Question 6 Which of the following is the graph of f(x) = x² = 5x + 4?

Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

Thus, for any vector x = (x1, x2, x3) in R3, we have: L(x) = Ax where A is the matrix given above.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used extensively in mathematics, science, engineering, and computer science to represent and manipulate linear equations, systems of equations, vectors, and other mathematical objects. Matrices can be added, subtracted, multiplied, inverted, and transformed in various ways to solve problems in algebra, calculus, statistics, and other fields. Matrices are also used in computer graphics, machine learning, and other areas of artificial intelligence to represent data, images, and other information. The size of a matrix is given by its number of rows and columns, and matrices can be classified as square (when they have the same number of rows and columns) or rectangular (when they have different numbers of rows and columns).

Here,

To find the matrix A that corresponds to the linear transformation L, we need to write L(e1), L(e2), and L(e3) as linear combinations of the standard basis vectors in R2.

L(e1) = (1+0, 0+0) = (1, 0)

L(e2) = (0+1, 1+0) = (1, 1)

L(e3) = (0+0, 1+0) = (0, 1)

So we can write:

L(x) = L(x1 e1 + x2 e2 + x3 e3)

= x1 L(e1) + x2 L(e2) + x3 L(e3)

Now we can assemble the coefficients of this linear combination into a matrix A:

A=  \(\left[\begin{array}{ccc}1&1&0\\0&1&1\end{array}\right]\)

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Using bisection, the measure of angle ABD is of m<ABD = 50º.

The bisection of an angle is when the angle is divided into two angles of equal measure.

In the context of this problem, we have that the angle BE bisects the angle DBC, hence the measures of these angles are given as follows:

mDBE = mEBC = 2x + 15.

As shown in the diagram, the entire line forms a ray, meaning that the sum of the measures of the angles is of 180º, hence we can solve for x as follows:

2x + 2(2x + 15) = 180º

2x + 4x + 30 = 180º

6x = 150º

x = 150º/6

x = 25º.

Then the measure of angle ABD is found as follows:

m<ABD = 2x = 2(25) = 50º.

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Answer:

X=1

Step-by-step explanation:

6(x+4)=30

first you do the foil method with the 6(x+4) to get 6x+24.

Your new equation is now 6x+24= 30

Now you subtract 24 from 30 to get 6.

Now your equation is 6x=6.

From there you divide 6 from 6 to get 1. Therefore x=1

Answer:

D = 25

Step-by-step explanation:

For 2 lines to be parallel, they must have the same sloe;

Given the coordinates (-2,4)and (5,D)

Slope = D-4/5-(-2)

Slope = D-4/5+2

Slope = D-4/7

Given the equation y = 3x + 4, comparing to y = mx+b

mx = 3x

m = 3

Hence the slope is 3

Equating the slopes

D-4/7 = 3

D-4 = 3*7

D-4 = 21

D = 21+4

D = 25

Hence the value of D is 25

Answer:

1 solution

Step-by-step explanation:

-5 - 11r = 6 ( -2r - 3 )

Distribute:

-5 - 11r = -12r - 18

Add 18 to both sides:

13 - 11r = -12r

Add -11r to both sides:

13 = -r

Divide each side by -1:

-13 = r

1 is your answer

Hope this helps!

The quantity of each colour beads that are in the necklace include the following:

Purple beads = 56

Purple beads = 56silver beads = 24

A ratio is defined as the mathematical expression that shows the number of times one value is contained in another value.

The number of purple beads = 14

The number of silver beads ,= 6

The total quantity of beads = 80

Therefore the total combination = 14+6 = 20

For purple beads = 14/20 × 80/1

= 1120/20 = 56

For silver beads = 6/20×80/1

= 480/20= 24

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Answer:

\(5a^6b^2c^6\)

Step-by-step explanation:

A two-dimensional number line, such as two perpendicular axes, can be thought of as a coordinate system.

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Answer:

The slope, m is -3

\({ \tt{ = \frac{3 - 0}{0 - 1} }} \\ = - 3\)

The y-intercept is b = 3

Symbol of inequality:

\({ \tt{x \geqslant 1}} \\ or : \\ { \tt{y \geqslant 3}}\)

Answer:

base: 8 cm

height: 48cm

Step-by-step explanation:

Let the base of the triangle = b.

You know that the formula for the area of a triangle is 1/2(b)(h), where b is the base and h is the height. So just substitute:

1/2(b)(h) = 192         replace the height with 6b, because it is 6 times the base

1/2(b)(6b) = 192

1/2(6b^2) = 192       multiply both sides by 2 to remove the 1/2

6b^2 = 384             now divide both sides by 6 to remove the 6

b^2 = 64

b = 8

6(8) = 48 = height

Answer:

Hello! Your answer is 9/14.

Answer:

C. sqrt((-3-6)² + (4+2)²)

Step-by-step explanation:

as we are using Pythagoras and asking for the distance as a side length (actually the Hypotenuse, the side opposite of the 90 degree angle) in a right-angled triangle, only an expression of a square root of a sum of squares can be right.

so, A and B are automatically out without even further analysis.

for the distance between 2 points on a coordination grid we build the mentioned right-angled triangle with the difference in x-direction as one side (e.g. "a"), the difference in y-direction as a second side (e.g. "b").

and the direct distance is then the Hypotenuse "c".

you remember Pythagoras :

c² = a² + b²

and therefore

c = sqrt(a² + b²)

in our example "a" is the difference between the 2 x-values.

a = (-3 - 6)

and "b" is the difference between the 2 y-values.

b = (4 - -2) = (4 + 2)

since we have to square them for the formula, the direction of what is subtracted from what is irrelevant, as the square of a negative value is also positive.

c = sqrt((-3 - 6)² + (4 + 2)²)

and that is answer option C

Answer: 28.25%

Step-by-step explanation:

113/400=0.2825=28.25%

45.455% is  the percentage of distance travelled by her in the train .

In math, what is a distance?

The length of the line segment connecting the two sites is used to measure distance between them.

                               The shortest segment of a line connecting a point to a line will have a length equal to the distance between them.

Distance travelled by bus = 3 miles

Distance travelled by train  = 5 miles

Distance travelled by car = 3 miles

Total distance travelled = 3 + 5 + 3 = 11 miles

the percentage of distance travelled by her in the train = 5/11  * 100

                                             = 45.455%

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Step-by-step explanation:

6⅓ + 4¾ + 3 7/12

Convert to improper fraction

= 19/3 + 19/4 + 43/12

LCM= 12

= 76 + 57 + 43

12

= 176/12

= 44/3

Answer

The two consecutive integers such that their sum is 141 will be 70 and 71.

The number system is a way to represent or express numbers.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Let's say that two consecutive integers are x and x + 1.

x + x + 1 = 141

2x + 1 = 141

2x = 140

x = 70

So, x + 1 = 71

Thus, it will be 70 and 71.

Hence "The two consecutive integers such that their sum is 141 will be 70 and 71".

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

-0.75

Step-by-step explanation:

Answer:

5/8 =0.625

Step-by-step explanation:

Hope this helps

Answer:

First, we rearrange the equation to isolate the y-term on one side:

dy/dx + ytanx = secx

Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1

Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1

Integrating both sides with respect to x, we get:  y |secx| = x + C

where C is the constant of integration. Solving for y, we have:

y = (x + C)/|secx|

Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined

The smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.

A figure known as an angle is created by two rays or line segments that meet at a place known as the vertex of the angle. The sides or legs of the angle are other names for the rays or line segments.

To determine the smaller angle made by the two hands of a clock when it is 3 o'clock, we can use the following formula:

angle = |(11/2) * m - 30h|

where:

m is the number of minutes past the hour (in this case, since it is 3 o'clock, m = 0)

h is the hour (in this case, h = 3)

By using this formula, we get:

angle = |(11/2) * 0 - 30(3)| = |0 - 90| = 90

Therefore, the smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.

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Answer:

b and c

Step-by-step explanation:

i took the test

Answer:

0.00085

Hope this helps

Answer:

0.00085

Step-by-step explanation:

2/2348= 0.00085

Answer: 7x + 1

Step-by-step explanation:

(6x-4)+(x+5)

Step 1: Remove Parentheses:

              6x-4+x+5

Step 2: Combine Like Terms:

             7x +1

To calculate how much Rachel and Dustin Lutts pay each quarter, we need to add up the annual premiums for the PPO insurance, dental plan, and vision plan, and then divide the total by the number of quarters in a year.

PPO insurance premium: $12,640

Dental plan premium: $866

Vision plan premium: $444

Total annual premium = PPO premium + Dental premium + Vision premium

Total annual premium = $12,640 + $866 + $444

Total annual premium = $13,950

Number of quarters in a year = 4

Quarterly premium = Total annual premium / Number of quarters

Quarterly premium = $13,950 / 4

Quarterly premium ≈ $3,487.50

Therefore, Rachel and Dustin Lutts pay approximately $3,487.50 each quarter for their insurance premiums.

To find out how much Rachel and Dustin pay each quarter, we need to first add up the cost of their insurance plans and divide by 4.

The PPO insurance premium is $12,640 annually, so the quarterly cost is:

$12,640 / 4 = $3,160

The dental plan costs $866 annually, so the quarterly cost is:

$866 / 4 = $216.50

The vision plan costs $444 annually, so the quarterly cost is:

$444 / 4 = $111

Adding these costs together, we get:

$3,160 + $216.50 + $111 = $3,487.50

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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Answer:

write 7  then write - 420   the answer is 45

Step-by-step explanation:

Answer:

First step

√15x + 4 = 16

Second step

15x + 4 = 256

Third step

15x = 252

Last step

x = 16.8

First step

8x + 12 - 7 = 13

Second step

8x + 5 = 13

Third step

8x = 8

Last step

x = 1

Hope this helps you

Instantaneous velocity represents the velocity at a particular point.

The instantaneous velocity at t = 3 is 7.7 ft/s

The table is given as:

\(\left[\begin{array}{cccccccc}t&0&1&2&3&4&5&6\\s&0&4.9&10.7&23.2&50.4&109.4&237.8\end{array}\right]\)

To calculate the instantaneous velocity at \(t = 0\)

We get the distance at \(t = 3\)

At \(t = 3\), the distance (s) is:

\(s = 23.2\)

So, the instantaneous velocity (v) is:

\(v = \frac st\)

This gives

\(v = \frac{23.2}3\)

Divide 23.2 by 3

\(v = 7.7\)

Hence, the instantaneous velocity at t = 3 is 7.7 ft/s

See attachment for the required graph

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