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3 years ago

Find the values of x and y in the figure below. Enter the answers as numbers.

Mathematics

1 answer:

ella [17]3 years ago

8 0

Answer: $x=79^{\circ}\ and\ y=101^{\circ}$

Step-by-step explanation:

In the given picture, a parallelogram PQRS is given with angle 101°.

In a parallelogram opposite angles are equal.

Since, y is opposite to 101°.

Therefore y=101°

Also, the sum of the adjacent angles of a parallelogram is 180°

$\\\Rightarrow\ x+101^{\circ}=180^{\circ}\\\Rightarrow\ x=180^{\circ}-101^{\circ}\\\Rightarrow\ x=79^{\circ}$

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Let p be the population proportion for the following condition. Find the point estimates for p and q. In a survey of 1226 adults

weeeeeb [17]

Answer:

(a)0.3303

(b)0.6697

Step-by-step explanation:

Point estimation is the use of sample data to calculate a single value which serves as a best estimate of a given unknown population parameter.

Total Sample=1226

Number who said that they were not confident that the food they eat in country A is safe=405.

The point estimate of those who said that they were not confident that the food they eat in country A is safe is given as $\^{p}$

(a)Point Estimate for p,

$\^{p}=\frac{405}{1226} =0.3303$

(b)Point estimate for q, $\^{q}=$ 1- (point estimate for p)

=1-0.3303

=0.6697

8 0

3 years ago

Substitue the expression 5-3x into the second equation

Rina8888 [55]

Answer:

Step-by-step explanation:

you substitute for y since you know what y equals.

so, it will then be

5x -4(5 -3x) = -3

you then multiply -4 by everything in the parenthesis

so then it will be

5x - 20 + 12x = -3

Then combine like terms

5x + 12x = 17x

then the new equation is

17x -20 = -3

the next step is to and 20 to both sides since it is negative you do the opposite.

17x - 20 = -3

17x = 17 divide 17 by both sides sice 17 is being multiplied by x you do the opposite and divide and you get 1.

4 0

3 years ago

Jenny multiplies the square root of her favorite positive integer by $\sqrt{2}$. Her product is an integer. a) Name three number

Dmitry [639]

Answer:

Part a) $2,50,18$

Part b) When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she gets an integer

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For $x=2$

$\sqrt{2}*\sqrt{2}=\sqrt{4}=2$ -----> the product is an integer

The number $x=2$ could be Jenny favorite positive integer

2) For $x=50$

$\sqrt{50}*\sqrt{2}=\sqrt{100}=10$ -----> the product is an integer

The number $x=50$ could be Jenny favorite positive integer

3) For $x=18$

$\sqrt{18}*\sqrt{2}=\sqrt{36}=6$ -----> the product is an integer

The number $x=18$ could be Jenny favorite positive integer

Part B)

1) For $x=2$

$\sqrt{2}/\sqrt{2}=\sqrt{1}=1$ -----> the result is an integer

2) For $x=50$

$\sqrt{50}/\sqrt{2}=\sqrt{25}=5$ -----> the result is an integer

3) For $x=18$

$\sqrt{18}/\sqrt{2}=\sqrt{9}=3$ -----> the result is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she gets an integer

4 0

3 years ago

True or false and why: if a and b are irrational, then a^b is irrational

FrozenT [24]

False

b could be the logarithm of a rational number to the base a. For example,

$b=\log_\pi{(4)}$ will be irrational, but π^b = 4, a rational number

7 0

3 years ago

2. Maria is monitoring the temperature of

stiks02 [169]

Here, we are required to determine after how many minutes will the two substances be at the same temperature.

The equation of when the two substances will be at the same temperature and the solution are as follows;

(a) The equation is 96.2 + 1.5(x) = 98.5 + 0.8(x).

(b) The solution is, x = 3.285minutes.

For substance A which is currently at 96.2° and rising at 1.5° each minute; It's temperature after x minutes is given as;

T(a) = 96.2 + 1.5(x)

For substance B which is currently at 98.5° and rising at 0.8° each minute; It's temperature after x minutes is given as;

T(b) = 98.5 + 0.8(x)

(a) For the two substances to be at the same temperature; T(a) must be equal to T(b).

T(a) = T(b)

The equation is therefore;.

96.2 + 1.5(x) = 98.5 + 0.8(x)

(b) To determine the solution;

1.5x - 0.8x = 98.5 - 96.2

0.7x = 2.3

x = 2.3/0.7

x = 3.285minutes.

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1 year ago