Eliminate the y in the following system of equations. What is the result when you add the two equations? \(x + y = 8 \\ 5x - 3y = 24\)A: 6x = 32B: 8x = 32 C: x = 0D: 8x = 48

The area of the exposed surface is 442 square feet

A right square pyramid is a polyhedron with 5 faces consisting of four triangles and a square base.

Analysis:

The exposed surface is the area of the four triangles.

The perpendicular height of the triangles is same and it is the slant length of the shape = 17ft

Area of 4 triangles = 1/2 bh = 1/2 x 17 x 13 x 4 = 442 square feet.

In conclusion, area of exposed surface is 442 square feet.

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Considering that it has an angle of 90º degrees, the triangle is classified as:

B. right

In this problem, two angles are 40º and 50º. Since the sum of the angles is of 180º, we have that:

x + 50 + 40 = 180

x = 90º.

Hence, it is a right triangle, and option B is correct.

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The two triangles are similar, so the ratio of their corresponding sides is equal. Let $x$ be the width of the river. Then, the ratio of the corresponding sides of the triangles is $\frac{x}{61} = \frac{23.4}{31}$. Solving for $x$, we get $x = \frac{23.4}{31} \cdot 61 = \boxed{46}$ meters.

Answer:

Clockwise rotation of 90 degrees and reflection across a vertical line. (as shown in picture)

Step-by-step explanation:

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day! :)

Answer:

I think the answer is thirty nine (39)

Step-by-step explanation:

because if you draw that on a book and you measure it using a protractor you get 39.

We know that the prices of the clothing are

Shirt $23

Belt $9

Sweater $38

Pair of Jeans $42

And we must find how much money Ming spent if Ming bought 8 belts.

Since Ming bought 8 belts we can find the money spent multiplying 8 by the cost of one belt

In order to make the multiplication more easy we can rewrite 8 as 4*2

Finally, the money spent will be

So, Ming spent $72

Answer

0.00336

Step-by-step explanation:

Given :

P(Brown), P(Br) = 0.4

P(Blue) = P(b= 0.35

P(green,) = P(g) = 0.12

P(gray), P(Gr) = 0.07

If 3 individuals are selected, the probability that one has brown eye, 1 has Grey and one has green.

Since the probabilities are independent :

P(Br) * P(Gr) * P( g)

0.3 * 0.07 * 0.12

= 0.00336

Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.

We use the fact that parallel lines have the same slope to determine the equation of a line that is perpendicular to a given line and passes through a point. provided that it takes the form y = mx + b, where m is the slope, the provided line has a slope of -8/7. The parallel line will therefore similarly have a slope of -8/7.

The point-slope form of a line is used to determine the y-intercept of a parallel line: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. We obtain: y - 4 = (-8/7)(x + 6) by substituting (-6, 4) and -8/7 for m.

This equation can be simplified to y = (-8/7)x - 40/7.

We make use of the fact that perpendicular lines have opposing reciprocal slopes to determine the equation of a line that is perpendicular to the supplied line and passes through (-6, 4). provided that the provided line has a slope of -8/7, the perpendicular line will have a slope of 7/8.

Again using the point-slope representation of a line, we arrive at: y - 4 = (7/8)(x + 6)

This equation can be simplified to: y = (7/8)x + 25/4

Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.

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Answer:

5000 ;

11125

Step-by-step explanation:

Given :

Total principal = 16125

Rates = 8.5% and 4%

Period, t = 2 years

Total interest = 1740

Let :

Principal amount invested at 8.5% = x

Principal amount invested at 4% = 16125 - x

Interest formula :

Interest = principal * rate * time

Hence, mathematically ;

(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740

(0.17x + 1290 - 0.08x ) = 1740

0.09x + 1290 = 1740

0.09x = 1740 - 1290

0.09x = 450

x = 450 / 0.09

x = 5000

Amount invested at 4% :

16125 - 5000 = 11125

Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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The required possible dimensions of the​ rug are 11   by  \(\frac{r^2 - 8r - 33}{11}\).

The area of the rectangular rug is given by the trinomial:

\($r^2 - 8r - 33$\)

To find the possible dimensions of the rug, we need to factor this trinomial. We can do this by finding two numbers that multiply to -33 and add up to -8. These numbers are -11 and 3:

\($r^2 - 8r - 33 = (r - 11)(r + 3)$\)

Therefore, the possible dimensions of the rug are:

\($r - 11 = 0$\) or \($r + 3 = 0$\)

\($r = 11$\)or $\($r = -3$\)

Since the dimensions of the rug cannot be negative, we can only take the positive value of r, which is r = 11.

Therefore, the possible dimensions of the rug are:

11   by  \(\frac{r^2 - 8r - 33}{11}\)

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Answer:

b= 23.4,. γ = 70°, c= 28.9

Step-by-step explanation:

To solve the triangle with given α = 65°, β = 45°, and a = 30, we can use the law of sines:

b/sin(β) = a/sin(α)

b/sin(45°) = 30/sin(65°)

b ≈ 23.4

Then, to find angle γ, we can use the fact that the sum of angles in a triangle is 180°:

γ = 180° - α - β

γ ≈ 70°

To find side c, we can again use the law of sines:

c/sin(γ) = a/sin(α)

c/sin(70°) = 30/sin(65°)

c ≈ 28.9

Therefore, the solution is b = 23.4, γ = 70°, and c = 28.9.

Note that there is no other possible solution, as the given angles and side lengths do not allow for multiple triangles to be formed.

The number of hours it will take the same dog to run 26 1/10 miles is 7.2 hours

7 1/4 miles in 2 hours

26 1/10 miles in x hours

Equate miles ratio hours

7 ¼ miles : 2 hours = 26 ⅒ miles : x hours

7.25 / 2 = 26.10 / x

cross product

7.25 × x = 26.10 × 2

7.25x = 52.20

divide both sides by 7.25

x = 52.20 / 7.25

x = 7.2 hours

Ultimately, it will take 7.2 hours for the dog to run 26⅒ miles.

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Answer:

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The diagram is shown below.

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

Work Shown:

tan(angle) = opposite/adjacent

tan(theta) = 12.5/18

theta = arctan(12.5/18)

theta = 34.7778313663639

theta = 34.8 degrees

Round this value however your teacher instructs. I decided to round to one decimal place because the 12.5 is to one decimal place. Make sure your calculator is in degree mode.

The notation arctan refers to arctangent. It is the same as inverse tangent, and it is often shown as \(\tan^{-1}\) on many calculators.

Answer:

\(\displaystyle 35\degree\)

Step-by-step explanation:

When drawn out, you will notise you must use the inverce cotangent trigonometric ratio:

\(\displaystyle ? = cot^{-1}\:\frac{18}{12,5}; 34,777831366...\degree \\ \\ \boxed{35\degree \approx\:?} \\ \\ \\ OR \\ \\ \\ ? = tan^{-1}\:\frac{12,5}{18}; 34,777831366...\degree \\ \\ \boxed{35\degree \approx\:?}\)

I am joyous to assist you at any time.

Extended information on trigonometric ratios

\(\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:\theta \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:\theta \\ \frac{OPPOCITE}{ADJACENT} = tan\:\theta \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:\theta \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:\theta \\ \frac{ADJACENT}{OPPOCITE} = cot\:\theta\)

Answer:

Counfounding variable phenomenon

Step-by-step explanation:

The correlation or positive relationship observed between ice cream consumption and crime rate is one of the scenarios which buttresses the point they correlation does not imply causation. Because, from the study, ice cream consumption rises and falls in hot and cold seasons respectively and crime rate also behaves accordingly. However, there is no logical reason why crime should be committed due to consumption of ice cream. However, from further studies, it was deduced that a third variable is at work here, which isn't considered in the initial study, which is temperature. During hot weather, rate of dehydration increases and the need to take ice chilled drinks to cool off rises; similarly temper seems to flare with rising temperature due to heat which might probably cause an imbalance system and ultimately lead people into committing crimes. Hence, the common variable which simultaneously affects both ice cream consumption and crime rate is temperature which is a confounding variable.

The last option which says  the roots of the auxiliary equation are √6 and -√6 is the correct one.

Auxiliary equation is the equation of characteristic polynomial which is calculated by substituting the right member of a standard differential equation by zero.

The roots of the equation is helpful in determining the nature of the general solution of the given differential equation.

We have the differential equation given in the question,

d²y / dx²  - 6y = 0

Now we can replace d²y / dx² as y''.

y'' - 6y = 0, where y'' is the second derivative of y.

Now we have to find the roots of the auxiliary equation.

Let c = y', then c² = y''

c² - 6 = 0

c² = 6

c = +√6 and -√6

So the roots of the equation are √6 and -√6.

Hence the roots of the auxiliary equation of the differential equation given are +√6 and -√6.

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Answer:

Below

Step-by-step explanation:

The equation to use for CONTINUOUS compounding is :

FV = PV e^(it)

18532.08 = 8327 * e^( i*10)        where i is the interest in decimal form

18532.08/8327  = e^(10i)

2.225541 = e^(10i)             now take natural log  (ln) of both sides to get

.8000 = 10i

i = .08     or 8% interest

Answer:

36w

Step-by-step explanation:

Answer:

A - A rotation 90° counterclockwise

Step-by-step explanation:

Translations change orientation. Dilations change size. Reflection over the *Y-AXIS* would be from Q4 to Q3. Rotations do not change orientation.

Answer:

-3.

Step-by-step explanation:

=  6(Sum+8) = 30

=  6Sum + 48 = 30

= 6Sum = -18

= Sum = -3

Hope this helps you :)

Answer:

the answer to this is 6(-3+8)=30

To graph the equation y = 12.3x, identify and locate the vertical and horizontal intercepts. To do this, set x equal to zero to find the vertical intercept, which is y = 12.3(0) = 0. Then, set y equal to zero to find the horizontal intercept, which is x = 0/12.3 = 0.

To graph the equation y = 12.3x, we need to identify and locate the vertical and horizontal intercepts. The vertical intercept is found by setting x equal to zero, which gives us y = 12.3(0) = 0. This means the vertical intercept is at the point (0,0). The horizontal intercept is found by setting y equal to zero, which gives us x = 0/12.3 = 0. This means the horizontal intercept is at the point (0,12.3). We can then plot these two points to graph the equation. Drawing a line through the points, we can see that the equation is a straight line that goes through the origin with a positive slope, meaning that as x increases, so does y. This line has a y-intercept of 0 and an x-intercept of 12.3.

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The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Answer:

: Gumuhit ng tatlong bagay na sa alam mo ay naging epekto ng digmaan. Iguhit ito Sa loob

ng mga bilog.

Step-by-step explanation:

Let's Write!

Directions: Write at least a five-sentence paragraph about the issue conveyed in the

picture using a pattern of idea development with its appropriate grammatical signals. A

rubric is given below for your guidance. Write your paragraph on a separate sheet of

paper.Directions: Write the word "TRUE” if the statement is true and write "FALSE” if the statement

is false. Write your answer on your answer sheet.

1. Always follow the routine “clean up while in use and clean up before keeping it”.

2. Manufacturer's instructions for operation and maintenance should be followed.

3. Employers have some control over potential hazards.

4. Before the vacuum cleaner becomes overloaded, throw dust bags after each use.

5. For the equipment with wheels, clean and check wheel-driven gears.

6. For proper storage/safekeeping of hand tools and equipment, surfaces of cutting tools

should be displayed for easy used and reach.

7. Only qualified people should carry out the maintenance and they should also keep

records of their inspections.

8. Check-up equipment irregularly to prevent serious breakdown.

9. Place guards on machinery to protect fingers and limbs.

10. Store electrical equipment outdoors.Directions: Write the word "TRUE” if the statement is true and write "FALSE” if the statement

is false. Write your answer on your answer sheet.

1. Always follow the routine “clean up while in use and clean up before keeping it”.

2. Manufacturer's instructions for operation and maintenance should be followed.

3. Employers have some control over potential hazards.

4. Before the vacuum cleaner becomes overloaded, throw dust bags after each use.

5. For the equipment with wheels, clean and check wheel-driven gears.

6. For proper storage/safekeeping of hand tools and equipment, surfaces of cutting tools

should be displayed for easy used and reach.

7. Only qualified people should carry out the maintenance and they should also keep

records of their inspections.

8. Check-up equipment irregularly to prevent serious breakdown.

9. Place guards on machinery to protect fingers and limbs.

10. Store electrical equipment outdoors.WORK #1

Direction: List 1 Digestive System disease. Identify its causes, symptoms, and treatment. Use the template

below.

Digestive Disease

Causes

Symptoms

TreatmentWRITTEN WORK #1

Direction: List 1 Digestive System disease. Identify its causes, symptoms, and treatment. Use the template

below.

Digestive Disease

Causes

Symptoms

Treatment

Answer:

20:9

Step-by-step explanation:

Here we will simplify the ratio to 40:18 for you and show you how we did it.

To simplify the ratio 40:18, we find the greatest common divisor of 40 and 18, and then we divide 40 and 18 by the greatest common divisor.

The greatest common divisor that you can use to simplify 40:18 is 2. This means the answer to ratio 40:18 simplified is:

20:9

The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Based on the price that Augusta Enterprises issued the bonds, the journal entries would be:

Date                  Account title                              Debit                Credit

July 1, 20x5       Cash                                      $97,000

                         Discount on Bonds payable $3,000

                         Bonds payable                                               $1,000,000

Date                  Account title                              Debit                Credit

July 1, 20x5       Cash                                     $1,020,000

                         Premium on Bonds payable                           $20,000

                         Bonds payable                                              $1,000,000

The cash received from the discounted bond is:

= 1,000,000 x 97%

= $970,000

The cash received from the premium bond is:

= 1,000,000 x 102/100

= $1,020,000

The premium is:

= 1,020,000 - 1,000,000

= $20,000

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Answer: In point C.

Step-by-step explanation:

Plane ADB is the plane that contains the points A, D and B.

If you look in the image, you can see that point C also does belong to this plane.

Line EC is the line that connects the points E and C.

Now, remember that Point C does belong to the plane ADB, then the point where the plane ADB and line EC intersect is in point C, because it is a common point to both elements.