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2 years ago

11

Hurry ASAP) Graph the system of equations. f ( x) = x^2 - 5x + 7 and g(x)=2x + 1. Which statements are true about the solutions

to the system of equations? Select each correct answer. ( I accidentally clicked on option A but I don't know the answer at all). Will Mark Brainliest.

1 answer:

N76 [4]2 years ago

7 0

Answer:

Options (2), (4) and (6)

Step-by-step explanation:

Given system of equations is,

f(x) = x² - 5x + 7

g(x) = 2x + 1

By equating both the functions,

f(x) = g(x)

x²- 5x + 7 = 2x + 1

x² - 5x - 2x + 7 - 1 = 0

x² - 7x + 6 = 0

x² - 6x - x + 6 = 0

x(x - 6) - 1(x - 6) = 0

(x - 1)(x - 6) = 0

x = 1, 6

For x = 1,

g(x) = 2x + 1

g(1) = 2(1) + 1

= 3

For x = 6,

g(6) = 2(6) + 1

= 13

Common points (solutions) of both the functions 'f' and 'g' are (1, 3) and (6, 13).

Both the solutions lie in quadrant 1.

x-coordinate of the solution (1, 3) is x = 1.

y-coordinate of the solution (1, 3) is y = 3.

Therefore, options (2), (4) and (6) are the correct options.

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I need help I don’t know how to do complementary and supplementary angles

madreJ [45]

Answer: supplementary angles add up to 180 degrees, and complimetary angles add up to 90 degrees

Step-by-step explanation: It depends on what u want

6 0

2 years ago

A new vehicle is worth $2500. If it depreciates records in value 12% per year, after 6 years what will it be worth

Margaret [11]

Answer:

Step-by-step explanation:

2500 - 12%

12% of 2500 = 300

2500 - 300 = 2200

12% of 2200 = 264

2200-264=1936

Repeat another 4 times

8 0

2 years ago

The back of Dante's property is a creek. Dante would like to enclose a rectangular area, using the creek as one side and fencing

Allushta [10]

The correct value is 720 ft of fencing.

Answer:

Max Area = 64800 sq.ft

Step-by-step explanation:

A square will always give us the maximum area.

Thus, one side would be;

720/4 = 180 feet

So, we want a square 180 ft by 180 ft

however, from the question, we are to use the creek as one side. So, we'll take the 180 ft that we don't need because of the creek and then add it to the opposite side to get 180 + 180 = 360 ft.

Thus,we now have a rectangle with dimensions: 180 ft by 360 ft

Area is given by;

area = length × width

Maximum Area = 180 × 360

Max Area = 64800 sq.ft

6 0

3 years ago

A swim coach has at most $800 to buy equipment for the swim team. Each pull buoy costs $5.50 and each kickboard costs $10. Let x

MissTica

Answer:

5.50x+10y≤800

Step-by-step explanation:

The pull bouys are $5.50 each (5.50x)

The kickboards are $10 each (10y)

And the words "at most" mean less than or equal to

Hope this helps

(can I plz have a brainliest)

3 0

3 years ago

The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

2 years ago