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3 years ago

If y varies directly as x, and y is 400 when x is n and y is n when x is 4, what is the value of n?

Mathematics

1 answer:

ArbitrLikvidat [17]3 years ago

7 0

Answer:

100

Step-by-step explanation:

4xy times 100n the variable of 4xy would be times in the related number of 100n to get the answer 400

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F(x)= |3x-4|+2, find f(-10)

Zarrin [17]

$f(x)=|3x-4|+2 \\ \\
f(-10)=|3 \times (-10) -4|+2=|-30-4|+2=|-34|+2=34+2 \\ f(-10)=36$

7 0

4 years ago

−4x+7y+5=0 x−3y=−5 How many solutions does the system have?

xeze [42]

Solution:

Using Substitution Method:

-4x+7y=-5 (Equation 1)

x-3y=-5 (Equation 2)

get the value of x from Equation 2

x=3y-5 (Equation 3)

Put the value of x from Equation 3 in Equation 1

-4(3y-5)+7y=-5

-4(3y)+20+7y=-5

-12y+7y=-5-20

-5y=-25

Negative sign on both sides cancels each other

y=25/5

y=5

Putting value of y in equation 3

x=3(5)-5

x=15-5

x=10

Therefore, [x,y]=[10,5]

Using Elimination Method

-4x+7y=-5 (Equation 1)

x-3y=-5 (Equation 2)

Multiply equation 2 with -4 in order to eliminate the x term

-4(x-3y)=-5*4

-4x+12y=20 (Equation 3)

Adding Equation 1 and 3

-4x+7y=-5

-4x+12y=20

+ - = - (Change Of Sign with x and y terms)

-----------------

0x-5y = -25

-5y=-25

y=5

Substituting y’s value is Equation 1

-4x+7(5)=-5

-4x+35=-5

-4x=-40

Cancellation of negative sign on both sides

x=40/4

x=10

[x,y]=[10,5]

3 0

3 years ago

For some constants a and b let \[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x

Viktor [21]

Answer:

The value of a+b is 4.

Step-by-step explanation:

The given function is

$f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.$

It is given that for some constants a and b the function f has the property that f(f(x))=x for all x.

For x≤3,

$f(x)=9-2x$

For x>3,

$f(x)=ax+b$

At x=0,

$f(0)=9-2(0)=9$

$f(f(0))=f(9)\Rightarrow a(9)+b=9a+b$

Using property f(f(x))=x,

$f(f(0))=0$

$9a+b=0$ .... (1)

At x=1,

$f(1)=9-2(1)=7$

$f(f(1))=f(7)\Rightarrow a(7)+b=7a+b$

Using property f(f(x))=x,

$f(f(1))=1$

$7a+b=1$ .... (2)

Subtract equation (2) from equation (1).

$9a+b-(7a+b)=0-1$

$2a=-1$

Divide both sides by 2.

$a=-\frac{1}{2}$

Substitute this value in equation (1).

$9(-\frac{1}{2})+b=0$

$b=\frac{9}{2}$

The value of a is $-\frac{1}{2}$ and value of b is $\frac{9}{2}$ . The value of a+b is

$a+b=-\frac{1}{2}+\frac{9}{2}$

$a+b=4$

Therefore the value of a+b is 4.

5 0

3 years ago

Need answer ASAP *MARKING BRAINLIEST

german

Answer:

Step-by-step explanation:

To the tenth term in the sequence we need to change all the n's to 10.

so...

a₁₀ = 4 + ( -1 )¹⁰ =

4 + (-1) = (Because -1¹⁰ = -1)

4 - 1 = 3

3 0

3 years ago

Read 2 more answers

A display number cube measures 20 inches on a side. The sides are numbered 1-6. The odd numbered sides are covered in blue fabri

Masja [62]

There are six sides or faces of a cube, each measuring 20 inches. If even numbered sides are covered with red fabric, then a total of 60 inches of red fabric was used. This is based from 3 even numbered sides multiplied to 20 inches as a measurement of each side.

5 0

3 years ago