A line contains the point (-4,6) and has a slope of -2/3 write the equation of the line using point-slope form

Answer:

Samantha worked 26 hours and Adriana worked 13 hours.

Step-by-step explanation:

Let s = the number of hours that Samantha worked

Let a = the number of hours that Adriana worked

s = 2a

s + a = 39

2a + a = 39

3a = 39

a = 13

In order to calculate the diameter of the soap bubble, we need to use the Laplace equation and solve for the radius of the bubble.The diameter of the soap bubble is 8.04 x 10⁻⁴ mm.

We will then double the radius to get the diameter of the bubble.Here's the solution:

Given that:

Radius of the soap bubble =

r = 0.065 mm

= 6.5 x 10⁻⁵ m

Surface tension of soap in air =

σ = 0.019 N/m

Pressure outside the bubble =

P₂ = 75.0 kPa

= 75,000 Pa

Ambient temperature =

T = 300 K

Atmospheric pressure =

P₁ = 1 atm = 101,325 Pa

Laplace's equation states that the pressure inside the bubble is given by:

Pinside = Poutside + (2σ/r)

where σ is the surface tension and r is the radius of the bubble.

Rearranging the above equation to solve for the radius of the bubble:

2σ/r = Pinside - Poutside

r = 2σ/(Pinside - Poutside)

Substituting the given values into the above equation:

r = [2 x 0.019] / [Pinside - 101325]

After the soap bubble rises up, the pressure outside the bubble becomes 75 kPa.

Therefore:

Pinside - 101325 = 75000

Pinside = 176325 Pa

Substituting this value of Pinside into the above equation:

r = [2 x 0.019] / [176325 - 101325]

= 4.02 x 10⁻⁷ m

The diameter of the soap bubble is twice the radius:

D = 2r = 2 x 4.02 x 10⁻⁷ m

= 8.04 x 10⁻⁷ m

Converting the diameter to mm:

D = 8.04 x 10⁻⁷ m x 1000 mm/m

= 8.04 x 10⁻⁴ mm (answer)

Therefore, the diameter of the soap bubble is 8.04 x 10⁻⁴ mm.

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The volume of right prism is equal to 464 cubic inches.

Volume of right prisms (V), in cubic inches, is equal to the product of cross area (A), in square inches, and height (h), in inches:

V = A · h

According to figure, cross area is the result of adding the areas of three rectangles. Area formula for rectangles is:

A' = w · l

Where:

First, determine the cross area of the prism:

A = 2 · (3 in) · (7 in) + (4 in)²

A = 42 in² + 16 in²

A = 58 in²

Second, calculate the volume of the right prism:

V = (58 in²) · (8 in)

V = 464 in³

The right prism has a volume of 464 cubic inches.

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Answer:

C is correct

Step-by-step explanation:

The matrix equation that could show the total books is \(\left[\begin{array}{cc}7&1\\2&6\end{array}\right] + \left[\begin{array}{cc}4&3\\6&1\end{array}\right] = \left[\begin{array}{cc}11&4\\8&7\end{array}\right]\)

The given parameters are the two-way tables attached to the question.

From the tables, we have the following matrices

\(June = \left[\begin{array}{cc}7&1\\2&6\end{array}\right]\)

\(July = \left[\begin{array}{cc}4&3\\6&1\end{array}\right]\)

The sum of these matrices is represented as:

June + July =  Total

So, we have:

\(\left[\begin{array}{cc}7&1\\2&6\end{array}\right] + \left[\begin{array}{cc}4&3\\6&1\end{array}\right]\)

Add the elements at corresponding positions

\(\left[\begin{array}{cc}11&4\\8&7\end{array}\right]\)

Hence, the matrix equation is \(\left[\begin{array}{cc}7&1\\2&6\end{array}\right] + \left[\begin{array}{cc}4&3\\6&1\end{array}\right] = \left[\begin{array}{cc}11&4\\8&7\end{array}\right]\)

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Answer: False

Step-by-step explanation:

In Boolean algebra, the symbol "+" represents logical OR operation, not regular addition as in linear algebra. The logical OR operation is used to combine two or more logical statements into a single statement that is true if at least one of the statements is true.

For example, if A and B are two logical statements, then A+B is true if A is true, or B is true, or both A and B are true.

Therefore, it is important to understand the context in which the symbol "+" is being used, whether it is in the context of regular addition or logical OR operation.

Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

A cylindrical object is 3.13 cm in diameter and 8.94 cm long and weighs 60.0 g. The density of the cylindrical object is 0.849 g/cm^3.

To calculate the density, we first need to find the volume of the cylindrical object. The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius (half of the diameter) and h is the height (length) of the cylinder.

Given that the diameter is 3.13 cm, the radius is half of that, which is 3.13/2 = 1.565 cm. The length of the cylinder is 8.94 cm.

Using the values obtained, we can calculate the volume: V = π * (1.565 cm)^2 * 8.94 cm = 70.672 cm^3.

The density is calculated by dividing the weight (mass) of the object by its volume. In this case, the weight is given as 60.0 g. Therefore, the density is: Density = 60.0 g / 70.672 cm^3 = 0.849 g/cm^3.

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Answer:

3

Step-by-step explanation:

In a triangle, The value of x is, 40°

And, The value of y is, 50°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The triangle is show in figure.

We know that;

In a triangle, the pair of two opposite sides are equal then there corresponding angles are also equal.

Now, By figure we can formulate;

⇒ x + x + 100 = 180

Solve for x;

⇒ 2x + 100 = 180

⇒ 2x = 180 - 100

⇒ 2x = 80

⇒ x = 40

Thus, The value of x = 40°

And, We get;

⇒ x° + y° + 90° = 180°

⇒ 40 + y + 90 = 180

⇒ y + 130 = 180

⇒ y = 180 - 130

⇒ y = 50°

Thus, The value of y = 50°

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Answer: 12.65 cm

Step-by-step explanation:

Use the Pythagoras theorem,

a^2 + b^2= c^2

You are given the hypotenuse , which is c and another leg which is either a or b, does not particularly matter- rearrange to find the missing length

c^2 - b^2 = a^2

14^2 - 6^2 = 160

Square root 160 to find the missing length

12.65

Hope this helped :)

Answer: 63

Step-by-step explanation:

Answer:

so that means you would divide 300 by 10 and that means she reads 30 pages in 1 hour so if you do 30 divided by 60 or 1 hour you get 0.5 pages so she reads 100 words in 1 minutes

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

So if there is 200 word per page it will be 200×300, which is 60,000. We are trying to find words per minute, so we do; 10×60 (1 hour=60minutes) which is 600. so to find the words per minute we do:

60,000÷600=100

Answer:

-3

Step-by-step explanation:

After subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

So, we have:

(x+7) and (3x+4)

We have to subtract as:

(3x+4) - (x+7)

Now, subtract as follows:

(3x+4) - (x+7)

3x+4 - x-7

2x-3

Therefore, after subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

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We have to find the equation of a line fo which we know two points, using the point-slope form.

The point-slope let us write the equation of the line knowing the value of the slope m and the coordinates of one point (x0,y0) of the line:

We use the two known points to calculate the slope m:

Using the point (-1,7), we can write the equation as:

Answer: From the options, the right ones are:

y-7=-1(x-(-1))

y-4=-1(x-2) --> this one would have been used if we picked the point (2,4) instead of (-1,7)

y=-x+6

The within-group estimate of variance is the estimate of the variance of the population of individuals based on the variation among the scores in each of the actual groups studied.

The within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Scores in each of the actual groups studied.
This estimate represents the variation within each group and helps in understanding the population's variance by looking at individual differences within the groups.

The estimated within-group variance is the sum of the within-group variances for each group in the model. Effectively, this is the sum of the variance of each value (j) from its group (i) divided by the sample size minus one.

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Answer:  (x, y) = (-12, 3)

This means x = -12 and y = 3 pair up together to form the solution.

========================================================

Work Shown

1/2 = 0.5

0.5x + 6y = 12

0.5x + 6(x+15) = 12 .... plug in y = x+15

0.5x+6x+90 = 12

6.5x + 90 = 12

6.5x = 12-90

6.5x = -78

x = -78/(6.5)

x = -12

Then,

y = x+15

y = -12+15

y = 3

The solution as an ordered pair is (x, y) = (-12, 3)

That is the shorthand way to indicate x = -12 and y = 3 pair up together to form the full solution.

-----------------

Check:

Plug x = -12 and y = 3 into the first equation. Simplify both sides.

0.5x + 6y = 12

0.5*(-12) + 6*3 = 12

-6 + 18 = 12

12 = 12

We reached a true statement, which confirms the first equation is true when x = -12 and y = 3.

Repeat for the second equation.

y = x+15

-3 = -12+15

-3 = -3

This equation is true as well. Both equations are confirmed.

A visual way to confirm the answer is to graph the original equations on the same xy grid. The two lines intersect at (-12, 3). See the diagram below. I used GeoGebra to make the graph. Desmos is another option.

the answers for this expression is 4329

please mark as brainelist

Answer:

4329

Step-by-step explanation:

first, simplify the exponents

6^2=36

5^2-4^2=25-16=9

13(36(9)+9)

36*9=324

13(324+9)

13(333)

13*333=4329

Answer:

8.77

Step-by-step explanation:

Answer:

I believe the answer is A) $8.77

step1) multiply the cost of peaches oer pound by 18.4

step2) add the cost for the peaches to the cost for the pineapple

step3)divide the cost by 4

The communicable diseases that are known for targeting the human respiratory system are C. I, II, and III.

There are several diseases that target the human respiratory system and a lot of them are communicable . One of the most popular of these is the Coronavirus infection which forced the world into various lockdowns to prevent its spread.

Then there is Influenza II which is one of the most communicable diseases in existence. It also attacks the human respiratory system much like Tuberculosis III.

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Answer:

54 sq. in.

Step-by-step explanation:

(15.1 + 6.5)/2 * 5

The effective rate for A is 2.824% and the effective rate for  B is  3.322%.

The Option B is better.

Since, compound interest:

\(A = P(1 + r/n)^{nt}\)

Option A:

Given that the interest rate is 2.8% compounded monthly, that is r = 0.028, n is monthly compounding that is, n = 12 and t = 1 year.

Put the values in formula:

\(A = P(1 + 0.028/12)^{12 \times 1}\\A = P(1 + 0.002333)^{12}\\A = P(1.002333)^{12\)

The effective rate for Option A is \((1.002333)^{12} - 1\), which can be calculated as follows:

Effective rate:

option  A = \((1.002333)^{12} - 1\)

Option A ≈ 0.02824

Therefore, the effective rate for A is 2.824%.

Option (B):

Given that the interest rate is 3.3% or 0.033 compounded semi-annually.

r = 0.033, n is semi-annual compounding, that is, n = 2 and t = 1 year.

Since,

\(A = P(1 + r/n)^{nt}\\A = P(1 + 0.033/2)^{2 \times 1}\\A = P(1 + 0.0165)^2\\A = P(1.0165)^2\)

The effective rate for Option B is \((1.0165)^2 - 1\), which can be calculated as follows:

Effective rate:

Option B = \((1.0165)^2 - 1\)

Option B ≈ 0.0332225

Therefore, the effective rate for  B is  3.322%.

Since,  effective rate is higher for Option B (3.322%)  than Option A (2.824%).

Hence, Option B is better, because Option B has a higher interest rate and would be the better option for earning more interest on the savings account.

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The answer is option b) $830.31.

To calculate Greg's total balance after making the monthly payment for July, we need to consider the interest accrued on his outstanding balance for May, June, and July. Assuming a constant interest rate, the interest for each month is calculated by multiplying the outstanding balance by the monthly interest rate. After calculating the interest for each month, we subtract the monthly payment from the outstanding balance to get the new balance for the following month.

Given that the minimum monthly payment is applied at the end of the month, the interest for May, June, and July is calculated on the initial balance. After calculating the interest and subtracting the monthly payment for each month, we find that Greg's total balance after making the July payment is approximately $830.31. Therefore, option b) is the correct answer.

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okay so since the area is 22cm^2 , you will need to simplify it.

Which you will get 22*22 and the total would be 484. Which u will divide by 4 ( Square) to get each of the side your looking for.

So your answer is... 121

Answer:

A and C

Step-by-step explanation:

Answer:

904.32 cubic ft

Step-by-step explanation:

To find the volume of a sphere, the formula is \(4\pi\frac{r^3}{3}\)

First, 3.14 * 4 for 12.56.

The radius is 6, and that cubed is 216.

After that, divide 216 by 3 for 72

Then, 12.56 times 72, which gets you the final answer of  904.32 cubic ft.

(10 * 72) + (2 * 72) + (0.5 * 72) + (0.06 * 72)

720 + 144 = 864

864 + 36 = 900

900 + 4.32 = 904.32

Your answer is D, I took the test.

The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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Answer:

The dollar bills d are the independent variable while the number of quarters q are the dependent variable

Step-by-step explanation:

Here, we want to state the variable that is dependent and the one that is independent

from the question, she has to put in dollars to get the quarters

so the number of quarters she gets is dependent on the number of dollars put into the machine

Thus, we can conclude that;

The dollar bills are the independent variable while the number of quarters q are the dependent variable

Independent variables are those who are not dependent on other variables. In contrast, their exists dependent variables whose value depends on some other variable(s)' value(s).

For given case, the number of dollar bills 'd' is independent variable with respect to variable 'q'.

The number of quarters 'q' is dependent variable.

Independent variables are those who are not dependent on other variables for their evaluation.

Those variables whose value is decided by the values of other variables. This shows that the variable in consideration is dependent on other variables for its values, thus called dependent variable.

If you see it carefully, you'll see that the quarters received from the change machine is depending on how much dollar bills you're feeding to the machine.

Thus, the value of 'q' is dependent on the value of d.

But since d takes its value independent of q (it exists before q exists and doesn't need q to get its values), thus, d is not dependent on q or is independent variable with respect to q(i said "with respect to q" since d might be dependent on some other variable which we do not know right know)

Thus:

The variable 'q' is dependent variable (depends on d)

The variable 'd' is independent variable with respect to 'q.

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