Algebra 2 - F - Homework #7
Solve the following systems of equations. Graph the lines to check your
solutions. Make sure you show all the work:


1.{2x+y=2
{5x+3y − 9

2. {5x - 2y = -2
{3x + 4y − 30

3. {-x+2y =
{3x + y = 15

Please help

The surface area of the prism is 60 sq meters.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

We know, The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given prism has 9 m of length, 6 m of width, and 2 m of height.

Therefore, The surface area of the prism is,

= 2(9 + 6)×2 sq meters.

= 2×15×2 sq meters.

= 60 sq meters.

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The formula for the volume of a square prism is given as V = s^2 * h. V = s^2 * h = 1.5^2 * 8 = 2.25 * 8 = 18 cm^3 So the volume of the square prism is 18 cubic centimeters.

this is what weegy answered

If Keshawn is 1.45 meters tall. At 12 noon, he measures the length of a tree's shadow to be 15.05 meters. the height of the tree to the nearest hundredth of a meter is 2.02 meters.

To find the height of the tree, we can use the similar triangles method. Let's call the height of the tree "h".

Since Keshawn and the tree are standing in the same spot, the same light source is casting their shadows, so the ratios of their shadow lengths to their heights are equal. This means we can set up the following proportion:

1.45 / h = 15.05 / 10.8

We can solve for "h" by cross-multiplying:

h = 15.05 * 1.45 / 10.8

h = 2.02 meters

Therefore, the height of the tree to the nearest hundredth of a meter is approximately 2.02 meters.

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Answer: 5.13

Step-by-step explanation:

The surface area of a square pyramid net can be found by adding the areas of the base and the four triangular faces.

First, find the area of the base by multiplying the length and width of the square base.

Area of base = length × width

Next, find the area of one of the triangular faces by using the formula:

Area of triangle = 0.5 × base × height

Since there are four triangular faces in a square pyramid, multiply the area of one triangle by four to find the total area of the triangular faces.

Area of triangular faces = 4 × (0.5 × base × height)

Finally, add the area of the base and the area of the triangular faces to find the total surface area of the square pyramid net.

Surface area = Area of base + Area of triangular faces

= (length × width) + (4 × (0.5 × base × height))

= (length × width) + (2 × base × height)

So, the surface area of a square pyramid net is the sum of the area of the base and the area of the four triangular faces.

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The ratio 3:4 into percentage is 75%.

3/4 is expressed as 75% in terms of percentage.

Percentage:

In mathematics, a percentage is a number or ratio that represents a fraction of 100. This is one way of representing a dimensionless ratio between two numbers. Other methods include ratios, fractions, and decimals. Percentage is often indicated by writing a "%" sign after the number.

According to the Question:

The fraction 3/4 to an equivalent fraction with the denominator equal to 100

(3 × 25) / (4 × 25) = 75/100

Now,

75/100 is expressed as 75% in terms of percentage.

Another simple way to convert a fraction to a percentage is by multiplying the fraction by 100.

In this case, 3/4 × 100 = 75%

Thus, 3/4 is expressed as 75% in terms of percentage.

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The given expression is a fifth-degree polynomial.

An expression represents a polynomial when these following conditions are satisfied:

The exponents for this problem are given as follows:

5, 2 and 1.

Hence the function represents a polynomial, of the fifth degree, as the highest exponent is of 5.

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The required derivative of f(x) = ln(1 - x) is f'(x) = -1 / (1 - x).

A derivative is a two-party contract whose price or value is based on an underlying asset. Futures, options, forward contracts, and swaps are the four most popular types of derivatives. It is a financial instrument whose price and value are determined by the underlying assets.

The derivative of the natural logarithmic function is given by:

d/dx [ln(u(x))] = 1/u(x) * du/dx

So, to find the derivative of f(x) = ln(1 - x), we need to find the derivative of the inside function, which is 1 - x:

f'(x) = 1/[1 - x] * d/dx [1 - x]

= 1/[1 - x] * (-1)

= -1 / (1 - x)

So the derivative of f(x) = ln(1 - x) is f'(x) = -1 / (1 - x).

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Answer:

Each crust is 1.2 inches

Step-by-step explanation:

12/10 is 1.2

Answer:

Each crust is 1.2 inches.

Step-by-step explanation:

12 ÷ 10 = 1.2

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Since the two parallel lines are cut by a transversal and m∠3 = 41°, the measure of angles m∠6 and m∠8 include the following:

m∠6 = 139°.

m∠8 = 139°.

In Mathematics, parallel lines are two lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:

m∠3 = m∠5 (alternate interior angles)

m∠5 + m∠6 = 180° (linear pair postulate).

41° + m∠6 = 180°.

m∠6 = 180° - 41°

m∠6 = 139°

m∠6 = m∠8 (vertical angles theorem).

m∠8 = 139°.

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The value of the fraction is A = 20 / 9

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction be represented as A

Now , the first fraction is p = 5/6

Let the second fraction be q = 3/8

Now , the equation is A = p/q

On simplifying , we get

A = ( 5/6 ) / ( 3/8 )

A = ( 5/6 ) x ( 8/3 )

On further simplification , we get

The fraction A = ( 20 / 9 )

Hence , the fraction is A = 20/9

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Answer: B- about 349,471 deer.

To calculate the population after 12 years, we can use the formula:

N = N0 * (1 + r)^t

where N0 is the initial population (15,000), r is the growth rate (3%), and t is the number of years (12).

Plugging in the values:

N = 15,000 * (1 + 0.03)^12 = 15,000 * 1.95863 = 29,379.45 ≈ 349,471

Step-by-step explanation:

Answer:

$1.80 per 4 mini muffins

Step-by-step explanation:

12 mini muffins = 5.40

divide by 3

4 mini muffins = 1.80

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Answer:

If 68.3% of Americans believe that some psychics can help solve murder cases, then the percentage of Americans who do not believe this is:

100% - 68.3% = 31.7%

Therefore, the probability of randomly selecting someone who does not believe that some psychics can help solve murder cases is 31.7%.

Step-by-step explanation:

Answer

lines passing through the midpoint of each side which are perpendicular to the given side

Step-by-step explanation:

Answer:

d. 1/36

Step-by-step explanation:

as total outcomes is 36

and we can get 1 on both the dice just once

The composite figure has a total area of 258 square centimeters.

The diagram is the made up of a rectangle and two triangles.

A triangle's area is given by the formula

Triangle 1

= 1/2 x base x height.

= 1/2 × 4 × 12

= 24

Triangle 2

=  1/2 × 12 × 3

= 18

Area of a rectangle

= length x width

= 18 × 12

= 216

The total area

= 24 + 18 + 216

= 258 squared centimeter

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Answer:

180

Step-by-step explanation:

since both triangles are 90 degrees 90 plus 90 make 180

(-3, 4) is the solution to the given system of simultaneous equation

Given the system of equation

y = -x + 1

y = -1/3x + 3​

When solving graphically, the point of intersection of both lines on an xy plane is the solution to the system of equation.

According to the graph attached, the solution to the system of equation is (-3, 4).

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⇒ The general formula of a geometric sequence is [tex]ar^{n-1}[/tex] where a is the first term and r is the common ratio, now in the given a which is 3 and the common ratio r which is 3.

to get the 10th term we use the same general formula

[tex]a_{n} =ar^{n-1}[/tex]

where [tex]T_{n}[/tex] is the nth term that is then output and n is the place of the nth term in the general sequence.

For the 10th term we substitute  10 in the place of n and simplify to find the value of the output.

[tex]a_{10} =ar^{(10-1)} \\a_{10} =ar^{9} \\[/tex]

Now since we know which formula to use to get the 10th term we can substitute the known values of the variables to get the output .

[tex]a_{10} =(3)(3)^{9} \\a_{10} =59049[/tex]

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Answer:

She must score an 87 to obtain an average of 75.

Step-by-step explanation:

(66+72+x) / 3 = 75

x = 87

The value of the square root of 9 is 3.

The square root of a number is the value that, when multiplied by itself, gives the original number. In this case, we want to find the square root of 9.

We can start by finding the perfect squares that are less than 9. The perfect squares less than 9 are 1 and 4. We can see that 3 is between these two numbers, so the square root of 9 must be somewhere between 1 and 3.

We can test whether 3 is the square root of 9 by squaring it: 3 x 3 = 9. This confirms that 3 is indeed the square root of 9.

Another way to find the square root of 9 is to use a calculator or a mathematical formula. The formula for finding the square root of a number is √x = y, where y is the square root of x. In this case, x is 9, so we have √9 = 3.

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The Grade Point Average at Purdue University is determined using a 4.0 scale (GPA).

By using the Grade Point Average at Purdue University is determined using a 4.0 scale (GPA). By allocating each course a specific number of credit hours, which is normally decided by the number of hours the course meets per week, the GPA is generated. The student's letter grades for each subject are then translated into a number value on a 4.0 scale, as seen below:

A = 4.0 A- = 3.67 B = 3.0 B- = 2.67 C = 2.0 C- = 1.67 D = 1.0 F = 0.0

The sum of the products of the credit hours and the numerical values of the letter grades obtained is used to compute the student's GPA after each letter grade has been given a numerical value.

The Grade Point Average at Purdue University is determined using a 4.0 scale (GPA). By allocating each course a specific number of credit hours, which is normally decided by the number of hours the course meets per week, the GPA is generated.

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Answer: 60%

Step-by-step explanation:

2,400/4,000 x 100/1

0.6 x 100 = 60%

The amount of KES that one would have to get for R150 is given as 1053.54 KES

​The KES tells us of the Kenyan currency. That is the Kenyan shillings. The R is the name that is used to refer to the Rands

Hence we would have to convert rands to KES

1 south African Rand is given as 7.0236

then 150 rand would be = ?

Hence the amount you would get of KES is: 7.0236 * 150

= 1053.54 KES

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The conversion of 73 Kilogram (kg) pounds (lbs) is 160.9358 lbs

The standard metric conversion of a unit weight from one S.I. unit to another follows a standard approach that is universally acceptable and timeless. For the conversion of 1 kilogram to pounds, 1 kg is equivalent to  2.2046 lbs.

To convert 73 kilograms to pounds, multiply 73 kilograms by 2.2046 lbs. Mathematically;

[tex]=73 \ kg \times \dfrac{2.2046 \ lbs}{1 \ kg}[/tex]

Cancel the common units

[tex]=73 \times \dfrac{2.2046 \ lbs}{1}[/tex]

= 160.9358 lbs

Therefore, we can conclude that the conversion of 73 kilograms (kg) to metric pounds (lbs) is 160.9358 lbs.

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Since, 1 Tablespoon is equal to 15 Gram.

Therefore, 2 Tablespoon is equal to 1/8 cups or 29.5 grams.

Gram:

The gram (originally gram; SI unit symbol g) is a unit of mass in the International System of Units (SI), equal to one thousandth of a kilogram.

Originally defined in 1795 as "the absolute weight of a volume of pure water equal to one hundredth of a meter at the temperature at which ice melts." The positive temperature (~0 °C) was later changed to 4 °C, the temperature of maximum density of water.

However, towards the end of the 19th century, attempts were made to make the kilogram the base unit and the gram the derived unit. In 1960, the new International System of Units defined the gram as one thousandth of a kilogram (i.e., 1 gram equals 1 × 10-3 kg. As of 2019, the kilogram is defined by the International Bureau of Weights and Measures based on the fixed value of Planck's constant (h),  

6.62607015 × 10-34 kg⋅m2⋅s-1.

According to the Question:

Convert from tablespoons to grams by multiplying the volume by 14.786765 times the density of the ingredient or material.

Using this simple formula, it can be converted to:

Grams = Tablespoons × 14.786765 × Ingredient Density

Therefore,

Grams = 02 × 14.786765

           = 29.57353

So the volume in grams is equal to the number of tablespoons times the density of the material or material times 14.786765.

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Answer:

Two ways.

(1) 4 notebooks,3 pencils, have change $12;

(2)3 notebooks, 5 pencils, have no change.

Step-by-step explanation:

set student buy x notebooks and y pencils,

x≥3,y≥3,

60x+36y≤360

if x=3, 180+36y≤360

         36y≤180

             y≤5

and y≥3, so y={3,4,5}

(1)when y=3, 60x≤360-36x3=252, x≤4.2,so x=4,

and change=360-36x3-60x4=12

(2)when y=4, 60x≤360-36x4=216, x≤3.6,so x=3,

and change=360-36x4-60x3=36, since student have to spend as much as possible of his money, $36 can buy a pencil, so this is not accepted.

(3)when y=5, 60x≤360-36x5=180, x≤3, so x=3,

and change =360-36x5-60x3=0

The student has two ways to spend his money on notebooks and pens. In one option, she can buy 4 notebooks and 3 pens and in the other option she can buy 3 notebooks and 5 pens.

To find the student's possibilities to buy pens and notebooks we must take into account his total budget of $360. Additionally, the values of the notebooks and pens that are: $60 and $36 respectively.

We must multiply the value of the notebooks by the number of notebooks that we believe the student can buy, this would be a range between 3 and 4 notebooks. Additionally, once we decide the number of notebooks we can divide the remaining money in the value of the pens to find the number of pens that the student can buy. According to the above:

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The area of the enclosure is approximately 128.6 acres

To find the area of the trapezoid ABCD, we first need to find the lengths of its parallel sides. Let's use the fact that the angles of a quadrilateral add up to 360 degrees:

Angle ABC = 124 degrees

Angle BCD = 85 degrees

Angle CDA = 96 degrees

Angle DAB = 360 - 124 - 85 - 96 = 55 degrees

Now we can use the tangent function to find the lengths of the sides:

tan(2 degrees) = (height of AB) / (distance between Anna and Benito)

(height of AB) = (distance between Anna and Benito) × tan(2 degrees)

(distance between Anna and Benito) = (713 - 690) / tan(2 degrees) ≈ 18490.3 ft

(height of AB) ≈ 429.4 ft

Similarly, we can find the height of CD:

tan(3 degrees) = (height of AD) / (distance between Anna and Deon)

(height of AD) = (distance between Anna and Deon) × tan(3 degrees)

(distance between Anna and Deon) = (725 - 690) / tan(3 degrees) ≈ 8639.5 ft

(height of AD) ≈ 459.6 ft

Now we can use the trapezoid area formula:

Area = (height of AB + height of CD) × (sum of the parallel sides) / 2

Area = (429.4 + 459.6) × ((18490.3 + 8639.5) / 2) / 5280 ≈ 128.6 acres

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The area of the polygon will be equal to 58.1 square units.

A polygon's area is the region that it occupies. Polygons can be both regular and irregular in shape. Triangles, squares, rectangles, pentagons, hexagons, and other basic polygons are used in geometry. Each of these polygons has its own area.

A pentagon is a given polygon. The apothem is the perpendicular line drawn from the octagon's midpoint to the base of one of its sides.

The formula for determining the area of a regular polygon is expressed as

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 5

Area = 4² × 5 × tan(180/5)

Area = 80 × tan 36

Area = 58.1 Square units

Hence, the polygon will have an area of 58.1 Square units.

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Answer:

11/x because split is the same as divide so she split 11 pieces with x people

Step-by-step explanation: