All categories

3 years ago

8.

Mathematics

1 answer:

Goshia [24]3 years ago

3 0

Answer:

x = 25

$m\angle \: MPQ = 125 \degree$

Step-by-step explanation:

$5x \degree = (3x + 50) \degree \\(corresponding \:\angle s) \\\\ 5x = 3x + 50 \\ \\ 5x - 3x = 50 \\ \\ 2x = 50 \\ \\ x = \frac{50}{2} \\ \\ x = 25 \\ \\ m\angle MPQ = (3x + 50) \degree \\ \\ m\angle MPQ = (3 \times 25 + 50) \degree \\ \\ m\angle \: MPQ = (75 + 50) \degree \\ \\ m\angle \: MPQ = 125 \degree \\ \\$

You might be interested in

Phyllis invested $10,500 a portion earning a simple interest rate of 9(1/5)% per year and the rest earning a rate of 9% per year

Alenkinab [10]

Total investment = $10,500

Let x = amount of first investment, and y the amount of the second investment.

First investment:
Interest rate = 9 (1/5)% = 0.092
Earned interest = 0.092x

Second investment:
Interest rate = 9% = 0.09
Earned interest = 0.09y

Total interest after one year is $957.00, therefore
0.092x + 0.09y = 957
or
1.0222x + y = 10633.33 (1)

Also,
x + y = 10500 (2)

Subtract (2) from (1).
0.0222x = 133.33
x = 6000
y = 10500 - x = 4500

Answer:
The first investment is $6,000 at 9 (1/5)% rate;
The second investment is $4,500 at 9% rate.

7 0

3 years ago

One-half of Heather's age 2 years from now plus one-third of her age three years ago is twenty years. How old is she now?

viktelen [127]

She is 24
24+2=26
26(1/2)=13
13+((24-3)1/3)
13+(21*1/3)
13+7=20
Therefore she is 24

4 0

3 years ago

Nine times the product of a negative two and a number

Aleksandr-060686 [28]

The statement written as a simplified mathematical expression is -18x

<h3>Writing mathematical expression</h3>

From the question, we are to write the given statement as a mathematical expression

The given expression is,

"<em>Nine times the product of a negative two and a number</em>"

Let the number be x

Thus,

The product of negative 2 and a number means

-2 × x = -2x

Then,

Nine times the product of a negative two and a number is

9 × -2x = -18x

Hence, the statement written as a simplified mathematical expression is -18x

Learn more on Writing mathematical expressions here: brainly.com/question/4344214

#SPJ1

7 0

2 years ago

Pleaseee I needddd helppp

Pachacha [2.7K]

Answer:

car b has a steeper slope tho... so it's car b

5 0

3 years ago

Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2.

insens350 [35]

Answer:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

Step-by-step explanation:

Given

$p(x) = \frac{x^2-2x-3}{x+2}$ -- Missing from the question

Required

The behavior of the function around its vertical asymptote at $x = -2$

$p(x) = \frac{x^2-2x-3}{x+2}$

Expand the numerator

$p(x) = \frac{x^2 + x -3x - 3}{x+2}$

Factorize

$p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}$

Factor out x + 1

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)

We are only interested in the sign of the result

----------------------------------------------------------------------------------------------------------

As x approaches -2 implies that:

$x -> -2^{-}$ Say x = -3

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

$p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12$

We have a negative value (-12); This will be called negative infinity

This implies that as x approaches -2, p(x) approaches negative infinity

$x->-2^{-}, p(x)->-\infty$

Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)

As x leaves -2 implies that: $x>-2$

Say x = -2.1

$p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1$

We have a negative value (-56.1); This will be called negative infinity

This implies that as x leaves -2, p(x) approaches negative infinity

$x->-2^{+}, p(x)->-\infty$

So, the behavior is:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

6 0

3 years ago