I’m kinda confused. Can someone help.

Mathematics

1 answer:

horsena [70]3 years ago

5 0

Answer:

PQ = $PM\cos MPQ + MQ\cos MQP=2PM\cos MQP$

Step-by-step explanation:

given MQR = 60, PQR = 75

MQP = 75 -60= 15 $QR = ((18(1+\cos 30))^{2}-(2\cos 15)^{2})^{\frac{1}{2}}$

WE KNOW THAT MQR +QRM +QMR = 180

MPQ = MQP AS ANGLE OPPOSITE TO EQUAL SIDES ARE EQUAL

THEREFORE QMR = 90 - 60 = 30

therefore PQM = 75 - 60 = 15

PM = PQ because M is the mid point

therefore PR = PM + $MQ\cos QMR$

PR = $18(1+\cos 30)$

$QR = (PR^{2}-PQ^{2}))^{\frac{1}{2}}$

PQ = $PM\cos MPQ + MQ\cos MQP=2PM\cos MQP$

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Honey's blueberry muffin recipe calls for 3 1/4 pounds of blueberries and 2 1/2 cups of muffin mix. How many cups of muffin mix

astra-53 [7]

For this case we convert the mixed numbers to improper fractions: $3 \frac {1} {4} = \frac {4 * 3 + 1} {4} = \frac {12 + 1} {4} = \frac {13} {4}\\2 \frac {1} {2} = \frac {2 * 2 + 1} {2} = \frac {4 + 1} {2} = \frac {5} {2}$

Now, we propose a rule of three:

$\frac {13} {4}$ pounds of blueberries -------------> $\frac {5} {2}$ cups of muffin mix

7 pounds of blueberries -----------------------------> x

Where the variable "x" represents the number of cups of muffin mix that Honey should use.

$x = \frac {7 * \frac {5} {2}} {\frac {13} {4}}\\x = \frac {\frac {35} {2}} {\frac {13} {4}}\\x = \frac {35 * 4} {2 * 13}\\x = \frac {140} {26}\\x = \frac {70} {13}\\x = 5.38$