solve for x 7(x+2) =6(x+5)

Answer:

x = 8 and -4

Step-by-step explanation:

3x² - 12x = 96

3(x² - 4x +  4 = 32 + 4)

3[(x - 2)² = 6²]

x - 2 = +/- 6

x = 8

x = -4

Answer:

The third table is the correct answer

Step-by-step explanation:

Here in this question, we are concerned with determine which of the tables correctly represents what an exponential function is.

An exponential function is a function of the form;

y = x^n

where the independent variable x in this case is raised to a certain exponent so as to give the results on the dependent variable axis (y-axis)

In the table, we can see that we have 2 segments, one that contains digits 1,2 and so on while the other contains purely the powers of 10.

Now, let’s set up an exponential outlook;

y = 10^x

So we have;

1 = 10^0

10 = 10^1

1/10 = 10^-1

1000 = 10^3

1/100 = 10^-2

We can clearly see here that we have an increase in the value of y, depending on the value of the exponent.

However it is only this table that responds to this successive correctness as the other tables in the answer do have a point where they fail.

For example;

10^-2 is not 10 which makes the fourth table wrong

10^4 is not 100 which makes the first table wrong

we have same error on second table too

Greetings from Brasil...

In a triangle the sum of the internal angles is 180 °.... Thus,

Ô = 180 - 30

Ô = 60

The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60

A1 = area of the rectangle triangle

TG B = OA/AB

AB = OA / TG B

AB = 6 / TG 30

AB = 6√3

A1 = (AB . OA)/2

A1 = (6√3 . 6)/2

A2 = area of the circular sector

(rule of 3)

 º                       area

360    ------------   πR²

60     ------------    X

X = 60πR²/360

X = 6π

So,

Then the area shaded is:

A = A1 - A2

Answer:

the speed of the plane with no wind is 700 km/h and the speed of the wind is 100 km/h

Step-by-step explanation:

Let V be the speed of the plane and v the speed of the wind. Down current, they are in opposite directions, and the plane travels a a distance of 4000 km in 5 hours,so

5(V - v) = 4000

V - v = 800    (1)

For upwind movement, since the plane travels 3000 km in 5 hours, so

5(V + v) = 3000

V + v = 600 (2)

adding equations (1) and (2), we have

V - v = 800

+

V + v = 600

2V = 1400

V = 1400/2 = 700 km/h

subtracting equations (2) from (1), we have

V - v = 800

-

V + v = 600

-2v = 200

v = -200/2 = -100 km/h

So, the speed of the plane with no wind is 700 km/h and the speed of the wind is 100 km/h

Answer:

The present age of the woman is 37 years and her daughter is 7 years

Step-by-step explanation:

two years ago a woman was 7 times old as her daughter, but in 3 years time she would be 4 times old as the girl. how old are they now

Two years ago a woman wad 7 times as old as her daughter

Let her daughter=x-2

The woman=y-2

x-2

7(y-2)=7y-14

x-2=7y-14

x-7y=-14+2

x-7y= -12 (1)

but in 3 years time she would be 4 times as old as the girl.

x+3

y+3

x+3

4(y+3)=4y+12

x+3=4y+12

x-4y=12-3

x-4y=9. (2)

x-7y= -12 (1)

x-4y=9. (2)

Subtract (1) from (2)

4y-(-7y)=9-(-12)

-4y+7y=9+12

3y=21

y=21/3

y=7

Substitute

y=7 into (1)

x-7y= -12

x-7(7)=-12

x-49=-12

x= -12+49

=37

The present age of the woman is 37 years and her daughter is 7 years

Answer:

p= 25/100 = 180/x

Step-by-step explanation:

In order to find the computer's original price, you must use the equation p= 25/100 = 180/x and solve for x.

Answer:

0.75p=p-180

Step-by-step explanation:

0.75p=p-180 is your answer

Answer:

d. $50,499

Step-by-step explanation:

Given:

S = 40,000 (1.06)^t

Where,

t=4 years

S=40,000(1.06)^4

=40,000(1.26247696)

=50,499.0784

To the nearest dollar

S=$50,499

The answer is d. $50,499

Answer:

120

Step-by-step explanation:

Got it right on the assigment

Answer:

c. 120

Step-by-step explanation:

Step-by-step explanation:

Answer:

$12.10 / hour

Step-by-step explanation:

42 - 31 =

1.3(11)r + 31r = 548.13

14.3r + 31r = 548.13

45.3r = 548.13

r = 12.1 / hour

Answer:

Step-by-step explanation:

y = r x

r is the constant of proportionality

To find r pick any values of x and y provided and substitute it into the above formula and solve for r.

That's

using

x = 2

y = 22

We have

22 = 2r

Divide both sides by 2

Therefore the constant of proportionality is 11

Hope this helps you

Answer:

x² = 900

Step-by-step explanation:

ΔABC is an equilateral triangle because its sides are equal lengths

this means their angles are also equal.

180 / 3 = 60

∠BCA and ∠DCA are supplementary angles - add up to 180º

if ∠BCA = 60º, then ∠DCA = 120º

ΔACD is an isosceles triangle because two sides are equal lengths. this means their angles are equal.

∠CAD ≅ ∠CDA

180 - ∠DCA = 2(∠CAD)

180 - 120 = 60

60 / 2 = 30º

x = 30º

x² = 900

Answer:

the 4th and 6th one

Step-by-step explanation:

A function is when there are x- and y-values but each x value has only 1      y-value

Simple: If the x-value is repeated its not a function

Answer:

Step-by-step explanation:

1,2,3

Answer:

x = -7

Step-by-step explanation:

DE + EF + FG = DG

2x+17 + 8+2 = x+20

Combine like terms

2x+ 27 = x+20

Subtract x from each side

2x+27-x = x+20-x

x+27 = 20

Subtract 27 from each side

x+27-27 = 20-27

x = -7

Step-by-step explanation:

[tex]\text{Discriminant} =\Delta = b^2-4ac\\

\implies \Delta = 7^2-4(1)(10)=49-40=9\\

\therefore \Delta >0\\[/tex]

Since the discriminant is greater than zero, there are two real solutions.

Also, the solutions are $x=5$ and $x=2$

Answer:

w = 100°

Step-by-step explanation:

Opposite angles in an inscribed quadrilateral in a circle are supplementary.

Therefore, [tex] w + 80 = 180 [/tex]

Subtract 80 from both sides

[tex] w + 80 - 80 = 180 - 80 [/tex]

[tex] w = 100 [/tex]

The value of w = 100°

Answer:

60 ships.

Step-by-step explanation:

Let the total number of ships in the naval fleet be represented by x

One-third of the fleet was captured = 1/3x

One-sixth was sunk = 1/6x

Two ships were destroyed by fire = 2

Let surviving ships be represented by y

One-seventh of the surviving ships were lost in a storm after the battle = 1/7y

Finally, the twenty-four remaining ships sailed home

The 24 remaining ships that sailed home =

y - 1/7y = 6/7y of the surviving fleet sailed home.

Hence

24 = 6/7y

24 = 6y/7

24 × 7/ 6

y = 168/6

y = 28

Therefore, total number of ships that survived is 28.

Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4

Total number of ships in the fleet(x) =

x = 1/3x + 1/6x + 2 + 28

Collect like terms

x - (1/3x + 1/6x) = 30

x - (1/2x) = 30

1/2x = 30

x = 30 ÷ 1/2

x = 30 × 2

x = 60

Therefore, ships that were in the fleet before the engagement were 60 ships.

Answer: 0.008

Step-by-step explanation:

We have 3 experiments.

Each experiment is exactly the same: "Drawing the card with the number 5, out of a bag with five cards".

in a random selection all the cards have exactly the same probability of being drawn, so the probability of drawing the 5, is equal to the quotient between the number of cards with the 5 (only one) and the total number of cards in the bag (5) then the probability is:

p = 1/5.

And we want this event to happen 3 consecutive times, then the total probability is equal to the product of the probabilities for each event:

P = (1/5)*(1/5)*(1/5) = 1/125 = 0.008

Answer:

(x-12)² + (y-6)² = 36 (Option C)

Step-by-step explanation:

use circle formula

(x-h)² + (y-k)²= r²

h= 12 and k= 6 and r= 6

(x-12)² + (y-6)² = 6²

6 squared = 36 (6·6)

(x-12)² + (y-6)² = 36

Answer:

m = -1/2 and b = 6.5

Step-by-step explanation:

To find the slope of the original line segment, we have to do the change in y/the change in x:

(4-8)/(-5--3) = -4/-2 = 2

2 is the slope of the original line segment, but since this is the perpendicular bisector, we have to take the negative reciprocal of 2 so m = -1/2

To find b we substitute the values of x, y, and m into the equation. Let's use the x value of -3 and the y value of 8:

y = mx + b

8 = -1/2(-3) + b

8 = 3/2 + b

6.5 = b

Answer:

a. 9

b. 9.

Step-by-step explanation:

a) √1098 = 33.136

33^3 = 1089

So the answer is 1098 - 1089

= 9.

b) √4498 = 67.067

67^2 =  4489

Answer = 9.

Answer:

a). 9

b). 9

Step-by-step explanation:

a) If you try to subtract 1 to 8 from 1098, it won't make a perfect square. But if you subtract 9 from 1098 (that will make it 1089), it will make a perfect square.

√1089 = 33

33² = 33 × 33 = 1089

So the answer is 9.

b). If you try to subtract 1 to 8 from 4498, it won't make a perfect square. But if you subtract 9 from 4498 (that will make it 4489), it will make a perfect square.

√4489 = 67

67² = 67 × 67 = 4489

So the answer is 9.

Hope you understand ◉‿◉ (◠‿◕)

Answer:

Hey there!

1 person can fix 1/3 of the road in 5 hours.

1 person can fix 1/15 of the road in 1 hour.

4 people can fix the road in 15/4, or 3.75 hours.

This is equal to 225 minutes.

Let me know if this helps :)

3 people - 5 h

4 people - x h

[tex]4\cdot x=3\cdot 5\\4x=15\\\\x=\dfrac{15}{4}=3,75[/tex]

3.75 h

Answer:

65.94 square inches

Step-by-step explanation:

Surface area of a cone=πr(r+√h^2+r^2)

π=3.14

r=diameter/2

=14/2

=7 in

h=?

h=a

To find h using Pythagoras theorem

c^2 = a^2 + b^2

14^2 = a^2 + 7^2

14^2 - 7^2= a^2

196-49=a^2

147=a^2

Square root both sides

√147=√a^2

12.12=a

a=12.12 in

Surface area of a cone=πr(r+√h^2+r^2)

=3.14(7+√12.12^2+7^2)

=3.14(7+√147+49)

=3.14(7+√196)

=3.14(7+14)

=3.14(21)

=65.94 square inches

Answer: A) 1716   B) 1235520

Step-by-step explanation:

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]

Given, Total distinct letters = 13

To choose = 6 letters

A) Number of ways to choose (if order does not matter)=[tex]^{13}C_6[/tex]

[tex]=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= $$1716[/tex]

B) Number of ways to choose (if order matters)=[tex]^{13}P_6[/tex]

[tex]=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= $$1235520[/tex]

Hence, A) 1716   B) 1235520

Answer:

D.0.25 inches per months

Step-by-step explanation:

The average rate or speed of human hair growth is about 0.25inches per month.

Answer:

x = -2

Step-by-step explanation:

To solve for x always get x on one side

First add 4 on each side, 4 + 7x - 4 = -18 + 4

Next subtract 18 from 4, making it -14    7x = -14

Now divide 7 on each side, x = -2

Answer:

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

Step-by-step explanation:

[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]

Factorizing the expressions we have

[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]

[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]

[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]

Cancelling out the like factors, (x -1) and (x - 2), we have

[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]

= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

Answer:

Acute.

Step-by-step explanation:

An angle of measure between 0 and 90 degrees is an acute angle.

Step-by-step explanation:

Since Ca(OH)2 is Basic, we need to find pOH:

pOH = - log [OH-]

pOH = - log(0.0001)

pOH = - ( - 4)

pOH = 4

Since, pH + pOH = 14

Therefore,

pH of 0.0001M sol. of Ca(OH)2 = 10

Answer: the ratio of the bike is 3

Step-by-step explanation:

its simply easy all you have to do is divide 36/12

Hey There!!

The answer to this is: (3:1) 36:12. 36 is the teeth on the front socket and 12 is the teeth on the rear socket. All you need to do is simplify by finding the greatest common factor (GCF) of 36 and 12-which is 12, then divide by the GCF. This gives you 3:1. The gear ratio for the bike is 3 teeth on the front socket for every 1 teeth on the rear socket (3:1).

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

The next step is;

Label the two intersection points

Step-by-step explanation:

To make a copy of an angle, the steps are;

1) Draw the rays of the original angle passing through the point B

2) Open the compass slightly and place the compass point on the vertices G where the two rays meet to draw an arc that intersect both rays

3) Label the point of intersection of both rays points C and D

4) With the compass still opened to the same width, move the compass to the point B on the line the angle is to be copied and draw a similar arc intersecting the ray at J

5) Open the compass to the width of C and D on the original angle and place the compass at point J to mark the arc on the copied angle location at M

6) Draw a line from B passing through M to complete the second ay of the copied angle.