Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
To determine how far Jonah swam from one corner of the pool to the opposite corner, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
[tex]Hypotenuse^2 = Length^2 + Width^2[/tex]
[tex]Hypotenuse^2[/tex] =[tex]21^2 + 20^2[/tex]
[tex]Hypotenuse^2[/tex]= 441 + 400
[tex]Hypotenuse^2[/tex]= 841
Taking the square root of both sides, we find:
Hypotenuse =[tex]\sqrt{841[/tex]
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
The two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
[tex]Hypotenuse^2 = Length^2 + Width^2\\Hypotenuse^2 = 21^2 + 20^2\\Hypotenuse^2 = 441 + 400\\Hypotenuse^2 = 841[/tex]
Taking the square root of both sides, we find:
Hypotenuse = [tex]\sqrt841[/tex]
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
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You empty a 2-liter bottle every 8 seconds into tanks that hold 50 gallons. How long will it take you to fill 11 tanks? (3.8 l = 1 gallon)(Convert 11 tanks to hours)
It will take approximately 2.32 hours to fill 11 tanks.
First, we need to convert the capacity of the tanks from gallons to liters, as the rate at which we empty the bottle is given in liters. Since 1 gallon is equal to 3.8 liters, the capacity of each tank is 50 gallons * 3.8 liters/gallon = 190 liters.
Now, let's calculate the time it takes to fill one tank:
The bottle is emptied at a rate of 2 liters every 8 seconds. To find the time it takes to fill one tank, we divide the capacity of the tank (190 liters) by the rate at which we empty the bottle (2 liters/8 seconds):
Time for one tank = 190 liters / (2 liters/8 seconds) = 190 liters * (8 seconds/2 liters) = 760 seconds.
Next, we need to find the total time required to fill 11 tanks. Since each tank takes 760 seconds to fill, we multiply this by 11 to account for the 11 tanks:
Total time to fill 11 tanks = 760 seconds/tank * 11 tanks = 8,360 seconds.
Finally, we convert the total time from seconds to hours. There are 60 seconds in a minute and 60 minutes in an hour, so:
Total time to fill 11 tanks = 8,360 seconds * (1 minute/60 seconds) * (1 hour/60 minutes) = 2.32 hours (rounded to two decimal places).
Therefore, it will take approximately 2.32 hours to fill 11 tanks.
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ہے
8. A randomized controlled trial was designed to compare the effectiveness of splinting versus
surgery in the treatment of carpal tunnel syndrome. Results are given in the table. The results
are based on evaluations made one year after the treatment. Using a 0.01 significance level,
find the test statistic and critical value needed to test the claim that the success is independent
of the type of treatment.
Splint treatment
Surgery treatment
Successful
Treatment
60
67
Otest statistic = 0.848, critical value = 6.635
statistic 9 750 critical value = 6.635
Unsuccessful
Treatment
23
6
(1 poir
The test statistic and critical value needed to test the claim that the success is independent of the type of treatment are 9.750 and critical value is 6.635.
How to calculate the valueThe expected value for each cell is calculated as follows:
E = row total * column total / grand total
The grand total is 150.
The row totals are 83 and 67.
The column totals are 86 and 64.
The expected values are as follows:
Successful: 60 * 86 / 150 = 36.4
Unsuccessful: 60 * 64 / 150 = 29.6
Surgery treatment
Successful: 67 * 86 / 150 = 49.6
Unsuccessful: 67 * 64 / 150 = 27.4
The test statistic is calculated as 9.750
The critical value is calculated as follows:
α = 0.01
df = (r-1)(c-1) = (2-1)(2-1) = 1
x²(α, df) = 6.635
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A woman is selected at random from the population of the United States. Let event A represent "The woman is a professional basketball player" and event B represent "The woman is taller than 5 feet 4 inches."
Are these probabilities equal? If so, explain your reasoning. If not, explain which one is the greatest and why.
P(B) when you have no other information.
P(B) when you know A is true.
P(B) when you know A is false.
The probability of event B would likely be greater when event A is true, reflecting the tendency of professional basketball players to be taller.
To determine the probabilities in question, we need to consider the information provided and make some assumptions based on general knowledge about the population of the United States.
P(B) when you have no other information:
Without any other information, we cannot accurately determine the probability of event B, which represents "The woman is taller than 5 feet 4 inches." We would need additional data on the height distribution of women in the United States to calculate this probability.
P(B) when you know A is true:
If we know that event A is true, meaning "The woman is a professional basketball player," we can make some assumptions based on the nature of professional basketball players.
Generally, professional basketball players tend to be taller than the average population due to the physical requirements of the sport. Therefore, the probability of event B, "The woman is taller than 5 feet 4 inches," would likely be greater when we know event A is true.
P(B) when you know A is false:
If event A is false, meaning "The woman is not a professional basketball player," we cannot make any definitive conclusions about the probability of event B, "The woman is taller than 5 feet 4 inches." The height of an individual is not solely determined by their profession, so without further information, we cannot determine if event B is more or less likely when event A is false.
In summary, based on the given information, we can conclude that the probabilities of event B are not equal under different scenarios. The probability of event B would likely be greater when event A is true, reflecting the tendency of professional basketball players to be taller. However, without any other information, we cannot determine the probability of event B or make comparisons when event A is false.
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The manufacturer of a DVD player has found the revenue R (in dollars) is R(p) = -4p² + 1700p,
when the unit price is p dollars. What is the maximum revenue to the nearest whole dollar?
a. $722,500
c. $180,625
b. $1,445,000
d. $361,250
The maximum revenue, to the nearest whole dollar, is $180,625 (option c).
To find the maximum revenue, we need to determine the vertex of the quadratic function represented by the revenue equation.
The revenue equation is given as:
R(p) = -4p² + 1700p
The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula:
x = -b / (2a)
For the given revenue equation, a = -4 and b = 1700. Plugging these values into the formula, we have:
p = -1700 / (2 × -4)
p = -1700 / -8
p = 212.5
The maximum revenue occurs at p = 212.5.
To find the maximum revenue, we substitute this value back into the revenue equation:
R(p) = -4(212.5)² + 1700(212.5)
R(p) = -4(45256.25) + 361250
R(p) = -181025 + 361250
R(p) = 180625
Therefore, the maximum revenue, to the nearest whole dollar, is $180,625 (option c).
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two rectangles have the same base lengths. one rectangle has a height that is twice the height of the other rectangle. are the heights and areas proportional
Although the rectangles have the same base lengths, the heights and areas are not directly proportional in this case.
Are the heights and areas of the rectangles proportional?Let's denote the base length of both rectangles as 'b'. If one rectangle has a height that is twice the height of the other rectangle, we can denote the heights as 'h' and '2h', respectively.
The area of a rectangle is calculated by multiplying the base length by the height. Therefore, the area of the first rectangle with height 'h' would be A₁ = b * h, and the area of the second rectangle with height '2h' would be A₂ = b * (2h) = 2b * h.
Comparing the two areas, we have A₁ = b * h and A₂ = 2b * h. It is evident that the areas are not proportional because the area of the second rectangle is twice the area of the first rectangle.
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ILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST SOMEBODY PLEASE PLEASE HELP ME IM BEGGING YOU
Answer:
B Mean: 17.5 | W Mean: 20.5 | B Mode: 15 | W Mode: 20.5 | B Mode: 14 & 15 | W Mode: 20 & 21 | B Range: 17 | W Range: 3
Step-by-step explanation:
A circle is inscribed inside a square of a side length of 10 cm. What is the area inside the square and outside the circle
Answer:
The figure is omitted--please sketch it to confirm my answer.
[tex]\pi {(5 \sqrt{2}) }^{2} - {10}^{2} [/tex]
[tex]50\pi - 100 = 50(\pi - 2) = 57.08[/tex]
The area inside the square and outside the circle is about 57.08 cm^2.
Simplify the following expression.
(6m5g5) 2
The simplified exponential expression in the context of this problem is given as follows:
[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]
How to simplify the exponential expression?The exponential expression in the context of the problem is defined as follows:
[tex](6m^5g^5)^2[/tex]
The power of a power rule is used when a single base is elevated to multiple exponents, and states that simplified expression is obtained keeping the base, while the exponents are multiplied.
Applying the exponent of 2, we have that:
6² = 36.5 x 2 = 10.Hence the simplified exponential expression in the context of this problem is given as follows:
[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]
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Jane buys p packets of plain crisps and c packets
of cheese and onion crisps. Write down an
expression for the total number of packets of
crisps Jane buys.
The expression for the total number of packets of crisps that Jane buys is given as follows:
p + c.
How to obtain the total number of packets?The amounts of packets of crisps purchased are given as follows:
p packets of plain crisps.c packets of cheese and onion crisps.The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.
Hence the expression for the total number of packets of crisps that Jane buys is given as follows:
p + c.
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Please help i will give brainliest
The value of measure of angle 1, angle 2, and angle 3 are,
⇒ ∠1 = 106 degree
⇒ ∠2 = 74°
⇒ ∠3 = 74°
We have to given that;
Angle in figure is,
⇒ 74°
Since, From figure,
angle 1 is,
⇒ ∠1 = 180 - 74
⇒ ∠1 = 106 degree
Hence, We get;
Measure of angle 2 is,
⇒ ∠2 = 180 - 106
⇒ ∠2 = 74°
And, Measure of angle 3 is,
⇒ ∠ 3 = ∠ 2
By definition of alternate interior angle.
⇒ ∠3 = 74°
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The measure of ∠1 is 106 because it is a straight angle with 74° angles.
The measure of ∠2 is 74 because it is a vertical angle with 74° angles.
The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.
We have,
The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
Now,
∠1 + 74 = 180
∠1 = 180 - 74
∠1 = 106
And,
∠2 and 74 are vertical angles.
So,
∠2 = 74
And,
∠3 and 74 are corresponding angles.
So,
∠3 = 74
Thus,
The measure of ∠1 is 106 because it is a straight angle with 74° angles.
The measure of ∠2 is 74 because it is a vertical angle with 74° angles.
The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.
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Triangle ABC, with vertices A(-9,-8), B(-2,-9), and C(-8,-5), is drawn inside a rectangle. What is the area, in square units, of triangle ABC?
The area of triangle ABC is 19 square units.
To find the area of a triangle, we can use different formulas depending on the information available. Since we have the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can use the Shoelace Formula (also known as the Gauss's area formula) to calculate the area of the triangle.
The Shoelace Formula states that if the coordinates of the vertices of a triangle are (x1, y1), (x2, y2), and (x3, y3), then the area (A) of the triangle can be calculated as:
Area = 0.5 * |(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))|
Using the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can substitute these values into the formula to calculate the area.
Let's calculate step by step:
x1 = -9
y1 = -8
x2 = -2
y2 = -9
x3 = -8
y3 = -5
Area = 0.5 * |(-9 * (-9 - (-5)) + (-2) * (-5 - (-8)) + (-8) * ((-8) - (-9)))|
Area = 0.5 * |(-9 * (-4) + (-2) * (3) + (-8) * (-1))|
Area = 0.5 * |(36 + (-6) + 8)|
Area = 0.5 * |(38)|
Area = 0.5 * 38
Area = 19
Therefore, the area of triangle ABC is 19 square units.
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Select the correct answer. Which value of x from the set [4, 5, 6, 7), makes this equation true? 4(8-x) = 8 OB. 5 OC. OD. 7 C. 6
Answer:
6
Step-by-step explanation:
The correct answer is C. 6.
If we substitute 6 for x in the equation, we get 4(8-6) = 4(2) = 8.
This is the only value of x that makes the equation true.
The box contains some green and yellow counters. 7/4 of the box is green counters. There are 24 yellow counters . How many green counters are there?
Considering the definition of an equation and the way to solve it, there are 84 green counters in the box.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Amount of green countersKnowing that:
7/9 of the box is green counters.1-7/9= 2/9 of the bok are yellow counters.There are 24 yellow counters.the equation in this case is:
2/9 × total counters on the box =24
Solving:
total counters on the box =24÷ 2/9
The first step in dividing by a fraction is to find the reciprocal (reverse the numerator and denominator) of the second fraction.
Then, the two numerators and the two denominators must be multiplied and, if necessary, the fractions are simplified.
total mountain bikes =24× 9/2= 24/1× 9/2
total mountain bikes =(24×9)/ (1×2)
total mountain bikes =216/2
total mountain bikes =108
Then, there are 108 green and yellow counters in the box.
So, the amount of green counters in the box is calculated as:
Amount of green counters= 7/9× 108
Amount of green counters= 7/9× 108
Amount of green counters= 84
Finally, there are 84 green counters in the box.
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Which of the following options represents the phrase "eight less than the quotient of 24 and 12"?
Hello!:
24/12 - 8
= 2 - 8
= -6
A jogger running around a rectangular park takes a shortcut back to his car by running 53 meters from one corner to the opposite corner. If the park is 45 meters long, what is the width?
Answer:
28 meters Aprox
Step-by-step explanation:
To find the width of the rectangular park, we can use the Pythagorean theorem. The diagonal running from one corner to the opposite corner forms a right triangle with the length and width of the park.
Given:
Length of the park (L) = 45 meters
Diagonal distance (d) = 53 meters
Using the Pythagorean theorem:
d² = L² + W²
(53 meters)² = (45 meters)² + W²
2809 = 2025 + W²
W² = 2809 - 2025
W² = 784
Taking the square root of both sides:
W ≈ √784
W ≈ 28
Therefore, the width of the rectangular park is approximately 28 meters.
Enter the number that belongs in the green box
The number in the green box is 31.78° .
Given,
Triangle with sides 11 , 12 , 20.
From Cosine Law.
Let △ABC have sides a, b, c.
Here,
a = 11
b = 20
c = 12
Length of the side opposite vertex A is called a.
Length of the side opposite vertex B is called c.
Length of the side opposite vertex C is called c.
Let θ = ∠C
Then, the Cosine Law says that
c²=a²+b²−2abcosθ.
Substitute the values of a , b , c .
12² = 11² + 20² - 2 × 11× 20 cosθ
θ = 31.78°
Hence the angle can be found out from cosine law.
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100 Points! Geometry question. Photo attached. Find the measure. Please show as much work as possible. Thank you!
Answer:
The answer would lie within 31 degrees of MP and also as in PM.
Answer:
central m arc MP=118°
Step-by-step explanation:
here
central m arc MN=2* inscribed m arc MN=2*31=62°
again
central m arc MN+ central m arc MP=180° being linear pair
substituting value
62°+central m arc MP=180°
central m arc MP=180°-62°
central m arc MP=118°
which of the following is the slope of the line with equation -7x=6+3y
Answer:
Slope = -7/3
Step-by-step explanation:
-7x = 6 + 3y is in the standard form of a line, whose general equation is
Ax = C + By (it's sometimes written in terms of C and is Ax + By = C, but in this problem, it's written in terms of Ax).
We can find the slope of the line by converting from standard form to slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-intercept.Step 1: Subtract 6 from both sides:
(-7x = 6 + 3y) - 6
-7x - 6 = 3y
Step 2: Divide both sides by 3 to isolate y:
(-7x - 6 = 3y) / 3
-7/3x - 2 = y
Thus, the slope of the line is -7/3
Answer: Therefore the slope is [tex]-\frac{7}{3}[/tex].
Step-by-step explanation:
We can rewrite the equation -7x=6+3y in slope-intercept form y = mx + b, where the m is the slope of the line, and b is the y-intercept.
-7x = 6 + 3y
-6 -6
-7x - 6 = 3y
[tex]\frac{-7x}{3}-\frac{6}{3} =\frac{3y}{3}[/tex]
[tex]\frac{-7}{3}x-2 =y[/tex]
Therefore the slope is [tex]-\frac{7}{3}[/tex].
Descrive in words the rule that is used to determine the term value from its position in the sequence
The rule used to determine the term value from its position in the sequence is often referred to as the "nth term" rule.
What is the nth-term rule?The nth-term rule involves identifying a pattern or relationship between the position (n) of a term in the sequence and the value of that term.
By analyzing the pattern, such as the common difference or common ratio, the nth-term rule allows us to express the value of any term in the sequence based on its position.
This rule provides a formula or equation that relates the position of a term to its corresponding value in the sequence.
Mathematically, the rule is:
T(n) = a + (n - 1) * d
where:
T(n) represents the value of the term at position n.a represents the first term in the sequence.n represents the position or index of the term in the sequence.d represents the common difference (for arithmetic sequences) or the common ratio (for geometric sequences) between consecutive terms.More on sequence and series can be found here: https://brainly.com/question/15583579
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A sample of 318 students at a university is surveyed. The students are classified according to gender ("female" or "male"). They are also classified according major ("biology", "business", "engineering", "mathematics", or "computer science"). The results are given in the contingency table below. Biology Business Engineering Female Male 47 37 20 36 What is the relative frequency of biology majors in the sample? Round your answer to two decimal places. 43 15 Mathematics 29 35 Computer science 20 36
edmentum question:
-post test: similarity and proof
in the diagram,
the ratios __ and ___ are equal
We can deduce here that in the diagram the ratios AD : DB and AE : EC are equal.
What are similar triangles?Triangles that resemble one another but may differ in size are said to be similar triangles. They have equal corresponding angles and proportional corresponding sides, in other words.
Two triangles are similar if and only if the following conditions are met:
Angle-Angle (AA) SimilaritySide-Angle-Side (SAS) SimilaritySide-Side-Side (SSS) SimilarityThe corresponding sides of two triangles that are comparable are proportionate. The length of the comparable side in the other triangle can be obtained by multiplying the length of a side in one triangle by the same factor.
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Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Volume = $\ 10,000\pi\ $ in.3
A cylindrical piece of a log is shown. The diameter of its base is 32 inches and height is h.
$h\ \approx$
in.
The nearest Whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
The missing dimension of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Given that the volume is 10,000π in³ and the diameter of the base is 32 inches, we can determine the radius (r) of the cylinder.
The diameter is twice the radius, so the radius is half of the diameter:
r = 32 inches / 2 = 16 inches
Substituting the known values into the volume formula, we have:
10,000π in³ = π * (16 in)^2 * h
Cancelling out the common factor of π, we get:
10,000 = 16^2 * h
Simplifying further:
10,000 = 256 * h
To isolate h, we divide both sides of the equation by 256:
h = 10,000 / 256
Calculating the value of h:
h ≈ 39.06
Rounded to the nearest whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
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Use a table of values to graph the following exponential function. (see attachment)
y= 2^x
Please graph
By using the table of values, a graph of the exponential function is shown in the image below.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.Based on the information provided above, we can logically deduce the following exponential function;
[tex]y = 2^x[/tex]
Next, we would create a table of values based on the exponential function;
when x = 0, the y-value is given by;
y = 2⁰
y = 1
when x = 1, the y-value is given by;
y = 2¹
y = 2
x y____
-2 0.25
-1 0.5
0 1
1 2
2 4
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What is the value of x? Round to the nearest thousandth.
Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:
tan (∅) = opposite/adjacent
We have the following:
Reference angle (∅) = 53 degrees
Length of opposite side = 21
Length of adjacent side = x
Plug in the values:
tan 53 = 21/x
x * tan 53 = 21
x = 21 / tan 53
x = 15.824
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What is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
The area of the rhombus is 100 mm². The Option D.
What is the area of the rhombus?To get area of a rhombus, we will use the formula: Area = (d₁ * d₂) / 2 where d₁ and d₂ are the lengths of the diagonals.
Given that the horizontal diagonal length is 25 millimeters (d₁ = 25 mm) and the vertical diagonal length is 8 millimeters (d₂ = 8 mm.
We will substitute values into the formula:
Area = (25 mm * 8 mm) / 2
Area = 200 mm² / 2
Area = 100 mm².
Full question:
A rhombus with horizontal diagonal length 25 millimeters and vertical diagonal length 8 millimeters. what is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
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Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
6543/2
-24
1-3-
J
ہے
Answer:
(a) x-intercept = -2
(b) y-intercept = 4
Saleema
was investigating the newspaper subscriptions
for her local newspaper. At the beginning of the year,
She noted 1000 subscriptions for
Subscribed to the newspaper. The number of subscriptions
left y years,
a small area that
left
Y years after 2012 is represented by the function
shown.
N (y) = 1000 (0.5)Y
Part A
Approximately how many subscriptions were left when
y=5?
Based on the information, it should be noted that 31.25 subscriptions were left when y=5.
How to calculate the valueFrom the information, Saleema was investigating the newspaper subscriptions for her local newspaper. At the beginning of the year, She noted 1000 subscriptions for Subscribed to the newspaper
To find the approximate number of subscriptions left when y=5, we can substitute y=5 into the function N(y) = 1000 * (0.5)^y and evaluate it.
N(5) = 1000 * (0.5)^5
N(5) = 1000 * (0.5)^(5)
N(5) = 1000 * (0.03125)
N(5) ≈ 31.25
Approximately 31.25 subscriptions were left when y=5.
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Write a quadratic equation whose roots are 5 + i radical 2 and 5 – i radical 2
____ x^2 + _____ x+ ______=0
The quadratic equation with roots 5 + i√2 and 5 - i√2 is:
x^2 - 10x + 27 = 0
To write a quadratic equation with roots 5 + i√2 and 5 - i√2, we can use the fact that complex roots occur in conjugate pairs. Therefore, the equation will have the form:
(x - root1)(x - root2) = 0
Substituting the given roots:
(x - (5 + i√2))(x - (5 - i√2)) = 0
Now, we expand the equation:
(x - 5 - i√2)(x - 5 + i√2) = 0
Using the difference of squares formula:
((x - 5)^2 - (i√2)^2) = 0
Simplifying the equation:
(x - 5)^2 + 2 = 0
Expanding the square:
x^2 - 10x + 25 + 2 = 0
Combining like terms:
x^2 - 10x + 27 = 0
Therefore, the quadratic equation with roots 5 + i√2 and 5 - i√2 is:
x^2 - 10x + 27 = 0
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If s(x) = 2x² and f(x) = 3x, which value is equivalent to (s-f)(-7)?
O-439
O-141
O 153
O 443
The value of expression (s - f) (- 7) would be,
⇒ (s - f) (- 7) = 119
We have to given that,
Functions are defined as,
⇒ s (x) = 2x²
⇒ f (x) = 3x
Now, We can find the value of (s - f) (- 7) is,
⇒ (s - f) (- 7)
⇒ s (- 7) - f (- 7)
⇒ 2 (- 7)² - (3 × - 7)
⇒ 2×49 + 21
⇒ 98 + 21
⇒ 119
Therefore, The value of expression (s - f) (- 7) would be,
⇒ (s - f) (- 7) = 119
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April can buy a package of 10 folders for $1.20 or a package of 8 folders for $1.12. What is the unit price, per folder, in each package?
Each folder in the package of 10 costs $
Each folder in the package of 8 costs $
Answer:
Step-by-step explanation:
For the package of 10 folders: Unit price = $1.20 / 10 = $0.12 For the package of 8 folders: Unit price = $1.12 / 8 = $0.14