Answer: 99.
If you take 275 and subtract it by 176, it should be 99, if I’m correct.
Which equations are true for x = –2 and x = 2? Select two options
O x2 – 4 = 0
O x2 = –4
O 3x2 + 12 = 0
O 4x2 = 16
O 2(x – 2)2 = 0
The only two options with equations that are true for x = –2 and x = 2 are;
Option A: x² - 4 = 0
Option D: 4x² = 16
How to identify the correct domain value?The domain of a function is the set of all input values for which the function is possible.
Now, we are given the domain values as x = –2 and x = 2.
a) x² - 4
f(-2) = (-2)² - 4
= 0
f(2) = (2)² - 2
= 0
b) x² = -4
f(-2) = (-2)²
= 4
f(2) = (2)²
= 4
c) 3x² + 12
f(-2) = 3(-2)² + 12
= 24
f(-2) = 3(2)² + 12
= 24
d) 4x²
f(-2) = 4(-2)²
= 16
f(2) = 4(2)²
= 16
e) 2(x - 2)²
f(-2) = 2(-2 - 2)²
= 32
f(2) = 2(2 - 2)²
= 0
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Can anyone solve this proof?
The proof for the Base Angles Theorem is explained below:
What is meant by Base Angles Theorem?A triangle's opposite angles are congruent if its two sides are congruent. We shall build the angle bisector through the vertex angle of an isosceles triangle in order to demonstrate the Base Angles Theorem. We created two congruent triangles by building the angle bisector, and then we utilized CPCTC to prove that the base angles are congruent. Base angles: The angles that include the base of an isosceles triangle are known as the "base angles."
Any triangle with at least two congruent sides is said to be isosceles. Legs are the isosceles triangle's congruent sides. The base is the other side. Base angles are the angles formed between the base and the legs.
Given: [tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]
Prove: ∠M≅∠N
According to the figure,
Given,
[tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]
By the definition of mid-point,
O is the mid-point of [tex]\bar{MN}[/tex]
Now, by joining the two points determine and draw a line of [tex]\bar{LO}[/tex]
Now, Again by the definition of mid-point
[tex]\bar{MO}[/tex]≅[tex]\bar{NO}[/tex]
Now, by using reflexive property,
[tex]\bar{LO}[/tex]≅ [tex]\bar{LO}[/tex]
By SSS rule,
ΔLMO≅ΔLNO
By CPCTC rule,
∠M≅∠N
Hence proved.
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 10(1.01)
The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.
What is the exponential growth function?An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.
It is represented by the formula,
y = a(1 + r)ˣ
Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.
Calculation:The given exponential function is y = 10(1.01)ˣ
Here we can write the function as
y = 10(1.01)ˣ
⇒ y = 10(1 + 0.01)ˣ
Since 1.01 > 1, it is an exponential growth function.
So, when comparing with the formula, we get the rate of increase,
r = 0.01
Converting it into fractions, we get 1/100
Then, the percentage rate of increase is 1%.
Therefore, the given exponential function grows with a rate of 1% increase.
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Find the surface area 5 4 7 6 8 triangular
The surface area of the triangular prism is 136 square units
How to determine the surface areaFrom the question, we have the following parameters that can be used in our computation (see attachment):
Rectangles (2) = 7 units by 5 unitsRectangles (1) = 7 units by 6 unitsTriangles (2) = 4 units by 6 unitsThe surface area of the triangular prism is the sum of the areas of the above shapes
So, we have
Surface area = 2 * area of rectangle 1 + 1 * area of rectangle 2 + 2 * area of triangle 1
Substitute the known values in the above equation, so, we have the following representation
Surface area = 2 * 7 * 5 + 1 * 7 * 6 + 2 * 0.5 * 4 * 6
Evaluate
Surface area = 136
Hence, the surface area is 136 square units
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A cryotherapy chamber uses extreme cold to reduce muscle soreness. A chamber is currently 0°F. The temperature in the chamber is dropping 2.5°F every second. Identify an inequality that represents the numbers of seconds $s$ that can pass for the temperature to drop below -20 °F
Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.
Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.
The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.
We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.
Dividing both sides by 2.5, we get the final inequality: $s$ > 7.
Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.
Angela is following this recipe to make biscuits.
Angela uses 0.9 litres of syrup.
How much margarine is needed in kg?
Recipe: Makes 10 biscuits
150 g margarine
180 g sugar
225 ml syrup
225 g oats
40 g sultanas
The amount of margarine needed in Kg for making biscuits is 0.6kg
What is proportions?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.
How to find the amount of margarine needed in KgThe amount of margarine needed in Kg is calculated using proportions
If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require
0.225 l = 0.15 kg
0.9 l = ?
cross multiplying
0.225 * ? = 0.9 * 0.15
? = 0.135 / 0.225
? = 0.6
Angela will require 0.6 kg of margarine
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A website offers a coupon to 50\%50%50, percent of its visitors, selected at random, each day. Yasemin visits the website for 444 days. What is the probability that yasemin will not be offered a coupon on at least one of the days she visits the website? round your answer to the nearest hundredth. P(\text{at least one day without coupon})=p(at least one day without coupon)=p, left parenthesis, start text, a, t, space, l, e, a, s, t, space, o, n, e, space, d, a, y, space, w, i, t, h, o, u, t, space, c, o, u, p, o, n, end text, right parenthesis, equals.
The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;
⇒ 0.9375
What is mean by Probability?The term probability refers to the likelihood of an event occurring
Given that;
The probability that a visitor is offered a coupon (p) = 50%
Now,
Since, The probability that a visitor is offered a coupon (p) = 50%
Hence, The probability that he gets coupon all 4 days is,
⇒ p (4) = p⁴
⇒ p (4) = (50%)⁴
⇒ p (4) = 0.0625
Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,
⇒ p' = 1 - 0.0625
⇒ p' = 0.9375
Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375
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Write the equation for a line that passes through the given points Write the equation in slope- intercept form
. (6,-4), (6,5)
The equation of the line, in slope-intercept form, that passes through the given points, (6,-4) and (6,5) is: x = 6.
How to Write the Equation of a Vertical Line?An vertical line can be written in slope-intercept form as x = a, because the line has no y-intercept and the change in x values in the slope formula is equal to zero.
The value of a in the equation is the point on the x-axis where the vertical line intercept, irrespective of the change in y-values up the line.
Given the line goes through the points, (6, -4) and (6, 5), it means the line is a horizontal line because they both have the same x-value, 6.
Therefore, the value of a is 6. The equation of the line would be x = 6.
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What is the cubic polynomial with zeros (3,0), (-6,0), and (1,0)?
(Question 15)
Answer:
D
Step-by-step explanation:
when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.
f(x) = (x - 3)(x + 6)(x - 1)
we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :
-3 × +6 × -1 = +18
and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).
By rounding to 1 significant figure, estimate
101
×
52
The significant figure by multiplying 101 with 52 is 5000.
What is significant figures?The number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value is referred to as significant figures. At the first non-zero digit, we begin counting significant figures.A number's first significant figure is the first digit that is not zero.To round to the nearest one, ten, hundred, thousand, and so on, change all digits to the right of the rounding digit to zeroes.Here given,
101 x 52
Round 101 to 100 and 52 to 50, then multiply together to get 5000.
Significant Figures: 1
Decimals: 0
The significant notation: 5e+3
Therefore the significant notation is 5000.
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. Solve for x: log₂ (x+4) + log₂ (x + 3) = 1. Pleasee
The value of x for the expression is equal to -5 and -2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the logarithmic expression is log₂ (x+4) + log₂ (x + 3) = 1. The value of x will be calculated as,
log₂ (x+4) + log₂ (x + 3) = 1
log₂ { (x+4)(x + 3) } = 1
x² + 7x + 12 = 2
x²+ 7x + 10 = 0
Solve the above quadratic equation,
x²+ 7x + 10 = 0
x² + 5x + 2x + 10 =0
x ( x + 5 ) + 2 ( x + 5 ) = 0
(x + 5 ) ( x + 2 ) = 0
x = -5 and -2
The values of x are -5 and -2.
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When solving an equation, Henry gets to the last line of his work and is left with “3 = 3”. What does this mean? * 4 points A. The solution is 3. B. There is only one solution. C. There is no solution. D. There are infinite solutions.
This mean there are infinite solutions.
What does this mean?Each side is equally satisfied in an endless solution. Infinite is a symbol for boundlessness or limitlessness. Typically, the sign "" is used to denote it.
Solving an equation, Henry gets to the last line of his work and is left with “3 = 3”.
Any value for the Variable would make the equation true, according to infinite solutions.
We can tell which instance it is by examining our findings. If both sides of the equal sign end up having the same word,
such as
3=3 or 3x=3x, then. Finite solutions exist.
This mean there are infinite solutions.
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What is the cubic polynomial with zeros (3,0), (-6,0), and (1,0)?
Question 15
The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:
D. x³ + 2x² - 21x + 18.
How to obtain the cubic polynomial?We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.
The zeros of the polynomial are given as follows:
x = 3, x = -6, x = 1.
Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:
(x - 3)(x + 6)(x - 1)
(x² + 3x - 18)(x - 1)
x³ + 2x² - 21x + 18.
Meaning that option D is correct.
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(50 points) Mariel and Sam Trent's savings account had a balance of $9,544 on May 1. The account earns interest at a rate of 5.25% compounded monthly until the end of August.
Answer:
$9,712.12 (nearest cent)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
P = $9,544r = 5.25% = 0.0525n = 12 (monthly)t = 4 months = 1/3 yearSubstitute the given values into the formula and solve for A:
[tex]\implies A=9544\left(1+\frac{0.0525}{12}\right)^{12 \cdot \frac{1}{3}}[/tex]
[tex]\implies A=9544\left(1.004375\right)^{4}[/tex]
[tex]\implies A=9544\left(1.017615179\right)[/tex]
[tex]\implies A=9712.119269[/tex]
The balance of the account at the end of August will be $9,712.12 (nearest cent).
A) a wooden block is formed in a the shape shown by cutting a right rectangular solid from a larger one. What is the volume of the block
B) check your calculations by using a second method to solve the problem
The volume of the rectangular block in this problem is given as follows:
1300 cm³.
How to obtain the volume of the block?The block is a rectangular prism, hence it's volume is given by the multiplication of it's dimensions, as follows:
V = length x width x height.
The dimensions for this block are given as follows:
Length: 16 cm.Width: 10 cm.Height: 10 cm.However, there is a small rectangular block that is removed from the prism, with the dimensions given as follows:
Length: 6 cm.Width: 10 cm.Height: 5 cm.Hence the volume of the rectangular block can be calculated as follows:
V = 16 x 10² - 6 x 5 x 10 = 1300 cm³.
(total volume subtracted by the removed volume from the empty space at the middle).
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What is the solution of the equation x2 - 12x = 8?
The solution of the equation is x = 6±2√11.
What is a quadratic equation?
The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.
Here, we have
Given: x² - 12x = 8
Now, we factorize the given equation and find the solution.
x² - 12x = 8
x² - 12x - 8 = 0
We apply here the quadratic formula.
= (-b ±√b²-4ac)/2
= (12 ±√12²-4×1×(-8))/2
= (12±√144+32)/2
= (12±√176)/2
= (12±4√11)/2
= 6±2√11
Hence, the solution of the equation x² - 12x = 8 is 6±2√11.
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2. Divide. Write the answer in simplest
form.
6 2/3 divided by 4 1/5
Answer:
100/63
Step-by-step explanation:
6 2/3 ÷4 1/5
20/3÷21/5
20/3×5/21
1 37/63 or 100/63 or 1.587301587
so the answer is one (whole number) thirty seven over sixty three
luka is making lemonade to sell at a school fundraiser. his recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. he uses 3 cups of lemon juice. how many cups of water does he need?
Luka will require 24 cups of water to make lemonades as calculated from the data given.
The quantity of sugar which he use is twice the amount of lemon which he us ,
= 2 x 3 = 6
and ,
as we know the amount of water is 4 times as much as lemon juice
Therefore, amount of water
= 4 * 6
= 24
A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.
A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.
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which of the following statements is a proposition? (a) get me a glass of milk (b) god bless you! (c) what is the time now? (d) the only odd prime number is 2
The proposition ststement is: the only prime number that is odd is 2.
The correct answer is an option (d)
In this question we have been given some statements.
we need to identify the proposition statement.
We know that a proposition is a declarative statement. In mathematics proposition gives a clear inference of whether a sentence is true or false. The proposition statement cannot be stated in two ways. The statement must be either correct or incorrect.
a) get me a glass of milkshake.
It is a commanding statement.
b) god bless you!
It is a type of optative statement.
c) what is the time now?
It is a question sentence.
d) the only odd prime number is 2.
It is a false proposition statement.
Therefore, option (d) is a proposition statement.
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cross-tabulation can only be used for two variables; each variable must have well-defined labels. true false
The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false
The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that that present the results of the entire group of respondents
The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "
The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables
The cross tabulation can be used for two or more variables
Therefore, the the given statement is false
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What is the product of the two largest one-digit primes and the largest two-digit prime?
Answer:
see below
Step-by-step explanation:
A prime number is a whole number that cannot be exactly divided by another number other than itself and 1.
The two largest one digit prime numbers are 7 and 5. The product of them is 7×5=35.
The two largest two digit prime numbers are: 89 and 97.
89×97=8633
4 Describe at least two different transformations or sequences of transformations that
transform square A to square B.
The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0).
Does the order of transformations matter in functions?
Order is not important. According to algebra, y=12f (x3). Our four transformations are (1), (3), (2), and (4); all four are in the x direction. When we combine a stretch and a translation in the same direction, the sequence counts.
The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.
ABCD can be transformed to A'B'C'D' by ...
rotation 90° CCW about the point (-1, -1)
Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...
reflection across the line y=x
reflection across the line x=-1
Complete question: A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.
b.) There is more than one way to transform quadrilateral ABCD into quadrilateral A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.
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Indigo goes out to lunch. The bill, before tax and tip, was $10.85. A sales tax of 3%
was added on. Indigo tipped 18% on the amount after the sales tax was added. The
total cost of the meal plus tip and tax was more than the cost of the bill by what
percent? Round to the nearest whole number.
The total cost of the meal plus tip and tax was more than 122% of the cost of the bill.
What is percent?
A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.
Indigo goes out to lunch.
The bill, before tax and tip, was $10.85.
A sales tax of 3% was added on.
Indigo tipped 18% on the amount after the sales tax was added.
The amount after adding sales tax is,
$10.85 x 3% = 0.3255
⇒ $10.85 + 0.3255 = $11.1755
Now to find the amount after tipped 18% on the amount after the sales tax was added.
$11.1755 x 18% = 2.01159
⇒ $11.1755 + 2.01159 = $13.18709
Hence, the amount after tipped 18% on the amount after the sales tax was added is $13.18709.
Let x be the percent of more than the cost of the bill of $13.18709.
⇒
[tex]\frac{10.85(x)}{100} = 13.18709\\ x = \frac{100 (13.18709)}{10.85}\\ x = 121.54[/tex]
Hence, the total cost of the meal plus tip and tax was more than 122% of the cost of the bill.
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Which ordered pair is a solution of the
equation?
-3x + 5y = 2x + 3y
Answer:
Solve the equation for [tex]{y}[/tex].
[tex]y=\frac{5x}{2}[/tex]
Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.
Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex]{(0,0)}[/tex]
Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex](1,\frac{5}{2})[/tex]
Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex]{(2,5)}[/tex]
These are three possible solutions to the equation.
[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]
STANDARD FORM MATHS HELP. POINTS
Answer:
1.64×10⁷ km16,400,000 km ("standard form" in the US)Step-by-step explanation:
You want the length of the hypotenuse of a right triangle with sides given as 3.6×10⁶ km and 1.6×10⁷ km.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the side lengths and the hypotenuse of a right triangle:
c² = a² +b²
RQ² = PQ² +PR²
RQ = √((3.6×10⁶)² +(1.6×10⁷)²) = 1.64×10⁷ . . . . . use numbers, take the root
The distance between planets Q and R is 1.64×10⁷ km.
__
Additional comment
The "standard form" of a number is different by location. In the US, it is written with the decimal point to the right of the units digit. In other places, "standard form" has the decimal point to the right of the most-significant digit, and a power of ten as a multiplier.
You may recognize the ratio of the given numbers is 9:40, telling you these lengths are a multiple of the {9, 40, 41} Pythagorean triple. That is, the distance RQ is 41/40 times the distance RP.
Any spreadsheet or scientific or graphing calculator can do the necessary arithmetic using the numbers in "scientific notation" format. Spreadsheets, in particular, use E() to signify ×10^(). That is, 3.6×10⁶ is entered into a spreadsheet as 3.6E6. The attached calculator display shows it can use the same sort of format.
Just use Pythagoras theorem to find the shortest distance between the two planets, (as it is along its hypotenuse)
The distance QR is :
[tex] \qquad \sf \rightarrow d = \sqrt{(1.6 \times 10 {}^{7}) {}^{2} + (3.6 \times 10 {}^{6} ) {}^{2} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{2.56 \times 10 {}^{14} + 12.96 \times 10 {}^{12} {}^{} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{256\times 10 {}^{12} + 12.96 \times 10 {}^{12} {}^{} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{(256 + 12.96 )\times 10 {}^{12} {}^{} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{(268.96 )\times 10 {}^{12} {}^{} } [/tex]
[tex]\qquad \sf \rightarrow d = 16.4\times 10 {}^{6} {}^{} [/tex]
Help meee please !!!???
Answer:
Step-by-step explanation:
it is c
Graph the inequality on the axes below
x+ 5y <-30
The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).
What is an inequality?Inequality is defined as a relationship between two expressions or values that are not equal to each other.In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).Here given the inequality.
x + 5y ≤ 30
To find the x-intercepts.
We have to substitute 0 for y and solve x to determine the x-intercepts.
x + 5 × 0 = 30
By solving the equation.
x = 30
( 30, 0 ) is the x-intercepts.
To find the y-intercepts.
By substituting 0 for x and solving y will get the y-intercept(s).
0 + 5y = 30
5y =30
y = 30/5
y = 6
In the point form, y-intercept.
Y-intercept(s): ( 0, 6 )
(30, 0) is the x-intercept.
Y-intercepts at : ( 0, 6 ).
The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).
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See the attached image.
The value of x will be 1.17 inches and the maximum volume of the box is 1.6 cubic inches.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.
Given that the rectangular box is made from cardboard the thickness is x.
The length of the box will be,
L = 4.5 - 3x
The width of the box will be,
W = 4 - 2x
The thickness of the box is,
H = x
The volume of the box will be calculated as,
V = ( 4.5 - 3x) ( 4 - 2x ) (x)
V = ( 4.5 - 3x) ( 4 - 2x ) (x)
V = ( 18 - 12x - 9x + 6x² ) x
V = 6x³ -21x² + 18x
For maximum volume differentiate the volume with respect to x and get the value of x,
dV / dx = d / dx ( 6x³ -21x² + 18x ) = 0
d / dx ( 6x³ -21x² + 18x ) = 0
18x² - 42x + 12 = 0
3x² - 7x + 6 = 0
Solve the above quadratic equation as,
x = [ -b ±√(b² - 4ac) ] / 2a
x = [ -7 ± √ (-7² - 4 x 3 x 6 ) ] / ( 2 x 3 )
x = 1.17
The value of x is 1.17 inches by solving the above quadratic equation. The maximum volume will be calculated as,
V = 6x³ -21x² + 18x
V = 6(1.17)³ -21(1.17)² + 18(1.17)
V = 9.6 - 28.7 + 21.06
V = 1.96 cubic inches
The maximum volume is 1.96 cubic inches and the value of x is 1.17 inches.
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What is the value of 5/9 ÷ 5/6? Responses
Answer:
2/3 or 0.667
Step-by-step explanation:
5/9 ÷ 5/6
5/9 * 6/5
1/3 * 2/1 (after cancelling off)
= 2/3
how do you solve this?
According to Euclidean geometry, the geometric system consisting in isosceles triangle has an angle x whose measure is equal to 74°.
How to solve a variable in an isosceles triangle
In this problem we find a geometric system consisting in a triangle, where two sides are congruent and the measure of an angle equals 74°.
According to Euclidean geometry, a triangle represented by the geometric system, with such features represents an isosceles triangle, that is, a triangle with two congruent sides and two congruent angles between the base side and each of the two congruent sides. Thus:
m ∠ x = 74°
x = 74°
Therefore, the measure of angle x, opposite to the angle whose measure is 74°, must be also equal to 74°.
The measure of angle x associated with the geometric system consisting in an isosceles triangle is equal to 74°.
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