Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are . If point D divides in the ratio 4 : 5, the coordinates of point D are

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: 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.

Two consecutive integers are - 7 and - 8.

Here,

We have to find the two consecutive integers.

What are Integers?

An integer is a number which includes negative and positive numbers, including zero.

Now,

Let the smaller number is x.

Then, the larger is nine more than twice the smaller.

So, Larger number = 2x + 9

Since, The difference of two consecutive number are always 1.

So,

2x + 9 - x = 1

x + 9 = 1

x = -8

Therefore, The larger number = 2x + 9 = 2*-8 + 9 = -16 + 9 = -7

Hence,

Two consecutive integers are - 7 and - 8.

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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 temperature at 4:00 pm will be 66° F.

What are Integers?

An integer is a number with no decimal number or fractional part.

Given that;

At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.

Now, The temperature at 4:00 pm is calculated as;

= 28° F + 38° F

= 66° F.

Thus, The temperature at 4:00 pm will be 66° F.

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The complete question is this;

At 4:00 am, the outside temperature was 28*F. By 4:00 P.M. it rose 38 degrees. What was the temperature at 4:00 P.M. ?

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:

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.

Answer:

B

Step-by-step explanation:

To write the equation of the line, use the slope formula to find the slope. Then substitute the slope and a point into the point slope form. Simplify using the distributive property to write in slope intercept form.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{25 - 17}{7-3} = \frac{8}{4} = 2[/tex]

Using the point slope form of a line equation, substitute m = 2 and the point (3,17).

[tex]y - y_1 = m(x-x_1)\\y -17 = 2(x - 3)\\y - 17 = 2x - 6 \\ y = 2x - 6 + 17 \\ y = 2x + 11 [/tex]

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:

Hence, the monthly payment to the nearest cent is 510.31

Step-by-step explanation:

Consider the provided information,

A college student borrow ​$1,500 for 3 months to pay for a semester of school.

Let us consider the monthly payment is $x.

If he pay $x for next 3 months, then the total amount student paid in 3 month is: 3x

The interest is ​$30.94 for 3 months.

Student pay all the borrowed money and interest in 3 months.

That means he pay $1,500 + $30.94 in 3 months while the monthly payment was 3x.

This can be written as:

[tex]3x = 1500+30.94[/tex]

[tex]3x = 1530.94[/tex]

[tex]x = \frac{1530.94}{3}[/tex]

[tex]x = 510.31[/tex]

Hence, the monthly payment to the nearest cent is 510.31

The reasonable estimate for multiplying 94 by 689 is found by rounding the numbers to the nearest convenient figures, which gives an estimated result of 70,000.

To estimate the product of 94 and 689, you can round each number to its nearest simple form and then multiply. Round 94 to 100 because it is close to that multiple of ten. Round 689 to 700, as it is close to this hundred mark. When you multiply 100 by 700, you get 70,000.

This process of rounding to the nearest convenient number simplifies the multiplication and gives us an answer that is easy to calculate and understand. Hence, by rounding the numbers before multiplying, the reasonable estimate for the problem 94 · 689 is 70,000.

Final answer:

By rounding the numbers and multiplying, a reasonable estimate for the product of 94 and 689 is 70,000.

Explanation:

To estimate the product of 94 · 689, we can round the numbers to the nearest ten or hundred and then multiply. For estimation purposes, we can approximate 94 to 100 (since it's closer to 100 than 90) and 689 to 700 (since it's closer to 700 than 600).

Multiplying these rounded figures: 100 × 700 equals 70,000. Therefore, 70,000 is a reasonable estimate for the product of 94 and 689.