Answer:
17 paintings are displayed
Step-by-step explanation:
difference of two sqaures
The difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).
What is a difference of two squares?
Difference of two squares is a particular case of a second order polynomial whose form is the following:
a² - b² = (a + b) · (a - b)
Now we proceed to demostrate the equivalence between the two expressions:
a² - b² → (a + b) · (a - b)
a² - b² Given
(a² - b²) + 0 Modulative property
(a² - b²) + a · b - a · b Existence of additive inverse
(a² + a · b) + (- b² - a · b) Associative property
a · (a + b) - b · (a + b) Definition of power / Distributive property / (- a) · b = - a · b
(a + b) · (a - b) Commutative and distributive property /
(a + b) · (a - b) → a² - b²
(a + b) · (a - b) Given
(a + b) · a + (a + b) · (- b) Distributive property
a² + a · b - a · b - b² Distributive property / (- a) · b = - a · b / Definition of power
(a² - b²) + (a · b - a · b) Associative property
a² - b² Existence of the additive inverse / Modulative property / Result
Hence, the difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).
RemarksThe statement is incomplete. The complete form is: What is a difference of two squares?
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dell has a small bag containing 50 centimeters of potting soil. her planter has a volume of 46,300 cubic millimeters. does dell have enough soil to fill the planter? explain.
Answer:
No, Dell does not have enough soil to fill the planter.
Step-by-step explanation:
f(x) = 13 - x
h(x) = x² - 6x - 18
Write (fo h) (x) as an expression in terms of a x.
(ƒ○h)(x) =
Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks. He must arrive at his friend’s house by 7:00 p.m. What is the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time?
The latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m
How to find the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time?Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks and He must arrive at his friend’s house by 7:00 p.m.
The time it takes Lyle to drive to his friend's house is given by t = d/v where
d = distance travelled and v = average speedGiven that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, we have that
d = 720 km and v = 80 km/hSubstituting the values of the variables into t, we have
t = d/v
= 720 km/80 km/h
= 9 h
So, it takes Lyle 9 hours to drive.
Now, since Lyle takes an hour for Lunch and two 15 minutes breakes, this extra time is t' = 1 h + 2 × 15 min
= 1 h + 30 min
= 1 h + 30 min/60 min × 1h
= 1 h + 0.5 h
= 1.5 h
So, the total time Lyle takes to reach his friend's house is T = t + t'
= 9 h + 1.5 h
= 10.5 h
Since Lyle must reach his friend's place no later than 7:00 pm, 10.5 hrs from 7:00 pm is 8:30 am.
So, Lyle must leave no later than 8:30 a.m
So, the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m
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What is the inverse function of f(x) = 4 - x/6?
Answer:
f^-1 (x)= -6x+24
Step-by-step explanation:
the inverse function would be negative six (x) plus 24
If line B is drawn such that it passes through Point P and is parralel to line A, what is the equation of line B?
Equation of line B is y=7/2x
A line is simply an object in geometry that is characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.
Straight line formulas= y=mx+ c
= y-y1=m(x-x1)
slope, m= (y1-y2)/(x1-x2)
given that, B passes through P and parallel to A
so one of the points on the line is P(2,7)
and one more point is O(0,0) if we extend line B parallelly to A
So we can conclude that B passes through O and P
we know equation of straight line is y-y1=m(x-x1)
on solving we get equation of line B is, y=7/2x
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Answer:
Line B's equation is y=7/2x.
Step-by-step explanation:
An object in geometry known as a line is simply one that extends on all sides and has zero width. Simply put, a straight line is a line devoid of curves. A straight line is one that does not curve and extends to infinity on both sides.
Straight line formulas= y=mx+ c
= y-y1=m(x-x1)
slope, m= (y1-y2)/(x1-x2)
given that, B passes through P and parallel to A
so one of the points on the line is P(2,7)
Moreover, if we stretch line B parallel to A, the final position is O(0,0).
Therefore, we can say that B goes through O and P.
Y-y1=m is the straight line's known equation (x-x1)
After solving, we obtain the equation y=7/2x for line B.
Help pls I really need if help then thank you you really help
Which input value produces the same output value for
the two functions?
O x=-3
O x=-1
O x=0
O x = 1
x = -2 is input value produces the same output value for the two functions .
What are the function's input values?
The domain of the function is the collection of input values. The range of the function is the collection of output values.
What input and output functions are used?
The fundamental functions for input and output are getchar, putchar, puts, scanf, and printf. To transfer single characters, utilize the first two functions, getchar and putchar.
Which four sorts of functions are there?
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
The input value which produces the same input .
value for two function is x = -2
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Write an explicit formula for each sequence. Then generate the first five terms. a₁ =4, r=0.1
The given geometric sequence, with first term = 4 and ratio = 0.1, has the formula for its nth term: a(n) = 4 . 0.1ⁿ⁻¹. The first five terms are: 4, 0.4, 0.04, 0.004, 0.0004
The formula of the nth term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
with a₁ is the first term and r is the ratio. In a geometric sequence, the ratio is constant and equal to a(n)/a(n-1).
In the given problem, a₁ =4, r=0.1, therefore:
a(n) = a₁ . r^(n-1)
a(n) = 4 . 0.1ⁿ⁻¹
To find the first five terms, replace n with 1, 2, 3, 4, and 5.
a₁ = 4
a(2) = 4 . 0.1²⁻¹
= 4 . 0.1¹ = 0.4
a(3) = 4 . 0.1³⁻¹
= 4 . 0.1² = 0.04
a(4) = 4 . 0.1⁴⁻¹
= 4 . 0.1³ = 0.004
a(5) = 4 . 0.1⁵⁻¹
= 4 . 0.1⁴ = 0.0004
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Solve equation by using the Quadratic Formula. Round to the nearest tenth if necessary. x² = x + 12
The quadratic equation of the form ax² + bx + c = 0.
The value of x = 4 and x = -3
No solution
No real-valued solution
What is meant by quadratic equation?The quadratic equation of the form
ax² + bx + c = 0.
The form is called the standard form of the quadratic equation.
Let the given equation be x² = x + 12
By using quadratic equation, ax² + bx + c = 0
ax² + bx + 12 = 0
x² = x + 12
⇒ x² - x - 12 = 0
Let the quadratic equation be
[tex]$x=\frac{\left(-b\right)\pm \sqrt{\left(b)^2-4\cdot \:a\cdot \left(c)}}{2\cdot \:a}[/tex]
a = 1, b = -1 and c = -12
Substitute the values in the above equation, we get
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-12\right)}}{2\cdot \:1}[/tex]
simplifying the above equation, we get
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \:7}{2\cdot \:1}[/tex] and
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a++ \:7}{2\cdot \:1}[/tex]
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a+- \:7}{2\cdot \:1}[/tex]
x = 4 and x = -3
Therefore, the value of x = 4 and x = -3
No solution
No real-valued solution
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Given the m∠5=82° use the image below to find the measures of the other angles.
The value of the other angles
∠1 = 180 - 82°
∠2 = ∠1 = 98°
∠3 = ∠ = 98°
∠4 = ∠5 = 82°
According to the given data,
m∠5=82° given
∠5 = ∠7 = ∠4 = ∠8 = ∠6 = ∠12
∠1 = ∠10 = ∠2 = ∠11 = ∠3 = ∠ 12 = 180° - ∠5
we get, measures of other angles
∠1 = 180 - 82°
∠2 = ∠1 = 98°
∠3 = ∠ = 98 °
∠4 = ∠5 = 82°
A transversal is a line that intersects two coplanar lines at two different points. In the figure,
line t is a transversal. The table summarizes the names of angle pairs formed by a transversal.
Corresponding angles lie on the same side of the transversal and on the same
sides of the intersected lines. ∠1 and ∠5
Same-side interior angles lie on the same side of the transversal and between
the intersected lines. ∠3 and ∠6
Alternate interior angles are nonadjacent angles that lie on opposite sides of
the transversal between the intersected lines. ∠3 and ∠5
Alternate exterior angles lie on opposite sides of the transversal and outside
the intersected lines. ∠1 and ∠7
Same-Side Interior Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure.
Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of corresponding angles have the same measure.
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Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. 23,27,31,35,39, . . . .
The sequence 23,27,31,35,39, . . . . is arithmetic and the tenth term is: 59
We can determine that the sequence is arithmetic, because two consecutive terms differ by "d".
To solve this exercise we are going to apply the formula of the arithmetic sequence:
aₙ= a + (n-1) * dd = aₙ₊₁ - aₙWhere:
a = first termd = common difference of the sequencen= number of termsInformation about the problem:
Sequence = 23,27,31,35,39, . . . . Tenth term = ?Calculating the "d" term, we have:
d = aₙ₊₁ - aₙ
d = 27 - 23
d = 4
Calculating the tenth term, we get:
aₙ= a + (n-1) * d
a₁₀= 23 + (10-1) * 4
a₁₀= 23 + (9) * 4
a₁₀= 23 + 36
a₁₀= 59
What is an arithmetic sequence?It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.
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Select the correct answer.
Triangle ABC represents a triangular property lot where the measure of ZA is 50°, the measure of ZB is 68°, and the measure of ZC
is 62⁰:
What is the longest side of the property?
Cannot be determined
O
BC
O AC
O
AB
Answer:
AC is the longest side
Step-by-step explanation:
• the longest side is side opposite largest angle in the triangle
• the shortest side is opposite the smallest angle in the triangle
the largest angle is ∠ B = 68°
the longest side is then AC
Find the geometric mean between pair of numbers.
36 and 24
The value of the geometric mean of the numbers 36 and 24 is.
Gm ( 36, 24) = 12√6
How is the geoemetric mean determined?The definition of geometric mean is a calculation that is performed on a set of numbers which consists of calculating the square root of the product between them, the equation is as follows:
Gm (a,b) = √ab
Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b
a = 36b = 24We substitute and solve for the square root
Gm (36, 24) = √ab = √36×24
Gm (36, 24) = √864
Gm (36, 24) = √6×144
Gm ( 36, 24) = 12√6
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Solve each equation for y .
12 y=3 x
After solving the equation, the value of y = x/4 for the equation 12 y=3 x.
⇒ 12 y=3 x
⇒ y = 3x/12
⇒ y = x/4
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Here is the picture it says xxxxxxxxxxxxxxxxxxx
Answer:
Step-by-step explanation:
given: 5^3/5^7
= 1/5^(7-3)
= 1/5^4
= 1/625
final answer: 1/625
Answer:
[tex]5^{-4}[/tex]
Step-by-step explanation:
using the rules of exponents
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
given
[tex]\frac{5^{3} }{5^{7} }[/tex]
= [tex]5^{(3-7)}[/tex]
= [tex]5^{-4}[/tex]
= [tex]\frac{1}{5^{4} }[/tex] ← if required with a positive exponent
Which is one condition that must be present for an inverse relation to be a function?
A- The inverse relation must be a straight line.
B- The function must be a straight line.
C-The function must pass the vertical line test.
D- The inverse relation must pass the vertical line test.
the correct option is D, the inverse relation is only a function if it passes the vertical line test.
When an inverse relation is a function?A relation maps elements from one set (called the domain) into elements of another set (called the range).
A relation is a function only if each element in the domain is mapped into only one element of the range. So, there is something called the vertical line test.
It says that if at any part of the graph of the relation you can draw a vertical line that intercepts the graph of the relation more than once, then it is not a function. Passing the vertical line test means that no vertical line intercepts the graph more than once.
Then the correct option is D, the inverse relation is only a function if it passes the vertical line test.
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Can y’all please help me on question 23 please I need help
1. Round 68.14 to the nearest tenth. 2.round 61.98265 to the nearest thousandth
Answer:
1. 68.1
2. 61.983
Step-by-step explanation:
nearest tenth is one digit after the decimal. nearest thousandth is three digits after the decimal. since 4 is less than 5, the 1 remains the same. in the second problem, the fourth digit is 6 which is greater than 5 so you change the 2 to a 3.
Consider the line -9x-6y=8.
What is the slope of a line perpendicular to this line
What is the slope of a line parallel to this line?
Slope of a perpendicular line:
Slope of a parallel line:
Answer:
Slope of a perpendicular line:
[tex]\boldsymbol{\dfrac{1}{9}}[/tex]
Slope of a parallel line:
[tex]\boldsymbol{-9}[/tex]
Step-by-step explanation:
A line perpendicular to a line y = mx + b will have its slope as[tex]-\dfrac{1}{m}[/tex]
Here slope of given line = -9
[tex]\displaystyle \mathrm {reciprocal\; of\;} -9 = -\dfrac{1}{9}[/tex]
[tex]\mathrm {negative\; of \;reciprocal\;}= -\left(-\dfrac{1}{9}\right) = \dfrac{1}{9}\\[/tex]
parallel lines have the same slope so a parallel line will have slope = -9
Every day, the Randolph Pet Store uses 2/3 of a bag of dog food to feed the dogs. How many days will 1 1/3 bags of dog food last?
Write your answer as a fraction or as a whole or mixed number.
A question paper has two parts, a and b, each containing 10 questions. if a student has to choose 7 from part a and 4 from part b, in how many ways can he choose the questions?
Combinations exist ways to select elements from a collection in mathematics where the order of the selection exists irrelevant. He can choose the question in 28 ways.
What is meant by combinations?
Combinations exist mathematical operations that count the number of potential configurations for a set of elements when the order of the selection exists is irrelevant. You can select the components of combos in any order.
The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.
Given: Number of questions in part A = 10
Number of questions in part B = 10
A student chooses 7 from part A and 4 from part B
Required number of ways = ( 10C7 × 10C4) × ( 10C3 × 10C6)
= 5040 × 24/ 6 × 720
= 28
He can choose the question in 28 ways.
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Part 3 of 3 Graph the equation y=49x, where y represents the distance traveled over time, z, in hours is the relationship proportional? How many miles from home is the family after 5 hours?
Refer to the graph below for the graphical representation of the given equation y = 49x.
What is an equation, exactly?An equation, in its most basic form, is a mathematical statement that proves two mathematical expressions appear to be equal.The expressions 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14.Graph:
A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that depicts the variation of one variable in comparison to another. A grouping of all points whose coordinates satisfy a given relationship (such as a function).Refer to the graph given below for the equation y=49x.
Therefore, the graph of the given equation y=49x is shown below.
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Directions: Using the digits 1 to 9 at most one time each, fill in the blanks to make the largest quotient.
Using the digits 1 to 9 at most one time each to make the largest quotient is 98 ÷ 12 .
According to the question we have to use digits 1 to 9 at most one time each to make the largest quotient.
Now we know that the number that is being divided is known as the dividend and the number by which we divide is known as the divisor.
Now dividend should be greater than the divisor.
So tot make the largest quotient the dividend and the divisor will be
98 and 12 respectively.
That is, 98 ÷ 12 = 8.2 which is the largest quotient.
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Marsha pays $20 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 6 months of having the membership?
|−20| − 6 = $14
|−20| − |6| = $14
−6|20| = −$120
6|−20| = $120
The total amount subtracted from her account after 6 months of having the membership is −6|20| = −$120. option C
Given:
Cost of membership
Cost per month for a car wash membership = $20
Number of months = 6 months
Total amount subtracted from her account = Number of months × Cost per month for a car wash membership
= 6 (-20)
= -120
Therefore, the total amount subtracted from her account after 4 months of having the membership is −6|20| = −$120.
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The formula used to convert degrees Celsius to degrees Fahrenheit is F=95C+32F= 59 C+32.Convert 68°F to degrees Celsius. Solve the formula for C, and then use it to convert the temperature.Which is the correct formula and conversion
Answer:
Step-by-step explanation:
F = 9/5 C + 32 is the correct formula.
9/5 C = F - 32
C = 5/9(F - 32)
So, 68 degrees Fahrenheit
= 5/9(68 - 32)
= 5/9 * 36
= 20 degrees C.
p²m ÷ 4; use m = 4, and p = 7
Answer:
[tex] \sf{49}[/tex]
Step-by-step explanation:
Given that,
m => 4
p => 7
Let us solve the given expression by using the given values.
[tex] \sf \: {p}^{2} m \div 4 \: \: \: \: \: \\ \sf{(7)}^{2} \times 4 \div 4 \\ \sf 49 \times 4 \div 4 \\ \sf196 \div 4 \: \: \: \: \: \: \\ \sf49 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
In an examination for the final year student of a school 60 offered history 50 offered economics and 48 offered literature,30 offered history and economics 16 offered history and literature 22 offered economics and literature if 10 candidate offered all the three subject find the number that offered only history
Answer:
Step-by-step explanation:
History(H),Economics(E),Literature(L)
1a).To find History(H) only is
H only =H-HE-HL+HEL
H only =60-30-16+10=24
b).E only=50-30-22+10=8
c). L only=48-22-16+10=20
2).no of candidates who sat for the exam is 24+8+20=52
The focus of a parabola is (0, -1). The directrix is the line y = 0. What is the equation of the parabola in vertex form?
In the equation y = (-k)² +h, the value of pls
The vertex of the parabola is the point (
The equation of this parabola in vertex form is y =
).
x²-1
The equation of the parabola in vertex form is
P is -[tex]\frac{1}{2}[/tex]
(0,-[tex]\frac{1}{2}[/tex])
y=[tex]\frac{-1}{2}[/tex][tex]x^{2}[/tex] -[tex]\frac{1}{2}[/tex]
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a variety of seemingly unrelated mathematical descriptions, all of which may be shown to define the same curves.
One definition of a parabola includes a line and some extent (the focus) (the directrix). The directrix isn't the main focus. The locus of points therein plane that is equally spaced apart from the directrix and the focus is known as the parabola. A right circular conical surface and a plane parallel to a different plane that is tangential to the conical surface intersect to form a parabola, which is additionally known as a conic section.
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The right-angled triangle ABC has an angle BAC of 30º. Taking the length of BC to be one unit:
a. work out the length of AC
b. use Pythagoras' theorem to obtain the length of AB
Answer:
a) [tex]\sqrt{3}[/tex]
b) 2
Step-by-step explanation:
a) tan 30 = opposite side / adjacent side 1/[tex]\sqrt{3}[/tex] so AC is [tex]\sqrt{3}[/tex]
b)3
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]1^{2}[/tex] +[tex]\sqrt{3} ^{2}[/tex] = [tex]c^{2}[/tex]
1 + 3 = [tex]c^{2}[/tex]
4 = [tex]c^{2}[/tex]
[tex]\sqrt{4}[/tex] =[tex]\sqrt{c^{2} }[/tex]
2 = c
The length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The right-angled triangle ABC has an angle BAC of 30º.
The length of BC be one unit
We have to find the length of AC
tan (30)= opposite side/ adjacent side
1/√3 = opposite side/ adjacent side
The adjacent side is √3 which is length of AC
Now let us find the length of AB by using pythagoras theorem
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
AB² = AC² + BC²
AB²=√3² + 1²
AB²= 4
AB = 2 units
Hence, the length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem
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