Which equation can be used to solve for b? Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 30 degrees. The length of side B C is 8 feet, the length of B A is c, and the length of C A is b.

Answer:

[tex]n = 500e^{-4.1589x}[/tex]

Step-by-step explanation:

Using the exponential growth equation [tex]N(t) = N_0e^{-kt}[/tex] where;

N₀ is the initial population of the bacteria

N(t) is the population of the bacteria during time t

If a biologist puts an initial population of 500 bacteria into a growth plate, this means that N₀ = 500 at t = 0

[tex]N(t) = N_0e^{-kt}\\N(t) = 500e^{-k(0)}\\N(t) = 500e^0\\N(t) = 500[/tex]

If the population is expected to double every 4 hours, this means when t = 4, N₀  = 2(500) = 1000

[tex]N(t) = N_0e^{-kt}\\500 = 1000e^{-4k}\\\frac{500}{1000} = e^{-4k}\\0.5 = e^{-4k}\\ln(0.5) = lne^{-4k}\\ln(0.5) = -4k\\k = \frac{ln0.5}{-4} \\k = 0.1733[/tex]

The equation that will give the expected number of bacteria, n, after x days, can be gotten by substituting N(t) = n and t = x days = 24x hours

[tex]N(t) = N_0e^{-kt}\\n = N_0e^{-0.1733(24x)}\\n = 500e^{-4.1589x}[/tex]

Hence the equation that will give the expected number of bacteria, n, after x days is [tex]n = 500e^{-4.1589x}[/tex]

Answer:

-8

Step-by-step explanation:

Answer:

a = -4

a= -8

Step-by-step explanation:

[tex]a^2+12a=-32\\\\\mathrm{Add\:}32\mathrm{\:to\:both\:sides}\\a^2+12a+32=-32+32\\\\Simplify\\a^2+12a+32=0\\\\Solve\:by\:factoring\\\mathrm{Factor\:}a^2+12a+32:\quad \left(a+4\right)\left(a+8\right)\\\\\mathrm{Solve\:}\:a+4=0:\quad a=-4\\\mathrm{Solve\:}\:a+8=0:\quad a=-8\\\\a=-4,\:a=-8[/tex]

Answer: 9(3+2)

Step-by-step explanation:

The GCF of 27 and 18 is 9  because the factors of 27 are, 1,3,9 and 27 and the the factors of 18 are, 1,2,3,9 and 18.

The greatest factor that they both share is 9.

And 9 times three is 27 and 9 times 2 is 18.

Answer:

Step-by-step explanation:

[tex]-2x-14=7x+6\\\\\mathrm{Add\:}14\mathrm{\:to\:both\:sides}\\-2x-14+14=7x+6+14\\\\Simplify\\-2x=7x+20\\\\\mathrm{Subtract\:}7x\mathrm{\:from\:both\:sides}\\-2x-7x=7x+20-7x\\\\Simplify\\-9x=20\\\\\mathrm{Divide\:both\:sides\:by\:}-9\\\frac{-9x}{-9}=\frac{20}{-9}\\\\x=-\frac{20}{9}\\\left(\mathrm{Decimal}:\quad x=-2.22222\dots \right)\\x =-2.2[/tex]

Answer:

x = -2.2

Step-by-step explanation:

-2x - 14 = 7x + 6

-2x - 7x = 6 + 14

-9x = 20

x = 20/-9

x = -2.2222

x = -2.2   (nearest tenth)

  Check

-2*-2.2 - 14 = 7*-2.2 + 6

4.4 - 14 = -15.4 + 6 = -9.6

Answer:

3

Step-by-step explanation:

3 because 3 is a good number....lol

Answer:

4

Step-by-step explanation:

Answer:

[tex] \frac{3}{2} \: or \: 1.5 [/tex]

Step-by-step explanation:

[tex] \frac{12}{6 + 2} = \frac{12}{6 + 2} = \frac{12}{8} = \frac{6}{4} = \ \frac{3}{2} \: or \: 1.5[/tex]

Answer:

15

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

So we want to convert 59°F to Celsius using the given formula:

[tex]C=\frac{5}{9}(F-32)[/tex]

Thus, substitute F for 59:

[tex]C=\frac{5}{9}(59-32)[/tex]

Subtract:

[tex]C=\frac{5}{9}(27)\\[/tex]

Simplify:

[tex]C=\frac{135}{9}=15\textdegree F[/tex]

The answer is A

Answer:

[tex]\huge\boxed{15 \° C}[/tex]

Step-by-step explanation:

[tex]C = \frac{5}{9} ( F - 32)[/tex]

Where F = 59 °F

[tex]\sf C = \frac{5}{9} (59-32)\\C = \frac{5}{9} ( 27)\\C = 5 * 3\\C = 15 \ degrees \ Celsius[/tex]

Answer:

-15 meters

Step-by-step explanation:

If it goes up 50 meters from the ground, it will be 0+50 which is 50.

Then it says it drops 65 meters into an underground tunnel.  So at 50 meters, it dropped 65 meters.  That means you subtract this: 50-65, which equals -15 meters because 50 goes into 65 but there is still 15 left, so the 15 is negative.

The ground level is at 0.  And we just found out that the tunnel is at -15 meters.  To find out how many meters the tunnel is below the ground, just do 0-15, which is still -15 meters.   :)

Answer:

25

Step-by-step explanation:

Hello, please consider the following.

[tex]\text{Let's note the 7 digits } x_i \text{ for }i = 0,1,2,3,4,5,6\\\\\text{We can write 7 equations as below.}\\\\(1) \ x_0+x_1+x_2+x_3=16\\\\(2) \ x_1+x_2+x_3+x_4=16\\\\(3) \ x_2+x_3+x_4+x_5=16\\\\(4) \ x_3+x_4+x_5+x_6=16\\\\(5) \ x_0+x_1+x_2+x_3+x_4=19\\\\(6) \ x_1+x_2+x_3+x_4+x_5=19\\\\(7) \ x_2+x_3+x_4+x_5+x_6=19[/tex]

This is the translation in mathematical equations.

(5)-(1) gives [tex]x_4=19-16=3[/tex]

(6)-(2) gives [tex]x_5=19-16=3[/tex]

(7)-(3) gives [tex]x_6=19-16=3[/tex]

So, by using (1)

[tex]x_0+x_1+x_2+x_3+x_4+x_5+x_6=(x_0+x_1+x_2+x_3)+3+3+3=16+9=25[/tex]

Thank you

PS: If we go a little bit further it is not so hard to find that the number actually is 3337333

Answer: x=12

Step-by-step explanation:

Given

-10x-5=-125

Add 5 on both sides (addition property of equality)

-10x=-120

Divide -10 on both sides (division property of equality)

x=12

Hope this helps!! :)

Please let me know if you have any question

Answer: X=12

Step-by-step explanation:

Clear the X first to solve this problem

-10x - 5 = -125

125 - 5 = 10x

120/10 = x

12 = x

Answer:

2(x+4)

Step-by-step explanation:

Tom ate four more pieces of fruit than Janet. Sylvia ate twice as many pieces of fruit as Tom. If x represents the number of pieces of fruit that Janet ate, write an expression to represent the amount of fruit that Sylvia ate.

Janet: (X)

Tom: X+4

Sylvia: 2(X+4)

I started by making listing out who did what. Janet is stated as clearly X, so that's all we need for her.

The question says Tom ate four more pieces of fruit than Janet. This is simple addition since you're adding four to Janet's amount of fruit. Therefore this makes Tom's equation X+4.

Then Sylvia eats TWICE the amount as Tom. In simpler terms, she's doubling the amount of food Tom eats. Doubling something is simply multiplying it by two. Therefore, we take Tom's amount eaten, which we made into an equation in the paragraph before this one, and multiply it by two.

Placing parenthesis around Tom's equation means that that part is solved before its multiplied. We do this because we need to acknowledge that X+4 is its own equation that needs to be clarified/solved before being doubled. So, the answer is 2(X+4)

Answer:

[tex]k=5.2[/tex]

Step-by-step explanation:

So we have the equation:

[tex]9.3=k+4.1[/tex]

To solve for k, subtract 4.1 from both sides:

[tex](9.3)-4.1=(k+4.1)-4.1[/tex]

The right cancels. Simplify the left:

[tex]5.2=k\\k=5.2[/tex]

Thus, the value of k is 5.2

Answer:

[tex]\huge \boxed{k=5.2}[/tex]

Step-by-step explanation:

[tex]9.3=k+4.1[/tex]

Subtract 4.1 from both sides.

[tex]9.3-4.1=k+4.1-4.1[/tex]

[tex]5.2=k[/tex]

Step-by-step explanation:

(1 − cos x)(1 + cos x)

1 − cos²x

sin²x

Answer:

C. 14%

Step-by-step explanation:

We know that Dallas's wage increased from $9 to $10.25.

Let's say the percent increase is x. Then we write the expression:

9 + x * 9 = 10.25

Divide by 9 from both sides:

1 + x = 10.25 / 9 ≈ 1.14

Subtract 1 from both sides:

x = 1.14 - 1 = 0.14

Since x is a percent, that means x = k/100, where k is an integer. So we have:

x = k/100 = 0.14

Multiply both sides by 100:

k = 0.14 * 100 = 14%

The answer is thus C.

~ an aesthetics lover

Answer:

Step-by-step explanation:

[tex]Original\:price = \$9\\New\:price =\$10.25\\\\Increase = 10.25-9\\Increase = 1.25\\\\Increase \: \% = \frac{Increase}{Original \:price} \:\times 100\\\\= \frac{1.25}{9} \times 100\\\\= \frac{125}{9}\\ \\= 13.888\\= 14\%[/tex]

Answer:

Height of the triangle is 6 feet and base of the triangle is 4 feet.

Step-by-step explanation:

Area of a triangle is given by the formula,

Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

Let the height of triangle = h feet

Since, base of the triangle is 2 feet less than its height then base of the triangle = (h - 2) feet

Area = [tex]\frac{1}{2}h(h-2)[/tex]

[tex]12=\frac{1}{2}h(h-2)[/tex]

h² - 2h - 24 = 0

h² - 6h + 4h - 24 = 0

h(h - 6) + 4(h - 6) = 0

(h + 4)(h - 6) = 0

h = -4, 6 feet

Since height of the triangle can not be negative, therefore, height of the triangle = 6 feet.

And base of the triangle = (h - 2) = 6 - 2

                                         = 4 feet

Height of the triangle is 6 feet and base of the triangle is 4 feet.

Step-by-step explanation:

Number of apples = A

Number of boxes = B

Amount of apples in each box

[tex] =\frac{A}{B}\\

=\frac{200}{5}\\

= 40[/tex]

Answer:

Nocomplanar? Right because they’re not all in the same place?

Step-by-step explanation:

Answer:

width = 6 ft

Step-by-step explanation:

let  A = 24 3/5 = (24*5 +3)/5 = 123/5 ft^2 the area

l = 4 1/10 = (4*10 + 1)/10 = 41/10 ft the length

w = the width, w>0

since the area = length*width we have:

l*w = A

(41/10)*w = 123/5

by solving we find:

w = 6 ft

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

(3,0)

Step-by-step explanation:

Co-ordinates of J =(4,3)

Co-ordinates of K = (2,-3)

Midpoint formula :

 = [tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1} +y_{2} }{2} \\ \frac{4+2}{2} ,\frac{3+(-3)}{2}\\\frac{6}{2},\frac{3-3}{2}\\3, 0[/tex]

Coordinates of the midpoint M (3,0)

The coordinates of the midpoint M is (3,0) and the distance between J(4,3) and K(2,-3) is 6.32 units.

The distance between two points of the xy-plane can be found using the distance formula. The distance formula is:

√[(x₂ - x₁)² + (y₂ - y₁)²].

Now given coordinates of two points are,

J(4,3) and K(2,-3)

Therefore we have,

x₁ = 4

y₁ = 3

x₂ = 2

y₂ = -3

To find the midpoint between J and K we have,

{[(x₁+x₂ )/2] , [(y₁+y₂ )/2]}

Put the values, we get

{[(4+2)/2] , [(3+(-3)/2]}

solving them,

{(6/2) ,(0/2)}

or,

(3,0)

which is the required midpoint M.

Now distance between J(4,3) and K(2,-3) = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 4)² + (-3 - 3)²]

= √[(- 2)² + (-6)²]

= √4 +36

= √40

= 6.32 units

Thus, the coordinates of the midpoint M is (3,0) and the distance between J(4,3) and K(2,-3) is 6.32 units.

To learn more about midpoints :

https://brainly.com/question/15192654

#SPJ2

Answer:

3.64 hr, or 3 hr 38 min

Step-by-step explanation:

Recall that distance = (rate)(time).  Thus,

time = (distance) / (rate)

Here we have:

time = (200 km) / (55 km/hr) = 3.64 hr, or 3 hr 38 min

Answer:

I will answer in English:

We first have a rational number, the quotient between 2 positive integer numbers is 0.57....

And we want to find which number we should add in order to get 1.

Then we have:

A/B = 0.5757...

So if we have:

x = 0.5757....

we have two periodic decimals, then we multiply by 100 (the number of zeros is equal to the number of periodic decimals)

100*x = 57.575757

Now we subtract the original number:

100*x - x = 99*x = 57.575757... - 0.5757 = 57.

Then we have:

99*0.5757... = 57

0.575757... = 57/99

Now that we know the original fraction, if we want to find a fraction such that:

0.57... + a/b = 1

57/99 + a/b = 1

we should use the same denominator in both fractions:

b = 99

57/99 + a/99 = 1

57 + a = 99

a = 99 - 57 = 42

Then the fraction is 42/99

Answer:

7

Step-by-step explanation:

A line segment partitioned by a ratio of 3:4 can be thought of as having 7 congruent sections

According to the ratio in which it is partitioned, the line segment can be thought as having 7 congruent sections.

If it can be divided into a ratio of a:b, it can be partitioned into a + b congruent segments.

In this problem, it has a ratio of 3:4, hence, the line segment can be thought as having 7 congruent sections.

More can be learned about line segments at https://brainly.com/question/4854238

Answer:

Step-by-step explanation:

[tex]\begin{bmatrix}2x-y=0\\ x+3y=-14\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:2x-y=0:\quad x=\frac{y}{2}\\\\\mathrm{Subsititute\:}x=\frac{y}{2}\\\\\begin{bmatrix}\frac{y}{2}+3y=-14\end{bmatrix}\\\\\mathrm{Simplify}\\\\\begin{bmatrix}\frac{7y}{2}=-14\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:\frac{7y}{2}=-14:\quad y=-4\\\\\mathrm{For\:}x=\frac{y}{2}\\\\\mathrm{Subsititute\:}y=-4\\x=\frac{-4}{2}\\\\\frac{-4}{2}=-2\\\\x=-2,\:y=-4[/tex]

Answer:

(-2,-4)

Step-by-step explanation:

2x-y=0

-2(x+3y=-14)

-2x-6y=28

x terms cancel

-y+-12y=-13y

0+28=28

-7y=28

28/-7

y=-4

plug into the orginal equation

2x-(-4)=0

simply: 2x+4=0

elimante the 4

2x=-4

divide by 2

x=-2

Answer:

3/6

Step-by-step explanation:

A coin has 2 sides

3 coins = 6 sides

3 heads 3 tails

3 chances out of 6 to get heads

3 chances out of 6 to get tails

3/6 for both

Answer: True

Step-by-step explanation: both equal 7

Answer:

Step-by-step explanation:

x  - total of population

35%x - women

1560 - men

35%x + 1560 = x

0.35x + 1560 = x

1560 = x - 0.35x

0.65x  =  1560

÷0.65     ÷0.65

x = 2400

Answer:

the answwr is C. the sum is zero