By applying the definite integral concept, it can be concluded that ∫₀¹²⁰ r(t) dt represents the number of gallons of oil that leaked from the tank in the first two hours.
Integral is a form of continuous addition that is the inverse of the derivative (anti-derivative)
Definite integral is an integral form in which the integration variables have limits (upper and lower limits) written at the top and bottom of the integral notation.
If y = f(x) is continuous on the interval a ≤ x ≤ b, where a is the lower limit and b is the upper limit, then:
∫ₐᵇ f(x) dx = F(x) |ₐᵇ
= F(b) - F(a) , where
F(x) = anti-derivative of f(x) on the interval a ≤ x ≤ b
In everyday life, integrals can be used to calculate the volume of a container when the flow rate is known.
r(t) = V'(t) , where:
r(t) = flow rate
V'(t) = anti-derivative of volume
We have a function ∫₀¹²⁰ r(t) dt where r(t) is the oil leaks rate.
As we know that r(t) = V'(t), we can substitute this into the function:
∫₀¹²⁰ r(t) dt = ∫₀¹²⁰ V'(t) dt
= V(120) - V(0)
Now we understand that this function represents the change of volume from t = 0 to t = 120 minutes (2 hours).
Or in the other words, this function represents the number of gallons of oil that leaked from the tank in the first two hours.
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A 16m long ladder reaches a window that is 12 m high in building a on one side of the street. If the ladder is placed on the other side of the street‚ with the base of the ladder being held in the same position, it will reach a window 14 m high in building b. How wide is the street from building a to building b?
The wide of the street from building a to building b is 18.32m
The Pythagoras theorem states that if a triangle is right-angled then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The three sides of a triangle are collectively called Pythagoras triples.
The formula is measured as:
c²= a²+ b²
Where
'c' = hypotenuse of the right triangle
'a' and 'b' are the other two legs.
First, let's consider △ADC,
AD²+AC²=CD²
12²+AC²=16²
AC²=256−144
AC=10.58 m
Again consider △BEC,
EC²=BC²+BE²
16²=14²+BC²
256−196=BC²
BC=7.745m
Width of the road= AC+BC = 10.58+7.74=18.32m
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given y′=16x with y(e)=53. find y(e2).
y(e2) = 4e^2 + (53 - 4e^2)e^(-16e^2), found by integrating the ODE y′ = 16x and using the initial condition y(e) = 53.
What is differential equation ?
A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable.
mu(x) = e^(int 16 dx) = e^(16x^2/2)
multiply both sides of the differential equation by the integrating factor to obtain:
mu(x) * y′ = 16x * mu(x)
Integrating both sides with respect to x, we get:
mu(x) * y = 8x^2 + C
Dividing both sides by the integrating factor, we get:
y = 4x^2 + Ce^(-16x^2/2)
Using the initial condition y(e) = 53, we can find the value of the constant C:
53 = 4e^2 + Ce^(-16e^2/2)
Solving for C, we get:
C = 53 - 4e^2
So the general solution for the differential equation is:
y = 4x^2 + (53 - 4e^2)e^(-16x^2/2)
Finally, to find y(e2), we plug in x = e2 into the general solution:
y(e2) = 4e^2 + (53 - 4e^2)e^(-16e^2)
And that gives us the value of y at x = e2.
y(e2) = 4e^2 + (53 - 4e^2)e^(-16e^2), found by integrating the ODE y′ = 16x and using the initial condition y(e) = 53.
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The wandering albatross can fly at speeds of up to 32 m/s (the speed limit on motorways!). One
albatross was found to have flown 16 250 km in 10 days.
Calculate its average speed in metres per second.
Answer:
Average speed = Total distance ÷ Total time
Average speed = 16250 km ÷ 10 days = 1625 km/day
1 km = 1000 m
1625 km = 1625 × 1000 m = 1,625,000 m
1 day = 24 hours = 24 × 60 minutes = 1440 minutes
10 days = 10 × 1440 minutes = 14400 minutes
Average speed = 1,625,000 m ÷ 14400 minutes = 113.19 m/min
1 minute = 60 seconds
Average speed = 113.19 m/min ÷ 60 seconds/min = 1.8865 m/s.
Step-by-step explanation:
Prompt #1: Given the following right triangle, solve for the missing side using trigonometric ratios
to the nearest hundredth. Then solve for the missing angle, H, to the nearest tenth.
G
?
H
15
53. 12
we used the Pythagorean Theorem to solve for the missing side, G, of the right triangle, which is 17.76. Then, using the SOHCAHTOA trigonometric ratio, we solved for the missing angle, H, which is 89.4 degrees.
Using the Pythagorean Theorem, we can solve for the missing side, G. The equation is a^2 + b^2 = c^2. In this case, the two known sides are 12 and 15, so we have 12^2 + 15^2 = G^2. We can solve this equation to get G = 17.76.
To solve for the missing angle, H, we can use the trigonometric ratio SOHCAHTOA. The ratio for finding the angle of a right triangle is opposite over hypotenuse, or H/G. We can use this ratio to solve for H: H = 15 * (53/17.76) = 89.37 degrees. Rounding to the nearest tenth, H = 89.4 degrees.
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The area of the circular base of a cone is 167 cm², and the slant height of the cone is 4 times the radius of the cone.
What is the approximate lateral area of the cone?
Use ≈ 3.14
Enter your answer rounded to the nearest whole number in the box.
cm²
thickness measurements of a coating process are made to the nearest hundredth of a millimeter. the thickness measurements are uniformly distributed with values 0.12, 0.13, 0.14, 0.15, 0.16. determine the mean and variance of the coating thickness for this process. round your answers to four decimal places (e.g. 98.7654). (a) mean (in millimeters) (b) variance (in millimeters2)
The mean of the given data be 0.17.
What is the difference between mean and variance?Variance is a measure of dispersion that considers the spread of all data points in a data collection, in contrast to range and interquartile range. The standard deviation, which is just the square root of the variance, is the other often used measure of dispersion.
A measure of variability is the variance. It is determined by averaging the squared deviations from the mean. Your data set's variability is shown by its variance. The variance is greater in respect to the mean when the data are more dispersed.
Since the data are stated in the question to be evenly distributed, the mean will be determined using the formula.
Mean = a + b /2
Where, a be the minimum value and b be the maximum value
for the data: 0.15,0.16,0.17,0.18, and 0.19
The value of a = 0.15 and b = 0.19
Substitute the values in the above equation, we get
Mean = (0.15 + 0.19) /2
simplifying the above equation, we get
Mean = 0.34/2
Mean = 0.17
Therefore, the mean of the given data be 0.17.
The complete question is:
Thickness measurements of a coating process are made to the nearest hundredth of a millimeter. The thickness measurements are uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19. Determine the mean and variance of the coating thickness for this process.
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Simplify. Assume all variables are positive.
Answer: The answer will be 7b^3
Answer:
the answer is 7 root 3
Step-by-step explanation:
I’ll give u $20 if u help me with these two
(Ignore my writing)
Check the picture below.
notice, it says that PT is perpendicular to SQ.
now onto the other one
well, a parallelogram with one right-angle and at least one pair of congruent sides, hell a rectangle is that, so is an square, so no dice.
a rhombus that has congruent diagonals, well, a square is that but so is a rectangle, no dice.
a parallelogram whose diagonals bisect each other, well, a square has that, sure, a rhombus too and a rectangle too, no dice.
a rectangle with perpendicular diagonals, well, a rhombus has perpendicular diagonals, however is not a rectangle, a square is a rectangle also with perpendicular diagonals too.
julio has 3 yards of wood he needs 2/5 of a yard to make a skateboard how many skateboards can he make SOLVE PLEASE AND EXPLAIN
The maximum number of skateboards Julio can make is 7.
What is division?A division is a process of splitting a specific amount into equal parts.
Given that, Julio has 3 yards of wood he needs 2/5 of a yard to make a skateboard, we need to find how many skateboards can be made,
So, to find the number of skateboards we will divide total length of wood to the length of on skateboard,
Therefore,
The number of skateboards = 3 / 2÷5
= 3×5/2
= 15/2
= 7.5
Hence, the maximum number of skateboards Julio can make is 7.
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you have been working on an item for a while and after a few missteps you've come up with an answer. however, there is one particular thing that you're not 100 %% sure of. what should you do? select all that apply.
We solved a problem after several missteps. One thing we are not certain of. We should:
"Check for any hints that address the part of the calculation you're unsure about." (A)"Return to the question after you've spoken with an instructor or classmate." (B)"Submit your answer and then adjust it according to any feedback you receive." (C)When we are unsure about a part of a calculation, it is a good idea to check for hints that address that part of the calculation. This can help us confirm or correct your understanding of the problem. In addition, speaking with an instructor or classmate can provide valuable insight and help clarify any confusion.
Finally, if we still feel unsure, submitting our answer and then adjusting it based on feedback can help us improve our understanding and knowledge of the material. All of these options can help ensure that we have the most accurate and complete understanding of the problem.
This question should be provided with answer choices, which are:
A. Check for any hints that address the part of the calculation you're unsure about.B. Return to the question after you've spoken with an instructor or classmate.C. Submit your answer and then adjust it according to any feedback you receive.D. None of the above.Learn more about problem solving process here: brainly.com/question/10708306
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A sailor is up a mast so that her eyes are 10 meters above water. A lighthouse is 40 meters tall. From how far away will the sailor first see the lighthouse?
The sailor is 10 meters above the water and the lighthouse is 40 meters tall, so the total height between the two is 50 meters. Therefore, the sailor will first see the lighthouse from 50 meters away.
Assuming the lighthouse is directly in front of the sailor, the light from the lighthouse will reach the sailor first when the total distance between them is 50 meters. This means the sailor will first see the lighthouse from 50 meters away. In addition, the angle between the sailor and the lighthouse will be equal to the angle of the light when it reaches the sailor's eyes. The angle of the light will depend on the curvature of the earth, the height of the lighthouse, and the height of the sailor.
Assuming the lighthouse is at sea level, the angle of the light when it reaches the sailor's eyes can be calculated using the following equation:
Angle
= arcsin (50 / (2 * 6371))
Where 6371 is the radius of the earth in km.
This calculation gives an angle of 0.0058°. This means the light from the lighthouse will reach the sailor from a distance of 50 meters with an angle of 0.0058°.
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Use the given scale factor and the side lengths of the scale drawing to
determine the side lengths of the real object.
Scale factor: 5:1
35 in
30 in
N
15 in
. side is inches long, side is inches
long,and side is inches long
Here is the complete question. Please find
attached a diagram showing the scaled and real
drawing
Use the given and the of
the scale drawing to determine the side lengths
of the real object
. side a is 7 inches long, side b is 6 inches
long,and side c is 3 inches long
. side a is 30 inches long, side b is 25 inches
long, and side c is 20 inches long
. side a is 40 inches long, side b is 35 inches
long,and side c is 20 inches long
. side a is 175 inches long,side b is 150 inches
long, and side c is inches long
A scale drawing is a reduced form in terms of
of an original image / building / object
the scale drawing is usually reduced at a constant
dimension
= original dimensions /
dimensions of the scale drawing
The scaled drawing is an enlarged image of the
original triangle.
It is enlarged at a ratio of :
original dimensions
a = 35/5 =
b = 30/5=
c = 15/5 =
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The side lengths of the real object will be 175 in, 150 in, and 75 in, respectively.
To determine the side lengths of the real object, we need to use the given scale factor and the side lengths of the scale drawing. The scale factor given is 5:1, which tells us that the scale drawing is 5 times smaller than the real object. Therefore, we can use this ratio to determine the side lengths of the real object. For example, if the side length of the scale drawing is 35 in, then the side length of the real object will be 5 times larger, which is 175 in. We can use this same ratio for the other side lengths of the scale drawing. The side length of the scale drawing is 30 in, so the side length of the real object will be 150 in. The side length of the scale drawing is 15 in, so the side length of the real object will be 75 in. Therefore, the side lengths of the real object will be 175 in, 150 in, and 75 in, respectively.
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In 2016 there were 34661 burger restaurants worldwide with 12194 them located in a country determine the percent of burger restaurants in that country in 2016
The percent of burger restaurants in that country in 2016 was:
35.1%
To calculate the percentage of burger restaurants in a specific country in 2016, we can divide the number of burger restaurants in that country by the total number of burger restaurants worldwide, then multiply the result by 100.
Percentage of burger restaurants in a specific country
= (Number of burger restaurants in that country / Total number of burger restaurants worldwide) * 100Percentage of burger restaurants in the specific country
= (12194 / 34661) * 100 = 35.1%So, in 2016 there were approximately 35.1% of all burger restaurants in the world located in that country.
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sketch the region enclosed by the given curves. y = |9x|, y = x2 − 10
Using points of intersection, The resulting sketch should look like a parabolic arch opening upwards with its vertex at (-3, 9) and endpoints at (5, 45) and (-3, 9), with the region below the x axis for x < -3 and above the x axis for x > 5.
What are the intersection points?The locations on the coordinate plane where two curves meet or intersect are known as the points of intersection.
By locating the places where the two curves overlap and then sketching the area in between, the area bounded by the curves y = |9x| and y = x2 - 10 may be determined.
First, let's find the points of intersection:
y = |9x| = x² - 10
If 9x >= 0, then |9x| = 9x, and we have:
9x = x² - 10
x² - 9x - 10 = 0
This is a quadratic equation and can be solved using the quadratic formula:
x = (9 ± √(81 + 40)) / 2 = (9 ± √(121)) / 2 = (9 ± 11) / 2 = 5 or -3
If 9x < 0, then |9x| = -9x, and we have:
-9x = x² - 10
x² + 9x - 10 = 0
This is a quadratic equation as well and can be solved using the quadratic formula:
x = (-9 ± √(81 - 40)) / 2 = (-9 ± √(41)) / 2 = (-9 ± 6.4) / 2 = -3 or -1.2
So the two curves intersect at the points (5, 45) and (-3, 9).
Next, we can sketch the region enclosed by the curves:
For x < -3, y = |9x| is below y = x² - 10, so the region is below the x axis.
For -3 <= x <= 5, y = x² - 10 is above y = |9x|, so the region is above the x axis.
For x > 5, y = |9x| is above y = x² - 10, so the region is above the x axis.
The resulting sketch should look like a parabolic arch opening upwards with its vertex at (-3, 9) and endpoints at (5, 45) and (-3, 9), with the region below the x axis for x < -3 and above the x axis for x > 5.
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what is the identetive property of vx0=0
The identity property of multiplication is that the result of the multiplication of any number and one results in the number one.
What are the properties of multiplication?The multiplication operation have multiple properties, which are presented as follows:
Commutative property: the order of two factors do not change the result.Associative property: with more than two terms, the order in which the terms are multiplied does not change the product.Neutral property: a number multiplied by zero will always result in a product of zero.Identity property: the result of the multiplication of any number and one results in the number one.More can be learned about the identity property of multiplication at https://brainly.com/question/2364391
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Write a short explanation to another students who is not in the class about
how to identify what values of x make V(x) = 0.
Students will learn how to construct simple equations corresponding to practical situations and thus finding the solution of the equations .
How to identify what values of x make V(x) = 0.In the time-independent Schrödinger equation it is stated that
[tex]-h/2m.d²ψ(x)/dx²+V(x)ψ(x)=Eψ(x)[/tex]
And it is common to give V(x)
some standard "forms": the infinite well, the finite square well, etc.
The problem is that I'm finding it pretty difficult to get what V(x)
actually is. I've read in books that it is the potential energy, but...
As far as I know, the potential energy depends on the properties of the particle itself (its mass, its charge), but, for instance, the finite square well is defined as
[tex]V(x)={−V0 if -a < x < a[/tex]
[tex]{0 if|x| > a[/tex]
where V0 is a positive constant. In this case,V0 seems to be fixed, but wouldn't it depend on the properties of the particle.
A concrete and intuitive example of this would be appreciated.
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how to find x and y intercepts
The x-intercept and y-intercept can find by using graphically and solving the equation.
What is the x-intercept?
A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.
If we have an equation, then there are two ways to find x-intercepts and y-intercepts.
1) Graphically
2) Solving the equation
Graphically:
If we have a graph of an equation, then find the points where the graph cuts the x-axis. The points are known as x-intercepts. The graph that cuts the y-axis is the y-intercepts.
Solving the equation:
Putting x = 0 in the equation to find the value y-intercept.
Put y = 0 in the equation to find the value x-intercept.
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Select the correct answer from each drop-down menu.
7/5
The area of the shaded square is 125 squared inches. The length of the unshaded rectangle is 75 inches.
The estimated value of the length of the shaded square is Inches. The estimated value of the area of the unshaded rectangle is
square Inches
The estimated area of the unshaded rectangle is 5625 square inches.
The formula for calculating the area of a rectangle. Rectangle surface area. A = l × b.
Once the length and breadth of a rectangle are determined, the area is computed.
The area of a rectangle may be calculated by multiplying its length and width.
The estimated value of the length of the shaded square is: 11 inches
The estimated value of the area of the unshaded rectangle is: 5625 square inches.
To find the estimated length of the shaded square,
We can use the square root of the area:
√(125) = 11
To find the estimated area of the unshaded rectangle,
We can multiply the length by the width:
75 * 11 = 825
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Mrs. Adesso wants to take her class on a trip to either the science center or natural history museum. The science center charges $8 per student, plus a flat fee of $5 for a group tour. The natural history museum charges $5 per student, plus a flat fee of $20 for a group tour. For what number of students is the cost of the trip the same at each museum?
The number of students is the cost of the trip the same at each museum is 25
What number of students is the cost?When we write expressions for the total cost of each field visit and set them equal, we find the solution to be the ratio of the difference in fixed cost to the difference in variable cost.
y = 75 +7x . . . . . cost for x students to visit the science center
y = 50 +8x . . . . cost for x students to visit the natural history museum
Subtracting the first equation from the second, we get
0 = -25 +x
25 = x . . . . . add 25; the number of students such that costs are equal
The cost will be the same either place for 25 students.
Here, the fixed cost difference is 75-50=25, and the variable cost difference is 8-7=1. The ratio of these costs is
$25/($1 /student) = 25 students.
This relationship only holds when the higher fixed cost is associated with the lower variable cost. Charges are such that one place caters to larger numbers of students (science center), and one prefers fewer students (natural history museum).
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Using mathematical expressions, for the cost of the trip to be the same at each museum, the number of students must be 5.
What are mathematical expressions?Mathematical expressions combine variables, constants or numbers, and mathematical operators., without the equation or inequality symbols.
Science Center History Museum
Cost per student $8 $5
Fixed cost $5 $20
Let the number of students = x
The total cost at the Science Center = 5 + 8x
The total cost at the History Museum = 20 + 5x
For the cost to be the same at either center:
5 + 8x = 20 + 5x
3x = 15
x = 5
Thus, when the number of students attending either museum is 5, the cost is the same.
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a rectangle has a width of 9 units and a length of 40 units. what is the length of a diagonal?31 units39 units41 units
The length of the diagonal of the rectangle is 41 units.
To find the length of a diagonal of a rectangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
In this case, the rectangle is the right triangle, and the lengths of the two shorter sides are 9 and 40 units. So we can write the equation:
9² + 40² = d²
Expanding both sides:
81 + 1600 = d²
Adding the two sides:
1681 = d²
Taking the square root of both sides:
d = 41 units
So the length of the diagonal of the rectangle is 41 units.
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The length of the diagonal of the rectangle is 41 units.
To find the length of a diagonal of a rectangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
In this case, the rectangle is the right triangle, and the lengths of the two shorter sides are 9 and 40 units. So we can write the equation:
9² + 40² = d²
Expanding both sides:
81 + 1600 = d²
Adding the two sides:
1681 = d²
Taking the square root of both sides:
d = 41 units
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which statements are true about the reflectional symmetry of a regular heptagon? select two options.
There are seven lines of symmetry in a heptagon. In a heptagon, the sides and angles are equal. Each vertex and the center of a regular heptagon are where the line of symmetry crosses.
What is Reflectional Symmetry ?
Any symmetry with regard to a reflection is referred to as reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry. In other words, a figure with reflectional symmetry does not alter when it is reflected. There is a line/axis of symmetry in 2D and a plane of symmetry in 3D. When a form or pattern is mirrored in a line of symmetry or a mirror line, this is known as reflective symmetry. The reflected form will have the same size, distance from the mirror line, and other characteristics as the original shape. When a figure can be split into two equal halves that match, it has line symmetry or reflection symmetry.
If a figure can be reflected over a line and retain its original appearance, it possesses reflection symmetry. If a figure can be altered while maintaining its appearance, it possesses symmetry.
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Complete question
Which statements are true about the reflectional symmetry of a regular heptagon? Check all that apply. It has only 1 line of reflectional symmetry. A line of symmetry will connect 2 vertices. A line of symmetry will connect a vertex and a midpoint of an opposite side. It has 7-fold symmetry. A line of symmetry will connect the midpoints of 2 opposite sides.
Recall that |x - 1| <5 can be written as –5 < x – 1 < 5. Which of the following represents the solutions of t | x - 1 | <5?
The inequality equation is -4 < x < 6
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the modulus function be represented as A
Now , the equation will be
| x - 1 | < 5 be equation (1)
Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.The value of the modulus function is always non-negative.
So , -5 < x - 1 < 5
On simplifying the equation , we get
Adding 1 on both sides of the equation , we get
-5 + 1 < x - 1 + 1 < 5 + 1
-4 < x < 6
Hence , the number line will denote the inequality having x more than -4 and less than 6
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Select the correct answer. Simon used these steps to solve an equation: Step 1: -6(x + 7) = 2(x − 11) Step 2: -6x − 42 = 2x − 22 Step 3: -8x − 42 = -22 Step 4: -8x = 20 Which property did he use to get from step 3 to step 4?
Answer:
Simon used the distributive property to get from step 3 to step 4. This is because in step 3, he multiplied both sides of the equation by -8, which is an example of the distributive property.
Step-by-step explanation:
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Write 4,511,000 in scientific notation.
assume that ⋅=2, ‖‖=4, and ‖‖=5. what is the value of 10⋅(10−4)?
The value of 10⋅(10−4) is equal to 60. This is because 10 multiplied by the difference between 10 and 4 (which is 6) is equal to 60.
10⋅(10−4) is an expression that can be expanded by multiplying 10 by each term inside the parentheses. Since ⋅=2, 10 multiplied by 10 is equal to 10⋅10, which is equal to 100. 10 multiplied by 4 is equal to 10⋅4, which is equal to 40. Therefore, 10 multiplied by the difference between 10 and 4, which is 6, is equal to 10⋅6, which is equal to 60. Therefore, the answer to 10⋅(10−4) is equal to 60.
To solve this expression, it is important to understand the order of operations. First, anything inside of parentheses must be solved first. Then, multiplication must be solved before addition or subtraction. Because there is only one operation inside the parentheses, which is subtraction, it is easy to solve 10⋅(10−4) by multiplying 10 by each of the terms inside the parentheses. Since 10 multiplied by 10 is equal to 100 and 10 multiplied by 4 is equal to 40, 10 multiplied by the difference between 10 and 4 is equal to 10 multiplied by 6, which is equal to 60. Therefore, the answer to 10⋅(10−4) is equal to 60.
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PLSSS HELP IF YOU TULRY KNOW THISSS
Answer:
[tex] \sf \: x = 8[/tex]
Step-by-step explanation:
Given equation,
→ x + 10 = 18
Now the value of x will be,
→ x + 10 = 18
→ x = 18 - 10
→ [ x = 8 ]
Hence, the value of x is 8.
what is the slope of the line tangent to the polar curve r=4θ2 at the point where θ=π4 ?
The slope of the tangent is 2π.
What is slope of a line?The slope of a line, often denoted by the letter "m," is a measure of how steep or inclined the line is. It represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
To find the slope of the line tangent to the polar curve at a specific point, we need to differentiate the polar equation with respect to θ and evaluate it at the given value of θ.
The polar equation given is r = 4θ². To differentiate this equation with respect to θ, we need to express r in terms of θ and then differentiate. Since r = 4θ², we can rewrite it as:
r = 4θ² = 4(θ²)
Now, we can differentiate both sides of the equation with respect to θ:
dr/dθ = d(4θ²)/dθ
Using the power rule for differentiation, the derivative of θ² with respect to θ is 2θ:
dr/dθ = 4(2θ)
Simplifying, we get:
dr/dθ = 8θ
Now, we can evaluate this derivative at the given value θ = π/4:
dr/dθ = 8(π/4) = 2π
Therefore, the slope of the line tangent to the polar curve r = 4θ² at the point where θ = π/4 is 2π.
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the table shows Rudy's score for a card game that he plays with his sister. They keep score each week. What integer represents Rudy's score for the two weeks?
Integer -17 represents Rudy's score for 2 weeks.
What do integers mean?A negative integer with a minus sign, a zero, or a positive natural number are all examples of integers.
The additive inverses of their positive counterparts are the negative numbers.
In mathematical notation, the Z is widely used to represent the set of numbers.
Rudy's scores:
Week 1: 15Week 2: -32Then, add 15 and -32 as follows:
= 15 + (-32)
= 15 - 32
= - 17
Therefore, integer -17 represents Rudy's score for 2 weeks.
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Did more students buy lunch on Thursday or on Wednesday?
Did more students buy lunch on Monday or on Friday?
PLEASE HELP ME ASAP I HAVE 7 MORE MINUTES TO DO THIS!!!
Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing thro ugh the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
A relationship that has a zero slope include the following: A. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2.
How to calculate the slope of a line?In Mathematics, the slope of a linear relationship can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following slope and data points on the line:
Points on x-axis = (-3, -1).Points on y-axis = (2, 2).Substituting the given data points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (2 - 2)/(-1 - (-3))
Slope, m = 0/2
Slope, m = 0.
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Answer:
IT IS C!!! ITS RIGHTTTTTTT