The sum of the digits of a certain two-digit number is 3. Reversing its digits decreases the number by 27. Find the number.

A solution of the equation is an ordered pair where the y-value is equal to the equation when the x-value is plugged in. An example of a solution for the equation y = 3x + 5 is the ordered pair (2, 11), because when 2 is plugged in for x, the y-value is 11 (3 * 2 + 5 = 11).

A solution of the equation y = 3x + 5 is an ordered pair of values that satisfies the equation. In other words, when the x-value of the ordered pair is plugged into the equation, the resulting y-value should be the same as the y-value of the ordered pair. For example, the ordered pair (2, 11) is a solution of the equation because when 2 is plugged into the equation, the result is 11 (3 * 2 + 5 = 11). This is true for any ordered pair that satisfies the equation, as the y-value of the ordered pair should always be equal to the result of the equation when the x-value is plugged in. Solutions of equations can be found by solving for the x-value and then plugging it into the equation to find the corresponding y-value. This is the same for any equation, not just y = 3x + 5.

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The explicit formula for the nth term of the sequence 7, 35, 175 is:

[tex]a_n = 7 * 5^{n-1}[/tex]

What is the geometric sequence?

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number called the common ratio. The general formula for a geometric sequence is:

a, ar, ar², ar³, ...

where a is the first term and r is the common ratio.

To find the explicit formula for the sequence 7, 35, 175, we need to identify the pattern in the sequence.

Notice that each term is obtained by multiplying the previous term by 5. Specifically, the first term (7) is multiplied by 5 to get the second term (35), and the second term is multiplied by 5 to get the third term (175).

So, the sequence is a geometric sequence with a common ratio of 5.

To find the explicit formula for a_n, we can use the formula:

[tex]a_n = a_1 * r^{n-1}[/tex]

where a1 is the first term, r is the common ratio, and n is the term we want to find.

In this case, a1 = 7 and r = 5.

Substituting these values into the formula, we get:

[tex]a_n = 7 * 5^{n-1}[/tex]

Therefore, the explicit formula for the nth term of the sequence 7, 35, 175 is:

[tex]a_n = 7 * 5^{n-1}[/tex]

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The predicted population of the school in 2012 is P = 1060 + 78.14(12) = 2002.68 students. We can round this up to 2003 students.

1. The population grew by _____students.

The population in 2001 was 1138 students, and in 2008, it had risen to 1691 students. Therefore, the population increased by 1691-1138 = 553 students.

2. The population took _____ years to grow from 1138 students to 1691 students.

From the year 2001 to the year 2008, the population increased from 1138 to 1691 students. The number of years it took for this growth is 2008-2001 = 7 years.

3. The average population growth per year is _____ students per year.

To obtain the average growth rate per year, divide the total growth in the population by the number of years between the starting year and the ending year. Therefore, the average population growth per year = (1691 - 1138) / 7 = 78.14 students per year.

4. The population in the year 2000 was _____ students.

Since the population was given for the year 2001, we'll have to work our way backward to find the population in the year 2000. It took 7 years for the population to increase from 1138 to 1691, so if we go back another year, we'll have to subtract the average yearly growth rate, which is 78.14 students. Therefore, the population in 2000 = 1138 - 78.14 = 1059.86 students, which we can round up to 1060 students.

5. An equation for the population P of the school t years after 2000 is P = _____.

We can use the formula for linear growth to determine the population of the school t years after 2000. The formula is P = P0 + rt, where P0 is the initial population (in the year 2000), r is the average annual growth rate, and t is the number of years. Therefore, the equation for the population P of the school t years after 2000 is P = 1060 + 78.14t.

6. The predicted population of the school in 2012 is _____ students.

To predict the population of the school in 2012 using the equation, we need to substitute t = 12 - 2000 = 12 into the equation we derived in part 5. Therefore, the predicted population of the school in 2012 is P = 1060 + 78.14(12) = 2002.68 students. We can round this up to 2003 students.

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Answer:

Full answer: 0.26385224274406332453825857519789 Rounded to the nearest hundredth: 0.26 Rounded to the nearest tenth: 0.3

Step-by-step explanation:

The correct equivalent form of 8⁵/8² is Adam made an error in step 2. The denominator should be 1, not 8¹. Option B is correct.

In step 2, Adam used the property of exponents that states: [tex]a^{(m-n)}[/tex] = [tex]a^{m}[/tex] / [tex]a^{n}[/tex]. However, he made a mistake by writing 8¹in the denominator instead of 1.

The correct expression after step 2 should be:

[tex]8^{5-2}[/tex] /1 = 8³

Then, in step 3, Adam used the property of exponents that states: [tex]a^{m}[/tex] / a =   [tex]a^{m-1}[/tex]. This step is correct, and the expression becomes:

[tex]8^{3/8}[/tex]

Finally, in step 4, Adam simplified the expression by dividing 8³ by 8². This step is also correct, and the expression simplifies to:

8¹ = 8

Therefore, the correct equivalent form of 8⁵/8² is 8.

Hence, B. Adam made an error in step 2. The denominator should be 1, not 8¹ is the correct option.

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--The given question is incomplete, the complete question is

"Adam is rewriting the expression 8^5/8^2 in equivalent form. His steps are shown: step 1: 8^5/8^2, step 2:  8^(5-2)/8^1, step 3: 8^3/8, step 4: /8^2. which statement describes the step and the error Adam made in that step? A) Adam made an error in step 2. The exponent in the numerator should be 5+2 B) Adam made an error in step 2. The denominator should be 1, not 8^1 C)  Adam made an error in step 3. The value of 8^1 is 1, not 8."--

The solution to the system of equations is x=\frac{19}{9} and y=\frac{2}{9}

To solve the system of equations, we can use the substitution method.

Step 1: Solve one equation for one variable. Let's choose the second equation, 2x-y=4, and solve for y:
\[y=2x-4\]

Step 2: Substitute the expression for y into the other equations and solve for x:
\[3x-6(2x-4)=5\]
\[3x-12x+24=5\]
\[-9x=-19\]
\[x=\frac{19}{9}\]

Step 3: Substitute the value of x back into the equation for y to find the value of y:
\[y=2(\frac{19}{9})-4\]
\[y=\frac{38}{9}-\frac{36}{9}\]
\[y=\frac{2}{9}\]

Step 4: Check the solution by plugging the values of x and y back into the original equations:
\[3(\frac{19}{9})-6(\frac{2}{9})=5\]
\[6.33-1.33=5\]
\[5=5\]

\[2(\frac{19}{9})-(\frac{2}{9})=4\]
\[4.22-0.22=4\]
\[4=4\]

Therefore, the solution to the system of equations is x=\frac{19}{9} and y=\frac{2}{9}.

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The probability that a randomly selected person had French toast for breakfast is 20%.

Probability describes the result of a random event based on the expected successes or outcomes.

Probability is computed as the quotient of the expected outcomes, events, or successes out of many possible outcomes, events, or successes.

Probability values lie between zero and one based on the degree of certainty or otherwise and can be depicted as percentages, decimals, or fractions.

The total number of survey participants = 20

The number of participants found to be having French toast for breakfast = 4

The probability of selecting a person having French toast for breakfast = 20%,or 0.2, or 1/5 (4/20 x 100)

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The answer is [tex]y = (3/7)x - 20[/tex]

To find the equation of the line that passes through the point (14,-14) and is parallel to the given line, we will use the slope-intercept form of an equation, which is [tex]y = mx + b[/tex], where m is the slope and b is the y-intercept.

First, we need to find the slope of the given line. To do this, we will rearrange the equation to get it in slope-intercept form:

[tex]7y - 10 = -3(5 - x)[/tex]

[tex]7y - 10 = -15 + 3x[/tex]

[tex]7y = 3x + 5[/tex]

[tex]y = (3/7)x + (5/7)[/tex]

The slope of the given line is 3/7.

Since the new line is parallel to the given line, it will have the same slope. So, the slope of the new line is also 3/7.

Now, we will use the point-slope form of an equation to find the equation of the new line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Plugging in the point (14,-14) and the slope 3/7, we get:

[tex]y - (-14) = (3/7)(x - 14)[/tex]

[tex]y + 14 = (3/7)x - 6[/tex]

[tex]y = (3/7)x - 20[/tex]

This is the equation of the new line in slope-intercept form. The slope is 3/7 and the y-intercept is -20.

So, the final answer is [tex]y = (3/7)x - 20[/tex].

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The percent of change from 9 points to 4 points is a decrease of 55.56%.

In an experimental research, an independent variable is one that you change or alter to examine its effects. It is named "independent" because it is unaffected by any other research factors.

A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.

The percent change is given as:

Percent change = (Difference)/(Original) (100)

Percent change = (9 - 4) / 9 (100) = 55.56%.

Hence, the percent of change from 9 points to 4 points is a decrease of 55.56%.

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The most appropriate formula to use in this situation (patient with a bacterial infection and prescribed with Amoxicillin) is Clark's rule, and the dose to administer every 12 hours would be 108.4 mg.

The best formula to use in this situation is the Clark's rule, which is used to calculate the dose of medication for a child based on their weight and the adult dose. The formula is as follows:

In this case, the weight of the child is 21.1 pounds and the adult dose is 771 mg every 12 hours. Plugging these values into the formula, we get:

Rounding to the nearest tenth of a milligram, the child dose would be 108.4 mg and to administer every 12 hours.

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Answer:

Blank 1: DE=59

Blank 2: EB=59

Blank 3: DB=118

Step-by-step explanation:

Set DE and EB equal to each other.

Solve for x.

9x-4=5x+24

-5x. -5x

4x-4=24

+4 +4

4x=28

x=7

Substitute 7 in for x.

DE: 9(7)-4=59

EB: 5(7)+24=59

DE+EB=59+59=118

The inequality that represents the maximum possible height that Raimundo reached is given as follows:

h - (-10) ≤ 40.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The difference between the maximum height and the maximum depth is given as follows:

h - (-10).

As the maximum depth is of 10 feet below.

The difference is at most 40 feet, hence the inequality is given as follows:

h - (-10) ≤ 40.

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The equatiοn fοr the number οf eggs in the refrigeratοr e decreased by 3 equals 15 is, e - 3 = 15.

A statement demοnstrating the equality οf twο expressiοns is knοwn as an equatiοn. Variables, cοnstants, and mathematical οperatiοns are οften included. Equatiοns are tοοls fοr prοblem-sοlving and representing relatiοnships between quantities.

Accοrding tο the questiοn states that the number οf eggs in the refrigeratοr e decreased by 3 equals 15.

It means that the equatiοn can be represented as,

e - 3 = 15

e = 18

Therefοre, the equatiοn is, e - 3 = 15.

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The names of the pair of angles are:

∠3 and ∠6: alternate interior

∠7 and ∠3: supplementary

∠5 and ∠4: alternate exterior

∠5 and ∠4: corresponding

Alternate interior angles are pairs of nonadjacent angles located on opposite sides of a transversal and inside the two parallel lines, while alternate exterior angles are pairs of nonadjacent angles located on opposite sides of a transversal and outside the two parallel lines.

Therefore, the pair of angles can be named as shown below:

∠3 and ∠6 are alternate interior angles

∠7 and ∠3 are supplementary

∠5 and ∠4 are alternate exterior angles

∠5 and ∠4 are corresponding angles

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The possible rational zeros of [tex]f(x) = 5x^(4) - 9x^(3) - 7x^(2) + 9x - 2[/tex] are [tex]±1, ±2, ±1/5, and ±2/5.[/tex]

According to the Rational Zeros Theorem, the possible rational zeros of a polynomial function are the ratios of the factors of the constant term to the factors of the leading coefficient. In this case, the constant term is -2 and the leading coefficient is 5.

The factors of -2 are ±1 and ±2. The factors of 5 are ±1 and ±5. So, the possible rational zeros are:

[tex]±1/1, ±2/1, ±1/5, ±2/5[/tex]

Simplifying these gives us the following list of possible rational zeros:

[tex]±1, ±2, ±1/5, ±2/5[/tex]

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By answering the above question, we may state that It is challenging to graphs offer a more precise interpretation of the graph without additional context and information about its intended use.

Mathematicians make graphs to visually express or chart facts or values in a logical way. Usually, a graph point will convey the connection between two or more objects. A graph is a non-linear data arrangement comprised of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as charts and graphs, pie charts, and line graphs. a triangle-shaped logarithmic graph.

Giving a precise interpretation is challenging without knowing the line's equation or the context of the graph. However, generally speaking, the fact that the line passes through the point (-10, 2) indicates that it is on the line.

The graph could compare two distinct types of data or separate variables, such time and distance. The point (-10, 2) on the line, for instance, may indicate that if someone worked for 10 hours, they would receive $2. This is an example of a graph demonstrating the link between the number of hours worked and the amount of money made.

It is challenging to offer a more precise interpretation of the graph without additional context and information about its intended use.

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To the nearest foot, the tree is 60 feet tall.

Angle of elevation refers to the angle formed between the horizontal line and an object or point when the observer is looking upward. This angle is measured from the horizontal plane up to the observer's line of sight. The angle of elevation is commonly used in navigation, surveying, and astronomy to determine the position of objects in the sky, such as stars and planets, and to calculate the height or distance of objects on the ground, such as buildings, trees, or mountains. It is also used in sports, such as archery and basketball, to aim accurately at a target.

Let's represent the height of the tree as 'h'.

From the given information, we can form a right triangle with the tree, its shadow, and the sun. The angle of elevation of the sun is the angle between the sun's rays and the horizontal ground. Therefore, the angle between the tree and its shadow (the angle of depression) is 90 - 63 = 27 degrees.

Using trigonometry, we can set up the following equation:

tan(63) = h / 27

Solving for 'h', we get:

h = 27 * tan(63) ≈ 60 feet

Therefore, to the nearest foot, the tree is 60 feet tall.

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Answer: 112°

Step-by-step explanation:

The angles are supplementary so add to 180°

(2x) + (3x + 10) = 180

Combine Like Terms leaves:

5x + 10 = 180

Subtract 10 from each side:

5x = 170

Divide 5 on each side:

x = 34

Plug x into the large angle

3(34) + 10

Solve:

102 + 10 = 112

The large angle is 112°

Hope this helps!

1,800,000

We have to do 6 x 300,000, which gives us 1,800,000

Answer:

16-year-old horse is equivalent to a 48-year-old human. x = 48

Step-by-step explanation:

We can set up a proportion to solve this problem:

horse age / human age = k

where k is the constant of proportionality. We're told that a 5-year-old horse is equivalent to a 15-year-old human, so we can use this information to find k:

5 / 15 = k

k = 1/3

Now we can use this value of k to find the equivalent human age for a 16-year-old horse:

16 / x = 1/3

Multiplying both sides by x:

16 = x/3

Multiplying both sides by 3:

x = 48

So a 16-year-old horse is equivalent to a 48-year-old human.

The number of bacteria in the refrigerated food product at T = 3 is -100.5.

The number of bacteria in a refrigerated food product is given by the equation N(T) = 27T^2 - 148T + 100.5. This equation can be used to determine the number of bacteria in the product at any given time, T.

To find the number of bacteria at a specific time, simply plug in the value of T into the equation and solve for N(T). For example, if we want to find the number of bacteria at T = 3, we would plug in 3 for T and solve:

N(3) = 27(3)^2 - 148(3) + 100.5
N(3) = 27(9) - 444 + 100.5
N(3) = 243 - 444 + 100.5
N(3) = -100.5

Therefore, the number of bacteria in the refrigerated food product at T = 3 is -100.5. It is important to note that the number of bacteria cannot be negative, so this equation may not be valid for all values of T. It is important to check the validity of the equation for the specific time period in question.

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B3 is in the image of A, and the vector x that demonstrates this is x = [ 5 ][ 2 ] [ 2 ].

To determine whether a vector is in the image of A, we need to solve the equation Ax = b for x. If there is a solution for x, then the vector is in the image of A.

For b1:
A x = [ 2 ]
[ 4 ] [ -7]
We can set up a system of equations:
0x + 1y - 1z = 2
0x + 2y - 2z = 4
1x + 2y + 3z = -7
Solving this system, we find that there is no solution for x, y, and z. Therefore, b1 is not in the image of A.

For b2:
A x = [ 3 ]
[ -10 ] [ 4 ]
We can set up a system of equations:
0x + 1y - 1z = 3
0x + 2y - 2z = -10
1x + 2y + 3z = 4
Solving this system, we find that there is no solution for x, y, and z. Therefore, b2 is not in the image of A.

For b3:
A x = [ 0 ]
[ 0 ] [ 11 ]
We can set up a system of equations:
0x + 1y - 1z = 0
0x + 2y - 2z = 0
1x + 2y + 3z = 11
Solving this system, we find that there is a solution for x, y, and z: x = 5, y = 2, and z = 2. Therefore, b3 is in the image of A, and the vector x that demonstrates this is x = [ 5 ]
[ 2 ] [ 2 ].

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The value of sin A in the triangle is 7/9

The complete question is added as an attachment

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

The triangle ABC

Using the sine rule, we have

sin(A) = Opposite/Hypotenuse

Substitute the known values in the above equation, so, we have the following representation

sin(A) = 7/9

Hence, the solution is 7/9

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The measure of m∠G of the trapezoid is 60°

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the trapezium be represented as EFGH

Now , the measure of m∠F = 150°

The measure of m∠H = 90°

Now , the measures of the sides EF = measure of side FG

So , the measures of angles are also equal

Now , the total internal angle of trapezoid is 360°

So , 2x + 150° + 90° = 360°

On simplifying , we get

2x = 360° - 240°

2x = 120°

x = 60°

Therefore , the measure of n = 60°

Hence , the measure of the angle of trapezoid ∠G = 60°

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Answer: D: 3 to 4

Step-by-step explanation:

Answer:

In Sharla's computer club, 4 out of every 7 members and girls. What is the ratio of boys to girls in the club?

Maria filled her bathtub with 15 gallons of water. How many pints of water did she put in the tub?

Step-by-step explanation:

You're welcome.

Answer:

Step-by-step explanation:

Q has y-coordinate of 4 => the distance from origin to y-coordinate is 4 units, which is one leg of the right triangle

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c^2 = a^2 + b^2

with c = 5, a = 4

5^2 = 4^2 + b^2

b^2 = 25 - 16 = 9

b = √9 = 3

so Q has coordinates (-3,4)

Answer:

look in the comments and have a good day

The given function, f(x) = x + 4 is increasing on the entire interval of 2≤x≤5

From the question, we are to determine if the given function is increasing or decreasing over the given interval

The given function is

f(x) = x + 4

To determine if the function f(x)=x+4 is increasing or decreasing on the interval of 2≤x≤5, we need to look at the sign of the first derivative of the function on that interval.

The first derivative of the function is

f'(x) = 1

Which is always positive

This means that the function is increasing on the entire interval of 2≤x≤5.

To justify this, we can also look at the graph of the function, which is a straight line with a positive slope. Any line with a positive slope is always increasing, so this confirms our conclusion that the function is increasing on the given interval.

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Solution: