Solve the triangle: a=100, b=90, a 29 degrees If it is not possible, say so.

Answer:

\(\frac{19351}{11220}\)

Step-by-step explanation:

\(\frac{2640+3366+5049+3060+5236}{11220} = \frac{19251}{11220}\)

Answer:

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Step-by-step explanation:

hope its right

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

There are 40 apples in the basket.

This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.

I hope this helped you, have an amazing day! :)

Answer:

perimeter: 2

Step-by-step explanation:

8x-3 = 6x

8x – 6x = 3

2x = 3

x = 3/2

The required algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The difference between the perimeter of Tamara's suitcase and Anna's suitcase can be found by subtracting the expression for the perimeter of Anna's suitcase from the expression for the perimeter of Tamara's suitcase:

(8x - 3) - (3x + 2)

Simplifying the expression by removing the parentheses and combining like terms, we get:

8x - 3 - 3x - 2

= 5x - 5

Therefore, the algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

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The sales tax on the item listed price of $45 is $3.15 .

To calculate sales tax, you must first convert the tax rate to a decimal value by dividing it by 100% , we get

 7/100=0.07

The total cost of the items is $45. To calculate sales tax, simply multiply this price by the previously calculated decimal number , we get

45 × 0.07 = $3.15

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Convert the problem to standard form and write the initial tableau with slack variables:

Maximize

\(Z = 7*3 + 6*4 + 18*5 + 14*6 - 3*1 - 3*2 - 4*5 - 4*6\)

Subject to:

\(x1 + x2 + s1 = 4000\\x3 - (1/3)*1 + (1/3)*5 = 0\\x4 - (1/3)*2 + (1/2)*6 = 0\\x3*1 + 3*2 + 3*3 + 3*4 + 3*5 + 2*6 + s2 = 6000\)

All variables are non-negative.

Tableau

 x1  x2  x3  x4  x5  x6  s1  s2   b

Z -3 -3 7 6 18 14 0 0 0

s1 1 1 0 0 0 0 1 0 4000

s2 3 3 3 3 3 2 0 1 6000

x5 0 0 1 0 1/3 0 0 0 0

x6 0 0 0 1 0 1/2 0 0 0

The basic variables are s1, s2, x5, and x6.

Step 1: Choose  entering variable. The most positive coefficient in objective row is 18, corresponding to x5. x5 enters the basis.

Step 2: Choose the leaving variable. The minimum ratio of right-hand side to coefficient of x5 is 12000/(1/3) = 36000,

corresponding to s1. s1 leaves the basis.

Step 3: Perform, pivot operation to make x5 the basic variable for s1. Divide, pivot row by 1/3 and subtract appropriate multiples of the pivot row from other rows to make other entries in column 5 zero.

 x1    x2    x3    x4     x5     x6   s1    s2       b

Z -3 -3 7 6 18 14 0 0 0

x5 0 0 1 0 1/3 0 0 0 0

s2 3 3 3 3 2 2/3 2/3 0 1/3 24000

x3 1 0 1/3 0 1/3 0 -1/3 0 0

x4 0 1 0 1/3 0 1/2 -1/6 0 0

The basic variables are x5, x3, x4, and s2.

Step 4: Choose the entering variable. The most positive coefficient in the objective row is 7, corresponding to x3. x3 enters the basis.

Step 5: Determine the leaving variable. The right-hand side's minimum ratio to the coefficient of x3 is 0, indicating that x3 can be increased without bound. This implies that the optimal solution is unbounded and that there is no finite optimal value for the problem.

As a result, the simplex algorithm demonstrates that the given linear programming problem lacks a feasible solution. This means that it is not possible to meet all of the constraints at the same time.

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Answer:

Step-by-step explanation:

To find the two consecutive natural numbers whose sum is 575, we can set up the following equation:

x + (x+1) = 575

where x and x+1 are the two consecutive natural numbers.

We can solve this equation by combining like terms:

2x + 1 = 575

Subtracting 1 from both sides, we get:

2x = 574

Dividing both sides by 2, we get:

x = 287

Therefore, the two consecutive natural numbers are 287 and 288. Our final answer is 287, 288.

Answer:

287,288

Step-by-step explanation:

Question

The sum of two consecutive natural numbers is 575. Find the numbers

soln

x +( x + 1) = 575

x + x + 1 = 575

2x + 1 = 575

2x = 575 – 1

2x = 574

\( \frac{2x}{2} = \frac{574}{2} \)

x = 287

since we got x as 287, lets solve(x+1)

by substituting

287 + 1 = 288

hence the consecutive numbers are 287,288

Check

287 + 288 = 575

we are correct.

i hope this helps

360 square feet is the surface area of the prism.

You must sum up the areas of all six faces to determine the rectangular prism's surface area. The formula for a rectangular prism's surface area is:

2lw + 2lh + 2wh = Surface Area

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

The dimensions of this issue are 10 feet in height, 10 feet in length, and 4 feet in breadth. Hence, the prism's surface area is as follows:

Surface Area =  2(10)(4) + 2(10)(10) + 2(4)(10)

Area of Surface = 80 + 200 + 80

Surface Area = 360 square feet

The prism's surface area is 360 square feet as a result.

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Answer:

3.65

Step-by-step explanation:

The square root of 2 is 1.4 and the square root of 5 is 2.2 adding that together you get 3.6

Answer:

Option A

Step-by-step explanation:

       Pick any two points on the line.

       (3 , 0) ⇒ x₁ = 3 & y₁ = 0

        (0,-2) ⇒ x₂ = 0 & y₂ = -2

Find the slope using the formula,

      \(\boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}\)  

                   \(\sf =\dfrac{-2-0}{0-3}\\\\\\=\dfrac{-2}{-3}\\\\\\=\dfrac{2}{3}\)

      Slope-point form of a line: y - y₁ = m(x - x₁)

Substitute slope and the point in the above equation,

              \(y - 0 = \dfrac{2}{3}(x - 3)\\\\ ~~~~~~ y= \dfrac{2}{3}x-\dfrac{2}{3}*3\\\\\\~~~~~~\boxed{ y = \dfrac{2}{3}x-2}\)

This is in slope intercept form: y = mx + b.

Answer:

$136.85

Step-by-step explanation:

You want to find 30% of 230 and then subtract it from 230.

30% of 230 is 69.

230 - 69 = 161

Then you find 15% of 161

15% of 161 is 24.15.

161 - 24.15 = $136.85

I checked my answer with this:

Answer:

\(8.5x+4y=99.5,\ x+y=17\)

Step-by-step explanation:

\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)

Answer:

the scale factor is 4 as from the table

The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

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Answer:

Didn't you mean A = (1/2)d1d2 ?

If so, clear out the fraction by mult. both sides of the eqn by 2:

2A = d1*d2

Now isolate d1 by div. both sides of this result by d2:

2A

------ = d1        (answer)

d2

Step-by-step explanation:

Answer:

The width of a block of wood with rectangular cross section is x cm. its height is 2/3 its width and its length is 4times its height what is its volume in cm3

m = n+ x/p

m (*p) = n (*p) + x/p (*p)

mp = np + x

x= mp - np

x= p ( m - n)

Answer:

x = 3 only

Step-by-step explanation:

\(\sqrt{2x-5} =1+\sqrt{x-3}\)

\(\implies 2x-5=(1+\sqrt{x-3})^2\\\\ \implies 2x-5=x+2\sqrt{x-3} -2\)

\(\implies x-3=2\sqrt{x-3}\)

\(\implies (x-3)^2=(2\sqrt{x-3})^2\)

\(\implies x^2-6x+9=4x-12\)

\(\implies x^2-10x+21=0\)

\(\implies (x-3)(x-7)=0\)

\(\implies x=3, x=7\)

Check by substituting found values of x into original equation:

\(x=3 \implies \sqrt{2(3)-5} =1+\sqrt{3-3} \implies 1 = 1 \ \ \ \checkmark\)

\(x=7 \implies \sqrt{2(7)-5} =1+\sqrt{7-3} \implies 3\neq 2 \ \ \ \ incorrect\)

Answer:

54

Step-by-step explanation:

46+80=126 and every triangle adds up to 180 so subtract 180 from 126 (180-126=54)

Hope this helped!

Answer:

c)54 degrees

Step-by-step explanation:

A triangle has to be 180 degrees.

46+80=126

180-126=54

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Answer:it might be A

Answer:

The third one, with the sideways "z" shape.

Step-by-step explanation:

When folded, this net shape will become the new figure.

Answer:

y - (18x - 6y)/3  

Step-by-step explanation:

y - (2/3)(9x - 3y)

y - [(2)(9x - 3y)]3

y - (18x - 6y)/3

y + (-18x + 6y)/3

y - 6x + 2y

-6 + 3y

Answer:

B. x= 2 is the correct answer

The solution for the given expression is  7 + 5/12

First we need to write the expression, using fractions, we will get:

(5 + 6/8) + (4 + 4/15) - (2 + 6/10)

We can group like terms, and we will get:

(5 + 6/8) + (4 + 4/15) - (2 + 6/10) = (5 + 4 -2) + (6/8 + 4/15 - 6/10)

Now just simplify that to get.

(5 + 4 -2) + (6/8 + 4/15 - 6/10) =  7 + 3/4 + 4/15 - 3/5

                                                =  7 + 3/4 + 4/15 - 9/15

                                                = 7 + 3/4 - 5/15

                                                = 7 + 9/12 - 4/12

                                                 = 7 + 5/12

That is the answer.

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The surface area of a similar cylinder with a diameter 3 cm is  8.4375π cm².

If two figures have the same shape, they are said to be comparable. In more formal terms, two figures are said to be similar if their respective angles are congruent and their corresponding side length ratios are identical.

Given a cylinder with a diameter 8 cm and a surface area 60π cm²

let the radius be  R = dia/2 = 8/2= 4 cm

and let the height be H

total surface area of cylinder  = 2πR(H + R)

60π = 2π(4)(4 + H)

4 + H = 60/8

H = 7.5 - 4

h = 3.5 cm

and a cylinder is similar to given cylinder,

let radius be r and height be h

given dia = 3 cm

r = 3/2 = 1.5 cm

since both cylinders are similar so the ratio of their height to radius is equal,

R/H = r/h

h = Hr/R

h = (3.5)(1.5)/4

h = 1.3125 cm

total surface area of cylinder  = 2πr(h + r)

total surface area of cylinder  = 2π(1.5)(1.5 + 1.3125)

the total surface area of the cylinder  = 8.4375π cm²

Hence the area of a cylinder is 8.4375π cm².

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By definition, a Power has the following form:

Where "b" is the base and "n" is the exponent.

Powers represent repeated multiplication. For example:

In this case, you have the following Power:

Based on the explained above, you can identify that:

- The base of the Power is:

- And the exponent is:

Therefore, that means that to get the result, you must multiply 10 times the base 0.5

The answers are:

1. Power.

2. Base.

3. Exponent.

4. Repeated multiplication.

The average cost of your item, based on a gross margin of 3%, is $108.20.

The average cost is the cost per unit.

It can be computed as the quotient of the total cost and the number of units.

The gross margin is the percentage difference between the cost of goods sold and the sales revenue.

The gross margin percentage is expressed as a quotient of the sales revenue multiplied by 100.

Selling price = $111.55

Gross margin = 3%

Selling price = 100%

Cost of goods sold = 97% (100 - 3)

Average cost (cost per unit) = Selling Price x Percentage Cost/Selling Price Percentage

$108.20 ($111.55 x 97/100)

Thus, the average cost of the product is $108.20.

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