Show that ∶ [– 1, 1] → ℝ, given by () =
(2+)
is one-one. Find the inverse of the function
∶ [– 1, 1] → Range . (Hint: For ∈ Range , = () =
(2+)
, for some in [– 1, 1], i.e., =

(2+)

Answer:

  c. √2/30

  f. 13√3/14

  i. -11√10/24

Step-by-step explanation:

You want the sums of the fractions shown.

Two fractions can be added like this:

  [tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]

If the denominators have a common factor (k), then this can be reduced to ...

  [tex]\dfrac{a}{bk}+\dfrac{c}{dk}=\dfrac{ad+bc}{bdk}[/tex]

The product bdk is the least common denominator when k is the greatest common factor.

Here, the numerators have a common factor, so we can factor that out, perform the sum, then multiply the result by that numerator factor.

  [tex]\dfrac{\sqrt{2}}{5}-\dfrac{\sqrt{2}}{6}=\sqrt{2}\left(\dfrac{1}{5}-\dfrac{1}{6}\right)=\sqrt{2}\cdot\dfrac{6-5}{5\cdot6}=\boxed{\dfrac{\sqrt{2}}{30}}[/tex]

  [tex]\dfrac{3\sqrt{3}}{7}+\dfrac{\sqrt{3}}{2}=\sqrt{3}\left(\dfrac{3}{7}+\dfrac{1}{2}\right)=\sqrt{3}\cdot\dfrac{3\cdot2+7}{7\cdot2}=\boxed{\dfrac{13\sqrt{3}}{14}}[/tex]

The denominators have a common factor of 2: 6=3·2, 8=4·2.

  [tex]\dfrac{-5\sqrt{10}}{6}+\dfrac{3\sqrt{10}}{8}=\sqrt{10}\left(\dfrac{-5}{6}+\dfrac{3}{8}\right)=\sqrt{10}\cdot\dfrac{-5\cdot4+3\cdot3}{3\cdot4\cdot2}=\boxed{-\dfrac{11\sqrt{10}}{24}}[/tex]

The measure of angle ABC in the figure of triangle attached is

In geometry, a perpendicular bisector is a line or line segment that divides another line segment into two equal parts and is perpendicular to it.

From the definition of perpendicular bisector, we have that

< A = < C

and using triangle ABD

< A + < ABD = 90

< A + 28 = 90

< A = 90 - 28

< A = 62

Using triangle ABC

< A + < ABC + < C = 180

62 + < ABC + 62 = 180

< ABC = 180 - 62 - 62

< ABC = 56

OR

< ABD = < DBC = 28 degrees

and < ABC = < ABD + < DBC adjacent angles

< ABC = < ABD + < DBC

< ABC = 28 + 28

< ABC = 56 degrees

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complete question

The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if measurement of angle CBD=16 degrees and measurement of angle ACB=118 degrees

Step-by-step explanation:

Since every single mile it descends the same amount (which is 500ft), that means it's linear, so we'll use that they gave us, the h(x) = mx+b

To find m, we use the following equation

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

to find b, we have to find out the starting point. luckily they gave it to us, which is 4,000ft. B = 4000

Now every 500 feet, we go down 1 mile

Which means at 1000 feet, we go down 2 miles

500 and 1000 can be our y1 and y2

1 and 2 can be our x1 and x2

[tex] \frac{1000 - 500}{2 - 1} = \frac{500}{1} = 500 = m[/tex]

Now that we have our m and b, we just put it together

[tex]h(x) = - 500x + 4000[/tex]

A negative was placed before the 500 because they are descending, not ascending.

Answer: 1200g

Step-by-step explanation:

1 kilogram is equal to 1000 grams, so since you want 1.2, simply multiply by that quantity. So the answer is 1200 grams.

The initial balance of the account was approximately $3541.83.

This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.

We can utilise the compound interest formula to find a solution to this issue:

A = P(1 + r/n)ⁿⁿ

In this case, we have P = the initial balance of the account, r = 0.23 (23% expressed as a decimal), n = 4 (since interest is compounded quarterly), t = 3 years, and A = $6258. We can solve for P by rearranging the formula:

P = A / (1 + r/n)ⁿⁿ

Substituting the values we know, we get:

P = 6258 / (1 + 0.23/4)⁴ˣ³

Simplifying this expression gives:

P = 6258 / 1.76757

P ≈ $3541.83

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A. The value of cos 240° = [tex]\frac{-1}{2}[/tex]

B. The value of sin 240° = [tex]-\frac{\sqrt{3} }{2}[/tex]

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

Part A:

we know that, cos (a +b)=cos a cos b - sin a sin b

cos 240° = cos (60° +180°)

=cos 60° cos 180° - sin 60° sin 180°

=[tex]\frac{1}{2} *(-1)-\frac{\sqrt{3} }{2} *0[/tex]

=[tex]\frac{-1}{2}[/tex]

Part B:

we know that, sin(a- b)=sin a cos b - cos a sin b

sin 240° = sin(270° - 30°)

=sin 270° cos 30° - cos 270° sin 30°

=[tex]-1 *\frac{\sqrt{3} }{2}-0*\frac{1}{2}[/tex]

=[tex]-\frac{\sqrt{3} }{2}[/tex]

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The same shape and similar are relationship between ΔXYZ and ΔUVW options (A) and (D) are correct.

What is the similarity law for triangles?

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the complementary angles are congruent.

We have given two triangles with dimensions.

Take the ratio of the corresponding sides:

12/24 = 5/10 = 13/26 = 1/2

The ratios of the corresponding sides are same which means the triangle are similar and having same shape.

Hence, the same shape and similar are relationship between ΔXYZ and ΔUVW option (A) and (D) are correct.

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The complete question is in the attached image.

Answer:

need help looking for the anwser here it's the 2.5

The interquartile range is 4 and the median is 27.

The interquartile range is the difference between the third quartile and the first quartile. On a box plot, the interquartile range is the difference between the first line and the third line on the box.

Interquartile range = 28 - 24 =4

Median is the central value of a data set. On a box plot, the median is the second line on the box.

The median is 27.

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The triangle's perimeter is roughly 25.29 cm.

The area around a form's edge is known as its perimeter. The perimeter of various forms can be calculated by summing the lengths of their sides.

Let's call the right triangle's shorter leg "x" for short.

The longer leg is then 5 cm longer than x, or x + 5, according to the situation.

The hypotenuse measures x + 10 cm longer than x.

By the Pythagorean theorem, we know that:

x² + (x+5)² = (x+10)²

Expanding and simplifying this equation gives:

2x² + 10x - 75 = 0

Dividing both sides by 2 gives:

x² + 5x - 37.5 = 0

We can find the value of x by using the quadratic formula:

x = (-5 ± sqrt(5² - 4(1)(-37.5))) / 2

x = (-5 ± sqrt(175)) / 2

x ≈ -8.68 or x ≈ 3.43

Since x represents a length, we must choose the positive solution x = 3.43 cm.

Therefore, the shorter leg of the triangle is 3.43 cm, the longer leg is 8.43 cm (3.43 + 5), and the hypotenuse is 13.43 cm (3.43 + 10). The perimeter of the triangle is the sum of the three sides, which is:

3.43 + 8.43 + 13.43 = 25.29 cm

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Answer:

Below

Step-by-step explanation:

Instead of x , I assume you want the angle For RIGHT triangles, remember

cos (angle ) = adjacent leg / hypotenuse

cos ( angle ) = 5 /12    

      angle = arccos( 5/12) = 65 °

You could also use pythagorean theorem to calculate the misssing side....then use cos law to calculate the angle.

Find the total distance that Ramesh ran is 23km. His average running speed for the whole journey is 3 5/6 km/h.

To find the average speed,

We find the total distance and divide it by the total time.

During the first part of the run, she ran 3 hours at a speed of 7 km/h.  

To find the the distance she ran, multiply the speed times the time:  3 x 7 = 21 km.

From the second part of the run, she ran 2km.

So the total distance he ran is 21 + 2 = 23km.

The total time was 6 hours.

To find the the average speed;  

Divide 23 by 6 to get the average speed, which comes to 3 5/6 km/h.

hence, the average speed is 3 5/6 km/h.

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If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?

I believe that is what type of story you needed, if wrong let me know.

Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6

Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.

for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.

The answer after multiplying it is 6/24 or 1/4.  

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The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).

From the attached graph :

The area of the shaded region :

x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :

= [tex]\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy[/tex]

=  [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ][tex]| \limits^1_0[/tex]

Substitute the lower limit and upper limit we get,

= (5 /3 )( 1 )³ - 0  - ( 5 / 4 )( 1⁴) + 0

= ( 5 / 3 ) - ( 5 / 4 )

= ( 20 - 15 ) / 12

= 5 / 12

Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .

The given question is incomplete, I answer the question in general according to my knowledge:

Find the total area of the shaded region x = 5y³ , x = 5y² for the interval

( 5, 1 ).

Graph is attached.

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Answer:

Step-by-step explanation:

15 into 300 is 20

300÷ 15 = 20

Answer:

∠1 = ∠2 = 135

Step-by-step explanation:

We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180° = 3 x 180°= 540°. Hence, the sum of interior angles of a pentagon is 540°.

so ∠1 + ∠2 + 3(90°) = 540°

since ∠1 = ∠2

∠1 + ∠1 + 3(90) = 540

2∠1 + 270 = 540

2∠1 = 540 - 270

2∠1 = 270

∠1 = 270/2 = 135

Answer:

48ft²

Step-by-step explanation:

Visualize the trapezoid as consisting of a rectangle with two triangles on either side. To find its total area, find the area of each and add them up.

Note that the formula for the area of a square is (base*height) and the formula for the area of a triangle is (0.5*base*height). The bottom of the trapezoid is 15ft and the top is 9ft, which makes the combined bases of the two triangles 15-9=6ft, meaning each triangle's base is 3ft.

Area of left triangle = 0.5*3*4 = 6ft²

Area of square = 4*9 = 36ft²

Area of right triangle = 0.5*3*4 = 6ft²

Therefore the total area is: 6ft² + 36ft² + 6ft² = 48ft²

Answer:

48ft?

Visualize the trapezoid as consisting of

a rectangle with two triangles on either

side. To find its total area, find the area of

each and add them up.

Answer:

-

Step-by-step explanation:

the question isn't clear enough to answer it

The position of G in the given line segment is at point 1, which is between points F and D and the line segment between F and D in the ratio 8:5.

What is meant by line segment?

Two unique points on a line define the boundaries of a line segment. A line segment is a section of the path a line takes to join two locations. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

Given, the locations of D  and F on the line segment.

D = -4

F = 9

Number of units between F and D = 9 - (-4) = 13

Point G partitions the line segment from F to D in the ratio 8:5.

So distance of G from F = [8/(8+5)] * 13 = 8

Distance of G from D =  [5/(8+5)] * 13 = 5

So from F, it is 8 units behind F = 9 - 8 = 1

from D, it is 5 units in front of D = -4 + 5 = 1

Therefore the position of G in the given line segment is at point 1.

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The volume, V of the solid obtained by rotating the region bounded by the graphs of the expressions, y² = x, x = 3y; about the y-axis is equals to the 162π/5 cubic units.

We have a region bounded by the graphs of two expressions. These expressios are y² = x, x = 3y. We have to calculate the volume of solid obtained by rotating the bounded region about the y-axis. First determine the intersection points of

y² = x, x = 3y.

=> x = 3y --(1)

=> y² = 3y

=> y² - 3y = 0

=> y( y - 3 ) = 0

=> y = 0 or y - 3 = 0

=> y = 0 , y = 3

from (1), x = 3y => x = 0, x = 9

Let the intersection points be O(0,0) and P(3,9). Now, the volume of rotating region or due to shaded region is

[tex]V = π\int_{0}^{3} (R² - r²) dy [/tex]

where R = 3y , r = y²

[tex]V = π\int_{0}^{3} [(3y)² - (y²)²]dy [/tex]

[tex]V = π \int_{0}^{3} (9y² - y⁴)dy [/tex]

[tex]V = π[ \frac{9y³}{3}- \frac{y⁵}{5} ]_{0}^{3} [/tex]

[tex]V = π[ \frac{9(3)³}{3}- \frac{{3}^{5} }{5} - 0- 0 ][/tex]

[tex]V = π(81 - \frac{243}{5} ) = \frac{162π}{5} [/tex]

Hence, the required volume is 162π/5 cubic units.

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Answer:

Step-by-step explanation:

The number of ways to arrange the letters in "HEDGEHOG" is 8!/(2!3!). The exclamation mark (!) means factorial, which is the product of all positive integers up to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

In this case, we have two H's and three E's, so we have to divide the total number of arrangements by the number of arrangements of H's and the number of arrangements of E's to avoid overcounting.

The total number of arrangements of the eight letters is 8!:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

The number of arrangements of H's is 2!:

2! = 2 x 1 = 2

The number of arrangements of E's is 3!:

3! = 3 x 2 x 1 = 6

So the number of arrangements of the letters in "HEDGEHOG" that avoid overcounting is:

40320 / (2 x 6) = 40320 / 12 = 3360.

Therefore, there are 3360 ways to arrange the letters in "HEDGEHOG".

Answer:

the ans is advanced

I hope you get your ans

The volume of the cube  is 444.19 in³

The volume of the rectangular prism is 661.2 ft³

The volume of the triangular prism is 30.04 yd³

The volume of the cylinder is 380.57 km³

Volume of a cube is solved using the formula

= length³

= 7.63³

= 444.19 in³

Volume of a rectangular prism is solved using the formula

= Area of base * height

= 9.5 * 8.7 * 8

= 661.2 ft³

Volume of a triangular prism is solved using the formula

= 1/2 × base × height × length

= 1/2 * 5.84 * 3.08 * 3.34

= 30.04 yd³

Volume of a cylinder is solved using the formula

= π * radius² * height

= π * 3² * 13.46

= 380.57 km³

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Answer:

268 pounds

Step-by-step explanation:

Two unit multipliers to be used for this unit conversion:

[tex]\frac{7.48 gallons}{1ft^{3}}[/tex] and [tex]\frac{8.33 pounds}{1 gallon}[/tex]

4.3 cubic feet = [tex](4.3ft^{3})[/tex]×[tex](\frac{7.48 gallons}{1ft^{3}})[/tex] ×[tex](\frac{8.33 pounds}{1ft^{3}})[/tex]

                     
The cubic feet units in the numerator and denominator will cancel each other out. The gallons units in the numerator and denominator will cancel each other out.
             = 268  pounds of water (Rounded to 3 significant figures)

On first evening she receives 19 calls and on second evening  she receives 11 calls while on 3rd evening she receives 38 calls.

A mathematical equation is a fοrmula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences oοn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol, fοr instance, 2x – 4 = 2.

X, Y, and Z represents the 1st , 2nd, and 3rd evenings

X + Y + Z = 68

⇒ X = Y + 8

⇒ Z = 2(Y + 8)

⇒ Y + Y + 8 + 2(Y + 8) = 68

Y = 11 calls

And

X = (11)+ 8 = 19 calls

Z = 2((11) + 8) = 38 calls

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Answer: $272.60

Step-by-step explanation:

9.75x5.4= 52.65

52.65+15.50=68.15

68.15x4=272.6

The height of the tree to the nearest hundredth of a meter is 10.77m.

Detailed explanation:

An illustration of identical triangles is shown in the diagram. View the illustration I included with my response to see how triangles can be used to solve this issue.

Because they both share an internal angle, the triangles made by Alyssa and her shadow and the triangle created by the tree and its shadow are examples of comparable triangles.

The ratios of the comparable sides on both sides are proportionate according to the similar triangles theorem.

Therefore, in order to determine the height of the tree, we must make a percentage of the corresponding sides of both triangles. Let x equal the tree's height.

[tex]\frac{BE}{BC} =\frac{DE}{AC}[/tex]

BE = 4.25 meters

DE = 1.65 meters

BC = 27.75 meters

AC = x meters

[tex]\frac{4.25}{27.75} =\frac{1.65}{x}[/tex]

Cross multiply is now used to find x.

4.25x= 1.65(27.75)

x = 10.77

Therefore, the height of the tree is 10.77 meters.

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Complete question:

Alyssa is 1. 65 meters tall. At 11 a. M. , she measures the length of a tree's shadow to be 27. 75 meters. She stands 23. 5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

A. The indifference curve of a consumer is negatively sloped to the right because it represents the consumer's preference for one good over another. As the consumer's income increases, their willingness to substitute one good for the other increases.

B. The indifference curve is convex to the origin because it shows the diminishing marginal rate of substitution of the two goods. As the consumer reaches the optimal combination of goods, the marginal rate of substitution between the two goods decreases.

C. Using the Lagrange method, the optimum combination of goods can be determined as follows:

Let L(X,Y) be the Lagrangian of this problem:

L(X,Y) = √X² + Y² - λ(200 - 3X - 4Y)

Where λ is the Lagrange multiplier.

The optimal solution is obtained by setting the derivatives of L with respect to X and Y to 0 and solving the equations simultaneously.

∂L/∂X = 0 -> X = 11.85

∂L/∂Y = 0 -> Y = 8.57

Therefore, the optimum combination of goods is X = 11.85 and Y = 8.57.

D. The slope of the indifference curve is equal to the slope of the budget line. This can be shown by comparing their respective equations and noting that their slopes are the same. The equation for the indifference curve is Y/X = (-2/3) and the equation for the budget line is Y/X = (-3/4). Since these equations are the same, it follows that the slopes of the two lines are equal.