Solve for x:2/7(x − 2) = 4x

Answer:

20°

Step-by-step explanation:

The sum of angles in a ∆ = 180°

Therefore, [tex] (17x - 1) + (3x - 4) + 25 = 180 [/tex]

Use this expression to find the value of x, then find the measure of angle A.

[tex] 17x - 1 + 3x - 4 + 25 = 180 [/tex]

[tex] 17x + 3x - 1 - 4 + 25 = 180 [/tex]

[tex] 20x + 20 = 180 [/tex]

Subtract 20 from both sides

[tex] 20x + 20 - 20 = 180 - 20 [/tex]

[tex] 20x = 160 [/tex]

Divide both sides by 20

[tex] \frac{20x} = \frac{160}{20} [/tex]

[tex] x = 8 [/tex]

Find measure of angle A.

Angle A is given as [tex] 3x - 4 [/tex]

Plug in the value of x and solve

[tex] A = 3(8) - 4 = 24 - 4 = 20 [/tex]

Answer:

(x - 3)(x - 2)(x + 2)

Step-by-step explanation:

Given

x³ - 3x² - 4x + 12 ( factor the first/second and third/fourth terms )

= x²(x - 3) - 4(x - 3) ← factor out (x - 3) from each term

= (x - 3)(x² - 4) ← x² - 4 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 4

= x² - 2²

= (x - 2)(x + 2)

Thus

x³ - 3x² - 4x + 12 = (x - 3)(x - 2)(x + 2) ← in factored form

Answer:

(x - 2)(x - 3)(x + 2).

Step-by-step explanation:

The Factor Theorem states that if x - a is a factor of f(x) the f(a) = 0.

f(x) = x^3 - 3x^2 - 4x + 12​

We try the factors of 12:

f(2) =  2^3 - 3*4 - 8 +12

= 8 - 12 - 8 + 12  = 0

- so (x - 2) is a factor of f(x)

Dividing:

        x^2  -  x -  6            <-----------Quotient

       -----------------------------

x - 2 )x^3 - 3x^2 - 4x + 12​

        x^3 - 2x^2

                  -x^2 - 4x

                  -x^2 + 2x

                          -6x + 12

                          -6x + 12

So we factor x^2 - x - 6:

= (x - 3)(x + 2)

Answer:

[tex]\Huge \boxed{\mathrm{3.91 \ cm}}[/tex]

Step-by-step explanation:

The triangle BDE is a right triangle.

Line segment DE = 2.5 cm

Line segment BE = 3 cm

We can apply Pythagorean theorem to solve for the diameter of the pipe or the hypotenuse of the right triangle BDE.

[tex]c=\sqrt{2.5^2 +3^2 }[/tex]

[tex]c=\sqrt{15.25} = 3.90512483795...[/tex]

We can round up the length to nearest hundredth.

[tex]3.90512483795 \approx 3.91[/tex]

The diameter of the pipe is 3.91 cm.

The smallest diameter of pipe that will fit the fiber optic line is 3.91 cm if the company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 2.5 cm and segment BE = 3 cm option (B) is correct.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

We have:

A company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 2.5 cm and segment BE = 3 cm.

As we know, the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides is known as the Pythagoras theorem.

Applying Pythagoras theorem in the triangle DEB:

DE² + BE² = DB²

2.5² + 3² = DB²

DB² = 6.25 + 9

DB² = 15.25

DB = 3.905 ≈ 3.91 cm

Thus, the smallest diameter of pipe that will fit the fiber optic line is 3.91 cm if the company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 2.5 cm and segment BE = 3 cm option (B) is correct.

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ5

Answer:

width = 8 inches

length = 10 inches

Step-by-step explanation:

width= 12/1.5

= 8

length = 15/1.5

= 10

Answer:

C. 4x = 12

Step-by-step explanation:

You and three friends= you + 3 friends=4 people

Pizza= 12 pieces

Each person eats equal pieces of pizza

x= number of pieces each person ate

Equation

4x=12

Divide both sides by 4

x=12/4

=3

x=3

Therefore, each person ate 3 pieces of pizza each

Check:

4x=12

4(3)=12

12=12

Answer:

SinB = 1/2, SinC = √3/2 and

TanC = √3

Step-by-step explanation:

The question lacks options. Find the complete question in the comment section.

Given triangle ABC, we will use the SOH, CAH, TOA trig identity to get the correct ratio.

Given the hypotenuse BC = 18 and one of the other two sides AC = 9, we can get the third side AB using Pythagoras theorem.

BC² = AC²+AB²

18² = 9²+AB²

2² = 1²+AB²

AB² = 4-1

AB² = 3.

AB = √3

Making <ABC as reference angle, AC will be opposite and AB will be the adjacent.

Sin<ABC = opp/hyp = AC/BC

Sin<ABC = 1/2

Cos<ABC = adj/hyp = AB/BC

Cos<ABC = √3/2

Tan<ABC = opp/adj = AC/AB

Tan<ABC = 1/√3

Making <BCA as reference angle, AB will be opposite and AC will be the adjacent.

Sin<BCA = opp/hyp = AB/BC

Sin<BCA = √3/2

Cos<BCA = adj/hyp = AC/BC

Cos<BCA = 1/2

Tan<BCA = opp/adj = AC/AB

Tan<BCA = √3

Frim the above calculation, the correct options are sin<ABC = 1/2, Sin<BCA = √3/2 and Tan<BCA = √3

Answer:

C.

Step-by-step explanation:

Will end up being 0 since it is the final number in the equation and goes along with PEMDAS sequence.

Answer:

the answer is 567

Step-by-step explanation:

20+30(11)+5+2(106)

20+330+5+212

= 567

Answer:

-48

Step-by-step explanation:

Plug x and y in to the expression,

-4(5) + (7)(-4) = -20 - 28 = -48

Answer:

=-4xy+8yx-8yx

=-4xy

Step-by-step explanation:

+×-=-

Answer:

1. [tex] \{ \bold{ \sf{Expenditure \: on \: food = \:1200 dollars\: }}[/tex]

2. [tex] \sf{a \: : \: c \: = 18 \: : \: 5}[/tex]

Step-by-step explanation:

1. [tex] \sf{here \: total \: expenditure = 3000 \: dollars}[/tex]

[tex] \sf{expenditure \: on \: food \: = \: \frac{3000}{360} \times 144}[/tex]

[tex] \sf{expenditure \: on \: food{ = 1200 \: dollars}}[/tex]

Note : Whole circle represents the total expenditure.

i.e 360° represents $ 3000

1° represents $ [tex] \sf{ \frac{3000}{360} }[/tex]

144 ° represents $ [tex] \sf{ \frac{3000}{360} \times 144}[/tex]

-------------------------------------------------------------

2. [tex] \sf{here \: a:b \: = 6:5 \: = \: \frac{6}{5} }[/tex]

[tex] \sf{b : \: c \ \: = 18 \: : \: 6} \: = \: \frac{18}{6} [/tex]

[tex] \sf{now \: a:b \times b:c = \frac{a}{b} \times \frac{b}{c} = \frac{a}{c} }[/tex]

⇒[tex] \sf{a:c = \frac{6}{5} \times \frac{18}{6} }[/tex]

⇒[tex] \sf{a:c = \frac{18}{5} }[/tex]

⇒[tex] \sf{a:c = 18:5}[/tex]

Hope I helped!

Best regards!!

Answer: Choice A)

Approximately 0.4 units or about 24 miles approximately

=========================================================

Explanation:

B = Santa Barbara's location

C = Santa Cruz Island's location

Point B is located at (34.4, 119.714)

Point C is located at (34, 119.726)

Use the distance formula to find the distance from B to C

[tex]d = \sqrt{ (x_1-x_2)^2 + (y_1-y_2)^2}\\\\d = \sqrt{ (34.4-34)^2 + (119.714-119.726)^2}\\\\d = \sqrt{0.160144 }\\\\d \approx 0.40017995951821\\\\d \approx 0.4\\\\[/tex]

Unfortunately, there isn't enough info to be able to go from 0.4 units to roughly 24 miles, so I don't know how your teacher is doing that step. But luckily, only choice A mentions 0.4, so this has to be the answer.

Answer:

660 exchanges

Step-by-step explanation:

Number of relatives = 12

Number of years = 5

Since each relative gives gift to one another each year:

Then each relative hands out 11 gifts (person giving out the gift will not be counted) to the others, and others also do the same.

Therefore, yearly exchange :

(Number of relatives * number of gifts given out per person)

(12 × 11) = 132

Number of exchanges after 5 years :

(Number of yearly exchanges × number of years)

(132 × 5) = 660

Answer:

  21040

Step-by-step explanation:

As with base-10 addition, when the sum is equal to the base or more, a "carry" is generated into the next place value column. Useful equivalents here are ...

  5₁₀ = 10₅

  6₁₀ = 11₅

  7₁₀ = 12₅

  9₁₀ = 14₅

  10₁₀ = 20₅

The addition is shown in the attachment. The sum is 21040₅.

_____

The equivalent decimal addition problem is 433+499+463=1395.

Answer:

£20.44

Step-by-step explanation:

Step 1: find the area of the total area of the garden.

Total area = l*w

Where,

l = 10 m

w = 6 m

Total area of garden = 10*6 = 60m²

Step 2: find the area of the vegetable patch.

Area of vegetable patch = l*w = 2*1.5 = 3m²

Step 3: find the area covered by pond.

Area covered by pond = πr²

Take π as 3.14

r = 2m

Area of pond = 3.14*2² = 12.56 m²

Step 4: find the area of the remainder of the garden to be reseeded.

Area of the remainder of the garden = total area of the garden - (area of the vegetable patch + area of pond)

= 60 - (3 + 12.56)

= 60 - 15.56

Area of the remainder of the garden = 44.44 m²

Step 5: calculate the total cost to reseed the garden.

Given that a bag of seed to cover 10m² is £4.60, total cost to reseed the remainder of the garden measuring 44.44 m² can be calculated bas follows:

10 m² = £4.60

44.44 m² = [tex] \frac{44.44*4.60}{10} = 20.44 [/tex]

The answer is £20.44

Answer:

I don't know how to insert a number line, but you have to put on it x<-3. You have to plot it, then put a open circle at -3, and draw an arrow, pointing it farther into the negitive side of the number line.

Step-by-step explanation:

Answer:

2x +5y -20

Step-by-step explanation:

-x - 3y - 20 + 3x + 8y

Combine like terms

-x+ 3x  - 3y+ 8y - 20

2x +5y -20

Answer:

2x + 5y - 20

Step-by-step explanation:

-x + 3x = 2x

-3y + 8y = 5y

Answer:

(3,5)

∧

this is x number

Step-by-step explanation:

the x number is left and right movement. if you move 3 units left you would subtract 3 from the x number. so 6-3=3 and you don't have to do anything on the y value because you don't move it.

Answer:

(3,5)

Step-by-step explanation:

When using graphs:

X-axis:

Y-axis:

When writing points on a graph, it should be (X,Y)

So (6,5) all you have to do is subtract 3 from 6(6-3=3) so your final answer should be (3,5)

Hopefully this helps :)

Answer:

1. $66

2. 30 + 4r

Step-by-step explanation:

Let

Price of admission into the park=$30

Price of every ride in the park=$4

Number of rides =x

Total cost of going to the park= 30+4x

1. How much money would Claire have to pay in total if she goes on 9 rides

Total cost of going to the park= 30+4x

When x=9

=30+4x

= 30 + 4(9)

=30 + 36

=$66

2. How much would she have to pay if she goes on r rides?

When x=r

Total cost of going to the park= 30+4x

= 30 + 4(r)

=30 + 4r

Answer:

Cost for 9 rides=$66, Cost for r rides=30+4r

Step-by-step explanation:

Cost for 9 rides: 30+4(9)=66

Cost for r rides: 30+4r

Answer:

its the third one. just multiply every number by 1.5 not that hard

Step-by-step explanation:

Answer:

The indoor pool has a higher temperature and also has the greatest absolute value.

Step-by-step explanation:

The indoor pool has a higher temperature becasue 24 is greater than 23.  It also has a bigger absolute value because the absolute value how much a number is from 0.

So the absolute value of 24 is 24.

The absolute value of 23 is 23.

24 is greater so the indoor pool also has a bigger absolute value.

Answer:

t= -3.7

Step-by-step explanation:

1. 5( t+3)= -3.5

2. 5t+15= -3.5

3. 5t= -18.5

4. t= -3.7

Answer:

33°

Step-by-step explanation:

A right triangle is formed based on the information given.

Use trigonometric ratio formula to find the number of degrees of the angle indicated with "?".

Let the angle = x°

162.5 yds is opposite to x°

298 yds is the hypotenuse of the right triangle formed.

Therefore, [tex] sin(x) = \frac{opposite}{hypotenuse} [/tex]

[tex] sin(x) = \frac{162.5}{298} [/tex]

[tex] sin(x) = 0.5453 [/tex]

[tex] x = sin^{-1}(0.5453) [/tex]

[tex] x = 0.5453 [/tex]

[tex] x = 33.0 [/tex]

Answer:

Step-by-step explanation:

total quantity of oil = 37 litres

quantity of oil in first tank = 11 litres

quantity of oil in second tank = 12 litres

Total quantity of oil in first and second tanks = 11 + 12 = 23 litres

∴ quantity of oil in the third tank = 37 - 23

= 14 litres

Hope this helps

plz mark as brainliest!!!!!!!!!!!

Answer:

P[ x >= 5 ]  = 0,005487  

Step-by-step explanation:

The possibility of the student to answer correctly one question is 1/3

We have three answers and only one is right.

The possibility of answer at least 5 right question is:

Possibility of answer 6 question plus the possibility of answer 5 questions

The possibility of answering at least 5 answers are correct is:

To answer 2 questions  1/3*1/3   =  1/9

To answer three    1/3*1/3*1/3   =  1/ 27

To answer 5   is  1/3*1/3*1/3*1/3*1/3   =  1/243

And to answer all the question right is (6) is  1/729

Therefore probability of answer at least 5 right questions is

P[ x >= 5 ]  = P [5] + P [6]

P[ x >= 5 ]  =  1/ 243  + 1/729

P[ x >= 5 ]  = 972/ 177147

P[ x >= 5 ]  = 0,005487            

Answer:

EQUATION IS GIVEN BELOW.

Step-by-step explanation:

let the number be 'x'

now,

x+12 =36

or, x=36-12

therefore,x=24

Part (i)

Plug in theta = pi/3 to get

h(theta) = sin(3theta)

h(pi/3) = sin(3*pi/3)

h(pi/3) = sin(pi)

h(pi/3) = 0 ... use a calculator or the unit circle

=================================================

Part (ii)

Plug in h = pi/2

h(theta) = sin(3theta)

h(pi/2) = sin(3pi/2)

h(pi/2) = -1

Answer:

Square= 12 units

Triangle long sides= 19 units

Triamgle short side= 10 units

Step-by-step explanation:

It is a square, so all sides are the same.  That means 3x+3 equals 4x.  What number can be subsituted into x to equal 4?  If x is 3, then 3x+3 would be 3(3)+3.  It equals 12.  4 times 3 is also 12.  It works!  That also means the square's side is 12 units.

Square= 12 units

So, x=3

The triangle's longer sides are 7x-2.  Subsitute x in, which is 3, and you get 7(3)-2.  It equals 19.  The two longer sides of the triangle are the same length, so both are 19 units.

Triangle long sides= 19 units

The triangles shorter side is 2x+4.  Subsitute 3 in for x and you get 2(3)+4.  It equals 10, so the shorter side is 10 units.

Triangle short side= 10 units

Answer:

Square: 12 unites

triangle shorter side: 10 units

triangle longer sides: 19 units, 19 units

Step-by-step explanation:

Hello!

First, we make the equations to find the perimeters of each shape by adding all the sides

Square: 4x + 4x + (3x+ 3) + (3x + 3)

Triangle: (7x - 2) + (7x - 2) + (2x + 4)

Since the perimeters are equal we can show that

4x + 4x + (3x+ 3) + (3x + 3) = (7x - 2) + (7x - 2) + (2x + 4)

Now we can solve for x.

Combine like terms

14x + 6 = 16x

Subtract 14x from both sides

6 = 2x

Divide both sides by 2

3 = x

Now we know what x is we can put that into the sides of the shapes

Square

4(x)

Put in x

4(3) = 12

The Square is 12 units

Triangle Short Side

2x + 4

Put in x

2(3) + 4

6 + 4

10

The shorter side of the triangle is 10 units

Triangle Longer Side

7x - 2

Put in x

7(3) - 2

21 - 2

19

The longer sides are 19 units

Hope This Helps!