Alex, Stephen and Bridget share some sweets in the ratio 5:4:2. Alex gets 21 more sweets than Bridget. How many sweets are there altogether?

The equation of the required perpendicular line is y = (-5/4)x - 30.

We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation of the given straight line is y = (4/5)x + 23. We need to find the equation of the straight line that is perpendicular to the given line and passes through the point that has coordinates (-40, 20).

The slope of the given line is 45. Let the slope of the required perpendicular line be represented by the variable "m". The slope of the perpendicular line must be the negative reciprocal of the slope of the given line.

m = -1/(4/5)

m = -5/4

The equation of the required line is of the form y = mx + c.

y = (-5/4)x + c

We know that this line passes the point (-40, 20).

20 = (-5/4)(-40) + c

20 = 50 + c

c = -30

Hence, the equation of the required line is y = (-5/4)x - 30.

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The ratio that can be used to find x is sin 21 = x/22.

The trigonometric ratios are the ratios that we can use to obtain the sides and the angles that are in a right angled triangle. The term right angled triangle has to do with a triangle that has one of its angles as 90 degrees.

Now;

Given that;

Sin θ = opposite/hypotenuse

opposite = x

hypotenuse = 22

θ  = 21 degrees

It now follows that to obtain the side x we have to use;

sin 21 = x/22

Hence, in looking for the side x, we have to use sin 21 = x/22

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Answer:

A) $75

B) y = 30x + 15

C) (24, 735) **graph below

D) Yes, there is a proportional relationship

Step-by-step explanation:

We can represent this relationship with an equation.

y = 30x + 15

where x would represent the months and y would be the total cost. The 15 would be the initial fee, which only occurs once.

A) Using the relationship [tex]y = 30x + 15[/tex], we can substitute 2 for x, since that would represent the months.

[tex]y = 30x + 15\\y = 30(2) + 15\\y = 75[/tex]

It would be 75 dollars.

B) The total cost for x months would just be the relationship

[tex]y = 30x + 15[/tex]

C) 2 years would represent 24 months. The screen shot below would represent the relationship. The y axis would be the total cost in dollars and the x axis would be the months. (24, 735)

D) Yes, there is a proportional relationship because as the time (months) progress or increases so does the price (dollars). The graph is linear too, which means it increases.

The equation for the rational function will be f(x) = (x² - 16)/(x - 2) and the denominator cannot be zero.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The rational function with an x-intercept at (–4, 0) and (4, 0), a vertical asymptote at x = 2, and an oblique asymptote at y = x + 2.

The rational function has x-2 in the denominator.

The denominator cannot be zero.

The rational function will be:

[tex]y=\dfrac{\left(x^{2}-16\right)}{x-2}[/tex]

Thus, the equation for the rational function will be f(x) = (x² - 16)/(x - 2) and the denominator cannot be zero.

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Answer:

its a

Step-by-step explanation:

Answer:

Answer D

Step-by-step explanation:

Multiply them all out. D is 4.04

Answer: D is correct I took the test without having to see the answer just wanted to help u out:)

Step-by-step explanation:

The number nickel is 12, and the number dimes are 8 if Jill has 20 coins, consisting of nickels and dimes totaling $1.40.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Jill has 20 coins, consisting of nickels and dimes totaling $1.40.

Let the number of nickels be n, and the number of dimes is 20 - n.

$1 = 10 dimes

$1 = 20 nickels

(1/20)n + (1/10)(20 - n) = 1.40

After solving:

n = 12

The number nickel = 12

The number dimes = 20 - 12 = 8

Thus, the number nickel is 12, and the number dimes are 8 if Jill has 20 coins, consisting of nickels and dimes totalling $1.40.

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The coordinates that represents the position of the library is (0, -8)

Each unit on the grid represents 1 mile

Tia is going from park to library

The coordinates of the park = (5, -5)

First she must go 3 miles to the south, Therefore there will be change in the y coordinates and the x coordinates will be same

New coordinate of the Tia's position = (5, -8)

Then she must go 5 miles west, there will be change in the x coordinates and the y coordinates will be same

New coordinates of the Tia's position = (0, -8)

Hence, the coordinates that represents the position of the library is (0, -8)

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The initial bird population density is 3713.

Given info;

A certain county received a new species of bird 25 years ago. According to biologists, the population doubles every ten years and is currently 21,000 people.

To get the initial size of the bird population;

We use the formula,

[tex]P(t)=Po* 2^\frac{t}{10}[/tex]

Where Po is the initial population and t is the time in years.

[tex]21000= P(25)=Po*2^\frac{25}{10}[/tex]

[tex]21000= Po*2^\frac{5}{2}[/tex]

[tex]21000= 4\sqrt{2}*Po[/tex]

[tex]Po = 21000/4\sqrt{2}[/tex]

[tex]Po = 3712.31\\Po = 3713[/tex]

Hence, the initial size of the bird population is 3713.

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With deceleration of 6 ft/s² and initial speed of 66 ft/s, the airplane will stop after travelling 363 ft.

Use the equation of motion:

v² = u² + 2 · a · s

Where:

v = final velocity

a = acceleration

u = initial velocity

s = distance

Deceleration is a negative acceleration.

Parameters given from the problem:

u = 66 ft/s

a = - 6 ft/s²

v = 0  since the airplane stops.

Plug these parameters into the formula:

v² = u² + 2 · a · s

0 = 66² + 2 · (-6)· s

s = 66² / 12

s = 363 ft.

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Answer:

Rs. 450

Step-by-step explanation:

Selling Price ----- 750

Reduced by 40% therefore 40/100 x 750

=300

750-300= 450

Answer:

$450

Step-by-step explanation:

40 percent *750 =

(40:100)*750 =

(40*750):100 =

30000:100 = 300

750-300=$450

Using combination formula , total 987 ways or outcomes are possible /involve atleast 8 heads.

We have given that, a coin is tossed 10 times .

total possble outcomes = 2¹⁰ = 1024

here, the chances of occurrence of tail and heads and equal so, this is independent event .

we want to calculate total numbers of possble wats atleast 8 heads occurs .

At least 8 heads means exactly two toss gives Tail as a result.

here we count sequences with exactly 8 heads, and also count sequences with more than three heads. We could compute this by equivalent, by subtracting from 1025 the number of sequences with no head, only one head, and only 2 heads

= 1024 - ⁸C₀ ( + ⁸C₁ + ⁸C₂ )

= 1024 - ( 1+8+28) = 1024 - 37

= 987

Hence , 987 outcomes involve atleast 8 heads.

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Answer:

x y

-2 -9

0 1

2 -9

4 -19

explanation:

you simply replace the x with the figure given in the x table or columns or rows

Answer:

so -2024y0000 division is s

The simplified expression to represent the number of members this year is 1.15m

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, the membership in the volunteers Club increased by 15% from last year. If the number of members last year was m.

The number of members will be:

= Old members+ Increase in members

= m + (15% × m)

= m + 0.15m

= 1.15m

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Answer:

D

Step-by-step explanation:

The slope if before the x so in this case it's -3.

The y-intercept is at the end so it's -2.

Answer:

D. slope = -3 and y-intercept = -2

Step-by-step explanation:

Slope Intercept Form:

The variables:

y = -3x -2

Answer:

121-129 F is in between

Step-by-step explanation:

Answer: 274.05 dollars

Step-by-step explanation:

9.45 x 5 x 3 = 141.75

9.45 x 7 x 2 = 132.3

141.75 + 132.3 = 274.05

Brainliest by any chance?

Answer:

equilateral acute

Step-by-step explanation:

equilateral-- all the sides have the same length

acute-- all the angles are below 90 degree

Answer:

Step-by-step explanation:

You'r answer should be an equilateral acute.

You invest $892 at the end of each year in an investment with annual rate of return 6%. Then  the investment worth after 15 year will be 14182.8 dollar

we know that

SI = prt

where

SI= simple interest

A= amount

P= principal

r= rate

t= number of year

according to the question

SI= 892* 0.06*1

 = 53.52

 A =  892+53.52

    = 945.52

after 15 years amount will be

A= 945.52*15

  = 14182.8

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Probability that the second card is an ace, given that the first card is an ace is 1/ 221

Without replacement means drawing the card first but not putting back to the deck and then drawing again.

Total number of cards in a deck = 52

Number of an ace in whole deck = 4

let event of getting an ace in first draw be A

and event of getting an ace in second draw be B

P(A) = 4 / 52 = 1 /13

drawing without replacement

P(B) = 3 / 51 = 1 / 17

Probability that second card is an ace given that first card is an ace is

P(A).P(B) =

1/13 × 1/ 17 = 1 / 221

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x=14/3 and y=-28 when  x = -6. and  y = 20 for equation y = 6x +8

x=30 and y=-4 for when  x = -6. and  y = 20 for equation  y = 2/3x

x=-15 and y=11,  when  x = -6. and  y = 20 for equation   y = -x + 5

x=2 and y=-2 ,  when  x = -6. and  y = 20 for equation  y = 6.5x + 7

Two or more expressions with an Equal sign is called as Equation.

For equation y = 6x +8

When x=-6

y=6(-6)+8=-36+8=-28

when y =20

20=6x+8

28=6x

x=28/6=14/3

x=14/3 and y=-28 when  x = -6. and  y = 20 for equation y = 6x +8

For equation y = 2/3x

When x=-6, y=2/3(-6)=-4

y=20, 20=2/3x

60=2x

x=30

x=30 and y=-4 for when  x = -6. and  y = 20 for equation  y = 2/3x

For equation y = -x + 5

When x=-6, y=6+5=11

When y=20,

20=-x+5

15=-x

x=-15

x=-15 and y=11,  when  x = -6. and  y = 20 for equation   y = -x + 5

For equation y = 6.5x + 7

When x=-6

y=6.5(-6)+7

y=-39+7=-2

When y=20

20=6.5x+7

13=6.5x

2=x

x=2 and y=-2 ,  when  x = -6. and  y = 20 for equation  y = 6.5x + 7

Hence,

x=14/3 and y=-28 when  x = -6. and  y = 20 for equation y = 6x +8

x=30 and y=-4 for when  x = -6. and  y = 20 for equation  y = 2/3x

x=-15 and y=11,  when  x = -6. and  y = 20 for equation   y = -x + 5

x=2 and y=-2 ,  when  x = -6. and  y = 20 for equation  y = 6.5x + 7

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Answer:

66

Step-by-step explanation:

The angle 108 is equal to the angle 42 plus the vertical angle to x

108-42 = 66 this is the measurement for the vertical angle to x. Vertical angles are congruent so angle x is 66

Answer:

508.94

Step-by-step explanation:

V = 1/3pi(r^2)(h)

plug in the values of r and h

V = 1/3(pi)(9^2)(6)

simplify

V = 508. 9380099

Round to nearest hundredth

V = 508.94

The third graphical representation is that of the function y = 1/2[x] .

The given function is y = 1/2[x] .

This is called the box function or the greatest integer function.

So for the equation of the line y = 1/2 x the graph passes through origin and through the points (2,1) , (4,2) and many more.

Now for the greatest integer function will take all the values of x greater than 1 up to 2 and round it off to 2.

so the points on the graph will be.

(2,1) , (3,1.5) , (4,2)....

This is clearly seen in the third option.

The integer function that returns an integer closest to the given real number is the largest integer function. also referred to as the step function. The greatest integer function rounds the input to the nearest integer. As a result, the equation to get the greatest integer is rather simple. It has the sign x, where x can represent any value.

The letter "x" denotes the biggest integer function for each real function. Real values are rounded to the nearest integer that is smaller than the input value by the function. Another term for this function is the floor function.

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The equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit is

y = (-2m/s^2)t^2 + (-2m/s)t + 6m

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given,

Assume for the moment that the hole is located at y = 0m, where x represents the time variable.

We are aware of:

The vertices are (-1s, 8m).

x in seconds and y in meters, I presume

The ball enters the hole at time x = 1s, hence we also have the following point:

(1s, 0m).

The vertex of the quadratic equation y = ax2 + bx + c is located at:

x = -b/2a,

Next, we have:

-1 = -b/2a.

Next, we have equations for trees:

8m = a(-1s)2, b(-1s), and c

0m = (a(1s)2) + (b(1s)2) + (c)

-1s = -b/2a.

The third equation should have one variable isolated first, and then it should be substituted in one of the other two:

1s2a = b.

Therefore, we can change b to bi 1s2a in the first two equations.

8m = 1s×2a×1s - a×1s2a1s + c

0m = 1s×2a×1s + a×1s×2a + c

We can combine the two equations to get:

8m is equal to a(1s2 - 2s2) + c, or a×1s2 - c.

0m is equal to a(1s2 + 2s2) + c, or a×3s2 + c.

We may quickly remove c from the second equation and then substitute it in the first equation:

c = -a3s^2

The initial equation is now:

8m is equal to -a×1s2 - a×3s2 - a×4s2.

a = 8m/-4s^2 = -2m/s^2.

We can now determine the values of c and b using a.

c = -(-(-2m/s2)*3s2)*3s2 = 6m.

B is equal to 1s*2a = 1s*(-2m/s2) = -2m/s.

The equation is then:

y = (-2m/s^2)t^2 + (-2m/s)t + 6m

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Answer: 8

Step-by-step explanation:

= (-100) ÷ (200 - (14 + 16) x 5) + 10

= (-100) ÷ (200 - 30 x 5) + 10

= (-100) ÷ (200 - 150) +10

= (-100) ÷ 50 + 10

= -2 + 10

=8

Answer:   8

Step-by-step explanation:    Remember BIDMAS, order of operations (brackets, indices, division, multiplication, addition, subtraction), since we have multiple brackets inside one another we'll start with the most inner brackets and then work from there.

14-(-16) = 30

30 x 5 = 150

200 - 150 = 50

(-100) ÷ 50 = -2

-2 + 10 = 8

Answer and Explanation:

m∠1 = 43° because opposite angles are congruent

m∠2 = 137° because ∠2 and 43° are supplementary, so m∠2 + 43° = 180°

m∠3 = 137° because opposite angles are congruent, so m∠3 = m∠2

m∠5 = 43° because alternate angles are congruent

m∠6 = 137° because ∠5 and ∠6 are supplementary, so 43° + m∠6 = 180°

m∠7 = 137° because alternate exterior angles are congruent, so m∠7 = m∠2

m∠8 = 43° because alternate exterior angles are congruent, so m∠8 = m∠1

Answer:

angle 1: 43

angle 2: 137

Step-by-step explanation:

Lets find angle 1 first :)

Since oposite diagonal angles are the same, this will make angle 1 43 degrees :)

Now lets find angle 2!

Since 1 was 43 degrees, and a flat line is 180 degrees we must subtract!

Lets do that now!

180 - 43 = 137

Angle 2 will be 137 degrees!

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JKL with vertices J(1, 3), K(5, 0), and L(7, 4) and its image after the glide reflection with a translation along <0,-3> and areflection in the y-axis is J'(-1, 0), K'(-5, -3), L'(-7, 1).

In the given question we have to graph JKL with vertices J(1, 3), K(5, 0), and L(7, 4) and its image after the glide reflection with a translation along <0,-3> and areflection in the y-axis.

The given vertices are J(1, 3), K(5, 0), and L(7, 4).

Firstly translation along (0,-3).

So translation is (x,y)→(x,y-3)

J'=(1, 3-3)=(1, 0)

K'=(5, 0-3)=(5, -3)

L'=(7, 4-3)=(7, 1)

We have to find the reflection in the y-axis so (x,y)→(-x,y).

Now the points are J'(-1, 0), K'(-5, -3), L'(-7, 1).

The graph of the glide reflection with a translation along <0,-3> and a reflection in the y-axis is given below.

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The standard error of the mean is 11.99

Given,

In the question :

No. of observation is  100

The sample mean is = 1234

Standard Deviation is = 120

To find the standard error of the mean.

Noe, According to the question:

No. of observation:

N = [tex](C_{v}[/tex] / ∈[tex])[/tex] ^2

Where,

∈ = allowance % error of mean

[tex]C_{v}[/tex] = coefficient of variation

[tex]C_{v} =[/tex] σ / x bar × 100

σ = standard deviation and x bar = mean

x bar = 1234 , σ = 120 and N = 100

[tex]C_{v} = \frac{120}{1234}[/tex]  × 100

[tex]C_{v}[/tex] = 9.72%

N = [tex](C_{v}[/tex] / ∈[tex])[/tex] ^2

100 = (9.72/∈)^2

100∈^2 = (9.72)^2

∈^2  = 0.944784

∈ = 0.972%

The standard error of mean = mean x percentage of absolute mean error

= 1234 x 0.972/100

= 11.99

Hence, The standard error of the mean is 11.99

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8 AM to 3 PM is 7 hours = 420 mins

Find how many rotations:
420 / 36 = 11.66666 rotations

Using ratio

1 rotation : 360 degrees

11.66666 : x degrees

x = 11.66666 / 1 * 360 = 4200 degrees