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3 years ago

Graph the linear inequality. x + 2y = 5

2 answers:

8 0

we can graph the linear function by finding first the x and y intercepts.
x-intercept
x + 0 = 5; x =5P ( 5,0)
y-intercept0 + 2y = 5y = 5/2P(0,5/2)
We connect the two points and extend the line infinitely

choli [55]3 years ago

5 0

So you always want y in front of the equation no matter what so you have x +2y=5 so you take the x and you subtract it to both side making it 2y= 5-x so then you just have to take the 2 to both side so you have to divide it and you will get y= 5/2-x/2 so then to graph it you start with the b which is -x/2 so you go down -1 and over 2 and place your dot adn then go up 5 over 2 and then place you dot and connect them together

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is a 50 percent increase followed by a 33 1/2 percent decrease same less or greatter than the original value

Nitella [24]

Answer:less than

Step-by-step explanation:

3 0

3 years ago

Slove the simoltanous equation by using substitution or elimination method 5x-3y=1 3x+2y=1

xxTIMURxx [149]

By substitution method 

5x - 3y =1

3x + 2y = 1

_____o____o____

$5x - 3y = 1 \\ 5x = 1 + 3y \\ x = \frac{1 + 3y}{5}$

______o____o_____

$3x + 2y = 1 \\ 3( \frac{1 + 3y}{5} ) + 2y = 1 \\ \frac{3 + 9y}{5} + 2y = 1 \\ \frac{3 +9y + 10y}{5} = 1 \\ \frac{3 + 19y}{5} = 1 \\ 3 + 19y = (1)(5) \\ 3 + 19y = 5 \\ 19y = 5 - 3 \\ 19y = 2 \\ y = \frac{2}{19}$

______o_____o____

$x = \frac{1 + 3y}{5} = \frac{1 + 3 \frac{2}{19} }{5} \\ x = \frac{1 + \frac{6}{19} }{5} = \frac{ \frac{19 + 6}{19} }{5} = \frac{ \frac{25}{19} }{5} \\ x = \frac{25}{19} \div 5 \\ x = \frac{25}{19} \times \frac{1}{5} \\ x = \frac{5}{19}$

I hope I helped you^_^

7 0

2 years ago

The function h(t) = −5t2 + 20t shown in the graph models the curvature of a satellite dish: graph of parabola starting at zero c

ipn [44]

Answer:

Part 1) Option B: 0 ≤ x ≤ 4

Part 2) Option C: (5x − 1)(2x − 3)

Part 3) Option C: The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) Option B: f(x) = (2x + 1)(2x − 1)

Part 5) Option A: The company earned 85 billion dollars in 2008

Part 6) Option C: (3, 0) and (5, 0)

Step-by-step explanation:

Part 1) we have

$h(t)=-5t^{2}+20t$

This is a vertical parabola open downward

The vertex is a maximum

The x-intercepts are the points (0,0) and (4,0)

The vertex is the point (2,20) ---> The x-coordinate of the vertex is the midpoint of the x-intercepts

The domain is the interval ----> [0,4]

$0\leq t\leq 4$

The range is the interval ----> [0,20]

$0\leq h(t)\leq 20$

Part 2) we have

$V=10x^{2} -17x+13$

where

x is the time in minutes

V is the volume in gallons

we know that

When the trough is empty, the volume is equal to zero

For V=0

$10x^{2} -17x+3=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$10x^{2} -17x+3=0$

$a=10\\b=-17\\c=3$

substitute in the formula

$x=\frac{-(-17)(+/-)\sqrt{-17^{2}-4(10)(3)}} {2(10)}$

$x=\frac{17(+/-)\sqrt{169}} {20}$

$x=\frac{17(+/-)13} {20}$

$x=\frac{17(+)13} {20}=\frac{3}{2}$

$x=\frac{17(-)13} {20}=\frac{1}{5}$

$10x^{2} -17x+3=10(x-\frac{3}{2})(x-\frac{1}{5})$

simplify

$10(x-\frac{3}{2})(x-\frac{1}{5})=(2x-3)(5x-1)$

Part 3) we have

$f(x)=-x^{2}+20x+100$

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change is equal to

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$f(a)=f(10)=-(10)^{2}+20(10)+100=200$

$f(b)=f(20)=-(20)^{2}+20(20)+100=100$

$a=10$

$b=20$

Substitute

$\frac{100-200}{20-10}$

$-\frac{100}{10}=-10$ ----> is a decreasing function

therefore

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) we have

$f(x)=4x^{2} -1$

Find out the x-intercepts

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

For f(x)=0

$4x^{2} -1=0$

Solve for x

$4x^{2}=1$

$x^{2}=\frac{1}{4}$

take square root both sides

$x=(+/-)\frac{1}{2}$

$f(x)=4x^{2} -1=4(x-\frac{1}{2})(x+\frac{1}{2})=(2x-1)(2x+1)$

Part 5) we have

$t^{2}+14t+85$

Remember that

The y-intercept of a function is the value of the function (output value) when the value of x (input value) is equal to zero

In this problem

The expression represent a company's net sales, in billions, from 2008 to 2018

t is the number of years since the end of 2008

For t=0 -----> represent the end of 2008

$(0)^{2}+14(0)+85=85\ billion\ dollars$

therefore

The company earned 85 billion dollars in 2008.

Part 6) What are the x-intercepts of the parabola?

we have the points (2,3),(4,-1),(6,3)

This is a vertical parabola open upward

The vertex represent a minimum

In this problem the vertex is the point (4,-1)

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

we have

(h,k)=(4,-1)

substitute

$y=a(x-4)^2-1$

take the point (2,3) and substitute in the quadratic equation to solve for a

For x=2, y=3

$3=a(2-4)^2-1$

$3=4a-1$

$4a=4$

$a=1$

The quadratic equation is

$y=(x-4)^2-1$

Find out the x-intercepts

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

For y=0

$(x-4)^2-1=0$

Solve for x

$(x-4)^2=1$

take square root both sides

$(x-4)=(+/-)1$

$x=4(+/-)1$

$x=4+1=5\\x=4-1=3$

therefore

The x-intercepts are the points (3,0) and (5,0)

7 0

3 years ago

Read 2 more answers

Kylie draws a triangle on a coordinate grid. She then performs the following

zmey [24]

B PLEASE GIVE BRAINLIEST

7 0

2 years ago

If F (7) 22, Then F(f-1(22))

jeka57 [31]

Answer:

$\boxed{\boxed{f(f^{-1}(22))=22}}$

Step-by-step explanation:

$\text{If we have}\ f(x)\ \text{and}\ f^{-1}(x),\ \text{then}\\\\\text{if}\ f(a)=b,\ \text{then}\ f^{-1}(b)=a.\\\\\text{Therefore, if}\ f(7)=22,\ \text{then}\ f^{-1}(22)=7.\\\\f(\underbrace{f^{-1}(22)}_{=7})=f(7)=22$

6 0

3 years ago