situation #4
It is known that ∆BIG~∆FUN.


4a. Angle N is congruent to which
angle? [Letter Only]



4b. Using situation #4, what should
go in the place of the smiley face in
this proportion?

NF ☆ ☾
---- = ---- = ----
☻ IB ♡


4c. Using situation #4, what should
go in the place of the moon in this
proportion?

NF ☆ ☾
---- = ---- = ----
☻ IB ♡

Answer:

[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}

Step-by-step explanation:

Solution Given:

To find the inverse we need to exchange Domain to Range and vice-versa.

so

[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}

Distribute the summation over the sum.

[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i[/tex]

Now plug in the known sums and simplify.

[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}[/tex]

Answer:

7 14/45

Step-by-step explanation:

9 1/9 - 1 4/5

82/9 - 9/5

410/45 - 81/45

329/45

7 14/45

Answer:

●7.31

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Answer:

220

Step-by-step explanation :

11 = 5%

100 ÷ 5 = 20

11 × 20 = 220

0.05 × 220 = 11 ✓

0.05 = decimal multiplier of 5%

Answer:

a) [tex]f(x) = x + 3[/tex]

b) [tex]f(x) = -x - 5[/tex]

c) [tex]f(x) = 2x + 6[/tex]

Step-by-step explanation:

To determine the equation of a straight line, we need two things:

1. two known points (coordinates) on the line, used to calculate the gradient

2. the y-intercept of the line (the y-coordinate of the point at which the line crosses the y-axis)

Then we can use the equation:

[tex]\boxed {f(x) = ax + q}[/tex]

where a is the gradient and q is the y-intercept, to determine the equation of the line.

a) known points: (0, 3), (-4, -1)

y-intercept: 3

gradient = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

             ⇒ [tex]\frac{3 - (-1)}{0 - (-4)}[/tex]

             ⇒ [tex]\bf 1[/tex]

∴ a = 1 , q = 3

∴ equation:

[tex]{f(x) = ax + q}[/tex]

[tex]f(x) = 1x + 3[/tex]

⇒ [tex]\bf f(x) = x + 3[/tex]

b) known points: (-7, 2) , (0, -5)

y-intercept = -5

gradient = [tex]\frac{2 - (-5)}{-7 - 0}[/tex]

             ⇒ [tex]\bf -1[/tex]

∴ equation:

[tex]f(x) = -1x + (-5)[/tex]

⇒ [tex]\bf f(x) = -x - 5[/tex]

c) known points: (-3, 0), (0, 6)

y-intercept = 6

gradient = [tex]\frac{6 - 0}{0 - (-3)}[/tex]

             ⇒ [tex]\bf 2[/tex]

∴ equation:

[tex]\bf f(x) = 2x + 6[/tex]

A circle is a figure bounded by a curved side which is referred to as circumference. Thus the area of the shaded region is option D. 81.65.

A circle is a figure bounded by a curved side which is referred to as circumference. Some of its parts are radius, diameter, sector, arc, etc.

The area of a circle can be determined by the given expression:

Area = π[tex]r^{2}[/tex]

where r is the radius of the circle and π = [tex]\frac{22}{7}[/tex]

So, the area of the shaded region can be determined as:

Area of the shaded region = area of the larger circle - area of the smaller circle

Area of the shaded region = π[tex](6.8)^{2}[/tex] - π[tex](4.5)^{2}[/tex]

                                            = π (46.24 - 20.25)

                                            = [tex]\frac{22}{7}[/tex] x 25.99

                                            = [tex]\frac{571.78}{7}[/tex]

Area of the shaded region = 81.683

Thus the appropriate answer to the question is option D. 81.65.

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Using simple interest, it is found that the APR is of 4.472%.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

The parameters are given as follows:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

Hence the APR is found as follows:

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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Answer:

x = 2/7

x = -6

Step-by-step explanation:

You can solve the equation by setting each set of parentheses equal to 0 and simplifying.

7x - 2 = 0                                <----- First set of parentheses

7x = 2                                      <----- Add 2 to both sides

x = 2/7                                    <----- Divide both sides by 7

x + 6 = 0                                 <----- Second set of parentheses

x = -6                                      <----- Subtract 6 from both sides

Answer:

its -14

Step-by-step explanation:

Step-by-step explanation:

the equation of a circle centered at the origin is

x² + y² = r²

r being the radius (the distance of the center to every point on the circle's arc).

so, we get a point on the arc : (0, -5).

what is its distance to the origin ?

the origin is (0, 0).

we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.

that means there is no distance between them in x direction.

the only distance is in y direction : 0 to -5.

a distance is always positive (no matter in what direction).

so, the distance from 0 to -5 is : 5 units.

that means r = 5.

and our equation is

x² + y² = 5² = 25

The pizza originally have 30 slices.

What is linear equation?

An equation in which the highest power of the variable is one is known as linear equation.

We will find number of pizza slices as shown below:

Let pizza originally have x slices.

Adam eats 20% of a pizza

= 0.2x

Bethany eats 1/3 of pizza

=1/3(x)

Charlie eats the remaining 14 slices

0.2x+1/3(x)+14=x

14 = x - 0.2x - 1/3(x)

14 = x - x/5 - x/3

14 = (15x - 3x - 5x)/15

14*15 = 7x

By dividing both sides by 7, we get

30 = x

x = 30

Hence, the pizza originally have 30 slices.

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66.90% of the total bankruptcy fillings are not chapter 13 fillings.

What is bankruptcy?

This is a situation where the management of a company declares that it could no longer pay its debt obligations as it does have the cash resources to do so.

In this case, the total number of bankruptcy fillings is 936,795, out of which 310,061 are chapter 13 filings

fillings that were not chapter 13=936,795-310,061

fillings that were not chapter 13=626,734

fillings that were not chapter 13 as % of total fillings=626,734/936,795

fillings that were not chapter 13 as % of total fillings=66.90%

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The value of angle TUS based on the information given about the circle will be 49°.

It should be noted that a circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Equivalently, a circle is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

The radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

Here, the value of TUS will be:

= 1/2 × TRS

= 1/2 × 98°

= 49°

In conclusion, the correct option is 49°.

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Complete question:

Circle R has a radius of 6 inches. Points S, T, and U lie on circle R, clockwise in alphabetical order. If m∠TRS = 98°, what is m∠TUS?

The amount that will be in the account after 30 years is $188,921.57.

When an amount is compounded annually, it means that once a year, the amount invested and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.

The formula that can be used to determine the future value of the deposit in 30 years is : annuity factor x yearly deposit

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$2000 x [{(1.07^30) - 1} / 0.07] = $188,921.57

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These are the laws of indices. You just have to memorise it, sorry : (

Hope it helps : )

Answer:

c

Step-by-step explanation:

because I had a test on these

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution of system B will be the same as the solution of system A.

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

System A:

x + 6y = 5 and; 3x - 7y = -35

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3.

System B:

x + 6y = 5 and; - 25y = -50

The solution of system B will be the same as the solution of system A.

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From the given system of linear equations, we have;

a. The system of linear equations can be expressed as follows;

y = 22•x - 9.5

y = 2.5•x + 4.1

Rewriting the equations to have the constants on the right, we have;

y - 22•x = - 9.5

y - 2.5•x = 4.1

Solving the above equations using matrices method on a calculator gives;

By direct solving, we have;

22•x - 9.5 = 2.5•x + 4.1

22•x - 2.5•x = 4.1 + 9.5

19.5•x = 13.6

x = 13.6 ÷ 19.5 ≈ 0.697

y = 22•x - 9.5

y = 22×(13.6/19.5) - 9.5 ≈ 5.84

b. 8•x + y - 18 = 0

5•x + 9•y + 4 = 0

Rewriting gives;

8•x + y = 18

5•x + 9•y = -4

Solving with technology gives,;

Solving directly gives;

Which gives;

18 - 8•x = -(5•x + 4)/9

9×(18 - 8•x) = -(5•x + 4)

162 - 72•x = -(5•x + 4)

5•x - 72•x = -162 - 4 = -166

67•x = 166

x = 166 ÷ 67 ≈ 2.478

y = 18 - 8•x

Therefore;

y = 18 - 8 × (166 ÷ 67) ≈ -1.82

c. 6•x + y = 12

5•x + 8•y = -100

Solving the above linear system using technology, we have;

Solving directly, we have;

y = 12 - 6•x

5•x + 8•y = -100

y = (-100 - 5•x)/8

12 - 6•x = (-100 - 5•x)/8

8 × (12 - 6•x) = (-100 - 5•x)

96 - 48•x = (-100 - 5•x)

48•x - 5•x = 96 + 100

43•x = 196

x = 196/43 ≈ 4.56

y = 12 - 6•x

Therefore;

y = 12 - 6×(196/43) ≈ -15.35

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Answer:

√2² cannot be answer yesah

electronic data interchange

Answer:

  1.14200738982×10^26

Step-by-step explanation:

Substitution can make this integral much easier to evaluate.

Let u = 7x² -x. Then du = (14x -1)dx. The limits on x become different limits for u:

  for x = 1: u = 7(1²) -1 = 6

  for x = 3: u = 7(3²) -3 = 60

  [tex]\displaystyle\int_1^3{(14x-1)e^{(7x^2-x)}}\,dx=\int_6^{60}{e^u}\,du=\left.e^u\right|^{60}_6\\\\=e^{60}-e^6\approx e^{60}\approx\boxed{1.14200738982\times10^{26}}[/tex]

The value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

The question has to do with definite integrals

Definite integrals are integrals obtained within a range of values (or limits) of the independent variable.

Given that

For any integral  [tex]\int\limits^a_c {g(x)} \, dx = \int\limits^a_b {g(x)} \, dx + \int\limits^b_c {g(x)} \, dx[/tex]

So,  [tex]\int\limits^{10}_3 {g(x)} \, dx = \int\limits^5_3 {g(x)} \, dx + \int\limits^{10}_5 {g(x)} \, dx[/tex]

So,   [tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

Since

Substituting the values of the variables into the equation, we have

[tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

[tex]\int\limits^{10}_5 {g(x)} \, dx = 36 - 18 \\\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

So, the value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

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The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

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

A geometric sequence is in the form aₙ = ar⁽ⁿ⁻¹⁾, where a is the first term and r is the common ratio.

The geometric sequence 81, 27, 9, 3, … has common ratio:

r = 27/81 = 1/3

The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

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The experiment is not a binomial experiment.

A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a yes or a no.

The conditions for a binomial experiment include:

1. Each trial should be classified either as a success or a failure.

2. There are a fixed number of observations

3. The trials are independent.

4. The number of trials are fixed.

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The scaled copy of the polygon is added as an attachment

The complete question is added as an attachment

The coordinates of the polygon are

A = (-7, 6)

B = (-10, 8)

C = (-10, 10)

D = (-6, 10)

The scale factor is 3.

So, the rule of dilation is

(x, y) = (3x, 3y)

Using the above rule, we have:

A' = (-21, 18)

B' = (-30, 24)

C' = (-30, 30)

D' = (-18, 30)

See attachment for the scaled copy of the polygon

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Answer:

17 & 26

Step-by-step explanation:

The equation

[tex]x+(x+9)=43\\2x+9=43[/tex]

[tex]2x=43-9\\2x=34[/tex]

[tex]x=34/2=17[/tex]

One number is 17

The other number is:

[tex]x+9=17+9=26[/tex]

Hope this helps

Answer:

[tex]\frac{16}{32}[/tex]

Step-by-step explanation:

given

[tex]\frac{1}{2}[/tex] ← multiply numerator and denominator by 16 (2 × 16 = 32 )

= [tex]\frac{16}{32}[/tex]