5. Let F: V→ W and G: W→ U be isomorphisms of vector spaces over K. Show that GF: V→U is an isomorphism.​

Answer:

Both

Step-by-step explanation:

After cutting the paper, both Calvin and Matthew have the same area. Calvin cut his into two rectangles that are each half the area of the original piece of paper. Matthew cut his paper into two equivalent right triangles that are also half the area of the original piece of paper.

1. The length of side AC is 21.5 units.

2. The magnitude of ∠R is 36.9°

3. The length of side ML is 7.5 units.

3. The length of side JK is 8.5 units.

In order to determine the length of side AC, we would apply sine trigonometric ratio because the given side lengths represent the opposite side and hypotenuse of a right-angled triangle;

sin(θ) = Opp/Hyp

Where:

By substituting the given side lengths, we have:

sin(34) = 12/x

x = 12/sin(34)

x = 21.5 units.

Question 2.

For the magnitude of ∠R, we have:

TanR = opposite side/adjacent side

TanR = 6/8

∠R = tan⁻¹(0.75)

∠R = 36.9°.

Question 3.

For side length ML, we have the following:

Tan28 = 4/ML

ML = 4/tan28

ML = 7.5 units.

Question 4.

For side length JK, we have the following:

cos(θ) = Adjacent side/Hypotenuse

cos(58) = JK/16

JK = 16cos(58)

JK = 8.5 units.

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Ben read at least 145 pages.

Ben read book , rounded to the nearest ten , 150 pages.

What is rounding off of a number?

Rounding off means a number is made simpler by keeping its value intact but closer to the next number.

Now,

We know that below the number 145 we cannot round it 150 for rounding of nearest ten.

Therefore, 145 is the smallest number which can be rounded (nearest ten) to 150.

Thus, he could read at least 145 pages.

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Answer:

the axis of symmerty is 4 and vertex is (4,3) correct me if i am wrong and you can use desmos to help you it is a graphing calculator

Step-by-step explanation:

Answer:

AB = 20 ft

AC = 40 ft

Step-by-step explanation:

==>Given:

Rectangular window ABCD, where,

side AB = ½ of side AC

Perimeter = 120ft

==>Required:

Length of side AB and side AC

==>Solution:

Let AB = x

If x = ½ of AC

AC = 2x

Perimeter = 2(AB + AC)

Thus,

120 = 2(x+2x)

120 = 2(3x)

120 = 6x

Divide both sides by 6 to solve for x

120/6 = x

20 = x

AB = x = 20 ft

AC = 2x = 2(20) = 40ft

Answer:

3.06 = AC

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 40 = AC / 4

4 cos 40 = AC

3.064177772 = AC

To the nearest hundredth

3.06 = AC

Answer:

The confidence Interval = (0.329, 0.391)

Step-by-step explanation:

Formula for the Confidence Interval for proportion =

p ± z × √p(1 - p)/n

where

p = x/n

From the question

n = 900 people

x = 36% of 900 people

= 36/100 × 900

= 324

z = z score of 95% confidence Interval

z = 1.98

p = x/n

= 324/900

= 0.36

Confidence Interval = p ± z × √p(1 - p)/n

= 0.36 ± 1.96 × √0.36 (1 - 0.36)/900

= 0.36 ± 1.96 ×√0.36 (0.64)/900

= 0.36 ± 1.96 × √0.000256

= 0.36 ± 1.96 × 0.016

= 0.36 ± 0.03136

Confidence Interval = 0.36 ± 0.03136

= 0.36 - 0.03136

= 0.32864

Approximately to 3 decimal places = 0.329

= 0.36 + 0.03136

= 0.39136

Approximately to 3 decimal places = 0.391

Therefore, the 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws = (0.329, 0.391)

Answer:

\(-\frac{5}{2} ;1.\)

Step-by-step explanation:

2x² + 3x-5=0;

\(\left[\begin{array}{ccc}x=\frac{-3-\sqrt{3^2+4*5*2}}{2*2} \\x=\frac{-3+\sqrt{3^2+4*5*2} }{2*2} \end{array} \ = > \ \left[\begin{array}{ccc}x=-\frac{5}{2} \\x=1\end{array}\)

The roots of the quadratic equation 2x² + 3x - 5 = 0 are \(-\frac{5}{2}\) and 1.

A quadratic equation is a polynomial of degree 2 as the highest power in such equations is 2. Generally, these equations are of the form ax² + bx + c = 0. Such equations have two roots whose nature depends upon the nature of the discriminant, D = \(\sqrt{b^2-4ac}\).

The given quadratic equation is

2x² + 3x - 5 = 0.

Use the quadratic formula:

\(x = \dfrac{-b\ \pm\ \sqrt{b^2-4ac}}{2a}\)

  \(= \dfrac{-3\ \pm\ \sqrt{3^2-4\times2\times(-5)}}{2\times2}\\= \dfrac{-3\ \pm\ \sqrt{9+40}}{4}\\= \dfrac{-3\ \pm\ \sqrt{49}}{4}\\= \dfrac{-3\ \pm\ 7}{4}\)

\(x = \dfrac{-3-7}{4}\) or \(x = \dfrac{-3+7}{4}\)

\(x = \dfrac{-10}{4}\) or \(x = \dfrac4{4}\)

\(x = \dfrac{-5}{2}\) or \(x =1\).

The given quadratic equation has two distinct roots that are \(-\frac{5}{2}\) and 1.

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Answer:

i have no idea just letting you know

Answer:

1808.64 IN^3

Step-by-step explanation:

Helium needed = volume of spherical shaped ice cream + volume of cone

Volume of a sphere = 4/3 x pi x r^3

4/3 x 3.14 x 6^3 = 904.32 ft^3

Volume of a cone 1/3 x (nr^2h)

n = 22/7

r = radius  = 12/2 = 6

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

h = height

1/3 x 3.14 x 6^2 x 24 = 904.32

helium needed = 2 x 904.32 = 1808.64 in^3

Answer:

after 13 hours

Step-by-step explanation:

Since the monthly fee is $4.25

so

● $4.25 + ( 2.75 × Number of hours) = 40

● ( 2.75 × Number of hours) = $40 - $4.25

● 35.75/ 2.75 = 13

Answer:

42

Step-by-step explanation:

LCM=2×2×3×5=2×6×5=2×30=60

Step-by-step explanation:

\(\large \boldsymbol{} \sf 6=\bold3\cdot \underline2 \\\\12=\bold3\cdot \underline2\cdot 2\\\\15=5\cdot\bold 3 \\\\ LCM(6 ; 12 ; 15) =\bold{3\cdot 2}\cdot 2\cdot 5=60\)

Answer:

7/8 or the bottom right

Step-by-step explanation:

Answer:

250 in²

Step-by-step explanation:

There are four identical rectangles so therefore area of one rectangle times 4. Then add the sum of the areas of the two identical squares.

4( l x b) + 2( l x b)

4( 10 x 5) + 2(5 x 5)

4(50) + 2(25)

200 + 50

Therefore 250 in²

Answer:

c.

Step-by-step explanation:

The pattern is supposed to be -4.

Gianna has 76 stamps left after 6 packages and pattern of decreasing stamps can be calculated as 100, 96, 92, 88, 84, 80, 76. Hence option c is correct

Gianna uses 100 stamps each day for her business. If she begins each day with 100 stamps, and after each package that is shipped has 4 less stamps,

In mathematics it deals with numbers of operations according to the statements.

As per question, after each package that is shipped has 4 less stamps.
Now,  for nth term of an arithmetic progression.
nth term = a + nd
Here, we have a = 100, d = -4 and  n = 6
So after 6th package shipped the number of stamps left.
= 100 - 6 x 4
= 76
And pattern of decreasing stamps can be calculated as 100, 96,92,88,84,80,76.

Thus, Gianna has 76 stamps left after 6 packages and pattern of decreasing stamps can be calculated as 100, 96,92,88,84,80,76.

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The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol

The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.

The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.

The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.

The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.

The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.

To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.

Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.

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Answer:

Take the X as S

Step-by-step explanation:

Hope's this helps

Answer:

[See Below]

Step-by-step explanation:

✦ \(\sqrt{95} =9.74679434\)

~Hope this helps Mate. If you need anything feel free to message me.

-I have included a number line as well...

Answer:

A

Step-by-step explanation:

To answer this question, we can use the following co-function identity:

\(\sin(\theta)=\cos(90\textdegree-\theta)\)

We know that sin(21°) is 0.36. This means that:

\(0.36=\sin(21\textdegree)=\cos(90\textdegree-21\textdegree)\)

Subtract within the cosine:

\(0.36=\sin(21\textdegree)=\cos(69\textdegree)\)

We can remove our second term:

\(\cos(69\textdegree)=0.36\)

So, our answer is A.

And we're done!

Answer: \((ab)(x)\)

Step-by-step explanation:

The degree of \((ab)(x)\) is the sum of the degrees of each of the functions \(a\) and \(b\).

Answer:

124.99 if i am right pls like my answer and rate it

Step-by-step explanation:

Step-by-step explanation:

24 hours and 29 minutes

Answer:

1.5 % is same as 1.50

explanation:

because 1.5 means that the equipment used to measure the number could not measure .It's equal, 1.50 is the same thing just with an added zero.

If a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B', then the current coordinates of B' are (3, -2).

As per the question statement, a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B'.

We are required to calculate the coordinates of B'.

To solve this question, we need to know what Translation (a, b) to (x, y) and (-a, -b) to (x, y) means. Translation (a, b) to (x, y) means the abscissa "x" is to be shifted to the right by "a" units while the ordinate "y" is to be shifted to the right by "b" units, i.e., after translation, the new coordinates become [(a + x), (b + x)]. On the other hand, Translation (-a, -b) to (x, y) means the abscissa "x" is to be shifted to the left by "a" units while the ordinate "y" is to be shifted to the left by "b" units, i.e., after translation, the new coordinates become [(a - x), (b - x)].

Here, as per the above mentioned concept, a translation of T (2, -7) if applied to the point B (1, 5), the new point B' will be at \([(1+2), (5+(-7)]=[3, (-2)]\).

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Answer: D (3,-12)

Step-by-step explanation:

Answer:

7250%

Step-by-step explanation:

To express 72 1/2 as a percentage, you need to convert it to a decimal first and then multiply by 100.

72 1/2 is equivalent to 72.5 as a decimal.

To convert it to a percentage:

72.5 * 100 = 7250

Therefore, 72 1/2 is equal to 7250% when expressed as a percentage.

let me know it is helpful for you or not

Answer:

B.

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

B) 5

Step-by-step explanation:

a(x)=1/9(90-x)

x=45

1/9(90-45)

1/9(45)

5

Hope this helps plz hit the crown :D

Answer:

The value of h(45) ⇨ 5  | B Choice.

Step-by-step explanation:

\(h(x)=\frac{1}{9}(90-x)\)

⟺ Find the value of h(45), substitute x = 45 in h(x)

\(h(45) = \frac{1}{9}(90-45)\\h(45)=\frac{1}{9}(45)\\h(45)=5\)

Thus, the answer is 5.

The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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