5- Solve the following expression and write the answers in the lowest term possible. [1
point]
a.
(m-8)²
m-4
n²-12m+32
2m
X
2m²-16m
m²-8m+161

The value of P in the equation (10011 base 2 + P + 11100 base 2 + 101 base 2 = 1001111 base 2) is 11011 base 2.

The value of P in the equation is found as follows from the given equation:

10011 base 2 + P + 11100 base 2 + 101 base 2 = 1001111 base 2

Hence;

P = 1001111 base 2 - (10011 base 2 + 11100 base 2 + 101 base 2)

Summing the values in the bracket: 10011 + 11100 + 101 = 110100

Then the value of  P will be:

P = 1001111 base 2 - 110100 base 2

P = 11011 base 2

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The value of x measure as 90 degree. the solution would be sinx = 1.

Since it is known that Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

WE are given the trigonometric functions as;

(sin2x)/(cosx)=2 for 0≤x≤2π

We know that sin 2x = 2 sinx cosx

Therefore,

(sin2x)/(cosx)=2

(2 sinx cosx)/(cosx)=2

sinx = 2/2

sinx = 1

Thus sin 90 = 1

x = 90 degree

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The simplified form of trigonometric functions by trigonometric formulas are listed below:

Case 1: 0.5√(2 - √3)

Case 2: (0.5√2) / (1 + 0.5√2)

Case 3: sin 6x

Case 4: sin θ

In this problem we must simplify and evaluate trigonometric functions by means of trigonometric formulas. The first two expressions must be simplified and evaluated by of half angle formulas:

Case 1

sin 15° = √[(1 - cos 30°) / 2]

sin 15° = √[(1 - √3 / 2) / 2]

sin 15° = √[(2 - √3) / 4]

sin 15° = 0.5√(2 - √3)

Case 2

tan 22.5° = sin 45° / (1 + cos 45°)

tan 22.5° = (0.5√2) / (1 + 0.5√2)

The last two expressions are simplified and evaluated by double angle formulas:

Case 3

2 · sin 3x · cos 3x

sin 6x

Case 4

2 · sin 0.5θ · cos 0.5θ

sin θ

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A) The best graphical representatiοn tο display the data wοuld be a histοgram.

B) The resulting histοgram shοuld shοw the distributiοn οf the grades and allοw fοr easy cοmparisοn οf the frequency οf grades in different ranges.

A) The best graphical representatiοn tο display the data wοuld be a histοgram. This is because a histοgram is a bar graph-like representatiοn οf data that grοups a range οf values intο intervals called bins οr classes. The height οf each bar represents the frequency οr number οf data pοints that fall within that bin οr class. A histοgram is an apprοpriate display fοr the data because it shοws the distributiοn οf the grades and allοws fοr easy cοmparisοn οf the frequency οf grades in different ranges.

Part B: Tο create a histοgram οf the data, the steps are as follows:

Step 1: Chοοse a title fοr the histοgram, such as "Distributiοn οf 7th Grade Math Exam Grades".

Step 2: Determine the range οf the data by finding the minimum and maximum values. In this case, the minimum grade is 61 and the maximum grade is 98.

Step 3: Divide the range intο a suitable number οf bins οr classes. A cοmmοn rule οf thumb is tο use between 5 and 20 bins, depending οn the range and distributiοn οf the data. Fοr this data, we can use 10 bins, with a bin width οf 3 (rοunded up frοm 2.9).

Step 4: Label the x-axis with the range οf grades, and label the y-axis with the frequency οr number οf grades.

Step 5: Draw the histοgram by drawing a bar fοr each bin, with the height οf the bar representing the frequency οf grades in that bin. Fοr example, the first bin wοuld be fοr grades between 60 and 62, the secοnd bin wοuld be fοr grades between 63 and 65, and sο οn. Cοunt the number οf grades that fall within each bin, and draw a bar with that height οn the y-axis.

Therefοre, The resulting histοgram shοuld shοw the distributiοn οf the grades and allοw fοr easy cοmparisοn οf the frequency οf grades in different ranges.

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Result:

The total cost of the jeans and shirts  = 5(x + y)

Let's use variables (x and y) to show the total cost of one pair of jeans and one T-shirt, respectively.

Let x = the cost of one pair of jeans.

Let y = e the cost of one T-shirt.

Given:

Maria bought 3 pairs of jeans and 4 T-shirts, all at the same price. That is:

3x = cost of Maria's jeans

4y = cost of Maria's T-shirts

Joan bought 2 pairs of jeans and 1 T-shirt, all at the same price. That is:

2x = cost of Joan's jeans

y = cost of Joan's T-shirt

To find the total cost of all they bought, add up the costs:

Total cost = Maria's cost + Joan's cost

Total cost = 3x + 4y + 2x + y

Total cost = 5x + 5y

So the total cost is 5 times the sum of the cost of one pair of jeans and one T-shirt.

Simplify the expression by factoring out a common factor of 5, and we get:

Therefore, total cost = 5(x + y)

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1) Matrices that have determinants are square matrices

2) Due to the inverse matrix's calculation utilizing a matrix's determinant, the determinant and the inverse matrix are connected.

3) The determinant affects whether a matrix has an inverse.

A matrix is a collection of numbers that have been sorted into rows and columns to create a rectangular array. The elements, or entries, of the matrix are the integers.

If and only if the determinant of a square matrix A is nonzero, the matrix has an inverse. The matrix A is referred to as singular and devoid of an inverse if its determinant is zero.

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Answer:

Step-by-step explanation:

The solution for y in the given equation x + 3y = 6 and 2x - y = 10 is 2/7.

hmm im not sure, but I'm going to try to help you!! but I think it is B or D. Maybe but I'm not too sure. though. :((

Answer: 226.795 paperclips

Step-by-step explanation:

    First, we need to know how many grams are in a pound.

[tex]\boxed{\text{1 pound = 453.59 grams}}[/tex]

    Next, we will divide 453.59 grams by the 2 grams per paper clip to see how many paper clips would balance the scale with one pound.

     453.59 / 2 = 226.795 paperclips

The requried, intersection points are (√5, 5), (-√5, 5), (√2, 2), and (-√2, 2).

To find the intersection points of the parabola y = x² and the circle with radius √6 and center at (0,4), we need to solve the system of equations:

x² + (y - 4)² = 6 (equation of circle)

y = x² (equation of parabola)

We can substitute y = x² into the equation of the circle and obtain a quadratic equation in x:

x² + (x² - 4)² = 6

x⁴ - 7x² + 10 = 0

This equation can be factored as:

(x² - 5)(x² - 2) = 0

Therefore, the solutions for x are x = ±√5 and x = ±√2. To find the corresponding values of y, we can substitute these values of x into the equation of the parabola:

y = x²

For x = √5, we have y = (√5)² = 5, and for x = -√5, we have y = (-√5)² = 5.

For x = √2, we have y = (√2)² = 2, and for x = -√2, we have y = (-√2)² = 2.

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The composite figure has an area of 142 square yards

The composite figure has one square, right triangle, two rectangles

Area of square = side × side

=8×8

=64 yards

Area of triangle =1/2×8×6

=24 square yards

Area of 1st rectangle = 3×6

=18 square yards

Area of 2 nd rectangle = 9×4

=36 square yards

Total area is sum of square, rectangles and triangle

total area = 64+24+18+36

=142 square yards

Hence, the composite figure has an area of 142 square yards

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The correct groupings for each probability are given below as follows:

The possibility of two events occurring simultaneously and at the same time is known as joint probability.

Joint probability is the likelihood that event Y will take place at the same time as event X.

An example of a joint probability is the probability that you eat at the restaurant and have no commute

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Answer: 226

Step-by-step explanation:

The angle is half of the arc angle

so mDGF is 2 times as big as the angle

mDGF=113*2

mDGF=226

The value of X, given the matrices, can be found to be X = [ [ 4 ], [-1.5 ] ].

We are told that the value of X can be found to be :
2X + A = B

Solving this would give:
X = (B - A) / 2

We can then apply this to the matrices to give:
B - A = [ [ 11 - 3 ], [1 - 4 ] ]

B - A =  [[ 8 ],  [ -3 ] ]

X = [ [ 8 / 2 ], [ -3/2 ] ]

X = [ [ 4 ], [-1.5 ] ]

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The length of MN to the nearest tenth is 11.4 units

From the question, we have the following parameters that can be used in our computation:

cos E = 4/7

MP = 20

Because the triangles are similar triangles, we have

cos M = cos E = 4/7

So, we have

cos M = MN/MP

This gives

MN/MP = 4/7

So, we have

MN/20 = 4/7

Evaluate

MN = 20 * 4/7

So, we have

MN = 11.4

Hence, the length is 11.4

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The value of x in the heptagon is 38.6 degrees.

An heptagon is a polygon with 7 sides. A regular heptagon is an heptagon with all sides equal to each other.

Therefore,  sum of angles in an heptagon is equal to 900 degrees.

Let's find each angle of the heptagon.

each angle in the regular heptagon = 900 / 7

each angle in the regular heptagon = 128.57 degrees

Therefore, each angle of a square is 90 degrees.

Hence,

x = 128.57 - 90

x = 38.5714285714

Finally,

x = 38.6 degrees

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The area of the original figure is 1/9 times the area of the new figure

The perimeter of the original figure is 1/2 times the perimeter of the new figure

From the question, we have the following parameters that can be used in our computation:

The figures

The areas of the new figures is calculated as

Area = Old area * scale factor

So, we have

Area Figure 1 = (1 * 3) * 3

Area Figure 1 = 9

The perimeter of the new figures is calculated as

Perimeter = Old Perimeter * scale factor

So, we have

Perimeter Figure 2 = (4 * 4 + 4 * (2 + 3)) * 1/2

Perimeter Figure 2 = 18

See attachment for the dilates figures

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The segments AB and CD are, parallel, perpendicular or neither, depending on the slopes obtained from the coordinates on the segments as follows;

Parallel lines or line segments are line segments that have the same slope.

1. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 13)/(0 - (-2)) = -10/2 = -5

The slope of the segment [tex]\overline{CD}[/tex] is;  (3 - 0)/(10 - (-5)) = 3/15 = 1/5

The slope of  [tex]\overline{AB}[/tex] is the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

[tex]\overline{AB}[/tex] ⊥  [tex]\overline{CD}[/tex],   [tex]\overline{AB}[/tex] is perpendicular to  [tex]\overline{CD}[/tex]

2. The slope of the segment [tex]\overline{AB}[/tex] is; (1 - 7)/(-6 - 3) = -6/-9 = 2/3

The slope of the segment [tex]\overline{CD}[/tex] is;  (-1 - (-5))/(0 - (-6)) = 4/6 = 2/3

The slope of  [tex]\overline{AB}[/tex] is the same as the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex],   [tex]\overline{AB}[/tex] is parallel to [tex]\overline{CD}[/tex]

3. The slope of the segment [tex]\overline{AB}[/tex] is; (4 - 2)/(-2 - (-6)) = 2/4 = 1/2

The slope of the segment [tex]\overline{CD}[/tex] is;  (-7 - 11))/(5 - (-1)) = -18/6 = -3

The slope of [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular

4. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 8)/(2 - (-3)) = -5/5 = -1

The slope of the segment [tex]\overline{CD}[/tex] is;  (2 - 6)/(-8 - (-4)) = -4/(-4) = 1

The slope of  [tex]\overline{AB}[/tex] is the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ⊥ [tex]\overline{CD}[/tex]

5. The slope of the segment [tex]\overline{AB}[/tex] is; (2 - (-1))/(-4 - (-8)) = 3/4

The slope of the segment [tex]\overline{CD}[/tex] is;  (6 - (-3))/(12 - 0) = 9/12 = 3/4

The slope of  [tex]\overline{AB}[/tex] is the same as the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ║  [tex]\overline{CD}[/tex]

6. The slope of the segment [tex]\overline{AB}[/tex] is; (-1 - 5)/(3 - 6) = -6/-3 = 2

The slope of the segment [tex]\overline{CD}[/tex] is;  (7 - (-5))/(-4 - 2)) = 12/(-6) = -2

The slope of  [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] and  [tex]\overline{CD}[/tex] are neither parallel nor perpendicular.

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The probability values are P(A) = 0.722 and P(B) = 0.50

From the question, we have the following parameters that can be used in our computation:

A fair die

The sample space of the events are

A = Sum is greater than 5

B = Sum is an even number

From the sample space of the sum of outcomes, we have

n(A) = 26

n(B) = 18

So, we have

P(A) = 26/36 = 0.722

n(B) = 18/36 = 0.50

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The volume of the cylinder is 238. 7m³

The formula that is used for calculating the cross-sectional area of a cylinder is expressed with the equation;

A = πr²

Such that;

From the information given, we have that;

17 = 3.14 × r²

Divide the values

r² = 5. 414

Find square root

r = 2.33 m

The volume of a cylinder is given as;

Volume = πr²h

Substitute the values

Volume = 3.14 × 2.33² × 14

Multiply the values

Volume = 238. 7m³

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An inequality for each of the constraints (one for frames, one for hours for assembly, and 2 non-negative inequalities describing the products is:

x + y ≤ 300

x1 + y3 ≤ 360

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.

Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

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Answer:

n = -6

Step-by-step explanation:

We can allow n to represent the unknown number.

Now, we can set the two expressions equal to each other to find the number, n:

[tex]2n-1=4n+11\\2n=4n+12\\-2n=12\\n=-6[/tex]

Finally, we can check if the number fits the equation and the verbal expression by plugging in -6 for n:

Algebraically:

2(-6) - 1 = 4(-6) + 11

-12 - 1 = -24 + 11

-13 = -13

Verbally:

Two times the number -6 is -12 and 1 less than - 12 is -13

Four times the number -6 is -24 and 11 more than this is -13

Answer: x= -6

Step-by-step explanation:

Each word in a word problem translates to a mathematical symbol

> 1 less than =>  - 1

> two times a number => 2x

put that together 1 less than two times a number means:

2x-1

> is => =

> 11 more  => 11+

> four times the number  => 4x

put it all together

2x-1=11+4x     bring all like terms to each side

-2x = 12         solve for x

x= -6

The measure of angle TDC in the triangle is 32 degrees.

The tangent CD forms a right angle with the radius CT of the circle. This forms a right angle triangle.

Therefore, the sum of angles in the triangle is 180 degrees.

Hence,

∠C = 90 degrees

Therefore,

3x + 14 + 8x + 10 + 90 = 180

11x + 114 = 180

11x = 180 - 114

11x = 66

divide both sides by 11

x = 66 / 11

x = 6

Therefore,

∠TDC = 3x + 14 = 3(6) + 14 = 18 + 14 = 32 degrees.

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Answer:

  9

Step-by-step explanation:

You want the number of non-congruent rectangles that can be drawn on a 4 × 4 geoboard.

A rectangle will have right-angle corners and opposite sides the same length. The attachment shows the 9 rectangles we believe exhaust the possibilities for a grid of 4 dots by 4 dots.

<95141404393>

[tex]\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) ~~ \begin{cases} r=radius\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=5\\ \theta =80 \end{cases} \\\\\\ A=\cfrac{5^2}{2}\left( ~~ \cfrac{\pi (80) }{180}-\sin(80^o ) ~~ \right)\implies A=\cfrac{25}{2}\left(\cfrac{4\pi }{9}- \sin(80^o) \right) \\\\\\ A=\cfrac{50\pi }{9}-\cfrac{25\sin(80^o)}{2}\implies A\approx 5.1~cm^2[/tex]

The expected number of people over 70 years old in that country in 2050 is given as follows:

D) 5.40 million.

The expected number of people over 70 years old in that country in 2050 is obtained applying the proportions in the context of the problem.

The expected population of that country in 2050 is given as follows:

180 million.

Hence the expected population of the country over 70 years old, equivalent to a percentage of 3%, is obtained as follows:

0.03 x 180 million = 5.4 million.

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The missing angle C of the given triangle using law of cosine is: 62.1°

The Law of Cosines is defined as a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.

Numerically, the Law of Cosines can be communicated as:

c² = a² + b² - 2abcos(C),

where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

Thus:

90² = 55² + 50² - 2(55 * 50)cos(C),

2575 = 5500 cos C

2575/5500 = cos C

cos C = 0.4682

C = cos⁻¹0.4682

C = 62.1°

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The graph that represents f(2x) is given by option B.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The parent function in this problem is given as follows:

f(x) = x².

For the transformation, we want the numeric value of the function at x = 2x, hence:

f(2x) = [2x]²

f(2x) = 4x².

Which is given by option b, representing an horizontal compression by a factor of 1/4 = vertical stretch by a factor of 4 of the graph of the parent function y = x².

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Answer: The height is 4.5 in

Step-by-step explanation:

       We can use the given formula for volume, transform it to solve for height (h), and then substitute our given values to solve.

Given formula:

[tex]\displaystyle V=\pi r^2h[/tex]

Transformed to solve for height:

[tex]\displaystyle h=\frac{V}{\pi r^2}[/tex]

Substitute given points:

[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.75\; \text{inches})^2}[/tex]

Square:

[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.5625)}[/tex]

Multiply:

[tex]\displaystyle h=\frac{8}{1.767146}[/tex]

Divide:

[tex]\displaystyle h=4.527[/tex]

Round to the nearest tenth:

[tex]\displaystyle h=4.5[/tex]