What is 100009 + 98710?

A student tried to solve the following equation but made a mistake.

Vesnalui [34]

9514 1404 393

Answer:

in Step 2, the student added 4 on the right and subtracted 4 on the left

Step-by-step explanation:

In Step 2, the student subtracted 4 on the left side of the equation, but incorrectly added 4 on the right. (The same operation needs to be performed on both sides of the equation.) The correct step 2 would be ...

-8x = -32 . . . . correct step 2

x = 4 . . . . . correct step 3

3 0

3 years ago

A certain company recently sold five-year $1000 bonds with an annual yield of 9.75%. After how much time could they be sold for

Brut [27]

Answer:

After 7 years and 5 months.

Step-by-step explanation:

Let x represent number of years.

We have been given that a certain company recently sold five-year $1000 bonds with an annual yield of 9.75%.

We can see that the value of bond is increasing exponentially, so we will use exponential growth formula to solve our given problem.

$y=a\cdot (1+r)^x$ , where,

y = Final value,

a = Initial value,

r = Rate in decimal form,

x = Time

$9.75\%=\frac{9.75}{100}=0.0975$

Substituting given values:

$y=1000\cdot (1+0.0975)^x$

$y=1000\cdot (1.0975)^x$

Since we need the selling price to be twice the original price, so we will substitute $y=2000$ in above equation as:

$2000=1000\cdot (1.0975)^x$

$\frac{2000}{1000}=\frac{1000\cdot (1.0975)^x}{1000}$

$2=1.0975^x$

Switch sides:

$1.0975^x=2$

Take natural log of both sides:

$\text{ln}(1.0975^x)=\text{ln}(2)$

Applying rule $\text{ln}(a^b)=b\cdot \text{ln}(a)$ :

$x\cdot \text{ln}(1.0975)=\text{ln}(2)$

$\frac{x\cdot \text{ln}(1.0975)}{\text{ln}(1.0975)}=\frac{\text{ln}(2)}{\text{ln}(1.0975)}$

$x=\frac{0.6931471805599453}{0.0930348659671894}$

$x=7.45040231265$

$x\approx 7.4504$

Since x represents time in years, so we need to convert decimal part into months by multiplying .4504 by 12 as 1 year equals 12 months.

7 years and 12*0.4504023 months = 7 years 5.4 months = 7 years 5 months

Therefore, after 7 years and 5 months the company could sold the bonds for twice their original price.

8 0

3 years ago

Solve each given equation and show your work. Tell weather each equation has one solution, an infinite number of solutions, or n

galben [10]

Hello!

To solve algebraic equations, you need to SADMEP it. SADMEP is only used to solve these equations, and it is an acronym for subtraction, addition, division, multiplication, exponents, and parentheses. The goal here is to get x on one side of the equation.

(a) 4x + 2(x - 1) = 10 + 2x (use the distributive property)

4x + 2x - 2 = 10 + 2x (add alike terms)

6x - 2 = 10 + 2x (subtract 2x from both sides)

4x - 2 = 10 (add 2 to both sides)

4x = 12 (divide both sides by 4)

x = 3

This equation has one solution because if you substitute 3 for x into the original equation, then both sides of the equation will be equal.

(b) 30 - x = 10 + -1(6x + 10) (use the distributive property)

30 - x = 10 + -6x - 10 (simplify)

30 - x = -6x (add x to both sides)

30 = -5x (divide both sides by -5)

x = -6

This equation has one solution because if you substitute x = -6 into the given equation, then the left and right side of the equation will be equivalent to each other.

(c) 8x = 4x + 4x + 10(x - x) (simplify - add and subtract)

8x = 8x + 10(0) (multiply)

8x = 8x

This equation has an infinite number of solutions because if you substitute any number into the given equation, both sides of the equation will be equal.

5 0

3 years ago

Write an equation of the line shown in the graph in slope intercept form (y = mx + b). Show

Lena [83]

Answer:

y = 2x - 2

Step-by-step explanation:

Points on graph: (4,6) and (2, 2)

Slope:

m=(y2-y1)/(x2-x1)

m=(2-6)/(2-4)

m=(-4)/(-2)

m = 2

Slope-intercept:

y - y1 = m(x - x1)

y - 6 = 2(x - 4)

y - 6 = 2x - 8

y = 2x - 2

8 0

3 years ago

All the while the dog sat in the snow, its wolf-brush of a tail curled around warmly over its forefeet, its wolf-ears are forwar

slavikrds [6]

Answer:

The man is envious because he's jealous of the dog's fur. For he has natural covering and is kept warm because of it. The man has to wear several layers of clothing to be warm while the dog is warm enough with his fur/natural covering.

8 0

3 years ago