Alma is solving the equation 4a-5=2a-3 Circle her mistake and correct it.

4a-5=2a-3
4a-2a-5=3
2a-5=3
2a=8

The rock will hit the water after approximately 2 seconds.

The time it takes for the rock to hit the water, we need to set the height h equal to zero and solve for t . The equation representing the height of the rock is given by:

[tex]\[ h = -16t^2 + 12t + 40 \][/tex]

Setting h to zero:

[tex]\[ 0 = -16t^2 + 12t + 40 \][/tex]

Now, we have a quadratic equation.

To solve for t , we can use the quadratic formula:

[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

In this equation, [tex]\( a \), \( b \), and \( c \)[/tex] are the coefficients from the quadratic equation [tex]\( at^2 + bt + c = 0 \).[/tex]In our case:

[tex]\[ a = -16, \quad b = 12, \quad c = 40 \][/tex]

Substitute these values into the quadratic formula:

[tex]\[ t = \frac{-12 \pm \sqrt{12^2 - 4(-16)(40)}}{2(-16)} \]\\[/tex]

Now, calculate the values under the square root:

[tex]\[ t = \frac{-12 \pm \sqrt{144 + 2560}}{-32} \][/tex]

[tex]\[ t = \frac{-12 \pm \sqrt{2704}}{-32} \][/tex]

[tex]\[ t = \frac{-12 \pm 52}{-32} \][/tex]

Now, consider both the positive and negative roots:

1. For the positive root:

[tex]\[ t_1 = \frac{-12 + 52}{-32} = \frac{40}{-32} = -\frac{5}{4} \][/tex]

2. For the negative root:

[tex]\[ t_2 = \frac{-12 - 52}{-32} = \frac{-64}{-32} = 2 \][/tex]

Since time cannot be negative in this context, we discard the negative root.

Therefore, the rock will hit the water after approximately t = 2 seconds.

Where B₁ and B₂ are the areas of the bases, the volume of the frustum is given by

... V = (1/3)(B₁ +B₂ +√(B₁B₂))h

For your dimensions, the volume is

... V = (1/3)(100 + 25 + √(100·25))·12 = (1/3)·175·12 = 700

The appropriate choice for the volume of the frustum is

... B. 700 in³

Answer: 3 × 5

Step-by-step explanation: To find the prime factorization of 15, first create a factor tree with two branches.

Since 15 divided by 3 gives us 5, we know that  and 5 are factors of 15. This means that we can write 3 and 5 at the bottom of our branches.

While 1 and 15 are also factors of 15, we don't use them in our factor tree. This because when finding a prime factorization, we only want factors other than 1 and the number itself.

Next, we circle any prime numbers in our factor tree. Since 3 and 5 are both prime numbers, we circle both 3 and 5. Since we have circles at the bottom of our branches, we are finished.

Therefore, the prime factorization of 15 is 3 × 5.

Final answer:

The baker's revenue R can be expressed as R = x * 6.50, and the cost C can be expressed as C = 45 + 25 + (x * 1.75). To find the number of cakes he needs to sell before making a profit, we set the revenue equal to the cost and solve for x. The baker will need to sell at least 15 cakes before making a profit.

Explanation:

To express the revenue R as a function of x, we can use the equation R = x * 6.50. This is because the revenue is the number of cakes sold multiplied by the price per cake. So, every cake sold contributes $6.50 to the revenue.

To express the cost C as a function of x, we can use the equation C = 45 + 25 + (x * 1.75). The initial fixed costs of $45 for reserving a booth and $25 for traveling expenses are added to the variable costs of $1.75 per cake multiplied by the number of cakes sold.

To find the number of cakes he needs to sell before making a profit, we need to set the revenue equal to the cost and solve for x:

R = C => x * 6.50 = 45 + 25 + (x * 1.75)

Combining like terms, we get:

4.75x = 70

x = 70 / 4.75

x ≈ 14.74

Since you cannot sell a fraction of a cake, the baker will need to sell at least 15 cakes before making a profit.

The gross pay for Alisson this week is $432.22. So option (d) is correct.

To calculate her gross pay, we first need to find the total number of hours worked during the week. We add up the hours worked each day:

1. Monday: 8:03 am to 5:13 pm = 9 hours and 10 minutes

2. Tuesday: 7:58 am to 4:49 pm = 8 hours and 51 minutes

3. Wednesday: 7:46 am to 4:41 pm = 8 hours and 55 minutes

4. Thursday: 8:32 am to 4:50 pm = 8 hours and 18 minutes

5. Friday: 7:31 am to 4:32 pm = 9 hours and 1 minute

Total hours worked = 43 hours and 15 minutes.

Since Alisson worked more than 40 hours this week, any hours beyond 40 are paid at time and a half. So, she worked 40 regular hours and 3 hours and 15 minutes of overtime.

Her regular pay = 40 hours * $9.32/hour = $372.80

Her overtime pay = 3.25 hours * ($9.32/hour * 1.5) = $59.42

Therefore, her total gross pay for the week is $372.80 + $59.42 = $432.22.

Complete Question;

If Alisson worked the times in the table and makes $9.32 an hour, how much was her gross pay this week?

8:03 am 5:13 pm

7:58 am 4:49 pm

7:46 am 4:41 pm

8:32 am 4:50 pm

7:31 am 4:32 pm

Remember that any time worked over 40 hours is paid at time and a half.

(a) $372.80

(b) $410.08

(c) $412.41

(d) $432.22

This question pertains to the voting options and procedures during a homeowners association meeting, covered under the broader subject of Social Studies in the context of High School education. It involves understanding quorum requirements and voting rules as per bylaws for decision-making on motions.

The question revolves around a homeowners association meeting where a board member has three options to participate in a vote: vote yes, vote no, or abstain from a motion. There are three motions for which each board member must decide how to vote. In such meetings, the rules outlined typically require a quorum to conduct business, the ability to make amendments to bylaws, and procedures for electing members, as seen in various articles of an organization's bylaws and rules of procedure. These rules ensure that the organization conducts its affairs in an orderly and democratic manner, often requiring a majority or unanimous consent for certain actions.

Meetings like these are essential, as they also involve critical decisions such as annual meetings, bylaw amendments, or the dissolution of the organization, each depending on the vote of the board members or the members of the organization. Membership eligibility and voting rights are typically determined by the board of directors or outlined within the bylaws. Furthermore, certain organizational procedures such as elections, member qualifications, and the transparency measures such as keeping a journal of proceedings of each meeting are often mandated.

Answer:

[tex]4x^2[/tex]

Step-by-step explanation:

We are asked to find the GCF of [tex]28x^3[/tex] and [tex]16x^2y^2[/tex].

The greatest common factor of numerical part would be GCF of 28 and 16.

Factors of 28: 1, 2, 4, 7, 14, 28.

Factors of 16: 1, 2, 4, 8, 16.

The greatest common factor of 28 and 16 is 4.

The GCF of variable part:

[tex]x^3=x\cdot x\cdot x[/tex]

[tex]x^2y^2=x\cdot x\cdot y\cdot y[/tex]

The greatest common factor of [tex]x^3[/tex] and [tex]x^2y^2[/tex] is [tex]x^2[/tex].

Upon combining the GCF of numerical part and algebraic part, we will get:[tex]4x^2[/tex]

Therefore, the greatest common factor of both expressions is [tex]4x^2[/tex].

Answer:

Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.

Step-by-step explanation:

Given Expression of the Sum of the all interior angles of a regular polygon

40x² - 65x + 50

We need to find expression representing the measure of the two angles.

We know that regular polygons have all side and all angles equal.

Number of side or angles in regular polygon = 5

So, when we divide given expression by 5 we get expression for an angle of the regular polygon.

[tex]\frac{40x^2-65x+50}{5}=\frac{5(8x^2-13x+10)}{5}=8x^2-13x+10[/tex]

Expression for an angle of regular pentagon = 8x² - 13x + 10

Now, For 2 angles  = 2( 8x² - 13x + 10 ) = 16x² - 26x + 20

Therefore, Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.