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Lemur [1.5K]
3 years ago
13

Two architects bid for a small government project, both

Mathematics
1 answer:
blondinia [14]3 years ago
4 0

Answer:

10 hours

Step-by-step explanation:

let x be the total number of hours

Amazing design total charge = 45x+250

super structures total charge = 60x+100

both companies charge the same amount when both equation equals

45x+250=60x+100

60x-45x=250-100

15x=150

x=10

therefore at 10 hours both companies will charge the same amount

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In Triangle BCD, BC=BD, and angle B =13x-35, angle C = 5x-19, angle D=2x+14. Find the measure of each angle
aleksandr82 [10.1K]

Answer:

B = 108

C = 36

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Step-by-step explanation:

Given

B =13x - 35

C = 5x - 19

D=2x+14

BC = BD

Required

Determine the measure of each angle

The angles in a triangle sum up t 180. i.e.

B + C + D = 180

Since BC = BD, then C = D

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B + C + C = 180

B + 2C = 180

Substitute values for B and C

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Open Bracket

13x - 35 + 10x - 38 = 180

Collect Like Terms

13x + 10x = 180 + 38 + 35

23x= 253

Divide both sides by 23

x = 11

To get the measure of each angle, substitute 11 for x in the expressions of B, C and D

B =13x - 35

B = 13 * 11 - 35

B = 108

C = 5x - 19

C = 5 * 11 - 19

C = 36

D=2x+14

D = 2 * 11 + 14

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5 0
3 years ago
A parabola has its focus at (1,2) and its directrix is y = −2. The equation of this parabola could be...?
Rudik [331]

9514 1404 393

Answer:

  y =1/8(x -1)^2

Step-by-step explanation:

The vertex is halfway between the focus and directrix, so has y-coordinate (2-2)/2 = 0. The x-coordinate of the vertex is the same as that of the focus. The focus-vertex distance (p) is 2-0 = 2. Where the vertex is (h, k), the equation is ...

  y = 1/(4p)(x -h)^2 +k

For p=2, (h, k) = (1, 0), the equation of the parabola is ...

  y = 1/8(x -1)^2

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3 years ago
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