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3 years ago

The variable Z is inversely proportional to X. When X is 6, Z has the value 2.

1 answer:

6 0

Inverse proportion is of the form:

y=k/x, in this case the variables are

z=k/x, and we are given the point (6,2) so we can solve for k

2=k/6

12=k, so our equation is:

z=12/x, so when x=13

z=12/13

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Can y’all help me please? :))

german

Answer:

3.75

Step-by-step explanation:

1.25x3=3.75 easy. you just need to times the height by length

6 0

3 years ago

Image attachment below, Algebra 1 stuff

chubhunter [2.5K]

I know you didn't want an explanation, but I'll give you one anyway.
So, for a function, when you have f(5) = , then you'll put that 5 in for all of the x's in the function.

The first batch of problems gave you the equation f(x) = $\frac{x}{2}$ + 3. Now, plug in the numbers given for s and solve.

1. f(5) = $\frac{x}{2}$ + 3 Plug in 5 for x
 = $\frac{5}{2}$ + 3 Make three into a fraction over 2
= $\frac{5}{2}$ + $\frac{6}{2}$ Add
= $\frac{11}{2}$

2. f(-4) = $\frac{x}{2}$ + 3 Plug in -4 for x
= $\frac{-4}{2}$ + 3 Divide -4 by 2
= -2 + 3 Add
= 1

For the next set, you have g(x) = x² + 1.

3. Let's split this up. Solve the first equation, then the second, and then put the answers together to solve it.

g(4) = x² + 1 Plug in 4 for x
= 4² + 1 Square
= 16 + 1 Add
= 17

g(3) = x² + 1 Plug in 3 for x
= 3² + 1 Square
= 9 + 1 Add
= 10

Now, put the two together.

g(4) + g(3) = Substitute in the answers you just got.
17 + 10 = Add
= 27

4. g(-1) = x² + 1 Substitute in -1 for x
= (-1)² + 1 Square
= 1 + 1 Add
= 2

5. g(-6) = x² + 1 Plug in -6 for x
= (-6)² + 1 Square
= 36 + 1 Add
= 37

For the last set, we have h(x) = x² + 7 and k(x) = 4x - 5. We'll have to pay close attention to the starting variables here.

6. h(-6) = x² + 7 Plug in -6 for x
= (-6)² + 7 Square
= 36 + 7 Add
= 43

k(4) = 4x - 5 Plug in 4 for x
= 4(4) - 5 Multiply
= 16 - 5 Subtract
= 11

Put the two answers into the final equation.

h(-6) + k(4) = Substitute in the answers you got
43 + 11 = Add
= 54

7. k(10) = 4x - 5 Plug in 10 for x
= 4(10) - 5 Multiply
= 40 - 5 Subtract
= 35

h(2) = x² + 7 Plug in 2 for x
= 2² + 7 Square
= 4 + 7 Add
= 11

Now, put those into the equation.

k(10) - h(2) = Plug in the answers you got
35 - 11 = Subtract
= 24

8. For this one, it wants you to add h(x) and k(x). We don't need to plug anything into the equations this time because they're both already solved for x! So, you can just set this up like a standard find-x equation.

(x² + 7) + (4x - 5) =
x² + 7 + 4x - 5 = Combine like terms (7 and -5)
x² + 2 + 4x = Reorder so the variables come first
= x² + 4x + 2

4 0

3 years ago

Read 2 more answers

Which axiom is used to prove that the product of two rational numbers is rational

aliina [53]

Answer:

First, a rational number is defined as the quotient between two integer numbers, such that:

N = a/b

where a and b are integers.

Now, the axiom that we need to use is:

"The integers are closed under the multiplication".

this says that if we have two integers, x and y, their product is also an integer:

if x, y ∈ Z ⇒ x*y ∈ Z

So, if now we have two rational numbers:

a/b and c/d

where a, b, c, and d ∈ Z

then the product of those two can be written as:

(a/b)*(c/d) = (a*c)/(b*d)

And by the previous axiom, we know that a*c is an integer and b*d is also an integer, then:

(a*c)/(b*d)

is the quotient between two integers, then this is a rational number.

5 0

3 years ago

It's possible to build a triangle with a side lengths of 5, 5, and 10

yawa3891 [41]

Yeah, base is ten and the two sides are 5...

7 0

3 years ago

Read 2 more answers

How do you solve sin (5pi/3) without a calculator?

Savatey [412]

very simple, we use the formula sin(a+b)=sinacosb + sinbcosa and sin(20)=2sinacosa

5pi = 2pi/3+3pi/3,

First, we use sin(a+b)=sinacosb + sinbcosa

sin(5pi/3)=sin(2pi/3+3pi/3)= sin(2pi/3+pi)= sin(2pi/3)cos(pi) +sin(pi)cos(2pi/3)

but we know that sin(pi)= 0, and cos (pi) = -1, so sin(5pi/3)= - sin(2pi/3)

now, use sin(2a)=2sinacosa, sin(5pi/3)= - sin(2pi/3)= -2sin(pi/3)cos(pi/3)

sin(5pi/3)= -2sin(pi/3)cos(pi/3)

sin(pi/3)= 0.86, cos(pi/3)=0.5, finally we have sin(5pi/3)= -0.86 x 0.5= -0.43

5 0

4 years ago

Read 2 more answers