Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is obtuse.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
4 + 12 > 14
12 + 14 > 4
14 + 4 > 12
Hence, these set of numbers can be the measures of the sides of a triangle.
According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:
acute if [tex]c^{2} < a^{2} + b^{2}[/tex]
obtuse if [tex]c^{2} > a^{2} + b^{2}[/tex]
right if [tex]c^{2} = a^{2} + b^{2}[/tex]
∴The longest side is 14.
Hence, a = 4, b = 12 and c = 14;
Consider [tex]a^{2} + b^{2}[/tex] :
[tex]= 4^{2} + 12^{2}[/tex]
= 160.
Now consider [tex]c^{2}[/tex] :
= [tex]14^{2}[/tex]
= 196.
Thus, [tex]c^{2} > a^{2} + b^{2}[/tex]
Hence, the triangle is obtuse.
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Determine the values of x in the equation x2 = 49.
Answer:
x = 7
Step-by-step explanation:
➟ x² = 49
in order to find the value of x will have to take square root of both side
➟ [tex] \sf \sqrt{x} = \sqrt{49} [/tex]
Calculate
➟ [tex] \sf \: x = 7[/tex]
Find the least common multiple of each pair of polynomials.
9(x+2)(2 x-1) and 3(x+2)
The least common multiple of the given polynomial 9(x+2)(2 x-1) and 3(x+2) is 3(x + 2).
According to the given question.
We have two polynomials 9(x + 2)(2x - 1) and 3(x + 2).
Since, we have to find the least common multiple of 9(x + 2)(2x -1) and 3(x+2).
As we know that, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.
From the definition of least common multiple, we can say that the least common multiple of 9 and 3 is 3 and (x +2)(2x -1) and (x + 2) is (x + 2).
Thereofrore, the least common multiple of the given polynomial 9(x+2)(2 x-1) and 3(x+2) is 3(x + 2).
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Sean is thinking of a 3 digit number. the digit in the hundreds place is 1 more than the digit in the ones place. the value of the digit in the ones place is 25 less than the value of the digit in the tens place. what number is sean thinking of?
635 is the 3 digit number Sean is thinking of.
What is a digit?A digit is one of the elements of a set that makes up a numeration system. Thus, in a certain context, a digit is a number. The digits in the decimal (base-10) Arabic numbering system are the constituents in the set 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Let a, b , c the digits of hundreds place, tens place and ones places.
Let the digit in the tens place be x, thus b = x
The digit in ones place is 25 less than the value of the digit in the tens place
c = x - 25
And finally, he digit in the hundreds place is 1 more than the digit in the ones place
a = (x - 25) +1
If a, b , c are digits of there respective places the the value of their digits are
a(100), b(10) c(1)
Now, b can be any no. which is more than 25 so as to make positive ones place, lets say 30
b = 30 = x
Thus x = 3, so
a = ( x - 25) +1
= ( 30 - 25) +1
= 6
c = 30 - 25
= 5
Thus, 635 is the 3 digit number Sean is thinking
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The points (-10, q) and (10, -9) fall on a line with a slope of -1/5. What is the value of q?
I need ur help please explain i don't understand check attachment
The graph of the given piecewise function is given at the end of the answer.
What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For this problem, the function is defined as follows:
f(x) = 2/3x, for x ≤ 0.f(x) = 3, for 1 ≤ x ≤ 3.f(x) = -2x + 5, for x ≥ 4.Hence:
To the left of x = 0, the function is increasing and linear.Between x = 1 and x = 3, the function is constant at x = 3.To the right of x = 4, the function is decreasing and linear.The function is given at the graph with the end of answer, with holes where the function is not defined, and multiple behaviors as it is piecewise.
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11
Collaborato
05 Use Math Tools Work with a partner, if the
the figure at the right is 40", determine the me
angle without using a protractor.
Answer:
1) 140°
2) 40°
3) 140°
4) 40°
5) 140°
6) 40°
7) 140°
Step-by-step explanation:
1) Angles on a straight line = 180°
180° - 40° = 140°
2) Angle 3 is Vertically opposite to Angle 1
So they are the same Angle
3) Angle 4 is Vertically opposite to Angle 2
So they are the same Angle
4) Angle 5 is corresponding to Angle 1
So they are the same angle
5) Angle 6 is corresponding to Angle 2
So they are the same angle
6) Angle 7 is corresponding to Angle 3
So they are the same angle
7) Angle 7 is corresponding to Angle 4
So they are the same angle
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
also show regular work
What is 1 5/17 as a decimal
What is 2 3/8 as a decimal
Answer:69999
Step-by-step explanation:your gay
Tanya bought the least expensive brand of dog food. Eddie bought the most expensive brand of dog food. Which brand did each person buy?
Tanya - Iams ProActive Lamb & Rice
Eddie - Ultimate Pet Nutrition Nutra Complete
y=x-3
y=-4x+3
Determine whether the pair of lines listed is parallel, perpendicular or neither.
The given equations are neither parallel nor perpendicular with each other.
According to the question, to calculate the slope of the given equations.
y = x - 3 and Y = 4x + 3
Now, equate the given equations with the standard slope equation that is: y = mx + c
Using above equation, the slope for first equation is: m1 = 1
And the slope for the second equation is: m2 = 4
When the value of the slopes are equal, means lines are parallel. Similarly, when the value is negative one, then the lines are perpendicular to each other otherwise neither parallel nor perpendicular.
Hence, the given equations are neither parallel nor perpendicular with each other.
What is the slope of a line?
The slope of a line is the ratio of the y-axis coordinates and the x-axis coordinates. It is also called as gradient which tells the steepness of a straight line. Depending upon the values, it is categorized as parallel, perpendicular or no line.
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Can y’all help me please
Step-by-step explanation:
least value is q
greatest value is n-q
close to zero is q-n
point C is on a line segment BD .Given BD = 5x , BC = 4x and CD = 4 determine the numerical length of BD
The numerical length of BD is 20.
We have a Line Segment BD and a point C on it.
We have to determine the numerical length of BD.
What is Line Segment?A line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
According to question, we have -
BD = 5x
BC = 4x
CD = 4
Now,
BD = BC + CD
5x = 4x + 4
x = 4
Therefore - BD = 5x = 5 x 4 = 20
Hence, the numerical length of BD is 40.
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Write the following quantities in second .
5•10⁷ µs
The value of 5•10⁷ µs quantity in second is 50 .
The unitary methodology could be a methodology within which you discover the worth of a unit then the worth of a needed range of units.For simplification, invariably write the items to be calculated on the right-hand aspect and things illustrious on the left-hand aspect.In the unitary method, the value of many things is given and we need to either find the value of more or fewer things. In order to try to to that, we have a tendency to should initial realize the worth of 1 issue by division so realize the worth of additional or fewer things by multiplication.We know that 10⁶μs is equal to 1 second .
Using unitary method , we get
1 μs have = 10⁻⁶ second
5•10⁷ µs have = 5 × 10⁷ × 10⁻⁶
= 50 second
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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point.
y=-x^2-6x-16
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-16} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -6}{2(-1)}~~~~ ,~~~~ -16-\cfrac{ (-6)^2}{4(-1)}\right) \implies \left( - \cfrac{ -6 }{ -2 }~~,~~-16 - \cfrac{ 36 }{ -4 } \right) \\\\\\ (-3~~,~~-16+9)\implies (-3~~,~~-7)[/tex]
!!100 points!!
determine whether each equation represents a linear function.
-4x + 2y = 10
y = 2x^2 - 3x + 5
x = -5
y = 1.5x
!!!!please explain your reasoning!!!!
The equation -4x + 2y = 10 represents a linear function
[tex]y = 2x^2 - 3x + 5[/tex] represents a non-linear function
x = -5 represents a linear function
y = 1.5x represents a linear function
The linear functions don't have any exponents higher than 1. Some of them don't have variables at all, and if they do, they have just plain x, which is equal to x to the first power.
When a linear function is written in its simplest form, it looks like y = a + bx, where a and b are both constants.
-4x + 2y = 10 represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
[tex]y = 2x^2 - 3x + 5\\[/tex] represents a non-linear functions as it lies in the plain (x-y) and it has power higher than 1. The highest power of the exponent is 2.
x = -5 represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
y = 1.5x represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
Therefore, equations -4x + 2y = 10 , x = -5 , y = 1.5x are linear functions.
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The equation -4x + 2y = 10 represents a linear function
[tex]y = 2x^2 - 3x + 5[/tex] represents a non-linear function
x = -5 represents a linear function
y = 1.5x represents a linear function
The linear functions don't have any exponents higher than 1. Some of them don't have variables at all, and if they do, they have just plain x, which is equal to x to the first power.
When a linear function is written in its simplest form, it looks like y = a + bx, where a and b are both constants.
-4x + 2y = 10 represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
[tex]y = 2x^2 - 3x + 5[/tex] represents a non-linear functions as it lies in the plain (x-y) and it has power higher than 1. The highest power of the exponent is 2.
x = -5 represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
y = 1.5x represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
Therefore, equations -4x + 2y = 10 , x = -5 , y = 1.5x are linear functions.
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The vertex of a parabola is (−2, 6) and its y-intercept is (0, 2). The parabola is the boundary of a quadratic inequality. The boundary is drawn with a dashed line, and the interior of the parabola is shaded.
The compound inequality in this problem is represented by:
y > -(x + 2)² + 6.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the vertex is at (-2,6), hence:
h = -2, k = 6.
y = a(x + 2)² + 6.
When x = 0, y = 2, hence we use it to find a as follows:
2 = 4a + 6
a = -1.
Hence:
y = -(x + 2)² + 6.
The inequality is the interior of the parabola, hence values greater, and the parabola is dashed, hence it is an open interval and the inequality is given by:
y > -(x + 2)² + 6.
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Solve the following inequality algebraically.
x^2+2x-24< 0
Answer:
-6<x<4
Step-by-step explanation:
x^2+2x-24=0
(x-4)(x+6)=0
x-4=0
x+6=0
x=-6,4
x<-6 false
-6<x<4 true
x>4 false
so -6<x<4
Help me please please
Evaluate the sum of the finite geometric series. Σ⁴ n=1 (2/3)ⁿ⁻¹
Sn = a(1 - rⁿ)/(1 - r) is the formula for the sum of a finite number of terms in a geometric series, where is the number of terms, is the first term, and is the common ratio.
The sum of the finite geometric series, Σ⁴ n=1 (2/3)ⁿ⁻¹ be 2.407.
What is meant by finite geometric series?The equation be Sn = a(1 - rⁿ)/(1 - r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an finite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.
Let the series be Σ⁴ n=1 (2/3)ⁿ⁻¹
Σ⁴ n=1 (2/3)ⁿ⁻¹ = (2/3)¹⁻¹ + (2/3)²⁻¹ + (2/3)³⁻¹ + (2/3)⁴⁻¹
= 1 + (2/3) + (2/3)² + (2/3)³
= 1 + (2/3) +(4/9) +(8/27)
Where, the first term is a = 1
common ratio be r = 2/3
n th term be n = 4
Let the equation be Sn = a(1 - rⁿ)/(1 - r)
substitute the values in the above equation, we get
S4 = 1(1 - (2/3)⁴)/(1 - (2/3))
S4 = 1(1 - (16/81)⁴)/(1/3)
S4 = (65/81) × 3
S4 = (65/27) = 2.407
Therefore, the sum of the finite geometric series, Σ⁴ n=1 (2/3)ⁿ⁻¹ is 2.407.
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Write an explicit and a recursive formula for each sequence. 0,6,12,18,24, . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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There was a base fee of $17.95 and there was an additional charge of 92 cents for each mile driven. Shen had to pay $173.43 when he returned the truck. For how many miles did he drive the truck?
Th number of miles driven by truck is 169.
What is defined as the unitary method?The unitary method is an approach that involves determining the value of a single unit and then calculating the value of the necessary number of units based on that value.The unitary method's formula is to identify the value of a single unit and afterwards multiply that value by the number of units to get the required value.For the given question:
The base fee of the drive = $17.95.
The additional charges are 92 cents for each mile driven.
The additional charges = $0.92
Let 'x' be the miles driven by the truck.
Thus, the total additional charges for the drive of x miles will be: 0.92x.
So, the total charge for truck drive is;
The total charge are given as $173.43.
Total charge = base charge + additional charge
$173.43 = $17.95 + 0.92x
0.92x = $173.43 - $17.95
0.92x = 155.53
x = 169.05
x = 169 miles.
Thus, the total number of miles driven by the truck are 169 miles.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write
3 2/3
as an improper fraction. You must show your work to receive all possible points.
The fraction converted to an improper fraction is 11/3
What is an improper fraction?An improper fraction can be defined as a type of fraction whose numerator is equal to or is greater than its denominator.
Examples of improper fractions are;
5/ 3, 8/2 , 11/ 7, 20/ 5, 4/ 1, 2/ 2, 5/ 3
Given the fraction;
3 2/3; this is a mixed fraction
To convert to improper fraction, we take the steps
Multiply the whole number by the denominator;
= 3 × 3 = 9
Add the value to the numerator
= 9 + 2 = 11
Divide by the denominator
= 11/ 3
Thus, the fraction 3 2/3 converted to an improper fraction is 11/3
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Two similar pyramids have slant heights of 6 inches and 12 inches. What is the ratio of the surface area of the small pyramid to the surface area of the large pyramid?
The Volume of the requested pyramid is 68.5 in³.
What is the scalar factor?The scale factor is a dimensionless number that allows us to relate dimensions in figures, it is also known as numerical ratio or proportion.
We must determine the scale factor with the data of the inclined heights of each of the pyramids:
a/b = slant height (small) / slant height (large) = 6/12 = 3/6 = 1/2a/b = 1/2If the scale factor is a/b, the reason of the volume will be:;
(a/b)³ = 1/8
1/8 = V/540
V = 1/8 x 540
V = 68.5
V = 68.5in³
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Michael is driving to Dallas. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Michael has 61 miles to his destination after 15 minutes of driving, and he has 49.8 miles to his destination after 29 minutes of driving. How many miles will he have to his destination after 33 minutes of driving?
In linear equation, 16.6 miles will he have to his destination after 33 minutes of driving.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."for linear equation rate of change is constant .
rate of change of distance from destination with respect to time
= 49.8 - 61/29 - 15
= -11.2/14
= -0.8
now the distance from destination after 57 minutes driving
= 49.8 + (-0.8)( 33 - 29 )
= 19.8 -3.2
= 16.6 miles
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pls help, i rlly dont know what this is
Answer:B
Step-by-step explanation:
Answer:
Step-by-step explanation:
option b is correct
9/4 = 2.25
13.5/6 = 2.25
do the last one yourself
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
Angles 1 and 7 are alternate exterior angles.
The statement "∠1 and ∠7 are alternate exterior angles" is true
Given,
The statement "∠1 and ∠7 are alternate exterior angles"
Here,
∠1 and ∠7 are lie on opposite sides of the transversal and both are nonadjacent exterior angles
So, ∠1 and ∠7 are alternate exterior angles.
Hence, the statement "∠1 and ∠7 are alternate exterior angles" is true
The complete question is:
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
Angles 1 and 7 are alternate exterior angles.
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Derek paid $3.20 for a 4 pack of Gatorade.
What is the cost per bottle?
Answer:
80¢ / 80centsStep-by-step explanation:
80¢ is your answer because Derek paid $3.20 for a pack of 4 Gatorade so you would have to divide $3.20 by 4 which will be 80¢
So your answer would be 80¢ per bottle.
Evaluate each expression for a=3 and b=-5 . 3(a-b)
Evaluating the expression 3(a - b) for a = 3 and b = -5 is equal to 24.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.
Given the expression 3(a - b), substitute the value of the variable a and the value of variable b.
3(a - b)
3[3 - (-5)]
Performing the arithmetic operations, we can have the value of the expression.
3[3 - (-5)]
= 3(3 + 5)
= 3(8)
= 24
Hence, the expression 3(a - b) when a = 3 and b = -5 is equal to 24.
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how many 0.8-liter glasses of waters does it take to fill up a 10.4-liters pitcher
13 litres of 0.8-liter glasses of waters does it take to fill up a 10.4-liters pitcher.
Concept: In simple words, division can be defined as the splitting of a large group into smaller groups such that every group will have an equal number of items. It is an operation used for equal grouping and equal sharing in math.
Quantity of 1 glass of water= 0.8 liters
Quantity to be filled completely = 10.4 liters
No . of 0.8-liter glasses of waters does it take to fill up a 10.4-liters pitcher = 10.8/0.4 = 13
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12 Express this product in scientific notation: (11 x 10¹¹) (12 × 10¹²).
A. 1.32 × 1023
B . 13.2 x 1025
C. 132 x 1025
D. -1.32 x 1025
Answer: The answer is c 1.32 x 10^25
Step-by-step explanation:
