The expression ((-8x⁵)(x⁻³))/(20x²) when simplified, making all exponents positive, will become -2/5.
To simplify the expression ((-8x⁵)(x⁻³))/(20x²), we need to apply the rules of exponents and simplify the coefficients.
First, let's simplify the coefficients:
-8/20 = -2/5
Next, let's apply the rules of exponents:
Product Rule: When multiplying two exponential expressions with the same base, you can add the exponents. That is, xᵃ · xᵇ = xᵃ⁺ᵇ
Quotient Rule: When dividing two exponential expressions with the same base, you can subtract the exponents. That is, xᵃ / xᵇ = xᵃ⁻ᵇ
(x⁵)(x⁻³) = x⁵⁺⁽⁻³⁾ = x²
x²/x² = x²⁻² = x⁰ = 1
So the expression simplifies to:
(-2/5)(1) = -2/5
Therefore, the simplified expression is -2/5.
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A food company conducted a survey and found that 4 out of 20 people had french toast for
breakfast yesterday.
What is the probability that a randomly selected person had french toast for breakfast?
The probability that a randomly selected person had French toast for breakfast is 20%.
What is the probability?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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HW. Solve system of eq. 1. \[ \begin{array}{r} 3 x-6 y=5 \quad 2 . \\ 2 x-y=4 \\ \text { 3. } 4 x-2 y=5 \\ 2 x-y=11 \end{array} \] \[ \text { 2. } x-3 y=8 \] \[ 2 x-6 y=16 \]
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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How much of a 12% salt solution must combined with a 26% salt solution to make 2 gallons of a 20% salt solution?
The final answer is 0.857 gallons of the 12% solution and 1.143 gallons of the 26% solution.
To find how much of a 12% salt solution must be combined with a 26% salt solution to make 2 gallons of a 20% salt solution,
We can use the equation:
x(12%) + (2 - x)(26%) = 2(20%)
where x is the amount of the 12% solution needed.
Simplifying the equation gives us:
12x + 52 - 26x = 40
-14x = -12
x = 0.857 gallons
Therefore, we need 0.857 gallons of the 12% salt solution and 1.143 gallons of the 26% salt solution to make 2 gallons of a 20% salt solution.
Answer: 0.857 gallons of the 12% solution and 1.143 gallons of the 26% solution.
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ANSWER FAST BECUASE I NEED THE ANSWER FASTTTTTTTTTTTTT
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!
17. In right triangle AABC shown below, the given lengths
are in millimeters. What is sin A ?
A.
B.
C.
D.
4√2
9
4√2
7
7√/2
8
779927
E. 2/7
A
4√2
9
B 7
C
The value of sin A in the triangle is 7/9
How to determine the value of sin AThe 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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You work for a company that wants to distribute 1.25 L cylindrical water bottles. Find dimensions of a cylinder that will result in the desired volume if the height must be between 4 to 6 times the radius.
To find the dimensions of a cylinder with a specific volume and height to radius ratio, we can use the formula for the volume of a cylinder, V = πr^2h, where V is the volume, r is the radius, and h is the height. We can also use the given information that the height must be between 4 to 6 times the radius, or 4r ≤ h ≤ 6r.
We can start by plugging in the given volume and the height to radius ratio into the formula:
1.25 L = πr^2(4r)
Dividing both sides by 4π gives us:
r^3 = 1.25 L / (4π)
Taking the cube root of both sides gives us the radius:
r = (1.25 L / (4π))^(1/3)
Now we can use the height to radius ratio to find the height:
h = 4r = 4(1.25 L / (4π))^(1/3)
So the dimensions of the cylinder are:
r = (1.25 L / (4π))^(1/3)
h = 4(1.25 L / (4π))^(1/3)
These dimensions will result in the desired volume of 1.25 L and a height that is between 4 to 6 times the radius.
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Q1.Identify the percent of change as an increase or a decrease. 9 points to 4 points
Q2.Find the percent of change. Round to the nearest tenth of a percent if necessary
The percent of change from 9 points to 4 points is a decrease of 55.56%.
What is the difference between a dependent and independent variable?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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Hi, can anyone please answers this. I appreciate it very much. I need the answer and solution of (b) only
Answer:
[tex]\frac{\sqrt{x+3} }{x+1}[/tex]
Step-by-step explanation:
nothing further can happen.
In studies looking at the movement patterns of penguins, penguins are often monitored by placing a metal tag on their flipper. A group of scientists were concerned that these metal tags may be negatively affecting the survival of penguins (Saraux et al. 2011, "The Reliability of flipper-banded penguins as indicators of climate change", Nature 469, 203- 206). They conducted a small study with a total of 1983 penguins to determine whether the type of tag (metal or electronic) influenced the 5-year survival of penguins. In total, the study included 957 penguins that wore metal tags, 540 penguins that wore metal tags and survived, and 301 penguins that wore electronic tags and died.
a) Assuming that the type of tag and penguin survival are independent of one another, what 2x2 table do we expect to see? Is the observed data consistent with this assump- tion of independence? Carry out a chi-squared test to address this question. Give all your steps, and state as clearly as you can what hypotheses you are testing, your p-value, and what you conclude.
b) Suppose a condition was specified in the null hypothesis through prior knowledge that the probability of survival is 0.637 and that the probability of a penguin wearing a metal tag is 0.483. Would anything in your analysis in (a) change? Is there any change in your conclusion from (a)?
c) Suppose a separate study had only included 21 penguins in total, 12 penguins that wore electronic tags, 4 penguins that wore metal tags and survived, and 5 penguins that wore electronic tags and died. Explain what reservations (if any) you may have with performing a chi-squared test. Carry out an appropriate test to address the question of independence between survival and tag type for the new data. Give all your steps, and state as clearly as you can what hypotheses you are testing, your p-value, and what you conclude.
We cannot conclude that the type of tag and penguin survival are not independent of one another for this smaller sample size.
a) The expected 2x2 table would look like this:
| | Metal Tag | Electronic Tag |
|------------|-----------|----------------|
| Survived | 483.637 | 456.363 |
| Not Survived | 473.363 | 569.637 |
The observed data is not consistent with the assumption of independence, as the observed values are different from the expected values. To carry out a chi-squared test, we need to calculate the chi-squared statistic:
X^2 = (957-483.637)^2/483.637 + (540-456.363)^2/456.363 + (301-473.363)^2/473.363 + (185-569.637)^2/569.637 = 237.525
The degrees of freedom for this test are (2-1)(2-1) = 1. Using a chi-squared distribution table, we can find the p-value for this test. The p-value is less than 0.001, which is very small. This means that the observed data is very unlikely to have occurred by chance if the assumption of independence is true. Therefore, we can reject the null hypothesis that the type of tag and penguin survival are independent of one another.
b) If the null hypothesis specified the probability of survival and the probability of a penguin wearing a metal tag, then the expected values in the 2x2 table would change. The new expected values would be:
| | Metal Tag | Electronic Tag |
|------------|-----------|----------------|
| Survived | 609.711 | 330.289 |
| Not Survived | 347.289 | 695.711 |
The chi-squared statistic would also change:
X^2 = (957-609.711)^2/609.711 + (540-330.289)^2/330.289 + (301-347.289)^2/347.289 + (185-695.711)^2/695.711 = 444.787
The p-value for this test would still be less than 0.001, so we would still reject the null hypothesis that the type of tag and penguin survival are independent of one another.
c) With a smaller sample size, the chi-squared test may not be appropriate. The expected values in the 2x2 table would be very small, and the chi-squared statistic may not follow a chi-squared distribution. Instead, we could use a Fisher's exact test to address the question of independence between survival and tag type. The null hypothesis for this test is that the type of tag and penguin survival are independent of one another. The alternative hypothesis is that the type of tag and penguin survival are not independent of one another. The p-value for this test is 0.657, which is not small enough to reject the null hypothesis. Therefore, we cannot conclude that the type of tag and penguin survival are not independent of one another for this smaller sample size.
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Determine if the function f(x)=x+4 is increasing or decreasing on the interval of 2≤x≤5
. Justify your answer.
The given function, f(x) = x + 4 is increasing on the entire interval of 2≤x≤5
Determining if a function is increasing or decreasing on the intervalFrom 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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You are stranded on a boat in the middle of the ocean with no fresh water on board. However, you are not alone, and some of those with you want to drink the ocean water. You tell them they should not do that but they don’t believe you. Use your understanding of osmosis to convince them WHY drinking salt water is very bad and a potentially deadly idea.
You can't drink salt water as it leads to dehydration and damage to our organs due to the high concentration of salt.
Why it is not recommended to drink salt water?Drinking salt water can be a potentially deadly mistake because of a phenomenon called osmosis. Osmosis is the movement of water molecules across a semi-permeable membrane, from an area of low solute concentration to an area of high solute concentration.
When we drink salt water, we introduce a high concentration of salt into our bodies. This high concentration of salt draws water out of our cells and tissues, causing dehydration. This is because our bodies require water to dilute the salt concentration and maintain a balance of solutes both inside and outside the cells.
The more salt water a person drinks, the greater the concentration of salt in their body becomes, leading to an increased loss of water through osmosis. This can lead to a vicious cycle where the more a person drinks salt water, the more dehydrated they become, thus damaging the organs of the person.
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Use the rational zeros theorem to list all possible rational zeros of the following. f(x)=5x^(4)-9x^(3)-7x^(2)+9x-2
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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Drag each set of coordinates to the correct location on the table. Calculate the distance between the pairs of coordinates, and classify them according to the distance between them. (3, 4) and (2, 1) (3, 7) and (5, 2) (5, -2) and (3, 3) (-2, 3) and (1, 2) (-4, -2) and (-3, 1) (4, -1) and (-1, 1)
The distances based on their values, we have:
Distances of approximately 1 to 2 units: (-3, 1) and (-4, -2)
Distances of approximately 3 units: (2, 1) and (1, 2)
Distances of approximately 5 units: (3, 7) and (4, -1), (5, -2) and (3, 3), and (-1, 1) and (4, -1).
Coordinates (3, 4) (3, 7) (5, -2) (-2, 3) (-4, -2) (4, -1)
(2, 1) 3.16
(5, 2) 5.39
(3, 3) 5.1
(1, 2) 3.16
(-3, 1) 1.41
(-1, 1) 5.1
We may use the distance formula to determine the separation between each pair of coordinates:
Distance is equal to sqrt((x2 - x1) + (y2 - y1))
Using the values to categorise the distances, we have:
About 1 to 2 unit distances are (-3, 1) and (-4, -2)
Distances roughly 3 units apart: (2, 1) and (1, 2) Distances roughly 5 units apart: (3, 7) and (4, -1), (5, -2) and (3, 3), and (-1, 1) and (4, -1).
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Hello again can you y’all help me again cuz I told u my three brain cells can’t can you check if I did the math right your supposed name the four types of angels alternate interior alternate exterior supplementary and corresponding
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
What are Alternate Interior and Exterior Angles?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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Please help I tried to answer this problem 10 times but got it wrong.
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.
A number is equal to the sum of half a sebond number and 3. The first number is also equal to the sum of one-quarter of the second number and 5. The situation can be represented by using the graph below, where x represents the second number.
The number of bacteria in a refrigerated food product is given byN(T)=27T2−148T+100,5
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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This is another math question, please help!!
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
If a=6 and b=24 eat is the calculation of b/a
Solution:
[tex]value \: of \: a = 6[/tex][tex]value \: of \: b = 24[/tex][tex] \frac{b}{a} = \frac{24}{6} [/tex][tex] = \frac{4}{1} = 4[/tex]The final value of b/a = 47y−10=−3(5−x)
Step 2 of 2 : Find the equation of the line which passes through the point
(14,−14)(14,−14) and is parallel to the given
line. Express your answer in slope-intercept form. Si
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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Big ideas 7.5 question
The measure of m∠G of the trapezoid is 60°
What is a trapezoid?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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if you get it correct you will get more points
The inequality that represents the maximum possible height that Raimundo reached is given as follows:
h - (-10) ≤ 40.
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.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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0.21 divided by 0.7959
Answer:
Full answer: 0.26385224274406332453825857519789 Rounded to the nearest hundredth: 0.26 Rounded to the nearest tenth: 0.3
Step-by-step explanation:
for
the function f(x) = x^2 - 2x, what are the intervals for which f(x)
is greater than or equal to zero?
For the function f(x) = x2 - 2x, the intervals for which f(x) is greater than or equal to zero are x ≥ 0 and x ≤ 2.
We can solve this equation by setting f(x) equal to zero and solving for x:
x2 - 2x = 0
x(x - 2) = 0
x = 0 or x = 2
Therefore, the intervals for which f(x) is greater than or equal to zero are x ≥ 0 and x ≤ 2.
Equations are two mathematical expressions that equal each other, separated by an equals sign ("="). In equations, we can find data that may or may not be known.
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may someone help me with this????
Answer:
The answer would be at 11 30 the temperature would be at 3°C
Helpppppp meeee and thank uuuuuuu
Answer:
look in the comments and have a good day
find the missing segment in the image below
In the triangle ABC, the value of BD is obtained as 34 units.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
A triangle ABC is given.
A line segment DE divides the triangle.
The measure of AD is given as 51 units.
The measure of BE is given as 16 units.
The measure of CE is given as 24 units.
According to the indirect measurement -
AD / BD = CE / BE
Substitute the values in the equation -
51 / BD = 24 / 16
24 BD = 51 × 16
BD = 17 × 2
BD = 34
Therefore, the value of BD is obtained as 34 units.
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Answer: 34
Step-by-step explanation:
Which ordered pair is a solution of the equation? y = 3 x + 5
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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When the angle of elevation of the sun is 63°, a tree casts a shadow that is 27 feet long. To the nearest foot, how tall is the tree?
To the nearest foot, the tree is 60 feet tall.
Describe Angle of elevation?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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Write an explicit formula for � � a n , the � th n th term of the sequence 7 , 35 , 175
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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