By applying the Triangle Inequality Theorem, the number of non-identical triangles that can be made using the given side lengths is one.
What is the Triangle Inequality Theorem?In Mathematics, the Triangle Inequality Theorem can be defined as a type of theorem which states that the sum of any two (2) side lengths of a triangle must be greater than the measure of the third (2) side.
This ultimately implies that, the sum of the lengths of any two (2) sides of a triangle cannot be less than the length of the third (3) side of the triangle in accordance with the Triangle Inequality Theorem, as represented by this mathematical expression:
b - c < a < b + c
Where:
a, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem to the side lengths of this triangle, the number of non-identical triangles is given by:
5 + 7 > 10
12 > 10 (True).
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solve for N
6n−6=−9n+54
n=
Answer:
[tex]n=4[/tex]
Step-by-step explanation:
[tex]6n-6=-9n+54[/tex]
Shifting the like terms:
[tex]6n+9n=54+6[/tex]
Simplify the equation:
[tex]15n=60[/tex]
Solve for n:
[tex]n=\frac{60}{15}[/tex]
The final answer is:
[tex]n=4[/tex]
Express the ratio below in its simplest form. 2:4
Answer:
1:2
Step-by-step explanation:
we divide both numbers by 2
I believe that the ratio written in its simplest form would be 1:2 in ratio form.
Hope this helps!
how do i answer this?????
answer:
8.037m
step-by-step explanation:
the total of two or more addends is the sum of the numbers added.
your two addends are 5.89 and 2.147, so add them together.
5.89+2.147
=5.89+2.147
=8.037
the answer is 8.037m
Which of the following does the Pythagorean Theorem reveal
According to the Pythagorean theorem, "in a right-angled triangle, the squares of the hypotenuse side is equivalent to the sum of squares of the other two sides," the hypotenuse side is the longest side of the triangle.
This is further explained below.
What is Pythagorean Theorem?Generally, The Pythagorean theorem is a well-known geometric theorem that states the number of squares just on the legs of a right triangle is equal to the square just on the hypotenuse (the side that is opposite the right angle).
This theorem can also be expressed in the familiar algebraic notation of a2 + b2 = c2, where a and b are the lengths of the legs of the triangle.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is an essential connection in Euclidean geometry that describes the relationships between the three sides of a right triangle.
It indicates that the total of the areas of the squares on the other two sides is equal to the area of the square whose side is the hypotenuse.
In conclusion, This means that the area of the square whose side is the hypotenuse is equal to that amount.
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CQ Not found: Answered Generally
The diagonals of parallelogram LMNO intersect at point P. If MP = 2x + 5 and OP = 3x − 7, what is MP?
The value of MP in the parallelogram is 29 units.
How to find the diagonal of a parallelogram?A parallelogram is a quadrilateral with opposite sides equal to each other and opposite side parallel to each other.
Therefore,
The diagonals of parallelogram LMNO intersect at point P.
The diagonals of parallelogram LMNO are LN and MO.
The point P of the parallelogram divides each diagonal into exactly two equal parts.
Hence,
MP = OP
MP = 2x + 5
OP = 3x - 7
2x + 5 = 3x - 7
2x - 3x = -7 - 5
- x = - 12
x = 12
Therefore,
MP = 2(12) + 5
MP = 24 + 5
MP = 29
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Adam buyed 8 new video games each costing $19.97. How can you represent the total amount that will be withdrawn from his bank account?
Answer:
8*19.97=159.76
Step-by-step explanation:
Answer:
8*19.97=159.76
Step-by-step explanation:
In triangle NAP, measure of N= 45 and the measure of A= 70. Which statement best describes triangle NAP?
1. Segment NA is the longest side
2. Segment NP is the longest side
3. Segment AP is the longest side
4. Segment AP and segment NP are the longest sides and are congruent
Answer:
2. NP is the longest side
Step-by-step explanation:
I assume the messages of N and A are degrees if the angles there.
angle A = 70°
angle N = 45°
that means
angle P = 180 - 70 - 45 = 65°
because the sum of all angles in a triangle is always 180°.
and that means A is the largest angle, and its opposite side is therefore the longest in the triangle.
the side opposite of A is NP.
Lowes carries 3 types of plants. 1/10 of the plants are fruit bearing,
1/2 of the plants are flower bearing, the rest are
vegetable bearing plants. How many are vegetable bearing plants?
This problem is asking me to determine?
Write the equation you will be using to solve.
The number of vegetable-bearing plants is 12/5.
How to find the number of vegetable-bearing plants?Lowes carries 3 types of plants.
1/10 of the plants are fruit bearing
1/2 of the plants are flower-bearing
The rest are vegetable-bearing plants.
Solution:
Let x be the no of vegetable-bearing plants.
The total number of plants = Number of plants that are fruit-bearing + Number of plants that are flower-bearing + Number of plants that are vegetable-bearing.
3 = 1/10+1/2+x
Taking L.C.M.,
3 = 1+5+10x/10
3 = 6+10x/10
30 = 6+10x
30-6 = 10x
24 = 10x
x = 12/5
Therefore, 12/5 of plants are vegetable-bearing.
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Question content area top Part 1 In a certain chemical, the ratio of zinc to copper is 3 to 11 . A jar of the chemical contains 363 of copper. How many grams of zinc does it contain?
We need to know about ratio to solve this problem. The number of grams of zinc is 1331 grams.
Ratio in simple terms mean how many times one number contains another. In this question we know that the ratio of copper and zinc is 3 to 11 which means that in the chemical there are 3 parts of copper and 11 parts of zinc. The ratio between two things can be obtained by dividing one by the other and reducing it to the simplest fraction. We know that 363 grams of copper is present, we need to find the amount of zinc. Let us consider the amount of zinc to be x
363/x=3/11
x=363x11/3=121x11=1331
Therefore the amount of zinc present is 1331 grams.
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. Describe and correct the error in finding the sum.
X
8 65+ (−16)
(-1)
15
30
6
+
8
15
=
13
6
+
||
11
49
30
19
= 1-
30
It’s the super long problem, sorry I couldn’t crop the other stuff out
Answer: see below
Step-by-step explanation:
I can’t see the whole problem, however 2 and 5/6 does not equal 13/6, it equals 17/6, if that helps.
(URGENT!) The function g is defined by the following rule. Complete the function table. g(x)=4x-2 (The table is in the image)
!!!!!!!
Using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal to each other. After solving for x, her teacher said she got the wrong value for x. Explain where Maggie made her mistake when solving for x.
Answer:
Step-by-step explanation:
When subtracting 7x from both sides in the first step, she said [tex]4x-7x=3x[/tex], even though [tex]4x-7x[/tex] is actually equal to [tex]-3x[/tex].
Question
What numbers are a distance of 23 unit from 12 on a number line
Identify the element in Group 17, Period 6
Answer:
ima say Chlorine
Step-by-step explanation:
Q's Which element is located in Group 17 and Period 6?
Chlorine is in group 17 of periodic table, also called the halogens, and is not found as the element in nature.
Answer:
Group 17 Elements: On the periodic table, the halogens are to the left of the noble gases. Fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (A) are the five poisonous non-metallic elements that make up Group 17 of the periodic table (At). Despite the fact that astatine is radioactive and has only short-lived isotopes, it behaves similarly to iodine and is frequently classified as a halogen. Because halogen elements have seven valence electrons, forming a complete octet requires only one extra electron. Because of this, they are more reactive than other non-metal groups.
In the periodic table, the Group 17 elements exist as the second column from the right side. The group 17 elements consist of Fluorine, Chlorine, Bromine, Iodine, Astatine, and Tennessine. The group 17 elements are called halogens. We will study the importance of group 17 elements, their properties, and their uses in this article. Some of the classic uses of halogens are as follows: Iodine is used as an antiseptic, chlorine is a disinfectant, fluorine is used in toothpaste in the form of sodium fluoride as it prevents tooth decays.
Step-by-step explanation:
Khan academy question. Can you help?
The point slope equation of the line that passes through (1, 0) and (6, -3) is y - (-3) = - 3 / 5 (x - 6)
How to represent point slope equation?The point slope equation can be represented as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinatesThe line passes through (1, 0) and (6, -3).
Therefore, the point slope equation can be represented as follows:
m = y₂ - y₁ / x₂ - x₁
Hence,
m = -3 - 0 / 6 - 1
m = -3 / 5
m = - 3 / 5
Using (6, -3) the point slope equation is y - (-3) = - 3 / 5 (x - 6)
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if you were to extract 15000 mcubic from a lake each year for 15 years, how far would the lake level fall? total volume of water given as 5400000 m cubic and water depth of the lake is 4 m
Answer:
[tex]d=0.17m[/tex]Explanation: Each year a volume of 15,000 cubic meters is taken from the lake for 15 years, the lake has a surface area of 1.35 square kilometers and a depth of 4m. We have to find the fall in the depth of the river after 15 years:
The total water taken out of the lake in 15 years is:
[tex]\begin{gathered} T=(15,000m^3)\times15=225,000m^3 \\ \\ T_w=225,000m^3 \end{gathered}[/tex]Therefore the fall in height is:
[tex]\begin{gathered} A\times d=(225,000m^3) \\ \\ \\ A=1.35km^2=1,350,000m^2 \\ \\ \\ A=1,350,000m^2 \\ \\ \\ \therefore\Rightarrow \\ \\ \\ (1,350,000m^2)d=(225,000m^3) \\ \\ \\ \\ d=\frac{(225,000m3)}{(1,350,000m^2)}=0.1666666666 \\ \\ \\ \\ d\approx0.17m \\ \end{gathered}[/tex]Therefore the height of the lake will reduce by 0.17me.
In a fruit cocktail, for every 30 ml of orange
juice you need 20 ml of apple juice and 50
ml of coconut milk. What proportion of the
cocktail is apple juice?
Give your answer as a fraction in its
simplest form
Answer:
1/5
Step-by-step explanation:
If you mix 30 ml of orange juice, 20 ml of apple juice and 50 ml of coconut milk you will get a total of 30 + 20 + 50 = 100 ml of cocktail
The proportion of apple juice in the cocktail is merely the volume of apple juice added to the total volume of cocktail
= 20/100 = 1/5
find the slope of the line
Answer:
0.5
Step-by-step explanation:
want an explanation?
What is the value of p when p = 6r² and r=3
Answer:
p = 54Step-by-step explanation:
What is the value of p when p = 6r² and r=3
p = 6r²
p = 6 * 3²
P = 6 * 9
p = 54
---------------
the circumference of a circle is 60cm what is the area
step by step explanation please
The area of a circle with a circumference of 60cm is 286. 38cm²
How to determine the area of the circleThe formula for calculating the circumference of a circle is expressed as;
Circumference = 2 πr
Where;
π has the value pie in decimal form is = 3. 14 and in fraction form is 22/7r is the radius of a circleNow, let's put and substitute the value of circumference of the circle as 60cm in the formula
We have;
60 = 2 πr
Interchange the value for π as 3.14, we have;
60 = 2× 3.14r
Multiply the values
60 = 6.28r
Make 'r' the subject of formula by dividing both sides by the coefficient of the variable 'r'
r = 60/6.28
Find the quotient
r = 9.55cm
But we have that the formula for area of a circle is expressed as;
Area = πr²
Substitute or put the value of radius into the formula
Area = 3. 14(9.55)²
Determine the square of the value
Area = 3.14(91. 20)
Find the product
Area = 286. 38cm²
Thus, the area is 286. 38cm²
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Solve the following inequality for r. Write your answer in
simplest form.
5r - 5(-7r +9) ≥ −10r +9 – 6r
Step-by-step explanation:
10r 7r-1 r-9 7r-7=10 5r²2
x-3/4+2/3=17/12 true?
1) 8
2) 6
3) 0
4) 4
The solution for the linear equation is x = 6, thus the correct option is the second one.
Which value of x makes the equation true?
Here we have the linear equation:
(x - 3)/4 + 2/3 = 17/12
To solve this we need to isolate the variable, x, in one of the sides of the equation.
(x - 3)/4 + 2/3 = 17/12
(x - 3)/4 = -2/3 + 17/12 = -8/12 + 17/12 = 9/12 = 3/4
(x - 3)/4 = 3/4
x - 3= 4*(3/4) = 3
x = 3 + 3
x = 6
The solution is x = 6, thus the correct option is the second one.
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Which among the given set is a function A = [(4,6), (A, B), (A, 6)]C = {(6,9), (6,6), (6,9)B = [(1, Z), ( 2, Y), (3, X)]
The set which is a function is B = [(1, Z), ( 2, Y), (3, X)]
What is a function ?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Since, we know that function does not repeat any x coordinate
Which means, the first coordinate of every pair does not repeat
Therefore the first coordinates which is repeated is not a function
Now, let's check out the given sets and check whether its a function or not
A = [(4,6), (A, B), (A, 6)], is not a function
Since, its first coordinate is repeated
C = {(6,9), (6,6), (6,9), is not a function
Since, its first coordinate is repeated
B = [(1, Z), ( 2, Y), (3, X)], is a function
Because, its first coordinate is not repeated
Hence, B = [(1, Z), ( 2, Y), (3, X)], is a function
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what is the y-intercept of 3x+5y=−30 ? responses
A. (0,−6)
B. (−6,0)
C. (0,10)
D. (10,−6)
In 1787 the French scientist Jacques Charles observed that when he plotted the graph of volume of a fixed amount of air versus the temperature of the air, the points lay along a straight line. Therefore, he concluded that volume of a gas varies linearly with temperature. Suppose that at 27º C a certain amount of air occupies a volume of 500 cm3. When it is warmed to 90º C, it occupies 605 cm3.
a) Write the particular equation in slope-intercept form expressing volume in terms of temperature.
b) Predict the volume at 60º C.
c) The process of predicting a value between two data points is called “interpolation”.
What is the origin of the word?
d) Predict the volume at 300º C.
e) The process of predicting a value beyond any given data points is called
“extrapolation”. What is the origin of this word?
f) Extrapolate your mathematical model back to the point where the volume is zero.
That is, find the temperature-intercept.
g) What is the special name given to the temperature in part f)?
The relationship between the volume, V, and temperature, T, of a given mass of gas, found by the French scientist Jacques Charles, gives;
a) The slope–intercept form of the equation that expresses the volume in terms of the temperature of the gas is; [tex] \displaystyle{ V = 1. \bar 6 \cdot T + 455}[/tex]
b) The volume at 60 °C is 555 cm³
c) Interpolation originates from the verb interpolare
d) The temperature at 300 °Cis 955 cm³
e) Extrapolation originates from 'extra' (meaning outside) and the shortened form of Interpolation
f) The temperature–intercept is -273 °C
g) The special name is the absolute zero temperature
What is Charles law for gases?Charles law states that the volume of a given mass of gas is directly proportional to its temperature given in Kelvin.
Mathematically, Charles Law states that; V = K•T
Where;
V = The volume of the gas
T = The gas temperature
K = The proportionality constant
The volume occupied by the gas at 27 °C = 500 cm³
The volume occupied at 90 °C = 605 cm³
a) To write the equation in slope–intercept form, we have;
[tex] \displaystyle{ Slope = \frac{605 - 500}{90 - 27} =1. \bar{6} =1. \bar{6}}[/tex]
The equation of the line in point and slope form is therefore;
Point–slope form; [tex] \displaystyle{ V - 500 = 1. \bar{6} \times (T - 27) }[/tex]
[tex] \displaystyle{ V = 1. \bar{6} \cdot T -45 + 500 = 1. \bar{6} \cdot T + 455}[/tex]
The equation in slope–intercept form of expressing the volume, V, in terms of the temperature, T, is therefore;
Volume equation; [tex] \displaystyle{ V = 1. \bar{6} \cdot T + 455}[/tex]
b) The volume at 60 °C is given from the equation that gives the volume, V, in terms of time, T as follows;
[tex] \displaystyle{ V(T) = 1. \bar{6} \cdot T + 455}[/tex]
When T = 60 °C
[tex] \displaystyle{ V(60) = 1. \bar{6} \times 60 + 455=555}[/tex]
The volume occupied by the gas at 60 °C is 555 cm³c) The word interpolate originated from the Latin word interpolare which means to alter or refurbish
d) The volume occupied by the gas at 300 °C is given by the function for the volume, V, in terms of temperature, T, equation as follows;
When T = 300 °C
[tex] \displaystyle{ V(300) = 1. \bar{6} \times 300 + 455 = 955}[/tex]
The volume of the gas at 300 °C is 955 cm³e) Extrapolation originate from the word 'extra' which refers to the outside of an area. Extra is combined with a short form of interpolate to give the word, extrapolation
f) When the volume is zero, the volume function equation can be used to find the temperature as follows;
Volume function; [tex] \displaystyle{ V = 1. \bar{6} \cdot T + 455}[/tex]
When V = 0
[tex] \displaystyle{ V = 0 =1. \bar{6} \cdot T + 455}[/tex]
[tex] \displaystyle{ -455 = 1. \bar{6} \cdot T }[/tex]
[tex] \displaystyle{T = \frac{3 \times (-455)}{5}= -273 }[/tex]
The temperature at which the volume of the gas is zero is -273 °Cg) The special name given to -273 °C of the gas is the absolute zero temperature.
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Rachel earns 52 dollars per week working part-time at a book store. She makes one dollar more for each book that she sells. The amount, A (in dollars), that
Rachel earns in a week if she sells b books is given by the following function.
A (b) = 52+b
How much does Rachel earn in a week if she sells 37 books?
dollars
X
Ś
Answer:
Step-by-step explanation:
x
The sum of two numbers is 140. The difference between the numbers is 32. Which system of equations can be used to find the larger number, x, and the smaller number, y.
Group of answer choices
x + y = 140
y – x = 32
y – x = 140
x + y = 32
x + y = 140
x – y = 32
x – y = 140
x + y = 32
Answer:
third option
Step-by-step explanation:
the sum of x and y is 140 , that is
x + y = 140
the difference between x and y is 32 ( y is smaller ) , then
x - y = 32
the system to solve for x and y is
x + y = 140
x - y = 32
Answer:
3rd one trust me
12 ejrid the rude
Help solve please im struggling
Answer:
The domain should be "All Real Numbers" and the Range should be "y is greater than or equal to 0"
The side that is adjacent to angel f has a length of 3 4 5
[tex]5^{2}[/tex]= 25, forming the right triangle of 3 4 5.
what is adjacent angle?When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have a same vertex and side, they can be a complimentary angle or supplemental angle.
what is adjacent rule angle?If two angles share a side and a vertex, they are said to be neighboring in geometry. In other words, neighboring angles do not overlap and are placed next to one another immediately.
Remember that a2 + b2 = c2.
[tex]5^{2}[/tex] = 25, so the 3 4 5 right triangle .
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Given g(x) = 2x- 4, find g(2).
Answer:
0
Step-by-step explanation:
So repalce the x with 2 so now its 2(2)-4 you multiple the 2 times 2 which is 4 now 4-4is 0