Given ADC ACB and BDC BCA prove a squared + b squared = c squared. Use the two Column proof.

Answer:

[tex] \mathsf{ {5x}^{2} + 28x + 21}[/tex]

Option A is the right option.

Step-by-step explanation:

Let's find the area of large rectangle:

[tex] \mathsf{(3x + 6)(2x + 4)}[/tex]

Multiply each term in the first parentheses by each term in the second parentheses

[tex] \mathsf{ = 3x(2x + 4) + 6(2x + 4)}[/tex]

Calculate the product

[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 6 \times 4}[/tex]

Multiply the numbers

[tex] \mathsf{ = 6 {x}^{2} + 12x + 12x + 24}[/tex]

Collect like terms

[tex] \mathsf{ = {6x}^{2} + 24x + 24}[/tex]

Let's find the area of small rectangle

[tex] \mathsf{(x - 3)(x - 1)}[/tex]

Multiply each term in the first parentheses by each term in the second parentheses

[tex] \mathsf{ = x( x - 1) - 3(x - 1)}[/tex]

Calculate the product

[tex] \mathsf{ = {x}^{2} - x - 3x - 3 \times ( - 1)}[/tex]

Multiply the numbers

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

Collect like terms

[tex] \mathsf{ = {x}^{2} - 4x + 3}[/tex]

Now, let's find the area of shaded region:

Area of large rectangle - Area of smaller rectangle

[tex] \mathsf{6 {x}^{2} + 24x + 24 - ( {x}^{2} - 4x + 3)}[/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \mathsf{ = {6x}^{2} + 24x + 24 - {x}^{2} + 4x - 3}[/tex]

Collect like terms

[tex] \mathsf{ = {5x}^{2} + 28x + 21}[/tex]

Hope I helped!

Best regards!

Answer:

3

Step-by-step explanation:

We are adding 2 each time

-3 +2 = -1

-1 +2 = 1

To get the next term add 2

1 +2 = 3

Answer: 3

Step-by-step explanation:

Answer:

Check the answer below.

Step-by-step explanation:

This is a very trivial but professional question. Note that all of millimetre, centimetre and metres are acceptable metric units but the millimetre is more preferable by builders and architects because:

1. It is easier to work with integer values on building and architectural plans, an advantage given by measuring and recording in millimetre.

2. working in millimetre allows for precision. The builder will record values that are very close to the true value

3. The measurement will be easily readable by anybody that sees it.

Answer:

w²-30w+210=0

Step-by-step explanation:

2w + 2l = 60 , w + l = 30, l = 30 - w

wl = 210

w(30-w) -210 = 0

30w - w²-210 = 0

w²-30w+210=0

Answer:

b. Contains four right angles.

Step-by-step explanation:

A parallelogram has two pairs of opposite sides that are both congruent and parallel, as does a rectangle.

A parallelogram usually does NOT have four right angles, but a rectangle does. b Contains four right angles is the difference between a parallelogram and a rectangle.

The diagonals of a parallelogram bisect each other, and so do the rectangle's diagonals.

The opposite angles of parallelograms are congruent, and all four angles of a rectangle are congruent, so this is a similar aspect of both a parallelogram and a rectangle.

Hope this helps!

Answer:

11√6

Step-by-step explanation:

5√6 +6√6 will equal to 11√6, because since √6 is the same, you just add the number on the outside

Answer:

Yes, because each x-value corresponds to one y value.

Step-by-step explanation:

If you look at the table, you notice that there is one output (y) for every input (x). This means that it is a function. It would NOT be a function if you had two outputs for an input. For example, there are two x values that are 6. For one coordinate pair, the table says (6,9) and (6,8). Since there are two values for the same input- it wouldn't be a function. In this case, there is an input of 4 and 5 with the same output. That is okay! Even though they have the same y value, those inputs still only have ONE output.

Answer:

$4

Step-by-step explanation:

2 Bracelets + 3 rings = $26

2 rings = $12

3 rings = x

To get the cost of 1 ring you divide 12 by 2 and the answer you get is 6.

The total cost of the 3 rings is $18( $6*3)

Then you subtract the cost of both 2 bracelets and 3 rings($26) from the cost of 3 rings($18). The answer is $8. ( THIS IS THE COST OF 2 BRACELETS)

1 BRACELET= $4( $8/2)

Answer:

-4.81647993062

Step-by-step explanation:

Look at the image below ↓

Based on the mathematical analysis, the value of log 0.5^16 is -4.816.

A logarithm is a mathematical term that is used to describe the exponent or power to which a base must be raised to yield a given number.

In this case, to calculate the value of log0.5^16 use logarithm properties.

rewrite the expression as log(0.5)^(16).

=> log(a^b) = b * log(a)

=> 16 * log(0.5).

Given that the Logarithm is the inverse of exponentiation => log(0.5) is equal to -0.301.

Substitute this value back into the expression:

16 * (-0.301) = -4.816.

Hence, in this case, it is concluded that the correct answer to the value of log 0.5^16 is -4.816.

Learn more about Logarithms here: https://brainly.com/question/30226560

#SPJ6

Answer:

3/2

Step-by-step explanation:

Perpendicular lines have slopes that multiply to -1

m * -2/3  =-1

Multiply by -3/2 to isolate m

m * -2/3 * -3/2 = -1 * -3/2

m = 3/2

The perpendicular line has a slope of 3/2

In the language of modular arithmetic, we're given

[tex]x-3\equiv0\pmod7\implies x\equiv3\pmod7[/tex]

[tex]y+3\equiv0\pmod7\implies y\equiv-3\equiv4\pmod7[/tex]

Then x = 7a + 3 and y = 7b + 4 for integers a and b.

Substitute these into the quadratic expression and simplify:

[tex]x^2+xy+y^2+n\equiv0\pmod7[/tex]

[tex](7a+3)^2+(7a+3)(7b+4)+(7b+4)^2+n\equiv0\pmod7[/tex]

[tex]49a^2+42a+9+49ab+28a+21b+12+49b^2+56b+16+n \equiv 0\pmod7[/tex]

[tex]37+n\equiv 0\pmod7[/tex]

[tex]n\equiv-2\equiv5\pmod7[/tex]

which means the smallest positive integer n we are looking for is 5.

Answer: C

Step-by-step explanation:

The open dot means its not equal to X and the placement is -14.5

Answer:

[tex]a^2+3\,a\,b-5\,a\,b-15\,b^2=(a-5\,b)\,(a+3\,b)[/tex]

Step-by-step explanation:

Work via factoring by groups:

!) re arrange the terms as follows:

[tex]a^2-5ab+3ab-15b^2[/tex]

then extract the common factor for the first two terms (a), and separately the common factors for the last two terms (3 b):

[tex]a^2-5ab+3ab-15b^2\\a\,(a-5\,b)+3\,b\,(a-5\,b)[/tex]

Now notice that the binomial factor (a-5 b) is in both expressions, so extract it:

[tex]a\,(a-5\,b)+3\,b\,(a-5\,b)\\(a-5\,b)\,(a+3\,b)[/tex]

which is the final factorization.

Answer:

[tex] \boxed{\sf (a + 3b)(a - 5b)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf Grouping \: like \: terms, \\ \sf {a}^{2} + 3ab - 5ab - 15 {b}^{2} = {a}^{2} + (3ab - 5ab) - 15 {b}^{2} : \\ \sf \implies {a}^{2} + (3ab - 5ab) - 15 {b}^{2} \\ \\ \sf 3ab - 5ab = - 2ab : \\ \sf \implies {a}^{2} - 2ab - 15 {b}^{2} \\ \\ \sf The \: factors \: of \: - 15 \: that \: sum \: to \: - 2 \: are \: 3 \: and \: - 5. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 - 5)ab - 15 {b}^{2} \\ \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf \implies a(a + 3b) - 5b(a + 3b) \\ \\ \sf \implies (a + 3b)(a - 5b)[/tex]

Answer:

Step-by-step explanation:

It depends on how it is written. By definition

[tex]\csc(x) = (\sin(x))^{-1} = \frac{1}{\sin(x)}[/tex]

[tex]\sec(x) = (\cos(x))^{-1} = \frac{1}{\cos(x)}[/tex]

[tex]\cot(x) = (\tan(x))^{-1} = \frac{1}{\tan(x)}[/tex]

however the functions

[tex]\sin^{-1}(x), \cos^{-1}(x), \tan^{-1}(x)[/tex] are the inverse functions of sine, cosine and tangent respectively. So, they are not equivalent functions

Answer:

Length = 8x - 3.2

Step-by-step explanation:

Perimeter = 4(Length)   [Since it's a square so all the sides are equal]

Given that Perimeter = 32x - 12.8

32x - 12.8 = 4(Length)

Dividing both sides by 4

=> Length = [tex]\frac{4(8x-3.2)}{4}[/tex]

=> Length = 8x - 3.2

Now, Three equivalent expressions to find the perimeter

=> Perimeter = 32x - 12.8

=> Perimeter = 4(8x - 3.2)   [Perimeter = 4 (Length)]

=> Perimeter = 2(16x - 6.4)

Answer:

[tex]\boxed{8x-3.2}[/tex]

Step-by-step explanation:

The perimeter is 32x - 12.8 of a square.

Use formula for perimeter of a square.

[tex]P=4a[/tex]

[tex]P=perimeter\\a=side \: length[/tex]

[tex]32x - 12.8=4a[/tex]

Solve for side length.

[tex]\frac{32x - 12.8}{4} =a[/tex]

[tex]8x-3.2=a[/tex]

Three equivalent expressions for perimeter:

32x - 12.8

⇒ 8(4x - 1.6)

⇒ 4(8x - 3.2)

⇒ 2(16x - 6.4)

Answer:

it is c because i took test review

Step-by-step explanation:

Answer:

C The solution should be 6, and the cyclists will need to ride 6 laps before the sprint to the finish.

Answer:

divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer

2

Step-by-step explanation

The radius of the large sphere is double the radius of the small sphere

Answer:

3

1/5

3/4

3/4

Step-by-step explanation:

Coefficient is a number that is always written in front of a term.

3xy^3=3

xy/5=1/5

3/4xy=3/4

3/4x^2y=3/4

Hope this helps ;) ❤❤❤

Answer: 6 animals should go in each pen.

Step-by-step explanation:

Total sheep = 54

Total cows = 24

Total pigs = 30

Highest number of animals are possible in each pen such that animals are distributed in pens with the same number = Greatest common divisior (54,24, 30)

54= 6 x 9

24= 6 x 4

30 = 6 x 5

So, Greatest common divisior (54,24, 30) = 6

Hence, 6 animals should go in each pen.

Answer:

arc KL=minor arc

arc LJK=major arc

Step-by-step explanation:

so minor arc is a arc which is larger than a semicircle .

a major arc is a circle having measure less than radians.

Answer:

A. Volume = 462 cm³; Surface Area = 458 cm²

B. Volume

C. Surface area

Step-by-step explanation:

A. Given a rectangular box:

[tex] Width (w) = 3 cm [/tex]

[tex] Height (h) = 14 cm [/tex]

[tex] length (l) = 11 cm [/tex]

=>Volume of the juice box

[tex] Volume (V) = whl [/tex]

[tex] Volume (V) = 3*14*11 [/tex]

[tex] = 3*14*11 = 462 [/tex]

Volume of juice box = 462 cm³

=>Surface area (S.A) of juice box:

[tex] S.A = 2(wl + hl + hw) [/tex]

[tex] S.A = 2(3*11 + 14*11 + 14*3) [/tex]

[tex] S.A = 2(33 + 154 + 42) [/tex]

[tex] S.A = 2(229) [/tex]

[tex] S.A = 458 cm^2 [/tex]

Surface area of juice box = 458 cm²

B. Volume would be used to find the amount of juice the box can hold

C. Surface area would be used to know how much wax to buy to use in coating the box.

Answer:

927.0 cm²

Step-by-step explanation:

Step 1: find Z

m < Z = 180 - (28 + 118) (sum of ∆)

= 180 - 146

Z = 34°

Step 2: Find side XY using the law of sines

[tex] \frac{XY}{sin(34)} = \frac{42}{sin(28)} [/tex]

Cross multiply

[tex] XY*sin(28) = 42*sin(34) [/tex]

[tex]XY*0.469 = 42*0.559[/tex]

Divide both sides by 0.469

[tex]\frac{XY*0.469}{0.469} = \frac{42*0.559}{0.469}[/tex]

[tex]XY = 50.06[/tex]

XY ≈ 50 cm

Step 3: find the area.

Area of ∆ = ½*XY*YZ*sin(Y)

XY ≈ 50 cm

= ½*50*42*sin(118)

= 25*42*0.8829

Area = 927.045

Area ≈ 927.0 cm² (nearest tenth)

Answer:

[tex]\dfrac{10}{4} \ hour[/tex]

Step-by-step explanation:

Given that :

Jack had 4 hours of school.

He spent 45 minutes in the library

1/2 hour on a science lecture  and;

had a lunch break of 25 minutes

The objective is to determine how much time is left for the school to get over and we are to write the answer as a fraction.

In order to do that, we will have to convert the minutes into hours,

we all know that; 60 minutes = 1 hour.

Then,

45 minutes = (45/60)hour = 3/4 hour

25/60 minutes = 1/4 hour

Therefore, the amount of time left  for the school to get over is:

= [tex]4 - (\dfrac{3}{4}+\dfrac{1}{2}+ \dfrac{1}{4})[/tex]

=  [tex]\dfrac{16-(3+2+1)}{4}[/tex]

= [tex]\dfrac{16-6}{4}[/tex]

= [tex]\dfrac{10}{4} \ hour[/tex]

Answer:

1

Step-by-step explanation:

1 to the tenth power is also 1 multiplied by 1 10 times.

1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 = 1

1 to any power will always have the answer of 1.

Answer:

56

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{35+20}{20}[/tex] = [tex]\frac{32+?}{32}[/tex] ( cross- multiply )

20(32 + ?) = 1760 ( divide both sides by 20 )

32 + ? = 88 ( subtract 32 from both sides )

? = 56

Answer:

[tex]\boxed{56}[/tex]

Step-by-step explanation:

We can use ratios to solve since the triangles are similar.

[tex]\frac{20}{32} =\frac{35}{x}[/tex]

Cross multiplication.

[tex]20x=35 \times 32[/tex]

Divide both sides by 20.

[tex]\frac{20x}{20} = \frac{35 \times 32}{20}[/tex]

[tex]x=56[/tex]

Answer:

Hey there!

The solution is where the lines intersect, and here we see that would be (-4,3)

Hope this helps :)

Answer: 22

Step-by-step explanation:

She sold two tubs of Oatmeal Raisins and it's 6 dollars a tub so we can do 6*2 or 6+6 (doesn't matter). We get $12. Then, she also sells 2 tubs of Peanut Butter, and since it's $5 a tub, then we do 5*2 or 5+5 to get 10. We add 12 and 10 (12+10) and get 22.

I'm not sure if this is right because you added $22, $24, $20, and $11 and I'm not sure what the purposes of those are.

Answer:

34 adults and 11 children

Step-by-step explanation:

15 times 11 is 165dollars for kids

25 times 34 adults equals 850 dollars

add it and its 1015

Answer:

34 and 11

Step-by-step explanation: