The sum of two consecutive odd integers is 56. what is the smaller number?

Final answer:

To write 90 as a product of prime factors, divide it by the smallest prime numbers in sequence: 90 = 2 × 3 × 3 × 5, which can also be expressed using exponents as 90 = 2 × 3² × 5.

Explanation:

Writing 90 as a product of prime factors involves breaking down the number into its prime number components. To do this, we start by finding the smallest prime number that divides into 90, which is 2. We then divide 90 by 2 to get 45. Since 45 is not a prime number, we continue the process and find the smallest prime number that divides into 45, which is 3. Dividing 45 by 3 gives us 15. Again, 15 is not prime, so we divide it by its smallest prime divisor, 3, which results in 5. Now, 5 is a prime number, so we have now expressed 90 as a product of prime factors:

90 = 2 × 3 × 3 × 5

Step-by-Step Process:

Divide 90 by the smallest prime number 2, resulting in 45.

Divide 45 by the smallest prime number 3, resulting in 15.

Divide 15 by 3 again, resulting in 5.

Write down the result as a multiplication of these prime factors: 2 × 3 × 3 × 5.

This factorization can also be written with exponents to show repeated factors: 90 = 2 × 3² × 5.

Answer:

2

Step-by-step explanation:

answer below, do the math and draw it out then it's easy.

Applying implicit differentiation, it is found that:

[tex]\frac{d^2y}{dx^2}(4,3) = \frac{7}{27}[/tex]

The curve given is:

[tex]x^2 + y^2 = 25[/tex]

Applying implicit differentiation, we have that the first derivative is:

[tex]2x\frac{dx}{dx} + 2y\frac{dy}{dx} = 0[/tex]

[tex]2y\frac{dy}{dx} = -2x[/tex]

[tex]\frac{dy}{dx} = -\frac{x}{y}[/tex]

Again applying implicit differentiation, the second derivative is:

[tex]\frac{d^2y}{dx^2} = -\frac{y\frac{dx}{dx} - x\frac{dy}{dx}}{y^2}[/tex]

Since [tex]\frac{dy}{dx} = -\frac{x}{y}[/tex]

[tex]\frac{d^2y}{dx^2} = -\frac{y - \frac{x^2}{y}}{y^2}[/tex]

[tex]\frac{d^2y}{dx^2} = \frac{x^2 - y^2}{y^3}[/tex]

At point (4,3), [tex]x = 4, y = 3[/tex], then:

[tex]\frac{d^2y}{dx^2}(4,3) = \frac{4^2 - 3^2}{3^3} = \frac{7}{27}[/tex]

A similar problem is given at https://brainly.com/question/15278071

Final answer:

To simplify the expression sec(y) sin(π/2 - y) using basic identities, we can use the identity sec(y) = 1/cos(y) and expand the expression using the identity sin(a - b) = sin(a)cos(b) - cos(a)sin(b). The simplified expression is -tan(y).

Explanation:

To simplify the expression sec(y) sin(π/2 - y) using basic identities, we can start by using the identity sec(y) = 1/cos(y). So the expression becomes (1/cos(y)) sin(π/2 - y). Next, let's use the identity sin(a - b) = sin(a)cos(b) - cos(a)sin(b) to expand the expression. We have (1/cos(y)) (cos(y)cos(π/2) - sin(y)sin(π/2)). Since cos(π/2) = 0 and sin(π/2) = 1, the expression simplifies to (1/cos(y)) (0 - sin(y)(1)), which further simplifies to -sin(y)/cos(y). Therefore, the simplified expression is -tan(y).

The airplane must head approximately 16.7° east of due north to compensate for the westward wind blowing at 30 m/s while attempting to fly due north at 100 m/s.

To determine the heading (angle and direction) that the airplane should take to compensate for the wind and fly due north, we need to consider the velocity of the plane relative to the air and the velocity of the wind. The plane wants to fly due north at 100 m/s, but the wind is blowing from the west at 30 m/s. This problem involves vector addition and can be solved graphically or using trigonometry.

Graphically, we would draw a vector to represent the plane's intended velocity due north (100 m/s) and then a vector to represent the wind's velocity (30 m/s) to the east of the northward vector. The result is a right-angled triangle where the plane's velocity is the hypotenuse, and the wind's velocity is one of the sides. Using trigonometry, we can calculate the required heading of the plane.

To find the angle (θ) between the plane's heading and the due north direction, we can use the tangent function:

Calculator error is often in degrees or radians, so ensure which mode you are using. Assuming we need the angle in degrees, we find that:

Thus, the airplane must head 16.7° east of due north to compensate for the wind and fly due north.

Kathleen's unpaid balance is $101.81. The correct option (C) $101.81.

To find Kathleen's unpaid balance after making a payment and incurring new charges, follow these steps:

Initial Balance: Kathleen's last balance was [tex]\( \$89.70 \).[/tex]

Payment: She made a payment of [tex]\( \$20 \).[/tex]

[tex]\[ \text{Balance after payment} = 89.70 - 20 = \$69.70 \][/tex]

New Charges: Kathleen incurred new charges totalling [tex]\( \$32.11 \).[/tex]

[tex]\[ \text{New balance after charges} = 69.70 + 32.11 = \$101.81 \][/tex]

So, after accounting for the payment and new charges, Kathleen's unpaid balance is $101.81.

Answer:

The actual answer 160

Step-by-step explanation:

Answer:

its (6,-4)

Step-by-step explanation:

lol

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

In a 4 minute, the shower uses an average of 20-40 gallons of water,

If we consider the maximum gallons of water,

In 4 minutes, the maximum gallons of water = 40

In 1 minute, the maximum gallons of water is given by

[tex]\frac{40}{4}=10[/tex]

In 18 minutes, the maximum gallons of water is given by

[tex]18\times 10=180\ gallons[/tex]

Hence, Option 'D' is correct.

the one above is incorrect the real answer is 10 meters per second and you don't really need an equation for this (it's pretty obvious ) :)

Final answer:

Given that A is a subset of B and the intersection of A and B is the empty set, it is conclusive that A is the empty set, and we cannot infer anything about the elements of set B.

Explanation:

When considering sets, subset relation and intersection are fundamental concepts. If A ⊆ B(A is a subset of B) and A ∩ B = θ (the intersection of A and B is the empty set), we can conclude that every element in A is also in B, but since the intersection is empty, A has no elements. Therefore, A is the empty set, which means that A contains no elements. It is not possible to determine the contents of set B or to compare the cardinalities of A and B, since we only know that A is empty.

Observing our subset and intersection principles, while A is a subset of B, the fact that they have an empty intersection invariably means that A cannot contain any member, thereby being the empty set. The other options given in the question are incorrect based on our set theory principles. Set B can be any set; it might not be empty, and it is not possible to make any conclusions about the number of elements in B relative to A from the information given.

Answer:

Geometric sequence states that a sequence in which a number that follows the pattern were the next term is found by multiplying the constant common ratio term(r).

For the sequence: [tex]a, ar, ar^2, ar^3,.....[/tex]

The formula for the nth geometric sequence is given by:

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

where

a is the first term

r is the common ratio

n is the number of terms.

Given that:

A geometric sequence:

50, _[tex]a_2[/tex]___, 450

Here, a = first term = 50

[tex]a_3 = 450[/tex]

Using the nth geometric sequence formula:

[tex]a_3 = ar^2[/tex]

or

[tex]ar^2 = 450[/tex]

Substitute the value of a , to solve for r;

[tex]50r^2 = 450[/tex]

Divide both sides by 50 we get;

[tex]r^2 = 9[/tex]

[tex]r = \sqrt{9} = 3[/tex]

To find the term [tex]a_2[/tex];

[tex]a_2 = ar[/tex]

Substitute the given values we have;

[tex]a_2 = 50 \cdot 3 = 150[/tex]

Therefore, the possible value for the missing term of the geometric sequence is 150

Answer:

Step-by-step explanation:

One five zero

Answer:

The answer is 8:343

Step-by-step explanation:

Answer:

The answer would be 123.4

Step-by-step explanation:

Resiprical

The possible sets of two sides for the lengths of the other two sides of the triangle are: 5 cm and 8 cm, 6 cm and 7 cm, and 8 cm and 8 cm.

To determine which set of two sides is possible for the lengths of the other two sides of the triangle, we can use the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, if one side of the triangle is 13 cm, then the sum of the other two sides must be greater than 13 cm in order for the triangle to be valid.

Let's check each set of two sides:

Based on the Triangle Inequality Theorem, the sets of two sides that are possible are: 5 cm and 8 cm, 6 cm and 7 cm, and 8 cm and 8 cm.

Final answer:

The third piece of wood must be longer than 9 ft but shorter than 35 ft to make a triangular garden bed with the other two pieces, adhering to the Triangle Inequality Theorem.

Explanation:

To determine the possible length of the third piece of wood to create a triangular garden bed with the other two pieces measuring 22 ft and 13 ft, we need to recall the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Conversely, the difference between these two sides must be less than the length of the remaining side.

Step 1: Identify the lengths of the two given pieces: 22 ft and 13 ft.

Step 2: To find the minimum length of the third piece, subtract the shorter piece from the longer piece, then add a small value to avoid equality (as the sum must be greater).

Minimum length > 22 ft - 13 ft => 9 ft + a small value

Step 3: To find the maximum length of the third piece, sum the lengths of the two pieces and subtract a small value (as the length must be less than the sum of the other two pieces).

Maximum length < 22 ft + 13 ft => 35 ft - a small value

So, the third piece of wood must be longer than 9 ft but shorter than 35 ft to form a triangle with the other two pieces.

Answer:

D

Step-by-step explanation:

She showed that f(n) - f(n - 1) was a constant difference.

The definition of an arithmetic sequence is the difference between consecutive terms is constant, aka common difference.