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3 years ago

Which value is a solution of the inequalityx∕5 + 2 ≤ 6?

Mathematics

2 answers:

avanturin [10]3 years ago

6 0

Answer:

Step-by-step explanation

the answer comes to $x\leq 20$ and 15 is the only answer below 20

Burka [1]3 years ago

5 0

Answer:

B. x = 15

Step-by-step explanation:

Firstly we simplify the inequality, so we have x on the left side, and every number on the right side
$\frac{x}{5}+2\leq 6\\ \frac{x}{5}+2-(2)\leq 6-(2)$ so we take away 2 on both sides
$\frac{x}{5}\leq 4$ now this is the same as $\frac{1}{5}*x\leq 4$
Now we multiply by 5 on both sides
$5*\frac{1}{5}*x\leq 5*4$ which is $\frac{5}{5}*x \leq 20$ which is simply $x \leq 20$ since 5 divide by 5 is 1 and 1 times x is x
So the inequality $x \leq 20$ means "every number for x that is less than or equal to 20"
Now from the list, the only number that fits is 15. So that's our answer

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3 times the sum of a number and 4

Lyrx [107]

Answer:

3(4+x)

which can be simplified to 12+3x

4 0

3 years ago

Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t i

bixtya [17]

Answer:

length of the curve = 8

Step-by-step explanation:

Given parametric equations are x = t + sin(t) and y = cos(t) and given interval is

−π ≤ t ≤ π

Given data the arrow the direction in which the curve is traces means

the length of the curve of the given parametric equations.

The formula of length of the curve is

$\int\limits^a_b {\sqrt{\frac{(dx}{dt}) ^{2}+(\frac{dy}{dt}) ^2 } } \, dx$

Given limits values are −π ≤ t ≤ π

x = t + sin(t) ...….. (1)

y = cos(t).......(2)

differentiating equation (1) with respective to 'x'

$\frac{dx}{dt} = 1+cost$

differentiating equation (2) with respective to 'y'

$\frac{dy}{dt} = -sint$

The length of curve is

$\int\limits^\pi_\pi {\sqrt{(1+cost)^{2}+(-sint)^2 } } \, dt$

$\int\limits^\pi_\pi \, {\sqrt{(1+cost)^{2}+2cost+(sint)^2 } } \, dt$

on simplification , we get

here using sin^2(t) +cos^2(t) =1 and after simplification , we get

$\int\limits^\pi_\pi \, {\sqrt{(2+2cost } } \, dt$

$\sqrt{2} \int\limits^\pi_\pi \, {\sqrt{(1+1cost } } \, dt$

again using formula, 1+cost = 2cos^2(t/2)

$\sqrt{2} \int\limits^\pi _\pi {\sqrt{2cos^2\frac{t}{2} } } \, dt$

Taking common $\sqrt{2}$ we get ,

$\sqrt{2}\sqrt{2} \int\limits^\pi _\pi ( {\sqrt{cos^2\frac{t}{2} } } \, dt$

$2(\int\limits^\pi _\pi {cos\frac{t}{2} } \, dt$

$2(\frac{sin(\frac{t}{2} }{\frac{t}{2} } )^{\pi } _{-\pi }$

length of curve = $4(sin(\frac{\pi }{2} )- sin(\frac{-\pi }{2} ))$

length of the curve is = 4(1+1) = 8

conclusion:-

The arrow of the direction or the length of curve = 8

7 0

3 years ago

Jared is going to plant 20 small plants around the edge of a circular garden that is 8 feet in diameter. If he spaces the plants

Hatshy [7]

Answer:

The space between the plants is approximately 1.26ft

Step-by-step explanation:

Given

Circular Garden

Number of plants = 20

Diameter of garden = 8ft

First, the circumference of the garden needs to be calculated; This is so because the plants that will be placed at the edge of the garden will occupy the circumference of the circle.

Calculating the circumference....

Circumference = 2πr

Where r = radius

r = ½ * diameter.

r = ½ * 8ft

r = 4ft

So,

Circumference = 2π * 4

Circumference = 8π ft

Given that the plants will be spaced evenly.

The distance between them = Circumference ÷ Number of plants

Distance = 8π/20

Distance = 0.4π ft.

Solving further to get actual distance (take π as 22/7)

Distance = 0.4 * 22/7

Distance = 8.8/7

Distance = 1.2571428571 ft

Distance = 1.26ft (Approximated)

Hence, the space between the plants is approximately 1.26ft

3 0

3 years ago

The composite figure is made up of three simpler shapes. What is the area of the figure?

Flauer [41]

4 × 3
−−−− = 6cm²
2

6 × 3 = 18cm²

10 × 5 = 50cm²

50 + 18 + 6 = 72cm²

7 0

2 years ago

Read 2 more answers

5. Solve the system of equations. 2x+3y=0 x-2y=-7 1-5y =

ra1l [238]

-9 is the answer to this equation

6 0

3 years ago