What is the solution for
8y ≥ 56

Answer:

x = 20√2 ft and y = 40/√2 ft

Step-by-step explanation:

Let; x = length of steel fencing

y = length of a wood fence that is perpendicular to the store

Thus, since area is 800 ft², then;

xy = 800

Length of fence; L = x + 2y

From earlier, xy = 800

y = 800/x

Thus;

L = x + 2(800/x)

L = x + 1600/x

Now, steel fencing costing $6 per foot and the other two sides will be constructed with wood fencing costing $3 per foot. Thus, total cost is;

C(x) = 6x + 3(2y)

But y = 800/x. Thus;

C(x) = 6x + 3(1600/x))

C(x) = 6x + 4800/x

C'(x) = 6 - 4800/x²

At C'(x) = 0, the cost is minimized.

Thus=

6 - 4800/x² = 0

6x² = 4800

x² = 4800/6

x² = 800

x = √800

x = 20√2

When 0 < x < 20√2, C'(x) < 0, so we say that C(x) is decreasing

When x > 20√2, C'(x) > 0, so we say that C(x) is increasing

Thus, the cost is minimized when x = 20√2

Thus, putting 20√2 for x in y = 800/x, we have;

y = 800/(20√2)

y = 40/√2

Thus, dimensions that will minimize cost are;

x = 20√2 ft and y = 40/√2 ft

Answer:

P1.H.x²+y²=34

centre[h,k]=(0,0)

point=[3,5]

now

radius=[tex]\sqrt{(0-3)²+(0-5)²}=\sqrt{34}[/tex]

now

equation of a circle is;

(x-h)²+(y-k)²=[tex]\sqrt{34}²[/tex]

x²+y²=34

P:2I.(x-6)²+(y+7)²=121

centre[h,k]=(6,-7)

diameter=22

radius[r]=22/2=11

now

equation of a circle is;

(x-h)²+(y-k)²=r²

(x-6)²+(y+7)²=11²

(x-6)²+(y+7)²=121

Answer:

x = 89

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

x+32+ 59 = 180

Combine like terms

x + 91 = 180

Subtract 91 from each side

x +91-91= 180-91

x = 89

Answer:

Step-by-step explanation:

L : y = -4x + 3

with a slope of -4.

Any line perpendicular to L will have a slope m such that

m ( -4) = -1, or m = 1/4

Any line perpendicular to L passing through point (a,b) will therefore have the form

P : (y-b) = (x-a)/4

When (a,b) = (8,1) as given, then substitute in P to get

P : (y-1) = (x-8)/4

y=x/4 -2 + 1

y = x/4 -1

Answer:

[tex]-\frac{3}{x} + \frac{7y}{x} = \frac{-3+ 7y}{x}[/tex]

Step-by-step explanation:

Given

[tex]-\frac{3}{x} , \frac{7y}{x}[/tex]

Required

Add

The statement can be interpreted as:

[tex]-\frac{3}{x} + \frac{7y}{x}[/tex]

Take LCM

[tex]-\frac{3}{x} + \frac{7y}{x} = \frac{-3+ 7y}{x}[/tex]

Answer:

x ≥ 40

Step-by-step explanation:

3x - 55 ≥ 65

combine like terms

3x  ≥ 65 + 55

3x  ≥120

divide both sides of the equation by 3

x  ≥ 40

Answer:i dont know

Step-by-step explanation:lol

Answer:

tmabm queria saber

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Francis borrowed 20$ and gives his dad 8$ he owes 12$ I hope it helps :)

Answer:

D. 2.33.

Step-by-step explanation:

Given;

the weight distribution of the bottles = 4, 2, 5, 4, 5, 2, and 6

sum of the weights = 28

the mean (x) = 28/7

                 x = 4

the sum of square of the mean deviation is calculated as:

= (4 - 4)² + (2 - 4)² + (5 - 4)² + (4 - 4)² + (5 - 4)² + (2 - 4)² + (6 - 4)²

= 0 + 4 + 1 + 0 + 1  + 4 + 4

= 14

[tex]the \ variance \ is \ calculated \ as:\\\\\sigma ^2 = \frac{\sum (x-\bar x)^2}{n-1} \\\\\sigma ^2 = \frac{14}{7-1} = \frac{14}{6} = 2.33[/tex]

Therefore, the correct answer is D

Answer:

where is the question

Step-by-step explanation:

send question

Answer:

The answer is B: 67/10x + 9

Step-by-step explanation:

I did the test

Answer:

[tex]\frac{1}{3}x-3=-x+1[/tex]

Step-by-step explanation:

Since there are plenty of lines that can pass through a single point, he only way to solve this question is by substituting values of [tex]3[/tex] into each equation and seeing if both equations return a value of [tex]-2[/tex].

Starting with the first answer choice:

[tex]-\frac{1}{3}(3)+3=3-1,\\-1+3=3-1,\\2=2[/tex]

Since none of the equations here return a value of [tex]-2[/tex], the correct answer must not include [tex]-\frac{1}{3}x+3[/tex] or [tex]x-1[/tex].

Thus, we can eliminate answer choices A, C, and D, hence the correct answer is [tex]\boxed{\text{B. }\frac{1}{3}x-3=-x+1}[/tex]

Answer:  B is the correct answer.

Answer:

so we have to use the formula 4/3PiR^3

which if we do we get the volume of

V≈97478.08

Answer:

V≈97478.08cm³

Step-by-step explanation:

Using the formulas

V=4/3πr3

d=2r

V=1/6πd3

D=1

1/6·πd3 1/6π ·57.13≈97478.07565cm³

I hope this helps. I worked hard on this one.

Answer:

B) 8 and 24.

Step-by-step explanation:

Just by looking at the answer choices, since one number must be three times the other, we can determine that the correct answer is B.

Regardless, let's work this out mathematically. Let the first number be a and the second number be b.

Their difference is 16. Hence:

[tex]a-b=16[/tex]

The first number is three times the second number. So:

[tex]a=3b[/tex]

Substitute:

[tex]3b-b=16[/tex]

Solve for b. Subtract:

[tex]2b=16[/tex]

And divide both sides by two:

[tex]b=8[/tex]

So, the second number is 8.

And since the first number is three times the second, the first number is 24.

Our answer is B as expected.

Answer:

bottle top

Step-by-step explanation:

Step-by-step explanation:

-5(4)+2

-20+2

-18

just put 4 on the place of x

Answer:

[tex]=-18[/tex]

Step-by-step explanation:

[tex]g(x)=-5x+2[/tex]

Let's substitute 4 for x and solve.

[tex]g(4)=-5(4)+2[/tex]

[tex]g(4)=-20+2[/tex]

[tex]g(4)=-18[/tex]

This means that when the function of [tex]g[/tex] is 4, then the [tex]x[/tex] value is [tex]-18[/tex]

Hope this helps.

Answer:

52,047.96

Step-by-step explanation:

Answer:

The answer is 30/10

Step-by-step explanation:

30 divided by 10 is 3.

Answer:

126 cm^3

Step-by-step explanation:

Use volume formula (Bh=V): 21×6=126

The volume of the pentagonal prism is 126 cm³

Pentagonal prism has two pentagonal bases, top and bottom and five rectangular sides.

Volume of the pentagonal prism = Area of the pentagon• height of the prism

Given:

Area of the pentagon = 21 cm²

Height of the prism = 6 cm

The volume of pentagonal prism = Area of the pentagon * Height of the prism

The volume of pentagonal prism = 21 cm² × 6 cm = 126 cm³

Therefore, the volume of pentagonal prism is 126 cm³

Learn more about the volume of pentagonal prism here:

https://brainly.com/question/31028600

#SPJ6

Answer:

[tex] \rm \displaystyle y _{ \rm tangent} = - \frac{8}{5} x - \frac{5}{2} a[/tex]

[tex] \rm \displaystyle y _{ \rm normal} = \frac{5}{8} x - \frac{765}{128} a[/tex]

Step-by-step explanation:

we are given a equation of parabola and we want to find the equation of tangent and normal lines of the Parabola

finding the tangent line

equation of a line given by:

[tex] \displaystyle y = mx + b[/tex]

where:

to find m take derivative In both sides of the equation of parabola

[tex] \displaystyle \frac{d}{dx} {y}^{2} = \frac{d}{dx} 16ax [/tex]

[tex] \displaystyle 2y\frac{dy}{dx}= 16a[/tex]

divide both sides by 2y:

[tex] \displaystyle \frac{dy}{dx}= \frac{16a}{2y}[/tex]

substitute the given value of y:

[tex] \displaystyle \frac{dy}{dx}= \frac{16a}{2( - 5a)}[/tex]

simplify:

[tex] \displaystyle \frac{dy}{dx}= - \frac{8}{5}[/tex]

therefore

[tex] \displaystyle m_{ \rm tangent} = - \frac{8}{5}[/tex]

now we need to figure out the x coordinate to do so we can use the Parabola equation

[tex] \displaystyle ( - 5a {)}^{2} = 16ax [/tex]

simplify:

[tex] \displaystyle x = \frac{25}{16} a[/tex]

we'll use point-slope form of linear equation to get the equation and to get so substitute what we got

[tex] \rm \displaystyle y - ( - 5a)= - \frac{8}{5} (x - \frac{25}{16} a)[/tex]

simplify which yields:

[tex] \rm \displaystyle y = - \frac{8}{5} x - \frac{5}{2} a[/tex]

finding the equation of the normal line

normal line has negative reciprocal slope of tangent line therefore

[tex] \displaystyle m_{ \rm normal} = \frac{5}{8}[/tex]

once again we'll use point-slope form of linear equation to get the equation and to get so substitute what we got

[tex] \rm \displaystyle y - ( - 5a)= \frac{5}{8} (x - \frac{25}{16} a)[/tex]

simplify which yields:

[tex] \rm \displaystyle y = \frac{5}{8} x - \frac{765}{128} a[/tex]

and we're done!

( please note that "a" can't be specified and for any value of "a" the equations fulfill the conditions)

Answer:

In attachment

Step-by-step explanation:

For answer refer to attachment .

Answer:583

Step-by-step explanation:

I took the test

Answer:

The answer is [tex]t\geq 20[/tex].

Step-by-step explanation:

To solve the inequality, start by solving for the variable [tex]t[/tex].

To solve for the variable [tex]t[/tex], subtract [tex]3.5t[/tex] from both sides. The inequality will look like [tex]6.5t\geq 130[/tex].

Then, divide both sides by 6.5 in order to get the variable [tex]t[/tex] by itself. The inequality answer will look like [tex]t\geq 20[/tex].

Answer:

[tex]y(t) =10t[/tex]

Step-by-step explanation:

The summary of the given parameters are:

[tex]a = 0[/tex] --- initial savings

[tex]m = 10[/tex] --- monthly savings

[tex]t \to[/tex] months

Required

The linear function

The linear function is calculated using:

y(t) = Initial Savings + Monthly Savings * Months

So, we have:

[tex]y(t) =a + m*t[/tex]

[tex]y(t) =0 + 10*t[/tex]

[tex]y(t) =10t[/tex]

Answer: Hello the options related to this question is missing below are the missing options

A. Themes

B. Excerpts

C. Descriptors

D. Codes

answer:

Descriptors

Step-by-step explanation:

Descriptors is a piece of data used to describe how other data are to be stored or stored. they are very necessary in Dedoose for producing mixed methods research

while a mixed method research is a type of research that uses past research data. using all possible ways

Answer:

75

Step-by-step explanation:

this problem statement tries to confuse us. there is no pi involved - also because there are no round surfaces and edges involved.

what do you think the surface area of such a 4-sided pyramid consists of ?

think !

there are the 4 walls or sides. and then there is the bottom too (if you lift the pyramid up, yes, the "floor" or bottom also belongs to the surface area).

each "wall" or side is actually a triangle.

and the bottom is a square.

what is the area of a triangle (At) ?

At = base length × height / 2 = 3×11/2 = 33/2 in²

what is the area of a square (As) ?

it is a special form of a rectangle, where length = width.

the area of a rectangle (Ar) = length × width.

and the area of a square (As), where length = width is

As = side length × side length = length² = 3² = 9 in²

our pyramid now has 4 "walls", all of the same size, so we need 4 times the area of such a single triangle.

and then add the bottom area.

=> the pyramid surface area (Ap) is

Ap = 4 × At + As = 4×33/2 + 9 = 132/2 + 9 = 66+9 = 75 in²

Answer:

48

Step-by-step explanation:

16×3=48

therefore the answer is forty eight

Answer:

np

Step-by-step explanation:

3.14(rs + r2)

3.14 (r= 2 x s= 3 + r =2 x 2)

3.14 ( 6+4)

3.14 (10)

3.14 x 10 = 31.4 units ² I guess

Answer:

9

Step-by-step explanation:

the 2 angles create a right angle ( indicated by the little square.)

right angles have a measure of 90 degrees

hence, 90 = 72 + 2x

( note that we just created an equation that we can use to solve for x )

we now solve for x using the equation we created.

90 = 72 + 2x

step 1 subtract 72 from each side

90 - 72 = 18

72 - 72 cancels out

we now have 18 = 2x

step 2 divide each side by 2

18 / 2 = 9

2x / 2 = x

we're left with x = 9