Which ordered pair is a solution to the system of inequalties?
y > –x
y ≤ x + 1

Linear equations are typically organized in slope-intercept form:

[tex]y=mx+b[/tex]

To determine a linear equation in slope-intercept form:

We're given:

First, find the slope of the line (m):

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

⇒ Plug in the given points (-1,-4) and (5,-2):

[tex]m=\dfrac{-2-(-4)}{5-(-1)}\\\\m=\dfrac{-2+4}{5+1}\\\\m=\dfrac{2}{6}\\\\m=\dfrac{1}{3}[/tex]

⇒ Therefore, the slope of the line is [tex]\dfrac{1}{3}[/tex]. Plug this into y=mx+b:

[tex]y=\dfrac{1}{3}x+b[/tex]

Now, determine the y-intercept (b):

[tex]y=\dfrac{1}{3}x+b[/tex]

⇒ Plug in one of the points and solve for b:

[tex]-4=\dfrac{1}{3}(-1)+b\\\\-4=-\dfrac{1}{3}+b\\\\-4+\dfrac{1}{3}=b\\\\b=-\dfrac{11}{3}[/tex]

⇒ Therefore, the y-intercept is [tex]-\dfrac{11}{3}[/tex]. Plug this back into our original equation:

[tex]y=\dfrac{1}{3}x-\dfrac{11}{3}[/tex]

[tex]y=\dfrac{1}{3}x-\dfrac{11}{3}[/tex]

The function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is a rational function

The simplified expression of the function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is [tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]

The function expression is given as:

f(x) =x - 4/x^2 + 13x + 36

Rewrite properly as:

[tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex]

Expand the denominator

[tex]f(x) =\frac{x - 4}{x^2 + 4x + 9x + 36}[/tex]

Factorize the denominator

[tex]f(x) =\frac{x - 4}{x(x + 4) + 9(x + 4)}[/tex]

Factor out x + 9

[tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]

Hence, the simplified expression of the function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is

[tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]

Read more about rational functions at:

https://brainly.com/question/1851758

Answer: f(x) is increasing for all x > -4

Proof of validity is shown below.

Answer:

the answer is c

Step-by-step explanation:

its c i dont know what the words say tho i need to read what it say first.

Answer:

the answer to that question is 14.09

Answer:

5 feet

Step-by-step explanation:

Hello!

We can use the Pythagorean theorem to solve this.

Formula: a² + b² = c²

Solve:

The diagonal is 5 feet.

Answer:

B) 5 ft

Step-by-step explanation:

Answer:

y can only be greater than x if x has a variable less than y so the answers is ly- lx

Step-by-step explanation:

Answer:

The length is 19 inches

Step-by-step explanation:

Step 1:  Determine the length

Perimeter = 2(L + W)

Step 2:  Solve for L

60 /2 = 2(L + 11) / 2

30 - 11 = L + 11 - 11

19 = L

Answer:  The length is 19 inches

Answer:

Step-by-step explanation:

Perimeter : 2(L + W) = 60

Answer:

16 times

Step-by-step explanation:

This problem is solved by ratio. Since the ratio of 28 out of 25 times is 4:5, he has to catch the ball 4:5 or 4 of 5 times. You multiply both 5 and 4 by 4, because that's how many times he's gonna catch it. 4 x 4 = 16, so the answer is 16 times.

Answer:

(4/5)^20

Step-by-step explanation:

1) First, write the numbers of times Raymond caught the football out of 35 attempts. This is a necessary step in order to obtain an appropriate operand.

28

35

2) Reduce the fraction to lowest terms. This is an optional step but it simplifies the problem.

28   /  4

35      4

= 4

  5

3) Raise the fraction to the 20th power. If the ball is thrown at him 20 times, the probability of him successfully catching the ball must be (4/5)^20.

= (4)^2

  (5)

Answer:

(8/3,11/3) is the centroid of the given triangle

pls do mention in comment if u need full solution

Answer:

(8/3, 11/3)

Step-by-step explanation:

Formula of the centroid

Points

Solving :

The entrance fee is d dollars, and the meal ticket is $4 less than the entrance fee -> Each meal ticket is d - 4

So, the total amount that the friends pay is 5(d-4)

Answer:

36 km^2

Step-by-step explanation:

We will use the way to find the area of trapezoids which is b+b/2 *h and that is 3+5/2 * 9 so 8/2 is 4 and 4*9=36

so her University costs are $22,500

however she gets some help because

◉ academic scholarship pays 10,000 off of that

◉ other scholarships pay 4,400 off of that

◉ and her parents pay 1800 off of that

what's left? well, what's left is 22500 - 10000 - 4400 - 1800 = 6300 bucks.

so for the next 10 months she needs to cover 6300 bucks of her expenses, now 6300 spread over 10 months is 630 a pop.

Answer:

See below

Step-by-step explanation:

Remember    S-O-H-C-A-H-T-O-A

   Sin = Opp / Hyp

    Cos = Adjacent  / Hyp

      Tan =Opp / Adj

You didn't say WHICH angle is X  , so you will have to finish this !

Scale of the new blueprint: 2 inches = 2.5 feet (or 4 inches = 5 feet)

Width of the new blueprint: 14.4 inches

Answer:

144040.3333

Step-by-step explanation:

275*523 = 143825

19x34/3 = 215.3333333

so add them up to get 144040.3333

Answer:

144040.333333

Step-by-step explanation:

start with parenthesis (275x523)

This would get you, 143825.

Next, you would do, (19x34/3)

That would get you, 215.333333333.

Finally, you would add the two numbers together and get a product of 144040.333333.

Answer:

Yes it does.

Step-by-step explanation:

I gives an estimate of what the weather is.

Answer:

the first one is the answer

Answer:

The answers are: 35 hot dogs & 52 sodas.

The plane has intercepts

y = z = 0   ⇒   3x = 6   ⇒   x = 2

x = z = 0   ⇒   2y = 6   ⇒   y = 3

x = y = 0   ⇒   z = 6

and thus passes through the points (2, 0, 0), (0, 3, 0), and (0, 0, 6).

Parameterize the portion of the plane (call it P) by the vector function,

[tex]\vec r(s,t) = \left\langle 2(1-s)(1-t), 3s(1-t), 6t \right\rangle[/tex]

where 0 ≤ s ≤ 1 and 0 ≤ t ≤ 1.

Compute the normal vector to P :

[tex]\vec n = \dfrac{\partial \vec r}{\partial t} \times \dfrac{\partial \vec r}{\partial s} = -\left\langle 18-18t, 12-12t, 6-6t \right\rangle[/tex]

Then the flux of F through P is given by the surface integral,

[tex]\displaystyle \iint_P \vec F \cdot d\vec S = \int_0^1 \int_0^1 \left\langle 6s(1-s)(1-t)^2, 90st(1-t), 72t(1-s)(1-t) \right\rangle \cdot \vec n \, ds \, dt \\\\ = - \int_0^1 \int_0^1 \left(108(t-1)^3 s^2 + 108(t-1)^2(5t+1) s + 432t(t-1)^2\right) \, ds \, dt \\\\ = - \int_0^1 18(t-1)^2(41t+1) \, dt \\\\ = \boxed{-\frac{135}2}[/tex]

Answer:

The mean is 6. When you add all the numbers you get 66 and then youre suppose to divide 66 by 10 in order to get the mean which is 6.

Step-by-step explanation:

4 + 5 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 = 66

66 ÷ 10 = 6

Answer:

That question is statistical because there can be multiple answers such as, biking, walking, carpooling, and taking a bus.

Step-by-step explanation:

[tex]\begin{cases} f(x)=x^2\\ g(x)=x-3 \end{cases}\qquad \qquad (g\circ f)(x)\implies g(~~ f(x)~~) \\\\[-0.35em] ~\dotfill\\\\ f(3.5)=(3.5)^2\implies f(3.5)=12.25 \\\\\\ g(~~ f(3.5)~~)\implies g(~~ 12.25~~)=(12.25)-3\implies \stackrel{(g\circ f)(3.5)}{g(~~ 12.25~~)}=9.25[/tex]

Answer:

67

Step-by-step explanation:

Complementary angles add to 90 degrees

<A + <B = 90

x+10  + 3x+28 = 90

Combine like terms

4x+38 =90

Subtract 38 from each side

4x+38-38 = 90-38

4x = 52

Divide by 4

4x/4 = 52/4

x = 13

We want to find <B

<B = 3x+28

   = 3(13) +28

   = 39+28

  =67

Answer:

Y =4x^4 + 4x^3 − 37x^2 + 41x −12

Step-by-step explanation:

Y = (2x - 1 ) (x + 4) (2x - 3) (x - 1)

Using commutative property we can re-arrange RHS,

Y= (2x - 1) (2x - 3) (x + 4) (x - 1)

Using the property

[(x+a) (x+b) = x^2 + (a+b)*x +ab],

Y =

[(2x)^2 + (-1 - 3)*2x + (-1 )*(-3)] [x^2 + (4 - 1)*x + 4*(-1)]

From here onwards I would recommend u to do the calculation by your own bc I might have made mistakes

in the steps but I got right but still just check yourself if u copy all the steps as it is

Y = (4x^2 -8x + 3) (x^2 + 3x -4)

Y = 4x^4 + 12x^3 - 16x^2 -8x^3 -24x^2 + 32x + 3x^2 + 9x - 12

Y = 4x^4 + 4x^3 -37x^2 + 41x - 12

Here I got the answer right so my calculations will also might be right

I checked my answer if it's right using an app called "MathPapa" and it's a great app to solve algebra questions like urs. The screenshot of the answer using this app is here on the top. This is the longest question I have solved for anyone, bye and have a nice day ahead!

Answer:

outside the circle

sorry if I'm wrong

Answer:

16.2

Step-by-step explanation:

By geometric mean theorem:

[tex] {9}^{2} = 5(x) \\ \\ \implies \: 81 = 5x \\ \\ \implies \: x= \frac{81}{5} \\ \\ \implies \: x=16.2[/tex]

Answer: T-R

Step-by-step explanation:

The surface area of this rectangular prism of dimensions 26 inches by 10 inches by 8 inches is 1096 square inches.

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The surface area of this rectangular prism = 2( lb + bh + hl)

The dimensions of a rectangular prism are 26 inches by 10 inches by 8 inches.

The surface area of this rectangular prism = 2( lb + bh + hl)

  = 2( 26 x 10 + 10 x 8 + 26 x 8)

  = 2(260 + 80 + 208)

  = 2 x 548

  = 1096

Thus, The surface area of this rectangular prism is 1096 square inches.

Learn more about the area;

https://brainly.com/question/6754997

#SPJ1