any
ete the equivalent ratio table.
D
B
(Equivalent Ratio
21
35
20 50
27
70
12:13
17:5
23
S
9
11
2
18
22

This is a geometric progression

So

The general formUla is

[tex]\\ \rm\Rrightarrow a(n)=ar^{n-1}[/tex]

[tex]\\ \rm\Rrightarrow a(n)=\dfrac{1}{4}\left(\dfrac{1}{4}\right)^{n-1}[/tex]

Answer:

[tex]\displaystyle \lim_{n \to \infty} \dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)[/tex]

Step-by-step explanation:

Series: the sum of the elements of a sequence.

Therefore, as the numbers have been defined as a series and we need to find [tex]S_n[/tex]:

[tex]\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}+...[/tex]

First determine if the sequence is arithmetic or geometric.

If it is an arithmetic sequence, there will be a common difference between consecutive terms.

if it is a geometric sequence, there will be a common ratio between consecutive terms.

From inspection of the terms, we can see that there is a common ratio of 1/4, as each term is the previous term multiplied by 1/4, so it is a geometric series.

Sum of the first n terms of a geometric series:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Given:

[tex]a=\dfrac{1}{4}[/tex]

[tex]r=\dfrac{1}{4}[/tex]

Substitute the values of a and r into the formula:

[tex]\implies S_n=\dfrac{\frac{1}{4}\left(1-\left(\frac{1}{4}\right)^n\right)}{1-\frac{1}{4}}[/tex]

[tex]\implies S_n=\dfrac{\frac{1}{4}\left(1-\left(\frac{1}{4}\right)^n\right)}{\frac{3}{4}}[/tex]

[tex]\implies S_n=\dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)[/tex]

Therefore:

[tex]\displaystyle \lim_{n \to \infty} \dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)[/tex]

Step-by-step explanation:

4.500 mm³ → cm³

1 cm³ = 1.000 mm³

= 4.500 ÷ 1.000

= 4,5 cm³ IS THE ANSWER

Answer:

A = 50x^2+3

B = 75

C = 55

Step-by-step explanation:

[tex]f(x)=2x^2+3\\g(x)=5x[/tex]

A. f(g(x))

[tex]2(5x)^2+3\\2(25x^2)+3\\=50x^2+3[/tex]

B. g(g(3))

[tex]5(5(3))\\5(15)\\=75[/tex]

C. g(f(-2))

[tex]g(2(-2)^2+3)\\g(8+3)\\g(11)\\5(11)\\=55[/tex]

Answer:

3.2

The value of C when B is 5 is 3.2

Step-by-step explanation:

Answer:

1 (2/3) or 1.66666667

Step-by-step explanation:

The slope of a line is found by using the equation :

y2 - y 1 / x2 - x1

So all we have to do is plug in our values given.

To find which belongs with which variable (such as x2 or y1), we do the following:

We know that the coordinates of a point are represented by (x, y). So we must assign a number to each points number.

(2, 8) will be x1 and y1.

(5, 13) will be x2 and y2

Plug in the values :

13 - 8 = 5

5 - 2 = 3

5 / 3 = 1 (2/3)

So, the slope of the line is 1.66666667 or 1 and (2/3)s

Answer:

Step-by-step explanation:

Answer:

15 ($20 dollar bills) and 19 ($10 dollar bills) ! Pretty sure this is correct, if wrong let me know and i'll make a question for you to give your points back, i dont know if i can do that but i can try!! Have a good day.

Answer:

Graph C

Step-by-step explanation:

Rearrange the terms so the equation is in slope-intercept form:
4x + y = 7
y = -4x + 7
The slope is -4, and the only graph that has a slope of -4 is graph C.

Triangles FGH and ABC are congruent because of the: AAS congruence theorem.

The AAS congruence theorem states that when two angles and one non-included side in one triangle are congruent to corresponding two angles and one non-included side in another triangle, then both triangles are congruent.

In the proof given, it is established that both triangles have two corresponding congruent angles, and also, BC ≅ GH which are non-included sides.

Therefore, both triangles are congruent because of the AAS congruence theorem.

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The complete question is

"What is the component form of the vector represented by 2a when a =⟨−2,3⟩?"

The Component form of the vector represented by 2a is (-4,6)

The component form of a vector is represented by (x, y) that has gone x units left to the origin and y units up from the origin.

Given, a=(-2,3)

By using scalar multiplication,

2a = (2(-2), 2(3))

2a = (-4,6).

Therefore the component form of 2a=(-4,6)

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Answer:

330.6

Step-by-step explanation:

You have to enter 290 for x.

T(290) = 290 + 0.14(290)

T(290) = 290 + 40.6

T(290) = 330.6

Answer:

-69

Step-by-step explanation:

inches:-69

-5 9/12 (-5 3/4 clearer) feet

Explanation in detail:

Write the equation down and distribute it.

3x - 1 = 2(x + 34)

3x - 1 = 2x + 68

Remove the variable on one side first (it makes solving the equation less complicated.)

3x - 1 = 2x + 68

-3x -3x

-1 = -x + 68

On all sides, subtract 68.

-1 = -x + 68

-68 -68

-69 = x

I'm guessing the answer in feet and inches is...

inches:-69

-5 9/12 (-5 3/4 simplified) feet

Answer:

c

Step-by-step explanation:

Answer:

a) The mass of a box of bolts is greater.

b) 3/20 kg

Step-by-step explanation:

a) Firstly, you have to make the denominators of the two fractions the same (by finding the LCM of the denominators).

The LCM of 4 and 5 is 20.

Converting 3/4 into denominator 20:

[tex]\frac{3 * 5}{4 * 5}[/tex]

= 15/20

Converting 3/5 into denominator 20:

[tex]\frac{3 * 4}{5 * 4}[/tex]

= 12/20

Now comparing the numerators:

15 > 12

Hence,

3/4 > 3/5

b) Difference of the boxes can be done by subtracting the numbers with the same denominator:

15/20 - 12/20

= 3/20 kg

Hope this helps and feel free to give me brainliest! :)

Answer:

the LCM of 18 25 40 80 81 and 72 is 226800

i hope this helps you

Step-by-step explanation:

by which method

prime factorization , division or defination method

The activity series is an arrangement of species in order of reactivity.

The activity series is an arrangement of species in order of reactivity. The position of a specie in the series determines the possibility of certain reactions.

The following are the fates of these reactions;

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Answer:

The answer is figure A, B, C, D.

Step-by-step explanation:

Because, polygon means a shape with more then 1 side, and in your pic all of the figures have more than one side, so that's the answer.

LHL in not equal to RHL , Therefore the limit does not exists , Option D is the answer.(none)

The limit of a function at a certain point is the value that the function approaches as the argument of the function approaches the same point.

It is given that

lim x->2 for f(x)

[tex]\lim_{x \rightarrow 2^-}f(x) = \lim_{x\rightarrow 2^+}f(x)[/tex]

f(x) = 2x+1 x ≤2

f(x)= x² , x >2

When both the function tends to 2

Left Hand Limit

f(x) = 2 *2 +1

f(x) = 5

Right Hand Limit

f(x) = x² ,

f(x) = 4

LHL in not equal to RHL , Therefore the limit does not exists.

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Answer:

[tex]\boxed{\bf B. \: c = 4 \sqrt{3} }[/tex]

Step-by-step explanation:

Since a = 6, then, b = 3.47 ( opposite of 30°).

By applying the pythagoras theorem..

Answer:

4√3 or B

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: f(0) = -3 [/tex]

[tex]\qquad \tt \rightarrow \: f(2) = 1[/tex]

[tex]\qquad \tt \rightarrow \: f(4) = 1 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

F(x) represents the value of y on curve for given value of x

[tex] \textsf{\large First -} [/tex]

[tex]\qquad \tt \rightarrow \: f(0) =( 0) {}^{2} - 3[/tex]

[ since 0 < 2 ]

[tex]\qquad \tt \rightarrow \: f(0) = 0 {}^{} - 3[/tex]

[tex]\qquad \tt \rightarrow \: f(0) = - 3[/tex]

[tex] \textsf{\large Second} [/tex]

[tex]\qquad \tt \rightarrow \: f(2) = (2) {}^{2} - 3[/tex]

[ since 2 = 2 ]

[tex]\qquad \tt \rightarrow \: f(2) = 4{}^{} - 3[/tex]

[tex]\qquad \tt \rightarrow \: f(2) = 1[/tex]

[tex] \textsf{\large Third -} [/tex]

[tex]\qquad \tt \rightarrow \: f(4) = - 4 + 5[/tex]

[ since 4 > 2 ]

[tex]\qquad \tt \rightarrow \: f(4) = 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

34.3 square unit.

Step-by-step explanation:

[tex]calculate \: df \: using \: pythagoras \\ theorem \\ df {}^{2} = 8 {}^{2} + 6 {}^{2} \\ df {}^{2} = 64 + 36 \\ df {}^{2} = 100 \\ df = \sqrt{100} \\ df = 10 \\ calculating \: for \: the \: area \: of \: \\ angle \: \: dfg \\ using \: heros \: formular \\ \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{10 + 11 + 7}{2} = \frac{28}{2} = 14 \\ area = \sqrt{14(14 - 10)(14 - 11)14(14 - 7)} \\ area = \sqrt{14(4)(3)(7)} = \sqrt{14 \times 84} \\ area = \sqrt{1176} = 34.2928564 \\ to \: the \: nearest \: tenth \: = 34.3[/tex]

Here it is stated that, side DE = 8 units, side EF = 6 units, side FG = 7 units and side GD = 11 units. We have to find area of ∆DFG, here we will use heron's formula which is given by:

Area of ∆ = √[s(s – a) (s – b) (s – c)]

Here a, b, and c are sides of ∆. We have;

So firstly lets calculate a i.e DF by using Pythagoras theorem on ∆DEF:

➸ DF² = 8² + 6²

➸ DF² = (8 × 8) + (6 × 6)

➸ DF² = 64 + 36

➸ DF² = 100

➸ DF = √(100)

➸ DF = √(10 × 10)

➸ DF = 10 units

Now, lets calculate s i.e semi - perimeter:

Now, using heron's formula on ∆DFG to calculate its area:

➸ Area(∆DFG) = √[14(14 – 10) (14 – 7) (14 – 11)]

➸ Area(∆DFG) = √[14(4) (7) (3)

➸ Area(∆DFG) = √(14 × 4 × 7 × 3)

We can write it as;

➸ Area(∆DFG) = √(2 × 2 × 2 × 7 × 7 × 3)

➸ Area(∆DFG) = 2 × 7√(2 × 3)

➸ Area(∆DFG) = 14√(6)

➸ Area(∆DFG) = 14 × 2.449

➸ Area(∆DFG) = 34.28

➸ Area(∆DFG) = 34.3 square units (approx)

Answer:

(x+y)

Step-by-step explanation:

[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

Thus, the HCF is (x+y).

Answer:

(x + y)

Step-by-step explanation:

Factorizing both terms :

The HCF of the terms is (x + y).

Answer:

[tex]\boxed {a, b, c, d}[/tex]

Step-by-step explanation:

Rhombuses, parallelograms, rectangles, and squares cannot be classified as trapezoids as they have 2 pairs of parallel sides each. But quadrilaterals can be classified as trapezoids if they have a pair of parallel sides and a pair of non-parallel sides.

a) rhombuses

b) parallelograms

c) rectangles

d) squares

Answer:

A. (6x + 7)(6x - 7)

Step-by-step explanation:

use difference of squares, which says a^2 - b^2 =(a+b)(a-b)

take the square roots of the two numbers, 6x and 7, and use them as a and b

Answer:

7,853.982

Step-by-step explanation:

Edg 2022

By looking at the graph of the piecewise function, we can see that:

On the graph, we have a piecewise function, which we want to evaluate in some different values.

First we have x  = -0.0001

This value belongs to the interval (-5, 0), and by looking at the graph, you can see that the function on that interval is equal to -9, then:

G(-0.0001) = -9

x = 0

x = 0 belongs to the interval [0, 9). On that interval the function values -1. (x = 0 belongs to that interval because we have a closed dot). Then we conclude

G(0) = -1

x = 0.0001

This value also belongs to the interval  [0, 9)

Then G(0.0001) = -1

Finally, x = 9.

If you look at the domain of the function, you can see that there is an open dot at x = 9.

This means that x = 9 does not belong to that domain, so:

G(9) is not defined.

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Answer:

9

Step-by-step explanation:

The numerical length of GH is 20.

Given, FH=4x+8, FG=x and GH=5x.

We need to determine the numerical length of GH.

In geometry, a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line that is between its endpoints.

Given Point G is on the line segment FH, then FG + GH = FH.

Now, substitute the given values into the formula as shown:

x + 5x = 4x + 8

6x = 4x + 8

6x - 4x = 8

2x = 8

x=4

To get the length of GH substitute x=4 for 5x

That is, GH = 5(4)= 20

Hence, the numerical length of GH is 20.

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