What is the area of the following composite figure? All angles are right angles. 22 m 2 29 m 2 24 m 2 27 m 2

The value of the expressions are;

a. 2x² + 6

b. 3x² - 6x + 2x -6

c. y = 3

d. x = 2

From the information given, we have

a. 2x(x + 3)

expand the bracket

2x² + 6

b. (3x + 2)(x-3)

expand the bracket

3x² - 6x + 2x -6

c. 4y -2(6-y) = 6

expand the bracket

4y - 12 + 2y = 6

collect like terms

6y = 18

Then,

y = 3

d.  x(2x-4)= (2x + 1)(x-2)

expand bracket

2x² - 4x = 2x² - 4x + x - 2

collect like terms

x = 2

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The initial length of the scarf is 50 centimeters.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We can use the given information to find the rate at which Cassandra is knitting the scarf and the initial length of the scarf.

Let L be the initial length of the scarf in centimeters, and let r be the rate at which Cassandra is knitting the scarf in centimeters per hour. Then, we have:

L + 25h = length of scarf after h hours

Substituting h = 3 and the length of the scarf after 3 hours = 125, we get:

L + 25(3) = 125

L + 75 = 125

L = 50

Therefore, the initial length of the scarf is 50 centimeters.

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Cassandra is knitting a scarf. She increases the length of

the scarf by 25 centimeters each hour she knits. After 3

hours, the scarf is 125 centimeters long what is initial length of scarf.

X = 2 (two) students study all three subjects (physics, geography, and economics). This can be found by adding the number of students who study only two subjects (6 + 4 + 5 = 15) and subtracting that from the total number of students who study at least one subject (55 - 20 = 35), since each of these 15 students who study two subjects is counted twice in the totals for each subject.

The number of students who study physics only is 10. This can be found by subtracting the number of students who study physics and at least one other subject (21 - 6 - 5 - 2 = 8) from the total number of students who study physics (21).

The number of students who study exactly one of the two subjects is 25. This can be found by adding the number of students who study each subject only (10 + 11 + 9) and subtracting that from the total number of students (55 - 20 = 35).

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The time at which the rocket reaches its maximum height is 3.5 seconds. Therefore, b. is the correct answer.

An equation describing the relationship between the input (x) and the output (f(x)) is called the function f(x). Any equation that represents the connection between an input x and an output f is referred to as the function f(x) (x).

A function can be expressed as a graph or table in addition to the standard form of an equation. Functions can be stated using symbols and phrases in addition to equations. A function could be expressed, for instance, as "the square of x" or "f of x equals x squared."

Whatever form a function takes, it's critical to keep in mind that the input (x) always yields the same result (f(x)).

In the given question,

The maximum height of the rocket is achieved at the point when the velocity of the rocket is 112 feet. This can be determined by taking the derivative of the function S(t).

S'(t) = 112

Therefore, when S'(t) = 112, t = 3.5.

This means that the rocket reaches its maximum height at t = 3.5 seconds.

Therefore, the time at which the rocket reaches its maximum height is 3.5 seconds.

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Answer:

6g+3g=11+3-5

combine like terms

9g=11+3-5

calculate the sum of difference

9g=9

Step-by-step explanation:

reduce the greatest common factor on both sides

of the equation

g=1

Given that AC bisects ∠BCD, the complete flowchart proof is given below:

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

A geometer is a mathematician who specializes in geometry.

GIven the shape in the image, the flowchart proof has been completed above.

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The perimeter of one square which combined with other to form a rectangle of 288 cm² is 12 cm.

The area of rectangle is given by the formula -

Area = length × width

Now we know that all the sides of square are same. Also, the identical squares have been kept side by side. So, let us represent one dimension of square with b. Thus, length of rectangle will be (b + b)

Length of rectangle = 2b

Width of rectangle will be b. Now, finding the value of b first.

288 = 2b×b

Performing multiplication

2b² = 288

b² = 288/2

Performing division

b² = 144

b = ✓144

Taking square root

b = 12 cm

The perimeter of one square = 2(length + width)

Perimeter of one square = 2 ( 12 + 12)

Perimeter = 2 × 24

Performing multiplication

Perimeter = 48 cm

Thus, perimeter of one square is 48 cm.

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The solution is, x= StartFraction t Over 4 + 2 EndFraction, is equivalent to 4 x = t + 2.

An equation can be stated  a  mathematical statement that is made up of two expressions connected by an equal sign.  In its normal form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

4 x = t + 2

or, x = (t + 2) /4

or, x = t/4 + 2/4

or, x = t/4 + 2

Hence, The solution is, x= StartFraction t Over 4 + 2 EndFraction, is equivalent to 4 x = t + 2.

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What does this problem ask for:

 --> which statement is sufficient to prove that:

     ∠ADB ≅ ∠ABD

Let's separate this image into two triangles: ΔADC and ΔABC

   --> prove that these triangles are congruent

       --> thus proving that: ∠ADB ≅ ∠ABD

Let's consider what evidence we have:

             --> thus: ∠ADC = ∠ABC

The minimum information that we have:

  --> prove that one pair of sides on both triangles are congruent

      --> based on the SSA Triangle Formula

             --> Two triangles that have two sides and one angle that are

                   equal, are therefore congruent

Based on the choices given:

 --> if DA = BA or DA is congruent to BA

  --> then ΔADC = ΔABC

Thus:

--> ∠ADC = ∠ABC

Answer: DA is congruent to BA

It is a continuous variable, as it can take on any value within a certain range (i.e., any value between a positive delay and a negative early arrival).

The variable described is quantitative, as it represents a numerical measurement of time, which is a continuous variable that can take on any value within a certain range. The range includes both positive values, representing delays, and negative values, representing early arrivals. This variable is a useful metric for tracking the performance of transportation systems or airlines, as it provides an objective measure of the amount of time a flight is delayed or arrives early. By analyzing the distribution of arrival delay times, policymakers and transportation providers can identify patterns, trends, and potential areas for improvement in their service delivery.

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The coordinates of vertex D of the parallelogram is; (0, 1)

We are given the coordinates of the parallelogram as;

A(2,4), B(5,2) and C(3,-1)

Now, we know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the mid point of BD.

The formula for the midpoint between two coordinates is;

(x1 + x2)/2, (y1 + y2)/2

Thus;

Midpoint of AC = (2 + 3)/2, (4 - 1)/2 = 5/2, 3/2

Midpoint of BD = (5 + x)/2, (2 + y)/2

Thus;

(5 + x)/2 = 5/2

x = 0

(2 + y)/2 = 3/2

2 + y = 3

y = 1

Coordinate of D = (0, 1)

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Answer:

49ft

Step-by-step explanation:

Sketching out the problem, we get something like the diagram below. Assuming the canyon makes a roughly 90° angle with the ground, we can see that we have two right-angled triangles formed.

Focusing on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can also find the combined width of the ground and river (let's call this y) using cos:

cos38=230/y

0.7880107536=230/y

y=230/0.7880107536= 291.874189467ft

Focusing now on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can find the width of the ground (let's call this x) using cos:

cos19=230/x

0.94551857559=230/x

x=230/0.94551857559= 243.252756673ft

Therefore, the width of the river must be the difference between the combined width of the ground and river, minus the width of the ground:

291.874189467ft - 243.252756673ft = 48.621432794ft ≈ 49ft

Answer:

Step-by-step explanation:

Since they are congruent, you know that 8=x-3. 11-3=8. and 14=x+6=8. x is 8

There are System A has 0 solutions and System B has 1 solution.

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

System A:

Line 1: y = (1/2)x

Line 2: y = (1/2)x - 1

System B:

Line 1: y = -x - 1

Line 2: y = -2x - 1

Using these equations, we can determine the number of solutions for each system:

System A has two lines that do not intersect (they are parallel), so it has no solutions.

System B has two lines that intersect at a single point, so it has one solution.

Therefore, System A has 0 solutions and System B has 1 solution.

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Answer: Perimeter: [tex]10mn^2+4m^2[/tex]; Area : [tex]6m^3n^2[/tex]

Step-by-step explanation: For Perimeter add like terms 7mn^2 and 3mn^2 add but 4 m^2 isolates. For area multiply 3 mn^2 and 4m^2 to get 12 m^3n^2 and then divide by 2 because it is right triangle.

The area of an equilateral triangle having height 12 cm is 83.136 sq.cm.

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It is sometimes referred to as a regular triangle because it is a regular polygon.

if height h is given in equilateral triangle then first we have to find the length of side which can be solve by this formula like a right angle triangle where side of equilateral triangle is a and another side is a/2 and next is height which is given 12 cm.

[tex]a^{2} -(a/2)^{2} = 12^{2}[/tex]

[tex](3/4)a^{2} = 144[/tex]

[tex]a^{2} = 192\\a = \sqrt{192}[/tex]

a = 13.85

area of equilateral triangle = [tex]((\sqrt{3})/ 4 )a^{2}[/tex]

= 1.732*192/4

83.136 sq.cm

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The equation of the given information is y(x) = 5x+10

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between.

Given that cost of renting for different numbers of hours.

The initial cost, regardless of time, is; $10. then the cost will increase at a rate of $5 per hour that the boat is rented.

Therefore, the cost (y) of renting a paddle boat for 'x' hours is:

y(x) = 5x+10

here linear relationship between x and y, where 5 is the slope of the equation, 10 is the y-intercept, the number of hours is the independent variable, and the cost is the dependent variable.

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Answer:

25/50

will equal to 1/2

Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex] => AC = [tex]\sqrt{115}[/tex]

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.

Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.

Here, in this triangle by Pythagorean theorem

[tex]A^2 = B ^2 + c^2[/tex]

AC = [tex]\sqrt{14^2- 9^2}[/tex]

AC = [tex]\sqrt{196- 81}[/tex]

Ac = [tex]\sqrt{115}[/tex]

Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.

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If administrators at International University are curious how students' GAs after their first year compare to their high school GPs. The correct answer is: C. We cannot assume independence between the high school GPAs in the sample.

The GPAs of the students in the sample at the end of their first year at the university are likely to be correlated with their high school GPAs, as students with higher high school GPAs are likely to perform better in university as well.

Thus, the high school GPAs of the students in the sample are not independent of each other, and using the formula for the standard deviation of the sample would not be appropriate in this situation.

Therefore the correct option is C.

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The correct question is:

Administrators at International University are curious how students' GPAs after their fist year compare to their high school GPAs. They plan on taking an SRS of 80 of the 900 freshmen to look up their high school GPAs. They plan to look at the difference between the mean high school and the mean university GPA for students in the sample at the end of their first year. Why is it not appropriate to use the formula for the standard deviation of

The samples are not independent of each other.

We cannot assume independence between the university GPAs in the sample.

We cannot assume independence between the high school GPAs in the sample.

The samples are independent of each other.

Answer: A

Step-by-step explanation:

The sample is sampling the high school GPA and college GPA of the same students meaning the samples are not independent.

Answer:

The solution of the equation 4x + 2y = 6 and x − y = 3 will be D. (2, –1)

Step-by-step explanation:

4x + 2y = 6 ....… (1)

x − y = 3 …..... (2)

Example, for equation 2 is:

x - y = 3

x = 3 + y

Put in equation 1:

4(y + 3) + 2y = 6

4y + 12 + 2y = 6

6y = -6

y = -6/6

y = -1

We have the value of y, then the value of x will be:

x = 3 + y

= 3 + (-1)

= 3 - 1

= 2

So, the solution of the equation 4x + 2y = 6 and x − y = 3 will be (2, –1)

Answer:

7 traders sell oranges and mangoes alone.

Step-by-step explanation:

(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)

(107 – x = 100)

(x = 107 – 100 = 7)

Therefore, 7 traders sell oranges and mangoes alone.

(b) (312_{four} + 52_{x} = 96_{ten})

(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})

= (48 + 4 + 2 = 54_{10})

(52_{x} = 5 times x^{1} + 2 times x^{0})

= ((5x + 2)_{10})

(therefore 54 + (5x + 2) = 96)

(56 + 5x = 96 implies 5x = 96 – 56 = 40)

(x = 8)

(therefore 312_{4} + 52_{8} = 96_{10})

The area of field hockey is larger by 3162.85 [tex]m^2[/tex].

The amount of unit squares that cover an enclosed figure's surface is its area. Square units like [tex]cm^2[/tex] and [tex]m^2[/tex] are used to measure area. A shape's area is a two-dimensional measurement. The space inside the perimeter or boundaries of a closed shape is known as the "area."

The hockey surface given here is in rectangular shape, so,

Area = length x breadth

Area of the hockey surface at a community centre is,

= 61 m x 30.5 m

=1860.5 [tex]m^2[/tex]

Area of field hockey played at outdoors,

= 91.5 m x 54.9 m

= 5023.35    [tex]m^2[/tex]

Clearly, we can see that area of field hockey is larger.

Difference between both the areas = 5023.35 -1860.5 = 3162.85 [tex]m^2[/tex].

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The number of ways the letters can be permutated in the word SPEECHLESS is 100800.

What is meant by permutation?

An arrangement of items in a specific order is referred to as a permutation. A set can be permuted by arranging its components in a linear or sequential order, or by rearrangement of its components if the set is already ordered. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

The  number of letters in SPEECHLESS = 10

The letter E repeats 3 times

The letter S repeats 3 times

The letters P,C,H,L repeats one time.

When there are repeating letters in a word, the total number of distinct ways the letters in the words can be permutated is:

[tex]N= \frac{n!}{r_1!r_2!.....r_m!}[/tex]

where N = number of arrangements

 n = number of letters

r = total number of times one letter is repeated in the word

For SPEECHLESS,

Therefore the number of ways the letters can be permutated  is:

[tex]N= \frac{10!}{3!3!}[/tex] = 100800

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Answer:

2

Step-by-step explanation: this is because the plus sign splits the terms so simply 2 terms

Answer:

y = 2x - 3

Step-by-step explanation:

Pick two random points for slope

slope = m = rise/run = [tex]\frac{(-3-(-5))}{0-(-1)} = \frac{2}{1} = 2[/tex]

y intercept form:

y = 2x - 3

The correct classification of the statements is: False, True, False, True.

What is Function ?

Function can be defined in which it relates an input to output.

The point of symmetry on f-¹(x) is (4,6).

False. The point (4,6) is not on the graph of f-¹(x), so it cannot be the point of symmetry. We can verify that the function is not symmetric with respect to any vertical or horizontal line.

The domain of f-¹(x) is (-∞,4).

True. The cube root function is defined for all real numbers, so the expression inside the cube root must be nonnegative. Therefore, (z - 4) / 5 ≥ 0, which implies that z ≥ 4. This means that the domain of f-¹(x) is (-∞,4].

The graphs of f¹(x) and f(x) are reflections across the x-axis.

False. The graphs of f¹(x) and f(x) are not reflections across the x-axis. We can plot the functions to see that they have different shapes and are not symmetric with respect to the x-axis.

The range of f¹(x) is (-∞,∞).

True. The cube root function is defined for all real numbers, so f-¹(z) can take any real value. This means that the range of f¹(x) is (-∞,∞).

Therefore, the correct classification of the statements is: False, True, False, True.

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