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Phoenix [80]
3 years ago
10

Solve the system by using substitution. y = 2x – 10 and - 6x – 2y = -10

Mathematics
2 answers:
lesantik [10]3 years ago
4 0
Make them both as y=mx+b for then make them equal each other. Should look like the picture I took.

Ann [662]3 years ago
3 0

Answer:

(3, -4) or x = 3 and y = -4

Step-by-step explanation:

Hope this helps!

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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
6.Madeline made the wooden steps shown. What is the volume of the steps? The wooden steps have two parts, both of which are rect
Lelu [443]

Answer:

840 cubic inches

Step-by-step explanation:

Given:

The wooden steps have two parts.

Both of which are rectangular prisms.

The top part is 6 inches tall, 5 inches wide and 10 inches long.

The bottom part is 6 inches tall, 9 inches wide and 10 inches long.

Question asked:

What is the volume of the steps?

Solution:

<u>For top part</u>

Length = 10 inches

Width = 5 inches

Height = 6 inches

<u><em>As we know:</em></u>

<u><em /></u>Volume\ of\ rectangular\ prism =length\times width\times height

                                                 =10\times5\times6=300\ cubic\ inches

<u>For bottom part</u>

Length = 10 inches

Width = 9 inches

Height = 6 inches

Similarly

Volume\ of\ rectangular\ prism =length\times width\times height

                                                 =10\times9\times6=540\ cubic\ inches

Volume of two steps = 300 + 540 = 840 cubic inches

<em>Therefore, the volume of the steps are 840 cubic inches.</em>

<em></em>

8 0
3 years ago
Lines s, t, u, and v are cut by transversal r. Clockwise from top left, the angles formed by r and s are blank, 89 degrees, blan
Natali [406]

Answer:

its not b but i think its c

Step-by-step explanation:

because it is

8 0
3 years ago
Read 2 more answers
Please show your work! Thankyou!
ZanzabumX [31]
Log₄(y+2) = 3, transform it into exponent form:

(y+2) = 4³
y+2 = 64
 y= 62

5 0
3 years ago
What is the area of the triangle in square yards?<br> 6 yd.<br> 15 3/4 yd.
IceJOKER [234]

Answer:

6x15 2/4 yd dividedby 2

Step-by-step explanation:

do the math and u get ur answer

3 0
3 years ago
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