4. Factor:

j) x(x+2) + y (x + 2) - 5(x + 2)

k) 5y2 - 10y3

l) ax + ay + az

5. Factor:

m) yx(y+1) + 4x(y + 1) - 5(y + 1)

n) 6p2 - 3p3

o) 4x4 + 2x

Answer:

Step-by-step explanation:

2| 1   -3    -10  24

 |       2   -2   -24

_______________

   1   -1    -12  |0

b=2

c=-1

d=-2

The value of x in the triangle using the cosine rule is 22.1 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:

c² = a² + b² - 2ab cos C

Where a, b, c are the sides and C is the angle opposite side c.

Using cosine rule:

8² = 14² + 19² - 2(14)(19) * cos(x)

cos(x) = 0.9267

x = 22.1°

The value of x in the triangle using the cosine rule is 22.1 degrees.

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Using the law of Cosines, the value of x to the nearest tenth is 77.8

From the question, we are to determine the value of x

Using the law of Cosines

c² = a² + b² - 2ab cos C

c is the unknown side length  

a and b are the given side lengths

and C is the included angle

From the given information,

a = 63

b = 62

C = 142°

Then,

x² = 63² + 61² -2×63×61 cos 142°

x² = 3969 + 3721 -7686(-0.788)

x² = 7690 + 6056.568

x² = 13746.569

x = √13746.569

x = 77.8

Hence, the value of x to the nearest tenth is 77.8

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Answer:

1.  0.9925  (4 d.p.)

2.  17°

3.  67°

Step-by-step explanation:

Question 2

⇒ sin 83° = 0.9925461516...

⇒ sin 83° = 0.9925 (4 d.p.)

Question 3

[tex]\sf \implies \sin X=0.2923[/tex]

[tex]\sf \implies X=\sin^{-1}(0.2923)[/tex]

[tex]\implies \sf X=16.99570395...^{\circ}[/tex]

[tex]\implies \sf X=17^{\circ}\:\:(nearest\:degree)[/tex]

Question 4

Sine Ratio

[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]

where:

From inspection of the triangle:

Substitute the values into the formula and solve for W:

[tex]\implies \sf \sin(W)=\dfrac{24}{26}[/tex]

[tex]\implies \sf W= \sin^{-1}\left(\dfrac{24}{26}\right)[/tex]

[tex]\implies \sf W=67.38013505...^{\circ}[/tex]

[tex]\implies \sf W=67^{\circ}\:\:(nearest\:degree)[/tex]            

Answer:

$25.10

Step-by-step explanation:

lunch=$7.52

dinner=$9.74

breakfast=$5.16

money left=$2.68

make total money he began with ‘x’

to find the total money he began with it will be

x-lunch+dinner+breakfast=money left

x-$7.52+$9.74+$5.16=$2.68

x-$22.42=$2.68

x=$2.68+$22.42

x=$25.10

Answer:

Ring toss game

Step-by-step explanation:

[tex]2:7[/tex] can be rewritten as [tex]\frac{2}{7}[/tex], which is [tex]\approx0.286[/tex].

We can now compare the probabilities of winning for each game.

[tex]0.286 > 0.25[/tex]

This means the odds of winning the ring toss game ([tex]0.286[/tex]) are higher than the odds of winning the balloon dart game [tex](0.25)[/tex].

The value of x in all case is

1. The value of x is 2

2. The value of x is 1

3.The value of x is 57

4.The value of x is 93

If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

1. As the given angle is 90 degree i.e., complementary angle.

So,

54+10x+16=90

20=10x

x=2

2. 65x-12=43x+10  (Vertically opposite angle)

 22x= 22

x=1

3. 72= x+15  (Vertically opposite angle)

x= 57

4.x+244+23=360  (Complete angle)

 x=93

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Answer:

x = 140°

Step-by-step explanation:

the secant- secant angle 10° is half the difference of the intercepted arcs

10° = [tex]\frac{1}{2}[/tex] (30 - ? )° ( multiply both sides by 2 to clear the fraction )

20° = 30 - ? ( subtract 30° from both sides )

- 10 = - ? ( multiply both sides by - 1 )

10° = ?

the lower arc is a semicircle = 180°

the sum of the arcs in a circle = 360° , then

x = 360° - 180° - 30° - 10° = 360° - 220° = 140°

Answer:

Step-by-step explanation:

To convert a percent to a fraction, we have to remove the percent sign and divide the given number by 100

ex: 11% = 11/100

Answer:.5 for either side

Step-by-step explanation:there are two sides, both equally likely so their probability must be equal and sun to 1. This condition is met when both probabilities are .5

Answer:

50/50 probability

Step-by-step explanation:

The estimated probability that at least one student who have NO PETS is 1/4.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Onyx surveys students at his school and finds that 80% have a pet.

He wants to estimate the probability that, if he randomly selected 4 students, at least one student would NOT have a pet.

lets the numbers 1, 2, 3, and 4 represent a student who HAS a pet, and 5 represent a student who does NOT have a pet.

He then has a computer randomly select 4 numbers and repeats this 20 times.

The estimated probability that at least one student who have NO PETS

= 1/4

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Answer:

The length of one of the sides would be 14 cm.

Step-by-step explanation:

There are 4 sides to a square and the total perimeter is 56 cm meaning that we need to divide 56 by 4 to get the length of one side. 56 divided by 4 is equal to 14 cm, getting your answer. I hope this helps! Have a great day! :)

The statement that proves that quadrilateral JKLM is a kite is (b) LM = JM = 3 and JK = LK = √17

See attachment for the complete question, the graph and the options

The coordinates of the quadrilateral are:

J = (4,5)

K = (5,1)

L = (1,2)

M = (1,5)

Calculate the lengths of the kite using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]JK = \sqrt{(4 -5)^2 + (5 -1)^2} = \sqrt{17[/tex]

[tex]LK = \sqrt{(1 -5)^2 + (2 -1)^2} = \sqrt{17[/tex]

[tex]LM = \sqrt{(1 -1)^2 + (5 -2)^2} = 3[/tex]

[tex]JM = \sqrt{(1 -4)^2 + (5 -5)^2} = 3[/tex]

On a kite, the adjacent sides are of equal lengths

Because LM = JM = 3 and JK = LK = √17, we can conclude that the quadrilateral JKLM is a kite

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Answer:

First one: X= 11.5

Second one: W = 3

X= 41.4°

Third one: 516.8

Step-by-step explanation:

Remember SOH CAH TOA when dealing with trigonometry and study the diagrams well

The ordered pair that is 5 units away is (-1, -3)

What is a line?

A line is a distance between two points.

Analysis:

see attached file.

In conclusion, the ordered pair is (-1, -3)

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The polynomial written in standard from is -7xy³ - 3x³y + 8x²y² + 4x².

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

In other words the terms are arranged by decreasing order of degrees.

The degree of a polynomial is the exponential value of the variables.

Therefore, the polynomial written in standard from in the options is as follows:

-7xy³ - 3x³y + 8x²y² + 4x²

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What is the surface area? 2 mm 3 mm 1 mm square millimeters.

••••••••••••••••••••••••••••••••••••••••••••

- Hence,The square millimeters is 22sqm².

"Problem has been Solve"

(ノ^_^)ノ

Answer :

Surface area is 22mm²

Required solution :

After noticing the question we got to knew that we need to calculate the surface area of cuboid and we've been provided with the values of length, breadth and height of it.

★ Surface area of cuboid :

Substituting values,

>> S.A. = 2 (2 × 3 + 2 × 1 + 3 × 1)

>> S.A. = 2 (6 + 2 + 3)

>> S.A. = 2 (8 + 3)

>> S.A. = 2 (11)

>> S.A. = 2 × 11

>> S.A. = 22

The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The question is incomplete.

The complete question is attached in the picture, please refer picture.

We have an expression:

[tex]= \rm \dfrac{\left(14x^4y^6\right)}{\left(7x^8y^2\right)}[/tex]

[tex]\rm =\dfrac{7\cdot \:2x^4y^6}{7x^8y^2}[/tex]

[tex]\rm =\dfrac{2x^4y^6}{x^8y^2}[/tex]

[tex]\rm =\dfrac{2y^4}{x^4}[/tex]

Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

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Answer:

A

Step-by-step explanation:

imagine explaining

Answer:

1. P(2 or 4) - 2/3

2. P(multiple of 2) - 1

3. P(multiple of 3) 1/3

4. P(odd prime numbers) 0

Step-by-step explanation:

Good luck lol

P(2 or 4) = 2/3

P( multiple of 2) = 1

P( multiple of 3) = 1/3

P(odd prime numbers) = 0

Probability is the likelihood of an event happening or not.

Analysis:

possible outcome = (2,2,4,4,6,6) = 6

P(2 or 4)

n( 2) = required outcome = (2,2) = 2

P(2) = 2/6 = 1/3

n(4) = (4,4) = 2

P(4) = 2/6 = 1/3

P(2 or 4) = 1/3 + 1/3 = 2/3

n( multiple of 2) = (2,2,4,4,6,6) = 6

P( multiple of 2) = 6/6 = 1

n(multiple of 3) = (6,6) = 2

P(multiple of 3) = 2/6 = 1/3

P(odd prime numbers) = 0

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Check the picture below.

Answer:

A. 55

Step-by-step explanation:

P(B|A) expressed in simplest form is  8/105.

Probability determines the chances that an event would happen. The chance of the event happening lies between 0 and 1.

P(B|A)  = (number of blue balls / total number of balls) x (number of white balls / total number of balls - 1 )

(4/15) x 4/14 = 8/105

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Answer:

5.3

Step-by-step explanation:

Since they are similar triangles, we assume the ratio between AM/AN is equal to the ratio between MB/NC.
AM/AN = 6/8 = 3/4
If MB is 4
3/4 = MB/NC = 4/NC
3/4 = 4/NC

3NC = 16
NC = 16/3
16/3 = 5.333333

Answer:

1/3

Step-by-step explanation:

probability = favorable outcomes/total possible outcomes

There are two favorable outcomes, 2 and 5.

There are 6 total possible outcomes.

Make your fraction.

2/6

reduce

1/3

The amount of money Jade and chet will have to purchase the app is $11.6

Where,

x = $2.50

Amount each earned:

Jade = 8 + 2x

= 8 + 2(2.50)

= 8 + 5

= $13

Chet = 4x + 6

= 4(2.50) + 6

= 10 + 6

= $16

Combined earnings = $13 + $16

= $29

Amount planned to save = 40% of combined earnings

= 40% × $29

= 0.4 × 29

= $11.6

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Answer:

1.93 or 2 years old

Step-by-step explanation:

First divide 1,000,000 by 60 to get the hours then by 24 to get the days then by 30 to get the months then by 12 to get the years.

Answer:

2 years old(Rounded)

Keys:

Where Y is Years, m is minutes, and v is the default value for dividing minutes into years.

Step-by-step explanation:

Y = m ÷ v

m = 1,000,000

v = 525,600

m ÷ v = 1.903

Answer:

ill answer

Step-by-step explanation:

but what is the question please make me brillianist