Simplify (x + 3) - 2(4 + x) + 5x - 4

Answer:

[tex]\frac{x^2}{2}[/tex] square units        [one-half x squared square units]

Step-by-step explanation:

As shown in the diagram attached to this response,

Since a square has all sides equal, let the sides of the square be each of a units.

The area, A, of the square = a x a = a²

i.e

A = a²    --------------(i)

Now,

The diagonal is x units such that applying Pythagoras rule gives;

x² = a² + a²

x² = 2a²

a² = [tex]\frac{x^2}{2}[/tex]           ----------------(ii)

Substitute the value of a² in equation (ii) into equation (i) to get;

A = [tex]\frac{x^2}{2}[/tex]

Therefore, the area of the square is [tex]\frac{x^2}{2}[/tex] square units

Answer:

1/2x^2 square units

Step-by-step explanation:

Answer:

(-2.3, 0.5)

Step-by-step explanation:

Step 1: Write out systems of equations

8x - 10y = -23

9x + 10y = -16

Step 2: Elimination (add the 2 equations together)

17x = -39

x = -39/17 = -2.29412 ≈ -2.3

Step 3: Plug in x to find y

8(-39/17) - 10y = -23

-312/17 - 10y = -23

-10y = -79/17

y = 79/170 = 0.464706 ≈ 0.5

Answer:

(-2.3, 0.5)

Step-by-step explanation:

Step 1: Write out systems of equations

8x - 10y = -23

9x + 10y = -16

Step 2: Elimination (add the 2 equations together)

17x = -39

x = -39/17 = -2.29412 ≈ -2.3

Step 3: Plug in x to find y

8(-39/17) - 10y = -23

-312/17 - 10y = -23

-10y = -79/17

y = 79/170 = 0.464706 ≈ 0.5

Step-by-step explanation:

Answer:

Hey there!

We have tan 9= 21/BW

tan 9 (BW)=21

BW= 21/tan 9

BW= 132. 59

Hope this helps  :)

Answer:

A- 132.59

Step-by-step explanation:

since we have to find the adjacent and already have the opposite we'll use tanθ = opp/adj

tan(9)= 21/WB

WB = 21/tan(9)   (make WB the subject)

WB = 132.5887818   or   132.59

Answer:

The ratio is 4:12:15.

Step-by-step explanation:

we need to make the first ratio (Sylvia's to John's) comparable to second one (John's to Peter's). Since John is in both ratios, we use his number to make it the same. 3 and 4 can both be multiplied into 12. So, multiply the first ratio by 4 and the second by 3.

[tex](1:3) * 4 = 4:12\\(4:5) * 3 = 12:15[/tex]

Put it together, and you get 4:12:15.

Hope it helps :P

Answer:

1st option

2,4,8,16

Step-by-step explanation:

1st option is not an Arithmetic sequence, it is geometric sequence. Because, the common ratio is 2

the 2nd option has a common difference of 7, so it is arithmetic

the 3rd option has a common difference of 0.5,  so it is arithmetic

and 4th option has a common difference of -4.  so it is arithmetic

It is approximately equal to 0.1111

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

To get this answer, we use the rule

[tex]x^{-k} = \frac{1}{x^k}[/tex]

The negative exponent tells us to apply the reciprocal to get the exponent to be positive.

So,

[tex](-3)^{-2} = \frac{1}{(-3)^2}\\\\(-3)^{-2} = \frac{1}{9}[/tex]

Squaring -3 means you square the negative as well

[tex](-3)^2 = (-3)*(-3) = 9[/tex]

Answer:

1/9

Step-by-step explanation:

(-3)^-2 would be better written as (-3)^(-2).

                                                                                       1

(-3)^(-2) would be easier to evaluate if written as -------------

                                                                                   (-3)^2

The final answer is 1/9.

Answer: 69.6 m

Step-by-step explanation:

Sin 55 deg = opposite side/hypotenuse

0.819 = height/string length

0.819 * 85= height

height = 69.6 m

Answer:   4.3 miles

The decimal 4.3 is equivalent to the mixed number 4 & 3/10

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

Explanation:

Fractions are often a pain, so I find it helpful to convert to decimal form whenever possible.

1/2 = 0.5

21 & 1/2 = 21 + 1/2 = 21 + 0.5 = 21.5

21 & 1/2 miles = 21.5 miles

The object travels 21.5 miles in 5 hours. Divide the distance over the time value to get the speed (or rate). This is exactly identical to finding the number of miles traveled in one hour (since each hour the object travels the same amount of distance)

speed = distance/time = 21.5/5 = 4.3 mph

4.3 = 4 + 0.3 = 4 + 3/10 = 4 & 3/10

In my opinion, it is much easier to use decimals. Saying "the object traveled a distance of 4 & 3/10 miles" seems very clunky to me.

Therefore, each hour, the object travels 4.3 miles.

Answer:

102.88m

Step-by-step explanation:

draw a rectangle and draw a diagonal line from each corner down. You will get 2 right triangles. The height is 91 and the base is 48

[tex]\sqrt{91^2+48^2}= 102..88[/tex]

Answer:

$2,459.21

Step-by-step explanation:

(see attached for reference)

recall that the formula for compound interest is:

A = P [ 1 + (r/n)^ (nt) ]

where,

A = Final amount ( we are asked to find this)

P = principal amount = given as $2,340

r = Annual Interest Rate = given as 5% = 0.05

n = number of times compounded in a year = 4 (compounded quarterly)

t= time = 1 year

Substituting the values into the equation,

A = P [ 1 + (r/n)^ (nt) ]

A = 2,340 [ 1 + (0.05/4)^ (4·1) ]

A = $2,459.21

Answer: a (see explanation below) .b.) rhombus .c) trapezoid in USA or trapezium elsewhere in the world

Step-by-step explanation:

For  a.)  Draw a horizontal from the bottom vertex, extending 2 units to the right. Then form a triangle by connecting a line from the right end of that line up to the right angle at the top of the original triangle

As per the given diagram

(a) represents a parallelogram not rectangle as shown in construction.

(b) Shape made by three congruent triangles on the grid below represents trapezium.

(c) Four congruent triangle in the grid below represents rhombus.

"Two triangles are said to be congruent if the measure of all the three corresponding sides and angles of one triangle are equal to that of other triangle."

According to the question,

(a) First diagram we have to construct a triangle with given triangle in such a way it forms a parallelogram but not rectangle.

As shown in the constructed diagram.

(b) In the fourth diagram given quadrilateral having one pair of parallel line , therefore trapezium.

(c) In the second diagram all the four sides are congruent and parallel to each other and diagonals bisects each other at 90°, therefore it is rhombus.

Hence, (a) as shown in construction ,(b) trapezium and (c) rhombus is the correct answer.

Learn more about congruent triangles here

https://brainly.com/question/12413243

#SPJ2

Answer:

thats the answer to rhjs problem

Answer:

18π

Step-by-step explanation:

the area of a circle is :

A= r²*π     where r is the radius

here r²  =81⇒ r= 9

the circumference of a circle is :

P= 2*r*π

P= 18π

Answer:

18 pi inches

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

81 pi = pi r^2

Divide by pi

81 = r^2

Take the square root of each side

sqrt(81) = sqrt (r^2)

9 = r

We want the circumference

C = 2 * pi * r

C = 2 * pi * 9

C = 18 pi

Step-by-step explanation:

Use pythagoras theorem

a^2=b^2+c^2

a^2=64+36

a=10m

The length up to the wall of the ladder will be around 5.2915.

The Pythagoras theorem is a theorem used to find out any length of a right-angle triangle.

Pythogoroous theorem is

Hypotenuse² = base² + perpendicular²

Given that a ladder leans against a wall so the ladder will act like a hypotenuse.

Let 6m be the base then we have to find the perpendicular.

Hypotenuse² = base² + perpendicular²

perpendicular² = Hypotaneous² -  base²

perpendicular =  [tex]\sqrt{ (Hypotenuse)^2 - (base)^2}[/tex]

Given hypotenuse is 8m and the base is 6m.

perpendicular² = 8² - 6²

perpendicular² = 28

perpendicular = √(28) = 5.2915 hence this much be far up the wall does the ladder reach.

For more information about Pythagoras theorem.

https://brainly.com/question/343682

#SPJ5

Answer:

(0,-6), (-2,0)

Step-by-step explanation:

-3x-y=6

-y=6+3x

y=-3x-6

when x=0, y=-6

when y=0 x=-2

Answer:

So for the table , .3 + .1 + .25 + .35= 1.

and 10 green pins. read my explanation please cause i worked a lot on this.

Step-by-step explanation:

So first we add the probability of purple and gray getting picked.

.35 + .25= .6

And we know that the probability of green is 3 times yellow.

So. yellow can be x. and the equation would look like this.

3x + x +.6= 1

x equals .1, because 3x + x or 3(.1) + .1= .4

So, .3 + .1 + .25 + .35= 1.

This should be enough info to complete the table. Now b.)

So we know 14 purple pins... and the probability of that is .35

so if 14 = .35 what equals .25?

(I'm going to convert these decimals into percents for problem b until we get the answer, and then i'll make it back to a decimal form)

Okay, so

14= 35%

and that means .4 equals 1% or .01 probability

so now we times .4 to 25% to find out how many green pins are there.

.4 * 25= 10

So there are 10 green pins.

Answer:

Original number is 52.

Step-by-step explanation:

1) Two digit number xy,

it can be written as 10x + y.

2) The sum of the digits of a two-digit number is 7.

x + y = 7

3) The digits are interchanged the reversed number is yx,

the new number can be written as 10y + x.

4)  The original number is 10x + y, so the tens digit of the original number  is x.

5) Five times the tens digit of the original number is 5*x.

6) The reversed number is five times the tens digit of the original number:

10y + x = 5*x

7) We have system of two equations

x + y = 7  ---->  x = 7 - y

10y + x = 5*x --->   10y - 4x = 0

10y - 4x = 0

10y - 4(7 - y) =0

10y - 28 + 4y = 0

14y = 28

y = 2

x = 7 - y = 7 - 2 = 5

x = 5

Original number is 52.

New number 25.

Check:

Original number is 52, the tens digit is 5.

The reversed number (25) is five times the tens digit of the original number find the original number .

25 = 5*5 True

Answer:

We operate the principle of sets to solve the problem. We are given the number of women to be 28 and men to be 23. The intersection will be while the union of both sets will be 24. To calculate the number of women teachers attending the lecture we first sum up the number of women and men and subtract from the intersection of both sets which gives us 3. Therefore, the number of teachers that are men are 3 while the number of women teachers are 1.

Step by step explaination:

Given the following, Let the set for men be represented by MM, that of women be represented by WW and that of teachers represented by TT.

Therefore, number of men i.e n(MM)= 23,

number of women i.e n(WW)= 29

number of teachers i.e n(TT)=4

number of  men or teachers i.e n(MM U TT)= 24

Therefore, we have:

n(MM U TT)=n(MM) + n(TT) - n(MM n TT)

Therefore:

n(MM n TT)=n(MM) + n(TT) -n(MM U TT)

n(MM n TT)= 23+ 4 - 24 = 3

There fore number of men that are teachers are n(MM n TT)= 3 .

Therefore, from the number of teachers n(TT)=4

the number of teachers that are men are 3 while the number of women teachers are 1.

Answer:

9 roots

Step-by-step explanation:

(x+10)^9 = 0

If you would multiply it out, the highest power is x^9 so the equation has 9 roots

Solving (x+10)^9 =0

Taking the 9th root of each sdie

x+10 = 0

x = -10

The root is -10 with multiplicity of 9

Answer:

Step-by-step explanation:

George: x

Alex: x + 12

Carl: 3(x+12)

3x+36+x+x+12= 68

5x + 48 = 68

5x = 20

x = 4; George's age

4 + 12 =  16; Alex's age

3(4+12)= 3(16)= 48; Carl's age  

George to Alex: 4:16 = 1:4

Alex to Carl: 16:48= 1:3

George to Carl 4:48= 1:12

Carl to Alex: 48:16 = 3:1

Answer:

B. (9x - 5y)(9x + 5y)

Step-by-step explanation:

Rewrite the binomial as:

(9x)² - (5y)²

Apply difference of two squares formula.

x² - y² = (x - y)(x + y)

(9x)² - (5y)² = (9x - 5y)(9x + 5y)

Answer:

Step-by-step explanation:

n could be : -14, -13, -12... -1, 0 , 1, 2, 3 ,4,5

Answer:

Step-by-step explanation:

let x= time period in years between age now and when  father's age=2* the samad's age

in x years father's age will be 40 + x years old

in x years samad's age will be 12+x years old

at a certain point in time, the father's age = 2*the samad's age

40+x=2*(12+x)

or, 40 +x=24 + 2x

or, 40-24 = x

   x=16

test:

father=40+16=56

son=12+16=28

hence , after 16 years samad's father will be twice as old as samad

Answer:

The correct answer is:

[tex]+6x^{2}\\-9y^2[/tex]

Step-by-step explanation:

We are given the term:

[tex]3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6 = 9x^{2} -y^{2} +9[/tex]

We have to fill in to the empty spaces such that the above equation gets satisfied.

First of all, let us simplify the LHS (Left Hand Side):

[tex]3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6\\\Rightarrow 3x^{2} +5y^{2} +4y^{2} [\text{ \ }] [\text{ \ }] +6 +3\\\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9[/tex]

Now, let us equate the LHS and  RHS (Right Hand Side):

[tex]\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9 = 9x^{2} -y^{2} +9[/tex]

Equating the coefficients of [tex]x^{2}\ and\ y^{2}[/tex] in LHS and RHS:

One box will have value = [tex]9x^{2} -3x^{2} =+6x^{2}[/tex]

Other box will have value = [tex]-y^{2} -9y^{2} =-10y^{2}[/tex]

The correct answer is:

[tex]+6x^{2}\\-9y^2[/tex]

So, if we fill the boxes with above values, the expression will be simplified as given.

Answer:

The correct answer is B. Positive 6 x squared and Negative 10 y squared

Step-by-step explanation:

Answer:

None of the above

Step-by-step explanation:

the x coordinate tells us the duration, and the y-coordinate tells us the total cost of a phone call. The y coordinate of point aA represents the total cost of an 8 minutes phone call. not 8 phone calls. point a tells us that the cost is $2 for an 8-minute phone call, so the cost per minute is 2/8=$0.25, not $0.3.

Hope this helps!

Answer:

12 and 93.

Step-by-step explanation:

Let the grandsons age be x then Mr. Roger's age = 8x - 3.

Five years ago the grandson's age was x-5 and Mr Rogers was 8x - 8 years old , so:

8x - 8 - (x - 5) = 81

8x - 8 - x + 5 = 81

7x = 81 + 8 - 5 = 84

x = 12.

So the grandson is 12 and Mt Rogers is  8*12 - 3 = 93.

Answer:

C

Step-by-step explanation:

Most of the times C is the answer on a test

Answer:

its D

Step-by-step explanation:

brainly tests

Answer:

x = -20

Step-by-step explanation:

These angles are opposite therefore they are the same angle/degree

so we can look at this problem as

6x+238=3x+178

(subtract 238)

6x=3x-60

(subtract 3x)

3x=-60

(divide by 3)

x=-20

Answer: 3.5

Step-by-step explanation:

Given: Dimensions of larger prism = length of  4.2 cm, a width of 5.8 cm, and a height of 9.6 cm.

Dimensions of smaller prism = length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm.

Scale factor = [tex]\dfrac{\text{Size of image}}{\text{Size of original figure}}[/tex]

Since, smaller figure is the original figure and the bigger one is the image.

So, scale factor = [tex]\dfrac{14.7}{4.2}=3.5[/tex]  [Taking lengths

Hence, the factor to produce the corresponding dimensions of the larger prism = 3.5

Answer:

A

Step-by-step explanation:

Answer:

-x+3

Step-by-step explanation:

3 plus signs so 1+1+1= 3