The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted. The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules.

Answer:

Step-by-step explanation:

You can start by drawing a diagram.  Then, you need to pick the shorter side and designate it as "x".  The longer side must be "x+8".

The formula for area of a rectangle is A=l*w.  Since the area is 84, then you can use the A=l*w formula.  84 = x(x+8) would be the equation to solve for x.

Now, you need to put the equation in standard form.  So, x2 + 8x - 84 = 0.

Since you can't solve this quadratic using factoring, you need to complete the square.

To complete the square you need to add 84 to both sides.  Now you have x2 + 8x = 84.  Take the coefficient for the x term (8) and divide by 2.  Now square it.  That would be 42, so 16.  Now you have x2 +8x +16 = 100.

Factor x2 +8x +16, so (x+4)2 = 100

If you use the square root property, you have x+4 = 10.  Therefore, x = 6 (the short side) and 14 is the long side.

I hope that helps.

Answer:

-b = √(3a+28)

Step-by-step explanation:

3a = -28 + b²

3a + 28 = b²

√(3a + 28) = √b²

negative solution:

-b = √(3a+28)

Therefore, they took in $43.10 selling watermelons that day.

Describe the dollar sign($)?

The dollar sign, also referred to as the peso sign, is a symbol that looks like a capital "S" crossed with one or two vertical strokes ($ or Cifro symbol depending on typeface), and it's used to denote the unit of many different currencies around the world, including the majority of currencies denominated in "pesos" and "dollars." The Portuguese word for the specifically double-barred Cifro symbol is cifro.

The sign is also present in a number of compound currency symbols, including those for the Nicaraguan córdoba (C$) and the Brazilian real (R$).

If they sold 5/6 of the watermelons, then they sold 8/6 of the watermelons. So, they sold 4/3 of the watermelons.

If they sold 4/3 of the watermelons for $5.75 each, then they sold each watermelon for $4.31.

They sold 5/6 of the watermelons for $5.75 each,

so they sold

5/6 × 4/3

= 20/18 = 10/9 of the watermelons for $4.31 each.

$4.31 * 10 = $43.10 That day.

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[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} t_1=0.5\\ t_2=0.75 \end{cases}\implies \cfrac{f(0.75)-f(0.5)}{0.75 - 0.5}\implies \cfrac{7.744-6.275}{0.75-0.5} \\\\\\ \cfrac{1.469}{0.25}\implies 5.876~\frac{meters}{second}[/tex]

The calculated surface area of the cuboid has a value of 192 square feet.

The surface area of a cuboid is the sum of the areas of all six faces.

In this case, the dimensions of the cuboid are 8 ft by 8 ft by 2 ft. So we can calculate the surface area as follows:

Therefore, the total surface area of the cuboid is:

= 2(64 sq ft) + 2(16 sq ft) + 2(16 sq ft)

= 128 sq ft + 32 sq ft + 32 sq ft

= 192 sq ft.

So the surface area of the given cuboid is 192 square feet.

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You roll a number cube two times. The theoretical probabilities are accurate is P(even number then odd number)= 1/4

Probability:

Probability is the likelihood of something happening. When we are unsure of the outcome of an event, we can talk about the likelihood of certain outcomes - how likely are they to occur. The analysis of events governed by probability is called statistics.

According to the Question:

Let P(E), P(H), and P(E and H) be the probabilities of rolling an even number on a die, heads on a coin, and heads, respectively.

We know,

P(E and H) = P(E)×P(H)

Now, to find P(E and H), we have to find P(E) and P(H).

Total number of possible results of a die roll = 6

Favorable results of an event E = {2, 4, 6}

∴ Number of favorable results of an event E = 3

Therefore,

P(E) = number of favorable results of an event event E / possible results The total number of

⇒ P(E)=3/6=1/2

There are two possibilities for tossing a coin = {H, T}

∴ Probability of heads on a flip coin = P(H)= 1/2

Finally, the probability that

Lewis gets an even number and flips heads =

1/2×1/2 = 1/4

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The intercepted arcs of the inscribed angle are in proportion to the inscribed angle itself. In other words, the larger the inscribed angle, the more significant the intercepted arc it cuts, and vice versa. So, in an equilateral triangle, each of the inscribed angles of the circle measures 60°, which is half of the central angle of 120° that intercepts the same arc.

The angle measure and intercepted arcs of inscribed angles in an equilateral triangle inscribed in a circle are related, and the relationship between inscribed angles and central angles in a circle is that the inscribed angles are half of the central angle. Let us have a more in-depth understanding of these two angles.An inscribed angle is an angle that has its vertex on the circle and is formed by two chords that intersect at that point. It is half of the central angle that intercepts the same arc.A central angle is an angle whose vertex is at the center of the circle, and the sides of the angle pass through any two points on the circumference of the circle.

For an equilateral triangle inscribed in a circle, each angle measures 60°, and the central angle measures 120°. So, each of the two inscribed angles measures half of the central angle, i.e., 60°.The relationship between inscribed angles and intercepted arcs.

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Answer:

The value of the percentage increase = 6.7% × 59

The new value = 59 + The value of the percentage increase

Step-by-step explanation:

The new value =

59 + The value of the percentage increase =

59 + (6.7% × 59) =

59 + 6.7% × 59 =

(1 + 6.7%) × 59 =

(100% + 6.7%) × 59 =

106.7% × 59 =

106.7 ÷ 100 × 59 =

106.7 × 59 ÷ 100 =

6,295.3 ÷ 100 =

62.953 ≈

62.95

Answer:

Select the one at the lowest point on the right of the y-axis. This point has an x value (horizontal) of 1 and 1/2, with a y value (vertical) of -5.

Hoped this helped.

Answer:

a) Account 2 will pay Lewis more interest after 15 years because it pays compound interest, which means that the interest is calculated on both the initial deposit and the accumulated interest from previous years. On the other hand, Account 1 pays simple interest, which means that the interest is calculated only on the initial deposit.

b) To calculate the amount of interest paid by each account, we can use the following formulas:

For Account 1: I = P × r × t, where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years.

I = 3100 × 0.07 × 15 = £3255

For Account 2: A = P × (1 + r/n)^(n × t), where A is the amount of money at the end of the investment period, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, n = 1 (compounded annually), so the formula simplifies to:

A = 3100 × (1 + 0.05)^15 = £5569.62

The interest earned by Account 2 is the difference between the final amount and the initial deposit:

I = A - P = £5569.62 - £3100 = £2469.62

Therefore, Account 2 will pay £2469.62 - £3255 = -£785.38 less in interest than Account 1 after 15 years.

Step-by-step explanation:

Answer:

The answer is Sin B

Step-by-step explanation:

I remember in 8th grade doing this

If Cody was 10 %, percent taller than he was on the first day of school last year then he was 150 cm tall on the first day of school last year.

 To find out the height of Cody on the first day of school last year, we need to perform a calculation as follows:

           Let's say their height of Cody on the first day of school last year is 'x'.

           His height of Cody on the first day of school this year is 165 cm.

           Cody is 10% taller than he was on the first day of school last year, so:

                      165 = x + (10% of x)

    Simplifying this equation will give

                        165 = x + 0.1 x 165

                               = 1.1xx

                               = 150

           Therefore, Cody was 150 cm tall on the first day of school last year.

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Answer:

3

Step-by-step explanation:

The probability of selecting green, blue, red, and yellow marbles from the bag is 1/35.

To find the probability of choosing specific marbles from the bag, we first need to find out the total number of ways in which four marbles can be selected from seven marbles.

The total number of ways in order to select 4 marbles from 7 marbles is given by the combination formula:

C(7,4) = 7!/(4!3!) = 35

There are 35 ways in which four marbles which will be selected from the bag. We need to find out the number of ways in which we can select green, blue, red, and yellow marbles.

We have only one way to select these specific four marbles from the bag. Number of ways to select green, blue, red, and yellow marbles is 1.

Probability of selecting green, blue, red, and yellow marbles:

P = (Number of ways to select green, blue, red, and yellow marbles) / (Total number of ways to select 4 marbles)

P = 1/35

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Step-by-step explanation:

The y-axis is where x = 0 ....so the y-axis intercept occurs at x = o

 put  in   '0' for 'x'

y = 0^2 + 2(0) + 10       <===== 10 is the y-axis intercept

Finally, use the sum of interior angles equation again to find the measure of angle Y:
m∠Y = 180° - m∠X - m∠Z

Hello! To find the measure of each angle in triangle XYZ, we need to use the fact that the sum of the interior angles of a triangle is 180°. We are given that m∠X = (32x)° and m∠Z = (6.5x)°. Let's represent the measure of angle Y as m∠Y.

Now we can write an equation:

m∠X + m∠Y + m∠Z = 180°
(32x)° + m∠Y + (6.5x)° = 180°

We need to find the value of x and m∠Y. First, combine the x terms:

38.5x° + m∠Y = 180°

Now, we'll solve for x and then find m∠Y using the equation above. To find x, subtract m∠Y from both sides:

38.5x° = 180° - m∠Y

After finding the value of x, substitute it back into the expressions for m∠X and m∠Z to find the measures of angles X and Z.

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Answer:

Step-by-step explanation:129412515968569028414 m

Required value of N is 1

This is a problem of simplification which is major part of Algebra.

Some Algebra's formulas:

[tex]{(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ {(x + y)}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ {x}^{2} + {y}^{2} = {(x - y)}^{2} + 2xy \\ {x}^{2} - {y}^{2} = {(x + y)}^{2} - 2xy \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )[/tex]

Given equation is [tex] - 3(8 \times N) = - 24[/tex]

We want to Simplify both side.

Multiplying (-3) and (8×N),

-24N = -24

Now we are dividing (-24) by (-24),

N = -24/-24

N = 1

Therefore, required value of N is 1.

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Answer:

We can use trigonometry to solve this problem. Let's call the distance from point A to the boat "x" and the distance from point B to the boat "y". Then we have:

In triangle AOC, tan(12) = OC / x

In triangle BOC, tan(64) = OC / y

We want to find the distance from point A to point B, which is the difference between x and y:

Distance AB = y - x

To solve for x and y, we need to eliminate OC. We can do this by setting the two expressions for OC equal to each other and solving for OC:

tan(12) = OC / x

OC = x tan(12)

tan(64) = OC / y

OC = y tan(64)

x tan(12) = y tan(64)

y = x tan(12) / tan(64)

Now we can substitute this expression for y into the equation for Distance AB:

Distance AB = y - x

Distance AB = x tan(12) / tan(64) - x

We can simplify this expression by factoring out an x:

Distance AB = x (tan(12) / tan(64) - 1)

Now we just need to plug in the values and calculate:

Distance AB = x (0.2174 - 1)

Distance AB = -0.7826 x

Since distance cannot be negative, we know that x > 0. Therefore, the boat is between point A and point B, and the distance from point A to point B is:

Distance AB = x (0.2174 - 1)

Distance AB = -0.7826 x

Distance AB ≈ 1.28 x

We don't know the actual value of x, but we can see that the distance from point A to point B is approximately 1.28 times the distance from point A to the boat when Jaxson measured the angle of depression to be 12 degrees.

Step-by-step explanation:

Answer:434

Step-by-step explanation:It’s correct

Therefore, the area of triangle XYZ is 2 square units.

Area is a measure of the size of a two-dimensional shape or surface. It is defined as the amount of space inside the boundary of a flat or planar figure, such as a triangle, square, rectangle, or circle. The unit of area is typically square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).

Here,

To determine the area of triangle XYZ with coordinates (6,1), (2,5), and (10,9), we can use the formula for the area of a triangle:

Area = (1/2) * base * height

where the base is any side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.

Distance between (6,1) and (2,5):

= √((6 - 2)² + (1 - 5)²)

= √(20)

So, the base of the triangle is √(20).

We can use the formula for the distance between a point and a line to do this:

Distance from (10,9) to line passing through (6,1) and (2,5):

= |(10 - 6)(5 - 1) - (2 - 6)(9 - 1)| / √((5 - 1)² + (6 - 2)²)

= 4 / √(20)

So, the height of the triangle is 4 / √(20).

Now, we can plug in the values for the base and height into the formula for the area of a triangle:

Area = (1/2) * base * height

= (1/2) * √(20) * (4 / √(20))

= 2

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The number of possible ways to select two vehicles = 55

Let m represents the number of cars and n represents the number of trucks.

An auto dealer has 5 different cars and 6 different trucks.

This means that m = 5 and n = 6

so, the total number of vehicles (t) would be,

t = m + n

t = 5 + 6

t = 11

Let us assume that p represents the number of possible ways to select two vehicles.

We use the combination formula.

[tex]^{n}C_r=\frac{n!}{r!(n-r)!}[/tex]

here, n = 11 and r = 2

Using combination formula,

p = [tex]^{11}C_2[/tex]

p = [tex]\frac{11!}{2!\times (11-2)!}[/tex]

p = 55

Therefore, the number of possible ways = 55

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Answer:

Step-by-step explanation:

[tex]x^2=17^2-15^2[/tex]     (Pythagoras Theorem)

[tex]x^2=64[/tex]

[tex]x=8[/tex]

Answer: 1.061

Step-by-step explanation:

1). Based on conditions, formulate: 1+6.1%

2). Then convert to a decimal: 1.061

Answer: the answer is A

reason:  224294 * 43 / 100 = around 96320

Answer: 2,000

Step-by-step explanation:

4 x 100 = 400

6 x 100= 600

400 + 600= 1,000

10 x 100= 1,000

1,000 + 1,000= 2,000

Answer:

80.925

Step-by-step explanation:

124.5 x 0.35 = 43.575

124.5 - 43.575 = 80.925

Answer:

[tex]\boxed{-\frac{1}{8} }[/tex]

Step-by-step explanation:

De acuerdo al inverso multiplicativo se cumple lo siguiente:

[tex]a\times \frac{1}{a}= \frac{a}{a}=1[/tex]

Por lo tanto:

[tex]-8 \times \frac{1}{-8}=1[/tex]

El número que cumple con el enunciado es [tex]-\frac{1}{8}[/tex]

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

We have shοwn algebraically that the sοlutiοns tο the system οf equatiοns F(x) = g(x) are [tex](-2, -3)[/tex] and [tex](1, 0)[/tex].

A system οf equatiοns in algebra is made up οf twο οr mοre equatiοns that are sοlved tοgether. "A grοup οf equatiοns satisfied by the same set οf variables are called a system οf linear equatiοns. Finding the values οf the variables emplοyed in the system οf equatiοns is the first step tοwards sοlving it.

While maintaining the balance οf the equatiοns οn bοth sides, we cοmpute the values οf the unknοwn variables. Finding a variable whοse value makes the cοnditiοn οf all the given equatiοns true is the primary gοal οf sοlving an equatiοn system.

Tο prοve that these cοοrdinate pοints are sοlutiοns, we need tο substitute them intο bοth equatiοns and verify that they satisfy the equatiοns. Let's start with (-2, -3):

[tex]F(-2) = (-2)^2 + 2(-2) - 1 = 4 - 4 - 1 = -1[/tex]

[tex]g(-2) = (-2) - 1 = -3[/tex]

We can see that [tex]F(-2) = g(-2)[/tex] , sο[tex](-2, -3)[/tex]is a sοlutiοn.

Nοw let's check (1, 0):

[tex]F(1) = 1^2 + 2(1) - 1 = 2[/tex]

[tex]g(1) = 1 - 1 = 0[/tex]

Again, we can see that F(1) = g(1), sο (1, 0) is alsο a sοlutiοn.

Therefοre, we have shοwn algebraically that the sοlutiοns tο the system οf equatiοns F(x) = g(x) are (-2, -3) and (1, 0).

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The cost of materials for the cheapest container is 69.6 dollars.

Let's first express the dimensions of the rectangular container in terms of a single variable. Let the width of the base be x meters, then the length of the base is 2x meters, and the height of the container is 10/(2x^2) = 5/x^2 meters, since the volume of the container is 10 cubic meters.

The area of the base is x * 2x = 2x^2 square meters, so the cost of the base is 10 * 2x^2 = 20x^2 dollars.

The area of each side of the container is (2x)(5/x^2) = 10/x square meters, so the cost of the four sides is 4 * (10/x) * 6 = 240/x dollars.

The total cost C of the materials is the sum of the cost of the base and the cost of the sides:

C = 20x^2 + 240/x

To find the value of x that minimizes this expression, we can take its derivative with respect to x and set it equal to zero:

dC/dx = 40x - 240/x^2 = 0

Solving for x, we get:

x^3 = 6

x = (6)^(1/3)

Substituting this value of x back into the expression for C, we get:

C = 20(6)^(2/3) + 240/(6)^(1/3) ≈ 69.6 dollars

Therefore, the cost of materials for the cheapest rectangular container is approximately 69.6 dollars.

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