Charlene is knitting a baby blanket. She wants its width, w, to be at least half its length, l. She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches. The system of inequalities shown represents the width of the blanket in inches, w, and the length in inches, l.

w ≥ 0.5l

2l + 2w ≤ 180

What is the maximum length possible for her blanket?

30 inches
45 inches
60 inches
90 inches

Answer:

Given That:

[tex]{ \large\longrightarrow { \rm{z = {x}^{2} + {y}^{2} }}}[/tex]

Partial differentiating both sides with respect to x, we get:

[tex]{ \large\longrightarrow { \rm{ \frac{∂z}{∂x} = 2x}}}[/tex]

Partial differentiating again with respect to x, we get:

[tex]{ \large\longrightarrow {{ \rm{ \frac{ {∂}^{2}z }{∂ {x}^{2} } \: = 2 \: \: \: \: \quad -(i) }}}}[/tex]

Consider again:

[tex]{ \large\longrightarrow {{ \rm{ z = {x}^{2} + {y}^{2} }}}}[/tex]

Partial differentiating both sides with respect to y, we get:

[tex]{ \large\longrightarrow { { \rm{ \frac{∂z}{∂y} = 2y}}}}[/tex]

Now, partial differentiating both sides with respect to x, we get:

[tex]{ \large\longrightarrow{ \rm{ \frac{ {∂}^{2}z }{∂x \:∂y } = 0 \: \: \: \quad - (ii) }}}[/tex]

Consider again:

[tex]{ \large\longrightarrow { \rm{ \frac{∂z}{∂y} = 2y}}}[/tex]

Partial differentiating both sides with respect to y, we get:

[tex]{ \large\longrightarrow{ \rm{ \frac{ {∂}^{2}z }{∂ {y}^{2} } = 2 \: \: \: \: \: \quad - (iii) }}}[/tex]

Now, consider Left Hand Side, we get:

[tex]{ \large{ \rm{ \longrightarrow {x}^{2} \frac{ {∂}^{2}z }{∂ {x}^{2} } + 2xy \frac{ {∂}^{2} x}{∂x \:∂y } + {y}^{2} \frac{ {∂}^{2}z }{∂ {y}^{2} } }}}[/tex]

From Equation (i),(ii) and (iii), we can write:

[tex]\longrightarrow{ \large{ \rm{ {2x}^{2} + 0 + {2y}^{2} }}}[/tex]

[tex]\longrightarrow \: { \large{ \rm{2( {x}^{2} + {y}^{2} ) }}}[/tex]

[tex]\longrightarrow{ \large{ \rm{2z}}}[/tex]

Therefore,

[tex]{ \large{\longrightarrow \: { \rm{{x}^{2} \frac{ {∂}^{2} z}{∂ {x}^{2} } + 2xy \frac{ {∂}^{2}x }{∂x \:∂y } + {y}^{2} \frac{ {∂}^{2}z }{∂ {y}^{2} } = 2z }}}}[/tex]

Hence Proved!!

[tex] \: [/tex]

[tex]\boxed{\begin{array}{c|c}\bf f(x)&\bf\dfrac{d}{dx}f(x)\\ \\ \frac{\qquad\qquad}{}&\frac{\qquad\qquad}{}\\ \sf k&\sf0\\ \\ \sf sin(x)&\sf cos(x)\\ \\ \sf cos(x)&\sf-sin(x)\\ \\ \sf tan(x)&\sf{sec}^{2}(x)\\ \\ \sf cot(x)&\sf-{cosec}^{2}(x)\\ \\ \sf sec(x)&\sf sec(x)tan(x)\\ \\ \sf cosec(x)&\sf-cosec(x)cot(x)\\ \\ \sf\sqrt{x}&\sf\dfrac{1}{2\sqrt{x}}\\ \\ \sf log(x)&\sf\dfrac{1}{x}\\ \\ \sf{e}^{x}&\sf{e}^{x}\end{array}}[/tex]

Refer to the attachments for answer

Answer:

■○■•♤•♤♤•》•♤~♤~♤~♤~♤♤~♤•♤○♤~

The area of the sector which has a central angle of 5π/7 radians and a diameter of 5.6 in is 8.79 in².

The area of a circular sector is the total space occupied by it. The sector area is half of the product of the square of radius of the circle and the central angle.

It can be calculated as,

[tex]A_{sector}=\dfrac{d^2\theta}{8}[/tex]

Here, (d) is the diameter of the circle and (θ) is the central angle.

The central angle of the sector is 5π/7 radians and the diameter of the sector is 5.6 in.

Put the values in the above formula as,

[tex]A_{sector}=\dfrac{(5.6)^2\times5\pi}{8\times7}\\A_{sector}=\dfrac{(5.6)^2\times5\pi}{8\times7}\\A_{sector}=8.79 \rm \; in^2[/tex]

Hence, the area of the sector which has a central angle of 5π/7 radians and a diameter of 5.6 in is 8.79 in².

Learn more about the area of a circular sector here;

https://brainly.com/question/1283563

Answer: is 4 you dontiy noweok

Step-by-step explanation: beacouse 2 + 2 is for silli sdlkfjasñldkas

sadfjlñsakdfjñsldfk

sdfsdlfksjañdlkfj234

23

42

34

23

4234

4

56

6

345

.

Answer:

E. 0.75%

Step-by-step explanation:

Convert to a fraction, then convert to a decimal by dividing the numerator by the denominator.

Answer: 20%

Step-by-step explanation: $1200 - $960 = $240

20% of 1200 is 240.

Answer:

1.23, -4.8

Step-by-step explanation:

-3.57 - 1.23 = -4.8

Hope this helps :)

Answer:

98.875

Step-by-step explanation:

Just add all the hours worked.

Hope this helps! :)

Answer:

300.2

7505/25=300.2 or300

Answer:

7(x-1)

Step-by-step explanation:

If you factor out 7 from each term,

you end up with 7([tex]\frac{7x}{7} -\frac{7}{7}[/tex])

or 7(x-1)

Veremos que el area del banderín es 930cm^2, entonces la opción correcta es A.

Luego de una pequeña busqueda online, pude ver que el banderin es un triangulo isósceles con base de 31cm y altura de 60 cm.

Recordar que para un triangulo de base b y altura h, el area es:

A = b*h/2

Entonces el area del banderín va a ser:

A = (31cm)*(60cm)/2 = 930cm^2

Entonces la opción correcta es A.

Sí quieres aprender más sobre triangulos, puedes leer:

https://brainly.com/question/2217700

Answer:

74

10x7=70

10-6=4

70+4=74

The result of the given mathematical expression is 74.

A mathematical expression consists of numbers, variables, and common mathematical operations such as addition, subtraction, multiplication, division, and more.

The given expression is:

{10 x 7} + (10 - 6)

= 70 + 4

= 74

Learn more about a mathematical expression here: https://brainly.com/question/23749699

#SPJ3

The probabilities for each case are:

There are 8 reservations for passengers that may go or not, such that the probability of arriving to the flight is P = 0.42, and the probability of not arriving is Q = 0.58

a) There will be overbooking if 7 or more passengers go to the flight, the probability that the 8 attend is:

P(8) = (0.42)^8

The probability that 7 attend is:

P(7) = 8*(0.42)^7*(0.58)

(where the factor 8 is because there are 8 permutations)

The total probability is:

P = P(8) + P(7) = 0.012

b) Will be empty seats if less than 6 people go.

The probability that exactly 6 of these people go to the flight is:

P(6) = (28)*(0.42)^6*(0.58)^2

Where there are 28 permutations, that is why we used that factor.

Then, the probability of having empty seats is:

P = 1 - P(6) - P(7) - P(8) = 0.937

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

Answer:

x = –3, x = –1, or x = 1

Step-by-step explanation:

when I put -3.-1,or 1 as x I get 0

Remainder Theorem Way :

x^3-3x^2-x-3

x^2 (x+3) -1(x+3) = 0

(x^2 -1) (x+3) = 0

(x+1) (x-1) (x+3) = 0

x= 1 x= -1 x= -3

https://brainly.com/question/3470351

Answer:

its b

Step-by-step explanation:

cause I took test

==============================

Explanation:

For problem 1, we will plot a closed circle at x = -2 to include this value in the shaded solution set. We include it because of the "or equal to". The shading is to the right because of the "greater than". So we're describing all x values that are either equal to -2 or larger than -2. You could say "x is -2 or larger".

---------------------

In problem 2, we'll exclude the endpoint since we don't have "or equal to". We shade to the left to visually show all values smaller than 3.

---------------------

In problem 3, we follow the same idea as the last problem. We have an open hole to exclude the endpoint and shade to the right of 12 to describe all values larger than 12.

---------------------

With problem 4, we now include the endpoint again. This is similar to problem 1. We shade to the left to describe x values that are either -15 or smaller.

Answer:

783

Step-by-step explanation:

There are 52 weeks in a year. Divide 40,716/52 and you get $783 weekly.

Answer:

7

Step-by-step explanation:

Because the lines are parrell and there is and a line intersecting both, you can say that the angles are interior corresponding angles. Thus you can have an equation 46=6x-2 then 48=6x divide x=7

The total finance charge for a $4,250 loan at 13. 25% interest compounded monthly for 24 months is $670.54.

What is Compound Interest?

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

A is the final amount, P is the Initial principal balance, r is the interest rate, n is the number of times interest is applied per time period, t is the number of time periods elapsed.

As it is given that the principal amount is $4,250 while the interest rate is 13.25% compounded monthly and the principal amount is taken for 24 months, therefore,

[tex]A = P(1 + \frac{r}{n})^{nt}\\\\A = 4,250(1 + \frac{0.1325}{12})^{24 \times 2}\\\\A = 5,531.54[/tex]

Now, the total amount that is needed to be paid is $5,531.54, while $4,250 was the principal amount therefore, the finance charge or the interest is,

Financial Charge = Final amount - Principal amount

Financial Charge = $5531.54 - $4861 = $670.54

Hence, the total finance charge for a $4,250 loan at 13. 25% interest compounded monthly for 24 months is $670.54.

Learn more about Compound Interest:

https://brainly.com/question/25857212

Answer:

the answer would be 3x+y-15

Answer:

8 red flyers and 8 blue flyers

Step-by-step explanation:

Packs of red flyers = 8

Blue flyers = 4

Jenny realizes that she gave out the same number of red and blue flyers

Find the lowest multiples of 8 and 4

8 = 8, 16, 24, 32

4 = 4, 8, 12, 16

The lowest common multiples of 8 and 4 is 8

Therefore,

The minimum number of flyers of each color is

8 red flyers and 8 blue flyers

Answer:

37

Step-by-step explanation:

239-17=222

222/6=37

37

Answer:

A=44 B=68

Step-by-step explanation:

There are two congruent sides, therefore the corresponding angles are also congruent.

Answer:

a and b both are 56 degree

Step-by-step explanation:

this is due to it's isosceles triangle. So, we take (180-68):2

Answer:

28.01

Step-by-step explanation:

Since x = 5.1

Substitute

5.1² + 2

=26.01+2

Add the numbers

=28.01

Hence, Answer = 28.01

~Learn with Lenvy~

Answer:

Option (C)

Step-by-step explanation:

Quadratic parent function has been given as,

f(x) = x²

If we reflect this function across the x-axis and vertically stretched by a scale factor of 'k',

g(x) = -kx²

This quadratic function passes through a point (1, -4),

g(1) = -k(1)²

-4 = -k

k = 4

Therefore, the new function after transformation will be,

g(x) = -4x²

Option (C) will be the correct option.  

The function g(x) is [tex]\rm g(x) = -4x^2\\[/tex].

Given that,

The function g(x) is a transformation of the quadratic parent function,

[tex]\rm f(x) = x^2[/tex]

We have to determine,

What function is g(x)?

According to the question,

The function f(x) is a transformation of the quadratic parent function,

[tex]\rm f(x) = x^2[/tex]

In the given figure the function g(x) reflect across the x-axis and is vertically stretched by a scale factor of 'k',

Then, The function g(x) is,

[tex]\rm g(x) = -kx^2[/tex]

Therefore,

The quadratic equation passes through the point (1,4),

[tex]\rm g(x) = -kx^2\\\\g(1) = -k(1)^2\\\\-4 = -k\\\\k= 4[/tex]

Therefore,

The function g(x) is,

[tex]\rm g(x) = -kx^2\\\\g(x) = -4x^2[/tex]

Hence, The required function g(x) is [tex]\rm g(x) = -4x^2\\[/tex].

For more details refer to the link given below.

https://brainly.com/question/411998

Answer:

1. 2c+9=m

Step-by-step explanation:

Answer:

Picture or graph? I need a graph to answer.

Answer:

a₇ = 797

Step-by-step explanation:

substitute n = 7 into the explicit formula

a₇ = 800 - 0.5(7 - 1) = 800 - 0.5(6) = 800 - 3 = 797