The absolute value expressions of the echo sounder are |r - w| and |w - r|
How to determine the absolute value expressions of the echo sounder?The statement in the question is represented as
The accuracy of an echo sounder is the positive difference between ...
To solve further, we use the following representations
Depth of water reading = r
Actual depth = w
So, the statement becomes
The accuracy of an echo sounder is the positive difference between r and w
The difference can be represented as
Difference = r - w or Difference = w - r
Represented as absolute value expressions
Difference = |r - w| or Difference = |w - r|
Hence, the expressions are |r - w| and |w - r|
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Select the correct answer.
Consider this function.
f(x) = 2x -2
Which graph represents the inverse of function f?
A. The first graph (Y)
B. The second graph (W)
C.The third graph (X)
D. The last graph (Z)
Answer:
option
Step-by-step explanation:
THE THIRD GRAPH(X)
Use the graph to estimate the number of school newspapers distributed in the third month 700250400500
Given the graph, you can identify that x-axis represents the number of the corresponding month, and the y-axis represents the Number of Newspapers distributed (in hundreds).
You know these points:
[tex]\begin{gathered} (2,2) \\ (4,3) \end{gathered}[/tex]Notice that 200 school newspapers were distributed in the second month, and 300 school newspapers were distributed in the fourth month. Therefore, you can conclude that the number of school newspapers that were distributed in the second month must be between 200 and 300. You can set up that, for:
[tex]x=2[/tex]The y-value is:
[tex]y\approx2.5[/tex]Hence, the answer is: Second option.
[tex]\sqrt{x} x^2+2x-3[/tex]
The result of the expression given is 3x - 3
Simplification of Linear EquationTo solve this problem, we have to simplify the equation, and write the expression.
Given that
[tex]\sqrt{x^2}+ 2x -3[/tex]
In the square root, we can eliminate the square and square root using the square root rule.
Lets apply that in this expression
[tex]\sqrt{x^2} + 2x - 3\\x + 2x - 3[/tex]
Lets solve the expression
[tex]x + 2x - 3\\3x - 3[/tex]
The value of the expression given is 3x - 3
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What do you call each part of an expression that is separated by a + or a -?
Write the equation of the line in the slope-intercept form which is parallel to
y = −2x +5 and passing through the point (1, −4)
The equation of the line that is parallel to the line y = −2x +5 and passing through the point (1, −4) is y = -2x - 2.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
The slope of two parallel lines is always the same.
The slope y-intercept form of an equation is y = mx + c where m is the slope.
Given the parallel equation y = -2x + 5 by compare slope = -2
Therefore,the equation will become y = -2x + c
Substitute,(1,-4) into this
-4 = -2(1) + c ⇒ c = -2
So equation converts as y = -2x - 2.
Hence "The equation of the line that is parallel to the line y = −2x +5 and passing through the point (1, −4) is y = -2x - 2".
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Rewrite without parentheses.
(4x²z² − 6x³)(-8xz¹)
-
Simplify your answer as much as possible
Answer:
Step-by-step explanation:-32x³z³+48x∧4z
SOS I NEED HELP ASAP I MEED IT NOW
Answer: do c to my very ecucated guess bc c is always right
Step-by-step explanation:
Step-by-step explanation:
Judy is 12 years old and is 8 years old mukta is 16 years old which of the following ratios best expresses the relationship between the ages 4 ratio 3 ratio to 2 ratio 3 ratio 4:3 ratio 2 ratio 4:3 ratio 4 ratio 2 ratio 4 ratio 3
Age of Judy = 12 yrs old
Age of x = 8 yrs old
Age of Mukta= 16 yrs old
Ratio between the 3 ages = 12 : 8 : 16
Since all the three numbers are divisible by 4
Therefore the ratio comes out to be 3 : 2 : 4 or 3 ratio 2 ratio 4
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Answer:
= 12 : 8 : 16
all the three numbers are divisible by 4
the ratio is 3 : 2 : 4
2/3 is what percent of 1/4? of 1/6
Let's first calculate the percentage for 1/4
[tex]\begin{gathered} P=\frac{2/3}{1/4} \\ P=\frac{8}{3} \\ P=2.666 \\ P=267\text{ \%} \end{gathered}[/tex]Let's first calculate the percentage for 1/6
[tex]\begin{gathered} P=\frac{2/3}{1/6} \\ P=\frac{12}{3} \\ P=4 \\ P=400\text{ \%} \end{gathered}[/tex]1. Priya's favorite kind of dark chocolate comes in a package shaped like a triangular. If the package can hold 144 cm of chocolate and the triangular faces have a base of 3 cm and a height of 4 cm, how tall is the entire package?
ok
Measures base = 3cm
height = 4cm
tall = x
volume = 144 cm^3
Volume = Area of the base * tall
Area of the base = (3 * 4) / 2 = 12/2 = 6 cm^2
144 = 6*x
x = 144/6
x = 24 cm
Result: The chocolate is 24 cm tall.
The table represents a continuous exponential function f(x). x 2 3 4 5 f(x) 9 3 1 one-third Graph f(x) and identify the y-intercept. 9 15 36 81
The exponential equation that represents the table is given as y = 81(3)^x.
What are exponential equations?Exponent-based equations in which the exponent or a portion of the exponent is a variable are known as exponential equations.
The standard exponential form is expressed according to the formula;
y= ab^x
Using the coordinate points (2, 9) and (3, 3) from the table, we can create simultaneous equation as shown;
9 = ab^2
3 = ab^3
Divide both equations
3/9 = ab^3/ab^2
1/3 = b^3/b^2
1/3 = b
Substitute b = 1/3 into any of the equations
3 = ab^3
3 = a(1/3)^3
3 = 1/27 a
a = 81
Determine the required equation
y = ab^x
y = 81(3)^x
This gives the required equation of the function.
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Answer: 81
Step-by-step explanation: Took the test & got it right :)
amazon is selling 24 pack of 3x3 sticky notes for 28.99 Each pack has 100 sticky notes. What is the price for each pack? How much is each single sticky note?
Given data:
Total packs 3x3 sticky notes: 24 packs
Cost of 24 packs: 28.99
Number of sticky notes in a pack: 100
With the information above, we can proceed to find the answers to the questions
Part A: What is the price for each pack?
Since 24 packs cost 28.99
Then 1 pack will cost =
[tex]\begin{gathered} \frac{28.99}{24}=1.208 \\ \text{which is appro}\xi mately\text{ 1.21} \end{gathered}[/tex]Hence, a pack will cost $1.21
Part B: How much is every single sticky note?
Since each pack cost 1.21, and each pack has 100 sticky notes, then
each sticky note will cost
[tex]\frac{1.21}{100}=0.0121[/tex]=> every single sticky note will cost $0.012
Alexis can run 5/2 miles in 1/4hrs. What is her speed in miles per hour?
Solution
We are given
Distance = 5/2 miles
Time = 1/4 hours
Answer:
The speed would [tex]10~\text{mph}[/tex].
Step-by-step explanation:
Step 1: State the formulas required
The formula for speed is:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
Step 2: Substitute the values into the formula
The distance is [tex]\frac{5}{2}~\text{miles}[/tex] and the time is [tex]\frac{1}{4}~\text{hours}[/tex].
Substitute these values into the formula:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\[/tex]
Step 3: Calculate
[tex]\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\div {\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\times 4\\\\\text{Speed}={\frac{20}{2}}\\\\\text{Speed}=10[/tex]
So, the speed is [tex]10~\text{miles per hour}[/tex] or [tex]10~\text{mph}[/tex].
Greg purchased furniture for his home. He purchased a chair for $320 and a lamp for $55. The store charges 7% sales tax. How much did Greg pay in tax?
Given:
Price of chair = $320
Price of lamp = $55
Total cost of furniture Greg purchased is = $320 + $55 = $375
Since the store charges a 7% sales tax, it means the amount Greg paid in tax is
7% of Total cost of furniture purchased.
Thus, the amount Greg paid in tax is:
[tex]\frac{7}{100}\times375=\text{ 0.07}\times375=26.25[/tex]The amount Greg paid in tax
1/3x - 7 = -8 what is x
Answer:
x = -3
Step-by-step explanation:
Add 7 to -8 = -1
1/3x = -1
Divide -1 by 1/3
x = -3
Answer:
x=-3
Step-by-step explanation:
Rewrite as x/3 -7 = -8Multiply the entire equation by 3 which results in : x -21 = -24Isolate the variable: x = -24 + 21Solve for x: x=-3All of the triangles are dilations of Triangle D. The dilations use the same center P, but different scale factors. 1) What do Triangles A, B, and C have in common? 2) What do Triangles E, F, and G have in common? 3) What does this tell us about the different scale factors used?
Triangles A, B, and C have a scale factor less than 1 in common
Triangles E, F, and G have a scale factor greater than 1 in commonDifferent scale factors would give different sizes after dilationWhat Triangles A, B, and C have in commonThe figure that completes the question is added as an attachment
From the figure, we can see that triangles A, B, and C are smaller than the original triangle i.e. the triangle D
This means that triangle D is dilated by a scale factor less than 1 to form each of these triangles
What Triangles E, F, and G have in commonThis has just a slight difference to (a)
From the figure, we can see that triangles E, F, and G are bigger than the original triangle i.e. the triangle D
This means that triangle D is dilated by a scale factor greater than 1 to form each of these triangles
What this tell us about the scale factorsThe conclusion about the scale factors is that
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Angle JKL and angle MKQ are complementary angles. The measures of angle JKL is twice the measure of angle MKQ.• Write one equation to find x, the measure of angle MKQ• Solve for X
Answer : x = 30 degrees
< JKL and < MKQ are complementary
Let < MKQ = x
Angle JKL is twice the measure of angle MKQ
JKL = 2 x MKQ
Sum of a complementary angles = 90 degrees
< JKL + < MKQ = 90
< JKL = 2MKQ
Substitute the value of < jkl
2(<2MKQ + Since, Therefore,
2x + x = 90
3x = 90
Divide both sides by 3
3x / 3 = 90/3
x = 30 degrees
Went to start the sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4 is Gwen correct explain why or why not
The sum of -1 (3/4) and 2 (1/2) is the same as the difference between 2 (1/2) and 1 (3/4).
Firstly, we will convert the mixed fractions into improper fractions.
-1 and 3/4 = -7/4
2 and 1/2 = 5/2
Addition of -1 (3/4) and 2 (1/2) = -7/4 + 5/2 = -7/4 + 10/4 = 3/4
Difference between 2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4
As both the values equal to 3/4 , we can say that the addition of -1 and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.
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The distance between the points (-2,y) and (3, -7) is 13 units.What are the possible values of y?
To calculate hte possible values of y you have to apply the Pythagoras theorem:
[tex]a^2+b^2=c^2[/tex]Where
c will be the distance between the given points, and the hypothenuse of a right triangle
a will be the base of a theoretical triangle below the hypothenuse, you calculate it as (x2-x1)
b= will be the heigth of said triangle, you calculate it using the y-coordinates (y2-y1)
So:
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ c=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]Replace the expression with the given measurements to calculate the y-coordinate of the first point:
[tex]\begin{gathered} c=\sqrt[]{(3_{}-(-2))^2+(-7-y)^2} \\ 13=(3+2)+(-7-y) \\ 13=5-7-y \\ 13=-2-y \\ 13+2=-y \\ -15=y \end{gathered}[/tex]The possible values for y, since its
p(x) = x^3 − 3x^2 − 10x + 24 , has a known factor of (x-4).
rewrite p(x) as the product of linear factors
The product of linear factors for p(x) is given as (x-4)(x^2+x-6).
What is the factor theorem?The factor theorem states that;
p(x) is divisible by x-a if and only if p(a)=0p(x) is divisible by x+a if and only if p(-a)=0From the question, given that x-4 is a factor of
p(x) = x^3 − 3x^2 − 10x + 24,
then it is divisible by x-4 and p(4)=0.
Dividing x^3 − 3x^2 − 10x + 24 by x-4 using the long division will result to another factor x^2+x-6 with a remainder of zero.
We can then conclude that (x-4)(x^2+x-6) is the product of linear factors for p(x).
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In the data set below, what are the lower quartile, the median, and the upper quartile? 30 45 49 50 63 75 75 77 84
In the data set {30,45,49,50,63,75,75,77,84} the lower quartile is 47, the median is 63 ,and the upper quartile is 76 .
In the question ,
the data set is given as {30,45,49,50,63,75,75,77,84}
as the data set has 9 terms , the median will be the central term that is 5th term .
so the median is 63 .
For finding the lower and upper quartile , we break the set into two half .
lower half = {30,45,49,50}
the lower quartile will be the central value ,that is (45+49)/2 = 47
so, the lower quartile(Q₁) is 47 .
upper half = {75,75,77,84}
the upper quartile will be the central value ,that is (75+77)/2 = 76
so, the upper quartile(Q₃) is 76 .
Therefore , in the data set {30,45,49,50,63,75,75,77,84} the lower quartile is 47, the median is 63 ,and the upper quartile is 76 .
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3w = 7.68 solve for w
Answer: w=2.56
Step-by-step explanation:
7.68/3=2.56
Which of the images above represents a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.
The image above represents a proof of the Pythagorean Theorem is image B.
What is Pythagorean Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship in Euclidean geometry between the three sides of a right triangle.
It states that the sum of the squares of the leg lengths equals the square of the hypotenuse length.
This is illustrated as:
a² = b² + c²
The values in image 2 will be used to ascertain this. Therefore,
5² + 12² = 13²
25 + 144 = 169
169 = 169
Therefore, B is correct as the value is gotten.
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Answer:
u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye
Step-by-step explanation:
two students each use a random number generator to pick an integer between 1 and 8 inclusive. what is the probability that they pick the same number? (enter your answer as a fraction.)
The probability that they pick the same number is 1/8.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
As given two students each use a random number generator to pick an integer between 1 and 8 inclusive.
So, the possible choices are,
8 - 1 + 1 = 8 Possible choices: 1, 2, 3, 4, 5, 6, 7, 8.
So, the probability is, 1/8.
Therefore, the probability that they pick the same number is 1/8.
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a bowling alley charges $14 for the first game $10 for the second game and $5 per game for every game after that which statement is true
The equation for the cost when the bowling alley charges $14 for the first game $10 for the second game is 24 + 5x.
What is a equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario
In this case, the bowling alley charges $14 for the first game $10 for the second game and $5 per game for every game after.
Let the number of games be illustrated as x.
Therefore, the equation will be:
14 + 10 + (5 × x)
= 24 + 5x
This illustrates the cost.
An overview was given as the information given is incomplete.
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PLEASE HELP!!!! Solve using the quadratic formula
Answer:
Step-by-step explanation:
Given Equation
3x^2 + x = - 2x - 7
Solution
Add 2x + 7 to both sides
3x^2 +x + 2x + 7 = -2x - 7 + 2x + 7 Combine like terms
3x^2 + 3x + 7 = 0
Givens
a = 3b = 3 c = 7x = (-b +/(√b^2 - 4ac))/2
x = (-3 +/- (√3^2 - 4(3 *7)) / 2*3
x = (- 3 +/- (9 - 84)) / 2 *3
x = (- 3 +/- √ (-75))/6
x = (- 3 +/- 8.660i ) / 6
x = -.5 +/-1.443i
Answer
x = -.5 + 1.443.i
x = -.5 - 1.443i
Line a is represented by the equation y=−7x+1.
How do these equations compare to line a?
Drag and drop the equations into the boxes to correctly complete the table.
Parallel to line a Perpendicular to line a Neither parallel nor perpendicular to line a
y = 7x - 5 y- = 7x + 3 y = 1/4x + 4
Answer:
Step-by-step explanation:
The volume of a gas in a container varies inversely with the pressure on the gas. If a gas has a volumeof 230 cubic inches under a pressure of 8 pounds per square inch, what will be its volume if thepressure is increased to 18 pounds per square inch? (Round off your answer to the nearest cubic inch.)
Answer:
Explanation:
The volume of a gas in a container varies inversely with the pressure on the gas
Let V represent volume
Let P represent Pressure
Rewrting the statement above Mathematically:
[tex]\begin{gathered} V\text{ }\alpha\text{ }\frac{1}{P} \\ V\text{ = k}\frac{1}{P} \end{gathered}[/tex]when V = 230 in³
P = 8 lb/in³
Substitute the value of P and V in the equation in order to ger k:
Does anyone know how to write a linear equation to find the length and width of a perimeter? Ex...
Write a linear equation to represent the given problem and then solve the problem.
The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensions.
The linear equation that represents the problem is 4w + 30 = 150.
The dimension(width and length) of the rectangle is 30 cm and 45 cm .
How to find the dimensions of a rectangle?A rectangle is a quadrilateral with 4 sides.
Opposite sides of a rectangle are equal to each other.
Opposite sides of a rectangle are parallel to each other.
Therefore,
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthHence, the perimeter of the rectangle is 150 cm. The length is 15cm greater than the width.
Therefore,
perimeter of rectangle = 150 cm
l = 15 + w
Hence,
150 = 2(15 + w + w)
150 = 2(15 + 2w)
150 = 30 + 4w
Therefore, the linear equation to represent the problem is 4w + 30 = 150.
Let's solve for the dimension of the rectangle.
4w + 30 = 150.
4w = 150 - 30
4w = 120
w = 120 / 4
w = 30 cm
L = 15 + 30 = 45 cm
Therefore,
length = 45 cm
width = 30 cm
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question : below pictureis attached
Answer:
the value of 2/3 ^-2 is 18