Solve:
[tex]sin^2(2x+3)+cos^2(2x+3)=2x+3[/tex]

During exercise, there was a substantial link between heart rate, coronary flow, and cardiac oxygen consumption. As heart rate increases, so does oxygen consumption, which seems to reach a maximum at very fast heart rates.

Your pulse and heart rate both serve as indicators of how your heart is working. Your heart rate is the number of times it beats in a minute. Your arteries widen as a result of the number of times your heart beats every minute.

In healthy people, heart rate, workload, and oxygen consumption are all linearly connected up to a certain point. The heart's reaction to physical exercise or stress is considered to be controlled by the sympathetic nervous system.

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The triangle formed by sides 24, 25 and 5 cm is not a right angled triangle.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Let us consider the triangle is a right angle triangle

so,  

24 and 5 will be the base and heights

[tex]\sqrt{24\x^{2} + 5\x^{2} } = 24.51\\[/tex]

so 25 is not equal 24.51 cm

so the triangle formed by sides 24, 25 and 5 cm is not a right angled triangle.

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i think its 4 x =2x +1

If two polygons are similar, it means that their corresponding angles are congruent (have the same measure) and their corresponding side lengths are in proportion to each other.

Similar polygons are two polygons that have the same shape but differ in size. Similar polygons have congruent congruent angles and proportional proportionate sides.

When two polygons are similar, their respective angles are congruent (have the same measure) and their corresponding side lengths are proportional to one another.

Additionally, the ratio of the length of any corresponding side of the two polygons is equal to the ratio of the length of any other corresponding side.

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B) 5x-4 = 3[tex]x^2[/tex] has no real solution

To check real solution of a quadratic equation we have to check for discriminant value of each equation a[tex]x^2[/tex] + bx +c is given by :

D =b^2 - 4ac.

if D<0 then equation have no solution.

now we need to check for each option the D value

Option A:

Therefore, the discriminant of the equation x^2 - 3x - 7 is (-3)^2 - 4(1)(-7) = 9 + 28 = 37.

Option B:

The discriminant of the quadratic equation 3x^2 - 5x + 4 is the value of b^2 - 4ac, which is (5)^2 - 4(3)(4) = 25 - 48 = -23. A negative discriminant (-23) would indicate that the equation has no real solutions, meaning it has no solutions in real numbers.

so option B  which is 5x-4 = 3[tex]x^2[/tex] have no real solution.

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Complete question:

Which of the following equations has no real solutions?

A. [tex]x^2[/tex] +3x=7

B. 5x-4 = 3[tex]x^2[/tex]

C. [tex]x^2[/tex] +1 = 3x

D. 2[tex]x^2[/tex] +5x=3

Answer:

I think it is 7 as well

Step-by-step explanation:

They look equal and they both have the same degree of angle. I hope this helps!

Answer:

I believe its A, correct me if i'm wrong.

Step-by-step explanation:

A hypothesis test involves a comparison between research results from a sample and a hypothesis about a population.

Thus, option (A) is correct.

In hypothesis testing, a researcher starts with a null hypothesis, which represents the assumption of no difference or no effect in the population.

The researcher collects data from a sample and performs statistical analysis to determine whether the evidence supports or rejects the null hypothesis in favor of an alternative hypothesis.

The research results obtained from the sample are compared to the hypothesis about the population to determine whether there is enough evidence to reject the null hypothesis and accept the alternative hypothesis.

Thus, option (A) is correct

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Colin will have a total amount of $ 675.90 with Colin.

The interest charged on a loan or deposit is known as compound interest. It is the idea that we used the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. 

The formula for compound interest is given by

Here we have

Colin invests $600 at a rate of 1.5% per year compound interest for 8 years

Here principal amount, p = $ 600

Rate of interest, r = 1.5% =

Number of compounds per year = 1

Time period, t = 8

By the Compound interest formula A = P (1 + r/n)^nt

A = 600( 1 + 0.015/1)⁽¹⁾⁽⁸⁾  

A = 600(1.015)⁸

A = $675.90  

Therefore,

Colin will have a total amount of $ 675.90.

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C. the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible.An unbounded problem is one for which the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible.

An unbounded problem is one for which the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible. This means that there may be more than one combination of decision variables that will maximize or minimize the objective, and there may not be exactly one solution that will result in the maximum or minimum objective value.

An unbounded problem is one for which the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible. This means that the problem has no finite upper or lower limit and is not subject to any specific constraints. As a result, there may be more than one combination of decision variables that will maximize or minimize the objective. In addition, there may not be exactly one solution that will result in the maximum or minimum objective value, as the solution set can be infinite. Thus, it is important to keep in mind that an unbounded problem has no specific solution and that different combinations of decision variables can result in the same objective value.

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Answer:

     [tex]c=\sqrt{61}[/tex]

Step-by-step explanation:

Assuming it's a right triangle, you would have to use the Pythagorean Theorem which states:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Assuming we're looking for the hypotenuse:

[tex]5^{2} +6^{2} =c^{2}[/tex]

[tex]25+36=c^{2}[/tex]

[tex]61=c^{2}[/tex]

[tex]\sqrt{61} =c[/tex]

The three types of loops that can be built using the while statement and other statements are The While Loop,The For Loop,The Do-While Loop.

Loop in math is a path or line that starts and ends at the same point. It can refer to a continuous curve, like a circle, or to a sequence of discrete points, like a polygonal line. It is a fundamental concept in mathematics, used to study various topics such as curves, surfaces, and solids. Loops are also used in graph theory to study networks.

1. The While Loop: This allows you to execute a set of instructions until a certain condition is met.
2. The For Loop: This is a pre-defined loop that is used to iterate through a list of elements and execute a set of instructions for each element.
3. The Do-While Loop: This is similar to the While Loop, but the set of instructions are executed at least once before the condition is checked. This allows for a set of instructions to always be executed at least once.

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The measures of angles m∠ABC = 36° and m∠CBD = 84°.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

The angle m∠ABD = 120° is the result for the sum of the two angles m∠ABC and m∠CBD so;

m∠ABC + m∠CBD = m∠ABD

2x + 5x - 6 = 120°

7x - 6 = 120° {add 6 to both sides}

7x = 120° + 6°

7x = 126° {divide through by 7}

x = 126°/7

x = 18

2x = 2(18) = 36°

5x - 6 = 5(18) - 6 = 84°

Therefore, the geometry question have the measure of angles m∠ABC = 36° and m∠CBD = 84°.

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Possible Question:

Find m∠ABC and m∠CBD if m∠ABD =120°, m∠ABC = 2x, m∠CBD = (5x - 6)°, and the angle m∠ABD is the sum of m∠ABC and m∠CBD.

Answer:

it will the the same shape you esrased but two more squares to the left

points (-3,1)(-5,1)(-4.5,3)(-6,5)

Answer:

B) y = -2/3x -2

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (-3,0) (0, -2); we see the y decrease by 2 and the x increase by 3, so the slope is

m = -2/3 = -2/3

The Y-intercept is located at (0, -2)

So, our answer is B) y = -2/3x -2

The slope of the given linear equation y = 2x + 10 is 2.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, c, of the line y = mx + c represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Now, if we equate the standard slope-intercept form of the equation with the given equation, we get

y = mx + c

y = 2x + 10

m = 2 and c = 10

As we know the m is the slope which is equal to 2.

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Our point A(x,y) rotates 270 degrees anticlockwise around the origin to become A' (y,-x). This implies that we reverse x and y and turn x negative.

A figure can be rotated 90 degrees anticlockwise by rotating it 270 degrees clockwise. It would now be (x, y) = (-y, x)

A translation in geometry is a type of transformation that shifts a geometric figure in a specific direction without altering its size or orientation. The figures are congruent before and after the transformation because it is a type of rigid transformation.

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The first step to solve the equation 3x/5 + 5 = 20,

3x/5 + 5 - 5 = 20 - 5

3x/5 (5/3) = 15 (5/3)

is known as Subtraction property of equality, So option B is correct.

It is a property of mathematics, in which we subtract the same number on both the sides of any equation.

for example, ax+b = c  ⇒ ax+b-5 = c-5

Given math equation,

3x/5 + 5  = 20

here we apply, Subtraction property of equality

So, we are subtracting -5 both the sides

3x/5 + 5 - 5 = 20 - 5

Hence, Used property is subtraction property of equality

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Step-by-step explanation:

e.g. there fit only max. 55 (< 56) people into a room (like a large conference room or a small movie theater).

or for a mathematical function like

1/(x - 56)

x < 56 can be the domain definition.

or it can be the climate (temperature in Fahrenheit) setting for a certain area at a zoo.

or, or, or ...

The correct option c. 5/7. The value of cos L is found to be 5 /7.

For the stated right angles triangle:

Cos L = base / hypotenuses

Cos L = 10 / 14

Cos L = 5/7

Thus, the value of cos L is found to be 5/7.

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The function g(n+4) = 10 + n/23 + 4n.

A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

g(x)=6+x/7+4x

g(n+4) = 6+n+4/7+4(n+4)

g(n+4) = 10 + n/7 + 4n + 16

g(n+4) = 10 + n/23 + 4n

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The value of 2 ½ is 2.5. As 2 ½ is the same as mixed fraction 2 ½ = 5/2.

2 ½ is a mixed number, it is a whole number combined with a fraction. In this case, 2 is the whole number and ½ is the fraction. The value of 2 ½ is calculated by adding the value of the whole number to the value of the fraction.

The value of the whole number 2 is 2, and the value of the fraction ½ is 0.5. To find the value of 2 ½, we add 2 to 0.5:

2 + 0.5 = 2.5

So, the value of 2 ½ is 2.5.

It's important to note that mixed numbers are used to represent numbers that are between two whole numbers, they consist of a whole number and a proper fraction. This mixed number representation is commonly used in everyday life, and it's easy to understand.

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The value of 625 is the numerical representation of the quantity.

It is a composite number, meaning it can be divided evenly by more than just 1 and itself (5 x 5 x 5 = 625). It is also a perfect cube, as it can be represented as 5 cubed (5³).

In mathematical operations, it can be used as a constant or as a variable in equations and formulas. It can also be represented in scientific notation as 6.25 x 10².

In terms of real-world applications, it may be used in measurements, such as area or volume, or as a quantity in various calculations or formulas.

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Answer:

A. 27

Step-by-step explanation:

mG=(180-126)/2=27

2.26 pounds equal one kilo of mass and hence, 121 pounds divided by 2.26 equals 53.09 kilograms.

Kg, the metric system's fundamental unit of mass The mass of 1,000 cubic centimeters of water is quite close to one kilogram; originally, it was supposed to be exactly equal. According to definitions, a pound is exactly equivalent to 0.45359237 kg. The kilogram (abbreviated "kg") is the SI Base Unit for calculating mass. One gram (g) is produced when you divide one kilogram by 1000, and one metric ton is produced when you multiply one kilogram by 1000. Consequently, 1000 grams equals 1 kilogram, and 1000 kilograms equal 1 ton.

given

kilogram (kg) weighs 2.2 times more than a pound (represented as lbs).

As a result, 2.26 pounds equal one kilo of mass.

hence, 121 pounds divided by 2.26 equals 53.09 kilograms.

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Answer: y= 120

Step-by-step explanation: y= 180 -2x30

=180-60

=120

Therefore , the solution of the given problem of table comes out to be the simplest table is of 1,2,3,4,5,6,7,8,9 and 10.

A statistic list is a group of figures that displays the results of a calculation with several inputs. Data is organized in rows and columns and is composed of descriptions and numbers. It is simple to remember the table and the pattern of 10. The numerals are 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50, in that order. Value mapping is a technique for displaying the relationships between various data elements. The values table can be useful in any science class.

Here,

The simple table is easy to remember and

the most simple table is of 1

=>1,2,3,4,5,6,7,8,9 and 10

Therefore , the solution of the given problem of table comes out to be the simplest table is of 1,2,3,4,5,6,7,8,9 and 10.

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Yes, it is possible to form a triangle with sides of 3.5cm, 4.5cm, and 7.5cm. This is because these triangle's sides adhere to the triangle inequality theorem.

The triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is because in order to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, otherwise it would be impossible to connect the three sides and form a closed shape.

In this case,

3.5 cm + 4.5 cm = 8 cm > 7.5 cm

3.5 cm + 7.5 cm = 11 cm > 4.5 cm

4.5 cm + 7.5 cm = 12 cm > 3.5 cm

So it is possible to form a triangle with these side lengths.

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The variable "area of the circle" would likely be classified as a continuous variable, as it can take on any value within a certain range (e.g. 0 to infinity), and the difference between any two values within that range can be any positive value.

The variable "number of equal slices in a pizza" would likely be classified as a discrete variable, as it can only take on certain integer values (e.g. 1, 2, 3, etc.). Similarly, the variable "portion of the pizza in one slice" would also be classified as a discrete variable, as it can only take on certain values (e.g. 1/2, 1/3, 1/4, etc.).

The variable "air temperature in Saint Paul, MN" would likely be classified as a continuous variable, as it can take on any value within a certain range (e.g. -40 to 120 degrees Fahrenheit), and the difference between any two values within that range can be any positive value.

The variable "last four digits of a Social Security number" would likely be classified as a discrete variable, as it can only take on certain integer values (e.g. 0001 to 9999).

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Answer:

[tex]a_{73}=367[/tex]

Step-by-step explanation:

[tex]a_n=a_1+(n-1)d\\a_{73}=7+(73-1)(5)\\a_{73}=7+(72)(5)\\a_{73}=7+360\\a_{73}=367[/tex]

The end behavior of a function is the way the graph of the function behaves as either x→∞ or x→−∞.

To calculate the end behavior of a function, we take the highest degree of the function and look at the leading coefficient. If the leading coefficient is positive, then the graph will go to positive infinity as x→∞ and will go to negative infinity as x→−∞. If the leading coefficient is negative, then the graph will go to negative infinity as x→∞ and will go to positive infinity as x→−∞. For example, if the function is f(x) = 2x^3 + 6x, then the highest power is 3 and the leading coefficient is 2, which is positive. Therefore, the graph of the function will go to positive infinity as x→∞ and will go to negative infinity as x→−∞.

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