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Mathematics

1 answer:

alex41 [277]3 years ago

7 0

Use the equivalence of opposite angles:

<PTS = <QTR

That gives you an equation with unknown y:

11(y-10)= 4y-5

solve for y:

11y -110 = 4y -5

7y = 105

y = 15

so m<PTS = 11(y-10) = 55 degrees

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A clothing designer had 173.4 meters of fabric to make identical sweaters, of all the same size. If each sweater used 3 meters o

s344n2d4d5 [400]

57 sweaters can be made from 173.4 meters of fabric

Step-by-step explanation:

Given,

Total fabric available = 173.4 meters

Fabric used for one sweater = 3 meters

Let,

x be the number of sweaters.

Fabric used for one sweater * Number of sweaters ≤ Total fabric available

$3x\leq 173.4$

Dividing both sides by 3

$\frac{3x}{3}\leq \frac{173.4}{3}\\x\leq 57.8$

57 sweaters can be made from 173.4 meters of fabric

Keywords: inequality, division

Learn more about inequalities at:

#LearnwithBrainly

8 0

3 years ago

He number of E.coli bacteria cells in a pond of stagnant water can be represented by the function below, where A represents the

denis-greek [22]

The function that represents the number of E.coli bacteria cells per 100 mL of water as t years elapses, and is missing in the question, is:

$A(t)=136(1.123)^{4t}$

Answer:

Option A. 59%

Explanation:

The base, 1.123, represents the multiplicative constant rate of change of the function, so you just must substitute 1 for t in the power part of the function::

$A(t)=136(1.123)^{4t}$

$rate=(1.123)^{4t}=(1.123)^4=1.590$

Then, the multiplicative rate of change is 1.590, which means that every year the number of E.coli bacteria cells per 100 mL of water increases by a factor of 1.590, and that is 1.59 - 1 = 0.590 or 59% increase.

You can calculate it also using two consecutive values for t. For instance, use t =1 and t = 1

$t=1\\\\ A(1)=136(1.123)^4\\\\\\t=2\\ \\ \\A(2)=136(1.123)^8\\ \\ \\A(2)/A(1)=1.123^8/1.1123^4=1.123^4=1.590$