Solve the equations.
\(3(x+4)^{2} =10x+32\\(x+4)^{2} =3x+40\\\frac{x^{2} -1}{2} -11x=11\)

Bacterial cell is smaller than the amoeba cell by 70 times or 7^ 10 times

What is mathematical expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

length of a bacterial cell = 5 x 10^-6 m

length of an amoeba cell = 3.5 x 10^-4 m

= 3.5 x 10^-4 x 100/100 m

= 350 x 10^-6 m

Now, comparing the length

= (350 x 10∧-6) / (5 x 10∧-6 )

= (350/5

= 70 times or 7^ 10 times

Therefore, bacterial cell is smaller than the amoeba cell by 70 times or 7^ 10 times

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Answer:

\( \pink{94.5}\)

Step-by-step explanation:

We have to solve this according to the BODMAS theorem.

That is,

B = brackets

O = of

D = division

M = multiplication

A = addition

S = subtraction

Let us solve now.

\( 2 \div 2 - 5 \times 9 + 159 \div 1 \times 3 \div 2 - 100 \\ 1 - 45 + 159 \times 1.5 - 100 \\ 1 - 45 + 238.5 - 100 \\ - 44 + 238.5 - 100 \\ 194.5 - 100 \\ 94.5\)

The area of the rectangle has a width of 5 1/3 yards long and 2 1/6 yards wide is 104/9 square yards or 11.56 square yards.

When calculating a rectangle's area, we multiply the length by the breadth of the rectangle.

A mixed fraction is one that is expressed by its quotient and remainder.

Area = length * breadth

Given: Length = \(5 \frac{1}{3}\) yards

           breadth = \(2 \frac{1}{6}\) yards

First, we need to convert a mixed number into the improper fraction

\(5 \frac{1}{3}\) = \(\frac{(5*3) + 1}{3}\) = \(\frac{16}{3}\)

\(2 \frac{1}{6} = \frac{(2*6) +1}{6} =\frac{13}{6}\)

Therefore the area of the rectangle = Length * width

= \(\frac{16}{3} * \frac{13}{6}\)

=\(\frac{104}{9}\)

=\(\frac{104}{9} yards^{2}\)

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Complete question:

The rectangle has \(5\frac{1}{3}\) yards long and \(2 \frac{1}{6} \\\) yards wide. What’s the area

The counselor's statement might be consistent with the regression evidence, but we would need more information to verify it and determine the range of values consistent with the regression.

Based on the given information, the high school counselor's statement suggests a correlation between the level of education and hourly earnings. In this context, regression analysis can be used to determine if the statement is consistent with the evidence.

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The answer that describes the polygon RSTU is as follows:

A quadrilateral is a polygon with 4 sides. Therefore, let's use the properties to find the name of the shape  RSTU as follows:

The polygon has 4 sides therefore, it is a quadrilateral.

The quadrilateral has opposite side parallel to each other. The opposite sides are RS and TU.

A trapezoid is a quadrilateral with only one pair of opposite side parallel to each other.

Therefore, the shapes that defines the polygon are as follows:

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Answer:

Yes

Step-by-step explanation:

Step 1: Define

12x - 10x⁵ - 7 + 3x⁴

-10x⁵ + 3x⁴ + 12x - 7

Step 2: Rearrange both equations into standard form

-10x⁵ + 3x⁴ + 12x - 7

-10x⁵ + 3x⁴ + 12x - 7

We see both are equivalent.

Answer:

x=2 or x= -1

Step-by-step explanation:

when  f(x) = 0

⇒| 2x-1 | =3

case(i)  (x>1/2)

2x-1=3

x=2

case(ii) (x<1/2)

-(2x-1)=3

2x-1=-3

x=-1

case(iii) (x=1/2)

\(0=3\) absurd.

Answer:

10,000-500=9,500 is  what it is worth

Step-by-step explanation:

The ratio is (J/W) = 7/6. Or. J= (7/6)• W .

Second line: J= (7/6)• 24. J= 28.

Third line: J= (7/6)• 18. J= 21

Answer:

b. (4,2)

Step-by-step explanation:

step one: isolate x in the first equation

substitute x=6-y: \(\begin{bmatrix}2\left(6-y\right)-2y=4\end{bmatrix}\)

\(\begin{bmatrix}12-4y=4\end{bmatrix}\)

\(-4y=-8\)

\(y=2\)

step two: isolate y in the second equation, substitute y=2

\(x=6-y\)

\(x=6-2\)

\(x=4\)

Answer:

b

Step-by-step explanation:

Given the 2 equations

3x + 3y = 18 → (2)

2x - 2y = 4 → (2)

Multiplying (1) by 2 and (2) by 3 and adding the result will eliminate the y- term

6x + 6y = 36 → (3)

6x - 6y = 12 → (4)

Add (3) and (4) term by term to eliminate y

12x + 0 = 48

12x = 48 ( divide both sides by 12 )

x = 4

Substitute x = 4 into either of the 2 equations and solve for y

Substituting into (1)

3(4) + 3y = 18

12 + 3y = 18 ( subtract 12 from both sides )

3y = 6 ( divide both sides by 3 )

y = 2

solution is (4, 2 ) → b

Answer:

y = -2x - 5

Step-by-step explanation:

1) Find the slope of the line.

The slope of the original line is the same as the slope of the parallel line.

Slope formula:

\(m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

In this case you can choose any 2 set of points on the table.

\(m = \frac{4 - 2}{-3 - (-2)}\) = \(\frac{4 - 2}{-3 + 2}\) = \(\frac{2}{-1}\) = -2

So the slope of the line is -2

2) Use the point-slope formula to find the equation of the line.

Point-slope formula:

\(y - y_{1} = m(x - x_{1})\)

Now plug in the point (0, -5) and the slope -2 into the equation.

y - (-5) = -2(x - 0)

y + 5 = -2(x - 0)

To solve the equation first apply the distributive property.

y + 5 = -2x + 0

y + 5 = -2x

Next, subtract 5 from sides.

y = -2x - 5

You know have your equation in point-slope form!

The length of IKE is 2x - 12.

A condition on a variable that is true for just one value of the variable is called an equation.

Since KITE is a kite, we know that KT = IT and KE = IE. Let's call the length of these diagonals d. Then we have:

KT + TI = d

KE + EI = d

Substituting in the given values, we get:

x + 6 + 2x = d

2x + IE = d

Solving for d in the first equation, we get:

3x + 6 = d

Substituting this into the second equation, we get:

2x + IE = 3x + 6

Solving for IE, we get:

IE = x + 6

Therefore, IKE is equal to:

IKE = IT - IE

IKE = (d - KT) - (x + 6)

IKE = (3x + 6 - x - 6) - (x + 6)

IKE = 2x - 12

So, the length of IKE is 2x - 12.

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3x + 27 =180

-27

3x = 153

÷3

x = 51

a=142

(vertically opposite angles are equal)

Reflex angles adds up to 360

360 - (142x2) = 76

76/2 = 38

t & c = 38

Hope this helps!

Answer:

Here you go :) if you need anything tell me!

Yes, we can find the area of the triangle by forming a parallelogram.

The area of a triangle is equal to half the area of a parallelogram.

The conditions are given below.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The area of the triangle can be calculated by forming a parallelogram under the conditions:

1)

If the triangle and the parallelogram are on the same base.

2)

If the triangle and the parallelogram are between the same parallels.

Then,

The area of the triangle is equal to half the area of a parallelogram.

Thus,

The area of the triangle is equal to half the area of a parallelogram.

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The probability that the exam scores are less than 35 is approximately 0.3745

The probability that the exam scores are less than 35 can be determined using the standard normal distribution.

To calculate this probability, we need to convert the exam scores to z-scores.

The z-score measures the number of standard deviations an observation is from the mean. The formula for calculating the z-score is:

z = (x - μ) / σ

where

x is the value we want to convert to a z-score,

μ is the mean of the distribution,

and σ is the standard deviation of the distribution.

In this case, the mean (μ) is 36.12 and the standard deviation (σ) is 3.53. We want to find the probability that the exam scores are less than 35, so x = 35.

First, let's calculate the z-score:

z = (35 - 36.12) / 3.53

z ≈ -0.3177

Next, we need to find the probability associated with this z-score using a standard normal distribution table or a calculator.

The probability corresponds to the area under the curve to the left of the z-score.

Looking up the z-score in a standard normal distribution table, we find that the probability associated with a z-score of -0.3177 is approximately 0.3745.

Therefore, the probability that the exam scores are less than 35 is approximately 0.3745.

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Answer:

Step-by-step explanation:

51 + 32 = 83 for DE

let's convert all mixed fractions to improper fractions, let's add all berries and then see how many times 1/2 go into that sum or namely division.

\(\stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} ~\hfill \stackrel{mixed}{4\frac{1}{2}} \implies \cfrac{4\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{9}{2}} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ strawberries }{\cfrac{13}{4}}~~ + ~~\stackrel{ blueberries }{\cfrac{9}{2}}\implies \cfrac{(1)13~~ + ~~(2)9}{\underset{\textit{using this LCD}}{4}}\implies \cfrac{13+18}{4}\implies \cfrac{31}{4} \\\\\\ \stackrel{\textit{now let's divide that sum by }\frac{1}{2}}{\cfrac{31}{4}\div \cfrac{1}{2}}\implies \cfrac{31}{4}\cdot \cfrac{2}{1}\implies \cfrac{31}{2}\implies {\Large \begin{array}{llll} 15\frac{1}{2} \end{array}}\)

Answer:

5.620

Step-by-step explanation:

I hope this helps you

Answer:

0.00025

Step-by-step explanation:

Here is a example

Gradient of tangent is 1/4. The correct option is (E) 2.

Given function is y = √√x + √y

Taking derivative of this function with respect to x

dy/dx = (1/2) * (1/2) * x^(-1/2) * (1/2) * y^(-1/2) * dy/dx + (1/2) * y^(-1/2) * dy/dx

Now, at point (4,1),  

dy/dx = 1/4

We need to find the value of gradient of tangent at this point.

dy/dx = (1/2) * (1/2) * 4^(-1/2) * (1/2) * 1^(-1/2) * (1/4) + (1/2) * 1^(-1/2) * (1/4)

Simplifying,

dy/dx = (1/8) + (1/8)

dy/dx = 1/4

Gradient of tangent is 1/4.

Hence, the correct option is (E) 2.

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The stage of group development that is characterized by disagreements and conflicts is called storming. During this stage, group members may have different ideas and opinions about how to approach tasks and goals, and they may struggle to find a common understanding.

Conflict can arise as individuals compete for leadership roles or try to assert their ideas over others. However, this stage is important for groups to progress towards their goals as it allows for open communication and the airing of different perspectives. Eventually, through negotiation and compromise, groups move on to the norming stage where a common understanding is established and roles are defined. From there, groups move on to performing, where they are able to work together effectively towards their goals.

Finally, the adjourning stage is where the group disbands after reaching their goals or completing their tasks.

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Answer:

its c.

rotate 90 ccw then mirror from y-axis

Step-by-step explanation:

Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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The real-world problem involving a related set of two equations is given below:

Problem: Cost of attending a concert  is made up of base price and variable price per ticket. You are planning to attend a concert with your friends and want to know the number of tickets to purchase for lowest overall cost.

The related set of two equations are:

Equation 1: The total cost (C) of attending the concert is given by:

The equation C = B + P x N,

where:

B  = the base price

P  = the price per ticket,

N = the number of tickets purchased.

Equation 2: The maximum budget (M) a person have for attending the concert is:

The  equation M = B + P*X

where:

X = the maximum number of tickets a person can afford.

So by using the values of B, P, and M, you can be able to find the optimal value of N that minimizes the cost C while staying within your own budget M. so, you can now determine ticket amount to minimize costs and stay within budget.

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Step-by-step explanation:

the correct answer is option a 6a-7

The system can be written as a vector equation as [5, 1, -3] [x1, x2, x3]^T = [8, 0]^T and as a matrix equation as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

To write the given system as a vector equation, we group the variables and the constants into vectors and write the equations in a matrix form. Thus, the system can be written as [5x1 + x2 - 3x3; 2x2 + 4x3] = [8; 0], which is a vector equation.

To write the system as a matrix equation, we can write the coefficients of the variables in a matrix A, the variables in a vector X, and the constants in a vector B. Thus, the system can be written as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

We can then solve for X by finding the inverse of A and multiplying both sides of the equation by it.

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Answer:

45h+ 4

Step-by-step explanation:

you got to divide but the expression is 45h+4

Answer:

The answer would be 15 cookies.

Step-by-step explanation:

Cookies = 24 cents each

Pop = 45 cents each

you would need about 2000 pennies to have enough to buy two cookies, 2000-50=1950, so if you have 50 cents you would need 1,950 more pennies to be able to get 2 cookies