The diagram below represents the net of a triangular prism.
3
6 cm
12 cm
6 cm
8 cm
10 cm
6 cm
(not drawn to scale]
What is the surface area of the triangular prism?
A
288 square centimeters
B
312 square centimeters
с
336 square centimeters
D
368 square centimeters

[tex]f(x) = \log_b(x)[/tex] is a decreasing function when [tex]0 < b < 1[/tex]

This is because we can use the change of base formula to say

[tex]\log_b(x) = \frac{\log(x)}{\log(b)}[/tex]

If b is between 0 and 1, not including either endpoint, notice how the log(b) term is negative.

For example, if b = 0.5, then log(b) = log(0.5) = -0.301 approximately. I'm using log base 10 to get log(0.5) = -0.301

So for b = 0.5, we have,

[tex]\log_{0.5}(x) = \frac{\log(x)}{\log(0.5)} \approx \frac{\log(x)}{-0.301} \approx -3.322\log(x)[/tex]

The log(x) part on its own is always increasing. The negative coefficient out front flips it to always decreasing.

By applying the behavior rules we notice that the expression [tex]F(x) = \log_{b} x[/tex]decreasing function if the base of the logarithm is 0 < b < 1. (Correct choice: D) #SPJ5

Logarithms are trascendent functions whose form is defined by the following expression:

[tex]\log _{b} x[/tex] such that [tex]x = b^{a}[/tex], where b > 0.

Where b is the base of the power.

Whose rules are described below:

By applying the behavior rules we notice that the expression [tex]F(x) = \log_{b} x[/tex] is a decreasing function if the base of the logarithm is 0 < b < 1. (Correct choice: D)

The statement is poorly formatted and reports several mistakes. Correct form is shown below:

For what values of b will [tex]F(x) = \log_{b} x[/tex] be a decreasing function?

A. b > 0

B. 0

C. b < 0

D. 0 < b < 1

To learn more on logarithms, we kindly invite to check this: https://brainly.com/question/20785664 #SPJ5

Answer:

The answer is below

Step-by-step explanation:

The area of the wall is 84 ft².

The width of the wallpaper is 18 in.

1 ft. = 12 in

Hence; 18 in = 18 in * 1 ft. per 12 in = 1.5 ft

The length of the wallpaper is 33 ft.

Therefore, the area of the wallpaper = length * width = 1.5 ft. * 33 ft. = 49.5 ft². This means that each roll of wallpaper has an area of 49.5 ft²

Therefore, the minimum amount of rolls of wallpaper needed = area of wall / area of wallpaper

Amount of wallpaper = 84 ft² / 49.5 ft² = 1.7 rolls

Answer:

He made the following mistake, he assumed that polynomial [tex](x^{2}+1) = (x^{2}-1)[/tex], having for granted that [tex]x^{2}+1[/tex] has two real roots, instead of two complex roots.

Step-by-step explanation:

He made the following mistake, he assumed that polynomial [tex](x^{2}+1) = (x^{2}-1)[/tex], having for granted that [tex]x^{2}+1[/tex] has two real roots, instead of two complex roots. The true factorized form of the fourth grade polynomial is:

[tex]r(x) = (x^{2}+1)\cdot (x^{2}-9)[/tex]

[tex]r(x) = (x- i)\cdot (x+i)\cdot (x+3)\cdot (x-3)[/tex]

Answer:

Part A

The volume of the triangular prism is 500 cm³

Part B

The total surface area of the prism is approximately 441.42 cm²

Step-by-step explanation:

The given details are;

The dimensions of the side length of the cube, s = 10 cm

The shape the cube was cut across to obtain = A prism

Part A

Whereby the prism obtained is a triangular prism, we have;

The cube can be cut in half to form a triangular prism

The volume of each triangular prism obtained = (1/2) × The volume of the cube

∴ The volume of the triangular prism = (1/2) × (10 cm)³ = 500 cm³

Part B

The height of the prism, h = 10 cm × sin(45°) = 5·√2 cm = (1/2) × The base width of the prism

The triangular cross sectional area of the prism, A₁ = 5·√2 × 5·√2 = 50

The square cross sectional area, A₂  = 10 × 10 = 100

The cross sectional area of the base, A₃ = 10·√2 × 10 = 100·√2

The total surface area of the prism, A = 2·A₁ + 2·A₂ + A₃

∴ A = 2×50 + 2×100 + 100·√2 = 300 + 100·√2 ≈ 441.42

The total surface area of the prism, A ≈ 441.42 cm²

Answer:

what do you mean for this question. What do you need help on?

Answer:

JMK

Step-by-step explanation:

Answer:

[tex]-\frac{1}{5}[/tex] is the slope of the line.

Step-by-step explanation:

(7 , 1) = (x1 , y1)

(-3 , 3) = (x2 , y2)

slope = y2 - y1/x2 - x1

=3 - 1/-3 - 7

=2/-10

=1/-5

=[tex]-\frac{1}{5}[/tex]

Step-by-step explanation:

if you draw an imaginary perpendicular line across the figure from the vertex which joins the line of 2 cm with the line that is making an angle of X then you can see that this figure is made up of two figures that is a triangle and a rectangle.

now from the angle given i.e X.

perpendicular= 5 cm

base = 14 -2= 12 cm

hypotenuse= ?

we know that,

h² = p²+b²

= 5²+12²=169

h= √169

h= 13

again,

cos X = b/h

= 12/13

Answer:

(8,5):

8 is x-axis

5 is y-axis

Answer:

A: 42

Step-by-step explanation: 10.5x4=42

Answer:

your answer is A 42

Step-by-step explanation:

make me brainliest

Answer:

12

Step-by-step explanation:

Answer:

to do this lets first solve this so

5*5*5*5=625

5^-3=0.008

0.008^2=0.000064

0.000064*625=0.4

so all equations that are equal to 0.4 are right which is C

Answer:

See Explanation

Step-by-step explanation:

You posted an incomplete question with little and unclear details.

I will answer this question with a more complete version (see attachment)

Given that:

[tex]Scores: 100\ 95\ 88\ 62\ 76\ 90\ 100\ 58\ 72\ 60\ 85\ 90\ 70\ 72\ 54\ 100\ 60\ 80\ 75\ 51[/tex]

Required

The fraction that passed the test

Rearrange the score in ascending order:

[tex]Scores: 51\ 54\ 58\ 60\ 60\ 62\ 70\ 72\ 72\ 75\ 76\ 80\ 85\ 88\ 90\ 90\ 95\ 100\ 100\ 100[/tex]

The total number of students is:

[tex]n =20[/tex]

Extract the students that passed (scored 70 and above)

[tex]Passed: 70\ 72\ 72\ 75\ 76\ 80\ 85\ 88\ 90\ 90\ 95\ 100\ 100\ 100[/tex]

Their numbers are:

[tex]Passed: 14[/tex]

So, the fraction of those that passed is:

[tex]Fraction = \frac{Passed}{n}[/tex]

[tex]Fraction = \frac{14}{20}[/tex]

Reduce fraction

[tex]Fraction = \frac{7}{10}[/tex]

Answer:

1

Step-by-step explanation:

that's a very vague question

Answer:

3  7/15

Step-by-step explanation:

1 4/5 + 2 2/3 - 16/15

9/5 + 8/3 - 16/15

27/15 + 40/15 - 16/15

52/15 = 3  7/15

Answer:

3 2/5

Step-by-step explanation:

STEP 1: Convert all fractions into improper fractions

9/5 + 8/3 - 16/15

Step 2: pass denominators

(9x3 + 8x5 - 16) / 15

=51/15

Step it into proper mixed number

3 2/5

Answer:

8 - 42x - 56y - 12xy

Step-by-step explanation:

Length = 4 - 7(3x + 4y)

= 4 - 21x - 28y

Width = 3x(-2y)

= -6xy

Perimeter of the rectangle = 2(length + width)

= 2{(4 - 21x - 28y) + ( -6xy)}

= 2(4 - 21x - 28y - 6xy)

= 8 - 42x - 56y - 12xy

Perimeter of the rectangle = 8 - 42x - 56y - 12xy

Answer:

$225

Step-by-step explanation:

mark rate = 80%

original price = $125

mark amount = 80% of $125

=80/100 *125

=10000/100

=$100

final price = $125 + $100

=$225

The lower the frequency the least common the average.

There are two frequencies that are 1, which would be the least common.

The answer is C. 0.320-0.329 and 0.360 -0.369

Answer:

option C

Step-by-step explanation:

option c is contains the two batting averages which have a frequency of 1, this means that they both only occurred once which is the least amount of times any of the batting averages has occurred.

Answer:

see explanation

Step-by-step explanation:

If (x - 1) is a factor then f(1) = 0

Given

f(x) = x³ - 13x² + 32x - 20 , then

f(1) = 1³ - 13(1)² + 32(1) - 20

     = 1 - 13 + 32 - 20

     = 0

Since f(1) = 0 then (x - 1) is a factor

Using Synthetic division

 1  | 1  - 13   32   - 20

      ↓    1   - 12      20    

     -----------------------------

      1    - 12   20     0 ← remainder

quotient = x² - 12x + 20 = (x - 2)(x - 10)

Then

x³ - 13x² + 32x - 20 = (x - 1)(x - 2)(x - 10) ← in factored form

Answer: 52x+4

Step-by-step explanation: Do 16(2x-1)+4(5x+5) and get 52x+4.

Answer:

Options : B & D

Step-by-step explanation:

E(x) = 10x - 30 , where x is the number of doors she knocks

Given she has to pay her own expense.

So whatever she earns $30 is reduced from it ,for her expense.

Option A: She can earn $10 even if she does not knock

any doors - False

                 That is, x = 0

                 When x = 0 , E (x) = 10 ( 0 ) - 30 = - 30

                 => she loses $30.

Option B :Her expenses are $ 30 per week - True

                E(x) = 10x  - 30

                 Expenses are reduced from her earnings.

Option C: She will lose $10 per week if she does not knock

any doors - False.

                 Already checked on option A that if she does not knock

                 on any door, means x = 0 , then loses $30.

Option D : If she does not knock on any doors at all during

the week , she will lose $30 - True

Answer:

13[tex]\sqrt{22}[/tex] / 44

Step-by-step explanation:

cos A = 9/13

here adjacent = 9 and hypotenuse = 13  opposite = ?

using pythagoras theorem to find opposite

a^2 + b^2 = c^2

9^2 + b^2 = 13^2

81 + b^2 = 169

b^2 = 169 - 81

b^2 = 88

b = [tex]\sqrt{88}[/tex]

b =  [tex]2\sqrt{22}[/tex]

therefore opposite =  [tex]2\sqrt{22}[/tex]

cosec A = hypotenuse/opposite

= 13/[tex]2\sqrt{22}[/tex]

rationalizing the denominator

=13/ [tex]2\sqrt{22}[/tex]  *  [tex]2\sqrt{22}[/tex] /  [tex]2\sqrt{22}[/tex]

=13 *[tex]2\sqrt{22}[/tex] /( [tex]2\sqrt{22}[/tex] )^2

=26 [tex]\sqrt{22}[/tex] / 4*22

=26 [tex]\sqrt{22}[/tex] / 88

=13[tex]\sqrt{22}[/tex] / 44

Answer:

[tex]cosec A = \frac{13}{\sqrt{88}}[/tex]

   OR

[tex]cosec A = \frac{13 \sqrt{22}}{44}[/tex]

Step-by-step explanation:

Formulas used:

[tex]cos^2 A = 1 - sin^2 A\\\\cosec A = \frac{1}{sin A}[/tex]

Given :

  [tex]cos A = \frac{9}{13}[/tex]

Find cosec A

   [tex]sin ^2 A = 1 - cos^2 A[/tex]

              [tex]= 1 - (\frac{9}{13})^2\\\\= 1 - \frac{81}{169}\\\\=\frac{169 - 81}{169}\\\\=\frac{88}{169}[/tex]

 [tex]sin A = \sqrt{\frac{88}{169}} = \frac{\sqrt{88}}{13}[/tex]

Therefore,

         [tex]cosec A = \frac{1}{sin A} = \frac{1}{ \frac{\sqrt{88}}{13}} = \frac{13}{ \sqrt{88}}[/tex]

OR In a simplified form :

[tex]cosec A = \frac{13}{\sqrt{88}} \times \frac{\sqrt{88}}{\sqrt{88}} = \frac {13 \times \sqrt{4 \times 22}}{88} = \frac{13 \times 2 \sqrt{22}} {88} = \frac{13 \sqrt{22}}{44}[/tex]        

Answer:

The amount paid as VAT is $ 12800.

Step-by-step explanation:

Sales = $ 80,000

VAT = 16 %

The amount of VAT paid to the government is

= 16 % of $ 80,000

= 0.16 x $ 80,000

= $ 12800

The amount paid as VAT is $ 12800.

Answer:

600.4 cm^2

Step-by-step explanation:

first we should find the base of samller triangle

hypotenuse = 35 cm

one side = 30 cm  whereas other has be be find

using pythagoras theorem

a^2 + b^2 = c^2

30^2 + b^2 = 35^2

900 + b^2 = 1225

b^2 = 1225 - 900

b^2 = 325

b = [tex]\sqrt{325}[/tex]

b = [tex]5\sqrt{13}[/tex]

area of big triangle

base = 22 + [tex]5\sqrt{13}[/tex]

area of a triangle = base * height / 2

= 30 (22 + [tex]5\sqrt{13}[/tex] ) /2

=30*22 + 30*[tex]5\sqrt{13}[/tex] / 2

=660 + 540.83 / 2

=1200.83 / 2

=600.415

=600.4 cm^2

9514 1404 393

Answer:

  330 cm²

Step-by-step explanation:

The formula for the area of a triangle is ...

  A = 1/2bh

where b is the base length and h is the height measured perpendicular to the base.

Here, the base length is 22 cm, and the height is 30 cm. The area is ...

  A = 1/2(22 cm)(30 cm) = 330 cm²

__

Additional comment

As is often the case with "overspecified" geometrical figures, the given dimensions are inconsistent. If the side lengths are taken as true, the height is closer to 33.1 cm, and the area is about 364.1 cm².

We assume the intended solution method is the one used above, as all it requires is to make use of a simple formula, and the calculation can be done mentally.

Answer:

v = 27,000 mm³

Step-by-step explanation:

v = s³

v = 30³

v = 27,000 mm³

Answer:

57

Step-by-step explanation:

5|x^³-2|+7

let x=-2

5|(-2)^3-2|+7

work inside the absolute value first

5|-8-2|+7

5|-10|+7

Take the absolute value, which make it positive

5 *10+7

multiply

50+7

=57

nakita ko lng po yan but hope that helpsツ