To pass a particular score a student has to achieve a mean of at least 50% in the ten pieces of work that form the assessment items. In the first nine of these pieces of work the student achieved a mean of 46%. What percentage mark must the student achieve in the tenth item if he is to pass the course?

By using properties of right triangles and trigonometric functions, we conclude that the length of the side BC is 19 units.

In this problem we can use trigonometric functions to determine the length of the side BC in three steps:

Step 1

BE = AB/tan 60°

BE = 19√2 /4

Step 2

BD = BE/cos 45°

BD = 19/2

Step 3

BC = BD/sin 30°

BC = 19

To learn more on trigonometric functions: https://brainly.com/question/6904750

#SPJ1

The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.

The given values exist

x,      f(x)

6,      -2

7,       4

8,       6

9,       4

10,      -2

The equation of the function in vertex form exists

f(x) = a(x - h)² + k

To estimate the values of a, h, and k,

When x = 6, f(x) = -2 then

-2 = a(6 - h)² + k

= (h²-12·h+36)·a + k.............(1)

When x = 7, f(x) = 4 then

4 = a( 7- h)² + k

= (h²-14·h+49)·a + k...........(2)

When x = 8, f(x) = 6

6 = a( 8- h)² + k ...........(3)

When x = 9, f(x) = 4.

4 = a( 9- h)² + k ..........(4)

When x = 10, f(x) = -2

-2 = a(10- h)² + k ...........(5)

Subtract equation (1) from (2)

4 - 2 = a( 7- h)² + k - (a(6 - h)² + k )

= 13·a - 2·a·h........(6)

Subtract equation (4) from (2)

a (9 - h)² + k - a( 7- h)² + k

32a -4ah = 0

Simplifying the equation, we get

4h = 32

h = 32/4 = 8

From equation (6) we have;

13·a - 2·a·8 = 6

-3a = 6

a = -2

From equation (1), we have;

-2 = -2 × ( 10- 8)² + k

-2 = -8 + k

k = 6

The value of k = 6.

The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.

To learn more about quadratic function refer to: https://brainly.com/question/25841119

#SPJ9

y=5(14-x)(x) quadratic equation best models the volume of the box .

What is volume of cuboid?

Perimeter = 2(width + length) =28

Let x=width of base, then length of base = (28/2)-x = 14-x

Volume of box = length*width*height

=x(14-x)*5  ⇒ 5x(14-x)(x)

Therefore, y=5(14-x)(x) quadratic equation best models the volume of the box .

Learn more about cuboid

brainly.com/question/19754639

#SPJ4

The expression that represents the height of the oblique prism is: 1/2x.

What is the Volume of a Prism?

Prism Volume = base area × height of the prism

Given that the oblique prism has:

Volume = 1/2x³ cubic units

edge length = x units

Therefore,

base area = x²

Thus:

1/2x³ = (x²)(height)

Divide both sides by x²

1/2x³ ÷ x² = height

1/2x³ × 1/x² = height

x³/2 × 1/x² = height

height = x³/2x²

height = x/2

Therefore, the expression that represents the height of the oblique prism is: 1/2x.

Learn more about oblique prism

brainly.com/question/20837986

#SPJ4

The complete question is -

An oblique prism with a square base of edge length x units has a volume of x3 cubic units. Which expression represents the height of the prism?

Answer:3 - x/4

Step-by-step explanation: quotient of x and 4 = x/4. 3 minus x/4 = 3 - x/4.

The expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].

We have a sentence - "3 minus the quotient of x and 4".

We have to determine the expression that represents the sentence.

The expression representing the above statement is -

x - y = π.

According to the question, we have -

3 minus the quotient of x and 4.

Using the Division Algorithm -

x = 4q + r

Substituting r = 0 by introducing decimals in the quotient, we get -

q = [tex]$\frac{x}{4}[/tex]

Therefore -

[tex]$3 -\frac{x}{4}[/tex]

Hence, the expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].

To solve more questions on Expression modelling, visit the link below-

brainly.com/question/20876878

#SPJ2

The inequality of the graph is expressed as: y > 1/2x + 2.

The graph given has a broken line and the shaded part is above the boundary line, therefore, we would use the sign, ">" in our inequality. The inequality would be expressed as y > mx + b.

Find the slope (m):

Slope (m) = rise/run = 1 units/2 units

m = 1/2

b = 2 (y-intercepts)

Substitute m = 1/2 and b = 2 into y > mx + b

y > 1/2x + 2.

Learn more about inequality on:

https://brainly.com/question/24372553

#SPJ1

The amount of cash needed to retire baldwin's bond early based on the brokerage will be $5427896.

It should be noted that from the information given, we are to calculate the amount of cash needed to retire baldwin's bond early based on the brokerage.

This will be:

= 6000 + (5756951 × 94.18/100)

= 6000 + 5421896.45

= 5427896

Therefore, the amount of cash needed to retire baldwin's bond early based on the brokerage will be $5427896.

Learn more about brokerage on:

brainly.com/question/14898119

#SPJ1

Answer:5

Step-by-step explanation:

321 123

Area of the base = 60 inches²

Height of the prism = 4 inches

perimeter of the base = 34 inches

Surface area of the rectangular prism =  256 inches²

The surface area of a rectangular prism can be calculated as follows;

area of the base = B = 12 × 5 = 60 inches²

Height of the prism = 4 inches

Perimeter of the base is the sum of the whole side of the base of the rectangular prism.

Therefore,

perimeter of the base = 12 + 12 + 5 + 5 = 34 inches

Surface area of the rectangular prism = 2B + ph

where

Therefore,

Surface area of the rectangular prism = 2(60) + 34(4)

Surface area of the rectangular prism = 120 + 136

Surface area of the rectangular prism =  256 inches²

learn more on rectangular prism here: https://brainly.com/question/9183590

#SPJ1

Answer:

The first option

Kindly award branliest

The quadrilaterals that describe DEFG include parallelogram, rhombus, and square

It should be noted that a quadrilateral simply means a close shape and a polygon that has four sides.

In this case, the quadrilaterals that describe DEFG include parallelogram, rhombus, and square. In a parallelogram, it should be noted that the sides are parallel to each other.

Therefore, the quadrilaterals that describe DEFG include parallelogram, rhombus, and square.

Learn more about quadrilateral on:

brainly.com/question/23935806

#SPJ1

The star system is pictured is  open cluster

A type of star cluster known as an open cluster is composed of up to a few thousand stars that are around the same age and originated from the same massive molecular cloud. Within the Milky Way galaxy, more than 1,100 open clusters have been found, and it is believed that there are many more.

The Sun and the things that circle it make up the gravitationally bound solar system. It was created 4.6 billion years ago when a massive interstellar molecular cloud collapsed because to gravity. The Sun is the system's primary mass source, while Jupiter is home to the majority of the system's leftover mass.

To know more about Open cluster visit:

https://brainly.com/question/9881073

#SPJ4

I understand that the question you are looking for is :

| Will mark brainliest | Which type of star system is pictured? |

A. globular cluster

B. open cluster

C. binary

Answer:

B

Step-by-step explanation:

open cluster

Answer:

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

The distance traveled by two planes in an hour is:

Let the rate of one plane be x, then the other plane's rate is x - 66.

The sum of two rates is the distance traveled in one hour:

So the rate of one plane is 926 km/h and of the other plane is:

Answer:

That's a reflection in the x axis.

Step-by-step explanation:

Triangle C is the mirror image  of B with the x axis acting as a mirror.

since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.

[tex]\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}[/tex]

The required length of the side BM is 29.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

In the given question,

Point M is the midpoint of line AB.

AM = 4x + 13,

and BM = 3x + 17

To find the length of MB, use midpoint property.

Since, Point M is the midpoint of AB,

Therefore, AM = MB

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

The length of MB = 3x + 17 = 3 × 4 + 17 = 12 + 17 = 29.

The length of MB, where M is midpoint of AB, is 29.

To know more about Algebra on:

https://brainly.com/question/24875240

#SPJ2

Answer:

1241

Step-by-step explanation:

∴

L.C.M. of 28, 36 and 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260

∴

the required number is 1260 - 19 = 1241

Hence, if we add 19 to 1241 we will get 1260 which is exactly divisible by 28, 36 and 45.

Answer:

[tex]\displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x=-4 \ln |x|+5 \ln|x-1|+\dfrac{3}{x-1}+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x[/tex]

Factor the denominator:

[tex]\begin{aligned}\implies x^3-2x^2+x & = x(x^2-2x+1)\\& = x(x^2-x-x+1)\\& = x(x(x-1)-1(x-1))\\ & = x((x-1)(x-1))\\& = x(x-1)^2\end{aligned}[/tex]

[tex]\implies \displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x=\displaystyle \int \dfrac{x^2-4}{x(x-1)^2}\:\:\text{d}x[/tex]

Take partial fractions of the given fraction by writing out the fraction as an identity:

[tex]\begin{aligned}\dfrac{x^2-4}{x(x-1)^2} & \equiv \dfrac{A}{x}+\dfrac{B}{(x-1)}+\dfrac{C}{(x-1)^2}\\\\ \implies \dfrac{x^2-4}{x(x-1)^2} & \equiv \dfrac{A(x-1)^2}{x(x-1)^2}+\dfrac{Bx(x-1)}{x(x-1)^2}+\dfrac{Cx}{x(x-1)^2}\\\\ \implies x^2-4 & \equiv A(x-1)^2+Bx(x-1)+Cx \end{aligned}[/tex]

Calculate the values of A and C using substitution:

[tex]\textsf{when }x=0 \implies -4=A(1)+B(0)+C(0) \implies A=-4[/tex]

[tex]\textsf{when }x=1 \implies -3=A(0)+B(0)+C(1) \implies C=-3[/tex]

Therefore:

[tex]\begin{aligned}\implies x^2-4 & \equiv -4(x-1)^2+Bx(x-1)-3x\\& \equiv -4(x^2-2x+1)+B(x^2-x)-3x\\& \equiv -4x^2+8x-4+Bx^2-Bx-3x\\& \equiv (B-4)x^2+(5-B)x-4\\\end{aligned}[/tex]

Compare constants to find B:

[tex]\implies 1=B-4 \implies B=5[/tex]

Substitute the found values of A, B and C:

[tex]\implies \displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x=\displaystyle \int -\dfrac{4}{x}+\dfrac{5}{(x-1)}-\dfrac{3}{(x-1)^2}\:\:\text{d}x[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]

[tex]\implies \displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x=\displaystyle \int -\dfrac{4}{x}+\dfrac{5}{(x-1)}-3(x-1)^{-2}}\:\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating} $\dfrac{1}{x}$\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $ax^n$}\\\\$\displaystyle \int ax^n\:\text{d}x=\dfrac{ax^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

[tex]\begin{aligned}\implies \displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x & =\displaystyle \int -\dfrac{4}{x}+\dfrac{5}{(x-1)}-3(x-1)^{-2}}\:\:\text{d}x\\\\& = \displaystyle -4\int \dfrac{1}{x}\:\:\text{d}x+5\int \dfrac{1}{(x-1)}\:\:\text{d}x-3 \int (x-1)^{-2}}\:\:\text{d}x\\\\& = \displaystyle -4 \ln |x|+5 \ln|x-1|-3 \int (x-1)^{-2}}\:\:\text{d}x\end{aligned}[/tex]

Use Integration by Substitution:

[tex]\textsf{Let }u=(x-1) \implies \dfrac{\text{d}u}{\text{d}x}=1 \implies \text{d}x=\text{d}u}[/tex]

Therefore:

[tex]\implies \displaystyle -4 \ln |x|+5 \ln|x-1|-3 \int (x-1)^{-2}}\:\:\text{d}x[/tex]

[tex]\implies \displaystyle -4 \ln |x|+5 \ln|x-1|-3 \int u^{-2}}\:\:\text{d}u[/tex]

[tex]\implies -4 \ln |x|+5 \ln|x-1|-\dfrac{3}{-1}u^{-2+1}+\text{C}[/tex]

[tex]\implies -4 \ln |x|+5 \ln|x-1|+3u^{-1}+\text{C}[/tex]

[tex]\implies -4 \ln |x|+5 \ln|x-1|+\dfrac{3}{u}+\text{C}[/tex]

Substitute back in u = (x - 1):

[tex]\implies -4 \ln |x|+5 \ln|x-1|+\dfrac{3}{x-1}+\text{C}[/tex]

Learn more about integration here:

https://brainly.com/question/27988986

https://brainly.com/question/27805589

Eliminate [tex]y[/tex].

[tex]u + v = (3x - 4y) + (x + 4y) = 4x \implies x = \dfrac{u+v}4[/tex]

Eliminate [tex]x[/tex].

[tex]u - 3v = (3x - 4y) - 3 (x + 4y) = -16y \implies y = \dfrac{3v-u}{16}[/tex]

The Jacobian for this change of coordinates is

[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} \dfrac14 & \dfrac14 \\\\ -\dfrac1{16} & \dfrac3{16} \end{bmatrix}[/tex]

with determinant

[tex]\det(J) = \dfrac14\cdot\dfrac3{16} - \dfrac14\cdot\left(-\dfrac1{16}\right) = \dfrac1{16}[/tex]

The explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21

The given parameters are:

The explicit form is for an arithmetic function.

An arithmetic function has an explicit form represented as:

f(n) = a + (n -1) * d

Substitute the values of n and a in the above equation

f(n) = 3 + (n -1) * -4

Evaluate the product i.e. multiply -4 by (n - 1)

f(n) = 3 -4(n - 1)

Rewrite the equation as

f(n) = -4(n - 1) + 3

The seventh term is then calculated as:

f(n) = -4(n - 1) + 3

Substitute 7 for n in the above equation

f(7) = -4(7 - 1) + 3

Evaluate

f(7) = -21

Hence, the explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21

Read more about arithmetic sequence at:

https://brainly.com/question/15412619

#SPJ1

Answer:

x = 1; y = 2

Step-by-step explanation:

y = 3x − 1

y = -4x + 6

In the first equation, y = 3x - 1.

Substitute 3x - 1 for y in the second equation.

3x - 1 = -4x + 6

7x = 7

x = 1

Substitute 1 for x in the first original equation.

y = 3x - 1

y = 3(1) - 1

y = 3 - 1

y = 2

Solution: x = 1; y = 2

The magnitude of the resulting vector, u - v, is approximately 5.83

and its angle of direction is approximately 59.04°.

We want to subtract vector v from vector u.

We are given;

v = <2, -3> = 2i - 3j

u = <5, 2> = 5i + 2j

u - v = 5i + 2j - (2i - 3j)

= 5i + 2j - 2i + 3j

= 3i + 5j

Resultant vector = √(3² + 5²)

Resultant vector = √34 ≈ 5.83

Angle of direction of resultant vector is;

tan θ = (5/3)

θ = tan⁻¹(5/3)

θ = 59.04°

Read more about Magnitude of Vector at; https://brainly.com/question/3184914

#SPJ1

Answer:

Step-by-step explanation:

6:1 i think

Answers

The ratio x:y:z is 10:5:3  

Ali got 20,000

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

Explanation:

Let

Those amounts add to 36,000

x+y+z = 36,000

We're told that x = 2y, so let's replace x with 2y in the equation above to get these steps

x+y+z = 36,000

2y+y+z = 36,000

3y+z = 36,000

We're also told that 3y = 5z, so we can replace that previously mentioned 3y with 5z to end up with one variable, in which we can solve for like shown below.

3y+z = 36,000

5z+z = 36,000

6z = 36,000

z = (36,000)/6

z = 6,000

This tells us that Chris got 6,000

Use this to find y

3y = 5z

3y = 5*6,000

3y = 30,000

y = (30,000)/3

y = 10,000

Ben received 10,000

Lastly, determine x.

x = 2y

x = 2*10,000

x = 20,000 which is the amount Ali got.

The ratio x:y:z turns into 20,000:10,000:6,000 which fully simplifies to 10:5:3 after dividing all three parts by the GCF 2000. It might be tempting to try to reduce the 10:5 portion into 2:1, but we cannot divide by 5 since it's not a factor of that 3 at the end.

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

Check:

Ali + Ben + Chris = 20,000 + 10,000 + 6,000 = 36,000

which helps confirm the answer.

The total amount Aisha would pay to paint her room is $54.

The first step is to determine the area of the walls. The walls have the shape of a rectangle. Thus, the formula for the area of a rectangle would be used to determine the area of the wall.

Area of the three walls without a door : 3 x (length x width)

3 x (2.4 x 5.2) = 37.44 m²

Area of the fourth wall with a door : area of the wall - area of the door

(2.4 x 5.2) - (2 x 0.8) = 10.88m²

Total area of the walls : area of the three walls + area of the wall with the door

10.88m² + 37.44 m² = 48.32 m²

The next step is to determine the number of tins that would be needed:

48.32 /12 = 4.03

5 tins would needed

Cost of the 5 tins: (4 x 12) + (0.5 x 12) = $54

To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449

#SPJ1

The simplified equivalent expression exists -1.9b + 7.8.

An equivalent expression exists an expression that contain the same value or worth as another expression, but does not look the same.

Combine the coefficient of the term b, we get

1.3b + 7.8–3.2b

= (1.3−3.2)⋅b + 7.8

simplifying the equation, we get

= (- 1.9) +b + 7.8

= −1.9b + 7.8

The simplified equivalent expression exists -1.9b + 7.8.

To learn more about equivalent expression refer to:

https://brainly.com/question/17175081

#SPJ4

The bags of candy that was sold is 6

The bags of cookies that was sold is 10.

$8.50c + $4.50o = 79 equation 1

o - c = 6

o = 6 + c  equation 2

Where:

Substitute for o in equation 1 using equation 2

$8.50c + $4.50(6 + c) = 79

$8.50c + 27 + 4.50c = 79

$8.50c + 4.50c = 79 - 27

$13c = 52

c = 52 / 13

c = 4

Substitute for c in equation 2

0 = 6 + 4 = 10

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

The athlete that has the shortest training ride is athlete A.

The athlete that has the shorter range is Athlete B.

The athlete that has the greater median is Athlete B.

The athlete that has the greater IQR is  athlete A.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The first whisker represents the minimum number and the second whisker represents the maximum number. The difference between the whiskers is known as range.

Range of Athlete A = 36 - 13 = 13

Range of Athlete B = 30 - 19 = 11

Training ride of  Athlete A = 16

Training ride of  Athlete B = 21

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Median of  Athlete A = 20

Median of  Athlete B = 25

IQR of  Athlete A = 30 - 16 = 14

IQR of  Athlete B = 28 - 21 = 7

To learn more about box plots, please check: https://brainly.com/question/27215146

#SPJ1

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{-\cfrac{2}{5}}(x-\stackrel{x_1}{10})[/tex]