Therefore , the solution of slope intercept comes out to be X intercept for the function is x = - 1
What does slope intercept mean?In math, the intersection is where the line's slope intersects the y-axis. a point on a line or curve where the y-axis crosses. The formula for the linear line is given as Y = mx+c, whereby m denotes the slope и c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercepting form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to appear to be slope detections. The slope and como are both modified to 1 if y=x is translated as y=1x+0, for example.
Here,
It is the point where a line or curve crosses the X axis
The function f(x) = x³ + x² - 6x = c
Let, y = f(x) = x³ + x²- 6x -c =0
at the X intercept, y = 0,
so, 0 = x³+ x²- 6x -6
x²(x +1) - 6(x +1) =0
(x +1) ( x²-6) = 0
x = -1, x = √6
X intercept is x = -1
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x + 2y = 2 y = −2x − 2
The solution of the system of equations is (-2, 2).
How to solve the system of equations?Here we want to find the solution of the system of equations:
x + 2y = 2
y = -2x- 2
To solve this, we can replace the second equation into the first one, then we will get:
x + 2*(-2x - 2) = 2
Now we can solve that for x:
x - 4x - 4 = 2
-3x = 2 + 4
-3x = 6
x = 6/-3 = -2
Thus, the value of y is:
y = -2*-2 - 2
y = 4 - 2 = 2
The solution of the system is (-2, 2)
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Complete question:
"Which is the solution of the system of equations?
x + 2y = 2
y = -2x- 2"
Identify the part, percent and base.
$37.60 interest earned on a $460 investment at 8%.
Part:
Percent:
Base:
The given information is,$37.60 interest earned on a $460 investment at 8%.
Part:The amount of interest earned is called the part. Here, the amount of interest earned is $37.60. Hence the part is $37.60.
Percent:The rate per 100 units of the base is called the percent. Here, the percent rate is 8%.
Base:The original amount invested or borrowed is called the base. Here, the original investment amount is $460. Hence the base is $460.
Thus,
Part: $37.60
Percent: 8%
Base: $460.
Part: The part is the interest earned, which is $37.60.
Percent: The percent is 8%, which represents the annual interest rate.
Base: The base is the amount of the investment, which is $460.
the box plot below represents some data set. what percentage of the data values are greater than 130
The percentage of the data values that are greater than 130 is 25%
What percentage of data values are greater than 130From the question, we have the following parameters that can be used in our computation:
The box plot
From the box plot, the five-number summary are
40, 70, 110, 130, and 150
In the above five-number summary, we have
Third quartile = 130
This means that the percentage of the data values that are greater than 130 is 25%
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Find the 5th term in the expansion of (3x + 1)7 in simplest form.
The 5th term in the expansion of [tex](3x + 1)^7[/tex] would be [tex]945x^3[/tex].
Binomial expansionTo find the 5th term in the expansion of [tex](3x + 1)^7[/tex], we use the binomial theorem formula:
[tex](a + b)^n = nC0 a^n b^0 + nC1 a^(n-1) b^1 + nC2 a^(n-2) b^2 + ... + nCn-1 a^1 b^(n-1) + nCn a^0 b^n[/tex]
where nCk represents the binomial coefficient, given by the formula:
nCk = n! / (k!(n-k)!)
In this case, a = 3x and b = 1, so we have:
[tex](3x + 1)^7 = 7C0 (3x)^7 1^0 + 7C1 (3x)^6 1^1 + 7C2 (3x)^5 1^2 + 7C3 (3x)^4 1^3 + 7C4 (3x)^3 1^4 + 7C5 (3x)^2 1^5 + 7C6 (3x)^1 1^6 + 7C7 (3x)^0 1^7[/tex]
To find the 5th term, we need to look at the term with k = 4, which is:
[tex]7C4 (3x)^3 1^4[/tex] = [tex]35 (3x)^3[/tex]
= [tex]35 (3x)^3[/tex]
= [tex]35 (27x^3)[/tex]
Therefore, the 5th term in the expansion of [tex](3x + 1)^7[/tex] is [tex]945x^3[/tex].
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Need help, show work please
Using the first two points we can get an exponential model:
[tex]y = (225/23)*(23/15)^x[/tex]
How to find the exponential equation?
The general exponential equation can be written as:
[tex]y = A*(b)^x[/tex]
We can replace any two values of the table to get the system of eqautions:
[tex]15 = A*(b)\\\\23 = A*(b)^2[/tex]
Taking the quotient between the second and the first equation we get:
[tex]23/15 = (A*b^2)/(A*b)\\\\23/15 = b[/tex]
Replacing that on the first equation we will get:
[tex]15 =A*(23/15)\\15*(15/23) = A\\225/23 = A[/tex]
Then an exponential model is:
[tex]y = (225/23)*(23/15)^x[/tex]
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Nancy flew home from vacation with a heavy bag. With the first airline she flew, Nancy had to pay $20 to check her bag, plus $5 for every pound that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Nancy had to pay $4 per pound that her bag was over the weight limit, in addition to the checked bag fee of $25. By coincidence, the fees ended up being the same with both airlines. How far over the weight limit was the bag? Write a system of equations, graph them, and type the solution.
Nancy's bag was 0.2kg over the weight limit.
What weight in which Nancy's bag exceeded limit?Let's denote the weight limit as x.
The total cost for the first airline can be expressed as:
Cost1 = 20x + 5
The total cost for the second airline is given by:
Cost2 = 25x + 4
As fees were same with both airlines, we will set up equation to find the weight difference:
20x + 5 = 25x + 4
20x-25x = 4-5
-5x = -1
x = -1/-5
x = 0.2kg
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Help Quickly! Which line in the graph contains the point (4,3) and has a slope of 2/5?
*Giving Brainlyest if correct*
A. line r
B. line p
C. line s
D. line t
Simplify the expression
log₂8³x
Answer:
We can simplify the expression log₂8³x using the following logarithmic rule:
logₐb^c = c * logₐb
Using this rule, we can rewrite the expression as:
log₂8³x = 3log₂8 + log₂x
We can further simplify by recognizing that 8 can be expressed as a power of 2:
8 = 2³
Substituting this in, we get:
3log₂8 + log₂x = 3log₂(2³) + log₂x = 3 * 3 + log₂x = 9 + log₂x
Therefore, the simplified expression is:
log₂8³x = 9 + log₂x
Step-by-step explanation:
The distribution for the life of refrigerators is approximately normal with a mean of 14 years and a standard deviation of 2.5 years. What percentage of refrigerators have lives between 11 years and 18 years?
The percentage of refrigerators that have lives between 11 years and 18 years is approximately 83.01%.
The values of 11 years and 18 years using the given mean and standard deviation, and then find the area under the standard normal curve between those two standardized values.
First, we standardize the value of 11 years:
z1 = (11 - 14) / 2.5 = -1.2
Next, we standardize the value of 18 years:
z2 = (18 - 14) / 2.5 = 1.6
Now we need to find the area under the standard normal curve between these two standardized values.
We can use a standard normal table or calculator to find this area.
Using a standard normal table, we can find the area between z = -1.2 and z = 1.6 by finding the area to the left of z = 1.6 and subtracting the area to the left of z = -1.2:
Area = P(-1.2 < z < 1.6) = P(z < 1.6) - P(z < -1.2)
Looking up these values in the standard normal table, we find:
P(z < 1.6) = 0.9452
P(z < -1.2) = 0.1151
Substituting these values, we get:
Area = 0.9452 - 0.1151 = 0.8301
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A car travels for 10minutes.
At the beginning of the trip, the car traveled at a speed
of 13 m/s. At the end of the trip the car was traveling at a speed of 6 m/s. What is
the acceleration of the car?
Answer:
0.01167 m/s^2
Step-by-step explanation:
Acceleration is chage in velocity with respect to time. Another way to think of acceleration is in the units: m/s^2, or as I like to say, (m/s) /s.
The strategy to solve this kind of problem is to find the change in velocity (which will be in units of m/s)... and then divide that by the time passed.
In this case:
Change in Velocity = (13 m/s) - (6 m/s) = 6 m/s
Time passed = 10 min
Converting units of time: 10 min * (60 s / 1 m) = 600 sec
Acceleration = Change in Velocity / Time Passed
Acceleration = (6 m/s) / (600 s)
Acceleration = 0.01167 m/s^2
Write an expression to show how much it will cost if Kenny buys x number of hotdogs and each hot dog costs $2.
The expression to show how much it will cost if Kenny buys x number of hotdogs is x * $2.
To find the total cost if Kenny buys x number of hotdogs, we can multiply the number of hotdogs (x) by the cost per hotdog ($2). The expression to calculate the cost would be:
Total Cost = x * $2
In this expression, x represents the number of hotdogs Kenny wants to buy, and $2 represents the cost per hotdog.
For example, if Kenny wants to buy 5 hotdogs, we can substitute x with 5 in the expression:
Total Cost = 5 * $2
Simplifying the expression:
Total Cost = $10
So, if Kenny buys 5 hotdogs, it will cost him $10 in total.
Similarly, if Kenny buys any other number of hotdogs, we can substitute that value for x in the expression to calculate the corresponding total cost.
In summary, the expression to show how much it will cost if Kenny buys x number of hotdogs is x * $2.
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LUUK al uit grapii velow.
Part B
-4
Part A
-3-2
Part C
3
2
-2
-3
Part D
Which part of the graph best represents the solution set to the system of
inequalities y ≥x+1 and y + x>-1? (5 points)
The solution set of given inequalities are represented by Part A.
The given inequalities are
⇒ y ≥ x + 1 and y + x > -1
Hence, The related equations of both inequalities are
y = x + 1
Put x=0, to find the y-intercept and put y=0, to find x intercept.
y = 0 + 1
y = 1
And, 0 = x + 1
x = - 1
Therefore, x-intercept of the equation is (-1,0) and y-intercept is (0,1).
Similarly, for the second related equation
y + x = - 1
y + 0 = - 1
y = - 1
0 + x = - 1
x = - 1
Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,-1).
Now, join the x and y-intercepts of both lines to draw the line.
Now check the given inequalities by (0,0).
0 ≥ 0 + 1
0 ≥ 1
It is a false statement, therefore the shaded region is in the opposite side of origin.
0 + 0 ≥ - 1
0 ≥ - 1
It is a true statement, therefore the shaded region is about the origin.
Hence, From the below figure we can say that the solution set of given inequalities are represented by Part A.
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Haleigh decides that instead of throwing away old candles, she can use the last bit of wax combined together to make new candles. Each candle has 10% of it's original wax left. How many 5 ounce candles can she make if she has five 20 oz candles, 5 five ounce candles, and twenty-five one-ounce candles?
Answer:she can make three 5 ounce candles. she had 15 ounces left over , 15/5=3 .
Step-by-step explanation: 5 of 10% of 20 ounces is 10 ounces, and both the 5 five ounce candles and the twenty five one ounce candles are each 2.5 extra ounces left. (5 for both), making a totalm of 15 ounces left to put into new candles.
At the beginning of the week, James has 8 quarts of milk. At the end of the week there are 412 cups of milk left.
How many cups of milk did James drink during the week?
James drank [tex]$27 \frac{1}{2}$[/tex] cups of milk during the week
To determine how many cups of milk James drank during the week, we need to find the difference between the initial amount of milk and the amount of milk left at the end of the week. The initial amount of milk: 8 quarts = [tex]$8 \times 4 = 32$[/tex] cupsThe remaining amount of milk: [tex]$4 \frac{1}{2}$[/tex] cupsTo find the amount of milk James drank, we subtract the remaining amount from the initial amount: [tex]$32 \text{ cups} - 4 \frac{1}{2} \text{ cups} = 27 \frac{1}{2}$[/tex] cupsThe concept used in this problem is subtraction. By subtracting the amount of milk left at the end of the week from the initial amount of milk, we can determine how much milk James consumed during the week. The difference between these two values represents the amount of milk that James drank.Therefore, James drank [tex]$27 \frac{1}{2}$[/tex] cups of milk during the week.
NOTE: The given question has wrong information. The correct question is:
"At the beginning of the week, James has 8 quarts of milk. At the end of the week, there are [tex]$4 \frac{1}{2}$[/tex] cups of milk left. How many cups of milk did James drink during the week?"
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Question 14 of 15
Which number line shows the solutions to x+8 > 15?
A number line that shows the solutions to x+8 > 15 include the following: B. number line B.
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Based on the information provided above, we have the following equation (inequality);
x + 8 > 15
By subtracting 8 from both sides of the equation (inequality), we have;
x + 8 - 8 > 15 - 8
x > 7
This ultimately implies that, the inequality must be shaded to the right with an open dot because the inequality symbol is greater than (>).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Convert
24 in = ___________ ft
700 cm. =__________m
Answer:
0.24ft
7m
Step-by-step explanation:
A school class went on a field trip to see a magician perform there were 17 females 20 males in the class the magicians randomly selected a volunteer from the audience in which had 52 females and 68 males given that the randomly selected audience member is a student from the class which equation can be used to find the probability p that the perdimos also a female?please help does anyone know the answer
2
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The probability p that the perdimos is also a female is 17/120
What is Conditional Probability?Conditional Probability is the possibility or likelihood of an event or outcome happening, based on the existence of a previous event or outcome.
How to determine this
When there were 17 females in class
And 20 male in class
When randomly selected, the female are 52
And males are 68
To calculate the selected volunteer is a student of the class.
= 20 + 17/52 + 68
= 37/120
To calculate the probability that the selected student is female.
= 17/52 + 68
= 17/120
= 0.14
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Flip a half a day league table in her kitchen, the lacewings from one corner of the table to the middle of the far side of the table. How long is the gateleg table?
The length of gateleg of the table whose leg swings from one corner of the table to the middle of the far side of the table top is 53 inches long.
The shape forms a trapezoid
The length of the parallel side = is 56 in
The length of the base = is 45 in
To the length of the triangle formed when the base of the gateleg is connected with the middle of the table
The length of the side when connected with the midpoint = 56/2 = 28
The length of gateleg = hypotenuse
Using Pythagorean theorem :
(hypotenuse)² = (base)² + (perpendicular)²
(hypotenuse)² = (45)² + (28)²
(hypotenuse)² = 2025 + 784
(hypotenuse)² = 2809
hypotenuse = 53
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The question is incomplete the complete question is :
Philippa has a gateleg table in her kitchen. The leg swings from one corner of the table to the middle of the far side of the tabletop, as shown in the sketch below.
Note: The figure is not drawn to scale.
How long is the gateleg of the table?
A.) 53 inches
B.) 49 inches
C.) 73 inches
D.) 72 inches
Select the correct answer from the drop-down menu. The missing term in the denominator is
Answer: where is the answer choices
Step-by-step explanation:
find the surface area of a regular hexagonal pyramid with the base edges of 10 and a slant height of 9 inches.
The surface area of the regular hexagonal pyramid is equal to 529.8 in² to the nearest tenth.
How to calculate for the surface area of the regular hexagonal pyramidArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of nonagon × (n)number of side
apothem = s/[2tan(180/n)]
apothem = 10in[2tan(180/6)]
apothem = 5√3in
perimeter = 6 sides × 10in = 60 in²
Area of the bottom hexagon = 1/2 × 5√3 × 60 in²
Area of the bottom hexagon = 259.8075 in²
Area of one triangle side face = 1/2 × 10in × 9in = 45 in²
Area of 6 triangle side faces = 6 × 45 in² = 270 in²
Surface area of the regular pyramid = 259.8075 in² + 270 in²
Surface area of the regular pyramid = 529.8 in²
Therefore, the surface area of the regular hexagonal pyramid is equal to 529.8 in²
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Suppose you pick 4 cards randomly from a well shuffled standard deck of 52 playing cards. The probability that you draw the 2,4,6, and 8 of spades in that order is
The probability of drawing the 2, 4, 6, and 8 of spades in that specific order is 0.0002.
What is the probability?The probability of drawing a specific card without replacement from a well-shuffled deck is 1/52 for the first card, 1/51 for the second card, 1/50 for the third card, and 1/49 for the fourth card.
We wish to draw the specific cards (2, 4, 6, and 8 of spades) in that specific order.
The probability will be:
Probability = (1/52) * (1/51) * (1/50) * (1/49)
probability = 0.0002.
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You are holding a kite string in your hand and your hand is 3 feet above the ground. The kite is 225 feet above the ground and the angle of elevation from your hand to the kite is 42°. How long is the kite string?
The kite string is 331.77 feet long.
How to find how long the kite string is?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Check the attached image for labeling. Where l represents the length of kite string.
h = 225 - 3 = 222 ft
Using trig. ratio:
sin 42° = 222/l
l = 222 / sin 42°
l = 331.77 feet
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There were 104 females and 78 males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.
Answer:
The ratio is 3:7
Step-by-step explanation:
You add 104+78
The un-simplified ratio is 78:182
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Extract the common factor from
(1) 2.x-2.y
(2) 5.x.x.x+5.3.x.y
Answer:
(1) 2x - 2y = 2(x - y)
(2) 5x^3 + 15xy = 5x(x^2 - 3y)
Find your answer on above picture ihope it will help you thank you.
The athletic department spent $1,204 on airline tickets and $600 on hotel costs for the 4 members of the tennis team. How much was spent for each member of the tennis team?
HELP ME ASAP PLEASE
Answer:
451$
Step-by-step explanation:
$1,204 + $600 = 1804$
Since there are 4 members on the team, we divide the total sum of costs by 4.
$1804/4 = 451$.
Answer:
The athletic department spent $1,204 on airline tickets and $600 on hotel costs for the 4 members of the tennis team. To find out how much was spent for each member of the tennis team, you can add the cost of airline tickets and hotel costs and then divide by the number of members.
So, the total cost for airline tickets and hotel costs is $1,204 + $600 = $1,804. Since there are 4 members on the tennis team, the cost per member is $1,804 ÷ 4 = $451.
Therefore, $451 was spent for each member of the tennis team.
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What the meaning of statement this?
The statement means that an n-ary operation on set X takes n inputs and produces a single output, with the operation defined by the function f:[tex]X^n[/tex] -> X.
The statement "An n-ary operation on x is functions f:X^n -> X" can be understood as follows:
In mathematics, an n-ary operation refers to an operation that takes n inputs and produces a single output. In this case, the operation is defined on a set X, and the inputs are elements from X. The result of the operation is also an element from X.
The symbol "f" represents the function that performs the n-ary operation. The function f takes n arguments, which are elements from the set X. The notation [tex]X^n[/tex] indicates the Cartesian product of X with itself n times, meaning that the inputs are taken from X and repeated n times as ordered tuples. The arrow "->" signifies that the function f maps the n-tuple of inputs to a single element in X.
To put it simply, the statement is describing a mathematical operation that takes n elements from a set X and combines them in some way to produce a single element, where the combination is determined by the function f. This function f can be defined explicitly based on the specific operation being considered.
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Solve 2(2x-5)=3x+x-2x
Answer:
5=x
Step-by-step explanation:
Q=2(2x-5)=3x+x-2x
SOLUTION:
4x-10=4x-2x
-10=2x-4x
-10= -2x
(-+-=+ so 10 and 2 are positive now)
10/2=x
5=x
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Answer:
1. x = 13.75
2. 17 degrees
3. a = 4, b = 2√2
Step-by-step explanation:
1. cos(37) = 11/x
since cos(37) = 4/5
4/5 = 11/x
4x = 55
x = 13.75
2. tan(0) = opp/adj
tan(0) = 4/13 = 0.30769
=> (0) = 17.1 degrees or 17 degrees
3. since the triangle is right triangle with 2 angles of 45 degress
=> isosceles right triangle
then b = 2√2
a^2 = (2√2)^2 + (2√2)^2
a^2 = = 8 + 8 = 16
a = √16= 4
increase a gross by 10%
The results of increasing a gross by 10% is 158.4.
What is percentage?Percentage refers to the amount, number or rate of something, regarded as part of a total of 100.
In mathematics, gross is written in figures as 144
increase a gross by 10%
= 144 + (10% × 144)
= 144 + (0.1 × 144)
= 144 + 14.4
= 158.4
Hence, 158.4 is the 10% increase in gross.
Complete question:
Calculate the increase in a gross by 10%.
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WORTH 25 points
Find the area of the parallelogram with given points.
(7,4)
(3,0)
(-4,9)
(13,0)