3 pounds of topsoil cost $5.76. What is the price per ounce?

Answer:

g = 7 + 13x-1 + -5x + x2

Step-by-step explanation:

Simplifying

g(x) = x3 + -5x2 + 7x + 13

Multiply g * x

gx = x3 + -5x2 + 7x + 13

Reorder the terms:

gx = 13 + 7x + -5x2 + x3

Solving

gx = 13 + 7x + -5x2 + x3

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Divide each side by 'x'.

g = 13x-1 + 7 + -5x + x2

Simplifying

g = 13x-1 + 7 + -5x + x2

Reorder the terms:

g = 7 + 13x-1 + -5x + x2

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

2) +20

4) +14

5) -100

6) -17

7) 10

8) -9

9) -8

10) +11

Step-by-step explanation:

look at the words and it will tell you whether it's positive or negative

ex. one hundred feet below sea level- it says below which means you would be going down

The actual consumer spending at a price of $27 per unit is $268.26.

Substitute the given price into the supply equation to get the corresponding quantity supplied:

p = q + 10

27 = q + 10

q = 17

Substitute q = 17 into the demand equation to get the corresponding price:

4q² + p² = 1405

4(17)² + p² = 1405

p² = 1405 - 1156

p² = 249

p = 15.78

The actual consumer spending can be calculated by multiplying the quantity demanded by the price:

Actual consumer spending = quantity demanded x price per unit

= 17 x 15.78

= $268.26

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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.

Relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides

a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

To widen or enlarge an opening or hollow structure beyond its usual size in simple way changes the the size.

The scale factors is the factor in which each linear measure of the figure is multiplied.

AC is a smaller triangle which is dilated to get A'C' and this A'C' is dilated to get A''C''.

the relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides with a scale factor.

Hence,  relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides

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Answer:

A,M,V

Step-by-step explanation:

Answer:

y=-45x + 100

Step-by-step explanation:

The slope-intercept form is y=mx+b where m is the slope and b is the y-intercept or in other words the initial amount (when x is 0). Since you start off with 100 dollars the y-intercept is going to be 100 since after 0 weeks (when you opened the account) you put 100 dollars in... so you should have 100 dollars. The slope is going to be -45 since you are withdrawing 45 each week so the value is going to be decreasing by 45 every week. If you put that together you get y=-45x+100

Answer:

Step-by-step explanation:

By HL congruence,  triangle ABC congruent to triangle DEF. Therefore, option D is the correct answer.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Consider the given triangles as ABC and DEF.

From the given triangles,

AC=DF=14 in.

BC=EF=20 in.

∠A=∠D=90°

The Hypotenuse-Leg (HL) Triangle Congruence Theorem is a special case that allows you to show that two right triangles are congruent. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

By HL congruence, ΔABC ≅ ΔDEF

Therefore, option D is the correct answer.

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Coefficient Cn is determined by Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

To find the coefficients Cn of the eigenfunction expansion of a function f(x), f(x) must be expanded with the eigenfunction yn(x). The expansion of f(x) with respect to the eigenfunction yn(x) is given by

f(x) = Σ[∞], n=1 cnyn(x)

To find the coefficient cn, we need to compute the dot product of f(x) and yn(x).

cn = (f,yn) = ∫[0,4]f(x)yn(x)dx

Since the eigenfunctions yn(x) are orthonormal, the scalar product is given by

cn = ∫[0,4]f(x)yn(x)dx = ∫[0,2]f(x)yn(x)dx + ∫[2,4]f(x)yn(x)dx

Since f(x) = 2/2 x for x in [0,2] and f(x) = 2 for x in [2,4], compute the coefficient cn as I can do it.

cn = ∫[0,2](2/2x)yn(x)dx + ∫[2,4](2)yn(x)dx

= ∫[0,2]xyn(x)dx + ∫[2,4]2yn(x)dx

= 1/2 ∫[0,2] (xyn(x) + 2yn(x)) dx

= 1/2 ∫[0,2] (x+2)yn(x) dx

Therefore, the coefficient Cn is given by

Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

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Answer:

Height, h = 20.99 millimeters.

Step-by-step explanation:

Given the following data;

Volume = 8792mm³

Radius = 20 mm

To find the height;

We know that the shape of an anthill is conical in nature.

Mathematically, the volume of a cone is given by the formula;

\( V = \frac{1}{3} \pi r^{2}h\)

Where;

Substituting into the equation, we have;

\( 8792 = \frac{1}{3} * 3.142*20^{2}*h \)

\( 8792 = \frac{1}{3} * 3.142*400*h \)

\( 8792 = \frac{1}{3} * 1256.8*h \)

\( 8792 = 418.93*h \)

\( Height, h = \frac {8792}{418.93}\)

Height, h = 20.99mm.

Therefore, the height of the cone is 20.99 millimeters.

The height of the skyscraper is D. 156.26 ft

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

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Answer:

answer this 5-y this the answer thanks for

Answer:

3xw+3xp+3y-9x-yw-yp

(I have no idea how it's ordered on your test)

Step-by-step explanation:

(3x-y)(w+p-3)

Multiply.

3xw+3xp-9x-yw-yp+3y

Reorder.

3xw+3xp+3y-9x-yw-yp

(me looking at this long a** expression like o.O)

---

hope it hope

52s is the maximum time that she can take on her last lap and still make the team.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).

The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.

We need to find the maximum time (in seconds) that she can take on her last lap and still make the team

Let x be the maximum time (in seconds) that she can take on her last lap

60=(63+62+65+58+x)/5

300=63+62+65+58+x

300=248+x

Subtract 248 on both sides

300-248=x

x=52s

Hence, 52s is the maximum time that she can take on her last lap and still make the team.

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4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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The answer to this problem is that we cannot determine the distance of beacon light and ship from point A to point B

What is tangent function ?

In trigonometry, tangent is one of the six basic trigonometric functions (along with sine, cosine, cosecant, secant, and cotangent). The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

In other words, if we have a right triangle with one acute angle θ, the tangent of θ is defined as:

tan(θ) = opposite / adjacent

where "opposite" refers to the length of the side opposite the angle θ, and "adjacent" refers to the length of the side adjacent to the angle θ.

According to the question:
From the information given, we can set up two right triangles: one with the boat, point A, and the lighthouse, and another with the boat, point B, and the lighthouse.

In the first triangle, we have:

tan(16°) = h/x

In the second triangle, we have:

tan(21°) = h/y

We want to find y - x, the distance traveled by the boat between the two measurements. We can set up an equation for this by subtracting the first equation from the second:

tan(21°) - tan(16°) = h/y - h/x

We know the height of the lighthouse is 0 feet, so h = 0. We can simplify the equation to:

tan(21°) - tan(16°) = 0/y - 0/x

To solve for y - x, we need to solve for y/x:

tan(21°) - tan(16°) = 0/y - 0/x

tan(21°) - tan(16°) = 0/(y-x)

Since 0/(y-x) = 0, we can simplify the equation to:

tan(21°) - tan(16°) = 0

We can solve this equation for the difference in distance, y - x:

y - x = 0/(tan(21°) - tan(16°))

y - x = 0

This tells us that the boat did not travel any distance between the two measurements. This doesn't make sense, so we must have made a mistake somewhere.

Looking back at the equations, we notice that we made a mistake when we set h = 0. The height of the lighthouse is actually given as "no feet above the water," which means h = 0 feet. We need to go back and redo the calculations with the correct value for h:

tan(16°) = h/x

tan(21°) = h/y

Substituting h = 0 into these equations, we get:

tan(16°) = 0/x

tan(21°) = 0/y

Solving for x and y, we get:

x = infinity (since tan(16°) is positive)

y = infinity (since tan(21°) is positive)

Therefore, the answer to this problem is that we cannot determine the distance from point A to point B.


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Answer:

The correct answer is x = 32.

Step-by-step explanation:

To solve this problem, we must remember the concept of supplementary angles.  Two angles that are supplementary together make an angle of 180 degrees (a straight line).

In this case, we can see that inside the triangle, we will have an angle of 80 degrees.  We know this because the angle at the top of the triangle is supplementary with the angle measuring 100 degrees, so its measure should be 180-100 = 80 degrees.

On the lower right hand of the triangle, a similar rationale can be applied.  The angle inside of the triangle must measure 68 degrees, since it is supplementary to an angle measuring 112 degrees, and 180-112=68.

Finally, to solve this problem, we must remember that the sum of the three interior angles of a triangle should be 180 degrees.  This lets us set up the following equation:

80+68+x = 180

Now, we can solve this equation. Our first step is to simplify the left side of the equation by adding together the constant terms.

148 + x = 180

Next, we should subtract 148 from both sides of the equation.

x = 180-148

x = 32

Therefore, the correct answer is x = 32 degrees.

Hope this helps!  

Answer:

IM GEORGE FLOYD

Step-by-step explanation:

Answer:

i would be 22.5 or 22 minutes and 30 seconds becuase 45 times 30 is 1350 and if you do it by 60 because thats how many seconds are in a minute you get 22.5 or 22 mins and 30 seconds

brainliest?! thank you !

Step-by-step explanation:

The part of a pyramid include the following: E. lateral faces.

In Mathematics and Geometry, the volume of a pyramid can be calculated by using the following formula:

Volume = 1/3 × b × h

Where:

Generally speaking, a pyramid is composed of three main parts and these include the following:

In conclusion, we can reasonably infer and logically deduce that lateral face is a part of any pyramid.

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The solution to the inequality 8(x-1) >12 - 2x is given as follows:

x > 2.

The inequality for this problem is defined as follows:

8(x-1) >12 - 2x.

Applying the distributive property to the left side, we have that:

8x - 8 > 12 - 2x.

Isolating the variable x, the solution is obtained as follows:

10x > 20

x > 20/10

x > 2.

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Answer: 22 tulips

Step-by-step explanation:

2 + 1 = 3

3 goes into 33 11 times, so you multiply each value by 11

2 * 11 = 22 tulips

22 tulips to 11 roses is 2:1 ratio

Answer:

x= 5 , y = 34

Step-by-step explanation:

8x-6=5x+9

3x-6=9

3x=15

x=5

-

8(x5) - 6 =

34

25(x5) +9 =

34

Answer:

x = 5 and y = 34

Step-by-step explanation:

I used substitution method and did this ;

8x - 6 = 5x + 9 .....put like terms together

8x - 5x = 9 + 6

3x = 15

x = 5

y = 8 (5) - 6

y = 40 - 6

y = 34

Answer:

The number 80 should go in the green box

Step-by-step explanation:

To solve this equation you will need to use the pythagorean theorem. Which is a^2 + b^2 = c^2. Also you will need to know where the legs and hypotenuse of the triangle are. The hypotenuse is the longest side of the triangle. So that would be the side marked 12. Then the other two sides are legs.

To solve for x you need to input your known numbers into the pythagorean theorem and solve. To know where the numbers go, a and b of the equation are the legs of the triangle and c is the hypotenuse. I solved the equation for you in the photo I inserted.

Hope that helped you!

Answer:

30 and 8

Step-by-step explanation:

30 - 8 = 22

Answer:

1. The mean amount that this farmer will earn over a long period of years is:

$57,100

2. It makes sense financially for the farmer to buy the insurance.   In a year of drought, he earns only $5,200.  If he spends on insurance premium, his earnings are reduced by $2,000 to $3,200 but the insurance reimbursement will take his overall net earnings to $23,200 ($3,200 + $20,000).  Incurring the insurance expense is highly justified.

Step-by-step explanation:

Earnings in a typical year = $75,000

Earnings in a wet year = $48,000

Earnings in a drought = $26,000

Pro

                         Typical            Wet           Drought

Earnings          $75,000       $48,000      $26,000

Probability        0.50              0.30             0.20

Expected

 earnings       $37,500       $14,400        $5,200

Mean earnings = $57,100

Insurance expense                                 $2,000

Net earnings after insurance expense $3,200

Insurance Reimbursement                  $20,000

Net earnings                                         $23,200

Answer:

See below.

Step-by-step explanation:

(x+y)(x-y)

(-3-5)(-3-(-5))

(-8)(-3+5)

(-8)(2)

-16

-hope it helps

The given sequence is

\(z_n = log(1 + (θ/(α + {i*cos(π/2) - i*sin(π/2)}))^n)\)

First, we need to simplify the expression inside the log. The term \({i*cos(π/2) - i*sin(π/2)}\) can be simplified to 0, since cos(π/2) = 0 and sin(π/2) = 1.

Therefore, the expression inside the log becomes \((1 + (\theta/\alpha)^n)\).

Now, we need to find the limit of this sequence as n approaches ∞.

If θ/α is less than 1, then (θ/α)^n will approach 0 as n approaches infinity, and the limit of the sequence will be log(1) = 0.

If θ/α is greater than 1, then (θ/α)^n will approach infinity as n approaches infinity, and the limit of the sequence will be log(infinity) = infinity.

If θ/α is equal to 1, then (θ/α)^n will always be 1, and the limit of the sequence will be log(2).

Therefore, the limit of the sequence depends on the values of θ and α. If θ/α < 1, the limit is 0. If θ/α > 1, the limit is infinity. If θ/α = 1, the limit is log(2).

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hm this is weird, i thought i answered the question. or maybe they're two different questions? line graph because i said so. i know im so helpful