Which statement is true about the diagram?

∠DEF is a right angle.
m∠DEA = m∠FEC
∠BEA ≅ ∠BEC
Ray E B bisects ∠AEF.

Step-by-step explanation:

B

\(6x + 8y = - 2 \\ \)

B is a multiple of A

\(3x + 4y = - 1 \\ if \: multiplied \: by \: 2 \\ = 6x + 4y = - 2\)

and since the two systems A and B

have

\(2x + y = 5\)

then the two systems have the same solution

Answer:

Step-by-step explanation:

The area is the product of the width and the length:

Correct choice is B

No cost price is given hence its not possible to calculate the actual answer.But don't worry I will simplify the equation till end that you can get the answer in fractions of sec

Solution:-

Let the Cost price be x

Mark up percent=40%

Now

Mark up=

\(\\ \sf\longmapsto 40\%\:of\:x\)

\(\\ \sf\longmapsto \dfrac{40}{100}\times x\)

\(\\ \sf\longmapsto \dfrac{40x}{100}\)

\(\\ \sf\longmapsto 0.04x\)

Just multiply The CP by 0.04 to get the answer

The variable assigned to strgrade when intscore equals 90 would likely be 'A'.

When the variable intscore equals 90, the corresponding value assigned to the variable strgrade would typically be 'A'. This suggests that a score of 90 is associated with the highest grade achievable in the given context. The specific mapping between integer scores and letter grades may vary depending on the grading system or criteria in place. It is important to note that without further information about the grading scale or specific rules defined within the system, it is difficult to determine the exact value of strgrade assigned to intscore of 90.

Learn more about variable

brainly.com/question/15078630

#SPJ11

Answer:

an open circle will be at -2(since the inequality sign does not include "equal to") and the line is drawn to the left of the circle (since the sign is "left than")

Step-by-step explanation:

Given the inequalities

17+4x < 9

Subtract 17 from both sides

17+4x -19 < 9 - 17

4x < -8

Divide both sides by 4

4x/4 < -8/4

x < -2

To represent the solution on a number line, an open circle will be at -2(since the inequality sign does not include "equal to") and the line is drawn to the left of the circle.

Answer:

270 students all together. First you divide 120 by the ratio of boys. That'll get you 30, then multiply 30 by 5 which is the girls ratio and you'll get 150. Finnaly add 150 + 120 then boom your answer

Even though dividing a fraction by a whole number might be challenging, it is simple to achieve with a few steps. By placing the full number above 1, you must first divide it into a fraction. After that, multiply the fraction you are dividing by the inverted version of the fraction. Lastly, simplify the response as much as possible.

For instance, to multiply 3/4 by 2:

Put 2 over 1, making it 2/1, to make it a fraction.

To get 1/2, invert 2/1.

To get 3/8, multiply 3/4 by 1/2.

Divide the numerator and denominator by 3 to get 1/4, which is the simplest representation of the fraction 3/8.

Hence, 1/4 is equivalent to 3/4 when divided by 2.

Learn more about fractions at

https://brainly.com/question/10354322

#SPJ4

We have to find a 4 x 4 matrix that represents in homogeneous coordinates the rotation by an angle about the x = y = 1, z = 0 line of R³.

A 4 x 4 matrix is required to represent the rotation using homogeneous coordinates of dimension 4.

To obtain the required matrix, the following steps should be taken:

1. A homogeneous coordinate system is introduced.

A 4 × 1 column vector can be used to represent each point in this coordinate system.

This column vector is written [x, y, z, w]T,

where T stands for transpose.

2. The 4 × 4 matrix A can be used to represent the transformation from one homogeneous coordinate system to another.

To get the transformation, A is multiplied on the right by the homogeneous coordinate vector.

3. The 4 × 4 matrix that represents the required transformation in homogeneous co-ordinates can be found as follows:

To represent a rotation by an angle about the x = y = 1, z = 0 line of R³, we'll use the following steps:

i. Determine the vector that is parallel to the rotation axis and normalize it.

ii. We'll take a point on the rotation axis as the origin.

iii. The axis vector is perpendicular to the plane of rotation;

therefore, we'll find two vectors that lie in the plane and are perpendicular to the axis vector.

iv. We'll use the three vectors to construct a 3 × 3 rotation matrix R that rotates vectors about the axis of rotation.

v. This matrix R is then placed in a 4 × 4 homogeneous coordinate matrix A with the fourth row and column consisting of zeros except for the fourth element, which is 1.

A 4 x 4 matrix that represents in homogeneous coordinates the rotation by an angle about the x = y = 1, z = 0 line of R³ is given by the matrix shown below;!

To know more about perpendicular  visit:

https://brainly.com/question/12746252

#SPJ11

Answer: 1

Step-by-step explanation:

Answer:

y ⁷

Step-by-step explanation:

y⁵ * y² = y ⁽ ⁵ ⁺ ² ⁾   (adding exponents)

          = y ⁷

A pair of integers (x, y) that satisfies the equation 61x + 41y = gcd(61, 41) is x = -2 and y = 3.

To find a pair of integers (x, y) that satisfies the equation 61x + 41y = gcd(61, 41), we can use the Extended Euclidean Algorithm.

This algorithm allows us to find the greatest common divisor (gcd) of two numbers (61 and 41 in this case) and express it as a linear combination of the two numbers.

Using the Extended Euclidean Algorithm, we can calculate the gcd(61, 41) as 1.

Along with the calculations, we keep track of the coefficients of 61 and 41, which will give us the values of x and y in the equation.

Starting with the initial values of 61 and 41, we perform the Euclidean Algorithm:

61 = 41 * 1 + 20

41 = 20 * 2 + 1

Working backwards, we substitute the remainders in terms of the previous values:

1 = 41 - 20 * 2

1 = 41 - (61 - 41 * 1) * 2

1 = 41 * 3 - 61 * 2

Comparing this equation to the original equation 61x + 41y = gcd(61, 41), we can see that x = -2 and y = 3.

Therefore, a pair of integers (x, y) that satisfies the equation 61x + 41y = gcd(61, 41) is x = -2 and y = 3.

Learn more about Euclidean Algorithm here:

https://brainly.com/question/14884820

#SPJ11

The required solution is x = (25/11) × log(70/17).

It is required to give exact answers, not decimals.

Therefore, the given equation is 1.7(2.8)⁴ˣ = 7(4.6)ˣ.

This can be simplified as follow

s;1.7 × (2⁹/5)⁴ˣ = 7 × (2⁴⁶/10)⁽ˣ/⁵⁾

1.7 × 2³⁶ˣ/25 = 7 × 2²³ˣ/5

Now, divide both sides of the equation by 2^23x/5;

1.7 × 2⁽³⁶ˣ/²⁵ ⁻ ²³ˣ/⁵⁾= 7

Simplify the left side;

1.7 × 2⁽¹¹ˣ/²⁵⁾ = 7

Now, divide both sides by 1.7;

2⁽¹¹ˣ/²⁵⁾ = 70/17

Take log on both sides;

log(2⁽¹¹ˣ/²⁵⁾)) = log(70/17)11x/25 × log(2) =

log(70/17)x = (25/11) × log(70/17)

Thus, the required solution is x = (25/11) × log(70/17).

Learn more about equation at

https://brainly.com/question/30811815.

#SPJ11

The simplification of the given expression will be  \((-3x^2-15x-30)\).

Given expression is

\(-3(x+2)^2 -3+3x\)

By applying  \((a+b)^2=a^2+2ab+b^2\)  we get

\(-3(x^2+6x+9)-3+3x\)

Multiplying by -3 into the whole bracket we get

\(-3x^2-18x-27-3+3x\)

\(-3x^2-18x-30+3x\)

\(-3x^2-15x-30\)

Thus the simplification of the given expression will be  \((-3x^2-15x-30)\)

To know more about Simplification follow

https://brainly.com/question/723406

Answer:

B. –3x^2 – 15x – 30

Step-by-step explanation:

Answer:

I got 5^10 x 2^14 x 3

Step-by-step explanation:

1. Do a tree to find 480 as a product of its prime factors

2. You should get 480= 5x2x3x2x2x2x2

3. 10 expressed as a product of its prime factors is 5x2

4. so 10^9 expressed as a product of its prime factors would be

5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2

5. You can then write out 480x10^9 as a product of its prime factors

5x2x3x2x2x2x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2

6. change this to use powers

5^10 x 2^14 x 3

N = 5^(10) × 2^(14) × 3

This is about prime factors

By definition, a prime factor is a factor of a number and that factor is also a prime number.

A prime number is one that is divisible by only itself and 1.

The number we have is; 480 × 10^(9)

Now, let's list the prime factors or 480 and they are;

2, 3, 5

Now, using these prime factors alone to get 480, we have;

5 × 3 × 2 × 2 × 2 × 2 × 2 = 480

In powers, gives;

5 × 3 × 2^(5)

Now,the 10^(9) with the 480 can also be expressed in terms of it's prime factors which are 2 and 5 as;

(5 × 2)^(9)

Expanding this gives; 5^(9) × 2^(9) = 10^(9)

Thus;

480 × 10^(9) = 5 × 3 × 2^(5) × 5^(9) × 2^(9)

This gives;

5^(10) × 2^(14) × 3

Read more at; brainly.com/question/4853862

Answer: 67

Step-by-step explanation:

We see a pattern where we multiply the number we added by previously by two.

For example, from 5 to 7, it is 2.

From 7 to 11, we add by 4.

From 11 to 19, we add by 8.

From 19 to 35, we add by 16.

This means the next number would be 32, adding 35 by 32 gives us 67,

Answer:

number 1 will be the Mean absolute deviation

Step-by-step explanation:

(i) To find the value of p, we need to find the magnitude of vector a:

|a| = √(2p^2i - 6p^2j + 3p^2k)

= √(2p^2 + 36p^2 + 9p^2)

= √(47p^2)

Since a is a unit vector, the magnitude of a must be 1. So, we can set up an equation to solve for p:

1 = √(47p^2)

p^2 = 1 / 47

p = √(1 / 47)

(ii) To find the dot product of a and b, we can use the formula:

a.b = |a| * |b| * cos(θ)

where θ is the angle between vectors a and b.

Since we know that a is a unit vector, the magnitude of a is 1. We can find the magnitude of b using the formula:

|b| = √(i^2 + j^2 + (-2k)^2)

= √(1 + 1 + 4)

= √(6)

So,

a.b = 1 * √(6) * cos(θ)

Answer:

Angle NOR is 127 degrees

Step-by-step explanation:

This is an example of the vertical angles theorem

Answer:

127

Step-by-step explanation:

This is ALSO called vertical angle. They are both congruent.

Nintendo switch dock = 15.60%

Nintendo Joy-Con = 17.53%

Nintendo Joy-Con Wrist Straps = 3.15%

Nintendo Joy-Con Grip = 7.01%

High Speed 4k HDMI Cable 6 Feet = 1.51%

Nintendo Switch AC Adapter = 2.60%

Nintendo Switch Console = 52.59%

Quadratic functions are those where the highest power of the variable is 2, and they are written in the form of f(x) = ax2 + bx + c, where a, b, and c are constants. Using the quadratic formula, we can solve quadratic equations to find their roots, as the formula for the roots of a quadratic equation is as follows: (-b ± √(b² - 4ac))/2a.

a. Let f(x) = (Tx + 10)(x - 3). Determine the root(s) of f.The roots of f(x) can be found by setting f(x) equal to 0, which gives(Tx + 10)(x - 3) = 0Therefore,

either (Tx + 10) = 0 or

(x - 3) = 0Solving

(Tx + 10) = 0 for x, we get

x = -10/T, which is one of the roots of f.Solving

(x - 3) = 0 for x, we get

x = 3, which is the other root of f.

Therefore, the roots of f(x) are -10/T and 3.b. Let g(x) = 2x² - 5x. Determine the root(s) of g.To find the roots of g(x), we set g(x) = 0. Thus,2x² - 5x = 0 Factorising out x, we getx(2x - 5) = 0Therefore, either x = 0 or

2x - 5 = 0Solving

2x - 5 = 0 for x, we get

x = 5/2, which is one of the roots of g.Solving

x = 0 for x, we get

x = 0, which is the other root of g.Therefore, the roots of g(x) are 0 and 5/2.c.

To know more about Quadratic visit:

https://brainly.com/question/22364785

#SPJ11

B. 5/3 is the evaluation of \(log_{8} 32\) using the base conversion method.

using the base conversion - \(log_{a} p= \frac{log_{b} p}{log_{b} a}\)

convert the base 8 into the base 2 algorithm

\(\frac{log_{2} 32}{log_{2} 8}\)

since 32=\(2^{5}\)

then, \(log_{2}(32)=5\)

similarly, since \(8=2^{3}\)

then, \(log_{2} (8)=3\)

this makes our expression 5/3.

know more about base conversion:

https://brainly.com/question/2845384

Answer:

5/3

Step-by-step explanation:

The change of base formula says logb b a = [logc c a] / [logc c b].

To evaluate log8 32, you need to use the following equation: log8 32 = x, where x is the unknown value.

This can be rewritten as 8^x = 32.

Solving for x gives x = 5/3.

To learn more about Base Formula

https://brainly.com/question/14407076

Michael is 33 years old and Brandon is 21 years old.

To find the current age of Michael and Brandon, we can use the information given in the problem to set up and solve a system of equations.

Let x be Brandon's current age, and y be Michael's current age.

From the problem, we know the following:

Michael is 12 years older than Brandon: y = x + 12

Seventeen years ago, Michael was 4 times as old as Brandon: y - 17 = 4(x - 17)

We can substitute the first equation into the second equation to eliminate y:

y - 17 = 4(x - 17)

x + 12 - 17 = 4(x - 17)

x - 5 = 4x - 68

3x = 63

x = 21

So, Brandon's current age is 21 years old.

We can use this information to find Michael's current age:

y = x + 12

y = 21 + 12

y = 33

So, Michael's current age is 33 years old.

Simultaneous equations are a set of two or more equations that contain the same variables. These equations must be solved together, or "simultaneously," in order to find the values of the variables. Solving simultaneous equations involves finding values for the variables that will make all the equations true at the same time.

The goal of solving a system of simultaneous equations is to find the values of the variables that satisfy all the equations in the system. The solution of the system of equations is the set of values that satisfy all the equations in the system.

In short, simultaneous equations are a set of two or more equations that contain the same variables. Solving simultaneous equations is to find the values of the variables that satisfy all the equations in the system. There are different methods to solve simultaneous equations such as substitution, elimination, and graphing.

Learn more simultaneous equations about here.

https://brainly.com/question/30319215

#SPJ1

Answer:

X = -5

Step-by-step explanation:

The solution of the sum of the numbers will be 5.

To make the addition easier, we can first simplify the fractions by finding a common denominator. The smallest common multiple of 2, 3, and 4 is 12. We can rewrite the fractions with this denominator:

7/4 = (7/4) x (3/3) = 21/12

1/2 = (1/2) x (6/6) = 6/12

5/3 = (5/3) x (4/4) = 20/12

1/3 = (1/3) x (4/4) = 4/12

1/4 = (1/4) x (3/3) = 3/12

1/2 = (1/2) x (6/6) = 6/12

Now we can add the fractions together:

21/12 + 6/12 + 20/12 + 4/12 + 3/12 + 6/12

Combining like terms, we get:

60/12 = 5

So the sum of the original fractions is equal to 5.

To know more about summation follow

https://brainly.com/question/542712

#SPJ1

Answer:

use mathwqy. it does all the math for u. i cant figure this out.

Step-by-step explanation:

*way

\( = \frac{ - 1}{ \: \: 2} x + 2 = x + 7\)

\( = \frac{ - 1}{ \: \: \: 2} x + 2 - x = 7\)

\( = \frac{ - 3}{ \: \: \: 2}x + 2 = 7\)

\( = \frac{ - 3}{ \: \ \: 2}x = 7 - 2 \)

\( = \frac{ - 3}{ \: \: \: 2} x = 5\)

\( x = 5 \: \div \frac{ - 3}{ \: \: \: 2} \)

\(x = 5 \times \frac{ \: \: \: 2}{ - 3} \)

\(x = \frac{ - 10}{ \: \: \: 3} \)

\(∴ \frac{ - 1}{ \: \: \: 2} \times \frac{ - 10}{ \: \: \: 3} = \frac{ - 10}{ \: \: \: 3} + 7

\)

Answer:

57.4

Step-by-step explanation:

Go to point A and draw a line straight down, perpendicular to HT.  Let's label the point where your drawn line hits AT as B.  Now you have the line segments HB, BT.  

HB + BT = 100

Solve for the height of the triangle, BA.

BA = sin35(80) = 45.9

HB = cos35(80) = 65.5

BT = 100 - 65.5 = 34.5

Now you can solve for AT, which is the hypotenuse of ΔBAT:

(AT)² = 45.9² + 34.5² = 3295

AT = √3295 = 57.4

Looking at the graph of g(x) (the red graph), we can see that it has the same format of f(x), but it is 9 units above it (f(x) passes through (0, -6) and g(x) passes through (0, 3)).

Therefore the graph of g(x) can be created using a translation of 9 units up from the graph of f(x).

That means we can write the following expression:

So the correct option is B.

a) The value of the sampling distribution of x is approximately equal to 81, and the standard deviation is approximately 2.

b) The probability P(z > 38.3333), which is virtually zero.

c) The probability P(z < 18.3333), which is virtually one.

d) P(7883.5) is not a valid probability

(a) The sampling distribution of x, the sample mean, can be approximated to be approximately normally distributed.

According to the central limit theorem, for a sufficiently large sample size, the distribution of the sample mean becomes approximately normal regardless of the shape of the population distribution.

In this case, since the sample size is 81, it meets the condition for the central limit theorem.

The standard deviation of the sampling distribution (also known as the standard error) can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, the sample size is 81.

The standard deviation of the sampling distribution (σx) = σ / \(\sqrt(n)\)

= 18 / \(\sqrt(81)\)

≈ 2

Therefore, the value of the sampling distribution of x is approximately equal to 81, and the standard deviation is approximately 2.

(b) To calculate P(x > 835), we need to convert the sample mean to a z-score and then find the corresponding probability from the standard normal distribution table or using a calculator. The formula for calculating the z-score is:

z = (x - μ) / (σ /\(\sqrt(n)\))

where x is the value of interest, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values:

z = (835 - 81) / (18 / \(\sqrt(81)\)) ≈ 38.3333

Using a standard normal distribution table or calculator, we can find the probability P(z > 38.3333), which is virtually zero.

(c) To calculate P(x < 576.1), we again need to convert the sample mean to a z-score and find the corresponding probability. Using the same formula as in part (b):

z = (576.1 - 81) / (18 / \(\sqrt(81)\)) ≈ 18.3333

Using a standard normal distribution table or calculator, we can find the probability P(z < 18.3333), which is virtually one.

(d) P(7883.5) is not a valid probability as it refers to a specific value and not a range. Probabilities are typically calculated for a range of values.

Learn more about probability and sampling distribution

brainly.com/question/23301074

#SPJ11