The perimeter of the triangle shown is 30 inches. What is the length of the longest side of the triangle

Answer:32 cm2

Step-by-step explanation:Use the formula A=BH, The 7 does not count because it isn't base or height. Use 4 times 8 which will make 32 cm2.

Area of the parallelogram is 32 cm²

Given that;

Base of parallelograms = 8 cm

Height of parallelograms = 4 cm

Find:

Area of the parallelogram

Computation:

Area of the parallelogram = l × b

Area of the parallelogram = 8 × 4

Area of the parallelogram = 32 cm²

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There are 990 different arrangements of president, vice-president, and secretary

The given parameters are:

Club members, n = 11

Members to arrange, r = 3

The number of arrangements is calculated using the following permutation equation

Ways = nPr

This gives

Ways = 11P3

Evaluate

Ways = 990

Hence, there are 990 different arrangements of president, vice-president, and secretary

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Final answer:

To find the number of different arrangements of president, vice-president, and secretary in a club of 11 members, we use the concept of permutations. Using the formula for permutations of distinct objects, we calculate P(11,3) = 990. Thus, there are 990 different arrangements possible.

Explanation:

To find the number of different arrangements of president, vice-president, and secretary, we can use the concept of permutations. Since the positions have different roles and can only be assigned to one person each, we use permutations. The number of permutations can be found using the formula for permutations of distinct objects: P(n,r) = n! / (n-r)!.

In this case, we have 11 members and need to assign them to 3 different positions (president, vice-president, and secretary). So, the number of arrangements is P(11,3) = 11! / (11-3)! = 11! / 8! = 11 x 10 x 9 = 990.

Therefore, there are 990 different arrangements of president, vice-president, and secretary possible.

25 % of the water had evaporated.

Answer:

20%

Step-by-step explanation:

Since the total amount of water is 2.5 million

And 2 million evaporated,

To determine the amount left,it will be total amount- evaporated

2.5-2=0.5

To determine the% of evaporated water

It will be evaporated/total amount ×100

0.5/2.5 × 100

50/2.5

20%

So the percentage of the evaporated water is 20%

Answer:

P=3x-14

Step-by-step explanation:

P=2(x+1/2 x-7)

=2x+x-14

or P=3x-14

The perimeter of the garden will be;

⇒ 3x - 7/2

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The garden is shown in figure.

Width of garden = 1/2x - 7

Length of garden = x

Now,

Since, Width of garden = 1/2x - 7

Length of garden = x

Hence, The perimeter of garden = 2 (Length + Width)

⇒ The perimeter of garden = 2 (x + 1/2x - 7)

⇒ The perimeter of garden = 2 (3/2x - 7)

⇒ The perimeter of garden = 3x - 7/2

Thus, The perimeter of the garden will be;

⇒ 3x - 7/2

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Answer:

C). 30 I just learned about this!

Step-by-step explanation:

If the smaller diamond is 12 and the bigger one is 36 then its times 3 and whatver you do to the top you do to the bottom so it would be 10 times 3 which would equal 30! (:

Answer:

C - 30

Step-by-step explanation:

Since one side of the smaller diamond is 12 and the side on the bigger diamond is 36 it is 3 times the perimeter on each side so since the side on the small diamond is 10 then you would times it by three to get the perimeter of the side on the bigger diamond , which is 30 .

Answer:

y   = 3x+3

Step-by-step explanation:

We know the y intercept since it crosses the y axis at (0,3) and we know the x intercept since it crosses the x axis at (-1,0)

We can fidn the slope

m = (y2-y1)/(x2-x1)  (0,3) (-1,0)

     =(0-3)/(-1-0)

     = -3/-1

      =3

The equation for the line is in the form

y = mx +b where m is the slope and b is the y intercept

y   = 3x+3

Answer:

x=1/2

Step-by-step explanation:

1.). add 7x to both sides

       12x=6

2.) divide by 12 to get x by itself.

       x=6/12

3.) simplify the fraction and you get the answer!

       x=1/2

The value of x is -9 and 3.Option D.

Step-by-step explanation:

Given,

[tex]-x^{2} +27 = 6x[/tex]

To find the value of x.

We will apply middle term factor formula.

The given equation can be written as,

[tex]x^{2} +6x-27 = 0[/tex]

or, [tex]x^{2}[/tex]+(9-3)x-27 = 0

or, x²+9x-3x-27= 0

or, x(x+9)-3(x+9)=0

or, (x+9)(x-3) = 0

So, x = -9 and x = 3

Hence,

The correct option is Option D.

Answer: -4

Step-by-step explanation:

If you replace x for 0 it will eliminate the variable. The only remaining term without a variable is -4

Answer:A. The graph is increasing by a common ratio of 3

C. As x increases, y increases

F. As x decreases, y approaches 0

Step-by-step explanation:

The true statements are:

A. The graph is increasing by a common ratio of 3

C. As x increases, y increases

F. As x decreases, y approaches 0

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Answer:52

Step-by-step explanation:

To find this

Total ratio=3+4

=7

Find the amount share

7/4×39

=91

So, to get a share's

3/7×91

=52

Answer:

[tex]x^{2} \\[/tex]+3x

Step-by-step explanation:

2x(2x+1)

x(x+1)

2[tex]x^{2}[/tex]+2x-[tex]x^{2}[/tex]+x

=[tex]x^{2}[/tex]+3x

Answer:

B. [tex]\left[\begin{array}{ccc}-18&10\\5&-3\end{array}\right][/tex]

Step-by-step explanation:

The question is off edg. it is supposed to be [tex]\left[\begin{array}{ccc}4&3\\-1&-1\end{array}\right] * \left[\begin{array}{ccc}-3&1\\-2&2\end{array}\right][/tex] with multiple options. I just used the matrix calculator on edg.

Answer:

3840 cubic inches

Step-by-step explanation:

10*24 = 240 in

240*16 = 3840 cubic in

Answer:

The probability of a student to be in the orchestra or the band is 0.07 or 7%.

Step-by-step explanation:

The probability of a student to be in the orchestra or the band is given by the following formula:

p(orchestra or band) = p(orchestra) + p(band) - p(orchestra and band)

p(orchestra or band) = 0.03 + 0.05 - 0.01

p(orchestra or band) = 0.08 - 0.01

p(orchestra or band) = 0.07

The probability of a student to be in the orchestra or the band is 0.07 or 7%.

Final answer:

The probability that a student is in orchestra or band is 7%.

Explanation:

To calculate the probability that a student at Lincoln High School is in either orchestra or band, we will use the formula for the probability of the union of two events, P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where P(A) is the probability of being in orchestra, P(B) is the probability of being in band, and P(A ∩ B) is the probability of being in both orchestra and band.

In this case, we have been given that 3% of students are in orchestra, 5% are in band, and 1% are in both.

Therefore, we have:

Applying the formula:

P(orchestra OR band) = P(orchestra) + P(band) - P(both orchestra and band) = 0.03 + 0.05 - 0.01 = 0.07

Therefore, the probability that a student is in either the orchestra or the band is 7%.

Ms. Joseph saves money for 12 weeks, starting with $1 and increasing the amount by $1 each week. By the 12th week, she adds $12. Therefore, she saves money for a total of 12 weeks.

To determine how many weeks Ms. Joseph is saving money, we need to look at the pattern of her savings. Each week, she adds one more dollar than the previous week:

We can see that this is an arithmetic sequence where the first term (a) is $1 and the common difference (d) is $1. The nth term of an arithmetic sequence can be found using the formula: aₙ = a + (n-1)d.

For 12 weeks, the amount saved each week would be: a₁₂= 1 + (12-1) ×1 = 12. Ms. Joseph adds $12 in the 12th week. Finally, the total weeks she saves money is 12 weeks.

Answer:

Option D - $81.75

Step-by-step explanation:

Given : Jake earns 15% commission on the total amount he sells. If he sells $545 worth of items.

To find : How much commission  does Jake earn?

Solution :

Using the commission formula,

[tex]\text{Commission}=\text{Sales}\times \text{Percentage}[/tex]

[tex]\text{Commission}=\$545\times 15\%[/tex]

[tex]\text{Commission}=545\times \frac{15}{100}[/tex]

[tex]\text{Commission}=81.75[/tex]

Therefore, commission  does Jake earn is $81.75.

So, option D is correct.

Answer:

150 ft/min

Step-by-step explanation:

The change in altitude per minute will have the units of ft/min.

We see that we are given the number of feet: 2250 ft, as well as the number of minutes: 15 min.

So, to get ft/min, we can divide 2250 ft (the distance) by 15 min (time) to get the rate: 2250/15 = 150 ft/min

Thus, the change in altitude per minute is 150 ft/min.

Hope this helps!

Answer:

-15 per minute

Step-by-step explanation:

2250/15 = 150

Since it's descending, height is decreasing.

Hence rate of change of height is -15 per minute

Answer:

Im 90% sure its H.

Step-by-step explanation:

Answer:

H) 9.6

Step-by-step explanation:

Use the pythagorean theorem to solve for a right triangle.

Pythagorean Theorem: a^2 + b^2 = c^2

So, 16^2= 12.8^2 + x ------> 256= 163.84 + x^2 (subtract 163.84 from both sides of the equation) -----> x^2= 92.16 (square root) -----> x=9.6

This is my first answer so I hoped it helped! :)

There is no picture but the fomula for volume is lengthxwidthxheight for a square or rectangle

Answer:

Price             Qd1     Qd2    Qs

25                     75000    60000    45000

30                    60000    55000    45000

35                    45000    50000    45000

40                     30000    45000    45000

45                      15000    40000    45000

[Find the attachment for the graph]

Final answer:

The equilibrium price for the Seattle Mariners baseball team's seats can be found using economic principles of supply and demand, taking into account factors that influence ticket demand, marginal revenue, and costs.

Explanation:

The question involves determining the equilibrium price for Seattle Mariners baseball team seats. This can be addressed using principles from Economics, specifically the supply and demand model. To determine the equilibrium price, one would need to establish the demand curve, which includes factors such as the population and income of the home city, the team's standing, and the number of superstars on the team. As economists such as Ferguson et al. suggest, the marginal cost for sports teams is often assumed to be zero due to the fixed costs of stadium operations. Therefore, the profit-maximizing quantity of seats sold is where marginal revenue is zero. This can be calculated and visualized with a graph showing both demand and marginal revenue curves. Additionally, adjustments such as the addition of new seats or external fees like licensing can affect the equilibrium dynamics, thus changing the equilibrium price and the total revenue.

Answer:

11x

Step-by-step explanation:

Answer:

If you take a number and 'subtract" it with another number, it means that you take your second number and remove that amount from the first number

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Answer:

Definition of subtraction sign. : a mathematical symbol used to indicate that a particular quantity is to be subtracted from another to which it is joined by the symbol : a symbolic representation of the relation of subtrahend and minuend —symbol −

Step-by-step explanation:

Answer:

13/8

Step-by-step explanation:

Answer:

Three and one fourth plus seven eigths

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

The equation of a circle gives the positions of points inside or on its circumference. A point is outside the circle if the substitution in the equation results in a value greater than the square of the circle's radius.

To understand this, we need first to understand the equation of a circle which is defined in the format (x-a)² + (y-b)² = r², where (a,b) is the center of the circle and r is the radius.

In this case, (a,b) = (5,-3) and r = 4. So, the equation of the circle becomes (x-5)² + (y+3)² = 16. Any point (X,Y) that satisfies this equation is inside or at the circumference of the circle. If the computation yields a result greater than 16, the point is outside the circle.

Let's take a point for example: (3,-1). Substituting the values gives (3-5)² + (-1+3)² = 4 + 4 = 8 which is less than 16, hence, lies inside the circle. But for a point like (10,0), it results in (10-5)² + (0+3)² = 25 + 9 = 34 which is greater than 16, so the point (10,0) is outside the circle.

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Answer:

63/380

Step-by-step explanation:

Initially,

# of Mysteries, M = 9

# of Biographies, B = 7

# of Sci. Fiction, S = 4

Total number of books = 9 + 7 + 4 = 20 books

P (first book selected is biography) = 7/20

After selecting 1 biography book,

# of Mysteries, M = 9

# of Biographies, B = 7 - 1 = 6

# of Sci. Fiction, S = 4

Total number of books remaining = 9 + 6 + 4 = 19 books

P (second book selected is a mystery) = 9/19

Hence (P first book is biography and 2nd book is mystery)

= (7/20 )(9/19)

= 63/380

The probability of selecting a biography then a mystery is 0.14.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Given that, a bookshelf contains 9 mysteries, 7 biographies, and 4 science fiction books.

Total number of outcomes = 9+7+4

= 20

The probability of selecting a biography = 7/20

The probability of selecting a mystery = 9/20

Probability of an event = 7/20 × 9/20

= 56/400

= 0.14

Therefore, the probability of selecting a biography then a mystery is 0.14.

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Final answer:

To find the value that goes in the empty cell, we need to multiply each value of x by 5. So, when x = -1, f(x) = 5*(-1) = -5. Therefore, the value that goes in the empty cell is -5.

Explanation:

The table represents the function f(x) = 5x. In the first column, we have the values of x, which are -1, 0, 1, and 2. In the second column, we have the values of f(x), which are blank, 0, 5, and 10. To find the value that goes in the empty cell, we need to multiply each value of x by 5. So, when x = -1, f(x) = 5*(-1) = -5. Therefore, the value that goes in the empty cell is -5.

Answer:

x=8

Step-by-step explanation:

The vertical asymptote is where the denominator goes to zero

3(x-8) =0

Divide by 3

(x-8) =0

Add 8 to each side

x-8+8=0+8

x=8

The vertical asymptote can be find by solving the 0 of the denominator.

3(x - 8) = 0

3x - 24 = 0

3x - 24 + 24 = 0 + 24

3x = 24

3x/3 = 24/3

x = 8

Besr of Luck!

Answer:

A

Step-by-step explanation:

vertical are always opposite each other

complementary are 180

supplementary are 90

Answer:

Step-by-step explanation:

Surface area = lateral area + 2(area of base)

Lateral area = perimeter of base * height.

Because it is a isosceles right triangle, both sides are equal.

[tex]x^{2} +x^{2}[/tex] = 72

2[tex]x^{2}[/tex] = 72. Divide both sides by 2

[tex]x^{2}[/tex] = 36.  Square both sides.

x = 6.

So the perimeter of the base = 6 + 6 +[tex]\sqrt{72}[/tex] = 20.485281374239

Lateral area = 20.485281374239 * 7 = 143.397 [tex]cm^{2}[/tex]

Area of base is (1/2)base * height.

(1/2)(6)(6) = 18

Using the surface area formula

surface area = 143.397 + 2(18) = 179.4 [tex]cm^{3}[/tex]

Final answer:

The surface area of the triangular prism can be calculated by finding the areas of the two triangular bases and the three rectangular sides. After calculations, the total surface area of the prism is found to be 2304 square centimeters.

Explanation:

The question asks us to find the surface area of a triangular prism whose base is an isosceles right triangle with a hypotenuse of √72 centimeters and a height of 7 centimeters. We'll use various formulas for geometry, area, and volume to solve this problem.

First, we need to find the legs of the isosceles right triangle which form the base of the prism. Since it is a right triangle, and the legs (a) are equal, we can use Pythagoras' theorem where [tex]a^2 + a^2 = (72)^2[/tex]

Solving this gives us each leg as 36 cm.

The area of the base triangle is then found using 1/2 × base × height, which gives us-

1/2 × 36 × 36 = 648 square centimeters

The prism has two such triangular bases, so their combined area is 2 × 648 = 1296 square centimeters.

For the three rectangular sides, we calculate their areas by using the formula for the area of a rectangle (length × width). Each side has a length of 7 cm (the height of the prism). The widths are equal to the sides of the triangular base: 36 cm, 36 cm, and √(362 + 362) = √2592 = 72 cm. Thus, the total area of these sides is-

2(36 × 7) + (72 × 7) = 504 + 504 = 1008 square centimeters.

The total surface area of the prism is the sum of the areas of the bases and the rectangular sides, which is 1296 + 1008 = 2304 square centimeters.