A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle θ. How should θ be chosen so that the gutter will carry the maximum amount of water?

Answer:

93°

Step-by-step explanation:

Angle ACB is a central angle.  The theorem regarding central angles and the arcs they intercept is that the angle and the arc are congruent.  That means that arc AB is also 93°

Answer:

Part A:

1/2 base * height

=1/2*4*1.5

=3cm

Part B:

1/2 b * h squared

=1/2*4*1.5

=3cm * 2

=6cm

Part C:

8cm*2.5cm

=20cm

Part D:

Length*Width

=8m*4cm

=32cm

(the comment answers, since someone already did the other ones)
(these are all plato answers btw..)
Part E

area of rectangle i = 20 cm²
area of rectangles i and iii = 2 × 20 cm²= 40 cm²

Part F

total area of the rectangles = 32 cm² + 20 cm² + 20 cm² = 72 cm²

Part G

To find the surface area of the prism, I need to know the areas of its bases and lateral faces, which are triangles i and ii and rectangles i, ii, and iii.

Part H

surface area of the prism = areas of bases and faces =
areas of two triangles + area of one large rectangle + areas of two smaller rectangles =
6 cm² + 32 cm² + 40 cm² =
78 cm2

Part I

This statement is false. Only two rectangles in the figure have equal areas. The third rectangle is larger than the other two.

Part J

This statement is true. The triangles are the bases of the prism, so they are congruent. Congruent triangles have the same area.            

Answer:

  4833.33

Step-by-step explanation:

The salary of $58,000 is Alex's pre-tax income. It is presumed to be divided evenly between the 12 months of the year, so his monthly income is ...

  $58,000/12 = $4833.33

Answer:

  Perpendicular

Step-by-step explanation:

Linear equations will describe parallel lines when the lines have the same slope. These equations are written in slope-intercept form, so we can easily determine that the slopes are ...

  f(x): slope is 5/6

  g(x): slope is -6/5

These are not the same, so the lines are not parallel.

__

The lines will be perpendicular when the product of their slopes is -1. Here, that product is ...

  (5/6)(-6/5) = -30/30 = -1

These equations describe lines that are perpendicular.

Answer:

The best represents a triangle is obtuse, because 6 + 10 > 12 ⇒ answer 4

Step-by-step explanation:

* Lets talk about some facts in the triangle

- The triangle is formed when the sum of the lengths of the shortest

 two side is greater then the length of the longest side

∵ The lengths of the sides are 6 cm , 10 cm , 12 cm

∵ 6 + 10 > 12

∴ 6 , 10 , 12 are the sides of a triangle

- Two know the type of the triangle use these rules

# The three sides of the triangle have lengths a , b , c where a and b

  are the shortest sides means a , b < c, then

- If a² + b² > c² , the triangle is acute triangle (its 3 angles are acute)

- If a² + b² = c² , the triangle is right triangle (the angle opposite to c is a

 right angle and the other 2 angles are acute angles)

- If a² + b² < c² , the triangle is obtuse triangle (the angle opposite to c is an

 obtuse angle and the other 2 angles are acute angles)

∵ (6)² + (10)² = 36 + 100 = 136

∵ (12)² = 144

∵ 136 < 144

∴ (6)² + (10)² < (12)²

∴ The triangle is obtuse

* The best represents a triangle is obtuse, because 6 + 10 > 12

Answer:

  (5, 3)

Step-by-step explanation:

Conventionally, the ordered pairs are (right, up). Then ...

Ming's = (0, 0) + (2, 5) = (2, 5)

Joe's = Ming's + (3, -2) = (2, 5) + (3, -2) = (2+3, 5-2)

Joe's = (5, 3)

Answer:

( 5,3 )

Step-by-step explanation:

i am doing this test too

Answer:x=13

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

Since the polygons are similar, their side lengths will be proportionate.

So, The ratio (x - 3)/2.5 will be proportionate to 16/4 (4).

That said, we can get that (x - 3)/2.5 = 4

Multiply: x - 3 = 10

Add: x = 13

You have a rectangle that is 8 ft by 10 ft

Area = 8 * 10 = 80 square feet.

Then there is a triangle 8 ft high with a base of 4 feet.

Area = /2 x 8 x 4 = 16 square feet.

Add together for total area:

80 + 16 = 96 square feet.

A simple method of calculating Area is multiplying the Length times the Width. It is much harder to calculate the entire thing all at once, so it is easier to rather keep the shapes separate.

10 x 8 = 80. This is the area of your first shape, the Rectangle.

You can do the same with the triangle, although triangles are only half a square. You also only multiply the flat sides, not the slanted side, the side with 8.9.

8 x 4 = 32. Because the shape is a triangle wedge, half a square, you divide your answer, 32, by 2, to get half of 32, which is 16.

Then add the two areas, 16 and 80, which is 96.

(The little box in the bottom right corner of the square is just an angle, it represents that it is a right angle, ignore it if you didn't know what it was.)

There all log base 3, the base won't matter as long as they're all the same.

log(x^2/y)=2log(x)-log(y)=2(4.5)-3=6

Answer: c. 6

Answer:

theoretical probability

Step-by-step explanation:

This is theoretical probability.  The 7 pieces of paper each bear one number from {1, 2, ... , 6, 7}.  There is only one piece of paper marked 7.  So the probability of drawing a 2 is  1/7.  

Answer:

  $35,000

Step-by-step explanation:

Let x represent the amount borrowed from Bank A. Then (55000-x) is the amount borrowed from Bank B. Kim's total 1-year interest is ...

  0.08x + 0.11(55000 -x) = 5000

  -0.03x + 6050 = 5000 . . . . . simplify

  -0.03x = -1050 . . . . . . . . . . . . subtract 6050

  x = 35,000 . . . . . . . . . . . . . . . divide by -0.03

Kim borrowed $35,000 from Bank A.

Answer:

The definition of a circle uses the undefined term  Arc

Step-by-step explanation:

There are three terms generally considered to be undefined in geometry: point, line and plane. A circle is the set of all points in a plane the same distance from a given point called the center. The only of our options that is used in this definition is plane.

Answer:

  1/64

Step-by-step explanation:

[tex]256^{-\frac{3}{4}}=2^{8(-\frac{3}{4})}=2^{-6}=\dfrac{1}{2^6}=\dfrac{1}{64}[/tex]

256^-3/4 can be converted into a positive fraction by interpreting the negative exponent as a reciprocal and the fractional exponent as a root. It simplifies to 1/(4th root of 256^3), which equals 1/64.

To express the numeral 256^-3/4 in the form of a fraction, we first need to understand how negative and fractional exponents work. The number is in the form of a^(-m/n) which is equivalent to the nth root of a^-m or 1/(nth root of a^m). The negative sign in the exponent implies a reciprocal of the number and the fractional exponent denotes a root of the number.

Now applying this understanding to our number which is 256^-3/4. Here, the base a is 256 and the fractions -m/n is -3/4. Therefore, it is equivalent to the 4th root of 256^-3, which can also be written as 1/(4th root of 256^3).

The 4th root of 256 is 4. So, the expression now becomes 1/(4^3), which after simplifying gives us the result 1/64.

So, the expression 256^-3/4 written as a positive fraction is 1/64.

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Answer:

The answer is E

Step-by-step explanation:

add all the numbers together then count how many numbers there are in tottally then divide

all the numbers added together is 64

there is a total of 16 numbers

64/16=4

Answer:

B)mean of data is closest to number 3.

Step-by-step explanation:

Given  : Histogram .

To find : Which of the following numbers is closest to the mean of this distribution.

Solution : We have given that histogram

We have data 1 , 2, 3, 4, 3, 2, 1.

Total number of data = 7

We need to find mean of the data

Mean = [tex]\frac{1+2+3+4+3+2+1}{7}[/tex].

Mean = [tex]\frac{16}{7}[/tex].

Mean = 2.2

Therefore, mean of data is closest to number 3.

Answer:

B

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Hence

[tex]log_{5}[/tex] 9 = x ⇒ 9 = [tex]5^{x}[/tex] → B

Answer:

its d 5 < x ≤ 9 .                                                                                                                                                                                                                                                            

If you live in the United States, then you live in Ohio.

False.

Answer with  explanation:

The converse of conditional statement "if p then q" is given by "if q then p".

The given conditional statement : If you live in Ohio, then you live in the United States.

Then , the converse of the given conditional statement will be :-

If you live in United states , then you live in Ohio.

, which is not true since there are so many states in United states other than Ohio.

Counter-example: If some one lives in Indiana, then he is also lives in United states.

The simplified ratio of Alice's measurements to Will's measurements is 26:19 when both measurements are converted to milliliters.

The ratio of Alice's measurements to Will's measurements can be found by converting both measurements to the same units and then simplifying the resulting fraction. Alice's measurement is in liters and Will's measurement is in milliliters. We know that 1 liter equals 1,000 milliliters, so Alice's measurement converted to milliliters is 6.5 liters * 1,000 = 6,500 milliliters.

Therefore, the ratio of Alice's measurement to Will's measurement in milliliters is 6,500:4750. To simplify this ratio, you can find the greatest common divisor (GCD) of the two numbers and divide both numbers by the GCD. In this case, the GCD of 6,500 and 4,750 is 250. Thus, the simplified ratio is 26:19.

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The ratio of Alice's measurements to Will's measurements is approximately [tex]\[ \frac{4750 \text{ milliliters}}{1000} = 4.75 \text{ liters} \][/tex]

To compare Alice's measurement to Will's, we need to express them using the same unit. Let's convert Will's measurement from milliliters to liters:

1 liter = 1000 milliliters

So, Will's measurement of 4750 milliliters is equivalent to:

[tex]\[ \frac{4750 \text{ milliliters}}{1000} = 4.75 \text{ liters} \][/tex]

Now, we can compare Alice's and Will's measurements:

Alice's measurement: 6.5 liters

Will's measurement: 4.75 liters

The ratio of Alice's measurements to Will's measurements is:

[tex]\[ \frac{\text{Alice's measurement}}{\text{Will's measurement}} = \frac{6.5}{4.75} \][/tex]

To simplify the ratio, we can multiply both the numerator and the denominator by 4 to get rid of the decimal in the denominator:

[tex]\[ \frac{6.5 \times 4}{4.75 \times 4} = \frac{26}{19} \][/tex]

So, the ratio of Alice's measurements to Will's measurements is [tex]\( \frac{26}{19} \)[/tex].

Answer:

(1/2)^3  

= (1/2) (1/2) (1/2)

= 1/4 (1/2)

= (1)(1)/(4)(2)

= 1/8

Step-by-step explanation:

Please mark brainliest!

Answer:

D

Step-by-step explanation:

This is a vertical opening parabola, since the focus is above the vertex on the axis of symmetry x = 2

The standard form of a vertically opening parabola is

(x - h)² = 4a(y - k)

where (h,k) are the coordinates of the vertex and a is the distance from the vertex to the focus.

here (h, k) = (2, - 1) and a = 4, hence

(x - 2)² = 16(x + 1) → D

Answer:

D

Step-by-step explanation:

Answer:

To maximize the income should be 30 buses and 150 cars

Step-by-step explanation:

Let

x-----> the number of cars

y ----> the number of bus

we know that

[tex]5x+32y\leq1,710[/tex] ------> inequality A

[tex]x+y\leq 180[/tex] ----> inequality B

The function of the cost to maximize is equal to

[tex]C=2x+6y[/tex]

Solve the system of inequalities by graphing

The solution is the shaded area

see the attached figure

The vertices of the solution are

(0,0),(0,53),(150,30),(180,0)

Verify

(0,53) ---> [tex]C=2(0)+6(53)=\$318[/tex]

(150,30) ---> [tex]C=2(150)+6(30)=\$480[/tex]

therefore

To maximize the income should be 30 buses and 150 cars

Answer:

Givens

To solve this problem we need to create a table to order all this information and express it as a system of inequations.

                     Car           Bus     Total Capcity

Sq. Meters      5c           32b            1710

N° vehicles      c              b                180                

Therefore, the inequalities are

[tex]5c+32b\leq 1710\\c+b\leq 180[/tex]

The expresion which represents the income is

[tex]I=2c+6b[/tex], because a car is $2.00 and a bus is $6.00.

Now, we first need to find the critical points of the solution of the inequality system, which is attached. Observe that the only points that can be a solution is (150,30), because there can't be just car or just buses.

Then, we replace this point in the income expression

[tex]I=2c+6b\\I=2(150)+6(30)=300+180=480[/tex]

Therefore, in order to maximize incomes, we need to park 150 cars and 30 buses, to make $480 income.

Answer:

figure four

Step-by-step explanation:

this is because 5.5/15 = 6.6/18 which means they are proportional making the two lines parallel.

Answer:

Lucy bought 4 placemats.

Step-by-step explanation:

Let n be the number of placemats Lucy bought.

1 doormat = $7

1 placemat = $2

n placemats = $2n

Total = $(7+2n)

Total number of objects bought = n+1

Average [tex]=\dfrac{\$(7+2n)}{n+1}[/tex]

So,

[tex]\dfrac{\$(7+2n)}{n+1}=\$3[/tex]

Solve this equation:

[tex]7+2n=3(n+1)\\ \\7+2n=3n+3\\ \\3n-2n=7-3\\ \\n=4[/tex]

Hence, Lucy bought 4 placemats.

Answer:

4

Step-by-step explanation:

is the answer

Answer:

x^4

Step-by-step explanation:

(x^(2/5))^10 is what I understand the words to mean

x^(2/5*10)

x^(20/5)

x^4

Answer:

The simplified form of given expression is [tex]x^4[/tex].

Step-by-step explanation:

The given expression is

[tex](x^\frac{2}{5})^{10}[/tex]

According to the power of power property of exponent, if x, a and b are any real number, then

[tex](x^a)^b=x^{ab}[/tex]

Using power of power property of exponent, the given expression can be written as

[tex](x^\frac{2}{5})^{10}=x^{\frac{2}{5}\times 10}[/tex]

[tex](x^\frac{2}{5})^{10}=x^{\frac{20}{5}}[/tex]

[tex](x^\frac{2}{5})^{10}=x^{4}[/tex]

Therefore the simplified form of given expression is [tex]x^4[/tex].

Answer:

12

Step-by-step explanation:

We can count the cubes.

One the right side there are 3 rows of 2 cubes each which is 6

There are 2 sets of identical " sets" of blocks

2*6 = 12

There are 12 blocks

1. Let S represent the cost of the sofa and C represent the cost of the chair.

If the sofa costs $50 less than three times the cost of the chair, then effectively we can write this as:

S = 3C - 50

If the sofa and chair together cost $650, we can write this as:

S + C = 650

2. Now, we can find out how much the sofa and chair cost by solving the two equations we obtained above for C, and substituting S = 3C - 50 into S + C = 650. Thus, we get:

S + C = 650

if S = 3C - 50, then:

3C - 50 + C = 650

4C - 50 = 650 (Add C and 3C)

4C = 700 (Add 50 to both sides)

C = 175 (Divide both sides by 4)

Thus, the cost of the chair is $175. Now, to find the cost of the sofa we need to simply substitute C = 175 into our first equation, S = 3C - 50:

S = 3(175) - 50

S = 525 - 50

S = 475

Thus, the sofa costs $475.

3. Now that we know that the sofa costs $475 and the chair costs $175, all we need to do is to subtract the cost of the chair from the cost of the sofa to find the difference in price:

475 - 175 = 300

Therefor, the sofa costs $300 more than the chair (answer C).

Answer:

  99°

Step-by-step explanation:

∠7 and ∠8 are a linear pair, so are supplementary. Numbers are assumed to be degrees.

  ∠7 + ∠8 = 180

  2x+15 + 3x = 180 . . . . . substitute given values

  5x = 165 . . . . . . . . . . . . subtract 15, collect terms

  x = 33 . . . . . . . . . . . . . . . divide by the coefficient of x

  ∠8 = 3x = 3·33 = 99 . . . . . degrees

Answer:

16c^2+56c+49

Step-by-step explanation:

(4c+7)^2 means (4c+7)(4c+7)

Use foil to multiply:  4c(4c)+4c(7)+7(4c)+7(7)

Simplifying            :   16c^2+28c+28c+49              

                                  16c^2+56c+49

[tex](4c + 7)^2=16c^2+56c+49[/tex]

Answer:

the probability of drawing three consecutive red marbles is based on how many red marbles you have and many marble there is in total.

Answer:

27/512

Step-by-step explanation:

P(3 consecutive red)=P(red)×P(red)*P(red)=3/8*3/8*3/8=27/512.

The reason P(red)=3/8 for each picking of marble us because you are putting the marble back in and there are 3 red while you have 8 marbles in all.

Answer:

The number of tables

Step-by-step explanation:

Let

z ----> the number of tables

y-----> the number of chairs

we know that

[tex]y=2z+3[/tex]

therefore

z represent the number of tables

Answer:

the number of tables :]

Step-by-step explanation:

The equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]

The vertices of the hyperbola are given as:

Vertices = (±4, 1)

The foci of the hyperbola are given as:

Foci = (±5, 1)

The coordinates of the vertices is represented as::

Vertices = (±a, n)

By comparing (±a, n) and (±4, 1), we have:

a = 4

n = 1

The coordinates of the foci is represented as::

Foci = (±c, n)

By comparing (±c, n) and (±5, n), we have:

c = 5

n = 1

Calculate b using:

b = √(c² - a²)

So, we have:

b = √(5² - 4²)

Evaluate

b = 3

The equation of a hyperbola is:

[tex]\frac{x^2}{a^2} - \frac{(y - n)^2}{b^2} = 1[/tex]

So, we have:

[tex]\frac{x^2}{4^2} - \frac{(y - 1)^2}{3^2} = 1[/tex]

Evaluate the exponent

[tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]

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