The side lengths 300 mm and 190 mm make a valid triangle because of the triangle inequality theorem
How to determine if the side lengths make a triangle?The side lengths are given as
300 mm and 190 mm
To solve this question, we make use of the triangle inequality theorem
The triangle inequality theorem states that
Given that the sides of a triangle are x, y and z.
The sum of any two sides of a triangle is greater than or equal to the third side;
This means that
x + y ≥ z
Using the above as a guide, we have the following inequality expressions
300 + 190 ≥ z
300 + z ≥ 190
z + 190 ≥ 300
Evaluate the inequality expressions
490 ≥ z
z ≥ -110
z ≥ 110
Remove the negative value
490 ≥ z
z ≥ 110
Combine the inequalities
110 ≤ z ≤ 490
The above inequality is a valid inequality expression
Hence, the side lengths 300 mm and 190 mm make a valid triangle
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These are the first four terms of a sequence, -2, 1, 8, 19. Write down the next term of this sequence.
24+6x=10x
PLS help ASAP!!!
Answer:
6?
Step-by-step explanation:
24=10x-6x
24=4x
6=x
Pls pls help whoever gets it right gets a crown
Answer:
Step-by-step explanation:
A. The common factor of the expression is 5[tex]x^{3}[/tex]y
B. In order to find a common factor, you find the prime factor. In this case, the biggest number that goes evenly into 40 and 25 is 5.
C. Divide the original problem by the common factor 5[tex]x^{3}[/tex]y
that gives you 5[tex]x^{3}[/tex]y(8x[tex]y^{2}[/tex]-5)
Hope this helps!
Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. When the frisbee is thrown, it follows a parabolic path that is modeled by the function h(t) = â€" 0. 145t2 0. 019t 5. 5. How many seconds will it take for the frisbee to hit the ground?
If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of seconds it will take for the frisbee to hit the ground is: 6.2 seconds.
Number of secondsGiven:
0.145t² + 0.019t + 5.5 = 0
Using almighty formula or quadratic formula
t=-b±√b²-4ac/2a
Where:
b²=19²
a=145
c=5500
Let plug in the formula
t=-19±√19²- 4(-145) (5500)/2(-145)
t=-19±√361+(3,190,000)/-290
t=-19±√3,190,361/-290
t=-19±1,786.158/-290
Hence,
-19-1,786.158/-290; -19+1,786.158/-290
t=6.2; 6.09
Therefore If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of seconds it will take for the frisbee to hit the ground is: 6.2 seconds.
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The number 6 comma 107 comma 200 can be expressed using scientific notation as ________.
The number 6 comma 107 comma 200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex].
Scientific notation is used to represent a very large number or a very small number in Simple way.
Steps to find scientific Notation of a number
Step (i) Move the decimal point until a number between 1 and 10 is created.
Step (ii) Count the number of times the decimal is moved .
Step (iii) If the decimal is moved n times then multiply the term by n times of 10.
In the given question
the number 6107200.
Step (i) We will move the decimal 6 place towards left.
number becomes 6.107200
Step (ii) The decimal is moved 6 place towards left.
Step (iii) we will multiply by [tex]10^{6}[/tex].
[tex]=6.1072*1000000[/tex]
So , the number becomes [tex]6.1072*10^{6}[/tex]
Therefore , the number 6107200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex]
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Oabc is a square o is 0,0 a is -2,2 b is 0,4 c is 2,2 A single transformation of oabc is such that A is mapped to c. C is mapped to a O and b are invariant points Describe fully transformation
Using translation concepts, it is found that the transformation is a reflection over the y-axis.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, we have that A is mapped to C and vice-versa. Since they are equidistant to the y-axis, we have that the rule is given by:
(x,y) -> (-x,y).
Meaning that the transformation is a reflection over the y-axis.
For O and B, the rules are given as follows:
O: (0,0) -> (-0,0) = (0,0).B: (0,4) -> (-0, 4) = (0,4).Showing that points O and B are invariant, keeping the same coordinates and confirming that the transformation is a reflection over the y-axis.
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The cost of Jake's cell phone bill is determined by how many megabytes of
data he uses each month, as shown in the graph below.
Jake's Cell Phone Bill
70
60
50
40
30
20
10
0
5
10
Data Usage (megabytes)
A. y = 0.5x + 40
B. y = 2x + 40
C. y 40x + 0.5
D. y = 40x + 2
15
X
Which equation represents the cost of Jake's cell phone bill, y, based on his
data usage in megabytes, x?
Step-by-step explanation:
Given that
The cost of Jake's cell phone bill is determined by how many megabytes of data he uses each monthas shown in the graphTo find
Which equation represents the cost of Jake's cell phone bill, y, based on his data usage in megabytes, x?So, according to the question
we have,
The co-ordinates of that line, from graph(0,40) and (15,70)
We have to find the equation of line
So, we know that
The equation of liney = mx + c, ---------------(1)
From graph,
c = 40 and
m = slope (we have to find it)
We kwon the slope of any two point
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where,
x₁ = 0 , and y₁ = 40
x₂ = 0 , and y₂ = 40
So,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{70-40}{15-0}[/tex]
m = [tex]\frac{30}{15}[/tex]
m = 2
Now putting the all values in equation (1)
We will get,
y = mx + c, ---------------(1)
y = 2x + 40
Answer:
The equation of line is y = 2x + 40. So option B is correct.To learn more about equation of line, please click on the link:
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Simplify by combining like terms. 3 a+b+a
The simplification by combining like terms of 3a + b + a is 4a + b.
According to the given question.
We have an expression 3a + b + a.
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression 3a + b + a.
Here 3a and a both are the like terms.
So, we add coeffcients of a to simplify the given expression.
Therefore, the simplification of 3a + b + a is given by
3a + b + a
= 3a + a + b
= 4a + b
Hence, the simplification by combining like terms of 3a + b + a is 4a + b.
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help i have to do this in likee 7 days
Write a recursive definition for each sequence. 5,22,39,56, . . . . .
This sequence follows the rules of Arithmetic Progression
Arithmetic Progression is an example of mathematical sequences. In this sequence, the next term is generated by adding the previous term to a fixed number which is called 'Common Difference'. This is generally represented by 'd'. It is calculated by subtracting any two consecutive terms in the sequence.
We can generally find out any term of the given statement. The [tex]n^{th}[/tex] term of a sequence is calculated by adding the previous term to the common difference. The formula to calculate the [tex]n^{th}[/tex] term of an Arithmetic Progression is :
=> [tex]a_{n} = a_{n-1} + d[/tex]
Here, n = No. of term, [tex]a_{n-1}[/tex] = previous term, and d = common difference
In the given sequence, 5,22,39,56......
Each term is separated by a common difference 'd'
Calculating d = a2-a1 => d = 22-5 => d = 17
Every term has a common difference of 17 so this is an Arithmetic Sequence
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Using the diagram above, how many lines are located on plane A? Group of answer choices 8 6 12 4
The number of lines located on plane A using the given diagram are 4.
As given in the question,
Number of lines located on plane A are as follow:
Point outside the plane A are T, W, S
Points located on plane A are as follow:
V, M, N, P
Lines formed by located points V, M, N, P on plane A
VM, VN, VP and MP
Therefore, number of lines located on plane A using the given diagram are 4.
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Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 3,-3,3,-3, . . . . . ..
In the given sequence, the next term is obtained by multiplying the next term by (-1), hence it is a geometric sequence with r = 1. The next two terms are 3, -3.
Arithmetic sequence.
In a arithmetic sequence, the next term = the previous term + common difference. Or mathematically:
a(n) = a(n-1) + d
or d = a(n) - a(n-1) for all n
Where d = common difference.
Geometric sequence.
In a geometric sequence, the next term = the previous term x common ratio. Or mathematically:
a(n) = a(n-1) . r
or r = a(n)/a(n-1) for all n
Where r = common ratio
The sequence given:
3,-3,3,-3, . . . . .
In this sequence:
a(1) = 3
a(2) = -3
a(3) = 3
a(4) = -3
Check whether it has a common differenceThe next two terms means a(5) and a(6). We already have a(4) = -3. Hence,
a(5) = a(4) . r = -3. (-1) = 3
a(6) = a(5) . r = 3. (-1) = -3
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I will mark BRAINLIEST AND GIVE EXTRA POINTS TO WHOEVER ANSWERS
I really don't understand this please help meh thanks :)
Answer: 1 ) other angle = 32.0°
2 ) A = ( -2, -2 )
B = ( 2, 5 )
C = ( 4, 2 )
Step-by-step explanation for first picture:
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
x + 58° = 90°
x = 90° - 58°
x = 32.0°
Step-by-step explanation for second picture:
( number on x line, number on y line )
A = ( 2, -2 )
B = ( -2, 5 )
C = ( -4, 2 )
reflection
A = ( -2, -2 )
B = ( 2, 5 )
C = ( 4, 2 )
Answer : second option
If your tire says P235/65R17, what is the diameter of your wheel? (Note: this should include the tire and the rim).
If the tire says P235/65R17, the diameter of your wheel will be 17 inches.
How to illustrate the information?The primary purposes of a car's tires are to carry the weight of the car, transmit traction and braking forces to the road surface, insulate against shocks from the road, and change and maintain the direction of motion.
It offers traction for braking and acceleration and reduces the number of road vibrations that reach the car's body.
It should be noted that the numbers that are written on the tire are vital in knowing the diameter that's illustrated.
In this case, when the tire says P235/65R17, the diameter of your wheel will be 17 inches.
In conclusion, it is 17 inches.
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Five million four thousand three hundred in standard form (maths watch)
(Laws of Exponents with Whole Number Exponents MC)
Evaluate one third raised to the seventh power divided by one third raised to the sixth power comma all raised to the second power.
one eighteenth
one ninth
1
one and one ninth
The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.
The given expression is [tex](\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}[/tex].
We need to evaluate the given expression.
What are the laws of exponents?Laws of exponents:
When multiplying like bases, keep the base the same and add the exponents. When raising a base with power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.Now, [tex](\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}=((\frac{1}{3})^{7-6})^{2}[/tex] (Because [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex])
[tex]=(\frac{1}{3})^{2}[/tex]
=1/9
The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.
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Audrey has $500 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $295.33. She buys 3 bicycle reflectors for $17.86 each and a pair of bike gloves for $33.62. She plans to spend some or all of the money she has left to buy new biking outfits for $55.17 each. Which inequality can be used to determine oo, the maximum number of outfits Audrey can purchase while staying within her budget?
The inequality that can be used to determine the maximum number of outfit she can purchase is 55.17oo ≤ 117.47.
What is the inequality?The first step is to determine which inequality sign would be used.
The following are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The sign that would be used is the less than or equal to sign- ≤ . This is because Audrey cannot spend more than her budget.
The next step is to determine the total cost of items bought:
Total cost = $295.33 + (17.86 x 3) + 33.62 = $382.53
Now determine the amount of money she has left : $500 - $382.53 = $117.47
(Total amount spent on outfit) amount left
(oo x $55.17) ≤ 117.47
55.17oo ≤ 117.47
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Pls pls help whoever gets it right gets a crown
Answer:
last one is the correct one
Mark please
please help!!!!!!! need the right answer in like before 15 minutes please
45 because it's 45 and I'm smart with a PhD in maths
Find the slope of the line that contains the points (7,2) and (3,4)
According to the given statement the slop of the given points are: -(1/2).
The line's slope is described as:The slope of the line is the mathematical ratio of overall rise to the run, or rise divided by the run. It expresses the slope of a line in the coordinate plane. Calculating the slope of a line is comparable to finding the slope between two separate places.
How do I calculate the slope of an equation?The procedure for calculating the slope from such an equation will vary based on the form of the equation presented to you. If the equation is written as y=mx+c, the slope (or gradient) is simply m. If the formula does not exist in this form, try rearrangement.
According to the given information:The slope of a line is easily calculated by hand using small, whole number coordinates.
so,
X1 = 7
X2 = 3
Y1 = 2
Y2 = 4
Applying the formula for slope:
slope = (y₂ - y₁) / (x₂ - x₁)
= (4 - 2) / (3 - 7)
= 2/(-4)
= - (1/2)
The slop of the given points are: -(1/2)
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Find the value of x for the given values of a and b .
\a+2 / b+13=5 x , for a=18 and b=-1
The value of x so that the equation based on a and b has a solution is x = -7/5
What is an equation?An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.
Equations can be graphed, they are used to model many problems and theories.
As we can see, we have the following equation:
(a + 2)b + 13 = 5x
and we have the values of the coefficients a and b, and these are:
a = 18b = -1We substitute these values in the equation:
(a + 2)b + 13 = 5x
(18 + 2)-1 + 13 = 5x We solve the equation
(20)-1 +13 = 5x
-20 + 13 = 5x
5x = -7
x = -7/5
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We have to simplify by factorizing
How to solve it
A, B, C and D are four towns.
B is 30 kilometres due East of A.
C is 30 kilometres due North of A.
D is 45 kilometres due South of A.
a) Work out the bearing of B from C.
b) Calculate the bearing of D from
Angle 213.7° the bearing of D from towns A, B, C and D .
What is an angle in math?
When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.The bearing of B from D is angle ADB, which is
∠ADB = arctan(30/45) ≈ 33.7°
The bearing of D from B is that angle plus 180°, so is
180° +33.7° = 213.7°
We use angle ADB because the reference direction for bearings is North.
The tangent of an angle (ADB) is the ratio of its opposite side (AB) to its adjacent side (AD).
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Which of the following expressions have the same value as the mixed number ( ), select ALL correct answers.
Answer:
C,D, and E
Step-by-step explanation:
-29/4 is an improper fraction version of -7 1/4
-7- 1/4 = -7 1/4
-(7 + 1/4) is -29/4
Just make -29/4 into a mixed number, which is -7 1/4
Answer:
Step-by-step explanation: the answer is the last 3 ones because if you add them together, you get -7 1/4. Remember that -(number) = -1(number). So, -(1) = -1(1).
Find the geometric mean between pair of numbers. 4√3 and 10√3
The geometric mean between pair of numbers 4√3 and 10√3 is 10.95
We know that for a sequence of numbers x1, x2, . . . , xn
The formula of geometric mean is,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have been given two numbers 4√3 and 10√3
We need to find the geometric mean between pair of numbers, 4√3 and 10√3.
Using the formula for the geometric mean,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have two numbers.
So, the value of n is 2.
[tex]\Pi=\sqrt{4\sqrt{3}\times 10\sqrt{3} } \\\\\Pi=\sqrt{4\times 10 \times \sqrt{3}\times \sqrt{3} } \\\\\Pi=\sqrt{40 \times 3 } \\\\\Pi=\sqrt{120}\\\\ \Pi=2\sqrt{30}\\\\\Pi=10.95[/tex]
Therefore, the geometric mean between pair of numbers 4√3 and 10√3 is 10.95
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solve this please and thank you
If A-P-B and if AP=2x-9,AB=32 and PB=1.5x+6. Find Pb
Main Answer:
The required value of PB is 21.
An equation is a mathematical statement with an equal symbol between two expressions that have equal values.
Given: If A-P-B and if AP=2x-9, AB=32, and PB=1.5x+6.
To find: Find PB.
According to the question,
AP + PB = AB
On putting the given values, we get,
(2x-9)+(1.5x+6) = 32
2x - 9 +1.5x + 6 = 32
3.5x - 3 = 32
3.5x = 32+3
3.5x= 35
x=10
Now, we will substitute the value of x=10 in the equation, we get,
PB= 1.5x+6
PB= 1.5 × 10 + 6
PB=15 + 6
PB=21
Final Answer:
The simplified value of PB = 1.5x + 6 is 21.
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Add or subtract. Simplify where possible. 4 / x²-36 + x / x-6
Add or subtract.Simplify where possible.
[tex]\frac{4}{x^{2}-36} +\frac{x}{x-6}[/tex] = [tex]\frac{4+x^{2}+6x}{(x+6)(x-6)}[/tex]
How the given expression is simplified?
[tex]\frac{4}{x^{2}-36} +\frac{x}{x-6} \\\\\text{On taking LCM of the denominator}\\\\\frac{4}{x^{2}-36} +\frac{x^{2}+6x }{x^{2}-36}\\\\\frac{4+x^{2}+6x}{x^{2}-36}\\\\\frac{4+x^{2}+6x}{(x+6)(x-6)}[/tex]
What is simplification?
A mathematical expression is simplified when it is expressed in the simplest way possible.Generally, the simplest form is one that makes use of basic mathematical concepts like exponents, algebraic principles, and so forth.Its goal is to simplify the expression by getting rid of any repetition or redundancy.To learn more about simplification, refer:
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Kole and his sister ordered ice cream. He spent $6.50 for his sundae. She ordered the same sundae with sprinkles, which were an extra $0.40. Kole pays for his ice cream and half of his sisters with $10. How much change will he get back?
Pls explain it step by step
Answer:
$6.95
Step-by-step explanation:
Kole: $ 6.50
His sister : $6.50+$0.40
= $6.90
Half of his sister: $6.90/2 =$3.45
$10-($6.50 +$3.45)
=$10-$3.05
=$6.95
Kara is standing about 50 feet from the base of her apartment building, looking up at it with an angle of elevation of 75^{\circ} . What is the approximate height of Kara's building?
When measuring height, it is necessary to represent both the vertical position and the separation between the minimum and maximum place or location. The height of Kara's building is 186.6 ft.
What is meant by height?In math, height can be defined as the vertical distance from the top to the base of the object. Height is the distance between an object's highest and lowest points.
The measurement of an object's height from the base to the top is known as the height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.
Mount Everest's summit serves as an illustration of height.
Ignoring the height of Kara,
h = 50 tan 75°
substituting the value of tan 75°, we get
= 50 × 3.7321
Height of building = 186.6 ft.
Therefore, the approximate height of Kara's building is 186.6 ft.
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