Find the value of each variable provide proofs

Answer:

look in the comments have a good day

Answer: If we let "the number of snakes" be represented by the variable "s", we can write the equation as:

s - 24 = 35

This can be simplified by adding 24 to both sides:

s = 59

Therefore, the number of snakes is 59.

Step-by-step explanation:

The equations that gives true value for x = -2 and x = 2 are option A: x² - 4 = 0 and option D: 4x² = 16.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equations that are true for x = -2 and x = 2 are -

x² - 4 = 0 (when x = -2, this becomes 4 - 4 = 0; when x = 2, this becomes 4 - 4 = 0)

4x² = 16 (when x = -2, this becomes 4(4) = 16; when x = 2, this becomes 4(4) = 16)

The other options are not true for x = -2 and x = 2.

Specifically -

x² = -4 is not true for any real value of x, since the square of any real number is always non-negative.

3x² + 12 = 0 is not true for x = -2 or x = 2, since plugging in these values gives 12 ≠ 0.

2(x - 2)² = 0 is only true for x = 2, but not for x = -2, since plugging in x = -2 gives 2(16) ≠ 0.

Therefore, the options x² - 4 = 0 and 4x² = 16 are the correct ones.

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We conclude that the physicists can change the temperature in 17 hours.

Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.

Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition.

We know that a physicist must make sure that the temperature of a metal at 0° C gets no colder than -51° C.

The physicist changes the metal's temperature at a steady rate of -3° C per hour.

We calculate how long can the physicists change the temperature.

We get:

-51-0 / -3-0

= 17

Hence, We conclude that the physicists can change the temperature in 17 hours.

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Answer: I think its true

explanation: Correct me if im wrong ty!

The height of a lean-to roof that has a slanted height of 325 cm and an angle of elevation of 22 degrees is 131.30 cm.

The tangent function in trigonometry describes the relationship between an angle's adjacent and opposing sides. The angle of elevation is the angle formed by a horizontal line and a line leading from the observer's eye to a higher-than-horizontal object. When calculating an object's height with the tangent function, we utilize the angle of elevation and the length of the neighbouring side (in this example, the slanted height) to get the length of the opposing side (the height). As a result, the height of the object increases with increasing tangent value and elevation angle.

Given that, a roof has slanted height of 325 cm and an angle of elevation of 22 degrees.

Using the trigonometric functions:

tan(22) = h / 325

h = 325 * tan(22)

h ≈ 131.30 cm

Hence, the height of a lean-to roof that has a slanted height of 325 cm and an angle of elevation of 22 degrees is 131.30 cm.

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Answer:

(-3,0), (1,0)

Step-by-step explanation:

The x-intercept is when the y = 0

In the graph, we see the line cross through the x-axis located at (-3,0), (1,0)

So, the x-intercepts are located at (-3,0) and (1,0)

Answer:

x intercepts are 1 and -3

Step-by-step explanation:

X intercepts are obtained by looking at a point where the parabola touches the x axis

The values of f(-10) = 20101 , f(2) = 17 , f(3) = 142.

An expression consisting of variables, coefficients, and non-negative integer exponents is known as polynomial. For example, 2x² + 3x - 5 is a polynomial with three terms. The highest exponent of the variable is the degree of a polynomial. Polynomials can be used to represent many mathematical and scientific concepts, such as curves and functions.

To find f(-10), we need to substitute -10 for x in the given polynomial:

F(-10) = 2(-10)⁴ + (-10)²-10(-10) + 1

= 20000+100+100+1

= 20101

To find f(2), we again substitute 2 for x in the polynomial:

F(2) = 2(2)⁴ + (2)² -10(2) + 1

= 32+4-20+1

= 17

To find f(3), we can use synthetic division with 3 as the divisor. The coefficients of the polynomial are 2, 0, 1, -10, and 1.

F(3) = 142

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The possible values of b are 1/10, 1/2, 9/12, here we have to learn graph of a function. Diagram of question given below.

The graph of a function f in mathematics is the collection of ordered pairs where display style f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical situation when x and f(x) are real integers.

Subset, If every element of a set P is also an element of a set Q, then set Q is a superset of set P and set A is a subset of set Q. P and Q might be equal; if not, then P is a legitimate subset of Q.

Here, when [tex]b=0,\ f(x) = a*0^{x} = 0[/tex]

[tex]b=1,\ f(x)=a*1^{x} = a[/tex]

[tex]b > 1,\ f(x)=a*b^{x}[/tex]

[tex]a < b < 1,\ f(x) = a*b^{x}[/tex]

[tex]So, b\in(0,1)=b=\frac{1}{10} ,\frac{1}{2} ,\frac{9}{10}.[/tex]

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Using the linear model, a puppy grows 6 pounds each month.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (2, 20), an equation of this line in slope-intercept form can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 20 = (80 - 20)/(12 - 2)(x - 2)

y = 60/10(x - 2) + 20

y = 6x - 12 + 20

y = 6x + 8

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The time it will take ;

a. 6 men is 1 hour

b. 5 men is 1 1/5 hours

c. 2 men is 3 hours

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)

If 3 men load for 2hours

1 will load for 2× 3 = 6hours

then;

a. for 6 men, they will load it for 6/6 = 1hour

b. for 5 men, they will load it for 6/5 = 1 1/5 hours

c for 2 men , they will load it for 6/2 = 3 hours

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For the given sequence we have.

We have a sequence where each term is the double of the previous one.

So if we start with 9, we have:

g(1) = 9

g(2) = 2*9 = 18

g(3) = 2*18 = 36

g(4) = 2*36 = 72

That is the value of g(4).

Now the recursive formulas are trivial:

g(n) = 2*g(n - 1)

g(n) = 4*g(n - 2)

g(n) = 8*g(n - 3)

And finally, the quotient, we can write:

g(24)/g(21) as:

g(n)/g(n - 3)

And by the last recursive formula,we know that:

g(n) = 8*g(n - 3)

g(n)/g(n -3) = 8

So that is the answer there.

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The total cost of Joeli's purchases is $45.35.

What is the addition?

Addition is a mathematical operation that combines two or more numbers or quantities to produce a sum. It is one of the four basic arithmetic operations, along with subtraction, multiplication, and division. In addition, the numbers being combined are called addends, and the result is called the sum. The addition operator is represented by the symbol "+".

To find the total cost of Joeli's purchases, we need to add the cost of the helmet to the cost of the elbow pads:

Total cost = helmet cost + elbow pads cost

Total cost = $27.57 + $17.78

Total cost = $45.35

Therefore, the total cost of Joeli's purchases is $45.35.

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The correct numerical expression for "12 times the sum of 5 and 25 minus 2" by simplification is option (b) , i.e 12 x (5 + 25) − 2.

Simplification means simplifying an expression by reducing it to a simpler form. Approximating means simplifying the formula to the nearest value, which is not exactly correct. 

BODMAS stands for Bracket, Off, Division, Multiplication, Addition, and Subtraction. BODMAS is used to describe the order of operations in formulas. In some areas, BODMAS is also known as PEDMAS. This represents parentheses, exponents, division, multiplication, addition, and subtraction. 

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Answer:

12 x (5 + 25) − 2

Step-by-step explanation:

hope this helps!

The correct equation is P = (a x b) ÷ 43, 560

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, an agricultural research assistant, you often need to calculate the amount of pesticide needed for test fields.

For each acre, b pounds of pesticide are required.

1 acre = 43,560 ft²

Pesticide needed for each acre = b / 43,560

Pesticide needed for the given area = 43,560 (a x b)

Therefore,

P = 43,560 (a x b)

Hence, the correct equation is P = (a x b) ÷ 43, 560

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We can infer that the function y = 3 log2x - 5 has the following end behaviour:

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

from the question:

We may look at what happens to the function as x gets closer to positive and negative infinity to figure out the final behavior of the function y = 3 log2x - 5.

The formula 3 log2x also approaches infinity as x moves closer to positive infinity, and log2x moves closer to infinity as well. As a result, y becomes closer to infinity as x gets closer to positive infinity. The following can be written:

lim x→∞ 3 log2x - 5 = ∞

Similar to how log2x approaches negative infinity, the complete phrase 3 log2x also does as x approaches 0 from the right. Hence, when x moves towards 0 from the right, y moves towards negative infinity. The following can be written:

lim x→0+ 3 log2x - 5 = -∞

We can then infer that the final behavior of the function y = 3 log2x - 5 is as follows:

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The base of the exponential function (1.75) is greater than 1, this represents exponential growth. As x increases, the value of the function will grow at an increasing rate.

Exponential growth is a mathematical concept that describes a process where a quantity grows at an increasing rate proportional to its current value. In other words, the larger the quantity, the faster it grows. This leads to a graph that is characterized by a rapid upward curve that becomes steeper and steeper over time.

Exponential growth is often represented by the equation y = abˣ, where y is the final amount, a is the initial amount, b is the growth factor or base, and x is the time or number of periods.

The function f(x) = a(1+r)ˣ represents exponential growth, where "a" is the initial value, "r" is the growth rate as a decimal, and "x" is the time variable.

In this case, the initial value is 50, and the growth rate is 75%, or 0.75 as a decimal. Therefore, the equation for the function becomes:

f(x) = 50(1+0.75)ˣ

Simplifying this expression, we have:

f(x) = 50(1.75)ˣ

Since the base of the exponential function (1.75) is greater than 1, this represents exponential growth. As x increases, the value of the function will grow at an increasing rate.

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Answer:

5.590

Step-by-step explanation:

To solve the equation 3/4x + 3 - 2x = -1/4 + 1/2x + 5, we first need to simplify both sides by combining like terms:

3/4x - 2x + 3 = -1/4 + 1/2x + 5

Next, we can simplify the fractions on the right side by finding a common denominator of 4:

3/4x - 2x + 3 = -1/4 + 2/4x + 20/4

Simplifying the right side further, we get:

3/4x - 2x + 3 = 19/4 + 1/2x

Now we can isolate the variable x by moving all the terms containing x to one side of the equation and all the constants to the other side:

3/4x - 2x - 1/2x = 19/4 - 3

Combining like terms:

-5/4x = 5/4

Finally, we can solve for x by multiplying both sides by the reciprocal of -5/4:

x = -1

Therefore, the solution to the equation is x = -1.

Answer:

Plot the temperature on the x-axis and the water consumption on the y-axis.

For each day, plot a point on the scatter plot with the temperature and water consumption values.

Use a regression tool or calculate the slope and intercept of the line of best fit manually.

Draw a straight line through the data points that represents the trend in the data.

The equation for the line of best fit can be used to make predictions about water consumption given a certain temperature.

Step-by-step explanation:

The scatter plot shows that there is a positive relationship between temperature and water consumption.

Here is the scatter plot of the data:

Temperature (°F) | Water Consumption (fl. oz.)

------- | --------

75 | 12

80 | 15

85 | 18

90 | 21

95 | 24

100 | 27

The line that is closest to all of the data points is a line with a positive slope. This means that as the temperature increases, the water consumption also increases. The line does not perfectly fit all of the data points, but it does a good job of capturing the general trend.

Here is an explanation of how to interpret the scatter plot:

The points that are closer to the line indicate that the relationship between temperature and water consumption is stronger for those points.

The points that are further away from the line indicate that the relationship between temperature and water consumption is weaker for those points.

The line itself indicates the general trend of the data.

In this case, the line indicates that as the temperature increases, the water consumption also increases. However, there are some points that do not follow this trend. For example, the point at 95°F has a water consumption of 24 fl. oz., which is lower than the water consumption for the points at 90°F and 100°F. This suggests that there may be other factors that affect water consumption, such as the humidity or the activity level of the person.

Overall, the scatter plot shows that there is a positive relationship between temperature and water consumption. However, there are some points that do not follow this trend, which suggests that there may be other factors that also affect water consumption.

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Answer:

First one is b second one is a thrid is c

Step-by-step explanation:

The coordinates of the roots of parabola are (2,0) and (4,0).

An equation that sets a point on a curve at the same distance from both a fixed point and a fixed line is known as a parabola. The focus and directrix of a parabola are its fixed point and fixed line, respectively. Another important thing to keep in mind is that the fixed point does not lie on the fixed line. Every position that is equally far from the focus and directrix of two given points is said to be the locus of a parabola. The vertex of a parabola is the location where it turns sharpest. A parabolic function has a maximum value if it is shaped like a "," else, it has a minimum value.

The roots of the parabola are the coordinates where the graph intersects the x-axis (y = 0).

As you can see, the vertex of the graph is above the x-axis, and opens down, meaning that there are two roots for the graph.

Points of intersection: (2,0),(4,0)

Therefore, the coordinates of the roots are (2,0) and (4,0).

Hence the equation of the parabola will be y=3/4 (x²-1).

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The requried, Chloe originally had 68 marbles.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

Let's assume that Chloe originally had "x" marbles.

According to the problem, Chloe added 36 marbles to her collection. This means that she now has x + 36 marbles.

And we also know that she now has a total of 104 marbles.

So, we can set up an equation:

x + 36 = 104

To solve for x, we can isolate x on one side of the equation by subtracting 36 from both sides:

x + 36 - 36 = 104 - 36

x = 68

Therefore, Chloe originally had 68 marbles.

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We can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.

What is Line point postulate ?

The line-point postulate, also known as the incidence postulate, is a fundamental axiom in geometry that states that for any two points in a plane, there exists exactly one line that contains both points.

In other words, the line-point postulate asserts that a line can be uniquely determined by two distinct points that lie on it. This is one of the most basic and intuitive principles in geometry, and it is essential for building a foundation for more advanced concepts such as angles, triangles, circles, and more.

The Line-Point Postulate states that a line can be uniquely determined by any two distinct points on the line. In this diagram, we can see an example of this postulate in action.

For instance, we can say that line $q$ passes through points $J$ and $K$, so according to the Line-Point Postulate, this is enough information to uniquely determine the line $q$. Similarly,

Therefore, we can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.

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Answer:

Step-by-step explanation:

To find the solutions to the equation x^3 + 2x^2 - x - 2 = log(x + 3), we need to find the points of intersection of the graphs of the two functions f(x) = x^3 + 2x^2 - x - 2 and g(x) = log(x + 3).

The statement that describes the relationship between the graphs and the solutions is:

The solutions are the x-coordinates of the points of intersection of the graphs.

This is because the solutions to the equation are the x-values where the two graphs intersect. At these points of intersection, the y-coordinates of the graphs will be equal, meaning that the left-hand side of the equation (f(x)) and the right-hand side of the equation (g(x)) will be equal. Therefore, we need to find the x-values where f(x) = g(x) in order to find the solutions to the equation.

To visualize this, we can graph the two functions on the same coordinate plane and look for the points where they intersect. The x-coordinates of these points will be the solutions to the equation.

The y-intercepts of the graphs (if they exist) have no relation to the solutions of the equation, as they are simply the points where the graphs cross the y-axis (i.e. where x = 0). Similarly, the x-intercepts of the graphs (if they exist) are not necessarily related to the solutions of the equation, as they only indicate where the graphs cross the x-axis (i.e. where y = 0).

In response to the aforementioned query, we may say that here, the exponent is [tex](x^2)^5 / (x^3)^2[/tex] = [tex]x^n[/tex] =>  [tex]x^4 = x^n[/tex] =>  so, n=4

Exponentiation, sometimes referred to as "b raised to the nth power," is a mathematical operation that includes two numbers: a base number, b, and an exponent, or power, n. It is represented by the sign bn. A number's exponent reveals how many times it has been multiplied by itself. For instance, the number 2-3 (written as 23) means 2 × 2 x 2 = 8. 2 + 3 = 6 does not equal 23. Remember that an integer multiplied by one equals itself. Exponents are a method for expressing large numbers as powers. The amount that shows how many times a number has been multiplied by itself is called an exponent. As an example, multiplying 6 by 4 results in 6 x 6 x 6.

here, the exponent is

[tex](x^2)^5 / (x^3)^2[/tex] = [tex]x^n[/tex]

[tex]x^{10} / x^{6}[/tex]

[tex]x^{10 - 6}[/tex]

[tex]x^4 = x^n[/tex]

so, n=4

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Cοmparing the medians fοund using the given bοx plοt, we fοund that the median οf eighth graders is greater than the median οf the seventh graders.

A bοx and whisker plοt, οften knοwn as a bοx plοt, shοws a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.

A bοx is drawn frοm the first quartile tο the third quartile in a bοx plοt.

At the median, a vertical line passes thrοugh the bοx. It is generally used tο shοw whether a distributiοn is skewed οr nοt and whether there are any pοtential οutliers, οr οdd οbservatiοns, in the data set.

When cοmparing οr invοlving numerοus data sets, bοxplοts are alsο highly helpful. Graphs can be used tο determine hοw widely the data values vary οr are spread οut.

Frοm the bοx plοt given, we can summarize the fοllοwing,

Fοr seventh graders,

The first quartile Q1 = 3

The third quartile Q3 = 4

Interquartile range = Q3 - Q1 = 4-3 = 1

The median = 3.5

Fοr eighth graders,

The first quartile Q1 = 3.5

The third quartile Q3 = 4.5

Interquartile range = Q3 - Q1 = 4.5 -3.5 = 1

The median = 4

Therefοre cοmparing the medians fοund using the given bοx plοt, we fοund that the median οf eighth graders is greater than the median οf the seventh graders.

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The music department can by less than or equal to 23 CD's for the given cost and shipping fee.

The set of values that fulfil an inequality is the solution to the inequality. For instance, the following formula can be used to solve the inequality

x + 3 < 7

Taking 3 away from both sides:

x < 4

Hence, the answer is any value of x that is less than 4. A number line with an open circle at 4 indicating that it is not part of the answer and an arrow pointing to the left indicating that all numbers lower than 4 are included in the solution may be used to graphically illustrate the solution.

Let us suppose the number of CD's purchased = x.

Given that, they cost $15 each and there is a $5 shipping fee for the order.

15x + 5 ≤ 350

15x ≤ 345

x ≤ 23.

Hence, the music department can by less than or equal to 23 CD's for the given cost and shipping fee.

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