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Vlad1618 [11]
3 years ago
9

What is the arc measure of AD in degrees?

Mathematics
1 answer:
ella [17]3 years ago
4 0
∠APD, ∠DPC, ∠CPB are supplementary angles (angles whose sum is 180°). ∠DPC is right angle (angle whose measurement 90°)

Make an expression based on the information above, then solve for x
∠APD + ∠DPC + ∠CPB = 180°
7x + 1 + 90 + 9x - 7 = 180

add like terms
7x + 9x + 1 + 90 - 7 = 180
16x + 84 = 180
16x = 180 - 84
16x = 96
 x = 96/16
 x = 6

The value of x is 6, substitute this value to APD's algebraic expression
∠APD = 7x + 1
∠APD = 7(6) + 1
∠APD = 42 + 1
∠APD = 43

The measurement of ∠APD is 43°
You might be interested in
(2n^3+20n^2+n)/10n^2
gizmo_the_mogwai [7]

The simplified form of this polynomial is (n(20n + 1))/5

3 0
3 years ago
The dimensions of the tank are 50 cm by 32 cm by 20 cm. The tank is full of water and sand. The ratio of the volume of water to
Sauron [17]

Given:

Dimensions of a tank are 50 cm by 32 cm by 20 cm

The tank is full of water and sand

Ratio of volume of water to the volume of sand is 5:1

To find:

Volume of water in the tank in liters

Solution:

Without loss of generality, let,

Length of tank = 50 cm

Breadth of tank = 32 cm

Height of tank = 20 cm

Then, we have,

Total Volume of the tank = Length * Breadth * Height

\Rightarrow Total Volume = 50*32*20 cc

\Rightarrow Total Volume = 32000 cc

It is given that,

Volume of water : Volume of sand = 5:1

\Rightarrow (Volume of water)/(Volume of sand) = 5/1

Cross multiplying, we have,

Volume of sand = (Volume of water)/5

It is also given that the tank is full of water and sand. This implies that,

Volume of water + Volume of sand = Total Volume

Using the value, we obtained, we get,

Volume of water + (Volume of water)/5 = Total Volume

\Rightarrow (6 * Volume of water)/5 = Total Volume

Plugging in the value of total volume, we get,

\Rightarrow (6 * Volume of water)/5 = 32000 cc

\Rightarrow Volume of water = \frac{32000*5}{6} cc

\Rightarrow Volume of water \approx 26,666.6667 cc

We know that,

1 cc = 0.001 liters

\Rightarrow 26,666.6667 cc = (26666.6667 * 0.001) liters

\Rightarrow 26,666.6667 cc \approx 26.667 liters

Thus, Volume of water in the tank is approximately 26.667 liters

Final Answer:

Volume of water in the tank (in liters) is approximately 26.667 liters

4 0
2 years ago
Mr. McKay wrote an algebra test with a total of 15 questions consisting of multiple choice and short response style questions. M
tankabanditka [31]

Step-by-step explanation:

x = number of multiple choice questions

y = number of short response questions

x + y = 15

5x + 10y = 100

=>

x + 2y = 20

let's subtract the first from the second equation :

x + 2y = 20

- x + y = 15

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

0 y = 5

x + y = 15

x + 5 = 15

x = 10

to graph you need to consider both equations as linear functions. and you need to transform them into e.g. a slope intercept form : y = ax + b

a is the slope, b is the y- intercept.

x + y = 15

transforms to

y = -x + 15

this line goes e.g. through the points (0, 15) and (1, 14).

and

x + 2y = 20

transforms to

2y = -x + 20

y = -x/2 + 10

this line goes e.g through (0, 10) and (2, 9).

the crossing point of both lines is the solution and should therefore be the point (10, 5) as calculated above.

5 0
2 years ago
1/4 times the sum of a number and −3.2 is 1.8. What is the number?
joja [24]

Answer:

10.4

Step-by-step explanation:

Let the number be x

Sum of  x  and -3.2 : x + (-3.2) = x - 3.2

1/4 times the sum of a number and −3.2 = (1/4) * (x - 3.2)

\dfrac{1}{4}* \left( x - 3.2 \right) = 1.8\\\\\Multiply \ the \ whole \ equation \ by \ 4 \\\\4*\dfrac{1}{4} *(x - 3.2) = 1.8*4\\\\\\x - 3.2 = 7.2\\\\Add \  3.2 \ to \ both \ sides\\\\\\x = 7.2 + 3.2\\

x = 10.4

5 0
3 years ago
What is the surface area of this right rectangular prIsm?
uranmaximum [27]

Answer:

28

Step-by-step explanation:

To find the area of a rectangle we multiply two edges together.

since we are looking for the surface area we are actually going to be finding 6 different areas and adding them together (since there are 6 sides to a rectangle)

ok so sides 1 and 2, the edges on the left and right will be equal, and then the four sides in the middle are all going to be equal

2(1x2) + 4(3x2) = 4 + 24 = 28

8 0
2 years ago
Read 2 more answers
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