Guang and Orion are doing an experiment in school for which they need to measure the density of a bacteria population after a certain solution has been introduced. Guang reports a density of 450045004500 bacteria per square centimeter and Orion reports a density of 505050 bacteria per square millimeter.

Answer:

The correct answer is h = 3.

Step-by-step explanation:

To solve this problem, we should first use the distributive property on the left side of the equation.  This means that we can multiply each of the terms inside the parentheses by -2 (be careful that you distribute the negative as well).  This is modeled below:

5h - 2(11 - h) = h - 4

5h - 22 + 2h = h - 4

Next, we can combine like terms on the left side of the equation.

7h - 22 = h - 4

Now, we can subtract h from both sides of the equation to move all of the variable terms to the left side of the equation.

6h - 22 = - 4

Next, we can add 22 to both sides of the equation to isolate the variable term on the left side of the equation.

6h = 18

Finally, we can divide both sides by 6 in order to get the variable completely isolated.

h = 3

Therefore, the correct answer is h = 3.

Hope this helps!

Answer:

r = 5 cm

Step-by-step explanation:

A = πr²

78.53 = (3.14)r²

divide by 3.14

25 = r²

r = ±5

r = 5

Your question has been heard loud and clear.

Slope formula when two points are given= y2-y1/x2-x1

Here y2= 2

X2=2

Y1= -4

X1= -1

= 2-(-4)/2-(-1)= 2

Slope of line= 2

Thank you.

Answer:

[tex]\huge \boxed{\mathrm{B. \ 2}}[/tex]

Step-by-step explanation:

The line crosses two points.

The two points are (-1, -4) and (2, 2).

The slope of a line can be found through two points.

[tex]\displaystyle \sf slope = \frac{rise}{run}[/tex]

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]y_2=2 \\ y_1 = -4 \\ x_2=2 \\ x_1=-1[/tex]

Plug in the values and evaluate.

[tex]\displaystyle m=\frac{2-(-4)}{2-(-1)}[/tex]

[tex]\displaystyle m=\frac{2+4}{2+1}[/tex]

[tex]\displaystyle m=\frac{6}{3}[/tex]

[tex]m=2[/tex]

The slope of the line is 2.

Answer:

12

Step-by-step explanation:

We are given the expression:

[tex]\frac{5z+x^2}{x}[/tex]

and asked to evaluate when x= 5 and z=7. Therefore, we must substitute 5 for x and z for 7.

[tex]\frac{(5(7)+(5)^2)}{5}[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

First, evaluate the exponent.

(5)²= 5*5= 25

[tex]\frac{(5(7)+25)}{5}[/tex]

Next, multiply 5 and 7.

5*7=35

[tex]\frac{(35+25)}{5}[/tex]

Next, add 35 and 25.

25+25=60

[tex]\frac{60}{5}[/tex]

Finally, divide 60 by 5.

[tex]12[/tex]

The expression (5z+x²)/x when x=5 and z=7 is 12.

Answer:

B

Given equation: [tex]x^2 = -8x -7[/tex]

To solve the quadratic equation, we will need to set one side of the equation equal to 0. This can be done by subtracting x² on both sides.

[tex]\implies x^2 - x^2= -8x -7 - x^2[/tex]

[tex]\implies 0= -8x -7 - x^2[/tex]

To further simplify, we can factor -1 from the expression on the R.H.S. Then, we can cancel the -1 since there is a 0 on the other side.

[tex]\implies 0= -1(8x + 7 + x^2)[/tex]

[tex]\implies 0= 8x + 7 + x^2 = x^2 + 8x + 7[/tex]

Finally, factor the expression on the right hand side.

Factoring a quadratic equation can be done in 2 ways.

In this method, we split the middle term into two suitable terms. The suitable terms must follow two conditions.

Then, we factor the first two terms of the expression and the last two terms of the expression. Eventually, we will get a common expression. So, we can further factorize to get a product of two expressions.

In this method, we will compare our equation with the standard form equation to determine the a, b, and c variables. Then, we plug the variables into the formula and simplify to get the roots (solutions).

[tex]\text{Quadratic Formula:} \ \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]

We can use any method to solve for the roots. First, let us check whether the middle term could be split into two suitable terms such that those terms could meet the criteria stated above.

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We can see that 8x is the middle term and it can be split into the sum of 7x and x. The product of the (middle term) coefficients is 7. The product of the coefficients (first and last terms) is also 7. Since both products match, we can use the splitting method to factorize the expression.

[tex]\implies 0= x^2 + 8x+ 7[/tex]

[tex]\implies 0= x^2 + x + 7x+ 7[/tex]

Now, factor the first two terms and the last two terms separately.

[tex]\implies 0= x^2 + x + 7x+ 7[/tex]

[tex]\implies 0= x(x + 1) + 7(x+ 1)[/tex]

We can see a common expression. Finally, let us factor the common expression to get a product of two expressions.

[tex]\implies 0= (x + 7)(x + 1)[/tex]

Since the factorized expression equals to 0, we can set each expression (inside the parentheses) equal to 0.

[tex]\implies x + 7 = 0; x + 1 = 0[/tex]

[tex]\implies x = -7; x = -1[/tex]

Now, let us try to solve using the Quadratic formula.

[tex]0= x^2 + 8x+ 7[/tex]

Tip: Standard form: 0 = ax² + bx + c

Comparing both equations will allow us to determine the a, b, c variables.

⇒ a = 1; b = 8; c = 7

Now, let us plug these values into the quadratic formula and simplify.

[tex]\implies \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]

[tex]\implies \dfrac{-8\ \± \sqrt{8^{2} - 4(1)(7)} }{2(1)}[/tex]

[tex]\implies \dfrac{-8\ \± \sqrt{64 - 28} }{2}[/tex]

[tex]\implies \dfrac{-8\ \± \sqrt{36}}{2} = \dfrac{-8\± 6}{2} = \dfrac{-8 + 6}{2},\ \dfrac{-8 - 6}{2} = \dfrac{-2}{2} ,\ \dfrac{-14}{2} = -1 , -7 \ \text{(B)}[/tex]

Therefore, in both methods, the answer is -1, -7 (B).

Learn more about quadratic formula: brainly.com/question/22364785

Learn more about splitting method: brainly.com/question/13874704

Answer:

14

Step-by-step explanation:

(multiply 2by7)

2×7

=14

Answer:

24 1/2

Step-by-step explanation:

Every 1/2 is 2 gallons.

1/2 x 2 gallons = 4 gallons.

The whole number in 6 1/2 is 6.

1 x 6 = 6.

Now, we multiply 6 by 4 because each 1 = 4 gallons.

6 x 4 = 24.

There is still an 1/2 left in 6 1/2.

You add that.

Your answer is 24 1/2.

Hope this helps you!

She paid $640 for the painting

Step-by-step explanation:

her selling price SP = 800

CP+25%of CP = 800

1.25CP=800

CP=640

Answer:

$640

Step-by-step explanation:

paint sold for $800

profit 25%

the price she paid for the painting = $800 / 1.25 = $640

Answer:

(A) 139°

Step-by-step explanation:

What we are trying to find here is the distance between -27 and 112.

To do this, we have to think of it as a number line.

The distance from -27 to 0 is 27 units, and the distance from 0 to 112 is 112 units.

So the total distance is [tex]112+27=139[/tex]

Hope this helped!

idek

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Answer:

The correct unit price can be calculated by dividing the total price paid by 84 that was the number of pairs of padded work gloves that were bought:

$102.48/84=$1.22

The correct unit price is $1.22.

-The error is that the person calculated the unit price by dividing the total price paid by 7 but the statement indicates that the contractor purchased 7 dozen pairs, which means: 7*12= 84. According to this, the contractor purchased 84 pairs of padded work gloves.

Answer:

l = 15 and w = 25

Step-by-step explanation:

[tex]l - w = - 10[/tex]

[tex]l + w = 40[/tex]

Adding both equations

[tex]2l = 30[/tex]

[tex]l = 15[/tex]

subtracting both equation

[tex]2w = 50[/tex]

[tex]w = 25[/tex]

Hope it helps..........

BRAINLIEST PLEASE

Answer:

Length=30 Width=10

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

plug in numbers to get 3+6

add them

boom

Answer:

D. 9

Step-by-step explanation:

Plug in 3 as x and -2 as y in the expression:

x - 3y

3 - 3(-2)

3 + 6

= 9

Answer:

Step-by-step explanation:

Given initial population of animals = 300 animals

If the population increases by 23% annualy, yearly increment will be expressed as:

Yearly increment = 23% of 300

Yearly increment = 0.23*300

Yearly increment for = 69

Let the total number of years of be x

Increment after x years = 69x

Increase in population of animals after x years with an annual rate of 23% = Initial population + Increment after x years

= 300 + 69x

Hence, the equation represents a population of 300 animals at the increase and an annual rate of 23% is expressed as 300 + 69x

please help me with my homework

Answer:

After 6 minutes, the oven temperature will be: [tex]125^o[/tex]

Step-by-step explanation:

If the increase in temperature is [tex]10^o[/tex] per minute, then in 6 minutes, the increase in temperature would be [tex]6\,*\,10^o=60^o[/tex], therefore, since the initial temperature of the oven was [tex]65^o[/tex], its temperature after 6 minutes would be:

[tex]65^o+60^o=125^o[/tex]

Answer:

-3

Step-by-step explanation:

3-x if x=6

3-6

-3

Hope this helps ;) ❤❤❤

Answer: -3

Step-by-step explanation: In this case, we are given that x = 6.

So we have 3 - 6 which is -3.

(-6,2)

Inbox me on fb for more help with math same name as my brainly

Answer:

(-6,2)

Step-by-step explanation:

Answer:

36, 29, 22, 15, 8

Step-by-step explanation:

Step 1: State known information

First difference is -7

Third term of the sequence is 22

Step 2: Find first 5 terms

You just need to add and subtract 7 to 22 and the answer 5 times

1. 36 +7

2. 29 +7

3. 22 <- We know 22 is the 3rd term

4. 15 -7

5. 8 -7

Therefore the first 5 terms of the sequence is 36, 29, 22, 15, 8

Answer:

i believe the answer is A

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

you can just plug this into a calculator.

OR you could take -3+1 and get -2 and then subtract that from 2 (-3+1=2) and then you get -4

Answer:

-4

Step-by-step explanation:

-3 + (+1)= -2

2(-3 + (+1)) = -4

Answer: find the answer in the explanation

Step-by-step explanation:

Given the function and its parent function, to describe the

transformation of g(x) = 1/3x^2

First sketch the graph of the parent function which is g(x) = x^2

For every value of x, g(x) will take the value it would have had at kx, that is, the graph of g(x) = x^2 is stretched by a factor of 1/3 in the x - direction.

Find the attached files for the graph and solution

Greetings from Brasil...

According to the statement, one figure is scaled in relation to another, so we can apply similarity to polygons.....

So

BIG/small = BIG/small

or

small/BIG = small/BIG

27/X = 45/35

OR

35/45 = X/27

27/X = 45/35

45X = 27·35

45X = 945

X = 945/45

Answer:

The expression is missing in the question.

The expression is 4x +450

The variable is x and the coefficient is 4

Step-by-step explanation:

In an expression, a variable is a quantity which is not fixed value and can be of any arbitrary value. A variable is the unknown in the expression. In any expression, the variable are represented by alphabets such as a, b, c, x, y or z etc.

The numeric quantity which lies in the front of a variable is known as a coefficient. It can be any numeric values. For example, 9x --- here 9 is the coefficient of variable x, 4x -- here 4 is the coefficient.

Answer:

120

Step-by-step explanation:

First find the discount

200 * 40%

200 * .40

80

Subtract the discount from the original price

200-80

120

The sale price is 120

Answer:

[tex]\huge \boxed{\mathrm{\$ \ 120}}[/tex]

Step-by-step explanation:

Calculating the discount on the jacket.

[tex]200 \cdot 40\% \\ \\ 200 \cdot 0.4 \\ \\ 80[/tex]

The discount on the jacket is $80.

Let’s find the sale price of the jacket.

[tex]\sf sale \ price = original \ price - discount.[/tex]

[tex]200-80 \\ \\ 120[/tex]

The sale price of the jacket is $120.

Answer: (-5)¹¹ of (-5)^11

Step-by-step explanation:

Since the base of the two exponents are teh same at -5, we can subtract the exponents.

5-(-6)=11

Now, we know that the new exponent will be 11, with the base staying the same.

Step-by-step explanation:

(6x^3 + 3x² + 3) + (2x^3 - 5x + 1)

6x^3 + 2x^3 = 8x^3

3x^2 + 0 = 3x^2

-5x + 0 = -5x

3 + 1 = 4

8x^3 + 3x^2 - 5x + 4 is the answer because you have to put all the terms that were solved together. This will lead to 8x^3 + 3x^2 - 5x + 4. And, standard form is ax^2 + bx + c. So, 8x^3 + 3x^2 - 5x + 4 is the answer.

8x^3 + 3x^2 - 5x + 4

Hope this helped,

Kavitha

Answer:

= 8x³ + 3x² - 5x + 4

Step-by-step explanation:

(6x³ + 3x² + 3) + (2x³ - 5x + 1)

= 6x³ + 3x² + 3 + 2x³ - 5x + 1    remove parentheses

= 6x³ + 2x³ + 3x² - 5x + 1          group like terms

= 8x³ + 3x² - 5x + 3 + 1              add similar elements

= 8x³ + 3x² - 5x + 4

Answer:

0

because -8 powered 2 and -8 powered 2 is same. 64-64=0

Step-by-step explanation:

Work Shown:

Angle PQR = (far arc - near arc)/2

Angle PQR = ( (major arc PR) - (minor arc PR) )/2

Angle PQR = ( (2x+252) - (2x+108) )/2

Angle PQR = 144/2

Angle PQR = 72

Notice how we didn't need to find the value of x at all.

Answer:

Step-by-step explanation:

coordinate of O(2,1),Y(3,-2),T(-3,-3)

let the reflected points are O',Y',T'

distance of O from y=2 is 1 unit.

∴ ordinate of O' =1+2(1)=3

or O' is (2,3)

distance of Y from y=2 is2+2=4

ordinate of Y'=-2+2(4)=6

so coordinate of Y' is (3,6)

distance of T from y=2 is (2+3)=5

so ordinate of T' =-3+2(5)=7

coordinate of T' is(-3,7)