[tex] = 2x(x - 3) - 5(x - 3) \\ = 2 {x}^{2} - 6x - 5x + 15 \\ = 2 {x}^{2} - 11x + 15 [/tex]
ATTACHED IS THE SOLUTION
a store increased the original price of a shirt by a certain percent and then decreased the new price by the same amount. given that the resulting price was 84% of the original price, by what percent was the price increased and decreased?
A retailer raised a shirt's original price by a certain percentage before lowering it by the same percentage. The price was increased and decreased by 40% as the final cost was 84% of the initial cost.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Here,
Let's say the shirt originally cost Rs 100, and we're adding t% to the price.
The new price of the shirt is therefore 100 + (t/100 * 100) = Rs. 100+t after the initial t% increase.
The price is then reduced by t%.
Cost of a new shirt: (100 + t) - (t/100)
[100+t] = (100+t)
[1-(t/100] = [(100+t)/100]
therefore, the final price is equal to 84% of Rs 100, or Rs 84.
10000 - t^2 = 84.
t^2 = 1600
t = 40
The price was thus raised and lowered by 40%.
The original price of a shirt was increased by a specific percentage before being decreased by the same percentage by the retailer. As the final price was 84% of the initial price, the price was both increased and decreased by 40%.
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Which of the following functions has a graph that is a
line
f(x) = Ixl
f(x) = x
f(x)=x²
With the help of equations we can say that function has a f(x) = x,straight line.
What is an equation?
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions.For instance, an équation is defined as having one or more variables in French.Finding the variables' values that cause the equality to be true is the first step in solving an equation with variables.The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfill the equality are known as the equation's solutions. Equations can be categorized as either identities or conditional equations.acc to our question-
f(x) = Ixl
f(x) = x
f(x)=x²
Hence, function f(x) = x is a line.
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Graph the parabola
y=3x^2-x-2
A parabola is a bowl-shaped figure. Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].
Since the additional point is [tex](3,22)[/tex]
What is a parabola?
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface: a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line. : something that is bowl-shaped.
Here the given quadratic equation is
[tex]y=3x^{2}-x-2[/tex]
The standard form of the quadratic equation is
[tex]y=ax^{2}+bx+c[/tex]
where [tex]a=3,b=-1,c=-2[/tex]
The axis of symmetry is the x-axis of the vertex
[tex]x=\frac{-b}{2a}\\x=\frac{1}{2(3)}\\x=\frac{1}{6}[/tex]
The y-value of the vertex is determined by substituting [tex]\frac{1}{6}[/tex] for [tex]x[/tex] into the equation and solving it for [tex]y[/tex].
[tex]y=3(\frac{1}{6})^{2}-\frac{1}{6}-2\\y=3(\frac{1}{36})-\frac{1}{6}-2\\y=\frac{3-6-72}{36}\\y=\frac{3-78}{36}\\y=\frac{-75}{36}[/tex]
Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
Since [tex]a < 0[/tex] the vertex is the maximum point and the parabola opens downward.
X-intercept values of [tex]x[/tex] when [tex]y=0[/tex]
Substituting [tex]0[/tex] for [tex]y[/tex] and solving for [tex]x[/tex] using the quadratic formula
[tex]0=3x^{2}-x-2\\x=\frac{-b+-\sqrt{b^{2}}-{4ac}}{2a}\\x=\frac{1+-\sqrt{1}-{4(3)(-2)}}{2(3)}\\\\x=\frac{1+-\sqrt({1}+{24})}{6}\\\\\\x=\frac{1+-\sqrt(25)}{6}\\\\\\\\x=\frac{1+-5}{6}\\\\\\x=\frac{1+5}{6} , x=\frac{1-5}{6}\\\x=\frac{1+5}{6},x=\frac{1-5}{6}\\\\\x=1,x=\frac{-2}{3}[/tex]
Y-intercept values of [tex]y[/tex] when [tex]x=0[/tex]
Substituting [tex]0[/tex] for [tex]x[/tex] and solving for [tex]y[/tex] using the quadratic formula
[tex]y=3(0)^{6}-0-2\\y=-2[/tex]
Y-intercept [tex](0,1)[/tex]
Now substitute [tex]3[/tex] for [tex]x[/tex] and solve for [tex]y[/tex]
[tex]y=3(3)^{2}-3-2\\y=3(9)-5\\y=27-5\\y=22[/tex]
So the point is [tex](3,22)[/tex].
Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].
Since the additional point is [tex](3,22)[/tex]
The parabola is of the form
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a marathon is a 26.2-mile race that commemorates the run made by a greek soldier, pheidippides, that took place in 490 bce. how many kilometers did he run? (note: 1 mi
He ran 42.1 kilometers.
Define conversion.A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet. The act or process of transforming something into a different condition or form is known as conversion. to convert a value or expression between two different forms. • Measurement: converting between different units, for as from inches to millimeters or liters to gallons. For instance, change 12 inches to millimeters. 304.8 millimeters are equal to 12 inches multiplied by the inch-to-millimeter ratio of 25.4.
Given,
A marathon is a 26.2-mile race that commemorates the run made by a greek soldier, pheidippides, that took place in 490 bce.
1 mile = 1.609
Converting miles into kilometer:
26.2 miles
= 26.2 × 1.609
= 42.1
He ran 42.1 kilometers.
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quick help me please
Answer:
calculate the difference ere
(3-22)+5
remove unnecessary parentheses
-19+5
calculate the sum
= -14
f(x) = |x|-3; vertical shrink by a factor of 1/3
An equation that represents a vertical shrinkage of the graph of g(x)=1/3|x|-1 by a factor of three.
What is vertical shrink?A vertical stretch/shrink by a factor of k also means that the point (x, y) on the f (x) graph is transformed to the point (x, ky) on the g graph (x). Vertical Stretches and Shrinks Examples Consider the base functions (1) f (x) = x2 - 2, and (2) g(x) = sin (x). Stretches and shrinks, unlike translations, effectively pull the base graph outward or compress the base graph inward, changing the overall dimensions of the base graph without changing its shape. Multiply or divide the output by a constant to stretch or shrink the graph in the y direction.Given,
f(x) = |x|-3;
vertical shrink by a factor of = 1/3
Therefore,
g(x)=1/3|x|-1
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For what values of x is the absolute value function ƒ(x) = |x + 1| − 3 increasing?
By identifying the vertex of the function, we conclude that it is increasing for:
x > -1
For what values of x is the function increasing?Here we have an absolute value function:
f(x) = |x + 1| - 3
This absolute value function has a positive coefficient, which means that the function opens upwards, so it looks like a regular "V" letter.
The function is increasing when, reading from left to right, we see that the line goes upwards. And for functions like this, this happens for values of x larger than the vertex x-value.
For:
f(x) = |x + 1| - 3
The vertex is at (-1, -3)
Then the function is increasing for x > -1
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x^3=x^2-1 find all the real zeros
Answer:
ask this braslate which matirias
a square tile is expanding as it is heated. right now, the 29 cm tile is growing by 1.625 cm per hour. at what rate is the area of the tile changing?
Using the concept of application of derivative it is concluded that the rate of change in the area of square tile is 94.25 cm²/hour.
What is the area of a square?The area of the square is defined as the square of its sides.
Let the side of the square is a then its area will be a².
Area of square figure = Side².
Let the side of the square is x= 29cm.
It is given that the side 29 cm tile is growing by 1.625 cm per hour on heating.
And the rate of change in side of square dx/dt = 1.625 cm/hour
We have to calculate the rate of change in an area of the square (A).
hen, area A = x²
On differentiating A with respect to time(t) we get a rate of change in area
dA/dt = d(x²)/dt
= 2x dx/dt
= 2×29×1.625
= 94.25 cm²/hour
Hence, the rate of change in the area of the square tile is 94.25 cm²/hour.
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the breaking strengths of a random sample of 20 bundles of wool fibers have a sample mean 436.5 and a sample standard deviation 11.9. (a) construct 90%, 95%, and 99% confidence intervals for the average breaking strength of the wool fibers. (b) compare the widths of the three confidence intervals. at which level of confidence do you have the widest interval? (c) do you think it is plausible that the average breaking strength is equal to 450?
With the help of standard deviation we can conclude our answer.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.acc to our question-
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A rectangular garden must have a perimeter of 540 feet and and area of at least
12,000 square feet. Describe the possible lengths of the garden. round to the nearest
whole number
I need help please!
The length of the garden is: l ≥ 6225ft.
Area = L multiplied by W. Since you measure the area in square feet, your final number should reflect that.
What is a Rectangle?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
Let l serve as a symbol for the garden's length.
Let w be the symbol for the garden's width.
The perimeter is 540 feet.
The rectangle's circumference is equal to
2(l + w)2(l + w) = 540 l + w = 270. (1)
The rectangle's area is equal to its length times its width, which equals 12000. (2)
Make the variable w the subject of the following equation:
w = 270 - l. (3)
Substitute equation (3) into equation (2)
(270 - l)(l) ≤ 12000
270l - l² ≤ 12000
0 ≤ l² - 270l + 12000
l² - 270l + 1200 ≥ 0
Solving the quadratic inequality above:
l ≥ 6225
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2. Communicate and Justify Why is the algebraic
expression x, equivalent to x ¹?
Expression x is equivalent to [tex]x^{1}[/tex] by using the exponent rule.
What do you mean by algebraic expression?
A mathematical expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are three primary categories of algebraic expressions, including:
Monomial expression
Binomial expression
Polynomial expression
An algebraic expression can be divided into two additional types in addition to the monomial, binomial, and polynomial types. These are:
Numeric Expression
Variable Expression
Numeric expression - A numeric expression consists of numbers and operations, but never include any variable.
Variable expression - A variable expression is an expression that contains variables along with numbers and operation to define an expression.
As we know, exponent form [tex]x^{n}[/tex] can be simplified as [tex]x \times x\times x\times ........n~ times[/tex]
In this way , [tex]x^{1}[/tex]can be written as x multiplied by 1 time which is equal to x
Therefore, expression x is equivalent to [tex]x^{1}[/tex].
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which contours are usually drawn darker than the other contours? group of answer choices index contours largest (max) value contour contour interval smallest (min) value contour
Index contours are usually drawn darker than the other contours.
Index Contours are darker and wider than the other regular contour lines for ease of identification. They are labeled with elevation and also have their altitude value mentioned on the dark lines and these values represent the altitudes of the particular contours. Index contours appears after every fifth contours. If the number with contours will increase then its elevation will also increase and similarly if the number associated with contours starts to decrease then its elevation also decreases.
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(14x - 2) - (11x-21)
Answer:
3x+19
Step-by-step explanation:
Distribute:
14 x − 2 − ( 11 x − 21 ) 1 4 − 2 − ( 1 1 − 2 1 )
14 x − 2 − 11 x + 21 1 4 − 2 − 1 1 + 2 1
Add the numbers:
14x−2−11x+21
14−2−11+2
Combine like terms:
14x+19−11x
14 +19−113x+193+19
Solution: 3x+19
Answer:
3x + 19
Example:
None.
y = -6x - 2
12x + 2y = −6
help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
pls help asap giving 50 points Farmer A planted green beans and corn at a ratio of 5:3. Farmer B planted green beans and corn at a ratio of 3:2.
Which farmer planted a greater ratio of green beans to corn?
Farmer A planted a greater ratio of green beans to corn
How to find the farmer that planted a greater ratio of green beans to corn?Ratio is defined as the comparison of two quantities (a and b) of the same units which indicates how much of one quantity is present in the other quantity. They are written a / b, where b does not equal 0
Given that: Farmer A planted green beans and corn at a ratio of 5:3 and farmer B planted green beans and corn at a ratio of 3:2
To find the greater ratio treat the ratio as a fraction:
Farmer A => 5:3 and Farmer B => 3:2
5/3 and 3/2 (LCM of 2 and 3 is 6)
10/6 and 9/6
10:6 and 9:6
Since 10:6 is greater than 9:6. Therefore, Farmer A planted a greater ratio of green beans to corn
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tan 30 x cos 30 in exact value
kara, who lives in canada, plays a popular online video game where every round has a winner. her best streak is 212121 wins in a row, and she wonders how that compares to other players. the game's website has a worldwide leaderboard of players with the longest win streaks for each month. kara finds that the top 200200200 longest streaks in the world in june had an average of about 636363 wins in a row. for which population is 636363 wins a legitimate estimate of the average longest streak?
For which population is 636363 wins a legitimate estimate of the average longest streak: Only the top 200200200 longest streaks worldwide in June
Mean = sum of data / Number of data
The 200200200 longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada, but they are the top 200200200 longest streaks of all players. So,
Only the top 200200200 longest streaks worldwide in June will win.
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Gerardo and his two friends order a pizza and decide to split the cost evenly. Each person ordered a drink for $1.50. How much was the pizza if each person paid $8?
19.50 cost of pizza
Step-by-step explanation:
$8.00-$1.50 = $6.50 × 3 =19.50
How many solutions does the
equation have?
3(d + 11) = 6(d + 33)
a. 0
b. 1
c. infinitely many
Answer: 1 solution
Step-by-step explanation:
3(d+11)=6(d+33)
simplifing the above equation
3d+33=6d+198
3d-6d=198-33
-3d=165
d= -165/3
d=-55
Answer:
b. 1
Step-by-step explanation:
3d + 33 = 6d + 198
3d - 6d = 198-33
-3d = 165
thus, d = -165/3
= -55
Answer 3,4,5,6 Thank you
B) The missing angle at the intersection point of both triangles is; x = 15°
C) The missing angle is gotten as; x = 61°
How to find the missing angles?B) In the second image given, we can see two angles;
Now, we know that sum of angles in a triangle is 180 degrees. Thus, for the interior angles, we have;
90 + 5x - 14 + y = 180
where y is the third interior angle
Now, we know that sum of angles on a straight line is equal to 180 degrees. Thus;
y = 180 - (9x + 16)
Put 180 - (9x + 16) for y into the first equation to get;
90 + 5x - 14 + 180 - (9x + 16) = 180
180 will cancel out to get;
90 + 5x - 14 - (9x + 16) = 0
4x = 90 - 14 - 16
4x = 60
x = 60/4
x = 15°
C) The missing angle of the triangle with side of 12y + 3 is an alternate angle to get;
Missing angle = 63°
Sum of angles in a triangle is 180 degrees. Thus;
56 + 63 + 3rd angle = 180
3rd angle = 180 - (56 + 63)
3rd angle = 61°
Thus, x = 61° because they are opposite angles
Also, the two given sides are equal to each other as shown. Thus;
51 = 12y + 3
12y = 51 - 3
12y = 48
y = 48/12
y = 4
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J.5 unit rates
96 kilometers in 3 hours = ?
The unit rate for 96 kilometers in 3 hours is 32 kilometer per hour.
What is unit rate?
A unit is one of a particular object. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Given in the question,
96 kilometer in 3 hours,
In order to find unit rate we have to change given values in kilometers per hour.
Do, 96 kilometer = 3 hours
96/3 kilometer = 1 hour
Therefore, unit rate is 32 kilometer per hour.
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Plssssss Help mewith a and b
a. The relationship between time and distance is not an arithmetic sequence, as the rate of change is not constant.
b. The distance is given by: d(n) = 5n².
What is an arithmetic sequence?An arithmetic sequence happens when the change in the output is always the same when the input changes by one, that is, the rate of change is constant.
From the table, the increases when the input(time) increases by one are given as follows:
15, 15, 35, 45.
The increases are not constant, hence the relationship between time and distance is not an arithmetic sequence.
What is the distance at t = n?The equation for the distance is given as follows:
d(t) = 0.5gt².
The constant is:
g = 10.
Hence:
d(t) = 5t².
At a time of n seconds, the distance is found replacing the lone instance of t by n, hence:
d(n) = 5n².
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Jerald i having drain iue at hi home and decide to call a plumber. The plumber charge $35 to come to hi houe and $60 for every hour they work. If the plumber charge Jerald a total of $305, how many hour did the plumber work?
Write and olve an equation to determine the number of hour worked by the plumber
The calculation for the plumber's total number of hours worked is 190 = 35 + 50x, where the result is 3.1 hours.
A linear equation is what?
It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.
It follows that:
Jerald chooses to call a plumber after discovering a problem with his home's drains.
The plumber bills him $35 to visit his home and $50 per hour of work.
Suppose there are x hours in a day:
190 = 35 + 50x
50x = 155
x=3.1 hours
As a result, the answer to the question of how many hours the plumber worked is 190 = 35 + 50x, which is 3.1 hours.
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pls help? i dont know any of this
Answer:
Round to the nearest tenth.
a. 0.54 + 0.278 = 0.5 +0.3 = 0.8
b. 2.65 + 28. 17= 2.70 + 28.20 = 30.9
c. 3.09 + 2.41 + 9.86 = 3.10+ 2.40 + 9.90= 15.4
d. 15.234 + 1.37 + 0.76 = 15.20 + 1.3 + 0.8 = 17.30
e. 39.18 + 2.48+ 0.84 = 39.20 + 2.5 + 0.8 = 42.5
Round to the nearest whole number.
f. 4.112 + 3.89 = 4 + 4 = 8
g. 23.14 + 7.6 + 3.67 = 23 + 8 + 4= 35
h. 53.2 + 3.08 + 27.51 = 53 + 3+ 28 = 84
i. 11.08 + 17.28 + 92.6 = 11 + 17 + 93 = 121
j. 24.08+ 7.9 + 3.06 = 24 + 8 + 3 = 35
Step-by-step explanation:
Hopefully it's right!!!
What is the equation in point-slope form of a line that passes through the point (6,5) and has a slope of 1? Convert to slope-intercept
Answer:
Point-slope: y-5=x-6
Slope intercept: y=x-1
Step-by-step explanation:
y-y1=m(x-x1) Point slope form
y-5=1(x-6)
y-5=x-6
y=x-1
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two
different proportional relationships represented in different ways.
Will give points to first correct answer that follows all the steps right.
Answer:
I Need Help On That Too
Step-by-step explanation:
an urn contains 8 white balls and 12 red balls. a sample of four balls is selected at random from the urn. what is the probability that the sample contains two white balls and two red ones? a) 0.3814 b) 0.3933 c) 0.0424 d) 0.1028 e) 0.1474 f) none of the above.
0.3814 is the probability that the sample contains two white balls and two red ones .
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Total number of balls = 8 + 12 = 20
Total number of elementary cases
= ( 20 4 )
Total number of favourable cases
= ( 8 2 ) * ( 12 2 )
Required probability
= ( 8 2 ) * ( 12 2 )/( 20 4 )
= 0.3814
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How do you find the distance between the points shown? (C: 6, -4) and (D: 6, -8)
A. Subtract the distance between each point and the x-axis
B. Add the distance between each point and the x-axis
C. Subtract the distance between each point and the y-axis
D. Add the distance between each point and the y-axis
Answer:
A. Subtract the distance between each point and the x-axis.
Step-by-step explanation:
As the two points have the same x-coordinate, x = 6, it means they lie on the vertical line x = 6.
Therefore, the distance between the points can be found by subtracting the distance between each point and the x-axis.
In the given example, the points are C(6, -4) and D(6, -8).
To find the distance between a point and the x-axis, we simply take the absolute value of the y-coordinate of the point:
Distance between point C and the x-axis = |-4| = 4
Distance between point D and the x-axis = |-8| = 8
Subtracting the distances, we get:
Distance = 8 - 4
Distance = 4
Therefore, the distance between points C and D is 4 units.