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3 years ago

Please help with steps as well!!

Mathematics

2 answers:

Andreas93 [3]3 years ago

6 0

Answer:

x=24

Step-by-step explanation:

x/2 -8=4

Add 8 to each side

x/2-8+8=4+8

x/2 =12

Multiply each side by 2

x/2*2 = 12*2

x=24

satela [25.4K]3 years ago

3 0

Answer:x=24

Step-by-step explanation:x/2-8=4

Add 8 to both sides

x/2=12

Multiply each side by 2

x=24

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Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is $z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$ .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be $z (x) = \cos x$ the base formula, where $x$ is measured in sexagesimal degrees. This expression must be transformed by using the following data:

$T = 180^{\circ}$ (Period)

$z_{min} = -4$ (Minimum)

$z_{max} = 5$ (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of $2\pi$ radians. In addition, the following considerations must be taken into account for transformations:

1) $x$ must be replaced by $\frac{2\pi\cdot x}{180^{\circ}}$ . (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

$\Delta z = \frac{z_{max}-z_{min}}{2}$

$\Delta z = \frac{5+4}{2}$

$\Delta z = \frac{9}{2}$

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

$z_{m} = \frac{z_{min}+z_{max}}{2}$

$z_{m} = \frac{1}{2}$

The new function is:

$z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)$

Given that $z_{m} = \frac{1}{2}$ , $\Delta z = \frac{9}{2}$ and $T = 180^{\circ}$ , the outcome is:

$z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

8 0

3 years ago

LaTanya leaves her house at 12:30pm and bikes at 12 mi/h to marta’s House she stays at marta’s House for 90mij both girls walk b

babymother [125]

Answer:

2.9 mi

Step-by-step explanation:

The time difference t between 12.30pm and 3.30pm is 3h.

Let the distance to Marat's house be s.

The equation to calculate velocity v is given by:

v = distance / time.

Now you can write an equation for the time difference t and use the two velocities and the 90 min(= 1.5h) she stays:

3 = s/12 + 1.5 + s/2.3

Solve this equation for s:

(1/12 + 10/23)* s = 1.5

s = 2.9

7 0

3 years ago

The Value of x in the system of equation at the right is -2 what is the value of a? use elimination to help you find the value.

sammy [17]

2x-4y=-16
ax+4y=6 +
--------------------
2x+ax=-10; for x=-2,
2(-2)+a(-2)=-10
-2a=-10+4
a=-6/-2
a=3

7 0

3 years ago

Solve each of the following equations for the missing variable.

Ierofanga [76]

The answer for -2.5x-10=40 would be:
x = - 20.

4 0

3 years ago

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Write a real-world problem that could be represented by the following inequality. 70 + 5x < 30 + 15x

kondaur [170]

Justin wants to paint his room. So he put together some quotations from two different painters. The first painter's total charge was based on the number of hours (denoted as x) worked was modeled as f( x ) = 70 + 5 x, while that of the second painter was g( x ) = 30 + 15 x. Justin knows that it will take more than 4 hours to decorate the house so he was certain to go with the first painter whose cost is low-priced when the number of hours is above 4 hours.

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3 years ago