The coefficient of x in the expansion of (x + 3)(x - 1) is
It’s either
2
-2
-3
4
Answers
Answer:
\({ \tt{(x + 3)(x - 1)}} \\ = { \tt{ {x}^{2} - x + 3x - 3 }} \\ = { \tt{ {x}^{2} + 2x - 3 }} \\ \\ { \boxed{ \bf{coefficient = 2}}}\)
Related Questions
A storage container in the shape of a square-based prism has a volume of 120 ft. If the sides of the square base are 4 ft in length, determine the height of the container.
Answers
9514 1404 393
Answer:
22.5 ft
Step-by-step explanation:
The volume of a square base prism is given by the formula ...
V = 1/3s²h
Then the height can be found to be ...
h = 3V/s² = 3(120 ft³)/(4 ft)² = 22.5 ft
The height of the container is 22.5 feet.
Oliver did the high jump three times. His scores were 7.016 feet, 5.42 feet, and 8.308 feet. How many feet did he jump in total? pleas help im in test
Answers
The total height of the three jumps is A = 20.744 feet
Given data ,
1st high jump score: 7.016 feet
2nd high jump score: 5.42 feet
3rd high jump score: 8.308 feet
On adding the scores , we get
7.016 + 5.42 + 8.308 = 20.744 feet
On simplifying the equation , we get
A = 20.744 feet
Hence , Oliver jumped a total of 20.744 feet in the three high jumps
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Mr. Martinez is buying hot dogs for a barbecue. Hot dogs are sold inpackages of 12 and hot dogs buns are sold in packages of 8. If he wants tohave an equal number of each, what is the LEAST number of hot dogs andbuns that Mr. Martinez will have to buy?
Answers
the batch of a hot dog contains 12 hot dogs
the batch of buns contains 8 buns
for equal no. of buns and hot dogs
so it will be the LCM of 12 and 8
4 x 2 x3 = 24
he has to buy 24 packets
I WILL MARK BRAINLIEST The account balance of each of three children at the end of a month is shown below: Kyle has -52.25 Jason has -52.00 Sue has as much savings in her account as the amount Kyle owes the bank. Part A: On a blank paper, draw a number line from -4 to +4. Plot points on the number line to show the account balances of the three children Label the points using the name of each of each child . describe in detail how you created and labeled this number line,and what it looks like in detail Part B: Determine whether Kyle or Jason owes the bank more Use absolute values and inequalities to write statements that justify your conclusion (5 points)
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Given:
Kyle's balance is -$2.25
Jason's balance is -$2.00
Sue's balance is: $2.25
Required:
A: plot and label the points on a number line from -4 to +4
describe how you did it
B: determine who owes more
Solution:
Part A: For the attached plot, we used the Desmos graphing calculator utility, giving it the points (-2.25, 0), (-2.00, 0), and (2.25, 0) to plot on x-y coordinates. The y-axis and minor grid lines are suppressed in order to better approximate a number line. The "label" facility is utilized to attach labels to the points.
Part B: Balances are owed to the bank when the balance is negative. The more negative it is, the more is owed. Kyle's point is farthest to the left on the number line (and is left of 0), so Kyle owes more. The ordering is ...
-2.25 < -2.00 < 0
where |-2.25| > |-2.00|. The number -2.25 is Kyle's balance, so he owes more.
Hello! The girl above me is correct :)
Brittany asked her classmates: How much time, in minutes, do you spend reading each day? Here are the results: 10, 20, 20, 20, 30, 30, 30, 30, 30, 40, 40, 40, 60, 60, 60 Display the data in a line plot, a histogram, and a box plot. Next to each graph, write down something you notice about the data. Upload your completed plots here.
Answers
The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.
Line Plot:
A line plot displays data points on a number line, representing the frequency or count of each value.
In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.
For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.
Histogram:
A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.
The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.
The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.
The height of each bar in the histogram will represent the number of students falling into each interval.
Box Plot:
A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.
The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.
The box will represent the interquartile range (IQR), showing the middle 50% of the data.
The line within the box will represent the median value.
The whiskers will indicate the minimum and maximum values, excluding outliers.
By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.
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22-3(4)
How do I answer this question?
Answers
Answer:
76
Step-by-step explanation:
22-3=19
19x4=76
22-3= 19
19 * 4= 76
I hope this helps! It’s my first time giving an answer
The table shows the number of admission tickets to an amusement park sold over the last 3 days.
Day Tickets Sold
Friday 2 to the power of 4 · 3 to the power of 2 · 5 to the power of 3
Saturday 2 to the power of 2 · 3 to the power of 4 · 7 · 13
Sunday 3 to the power of 6 · 5 · 7
How many more tickets were sold on Sunday than on Friday? Write your answer as a whole number.
HOW MANY tickets??!?
Answers
Answer:
There were 7515 more ticket sold on Sunday than on Friday.
Answer: There were 21915 sold on Sunday than on Friday.
EXPONENTIAL FUNCTIONS HELP Write the function for each graph described below. the graph of f(x) = 2x reflected across the x-axis. The graph of f(x)= 1/3x translated up 5 units. The graph of f(x) = 3x left 2 units, and down 3. The graph of f(x) = 1/2x translated down 2 units. The graph of f(x) = 4x stretched horizontally by a factor of 3. The graph of f(x) = 2x up 4 units, right 3.
Answers
Answer:
-2^x(1/3)^x +53^(x +2) -3(1/2)^x -24^(x/3)2^(x -3) +4Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
Answer:
-2^x
(1/3)^x +5
3^(x +2) -3
(1/2)^x -2
4^(x/3)
2^(x -3) +4
Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
Resuelva:
1) |3 x-1|-|2 x+5-(5-x)|=0
2) |2(x+1)-4|=|2-2(2-x)|
3) |x-2/4|-1/3=x
4) 1/2|x-3|-1=|x-3|+2
Answers
The solutions to the absolute functions |3x - 1| - |2x + 5 - (5 - x)| = 0, |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|, |(x - 2) / 4| - 1/3 = x and 1/2|x - 3| - 1 = |x - 3| + 2 are 1/6, 1, 2/15 and no solutions respectively
Absolute FunctionAn absolute value function is a function in algebra where the variable is inside the absolute value bars. This function is also known as the modulus function and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. Generally, we can represent the absolute value function as, f(x) = a |x - h| + k, where a represents how far the graph stretches vertically, h represents the horizontal shift and k represents the vertical shift from the graph of f(x) = |x|. If the value of 'a' is negative, the graph opens downwards and if it is positive, the graph opens upwards.
In the questions given;
Question 1
|3x - 1| - |2x + 5 - (5 - x)| = 0
x = 1/6
Question 2
|2(x + 1) - 4| - 4| = |2 - 2(2 - x)|
x = 1
Question 3
|(x - 2) / 4| - 1/3 = x
x = 2 / 15
Question 4
1/2|x - 3| - 1 = |x - 3| + 2
This equation does not have a solution
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I need help please... I don’t know the constant of proportionality... please I need this quick
Answers
Answer:
440 and 10
Step-by-step explanation:
i hop[e this is right
Is. She analyzes
st.
Martha graphs the data for the number of bracelets made, a, and the number of beads used,
y, and draws a line through the points.
Number of Beads Used
600
500
400
300
200
100
0
Bracelets Made
versus Beads Used
(31, 651)
(23, 483).
(10, 210)
5 10 15 20 25 30 35
Number of Bracelets Made
Write an equation that represents the relationship between the number of bracelets made
and the number of beads used. Show or explain how you found the slope and y-intercept.
Enter your equation and your work or explanation in the space provided.
You may use the drawing box to add a drawing to help explain your answer.
A
7
44
▶
Exhibits
P
Answers
The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.
First, the rate of change
= (483 - 210) / (23 - 10)
= 273 / 13
= 21
So, the equation for the relationship between the number of bracelets made and the number of beads used.
(y - 210) = 21 (x- 10)
y - 210 = 21x - 210
y = 21x
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Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 4p − 7 ≥ 9p + 8 true.
PLS HELP ME
Answers
The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5
Let's solve the inequality first
4p -7 \(\geq\) 9p +8
Taking p's on the same side we will get :
-7 - 8 \(\geq\) 9p - 4p
-15 \(\geq\) 5p
Divide by 5 into both sides
-3 \(\geq\) p
i.e. p \(\leq\) -3
Therefore p must be less than or equal to -3
From the set, we have the numbers -3,-4,-5 which are less than or equal to -3
Hence the integers -3,-4,-5 will make the inequality 4p-7 \(\geq\) 9p+8 true
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Estimate the slope of the tangent line (rate of change) to f(x) = ² at x = -1 by finding the slopes of
the secant lines through the points:
a. (-2,4) and (0,0)
secant slope, msec=
b. (-1.5, 2.25) and (-0.5, 0.25)
secant slope, msec=
Answers
a. The secant slope through (-2,4) and (0,0) is -2.
b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.
The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.
To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.
a. (-2,4) and (0,0):
The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:
msec = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
msec = (0 - 4) / (0 - (-2))
= -4 / 2
= -2
So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.
b. (-1.5, 2.25) and (-0.5, 0.25):
The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:
msec = (0.25 - 2.25) / (-0.5 - (-1.5))
= (-2) / (1)
= -2
So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.
By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.
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Gina charges an initial fee and an hourly fee to babysit. Using the table below find the hourly fee and the initial fee that
Gina charges to babysit. Show work.
Cost in Dollars
Answers
Answer:
13 dollars
Step-by-step explanation:
Enlargements math problem
Answers
Answer:
Step-by-step explanation:
What is Enlargement:
A transformation could involve enlargement. A transformation is a technique for moving or resizing a shape.
A center of enlargement is needed to enlarge a form.
When a shape is enlarged from a center of enlargement, the distances between each point and the center are multiplied by the scale factor.
So here We can see for A the length is 7-1 = 6.
The width of A is 5-2 = 7
and
The length of B is 5-3 = 2
The width of B is 9-8 = 1
So now,
A to B : Enlargement with a scale factor of \(\frac{2}{6}\) = \(\frac{1}{3}\)
From the image we can easily say that the center is at (11,4)
B to A: Enlargement with a scale factor of \(\frac{6}{2}\) = 3
From the image we can easily say that the center is at (11,4)
We can answer 2 questions from here:
1)What is enlargement ?
2)What is scale factor?
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Using the steps, we can find the lengths of the sides of the enlarged figure as follows: AB = 8cm , BC = 6cm ,AC = 10cm and CD = 12cm
What is Scale factor ?
Scale factor refers to a number that is used to multiply the dimensions of an object or system by a constant factor. This multiplication results in a proportional change in the size of the object or system while maintaining its shape.
This is a question related to enlargement in mathematics. To solve this problem, you can use the following steps:
Identify the scale factor by comparing the corresponding lengths in the original and the enlarged figure. In this case, we can see that the length of the side AB has been enlarged from 4cm to 8cm. So the scale factor is 8/4 = 2.
Use the scale factor to find the lengths of the other sides. For example, the length of BC in the original figure is 3cm. To find its length in the enlarged figure, we multiply it by the scale factor: 3 x 2 = 6cm. Similarly, we can find the lengths of the other sides: AC = 2 x 5 = 10cm and CD = 2 x 6 = 12cm.
Check that the angles have remained the same. Enlarging a figure using a scale factor does not change the angles, so we can check that the angles in the enlarged figure are the same as in the original figure.
Therefore, Using the steps, we can find the lengths of the sides of the enlarged figure as follows: AB = 8cm , BC = 6cm ,AC = 10cm and CD = 12cm
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Stuck on this one, help asap please
Answers
Answer:
Tan B = 24/10 = 12/5
Step-by-step explanation:
Tangent is opposite/adjacent. The side opposite of B is 24 and adjacent to that is 10.
HELP ASAP FOR LOTS OF POINTS AND BRAAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 4. What is the slope of any line that is parallel to the line 8x + 4y = 64?
A. 1/2
B. −2
C. −1/2
D. 2
Answers
Answer:
-2
Step-by-step explanation:
8x + 4y = 64 Put into slope intercept form
4y = -8x + 64
Divide by 4
y = -2x + 16
Slope is -2
whats is the spread of 4, 6, 7, 9, 9
Answers
So, the spread of the numbers 4, 6, 7, 9, 9 is 5.
What is spread?Spread can refer to different things depending on the context. Here are a few examples:
In finance, spread refers to the difference between the bid price and the ask price of a security or asset. The bid price is the highest price a buyer is willing to pay for a security, while the ask price is the lowest price a seller is willing to accept. The spread represents the cost of trading that security or asset and is typically measured in basis points (hundredths of a percentage point).
In sports betting, spread refers to the point spread or handicap that is assigned to a team in order to make the betting odds more even. For example, if a football team is favored to win by 7 points, they may be assigned a -7-point spread, meaning they would have to win by more than 7 points for a bet on them to be successful.
In epidemiology, spread refers to the transmission of a disease from one person to another. The spread of a disease can be influenced by a variety of factors, including the infectiousness of the disease, the proximity and frequency of contact between people, and the effectiveness of measures to prevent transmission (such as vaccines or masks).
In cooking, spread can refer to a variety of ingredients that are used to spread on bread or crackers, such as butter, jam, or peanut butter.
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In 2015, a city had a population of about 124,000. The population of the city increases by about 0.5% each year. Estimate the population of the city in 2032. Round your answer to the nearest thousand.
Answers
It is estimated that the population of the city will be about 135,000 in 2032.
What is the population of the city in 2032?To estimate the population of the city in 2032, we need to find the population after 17 years, since 2032 is 17 years after 2015.
First, we determine the annual increase in population due to the 0.5% growth rate.
We can do this by multiplying the current population by 0.5%:
annual increase = 0.5% × 124,000
annual increase = 0.5/100 × 124,000
annual increase = 0.5/100 × 124,000
annual increase = 620
This means that the population of the city will increase by approximately 620 people per year.
Next, we can estimate the population in 2032 by adding the total increase in population to the current population of 124,000:
estimated population in 2032 = 124,000 + (620 × 17)
estimated population in 2032 = 124,000 + 10,540
estimated population in 2032 = 134,540
Rounding to the nearest thousand,we get:
estimated population in 2032 = 135,000.
Therefore, it is estimated that the population of the city is 135,000.
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What is the ratio of 3 inches to 20 feet
Answers
Answer:
1/80
Step-by-step explanation:
Answer:
3 inches is 1/4th of one foot so to 20 ft is 1/80th
Step-by-step explanation:
Remember, 12 in.=1 FT
Hope this helps
;)
how do I find the indicated term in this geometric sequence?
Answers
A geometric sequence has a common ratio, in this case r = 0.1. The formula for the n term is aₙ = arⁿ⁻¹. where aₙ is the term of the sequence, a first term of the seuqence and r the commun ratio. So, aₙ = arⁿ⁻¹
a⁸ = (1,000,000) (0.1) ⁸⁻¹
a⁸ = (1,000,000) (0.1)⁷
a⁸ = 0.1
1 + 4 = 5
2 + 5 = 12
3 + 6 = 21
5 + 8 = ?
Answers
Hope this helps!!!!
Answer:
:)
Step-by-step explanation:
45
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how to find gcf's of numbers?
Answers
Answer: first list the prime factors of each number
Step-by-step explanation:
Suppose you stand 53 ft from a wind farm turbine. Your angle of elevation to the hub of the turbine is 56.5^{\circ} ∘ . Your eye level is 5.5 ft above the ground. To the nearest tenth, how tall is the turbine from the ground to its hub?
Answers
Let's denote the height of the turbine from the ground to its hub as "h". We can use trigonometry to solve for "h".
First, we need to find the distance from the observer's eye level to the base of the turbine. We can use the angle of elevation and the observer's distance from the turbine to find this distance.
Using the tangent function:
tan(56.5°) = h / (53 ft + 5.5 ft)
Simplifying and solving for "h":
h = tan(56.5°) * (53 ft + 5.5 ft)
h = 67.8 ft
Therefore, the height of the turbine from the ground to its hub is approximately 67.8 ft to the nearest tenth.
At the start of the day, a builder rested a 3 m ladder against a vertical wall so that the foot of the ladder was 70 cm away from the base of the wall. During the day, the ladder slipped down the wall, causing the foot of the ladder to move 50 cm further away from the base of the wall. How far down the wall, in centímetres, did the ladder slip? Give your answer to the nearest 1 cm. task Watch video
Answers
Answer:
17cm
70+50 =120cm
√(300^2 - 120^2) = 274.9cm
√(300^2 - 70^2) = 291.7cm
291.7 - 274.9 = 16.8cm ≈ 17cm
slope 0, passes through (0, –10)
a
y = –10
b
x = –10
c
y = –10x
d
y = x – 10
Answers
y=-10
Explanation:
The answer choices are all in slope-intercept form, which is this equation:
y=mx+b
Here’s what the variables mean:
Y=the y axis
M=the slope
X=the x axis
B=the point on the line that intercepts the y axis (the y-intercept)
We know the slope is 0, so 0 would be the m variable.
y=0x+b
We also know that the line passes through (0,-10), which means the y-intercept is -10.
y=0x+(-10)
0 multiplied by anything equals 0 and a negative and positive makes a negative, so we can rewrite the equation to be this:
y=-10
I hope this helps! Please comment if you have any questions.
Please help asap !!! I will give points !!!
Answers
The value of p when q is 2 is 1
What is inverse variation?Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.
This means that has x increases y will decrease and vice versa.
If p is inversely proportional to q , then p = kq
when p = 2, q = 4
2 = k4
k = 2/4
k = 1/2
When q = 2
p = 1/2 × 2
p = 1
Therefore the value of p is 1
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what's the answer?!!!
Answers
Answer:
6(y-2) would be 6y-12
Step-by-step explanation:
Verify that the given point is on the curve and find the lines that are a. tangent and b. normal to the curve at the given point.
Answers
Answer:
4, -4, 16, 16, truetangent: x - y = 8normal: y = -xStep-by-step explanation:
You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.
PointThe point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.
(a) TangentThe tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...
m = y/x = -4/4 = -1
The tangent line's slope is the opposite reciprocal of this:
m = -1/(-1) = 1
The point-slope form of the equation for the tangent line is ...
y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)
y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)
x -y = 8 . . . . . . . . . . add 4-y to put in standard form
The equation of the tangent line is x - y = 8.
(b) NormalIn the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...
y -0 = -1(x -0)
y = -x
The equation of the normal line is y = -x.
__
Additional comment
The normal line can also be written as x + y = 0.
The tangent line can also be written as y = x -8.
<95141404393>
Please see the attached
Answers
(a). The Tanakas paid a total of $523,906.40 for the townhome.
(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.
What is simple intresst?Simple interest is the type of interest that is calculated on the principal amount only.
It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.
(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.
Down payment = $41,000
Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40
Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40
(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.
Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000
Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40
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