3k(x+2)+2 = 5x+8
How do I solve for k while keeping x smaller then 3?

Answer:

Step-by-step explanation:

Analysis

Answer:

49 x 3 = 147

147 + 173 = 320

Step-by-step explanation:

Step 1 Henrik grew 3 times as many potatoes as Derek grew. Derek managed to grow 49 potatoes.

49 x 3 = 147

Step 2  Henrik already had 173 potatoes harvested from his other field.

173 + 147

Answer:

  e/f

Step-by-step explanation:

Common factors in the numerator and denominator cancel.

  [tex]\dfrac{e\times e\times e\times e\times f}{e\times e\times e\times f\times f}=\dfrac{e}{e}\times\dfrac{e}{e}\times\dfrac{e}{e}\times\dfrac{e}{f}\times\dfrac{f}{f}=1\times1\times1\times\dfrac{e}{f}\times1=\boxed{\dfrac{e}{f}}[/tex]

The required simplification of the expression is [tex]\dfrac{e}{f}[/tex].

We have to the given expression, e x e x e x e x f ÷ e x e x e x f x f.

The given expression is simplify in the following steps given below.

Expression; [tex]\dfrac{e \times e \times e \times e \times f}{e \times e \times e \times f \times f}[/tex]

Then,

The simplification of the given expression,

[tex]=\dfrac{e \times e \times e \times e \times f}{e \times e \times e \times f \times f}\\\\[/tex]

Cancel out the same term from denominator and numerator,

[tex]= \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{f}{f} \\\\= 1 \times 1 \times 1 \times \dfrac{e}{f} \times 1 \\\\= \dfrac{e}{f}[/tex]

Hence, The required simplification of the expression is [tex]\dfrac{e}{f}[/tex]

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Step-by-step explanation:

y isn't directly proportional with x because the graph doesn't cross O the origin, it starts from a y-intercept wich is not a property for proportional portions

Answer:

The answer is given below

Step-by-step explanation:

Given that the location of the points are W = (3, 1) , X = (7, -1), Y = (7, -3) and Z = (3,-3)

The distance between two points A(x1, y1) and B(x2, y2) is given by the formula:

[tex]|AB|=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Therefore, the side length of the quadrilaterals are:

[tex]|WX|=\sqrt{(-1-1)^2+(7-3)^2}=\sqrt{20} =4.47[/tex]

[tex]|XY|=\sqrt{(-3-(-1))^2+(7-7)^2}=\sqrt{20} =2\\\\|YZ|=\sqrt{(-3-(-3))^2+(3-7)^2}=\sqrt{20} =4\\\\|ZW|=\sqrt{(-3-1)^2+(3-3)^2}=\sqrt{20} =4[/tex]

The Perimeter of the quadrilateral = |WX| + |XY| + |YZ| + |ZX| = 4.47 + 2 + 4 + 4 = 14.47 units

Answer:

4.47,

2

4

14.47

Step-by-step explanation:

Answer:

Please find attached the required graph and

Step-by-step explanation:

The values for the information given can be written down as follows;

Time, seconds             Volume mL

0,                                    500

12,                                   450

24,                                  400

36,                                  350

48,                                  300

60,                                  250

72 250

84 250

96 250

108 250

120 250

132 250

144 250

156 250

168 250

180 250

192 250

204 250

216 250

228 250

240 250

252 250

264 250

276 250

288 250

300 250

312 225

324,                                        200

336,                                         175

348,                                         150

360,                                         125

372,                                         100

384,                                         75

396,                                        50

408,                                        25

420,                                        0

Answer:

Scale factor of dilation = 2

Step-by-step explanation:

The bigger triangle divided by 2 to get to the smaller triangle. If you count the tiles next to the bigger triangle and the smaller one you can see that it's dilated by 2.

Hope this helps!

Answer:

Step-by-step explanation:

The lengths of all the sides have decreased by half.

So

A-B = 3       A'-B' = 6

A-B = 3         Because 6/2 = 3

This proves the scale factor is 2.

Hope this helped!

Kavitha

Answer:

Children 188

Adults. 115

Step-by-step explanation:

Let the no. of children be x and adults be y

x + y = 303

x = 303 - y. .... .....(1)

1.75x + 4.80y = 881. ...........(2)

Substituting,

1.75(303-y) +4.80y = 881

530.25 -1.75y + 4.80y = 881

530.25 + 3.05y = 881

3.05y = 881 - 530.25

y = 350.75 / 3.05 = 115 = adults

Children = 303-115 = 188

Answer:

This sequence is a geometric sequence.

The common ratio of the sequence is

3/9 = 1/3

Hope this helps

Answer:

98

Step-by-step explanation:

7x+4 = 88 because they are vertical angles and vertical angles are equal

7x = 88-4

7x = 84

Divide by 7

7x/7 = 84/7

x = 12

<1 and 7x-2 are supplementary angles since they form a line

<1 + 7x-2 = 180

<1 + 7(12) -2 = 180

<1 +84-2 =180

<1 +82 = 180

<1 = 180-82

<1 = 98

Answer-

98

step by step explanation -

7x+4=88

7x=84

x=12

7x-12=7*(12)-2=82

angle 1=180-82 =

Answer:

option B is the correct option.

Solution,

[tex] {(x - 4)}^{2} = 5 \\ [/tex]

x-4=_+√5

X=4_+√5

Hope this helps...

Good luck on your assignment...

Answer:

(x-4)^2 =5

x^2-16=5

x^2=5+16

x^2=21

√x^2=√21

x=√21

Step-by-step explanation :

First of all open the bracket which has square

Secondly change the position of 16

Note: when a number changes its place , the symbol also changes

then when you get the value take the square root on both sides

and you'll get the answer

By using multiplication, [tex](2x+3)^{2}[/tex] =  [tex]4x^{2} +12x+9[/tex].

Multiplication is the method of finding the product of two or more numbers. It is a primary arithmetic operation that is used quite often in real life. Multiplication is used when we need to combine groups of equal sizes.

Given

[tex](2x+3)^{2}[/tex]

= (2x + 3)(2x + 3)

= 2x (2x) + 2x(3) + 3(2x) +3(3)

= [tex]4x^{2} +6x+6x+9[/tex]

= [tex]4x^{2} +12x+9[/tex]

Hence, by using multiplication, [tex](2x+3)^{2}[/tex] =  [tex]4x^{2} +12x+9[/tex].

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Answer:

see explanations below.

Step-by-step explanation:

The shown sides are all equal.

If it is a regular polygon, it must have all interior angles equal, and all sides equal.

IF

all sides are equal and all angles are equal,

THEN

it is a regular polygon, with 12 sides, because in regular polygons, all exterior angles are equal, and add up to 360 degrees.

No. of sides = 360/(180-150) = 360/30 = 12 sides.

Answer:

-15c - 30

Step-by-step explanation:

-5(3c+6)

Expand or distribute the term outside the bracket to the terms inside.

-5(3c) - 5(6)

-15c - 30

Answer:

The answer is -15c - 30

Step-by-step explanation:

You have to apply Distributive Law :

[tex]a(m + n) = am + an[/tex]

So for this question :

[tex] - 5(3c + 6)[/tex]

[tex] = - 5(3c) - 5(6)[/tex]

[tex] = - 15c - 30[/tex]

Answer:

the alternate interior angles theorem.

Hope this helps.. Good Luck!

Answer:

Option B.

Step-by-step explanation:

From the given graph it is clear that the related line passes through the points (0,3) and (2,4).

So, the equation of related line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-3=\dfrac{4-3}{2-0}(x-0)[/tex]

[tex]y-3=\dfrac{1}{2}x[/tex]

Add 3 on both sides, we get

[tex]y=\dfrac{1}{2}x+3[/tex]

The related line is a solid line and shaded portion lies below the line. So, the sign of inequality must be ≤.

[tex]y\leq \dfrac{1}{2}x+3[/tex]

Therefore, the correct option is B.

Answer:

y ≤ one-halfx + 3

Step-by-step explanation:

Answer:

557.75

Step-by-step explanation:

575 - 3% = 557.75 is the minimum amount in sales that has to be made

Answer:

The answer is

Step-by-step explanation:

To find the graph which shows (f + g)(x) we must first find (f + g)(x)

That's

f(x) = - x² + 3x + 5

g(x) = x² + 2x

To find (f + g)(x) add g(x) to f(x)

That's

(f + g)(x) = -x² + 3x + 5 + x² + 2x

Group like terms

(f + g)(x) = - x² + x² + 3x + 2x + 5

We have (f + g)(x) as

(f + g)(x) = 5x + 5

Since (f + g)(x) is linear the graph which shows (f + g)(x) is the last graph

Hope this helps you

Answer:

last graph or D

Step-by-step explanation:

Answer:

C has the largest area. It is 4.5 square units.

Step-by-step explanation:

A:

area = bh/2 = 2 * 3/2 = 3

B:

area = bh/2 = 2 * 3/2 = 3

C:

area = bh/2 = 3 * 3/2 = 4.5

C has the largest area. It is 4.5 square units.

Answer:

proved

Step-by-step explanation:

prove that : (sin^2 θ)/(1+cosθ)=1-cosθ

(sin^2θ)*(1−cosθ)/(1+cosθ)(1+cosθ) =

sin^2Ф)(1-cosФ)/1-cos^2Ф since 1-cos^2Ф=sin^2Ф then:

(sin^2Ф)(1-cosФ)/sin^2Ф =

1-cosФ     (sin^2Ф/sin^Ф=1)

proved

Answer:

Step-by-step explanation:

take it befor delete

Answer:

7. a = 50 degrees

b = 50 degrees

c= 50 degrees

d = 75 degrees

8.

Step-by-step explanation:

7.

a. Vertically opposite angles are equal

b. Vertically opposite angles are equal

c Alternate angles

d. Angles on a straight line.

8. 45 + 45 + 65 + 35 + 40 + 30 = 200m

Hope this helps

Answer:

Step-by-step explanation:

Permutation has to do with arrangement.

To form different word by rearranging the word KINDNESS, this can be done in the following way;

The total letters present in kindness = 8 letters

Repeated letters are 2N's and 2S's

The arrangement is done in [tex]\frac{8!}{2!2!}[/tex] ways

[tex]= \frac{8!}{2!2!} \\= \frac{8*7*6*5*4*3*2!}{2!*2}\\ = 8*7*3*5*4*3\\= 10,080 \ different\ words[/tex]

For MATHEMATICIAN;

The total letters present in kindness = 13 letters

Repeated letters are 2M's, 2T'S 2I'sand 3A's

The number of words formed =

[tex]\frac{13!}{2!2!2!3!} \\= \frac{13*12*11*10*9*8*7*6*5*4*3!}{6*3!}\\= 13*2*11*10*9*8*7*6*5*4\\= 172,972,800\ different\ words[/tex]

Answer:

See text below or attached figure

Step-by-step explanation:

Given arcs

AC=70

CR=18

therefore AR = 88

RB=80

BE=130

therefor EA = 360-(70+18+80+130) = 360-298 = 62

angles will be denoted (1) for angle 1, etc.

We ASSUME

ARD is a straight line

PFRB is a straight line

FCE is a straight line

Using inscribed angle theorem, angles subtended by chords/arcs equal to half the arc central angle.

Therefore

(4)=80/2=40

(13)=130/2=65

(12)=62/2=31

(11)=70/2=35

(5) = (70+18)/2 = 44

Consider triangle AEG,

(7)=(13)+(11)=65+35=100   [exterior angle]

Consider triangle EGB,

(10)=180-100-31 = 49      [sum of angles of a triangle]

Consider triangle AEH,

(3) = 180-(4)-(13)-(11) = 180-40-65-35 = 40  [sum of angles of a triangle]

From cyclic quadrilateral ARBE,

ARB+AEB=180 =>

ARB=180-AEB=180-(35+49) = 96

By the intersecting secants theorem,

(2) = (130-18)/2 = 56     [secants FE, FB]

(1) = (130+62 - (18+70))/2 = 104/2 = 52  [secants PA,PB]

(8) = (130+62 -80)/2 = 112/2 = 56

ARD is straight line  (see assumptions above)

(9) = 180-96 = 84    [sum of angles on a line]

ARP = (9) = 84     [vertically opposite angles]

Consider triangle ARP

(14) = 180-52-84 = 44

Consider tangent PA

(15) = 180-(44+40+65) = 31    [sum of angles of a triangle]

Consider triangle ABD

(6) = 180 - (40+44+56) = 40   [sum of angles of a triangle]

This completes the search for all sixteen angles, as shown in the diagram, or in the text above.

Answer:

The times are t = 9, t = 10, t = 11 and t = 12

Step-by-step explanation:

For the train to be more than 16 km South and since south is taken as negative,

d(t) > -16

t³ - 9t² + 6t > -16

t³ - 9t² + 6t + 16 > 0

Since -1 is a factor of 16, inserting t = -1 into the d(t), we have

d(-1) = (-1)³ - 9(-1)² + 6(-1)+ 16 = -1 - 9 - 6 + 16 = -16 + 16 = 0. By the factor theorem, t + 1 is a factor of d(t)

So, d(t)/(t + 1) = (t³ - 9t² + 6t + 16)/(t +1) = t² - 10t + 16

Factorizing  t² - 10t + 16, we have

t² - 2t - 8t + 16

= t(t - 2) - 8(t - 2)

= (t -2)(t - 8)

So t - 2 and t - 8 are factors of d(t)

So (t + 1)(t -2)(t - 8) > 0

when t < -1, example t = -2 ,(t + 1)(t -2)(t - 8) = (-2 + 1)(-2 -2)(-2 - 8) = (-1)(-4)(-10) = -40 < 0

when -1 < t < 2, example t = 0 ,(t + 1)(t -2)(t - 8) = (0 + 1)(0 -2)(0 - 8) = (1)(-2)(-8) = 16 > 0

when 2 < t < 8, example t = 3 ,(t + 1)(t -2)(t - 8) = (3 + 1)(3 -2)(3 - 8) = (4)(1)(-5) = -20 < 0

when t > 8, example t = 9,(t + 1)(t -2)(t - 8) = (9 + 1)(9 -2)(9 - 8) = (10)(7)(1) = 70 > 0

Since t cannot be negative, d(t) is positive in the interval 0 < t < 2 and t > 8

Since t ∈ (0, 12]

In the interval 0 < t < 2 the only value possible for t is t = 1

d(1) = t³ - 9t² + 6t = (1)³ - 9(1)² + 6(1) = 1 - 9 + 6 = -2

Since d(1) < -16 this is invalid

In the interval t > 8 , the only possible values of t are t = 9, t = 10.t = 11 and t = 12.

So,

d(9) = 9³ - 9(9)² + 6(9) = 0 + 54 = 54 km

d(10) = 10³ - 9(10)² + 6(10) = 1000 - 900 + 60 = 100 +60 = 160 km

d(11) = 11³ - 9(11)² + 6(11) = 1331 - 1089 + 66 = 242 + 66 = 308 km

d(12) = 12³ - 9(12)² + 6(12) = 1728 - 1296 + 72 = 432 + 72 = 504 km

Answer:

A

Step-by-step explanation:

in 1 years it grows 15% of $200= $30+200=$230

in x yrs it grows to $500

.... number of yrs= 500/230= 2.17 yrs

total number of pages = 550 pages

total amount of time to read the full book = 10 hours

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

Work Shown:

1 hour = 55 pages

4 hours = 220 pages ... multiply both sides by 4

After 4 hours, he had read 220 pages. Since he has 330 still left to read, this brings the total to 220+330 = 550 pages overall

550/55 = 10 hours is the total amount of time needed to read the entire book at a rate of 55 pages per hour. This is assuming the rate is kept constant.

While 10 hours is a lot, it's somewhat plausible to get the full book read in one continuous session. Though he is better off taking (short) breaks every now and then.

Answer:

550 pages

10 hrs

Step-by-step explanation:

he reads 55 pages per hour

4 hrs* 55 pages/hrs=220 pages

the book is 550 pages long

220 pages+330=550 pages

to find the time to read the whole book:

330/55=6 hrs +4 hrs=10

or

550/55=10 hrs

Answer:

13%

Step-by-step explanation:

[tex]percentage \: increase = \frac{565 - 500}{500} \times 100 \\ \\ = \frac{65}{500} \times 100 \\ \\ = \frac{65}{5} \\ = 13 \% [/tex]

Answer:

The population of the city was 25,000 in 1970 and 1983.

Step-by-step explanation:

In order to find the year at which the population was 25,000 we need to make p(t) equal to that number and solve for t as shown below.

[tex]25000 = 14*t^2 + 650*t + 32000\\14*t^2 + 650*t + 7000 = 0\\t^2 + 46.43*t + 500 = 0\\t_{1,2} = \frac{-46.43 \pm \sqrt{(46.43)^2 - 4*1*500}}{2}\\t_{1,2} = \frac{-46.43 \pm \sqrt{155.75}}{2}\\t_{1,2} = \frac{-46.43 \pm 12.48}{2}\\t_1 = \frac{-33.95}{2} = -16.98\\t_2 = \frac{-58.91}{2} =- 29.5[/tex]

Since t = 0 corresponds to the year 2000, then t1 = 1983 and t2 = 1970.

Answer:

x ≤ -4

Step-by-step explanation:

There is a closed circle at -4, which requires and equals sign

The line goes to the left, which is less than

x ≤ -4

Answer:

-b+2 or 2-b

Step-by-step explanation:

We first obtain 2 * b + 4. Next, we get 2b + 4 - 4b = -2b +4. Dividing this by two, we have -2/2b + 4/2 = 2/2 b + 4/2.

The final expression obtained after given operations is 2 - $b$.

Linear expressions are expressions involving constants and variables.

We are given that the person takes a variable $b$, doubles it, and adds four to it. He subtracts $4b$ from this and then divides the whole by 2.

So, we perform these operations on our variable $b$, to obtain the linear expression.

Variable: $b$

Doubles it, that is we multiply it by 2: 2*$b$

Adds 4: 2$b$ + 4.

Subtracts $4b$: 2$b$ + 4 - $4b$ = 4 - $2b$

Divides by 2: (4 - 2$b$)/2 = 2 - $b$

The expression now: 2 - $b$.

∴ The final expression obtained after given operations is 2 - $b$.

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