How many significant figures are in 10.659 22​

Answer:

Step-by-step explanation:

Answer:

√43

Step-by-step explanation:

Implement the Pythagorean formula to solve for sides of a right triangle: a^2 + b^2 = c^2, where "a" and "b" are the legs and "c" is the hypotenuse.

a = √6 and c = 49

√6^2 + b^2 = 49

6 + b^2 = 49

b^2 = 43

b = √43

Answer:

The square root of 43

Step-by-step explanation:

 I did this in class the other day

Answer:

Step-by-step explanation:

measure horizontally

measure vertically

measure depth..

The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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There 1365 ways to choose four people from the group of fifteen.

b. There are 70 ways to choose  four Republicans from the group of eight Republicans.

C. The probability is about  0.0513, or  5.13%.

a.  To know the ways that four people can be selected from this group of fifteen is by:

nCr = n! / (r! x (n-r)!),

Where:

n  = total number of items

r = is the number of items to be selected,

!  = the factorial of a number.

Putting in the values into the the formula:

15C4 = 15! / (4! x (15-4)!)

(15-4)! = 11!

15C4 = 1365

B.  Since:

n = 8

r = 4

Putting in the values into the the formula:

8C4 = 8! / (4!  x (8-4)!)

(8-4)! = 4!

8C4 = 70

c. The  Probability = Number of ways to choose four Republicans / Number of ways to choose four people

Hence  Probability = 70 / 1365

                             =  0.0513

Therefore, the probability that the selected group will consist of all Republicans is about  0.0513, or  5.13%.

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Given data:

The given expression.

The given expression is perfect square it means can be express in th form of (a+b)^2.

The expression for the (a+b)^2 is,

The given expression can be written as,

Thus, the unknow value is 81.

Answer: Distinct parallel lines

Step-by-step explanation:

The two equations of lines represent distinct parallel lines

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the first line be A

Now , the equation of line A , 5x + y = 3  

The equation A can be expressed as slope - intercept form

Subtracting 5x on both sides of the equation , we get

y = -5x + 3

So , the slope of the first line A is -5

Let the first second be B

Now , the equation of line B , 10x + 2y = -6  

The equation A can be expressed as slope - intercept form

Subtracting 10x on both sides of the equation , we get

2y = -10x - 6

Divide by 2 on both sides , we get

y = -5x - 6

So , the slope of the first line B is -5

Therefore , both the equations of lines have same slope but different y intercepts

So , the equations of lines represent distinct parallel lines

Hence , The two equations of lines represent distinct parallel lines

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The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Answer:

Cost of Washer = $696

Cost of Dryer = $232

Step-by-step explanation:

Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.

Put the equation together, so we can add the x variables together.

3x + x = 4x

The total cost will be what the '4x' is equal to.

4x = 928

Going back to algebra, we solve the equation by dividing both sides by 4.

x = 232

Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.

3x

3(232) = 696.

To check the answer, we can add them together to make sure we get the total cost.

696 + 232 = 928

The x-intercept of the function is (-1/3, 0) and (5, 0)

Given is a graph of a parabola having equation y = -3x²+14x+5, we need to find the x-intercept of the graph,

So to find the x-intercept put y = 0,

Therefore,

-3x²+14x+5 = 0

-3x²+15x-x+5 = 0

-3x(x-5)-1(x-5) = 0

(-3x-1)(x-5) = 0

Therefore,

x = -1/3 and x = 5

Hence the x-intercept of the function is (-1/3, 0) and (5, 0)

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Answer:

Hope this is right and helps :)

Step-by-step explanation:

Answer:

To find the rules for (fg)(x) and (gf)(x), we need to evaluate the composite functions.

(fg)(x) = f(g(x)) = f(sqrt(x - 5)) = (sqrt(x - 5))^2 + 5 = x - 5 + 5 = x

(gf)(x) = g(f(x)) = g(x^2 + 5) = sqrt(x^2 + 5 - 5) = sqrt(x^2) = |x|

Therefore, the rules for (fg)(x) and (gf)(x) are:

(fg)(x) = x

(gf)(x) = |x|

Step-by-step explanation:

Answer:

the unit rate for each pair is $1.13

Step-by-step explanation:

Okay this is how you would do this problem correctly:

we know that 4 dozen pairs of gloves cost $54.24 however we want to know what the cost is for one pair so we have to make a equation by dividing total cost by the number of glove pairs.

$54.24/4 dozen

the reason we are putting 4 dozen instead of just dividing $54.24 by 4 is because we want to know the unit price for each pair of gloves so it would actually look like this:

$54.24/4(12)

Dozen = 12

so we multiply 12 by 4 to get 48 pairs of gloves, we then divide $54.24 by 48 to find our unit rate of pricing for each pair:

$54.24/48 = 1.13

so now we place a dollar sign in front of 1.13 to get your answer:

for every pair bought it costs $1.13

So how did the Analysis A contractor get the wrong answer? well when she had bought the 4 dozen gloves she divided $54.24 by 4, which in this case would make it seem as though the gloves came in a 12 pack of gloves. However she was buying the gloves individually so she would have to multiply 4 by 12 before dividing the total number of gloves from $54.24.    

The area of the shaded which is obtained using the composite figure formed the shaded region and the area under the curve of the specified function is; (2·π - 3·√3)/2 square units

A composite figure is one that is composed of two or more simpler figures.

The area can be considered of comprising of a composite figure of the area under the curve of the function and the area of the shaded region

The function representing the curve under the shaded region can be presented as follows;

y = 3·cos(x) + 1

The interval specified under the curve can be expressed as follows;

0 ≤ x ≤ π/3

Therefore, the area under the curve can be found as follows;

\(\int\limits^\frac{\pi}{3} _3 {3\cdot cos(x) + 1} \, dx = [3\cdot sin(x) + x]^{\frac{\pi}{3} }_0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3} - 0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3}\)

sin(π/3) = (√3)/2

Therefore; 3·sin(π/3) + π/3 = 3·(√3)/2 + π/3 = (2·π + 9·√3)/6

The area of the rectangle = (4 - 0) × (π/3 - 0) = 4·π/3

The area of the shaded region = Area of the rectangle - Area under the curve of the specified function

Therefore, area of the shaded region = 4·π/3 - (2·π + 9·√3)/6 = (2·π - 3·√3)/2

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Answer:

(-b±√(b²-4ac))/(2a)

Step-by-step explanation:

Answer:

This is my alt

Step-by-step explanation:

Answer:

um whats m or y?

Step-by-step explanation:

Answer:

\(x=3m+y\)

Step-by-step explanation:

Let's solve for \(x\).

\(m=\frac{x-y}{3}\)

Step 1: Flip the equation.

\(\frac{1}{3}x+\frac{-1}{3}y=m\)

Step 2: Add \(\frac{1}{3}y\) to both sides.

\(\frac{1}{3}x+\frac{-1}{3}y+\frac{1}{3}y=m+\frac{1}{3}y\)

\(\frac{1}{3}x=m+\frac{1}{3}y\)

Step 3: Divide both sides by \(\frac{1}{3}\).

\(\frac{\frac{1}{3}x }{\frac{1}{3} } ={\frac{m+\frac{1}{3}y }{\frac{1}{3} }\)

\(x=3m+y\)

Answer:

\(x=3m+y\)

The fraction of total interest owed after the fifth month of a 12-month loan is 64.1%

From the question, we have the following parameters

After the fifth month, the equation of the numerator is:

Numerator = (1+11)+(1+10)+(1+9)+(1+8)+(1+7)

Numerator = 50

The equation of the denominator is:

Denominator = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Denominator = 78

The fraction of total interest is then calculated using:

Fraction = Numerator/Denominator

This gives

Fraction = 50/78

Express as percentage

Fraction = 64.1%

Hence, the fraction of total interest owed after the fifth month of a 12-month loan is 64.1%

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The length of line segment AB is 5 units.To find the length of line segment AB, we can use the distance formula, which is based on the Pythagorean theorem.

The distance formula calculates the distance between two points (x1, y1) and (x2, y2) in a coordinate plane.

Let's calculate the length of AB using the given coordinates for points A and B:

Coordinates of point A: A = (4, -5)

Coordinates of point B: B = (7, -9)

The distance formula is given by:

\(d = [(x2 - x1)^2 + (y2 - y1)^2]\)

Substituting the coordinates of A and B into the formula:

\(d = [(7 - 4)^2 + (-9 - (-5))^2]\\d =[(3)^2 + (-4)^2]\)

d = √[9 + 16]

d = √25

d = 5

Therefore, the length of line segment AB is 5 units.

The distance formula calculates the straight-line distance between two points in a two-dimensional space. In this case, it determines the distance between points A and B in the coordinate plane. By applying the formula and substituting the given coordinates, we find that the length of AB is 5 units.

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Answer:

angle 8 is congruent to angles 3, 6, and 1

Step-by-step explanation:

If n and q are parallel then corresponding and vertical angles would be congruent. So: angle 8 is congruent to angles 3, 6, and 1.

Answer:

Depends on the value of x. If x = 3, the triangle has sides 18, 6, 16 which satisfies the triangle inequality, so 2x+12 is longest in this case. If x is very large, the triangle inequality is still satisfied, and 6x-2 is the longest side.

Step-by-step explanation:

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer:

100 km

Step-by-step explanation:

Speed = distance/time

=> Speed × time = distance

=> Distance = speed × time

=> Distance = (40 km/h) × 2.5 hours

=> Distance = 100 km.h/h

=> Distance = 100 km

The constant of proportionality k, of the given equation y = (2/7)x  is 2/7.

Proportionality :

Proportion is a mathematical comparison between two numbers.

here

y=2/7x

y \(\ \propto\) 2

shows that y is  directly proportional  to 2.

y \(\ \propto\) 1/ 7x

shows that y is inversely proportional  to 7x.

The constant of proportionality is given as:

y = kx or  y = k/x

where k is the proportionality constant

The constant of proportionality k, of the given equation y = (2/7)x  is 2/7.

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The correct option is (D). On average, the number of breakdowns per day varies from the mean by about 0.28.

Because standard deviation represents the typical distance between each data point and the mean.

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is.

So, the correct answer is On average, the number of breakdowns per day varies from the mean by about 0.28.

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To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.

First, let's find the multiplicative inverse of (4/3 - 4/9):

Multiplicative inverse = 1 / (4/3 - 4/9)

To simplify the expression, we need a common denominator:

Multiplicative inverse = 1 / ((12/9) - (4/9))

= 1 / (8/9)

= 9/8

Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:

Subtracted value = (7/12 + 7/8) - (9/8)

To perform this calculation, we need a common denominator:

Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)

= (14/24 + 21/24) - (9/8)

= 35/24 - 9/8

To simplify further, we need a common denominator:

Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)

= 35/24 - 27/24

= 8/24

= 1/3

Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).

Answer:

\(\boxed{\sf \ \ f^{-1}(x)=\dfrac{x-5}{2} \ \ }\)

Step-by-step explanation:

hello,

the easiest way to understand what we have to do is the following in my opinion

we can write

\((fof^{-1})(x)=x\\<=>f(f^{-1}(x))=x\\<=>2f^{-1}(x)+5=x\\<=>2f^{-1}(x)+5-5=x-5 \ \ \ subtract \ \ 5\\<=> 2f^{-1}(x)=x-5 \\<=> f^{-1}(x)=\dfrac{x-5}{2} \ \ \ divide \ by \ 2\\\)

so to follow the pattern of your question

y = 2x + 5

we need to find x as a function of y, so let's swap x and y

x = 2y + 5

then subtract 5

x - 5 = 2y

then divide by 2

\(\dfrac{x-5}{2}=y\)

finally

\(f^{-1}(x)=\dfrac{x-5}{2} \\\)

hope this helps

Answer:

1. y= 2x + 5

2. x = 2y + 5

3. x - 5 = 2y

4. (x-5)/2 =u

5. f^-1(x) = (x-5)/2

Step-by-step explanation:

:)

The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.

To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.

Stock A:

High price = $105.19

Low price = $103.25

Close price = $103.38

Stock B:

High price = $145.18

Low price = $143.28

Close price = $144.05

The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.

To calculate the selling prices, we need to multiply the number of shares by the respective selling price.

Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50

Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50

Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50

Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00

Now, let's calculate the difference in overall gain or loss:

Difference in overall gain = Selling price at the high price - Selling price at the low price

= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)

= $16,148.00 - $15,908.50

= $239.50

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