Look at the warm-up document and determine your answer. Explain using a well thought out and complete sentence why you chose your answer

Answer:

x = 8

Step-by-step explanation:

4(x + 3) = 44 ( divide both sides by 4 )

x + 3 = 11 ( subtract 3 from both sides )

x = 8

The answer of the given question based on the equations are, the solution to the system of equations is (x,y) = (12,10).

An equation is  mathematical statement that shows that the two expressions are equal. An equation contains an equals sign (=) and consists of two expressions, referred to as the left-hand side (LHS) and the right-hand side (RHS), which are separated by the equals sign. The expressions on either side of the equals sign can include variables, constants, and mathematical operations like  addition, subtraction, multiplication, and division.

Multiply the first equation by 2 and the second equation by -1 to eliminate the x term.

4x - 6y + 12 = 0

-4x + 5y - 2 = 0

Add two equations to eliminate  x term.

-y + 10 = 0

y = 10

Substitute value of y back into one of original equations and solve for the x.

2x - 3y + 6 = 0 (using the first equation)

2x - 3(10) + 6 = 0

2x - 24 = 0

x = 12

Therefore, the solution to the system of equations is (x,y) = (12,10).

To know more about Expression visit:

https://brainly.com/question/1859113

#SPJ1

We know that:

Using this clue, we can find m∠1.

We have finally found the answer to the missing angle. The answer is 51°.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

Answer:

x = 1

Step-by-step explanation:

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

Answer:

2z-6w

Step-by-step explanation:

Answer:

-6w+2z

Step-by-step explanation:

The direction of the positive x-axis is ∫∫S F · n dS

\(\int 0^2 \int 0^(1-u^2/4) -2u^3 \sqrt {v/(1+4v^2)} dv du+ \int 0^2 \int 0^(1-u^2/4) u^2 \sqrt {v/(1+4v^2)} dv du+ \int 0^2 \int 0^(1-u^2/4) u^2\)

The surface integral need to parameterize the surface S of the cone and find the normal vector.

Then we can evaluate the dot product of the vector field F with the normal vector and integrate over the surface using the parameterization.

To parameterize the surface S can use the following parameterization:

r(x, y) = ⟨x, y, √(x² + y²)⟩ (x, y) is a point in the base of the cone.

The normal vector can take the cross product of the partial derivatives of r:

rₓ = ⟨1, 0, x/√(x² + y²)⟩

\(r_y\) = ⟨0, 1, y/√(x² + y²)⟩

n(x, y) = \(r_x \times r_y\)

= ⟨-x/√(x² + y²), -y/√(x² + y²), 1⟩

The direction of the normal vector to point outward from the cone, which is consistent with the orientation of the cone given in the problem.

To evaluate the surface integral need to compute the dot product of F with n and integrate over the surface S:

∫∫S F · n dS

Using the parameterization of S and the normal vector we found can write:

F · n = ⟨-tan(2xy²), x², x²⟩ · ⟨-x/√(x² + y²), -y/√(x² + y²), 1⟩

= -x³/√(x² + y²) tan(2xy²) - x² y/√(x² + y²) + x²

The trigonometric identity tan(2θ) = 2tan(θ)/(1-tan²(θ)):

F · n = -2x³ y/√(x² + y²) [1/(1+tan²(2xy²))] - x² y/√(x² + y²) + x²

To integrate over the surface S can use a change of variables to convert the double integral over the base of the cone to a double integral over a rectangular region in the xy-plane.

Letting u = x and v = y² the Jacobian of the transformation is:

∂(u,v)/∂(x,y) = det([1 0], [0 2y])

= 2y

The bounds of integration for the double integral over the base of the cone are 0 ≤ x ≤ 2 and 0 ≤ y ≤ √(1 - x²/4).

Substituting u = x and v = y² get the bounds 0 ≤ u ≤ 2 and 0 ≤ v ≤ 1 - u²/4.

For similar questions on direction

https://brainly.com/question/29248951

#SPJ11

The measure of the largest angle in the triangle is 64 degrees.

Let's assume that the measure of the two equal angles in the triangle is x degrees. According to the given information, the third angle is 6 degrees greater than each of the other two angles, so its measure is x + 6 degrees.

The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:

x + x + x + 6 = 180

Combining like terms, we get:

3x + 6 = 180

Next, we subtract 6 from both sides of the equation:

3x = 180 - 6

3x = 174

Finally, we divide both sides of the equation by 3 to solve for x:

x = 174 / 3

x ≈ 58

So, each of the two equal angles measures approximately 58 degrees. The third angle is 6 degrees greater than each of the other two, which means it measures 58 + 6 = 64 degrees.

To find the measure of the largest angle in the triangle, we take the maximum value among the three angles, which is 64 degrees.

Learn more about angle visit:

brainly.com/question/13954458

#SPJ11

Answer: B

Step-by-step explanation:

If we share $60 in the ratio 3:1, then each person will get is $45 and $15 respectively

Given,

The total amount = $60

The ratio = 3:1

Then the amount given to first person = 3x

The amount given to the second person = x

Given that the total amount is 60

Then  the equation will become

x+3x=60

4x=60

x=\(\frac{60}{4}\)

x=15

The amount given to the first person = 3x

Substitute the value of x in the equation

The amount given to the first person =3x

=3×15

= $45

The amount given to the second person =x

= $15

Hence, if we share $60 in the ratio 3:1, then each person will get is $45 and $15 respectively

Learn more about ratio here

brainly.com/question/13419413

#SPJ1

Answer:

(x²)² + 2(9)x² + 9²

(x² + 9)²

Step-by-step explanation:

Given expression in the question is,

(x⁴ + 18x²+ 81)

We have to factorize this expression.

We know the formula of (a + b)² = a² + 2ab + b²

Comparing this formula with the given expression,

a = x²

b = 9²

By substituting these values in the given formula,

Therefore, (x⁴ + 18x²+ 81) = (x²)² + 2(9)x² + 9²

                                         = (x² + 9)²

To show that A and AT have the same characteristic polynomial, we can use the property that the matrix det (A) = (-1)det (AT) and then use the formula AAT = 1.

A characteristic polynomial is a polynomial associated with a square matrix that is formed by taking the determinant of the matrix minus a scalar variable λ. The resulting polynomial is the characteristic polynomial of the matrix. It is used to find the eigenvalues of the matrix.The determinant of a matrix is a scalar value that can be calculated from the elements of the matrix. If two matrices have the same determinant, then they have the same characteristic polynomial. The correct answer is option A: Start with det (A) = (-1)det (AT). Then use the formula AAT = 1. The property of determinants to show that A and AT have the same characteristic polynomial is to start with det (A) = (-1)det (AT) and then use the formula AAT = 1. Therefore, to show that A and AT have the same characteristic polynomial, we can use the property that the matrix det (A) = (-1)det (AT) and then use the formula AAT = 1.

Learn more about matrix here, https://brainly.com/question/16751698

#SPJ11

Answer:

the anser and the

Step-by-step explanation:

Answer:

If im wrong just say but i think it B

Step-by-step explanation:

Answer:

B (3x / ( 5pi)) ^ 1/3 =  r

Step-by-step explanation:

x=5/3 pi r ^3

Multiply each side by 3/5

3/5 x= pi r ^3

Divide each side by pi

3x / ( 5pi) = pi r^3 /pi

3x / ( 5pi) =  r^3

Take the cube root of each side

(3x / ( 5pi)) ^ 1/3 =  r^3 ^ 1/3

(3x / ( 5pi)) ^ 1/3 =  r

Here, we just have to express r in terms of x when we are provided with the relation between x and r. We have to flip and sent it to the Right hand side.

We have,

Solving it further,

\( \large{ \longrightarrow{ \rm{x = \frac{5}{3} \pi {r}^{3} }}}\)

Taking 5/3 to the other side by dividing it,

\( \large{ \longrightarrow{ \rm{ \frac{3x}{5} = \pi {r}^{3} }}}\)

Now, taking π to the other side by dividing it,

\( \large{ \longrightarrow{ \rm{ \frac{3x}{5\pi} = {r}^{3} }}}\)

Cube rooting LHS to get r

\(\large{ \longrightarrow{ \rm{ \sqrt[3]{ \frac{3x}{5\pi} } = r}}}\)

Flipping it,

\(\large{ \longrightarrow{ \rm{r = \sqrt[3]{ \frac{3x}{5\pi} } }}}\)

So, the correct option:

\( \huge{ \boxed{ \bf{ \red{Option \: B}}}}\)

━━━━━━━━━━━━━━━━━━━━

To test the candy company's claim about the percentage of blue candies, a hypothesis test can be conducted using a significance level.

The null hypothesis would assume that the claimed percentage is true, while the alternative hypothesis would state that the claimed percentage is not true. The significance level will determine the threshold for rejecting the null hypothesis based on the observed data.

In hypothesis testing, the null hypothesis (H₀) represents the claim being tested, which in this case is that the percentage of blue candies is equal to a specific value. The alternative hypothesis (H₁) contradicts the null hypothesis and suggests that the claimed percentage is not true. Let's assume the claimed percentage is p. The test statistic used for comparing observed data with the null hypothesis is typically the z-score.

The next step is to determine the significance level, denoted as α. This value represents the probability of rejecting the null hypothesis when it is true. Commonly used significance levels are 0.05 (5%) and 0.01 (1%). Once the significance level is chosen, a critical region is established, which defines the range of values that would lead to rejecting the null hypothesis. The critical region is determined based on the chosen significance level and the distribution of the test statistic (in this case, the standard normal distribution).

Finally, the observed data is collected and analyzed. The test statistic is calculated using the observed proportion of blue candies, and it is compared to the critical values. If the test statistic falls within the critical region, the null hypothesis is rejected, indicating that there is evidence to support the claim that the percentage of blue candies is different from the claimed value. If the test statistic does not fall within the critical region, the null hypothesis is not rejected, suggesting that the claim made by the candy company is plausible.

Learn more about Hypothesis test here :

brainly.com/question/17099835

#SPJ11

$11

Step-by-step explanation:

$83 to begin with

-$6 for her lunch

$77 dollars leftover

If she bought 7 candles, each candle has to be $11 bc 77÷7=11

Hope this helped <3

Answer:

she spent 11 dollars on each candle

Step-by-step explanation:

Answer:

Step-by-step explanation:

Well, if you're in debt your amount of money can go into the negatives

Answer:

2.5

The lowest point on the graph, or the minimum is at f(x)= 2.5

The minimum value of the given periodic function is, 2.5

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

A periodic function,

Period  = 3π

The value of the function is in the range of (2.5, 4.5)

So,

Maximum value = 4.5

Minimum value  = 2.5

Thus, the minimum value is 2.5

To know more about Functions check:

https://brainly.com/question/5975436

#SPJ6

To determine the radius of the isotope's path in the mass spectrometer, we need to know the magnetic field strength and the charge of the isotope. Without this information, it is not possible to calculate the radius of the path.

In a mass spectrometer, the radius of the path is determined by the interplay between the magnetic field strength, the charge of the ion, and the mass-to-charge ratio (m/z) of the ion. The equation that relates these variables is:

r = (m/z) * (v / B)

Where:

r is the radius of the path,

m/z is the mass-to-charge ratio,

v is the velocity of the ion, and

B is the magnetic field strength.

Since we only have the mass of the isotope (2.51 x 10^(-26) kg) and not the charge or magnetic field strength, we cannot calculate the radius of the path.

A mass spectrometer is able to separate different isotopes based on the differences in their mass-to-charge ratios (m/z). Here's an overview of the process:

Ionization: The sample containing the isotopes is ionized, typically by methods like electron impact ionization or electrospray ionization. This process converts the atoms or molecules into positively charged ions.

Acceleration: The ions are then accelerated using an electric field, giving them a known kinetic energy. This acceleration helps to focus the ions into a beam.

The accelerated ions enter a magnetic field region where they experience a force perpendicular to their direction of motion. This force is known as the Lorentz force and is given by F = qvB, where q is the charge of the ion, v is its velocity, and B is the strength of the magnetic field.

Path Radius Determination: The radius of the curved path depends on the m/z ratio of the ions. Heavier ions (higher mass) experience less deflection and follow a larger radius, while lighter ions (lower mass) experience more deflection and follow a smaller radius.

Detection: The ions that have been separated based on their mass-to-charge ratios are detected at a specific position in the mass spectrometer. The detector records the arrival time or position of the ions, creating a mass spectrum.

By analyzing the mass spectrum, scientists can determine the relative abundance of different isotopes in the sample. Each isotope exhibits a distinct peak in the spectrum, allowing for the identification and quantification of isotopes present.

In summary, a mass spectrometer separates isotopes based on the mass-to-charge ratio of ions, utilizing the principles of ionization, acceleration, magnetic deflection, and detection to provide information about the isotopic composition of a sample.

to learn more about  isotopes

https://brainly.com/question/28039996

problem 1:

Annihilator found: (D-5); Particular solution: \(u_p\) = (1/2)exp(2x+C1) + 1 - (1/40)exp(-4x-2C1)

Problem 2:

Annihilator found: (D-3)(D-4); Particular solution: yp(x) = (1/7)exp(7x + C1) + (1/7)exp(C1) + (1/42)sin x

problem 1:

(a) To annihilate the nonhomogeneity cos(5x) + 10,

We need to find a differential operator that will make it equal to zero. Since cos(5x) is a solution to the homogeneous equation u'' - u' - 2u = 0 (i.e. the complementary equation),

We can use the operator (D - 5)² to make the entire nonhomogeneous equation equal to zero.

Here, D represents the differentiation operator.

(b) Now, we can use the annihilator found in part:

(a) to find the form of the particular solution.

Applying the operator (D - 5)² to both sides of the nonhomogeneous equation, we get:

(D - 5)²[u" - u' - 2u] = (D - 5)²[cos(5x) + 10]

Expanding the left side using the product rule, we get:

D²u - 2x5Du + 5²u - Du' + 2x5u' - 2u = 0

Now, we can solve for \(u_p\) by equating the coefficients of the terms on the right side of the equation. This gives us:

Du' - 2u = 0  (coefficient of cos(5x))

D²u - 2x5Du + 5²u - 2u = 10 (coefficient of 10)

Solving the first equation using separation of variables, we get:

ln|u'| - 2x = C1

Where C1 is the constant of integration.

Solving for u', we get:

u' = exp(2x + C1)

Integrating once more, we get:

u = (1/2)exp(2x + C1)² + C2

Where C2 is another constant of integration.

To solve for C2, we need to use the second equation we found for the coefficients.

Substituting in \(u_p\) = (1/2)exp(2x + C1)² + C2 and its derivatives into the equation, we get:

-20exp(2x + C1)² + 10 = 10

Solving for C2, we get:

C2 = 1 - (1/40)exp(-4x - 2C1)

Therefore, the form of the particular solution is:

\(u_p\) = (1/2)exp(2x + C1)² + 1 - (1/40)exp(-4x - 2C1)

Problem 2:

(a) To annihilate the nonhomogeneity exp(7x) - sin x,

We need to find a differential operator that will make it equal to zero. Since exp(3x) is a solution to the homogeneous equation

y'' + 12y' + 27y = 0,

We can use the operator (D - 3)(D - 4) to make the entire nonhomogeneous equation equal to zero.

Here, D represents the differentiation operator.

(b) Now, we can use the annihilator found in part (a) to find the form of the particular solution.

Applying the operator (D - 3)(D - 4) to both sides of the nonhomogeneous equation, we get:

(D - 3)(D - 4)(y") + 12(D - 3)(D - 4)(y') + 27(D - 3)(D - 4)(y) = (D - 3)(D - 4)(exp(x) - sin x)

Expanding the left side using the product rule, we get:

D²y - 7Dy + 12y - 4Dy' + 28y' - 27y + 3exp(x) - 3sin x

Now, we can solve for yp by equating the coefficients of the terms on the right side of the equation.

This gives us:

-4Dy' + 28y' = exp(x) (coefficient of exp(x))

D²y - 7Dy + 12y - 27y = -sin x (coefficient of sin x)

Solving the first equation using the separation of variables, we get:

ln|y'| - 7x = C1

Where C1 is the constant of integration. Solving for y', we get:

y' = exp(7x + C1)

Integrating once more, we get:

y = (1/7)exp(7x + C1) + C2

Where C2 is another constant of integration.

To solve for C2,

We need to use the second equation we found for the coefficients. Substituting in yp = (1/7)exp(7x + C1) + C2 and its derivatives into the equation, we get:

-42exp(7x + C1) = -sin x

Solving for C2, we get:

C2 = (1/7)exp(C1) + (1/42)sin x

Therefore, the form of the particular solution is:

yp(x) = (1/7)exp(7x + C1) + (1/7)exp(C1) + (1/42)sin x

To learn more about differential equation is,

https://brainly.com/question/30466257

#SPJ4

The functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.The given differential equation is, y''+4y'+4y=e^t ...(1)

We have to find the solutions of the differential equation. Let's solve the differential equation:(1) => r²+4r+4=0Now, solve the quadratic equation using the quadratic formula: r= (-(4)+√((4)²-4(1)(4))) / 2(1)= -2 (repeated)So, the solution of the corresponding homogeneous equation is:(2) yh= (c₁+c₂t)e^(-2t) ---------------(2)Now, we have to find a particular solution of the non-homogeneous differential equation (1).

Let, yp= Ae^t. Now, yp'= Ae^t, yp''= Ae^t. Substitute yp and its derivatives in the equation (1):yp''+4yp'+4yp= e^tAe^t+4Ae^t+4Ae^t= e^t9Ae^t= e^tA= 1/9Therefore, the particular solution is,(3) yp= e^t/9 ------------(3)

Hence, the general solution of the given differential equation is,(4) y= yh+yp= (c₁+c₂t)e^(-2t) + e^t/9Now, substitute the initial conditions in the general solution to get the constants c₁ and c₂:Let, y(0)=0 and y'(0)=0, then,c₁= -1/9 and c₂= 5/9Finally, the solution of the differential equation y''?4y'+4y=e^t is,(5) y= -(1/9)e^(-2t) + (5/9)te^(-2t) + e^t/9 =(e^(2t)+te^(2t))/9+ e^t ...

(Ans)The options that represent the functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.

To learn more about - Solutions of the differential equation y''?4y'+4y=e^t? : https://brainly.com/question/13260541

#SPJ11

if the number of times you take the test were independent variable of the chance you fail what could that mean the difficulty of the test is consistent and unchanging.

The difficulty of the test is consistent and unchanging, making it so that the chance of failing is solely determined by the individual's performance on the test. Factors such as knowledge of the subject and the ability to focus can play a role in a person's success, but the actual chance of failing is not affected by how many times the test is taken. This means that those who fail the test will have to work harder and prepare better in order to pass it on the next attempt. Taking the test multiple times does not guarantee a higher chance of success, as the difficulty remains the same each time due to independent variable.

Learn more about independent variable here

https://brainly.com/question/29430246

#SPJ4

Answer:

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

Let the amount deposited be x. It is assumed we are talking about simple interest.

After 4 years the interest amount is:

95% of this amount is Rs 4940:

Mrs Majhi deposited Rs 20000.

Mrs. Majhi deposited Rs 20000 in her bank account. This was calculated by first finding the total interest (before tax) and then using the formula for simple interest to determine the principal amount.

The question is based on the concepts of Simple Interest and taxation. We know that Mrs Majhi received Rs 4940 as net interest after 4 years and this amount is 95% of the total interest (since 5% was paid as income tax). The total interest can be calculated as (4940 / 95) * 100 = Rs 5200.

The rate of interest is given as 6.5% per annum. Thus, the money deposited (Principal) by her can be calculated using the formula for simple interest (I = PRT/100), where P is the Principal, R is the rate of interest, and T is the time. Re-arranged to calculate the Principal (P), it becomes P = I / (R*T) = 5200 / (6.5*4) = Rs 20000.

https://brainly.com/question/32543341

#SPJ2

The population variance is closest to 67.43, hence option C: 67.00, by referring the formula for population variance where N plays the number of data points.

The following gives the formula for population variance:

σ2 = (1 /N) ∑ (xi – μ) 2

Where:

σ2 refers to the population variance.

N refers to the total number of data points

∑ (xi – μ) 2 is the sum of the squared differences between each data point and the mean of the population.

For example, consider a population with data values of 12, 8, 28, 22, 12, 30, 14. The mean of this population is:

12+8+28+22+12+30+14)/7 = 18.

The population variance is calculated as follows:

σ2 = (1/7) [(12-18)2 + (8-18)2 + (28-18)2 + (22-18)2 + (12-18)2 + (30-18)2 + (14-18)2]

= 67.43

Therefore, the population variance is closest to 67.43.

To know more about population variance, refer:

https://brainly.com/question/30884734

#SPJ4

Complete question is:

Consider a population with data values of 12 8 28 22 12 30 14. The population variance is the closest to:

A. 8.00

B. 8.64

C. 67.00

D. 74.67

The inequality expression has a solution of "-8" greater than x

From the question, the inequality is given as

3 − (2x − 5) < −4(x + 2)

This gives

3 − 2x + 5 < −4x - 8

Collect the like terms in the above inequality

So, we have the following representation

4x - 2x < -8 - 3 - 5

Evaluate the like terms

So, we have the following representation

2x < -16

Divide by 2

x < -8

Rewrite the inequality as follows

So, we have the following representation

-8 > x

This is represented as

"-8" greater than x

Hence, the solution to the expression is "-8" greater than x

Read more about inequality at

brainly.com/question/25275758

#SPJ1

Answer:

17

Step-by-step explanation:

you multiply 5 and x and you get 15 plus 2 equals 17

Answer:

5

Step-by-step explanation:

5*2=10

10+1=11

Answer:

2x - 1 = 11

2x = 11 + 1

2x = 12 (divide both sides by 2 to get x)

2x/2 = 12/2

x = 6

Step-by-step explanation:

im not 100% sure