AB = 20 cm, m∠A = 30°, and m∠C = 45°. Express the number of centimeters in the length of BC in simplest radical form.

Pull out a common factor of 10⁷:

10⁹ + 10⁸ + 10⁷ = 10⁷ (10² + 10¹ + 10⁰)

… = 10⁷ × 111

Factorize 10 as 2 × 5, then distribute the power of 7:

… = 2⁷ × 5⁷ × 111

Pull out a factor of 5 and multiply it with 111:

… = 2⁷ × 5⁶ × 5 × 111

… = 2⁷ × 5⁶ × 555

So 555 divides 10⁹ + 10⁸ + 10⁷.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\dfrac{(9 \times5) 2}{3}}[/tex]

[tex]\huge\boxed{9 \times 5 = \bf 45}[/tex]

[tex]\huge\boxed{ = \dfrac{45(2)}{3}}[/tex]

[tex]\huge\boxed{45(2) = \bf 90}[/tex]

[tex]\huge\boxed{= \dfrac{90}{3}} \\\\\huge\boxed{= \dfrac{90\div3}{3\div3}}\\\\\huge\boxed{= \dfrac{30}{1}}[/tex]

[tex]\huge\boxed{= \bf 30}[/tex]

[tex]\huge\boxed{\rm{Answer: 30}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

30

Step-by-step explanation:

Multiply 9 and 5 to get 45.

Multiply 45 and 2 to get 90.

Divide 90 by 3 to get 30.

Answer: B) [tex]f\left(x\right)=\frac{1}{3}\left(-x-1\right)^{5}[/tex]

Step-by-step explanation:

When graphing x5 the parent function and plugging in the equation for B the only equation that fits the criteria of

*shifting left 1 unit

*vertically compressed by 1/3

*reflect over the y-axis

So the answer is B

The function after the transformation is f ( x ) = ( 1/3 ) ( -x + 1 )⁵

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x⁵

On reflecting over the y axis , we get

f ( x ) = ( -x )⁵

On vertically compressing by a factor of ( 1/3 ) , we get

f ( x ) = ( 1/3 ) ( -x )⁵

And , shifting 1 unit to the left , we get

f ( x ) = ( 1/3 ) ( -x + 1 )⁵

Hence , the transformed function is f ( x ) = ( 1/3 ) ( -x + 1 )⁵

To learn more about transformation of functions click :

https://brainly.com/question/26896273

#SPJ7

Hello,

we are going to use the theorem of the bissectrice. (if this word is good in english)

[tex]\dfrac{KL}{LM} =\dfrac{KN}{NM} \\\\\dfrac{8}{x} =\dfrac{14}{20-x} \\\\8(20-x)=14x\\\\160-8x=14x\\\\22x=160\\\\x=\frac{160}{22} \\\\x=\frac{80}{11} \\\\\\x=7.\overline{27}[/tex]

Answer:

no  c

Step-by-step explanation:

Answer:

44m

Step-by-step explanation:

add all 4 sides of the rectangle then multiply by 2 since each square is 2m.

Answer:

A 2

B 1

C 4

D 3

Step-by-step explanation:

( ) means not including (also used for infinity)

[ ] means including

The answer choices are in interval form, showing all the possible answer choices between two numbers and if the answer choice includes or excludes a number using the () []

Explanation for A:

x < 7.8 means x won't include 7.8 since the symbol is "less than" and not "less than or equal to".

x can be anything, it just has to be less than 7.8, so the answer is:

2 (-infinity, 7.8)

Explanation for B:

x <= 7.8 means x will include 7.8 since the symbol means "less than or equal to".

x can be anything, it just has to be less than or equal to 7.8, so the answer is:

1 (-infinity, 7.8]

Explanation for C:

x >= 7.8 means x will include 7.8 since the symbol means "greater than or equal to".

x can be anything, it just has to be greater than or equal to 7.8, so the answer is:

4 [7.8, infinity)

Explanation for D:

x > 7.8 means x won't include 7.8 since the symbol means "greater than" and not "greater than or equal to".

x can be anything, it just has to be greater than 7.8, so the answer is:

3 (7.8, infinity)

Hope it helps (●'◡'●)

Answer:

A:2 B:1 C:4 D:3

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

126+x=180

x=180-126=54

x=54

Answer:

1/ x = 22.5°

2/ x = 60°

Step-by-step explanation:

1/ We have: 3x + 2x + 3x = 180°

=> 8x = 180° => x = 22.5°

2/ We have: x + x + x = 3x = 180°

=> x = 60°

Answer:

1) x = 22.5

2) x = 60

Step-by-step explanation:

→ Add the angles together

1) 3x + 2x + 3x = 8x

2) x + x + x = 3x

→ Make it equal to 180

1) 8x = 180

2) 3x = 180

→ Divide both sides by 8 and 3

1) x = 22.5

2) x = 60

Answer:

6x 2 = 12

Step-by-step explanation:

Answer:

24

EXPLANATION:

there's 4 different outcomes for the Penny and Quarter combos

- P Heads and Q Heads

- P Tails and Q Heads

- P Heads and Q Tails

- P Tails and Q Tails

Each of those outcomes will have one of six numbers so I just figured

6 outcomes for number cube × 4 outcomes for P and Q (penny and quarter)

6 × 4 = 24

:)

Answer:

50 a^2 b c^2

Step-by-step explanation:

I'm quite confused about your question, but I try my best. I have attached the explanation above. Hopefully this will help

Answer:

points srru

Step-by-step explanation:

Answer:

Step-by-step explanation:

PQ=√((x-5)²+(-2-2)²)=√((x-5)²+16)=5

squaring

(x-5)²+16=25

(x-5)²=25-16=9

x-5=±3

x=-3+5,3+5

or x=2,8

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Answer:

A)2

Step-by-step explanation:

we would like to integrate the following definite Integral:

[tex] \displaystyle \int_{0} ^{1} 5x \sqrt{x} dx[/tex]

use constant integration rule which yields:

[tex] \displaystyle 5\int_{0} ^{1} x \sqrt{x} dx[/tex]

notice that we can rewrite √x using Law of exponent therefore we obtain:

[tex] \displaystyle 5\int_{0} ^{1} x \cdot {x}^{1/2} dx[/tex]

once again use law of exponent which yields:

[tex] \displaystyle 5\int_{0} ^{1} {x}^{ \frac{3}{2} } dx[/tex]

use exponent integration rule which yields;

[tex] \displaystyle 5 \left( \frac{{x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1} \right) \bigg| _{0} ^{1} [/tex]

simplify which yields:

[tex] \displaystyle 2 {x}^{2} \sqrt{x} \bigg| _{0} ^{1} [/tex]

recall fundamental theorem:

[tex] \displaystyle 2 ( {1}^{2}) (\sqrt{1} ) - 2( {0}^{2} )( \sqrt{0)} [/tex]

simplify:

[tex] \displaystyle 2 [/tex]

hence

our answer is A

9514 1404 393

Answer:

  (x, y) = (1.4, -3.6)

Step-by-step explanation:

4. We choose to substitute into the second equation because it has positive coefficients.

  7(1.4) +2.5y = 0.8

  9.8 +2.5y = 0.8 . . . . simplify

  2.5y = -9.0 . . . . . . . subtract 9.8

  y = -3.6 . . . . . . . . . . divide by 2.5

The solution to the system is (x, y) = (1.4, -3.6)

Answer:

1.75 × 10⁶

Step-by-step explanation:

7,000,000 ÷ 4 = 1750000

Which is 1.75 × 10⁶ in standard form

Answer:

C

Step-by-step explanation:

Answer:

94 cm^2

Hope it helps!

Answer:

The ball will reach the same height of 10 meters after 100 meters.

Part A)

100 meters.

Part B)

10 meters.

Step-by-step explanation:

The golf-ball hit by the Seven-Iron is modeled by the equation:

[tex]h=-0.002d^2+0.3d[/tex]

And the ball hit by the Nine-Iron is modeled by the equation:

[tex]h=-0.004d^2+0.5d[/tex]

Where h is the height of the ball after d meters.

When they are at the same height, the two equations will equal each other.

Graphically, this is where the two graphs will intersect.

To solve this using a Ti-84, you can follow these steps (I'm using the Ti-84 Plus Silver Edition):

1) Using [Y=], write and then [GRAPH] the two equations.

2) Press [ZOOM] and [ZOOM OUT] until you can see both graphs clearly.

3) To find the intersection point, press [2ND] and then [CALC] (above [TRACE]).

4) Choose [5) Intersect].

5) Using the arrow keys, click on one graph to choose it as your first curve and the other to choose it as your second curve. (In this case, it doesn't matter which one is which.)

6) When it asks you to guess, put the cursor to as close to the intersection point as possible. Ignore the intersection at the origin point.

7) Press [ENTER], and it should give you your solution.

Therefore, the intersection point (not counting (0,0)) is at (100, 10).

Therefore, the ball will reach the same height of 10 meters after 100 meters.

OPTION C

The graph is continuous because there can be fractional values for time

Answer:

(C) The graph is continuous because there can be fractional values for time.

Step-by-step explanation:

There can't be a negative altitude because when it reaches the ground, it has a altitude of zero and can't go further down. However, it's not B because a discrete graph would also mean there would be set times (represented by points on the graph) of the hot air balloon moving. This isn't true, because the hot air ballon moves as time continues, even fractional time values.

So it's C, "The graph is continuous because there can be fractinoal values for time".

Hope it helps (●'◡'●)

Answer:

78.5÷3.14=25

56.272×41.2=2318.4064

429×338×712=103241424

447÷513=0.8713450292

Step-by-step explanation:

hope it will help!

Answer:

x = –1

Step-by-step explanation:

From the question given above, the following data were obtained:

y = √(–2x + 7)

y = 3

x =?

The value of x can be obtained as follow:

y = √(–2x + 7)

3 = √(–2x + 7)

Take the square of both side

3² = –2x + 7

9 = –2x + 7

Collect like terms

9 – 7 = –2x

2 = –2x

Divide both side by –2

x = 2 / –2

x = –1

Answer:

- 0.1

Step-by-step explanation:

Step-by-step explanation:

you need to find the lenght and breadth of the rectangle

Answer:

313 ft

Step-by-step explanation:

It's hard to explain because its geometry, but there will be a right triangle with angle of 72 and another with angle of 25. do tan72 * 120 - tan25 * 120

The distance from point A to point B is given by the trigonometric relations and d = 313 feet

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the first triangle be represented as ΔAOD

Let the second triangle be represented as ΔBOD

where the distance from point A to point B = d

And , Riley is watching from a vertical distance of 120 feet above the water

Riley measures an angle of depression to the boat at point A to be 18 degrees

Riley takes another measurement and finds the angle of depression to the boat (now at point B) to be 65 degrees

So , ∠BOD = 25° and ∠AOD = 72°

From the trigonometric relations ,

tan θ = opposite / adjacent

tan AOD = AD / OD = tan 72°

tan 72° = 3.087

tan BOD = tan 25° = 0.47

Now , the measure of AD = 120 x 3.087 = 369.6 feet

And , the measure of BD = 120 x 0.74 = 56.4 feet

Therefore , the distance from A to B = 369.6 feet - 56.4 feet

d = 313 feet

Hence , the distance is 313 feet

To learn more about trigonometric relations click :

https://brainly.com/question/14746686

#SPJ2

Answer: She can either arrange them in 7 columns or 6 columns.

Step-by-step explanation:

We are given:

Total number of pots = 42

In order to arrange the pots in the same number of columns so that each column has an equal number of pots, we will find out the factors of 42.

42 = 6 × 7

42 = 1 × 42

Garima can arrange 6 pots in 7 columns or 7 pots in 6 columns so as to have equal number of pots.

Hence, she can either arrange them in 7 columns or 6 columns.