Find the exact length of side a.

 Find The Exact Length Of Side A.

Answers

Answer 1

The exact length of a which is equivalent to BC is 7units

Cosine rule

A triangle is a shape with 3 sides and angles. In order to determine the sides BC, we will use the cosine rule

c² = a² + b² - 2abcosC

Given the following parameters

b = 2

c = 5√3

theta = 30 degrees

Substitute

c² = 2² + (5√3)² - 2abcos30
c² = 4 + 75 - 2(2)(5√3)*√3/2

c² = 79 - 30
c² = 49
c = 7 units

Hence the exact length of a which is equivalent to BC is 7units

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Related Questions

Leslie buys a new pair of sneakers for
$43 and several pairs of laces, I, that
cost $6 each. Write an algebraic
expression to represent the total
amount she will spend.

Answers

Answer:

$43 + $6l

Step-by-step explanation:

Hello!

She spends $43 and bus several $6 laces.

We don't know how many she buys, but we know that we can represent that number using l.

That means she spends $43 + $6l.

The algebraic expression is $43 + $6l.

We can determine the price if we know the number of laces she buys. We can simply plug in the number of laces she bought, and we can plug it in for l in the equation.

Answer:

43= 6(x)

Explanation:

43 is the total,  and each of them are 6$ each. X is the variable that we don't know.

Which polynomial function could be represented by the graph below?


A. [tex]f(x) = x^2 - 4x[/tex]

B. [tex]f(x) = x^2 + 4x[/tex]

C. [tex]f(x) = -x^2 - 4x[/tex]

D. [tex]f(x) = -x^2 + 4x[/tex]

Answers

Answer:

[tex]f(x) = {x}^{2} + 4x[/tex]

Step-by-step explanation:

The graph is concave up, this means that the leading term x^2 is positive.

[tex]f(x) = {x}^{2} + 4x[/tex]

[tex]y = {x}^{2} + 4x[/tex]

For the x intercept, let y = 0

[tex] {x}^{2} + 4x = 0[/tex]

[tex]x(x + 4) = 0[/tex]

[tex]x = 0 \: \: \: or \: \: \: \: x = - 4[/tex]

The x intercepts are:

(0 , 0) and (-4 , 0)

For the y intercept, let x = 0

[tex]y = {0}^{2} + 4(0) = 0[/tex]

y intercept :

(0, 0)

For the turning point:

[tex]t.p = \frac{x1 + x2}{2} [/tex]

[tex]t.p = \frac{0 + ( - 4)}{2} = - 2[/tex]

[tex]f( - 2) = {( - 2)}^{2} + 4( - 2) = - 4[/tex]

Turning point:

(-2 , -4)

If you connect all these coordinates you will get the parabola shown in the picture.

You have been given data about gas prices in 15 states. Comparing the two data sets below, what does the larger standard deviation, range, and variance say about gas prices in 2022 compared to gas prices in 2018?

Gas Prices in 2018 Gas Prices in 2022
Max: $2.42

Min: $2.03

Mean: $2.098

Median: $2.06

Mode: $2.04

Variance: 0.0121

Standard Deviation: $0.11

Max: $5.87

Min: $4.48

Mean: $4.83

Median: $4.72

Mode: $4.72

Variance: 0.0142

Standard Deviation: $0.38

Answers

Comparing the two data sets shown below

What is standard deviation and variance?

Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.

Both the mean and the median can be used to describe where the “center” of a dataset is located.

So, the mean of data in 2022 is more than mean of data in 2018.

It’s best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers.

As the variance of 2022 more than in variance in 2018.

A high variance indicates that the data points are very spread out from the mean, and from one another.

As the standard deviation of 2022 more than in standard deviation in 2018.

The high standard deviation indicates data are more spread out.

The bigger the range, the more spread out the data.

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Consider function g.

g(x)={(6,-8<=(-2)<-2 ),(0,-2<=(-2)<4),(-4,4<=(-2)<10):}

What are the values of the function when x = -2 and when x = 4?

g(-2) = __
g(4) = __

Answers

By evaluating the piecewise function, we get:

g(-2) = 0.

g(4) = 4.

How to evaluate the piecewise function?

A piecewise function is a function that behaves differently in different parts of its domain.

Here, we first want to get g(-2). x = -2 belongs to the second domain, then we use that part:

g(-2) = 0.

For x = 4, it belongs to the third domain, then we have:

g(4) = 4.

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What is the name of the numeral system we use today?.

Answers

Answer :-Hindu - Arabic numeral systemThe hindu - Arabic numeral system, which orginated in India and is now used throughout the world is a positional base 10 system.

Please mark may be brainliest answer.

I need help in this question if highly appreciate it if someone can help me solve this problem

Answers

Answer:

The one you chose is correct.

Step-by-step explanation:

The scale factor is 1.5. We know QP is 5. QP is the corresponding side to KJ. So, we multiply 5 with 1.5 and get 7.5 which is equal to 15/2

I found the scale factor by dividing LK which was 9 and QR which was 6.

9/6=1.5.

Hope this helps

Simplify the expression to a + bi form:
√4+ √−4+√36 + √−4

Answers

Answer:

8 + 4i

Step-by-step explanation:

according to the bi form, the solution to the expression √4+ √−4+√36 + √−4 would be 8 + 4i

please answer, much appreciated!!!!!

Answers

Answer:

i don't understand your question

Step-by-step explanation:

What is the value of x? Do not round your answer.

Answers

Answer:

x = 3

Step-by-step explanation:

Setup a proportion

[tex]\frac{CB}{CA} =\frac{DB}{DA} \\\frac{4}{3} =\frac{x}{2.25} \\3x=9\\\frac{3x}{3} =\frac{9}{3} \\x=3[/tex]

Nashville is 595 feet above sea level. You board an airplane and the pilot ascended 39000 feet. Write the two integers that represent this scenario.

Answers

To solve this problem, let's simply find the difference in the distance between the two locations.

Equation

To express this integer, we need to define the locations with variables and then calculate the difference.

Nashville = A = 595ftPilot = B = 39000ft

The difference between the two location can be written as

[tex]Pilot - Nashville = B - A = 39000 - 595 = 38405ft[/tex]

The two integers that represent this scenario are 595 and 39000 respectively.

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the simplification lf (x^3+2x-3)-(x^2-2x+4)​

Answers

Answer:

x³ - x² + 4x - 7

Step-by-step explanation:

(x³ + 2x - 3) - (x² - 2x + 4)

remove first parenthesis and distribute second parenthesis by - 1

= x³ + 2x - 3 - x² + 2x - 4 ← collect like terms

= x³ - x² + 4x - 7 ← in standard form

What is the slope of the line that passes through the pair of points?
(5, 8), (9,-3)

Answers

Answer:

-11/4

Step-by-step explanation:

slope = [tex]\frac{-3-8}{9-5} =\frac{-11}{4}[/tex]

Hope this helps

Answer:

-11/4

Step-by-step explanation:

slope = (difference in y)/(difference in x)

slope = (-3 - 8)/(9 - 5) = -11/4


HELP PLEASEEE GEOMETRY

Answers

2. 17 because 15-12= and 20-3=17

What effect does the circled point have on the standard deviation of the residuals? This point will increase the value of the standard deviation of the residuals because it has a large positive residual. This point will increase the value of the standard deviation of the residuals because it has a large negative residual. This point will not affect the value of the standard deviation of the residuals because it has a large positive residual. This point will decrease the value of the standard deviation of the residuals because it has a large negative residual.

Answers

The effect of this circled point is that: A. it will increase the value of the standard deviation of the residuals because it has a large positive residual.

What is the standard deviation of residuals?

The standard deviation of residuals is also referred to as root mean square deviation and they are typically used in statistics to calculate the rate at which data points spread around a given regression line.

By critically observing the scatter plot shown in the image attached below, we can infer and logically deduce that the circled point will increase the value of the standard deviation of the residuals because it has a large positive residual.

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Complete Question:

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. What effect does the circled point have on the standard deviation of the residuals?

How to find a fraction from a decimal

Answers

Answer:

0.6= 6/10

[tex]0.6 = 6 \div 10[/tex]

Step-by-step explanation:

To convert a decimal to a fraction

 place the decimal number over its place value

For example

in 0.8 the 8is in the tenths place,

so we place 6 over 10 to create the equivalent fraction, 8/10.

example 2

=6.25

625/100

25/4

A shop has 4 fruits (bananas, oranges, apples, and grapes) and 2 dips (peanut butter and caramel).


Zeke's mom randomly buys 1 fruit and 1 dip for his lunch.


What is the probability that she selects his favorite option: bananas and peanut butter?

Answers

Answer:

total fruits and dips=4+2=6

P(select banana&peanut butter)=banana+peanut /total fruits and d

Step-by-step explanation:

total fruits and dips=4+2=6

P(select banana&peanut)=banana+peanut/total fruits and dips

P(select banana&peanut)=1+1=2/6

=1/3

Add the polynomials.

(3x^2+5x−3)+(4x^2+2x)


7x^2+7x−3
7x^2+5x+5
3x^2+9x−1
x^2+5x−3

Answers

The answer is 7x^2+7x-3.

Audrey takes a sheet of paper and makes a diagonal cut from one corner to the opposite
corner, making two triangles. The cut she makes is 87 inches long and the width of the paper
is 60 inches. What is the paper's length?

Answers

[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Solution:}}}}}}[/tex]

Let us take the width of the paper as base, the cut she made be hypotenuse and the paper's length be perpendicular.

Here,

Hypotenuse (H) = 87 inch

Base (B) = 60 inch

Perpendicular (P) = [To be calculated]

As, we can use Pythagoras theorem to find. So by using Pythagoras theorem :

H² = P² + B²

[tex] {87}^{2} = {P}^{2} + {60}^{2} \\ \\ \implies \: 7569 = {P}^{2} + 3600 \\ \\ \implies \: 7569 - 3600 = {P}^{2} \\ \\ \implies3969 = {P}^{2} \\ \\ \implies \: P = \sqrt{3969} \\ \\ \implies \: P = 63[/tex]

The length of the paper is 63 inches.

[tex] \boxed{ \frak \pink{BrainlyDamurai}}[/tex]

Write an equation for the line through the point (1,3) parallel to
the line y =
1/2x + 10.

Answers

Answer is, y=3 hope that helps

y=3

Answer:

y=1/2x+5/2

Step-by-step explanation:

The slope will not change if the line is parallel.

So start with 1/2x and plug in 1.

You will get 1/2 and you need to get a total of 6/2 to get a y of 3.

since you already have 1/2 the remanding value needed is 5/2 and once you add the two you will get 6/2 which equals a y of 3.

help im being timed plssss

Answers

The value of cos 45 in a right angle triangle is 1/√2.

What is the trigonometry ratio?

The trigonometry ratios are ratios that can be used to determine the side and angles of a triangle depending on the known parameter. The basic trigonometry ratios are denoted by the acronym: SOH CAH TOA

i.e.

Sin θ = opp/hypCos θ = adj/hypTan θ = opp/adj

From the given diagram, we are to find the Cos 45°

i.e.

θ = 45°

Let's recall the angle 45 45 90 theorem that states that right angles have the following values for the sides:

hypotenuse = √2opposite = 1adjacent = 1

Since

Cos θ = adj/hyp

Cos 45 = 1/√2

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For what value of x does 4 superscript x baseline = (one-eighth) superscript x 5?

Answers

An equation is formed of two equal expressions. The value of x for which 4ˣ=(1/8)ˣ⁺⁵ is 3.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of x for which 4ˣ=(1/8)ˣ⁺⁵ is,

4ˣ=(1/8)ˣ⁺⁵

(2²)ˣ = (2⁻³)ˣ⁺⁵

2²ˣ = 2⁽⁻³ˣ⁺¹⁵⁾

2x = -3x + 15

5x = 15

x = 3

Hence, the value of x for which 4ˣ=(1/8)ˣ⁺⁵ is 3.

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f(x) = 4x² + 5x - 3
g(x) = 4x³
3x² + 5
Find (f+g)(x).

Answers

Answer:

[tex]4x^3+7x^2+5x+2[/tex]

Step-by-step explanation:

Given:

[tex]f(x)=4x^2+5x-3[/tex]

[tex]g(x)=4x^3+3x^2+5[/tex]

[tex]\begin{aligned}\implies (f+g)(x)=f(x)+g(x) & = (4x^2+5x-3) + (4x^3+3x^2+5) \\& = 4x^2+5x-3+4x^3+3x^2+5 \\& = 4x^3+4x^2+3x^2+5x-3+5 \\& = 4x^3+7x^2+5x+2 \\\end{aligned}[/tex]

A map has the scale 1 : 200,000 and the distance between two villages on the map is 8 cm. What is the distance in metres between the towns in real life?

Answers

The distance in metres between the towns in real life is 1600000 meters

How to determine the distance in real life?

The scale ratio is given as:

Scale = 1 cm : 200000 m

The map distance of 8cm implies that:

8 cm : Real = 1 cm: 200000 m

Express as fraction

Real/8 = 200000 m/1

Multiply both sides by 8

Real = 1600000 m

Hence, the distance in metres between the towns in real life is 1600000 meters

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The diagram shows a rectangle. The area of the rectangle is 310 m². Work out the value of w when 5x-9 is the length and 3x+7 is the another length​

Answers

Answer:

w = 10

Step-by-step explanation:

First we take the two values for the breadth of the rectangle

So:

5x - 9 = 3x + 7

now we solve this equation as follows:

5x - 3x = 9 + 7

2x = 16

x = 8

now that we have found the value for x, we can substitute it in the equation, 5x - 9,or in the equation, 3x + 7.

when we substitute x in any of these equations, we get

5(8) - 9 = 31

3(8) + 7 = 31

now that we have the value for the breadth we can form the following equation:

31 × w = 310

31w = 310

w = 310/31 = 10

Answer:

10

Step-by-step explanation:

Firstly, we find the value of X

since 5X-9 and 3X+7 are lenghts

5X-9= 3X+7

5X-3X= 7+9

2X = 16

dividing bothsides by 2

2X/2= 16/2

X = 8

Hence,

5X-9= 5(8)-9= 40-9 = 31

3X+7=3(8)+7= 24+7= 31

To find the width

Area= lenght×width

310= 31×w

31w= 310

w= 310/31

W= 10

solve for x.
2-[x+4(6-x)+16]-10=38-8x

Answers

Exact form is x = 86/11

Mixed number form is x = 7 whole number 9/11

If x1 = 4, then x² + 1/x² =​

Answers

Answer:

257/16

Step-by-step explanation:

Given :

x¹ = 4

Then :

x² + 1/x²(x¹)² + 1/(x¹)²(4)² + 1/(4)²16 + 1/16257/16

how many significant figures are there in the number 11

Answers

Answer: the maximum of three

Step-by-step explanation: each number has  2 significant figures. so 10.85 has four significant figures and must be rounded to 11 so it can have a maximum of three

15.23*3.6=54.83

Johnni guessed on all 8 questions of a multiple-choice quiz. each question has 4 answer choices. what is the probability that she got exactly 3 questions correct? round the answer to the nearest thousandth. p (k successes) = subscript n baseline c subscript k baseline p superscript k baseline (1 minus p) superscript n minus k. subscript n baseline c subscript k baseline = startfraction n factorial over (n minus k) factorial times k factorial endfraction 0.004 0.208 0.422 0.792

Answers

The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.

What is Probability ?

Probability can be defined as the likeliness of

If you use the formula P(r)=[tex]^nC_r P^rq^{n-r}[/tex]

P is the probability of success =  3/4 = .25

the total number of questions is n = 8

the total number of questions that Johnni got correct is r  = 3

the probability of getting an answer wrong is q = 1-0.25 = 0.75

Substituting all of these values

[tex]^8C_3 P^3 (0.75)^{8-3}[/tex]

=  .208.

The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.

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Answer:

B. 0.208

Step-by-step explanation:

edge 2023

Write the following ratio using two other notations.
[tex] \frac{1}{3} [/tex]

Answers

Answer:

1:3

1 to 3

Step-by-step explanation:

The other notations a ratio [tex]\frac{a}{b}[/tex] can be written in are a:b and a to b.

From what we are given, a = 1 and b = 3, so in the form a:b, the ration would be 1:3 and in the form a to b it would be 1 to 3.

please help !!!! and please answer every question not just one part.

Answers

Answer:

1) C. x-1 tells us that it has decreased by a value

2) original number of apples

3) 4(x-1)=28. Divide by 4, then take the 1 over

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