Which number(s) below belong to the solution set of the inequality? Check all
that apply.
X+ 30 < 60
A. 30
B. 45
C. 1
D. 50
E 300
F 29

Answer:

400 ft^2

Step-by-step explanation:

It can be shown that a square area is the most efficient way in which to use fencing.  If the area is not square, the area will inevitably be smaller.  

Calculus is the tool most often used in higher math to solve optimization problems.  

But the same goal can be achieved in this problem by working with constraints:  

If x and y are the length and width respectively, then

2x + 2y = 80 ft, or x + y = 40, or x = 40 - y.  This is one constraint.  

The other constraint involves the area:  A = x*y, or A = (40 - y)*y.  To maximize this, we need to rewrite (40 - y)*y in standard form:

A = 40y - y^2, or, finally, A = -y^2 + 40 y.  The coefficients of this quadratic are -1, 40 and 0; the axis of symmetry is thus

x = -b/ [2a], or, in this case, x = -40/[2*(-1)], or x = 20.

Thus, If x = 20, y = 20 also, proving that the shape of the enclosed yard is that of a square.

Then Mrs. L' 80 feet of fencing is sufficient to construct a 20 ft by 20 ft space, which comes out to a maximum area of 400 ft^2.

40 -

Answer:

Answer:

Check the text of the exercise, there is something wrong

Step-by-step explanation:

y=10x-4

y=-2x+10

These are two stright lines, they meet in one point only, P(7/6, 23/3)

Answer:

y = 3x - 30

Step-by-step explanation:

First, put both equations into slope-intercept form.

x + 3y - 4 = 0

3y = -x + 4

y = (-1/3)x + (4/3)

2x + 5y - 20 = 0

5y = -2x + 20

y = (-2/5)x + 4

For a line to be perpendicular to y = (-1/3)x + (4/3), its slope should be the opposite and reciprocal of this line's slope.

The slope of y = (-1/3)x + (4/3) is (-1/3). The slope of a perpendicular line is 3.

To find the x-intercept of y = (-2/5)x + 4, plug in 0 for y and find x.

0 = (-2/5)x + 4

x = 10

The equation of the line right now is y = 3x + b

Plug in (10, 0) to find the y-intercept.

0 = 3(10) + b

b = -30

The equation of the line is y = 3x - 30

Answer:

12y

Step-by-step explanation:

Answer: 251.2 inches.

Step-by-step explanation: You have to multiply 4*2*π*radius. So, simply multiply 4*2*3.14*10. It would come out as 251.2 inches.

Answer:

13

Step-by-step explanation:

it just 13$ so yeah your welcome

Answer:

12.8

Step-by-step explanation:

Look at the zero in the end (hundreths place). Since it is zero keep everything the same!

If it is higher than 5, round up

If it is 5 or below round down.

0 is special because you can just keep everything the same.

Hope this helps!

Answer:

in this form, the "-r" would cause the result to decrease

I assume that the answer is "r"

if r = .1 (10 %) then 1-.1 = .9

if you have 100 items then y = 100(.9)^1 = 90

the total decreased by 10% ... y = 100(.9)^2 after 2 time periods

Step-by-step explanation:

Answer:

[tex]9\frac{3}{5}[/tex]

Step-by-step explanation:

3 3/4 = 15/4

[tex]\frac{36}{1}[/tex] ÷ [tex]\frac{15}{4}=[/tex]

[tex]\frac{36}{1} *\frac{4}{15}=[/tex]

[tex]\frac{12}{1} *\frac{4}{5}=[/tex]

[tex]=\frac{48}{5}[/tex]

[tex]=9\frac{3}{5}[/tex]

Hope this helps

The equation of red graph is [tex]F(x) = 2 -x^{2}[/tex].

The general equation of parabola is [tex]y = a(x-h)^{2} + k[/tex].

Where,

(h, k) are the vertices of the parabola.

According to the given question.

We have two graph.

The blue and red graph both represents the equation of downward parabola.

Since, blue graph represents the equation of downward parabola.

Whose equation is given

[tex]G(x) = 5 - x^{2}..(i)[/tex]

The general equation of a parabola is [tex]y = a(x-h)^{2} + k..(ii)[/tex]

Where, (h, k) are the vertices of the parabola.

Compare the equation (i) with (ii)

We get

(h, k) = (0, 5) and a = -1.

Now, the red graph which also represents the downward parabola whose vertices are (0, 2)

Therefore, the equation red graph is given by

[tex]F(x) = a(x-0)^{2} + 2[/tex]

⇒ [tex]F(x) = -1(x-0)^{2} + 2[/tex]

⇒ [tex]F(x) = 2 - x^{2}[/tex]

Hence, the equation of red graph is [tex]F(x) = 2 -x^{2}[/tex].

Find out more information about equation of parabola here:

https://brainly.com/question/4074088

#SPJ3

Answer:

[tex](q,p)=(1.948,4.156)[/tex]

Step-by-step explanation:

Given

[tex]p^2 - \frac{1}{3}q-4p=0[/tex] --- demand curve

[tex]2q + 8p -4p^3=2p^2[/tex] ------ supply curve

Required

The equilibrium point

To do this, we make use of the graphical method (see attachment for the demand and supply curve)

The points of intersection of both curves on the attached plot are:

[tex](q_1,p_1)=(1.948,4.156)[/tex]

[tex](q_2,p_2)=(0,0)[/tex]

[tex](q_3,p_3)=(-0.8766,0.0744)[/tex]

[tex](q_3,p_3)=(0.3802,-0.0314)[/tex]

Of the 4 points, only the points where [tex]p,q>0[/tex] can be selected as equilibrium points

The only point that satisfies this condition is:

[tex](q_1,p_1)=(1.948,4.156)[/tex]

Hence, the equilibrium points of the airline is: [tex](q,p)=(1.948,4.156)[/tex]

Answer:

you can do it

Step-by-step explanation:

by using your brain

Answer:

4z²+4z-15 Square Metre  

Step-by-step explanation:

According To The Question,

Area Of Garden = Length × Breadth

Area Of Garden = (2z+5) × (2z-3)

Area Of Garden = 4z²-6z+10z-15

Area Of Garden=4z²+4z-15 Square Metre

Answer:

(15+6)÷3

hope it helps!!

Answer:

(x+y)+2

hope this helps

Answer:

-2< x< 8

Step-by-step explanation:

|x-3|<5 <=> -5<x-3<5 <=> -2<x<8

..

Answer:

-2x<8

Step-by-step explanation:

|x-3|<5<=> -5<x-3<5 <=>-2<x<8

.....

Given:

Principal value = $2300

Rate of interest = 14% compounded continuously.

To find:

The time taken by Brad's investment to triple.

Solution:

The formula for amount after the compound interest (Continuously) is:

[tex]A=Pe^{rt}[/tex]

Where, P is the principal, r is the rate of interest in decimal and t is the time period.

Triple of Brad's investment is

[tex]3\times \$ 2300=\$ 6900[/tex]

Substituting [tex]A=6900,P=2300\ r=0.14[/tex], we get

[tex]6900=2300e^{0.14t}[/tex]

[tex]\dfrac{6900}{2300}=e^{0.14t}[/tex]

[tex]3=e^{0.14t}[/tex]

Taking natural log on both sides, we get

[tex]\ln 3=\ln e^{0.14t}[/tex]

[tex]1.0986=0.14t[/tex]                [tex][\because \ln e^x=x][/tex]

[tex]\dfrac{1.0986}{0.14}=t[/tex]

[tex]7.84714=t[/tex]

After approximating the value, we get

[tex]t\approx 7.85[/tex]

Therefore, Brad's investment will take 7.85 years to triple.

Answer:

$240

Step-by-step explanation:

They spend 5% of their monthly income on transportation, so you want to work out 5% of 4800.

An easy trick with 5% is to divide by 10 (drop the ending 0) and then divide by 2. This would be 4800/10/2, or 480/2, which gives 240.

**This content involves using percentages which you may wish to revise.

Answer:

69.825

Step-by-step explanation:

Answer:

The first one is B. 11.75

The second one is A. 4

Step-by-step explanation:

In order to find how many liters (L) of paint he used you need to do 2.5*5.5=13.75 Then to find out how much he has left you do 25-13.75=11.75 So your answer is 11.75.

The second one you have to do the reverse. So since it says 4*_=48, you do 48÷4=_=12. Then since it says 12*1/3=_ You can do 12÷3=_=4 So your answer is 4.

Answer:

54,280

Step-by-step explanation:

In Pic

Answer:

Associative property

Step-by-step explanation:

The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.

Hope this helps

Answer:

24

Step-by-step explanation:

4 times 4

8 times 8

Subtract the 2 #'s

Then divide your answer by 2.

Step-by-step explanation:

use Pythagoras theorem

hypotenuse² = base² + height²

8²=base²+4²

64-16=B²

√48=B

√2×3×2×2×2=B

2×2√3

4√3 = B

hope it helps

Answer:

-1 is the only number there that is an integer as all the rest of them are mixed fractions.

Answer:

- 1

Step-by-step explanation:

Answers:

The total profit expression is a binomial.

The total profit expression is a polynomial.

The total profit expression has a constant term.

The total profit expression is a polynomial

The total profit expression is a binomial

The total profit expression has a constant term

The first step to determining which type of function it is, is to add the profits in both theatres together

(t³ - t² + 2t - 100) + (t² - 2t - 300) = t³ - 400

A polynomial function is a mathematical expression that is made up of different types of variables. They include non-zero coefficients, positive exponents, and constants.

Types of polynomials include :

1. Linear polynomial function : a linear function is a function that has a single variable raised to the power of 1.

An example is x + 2

The variable x is raised to the power of 1. 2 is the constant terms

2.  Quadratic polynomial function - A quadratic function is a function that usually has a single variable and it is raised to the power of 2.

An example is 2x² + 10x + 25

3. Cubic polynomial function : this is a function that usually has a single variable raised to the power of 3.

An example is 5y³ + y²

4. Binominal function: this  is a function that contains only two terms.

An example is   t³ - 400

t³ - 400

The above equation of the total profit has a constant term which is -400

The above equation is a polynomial. This is because it has different types of variables.

The above equation is a binomial equation because it has only two terms  t³ and 400

In order to determine the type of expression the total profit is, the first step is to add the two profit expressions provided in the question. Based on the expression derived, the type of expression it is can then be deduced.

To learn more about polynomials, please check: https://brainly.com/question/17822016?referrer=searchResults

Answer:

The solution to the system is (-2,6)

Step-by-step explanation:

I said the solution to the system is (-2,6) because that is where both lines cross, meaning that's the solution.

Hope this is hepful.

Answer:

Option (1)

Step-by-step explanation:

We have to graph the system of inequalities given.

y > 2x + 1 -----(1)

y > |x| --------(2)

For inequality (1),

Solution area will be the area above the dotted line y = 2x + 1

Similarly, solution area of the second inequality will be the area above the dotted lines of y = |x|

Solution area of the system of inequalities will be the common area of both the graphs of the given system.

That will lie in quadrants 1 and 2.

Option (1) will be the answer.

Answer:

the answer is a 18 as 60 percent of 30 is 18

hope it helps

Answer:

Ax+By=C

Step-by-step explanation:

basically the standard form of any linear equation, y=mx+b. y is the y coordinate, m is the slope, x is the x coordinate, and b is the y-intercept (where x is 0 on the line).