You buy 40 of your favorite songs from a Web site that charges ​$0.97 for each song. What is the cost of 40 songs?

Using the sine function and known angle and ladder length, the distance up the building the ladder reaches is \(7\sqrt{2}\) feet.

The correct answer is option C) \(7\sqrt{2}\) feet.

To find how far up the building the ladder reaches, we can use trigonometric functions, specifically the sine function since we have the angle and the length of the ladder.

Given:

- Length of the ladder (hypotenuse) = 14 feet

- Angle with the building = 45 degrees

Let [tex]\(x\)[/tex]be the distance up the building that the ladder reaches.

Using the sine function [tex](\(\sin\))[/tex] in a right triangle:

[tex]\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \][/tex]

Substituting the known values:

[tex]\[ \sin(45^\circ) = \frac{x}{14} \][/tex]

Since [tex]\(\sin(45^\circ) = \frac{\sqrt{2}}{2}\),[/tex] we have:

[tex]\[ \frac{\sqrt{2}}{2} = \frac{x}{14} \][/tex]

To solve for [tex]\(x\),[/tex] multiply both sides by 14:

[tex]\[ x = 14 \times \frac{\sqrt{2}}{2} \][/tex]

[tex]\[ x = 7\sqrt{2} \, \text{feet} \][/tex]

Therefore, the ladder reaches [tex]\(7\sqrt{2}\)[/tex] feet up the building.

Therefore the correct answer is option C) [tex]\(7\sqrt{2}\)[/tex]feet.

The question probable may be:

A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How far up the building does the ladder reach?

A. 7 feet

B. 28sqrt(2) feet

c. 7sqrt(2) feet

D. 14sqrt(2) feet.

the answer is B hope it helps

The answer is 8 and 2 over 3.

Answer:

B. 5p³ - 2p² - 7p + 1

Step-by-step explanation:

Good luck! Hope it was found helpful to you!

The total impedance of the circuit is 8 + 2i.

The total impedance in a series circuit is the sum of the individual impedances. To find the total impedance of the circuit, add the real parts and imaginary parts separately. In this case, Z1 = 3 + 4i and Z2 = 5 - 2i. So, the total impedance Zt = (3 + 5) + (4 - 2)i. Simplifying this, Zt = 8 + 2i.

Final answer:

To solve the equation log2 (x) + log2(x+7) = 3, you can combine the logarithmic terms using the property log(a) + log(b) = log(a*b). By applying this property and solving the resulting quadratic equation, we find that x = 1.

Explanation:

To solve the equation log2 (x) + log2(x+7) = 3, we need to combine the logarithmic terms using the property log(a) + log(b) = log(a*b). Applying this property, we get log2 (x*(x+7)) = 3. Next, we can rewrite this equation in exponential form as 2^3 = x * (x+7). Simplifying further, we have 8 = x^2 + 7x. Rearranging the equation, we get a quadratic equation x^2 + 7x - 8 = 0. Solving this quadratic equation, we find that x = -8 or x = 1. However, since the logarithm of a negative number is undefined, the solution is x = 1.

the correct answer is x+5 :DDD it was also the correct answer on the test !

Final answer:

To determine which of the given options is a factor of the expression 2x⁴ + 22x³ + 60x², we can use synthetic division. The only option that is a factor of the given expression is x⁴.

Explanation:

To determine which of the given options is a factor of the expression  2x⁴ + 22x³ + 60x², we can use synthetic division. Let's test each option:

2x³: When we divide 2x⁴ + 22x³ + 60x² by 2x3, the remainder is not zero. Therefore, 2x3 is not a factor.

x⁴: When we divide  2x⁴ + 22x³ + 60x²by x4, the remainder is zero. Therefore, x4 is a factor.

x + 4: When we divide  2x⁴ + 22x³ + 60x² by x + 4, the remainder is not zero. Therefore, x + 4 is not a factor.

x + 5: When we divide  2x⁴ + 22x³ + 60x² by x + 5, the remainder is not zero. Therefore, x + 5 is not a factor.

Based on the results, the only option that is a factor of the given expression is x⁴.

b: neither arithmetic nor geometric

The given sequence describes the type of sequence that is neither arithmetic nor geometric. which is the correct answer would be an option (B).

An arithmetic sequence is defined as an arrangement of numbers that is a particular order.

The sequence is given in the question following as:

1, 6, 7, 13, ...

We have to identify the type of given sequence

As per the given question, we have

1, 6, 7, 13, ...

For checking as an arithmetic sequence :

Common difference between 1 and 6 is d = 6 - 1 = 5

Common difference between 6 and 7 is d = 7 - 6 = 1

Since the common difference between consecutive terms is not the same, this means it's not an arithmetic sequence.

For checking as a geometric sequence :

Common ratio between 1 and 6 is r = 6/1 = 6

Common ratio between 6 and 7 is r = 7/6

Since the common ratio between consecutive terms is not the same, this means it's not a geometric sequence

Thus, the given sequence describes the type of sequence that is neither arithmetic nor geometric.

Learn more about arithmetic sequence here:

brainly.com/question/21961097

#SPJ2

Final answer:

After finding the value of x by equating m<2 and m<4, we calculate m<4 and then use the property of supplementary angles in a parallelogram to find that m<3 is 163 degrees.

Explanation:

To solve for m<3 in the parallelogram with m<2 = 5x - 28 and m<4 = 3x - 10, we first find the value of x. Given that opposite angles in a parallelogram are equal (m<2 = m<4), we set the two equations equal to each other and solve for x:

5x - 28 = 3x - 10

5x - 3x = 18

2x = 18

x = 9

Now that we have the value of x, we can substitute it into the equation for either angle to find the measure of that angle. Since m<4 = 3x - 10:

m<4 = 3(9) - 10 = 27 - 10 = 17

In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Therefore, to find m<3, we subtract m<4 from 180 degrees:

m<3 = 180 - m<4

m<3 = 180 - 17 = 163

Thus, m<3 in the parallelogram is 163 degrees.

The measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 2x - 18 \).[/tex]

In a parallelogram, opposite angles are equal. Therefore, we can set up an equation based on the given angle measures:

[tex]\[ m\angle 2 + m\angle 3 = 180^\circ \][/tex]

Substitute the given expressions for[tex]\( m\angle 2 \) and \( m\angle 4 \):[/tex]

[tex]\[ (2 + 5x - 28) + (3x - 10) = 180 \][/tex]

Combine like terms:

[tex]\[ 5x + 3x - 28 - 10 + 2 = 180 \][/tex]

[tex]\[ 8x - 36 = 180 \][/tex]

Add 36 to both sides:

[tex]\[ 8x = 216 \][/tex]

Divide by 8:

[tex]\[ x = 27 \][/tex]

Now that we have the value for x, substitute it into the expression for \( [tex]m\angle 3 \):[/tex]

[tex]\[ m\angle 3 = 2(27) - 18 \][/tex]

[tex]\[ m\angle 3 = 54 - 18 \][/tex]

[tex]\[ m\angle 3 = 36 \][/tex]

Therefore, the measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 36^\circ \).[/tex]

The approximate probability of choosing one club followed by one heart from a standard deck of 52 playing cards is 5.9%.

The student's question pertains to the calculation of the probability of choosing one club and one heart from a standard deck of 52 playing cards. We start by recognizing that there are 13 clubs and 13 hearts in the deck, with each of the four suits represented equally.

Firstly, the probability of choosing a club (P(club)) is 13/52. After a club is chosen, there are 51 cards left in the deck. The number of hearts remains the same at 13 (since a club was chosen first). So, the probability of then picking a heart (P(heart)) is 13/51.

The two events, choosing a club and then a heart, are dependent events because the outcome of the second event depends on the outcome of the first. Hence, to find the combined probability, we multiply the probabilities of each event.

The probability of choosing one club followed by one heart is therefore P(club)  imes P(heart) = (13/52)  imes (13/51), which simplifies to approximately 0.059, or 5.9%.

Answer:

Complete Quick Check of...

Lesson 4: Graphing a Function Rule

Algebra 1 A: Unit 5

Step-by-step explanation:

1.C) x,0,1,2,3, y,3,-1,-5,-9

2.A) True

3.D) $698.75

4.C) cant write it out.

5.D) C = 11n; discrete

:) hope this helps!