find the geometric mean of 64 and 49

Answer:

804.25 cm² (corrected to 2 decimal places)

Step-by-step explanation:

Radius = diameter / 2

= 16/ 2

=8 cm

Surface area of sphere = 4πr²

= 4π8²

=804.25 cm² (corrected to 2 decimal places)

Answer:

B. (2, 2)

Step-by-step explanation:

In order for the coordinate to be a solution of the systems of inequalities, it has to be in the shaded region (not on the line since both are dotted). Only B fits in the shaded region.

Answer:

1.1 hour or 1 hour and 6 minutes

Step-by-step explanation:

Time is given by the distance divided by the velocity. If the time it takes the tugboat to travel 20 km downstream in the same time it takes it to travel 10 km upstream, then:

[tex]t_1=t_2\\\frac{20}{v_b+v_c}=\frac{10}{v_b-v_c}\\v_c=5\ km/h\\20v_b-100=10v_b+50\\10v_b=150\\v_b=15\ km/h[/tex]

The velocity of the boat is 15 km/h. When traveling downstream, the current will favor the boat, therefore, the time required for it to travel 22 km downstream is:

[tex]t=\frac{22}{v_b+v_c} \\\t=\frac{22}{15+5}\\ t=1.1\ hour[/tex]

It will take the boat 1.1 hour or 1 hour and 6 minutes.

Answer:

88° and 132°

Step-by-step explanation:

The sum of angles in a pentagon ( a 5-sided shape) is given as

= (5 - 2) 180°

= 540°

The angles ∠EAB and ∠AED are supplementary hence the sum is 180° Therefore,

∠AED + 110 = 180

∠AED = 180 - 110

= 70°

Given that the sum of the angles in a pentagon is 540° then

110 + 70 + 2k + 140 + 3k = 540

5k + 320 = 540

5k = 540 - 320

5k = 220

k = 220/5

= 44°

Hence the angle ∠ABC

= 2 × 44

= 88°

∠CDE

= 3 × 44

= 132°

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

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:

0.45 litres

Step-by-step explanation:

2/5 multiplied by 2 = 0.8

0.8+0.75= 1.55

2-1.55 = 0.45

Answer:

A

Step-by-step explanation:

We know that the y-coordinate has to be 1 so we can eliminate options C and D. If we plug y = 1 into y = -5x + 3 to solve for x we get:

1 = -5x + 3

-2 = -5x

x = 0.4 so the answer is A.

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:

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

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:

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:

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:

  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]

To know more about Multiplication click the link given below.

https://brainly.com/question/16871801

Answer:

Out of 8000 students, 10% take tuition in various subjects before the exam.

10% of 8000 is:

10/100 * 8000 = 800

Among the 800, 40% take tuition in English only and 20% take tuition in Math only.

80 students take tuition in other subjects, therefore, in percentage:

80/800 * 100 = 10%

Therefore, the percentage of students that take tuition in both Math and English is:

100% - (40% + 20% + 10%) = 100% - 70% = 30%

30% of the 800 students take tuition in both subjects. That is:

30/100 * 800 = 240 students

Therefore, among the 8000 students in the district, only 240 take tuition in both English and Math.

In percentage:

240/8000 * 100 = 3%

3% of students take tuition in both English and Math.

In Ratio:

3 : 100

3 out of 100 students take tuition in English and Math.

Answer:

9.35975609756

Step-by-step explanation:

Its about this I just put it into a calculator

Answer:9.353658

Step-by-step explanation:

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:

LJ = CB

Therefore, CJ is 50km

Answer:

x = 5.85641

Step-by-step explanation:

Step 1: Find missing leg of left triangle

sin30° = x/16

16sin30° = x

x = 8

Step 2: Find missing leg of right triangle

8² + b² = 16²

b² = 192

b = 8√3

Step 3: Find x by taking the difference

8√3 - 8 = 5.85641

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 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.

Step-by-step explanation:

last years was $2500.00

20% of $2500 = $500.00

profit this year is $3000.00

Answer:

D

Step-by-step explanation:

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 - $b$.

Learn more about linear expressions at

https://brainly.com/question/14323743

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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:

x=88° a=+3 b=4a-3

Step-by-step explanation:

as triangles ADE and BCE are congruent by sss axiom

so correponding angles are equal

i.e<AED = <BEC

and <DAE =90-60

=30°

so

62°+x+30°=180°

therefore x=88°

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:

[tex]\boxed{f(x) = x + 2}[/tex]

Step-by-step explanation:

The translation is horizontal translation.

The value of x is subtracted from 4, since the function is shifted 4 units to the right.

f(x - 4)

f(x) = (x - 4) + 6

f(x) = x + 2

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:

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 =