MATHEMATICS HIGH SCHOOL

A carpenter added a diagonal brace to gate. The gate is 8ft. Wide and 10 ft. Tall. How long is the brace

Answers

Answer 1
Answer:

Answer:

The brace is 2√(41) ft ≅ 12.806 ft long

Step-by-step explanation:

The length of the diagonal of a rectangle can be found using this rule

d=\sqrt{l^(2)+w^(2)} , where

  • l is its length
  • w is its width

∵ The gate has shaped a rectangle

∵ Its length = 10 ft

∵ Its width = 8 ft

∴ l = 10 and w = 8

∵ The brace is the diagonal

→ By using the rule above

∴ d=\sqrt{(10)^(2)+(8)^(2)}=√(100+64)=√(164)

∴ The length of the brace = 2√(41) ≅ 12.806 ft

∴ The brace is 2√(41) ≅12.806 ft long

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Goran made 6 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 6 necklaces was $33.60 . If the beads cost $2.90 for each necklace, how much did each pendant cost?

Answers

2.90*6=17.40
33.60-17.40=$16.20
16.20/6=$4.05

Mark and Nora both work at the same pet store. The inequality y less than or equal too 2x relates x, the number of hours Mark works each week, and y, the number of hours that Nora works. Which ordered pair must be included in the solution set of the inequality when interpreted in the context of the problem? please help(–7, 20)
(0, 0)
(8, 2)
(13, –28)

Answers

Answer:

y≤2x

Step-by-step explanation:

answer in comments

Raphael paid $652 for a camera during a 20% off sale. What was the camera's regular price? Please work the problem and show your work so I can understand it better.

Answers

The price the Rafael paid for the camera is 652 dollars which already has a discount which is 20%.
There are a lot of ways to solve it, however, I'll show you the easiest way.
=> 652 dollars is the 80% of the price since it lessen by 20%
=> 652 / 8 = 81.5 is the 10% of the price.
=> 81.5 * 10 = 815 dollars is the original price of the camera.

Write "P (x) = -36x^2 + 900x - 1584" in standard vertex form, help please!

Answers

y = a(x – h)2 + k, where (h, k) is the vertex;

in our case, P(x) = a(x + b/2a)^(2) - Δ/4a ;

a = -36; b = 900; c = -1584;

b/2a = 900/-72 = -12.5;

Δ = b^(2) - 4ac = 810000 - 144*1584 = 581904 => -Δ/4a = 4041;

P(x) = (-36)(x - 12.5)^2 + 4041, where (12.5 , 4041) is the vertex;

Answer:

y = a(x – h)2 + k, where (h, k) is the vertex;

in our case, P(x) = a Δ/4a ;

a = -36; b = 900; c = -1584;

b/2a = 900/-72 = -12.5;

Δ =  4ac = 810000 - 144*1584 = 581904 => -Δ/4a = 4041;

P(x) = (-36)(x - 12.5)^2 + 4041, where (12.5 , 4041) is the vertex;

For each number, name its opposite. a. -5 b. 28 c. -10.4 d. 0.875 e. 0 f. -8,003 answer as soon as possible

Answers

Answer:

5, -28, 10.4, -.875, 0, 8003

Step-by-step explanation:

ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)

Answers

we have that
Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2)
y - 3x = – 8-----> y=3x-8------> the slope m=3

we know that
if two lines are perpendicular 
then
m1*m2=-1
m1=3
so
m2=-1/3

with m=-1/3 and point (3, 2) find the equation of the line
y=mx+b
2=(-1/3)*3+b------> 2=-1+b-----> b=3

the equation of the line is
y=(-1/3)x+3

the answer is
y=(-1/3)x+3

see the attached figure
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