A summer camp wants to hire counselors aides to fill its staffing needs at minimum cost

Answer:

[tex]\cos(69)[/tex]

Step-by-step explanation:

We will use the co-function identity for sine, where:

[tex]\sin(x)=\cos(90-x)[/tex]

Since sin(21)=0.358=cos(x). This means that:

[tex]21=90-x[/tex]

Solve for x. Add x to both sides:

[tex]x+21=90[/tex]

Subtract 21 from both sides:

[tex]x=69\textdegree[/tex]

Hence:

[tex]\sin(21)=\cos(69)\approx0.358[/tex]

Answer:

(x+3)² = (x+3)(x+3)

When we distribute polynomials, we have to make sure each term mutliplies to all of the terms in the other polynomial.

x(x+3) + 3(x+3)

x² + 3x + 3x + 9

x² + 6x + 9

Methods such as FOIL (first, outside, inside, last) and creating a table can help you with this.

Step-by-step explanation:

Answer:

x^(2)+6x+9 also x=-3

Step-by-step explanation:

9514 1404 393

Answer:

  A) the curves are ellipses

  B) 161 yards

  C) 366 yards

Step-by-step explanation:

A) The general shape of the side marked c has the appearance of two quarter-ellipses. The major axis is approximately 125 yards, and the minor axis is approximately 80 yards. Paul could assume that the curves are quarter-ellipses.

__

B) For an ellipse with this eccentricity, its perimeter is within 2% of that of a circle with a diameter equal to the average of these dimensions.*

So, the approximate length of side c is ...

  c ≈ π(80 +125)/4 ≈ 161 . . . . yards; length of side c

__

C) The perimeter of the pond is the sum of the side lengths, so will be ...

  80 yds + 125 yds + 161 yds = 366 yds . . . pond perimeter

_____

* Indian mathematician Ramanujan developed an approximate formula for the circumference of an ellipse, which would otherwise need to be computed using an elliptic integral. it is ...

  C = π(a+b)(1 + 3λ²/(10 +√(4 -3λ²))

where λ = (a -b)/(a +b) and a, b are the semi-axis lengths.

For this ellipse, λ = 9/41, so the last factor is about 1.01208313. Using this factor, the circumference is expected to be good to about 7 significant digits. Continuing the calculation, we find ...

  C ≈ 325.904 . . . . circumference of an ellipse 125 yd long by 80 yd wide

This is twice the length we imagine for c, so c ≈ 163 yards. As we said, the approximation used above is within 2% of this value.

The attachment shows the shape if the curve is actually an ellipse.

Answer:

C

Step-by-step explanation:

I believe this is the correct one.

Answer:

C

Step-by-step explanation:

C has the point (-2, -3.5) and the point (0.5, -4)

Answer: Two sides of a triangle have lengths 2 and 7. Find all possible lengths of the third side. Show Answer. difference $$< x <$$ sum $$7 -2 < x < 7+2$$ Answer: $$5 < x < 9$$ Problem 7. Two sides of a triangle have lengths 12 and 5. Find all possible lengths of the third side

Step-by-step explanation: i hope i helped

Answer:  Part 1: y =10x+50

Part 2:  Jordan’s total cost = $90

Step-by-step explanation:

Given: Price of each large balloon = $25

Price of each small balloon = $10

Price of 2 large balloons = 2 (Price of each large balloon)

= $2 (25)

= $50

Part 1: Total cost = (Number of small balloons)(Price of each small balloon)  +  (Number of large balloons)(Price of each large balloon)

Let x = Number if small balloons , y=  total cost Jordan must pay in dollars.

Then, y= (x)(10)+(2)(25)

⇒ y =10x+50

Part 2: If she purchases 4 small balloon animals, put x=4

Then, y= 10(4)+50=40+50= 90

i.e. Jordan’s total cost = $90

Answer:

There are 50,000 decimeters in 5 kilometers

Step-by-step explanation:

as for showing my work not really sure what you want me to do it's pretty straightforward, butttttttt what i did was multiply the length value by 10,000, so [tex]10,000=10^4[/tex]

I'm not sure if that's what you're looking for but I hope this helps :)

Answer:

y = x - 1

Step-by-step explanation:

If it's parallel to x - y = 7, that means the slope of that equation is the slope for the equation you're looking for.  

To get the slope, you need to put the given equation into slope intercept form, so move x to the other side. You should get: -y = 7 - x

Then, to get the y positive, divide by -1:     y = -7 + x

Slope intercept form is as follows: y = mx + b, so whatever the number is in front of x is your slope. In this instance, your slope is 1.

You now have your slope, and a point in which your new line passed through. Using slope intercept form, y = mx + b, if you substitute in what you know, you can find your answer. Right now you know y, m, and x, and you're looking for b.  

x=1; y=0; m=1.  

So, substituting, you'd get 0 = (1)(1) + b

0=1+b     Solve

You should get b= -1, leaving your final answer as y = x - 1

y=x+1 is the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7.

The slope will be same as it is parallel.

x - y = 7.

-y=7-x

y=x-7

Slope is 1.

Now equation of line passing through (1,0)

0=1(1)+c

c=-1

y=x-(-1)

y=x+1

Hence y=x+1 is the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7.

To learn more on slope of line click:

https://brainly.com/question/14511992

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Answer:

4. The solution to the system of equations is: (2,-1)

5. The solution to the system of equations is: (3,5)

Step-by-step explanation:

4. What is the solution to the system of equations?

[tex]2x+3y=1\\-3x+4y=-10[/tex]

Let:

[tex]2x+3y=1--eq(1)\\-3x+4y=-10--eq(2)[/tex]

Multiply eq(1) by 3 and eq(2) by 2 and add both equations

[tex]6x+9y=3\\-6x+8y=-20\\---------\\0x+17y=-17\\y=\frac{-17}{17}\\y=-1[/tex]

So, value of y=-1

Now finding the value of x bu putting value of y in eq(1)

[tex]2x+3y=1\\2x+3(-1)=1\\2x=1+3\\2x=4\\x=\frac{4}{2}\\x=2[/tex]

So, value of x=2

The solution to the system of equations is: (2,-1)

5. What is the solution to the system of equations?

[tex]y=2x-1\\6x-y=13[/tex]

Let:

[tex]-2x+y=-1--eq(1)\\6x-y=13--eq(2)\\------\\4x=12\\x=\frac{12}{4}\\x=3[/tex]

So, value of x=3

Putting value of x in equation 1 to find value of y

[tex]y=2x-1\\y=2(3)-1\\y=6-1\\y=5[/tex]

So, value of y=5

The solution to the system of equations is: (3,5)

Answer:

Equation of a line through (15, 8) that is perpendicular to the line y =57 x −1 is [tex]\mathbf{y=-\frac{1}{57}x+\frac{157}{19}}[/tex]

Step-by-step explanation:

We need to write an equation of a line through (15, 8) that is perpendicular to the line y =57 x −1.

The equation will be in slope-intercept form: [tex]\mathbf{y=mx+b}[/tex]

Where m is slope and b is y-intercept.

Finding Slope of new line

We are given equation [tex]y =57x-1[/tex] of line, which is perpendicular to the line whose equation we need to find.

If the lines are perpendicular there slopes are inverse of each other i.e [tex]m_1=-\frac{1}{m_2}[/tex]

Slope of given line is m= 57 ( compare the given equation with standard slope-intercept form the value of m is 57

Slope of new line is m= [tex]-\frac{1}{57}[/tex]

Finding y-intercept of new line

Now finding y-intercept (b) for new line. It can be found using point (15,8) and slope m = [tex]-\frac{1}{57}[/tex]

[tex]y=mx+b\\8=-\frac{1}{57}(15)+b\\8=-\frac{15}{57}+b\\b=8+\frac{15}{57}\\b=\frac{8*57+15}{57}\\b=\frac{471}{57}\\b=\frac{157}{19}[/tex]

So, y-intercept b of new line is: [tex]b=\frac{157}{19}[/tex]

Equation of required line

Equation of line having slope m= [tex]-\frac{1}{57}[/tex] and y-intercept  [tex]b=\frac{157}{19}[/tex] is:

[tex]y=mx+b\\\mathbf{y=-\frac{1}{57}x+\frac{157}{19}}[/tex]

So, equation of a line through (15, 8) that is perpendicular to the line y =57 x −1 is [tex]\mathbf{y=-\frac{1}{57}x+\frac{157}{19}}[/tex]

Answer:

p(x) as a product of linear factors. [tex]p(x)=(x+3)(x-2)(x+6)[/tex]

Step-by-step explanation:

(x+3) is the factor of polynomial [tex]p(x) = x^3 + 7x^2 - 36[/tex]

So, we can divide [tex]p(x) = x^3 + 7x^2 - 36[/tex] by (x+3) to find other factors

The division is shown in figure attached.

The quotient is: x^2+4x-12

Now factoring the quotient to find linear factors

[tex]x^2+4x-12\\=x^2+6x-2x-12\\=x(x+6)-2(x+6)\\=(x-2)(x+6)[/tex]

The factors are [tex](x+3)(x-2)(x+6)[/tex]

So, p(x) as a product of linear factors. [tex]p(x)=(x+3)(x-2)(x+6)[/tex]

Answer:

24w - 21

Step-by-step explanation:

-8(2 - 3w) - 5

We first expand the -8

-16 + 24w - 5

We then add -16 to -5

-16 + -5

= -21

We get the 24w, put in in the equation and get 24w - 21

Answer:

24w−21

Step-by-step explanation:

Factoring  24w2+10w-21

The first term is,  24w2  its coefficient is  24 .

The middle term is,  +10w  its coefficient is  10 .

The last term, "the constant", is  -21

Step-1 : Multiply the coefficient of the first term by the constant   24 • -21 = -504

Step-2 : Find two factors of  -504  whose sum equals the coefficient of the middle term, which is   10 .

     -504    +    1    =    -503

     -252    +    2    =    -250

     -168    +    3    =    -165

     -126    +    4    =    -122

     -84    +    6    =    -78

     -72    +    7    =    -65

     -63    +    8    =    -55

     -56    +    9    =    -47

     -42    +    12    =    -30

     -36    +    14    =    -22

     -28    +    18    =    -10

     -24    +    21    =    -3

     -21    +    24    =    3

     -18    +    28    =    10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  28

                    24w2 - 18w + 28w - 21

Step-4 : Add up the first 2 terms, pulling out like factors :

                   6w • (4w-3)

             Add up the last 2 terms, pulling out common factors :

                   7 • (4w-3)

Step-5 : Add up the four terms of step 4 :

                   (6w+7)  •  (4w-3)

            Which is the desired factorization

Answer:

4, 11

Step-by-step explanation:

Q# 13 :

Let the first number be 'x'

the 2nd number would be ' x + 7'

x + x + 7 = 15

2x= 15-7

x= 8/2

x= 4

2nd number: x + 7

                    = 4+7

                    = 11

Answer:

5 hours

Equations:

first company: 17x+15

second company: 20x

Proof:

17(5)+15 => 85+15 => 100

20(5) => 100

Answer:

5 hours

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Measure of one interior angle of a regular polygon of n sides:

(n - 2)180/n

Measure of one exterior angle of a regular polygon if n sides:

360/n

"the interior angle is thrice the exterior angle"

(n - 2)180/n = 3 * 360/n

(n - 2)180 = 3 * 360

n - 2 = 3 * 2

n = 8

The number of sides is 8.

Answer:

1/8

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

Answer:

the answer is 2

Step-by-step explanation:

Bcz u choseine option and lose the next bet benefit

Answer:

Step-by-step explanation:

an isosceles triangle two adjacent sides are equal

so AB = BC

3x-4 = 5x-10

2x = 6

x= 3

so ,

3 ( 3 ) -4 = 5

5 ( 3 ) -10 = 5

Answer:

No, it does not

Step-by-step explanation:

Answer:

qs,wdnfm.ew fw v

Step-by-step explanation:

wdmc vw.mv / n,v

Answer:

B.

Step-by-step explanation:

The graphed line has a slope of 3 which is higher than the functions slope of 2. It also has a y-intercept of 4 while the functions y-intercept is -5, therefore it is higher.

Answer:

There you go cupcake!

Answer:

Step-by-step explanation:

Since we are not given the dimension. Let us say the shape of the patio is a rectangle with length 30m and width 18m.

Area of the rectangle = Length * Width

Area of the rectangle = 30 * 18

Area of the rectangle = 540m²

This means that 540m² of the patio costs $2276.35. To get the cost of each square metre of patio, we will say;

540m² = $2276.35

1m² = x

cross multiply;

540x = $2276.35

x = $2276.35/540

x = $4.22

Hence each square meter of patio will cost $4.22

Note that the dimension of patio was assumed. Same explanation can be employed for any dimension.

Answer:

2a^2 b^3(3a^2 b^3 - 4ab^2 + 6)

Answer:

10/3

Step-by-step explanation:

110/33

lowest term of 110/33 is 10/3

Answer:

2=53 employees(m)

4=91 employees(m)

6=129 employees(m)

8=167 employees(m)

Step-by-step explanation:

19x2=38+15= 53

19x4=76+15= 91

19x6=114+15=129

19x8=152+15=167

Answer: I disagree with the person that answers before. The answer is D, parliamentary democracy.

Here's why: The definition of parliamentary democracy is a democratic form of government in which the party with the greatest representation in the parliament (legislature) forms the government, its leader becoming prime minister. The United Kingdom is a unitary state with devolution that is governed within the framework of a parliamentary democracy under a constitutional monarchy in which the monarch, currently Queen Elizabeth II, is the head of state while the Prime Minister of the United Kingdom, is currently Boris Johnson  

Answer:

Step-by-step explanation:

X is -18

Answer:

49/27 i think

Step-by-step explanation:

Answer:

150 units woild fill the volume of the prism.

Answer:

The relationship between the angles would be parallel because they are the exact same degree now if they were different degrees their relationship would be perpendicular but with them being the same the answer is parallel