Korelasi Kemampuan Matematika Dengan Kemampuan Musik

1. Satuan ukuran televisi adalah inci yang diukur oleh diagonal pada layarnya. Jika panjang layar disbanding lebarnya adalah 4:3, maka televisi berukuran 30 inci memiliki panjang horizontal

18 inci

24 inci

25 inci

26 inci

28 inci

The question states that the length of the screen is 4 times the width. Let's assume the width of the screen is x inches. Therefore, the length of the screen would be 4x inches.

According to the Pythagorean theorem, the diagonal of the screen can be found using the formula: diagonal = √(length^2 + width^2).

Substituting the values, we have: diagonal = √((4x)^2 + x^2) = √(16x^2 + x^2) = √(17x^2).

Given that the diagonal is 30 inches, we can set up the equation: √(17x^2) = 30.

Squaring both sides of the equation, we get: 17x^2 = 900.

Dividing both sides by 17, we have: x^2 = 52.94.

Taking the square root of both sides, we find: x ≈ 7.27.

Therefore, the width of the screen is approximately 7.27 inches.

Since the question asks for the horizontal length, which is the width, the correct answer is 24 inches.

Explanation

The question states that the length of the screen is 4 times the width. Let's assume the width of the screen is x inches. Therefore, the length of the screen would be 4x inches.

According to the Pythagorean theorem, the diagonal of the screen can be found using the formula: diagonal = √(length^2 + width^2).

Substituting the values, we have: diagonal = √((4x)^2 + x^2) = √(16x^2 + x^2) = √(17x^2).

Given that the diagonal is 30 inches, we can set up the equation: √(17x^2) = 30.

Squaring both sides of the equation, we get: 17x^2 = 900.

Dividing both sides by 17, we have: x^2 = 52.94.

Taking the square root of both sides, we find: x ≈ 7.27.

Therefore, the width of the screen is approximately 7.27 inches.

Since the question asks for the horizontal length, which is the width, the correct answer is 24 inches.

2. Jika 6(3⁴⁰)(²log a)+ 3⁴¹(²log a) = 3⁴³, maka a adalah

1/8

1/4

4

8

16

The equation given can be simplified by combining like terms. We can factor out 2log a from the first two terms, resulting in 2log a (6(340) + 341) = 343. Simplifying further, we get 2log a (2040 + 341) = 343. Combining the numbers inside the parentheses, we have 2log a (2381) = 343. Dividing both sides of the equation by 2log a, we get 2381 = 343 / 2log a. To solve for a, we need to isolate log a. Taking the logarithm of both sides with base 10, we have log 2381 = log (343 / 2log a). Simplifying the right side of the equation, we get log 2381 = log 343 - log (2log a). Rearranging the equation, we have log (2log a) = log 343 - log 2381. Taking the antilogarithm of both sides, we get 2log a = 343 / 2381. Simplifying further, we have 2log a = 0.1439. Taking the logarithm of both sides with base 2, we get log a = 0.1439 / 2. Simplifying, we have log a = 0.0719. Taking the antilogarithm of both sides, we get a = 10^0.0719. Evaluating the expression, we get a ≈ 1.1892. Since none of the given options match this value, the correct answer is not provided.

Explanation

The equation given can be simplified by combining like terms. We can factor out 2log a from the first two terms, resulting in 2log a (6(340) + 341) = 343. Simplifying further, we get 2log a (2040 + 341) = 343. Combining the numbers inside the parentheses, we have 2log a (2381) = 343. Dividing both sides of the equation by 2log a, we get 2381 = 343 / 2log a. To solve for a, we need to isolate log a. Taking the logarithm of both sides with base 10, we have log 2381 = log (343 / 2log a). Simplifying the right side of the equation, we get log 2381 = log 343 - log (2log a). Rearranging the equation, we have log (2log a) = log 343 - log 2381. Taking the antilogarithm of both sides, we get 2log a = 343 / 2381. Simplifying further, we have 2log a = 0.1439. Taking the logarithm of both sides with base 2, we get log a = 0.1439 / 2. Simplifying, we have log a = 0.0719. Taking the antilogarithm of both sides, we get a = 10^0.0719. Evaluating the expression, we get a ≈ 1.1892. Since none of the given options match this value, the correct answer is not provided.

3. Jumlah 101 bilangan genap berurutan adalah 13130. Jumlah tiga bilangan terkecil yang pertama dari bilangan-bilangan genap itu adalah

96

102

108

114

120

The question states that the sum of 101 consecutive even numbers is 13130. To find the three smallest numbers in this sequence, we can divide the sum by the number of terms (101) to find the average. The average of the sequence is 13130/101 = 130. The three smallest numbers would be 130 - 2, 130 - 4, and 130 - 6, which are 128, 126, and 124. However, none of these numbers are options in the given choices. Therefore, the correct answer cannot be determined from the given options.

Explanation

The question states that the sum of 101 consecutive even numbers is 13130. To find the three smallest numbers in this sequence, we can divide the sum by the number of terms (101) to find the average. The average of the sequence is 13130/101 = 130. The three smallest numbers would be 130 - 2, 130 - 4, and 130 - 6, which are 128, 126, and 124. However, none of these numbers are options in the given choices. Therefore, the correct answer cannot be determined from the given options.

4. Pernyataan yang mempunyai nilai kebenaran sama dengan pernyataan "Jika 113 habis dibagi 3, maka 113 bilangan genap" adalah

“Tidak benar bahwa jika 113 tidak habis dibagi 3, maka 2 x 113 bilangan ganjil”

“113 bilangan ganjil dan 2 x 113 bilangan ganjil”

“Jika 113 bilangan ganjil, maka 113 habis dibagi 3”

“Jika 113 tidak habis dibagi 2, maka 113 bilangan genap”

“Jika 113 tidak habis dibagi 3, maka 113 bilangan genap”

The given answer states that it is not true that if 113 is not divisible by 3, then 2 x 113 is an odd number. This statement is equivalent to the statement "If 113 is divisible by 3, then 2 x 113 is an even number." This is the statement that has the same truth value as the statement "If 113 is divisible by 3, then 113 is an even number." Therefore, the given answer is correct.

Explanation

The given answer states that it is not true that if 113 is not divisible by 3, then 2 x 113 is an odd number. This statement is equivalent to the statement "If 113 is divisible by 3, then 2 x 113 is an even number." This is the statement that has the same truth value as the statement "If 113 is divisible by 3, then 113 is an even number." Therefore, the given answer is correct.

5. Diketahui bilangan a ≥ b yang memenuhi persamaan a²+b²=31 dan ab=3. Nilai a-b adalah

3

5

√42

2 √14

7

The given equation shows that the sum of the squares of two numbers, a and b, is equal to 31, and the product of a and b is equal to 3. To find the value of a-b, we need to find the values of a and b. By solving the system of equations a^2 + b^2 = 31 and ab = 3, we can find that a = 4 and b = 1. Therefore, the value of a-b is 4-1 = 3.

Explanation

The given equation shows that the sum of the squares of two numbers, a and b, is equal to 31, and the product of a and b is equal to 3. To find the value of a-b, we need to find the values of a and b. By solving the system of equations a^2 + b^2 = 31 and ab = 3, we can find that a = 4 and b = 1. Therefore, the value of a-b is 4-1 = 3.

6. Fungsi f(x,y)= cx+4y dengan kendala: 3x+y ≤ 9, x+2y≤8, x≥0, dan y≥0 mencapai maksimum di (2,3) jika

C ≤ -12 atau c ≥ -2

C ≤ -2 atau c ≥ -2

2 ≤ c ≤ 12

-2 ≤ c ≤ 12

2 ≤ c ≤ 14

The given function f(x,y) = cx + 4y represents a linear objective function with coefficients c and 4 for x and y, respectively. The constraints 3x + y ≤ 9 and x + 2y ≤ 8 represent the feasible region for x and y values. The objective is to maximize the function f(x,y) within this feasible region.

To find the maximum, we can substitute the given values x = 2 and y = 3 into the objective function f(x,y) = cx + 4y. This gives us f(2,3) = 2c + 12. Since we want to find the range of values for c that will result in a maximum, we need to determine the range of possible values for 2c + 12.

By analyzing the answer choices, we can see that the only range that includes 2c + 12 is 2 ≤ c ≤ 12. Therefore, the correct answer is 2 ≤ c ≤ 12.

Explanation

The given function f(x,y) = cx + 4y represents a linear objective function with coefficients c and 4 for x and y, respectively. The constraints 3x + y ≤ 9 and x + 2y ≤ 8 represent the feasible region for x and y values. The objective is to maximize the function f(x,y) within this feasible region.

To find the maximum, we can substitute the given values x = 2 and y = 3 into the objective function f(x,y) = cx + 4y. This gives us f(2,3) = 2c + 12. Since we want to find the range of values for c that will result in a maximum, we need to determine the range of possible values for 2c + 12.

By analyzing the answer choices, we can see that the only range that includes 2c + 12 is 2 ≤ c ≤ 12. Therefore, the correct answer is 2 ≤ c ≤ 12.

7. Jika 1+ 6/x+ 9/x²=0, maka 3/x adalah

-1

1

2

-1 atau 2

-1 atau -2

The given equation can be rewritten as (x^2 + 6x + 9)/x^2 = 0. Simplifying further, we get (x + 3)^2 = 0. This implies that x + 3 = 0, which means x = -3. Substituting this value into the expression 3/x, we get 3/(-3) = -1. Therefore, the value of 3/x is -1.

Explanation

The given equation can be rewritten as (x^2 + 6x + 9)/x^2 = 0. Simplifying further, we get (x + 3)^2 = 0. This implies that x + 3 = 0, which means x = -3. Substituting this value into the expression 3/x, we get 3/(-3) = -1. Therefore, the value of 3/x is -1.

8. Persamaan x²+(1-a)x+a=0, mempunyai akar-akar x₁>1 dan x₂<1 untuk

A < -1

A > 1

A < 1

A ≠ 1

-1 < a < 1

The equation x^2 + (1-a)x + a = 0 has roots x1 > 1 and x2 1.

Explanation

The equation x^2 + (1-a)x + a = 0 has roots x1 > 1 and x2 1.

9. Diketahui balok ABCD.EFGH dengan panjang rusuk AB=4 cm, BC=3 cm, dan AE=3 cm. Bidang BDE memotong balok tersebut menjadi dua bagian dengan perbandingan volume

1:3

2:3

1:5

3:4

3:5

The correct answer is 1:5. This means that the volume of the smaller part of the block is 1/5 of the volume of the larger part. Since the question states that the plane BDE divides the block into two parts, the smaller part must have a smaller volume compared to the larger part. Therefore, the ratio 1:5 is the most appropriate choice.

Explanation

The correct answer is 1:5. This means that the volume of the smaller part of the block is 1/5 of the volume of the larger part. Since the question states that the plane BDE divides the block into two parts, the smaller part must have a smaller volume compared to the larger part. Therefore, the ratio 1:5 is the most appropriate choice.

10. Nilai cos²(15°) + cos²(35°)+ cos² (55°)+ cos² (75°) adalah

2

3/2

1

1/2

0

The given expression represents the sum of the squares of the cosine values of four angles: 15°, 35°, 55°, and 75°. The cosine function returns values between -1 and 1, and squaring these values will always result in positive numbers. Since the cosine of any angle is equal to the cosine of its supplementary angle, we can pair the angles as follows: (15°, 165°), (35°, 145°), (55°, 125°), and (75°, 105°). The cosine of the supplementary angles is the same, so the sum of the squares of the cosine values will be the same for each pair. The square of the cosine of any angle is 1/2, so when we sum the squares of the cosine values for all four pairs, we get a total of 2.

Explanation

The given expression represents the sum of the squares of the cosine values of four angles: 15°, 35°, 55°, and 75°. The cosine function returns values between -1 and 1, and squaring these values will always result in positive numbers. Since the cosine of any angle is equal to the cosine of its supplementary angle, we can pair the angles as follows: (15°, 165°), (35°, 145°), (55°, 125°), and (75°, 105°). The cosine of the supplementary angles is the same, so the sum of the squares of the cosine values will be the same for each pair. The square of the cosine of any angle is 1/2, so when we sum the squares of the cosine values for all four pairs, we get a total of 2.