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3 years ago

4. Elena noticed that, nine years ago, her cousin Katie was twice as old as Elena was then,

Mathematics

1 answer:

kakasveta [241]3 years ago

4 0

Answer:

k - 2e + 9 = 0

k - e - 4 = 0

Step-by-step explanation:

Given that Elena is currently e years old and Katie is k years old. Now, nine years ago, Katie was twice as old as Elena was.

So, k - 9 = 2(e - 9)

⇒ k - 2e + 9 = 0 .............. (1)

And, in four years, Elena will be as old as Katie is now.

So, k = e + 4

⇒ k - e - 4 = 0 ............... (2)

Therefore, the equations (1) and (2) matches the conditions. (Answer)

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Need help! Will mark Brainiest!

kicyunya [14]

Option B: $y=-\sqrt[3]{x-4}+7$ is the new equation

Explanation:

The given equation is $y=-\sqrt[3]{x}$

We need to find the new graph which is shifted 7 units up and 4 units right.

First, we shall shift the graph 7 units up.

The general formula to shift the graph b units up is given by

$y=f(x)+b$

Thus, to shift the graph 7 units up, let us substitute $b=7$ and $f(x)=-\sqrt[3]{x}$ in the general formula, we have,

$y=$-\sqrt[3]{x}$+7$

Now, we shall shift the graph 4 units right.

The general formula to shift the graph b units right is given by

$y=f(x-b)$

Thus, to shift the graph 4 units right, let us substitute $b=4$ and $f(x)=$-\sqrt[3]{x}+7$$ in the above equation, we have,

$y=-\sqrt[3]{x-4}+7$

Therefore, the new equation is $y=-\sqrt[3]{x-4}+7$

Therefore, Option B is the correct answer.

5 0

3 years ago

HELP PLS The function of F is defined by f(x)=x+2 find F(n-4)

GalinKa [24]

Answer:

Step-by-step explanation:

f(n - 4)= n - 4 + 2 = n - 2

7 0

2 years ago

If u is a unit vector, find u · v and u · w. (assume v and w are also unit vectors.) equilateral triangle

serg [7]

solution:

we know that ,

u.v = ΙuΙ ΙvΙcosθ

here,

θ =60° (since the given triangle is equilateral triangle)

u.v = ΙuΙ ΙvΙcos60°

= 1 x 1 x 1/2

u.v = 1/2

now, u.w = ΙuΙ ΙwΙcosθ

= ΙuΙ x cos(60x2)

u.w = -1/2

5 0

4 years ago

Which statements are true about the ordered pair

Lostsunrise [7]

Answer:

-The ordered pair (-1, 5) is a solution to the first equation because it makes the first equation true.

-The ordered pair (-1, 5) is a solution to the second equation because it makes the second equation true.

-The ordered pair (-1, 5) is a solution to the system because it makes both equations true

Step-by-step explanation:

The correct question is

Which statements are true about the ordered pair (−1, 5) and the system of equations?

x+y=4

x−y=−6

we know that

If a ordered pair is a solution of a equation, then the ordered pair, must satisfy the equation (makes the equation true)

If a ordered pair is a solution of the system of equations, then the ordered pair, must satisfy the equations of the system (makes both equations true)

we have

$x+y=4$ ----> first equation

$x-y=-6$ ----> second equation

step 1

Verify if the ordered pair satisfy the first equation

Substitute the values of x and y of the ordered pair in the first equation

For x=-1, y=5

$-1+5=4$

$4=4$ ---> is true

The ordered pair satisfy the first equation

The ordered pair is a solution to the first equation because it makes the first equation true

step 2

Verify if the ordered pair satisfy the second equation

Substitute the values of x and y of the ordered pair in the second equation

For x=-1, y=5

$-1-5=-6$

$-6=-6$ ---> is true

The ordered pair satisfy the second equation

The ordered pair is a solution to the second equation because it makes the second equation true

therefore

The ordered pair (-1, 5) is a solution to the system because it makes both equations true

6 0

4 years ago

Find the slope, x-intercept, and y-intercept of the equation y = 10x - 20.

levacccp [35]

Answer:

slope=10, y-int=-20. x-int=2

Step-by-step explanation:

The equation y=10x-20 is in slope-intercept form, or y=mx+b with m being the slope and b being the y-int. In this scenarion, the m(the slope) is 10 and the b(the y-int) is -20. For the x-int, you have to find out what x is when y=0 and vice versa for the y-int. In this case, 0=10x-20 so x=2. Therefor the x-int is 2.

7 0

3 years ago