The sum of Eli's age and Cecil's age is 15 Eli is twice as old as Cecil

x = -4 - 4√2/6 and x = -4 + 4√2/6.

Hi there! The equation 3x5/3 + 96 = 0 can be rewritten as x5 + 32 = 0. In order to solve for the real solutions of this equation, we can use the Quadratic Formula, which states that for the equation ax2 + bx + c = 0, the real solutions are given by x = (-b ± √b2 - 4ac)/2a. Substituting the values for a, b, and c, we get x = (-32 ± √322 - 4*3*0)/6, which simplifies to x = (-32 ± √1024)/6, or x = -4 ± 4√2/6. Therefore, the real solutions for the equation are x = -4 - 4√2/6 and x = -4 + 4√2/6.

Learn more about variable equation

brainly.com/question/29209545

#SPJ11

Answer:

Using the difference of squares formula, we have:

(r³ - 6t¹) (r³ + 6t¹) = r³ × r³ - r³ × 6t¹ - 6t¹ × r³ - 6t¹ × 6t¹

= r^6 - 36t²

Therefore, the expression in simplest form is r^6 - 36t².

So the equation of the line in slope-intercept form is y = x + 2. The y-intercept is 2.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

In this problem, you are given a graph of a linear function. The graph shows two points on the line: (-2, 0) and (3, 5).

To find the slope of the line, we can use the formula:

slope = (change in y) / (change in x)

We can use the two points given to find the change in y and the change in x:

change in y = 5 - 0 = 5

change in x = 3 - (-2) = 5

Plugging these values into the formula, we get:

slope = 5/5 = 1

So the slope of the line is 1.

To find the y-intercept of the line, we can use one of the points on the line and the slope we just found. Let's use the point (-2, 0):

y - y1 = m(x - x1)

where (x1, y1) is the point (-2, 0) and m is the slope we just found:

y - 0 = 1(x - (-2))

y = x + 2

Therefore, the equation of the line in slope-intercept form is y = x + 2. The y-intercept is 2.

To learn more about Linear equation from given link.

https://brainly.com/question/29739212

#SPJ1

Answer:

Step-by-step explanation:

take and mulityply all of them the add them all up

The work performed on the steam in this compression process per kilogram is -50 kPa*V/kg.\

To find the work performed on the steam in this compression process per kilogram, we need to use the following formula:

W = PΔV

Where W is the work, P is the pressure, and ΔV is the change in volume.Since the process is isothermal, the pressure and volume are inversely proportional.

This means that if the pressure is doubled, the volume will be halved. In this case, the pressure is constant at 100 kPa, and the volume is halved because half of the vapour has condensed.

Therefore, the change in volume is:

ΔV = V/2 - V = -V/2

Substituting this into the formula for work, we get:

W = PΔV = (100 kPa)(-V/2) = -50 kPa*V

To find the work per kilogram, we need to divide the work by the mass of the steam. Since the mass is not given in the question, we can assume it is 1 kilogram. Therefore, the work per kilogram is:

-50 kPa*V/1 kg = -50 kPa*V/kg

So the work performed on the steam in this compression process per kilogram is -50 kPa*V/kg.\

For more about kilogram:

https://brainly.com/question/28844288

#SPJ11

Answer:

Step-by-step explanation:

rwerdfsdfsdfsdfsdfsdfsdfsdfsdfsd           56

The chart that cοuId be used tο dispIay the data is D. Bοx pIοt; because the data is categοricaI.

A bοx pIοt, οften knοwn as a bοxpIοt, is a methοd in descriptive statistics fοr graphicaIIy dispIaying the IοcaIizatiοn, spread, and skewness grοups οf numericaI data thrοugh their quartiIes.

Bοx pIοts are used tο depict the distributiοns οf numericaI data vaIues, particuIarIy when cοmparing them acrοss variοus grοups. They are designed tο cοnvey high-IeveI infοrmatiοn at a gIance, prοviding generaI infοrmatiοn abοut the symmetry, skew, variance, and οutIiers οf a grοup οf data.

In this case, since the data set Iists the favοrite chοice οf rοck bands, the bοx pIοt can be used.

Learn mοre abοut bοx plοt οn:

https://brainly.com/question/1523909

#SPJ1

Complete question:

A data set lists the favοrite chοice οf rοck bands. Which οf the fοllοwing charts cοuld be used tο display the data, and why?

Bar chart; because the data is categοrical

Bar chart; because the data is numerical

Bοx plοt; because the data is categοrical

Bοx plοt; because the data is numerical

The equation of the sine function is: y = 4 sin(1/4 x).

What is a sine function?

A sine function is a type of trigonometric function that relates the angle of a right triangle to the ratio of the length of its opposite side to its hypotenuse. It is defined as the ratio of the length of the opposite side of an angle in a right triangle to the length of the hypotenuse.

The general form of a sine function is:

y = A sin(Bx + C) + D

where A is the amplitude, B determines the period (B = 2π/period), C is the phase shift, and D is the vertical shift.

Substituting the given values, we get:

A = 4 (amplitude)

Period = 8π

B = 2π/Period = 2π/(8π) = 1/4

C = 0 (no phase shift)

D = 0 (no vertical shift)

the equation of the sine function is:

y = 4 sin(1/4 x)

Note that the value of B is the reciprocal of the period, since the formula for period is T = 2π/B, which can be rearranged to get B = 2π/T.

Hence, the equation of the sine function is: y = 4 sin(1/4 x).

To learn more about the sine function, visit:

https://brainly.com/question/3522842

#SPJ1

matrix is 0.3 x 4 = 1.10

To determine the determinant of this 3 x 3 matrix, you can use the Laplace Expansion method. First, cross out the third column and calculate the determinant of the 2 x 2 matrix that remains:

0.6 0.8

0.5 0

The determinant of this 2 x 2 matrix is 0.6 x 0 - 0.8 x 0.5 = 0.3.

Next, multiply this result by the last element of the third column, which is 4. So the determinant of the 3 x 3 matrix is 0.3 x 4 = 1.10.

Learn more about  Laplace Expansion method

brainly.com/question/12972484

#SPJ11

a)not linear

b)linear

c)not linear

d)linear

(i) T:R2→R2 defined by T(x,y)=(x,∣x+y∣): This transformation is not linear because it is not closed under addition and scalar multiplication.

(ii) T:Rn→R defined by T(x)=a⋅x, where a is a fixed vector of Rn: This transformation is linear because it is closed under addition and scalar multiplication.

(iii) T:P2(R)→P2(R) where (T(f))(x)=f(x)+x: This transformation is not linear because it is not closed under addition and scalar multiplication.

(iv) T:Rn→R defined by T(x)=xTa, where a is a fixed vector of Rn: This transformation is linear because it is closed under addition and scalar multiplication.

Learn more about linear transformation equation

brainly.com/question/30170459

#SPJ11

The T(αu + v) = αT(u) + T(v), and so T is linear.

(i) Transformation T: R2 → R2 defined by T(x,y) = (x,|x + y|) is not linear, as the following counterexample proves: let u = (1,1) and v = (−1,2) be vectors in R2. Then:
T(u) = T(1,1) = (1,|1 + 1|) = (1,2)
T(v) = T(−1,2) = (−1,|−1 + 2|) = (−1,1)
However,
T(u + v) = T(1 − 1, 1 + 2) = T(0,3) = (0,|0 + 3|) = (0,3)
T(u) + T(v) = (1,2) + (−1,1) = (0,3)
Thus, T(u + v) ≠ T(u) + T(v), and so T is not linear.

(ii) Transformation T: Rn → R defined by T(x) = a · x, where a is a fixed vector of Rn, is linear. This can be easily checked by verifying that for any vectors x and y in Rn and scalars α and β in R, we have:
T(αx + βy) = a · (αx + βy) = α(a · x) + β(a · y) = αT(x) + βT(y)

(iii) Transformation T: P2(R) → P2(R) where (T(f))(x) = f(x) + x is linear. We can prove this as follows. Let f and g be any polynomials in P2(R) and let α be any scalar in R. Then:
(T(αf + g))(x) = (αf + g)(x) + x = αf(x) + g(x) + x = α(T(f))(x) + (T(g))(x)
Thus, T(αf + g) = αT(f) + T(g), and so T is linear.

(iv) Transformation T: Rn → R defined by T(x) = xT a, where a is a fixed vector of Rn, is linear. We can prove this as follows. Let u and v be any vectors in Rn and let α be any scalar in R. Then:
T(αu + v) = (αu + v)T a = α(uT a) + vT a = αT(u) + T(v)
Thus, T(αu + v) = αT(u) + T(v), and so T is linear.

Learn more about Linear

brainly.com/question/15830007

#SPJ11

The fourth point has coordinates (-17, 0).

The x-coordinate of A remains constant but the sign of the y-coordinate changes if A is mirrored over the x-axis to form A'. Hence, if Has a coordinates (a, b), A' must also have coordinates (a, -b).

Given that A and A' are the corners of a rectangle that are opposite one another, the other two corners of the rectangle must be on a horizontal line that passes through A and A"s midpoint (a, 0). Since (a, 0) and the fourth point (let's call it C) are separated by 2|b|, the distance between A and A' is also 2|b|. This indicates that depending on which side of the line AA' C is on, it has coordinates of (a + 2|b|, 0) or (a - 2|b|, 0).

In this instance, the coordinates of A are (3, 5) and those of A' are (3, -5). The intersection of A and A' is (3, 0). A and A' are separated by 2|5|, which equals 10.

The fourth point, C, thus, has coordinates of either (3 + 2(10), 0) = (23, 0) or (3 - 2(10), 0) = (-17, 0).

The right response is (3 - 2(10), 0), which can be deduced from the graph since the rectangle is symmetric about the y-axis (-17, 0).

The fourth point therefore has coordinates (-17, 0).

To know more about vertices of rectangle visit:

https://brainly.com/question/16071215

#SPJ1

Answer:

In Explanation

Step-by-step explanation:

To convert grams to pounds, we need to first convert grams to kilograms, and then kilograms to pounds.

Given that 1 gram = 0.001 kilograms, we can convert 23,000 grams to kilograms as follows:

23,000 grams = 23,000 * 0.001 kilograms = 23 kilograms

Now, given that 1 kilogram ≈ 2.2 pounds, we can convert 23 kilograms to pounds as follows:

23 kilograms * 2.2 pounds/kilogram = 50.6 pounds

Therefore, 23,000 grams is equivalent to 50.6 pounds.

(Please give brainlist)

Sabrina needs to buy at least 8 pairs of socks to get free shipping, so the inequality will be x ≥ 8.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Sabrina needs to buy at least 100 dollars worth of items to get free shipping, and she already has a 70 dollar sweatshirt in her cart.

Let x be the number of pairs of socks she needs to buy.

Each pair of socks costs 4 dollars, so the cost of x pairs of socks is 4x dollars.

To get free shipping, the total cost of her items must be at least 100 dollars.

Therefore, we can write the inequality -

70 + 4x ≥ 100

Subtracting 70 from both sides, we get -

4x ≥ 30

Dividing both sides by 4, we get -

x ≥ 7.5

Since Sabrina cannot buy a fraction of a pair of socks, she needs to buy at least 8 pairs of socks to meet the minimum spending requirement for free shipping.

Therefore, the solution to the situation is x ≥ 8.

To learn more about inequality from the given link

https://brainly.com/question/11234618

#SPJ1

Step-by-step explanation:

To prove that the eqn provided passes through those points(coordinates..) we just have to inser the value of x and y. As a result we get the valid ans which stands ftrue for both the coordinates. Hence it's proved.

Step-by-step explanation:

when x=2

y=2(2)-1

y=4-1

Answer:

slope = -2, Y intercept = -1

Step-by-step explanation:

[tex]y = mx + c[/tex]

[tex]where \: m \: is \: the \: slope \: and \: c \: is \: the \: intercept[/tex]

So compare the equation with y= -2x-1

Therefore m = -2, c = -1

Correct statement: Two vectors are perpendicular if and only if the dot product of the two vectors is zero.

Explanation:

Two vectors are perpendicular if and only if the dot product of the two vectors is zero. This is equivalent to saying that the angle between the two vectors is 90 degrees. Therefore, the statement "Two vectors are perpendicular if and only if the angle between them is 90 degrees" is correct.

Every orthonormal set is linearly independent. This statement is also correct. An orthonormal set of vectors is a set of vectors that are pairwise perpendicular and have length 1.

Since the dot product of any two distinct vectors in an orthonormal set is 0, it follows that any linear combination of these vectors will also have a dot product of 0 with any other vector in the set.

Therefore, the only solution to a linear combination of these vectors being equal to the zero vector is for all the coefficients to be 0, which implies linear independence.

Every orthogonal set is linearly independent. This statement is also correct. An orthogonal set of vectors is a set of vectors that are pairwise perpendicular, but not necessarily of length 1.

Similar to the previous argument, the dot product of any two distinct vectors in an orthogonal set is 0, which implies linear independence.

R^n has an orthonormal basis. This statement is also correct. An orthonormal basis for a vector space is a basis consisting of orthonormal vectors. It can be shown that any finite-dimensional inner product space has an orthonormal basis, and R^n is a finite-dimensional inner product space with the standard dot product.

The zero vector is perpendicular to all other vectors. This statement is false. The zero vector is orthogonal to all other vectors, but not necessarily perpendicular, as the concept of perpendicularity requires the vectors to have a nonzero length.

Any orthonormal set in R^n is a basis. This statement is also correct. An orthonormal set of n vectors in R^n must span the entire space, as any vector in the space can be expressed as a linear combination of these vectors.

Furthermore, any set of n linearly independent vectors in R^n is a basis, so the fact that an orthonormal set is linearly independent (as shown in statement 2) implies that it is a basis.

For more questions like vectors visit the link below:

https://brainly.com/question/14262011

#SPJ11

Answer:

$9 an hour

Step-by-step explanation:

A) 1

B) 18

C) 4

D) 90

g can be made the subject of the formula as g = mv² / fr.

Subject of a formula is defined as the variable that we are going to find. This can be differentiated by putting in one side of the formula.

The given formula is,

f = mv² / gr

Here, f is the subject of the formula, as it is the only variable in the left hand side.

Now rearrange the equation that g is isolated in the left hand side.

Multiply both sides by gr.

f g r = mv²

g (fr) = mv²

Divide both sides by fr.

g = mv² / fr

Hence we can rearrange the formula as g = mv² / fr.

To learn more about Subject of Formula, click :

https://brainly.com/question/19107883

#SPJ1

The measures of those two angles are, 20° and 110°

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Two angles of a quadrilateral measure 180° and 50°.

And, The other two angles are in a ratio of 2:11.

Since, The other two angles are in a ratio of 2:11.

Hence, ,Measures of both angles are, 2x and 11x.

Now, We know that;

Sum of all interior angles of a quadrilateral are 360°.

Hence, We get;

⇒ 180 + 50 + 2x + 11x = 360

⇒ 230 + 13x = 360

⇒ 13x = 360 - 230

⇒ 13x = 130

⇒ x = 10

Thus, Measures of both angles are,

2x = 2 × 10 = 20°

and 11x = 11 × 10 = 110°

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ9

Answer:

4v - 9

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

multiply inside to the parentheses and add all commmon numbers getting you to, 5v -18 = 2 then add 18 5v=20 divided to v=4

Answer:

They have large leaves with holes in them that the Toucan can use to reach the fruit inside. The Toucan's beak is also used to break open hard-shelled fruits, such as coconuts. The Toucan's beak is also used for defence against predators, as it can be used to peck and jab at them. The adaptations of the rainforest plants are examples of convergent evolution. Both the Toucan and Monstera Plants have adapted to their environment in order to survive. The Toucan has a large beak that helps it to reach fruit in the canopy, while the Monstera Plant has long, grooved leaves with drip tips that allow water to run off and prevent mould. Both adaptations are beneficial for the survival of the species in the rainforest.

Step-by-step explanation:

Yes, an A is received on the test.

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

As per the given data:

x = number of multiple choice questions.

x = 20

y = correctly answered questions.

y = 18

Inequality for receiving A:

3x + 2y ≥ 93

For receiving A, x and y must satisfy the inequality:

3x + 2y ≥ 93

3(20) + 2(18) ≥ 93

96 ≥ 93

Hence, Yes, an A is received on the test.

To learn more about inequality, click:

brainly.com/question/30231190

#SPJ1

The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into the equivalent exponential statement [tex]4^(-2)=(1)/(16)[/tex].

The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into an equivalent exponential statement by using the definition of logarithms. The definition of logarithms states that if [tex]log_(b)(a)=c[/tex], then [tex]b^c=a.[/tex]

Using this definition, we can translate the logarithmic statement[tex]log_(4)(1)/(16)=-2[/tex] into an equivalent exponential statement by rearranging the terms.

The equivalent exponential statement would be[tex]4^(-2)=(1)/(16)[/tex]. This means that 4 raised to the power of -2 is equal to 1/16.

So, the logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex]can be translated into the equivalent exponential statement[tex]4^(-2)=(1)/(16)[/tex].

To know more about  logarithmic statement refer here:

https://brainly.com/question/29169815

#SPJ11

I may be wrong but, i think it may be C. due to how the question  states the answers and questions, Although it may also be B.

The given function will have a minor and major axis with length 6 and 8, respectively. The correct answer is B.

The given equation is (x²)/(9) - (y²)/(16) = 1 is in the form of (x²)/(a²) - (y²)/(b²) = 1. This is the equation of a hyperbola with a horizontal transverse axis.

The length of the major axis is 2a, and the length of the minor axis is 2b.

In this case, a = 3 and b = 4.

So, the length of the major axis is 2a = 2(3) = 6, and the length of the minor axis is 2b = 2(4) = 8.

Therefore, the correct answer is option b. 6,8.

Learn more about horizontal transverse axis here: https://brainly.com/question/28969949.

#SPJ11

The points of the equation are: (-3, 0), (-9, 0), and (0, 0). Be sure to select the appropriate number.

To find the points of the equation f(x) = (3x2 + 18x + 27)/(x2 + 3x4), you need to set the numerator and denominator of the equation equal to 0. Then you can solve for the points.

Setting the numerator equal to 0:
3x2 + 18x + 27 = 0
Solve for x: x = -3 and x = -9

Setting the denominator equal to 0:
x2 + 3x4 = 0
Solve for x: x = 0

Therefore, the points of the equation are: (-3, 0), (-9, 0), and (0, 0). Be sure to select the appropriate number.

Learn more about appropriate numbe

brainly.com/question/20653893

#SPJ11

The solutions to the equation are x=1.25 and x=0.5. These are the values of w that make the equation true.

To solve the quadratic equation [tex]8w^(2)-14w+5=0[/tex] using the quadratic formula, we first need to identify the values of a, b, and c. In this case, a=8, b=-14, and c=5. The quadratic formula is:

[tex]x = (-b ± √(b^(2)-4ac))/(2a)[/tex]

Plugging in the values of a, b, and c, we get:

[tex]x = (-(-14) ± √((-14)^(2)-4(8)(5)))/(2(8))[/tex]

Simplifying the equation, we get:

x = (14 ± √(196-160))/16

x = (14 ± √36)/16

x = (14 ± 6)/16

Now we can solve for the two possible values of x:

x = (14+6)/16 = 20/16 = 1.25

x = (14-6)/16 = 8/16 = 0.5

To know more about quadratic formula refer to-

brainly.com/question/9300679#
#SPJ11

Answer:

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

Simplify each expression including the given and compare.

Given expression:

Options simplify as:

A)

B)

C)

D)

Interest rates vary between lenders and can drastically change the monthly payment.

The interest rate is the cost of borrowing money from a lender. It determines how much extra you will pay on top of the principal amount borrowed.

The interest rate is a crucial factor to consider when shopping for loans because it directly affects the total cost of the loan.

Higher interest rates mean that you will pay more over the life of the loan, resulting in a higher monthly payment.

Lower interest rates mean that you will pay less over the life of the loan, resulting in a lower monthly payment.

Thus, choosing a loan with a lower interest rate can save you a significant amount of money in the long run.

Hence, Interest rates vary between lenders and can drastically change the monthly payment.

To learn more on Interest rate click:

https://brainly.com/question/14445709

#SPJ1

As per the unitary method, the bakery sold 2294 coffee buns.

Let us assume that the number of blueberry buns sold by the bakery is x. According to the problem, the number of coffee buns sold is 1560 more than the number of blueberry buns sold. Therefore, the number of coffee buns sold can be expressed as (x + 1560).

Now, we are given that the total number of buns sold (both coffee and blueberry) is 3028. Therefore, we can set up an equation based on the given information:

x + (x + 1560) = 3028

Simplifying this equation, we get:

2x + 1560 = 3028

2x = 1468

x = 734

Therefore, the number of blueberry buns sold by the bakery is 734. Now, we can use the unitary method to find the number of coffee buns sold. We know that the number of coffee buns sold is 1560 more than the number of blueberry buns sold, which is:

x + 1560 = 734 + 1560 = 2294

To know more about unitary method here

https://brainly.com/question/28276953

#SPJ4