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3 years ago

If ABCD congruent to QRST, measure of angle A = x – 10º, and measure of angle Q = 2x – 30º, what is the measure of angle A?

Mathematics

1 answer:

belka [17]3 years ago

3 0

Congruent means they are the same,

A and Q are both the first letters, which mean they would also be the same.

Set the two equations equal to each other, solve for x then solve for angle A.

x-10 = 2x-30

Add 30 to each side:

x+20 = 2x

Subtract 1x from each side:

x = 20

Now replace x with 20 in the equation for A

A = 20-10

Angle A = 10 degrees.

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A diameter of a circle has enpoints (-2, 10) and (6, -4) in the standard (x, y) coordinate plane. What is the center of the circ

wlad13 [49]

Answer:

The center of the circle is $C(x,y) = (2, 3)$ .

Step-by-step explanation:

The center of the circle is the midpoint of the segment between the endpoints. We can determine the location of the center by this vectorial expression:

$C(x,y) = \frac{1}{2}\cdot R_{1}(x,y)+ \frac{1}{2}\cdot R_{2}(x,y)$ (1)

Where:

$C(x,y)$ - Center.

$R_{1} (x,y)$ , $R_{2} (x,y)$ - Location of the endpoints.

If we know that $R_{1} (x,y) = (-2,10)$ and $R_{2} (x,y) = (6,-4)$ , then the location of the center of the circle is:

$C(x,y) = \frac{1}{2}\cdot (-2,10)+\frac{1}{2}\cdot (6,-4)$

$C(x,y) = (-1, 5) + (3, -2)$

$C(x,y) = (2, 3)$

The center of the circle is $C(x,y) = (2, 3)$ .

8 0

3 years ago

1. Write the equation of the piece-wise function graphed below.

DaniilM [7]

Problem 4

<h3>Answer:</h3>

$f(x) = \begin{cases}2x+4 \text{ if } x < 1\\x-3 \text{ if } x \ge 1\end{cases}$

------------------

Work Shown:

The left line goes through (-2,0) and (0,4)

The slope of this line is

m = (y2-y1)/(x2-x1)

m = (4-0)/(0-(-2))

m = (4-0)/(0+2)

m = 4/2

m = 2

The y intercept is b = 4

Since m = 2 and b = 4, this means y = mx+b turns into y = 2x+4. This portion is only done when x < 1. Note the open circle at the endpoint of this portion. So we do not include x = 1 as part of this piece.

---

The line on the right side goes through (1,-2) and (2,-1)

Slope

m = (y2-y1)/(x2-x1)

m = (-1-(-2))/(2-1)

m = (-1+2)/(2-1)

m = 1/1

m = 1

The y intercept is b = -3. You can see this if you extend the line until it crosses the y axis.

Alternatively, plug in (x,y) = (1,-2) and m = 1 into y = mx+b to find that b = -3

So y = mx+b turns into y = 1x+(-3) or just y = x-3

We combine both parts to end up with $f(x) = \begin{cases}2x+4 \text{ if } x < 1\\x-3 \text{ if } x \ge 1\end{cases}$

This is only graphed when $x \ge 1$ (note the closed or filled in circle for the endpoint of this portion).

===================================================

Problem 5

Answer:

<h3> $f(x) = \frac{1}{2}|x+3|$ is the absolute value function</h3><h3>while this is the piecewise function</h3>

$f(x) = \begin{cases}-\frac{1}{2}(x+3) \text{ if } x < -3\\\frac{1}{2}(x+3) \text{ if } x \ge -3\end{cases}\\$

------------------

Work Shown:

y = |x| .... parent function

y = |x+3| ... shift 3 units to the left

y = (1/2)*|x+3| .... vertically compress by factor of 1/2

f(x) = (1/2)*|x+3|

------

Break that down into a piecewise function

when x < -3, then y = -(1/2)(x+3)

when $x \ge -3$ , then y = (1/2)(x+3)

I'm using the rule that y = |x| turns into y = -x when x < 0 and y = x when $x \ge 0$

So that is how we get $f(x) = \begin{cases}-\frac{1}{2}(x+3) \text{ if } x < -3\\\frac{1}{2}(x+3) \text{ if } x \ge -3\end{cases}\\$ as the piecewise function.

8 0

3 years ago

Read 2 more answers

Jennifer is organising a street party. she needs to make 300 cakes. the recipe consist of : 50g icing, 150g butter, 120g caster

joja [24]

Answer:

1.25 kg of icing sugar

3.75 kg of butter

3 kgs of caster sugar

2.75 kgs flour

25 eggs

125g baking powder

Step-by-step explanation:

300/12 x (weight of ingredient)

4 0

3 years ago

Read 2 more answers

The area of a square is 49 square meters. How long is each side?

OLga [1]

Well if 49 is the area, and you get area by multiplying one side by another side, and its a square so the numbers are going to be the same, so you would be multiplying two of the same numbers. And two of the same numbers that equal 49 is 7.

4 0

3 years ago

A music website tracked the number of new users per day over 1 week. The number of new users for each day of the 7 days was 38,

enyata [817]

Part a)

MAD = median of absolute deviations

MAD = median of the set formed by : |each value - Median|

Then, first you have to find the median of the original set

The original set is (<span>38, 43, 45, 50, 51, 56, 67)

The median is the value of the middle (when the set is sorte). This is 50.

Now calculate the absolute deviation of each data from the median of the data.

1) |38 - 50| = 12
2) |43 - 50| = 7
3) |45 - 50| = 5
4) |50 - 50| = 0
5) |51 - 50| = 1
6) |56 - 50| = 6
7) |67 - 50| = 17

Now arrange the asolute deviations in order

(0, 1, 5, 6, 7, 12, 17)

The median is the value of the middle: 6.

Then the MAD is 6.

Part b) MAD represents the median of the of the absolute deviations from the median of the data.

</span>

3 0

3 years ago