Write fraction that represents the parts shaded red (indicated by "R*) in the figure shown below.
R
R
R
R
R
W
R
R
W

The surface area of the triangular prism is B. 1,008 \(cm^{2}\)

Triangular Prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.

How to determine this

The surface area of the triangular prism =  Area of the front Triangle + Area of the triangle + Each sides of the triangle by the length of the triangular prism.

Area of the front and back triangle will be the the same given the same base and height

To find the area of the triangle = 1/2 * Base * Height

Where base = 12 cm

Height = 9 cm

Area = 1/2 * 12 cm * 9 cm

Area = 6 * 9 \(cm^{2}\)

Area of the one triangle = 54 \(cm^{2}\)

So, by multiplying each sides of the triangle by the length

= Base * Length

= 12 cm * 25 cm

= 300\(cm^{2}\)

Height * Length

= 9 cm * 25 cm

= 225 \(cm^{2}\)

Then, Hypotenuse * Length

= 15 cm * 25 cm

= 375 \(cm^{2}\)

Surface area = 54\(cm^{2}\) + 54\(cm^{2}\) * 300\(cm^{2}\) + 225\(cm^{2}\) + 375\(cm^{2}\)

Surface Area = 1,008\(cm^{2}\)

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Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.

Weekly salary = Hourly pay rate * Number of hours worked

Weekly salary = $12/hour * 20 hours

Weekly salary = $240

So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

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Answer:

Step-by-step explanation:

use the distance formula

dist = sqrt[ (x2-x1)^2 + (y2-y1)^2 ]

where point one ,P1,  is A and point 2, P2,  is C, so

P1 = (x1,y1) = (-7,3)

P2 =(x2,y2) = (0,6)

then

dist = sqrt[ (0 - (-7))^2 + (6-3)^2 ]

dist = sqrt [ 7^2 + 3^2 ]

dist = sqrt [49 +9 ]

dist = sqrt [58]

dist = 7.6157....

AC = 7.6 ( rounded to nearest tenth)

Answer:

No

Step-by-step explanation:

There is no formula

There is no formula

Answer:

Step-by-step explanation:

We know that the sides in a square are equal length. We also know that you have to multiply length by width to get area. So if we know that the length of one side is 16 feet then all we have to do if multiply 16 by 16. Hence why the answer is 256 square feet of carpet.

Using a piece-wise function, the constraints are:

\(65x, x < 7\)

\(375 + 55x, x \geq 7\)

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

A piece-wise function is a function that has multiple definitions, depending on the value of the input.

In this problem:

Less than 7 days the rental price is $65 per day.

Thus, one constraint is:

\(65x, x < 7\)

Once a tenant stays  seven or more days, the price is $375 plus $55 per day past seven.

Thus, the other constraint is:

\(375 + 55x, x \geq 7\)

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Answer: a and d

Step-by-step explanation:

its easy. U can just solve the problem

The angles of a right angled triangle with acute angles of ratio 4:5 are as follows:

40 degrees = 0.698132 radian

50 degrees = 0.872665 radians

90 degrees = 1.5708 radians

Right angle triangle has one of its angle as 90 degrees. Therefore, the sum of the other two angles are less than 90 degrees.

The acute angle are in the ratio 4:5. Therefore,

The other angle = 90 - 40 = 50 degrees.

The angles in radian are as follows:

40 degrees = 0.698132 radian

50 degrees = 0.872665 radians

90 degrees = 1.5708 radians

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The shaded region of the rectangle is 242.9 cm² and the shaded region of the sector is 7.1 square units.

Question 17) is a figure of a rectangle and two inscribed circles.

The area of a rectangle is expressed as: A = length × width

The area of a circle is expressed as: A = πr²

Where r is the radius.

To determine the area of the shaded region, we simply subtract the areas of the two circles from the area of the rectangle.

Area = ( Length × width ) - 2( πr² )

Area = ( 40 × 10 ) - 2( π × 5² )

Area = ( 400 ) - 2( 25π )

Area = 400- 50π

Area = 242.9 cm²

Area of the shaded region is 242.9 squared centimeters.

Question 18) is the a figure a sector of a circle and a right triangle.

The area of a sector is expressed as: A = (θ/360º) × πr²

The area of a triangle  is expressed as: A = 1/2 × base × height

To determine the area of the shaded region, we simply subtract the areas of the triangle from the area of the sector.

Hence:

Area = ( (θ/360º) × πr² ) - ( 1/2 × base × height )

Plug in the values:

Area = ( (90/360º) × π × 5² ) - ( 1/2 × 5 × 5 )

Area = 25π/4 - 12.5

Area = 7.1

Therefore, the area of the shaded region is 7.1 square units.

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Answer:

y=-2x

Step-by-step explanation:

Therefore, the end behavior of the function f(x) is: f(x) → 0- as x → -∞ and f(x) → 1 as x → ∞.

In mathematics, a function is a rule that assigns a unique output value to each input value. Functions are often represented as equations or graphs that relate the input (also known as the independent variable) to the output (also known as the dependent variable). The input is usually denoted by the variable x, and the output is usually denoted by the variable y. Functions can be used to model relationships between different quantities, such as time and distance, or temperature and pressure. They are a fundamental concept in mathematics and are used in many fields, including physics, engineering, economics, and computer science.

Here,

To determine the end behavior of the function f(x) = (-4x³+ 7x + 9)/(8x⁶ - 9x⁴ - 2x), we need to consider the limit of the function as x approaches positive or negative infinity.

As x approaches negative infinity, the highest power of x in the numerator is -4x³, which will dominate the function. The highest power of x in the denominator is 8x⁶, which will also dominate the function. Therefore, we can simplify the function to:

f(x) ≈ (-4x³)/(8x⁶) = -1/(2x³)

As x approaches negative infinity, the denominator of this simplified function will become very large (since x³ becomes very negative), causing the function to approach 0 from the negative side:

f(x) → 0- as x → -∞

As x approaches positive infinity, the highest power of x in the numerator and denominator are both 8x⁶. Therefore, we can simplify the function to:

f(x) ≈ (8x⁶)/(8x⁶) = 1

As x approaches positive infinity, the function will approach 1 from the positive side:

f(x) → 1 as x → ∞

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Complete question:

Consider the following rational function fff. f(x)=\dfrac{-4x^3+7x+9}{8x^6-9x^4-2x}f(x)= 8x 6 −9x 4 −2x −4x 3 +7x+9 ​ f, left parenthesis, x, right parenthesis, equals, start fraction, minus, 4, x, cubed, plus, 7, x, plus, 9, divided by, 8, x, start superscript, 6, end superscript, minus, 9, x, start superscript, 4, end superscript, minus, 2, x, end fraction Determine fff's end behavior. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to -\inftyx→−∞x, \to, minus, infinity. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to \inftyx→∞x, \to, infinity.

Answer:

6x+7=13

2/3x+8= 8.66

Step-by-step explanation:

calculator and rule with a compass

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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\(\text{Let,}\\\\~~~~~~~x=1-4i,\\\\\implies x-1 = -4i\\ \\\implies (x-1)^2 =(-4i)^2\\\\\implies x^2 -2x +1 = -16\\\\\implies x^2 -2x +1 +16 = 0\\\\\implies x^2 -2x +17=0\\\\\text{So,}~ x^2 -2x +17 ~\text{is a factor of the 3 degree polynomial.}\\ \\\text{The polynomial is,}\\\\P(x) = (x-3)(x^2 -2x +17)\\\\~~~~~~~=x^3-2x^2+17x -3x^2 +6x -51\\\\~~~~~~~=x^3 -5x^2 +23x -51\)

Answer:

\(5xy\)

Step-by-step explanation:

\(\mathrm{Factor\:}:5x^2y\)

\(5\cdot \:x\cdot \:x\cdot \:y\)

\(\mathrm{Factor\:}:10xy^2\)

\(2\cdot \:5\cdot \:x\cdot \:y\cdot \:y\)

Common factor:-

\(5\cdot \:x\cdot \:y\)

OAmalOHopeO

Answer:

falseeeee

Step-by-step explanation:

im smart lol ight so so

3/1 · 2/3

3 times 2=6

6/3=2 not 3 my dude

Answer:

30

Step-by-step explanation:

150/5 = 30

30+30+30+30+30 = 150

Answer:

Step-by-step explanation:

given:

line f:  y+3 = \(\frac{1}{6}\)(x-2)

line g:   P1=(x1,y1) = ( -6,1)    and parallel to  f  ( same slope)

use point-slope, again  

y-y2 = m(x-x1)

y-1=\(\frac{1}{6}\)(x-(-6))

y-1 =\(\frac{1}{6}\)(x+6)

y-1 = \(\frac{1}{6}\)x +1

y = \(\frac{1}{6}\)x + 1 +1

y = \(\frac{1}{6}\)x + 2   ( in slope intercept form  y= mx+b)

The question that Diondra would ask that does not allow for variability is A. Which movie did her best friend like the most?

The other three questions ("How many awards did each movie win?", "What is the total dollar amount that each movie made from ticket sales?", and "How many weeks did each movie play in the theater?") all offer metrics by which a movie's popularity could be measured, and those measurements could vary from movie to movie.

However, the question about her best friend's favorite movie depends solely on the opinion of one individual, not a variable measure, and therefore doesn't allow for variability.

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Answer:

  1/2401

Step-by-step explanation:

  \(7^{-4}=\dfrac{1}{7^4}=\boxed{\dfrac{1}{2401}}\)

The perimeter of the pond is 2.92 meters.

A right-angled triangle is a triangle in which one of the angles measures exactly 90 degrees, also known as a right angle.

The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

The perimeter of a right-angled triangle is the sum of the lengths of its three sides.

Here we have

The Hypotenuse of the triangle is 1.46 m    

The angle between hypotenuse and perpendicular height = 73°

From triagonometric ratios,

=> cos A = Perpendicular height/ Hypotenuse.

=> cos (73) = Perpendicular height/1.46

=> Perpendicular height = 1.46 × 0.29 = 0.42 m

As we know from Pythagoras' theorem,

Hypotenuse² = side² + side²    

Side = √Hypotenuse² - side²  

= √[(1.46)²- (0.42)²]  = 1.04

Therefore, the sides of the pond are 1.46 m, 0.42 m, and 1.04

Hence, perimeter of the pond =  1.46 + 0.42 + 1.04 = 2.92 meters  

Therefore,

The perimeter of the pond is 2.92 meters.

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The complete Question is given below

The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

The given expression is 5x²+6x+4+x²+x

Simplifying the given expression

5x²+6x+4+x²+x

Firstly, put the similar terms together

5x²+x²+6x+x+4

Adding the similar terms

6x²+7x+4

∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.

Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

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Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

Answer: x<69

Step-by-step explanation:

For this problem, we solve is just as we would if it was an equal sign.

x+9<78       [subtract 9 on both sides]

x<69

Using proportions, it is found that 21/10 divided by 2 and 4/5 represents the number of shifts that Jammar worked.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

For this problem, we have that following rule of three:

One shift - 2 and 4/5 hours.

x shifts - 21/10 hours.

Applying cross multiplication, the number of shifts is found as follows:

2 4/5x = 21/10.

x = (21/10)/(2 4/5)

Hence 21/10 divided by 2 and 4/5 represents the number of shifts that Jammar worked.

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Answer:

Step-by-step explanation:

o the expression

21

10

÷

2

3

4

10

21

​

÷2

4

3

​

represents the length of each shift.

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.