Solve the system of equations using the substitution method.
4x + 5y = 7
y= 3x + 9
​

The expression that gives the number of bacteria after 3 hours is

500 x  1.2³.

Given,

The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour.

There were initially 500 bacteria.

We need to find an expression that gives the number of bacteria after 3 hours.

Suppose we have a number 3 that gets multiplied by 2 every 1 minute.

So in 3 minutes, we have,

3 x 2 = 6

6 x 2 = 12

12 x 2 = 24

We see that we need to multiply the previous answer by the required factor till the required number of times.

We have,

The initial number of bacteria = 500

The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour.

This means the number of bacteria after one hour:

= 500 x 1.2

= 600 bacteria

After two hours,

= 600 x 1.2

= 720 bacteria

After 3 hours

= 720 x 1.2

= 864 bacteria

The expression that gives the number of bacteria is 500 x [tex]1.2^{h}[/tex] where h is the number of hours.

Learn more about how to write expressions where the amount gets multiplied per hour here:

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The number of bacteria after 3 hours, given an initial count of 500 and a growth factor of 1.2 per hour, can be calculated as 500 × 1.2^3, resulting in 864 bacteria.

The number of bacteria in a petri dish growing exponentially can be modeled mathematically. If the number of bacteria is multiplied by a factor of 1.2 every hour, and we began with 500 bacteria, the expression for the number of bacteria after 3 hours can be found using exponential growth formula.

To find the number of bacteria after 3 hours, we would start with the initial amount of 500 bacteria and multiply it by 1.2 for each hour that passes. Therefore, after 3 hours, the expression would be:

Number of bacteria after 3 hours = Initial number × (growth factor)number of hours = 500 × 1.23

Using a calculator, we can compute this to find:

500 × 1.23 = 500 × 1.728 = 864

Thus, there would be 864 bacteria in the petri dish after 3 hours.

ln z + ln 7 = ln 63

When adding two logarithms of the same base, you can combine them into a single logarithm where the input is the product of both previous inputs

ln 7z = ln 63

Take the exponential of e to both sides

7z = 63

Divide both sides by 7

z = 9

Let me know if you need any clarifications, thanks!

Answer: OPTION A.

Step-by-step explanation:

Let be "e" the number of tickets that the radio station gave away to employees and "l" the number of tickets that the radio station gave away to listeners.

Based on the data given in the exercise, you can set up the following System of equations:

[tex]\left \{ {{e+l=192 } \atop {l=5e}} \right.[/tex]

Finally you must apply the Substitution Method to solve the System of equations.

To apply it, you must substitute the second equation into the first one and then you must for the variable "e".

Through this precedure you get the following value of "e":

[tex]e+l=192\\\\e+(5e)=192\\\\6e=192\\\\e=\frac{192}{6}\\\\e=32[/tex]

Answer:

4.

a)  [tex]4x^4-4x^3-16x^2+16x[/tex]

b)  [tex]4x^4-4x^3-16x^2+16x[/tex]

5. Yes

Step-by-step explanation:

The distributive property is:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

It can be extended to a lot of terms as well.

We will use this to multiply both of the probelms shown.

4 a)

[tex](4x^2-4x)(x^2-4)=(4x^2)(x^2)-(4)(4x^2)-(4x)(x^2)+(4x)(4)=4x^4-16x^2-4x^3+16x=4x^4-4x^3-16x^2+16x[/tex]

The answer is [tex]4x^4-4x^3-16x^2+16x[/tex]

4 b)

[tex](x^2+x-2)(4x^2-8x)=(x^2)(4x^2)-(8x)(x^2)+(x)(4x^2)-(8x)(x)-(2)(4x^2)+(2)(8x)=4x^4-8x^3+4x^3-8x^2-8x^2+16x=4x^4-4x^3-16x^2+16x[/tex]

The answer is  [tex]4x^4-4x^3-16x^2+16x[/tex]

5. Yes

Answer:

r ≥ 5

The solution includes all the numbers greater than or equal to 5.

Step-by-step explanation:

We are given an inequality and we have to solve that inequality and mark it on a graph.

The given inequality is

-1 + r ≥ 4

This is a rather simple inequality and we just need to rearrange it to get the answer.

Rearranging, we get

r ≥ 5

This represents all the numbers in the number line which are greater than 5.

This means r can take all the values greater than 5 but not which are less than 5.

Step-by-step explanation:

[tex]3\log x+\log2=\log3x-\log2\\\\\text{Domain:}\ x>0\\\\\text{Use}\\\\\log_ab^c=c\log_ab\\\\\log_ab+\log_ac=\log_a(bc)\\\\\log_ab-\log_ac=\log_a\left(\dfrac{b}{c}\right)\\===================\\\log x^3+\log2=\log\left(\dfrac{3x}{2}\right)\\\\\log(2x^3)=\log\left(\dfrac{3}{2}x\right)\iff2x^3=\dfrac{3}{2}x\qquad\text{subtract}\ \dfrac{3}{2}x\ \text{from both sides}\\\\2x^3-\dfrac{3}{2}x=0\qquad\text{multiply both sides by 2}\\\\4x^3-3x=0\qquad\text{use distributive property}\\\\x(4x^2-3)=0\iff x=0\ \vee\ 4x^2-3=0[/tex]

[tex]x=0\notin\ \text{Domain}\\\\4x^2-3=0\qquad\text{add 3 to both sides}\\\\4x^2=3\qquad\text{divide both sides by 4}\\\\x^2=\dfrac{3}{4}\Rightarrow x=\pm\sqrt{\dfrac{3}{4}}\\\\x=\pm\dfrac{\sqrt3}{\sqrt4}\\\\x=-\dfrac{\sqrt3}{2}\notin \text{Domain}\\\\\boxed{x=\dfrac{\sqrt3}{2}}\in \text{Domain}[/tex]

The equivalent equation to 3logx + log2 = log3x - log2 is x² = 3/4, which is derived by applying properties of logarithms such as combining log terms and setting the resulting expressions equal to each other.

The equation 3logx + log2 = log3x - log2 can be simplified using the properties of logarithms. To find the equivalent equation, we use the property that log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b). Applying these properties:

The equivalent equation is x² = 3/4 or x = ±√(3/4), provided that x ≠ 0 since the logarithm of zero is undefined.

Answer:

-4x^9-12x^4+2x^3-7x+8

Answer:

=−4x9−12x4+2x3−7x+8

Step-by-step explanation:

Distribute the Negative Sign:

=2−4x9+3x3+−1(7x+x3−6+12x4)

=2+−4x9+3x3+−1(7x)+−1x3+(−1)(−6)+−1(12x4)

=2+−4x9+3x3+−7x+−x3+6+−12x4

Combine Like Terms:

=2+−4x9+3x3+−7x+−x3+6+−12x4

=(−4x9)+(−12x4)+(3x3+−x3)+(−7x)+(2+6)

=−4x9+−12x4+2x3+−7x+8

Answer:

Lisa = 7 hours and 15 minutes

Naila = 10 hours and 45 minutes

Step-by-step explanation:

Naila = N

Lisa = L

Naila worked:

N = 3.5 + L

In total, they worked:

N + L = 18

Lisa worked:

L = h

Substitute values into the total equation

3.5 + L  + L = 18

Solve

2L = 14.5

L = 7.25 = 7 hours and 15 minutes

N = 7.25 + 3.5 = 10.75 = 10 hours and 45 minutes

Hope this helps :)

Answer:

The line which is parallel to the given line [tex]y=-\frac{\bf 4}{\bf 3}x+{\bf 1}[/tex] is [tex]y=-\frac{\bf 4}{\bf 3}x+{\bf 2}[/tex]

Step-by-step explanation:

Given that the equation of the line is

[tex]y=-\frac{4}{3}x+1\hfill (1)[/tex]

To find the equation of the line is parallel to the given line equation.

We know that the given equation is in the slope intercept form

y=mx+c where m is the slope and c is the intercept.

Compare with given equation(1) we get

[tex]m=-\frac{4}{3}[/tex]  and c=1

Now change the y intercept c=1 to a intercept of c= 2

Therefore (1) becomes

[tex]y=-\frac{4}{3}x+2[/tex]

The above equation of the line is the parallel line to the given equation of the line

Answer:

3x - 4y = -28

Step-by-step explanation:

Answer:

Step-by-step explanation:

7 + 3 + 5 + 15 = 30

Answer:

Step-by-step explaination:

I would try to help u but im not big brain and i really need the points

Answer:

y = 242.4 ft

Step-by-step explanation:

Since the lines are parallel then the angle at the right side of the triangle is 29° ( adjacent angles are congruent )

Using the sine ratio in the right triangle

sin29° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{500}[/tex]

Multiply both sides by 500

500 × sin29° = y, thus

y = 242.4 ft ( to the nearest tenth )

Answer:

4 miles

Step-by-step explanation:

Walking:

Distance  = d miles

Rate = 4 mph

Time = t hours

[tex]d=4\cdot t[/tex]

Biking:

Distance = d miles

Rate = 10 mph

Time [tex]=t-\dfrac{18}{60}=t-0.3[/tex] hours (convert minutes to hours)

[tex]d=10\cdot (t-0.3)[/tex]

Hence,

[tex]4t=10(t-0.3)\\ \\4t=10t-3\\ \\4t-10t=-3\\ \\-6t =-3\\ \\6t=3\\ \\t=\dfrac{3}{6}=\dfrac{1}{2}=0.5\ hour[/tex]

Therefore, the distance to friend's house is

[tex]d=4\cdot 0.5=2\ miles[/tex]

and the total distance of the round trip is

[tex]2+2=4\ miles[/tex]

Answer:

[tex]\angle CST,\angle TSC[/tex]

Step-by-step explanation:

we know that

You can name a specific angle by using the vertex point, and a point on each of the angle's rays. The name of the angle is simply the three letters representing those points, with the vertex point listed in the middle

In this problem

The vertex point is S and the points on each of the angle's rays are C and T

so

[tex]\angle z=\angle CST=\angle TSC[/tex]

therefore

[tex]\angle CST,\angle TSC[/tex]

Answer:

Step-by-step explanation:

Incomplete question.

If the boy has 10, and his sister has 2 1/2 times as many as him, you would first multiply 10 times 2 to get 20. After that you would automatically 1/2 of 10 is 5, which would bring you to the conclusion that his sister has 25 cookies. Thus, you answer is 25 cookies.

Answer:

25

Step-by-step explanation:

10×2.5=25

and heres some other random stuff so brainly will let me tell you this

Answer:

A)  The equation has no solution

B ) The equation has one solution

C ) The solution of equation is 1

D ) The solution of equation is 20

E ) The solution of inequality is  x [tex]<[/tex] 8

Step-by-step explanation:

Given as :

A ) The equation is written as

5 ( x - 9 ) = 5 x

So, solving the equation

i. e  5 x - 5 × 9 = 5 x

or, , (5 x - 5 x) - 45 = 0

or, (0) - 45 = 0

∵ The equation do not have any variable terms

So, the equation has no solution

B) The equation is written as

- 2 ( x - 1 ) = 2 x - 2

So, solving the equation

i.e - 2 x + 2 = 2 x - 2

or, ( - 2 x - 2 x ) = - 2 - 2

or, - 4 x = - 4

∴ x = [tex]\dfrac{-4}{-4}[/tex]

I.e x = 1

So, The equation has one solution

C) The equation is written as

3 x + 6 = 9

So, solving the equation

I.e 3 x = 9 - 6

or, 3 x = 3

∴ x = [tex]\dfrac{3}{3}[/tex]

I.e x = 1

So, The solution of equation is 1

D) The equation is written as

[tex]\dfrac{x}{4}[/tex] - 1 = 4

Or, [tex]\dfrac{x}{4}[/tex] = 1 + 4

or, [tex]\dfrac{x}{4}[/tex] = 5

∴ x = 5 × 4

I.e x = 20

So, The solution of equation is 20

E) The equation of inequality is written as

9 x [tex]<[/tex] 72

Or, x [tex]<[/tex] [tex]\dfrac{72}{9}[/tex]

∴  x [tex]<[/tex] 8

So, The solution of inequality is  x [tex]<[/tex] 8

Hence , A)  The equation has no solution

B ) The equation has one solution

C ) The solution of equation is 1

D ) The solution of equation is 20

E ) The solution of inequality is  x [tex]<[/tex] 8

Answer

Answer:

y = 0, 3

Step-by-step explanation:

1) Add 1 to both sides.

4 ∣ 2y −3 ∣ = 11 + 1

2) Simplify 11+1 to 12.

4 ∣ 2y − 3∣ = 12

3) Divide both sides by 4.

∣ 2y − 3∣ =​​ 12 / 4

4) Simplify 12/4 to 3.

∣ 2y − 3 ∣ = 3

5) Break down the problem into these 2 equations.

2y − 3  = 3

-(2y - 3 ) - 3

6) Solve the 1st equation: 2y − 3  = 3

y = 3

7) Solve the 2nd equation: -(2y - 3 ) - 3

y = 0

8) Collect all solutions.

y = 0, 3

Answer:

The maximum value of P is 34 and the minimum value of P is 0

Step-by-step explanation:

we have the following constraints

[tex]x+y \leq 6[/tex] ----> constraint A

[tex]2x+3y \leq 16[/tex] ----> constraint B

[tex]x\geq 0[/tex] ----> constraint C

[tex]y\geq 0[/tex] ----> constraint D

Solve the feasible region by graphing

Using a graphing tool

The vertices of the feasible region are

(0,0),(0,5.33),(2,4),(6,0)

see the  attached figure

To find out the maximum and minimum value of the objective function P, substitute the value of x and the value of y for each of the vertices in the objective function P, and then compare the results

we have

[tex]P=5x+6y[/tex]

For (0,0) ----> [tex]P=5(0)+6(0)=0[/tex]

For (0,5.33) ----> [tex]P=5(0)+6(5.33)=31.98[/tex]

For (2,4) ----> [tex]P=5(2)+6(4)=34[/tex]

For (6,0) ----> [tex]P=5(6)+6(0)=30[/tex]

therefore

The maximum value of P is 34 and the minimum value of P is 0

0+6/10+2/100+4/100

Hope this helped! (plz mark me brainliest)

Answer: B, D, E

Step-by-step explanation:

Using function concepts, it is found that the correct options are:

--------------------------------

A similar problem is given at https://brainly.com/question/13421430

Answer:

Step-by-step explanation:

Here, the "whole number" is the portion of the number to the left of the decimal point: 593.

The "remainder" is the portion left after the whole number is subtracted: 0.5625.

Answer:

B and D

Step-by-step explanation:

2 divided by 1

1                     3

Keep Change Flip

2 *  3   =   6

1      1

3/4 divided by 2/3= 1 1/8

Answer:

Step-by-step explanation:

[tex]\dfrac{a}{b}\times c=\dfrac{a\times c}{b}\\\\a\times\dfrac{b}{c}=\dfrac{a\times b}{c}\\\\\dfrac{a}{b}:c=\dfrac{a}{b}\times\dfrac{1}{c}=\dfrac{a}{b\times c}\\\\a:\dfrac{b}{c}=a\times\dfrac{c}{b}=\dfrac{a\times c}{b}\\\\\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{a\times c}{b\times d}\\\\\dfrac{a}{b}:\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}=\dfrac{a\times d}{b\times c}\\\\============================[/tex]

[tex]\bold{A}\\\\\dfrac{1}{3}\times2=\dfrac{1\times2}{3}=\dfrac{2}{3}<1\\\\\bold{B}\\\\2:\dfrac{1}{3}=2\times\dfrac{3}{1}=2\times3=6>1\\\\\bold{C}\\\\\dfrac{1}{4}\times\dfrac{2}{3}=\dfrac{1\times2}{4\times3}=\dfrac{2}{12}<1\\\\\bold{D}\\\\\dfrac{3}{4}:\dfrac{2}{3}=\dfrac{3}{4}\times\dfrac{3}{2}=\dfrac{3\times3}{4\times2}=\dfrac{9}{8}=1\dfrac{1}{8}>1\\\\\bold{E}\\\\\dfrac{2}{3}\times\dfrac{3}{4}=\dfrac{2\times3}{3\times4}=\dfrac{6}{12}<1\\\\\bold{F}\\\\\dfrac{2}{3}:\dfrac{3}{4}=\dfrac{2}{3}\times\dfrac{4}{3}=\dfrac{2\times4}{3\times3}=\dfrac{8}{9}<1[/tex]

Answer:

The solution is that there are 26 students in her class

Step-by-step explanation:

We know that 15 of her student are girls, and since there are more girls than boys in the class, there can at most be 15+14= 29 students in her class.

We need to find a number x between 16 (in the case where there is only one boy in the class) and 29, for which x/4 gives a remainder of 2, and x/5 gives a remainder of 1.

The numbers between 16 and 29, which when divided by 4 gives a remainder of 2 are:

18, 22, and 26

You can check yourself that these give a remainder of 2.

So it is one of these numbers. But the solution must also fulfill that the number divided by 5 gives a remainder of 1.

18/5 = 15 + remainder=3

22/5 = 4 + remainder=2

26/5 = 5 + remainder=1

Thus the only possible solution is 26.

To find the total number of students, we can use modular arithmetic and the Chinese Remainder Theorem. The number of students is 40k + 27, where 'k' is an integer.

To solve this problem, we can use the concept of modular arithmetic. Let's assume the number of students as 'x'. We are given that when the students are divided into groups of 4, there are 2 students left over. This can be written as x % 4 = 2. Similarly, when the students are divided into groups of 5, there is 1 student left over, which can be written as x % 5 = 1.

To find the value of 'x', we can solve these congruences simultaneously. One way to solve this is by brute force by trying different values of 'x'. However, a more efficient approach is to use the Chinese Remainder Theorem. By solving the congruences, we get x ≡ 21 (mod 20). This means that the number of students can be expressed as x = 20k + 21, where 'k' is an integer.

Since we are given that there are 15 girls and more girls than boys, we can say that the number of boys is 'x - 15'. Substituting the value of 'x' from the previous equation, we get the number of boys as 20k + 21 - 15 = 20k + 6. Therefore, the total number of students is 20k + 21 + 20k + 6 = 40k + 27.

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Answer:

A. h(x)= -5.86x^2 + 23.37x + 34

Step-by-step explanation:

If the scientist uses the same amount of pesticide on the two farms then the x's of the functions are the same.

Then, the combined yield [tex]h(x)[/tex] of the two farms is just the yield of the first farm plus the yield of the second farm:

[tex]h(x)=f(x)+g(x)[/tex].

Now, since

[tex]f(x)= -2.43x^2+10.37x+9[/tex]

and

[tex]g(x)= -3.43x^2+13x+25[/tex],

then

[tex]h(x)= (-2.43x^2+10.37x+9)+(-3.43x^2+13x+25)[/tex]

we add the coefficients of the  corresponding terms to get:

[tex]h(x)= (-2.43x^2-3.43x^2)+(10.37x+13x)+(9+25)[/tex]

[tex]\boxed {h(x)=-5.86 x^2 + 23.37 x + 34.}[/tex]

Which is choice A.

The question is missing the figure. So, the figure is attached below.

Answer:

The area of the base of the pyramid is 36 square inches.

Step-by-step explanation:

Given:

Volume of the pyramid is, [tex]V=108\ in^3[/tex]

The height of the pyramid is, [tex]h=9\ in[/tex]

Let the area of the base be 'A'.

So, the volume of the pyramid is given as:

[tex]V=\frac{1}{3}Ah[/tex]

Rewrite the given formula in terms of 'A'. This gives,

[tex]A=\frac{3V}{h}[/tex]

Now, plug in 108 for 'V', 9 for 'h' and solve for 'A'. This gives,

[tex]A=\frac{3\times 108}{9}\\\\A=3\times 12\\\\A=36\ in^2[/tex]

Therefore, the area of the base of the pyramid is 36 square inches.

Answer:

use photomath

Step-by-step explanation:

the variable qould b and aStep-by-step explanation:

Check the picture below.

Final answer:

To solve the multiplication problem 3/4 × 8/9, multiply the numerators and denominators, then simplify the fraction.

Explanation:

To solve the multiplication problem 3/4 × 8/9, we multiply the numerators (3 × 8) to get 24, and multiply the denominators (4 × 9) to get 36. So the result of the multiplication is 24/36. To simplify the fraction, we find the greatest common divisor of 24 and 36, which is 12. Dividing both the numerator and denominator by 12, we get 2/3. Therefore, the answer to the problem is 2/3.

Answer:

y = 1x + 2

please mark me as brainliest, thank you and have a good day!

Answer:

y = 5/8x + 9/4

but it can be

y=5/8x+6

or

y=5/8x+1

Explaination:

but there can be other solutions

First let's find the slope (5/8(

(-2,1) and (6,6)

let plug those numbers in

[tex]\frac{6-1}{6-(-2)}[/tex]

which becomes

[tex]\frac{5}{8}[/tex]

that's your slope, plug that into the slop-intercept equation

y = mx + b tp y = 5/8x + b

b can be either y-values (1 or 6) but 9/4 is also an answer