How many solutions does the equation 5x+1=-5x+10 have?<br> A. 0<br> B. 1<br> C. 2<br> D. Infinite

Alinara [238K]

627282638392926392928373

5 0

2 years ago

A report by the US Geological Survey indicates that glaciers in Glacier National Park, Montana, are shrinking. Recent estimates

postnew [5]

Answer

a) C

b) B

c) C, E

d) 15.5

e) 0.7

f) 67.7

Step-by-step explanation

a) A linear equation can be written as $y=mx+c$ where $m$ is the slope and $c$ is the intercept on the $y$ -axis. The slope describes how $y$ changes when $x$ changes. A negative value means the it is a decreasing change. In our case, $y$ is $A$ and $x$ is $t$ . Thus, the slope of the equation is $m=-0.062$ . This means that the area of glacier is decreasing by $0.062 \text{km}{}^2 = 62000 \text{m}{}^2$ every year since 2000.

b) The $A$ -intercept (= 16.2 $\text{km}{}^2$ ) represents the area covered when $t=0$ . But $t=0$ starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2 $\text{km}{}^2$ .

c) $A=f(t)$ means the area covered after year 2000. Setting it to 12 means the area covered after $t$ years is 12 $\text{km}{}^2$ ). $t$ is therefore the number of years since 2000 that the total area covered will be 12 $\text{km}{}^2$ ).

d) $f(12)=16.2−0.062\times12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2$ to 1 decimal place.

e) The term involving $t$ represents the disappearing area. In 12 years, the disappeared area is $0.062\times12=0.744 =0.7 \text{km}{}^2$ to 1 decimal place.

f) $f(t)=16.2−0.062t =12$

$0.062t = 16.2-12 = 4.2$

$t = \dfrac{4.2}{0.062}=67.7419\ldots =67.7$ years to 1 decimal place.

8 0

3 years ago

You have accepted a job offer at an annual salary of $36,980. This salary includes a year-end bonus of $2900. You are paid twice

Free_Kalibri [48]

Your gross pay will be $1595.2 for each paycheck

<h3>What are Arithmetic operations?</h3>

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 12 -2 = 10

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

You have accepted a job offer at an annual salary of $36,980.

This salary includes a year-end bonus of $2900

So your gross pay = 36980 + 2900 = 15952

You are paid twice per month

12 months × 2 checks = 24 paychecks

15952/ 25= 1595.2

Hence, your gross pay will be $1595.2 for each paycheck

Learn more about Arithmetic operations here:

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#SPJ1

8 0

1 year ago

The perimeter of a rectangle is 150 cm. the length is 4 cm greater than the width find the width and length

Fudgin [204]

Let's call the width of our rectangle $w$ and the length $l$ . We can say $l = w + 4$ , since the length is equal to 4 cm greater than the width.

Also remember that the perimeter of a rectangle is the sum of two times the width and two times the length, or $P = 2l + 2w$ . To solve this problem, we can substitute in the information we know, as shown below:

$150 = 2(w + 4) + 2w$

$150 = 4w + 8$

$142 = 4w$

$w = \frac{71}{2}$

Now, we can substitute in the width we found into the formula for length, which is $l = w + 4$ :

$l = \frac{71}{2} + 4$

$l = \frac{79}{2}$

The width of our rectangle is $\boxed{\frac{71}{2} \,\, \textrm{cm}}$ cm and the length of our rectangle is $\boxed{\frac{79}{2} \,\, \textrm{cm}}$

8 0

3 years ago

Cual es la constante de proporcionalidad de 1/2 ?

vivado [14]

Answer:

Therefore, the relationship given in the table is proportional. When we look at the above table when x gets increased, y also gets increased, so it is direct proportion. Substitute 2 for x and 1 for y. So, the constant of proportionality is 1/2.

8 0

2 years ago

How many solutions does the equation 5x+1=-5x+10 have? A. 0 B. 1 C. 2 D. Infinite