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2 years ago

Graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane.

Mathematics

1 answer:

Tamiku [17]2 years ago

8 0

Answer:

x = 2

Step-by-step explanation:

To solve the equation, you need to set both functions equal to each other and simplify to find the value of "x".

f(x) = 2x + 1

g(x) = -x + 7

f(x) = g(x) <----- Given equation

2x + 1 = -x + 7 <----- Insert functions

3x + 1 = 7 <----- Add "x" to both sides

3x = 6 <----- Subtract 1 from both sides

x = 2 <----- Divide both sides by 3

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What are the features of the parabola modeled by the equation f(x) = x2 - 114x ?

notsponge [240]

Answer:

Answers are in bold type

Step-by-step explanation:

f(x) = $x^{2} -144x$

The parabola opens up, so has a minimum at the vertex.

Let (h, k) be the vertex

h = -b/2a = - (-144)/2(1) = 57

k = 57^2 - 144(57) = 3249 - 6498 = -3249

Therefore, the vertex is (57, -3249)

The minimum value is -3249

The domain is the set of real numbers.

The range = {y | y ≥ -3249}

The function decreases when -∞ < x < 57 and increases when 57 > x > ∞

The x - intercepts: $x^{2} -144x$ = 0

x(x - 114x) = 0

x = 0 or x = 114

x-intercepts are (0, 0) and (0, 114)

When x = 0, then we get the y-intercept. So, 0^2 - 114(0) = 0

y-intercept is (0, 0)

3 0

3 years ago

What is the largest two-digit number that is a multiple of 5 and 10 at the same time?

alexandr402 [8]

Answer:

Step-by-step explanation:

90/10= 9

90/5= 18

No number larger than 90 would work.

5 0

3 years ago

Use the substitution method <br> Y=-2x+11 y=-3x+21

gogolik [260]

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Y = 2 y /3 − 3

x = − y /3 + 7

Hope this helped!

6 0

4 years ago

85% expressed as a fraction in simplest form is

Marizza181 [45]

Hello There!

85% = 85/100

85/100 = 0.85

0.85/1 * 100/100

85/100

SIMPLIFIED IS 17/20

8 0

3 years ago

Read 2 more answers

A worker was paid a salary of $10,500 in 1985. Each year, a salary increase of 6% of the previous year's salary was awarded. How

Mazyrski [523]

Note that 6% converted to a decimal number is 6/100=0.06. Also note that 6% of a certain quantity x is 0.06x.

Here is how much the worker earned each year:

In the year 1985 the worker earned <span>$10,500.

</span>In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:

$10,500(1+0.06).

In the year 1987 the worker earned

$10,500(1+0.06) + 0.06[$10,500(1+0.06)].

Now we can factorize $10,500(1+0.06) and write the earnings as:

$10,500(1+0.06) [1+0.06]= $$10,500(1.06)^2$ .

Similarly we can check that in the year 1987 the worker earned $$10,500(1.06)^3$ , which makes the pattern clear.

We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:

$10,500+10,500(1.06)^1+10,500(1.06)^2+10,500(1.06)^3...10,500(1.06)^{26}$ .

Factorizing, we have

$=10,500[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]=10,500\cdot[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]$

We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula

$\sum_{i=1}^{n} a_i= a(\frac{1-r^n}{1-r})$ (where a is the first term and r is the common ratio) we have:

$\sum_{i=1}^{26} a_i= 1(\frac{1-(1.06)^{26}}{1-1.06})= \frac{1-4.55}{-0.06}= 59.17$ .

Finally, multiplying 10,500 by 59.17 we have 621.285 ($).

The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating $(1.06)^{26}$ .

Answer: D

4 0

3 years ago