If a and b are 3 × 3 matrices, then det(a − b) = det(a) − det(b) then:_________

The expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.

The power-reducing formula, for cosine, is,

cos² θ = (1/2)[1 + cos 2θ].

In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.

We can do it as follows:

cos⁴ θ

= (cos² θ)²

= {(1/2)[1 + cos 2θ]}²

= (1/4)[1 + cos 2θ]²

= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}

= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)

= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]

= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8

= 3/8 + cos 2θ/4 + cos 4θ/8

= [ 3 + 2cos 2θ + cos 4θ]/8.

Thus, the expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.

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These are the effect on the PPC

1st pairs with a point original to PPC. and 2nd pairs with PPC shifts to the left. and 3rd pair with PPC shifts to the right.

According to the statement

we have given the some conditions and we have to match the each scenario with the effect of the PPC.

So, The given effect on the tiles are Tiles

- the PPC shifts to the right

- the PPC shifts to the left

- a point on the original PPC

- a point inside the PPC

- a point outside the PPC

And we have to join it with its pairs.

So,

First :

A manufacturing unit uses all its resources efficiently = A point on the original PPC

Second :

Andrew has 5 hours to complete his homework but uses only 3 hours, so he doesn’t complete it. = The PPC shifts to the left

Third :

A country acquires part of its neighboring country = The PPC shifts to the right

These are the conditions that satisfy the effect of PPC.

So, These are the effect on the PPC

1st pairs with a point original to PPC. and 2nd pairs with PPC shifts to the left. and 3rd pair with PPC shifts to the right.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Match each scenario with its effect on the PPC.

Tiles

- the PPC shifts to the right

- the PPC shifts to the left

- a point on the original PPC

- a point inside the PPC

- a point outside the PPC

Pairs

- A manufacturing unit uses all its

resources efficiently.

- Andrew has 5 hours to complete his

homework but uses only 3 hours, so

he doesn’t complete it.

- A country acquires part of its neighboring

country.

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^it doesn't need to be this complicated

The factored expression of the polynomial is (x - 3)(x + 4)

The polynomial expression is given as;

x^2 + x - 12

Expand the expression

x^2 + 4x - 3x - 12

Factorize the expression

x(x + 4) -3(x + 4)

Factor out x + 4

(x - 3)(x + 4)

Hence, the factored expression of the polynomial is (x - 3)(x + 4)

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The recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously is f(n + 1) = f(n) + 0.75

The general recursive function is expressed as:

an+1 = d + an

where

r is the common difference

Given the sequence below

1.5, 2.25, 3.0, 3.75, ...

Common difference =  2.25 - 1.5 = 0.75

Substitute

f(n + 1) = f(n) + d

f(n + 1) = f(n) + 0.75

Hence the recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously is f(n + 1) = f(n) + 0.75

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The measure of angle D in the inscribed triangle is as follows;

∠D = 63 degrees

The circle theorem can be use to find the ∠D as follows;

The triangle BCD is inscribed in the circle.

Using circle theorem,

The angle of each triangle is double the angle of the arc it create.

Therefore,

arc BC = m∠D

m∠B = 134 / 2 = 67 degrees.

Therefore, using sum of angles in a triangle.

67 + 50 + m∠D = 180

m∠D = 180 - 50 - 67

m∠D = 63 degrees.

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Answer:

x = 90°

Step-by-step explanation:

Hello!

The sum of angles on a straight line is 180°.

To find the value of angle x°, we can subtract all the given angles form 180°.

The value of x is 90°.

the value of 'x' is 0. 9

For the given triangle, we have the;

We want to find the value of x

Using the tangent ratio

Tan θ = opposite/adjacent

Let's substitute the value of theta, opposite and adjacent

Tan 60 = 13 + x / 7

1. 73 = 13+ x/ 7

cross multiply

1. 73 × 7 = 13 + x

12. 1 = 13 + x

x = 13 - 12. 1

x = 0. 9

We can see that the value of x is 0. 9

Thus, the value of 'x' is 0. 9

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By trigonometric functions we find that the measure of angle A is approximately 0.12π radians.

In this question we have a right triangle, of which the length of two sides are known (AB, BC). We can know the measure of angle A by trigonometric functions:

[tex]\tan A = \frac{BC}{AC}[/tex]

[tex]\tan A = \frac{2}{5}[/tex]

A ≈ 0.12π radians

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Answer:

b

Step-by-step explanation:

edge

Answer:

3x³ + 3x² - 30x - 48

Step-by-step explanation:

3(x + 2)(x² - x - 8) ← distribute (x + 2) by 3

= (3x + 6)(x² - x - 8)

each term in the second factor is multiplied by each term in the first factor

= 3x(x² - x - 8) + 6(x² - x - 8) ← distribute both parenthesis

= 3x³ - 3x² - 24x + 6x² - 6x - 48 ← collect like terms

= 3x³ + 3x² - 30x - 48

Answer:

A 0.08

Step-by-step explanation:

The price of the turkey based on the percentage given is $15.81.

It was stated that the cost is $15.50 but that there was a 2% increment in price.

Therefore, the new price will be:

= $15.50 + (2% × $15.50)

= $15.50 + $0.31

= $15.81

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Answer:

1/2

1/3

Step-by-step explanation:

x=1/2

x=-1/3

Answer:

[tex]x_{1} =-\frac{1}{3} \\x_{2} =\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]6x^{2} -x-1=0[/tex]

Factoring the equation:

[tex](3x+1)(2x-1)=0[/tex]

Extract the roots:

First factor

[tex]3x+1=0\\3x=-1\\x_{1} =-\frac{1}{3}[/tex]

Second factor

[tex]2x-1=0\\2x=1\\x_{2} =\frac{1}{2}[/tex]

Hope this helps

The number of angles that are alternate exterior with angle 5 is one, which is angle 11.

Alternate exterior angles are formed on the outside of the two parallel lines that are intersected by a transversal, each being located on the opposite side of the transversal.

The alternate exterior angle pairs are two angles that are supplementary. This means they add up to give a sum of 180 degrees.

Considering transversal s and parallel lines t and u, the angle that is an alternate angle to angle 5 is angle 11.

Angle 11 is the only angle that is alternate exterior angles with angle 5. therefore, we can conclude that, the number of angles that are alternate exterior with angle 5 is just 1, which is angle 11.

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Answer:

A

Step-by-step explanation:

Area of the rectangle is 15*20=300

Area of the triangle is 8*17/2=68

Total area is 300+68=368

Perimeter is 15+20+20+8+17=80

Answer:

[tex]\rm {P = 80 \space\ feet,\space\ A = 360 \space\ square \space\ feet}[/tex]

Step-by-step explanation:

The perimeter of a shape is the sum of all the sides of the shape.

• Perimeter of the polygon = 15 + 20 + 17 + 8 + 20

                                            = 80 feet

To find the area of the polygon, we can separately find the areas of the triangle and the rectangle and then add them together.

• Area of rectangle = length × breadth

                                = 15 × 20

                                = 300 square feet

• Area of triangle = [tex]\frac{1}{2}[/tex] × base × height

As the height of the triangle is not provided, we have to calculate it.
Let the height of triangle = [tex]x[/tex]

Using Pythagoras's theorem:
[tex]x^2 + 8^2 = 17^2[/tex]

⇒  [tex]x^2 = 17^2 - 8^2[/tex]

⇒  [tex]x = \sqrt{17^2 - 8^2}[/tex]

⇒ [tex]x=\bf15[/tex]

Now using this value of height, we can find the area of the triangle:

Area of triangle =  [tex]\frac{1}{2}[/tex]  × 8 × 15

                          = 60 square feet

• Finally, we can add the areas of the triangle and rectangle together to find the area of the polygon:

Area of polygon = 300 + 60

                           = 360 square feet

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

As per the given information ~

The given triangles are similar, so their corresponding sides should be in same ratio :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x}{4} = \cfrac{5}{x - 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{x}{2} = \cfrac{5}{x - 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x(x - 3) = 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 3x = 10 [/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 3x - 10 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 5x + 2x - 10 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: x(x - 5) + 2(x - 5) = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: (x + 2)(x - 5) = 0[/tex]

so, x = 5 or -2

but since side length can't be negative, we will take x = 5 neglecting the negative value (-2)

So, side lengths of unknown sides are :

[tex] \qquad \sf  \dashrightarrow \: {2x = 2 × 5 = 10 units} [/tex]

and

[tex]\qquad \sf  \dashrightarrow \: x - 3 = 5 - 3 = 2 \: \: units[/tex]

Answer:  0.0059   (choice C)

Explanation:

There are 4 jacks out of 52 cards total.

4/52 = 1/13 is the probability of getting a jack.

The same applies to an ace as well.

The probability of a jack followed by an ace is (1/13)*(1/13) = 0.0059 approximately, when we replace the first card. If the replacement wasn't done, then the second probability would be different from 1/13.

Answer:

we spend maths class in a. day =85m

.:we spend in a maths class in a 9 week period=85x9x7:- 24=223.125

Answer:

volume = 3549.203

Step-by-step explanation:

you need to subtract the volume of the cylinder from the volume of the box

cylinder:

[tex]vol=\pi r^2h\\V=\pi (5)^2(20)\\V=\pi (25)(20)\\V=500\pi[/tex]

box:

[tex]vol=(length)(width)(height)\\V=(20)(16)(16)\\V=5120[/tex]

subtract:

[tex]5120-500\pi =3549.203[/tex]

Answer:

10

Step-by-step explanation:

Answer:

You have to complete around 49 assignments everyday to finish in one week.

Step-by-step explanation:

• First, we have to calculate the number of assignments left to do:

Assignments remaining = 419 - 79

                                        = 340

• There are 7 days in a week, which means 340 assignments need to be completed in 7 days.

7 days  ⇒  340 assignments

1 day    ⇒   340 ÷ 7

            =    48.6

            ≅ 49 assignments

∴ You have to complete around 49 assignments everyday to finish in one week.

Answer:

30

Step-by-step explanation:

18/60 =.3 x 100 = 30

Answer:

70 degrees = a

Step-by-step explanation:

Triangle= 180 degrees.

Therefore, since a and the unmarked angle are congruent since it is an isosceles triangle, we subtract 40 from 180, with a result of 140. With 140, we divide by 2 to find the degrees for both the unmarked angle and angle a, since they are congruent. 140/2 = 70, Angle A will equal to 70 degrees

The correct equation of the given graph is; Option A: y = |x/2| - 5

From the given graph, we can see the following coordinates;

At x = 0, y = -5

At x = 1, y = -4.5

At x = -1, y = -4.5

At x = 2, y = -4

At x = -2, y = -4

Since the y-intercept is at y = -5, looking at the given options, the only one that is correct will be;

y = |x/2| - 5

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Answer:

x = 8

Step-by-step explanation:

complementary angles sum to 90°

sum the 2 angles and equate to 90

5x + 50 = 90 ( subtract 50 from both sides )

5x = 40 ( divide both sides by 5 )

x = 8

Answer:

1000.

Step-by-step explanation:

We need 4 weights where 3 of them add up to

900, 1400, 1600 or 1800g.

Not sure of the method for doing this!

Lets assume that the answer is 1000 g.

Then the  3 that make 1800 could be

1000 500 and 300

- then to make 900 we need a 100g tomato giving:

1000 500 300 and 100 grams

So the 1400 will be the 1000, 300 and 100 tomato

and the 1600 will be 1000, 500 and 100.

That seems to fit !!

The bearing to take is 134 degrees and the shortest distance is 14.3 km

The attached diagram represents a labelled version of the ship movement

The angle at Q is

Q = 180 - 155 + 90 + 120 - 90

This gives

Q = 145

The distance PR is calculated as:

PR^2 =PQ^2 + QR^2 - 2 * PQ * QR * cos(Q)

This gives

PR^2 = 9^2 + 6^2 - 2 * 9 * 6 * cos(145)

Evaluate

PR^2 = 205.46

Take the square root

PR = 14.3 km

The angle at P is then calculated as:

QR/sin(P) = PR/sin(Q)

This gives

6/sin(P) = 14.3/sin(145)

Evaluate the quotient

6/sin(P) = 24.93

Make sin(P) the subject

sin(P) = 6/24.93

Divide

sin(P) = 0.2407

Take the arc sin of both sides

P = 14

The bearing is then calculated as:

Bearing = P + 120

This gives

Bearing = 14 + 120

Evaluate

Bearing = 134

Hence, the bearing to take is 134 degrees

In (a), we have

PR = 14.3 km

This represents the shortest distance

Hence, the shortest distance is 14.3 km

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The equivalent expression after factoring 20a + 28b = ( a + 7b) using the distributive property is 19a + 21b = 0.

According to the distributive property, an expression in the form A (B + C) can be solved as A (B + C) = AB + AC. This distributive law applies to subtraction as well and is written as A (B - C) = AB - AC. This means that operand A is shared by the other two operands.

The given equation is  20a + 28b = ( a + 7b).

20a + 28b = ( a + 7b).
Now, subtract both sides by a.
20a - a + 28b = a + 7b - a.

19a + 28b = 7b.
Now, subtracting both sides by 7b.
19a + 28b - 7b = 7b - 7b.
19a + 21b = 0.
Therefore, the equivalent expression to  20a + 28b = ( a + 7b) is 19a + 21b = 0.

Answer: 30%

Step-by-step explanation: