Point T' has coordinates (-3, 4). If it was translated up 3 units, what were the coordinates of its pre-image?

(0, 4)
(-3, 7)
(-3, 1)
(-6, 4)

Answer:

b.

21

Step-by-step explanation:

The triangle is a right triangle as the sides follow the Pythagorean theorem. The angles opposite the sides are 90° (largest), 53.13°, and 36.87° (smallest), listed from largest to smallest based on side lengths.

The student's question involves a triangle with sides of lengths 3 cm, 4 cm, and 5 cm and asks for the angles to be listed from smallest to largest. Since these side lengths satisfy the Pythagorean theorem (32 + 42 = 52), the triangle is a right triangle, with the right angle opposite the longest side, MO. Using the properties of a right triangle, we can determine that the smallest angle is opposite the shortest side, NM, and the next larger angle is opposite the intermediate side, NO.

To find the actual angle measurements, we would typically use trigonometric ratios such as sine, cosine, or tangent. However, since this is a 3-4-5 triangle, we already know that the angles are 90° for the right angle, and 36.87° and 53.13° for the other two angles, respectively. Thus, the angle opposite NM (3 cm) is the smallest, the angle opposite NO (4 cm) is larger, and the angle opposite MO (5 cm) is the largest, at 90 degrees.

The angle measurements in a right triangle will always follow this pattern based on the lengths of the sides, making it a straightforward matter to list them from smallest to largest.

To find the exact length of the curve, we can use the concept of arc length. The formula for the arc length of a curve y = f(x) on the interval [a, b] is given by: L = ∫√(1 + (f'(x))^2) dx, where f'(x) is the derivative of f(x). In this case, y2 = 4(x + 1)3 can be rewritten as y = 2√(x + 1)^3. Taking the derivative of y with respect to x, we get y' = 3(x + 1)^(3/2). Plugging this into the formula for arc length: L = ∫√(1 + (3(x + 1)^(3/2))^2) dx = ∫√(1 + 9(x + 1)^3) dx. We can then evaluate this integral over the interval [0, 1] to find the exact length of the curve.

To find the exact length of the curve y2 = 4(x + 1)3, 0 ≤ x ≤ 1, y > 0, we can use the concept of arc length. The formula for the arc length of a curve y = f(x) on the interval [a, b] is given by:

L = ∫√(1 + (f'(x))^2) dx, where f'(x) is the derivative of f(x).

In this case, y2 = 4(x + 1)3 can be rewritten as y = 2√(x + 1)^3. Taking the derivative of y with respect to x, we get y' = 3(x + 1)^(3/2). Plugging this into the formula for arc length:

L = ∫√(1 + (3(x + 1)^(3/2))^2) dx = ∫√(1 + 9(x + 1)^3) dx

We can then evaluate this integral over the interval [0, 1] to find the exact length of the curve.

Based on the 80% figure, we'd expect 320 out of 400 adult smokers to have started before they turned 18. Observing 360 in this situation could be unusual but would require a statistical test to confirm.

This question pertains to concepts of probability and statistics. If 80% of adult smokers began smoking before they turned 18, then in a group of 400 randomly selected adult smokers, we would expect 80% (or 0.8) of that 400 to have started smoking before the age of 18. This means 320 out of the 400 individuals started smoking before turning 18.

As for the second part of the question, if we observed 360 smokers out of 400 who started smoking before turning 18, this number is higher than our expectation of 320. This could be seen as unusual, but it also might occur by chance. To determine how unusual it is, we would typically conduct a statistical test, which would require additional information not provided in the question.

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Jude's interest rate will be 3% for the principal of $1800 on an investment.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.

To find Jude's interest rate, we need to set up an equation using the information given. Let R be the interest rate.

The interest earned is equal to the principal times the interest rate, so the equation is:

Interest = Principal × Rate

Substituting the given values, we have:

54 = 1800 × R

Dividing both sides by 1800 gives:

R = 54 / 1800

R = 0.03, or 3%.

Therefore, for an investment of $1800, the interest rate will be 3%.

Learn more about the simple interest here:

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The consecutive even integers whose squares sum to 164 are [tex]\(8\) and \(10\) or \(-10\) and \(-8\).[/tex]

Let the two consecutive even integers be  [tex]\( x \) and \( x + 2 \).[/tex]

The sum of their squares is given by:

[tex]\[ x^2 + (x + 2)^2 = 164 \][/tex]

Expanding and simplifying this equation:

[tex]\[ x^2 + (x^2 + 4x + 4) = 164 \]\[ 2x^2 + 4x + 4 = 164 \]\[ 2x^2 + 4x + 4 - 164 = 0 \]\[ 2x^2 + 4x - 160 = 0 \]\[ x^2 + 2x - 80 = 0 \][/tex]

Now, solve the quadratic equation [tex]\( x^2 + 2x - 80 = 0 \).[/tex]  We use the quadratic formula  [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \),[/tex]  where [tex]\( a = 1 \), \( b = 2 \), and \( c = -80 \).[/tex]

[tex]\[ x = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 1 \cdot (-80)}}{2 \cdot 1} \]\[ x = \frac{-2 \pm \sqrt{4 + 320}}{2} \]\[ x = \frac{-2 \pm \sqrt{324}}{2} \]\[ x = \frac{-2 \pm 18}{2} \][/tex]

This gives us two solutions:

[tex]\[ x = \frac{-2 + 18}{2} = \frac{16}{2} = 8 \]\[ x = \frac{-2 - 18}{2} = \frac{-20}{2} = -10 \][/tex]

So, the two pairs of consecutive even integers are  [tex]\( 8 \) and \( 10 \), or \( -10 \) and \( -8 \).[/tex]

Therefore, the integers are [tex]\( 8 \) and \( 10 \), or \( -10 \) and \( -8 \).[/tex]

Diagram is in the attachment below

The width of the rectangular field is 88 yards.

To find the width of the rectangular field, we can use the formula for the area of a rectangle: Area = length x width.

In this case, the area is given as 8624 yd² and the length is given as 98 yards. So, we can rearrange the formula to solve for the width: width = Area / length.

Plugging in the values, we have width = 8624 yd² / 98 yds. Dividing these values gives us the width of the field: width = 88 yards.

Answer: 10% -APEX

2 year late answer lol.

Answer:

Step-by-step explanation:33

Final answer:

To determine the amount of almonds needed for a third of the recipe, if one full batch requires 3 cups, you would divide 3 cups by 3, resulting in 1 cup of almonds for a third of the recipe.

Explanation:

To calculate the amount of almonds needed for a third of the recipe, we first need to determine the total number of cups used for the full recipe. If the original recipe calls for 3 cups of almonds to make one batch, and the person is making 5 batches, they would initially need 15 cups of almonds (since 3 cups per batch multiplied by 5 batches equals 15 cups).

If they only want to make a third of one batch, we would take the amount needed for one batch, which is 3 cups, and divide it by 3 to find the required amount. So, 1 cup of almonds is needed for a third of the recipe, because 3 cups divided by 3 equals 1 cup.

The probability that a student earned an A on the last test is 7/12. This is found by dividing the number of students who earned an A by the total number of students and simplifying the fraction.

To find the probability that a randomly chosen student earned an A on the last test, we need to consider the total number of students and the number of students who earned an A.

The total number of students is 24, and 14 of them earned an A. The probability is calculated by dividing the number of students who earned an A by the total number of students:

Probability = Number of Students Who Earned an A / Total Number of Students = 14/24.

Next, we simplify the fraction 14/24 by finding the greatest common divisor (GCD) of 14 and 24, which is 2. Dividing both the numerator and the denominator by 2, we get:

Simplified Probability = (14 ÷ 2) / (24 ÷ 2) = 7/12.

Therefore, the probability that a student earned an A on the last test is 7/12.

Final answer:

The three consecutive odd integers whose sum is 243 are 79, 81, and 83. The integers were found using the algebraic expression for consecutive odd numbers and solving for the sum equal to 243.

Explanation:

To find three consecutive odd integers whose sum is 243, we can represent the first of these integers as 'n', the second as 'n + 2', and the third as 'n + 4', since each consecutive odd integer is 2 more than the previous one. The equation we would use to portray their sum is:

n + (n + 2) + (n + 4) = 243

Simplifying the equation, we combine like terms:

3n + 6 = 243

Next, we subtract 6 from both sides to isolate the 3n term:

3n = 243 - 6

3n = 237

Now we divide by 3 to solve for n:

n = 237 / 3

n = 79

The first odd integer is 79, the second odd integer is 79 + 2 = 81, and the third odd integer is 79 + 4 = 83.

Therefore, the three consecutive odd integers are 79, 81, and 83.