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hodyreva [135]
2 years ago
9

Am I correct with my answers?

Mathematics
1 answer:
Anni [7]2 years ago
6 0

Answer:

  • w = 70° . . . . alternate interior angles
  • x = 70° . . . . alternate interior angles
  • y = 40° . . . . angle sum in a triangle
  • z = ?? . . . . not enough information

Step-by-step explanation:

The alternate interior angles theorem, and the angle sum theorem can be used here.

<h3>Alternate interior angles</h3>

Alternate interior angles are found on either side of a transversal where it crosses a pair of parallel lines. They are between the parallel lines. Their vertices are at the junction of the transversal and the parallel lines. Alternate interior angles are congruent.

In this diagram, there are two pairs of alternate interior angles where the two transversals AD and BD cross parallel lines AB and CD.

At points A and D, the alternate interior angles are 70° and x, respectively. This tells you ...

  x = 70° . . . . alternate interior angles theorem

At points B and D, the alternate interior angles are w and 70°, respectively. This tells you ...

  w = 70° . . . . alternate interior angles theorem

<h3>Angle sum</h3>

The angle sum theorem tells you the sum of angles in a triangle is 180°. This fact can be used to find the measure of angle y.

  70° +w +y = 180°

  y = 180° -70° -w = 110° -70°

  y = 40° . . . . angle sum theorem

There is not enough information to determine the measure of angle z.

  z = indeterminate

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Answer:

After population (A) = 62,902 (Approx)

Step-by-step explanation:

Given:

Current population (P) = 19613

Number of years (n) = 2020 - 2000 = 20 year

Rate of growth (r) = 6% = 0.06

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After population (A)

Computation:

After\ population (A) = Current\ population (P)[1+r]^n \\\\After\ population (A) = 19613[1+0.06]^{20} \\\\After\ population (A) = 19613[1.06]^{20} \\\\After\ population (A) = 62,901.548

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Express your answer as a decimal.<br><br> 3÷2=
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5 0
2 years ago
In RSM camp, there are four counselors for every fifty seven students and three teachers for every five counselors.
Ray Of Light [21]

Answer:

Students : Counselors : Teachers = 285: 20 : 12

Step-by-step explanation:

In the camp, the ratio of:

( C: S )  Counselors : Students   is  4   :  57

( T: C )  Teachers :   Counselors  is  3   :  5

To determine the ratio of   -  Students : Counselors : Teachers

Here given      -  C : S  = 4 : 57

Multiplying both sides by 5, we get

C: S  = 4 x 5  : 57 x 5  = 20 : 285

So, for every 20 counselors, there are 285 students      ...... (1)

Similarly, given   Teachers :   Counselors  is  3   :  5

Multiplying both sides by 4, we get

T  : C  = 3 x 4  : 5 x 4  = 12  : 20

So, for every 12  teachers, there are 20 Counselors      ...... (2)

Hence, in both equation 1 and 2 the number of counselors is same = 20 .

Hence, both the ratios acne be combined.

So we get C : S  = 20 : 285      and T : C  = 12: 20

Inverting the values

⇒  S : C  = 285 : 20         and C : T  = 20 : 12

or, S : C : T  = 285: 20 : 12

or, Students : Counselors : Teachers = 285: 20 : 12

Hence, for every 285 students there are 20 counselors and 12 teachers.

4 0
3 years ago
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