Simplify 10√3x +4√3x +5√3x

Answer:

1, 17, 33, 49

Step-by-step explanation:

given the first term is 1 then the next 3 terms are

1 + d, 1 + 2d, 1 + 3d ( d is the common difference )

the sum of the first 4 terms is 100 , then

1 + 1 + d + 1 + 2d + 1 + 3d = 100 , that is

4 + 6d = 100 ( subtract 4 from both sides )

6d = 96 ( divide both sides by 6 )

d = 16

1 + d = 1 + 16 = 17

1 + 2d = 1 + 2(16) = 1 + 32 = 33

1 + 3d = 1 + 3(16) = 1 + 48 = 49

the first 4 terms are

1, 17, 33, 49

Answer:

see the file attached!!!!

Answer:

Polygon 3 and polygon 4 are similar to polygon 1.

Step-by-step explanation:

I believe this is the answer from the looks of it. If it's not 3, then try 2. I know one of them is definitely 4 though. I hope this helps!!

Step-by-step explanation:

hope it helps you and give me a brainliest

Step-by-step explanation:

[tex] = \frac{1}{5} + \frac{1}{10} \\ [/tex]

Now make the denominator same...

[tex] = \frac{1}{5} \times \frac{2}{2} + \frac{1}{10} \\ [/tex]

[tex] = \frac{2}{10} + \frac{1}{10} \\ [/tex]

[tex] = \frac{3}{10} \\ [/tex]

:)

..

Answer:

Step-by-step explanation:

The word in the problem that indicates that a negative sign should be used is "descend"

We know that he stops for water breaks four times, and between each water break, he descends 15 meters.

The written equation is:

4*(-15)m = -60m

Why the negative sign is used?

The negative sign is used because the hiker is descending, so its height is decreasing. The word in the problem that indicates that a negative sign should be used is "descend"

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Semiperimeter is used to find the area of various shapes including the equilateral triangle (False).

Semiperimeter is a term used in geometry to refer to half the perimeter of a polygon. It is generally used in formulas for triangles.

However, it is also part of calculations related to other geometric shapes. According to the above, it can be inferred that the semiperimeter can be used to find the area of various geometric figures.

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Step-by-step explanation:

Since we have a right triangle, we use the Pythagorean Theorem

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

or

[tex]c = \sqrt{ {a}^{2} + {b}^{2} } [/tex]

where a and b are the legs and c is the hypotenuse

Remember the legs are the sides that form that right angle, and the hypotenuse is the side opposite of the right angle.

So here the hypotenuse is 8, and one of the legs is 4. So we plug those values into the formula

[tex] 8 = \sqrt{ {b}^{2} + {4}^{2} } [/tex]

Answer:

Step-by-step explanation:

Answer:

(-2, 11) and (2, 3)

Step-by-step explanation:

Given system of equations:

1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3

2) f(x) = -2x + 7 ⇒ y = -2x + 7

Solve Using the Substitution Method:

Step 1: Substitute the the first equation into the second.

⇒ x² - 2x + 3 = -2x + 7

Step 2: Solve for x.

x² - 2x + 3 = -2x + 7 [ Add 2x to both sides. ]

x² - 2x + 2x + 3 = -2x + 2x + 7

⇒ x² + 3 = 7 [ Subtract 3 from both sides. ]

x² + 3 - 3 = 7 - 3

⇒ x² = 4 [ Take the square root of both sides. ]

√x² = √4

x = ± 2

⇒ x = -2, x = 2

Step 3: Solve for y.

Substitute the found x-values into one of the given equations.

y = -2x + 7 ⇒ y = -2(-2) + 7 ⇒ y = 4 + 7 ⇒ y = 11

y = -2x + 7 ⇒ y = -2(2) + 7 ⇒ y = -4 + 7 ⇒ y = 3

The solutions to the system of equations are: (-2, 11) and (2, 3).

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The correct answer is option C the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.

In the proof of the given question, it is given that the ∠AOP and ∠POB are complementary angles by linear pair of theorem but the linear pair of the theorem is applied to the angles with the sum of 180.

Therefore the correct answer is option C the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

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Answer: Both:

The linear pair theorem cannot be used to state ∠XMN is complementary to ∠NMY.

The linear pair theorem cannot be used to state ∠AOP is complementary to ∠POB.

Step-by-step explanation:

Edmentum/Plato

STEP 1 : Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered

|2x-1| < 11

STEP 2 : Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x-1|

For the Negative case we'll use -(2x-1)

For the Positive case we'll use (2x-1)

STEP 3 : Solve the Negative Case

-(2x-1) < 11

Multiply

-2x+1 < 11

Rearrange and Add up

-2x < 10

Divide both sides by 2

-x < 5

Multiply both sides by (-1)

Remember to flip the inequality sign

x > -5

Which is the solution for the Negative Case

STEP 4 : Solve the Positive Case

(2x-1) < 11

Rearrange and Add up

2x < 12

Divide both sides by 2

x < 6

Which is the solution for the Positive Case

STEP 5 : Wrap up the solution

-5 < x < 6

Solution in Interval Notation

(-5,6) .

Answer:

x=(y-3)/4

Step-by-step explanation:

y=4x+3

y-3=4x

x=(y-3)/4

Answer:

This point is not on the line, NOT TRUE

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

          b represents the y-intercept

where the format of a point is (x, y)

Given: y = 3x - 5.1, (-1.2, -3.1)

we can plug in the point (-1.2, -3.1)

-3.1 = 3(-1.2) - 5.1

-3.1 = -3.6 - 5.1

-3.1 = -8.7

-3.1 does not equal -8.7 so this point is not on the line

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Answer:

cost of old motor bike =$5675

he spent on repair =$453

cost that he sold =$7265

profit he made=$7265-$5675+$453

=$7265-$6128

=$1137

Step-by-step explanation:

The product of A and B matrix will be option D; BA = [tex]\left[\begin{array}{ccc}16&10&39\\-32&-30&-18\\-6&-6&-19\end{array}\right][/tex].

If [tex]A = \left[\begin{array}{ccc}-2&-4&2\\5&1&5\\-1&-3&-4\end{array}\right][/tex]and [tex]B = \left[\begin{array}{ccc}2&3&-5\\5&-4&2\\-1&-1&3\end{array}\right][/tex]

then,

BA = [tex]\left[\begin{array}{ccc}2&3&-5\\5&-4&2\\-1&-1&3\end{array}\right] \left[\begin{array}{ccc}-2&-4&2\\5&1&5\\-1&-3&-4\end{array}\right][/tex]

BA = [tex]\left[\begin{array}{ccc}16&10&39\\-32&-30&-18\\-6&-6&-19\end{array}\right][/tex]

Hence, the product of A and B matrix will be option D; BA = [tex]\left[\begin{array}{ccc}16&10&39\\-32&-30&-18\\-6&-6&-19\end{array}\right][/tex].

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The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

a) Yes it does, because the graph of their relationship is a Straight line

b) Independent variables are variables whose variation does not depend on another. Number of works does not depend on followers. Therefore, it is independent

C)number of followers depend on the number of locks passing. It is dependent.

D) Slope = (Y₂- Y₁)/(x₂-x₁) = (100-82)/ (3-0) =  18/3 = 6

It represents the increase in number of followers per week,

E) y-intercept is value of y when x=0

y-intercept = 82. It means his initial number of followers

F) Slope-intercept form → y = mx + c m = slope горе C = y-intercept y = no of followers x= weeks.

Y=6x+82

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Answer:

C

Step-by-step explanation:

SAS axiom

SAS axiom

SAS axiomSAS axiom

SAS axiom

The value of a is 1/64.

The rules of the exponent are

(a) [tex]a^m*a^n=a^{m+n[/tex]

(b)[tex]a^m/a^n=a^{m-n[/tex]

(c)[tex](a^b)^c=a^{bc}[/tex]

(d) [tex]\sqrt[n]{a}=a^{1/n[/tex]

(e) a⁻ⁿ=1/aⁿ

From the table it is clear that

By the rule of the exponent a⁻ⁿ=1/aⁿ

where a=2

2⁻¹ = 1/2¹ = 1/2

2⁻² =1/2² =1/4

2⁻³ =1/2³ =1/8

2⁻⁴ =1/2⁴ =1/16

2⁻⁵ =1/2⁵ =1/32

So we have to calculate the left one where it is given that we have to estimate the value for 2⁻⁶ which is a.

From the above, it is clear that 2⁻ⁿ =1/2ⁿ

using the above formula

2⁻⁶= 1/2⁶ =1/64= a

Therefore the value of a is 1/64.

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Surface area of old cube

Side of new cube

Surface area

Difference

Answer:

A)  6(x + y)² = 6x² + 12xy +6y²

B)  12xy +6y²

Step-by-step explanation:

Surface area of a cube = 6s²  (where s is the side length)

Part A

Given:

⇒ Surface area of the original cube = 6x²

If the side length of the cube is increased by y, then:

⇒ Surface area of the new cube = 6(x + y)²

Expand and simplify:

⇒ 6(x + y)²

⇒ 6(x + y)(x + y)

⇒ 6(x² + xy + xy + y²)

⇒ 6x² + 12xy +6y²

Part B

To find the difference between the surface areas of the new and original cubes, subtract the surface area of the original cube from the surface area of the new cube:

⇒ SA of new cube - SA of original cube

⇒ 6x² + 12xy +6y² - 6x²

⇒ 12xy +6y²

Answer:

1.00 + [(n - 1) × 0.20]

or

0.80 + [n × 0.20]

Step-by-step explanation:

week 1: 1.00

week 2: 1.20

week 3: 1.40

we could rewrite this as:

week 1:  1.00 + [0 × 0.20]

week 2: 1.00 + [1 × 0.20]

week 3: 1.00 + [2 × 0.20]

we can write this overall as:

week __ : 1.00 + [x × 0.20]

> x being the amount of weeks that have passed since week 1

but, we need to express this as in terms of nth, so, we need to figure out how the week is related to the x value

each week, we subtract 1 from the week number [to account for week 1]

so, we can write this as: 1.00 + [(n - 1) × 0.20]

or, we can backtrack from the first week, and start our counting at 0.80:

0.80 + [n × 0.20]

we can test this out:

(week 1)

1.00 + [(n - 1) × 0.20]

1.00 + [(1 - 1) × 0.20]

1.00 + [0 × 0.20]

1.00

or...

(week 1)

0.80 + [n × 0.20]

0.80 + [1 × 0.20]

0.80 + 0.20

= 1.00

So, nth week should be expressed as either:

1.00 + [(n - 1) × 0.20] or

0.80 + [n × 0.20]

(the second one is a little bit more simplified, but it depends on how you're supposed to write it)

hope this helps!!

Answer:

C

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

the y- intercept is the value of y where the line crosses the y- axis , then

y- intercept = 2

Answer:

Groceries Galore

Step-by-step explanation:

1) Find the value of 1 egg for each shop.

Max's Market:

2.04 ÷ 6

= £0.34

Groceries Galore:

2.64 ÷ 8

= £0.33

Fancy Foodstuffs:

4.08 ÷ 12

= £0.34

Therefore, Groceries Galore's price per egg is cheaper.

Answer:

Groceries Galore

Step-by-step explanation:

we have to calculate the price of 2 eggs

in each shop apart ,and then we can infer

which shop offers the cheaper price.

…………………………………………………………

• At Max's market :

2 egg costs 2,04÷3 = £0,68

• At Groceries Galore :

2 egg costs 2,64÷4 = £0,66

• At Fancy Foodstuffs :

4,08÷6 = £0,68

………………………………

Conclusion :

Groceries Galore Offers the Lower price.

Note : we can just determine

the price of one egg in each store ,and then compare.

The distance that edgar runs in a 5-day week will be 4.45 miles.

Distance is defined as the length between the two points it can be represented in mm,cm, meters,km, and miles.

Given that:-

Edgar runs 8/9 of a mile each day. what is the total distance that Edgar runs in a 5-day week?

The total distance will be calculated as:-

D = [tex]\dfrac{8}{9}[/tex] x 5

D = 4.45 miles

Therefore the distance that edgar runs in a 5-day week will be 4.45 miles.

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The proof will be given as:- [tex]\dfrac{tanx+Cotx}{Coscx Cosx} = Sec^2x[/tex].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The proof will be given as:-

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = \dfrac{tanx}{coscxCosx}+\dfrac{Cosx}{CoscxCosx}\\\\[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} =\dfrac{\dfrac{Sinx}{Cosx}}{\dfrac{Cosx}{Sinx}}+\dfrac{\dfrac{Cosx}{Sinx}}{\dfrac{Cosx}{Sinx}}[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = \dfrac{Sin^2x}{Cos^2x}+1[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = tan^2x+1}[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} =Sec^2x[/tex]

Therefore the proof will be given as:- [tex]\dfrac{tanx+Cotx}{Coscx Cosx} = Sec^2x[/tex].

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Answer: 1:2

Step-by-step explanation:

Well, if you're asking for the ratio, it is 1:2

For every 1 notebook bought, there would be 2 free pens.

Since she bought 8 notebooks, just multiply 2 by 8 which will result in 16.

The graph of the greatest integer function is graph A.

A graph is a diagram or a pictorial representation of data or values that show the relationship between quantities or objects.

Given are graphs we need to find the graph of the greatest integer function,

The graph of the greatest integer function is graph A because since it is a greatest integer function, it includes the highest integer, but excludes the lowest since it is the highest integer when x is less than or equal to an integer but greater than x-1.

Hence the graph of the greatest integer function is graph A.

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Answer:

3

Step-by-step explanation:

Factors of 15 are 1, 3, 5, 15

Factors or 6 are 1, 2, 3, 6

HCF = 3

Answer:

its right there.

Step-by-step explanation:

The 3 steps to solve the algebra equation have each sub step as explained and written below.

We are given the algebraic equation;

2x + 5 = 4x - 1

Step 1; After adding 1 to both sides, we have;

2x + 5 + 1 = 4x - 1 + 1

2x + 6 = 4x

Step 2; We subtract 3x from both sides to get;

2x - 2x + 6 = 4x - 2x

2x = 6

Step 3; Divide both sides by 3 to get;

2x/2 = 6/2

x = 3

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