The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
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One solution exists for the following system of equations. In this question, correct answer is option (5) which states the solution is point

(3 , 2).

There are many various ways to define an equation. The definition of an equation in algebra is a mathematical statement that illustrates the equality of two mathematical expressions.

As we know that when the system of equations are given in graph form ,

then the solution to them is the number of points they intersect each other.

Now in the given question,

In the given graph it can be clearly seen that graphs of equations meet at one point. The point at which the graph meets is (3 , 2).

We can see that option (5) is correct.

So the given system of equations have one solution.

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Answer: A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is constant. Let's call the common ratio "r". We can use this property to find "r" and then calculate other terms in the sequence.

Given that t3 = 24 and t9 = 1536, we can use the formula for the nth term in a geometric sequence: tn = t1 * r^(n-1), where t1 is the first term in the sequence.

Since we know t3 and t9, we can find r by dividing t9 by t3:

r = t9/t3 = 1536/24 = 64

Now that we have found "r", we can use it to find t1 by dividing t3 by r^(3-1):

t1 = t3 / r^(3-1) = 24 / 64^(3-1) = 24 / 64 = 3/2

Now that we know t1 and r, we can find any term in the sequence by using the formula: tn = t1 * r^(n-1).

Therefore, there are two possible sequences with two different first terms:

Sequence 1: t1 = 3/2, r = 64

Sequence 2: t1 = -3/2, r = -64

These are the two possible geometric sequences that satisfy the conditions t3 = 24 and t9 = 1536.

Step-by-step explanation:

The rate of change for Modis building stairwell is 0.68 feet per step.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Part A: In the Modis building, he climbs 22 steps for every 15 ft of horizontal travel.

Now, rate = 15/22

= 0.68 feet per step

In Sears Tower, he climbs 17 steps for every 7 ft of horizontal travel

Here, rate 7/17

= 0.41 feet per step

Part B: Sears Tower steps are easy to climb, because rate is lesser than Modis building steps.

Therefore, the rate of change for Modis building stairwell is 0.68 feet per step.

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Answer:7

Step-by-step explanation:

let P(a)=27, like cold tea,

    P(b)=42, like hot tea,

  P(a∪b)=62,

using formula,

P(a∩b)=P(a)+P(b)-P(a∪b)

            =27+42-62

             =7

Answer:

5 < x <  15

Step-by-step explanation:

The triangle inequality theorem states that the sum of the measures of any two sides of a triangle must be greater than the measure of the third side

In the given triangle we are provided measures of two of the sides as 10 and 5

Let the measure of the third side be x

So the three sides are 10, 5 and x

Then by the inequality theorem
10 + 5 > x

==>  15 > x or

x < 15    This is an upper bound for x

when we switch sides in an inequality > changes to < and < changes to >

We also have
x  + 5 > 10  ==> x > 10 - 5 ==> x > 5

and

x + 10 > 5 ==> x > -5

Since x > 5 is more restrictive than x > -5, we conclude that x > 5 or 5 < x is the lower bound on x

Combining all inequalities we get

5 < x <  15

Note

We could also state the lower and upper bound limits as

difference of two sides < x < sum of two sides
10 - 5 < x < 10 + 5

or

5 < x < 15

While this may seem easier to compute than the explanation given above, the derivation is left out and may confuse some students

The variable n in the original equation -2/3n = 7 + 15 is equal to -12.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable maybe pointed search is the energy.

In order to isolate the variable in the equation -2/3n = 7 + 15, the first step is to subtract 7 from each side of the equation. This results in -2/3n = 8. Next, multiply each side of the equation by 3 to cancel out the 3 in the denominator. This leaves -2n = 24. Finally, divide each side of the equation by -2 to isolate the variable n. This results in the equation n = -12. Therefore, the variable n in the original equation -2/3n = 7 + 15 is equal to -12.

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Answer: C= 24-4t

Step-by-step explanation: Since four were eaten each dat the blue is getting lower, use -4t to represent it. 24 is the total amount gotten by substitution.

The equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.

What is the equation in one variable?

An equation in one variable is a mathematical expression that contains a single variable, typically represented by x. The goal of solving an equation in one variable is to determine the value of the variable that makes the equation true.

To solve the equation -6(x+1)+8x=2(x-3), we can simplify the left-hand and right-hand sides of the equation and then solve for x. Here are the steps:

Distribute the -6 and 2 to the terms inside the parentheses: -6x - 6 + 8x = 2x - 6

Combine like terms on each side of the equation: 2x - 6 = 2x - 6

Subtract 2x from both sides of the equation: -6 = -6

At this point, we have a true statement (-6 = -6), but there is no variable present. This means that the equation has infinitely many solutions, and every real number is a solution to the equation.

Hence, the equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.

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The completed flowchart proof is that ΔΑΒΕ =  ΔCDE

Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and dimensions of objects in space. It is concerned with the properties of points, lines, curves, surfaces, and solids, as well as the relationships between them.

How to prove this:

<ABD = <BDC

(alternate angles)

<BAC = <ACD

(alternate angles)

Hence, BE = ED (given)

So, ΔΑΒΕ =  ΔCDE

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These terms describe various aspects of quantitative analysis and measurement in different scientific fields such as analytical chemistry, biology, and statistics.

A. Sensitivity - the ability of a measurement method or instrument to detect small changes in the quantity being measured.

B. Detection limit - the minimum amount of a substance that can be reliably detected by a measurement method or instrument.

C. LOQ (Limit of Quantitation) - the minimum concentration of a substance that can be accurately quantified by a measurement method or instrument.

D. Limit of Linearity - the range of concentrations of a substance over which the measurement method or instrument produces proportional results.

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Distinguish between the following terms:

A. sensitivity and detection limit

B. Log and limit of linearity

C. quantitation by calibration curve and the method of standard addition.

D. confidence interval and confidence limits

Answer: the number is 6

Step-by-step explanation: First, set up an equation. Two more means +2, 3 times a number means 3x. So your equation would be 3x+2=20. Then solve the equation for x.

Answer:

x = 6

Step-by-step explanation:

Let the number be 'x'

Then, the equation becomes,

2 + 3x = 20
3x = 20 - 2
3x = 18
x = 18/3
x = 6

Hope it helped :)

B, 222 units, is the correct answer.

The scale to figure out the heavier stack 2 gram higher.

To determine the heavier stack of coins, you will need to use the electronic scale. However, since you cannot weigh all the coins at once, you will have to use the concept of unitary method.

Based on this, you can calculate the total weight of the coins on the scale. Since each coin weighs 1 gram, the total weight of the coins should be equal to the sum of the natural numbers from 1 to 10, which is 55.

Next, you need to compare the weight of the coins on the scale to the expected weight of 55 grams. If the weight on the scale is less than 55 grams, then the stack of coins that you did not weigh is the heavier stack.

However, if the weight on the scale is more than 55 grams, you need to use the concept of unitary method again. Suppose the weight on the scale is 56 grams. This means that the heavier stack has one coin that weighs 2 grams, and the other stack has 10 coins that weigh 1 gram.

To determine which stack is heavier, you can subtract the expected weight of 55 grams from the weight on the scale (56 grams). The difference is 1 gram.

Now you need to divide the difference by 2 (since one coin weighs 2 grams). This gives you 0.5. This means that the heavier stack has 0.5 coins that weigh 2 grams.

Since you cannot have half a coin, this means that the stack with one coin that weighs 2 grams is the heavier stack.

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Using the log, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].

The power to which a number must be increased in order to obtain another number is known as a logarithm.

For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.

So, solve using a log as follows: (1/243) ^-x/3 = 4

[tex]\begin{aligned}& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4\end{aligned}[/tex]

[tex]\begin{aligned}& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4\end{aligned}[/tex]

[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=12\end{aligned}[/tex]

[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=12 \\& -x=\log _{\frac{1}{243}}(12) \\& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& -x=\log _{\frac{1}{243}}(12)\end{aligned}[/tex]

Therefore, using the log, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].

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On solving the provided question, we can say that by fractions,  the space from the edge of the wall to the picture = 17/4*1/2 = 17/8

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Simply subtract the length of the image from the length of the wall to get the total area below and above the picture from the edge of the wall. So.

[tex]14\frac{1}{2} - 10\frac{1}{4}[/tex]

29/2 - 41/2

17/2

the space from the edge of the wall to the picture = 17/4*1/2 = 17/8

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Answer: 63%

Step-by-step explanation:

22 divided by 35 times 100

Answer:

61/10

Step-by-step explanation:

Convert the mixed number to an improper fraction

28 / 5 + 1 / 2

= 61/10

Answer:

Simplified form: 6 1/10

Improper form: 61/10

Step-by-step explanation:

5 3/5 + 1/2

= 28/5 + 1/2

Then, you multiply both fractions so that the denominator is the same number. In this case, multiply the fraction (numerator and denominator) on the left by 2 and on the right by 5.

= 56/10 + 5/10

This way, you can add the numbers because they have the same denominator.

=61/10

Answer:

In the expression -17 + (-b) + (-25), the coefficient is a number that multiplies a variable. In this case, the coefficients are -17, -1 (which multiplies the variable "b"), and -25.

Step-by-step explanation:

Answer:

The solution is 9,913 × 10⁸

Step-by-step explanation:

9,72 × 10⁸ and 1,93 × 10⁷

9,72 × 10⁸ + 1,93 × 10⁷

Factor the shape

= 10⁷ (9,72 × 10 + 1,93)

= 10⁷ (97,2 + 1,93)

= 10⁷ × 99,13

= 9,913 × 10⁸

Answer:104

Step-by-step explanation:

If 1/2 d=52,

d/2=52

Multiply both sides by 2.

Thus, d=52×2= 104.

Hope this helps! :)

The product of 1/2 and 2/3 is equivalent to one third

Fractions are expressions written as a ratio of two integers. For instance a/b is a fraction

Given the expression below

1/2 of 2/3

This can also be written as;

1/2 of 2/3 = 1/2 of two thirds

Simplify

1/2 * 2/3 = 2/6

1/2 of 2/3 = 1/3

Hence the resulting value of the expression is one third

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A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34. 5-foot shadow then the building is approximately 95.2 feet tall.

What is similar triangles ?

Similar triangles are useful in geometry and other fields because they allow us to solve problems involving unknown distances or heights. We can use the known lengths and angles of one triangle to find the lengths and angles of the other triangle, as long as we know that the two triangles are similar. This can be done using the properties of proportional relationships and the rules of similar figures.

Let's use similar triangles to solve this problem. The height of the building and the height of the flagpole are proportional to the lengths of their shadows. We can set up the following equation:

height of building / length of building's shadow = height of flagpole / length of flagpole's shadow

Let x be the height of the building. Then we have:

x / 103 = 32 / 34.5

Simplifying this equation, we get:

x = 103 * (32 / 34.5) ≈ 95.23

Therefore, the building is approximately 95.2 feet tall.

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Paul records data that the number of hot chocolates sold increases as temperature outside decreases. The depiction of the finding is "There is a correlation between two variables". So, the correct option is A.

Specifically, the data suggest that there is a relationship between two variables - the number of hot chocolates sold and the temperature outside.

When the temperature outside decreases, more hot chocolates are sold, and when the temperature increases, fewer hot chocolates are sold. This indicates that there is a correlation between the two variables, as they appear to be related.

However, we cannot determine from this information alone whether the correlation is strong or weak, or whether it is positive or negative.

The strength of the correlation would depend on how much the sales of hot chocolate increase or decrease as the temperature changes, while the direction of the correlation (positive or negative) would depend on whether the increase or decrease in hot chocolate sales is associated with an increase or decrease in temperature, respectively.

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Complete question is:

Paul records data that indicate that the number of hot chocolates sold at a concession stand increases as temperature outside decreases. (for example, more hot chocolates are purchased during late fall than late spring) which statement is the most accurate depiction of this finding?

a) There is a correlation between two variables

b) There is a strong , positive correlation between two variables

c) There is a weak , positive correlation between two variables

d) There is a negative correlation between two variables

The following expressions rewritten below;

23 + 8b

No common terms or factors

= 23 + 8b

㎡ - 5g

No common terms or factors

= m² - 5g

1/8 q + 7a/3

= (3q + 56a) / 24

12k (g+h)

= 12kg + 12kh

(2x + 3)(2 - 5x)

= 4x - 10x² + 6 - 15x

combine like terms

= -10x² -11x + 6

Therefore, algebraic expressions are solved by multiplying and combining like terms.

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Answer:

Since ∠1 and ∠2 are vertical angles, they have equal measure. And since ∠3 and ∠4 are right vertical angles, they have measure 90° each.

Since ∠3 is adjacent to both ∠1 and ∠2, we can say that:

∠1 + ∠3 = 180°

∠2 + ∠3 = 180°

Adding these two equations together:

∠1 + ∠2 + 2∠3 = 360°

Substituting the values we have:

∠1 + ∠2 + 2(90°) = 360°

∠1 + ∠2 + 180° = 360°

Solving for ∠1 + ∠2:

∠1 + ∠2 = 180° - 180° = 0°

Finally, the sum of the measure of ∠4 and the measure of ∠1 minus the measure of ∠2 is:

∠4 + (∠1 - ∠2) = 90° + (∠1 - 0°) = 90° + ∠1

So the answer is 90° + ∠1.

Sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to underestimate the true population variance and standard deviation.

The reason for this is that the sample variance and standard deviation are based on a sample of the population, not the entire population. The sample may not accurately represent the entire population, and thus the sample variance and standard deviation may not accurately reflect the true population variance and standard deviation. To correct for this bias, a correction factor is usually added to the sample variance calculation. For example, when estimating the population variance from a sample of size n, the sample variance is divided by (n-1) instead of n. This correction factor helps to provide a more accurate estimate of the population variance. Similarly, the sample standard deviation is calculated as the square root of the sample variance, and the correction factor is also applied to the sample standard deviation calculation. This corrected sample standard deviation is known as the unbiased sample standard deviation.

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Complete Question

sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to: What?

The situation that matches the information in the graph is a boy rides a bicycle on flat ground and goes quickly down a large hill (option A).

The graph shows how the movement of a body changes over time. In general, it can be observed the movement is first linear as in moving on a flat surface, then the body goes down, then it goes up, and finally, the movement is linear again.

Based on this, it can be concluded that the option that describes the graph is a boy rides a bicycle on a flat group, then he goes down a large hill and finally he drives on flat ground again (option A).

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The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.

We have,

In an equilateral triangle,

- all three sides are of equal length

- the altitude drawn from any vertex bisects the opposite side into two equal segments, forming a right triangle.

Let's denote the side length of the equilateral triangle as "s."

When an altitude is drawn, it bisects the base into two equal segments, each measuring "s/2."

The altitude forms a right triangle with the base, where one leg is the altitude (15 m) and the other leg is half of the base (s/2).

So,

Using the Pythagorean theorem, the value of "s":

s² = (s/2)² + 15²

s² = s²/4 + 225

4s² = s² + 900

3s² = 900

s² = 300

s = √300 = 10√3

Now,

Perimeter = 3 * side length

Perimeter = 3 * 10√3

Perimeter = 30√3 meters

Thus,

The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.

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Answer:

x = 6, y = -3

Step-by-step explanation:

[tex]\frac{x}{y + 1} = -3\\\frac{y}{x-3} = -1[/tex]

x = -3(y+1) - Isolate for x or y (I chose x)

x = -3y -3

Plug in x into y

[tex]\frac{y}{x-3} = -1\\\frac{y}{(-3y -3) - 3} = -1\\\frac{y}{-3y -6} = -1\\y = -1(-3y - 6)\\y = 3y + 6\\-2y = 6\\y = -3[/tex]

Plug y back into equation

[tex]\frac{x}{y+ 1} = -3\\\frac{x}{(-3)+ 1} = -3\\\frac{x}{-2} = -3\\x = -3(-2)\\x = 6[/tex]