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Alina [70]
4 years ago
9

Brainliest! Fill in the blank with an appropriate inequality sign.

Mathematics
1 answer:
Maslowich4 years ago
7 0
A x-3 < 4
b 3x ≤ 21
c -3x ≤ -18
d -x > 6
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A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the rectangle is the intersection
svet-max [94.6K]

Answer:

x  =  2  cm

y  = 2  cm

A(max) =  4 cm²

Step-by-step explanation: See Annex

The right isosceles triangle has two 45° angles and the right angle.

tan 45°  =  1  =  x / 4 - y        or     x  =  4  -  y     y  =  4  -  x

A(r)  =  x* y

Area of the rectangle as a function of x

A(x)  =  x  *  (  4  -  x )       A(x)  =  4*x  -  x²

Tacking derivatives on both sides of the equation:

A´(x)  =  4 - 2*x             A´(x)  =  0            4   -  2*x  =  0

2*x  =  4

x  =  2  cm

And  y  =  4  - 2  =  2  cm

The rectangle of maximum area result to be a square of side 2 cm

A(max)  = 2*2  =  4 cm²

To find out if A(x) has a maximum in the point  x  =  2

We get the second derivative

A´´(x)  =  -2           A´´(x)  <  0   then A(x) has a maximum at  x = 2

5 0
3 years ago
A gym employee is paid monthly.after working for 3 months he had earned $4,500. To determine how much money he will make over a
Soloha48 [4]
He would make $9,000 in 6 months
6 0
3 years ago
One Step Equations<br> solve for x <br><br> 2.4+x=9.8
Simora [160]

Answer:

x=7.4

Step-by-step explanation:

2.4+x=9.8

(x=9.8-2.4)

x=7.4

7 0
3 years ago
Read 2 more answers
Solve the system of equations algebraically.
andrew11 [14]

Answer: d. (17, 20)

Step-by-step explanation:

We have the following system of equations:

x-3y=8 (1)

5x-4y=5 (2)

Isolating x from (1):

x=\frac{8+3y}{4} (3)

Substituting (3) in (2):

5(\frac{8+3y}{4})-4y=5 (4)

Isolating y:

\frac{40}{4}+\frac{15 y}{4}-4y=5 (5)

10-5=4y-\frac{15 y}{4} (6)

y=20 (7)

Substituting (7) in (1):

x-3(20)=8 (8)

Isolating x:

x=17 (9)

Hence, the correct option is d. (17, 20)

8 0
3 years ago
Which graph below shows the solutions for the linear inequality ys x-3?
liraira [26]

Answer:

Graph A.

Step-by-step explanation:

Given the inequality: y\leq \dfrac{1}{4}x-3

Since the sign is "less than or equal to", the line cannot be dotted. Therefore, Options C and D are incorrect.

Since the sign is a "less than" sign, the required region must be below the line. Therefore, the graph which shows the given inequality is Graph A.

4 0
3 years ago
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