What is the solution to the following equation? 12 + 3x+7 = 0

The statement which is true about the two equilateral triangles is b)The two triangles are the same shape but not the same size. So, correct option is b.

In calculation, a symmetrical triangle is a triangle where every one of the three sides have a similar length. In the natural Euclidean calculation, a symmetrical triangle is likewise equiangular; that is, every one of the three inward points are additionally compatible to one another and are each 60°. It is likewise an ordinary polygon, so it is additionally alluded to as a normal triangle.

Some of hypotheses which are made sense of utilizing symmetrical triangle:

The side length of the primary symmetrical triangle is 3 inches.The side-length of the second symmetrical triangle is 4 inches.Since both the triangles are symmetrical triangles, in this way they have same shape.

Be that as it may, the two triangles have different side lengths in this way they have different size.

Hence, option b is correct.

To know more about equilateral triangle, visit here:

https://brainly.com/question/3461022

#SPJ4

(Complete question) is:

on a piece of paper, use a protractor and a ruler to construct two equilateral triangles: one with a side length of 3 inches and one with a side length of 4 inches. which statement is true about the two triangles?

a. The two triangles are the same size but not the same shape.

b. The two triangles are the same shape but not the same size.

c. The two triangles are the same size and same shape.

d. It is impossible to construct equilateral triangles with these side lengths.

Answer:

Step-by-step explanation:

D

Answer:

Area=1,288.88m²

Step-by-step explanation:

A circular hall(big room) has a hemispherical roof.The greatest height is equal to the inner diameter.Find the area of the floor,given that the capacity of the hall is 43510 cubic meter

Solution

let

diameter = D

radius,r = D/2

Greatest height = D

height of cylindrical part (h)= D-r = r

radius of cylindrical part = r

area of floor = πr²

volume = volume of cylindrical part + volume of hemispherical part

= πr²h + 2/3 πr³

Recall h=r

volume = πr³ + 2/3 πr³

43510=5/3πr³

Make r the subject

r=3√(43510*3)/5π

=3√(130,530/15.7

=3√8,314.01

=20.26

Area of floor = πr²

=3.14*(20.26)²

=3.14*410.47

=1,288.88m²

Answer:2

2b√5ab

Step-by-step explanation:

Answer:

\( \sqrt{20a {b}^{3} } \\ = \sqrt{4 \times 5 \times ab {b}^{2} } \\ = 2b \sqrt{5ab} \\ thank \: you\)

Answer:

not sure if it's a or b but I think it's a

Answer:

2

Step-by-step explanation:

Answer:

10 miles long

Step-by-step explanation:

The length of the circular trail is calculated as: 10 miles.

We are told that Arthur walked around a circular trail twice in a total of 4.5 hrs.

Thus, he completed two full loops around the circular trail. Let's call the distance of the trail "d" (in miles) and the time it took for the first loop "t1" hours, and the time it took for the second loop "t2" hours.

So, we have:

t₁ + t₂ = 4.5

He walked the circle at 4 mph the first time and at 5 mph the second time.

The distance traveled is given by the formula:

Distance = Speed × Time.

For the first loop:

d = 4t₁

For the second loop:

d = 5t₂

From Equation 2 and Equation 3, we can set up an equation relating t₁ and t2:

4t₁ = 5t₂

Now, we can solve for t₁ in terms of t₂:

t₁ = (5/4)t₂

Substitute this value of t1 into Equation 1:

(5/4)t₂ + t₂ = 4.5

Combine the terms:

(9/4)t₂ = 4.5

Now, solve for t₂:

t₂ = (4.5 * 4) / 9

t₂ = 2

Now that we have the value of t₂, we can find t₁ using the equation

t₁ = (5/4)t₂

t₁  = (5/4) * 2

t₁  = 2.5

Now we can find the length of the trail using either Equation 2 or Equation 3:

d = 4t₁

d = 4 * 2.5

d = 10

So, the length of the circular trail is 10 miles.

Read more about Algebraic expressions at: https://brainly.com/question/434421

#SPJ3

The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

To know more about z-scores, here

https://brainly.com/question/15016913

#SPJ4

The system of equations general solution is denoted by the following notation:

\(\[x = c_1 \cdot e^{\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ \sqrt{51} - 5 \end{pmatrix} + c_2 \cdot e^{-\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ -\sqrt{51} - 5 \end{pmatrix}\]\)

where t stands for the independent variable (time) and c_1 and c_2 are arbitrary constants.

What is Linear algebra?

The study of vector spaces and linear transformations is the focus of the mathematical field known as linear algebra. It includes the geometric and algebraic characteristics of matrices and vectors.

Vectors are used in linear algebra to describe quantities that have both a magnitude and a direction. They can be multiplied by one another, scaled using scalars, and put through a variety of procedures. Contrarily, matrices are rectangular arrays of numbers that can be used to represent a variety of mathematical structures, including systems of equations and linear transformations.

Let's begin by reformatting the system of equations into a matrix form in order to get the general solution:

\(\[x' = \begin{pmatrix} 5 & 1 \\ -26 & -5 \end{pmatrix} x\]\)

where x is the (x, y) column vector.

We can determine the eigenvalues and eigenvectors of the coefficient matrix (5 1; -26 -5) to solve this system.

We begin by computing the eigenvalues by resolving the defining equation:

\(\[\det(A - \lambda I) = 0\]\)

where A is the matrix of coefficients and I is the matrix of identities.

The characteristic equation is \(\(\begin{pmatrix} 5 & 1 \\ -26 & -5 \end{pmatrix}\)\) using the coefficient matrix.

\(\[\begin{vmatrix} 5 - \lambda & 1 \\ -26 & -5 - \lambda \end{vmatrix} = 0\]\)

Increasing the determinant's scope:

\(\((5 - \lambda)(-5 - \lambda) - (-26)(1) = 0\)\)

Simplifying:

\(\((\lambda - 5)(\lambda + 5) - 26 = 0\)\(\lambda^2 - 25 - 26 = 0\)\(\lambda^2 - 51 = 0\)\)

We obtain two eigenvalues after solving for :

\(\(\lambda_1 = \sqrt{51}\)\(\lambda_2 = -\sqrt{51}\)\)

Then, for each eigenvalue, we identify the matching eigenvectors.

If \(\(\lambda_1 = \sqrt{51}\):\((A - \lambda_1 I)v_1 = 0\)\)

Changing the values:

\(\((5 - \sqrt{51})v_1 + v_2 = 0\)\(-26v_1 + (-5 - \sqrt{51})v_2 = 0\)\)

We can use the free variable v_1 = 1 to solve these equations:

\(\(v_2 = \sqrt{51} - 5\)\)

As a result,\(\(v_1 = \begin{pmatrix} 1 \\ \sqrt{51} - 5 \end{pmatrix}\).\) is the eigenvector corresponding to _1 = sqrt(51).

In the same way, for \(\(\lambda_2 = -\sqrt{51}\):\((A - \lambda_2 I)v_2 = 0\)\)

Changing the values:

\(\((5 + \sqrt{51})v_3 + v_4 = 0\)\(-26v_3 + (-5 + \sqrt{51})v_4 = 0\)\)

We can use the free variable\(\(v_3 = 1\)\) to solve these equations:

\(\(v_4 = -\sqrt{51} - 5\)\)

As a result, \(\(v_2 = \begin{pmatrix} 1 \\ -\sqrt{51} - 5 \end{pmatrix}\).\) is the eigenvector corresponding to\(\(\lambda_2 = -\sqrt{51}\)\)

The system of equations general solution is denoted by the following notation:

\(\[x = c_1 \cdot e^{\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ \sqrt{51} - 5 \end{pmatrix} + c_2 \cdot e^{-\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ -\sqrt{51} - 5 \end{pmatrix}\]\)

where t stands for the independent variable (time) and c_1 and c_2 are arbitrary constants.

To learn more about Linear algebra:

https://brainly.in/question/54116586

#SPJ4

We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

File < Options < (A) Formulas < Automatic

We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

Therefore, File < Options < (A) Formulas < Automatic

Know more about Formulas here:

https://brainly.com/question/21140562

#SPJ4

The complete question is given below:

What would you choose as X in the given series of clicks to calculate formulas automatically: File < Options < X < Automatic?

a. Formulas

b. Language

c. Proofing

d. Advanced

The answer is: 0.0362

The total number of Master's degree holders = 2848 (from the question)

In order to choose people 40 and above from this Master's degree holder subset,

You choose:

People 40-49 AND People 50 and over.

Number of people 40-49 = 475

Number of people 50 and over = 699

But we also need to take into consideration, the probability of picking a person 40-49 years old OR 50 and over

total Number of people 40 - 49 are 3518

The total Number of people 50 and above are 6518

Thus, we can write the probability as:

The final answer is: 0.0362

Answer:

A

Step-by-step explanation:

The scale factor can be defined as the ratio of new dimension of an object after scaling to the original  dimension. The are of the new circle is 49 times the area of the original circle. The correct answer is option C.

Scaling factor is a conversion factor used to change the size of a figure without changing its shape. When the size of a figure is increased, it called scaled up and when it decreases it is called as scaled down.

Given that, Scale factor of circle = 7.

Since, the scale factor of a circle is the ratio of new radius to original radius.

The new radius of circle can be written as,

r' = 7r

Thus, the area of new circle is π × (r')^2= π × (49r^2).

Hence, the area of new circle is 49 times the original circle.

To learn more about Scale factor click on,

https://brainly.com/question/22312172

#SPJ2

The Markov chain model for this system can be represented as follows:

State 0: Neither broker is on the phone

State 1: Broker 1 is on the phone, and Broker 2 is not

State 2: Broker 2 is on the phone, and Broker 1 is not

State 12: Both brokers are on the phone

The transition rates between states are as follows:

From state 0, a transition to state 1 occurs at rate λ1 = 1 per hour.

From state 0, a transition to state 2 occurs at rate λ2 = 1 per hour.

From state 1, a transition to state 0 occurs at rate μ1 = 3 per hour (call serviced).

From state 2, a transition to state 0 occurs at rate μ2 = 3 per hour (call serviced).

From state 1, a transition to state 12 occurs at rate λ2 = 1 per hour.

From state 2, a transition to state 12 occurs at rate λ1 = 1 per hour.

From state 12, a transition to state 0 occurs at rate μ1 = 3 per hour (call serviced) if Broker 1 finishes the call first.

From state 12, a transition to state 0 occurs at rate μ2 = 3 per hour (call serviced) if Broker 2 finishes the call first.

(b) To find the stationary distribution, we solve the system of equations:

π0λ1 = π1μ1 + π2μ2

π0λ2 = π2μ2 + π1μ1

π1λ2 = π12μ1

π2λ1 = π12μ2

π0 + π1 + π2 + π12 = 1

Solving these equations will give us the stationary distribution (π0, π1, π2, π12).

(c) With the upgraded telephone system, a call on one line that is busy is forwarded to the other phone and lost if that phone is busy. This implies that the system can no longer be in state 12 since both brokers cannot be on the phone simultaneously.

(d) To compare the rate at which calls are lost in the two systems, we need to analyze the transition rates and the probability of being in state 12 in the original system versus the upgraded system.

Learn more about Markov chain model from

https://brainly.com/question/30975299

#SPJ11

Given that there are 30 employees, 12 of them take public transit while 11 employees drive to work. In addition, 10 employees from the group are to be selected for a study. Note that employees take only public transit, drive to work, or do neither.

Let us use combination formulas to solve the given questions.1. How many different groups of 10 employees can be selected from the 30 employees The formula for combination is given as n Therefore, the number of different groups of 10 employees that can be selected from the 30 employees is given by 30C10=30045015. Thus, the number of different groups of 10 employees that can be selected from the 30 employees is 30C10=30045015.2. How many of the possible groups of 10 employees will consist only of employees that either take public transit or drive to work.

Since there are 12 employees that take public transit, 11 employees drive to work, and 30-12-11=7 employees that do neither, there are two choices Select 10 employees from the 12 employees that take public transit and 11 employees that drive to work. In this case, the total number of possible groups that consist of employees that either take public transit or drive to work is given by 23C10=1144066. Choose 10 employees from the 12 employees that take public transit, 7 employees that do neither, or 10 employees from 11 employees that drive to work and 7 employees that do neither .

To know more about employees visit :

https://brainly.com/question/30489954

#SPJ11

Answer:

B=28

Step-by-step explanation:

Answer:

\(y = 12 \tan(30 \degree ) \\ y = 6.92\)

\(x = \frac{12}{ \cos(30 \degree) } \\ x = 13.8\)

\( \small{ \star{ \underline{ \blue{becker}}}}\)

Consider the same figure as given above. It is observed that DP/PE = DQ/QF and also in the triangle DEF, the line PQ is parallel to the line EF.

So, ∠P = ∠E and ∠Q = ∠F.

Hence, we can write: DP/DE = DQ/DF= PQ/EF.

The above expression is written as

DP/DE = DQ/DF=BC/EF.

It means that PQ = BC.

Hence, the triangle ABC is congruent to the triangle DPQ.

(i.e) ∆ ABC ≅ ∆ DPQ.

Thus, by using the AAA criterion for similarity of the triangle, we can say that

∠A = ∠D, ∠B = ∠E and ∠C = ∠F.

To know more about triangle check the below link:

https://brainly.com/question/1058720

#SPJ4

It can be expect approximately 7.61 inches of rain for the rest of the month of April.

To determine how much more rain can be expected for the rest of the month, we need to calculate the total rainfall recorded for the three days and subtract it from the average rainfall for April.

The total rainfall recorded for the three days is:

1.25" + 0.7" + 3.09" = 5.04"

The average rainfall for April is given as 12.65".

To find how much more rain can be expected for the rest of the month, we subtract the total recorded rainfall from the average rainfall:

12.65" - 5.04" = 7.61"

Therefore, you can expect approximately 7.61 inches of rain for the rest of the month of April.

Learn more about average here:

https://brainly.com/question/24057012

#SPJ11

The correct question is:

Neil recorded the amount of rain that fell over the course of 3 days in April on one day he recorded 1.25" on day 2 he recorded 0.7" and on day 3 he recorded 3.09" the average rainfall for April is 12.65" how much more rain can you expect this month?

Answer:

Original value of investment = £500 (Approx.)

Step-by-step explanation:

Given:

Rate per year = 4%

Number of year = 3 years

Value of investment after 3 year = £562.43

Find:

Original value of investment

Computation:

A = P[1+r]ⁿ

562.43 = P[1+4%]³

562.43 = P[1+0.04]³

562.43 = P[1.04]³

562.43 = P[1.1248]

Original value of investment = 562.43 / 1.1248

Original value of investment = 500.026

Original value of investment = £500 (Approx.)

The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11

The height of the trapezoid is 9 yards. Therefore, the correct answer is option b. 9 yd.

To find the height of the trapezoid with the given area and base lengths, we will use the formula for the area of a trapezoid:

Area = (1/2) * (base1 + base2) * height

Here, the area is given as 126 square yards, base1 is 17 yards, and base2 is 11 yards. We need to find the height.

1. Substitute the given values into the formula:

126 = (1/2) * (17 + 11) * height

2. Simplify the equation:

126 = (1/2) * 28 * height

3. To isolate the height, divide both sides by (1/2) * 28:

height = 126 / ((1/2) * 28)

4. Calculate the result:

height = 126 / 14

height = 9

For more about height:

https://brainly.com/question/10726356

#SPJ4

Answer:

Ye i think ur correct just try pulging in the numbers

Step-by-step explanation:

Answer:

====================

Total number of outcomes is 16, count of all outcomes.

Number of outcomes with 3 or more tiles is 5:

The probability is:

Correct choice is D.

The missing reason in the flowchart would be SAS.

Option (D) is correct.

What is the SAS congruence theorem?

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

In the given figure,

Side RC ≅ Side TN ---- Given

Side HX ≅ Side XK ----Given

Angle RHK ≅ Side HKN --- Vertical angles are congruent.

Hence, ΔRHX ≅ NKXΔ ----- (SAS congruence)

Hence, the missing reason in the flowchart would be SAS.

To learn more about the SAS congruence theorem, visit:

https://brainly.com/question/18922904

#SPJ1

The number of elements in the sample space for this experiment is 969.

If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:

nCr = n! / [r!(n - r)!]

where n is the total number of items in the set and r is the number of items being chosen.

In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:

19C3 = 19! / [3!(19 - 3)!]

= 19! / (3!)(16!)

= 969

Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.

Learn more about combinations here: https://brainly.com/question/11732255

#SPJ4

Answer:

13 weeks

Step-by-step explanation:

475 - 150 =325

325 / 25 = 13

The root-mean-square of this group of molecules can be calculated using the formula: RMS = √[(16² + 17² + 18² + 19² + 20² + 21² + 22² + 23² + 24² + 25² + 26²)/11].

RMS = √[6726/11] = √611.45 = 24.7 m/s (rounded to one decimal place)

Therefore, the root-mean-square of this group of molecules is 24.7 meters per second.
To calculate the root-mean-square (RMS) speed of the group of molecules, follow these steps:

1. Square each speed: 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676
2. Find the average of these squared speeds: (256 + 289 + 324 + 361 + 400 + 441 + 484 + 529 + 576 + 625 + 676) / 11 = 4951 / 11 = 450.091

3. Take the square root of the average: √450.091 ≈ 21.2 m/s, So, the root-mean-square speed of this group of molecules is approximately 21.2 m/s with one decimal place.

To know more about decimal click here

brainly.com/question/29775125

#SPJ11

The expression that has a value of 13 is (18 ÷ 2) + 6 ÷ 6 + 3

In order to calculate the expression, we need to use the PEMDAS rule which states:

From the question, we are to get the expression equal to 13.

From the given expression,(18 ÷ 2) + 6 ÷ 6 + 3 is equivalent to 13;

(18 ÷ 2) + 6 ÷ 6 + 3

9 + 6  ÷ 6 + 3

9 + 1 + 3

13

Hence the expression that has a value of 13 is (18 ÷ 2) + 6 ÷ 6 + 3

Learn more on expansion here: https://brainly.com/question/26430239