What is the solution to the system of equations grahped below

Step-by-step explanation:

For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,

b^2 - 4ac must be positive.

b^2 - 4ac > 0

(k - 3)^2 - 4(3 - 2k) > 0

k^2 - 6k + 9 - 12 + 8k > 0

k^2 + 2k - 3 > 0

To show that k satisfies k² + 2k - 3 > 0 ,the discriminant is given as Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]

To have two distinct real roots, the discriminant of the quadratic equation must be positive. The discriminant is given by;

Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]

For two distinct real roots, Δ > 0. So, we have k² + 2k - 3 > 0. Thus, k satisfies the inequality k² + 2k - 3 > 0.

In summary, for the quadratic equation x² + (k - 3)x + (3 - 2k) = 0 to have two distinct real roots, the value of k must satisfy the inequality k² + 2k - 3 > 0

Learn about quadratic equations at: https://brainly.com/question/1214333

#SPJ3

Answer:

when -2 , y = 1

when 0, y = -5

when 2, y = -3

when 3, y = 1

when 4, y = 7

9514 1404 393

Answer:

  (c)  y = 36·5

Step-by-step explanation:

If x represents the number of chocolates, the given formula ...

  y = kx

with the values k = 36 and x = 5 inputted will look like ...

  y = 36·5

Answer:

1 1/5

Step-by-step explanation:

4/5 ÷ 2/3

4/5 × 3/2

12/10

6/5

1 1/5

Answer:

a) s[n] = 1.05s[n-1] +1000; s[0] = 50,000

 b) $83,421.88

 c) s[n] = 70000·1.05^n -20000

Step-by-step explanation:

a) Let s[n] represents the employee's salary in dollars n years after 2017. The salary in 2017 is given as $50,000, so ...

 s[0] = 50000 . . . . the recursion relation initial condition

The next year, the salary is multiplied by 1.05 and 1000 is added:

 s[1] = 1.05·s[0] +1000

This pattern repeats, so the recursion relation is ...

 s[n] = 1.05·s[n-1] +1000

__

c) It is convenient to find a formula for the salary before trying to compute the salary 8 years on. So, we work part (c) before part (b).

The base salary gets multiplied by 1.05 each year, so can be described by the exponential function ...

 base salary after n years = 50,000·1.05^n

The add-on to the raise becomes a geometric sequence whose common ratio is 1.05. The sum can be described by the formula for the sum of such a sequence:

 sum = a1(r^n -1)/(r -1) . . . . . (see note below)

 sum of add-ons = 1000(1.05^n -1)/(1.05 -1) = 20000(1.05^n -1)

So, the total salary after n years is ...

 s[n] = 50000·1.05^n + 20000(1.05^n -1)

The exponential terms can be combined, so we have the explicit formula ...

 s[n] = 70000·1.05^n -20000

__

b) The year 2025 is 8 years after 2017, so we want to find s[8].

 s[8] = 70000·1.05^8 -20000 = 70000·1.4774554 -20000

    = 103,421.88 -20000 = 83,421.88

In 2025, the employee's salary will be $83,421.88.

_____

Note on the sum of the add-ons

A geometric sequence starts with term a1 and gets multiplied by a ratio r to make the next term: a2=r·a1; a3=r²·a1, ....

The sum of such a geometric sequence has the formula

 Sn = a1·(r^n -1)/(r -1)

Here, the sequence starts in year 1 with a1=1000 and has a common ratio r=1.05. The denominator of the sum is r-1 = 0.05 = 1/20, so the sum can be written as

 Sn = 20000·(1.05^n -1).

Answer:

Corresponding

Step-by-step explanation:

They are on the same side which makes them corresponding angles

Answer:

1. 2/5

2. 3/20

3. 6 1/9

4. 1/5

5. 11

6. 1

7. 3/13

8. 1 5/11

9. 2

10. 6 1/2

11. 20/27

12. 2 3/16

13. 4 13/18

14. 1 45/98

Hope this helps!

Step-by-step explanation:

Answer:

Option C): f(x) = 3x - 4.

Step-by-step Explanation:

A linear function in slope-intercept form is given by f(x) = mx + b where:

We can solve for the slope by using the following formula:

[tex]\displaystyle\mathsf{Slope\:(m)\:=\:\frac{Rise}{Run}\:=\Bigg(\frac{y_2-y_1}{x_2 - x_1}\Bigg)}[/tex]

Choose two points from the graph and substitute their values into the slope formula.

[tex]\displaystyle\mathsf{Slope\:(m)\:=\Bigg(\frac{y_2-y_1}{x_2 - x_1}\Bigg)\:=\:\Bigg(\frac{2-(-4)}{2-0}\Bigg)\:=\:\Bigg(\frac{2+4}{2}\Bigg)\:=\:\frac{6}{2}\:\:=\:3}[/tex]

Therefore, the slope of the line is 3.

As defined in the previous section of this post, the y-intercept (0, b) is the point on the graph where it crosses the y-axis.  We can see that the line intersects the y-axis at point (0, -4). This means that the value of our y-intercept, b, is -4.

Alternatively, we can solve for the y-intercept (b) by choosing a point on the graph and substitute its values into the slope-intercept form.

We will use and substitute the values of (x₁, y₁) and the slope into the function to solve for b.

f(x) = mx + b

⇒  2 = 3(2) + b

⇒  2 = 6 + b

⇒  2 - 6 = 6 - 6 + b

⇒  -4 = 0 + b

⇒  - 4 = b

Hence, the value of the y-intercept is: b = 4.

Based from our calculations, we can infer that the linear function that matches the graph is Option C: f(x) = 3x - 4.

Linear functions

Linear equations

Slope-intercept form

_______________________________

Learn more about Linear Functions here: https://brainly.com/question/26351470

Learn more about Point-slope form here: https://brainly.com/question/26681302  

Answer:

f(x)=3x-4

Step-by-step explanation:

Answer:

1.45 x 10^2

Step-by-step explanation:

In scientific notation, you get the number down to 1 digit before the decimal place and all the rest after it, then multiply by 10 raised to a power in order to get it back to the original. An easy way to do it is to count the number of times you moved the decimal and remember which direction you did it. The number is the power (in this case 2) and the direction tells you if it's positive or negative (in this case it was to the left, so it's positive two.)

In simpler terms, slide the decimal to the right two places and make it 1.45, then multiply it by 10^2 (which is 100) to make it equal to 145. This leaves you with 1.45 x 10^2.

Answer:

domain: -7, -1, 0, 1

Range: -1, 0, 1, 2, 7

Step-by-step explanation:

I don't know the drop-down menu choices so I can't answer that one for you sorry :(

But I hope this helps :)

Divide 47 by 14:

Answer 3.357

Rounded to nearest hundredth: 3.36

Answer:

11

Step-by-step explanation:

f(16) = 7 + 16/4

= 7 + 4

= 11

Answer:

square roots are x, 8, 4x

Step-by-step explanation:

x^2 square root is x

64 square root is 8

16x square root is 4x

Answer:

ok so it will be 16-bit

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] - 3 - ( - 5) \\ - 3 + 5 \\ 2 \\ [/tex]

Answer:

712436 eggs were sold together

Step-by-step explanation:

429,382 + 283,054 = 712436

Answer: 50

Step-by-step explanation:

[6+√-64] × 3-√-16

(6+8i)(3-4i)

6(3-4i)+8i(3-4i)

18-24i+24i+32

18+32=50

Answer:

fifty

Step-by-step explanation:

fifty

Answer:

Missing reason/statements:

vâng vì phụ nữ là những người tán gẫu

Answer:

28.5

Step-by-step explanation:

1/2 is 0.5 as a decimal.

That would mean that 28 1/2 is the same as 28.5.

Hope this helps! Brainliest would be really appreciated!

Answer: A

Step-by-step explanation:

Using pythagoras;

[tex]25 = \sqrt{7^{2}+ x^{2} }\\25^{2}=7^{2} +x^{2} \\625 = 49 +x^{2} \\576 = x^{2} \\x = 24[/tex]

Please give me a brainliest answer

Answer:

Step-by-step explanation:

The Pythagoras theorem formula states that in a right triangle ABC, the square of the hypotenuse is equal to the sum of the square of the other two legs. If AB, BC, and AC are the sides of the triangle, then: BC2 = AB2 + AC2​. While if a, b, and c are the sides of the triangle, then ​c2 = a2 + b2.

√(25²-7²) =

√(625-49)=

√576=

24

Answer:

[tex] - \frac{8}{5} [/tex]

Step-by-step explanation:

[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]

(x₁, y₁) is the 1st coordinate while (x₂, y₂) is the 2nd coordinate.

Gradient of the line

[tex] = \frac{6 - ( - 2)}{ - 2 - 3} [/tex]

[tex] = \frac{6 + 2}{ - 5} [/tex]

[tex] = - \frac{8}{5} [/tex]

Answer:

=3x+5

Step-by-step explanation:

Let's simplify step-by-step.

5x+5−2x

=5x+5+−2x

Combine Like Terms:

=5x+5+−2x

=(5x+−2x)+(5)

=3x+5

Answer:

=3x+5

Answer:

[tex]\boxed{\boxed{\sf 3x+5 }}[/tex]

Step-by-step explanation:

[tex]\sf (5x+5)-2x[/tex]

[tex]\sf \left(a\right)=a[/tex]

⇒ First step is to get rid of expression parentheses:

[tex]\longmapsto[/tex] [tex]\sf 5x+5-2x[/tex]

⇒ Now, we need to combine like terms:

[tex]\longmapsto[/tex] [tex]\sf (5x-2x)[/tex] [tex](5)[/tex]

[tex]\longmapsto[/tex]  [tex]\sf 3x+5[/tex]

__________________________________

Answer:

306.

Step-by-step explanation:

Firstly, we are aware 100% of 680 is obviously 680,

Next, we know half of a 100% is 50% therefore half of 680 is 340.

Then, we know 45% is 5% less than 50%

To find 5% of a number mentally, divide it by 10 as 100÷5=20

680÷20=34

Lastly 50% subtracted by 5%: 340-34=306.

Now we know, 45% of 680 is 306.

Hope this helps.

Hope this helps.Please mark BRAINLIEST.

Answer:

13

Step-by-step explanation:

17-10+6

7+6=13

hope it helps

Step-by-step explanation:

we will add 3+37=40

40/8=5

mark me brainlist plz

Answer:

You have to add a certain amount of a number to 3 7/8 to make five. Or the easy way, 5 - 3 7/8 = 1 1/8

Step-by-step explanation:

If you want can you make me brainlyist?

Also, I hope this helped!

Answer:

8.75 per hour

Step-by-step explanation:

Since it is a linear function we can use the slope formula

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

  = ( 370-20)/(40-0)

  =350/40

 = 8.75