Mathematics, 14.02.2021 05:30 faithlopez209

Hector had 30 minutes to do a three-problem quiz. He spent 11 3 4 minutes on question A and 6 1 2 minutes on question B. How much time did he have left for question C?

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Answer from: itsyagirl11076

$11 \frac{3}{4}$ min

Step-by-step explanation:

In order to solve this problem, we must subtract the times he has already used from the time he has available, so we get:

$30-11 \frac{3}{4} - 6 \frac{1}{2}$

we can start solving this subtraction by turning all of the numbers into improper fractions so we get:

$\frac{30}{1}-\frac{11*4+3}{4}- \frac{6*2+1}{2}$

$\frac{30}{1}-\frac{47}{4}- \frac{13}{2}$

next, we can find a least common denominator. In this case it will be 4, so we need to turn all denominators into a 4, so we get:

$\frac{30*4}{1*4}-\frac{47}{4}- \frac{13*2}{2*2}$

$\frac{120}{4}-\frac{47}{4}- \frac{26}{4}$

and now we can subtract the numerators and copy the denominators so we get:

$\frac{120-47-26}{4}$

$\frac{47}{4}$

which can now be turned into a mixed number by dividing 47/4 which yields 11 with a remainder of 3, so the mixed number is:

$11 \frac{3}{4}$ min

and this is the amount of time he has available to solve the las problem.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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