So, the component form of vector u + v is (4, 7).
Final answer:
The component form of the sum of vector u = (5, 3) and vector v = (-1, 4) is found by adding corresponding components, yielding the sum vector u + v = (4, 7).
Explanation:
To find the component form of the sum of two vectors, vector u, and vector v, you simply add the corresponding components of each vector. The given vectors are vector u = (5, 3) and vector v = (-1, 4). By adding the x-components (5 and -1) and the y-components (3 and 4), we get the sum of the vectors.
The component form of vector u + vector v is calculated as follows:
Sum of x-components: 5 + (-1) = 4Sum of y-components: 3 + 4 = 7Therefore, the component form of vector u + vector v is (4, 7).
Marcus has a total of 10 nickels and dimes in his pocket. he has a total of 70 cents. how many dimes does he have in his pocket?
The graph of a quadratic function touches, but does not cross, the x-axis at x = 4. Which function represents this situation? y = x2 – 16 y = x2 – 4x y = x2 – 8x + 16 y = x2 + 8x + 16
The quadratic equation is y = x^2 - 8x + 16
How to determine the equation?From the question, we have:
x = 4
Since the graph only touches x = 4 and it does not cross it, then it means that the graph has a multiplicity of 2 at x = 4
The equation is then represented as:
y = (x - 4)^2
Expand
y = x^2 - 8x + 16
Hence, the quadratic equation is y = x^2 - 8x + 16
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If you were given the equation f ( x ) = 3x⁵+6x, what behavior would the ends of the graph have?
a. Both ends will point up
b. Both ends will point down
c. the left end will start down at a large negative and the right end will go upwards
d. the left end will start up at a large positive and the right end will go downwards EXPLAIN ANSWER
The ends of the graph of the function f(x) = 3x^5 + 6x will display the behavior described in option c. This is due to the highest power of x in the equation being an odd number and the coefficient being positive. As such, the left end of the graph will start down at a large negative and the right end will go upwards.
Explanation:The behavior of the ends of the graph of the function f(x) = 3x^5 + 6x is determined by the highest power of x in the equation, which is 5 in this case. The coefficient of x^5 is positive, so as x approaches positive infinity, f(x) also approaches positive infinity. Conversely, as x approaches negative infinity, the value of f(x) would approach negative infinity. We can describe this behavior as the left end of the graph starting at a large negative and the right end going upwards. Thus, answer c. 'the left end will start down at a large negative and the right end will go upwards' is correct.
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The perimeter of a square must be greater than 188 inches but less than 198 inches. find the range of possible side lengths that satisfy these conditions. (hint: the perimeter of a square is given by p=4s, where s represents the length of a side).
The range of possible side lengths for the square is from slightly more than 47 inches to slightly less than 49.5 inches. This is found by dividing the given perimeters by 4, using the formula p=4s.
Explanation:In this problem, we need to find the range of possible side lengths of a square where the perimeter is more than 188 inches but less than 198 inches. Remember that the perimeter of a square is found by multiplying the length of one side by 4 (p=4s).
First, let's find the side length for a square with a perimeter of 188 inches. We do this by dividing the perimeter by 4: 188 / 4 = 47 inches. So, any square with side lengths greater than 47 inches would have a perimeter more than 188 inches.
Next, we find the side length for a square with a perimeter of 198 inches. Similarly, we divide the perimeter by 4: 198 / 4 = 49.5 inches. So any square with side lengths less than 49.5 inches would have a perimeter less than 198 inches.
Therefore, the range of possible side lengths that satisfy these conditions is from slightly more than 47 inches to slightly less than 49.5 inches.
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Solve. 2m^2-7m-13=-10
[tex]2m^2-7m-13=-10\ \ \ |+10\\\\2m^2-7m-3=0[/tex]
[tex]a=2;\ b=-7;\ c=-3\\\\b^2-4ac=(-7)^2-4\cdot2\cdot(-3)=49+24=73\\\\m_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ m_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\m_1=\dfrac{-(-7)-\sqrt{73}}{2\cdot2}=\dfrac{7-\sqrt{73}}{4}\\\\m_2=\dfrac{-(-7)+\sqrt{73}}{2\cdot2}=\dfrac{7+\sqrt{73}}{4}[/tex]
Northbound buses with tourists leave Waco for Dallas at 10 minute intervals. The trip takes exactly one hour. Southbound tourist buses leave Dallas for Waco at the same moment as their northbound counterparts and arrive an hour later. How many southbound buses does a northbound bus encounter between Waco and Dallas, including the one that is arriving in Waco just as the northbound bus leaves for Dallas and the one that is departing from Dallas just as the northbound bus arrives there?
Given that (6,5) is on the graph of f(x), find the corresponding point for the function-2f(x)
Answer:
the person up is wrong
Step-by-step explanation:
i got it wrong on the test rn
Indicate a general rule for the [tex] n^{th}[/tex] term of this sequence.
-6a, -3a, 0a, 3a, 6a. . .
A.] [tex] a_{n}=3an+9a[/tex]
B.] [tex] a_{n}=-3an-9a[/tex]
C.] [tex] a_{n}=-3an+9a[/tex]
D.] [tex] a_{n}=3an-9a[/tex]
If side a has a length of 3 and side b has a length of 4, use the Pythagorean Theorem to find the length of side c. Round the answer to the nearest tenth.
Which is a monthly recurring cost associated with renting a house?
utility bills
property tax
insurance
A person at the top of a cliff 100 ft. tall sees Gilligan's boat. He sees the boat at an angle of depression of 10. How far is the boat from the base of the cliff.
At the start of a race, a runner’s velocity changes from 0 to 4.0 m/s. It takes him 2 seconds to speed up. His acceleration is ______ m/s2.
His acceleration is, 2 m/s^2!
Hope this helps! :)
What term can you add to 5/6x-4 to make it equivalent to 1/2x-4
Answer:
-1/3
Step-by-step explanation:
We need a c number that:
5/6x + cx = 1/2x
We clear the equation:
cx = 1/2x -5/6x
c = 1/2 -5/6
c= -2/6 = -1/3
The area of square abcd is 36 square units and the area of triangle ebf is 20 square units. if line eb is perpindicular to line bf and line ae is equal to 2 find the length of line cf
Final answer:
The length of line CF is 20 units.
Explanation:
Let's analyze the given information step by step:
The area of square ABCD is 36 square units, so each side of the square measures √(36) = 6 units.The area of triangle EBF is 20 square units.Line EB is perpendicular to line BF.Line AE is equal to 2 units.Since line EB is perpendicular to line BF, triangle EBF is a right triangle. Let's assume the length of line BF is x units. Using the area of a triangle formula, we have:
Area of triangle EBF = (1/2) * base * height
20 = (1/2) * x * 2
Simplifying the equation, we get:
20 = x
Therefore, the length of line BF (or CF) is 20 units.
If you were going to represent the top view of the figure, stated which boxed should be shaded.
Which transformation shows a reflection of ΔDEF?
The answer is B or the purple one
Answer:
The image B with purple figures is correct.
Step-by-step explanation:
We are given the figure DEF and we are required to find the figure which is obtained after reflecting it.
Now, reflection of a figure means to flip the figure over a line.
In the green figure, the points D and E are interchanged which is not possible in reflection.
In the blue figure, there is no change.
In the purple figure, the triangle is flipped over the line DE and so it is the correct answer.
Hence, the purple figure is obtained after reflecting the figure DEF.
18 points were scored by one figure skating pair that was 40% of your final score. What was the final score for that pair of figure skaters?
What scale factor was applied to the first rectangle to get the resulting image
Help me plsssssssssssssssssssssssssssssssssssssssssss!
A bakery sold 115 cupcakes in one day. The head baker predicted he would sell 95 cupcakes that day. What was the percent error of the baker's prediction?
The baker's prediction had a 17.39% error.
To calculate the percent error of the baker's prediction, we use the formula:
Percent Error = (|Actual Value - Predicted Value| / Actual Value) * 100%
In this case, the Actual Value is the number of cupcakes actually sold, 115. The Predicted Value is the number the baker predicted to sell, 95.
So, the computation will be:
Percent Error = (|115 - 95| / 115) * 100%
Percent Error = (20 / 115) * 100
Percent Error = 0.1739 * 100%
Percent Error = 17.39%
What is the derivative of e^(2x)
I am confused because the derivative e^x is e^x.
But they say you need to use the chain rule.
Which is f'(g(x))*g'(x).
I have used that on exponents but in this I just get, 2x * e^(2x-1) *e
Which is not the answer =/
I need help on #9. The help would be grateful appreciated.
Jana wants to navigate page 35 of her report. what is the quickest way to navigate?
To navigate to page 35 of a report, you can use the 'find' function in a web browser with CONTROL or COMMAND + F, utilize the table of contents with hyperlinks, or enter the page number in a navigator window's spin box, depending on the device and format.
To quickly navigate to page 35 of a report, you have several options depending on the format and the device you are using. If you are viewing the report on a web browser, you can usually press CONTROL or COMMAND and the letter F to open the 'find' function and type '35' to jump to page 35. Alternatively, if the document has a table of contents with hyperlinks, you can click on the relevant section to navigate quickly. For documents with a navigator window, enter '35' in the spin box to jump straight to that page. In a mobile reading environment, you may find a Contents button at the top of the screen; clicking this can allow you to select and jump to the desired page or section.
What is the solution set for the quadratic equation x2 - 16 = 0?
A)
{4}
B)
{-4, 4}
C)
{256}
D)
{-256, 256}
The height of a stack of dimes varies directly with the number of dimes in the stack. A stack of 4 dimes is 5.4 mm tall. How many millimeters tall is a stack of 15 dimes?
Choose the pair of numbers that is not a solution to the given equation.
y = 5 - 2x
My options are;
1,3
2,1
0,3
The graph shows the number of copies a copier can make. What is the unit rate?
A)
1
25
B) 5
C) 15
Eliminate
D) 25
Answer:
25
Step-by-step explanation:
Yu-Xi draws a triangle with two angles measuring 79 degrees and 23 degrees.What is the measure, in degrees, of the third angle?
Answer:
The Triangle Drawn by ,Yu-Xi,has measure of two angles ,79° and 23°.
All the Basic Learners who knows Math ,that,sum of Measures of three Interior angles of Triangle is 180°.
→79°+23°+Third Angle =180°
→102°+Third Angle =180°
→Third Angle =180° -102°
Third Angle =78°
Solve for x where a is an integer less than 0
How would you get the answer??
the ordered pairs below represent a relation between x and y.
(-3,0), (-2,4), (-1,8), (0,12), (1,16), (2,20)
could this set of ordered pairs have been generated by a linear function?
A. No, because the distance between consecutive x-value is different than the distance between consecutive x-values.
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
C. No, because the y-values decrease and then increase
D. Yes, because the distance between consecutive x-values is constant.
Answer:
Yes because the relative difference between y-values and x-values is the same no matter what which pairs of (x,y) values you use to calculate it
Step-by-step explanation:
Yes, this set of ordered pairs have been generated by a linear function because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
The correct option is (B)
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given are ordered pairs are: (-3,0) (-2,4)(-1,8)(0,12)(1,16)(2,20).
It can be seen that the there only unit increase in x coordinates and units increase in consecutive y- coordinates.
Now, if we set up the equation of line as:
Here, m =4 and b = 12
So the relationship is linear and represented by the equation
y=4x+12
Hence, the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
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