Difference between algebra 1 and pre-algebra

In the triangle with B = 36°, a = 41, c = 20, b ≈ 45.3, C ≈ 29.5, A ≈ 114.5.

To solve the triangle, we can use the Law of Sines and the fact that the sum of angles in a triangle is 180 degrees.

Given:

[tex]- Angle \( B = 36° \)[/tex]

[tex]- Side \( a = 41 \)[/tex]

[tex]- Side \( c = 20 \)[/tex]

First, we need to find angle [tex]\( A \)[/tex]. We can use the fact that the sum of angles in a triangle is 180 degrees:

[tex]\[ A = 180 - B - C \][/tex]

We can find angle [tex]\( C \)[/tex] using the Law of Sines:

[tex]\[ \frac{\sin C}{c} = \frac{\sin B}{b} \][/tex]

Solving for [tex]\( C \):[/tex]

[tex]\[ \sin C = \frac{c \times \sin B}{b} \][/tex]

[tex]\[ \sin C = \frac{20 \times \sin 36°}{b} \][/tex]

[tex]\[ \sin C = \frac{20 \times 0.5878}{b} \][/tex]

[tex]\[ \sin C = \frac{11.756}{b} \][/tex]

Now we can find angle [tex]\( C \)[/tex] using the inverse sine function:

[tex]\[ C = \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]

Now, we can substitute [tex]\( C \) i[/tex]nto the equation for [tex]\( A \)[/tex] and solve for [tex]\( b \):[/tex]

[tex]\[ A = 180 - B - C \][/tex]

[tex]\[ A = 180 - 36 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]

[tex]\[ A = 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]

Since we know all three angles of the triangle, we can find [tex]\( b \)[/tex] using the Law of Sines again:

[tex]\[ \frac{\sin A}{a} = \frac{\sin B}{b} \][/tex]

[tex]\[ \sin A = \frac{a \times \sin B}{b} \][/tex]

[tex]\[ \sin A = \frac{41 \times \sin 36}{b} \][/tex]

[tex]\[ \sin A = \frac{41 \times 0.5878}{b} \][/tex]

[tex]\[ \sin A = \frac{24.0678}{b} \][/tex]

Now, we can find [tex]\( b \)[/tex] using the inverse sine function:

[tex]\[ b = \frac{24.0678}{\sin A} \][/tex]

Finally, we'll use the given values and calculate the closest option:

[tex]\[ A \approx 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]

[tex]\[ b \approx \frac{24.0678}{\sin A} \][/tex]

[tex]\[ c \approx 20 \][/tex]

B = 36°

[tex]\[ a = 41 \][/tex]

After the calculation, the closest option is:

[tex]\[ b \approx 45.3, \ C \approx 29.5, \ A \approx 114.5 \][/tex]

Complete Question:

Solve the triangle.

B = 36°, a = 41, c = 20

choices:

b ≈ 27.5, C ≈ 115.5, A ≈ 28.5

b ≈ 45.3, C ≈ 25.5, A ≈ 118.5

b ≈ 45.3, C ≈ 29.5, A ≈ 114.5

b ≈ 27.5, C ≈ 25.5, A ≈ 118.5

Answer:

the correct answer is A 7,3

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

The first and second system have the same solutions, the are equivalent systems of equations. Let's calculate solutions to demonstrate it:

[tex]\left \{ {{4x - 5y = 2} \atop { 3x - y = 8}} \right.[/tex]

If we multiply the second equations by -5, we can eliminate one variable and find the first solution:

[tex]\left \{ {{4x - 5y = 2} \atop { -15x +5y = -40}} \right.\\-11x=-38\\x=\frac{38}{11}[/tex]

Now, we use this value to find the other solution:

[tex]3x - y = 8\\3(\frac{38}{11})-y=8\\\frac{114}{11}-8=y\\ y=\frac{114-88}{11}=\frac{26}{11}[/tex]

The solution of the first system is [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]

[tex]\left \{ {{4x - 5y = 2} \atop { 10x - 7y = 18}} \right.[/tex]

We do the same process than we did before, but this time we have to multiply by [tex]-\frac{5}{7}[/tex]:

[tex]\left \{ {{4x - 5y = 2} \atop { -\frac{50}{7}x + 5y = \frac{90}{7} }} \right.\\\frac{28x-50x}{7}=\frac{-90+14}{7}\\-22x=-76\\x=\frac{38}{11}[/tex]

Then,

[tex]4x - 5y = 2\\4(\frac{38}{11})-5y=2\\\frac{152}{11}-2=5y\\ 5y=\frac{152-22}{11}\\y=\frac{130}{5(11)}=\frac{26}{11}[/tex]

The solution of the second system is  [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]

Therefore, system 1 and system 2 are equivalent.

1 1/4 is 5 times larger than 1 /4

 so b is 5 times larger than 2

5*2 =10

so 1/4 is to 1 1/4 as 2 is to 10

b=10

Answer:

The correct option is D) 60°

Step-by-step explanation:

Consider the provided triangle.

From the provided figure it is given that one angle is 60° and we need to find the value of y.

As we know the sum of all interior angle in a triangle is 180°.

y°+y°+60°=180°

Now solve the above equation to find the value of y.

2y°+60°=180°

2y°=180°-60°

2y°=120°

y°=120°÷2

y°=60°

Hence, the value of y is 60°.

Thus, the correct option is D) 60°

Answer:

26 sq. units

Step-by-step explanation:

a-p-e-x

The area of the triangle is 26 sq.unit, the correct option is B.

A triangle is a polygon with three sides, angles and vertices.

The triangle is classified into various types on the basis of the angle and on the basis of the equality of the length of the sides, as obtuse , acute and right angled triangle and scalene, isosceles and equilateral triangle.

The triangle is shown in the figure has side 13 and height 4 units.

The area of the triangle whose base and height is given is calculated by using the formula:

Area = (1/2) * base * height

Substituting the value in the formula.

Area = (1/2) * 13 *4

Area = 13 * 2

Area = 26 sq.unit

To know more about Triangle

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Answer:3y is the answer

Step-by-step explanation:

Answer:

I believe the answer would be "Multiply the area of the triangular base by the prism’s height." i'm not sure tho

Step-by-step explanation:

you can correct me if im wrong

1st minute = 0.46

 additional minutes = 0.37

6.75 -0.46 = 6.29

6.29/0.37 =17

 17 +1 = 18 total minutes

Answer:

A

Step-by-step explanation:

Mary grew 15 tomatoes. A simple algebraic equation was formulated and solved to determine the quantity: m + 3m - 6 = 54, where m represents the number of tomatoes grown by Mary.

Given that Jolene had 3 times as many tomatoes as Mary and birds ate 6 of Jolene's tomatoes, and together they have 54 tomatoes, we need to set up an equation to solve for the number of tomatoes Mary grew.

Let's denote the number of tomatoes Mary grew as m. Therefore, Jolene grew 3m tomatoes. Since birds ate 6 of Jolene's tomatoes, we have 3m - 6 for the number of tomatoes left with Jolene. The equation representing the total number of tomatoes then becomes m (Mary's tomatoes) + (3m - 6) (Jolene's remaining tomatoes) = 54. Simplifying this equation:

m + 3m - 6 = 54

4m - 6 = 54

4m = 60

m = 15

Therefore, Mary grew 15 tomatoes.

To find the acute angle A when cosA=0.1045, use a calculator in degree mode to perform the inverse cosine operation and round the result to the nearest degree, which is approximately 84 degrees.

To find the measure of acute ">∠A when cosA=0.1045, we use the inverse cosine function (also known as arccos or cos-1). Make sure your calculator is in degree mode. The approximate measure of acute ∠A can be calculated as follows:

Using a calculator set to degree mode, the result for cos-1(0.1045) should be approximately 84 degrees, when rounded to the nearest whole degree.

Answer: Cylinder.

Step-by-step explanation: Lip-gloss tubes may have different shapes, but the usual form of a lip-gloss tube is, as the name says, a tube.

This means that it has a circular base and a circular top, and a given height that connects the base and the top, the geometrical shape that has this shape is called a cylinder.

Final answer:

To approximate solutions for the system of equations, enter them into graphing technology, look for intersection points, and match them to the provided coordinates, rounding to the nearest tenth.

Explanation:

To approximate the solution(s) to the system of equations using technology, such as a graphing calculator or graphing software, you typically enter the equations into the device or program and view their intersection points. These intersection points represent the solutions to the system of equations. To get an accurate approximation to the nearest tenth of a unit, you may zoom in on the graph to clearly see where the lines intersect or use the device's built-in features to find the intersection.

You would then compare the given coordinates to the intersection points you found graphically and select the ones that match:

(0,0)

(9.2, 1.5)

(9.6, 3.5)

(5.3, 9.8)

(3.5, 9.6)

Remember to round your values to the nearest tenth as required and to quickly check if these values make sense in the context of the original problem.

The point of intersection of lines represents the common solution of the system of linear equations. The solution of linear equations given in the graph is (0,2).

Linear equation represents a line on the graph. The system of linear equations represents couple/s of linear equations or lines.

The solution of system of linear equations means the common point satisfying the different linear equations.

Graphically, the point of intersection of two lines represents the common solution of these two lines or simply the solution of the system of linear equations.

So, the point of intersection from the given graph is (0,2).

Therefore, the solution of linear equations given in the graph is (0,2).

For more details, refer to the link:

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