The value of the line integral ∫C F · dr, where F = (x+z)i + zj + yk and C is the line from (2,4,4) to (1,5,2), is 2.
We need to evaluate the line integral ∫C F · dr, where F = (x+z)i + zj + yk and C is the line from (2,4,4) to (1,5,2). We can parameterize the line C as r(t) = (2-t)i + (4+t)j + (4-2t)k, where 0 ≤ t ≤ 1.
Then, the differential of r is dr = -i + j - 2k dt. We can substitute F, r(t), and dr into the formula for the line integral to get ∫C F · dr = ∫0^1 (2-t)+4-2t + (4-2t)(1) dt = ∫0^1 2 dt = 2. Therefore, the value of the line integral is 2.
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kylie uses the number 400 to represent a location 400 miles north of the equator she uses the number- 2000 to represent a location 2000 miles south of the equator which number would represent what number would represent a location on the equator
Answer:
0
Step-by-step explanation:
Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction. Using the direction chart we get the equator is at 0 distance away from the location of kylie.
Given-
Kylie uses the number 400 to represent 400 miles north of the equator.
Kylie uses the number -2000 to show 2000 miles south of the equator.
What is the direction?
Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction.
As Kylie use the number 400 to represent 400 miles north of the equator. Thus if he need to back at 400 towards the south to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.
Similarly Kylie uses the number -2000 to show 2000 miles south of the equator. Thus if he need to come back at 2000 towards the north to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.
Hence both the statement suggest that the equator is at 0 distance away from the location of kylie where he had started earlier.
Alexa created the line of best fit shown for the data points graphed. Is the line a good representation for this data? Explain your reasoning.
The line created by Alexa is not a good representation for this data
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the line divides the points on the line unevenly
A good line of best fit would have equal number of points on either sides
Hence, the line is not a good representation
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Which of the following are the solution to the equation 2x² 5x 3 0?(i) x = 3 (ii) x= –2(iii) x=-1/2 (iv) x=-1/3
The solution of the given equation is (i) x = 3 ,(iii) x=-1/2 .
What is root of quadratic equation?Quadratic equation's roots The roots of a quadratic equation are the values of the variables that satisfy the equation. In other words, if f() = 0, therefore x = is a root of the quadratic equation f(x). The x-coordinates of the points where the curve y = f(x) intersects the x-axis are the real solutions of an equation f(x) = 0.
So we can find the root of 2[tex]x^2[/tex]— 5x —3 = 0 by factorising them.
=> 2x² - 5x - 3 = 0
=> 2x² - 6x + x - 3 = 0
=> 2x(x - 3) + (x - 3) = 0
=> (x-3)(2x+1) = 0
so the value of x = 3 , - 1/2
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Complete question :
For 2[tex]x^2[/tex]— 5x —3 = 0, determine which of the following are solutions?
(i) x = 3 (ii) x= –2
(iii) x=-1/2 (iv) x=-1/3
I’ll give brainlist!!What is the restricted domain of the quadratic(y=(x+1)^2) that would ensure that the inverse is a function? Justify the answer
So, on solving the provided question, we cans ay that value o the quadratic equation (x+1)(x+1) => x = -1, -1
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation will be
[tex]y=(x+1)^2[/tex]
so,
(x+1)(x+1)
x = -1, -1
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The correct question is -
What is the restricted domain of the quadratic(y=(x+1)^2) that would ensure that the inverse is a function?
Solve 3x + 11 = kfor x.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \: 3x + 11 = k[/tex]
[tex]\qquad \sf \dashrightarrow \: 3x + 11 - 11 = k - 11[/tex]
[tex]\qquad \sf \dashrightarrow \: 3x = k - 11[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \dfrac{k - 11}{3} [/tex]
Determine the next three terms
-1 1/2, -1/4, 1/8
The next three terms of the alternating series are - 1 / 16, 1 / 32 and 1 / 64, respectively.
How to predict the next three terms of a series
Herein we find an alternating series of the form:
sₙ = (- 1)ⁿ · rⁿ⁻¹, for n = {1, 2, 3, ..., n}
Where:
n - Index of the n-th element of the series.r - Common ratio.By direct inspection, we find that r = 1 / 2 and the next three terms are: n = {5, 6, 7}
n = 5
s₅ = (- 1)⁵ · (1 / 2)⁵⁻¹
s₅ = - 1 · (1 / 16)
s₅ = - 1 / 16
n = 6
s₆ = (- 1)⁶ · (1 / 2)⁶⁻¹
s₆ = 1 · (1 / 32)
s₆ = 1 / 32
n = 7
s₇ = (- 1)⁷ · (1 / 2)⁷⁻¹
s₇ = 1 · (1 / 64)
s₇ = 1 / 64
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The owner of Nuts2U Snack Shack mixes cashews worth $6.25 a pound with peanuts worth $2.10 a pound to get a half-pound mixed nut bag worth $1.90. How much of each kind of nut is included in the mixed bag?
Answer:
I have solved it and attached in the explanation.
Step-by-step explanation:
The amount of Cashew nuts is 0.205
The amoun of Peanuts is 0.295
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Amount of Cashew nuts = x
Amoun of Peanuts = y
Now,
We can make two equations.
x + y = 1/2 ____(1)
x = 1/2 - y _____(20
Substituting (2) in (3)
6.25x + 2.10y = 1.90 _____(3)
6.25 (1/2 - y) + 2.10y = 1.90
3.125 - 6.25y + 2.10y = 1.90
3.125 - 4.15y = 1.90
3.125 - 1.90 = 4.15y
y = 1.225/4.15
y = 0.295
And,
x = 1/2 - y
x = 1/2 - 0.295
x = 0.205
Thus,
Amount of Cashew nuts = 0.205
Amoun of Peanuts = 0.295
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To prepare for a half-marathon, Colleen recently had 3 training runs. The table shows how far she ran in each session and how long it took.
Colleen's velocity increased from the first section to the second section, while it remained constant from the second section to the third section.
How to obtain the velocity?The measures in this problem are obtained considering the relation between velocity, distance and time.
The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:
v = d/t.
In which:
v is the velocity.d is the distance.t is the time.For session 1, considering decimal numbers, the parameters are given as follows:
Time of 2.2 hours, as 2 + 1/5 = 2 + 0.2 = 2.2.Distance of 9.9 miles.Hence the velocity is of:
v = 9.9/2.2 = 4.5 miles per hour.
For session 2, the parameters are given as follows:
Time of 2.5 hours.Distance of 11.875 miles.Hence the velocity is of:
v = 11.875/2.5 = 4.75 miles per hour.
For session 3, the parameters are given as follows:
Time of 3.25 hours.Distance of 15.4375 miles.Hence the velocity is of:
v = 15.4375/3.25 = 4.75 miles per hour.
Missing InformationThe table is given by the image presented at the end of the answer.
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The function f is continuous on the interval (0,16) and f is twice differential except at x=5 where the derivatives are undefined. Information about the first and second derivatives
Using it's definition, it is found that the function f(x) has a point of inflection at:
A. x = 8 only.
What are the points of inflection of a function?Inflection points are points where the function changes concavity.
The critical points of a function are the values of x for which:
f" (x) =0
Additionally, there has to be a change in the sign of f" (x)
Researching the problem on the internet, it is found that:
For 0 < x < 5, f"(X) > 0
For x = 5, f" (x) is undefined.
For 5 < x < 8, f (x) < 0
For x = 8, f"(x) = 0
For 8 < x < 12,f" (x) > 0
For x = 12, f (x) = 0
For 12 < x < 16, f"(x) > 0
The two conditions, f"(x) = 0 and a change in the signal of f" (x) are only respected at x = 8, which is the lone inflection point.
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Complete option
of f for values of x in the interval (0,16) is given in the table above. At what values of x in the interval (0,16) does the graph of f have a point of inflection?.
Help meee
A 10 pound bag of flour at C-Town cost $30. A 16 pound bag of flour at Food Bazaar
This means that C-Town flour is more expensive because it is only $1.88 per pound compared to Food Bazaar's $2.25 per pound.
What is cost?Cost is the amount of money or resources needed to acquire, maintain, or produce something. It can refer to either the expense of buying a good or service, the expense of labor, or the expense of resources such as time and materials. In a business context, cost is often used to refer to the total amount of money a company has spent on a particular activity or product.
C-Town's smaller bag size may make it a more convenient purchase, but it is not a good price compared to Food Bazaar.
In order to get the best deal, the shopper needs to compare prices and consider all of the factors. The size and quantity of the bags, the number of servings in each bag, the cost per serving, and the store's location are all important considerations. For example, C-Town may be closer geographically, but if the shopper needs more servings for their recipe, the extra cost to buy multiple bags at C-Town may be more expensive than buying a larger bag of flour at Food Bazaar.
In addition to the cost of the flour, other costs such as the cost of transportation to the store, the cost of any necessary packaging, the cost of any other ingredients needed for the recipe, and the cost of any other items purchased should also be taken into account.
Finally, shoppers should take the quality of the product into consideration. The type of flour, the freshness and shelf life of the product, and any special features of the product should also be taken into account. A low-cost bag of flour may be far less desirable than a more expensive bag of flour with higher quality ingredients.
Overall, to get the best deal on flour, shoppers need to consider all of these factors and compare prices between stores.
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How do you dilate a right triangle?
Dilation is a transformation that can be used to resize an item. Dilation can cause the items to grow or shrink.
What does dilation mean?Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.
You have most likely started labour when your cervix is 3 cm dilated. Your cervix slowly widens to around 6 cm during this phase. It can take anywhere from a few hours to a few days to complete this stage of labour, however it typically takes between 8 and 12 hours. An average woman can dilate between 0.5 and 0.7 cm per hour during the active stage of labour. Whether this is your first child or not will also influence how quickly your cervix dilates. Experienced mothers typically progress through labour more quickly.
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Think of a number. Add 8 to it. Multiply this sum by 3. The result is 48. What is the original number?
Answer:
The original number is 8.
Step-by-step explanation:
(x + 8) x 3 = 48
x + 8 = 48/3
x = 16 - 8
x = 8
Someone help!! HOW DOES IT DIFFER FROM THE DISTANCE AB
Therefore , the solution of the given problem of distance comes out to be D = 11.66.
Specify the distance.An object's travels are quantified by distance. Simply explained, distance, or t, is the amount of space an object covers within a specific period of time. Displacement is still the shortest distance a moving object can travel. We frequently take into account the concepts of distance et displacement.
Here,
provided parameters
Dimensions of A = (-4,5)
B's coordinate number is (2,-5)
Unknown:
Size of AB =?
Solution:
Use the formula below to calculate the distance between these two places;
D = √(y2-y1)²+(x2-x1)²
x₁ = -4
x₂ = 2
y₁ = 5
y₂ = -5
enter the parameters, then solve;
=> D = √(2-(-4)) ²+(-5-5) ²
=>D = √6² + (-10)² = 11.66
Therefore , the solution of the given problem of distance comes out to be D = 11.66.
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In right triangle xyz, ∠x and ∠z are complementary angles and cos(x) is . what is sin(z)? a. b. c. d.
So the sin(z) is approximately 0.4866.
In a right triangle, the two non-right angles are complementary, meaning that their measures add up to 90 degrees.
So, if ∠x is complementary to ∠z, then we can write the equation ∠x + ∠z = 90°
We also know that in a right triangle, the cosine of one angle is equal to the ratio of the adjacent side to the hypotenuse.
And the sine of one angle is equal to the ratio of the opposite side to the hypotenuse.
Given that cos(x) = 0.6.
We can find sin(z) by using the trigonometric identity, sin²(z) + cos²(z) = 1
sin²(z) = 1 - cos²(x)
sin²(z) = 1 - 0.6²
sin²(z) = 0.24
sin(z) = √0.24
sin(z) = 0.4866
So the sin(z) is approximately 0.4866.
It's important to note that the result is an approximation since the value of cos(x) is given as 0.6, which is not exact.
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5x^2+14x=x+6
HURRYY SOLVE BY FACTORING EXPLAIN AND SHOW EVER STEP
Answer:
(x+3) and (5x-2)
Step-by-step explanation:
first get everything onto one side
5x^2+13x-6=0
then multiply 5 by 6 to get 30 and 15 times 2 is thirty and 15-2=13
5x^2+15x-2x-6=0
then split in half and factor both sides
5x^2+15x factored is 5x(x+3)
-2x-6 factored is -2(x+3)
so the answer is (x+3) and (5x-2)
At a sale this week, a sofa is being sold for $220.40. This is a 38% discount from the original price. What is the original price? (Don't forget the dollar sign!!)
Answer:
$83.75
$220.40 x 38% =$83.75
which expression has a product greater than (2 1/6)
The expression has a product greater than (2 1/6) is 2 [tex]\frac{1}{6}[/tex] x 2 [tex]\frac{1}{6}[/tex] .
How to calculate the expression has a product greater than given number?The first step to calculate an expression with a product greater than a given number is to identify the expression. To do this, you need to identify any variables and constants that are present in the expression. Once you have identified these, you can then begin to calculate the expression.The next step is to determine the order of operations of the expression. This determines the order in which the operations should be performed in order to calculate the expression. Generally, the order of operations follows the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.Once the order of operations has been determined, you can begin to calculate the expression. When calculating an expression with a product greater than a given number, it is important to remember to multiply the terms in the expression first before adding or subtracting them. This is because multiplication has a higher order of operations than addition and subtraction.Once all the terms in the expression have been calculated, the final step is to compare the product of the expression with the given number. If the product of the expression is greater than the given number, then the expression is valid and can be used. If the product of the expression is less than the given number, then the expression needs to be modified. This can be done by adding constants or adjusting the coefficients of the variables in the expression.By following these steps, you can calculate any expression with a product greater than a given number. This is a useful skill to have when solving equations and can help you get the correct answer quickly.To learn more about product expression refer to:
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Can somebody help me on this?
Answer:
Translation, then Rotation
Step-by-step explanation:
It is first moved(translation), then rotated(rotation) around the left meeting point of the graph by about 90 degrees to the right.
What is not a function inverse?
A non-function inverse would be a mathematical operation that does not produce a new function.
A function inverse is a new function that can be used to "undo" the effects of an original function. An example of a function inverse would be the inverse sine function of sin(x).
A non-function inverse would be a mathematical operation that does not produce a new function. Examples of non-function inverses include division, subtraction, and multiplication. These operations can be used to undo the effects of an original function, but they do not create a new function. Division can be used to “undo” multiplication, for example. However, the end result is not a new function, but rather a number or set of numbers. Subtraction and multiplication can be used to “undo” addition and division, respectively, but again, the end result is a number or set of numbers, not a new function. Therefore, these operations are not function inverses.
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5. In order to graduate, you must take at least 13 core credits and 6 electives credits and you can take no more than a total of 27 credits. Write a system of inequalities that defines how many of each you can take.
a C ≥ 13, E ≥ 6, C + E ≤ 27
b C+ E ≥ 19, C + E ≤ 27
c C ≤ 13, E ≤ 6, C + E ≤ 27
d C + E ≥ 19, C + E < 27
The system of inequality the satisfies the given credit conditions is option a, C ≥ 13, E ≥ 6 and C+E ≤ 27.
What is system of inequality?One or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. A linear inequality's solution is an ordered pair that resolves all of the system's inequalities, and the inequality's graph is a representation of all of the system's solutions.
Given that to graduate the core credit must be at least 13 credits. This is represented as follows:
C ≥ 13.
The credit of the electives should be at least 6, this is represented as follows:
E ≥ 6
The total credits should be no more than 27, this is represented as:
C + E ≤ 27
Hence, the system of inequality the satisfies the given conditions is option a, C ≥ 13, E ≥ 6 and C+E ≤ 27.
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PLSSS HELPPP
What is the domain of the function?
The domain and range of the the function are given below -
Domain → [-5, 10)
Range → [-3, 3)
What is a function?A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.Given is a graph of the function.
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes. So, we can write the domain as -
Domain → [-5, 10)
Range → [-3, 3)
Therefore, the domain and range of the the function are given below -
Domain → [-5, 10)
Range → [-3, 3)
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Write 40.5 as a fraction
Answer:
40.5=40 1/2
Step-by-step explanation:
Answer: 40.5 as a fraction is 81/2. ✅
Step-by-step explanation:
Sure, here's a step-by-step explanation of how I got the fraction 81/2 for the decimal number 40.5:
Identify the number of decimal places in the decimal representation of 40.5, in this case, it's 1.
Write the decimal number as a fraction by placing the decimal number over a power of 10 that has the same number of zeroes as there are decimal places in the decimal representation. In this case, it's 40.5 / 10^1 (or 40.5/10).
Simplify the fraction if possible by dividing both the numerator and denominator by a common factor if one exists. In this case, the fraction is already in its simplest form.
The fraction representation of 40.5 is 405/10
Simplify the fraction again if possible by dividing both the numerator and denominator by a common factor if one exists. In this case, the fraction can be simplified further by dividing both the numerator and denominator by 5.
So, the fraction representation of 40.5 is 81/2
Hence, the fraction representation of 40.5 is 81/2.
Drag each part of the expression to categorize it as a term or a coefficient in the expression. −2/5h+7h+6
If the expression be −2/5h+7h+6 then the value of h be -10/11.
What is meant by expression?A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.
An expression in mathematics is made up of a number of variables, functions, and other elements (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.
Using mathematical operations like addition, subtraction, multiplication, and division, a combination of numbers and integers can be expressed numerically in mathematics.
Let the equation be -2/5h + 7h + 6 = 0
Move 6 to the right side
-2/5h + 7h = -6
Multiply both sides by 5
-2/5h × 5 + 7h × 5 = -6 × 5
Simplifying the above equation, we get
33h = -30
Divide both sides by 33
33h/33 = -30/33
Therefore, the value of h = -10/11.
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The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is 40 or older is chosen at random, what is the probability that they have completed a bachelor's or master's degree? Round your answer to the nearest thousandth.
If a resident who is 40 or older is chosen at random, the probability that they have completed a bachelor's or master's degree is given as follows:
0.436 = 43.6%.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The desired and total outcomes for the conditional probability in this problem are given as follows:
Desired outcomes: Bachelor's or master's degree and age 40 or older.Total outcomes: Age 40 or older.Hence the number of total outcomes is given as follows:
3827 + 7106 = 10933.
(40-49 + 50 and over).
The number of desired outcomes is given as follows:
726 + 655 + 2160 + 1226 = 4767.
(either master's or bachelor's degree's for both age intervals).
Hence the probability is calculated as follows:
p = 4767/10933
p = 0.436.
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A checking account is set up with an initial balance of $6,200, and $350 is removed from the account each month for rent (no other transactions occur on the account). Write an equation whose solution is the number of months, m
, it takes for the account balance to reach $2,700.
An equation, containing variable m that represents the situation described is:
An equation, containing variable m that represents the situation described is 2,700 = 6,200 - 350m.
What is an equation?An equation is a mathematical statement showing the equality or equivalence of two or more mathematical or algebraic expressions.
Equations go with the equal symbol (=) unlike mathematical expressions, which combine variables, numbers, constants, and values with the mathematical operands.
The initial balance in the checking account = $6,200
Monthly withdrawal = $350
The final account balance = $2,700
Let the number of months of withdrawal = m
Equation:2,700 = 6,200 - 350m
Check:
2,700 = 6,200 - 350m
350m = 3,500
m = 10 months
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In triangle ABC, angle A is 35° and angle B is 20°. Select all triangles which are similar to triangle ABC.
A. triangle DEF where angle D is 35° and angle E is 20°
B. triangle GHI where angle G is 35° and angle I is 30°
C. triangle JKL where angle J is 35° and angle L is 125°
D. triangle MNO where angle N is 20° and angle 0 is 125°
E. triangle PQR where angle Q is 20° and angle R is 30°
Triangles which are similar to triangle ABC is the triangle having same corresponding angles.
A) triangle DEF where angle D is 35º and angle E is 20°.
C) triangle JKL where angle J is 35º and angle L is 125°.
D) triangle MNO where angle N is 20° and angle O is 125°.
What is a triangle?
Triangle can be defined as a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.
We know the sum of all the interior angles in a triangle is 180°.
A triangle ABC, angle A is 35º and angle B is 20º.
∴ m∠C is 180° - (35 + 20)°.
m∠C = 180° - 55°.
m∠C = 125°.
∴ Triangles which are similar to triangle ABC is the triangle having the same corresponding angles.
Triangle DEF where angle D is 35º and angle E is 20°.
Triangle JKL where angle J is 35º and angle L is 125°.
Triangle MNO where angle N is 20° and angle O is 125°.
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Choose the correct verb form that completes this sentence: Nosotros _____ la ventana. Select one: a. compartimos b. abro c. escribimos d. abrimos
Answer: abrimos
Step-by-step explanation: That's what it is on my quiz.
In the sentence "Nosotros _____ la ventana", the correct verb form is "abrimos". The best answer is option D.
The verb "abrir" is a Spanish verb that means "to open", and the first person plural form of this verb is "abrimos". So the sentence "Nosotros abrimos la ventana" translates to "We open the window".
The other verb forms in the options ("compartimos", "abro", and "escribimos") do not fit the context of opening the window. "Compartimos" means "we share", "abro" means "I open" (first person singular), and "escribimos" means "we write". So these forms are not the correct form to complete the sentence.
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-x/5-8=12
Show work
And check
Answer:
[tex]\huge\boxed{\sf x = -100}[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle -\frac{x}{5} -8=12\\\\Add \ 8 \ to \ both \ sides\\\\-\frac{x}{5} = 12+ 8\\\\-\frac{x}{5} = 20\\\\Multiply \ both\ sides \ by \ 5\\\\-x = 20 \times 5\\\\-x = 100\\\\Multiply\ both \ sides \ by\ -1\\\\x = -100\\\\\rule[225]{225}{2}[/tex]
slope =-5, through (-2,4)
The equation of the line with given slope and passing through the given point is y = -5x - 6.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.
General form of slope intercept form of line is,
y = mx + d
Here d is the y intercept, which is the value of y coordinate when x coordinate is 0. And m is the slope.
Given that slope, m = -5
Also we have a point on the line (-2, 4)
Substituting these,
4 = (-5 × -2) + d
4 = 10 + d
d = -6
So the equation is y = -5x - 6.
Hence the equation of the line is y = -5x - 6.
Learn more about Slope here :
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Describe the transformation that is needed to obtain the graph of g(x)=3x−5 from the graph of g(x)=3x
Answer:
The graph of g(x) = 3x−5 is obtained from the graph of g(x) = 3x by applying the transformation (f(x) = f(x) + b) where b = -5. This transformation is a vertical shift of the graph of g(x) = 3x downward by 5 units.
The graph of g(x) = 3x is a line with a slope of 3 and y-intercept of 0. By subtracting 5 from each y-coordinate, the y-intercept of the graph is shifted downward by 5 units, resulting in a y-intercept of -5. The slope of the graph remains the same as the original function, 3. So the graph of g(x)=3x−5 is the same line as g(x)=3x, but shifted downward 5 units.
Step-by-step explanation: