y-k)^2=r^2$

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.

Since our center is (0, 5), <em>h</em> = 0 and <em>k</em> = 5. The radius is 3. So, <em>r</em> = 3. Substitute:

$(x-0)^2+(y-5)^2=(3)^2$

Simplify:

$x^2+(y-5)^2=9$

At the point where the two equations intersect, its <em>x-</em>coordinate and <em>y-</em>coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for <em>x</em>. So:

$x^2+((0.5x+5)-5)^2=9$

Simplify:

$x^2+(0.5x)^2=9$

Square:

$x^2+0.25x^2=9$

Combine like terms:

$\displaystyle 1.25x^2=\frac{5}{4}x^2=9$

Solve for <em>x: </em>

<em /> $\displaystyle \begin{aligned} x^2&=\frac{36}{5} \\ x&=\pm\sqrt{\frac{36}{5}} \\ x&\Rightarrow \frac{6}{\sqrt{5}}=\frac{6\sqrt{5}}{5}\approx2.68\end{aligned}$ <em />

Note that since we are looking for the point of intersection in QI, <em>x</em> should be positive. So, we can ignore the negative answer.

To find the <em>y-</em>coordinate, substitute the <em>x-</em>value back into either equation. Using the linear equation:

$\displaystyle y=0.5\left(\frac{6\sqrt{5}}{5}\right)+5=\frac{3\sqrt{5}}{5}+5\approx 6.34$

So, the point of intersection in QI is:

$\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)$

6 0

2 years ago

What is 3 1/8 - 1/2

irina1246 [14]

Answer:

$\frac{21}{8}$

Step-by-step explanation:

Given: $3\frac{1}{8} - \frac{1}{2}$

Let's changed that mixed number to an improper fraction. Now we get:

$\frac{25}{8} - \frac{1}{2}$

Let's find out least common denominator. This one is easy, the LCD is 8. Now that we know the LCD, let's convert both our fractions:

$\frac{25}{8} - \frac{4}{8}$

We can use $\frac{4}{8}$ because it is equal to $\frac{1}{2}$ . Now, all we need to do is subtract the numerators:

$\frac{25}{8} - \frac{4}{8}=\frac{21}{8}$

3 0

3 years ago

Read 2 more answers

2) Find the total cost (in dollars) of buying:

pantera1 [17]

Answer:

a=4

b=0.5p

c=py

Step-by-step explanation:

a) 8*0.5= 4

b) p*0.5= 0.5p

c) p*y= py

Hope this helps! :)

6 0

2 years ago

Read 2 more answers

The triangles are congruent by SSS or HL. The diagram shows the sequence of three rigid transformations used to map ABC onto A"B

Pani-rosa [81]

Answer:

The sequence of transformation used to map ABC onto A"B"C" is reflection, then rotation, then translation.

Step-by-step explanation:

To map ABC onto A"B"C" steps are:

step 1: Reflection of ABC

step 2: rotation of A'BC by some angle to obtain A'B'C'.

step 3: translation of A'B'C' by some units to the right to obtain the given transformation A"B"C".

7 0

3 years ago

Read 2 more answers

Write the expression in simplest form. (-11/2 x +3) - 2(-11/4 x - 5/2)

zhannawk [14.2K]

(-11/2x + 3) - 2(-11/4x - 5/2)
(-11/2x + 3) + (5.5x + 5)
(-5.5x + 3) + (5.5x + 5)
3 + 5
8

6 0

3 years ago