Twice the quotient of a number and -24 is -8 Find the number.

The number is ________.

Answer:

A, B, and C

Step-by-step explanation:

Answer:

a.) 2(x + 2) + 2 = 2(x + 3) + 1

b.) 2x + 3(x + 5) = 5(x – 3)

e.) 5(x + 4) – x = 4(x + 5) – 1

Step-by-step explanation:

a.) 2(x + 2) + 2 = 2(x + 3) + 1

0 ≠ 1

b.) 2x + 3(x + 5) = 5(x – 3)

0 ≠ -30

c.) 4(x + 3) = x + 12

x = 3

d.) 4 – (2x + 5) = (–4x – 2)

x = -½

e.) 5(x + 4) – x = 4(x + 5) – 1

0 ≠ -1

I hope this helps

The measure of angle a is:

a = (140° - 96°) / 2 = 44° / 2 = 22°

Therefore, the answer is 22.

1

If two secant lines intersect outside a circle, the measure of the angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.

In the given diagram, we can see that the intercepted arcs are 96° and 140°. Therefore, the measure of angle a is:

a = (140° - 96°) / 2 = 44° / 2 = 22°

Therefore, the answer is 22.

Answer: 22

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Answer:

$3,840

Step-by-step explanation:

9600 x 0.08 =  768 per years (assuming flat rate)

768x5= 3,840

Answer:

3840

Step-by-step explanation:

9600 * 8% * 5 = 3840

Hope this helps!

Thenks and mark me brainliest :))

14 diagonals  is the probability that they intersect inside the heptagon.

What are examples and probability?

there are 14 diagonals, not 30 diagonals.

This can be found by

            \(\frac{n(n - 3)}{2} = \frac{7 * 4}{2}\)   = 14 diagonals.

    = 28+42/182(5/13),

because we can choose the first diagonal is 14 ways, the second is 13.  

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Answer:

11/4

Step-by-step explanation:

3/2 can be re-written as 6/4. they now have the same denominator. 6/4 + 5/4 = 11/4

We want to find the value of cot(θ) given that sin(θ) = 3/8 and θ is an angle in a right triangle, we will get:

cot(θ) = (√55)/3

So we know that θ is an acute angle in a right triangle, and we get:

sin(θ) = 3/8

Remember that:

Then we have:

opposite cathetus = 3

hypotenuse = 8 = √(3^2 +  (adjacent cathetus)^2)

Now we can solve this for the adjacent cathetus, so we get:

adjacent cathetus = √(8^2 - 3^2) = √55

And we know that:

cot(θ) = (adjacent cathetus)/(opposite cathetus)

Then we get:

cot(θ) = (√55)/3

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The simple interest for the principal amount of $600 at the rate of 4% for 9 months will be equal to $216.

A quick and simple way to figure out interest on that money is to use the simple interest approach, which adds interest at the same rate for each daily cycle, and it is to the initial principal amount. A way to figure out how much interest will be charged on an amount of money at a specific rate and for a specific duration of time is by using simple interest.

As per the given information in the question,

Principle amount, P = $600

Time, T = 9 months

Rate, R = 4%

SI = (600 × 9 × 4)/100

SI = $216.

The SI will be $216.

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Answer:

16(base) x 15(height) x 1/2(basically just dividing by 2) = 120

120 x 2 = 240

17 x 17 = 289, 289 x 2 = 578

17 x 16 = 272

Add all given areas:

240 + 272 + 578 = 1,090 in2 is your answer

The cost of materials for the least expensive such container is 245.31 dollars .

Suppose the width of container is x (m),

length of the base of container is 2x (m)

the base area of container is (length × width)sq. m i.e 2x² meter².

Since the volume of container is 10 m³.

the height of container = area of container/ volume of container

height of container= 10/2x² m = 5/x² m

The cost of making such container is cost of base = 2x²*10 = 20x².

cost of sides of container = (2×2x × 5/x² + 2× x × 5/x²)×6 = 180/x

The overall cost is hence the sum of the base and the sides: f(x) = 20x² + 180/x

The get the minimum,

df(x)/dx = 20×(2x - 9/x²) = 0

so 2x = 9/x^2 => 2x = 2.0800 ==> x = 1.651 m

f(x) = 245.31 dollars

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Answer:

NAswer to what

Step-by-step explanation:

The extraneous solution of the equation x - 1 = √x + 1 is x = 0

From the question, we have the following parameters that can be used in our computation:

x - 1 = √x + 1

Take the square of both sides

So, we have

x² - 2x + 1 = x + 1

Evaluate the like terms

x² - 3x = 0

So, we have

x(x - 3) = 0

Solving for x, we have

x = 3 and x = 0

Substitute x = 3 and x = 0 in x - 1 = √x + 1

3 - 1 = √3 + 1

2 = 2 ---- true

0 - 1 = √0 + 1

-1 = 1 ---- false

Hence, the extraneous solution is x = 0

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since we cannot have a fraction of a serving, we can only make 9 servings of soup with 2 quarts (or 8 cups) of chicken broth.  Therefore, the proportion we should use is 5 cups of chicken broth to 6 servings of soup.

To answer this question, we need to convert 2 quarts to cups. Since there are 4 cups in a quart, 2 quarts would be 8 cups.

Now that we know we have 8 cups of chicken broth, we can set up a proportion to determine how many servings of soup we can make.

5 cups of chicken broth = 6 servings of soup

x cups of chicken broth = y servings of soup

To solve for x and y, we can cross-multiply:

5y = 6x

x = 8 cups of chicken broth

y = (6/5) * 8 = 9.6 servings of soup

However, since we cannot have a fraction of a serving, we can only make 9 servings of soup with 2 quarts (or 8 cups) of chicken broth.

Therefore, the proportion we should use is 5 cups of chicken broth to 6 servings of soup.

 To determine how many servings you can make with 2 quarts of chicken broth, you should set up a proportion using the given information: 6 servings require 5 cups of broth. First, convert 2 quarts to cups (1 quart = 4 cups, so 2 quarts = 8 cups). Now, set up the proportion:

6 servings / 5 cups = x servings / 8 cups

Here, x represents the number of servings you can make with 8 cups (2 quarts) of chicken broth. By cross-multiplying and solving for x, you will find the number of servings possible with the available broth.

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Answer:

18 and 9 are the numbers

Answer:

The total number of your ancestors for the past 42 generations would be 8,796,093,022,206.

Step-by-step explanation:

To calculate the total number of your ancestors for the past 42 generations, we can use the formula for the sum of a geometric sequence:

Sum = a * (1 - r^n) / (1 - r)

where: - a is the first term in the sequence - r is the common ratio between terms - n is the number of terms in the sequence

For this problem: - a = 2 (since you have 2 parents) - r = 2 (each generation doubles the number of ancestors) - n = 42 (the number of generations)

Now, plug these values into the formula:

Sum = 2 * (1 - 2^42) / (1 - 2) Sum = 2 * (1 - 4398046511104) / (-1) Sum = 2 * (4398046511103) / 1 Sum = 8796093022206

So, the total number of your ancestors for the past 42 generations would be 8,796,093,022,206.

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Answer:

1) 46 cases to 1 min

2) 50 cans to 1 min

3) Cans are made faster

Step-by-step explanation:

1) 2 min per 92 cases so that's 2/2 and 92/2  which is 1 to 46

2) Now canned juice is as it shows in the graph as 50 cans per min.

3) 50 cans can be made in a min while only 46 cases can be made in a min.

Answer:

23

Step-by-step explanation:

(x+4) ²-3 (Question)

x²+4x+16-3

x²+4x+13

(2)²+4(2)+13 (since x=2)

4+6+13

23

To find the equation of a line in slope-intercept form (y = mx + b) that passes through the points (-2, 2) and (7, -4), we first need to determine the slope (m) of the line.

The slope (m) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates (-2, 2) and (7, -4) into the formula, we get:

m = (-4 - 2) / (7 - (-2)) = -6 / 9 = -2/3

Now that we have the slope (m), we can use it along with one of the given points to find the y-intercept (b).

Let's use the point (-2, 2) and substitute the values into the slope-intercept form:

2 = (-2/3)(-2) + b

2 = 4/3 + b

b = 2 - 4/3

b = 2/3

Therefore, the equation of the line in slope-intercept form is:

y = (-2/3)x + 2/3

By using the formula for slope, we calculate the slope of the line passing through the given points. Substituting one of the points into the slope-intercept form equation, we solve for the y-intercept. Finally, we combine the slope and y-intercept to obtain the equation of the line in slope-intercept form, which is y = (-2/3)x + 2/3.

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The value of BA = 11.2

Here we use the condition CB/BA = DE/EF to determine the Length of BA

Substitute the lengthS of each side as per the given figure and solve the condition for the Length of the side BA.

Given that CB/BA = DE/EF

From the given figure,

CB = 7, DE = 5, and EF = 8  

Substitute the above values in the given condition

=> 7 /BA = 5 /8

Do cross multiplication

=> BA(5) = 7(8)

=> 5BA = 56

=> BA = 11.2

Therefore,

The value of BA = 11.2    

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The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

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The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is 18%.

To find the percent of the total area between two z-scores, we need to calculate the area under the standard normal curve between those two z-scores.

Using a standard normal distribution table or a statistical software, we can find the area to the left of each z-score and subtract the smaller area from the larger area to find the area between the z-scores.

For z = -1.5, the area to the left of z = -1.5 is approximately 0.0668.

For z = -0.7, the area to the left of z = -0.7 is approximately 0.2420.

The area between z = -1.5 and z = -0.7 is:

Area between z = -1.5 and z = -0.7 = Area to the left of z = -0.7 - Area to the left of z = -1.5

= 0.2420 - 0.0668

= 0.1752

To convert this area to a percentage, we multiply by 100:

Percentage of the total area between z = -1.5 and z = -0.7 = 0.1752 * 100 ≈ 17.52%

Rounding to the nearest integer, the percent of the total area between z = -1.5 and z = -0.7 is 18%.

The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is approximately 18%.

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The correct responses for the points, segments, lines, planes, are as follows;

1. M, S, X, and Y

2. Two lines are; \( \overleftrightarrow{SX}\), \( \overleftrightarrow{YR}\)

3. \( \overline {MX}, \overline{MY}, \overline {MS}, \overline{MR}\)

4. \(\overrightarrow{MT}\)

5. S, M, T

6. T

7. \( \overline{MT}\)

8. \( \overleftrightarrow{SX}\)

9. \( \overleftrightarrow{SX}\)

10. \( \overline{MR}\)

11. A line

12. A plane

13. A point

14. A plane

15. A ray

16. A segment

Please find attached the drawing for the figures in questions 17, 18, 19,and 20

1. A point in Euclidean geometry is a location in space.

Four points are; M, S, X, and Y

2. A line has no thickness and extends indefinitely in both directions.

Two lines are;

\( \overleftrightarrow{SX}\)

\( \overleftrightarrow{YR}\)

3. Four segments are;

\( \overline {MX}, \overline{MY}, \overline {MS}, \overline{MR}\)

4. A ray that has M as an endpoint is \overrightarrow{MT}

5. Three collinear points are; S, M, T

6. A point not on \( \overline{YR}\) is T

7. A segment with points T and M as its endpoints is \( \overline{MT}\)

8. A line that does not contain R is \( \overleftrightarrow{SX}\)

9. A line containing M is; \( \overleftrightarrow{SX}\)

10. A segment of lies on \( \overleftrightarrow{YR}\) is MR

11. A toothpick suggests a line

12. A floor suggests a plane

13. The tip of a pin suggests a point

14. The water surface of a swimming pool suggest a plane

15. A beam of light from a laser suggests a ray

16. A fence pole suggests a segment

Please find attached the drawing for the figures in questions 17, 18, 19, and 20

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(4x+3y=21\implies 3y=-4x+21\implies y=\cfrac{-4x+21}{3} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-4}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-4}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-4}\implies \cfrac{3}{4}}}\)

so we're really looking for the equation of a line whose slope is 3/4 and it passes through (4 , 2)

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{3}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-2=\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=\cfrac{3}{4}x-1 \end{array}}\)

Step-by-step explanation:

If you were asking what is the 3/4 the area of circle with radius 4 I can answer this.

The area of a circle with radius 4 is π4 ^2=16π

3/4*16π= 12π, thus your answer.

Answer:

The answer is 49 .

Step-by-step explanation:

Do i need to explain ?

a) The effective rate of interest on a mortgage at 8.15 percent compounded semi-annually is 8.23 percent.

b) It will take approximately 54.4 years to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly.

a) To find the effective rate of interest, we use the formula: Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods))^Number of Compounding Periods - 1.

For a mortgage at 8.15 percent compounded semi-annually, the nominal rate is 8.15 percent and the number of compounding periods is 2 per year.

Plugging these values into the formula, we get Effective Rate = (1 + (0.0815 / 2))^2 - 1 ≈ 0.0823, or 8.23 percent. Therefore, the effective rate of interest on the mortgage is 8.23 percent.

b) To determine how long it will take to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly, we can use the formula for the future value of an ordinary annuity: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of periods.

Rearranging the formula to solve for n, we have n = log(FV * r / P + 1) / log(1 + r). Plugging in the values $1,000,000 for FV, $200 for P, and 6 percent divided by 12 for r, we get n = log(1,000,000 * (0.06/12) / 200 + 1) / log(1 + (0.06/12)) ≈ 54.4 years.

Therefore, it will take approximately 54.4 years to save $1,000,000 for retirement under these conditions.

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Answer:

see explanation

Step-by-step explanation:

the radius r is the distance from the centre to a point on the circle.

calculate the radius using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = P (1, 2 ) and (x₂, y₂ ) = C (5, 8 )

r = \(\sqrt{(5-1)^2+(8-2)^2}\)

 = \(\sqrt{4^2+6^2}\)

 = \(\sqrt{16+36}\)

= \(\sqrt{52}\)

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = C (5, 8 ) and r = \(\sqrt{52}\) , then

(x - 5 )² + (y - 8 )² = ( \(\sqrt{52}\) )² , that is

(x - 5)² + (y - 8)² = 52