No. 2: Kennedy error is that he mistakenly distributed the negative sign when multiplying -3 and +3. The correct answer is x² - 9.
No. 3: The product (x + 6)(x - 6) is equivalent to the expression x² - 6².
No. 4: The pattern for the squares of binomial are: (a + b)² = a² + 2ab + b²
and (a - b)² = a² - 2ab + b².
Sum and difference pattern: (a + b)(a - b) = a² - b²
How to describe and correct Kennedy's error?No. 2
Kennedy made an error in multiplying (x - 3)(x + 3) because the correct result of this multiplication is x² - 9, not x² - 6x - 9.
This error occurred because Kennedy mistakenly distributed the negative sign when multiplying -3 and +3, resulting in an additional -6x term in the final answer.
The correct way to multiply (x - 3)(x + 3) is to use the FOIL method, which stands for First, Outer, Inner, Last. This gives us:
(x - 3)(x + 3) = x² + 3x - 3x - 9 = x² - 9
No. 3
The product (x + 6)(x - 6) is equivalent to the expression x² - 36, which is called the difference of two squares because it represents the difference between two perfect squares: x² and 6².
Specifically, (x + 6)(x - 6) can be written as x² - 6², and using the identity (a + b)(a - b) = a² - b² we can simplify this to x² - 36.
No. 4
The pattern for the squares of binomial are:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
The pattern for the product of a sum and a difference is:
(a + b)(a - b) = a² - b²
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The answer should be 3278 ft I just need help with how to get it and the work.
The Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.
What is a trapezoid?A trapezoid is a quadrilateral having two parallel bases and one set of other sides called legs.
To estimate the distance traveled by the Panther I, we need to approximate the area under the velocity curve between 0 and 25.7 seconds. We can divide the area into trapezoids using the data given in the table.
The first trapezoid has a height of 30 mph and a base of 1.8 seconds. The second trapezoid has a height of 40 mph and a base of 1.3 seconds (the difference between 3.1 and 1.8).
Continuing in this way, we get the following table:
Speed Height
Range (mph) Base (s) Area (mph * s)
0-30 30 1.8 54
30-40 40 1.3 52
40-50 50 1.1 55
50-60 60 1.3 78
60-70 70 1.9 133
70-80 80 1.8 144
80-90 90 2.3 207
90-100 100 3.1 310
100-120 120 6.3 756
120-130 130 4.8 624
To find the total area, we add up the areas of all the trapezoids:
54 + 52 + 55 + 78 + 133 + 144 + 207 + 310 + 756 + 624 = 2413
Therefore, the Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.
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What is the 10th term in this sequence 2,0, -2
Answer:
-16
Step-by-step explanation:
A ball is thrown upward with an initial velocity of 75 feet per second and an initial height of 4 feet. Given h(t) = −16t2 + v0t + h0, complete function h to model the vertical motion of the ball. Then find the ball’s maximum height, to the nearest foot.
The maximum height of the ball is given as follows:
92 feet.
How to model the height of the ball?The quadratic function modelling the height of the ball is given as follows:
h(t) = -16t² + v(0)t + h(0).
In which:
v(0) is the initial velocity.h(0) is the initial height.The parameters for this problem are given as follows:
v(0) = 75, h(0) = 4.
Hence the equation is:
h(t) = -16t² + 75t + 4.
The coefficients are given as follows:
a = -16, b = 75, c = 4.
As the quadratic equation is concave down, the maximum height is at the vertex.
The t-coordinate of the vertex is given as follows:
t = -b/2a
b = -75/-32
b = 2.34375s.
Hence the maximum height is of:
h(2.34375) = -16(2.34375)² + 75(2.34375) + 4.
h(2.34375) = 92 feet.
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(2x+3)(xexponent2 - 6x - 2)
Answer:
Step-by-step explanation:
We can use the distributive property and basic algebraic operations to multiply the given expression:
(2x+3)(x^2 - 6x - 2)
= 2x(x^2 - 6x - 2) + 3(x^2 - 6x - 2) // Distribute 2x and 3
= 2x^3 - 12x^2 - 4x + 3x^2 - 18x - 6 // Multiply each term
= 2x^3 - 9x^2 - 22x - 6 // Combine like terms
Therefore, (2x+3)(x^2 - 6x - 2) simplifies to 2x^3 - 9x^2 - 22x - 6.
If the short leg of a 30-60-90 triangle measures 203, the long leg measures how much ?
We can state this by responding to the provided question Hence, the triangle longer limb is around 351.42 in length.
What precisely is a triangle?A triangle is a polygon because it includes four or so additional parts. It features a simple rectangular shape. A rectangle having edges A, B, and C is referred to as a triangle. When the sides are actually not collinear, Euclidean geometry yields a single plane and cube. If a triangle contains three parts and three angles, it is a polygon. The intersections of a triangle's three sides are referred to as its corners. The sum of a triangle's sides is 180 degrees.
In a triangle with three legs measuring 30, 60, and 90, the shorter leg is half as long as the hypotenuse while the larger leg is sqrt3 times as long.
Let's name the larger leg's length "x" for simplicity. Thus, we are aware of:
The shorter leg measures 203 in length.
The hypotenuse measures 406 times the length of the shorter leg.
Using the proportion of the hypotenuse and leg lengths in a 30-60-90 triangle, we may find:
x = sqrt3 times ($) 203 = 351.42$
Hence, the longer limb is around 351.42 in length.
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у + 4 + 3(y + 2) =
A. 4y + 10
B. 4у + 6
C. 3у2 +6
D. 3у2 +10
Answer:
A. 4y + 10Step-by-step explanation:
[tex]\tt y+4+3\left(y+2\right)[/tex]
Expand by distributing terms:-
[tex]\tt y+4+3y+6[/tex]
Combine like terms:-
[tex]\boxed{\tt y+3y}+\boxed{\tt 4+6}[/tex]
[tex]\tt y+3y=\underline{\bf 4y}[/tex]
[tex]\tt 4+6=\underline{\bf 10}[/tex]
⇒ [tex]\underline{\bf 4y+10}[/tex]
Therefore, A. 4y + 10 is our answer!
_______________________
Hope this helps! :)
Answer:
4y+10
Step-by-step explanation:
у + 4 + 3(y + 2) =
y + 4 + 3y + 6
y + 10 + 3y
4y +10
What is the difference between the fractions of 1/9 and 1/2
Answer:
1/9 and 1/2 one is greater then
Step-by-step explanation:
so if u look at it you will know that 1/2 is less then and 1/9 is greater then.
9. At a scouts' camp. there is sufficient food to last 72 scouts for 6 days. If 18 scouts do not turn up for the camp, how much longer can the food last for the other scouts?
Answer:
9 54 divided by 9 = 6 72 - 18 = 54
Step-by-step explanation:
Jorge's 3/4 hr drive to a job was part city and part country driving 2/11 hr was city driving, how much time was spent on country driving?
The time spent on country driving is 25/44 hour
How to determine how much time was spent on country driving?From the question, we have the following parameters that can be used in our computation:
Total time = 3/4
City driving = 2/11
Given that 2/11 hour was spent on city driving, we can find the time spent on country driving as follows:
Time spent on country driving = Total driving time - Time spent on city driving
Time spent on country driving = 3/4 hour - 2/11 hour
So, we have
Time spent on country driving = 25/44
Hence, the time spent is 25/44
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Dividing integers, please help
Answer:
The percent of Dan's average did he score during this game is 11.11%
What percent of Dan's average did he score during this game?
Dan's score in the high school basketball team during last game= 18 points
Dan's score in the high school basketball team during this season = 20 points
Percent of Dan's score during this game = (20 - 18) / 18 × 100
= 2/18 × 100
= 11.11%
In conclusion, Dan scored an average percentage of 11.11% during this game.
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Find the discriminant for each Quadratic and state the types of roots.
2x² + 3x - 3=0
4x²-6x+2=y
0=x²-3x+8
y=5x²+4x+1
9. The discriminant is 33. And the roots are real and distinct.
10. The discriminant is 4. And the roots are real and distinct.
11. The discriminant is -23. And the roots are imaginary roots.
12. The discriminant is -4. And the roots are imaginary roots.
What is the discriminant?
The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,
D = b² - 4ac
If D > 0, then the roots are real and distinct root.If D = 0, then the roots are real and equal roots.If D < 0, then the roots are imaginary roots.9. 2x² + 3x - 3 = 0, the discriminant is given as,
D = 3² - 4 × 2 × (-3)
D = 33
Roots are real and distinct.
10. 4x² - 6x + 2 = y, the discriminant is given as,
D = (-6)² - 4 × 4 × (2)
D = 4
Roots are real and distinct.
11. 0 = x² - 3x + 8, the discriminant is given as,
D = (-3)² - 4 × 1 × (8)
D = - 23
Roots are imaginary.
12. y = 5x² + 4x + 1, the discriminant is given as,
D = (4)² - 4 × 5 × (1)
D = -4
Roots are imaginary.
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Question In the coordinate plane, what is the length of the line segment that connects points at (5, 4) and (−3, −1)? Enter your answer in the box. Round to the nearest hundredth. units?
The length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.
Explain about the distance formula?The distance formula is still a formula used to determine how far apart two places are from one another. The dimensions of these points are unlimited. For instance, you could need to determine the separation between two points in space, a plane, or a line (1, 2, or 3 dimensions) .Using the formula obtained from Pythagoras' theorem, distance can be computed.
The distance formula in coordinate geometry is:
(P, Q) = √ (x2 – x1)² + (y2 – y1)².
Given points: (5, 4) and (−3, −1)
d = √ (-3 - 5)² + (4 + 1)²
d = √ 64 + 25
d = √ 89
d = 9.43
Thus, the length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.
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3. If circle 2 were a glide reflection of circle 1, what transformations would be involved?
dilation and reflection
rotation and translation
translation and reflection
reflection and rotation
According to the Cartesian plane graph, it can be inferred that the circle was rotated and translated (option B).
How to identify the movements that were made to circle 1 to become 2?To identify the movements that were made to circle 1 to become 2 we must carefully observe the graph. Once we have analyzed this graph we can infer the movements that were made to the circle. In this case, the rotation was performed because it can be seen that it was rotated having the coordinate (-1.5, 0.5) as a reference or point of rotation.
However, it was also translated because it was shifted a bit down and to the left. So the correct answer would be option B.
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Answer: rotation and translation
Step-by-step explanation: I took the quiz
During a lab experiment, the temperature of a liquid changes from 6.4°F to 10.75°F.
What is the percent of increase in the temperature of the liquid?
Enter your answer in the box as a percent rounded to the nearest hundredth. Help pls
Answer:
67.97%
Step-by-step explanation:
Answer:
67.97%
Step-by-step explanation:
use any method to solve the system of equation: 6x + 27y = -9
20x + 90y = -30
The graph shows the total cost c of buying one large bucket of popcorn and d large drinks. Write an equation from the graph that could be used to find the total cost c if you buy one large bucket of popcorn and d large drinks.
Answer:
[tex]y = 4d + 8\\[/tex]
Step-by-step explanation:
Since d is the number of large drinks, and there is always a constant of 1 large popcorn, we go to (0, 8). This concludes that since we start off with the cost of 8 dollars with no large drink but a large popcorn, the popcorn will stay a constant cost of $8. (the equation for this scenario is as shown):
y = md + 8
y (total cost)
m (coefficient - in this sense the cost of the drinks.)
d (amount of drinks)
8 (the constant of 8 represents the cost of one large popcorn consistently)
Now, lets find the cost of the dink.
Go to (1, 12).
$12 dollars is the total cost, with one drink and one large popcorn bought.
We have already discussed that we will have a constant of 8 because no matter the amount of drinks we will get, we would have bought 1 large popcorn at $8.
Therefore, we must subtract 8 dollars from 12.
12 - 8 = 4
From the total cost of everything we bought (2 things) and subtracting it with the cost one of the things we bought, we get the cost of the other thing.
each drink will cost $4.
Therefore, with all the variables and their listed meanings, this will be our given equation:
y = 4d + 8
Truth Tables 5. Translate each statement from symbolic notation into English sentences. Let A represent “Elvis is alive” and let G represent “Elvis gained weight”. a. A ⋁ G b. ~(A ⋀ G) c. G → ~A d. A ↔ ~G
a. A ⋁ G: Elvis is alive or Elvis gained weight.
b. ~(A ⋀ G): Elvis is not both alive and gained weight.
c. G → ~A: If Elvis gained weight, then Elvis is not alive.
d. A ↔ ~G: Elvis is alive if and only if Elvis did not gain weight.
I need help in this please
The x-intercepts and y-intercepts of the graph include the following:
x-intercept: B. -1.
y-intercept: D. none.
The equations for all vertical and horizontal asymptotes are as follows;
Vertical asymptote: x = 1.
Horizontal asymptote: y = 4.
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
What is an asymptote?In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).
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How do I evaluate the limit? How do I know which theorems to use
In the polynomial function given, the value of the limit as it approached infinity is 5/3
What is the value of the limitTo evaluate this limit, we need to determine the behavior of the function as x approaches infinity. To do this, we can use the fact that for any polynomial p(x) and q(x) of the same degree, the limit of p(x)/q(x) as x approaches infinity is equal to the ratio of the leading coefficients.
In this case, both the numerator and denominator are polynomials of degree 2, so we can apply this property. The leading coefficient of the numerator is 6 and the leading coefficient of the denominator is 7. Therefore, the limit as x approaches infinity of the given expression is:
lim [ (6x² - 5) / (7x² + x - 3)]
x → ∞ = 5/3
Therefore, the limit of the given expression as x approaches infinity is equal to 5/3.
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Working 8 hours a day, 48 men can complete a job in 1 week. How many men working 6 hours a day will complete the same job in 16 days?
The number of men needed to complete the same job in 16 days working 6 hours a day is given as follows:
28 men.
How to obtain the number of men?The number of men is obtained applying the proportions in the context of the problem.
The rule of three is given as follows:
n/48 = 8/6 x 7/16.
(the time is inverse proportional to the number of men, hence the fractions are inverted).
Thus:
n/48 = 56/96
Applying cross multiplication, the number of men is obtained as follows:
96n = 48 x 56
n = 48 x 56/96
n = 28 men.
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9 inches of ribbon is needed for wrapping one present. How many presents can be wrapped with 8 yards of ribbon?
Answer: 32 presents can be wrapped with 8 yards of ribbon
Step-by-step explanation:
Convert yards to inches
1 yard = 36 inches
8 yards = 288 inches
Divide 288 inches by 9 inches
288/9 = 32
Answer: You can wrap 32 presents with 8 yards.
Step-by-step explanation:
So, first, you need to know how many inches are in a yard. There are 36 inches in 1 yard.
Then, do 36 inches times 8 yards to figure out how many yards are in 8 yards. So in 8 yards, there are 288 inches.
Finally, do 288 divided by 9 to figure out how many present you can wrap with 8 yards (288 inches).
You can wrap 32 presents with 8 yards.
I hope this helped!
This question is for Geometry. If you know the answer, please send.
The measure of side AC of the right triangle is 7.2 units.
What is the measure of side AC?The figure in the image is the of a right triangle.
Angle A = 51 degreeOpposite to angle A = BC = 8.9Adjacent to angle A = ACTo solve for the measure of side AC, we use trigonometric ratio.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Tangent = Opposite / Adjacent
tan( A ) = BC / AC
Plug in the values and solve for side AC.
tan( 51° ) = 8.9 / AC
AC = 8.9 / tan( 51° )
AC = 8.9 / 1.234897
AC = 7.2
Therefore, side AC has a value of 7.2 units.
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Translate the sentence into an equation using n as the unknown number. Then solve the equation for n. Two times a number increased by 5 is 15. a. 2n(5) = 15 n = 1.5 c. 2n + 5 = 15 n = 20 b. 2n + 5=15 n = 5 d. n + 5 = 15 n = 10 Please select the best answer from the choices provided
Which of the following are true about the graph of the function f(x) = 2 (0.33^x)? Select the two correct answers
AThere is no x-intercept.
BThe graph passes through the point (1, 2).
CThe z-intercept is (0, 0).
DThe f(z)-intercept is (0, 2).
EThe graph passes through the point (2, 1).
$5 dollar less on dinner than James.
Answer:
x - 5
Step-by-step explanation:
Okay to write this problem as an expression it would be x -5. x represents James and -5 represents less than.
Answer:
x-5
Step-by-step explanation:
we don't know how much James has but we know it is $5 less so what ever the original amount is we are putting as x for now and we will subtract 5 because it is $5 less making our x-5.
4) The length and width of a rectangular box
are 10 in. and 8 in., respectively. Another
rectangular box has a length of 15 in. and a
width of 12 in. respectively. Are the length
and width dimensions of the two rectangular
boxes similar?
Answer:
Step-by-step explanation:
Yes, the length and width dimensions of the two rectangular boxes are similar.
Two objects are considered similar if they have the same shape, but not necessarily the same size. The ratio of the corresponding sides of two similar objects is called the scale factor.
For the first rectangular box, the ratio of length to width is 10/8, which can be simplified to 5/4.
For the second rectangular box, the ratio of length to width is 15/12, which can be simplified to 5/4 as well.
Since the ratio of the corresponding sides of the two boxes is the same, namely 5/4, we can conclude that the length and width dimensions of the two rectangular boxes are similar.
The graph shows g(x), which is a translation of f(x)=x2. Write the function rule for g(x).
The function g(x) is translation of f(x) 9 units up. The solution has been obtained by using transformation.
What is transformation?An operation known as a transformation involves moving a polygon or other two-dimensional object on a plane or coordinate system.
We are given that the function g(x) is a translation of the function
f(x) = x².
In the graph, we can see that the vertex of the parabola is at (0, 9).
This means that the function g(x) is 9 units up from the function f(x).
So, g(x) = x² + 9
Hence, the function g(x) is translation of f(x) 9 units up.
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you need to think about which __________ __________ you need to use
According to the information we can infer that sentence is completed with the words mathematical procedure.
How to complete the sentence?To complete the sentence we must identify the central idea and establish the right words to complete it. In this case, it is referring to a mathematical procedure then we could infer that these are the words that complete the sentence. Then the complete sentence would be like this:
You need to think about which Mathematical Procedure you need to use.Note: This question is incomplete. Here is the complete information:
Complementary information:
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please answer this is
Answer:
Its answer number 4
Step-by-step explanation:
The table at right shows speed limits in some foreign countries in kilometers per hour. One kilometer is equal to 0.6 miles. What are these speed limits in miles per hour?
As an example, the 78-mph speed limit in the United States is equivalent to the 130 km/h restriction in Germany.
How quick is that speed?
A connection with a speed of 100 Mbps or higher is considered fast internet. Broadband internet speed is defined by the federal communications regulator (FCC) as 25 Mbps for downloading and 3 Mbps for upload.
We can increase each number by 0.6 to convert overall speed limitations from kilometers per hour into miles per hour. Here is the revised table:
Country Speed Limit (km/h) Speed Limit (mph)
Germany 130 78
France 110 66
Italy 150 90
Japan 100 60
Australia 110 66
United Kingdom 113 67.8
Hence, Because one kilometer is equivalent to 0.6 miles, it is evident that speed limits in the form of miles per hour were lower than those in kilometers per hour.
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