The total area of the two triangles is 28 square inches.
Step 1: Calculate the area of the first triangle.
The first triangle is a right triangle with a base of 4 inches and a height of 3 inches.
Area of a triangle = (1/2) * Base * Height
Area of the first triangle = (1/2) * 4 * 3 = 6 square inches.
Step 2: Calculate the area of the second triangle.
The second triangle is an isosceles triangle with a base of 4 inches and a height of 4 inches.
Area of a triangle = (1/2) * Base * Height
Area of the second triangle = (1/2) * 4 * 4 = 8 square inches.
Step 3: Add the areas of the two triangles.
Total area = 6 + 8 = 14 square inches.
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a mathematical organization is producing a set of commemorative license plates. each plate contains a sequence of five characters chosen from the four letters in aime and the four digits in $2007$. no character may appear in a sequence more times than it appears among the four letters in aime or the four digits in $2007$. a set of plates in which each possible sequence appears exactly once contains $n$ license plates. find $\frac{n}{10}$.
On solving the provided question we can say that there are 7!/(7-5)! potential sequences if 0 appears 0 or 1 times in the sequence.
what is a sequence?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.
N/10 has a value of 372.
The letters can be selected from the words "AIME" or "2007."
The only number that can be repeated twice is 0; there are seven different characters that can be chosen.
There are 7!/(7-5)! potential sequences if 0 appears 0 or 1 times in the sequence.
There are 2520 possible sequences if 0 appears 0 or 1 times in the sequence.
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Solve the system of equations – 8x + 6y = 14 and -5x + 2y = -7 by combining
the equations.
-
|(- 8x +y = 14)
(- 5a +2y =-7)
- 8x t6y = 14
-5 +2y =-7
0x + 0y
try
For the given system of equations the value of x is 0.27 and the value of y = 2.7.
What is system of equations?A system of equations in algebra consists of two or more equations and looks for common answers. A group of equations that have the same set of variables as solutions are referred to as a system of linear equations.
The given equations are:
-8x + 6y = 14 and
-5x + 2y = -7
For the equation -5x + 2y = -7 isolate the value of x:
-5x = 7 - 2y
x = - (7 - 2y) / 5
Substitute the value of x in the equation -8x + 6y = 14.
[tex]-8 (\frac{7-2y}{5} ) +6y =14\\\\-11.2 + 3.2y + 6y =14\\\\9.2y = 14 + 11.2\\\\y = 2.7[/tex]
Substitute the value of y in any one of the equations:
-8x + 6(2.7) = 14
-8x = 14 - 16.2
x = 0.27
Hence, the value of x is 0.27 and the value of y = 2.7.
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the hawks won 65% of their 60 games this year . how many games did they win ?
Answer: 24 games
Step-by-step explanation: 60-60%=24
how to do distributive law in factorization?
Answer: it’s lar and we can’t compete against each other
Step-by-step explanation:
Do the sides 7 cm 24 cm and 25 cm form a right-angled triangle give reason?
The sides 7cm , 24cm and 25cm ; forms a right angled triangle because the condition of Pythagoras Theorem is satisfied .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that the square of hypotnuse (longest sides) is equal to the sum of the square of the other two sides .
The sides are given as ⇒ 7cm , 24cm and 25cm ;
here the longest side (hypotnuse) is = 25 cm ;
According to Pythagoras theorem ,
⇒ [tex]25^{2} =24^{2} +7^{2}[/tex] ;
⇒ [tex]625=576+49[/tex] ;
⇒ [tex]625 = 625[/tex] ;
The condition of Pythagoras theorem is satisfied .
Therefore , the given sides can form a Right Angled Triangle .
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HELP can all regular polygons fit in a larger polygon?
The property of square depicted is not common for all regular polygon
What is a regular polygon?If a polygon's sides and angles are equal, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a regular quadrilateral is a square.
The property showed how the square was merged with every two sides fully overlapping to form a bigger square
The trapezium which can also be a regular polygon (quadrilateral) lacks such property of arranging four trapeziums side by side, making overlaps that will form a bigger trapezium.
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find a cartesian equation for the curve and identify it. r = 7 cos(θ)
The cartesian equation for the curve r = 7 cos(θ) is [x -(7/2)]²+y² = 49/4, which is the equation of a circle.
Given r =7 cosθ
Multiplying throughout by ‘r’,
r² =7r cos θ --- (1)
Consider x² + y² = r² and put x = r cos θ --- (2)
x² + y² = 7x
Using completing the square method:
x² - 7x + (7/2)² + y² = (7/2)²
[x - (7/2)]² + y² = 49/4
(x - 7/2)² + (y - 0)² = (7/2)²
This is the equation of the circle with a center (7/2, 0) and radius of 7/2.
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7 less than the product of a number n and 1/5 is no more than 95 .
ANSWER:
STEP-BY-STEP EXPLANATION:
We must interpret each sentence mathematically, just like this:
Less then would be a subtract
Product would be a multiplication
No more than would be equal or less than
Answer:
.2n-7≤95
.2n≤102
n≤510
hope this helps
claire jogs $6$ miles per hour and megan jogs $5$ miles per hour. they start together at their campsite and jog to an outpost $18$ miles away. when claire gets there, she immediately turns around and heads back towards megan. how many miles will they be from the outpost when they meet? express your answer as a mixed number.claire jogs $6$ miles per hour and megan jogs $5$ miles per hour. they start together at their campsite and jog to an outpost $18$ miles away. when claire gets there, she immediately turns around and heads back towards megan. how many miles will they be from the outpost when they meet? express your answer as a mixed number.
When Claire and Megan meet, they will be $13\frac{1}{2}$ miles away from the outpost.
What is speed?Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.
This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone $9$ miles, and Megan will have gone $8\frac{1}{2}$ miles. When they meet, they will have gone a total of $17\frac{1}{2}$ miles, leaving them $13\frac{1}{2}$ miles away from the outpost.
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When Claire and Megan meet, they will be [tex]13\frac{1}{2}[/tex] miles away from the outpost. This can be solved by applying the concept of speed.
What is speed?Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.
This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone 9 miles, and Megan will have gone [tex]8\frac{1}{2}[/tex] miles. When they meet, they will have gone a total of [tex]17\frac{1}{2}[/tex] miles, leaving them [tex]13\frac{1}{2}[/tex]miles away from the outpost.
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Determine the reactions at the roller A and pin B.B. 4 m 450 N 600 NmA. 2 m 3 m
The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N. To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N).
Reaction at Roller A:
2 m * 900 N = 1800 N
Reaction at Pin B:
3 m * 450 N + 600 N = 2450 N
To calculate the reaction at Roller A, you need to multiply the length of the roller (2 m) by the load (900 N). This gives you 1800 N.
To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N). This gives you 2450 N.
The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N.
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______ are measures of center that summarize a typical data point
in a data set.
A. Mean and median
B. Median and interquartile range
C. Mean and mean absolute deviation
D. Mean absolute deviation and interquartile range
PLEASE HELP WITH EXPLAINING ill give brainliest!
After Ms. Wilson pays her federal taxes, D. She will receive a refund of $ 258.
Why will she receive a tax refund ?A tax refund is given when an individual or business overpays their taxes to the government during the year. It happens when the taxes that an individual or business paid through the year (withholding taxes or estimated taxes) are more than their actual tax liability for the year.
Going by the table, Ms. Wilson at her Single filling status was meant to pay the tax amount of $ 5, 086 in federal taxes and instead paid $ 5, 344. She will therefore get a refund of :
= 5, 344 - 5, 086
= $ 258
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Question
Points A , B , and C are three vertices of a rectangle. Plot the three points. Then find the coordinates of the fourth point, D , to complete the rectangle. Finally, write the equation of the line that passes through points B and D and forms a diagonal of the rectangle. �
(
−
2
,
3
)
,
�
(
4
,
3
)
,
�
(
4
,
−
1
)
A(−2,3),B(4,3),C(4,−1)
The fourth co-ordinate of the rectangle is D (-2, -1). The equation of the line that passes through the points B and D is 3y = 2x + 3.
The given points are:
A(−2,3), B(4,3), C(4,−1)
When we plot these points on the graph we can easily estimate the fourth point which will be equidistant from A as the point C is from B and from the point C as the point A is from B.
Therefore, the diagonal points are B(4, 3) and D(-2, -1).
The equation of the line between these two points is:
(y - y1) = ((y2 - y1)/(x2 - x1)) (x - x1)
(y - 3) = ((-1 -3)/(-2 - 4)) ( x - 4)
y - 3 = (2/3) (x - 4)
3y - 9 = 2x - 8
3y = 2x + 1
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a library is having a book sale to raise money hardcover book scost $4 each and paperback books cost $2 each. a person spends $26 for 8 books. how many of each type of book did she buy
Answer: 5 hardcover and 3 paperback
Step-by-step explanation: To solve, we need to keep this question in mind:
"How many books can we buy for each without going over the initiate amount [$26]?"
So, let's start with the $4 books, so knowing our multiples of 4
ex. 4, 8, 12, 16, 20, 24, 28......
So, I listed the example of the multiples. So, it can be either 20 or 24. So, it would be 20, because it is under the initiate amount AND it is less with unincluded paperback books. So, 26-20 = 6. So, if each paperback book costs $2, we need to divide 6 by 2. That's 3. So, therefore, she can buy 5 hardcovers and 3 paperbacks by spending all the money. I hope this helps!
concept check 1. another word for mean is . margin centric statistic average product 2. which measure of central tendency is affected by outliers? mean median both mean and median mean, median, and mode 3. when would you calculate an expected value? when you need to know the exact outcome of a future, unknown event when your data points occur on different dates when you only have one data point when your data points have various probabilities of occurring 4. what is the median of the following set of numbers: 4, 0, -3, 5, 1, 3, -2? 3 5 1.14 1 5. true or false: the mode is universally an accurate representation of data sets because it captures the number that occurs most often. true false
Answer:
Another word for the mean is "average".
Which measure of central tendency is affected by outliers? Mean.
When would you calculate an expected value? when your data points have various probabilities of occurring.
What is the median of the following set of numbers: 4, 0, -3, 5, 1, 3, -2? 3.
True or false: The mode is universally an accurate representation of data sets because it captures the number that occurs most often. False. Mode is not always an accurate representation of data sets and it may not exist in certain data sets.
Step-by-step explanation:
Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase (y) for different number of tickets (x) in the table shown. Do not add any spaces when typing in the equation.
The equation that models this linear function is y = 12.5x + 7.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept.Next, we would determine the slope of the data points in this table as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (44.50 - 32.00)/(3 - 2)
Slope, m = 12.5/1
Slope, m = 12.5.
At point (2, 32.00), a linear equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - 32.00 = 12.5(x - 2)
y - 32.00 = 12.5x - 25
y = 12.5x - 25 + 32.00
y = 12.5x + 7
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Complete Question:
Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase (y) for different number of tickets (x) in the table shown. What is the equation that models this linear function?
Write the set using the descriptive method:
(5, 10, 15, 20, 25}
Answer: study dum ahh
Step-by-step explanation:
A quare piece of cloth i ize 25 m quare i cut into rectangle trip of 50 50 cm wide find the number of tate and their total length in metre
All of the rectangles together measure 1250 meters in length.
A textile square with a 25 square meter surface area. We are aware that the area of a square is determined by multiplying one side's length by itself. The square root of 25 square meters, or 5 meters, is the length of one side of the square in this instance.
Secondly, we are aware that the fabric is being cut into 50 cm-wide rectangles. We can use the following formula to determine each rectangle's length:
(Rectangle width) x (Square cloth length) / (Width of square cloth)
The equation in this instance is (50 cm) x (25 m) / (5 m) = 2500 cm or 25 meters.
Therefore, each rectangle is 25 meters long.
We divide the square cloth's length by each rectangle's width to get the total number of rectangles.
25m / 0.5m (50cm) = 50 rectangles.
Finally, we multiply the quantity of rectangles by the average length of each rectangle to determine the total length of all the rectangles:
50 m x 25 m = 1250 m
Therefore, a square piece of fabric that is 25 square meters in size and has been divided into 50 rectangles, each measuring 50 cm wide and 25 meters long.
Therefore the rectangles together measure 1250 meters in length.
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Aubree's car used 4 gallons to travel 120 miles. How many miles can the car go on one gallon of gas?
Aubree's car used 1 gallon to travel 30 miles.
The car used 4 gallons to travel 120 miles. We need to calculate the distance car can travel with 1 gallon of gas.
By unitary method;
The distance car can travel = (120/4)*1 =30
Aubree's car used 1 gallon to travel 30 miles.
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On 1 gallon of gas, Aubree`s car can go 30 miles.
This is a question of the unitary method. The unitary method is a technique for solving a problem by first finding the value of a single unit, [by dividing] and then finding the necessary value by multiplying the single unit value.
Aubree`s car used 4 gallons of gas to travel 120 miles. So, to find the miles it travelled on 1 gallon of gas. We can simply just divide the total miles the car travelled by the total litres of gas it used.
Therefore, 120/4=30 miles.
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how many liters of 10% salt solution must be added to 5 liters of 25% salt solution to obtain a 15% salt solution?
Answer: 10 liters
Step-by-step explanation:
Let the number of liters of 10% solution be [tex]x[/tex].
[tex]0.10x+5(0.25)=0.15(x+5)\\\\0.10x+1.25=0.15x+0.75\\\\1.25=0.05x+0.75\\\\0.05x=0.50\\\\x=10[/tex]
a right rectangular prism 3 in by 4.25 in by 18.25 in what is the total surface area of the prism
The total surface area of the prism will be 290.125 Square units.
What is a surface area of a rectangular prism?The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.
The surface area of a rectangular prism is given by:
SA = 2 (lh +wh + lw )
where
l = 3
w = 4.25
h = 18.25
SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)
SA = 2 (54.75 + 77.5625 + 12.75)
SA = 2 (146.0625)
SA = 290.125 square units
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algebra 25 focus: polynomial multiplication 66 3/3 correct problem level 25 algebra 125 xp resilience 86, stamina 95. suppose that $f$ is a quadratic polynomial and $g$ is a cubic polynomial, and both $f$ and $g$ have a leading coefficient of $1$. what is the maximum degree of the polynomial $(f(x))^3 - (g(x))^2 f(x) - 1$?
maximum degree f(x) = x2 + bx + c g(x) = x3 + wx2 + yx + z [f(x)]3 - [g(x)]2 + f(x) - 1 (x2+bx+c)3 - (x3+wx2..for the given polynomial
What is a polynomial class 9?
Polynomial Definition. Polynomials are expressions with one or more terms with a non-zero coefficient. A polynomial can have more than one term. An algebraic expression p(x) = a0xn + a1xn-1 + a2xn-2 + … an is a polynomial where a0, a1, ………. an are real numbers and n is non-negative integer.
Find the value of f(–9) and g(1) if f(x) = 8x + 6 and g(x) = 9x + 20x−2
polynomial f(x) = 8x + 6
f(–9) = 8(-9) + 6 = -66
g(x) = 9x + 20x − 2
g( 1 ) = 9( 1 ) + 20( 1 ) − 2 = 27
None of the given choices were correct (unless there's a typo error for — it's supposed to be g( 1 ) = 27 instead of 29?) because the value are: f(–9) = -66 and g( 1 ) = 27
f(–9) and g(–1) if f(x) = –3x – 2 and g(x) = 3x³ – 24x
f(x) = –3x – 2
f(–9) = –3(–9) – 2 = 25
g(x) = 3x³ – 24x
g(–1) = 3(–1)³ – 24(–1) = 21
Therefore, : f(–9) = 25, g(–1) = 21
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Which of the following r values indicates the strongest relationship between two variables? +0.45
-0.30
+0.03
-0.45
According to the given option +0.03 is the r values that indicates the strongest relationship between two variables. The option 3 is correct.
The strength of the association between two variables is gauged using correlation coefficients. Although there are other kinds of correlation coefficients, Pearson's is the most widely used. A correlation coefficient frequently used in linear regression is Pearson's correlation. Correlation coefficients typically lie in the range of -1.00 to +1.00.
The closest value to +1 (positive correlation) or -1 is taken into consideration as the strongest correlation, per the rule of correlation coefficients (negative correlation).
A high correlation coefficient means that one variable's value is directly correlated with another.
There is no relationship between the two variables if the correlation coefficient is zero.
A negative correlation coefficient shows an adverse relationship between the values of the two variables.
According to the given option +0.03 is the r values that indicates the strongest relationship between two variables.
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the half-life of strontium-90 is 28 years, meaning that after 28 years a given amount of the substance will have decayed to half the original amount. find the exponential decay midel of strontium-90
Answer:i had to
Step-by-step explanation: mb
Given the linear system:
5x + 3y = 17
-8x - 3y = 9
What is the correct formula for the solution to the linear system?
The solution to the linear system is [tex]x=\frac{\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,\ y=\frac{\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]}[/tex]
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
A linear system of equation:
Ax + By = C
Dx + Ey = F
Can be solved using:
[tex]x=\frac{\left[\begin{array}{cc}C&B\\F&E\end{array}\right]}{\left[\begin{array}{cc}A&B\\D&E\end{array}\right]} \\\\\\y=\frac{\left[\begin{array}{cc}A&C\\D&F\end{array}\right]}{\left[\begin{array}{cc}A&B\\D&E\end{array}\right]}[/tex]
Hence, for:
5x + 3y = 17
-8x - 3y = 9
[tex]x=\frac{\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} \\\\\\y=\frac{\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]}[/tex]
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Answer:
C
Step-by-step explanation:
a rectangle has its upper two vertices on the graph of and its lower two vertices on the -axis. what is the maximum possible area of the rectangle?
The maximum area of the rectangle is determined by the distance between the two points on the graph and the -axis.
What is rectangle?A rectangle is a four-sided shape with four right angles and two pairs of parallel sides. It is one of the most common shapes in the world, found in everything from building designs to artwork. Rectangles are also used in math, specifically to measure area and perimeter. Rectangles can also be classified according to their sides, with squares being a special type of rectangle with four equal sides.
To calculate the maximum possible area of the rectangle, we can use the formula A = (x2 - x1)(y2 - y1).
In this case, the two points on the graph have the same -coordinate, so the x2 - x1 part of the equation is zero. This means that the y2 - y1 part of the equation gives the maximum possible area of the rectangle. To calculate this, we need to take the difference between the two points on the graph.
For example, if the two points on the graph were (2,4) and (2,6), the maximum area of the rectangle would be (6 - 4) = 2.
Therefore, the maximum possible area of the rectangle is equal to the difference between the two points on the graph.
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Write an expression to represent the situation
Rhona got 114 more votes Tham Petro.
Matt took 10 minutes longer than twice as long as Bryce took to do his assignment.
A hamburger costs 29 cents less than half as much as a full meal.
someone please help asap tysm <333
The expression that represents the statements are
1. R = 114+P
2. M = 10+2B
3. H = 1/2M -29
What are linear expressions?Linear expressions are those statements that each term is either a constant or a variable raised to the first power.
In linear expressions, the highest power of the variable is 1.
In the first statement 'Rhona got 114 more votes Tham Petro'. Let's represent the votes for Rhona by R and for Pedro by P
therefore R = 114+ P
In the second statement 'Matt took 10 minutes longer than twice as long as Bryce took to do his assignment'
Let's represent the time it took Matt to do his assignment' by M and time it took Bryce by B.
then,
M = 10+2B
In the third statement 'A hamburger costs 29 cents less than half as much as a full meal'.
Let's represent the cost of hamburger by H and the cost of full meal' by M, then,
H = 1/2M -29
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I choose a random integer n between 1 and 10 inclusive. What is the probability that for the n I chose, there exist no real solutions to the equation x(x+5)=−n? Express your answer as a common fractio
The probability is 1/10.
The equation x(x+5) = -n can be rewritten as x^2 + 5x + n = 0. To find the solutions of this equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 5, and c = n.
For there to be no real solutions, the discriminant (b^2 - 4ac) must be negative. The discriminant is 5^2 - 4(1)(n) = 25 - 4n. So for there to be no real solutions, 25 - 4n < 0, or n > 6.25.
Since the integer n is between 1 and 10 inclusive, the only value that would not have a real solution is n = 7. Therefore, the probability that for the randomly chosen n there exist no real solutions is 1/10.
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helppppppppppppp pls.
someone asked tjis question before
Step-by-step explanation:
he needs 100ml to make 250ml, the explanation is somewhere on this app
Answer:
150ml
Step-by-step explanation:
250ml=100%
25ml=10%
times 25mls 6 times so that it become 60%=150ml
Find dy/dt for each pair of functions. y = x^2 - 2x, x = t^2 + 8 dy/dt =
[tex]dy/dt[/tex] for each pair of functions is [tex]4t^3 + 28t[/tex].
[tex]y[/tex] = [tex]x^2 - 2x[/tex]
[tex]x[/tex] = [tex]t^2 + 8[/tex]
[tex]y[/tex] = [tex](t^2+8)^2 - 2(t^2+8)[/tex]
[tex]dy/dt[/tex] = [tex]2(t^2+8)(2t) - 2(2t)[/tex]
= [tex]4t^3 + 32t - 4t[/tex]
[tex]dy/dt[/tex] = [tex]4t^3 + 28t[/tex]
The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value). Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.
When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable. The function closest to that input value is best approximated linearly by the tangent line.
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