The triangle having vertices X(-7,-3), Y(-2,-5), Z(-4,-1) is obtuse.
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]a^{2} + b^{2} < c^{2}[/tex]
obtuse if [tex]a^{2} + b^{2} > c^{2}[/tex]
right if [tex]a^{2} + b^{2} = c^{2}[/tex]
XY = [tex]\sqrt{(-2 + 7)^{2} + (-5 + 3)^{2} }[/tex]
∴ XY = 5.38
YZ = [tex]\sqrt{(-4 + 2)^{2} + (-1 + 5)^{2} }[/tex]
∴YZ = 4.47
ZX = [tex]\sqrt{(-4 + 7)^{2} + (-1 + 3)^{2} }[/tex]
∴ ZX = 3.60
∴The longest side is XY = 5.38.
Hence, a = YZ, b = ZX and c = XY;
Consider [tex]a^{2} + b^{2}[/tex] :
= [tex]4.47^{2} + 3.60^{2}[/tex]
= 32.94.
Now consider [tex]c^{2}[/tex]:
= [tex]5.38^{2}[/tex]
= 28.94.
Thus, [tex]a^{2} + b^{2} > c^{2}[/tex]
Hence, the triangle is obtuse.
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On Halloween night, Mack collects x pieces
of candy and then eats 7 pieces. The next day
he eats 10% of his candy pieces and has 63
pieces remaining. How many pieces of candy
did he collect on Halloween night?
Based on the number of candy pieces that Mack ate on the first and net day, the number of pieces of candy that he collected on Halloween night was 78 pieces of candy
How to find the number of candy pieces collected?The total pieces of candy that Mack had left on the next day was:
Number of candy pieces collected - 7 pieces of candy - (10% x Number of candy pieces collected) = 63
To find the number of candy pieces collected:
x - 7 - 10% × x = 63
x - 7 - 0.1x = 63
x - 0.1x = 63 + 7
0.9x = 70
x = 70 / 0.9
x = 77.7
= 78 pieces of candy
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Find the first five terms of each sequence. aₙ =-2 n-1
The first five terms of the sequence are -3, -5, -7, -9, -11
What is a sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given,
aₙ =-2 n-1
a1 = -2 - 1 = -3
a2 = -4 -1 = -5
a3 = -6 -1 = -7
a4 = -8 -1 = -9
a5 = -10 - 1 = -11
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The quantities X and Y are proportional
The quantities X and Y are proportional as y = rx then the constant of proportionality r is 1/9.
What is constant of proportionality?Firstly, there is proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called constant of proportionality.
WE have been given quantities X and Y are proportional
y = rx
Where r is constant of proportionality.
Then x = 45 and y = 5
Thus,
y = rx
5 = 45r
Now divide by 45 on both side;
r = 5/45
r = 1/9
Therefore, the constant of proportionality r is 1/9.
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1/2x+1/2x+x+1
I got to x+x+1 (if that's even right)
but how do you solve the rest?
The value of the expression ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.
A variable, a number, or a mix of numbers, operations, and numbers symbols make up an expression. Two expressions joined by an equal sign form an equation.
A formula called an equation uses the equals symbol (=) to denote the equality of two expressions.
Consider the expression,
1/2x + 1/2x + x + 1
Taking common out,
( 1/2 )x + ( 1/2 )x + x + 1 = ( 1/2) × [ x + x ] + x + 1
( 1/2 )x + ( 1/2 )x + x + 1 = (1/2x) × 2 + x + 1
( 1/2 )x + ( 1/2 )x + x + 1 = x + x + 1
( 1/2 )x + ( 1/2 )x + x + 1 = 2x + 1
Therefore, the value of ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.
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The function f(x) = ln(x) has a domain of all real numbers greater than zero and a range of all real numbers. the inverse of this function is fâ€""1(x) = ex. which conclusion can be drawn by comparing the two functions? the domain of fâ€""1(x) is all real numbers and the range is all real numbers. the domain of fâ€""1(x) is all real numbers greater than 0 and the range is all real numbers. the domain of fâ€""1(x) is all real numbers and the range is all real numbers greater than 0. the domain of fâ€""1(x) is all real numbers greater than 0 and the range is all real numbers greater than 0.
Comparing the functions f(x) = ln (x) and [tex]f^{-1}(x) = e^x[/tex], we can conclude that the domain of [tex]f^{-1}(x)[/tex] is all real numbers and the range is all real numbers greater than 0.
Given function is the logarithmic function f(x) = ln(x).
Now, f(x) has a domain(D) of all real numbers greater than zero and a range(R) of all real numbers.
i.e., f : D → R defined by f(x) = ln(x)
So if an inverse exist for f(x), then, [tex]f^{-1}(x)[/tex] will have R as its domain and D as its range.
i.e., [tex]f^{-1}[/tex] : R → D defined by [tex]f^{-1}(x) = e^x[/tex].
Because f( [tex]f^{-1}(x)[/tex] ) = ln([tex]e^x[/tex]) = x, that is the identity function.
So [tex]e^x[/tex] is the inverse of ln(x).
Also, the domain of [tex]f^{-1}(x)[/tex] is all real numbers and the range is all real numbers greater than 0.
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Answer:
C. The domain of f–1(x) is all real numbers and the range is all real numbers greater than 0.Step-by-step explanation:
(29x - 3)*
(13y - 17)
(15x + 7)*
The simplified value of the expression given as (29x - 3) + (13y - 17) - (15x + 7) is 14x + 13y -27
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
(29x - 3) + (13y - 17) - (15x + 7)
Open the bracket in the above expression
So, we have
(29x - 3) + (13y - 17) - (15x + 7) = 29x - 3 + 13y - 17 - 15x - 7
Collect the like terms in the above expression
So, we have
(29x - 3) + (13y - 17) - (15x + 7) = 29x - 15x + 13y - 3 - 17 - 7
Evaluate the like terms in the above expression
So, we have
(29x - 3) + (13y - 17) - (15x + 7) = 14x + 13y -27
Hence, the simplified value of the expression given as (29x - 3) + (13y - 17) - (15x + 7) is 14x + 13y -27
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Complete question
Evaluate the following expression
(29x - 3) + (13y - 17) - (15x + 7)
Jesse has been saving his earnings from his lemonade stand. Jesse has 47 dollars to spend. If He buys a new hat for 19 dollars, how many scarves can He buy with the remaining spending money if they cost 7 dollars each?
The remaining scarves he can spend is 4.
A mixture of constants, variables, and operators make up an algebraic expression. Algebraic expressions can be used to accomplish the four fundamental mathematical operations of addition, subtraction, multiplication, and division. Algebraic expression addition and subtraction are quite similar to addition and subtraction of numbers.
Jesse has a total of 47 dollars.
The cost of the new hat is = 19 dollars
The remaining dollars after buying the new hat is 47 dollars - 19 dollars = 28 dollars.
The cost of the scarves is 7 dollars
Thus total scarves for 28 dollars = 28/7 = 4 scarves.
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in straightedge and compass construction of the parallel line below which of the following reasons can you use to prove that JK and LN are parallel
The correct option is (C) ∠ MJK ≅ ∠ MKJ by construction.
When two parallel lines have a transversal cutting those parallel lines, the alternate angle theorem holds true. According to the alternate angle theorem, all alternate angles are equal.
We have a similar circumstance here, where we are employing the alternate angle theorem approach to design and build two parallel lines. To prove that the two alternate angles are equal and the lines are parallel, we must first identify the two alternate angles.
The two alternate angles are:
∠ MLN and ∠ MJK
Therefore, for the lines, JK and LN to be parallel the two angles must be congruent.
Hence, ∠ MLN ≅ ∠ MJK
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The complete question is mentioned below:
In the straightedge and compass construction of the parallel line below, which of the following reasons can you use to prove that JK and LN are parallel?
A. ∠ MLN ≅ ∠ MNL by construction.
B. ∠ NLJ ≅ ∠ MJK by construction.
C. ∠ MJK ≅ ∠ MKJ by construction.
D. ∠ MLN ≅ ∠ MJK by construction.
Help, plss. I must get the area of this irregular figure.
Step-by-step explanation:
Given that
Length is 3m .width is 2m.To find
The area of this irregular figure.So, according to the question
From figure we can say that there is present five rectangle of same size.
So far finding the area of this irregular figure we have to find the area of this single rectangle and multiply it by 5 so from that process we can calculate the area of this irregular figure.
Now first we have to learn about the area,
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
So, we know
The area of one rectangle = l x w
Now, putting the values = 3 x 2 = 6
So,
The area of this irregular figure = 5 ( The area of one rectangle )
= 5 x 6
= 30
Answer:
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What is the area of a section of pavement that is 10 ft wide and 80 yd long? Give your answer in square feet.
Answer:
The area of this section of pavement is 800 square feet
Step-by-step explanation:
10 ft times 80 ft = 800 square feet
Give me brainliest if that helped :)
need help with inequalities problem
ll and lll is the answer.
never said anything about
Suppose that R and S are points on the number line.
If RS =5 and R lies at 14, where could S be located?
The location of S will be at 9 and ₋19 .
When speaking of a straight line in mathematics, the term "number line" refers to the placement of numbers along some or all of the breadth. Any direction can be used to postpone a number line, which is frequently displayed horizontally.
Given, on a number line R and S are points on the number line.
RS = 5 and R is located at 14.
S is located at = ?
Let x be the coordinate of the point S. Then we have:
14 ₋ x = ±5
x = ± 5 ₋ 14
x = 5 ₋ 14 or ₋5₋14
x = 9 or ₋19
Then the location of point S will be at 9 and -19.
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Evaluate each logarithm. log₂ 16
A logarithm is a power that requires a number to be raised to another power.
The logarithmic equation given in the question can be written as
log2(16) =x
We will rewrite this equation in the exponential form by considering the definition of logarithm.
The definition states that,
If x and b are two positive real numbers and the value of b is not equal to 1, then the log of
log b (x)=y is equivalent to by=x
We will convert the given equation according to the above definition,
2x=16
The bases of all the values involved must be identical. So, we will create equivalent expressions in the equation that all have equal bases.
2x=24
Now we have the same bases; the two expressions can only be said equal if the exponents are also equal.
x=4
The variable x is equal to 4.
4
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C: (4, -8, 16, -32,...}
Find a 10
Answer:
i think 10 is in between -8 and
Step-by-step explanation:
hope this
3. Change the digit 5 to zero in each number. Show the operation that will make it zero
a. 478 578 = b. 353 897 = c. 294 025 = d. 500 000 = e. 893 257 = 0 1 2 3 4
Place value is defined as the value of a digit in a number which depends on its position in the number. On the other hand, Total value is the product of a digit and its place value.
Rounding off entails changing a number into an approximation such that it has fewer significant numbers. To change the digit 5 in this question to 0, we will need to round off the given numbers to the most appropriate place value.
a. 478 578
We round off to the nearest thousands, this becomes 479 000
b. 353 897
We round off to the nearest tens of thousands, this becomes 400 000
c. 294 025
We round off to the nearest ones, this becomes 294 030
d. 500 000
The 5 in this value cannot be converted to 0 since 5 is the largest place value in the number.
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Write an equation in point-slope form for each pair of points. (4,6) and (10,30)
The equation of point slope form of (4,6) and (10,30) is -4x + y + 10 = 0.
How to find the equation of point slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1, y1).
given that
the coordinates points are (4, 6) and (10, 30)
(x1,y1) = (4,6)
(x2, y2) = (10,30)
The formula of point-slope is
(y - y1) = m(x - x1)
Here,
x1 = 4 and y1 = 6 but we don't know the value of
m.
now,find the value of m using the following formula
[tex] m = \frac{(y2 - y1)}{(x2 - x1)}[/tex]
now, substitute the values, we get
[tex]m = \frac{(30 - 6)}{(10 - 4)}[/tex]
[tex]m = \frac{24}{6}[/tex]
m = 4
so, the value of m is 4.
substitute these values into the point-slope formula
(y - 6) = 4(x - 4)
y-6 = 4x - 16
y = 4x -16 + 6
y = 4x - 10
-4x + y + 10 =0
Hence, the equation of point slope form of (4,6) and (10,30) is -4x + y + 10 = 0.
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A rectangular sticker has a perimeter of 30 centimeters. Its area
is 54 square centimeters. What are the dimensions of the sticker?
The dimensions of the sticker are 6 centimeters and 9 centimeters, respectively.
What are the dimensions of a rectangular sticker?
According to the statement, we find a rectangular sticker whose perimeter and area are known. By the perimeter and area formulas of the rectangle we have the following system of equations:
x · y = 54 (1)
2 · (x + y) = 30 (2)
By (2):
2 · x + 2 · y = 30
2 · x = 30 - 2 · y
x = 15 - y
(2) in (1):
(15 - y) · y = 54
15 · y - y² = 54
y² - 15 · y + 54 = 0
(y - 9) · (y - 6) = 0
The solutions are y₁ = 9 and y₂ = 6, respectively.
By (2):
x₁ = 15 - y₁
x₁ = 15 - 9
x₁ = 6
x₂ = 15 - y₂
x₂ = 15 - 6
x₂ = 9
The solutions are x₁ = 6 and x₂ = 9, respectively.
The dimensions of the sticker are 6 centimeters and 9 centimeters, respectively.
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Please help!!
Will give brainliest!
Answer:
-10.08
Step-by-step explanation:
Using order of operations:
[tex] - 17 + (\frac{ - 2.3 + 8.12}{6} ) \times {4}^{2} - 8.6[/tex]
[tex] - 17 + \frac{5.82}{6} \times 16 - 8.6[/tex]
[tex] - 17 + .97 \times 16 - 8.6[/tex]
[tex] - 17 + 15.52 - 8.6[/tex]
[tex] - 10.08[/tex]
1.the data set represents the number of eggs produced by a small group of chickens each day for fifteen days 6,7,7,7,8,8,8,8,9,10,10,11,12,12,13
create a dot plot to represent the situation
2. from the data what would be the typical number of eggs produced in a day?
a. The dot plot that represents the situation is shown in the diagram attached below.
b. The typical number = 8.
How to Create a Dot Plot?-To create a dot plot, the frequency of each data point of the data distribution is represented by a "dot". The number of "dots" on a data point determines the number of times that data point appears in the data distribution.
Given the data for the number of eggs produced: 6,7,7,7,8,8,8,8,9,10,10,11,12,12,13, we have the following data points and their frequency:
6 - 1 dot
7 - 3 dots
8 - 4 dots
9 - 1 dot
10 - 2 dots
11 - 1 dot
12 - 2 dots
13 - 1 dot
a. The dot plot that represents the situation is shown in the diagram attached below.
b. The typical number of eggs is: 8.
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how long would it take someone to run 10km at 4 meters per second?
Answer: 41 minutes and 40 seconds
Step-by-step explanation:
1000 meters=1 km
10 km * 1000 meters/1 km=
10 * 1000/1=
10*1000=10000 meters
10000 meters * 1 second/4 meters=
10000 * 1/4=
10000/4=2500 seconds
60 seconds=1 minute
2500 seconds * 1 minute/60 seconds=
2500/60=
(2460+40)/60=
2460/60 + 40/60= 41 minutes and 40 seconds
What is an equation of the line that passes through the point (4,1)(4,1) and is perpendicular to the line 2x-y=42x−y=4?
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line is given below.
2x - y = 4
Then the slope of the perpendicular line will be
y = 2x - 4
m = 2
Then the equation of line will be
y = -(1/2)x + d
Then the line is passing through (4, 1), then we have
1 = -(1/2)4 + d
3 = d
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3
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The formula K=C+273.15 converts temperatures from Celsius C to Kelvin K.
a. Solve the formula for C.
Please help ASAP
Answer:
C° = K-273.15
Step-by-step explanation:
The goal is to get C by itself, so subtract 273.15 from both sides.
X a strawberry milk recipe uses 3 teaspoons of strawberry syrup for every 8 ounces of milk. how many teaspoons of strawberry syrup per ounce of milk does this recipe use? how many ounces of milk are needed per teaspoon of strawberry syrup? 1959 subm
Answer:
Step-by-step explanation:
So our ratio for this problem is
3/8
Now, to find how many teaspoons per ounce, we divide 3 by 8
3/8=0.375
Hope this helps!^^
To find ounces per teaspoon, we do 8/3
8/3 = 2.666666667
Hope this helps^^
Solve this multi-step problem. A runner completes of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?
The runner completes a 10 miles race in 16 minutes.
According to the question we have been given that,
Runner takes 8 minutes to complete = 5 miles race
We need to find that if the runner is in the same pace then how many miles the runner completes in 16 minutes
This multi-step problem can be solved using the unitary method. That is,
8 minutes = 5 miles
1 minute = 5/8 miles
16 minutes = 5/8*16 miles
= 5*2 miles
= 10 miles
Hence runner completes a 10miles race in 16 minutes
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Write a compound inequality for the graph
x<=-4 or x>=-1
A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.”
“And” indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements.
“Or” indicates that, as long as either statement is true, the entire compound sentence is true. It is the combination or union of the solution sets for the individual statements. A compound inequality that uses the word “and” is known as a conjunction.
By seeing the graph we can see that there are 2 inequalities. We have to solve them separately
Final answer: x<=-4 or x>=-1
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what is the quetient when (x+3) is divided into the polynomial 2x^2+x-15
The quetient is 2x - 5 with no remainder.
Step-by-step explanation:
The give polynomial is 2x² + x - 15
And the given divisor is (x + 3)
Now, Using divide rule of polynomials
x + 3 ) 2x² + x - 15 ( 2x - 5
2x² + 6x
- -
____________________
- 5x - 15
- 5x - 15
+ +
__________________
0
Hence, we get the quotient is 2x - 5 and the remainder is 0
Therefore, The correct answer 2x - 5 with no remainder.
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103^2 = (100 + ⋯ )^2 = 100^2 + ⋯ + ⋯
I need help Filling in the blank spaces, Urgent
Step-by-step explanation:
Notes;(a+b)² = (a+b) × (a+b)
= a(a+b) × b(a+b)
= a² +ab + ba + b²
= a² + b² + 2ab
similarly , (a-b) = a² + b² - 2ab so , The question :-103² = (100 + 3)²
= 100² + 3² + (2×100×3)
= 10000 + 9 + 600
= 10609
19m=3 how do I solve for M
Answer:
m=3/19
Step-by-step explanation:
Answer:
m = 3/19
Step-by-step explanation:
Let's solve your equation step-by-step.
19m = 3
Step 1: Divide both sides by 19.
19m/19 = 3/19
- You might be wondering, why do we need to divide both sides by 19? -
Well, to find m, you need to get it by itself. So by dividing 19m by 19, m stands alone. But again, what we do to one side, we need to do to the other. So 3 must also be divided by 19.
Answer:
m = 3/19
Write the slope intercept form of the equation for each line
The equation of the line in slope-intercept form is: y = -4/5x - 8/5.
How to Write the Slope-intercept Form Equation of a Line?Using two points on the line, say, (-2, 0) and (3, -4), follow the steps below to find the equation of the line:
Step 1: Find the slope of the line
Slope (m) = (-4 - 0)/(3 -(-2))
Slope (m) = -4/5
Step 2: Find the y-intercept (b)
Substitute m = -4/5 and (x, y) = (-2, 0) into y = mx + b
0 = -4/5(-2) + b
0 = 8/5 + b
0 - 8/5 = b
b = -8/5
Step 3: Substitute m = -4/5 and b = -8/5 into y = m + b
y = -4/5x - 8/5
Thus, the equation of the line in slope-intercept form is: y = -4/5x - 8/5.
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Suppose you pull a card from a standard 52-card deck. Find the probability of following event. The card is red.
