The angle of triangle ∠LMN = 60 degrees,
Right angle triangle MLN where at L it is a right angle ∠MLN=90 and the line LN of triangle MLN lies on the ray LO passes through LN it makes an exterior angle with MN it is given by 3x+15 degrees whereas angle M in the triangle MLN is given by ∠LMN = x+15 degrees.
By using the exterior angle relation that exterior angle =sum of two opposite internal angles,
Here, 3x+15=x+15+90,
We get x=45 degrees ,
So angle ∠LMN is x+15 which is 60,
Hence, The angle of triangle ∠LMN = 60 degrees.
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In Quadrilateral ABCD , AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠2=31°. What is m∠5? Enter your answer in the box. ° Trapezoid A B C D with segment B D. Angle A D B is angle 1. Angle B D C is angle 2. Angle C is angle 3. Angle A is angle 4. Angle A B D is angle 5. Angle C B D is angle 6.
The measure of m∠5 is 31 degrees.
What are alternate angles?
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal
Given that,
The AB is perpendicular to CD.
And, the m∠2=31°.
Based on the above information, the following information should be considered:
The alternate angles should be equal i.e. ∠2 = ∠5 and ∠1 and ∠6.
So, ∠5 = ∠2 = 31 degrees.
Therefore we can conclude that the measure of m∠5 is 31 degrees.
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Enola opened a savings account with $8400 that earns 1.8% simple interest annually. After how many years will the balance of the account be $9600? Round to the nearest tenth, if necessary.
After 8 years the balance of the account would be $9600.
What is simple interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest =(P×r×t)/100
where:
P =Principal
r = interest rate
t = time
Given:
Principal, P = $8400
Rate of interest, r = 1.8%
Final amount, A = $9600
Simple interest, S.I = Final amount - Principal = 9600 - 8400 = $ 1200
Now, 1.8% of 8400 = (1.8/100) × 8400 = 151.2
⇒ Interest of 1 year = $151.2
Interest after x years = $1200
x = 1200/151.2 = 7.94 ≈ 8 years
Therefore, after 8 years the balance of the account would be $9600.
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John wants to buy a new TV. The price is , and the sales tax is 5 percent.
Store A is offering a 10 percent discount and Store B is offering a rebate.
What would John's total cost be at each store? Make sure to record your answers to the nearest cent.
Total cost at Store A = $
Total cost at Store B = $
Price of Tv at Store A = $ 94.5
Price of Tv at Store B = $ 95
How to calculate the price?Given that
Price of tv player = $ 100
Sales Tax = 5%
The price of tv at store A after 10% discount = 100 - 10% of 100
The price of tv at store A after 10% discount:
= 100 - 0.1x100
= 100 - 10 = $90
Price of tv at store A after sales tax = 90 + 5% of 90
= 90 + 0.05x90
= 90 + 4.5
= $94.5
Now, lets calculate price of of tv at store B.
The price of tv at store B= 100
Price of tv at store B after sales tax:
= 100 + 5% of 100
Price of tv at store B after sales tax = 100 + 0.05x100
= 100 + 5
= $105
Price of tv at store B $10 rebate
= 105 - 10
= $95
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Complete questions
John wants to buy a tv. The price is $100, and the sales tax is 5 percent. Store A is offering a 10 percent discount and Store B is offering a $10 rebate. What would John's total cost be at the two stores? Total cost at Store A = Total cost at Store B =
Explain how proving two triangles congruent can help prove parts of the triangle congruent.
Answer:
If two triangles are congruent, then by the definition of congruent triangles, 3 pairs of sides are congruent and 3 pairs of angles are congruent. In all, this is 6 statements of congruence.
There are ways of proving triangles congruent that require only 3 statements of congruence of corresponding parts, such as ASA, SAS, AAS, etc.
Sometimes in order to prove two segments or two angles congruent, since these segment and angles are parts of triangles, you prove the triangles congruent using some other statements of congruence, not involving these parts, and then you get 6 statements of congruence that includes the parts you wanted to prove congruent. That is where you use "corresponding parts of congruent triangles are congruent", or CPCTC for short.
(-3, -2) and (x, 6); m = 2
Answer:
1
Step-by-step explanation:
(y2-y1)/(x2-x1) is the formula for slope (aka m)
6-(-2)/1-(-3) = 8/4 = 2
Does anyone know the answer?
Answer:
a. -13
b. 14
c. -6
Step-by-step explanation:
a.
Substitute x = -3 into the equation.
f(-3) = 2(-3) - 7
= - 6 - 7
= -13
b.
Substitute f(x) = 21 into the equation.
2x - 7 = 21
2x = 28
x = 14
c.
Substitute x = 1/2 into the equation.
f(1/2) = 2(1/2) - 7
= 1 - 7
= -6
in the parallelogram pqrs shown below, ps is 7 centimeters long. if the parallelogram's perimeter is - 40 centimeters, how many centimeters long is pq?
13 cm long is PQ in parallelogram .
What does parallelogram mean in a nutshell?
A parallelogram is a geometric shape with parallel sides that exists in two dimensions. The pair of parallel sides in this sort of polygon with four sides, also known as a quadrilateral, are of equal length. In a parallelogram, the sum of the adjacent angles is 180 degrees.Perimeter of ∥gm = - 40 cm
2(PQ+ PS) = - 40
2 ( PQ + 7 ) = 40
PQ + 7 = 20
PQ = 20 - 7
PQ = 13 cm
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A teacher buys 100 pencils to keep in her classroom at the beginning of the school year. She allows the students to borrow pencils, but they are not always returned. On average, she loses about 8 pencils a month. Which equation represents the number of pencils she has left y after a number of x months?.
A teacher buys pencils= 100
the equation is y=8x/100.
total number of pencils = 100
average number of pencil lost in months = 8
number of pencil lost in one month = 8/100
pencil left = y
months = x
so the equation would be:
y = 8x/100.
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4/5(-7x-1/2)=-2x-(4x-1)
Answer:
x = 7/2
Step-by-step explanation:
-28/5 x -2/5 = -2x -4x + 1
-28/5 x -2/5 = -6x + 1
-28 x -2 = -30x + 5
30 x -28 x = 5 + 2
2x = 7
2/2 x = 7/2
x = 7/2
Answer:
(7/2)
Step-by-step explanation:
I'll rewrite "4/5(-7x-1/2)=-2x-(4x-1)" to (4/5)(-7x-1/2)=-2x-(4x-1) to clarify the fraction (I am not interpreting it as 4/(5(-7x-12))). [The five is not part of the denominator in my rewrite]
(4/5)(-7x-1/2)=-2x-(4x-1)
(-28x-2)= 5*((-6x+1)) [multiply the numerator by 4 on the left side, and multiply both sides by 5]
-28x-2= -30x + 5 [Combine like terms]
2x = 7 [Put like terms together by adding 30x and +2 to both sides]
x = (7/2) This satidfies the equation.
1. Find the average rate of change on the interval [-2, 2] for each of the functions below.
a. a(x) = 2x + 1
b. b(x) = x² + 2
d. Which function has the greatest average rate of change over the interval x = -2 to x = 2?
c. c(x) = 2x - 1
The greatest average rate is. x^2+1
What is ROC?
The rate of change is measured by a line's slope.Rate of Change: How quickly a variable changes over a predetermined amount of time. It is frequently used while discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.acc toour question-
(1+4x)/2 f(2) = 9/2; f(-1) = -3/2 AROC = (9/2 - -3/2)/3 = 12/2 over 3 = 6 /3 or is it 1+ 4x/2 = 1+2x ??? f(2) = 5; f(-1) = -1; AROC = (5 - -1)/3 = 6/3 = 2 <--- YES !!!B) f(2) = 2^2 - 2 = 4 - 2 = 2 f(-1) = (-1)^2 - (-1) = 1 - (-1) = 1+1 = 2 AROC = (2-2)/3 = 0/3 = 0 <--- NOC) f(2) = 2^2 = 4; f(-1) = (-1)^2 = 1; AROC = (4-1)/3 = 3/3 = 1 <--- NOd) f(2) = 2^2 + 2 = 4+2=6 f(-1) = (-1)^2 + (-1) = 1+(-1) = 0 (6-0)/3 = 6/3 = 2Learn more about roc click here:
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hi! could i get some help on this pls! ty
Left Blue Dot (5,9)
Right Blue Dot (7,0)
m = (y2 - y1)/(x2-x1)
= (9-0)/(5-7)
=9/-2
m = -9/2
Don't know the y-intercept so use the formula below to calculate equation of line
y-b = m(x-a)
y-9 = -9/2(x-5)
y-9 = -9x/2 + 45/2
y = = -9x/2 + 45/2 + 18/2
y = -9x/2 + 63/2
What is the intermediate step in the form (x+a)^2=b(x+a)
2
=b as a result of completing the square for the following equation?
x^2-28=12x
The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64
Given,
The equation x² - 28 = 12x
We need to find the intermediate step in the form (x + a)² =b as a result of completing the square for the given equation
Equation; x² - 28 = 12x
Arrange the equation;
x² - 12x = 28
Take the coefficient of x
k = -12
Divide it by 2
k/2 = -6
Square both sides
(k/2)² = 36
Add 36 to both sides of x² - 12x = 28
x² - 12x + 36 = 28 + 36
(x - 6)² = 64
Therefore,
The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed is $10865, based on the given parameters
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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Find the -intercept and -intercept of the line.
3x + 5y = -6
Answer:
The intercept would be -6/5
Step-by-step explanation:
Answer:
y=-3 x=-3
Step-by-step explanation:
What is radius r length?.
A line segment that connects a circle, sphere, or other shape's center to its perimeter or border. Radius: 12 units
What is Pythagoras Theorem?According to the Pythagorean Theorem, a right triangle's hypotenuse (the side opposite the right angle) or, using conventional algebraic notation,[tex]a^{2} + b^{2} = c^{2}[/tex]
The Pythagorean theorem is well known for what reason?The Greeks established the existence of numbers that could not be expressed as rational numbers thanks to Pythagoras' theorem. For instance, if we assume that the two shorter sides of a right triangle are 1 and 1, we are left with a length hypotenuse that is not a rational number.
By Pythagoras theorem-
[tex]adjacent side^{2} + opposite side^{2} = hypotenuse^{2}[/tex]
35= opposite side
r= adjacent side
25+r= hypotenuse
[tex](25+r)^{2} = 35^{2} + r^{2}\\ 665 + r^{2} + 50r = 1225 + r^{2} \\50r = 600\\r=12 units[/tex]
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Mark buy 2 pound of ham and 4 pound of turkey for 40$. Gigi buy 5 pound of ham and 4 pound of turkey for 51$
How much i a pound of ham?
Based on Mark's and Gigi's expenditure, a pound of ham costs $3.67.
Let us represent 1 pound of ham by x and 1 pound of turkey by y. Forming equation based on Mark's ham and turkey
2x + 4y = 40 : Equation 1
Forming equation based on Gigi's ham and turkey
5x + 4y = 51 : Equation 2
Subtracting Equation 1 from equation 2
5x + 4y = 51
(-) 2x (-) + 4y = (-) 40
The result we get on subtraction -
3x = 11
x = 11/3
Performing division on Right Hand Side of the equation
x = 3.67
Thus, one pound of ham cost $3.67.
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What is the absolute value of +4?.
The absolute value of +4 will be 4 units as it is the distance from (0,0) to (4,0) in coordinate plane.
What is absolute value?Without taking into account direction, absolute value defines how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0. A number's absolute value is determined by how far it is from zero on the number line. For instance, the absolute value of -7 would be 7, as it is 7 units away from zero. Additionally, since 0 is 7 units distant, the value of 7 would likewise be 7.
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the expression 18+1.5x is 8 less than 36.5. What is the value of 4x
In the expression 1.5x + 18 = 36.5 - 8 x is 7, hence 4x is 28.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An expression 18 + 1.5x is 8 less than 36.5.
∴ 1.5x + 18 = 36.5 - 8.
1.5x = 36.5 - 8 - 18.
1.5x = 10.5.
x = 10.5/1.5.
x = 7.
Therefore 4x is equal to 4(7) = 28.
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Write an equation in slope-intercept form of the line that passes through (6,
-1) and (3,
-7).
Answer: y = 2x - 13
Step-by-step explanation:
y=mx + b
[tex]m= \frac{-7-(-1)}{3-6}[/tex]
[tex]= \frac{-6}{-3}[/tex]
[tex]m = 2[/tex]
y = 2x + b
(6, -1) <-- use to find "b" by substituting either one of the coordinates
-1 = 2(6) + b
-1 = 12 + b
-13 = b
y = 2x - 13
Describe the transformation of the parent
function f(x) = x².
f(x) = (x − 1)² +3
The transformation from the parent function is a translation by 1 unit right and 3 units up
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x²
f(x) = (x − 1)² + 3
First, we have the transformation to be:
From f(x) = x² to f(x) = (x − 1)²
This means the function is translated right by 1 unit
Next, we have:
From f(x) = (x − 1)² to f(x) = (x − 1)² + 3
This means the function is translated up by 3 units
Hence, the transformation is 1 unit right and 3 units up
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Each day last week you sold 32, 45, 47, 63, and 72 product accessories. What was the median number of accessories you sold for the week?".
The answer is 47.
Step-by-step explanation:
To find the median, you need to write the numbers in order from least to greatest. However, that is already done.
Then, you need to count the numbers from the ends to the middle.
For example, if the numbers were 2, 4, 8, 9, and 10, you would do it like this (see the example below)
So, you would go from 32 to 45 and 72 to 63, and from 45 to 47 and 63 to 47.
This means that the median is 47.
HELP MEEEE PLEASE TYYY
Answer:
241.9026
Step-by-step explanation:
2*pi*r
Answer:
241.9 cm
Step-by-step explanation:
circumference= [tex]\pi[/tex]d
circumference= [tex]\pi[/tex](77)
circumference= 241.9 cm
A study of the population of deer in a park finds that the population decreases by 1.2% each year. The deer population at the beginning of the study is 525. Write an equation to model the population of deer in the park after x years. After how many years will the population of deer in the park be less than 200?
The exponential decay of the function shows it will take approximately 81 years for the population to decrease to 200
Exponential FunctionAn exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. This could also be an exponential growth or exponential decay which depends on the situation.
The exponential function is an important mathematical function which is of the form f(x) = ax
The details given in this question are;
Rate = 1.2% Initial population (P) = 525Final population = 200Number of years = x.The exponential function to represent this will be given as
200 = 525(1 + 0.012)⁻ˣ
x = number of years
This can be simplified as
200 = 525(1.012)⁻ˣ
x = 80.9 years
It will take approximately 81 years
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On the grid below, draw the graph of y = 2 – 3x for values of x from – 3 to 3
The graph of the linear function f(x) = 2 - 3x is a straight line attached below
Graph of Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,
m = slope of the lineb = y-intercept of the linex = is the independent variabley (or f(x)) = dependent variableThe function given y = 2 - 3x can be plotted on a graph using function table
When x = -3
f(-3) = 2 - 3(-3)
f(-3) = 11
when x = -2
f(-2) = 8
when x = - 1
f(-1) = 1
when x = 0
f(0) = 2
when x = 1
f(1) = -1
when x = 2
f(2) = -4
when x = 3
f(3) = - 7
We can use this data and plot a graph.
Kindly find the attached graph of the function below
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what is the distribution of the number of fair coin tosses before one observed 3 heads in a row? markov chain
The distribution of the number of fair coin tosses before one observed three heads in a row is 14.
We have a coin. We have to find the number of fair coin tosses before one observes three heads in a row. We need to use the Markov chain. The probability of getting a head when a coin is flipped is 1/2. Let the probability be represented by the variable "p". Let the number of heads we want in a row be "n".
p = 1/2
n = 3
Using the Markov chain, the formula for getting "n" numbers of the same event in a row with the probability "p" is given below.
A(n) = [1 - p^(n)]/[(1 - p)*p^(n)]
We need to find the value of A(3).
A(3) = [1 - (0.5)^(3)]/[(1 - 0.5)*(0.5)^(3)]
A(3) = [1 - 0.125]/[(0.5)*(0.125)]
A(3) = 0.875/0.0625
A(3) = 14
Hence, the number of fair coin tosses before one observes three heads in a row is 14.
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Triangle xyz was translated up 2 and right 3 units, creating triangle cab. Which relationship between the parts of the two triangles must be true?.
The congruency relationship which hold true after transformation is
YZ ≅ AB
What is congruent ?
In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.
Explanation:
A translation is known as a rigid transformation. This is because it preserves congruence. Since CAB is created from XYZ, this tells us that:
X corresponds to C; Y corresponds to A; Z corresponds to B; XY corresponds to CA; YZ corresponds to AB; and XZ corresponds to CB.
Since the triangles are congruent, the corresponding pieces are congruent as well.
Out of these corresponding congruent pieces of triangles, the only one in our options is YZ ≅ AB.
Hence the answer is YZ≅AB.
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solve 2^(x+3)=(1/8)^(x+2) for x
Answer:
-9/4 Negative As a Fraction
How I got the answer:
2 (x+3) = (1/8) (x+2)
x+ 3 = -3 (x+ 2)
x = -9/4
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Which list of minerals is grouped based on color?
bornite, chalcopyrite, and hematite
chalcopyrite, pyrrhotite, and pyrite
hematite, bornite, and pyrite
pyrrhotite, goethite, and hematite
The list of minerals that is grouped based on color is B. chalcopyrite, pyrrhotite, and pyrite.
What minerals does chalcopyrite share a color with?Chalcopyrite is a mineral that has a high concentration of copper ore. As a result, it has a golden yellow color due to the copper in it. It also has crystals of a tetragonal form.
Pyrrhotite is a mineral with iron in it. It has the color of bronze yellow which means that it is similar in color to Chalcopyrite. We also have Pyrite which is brass yellow in color and looks golden. This puts it in the same color group as Chalcopyrite.
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(2x + 6)
The perimeter (adding up all the sides) of a rectangular
piece of land is 228 feet. The length of the land can be
shown by x and its width can be shown by (2x + 6).
Solve for x, and then plug it back in to find the Length
and the Width of the land.
The value of x is 36 feet and the length of the rectangle is 36 feet and the width is 78 feet.
According to the question,
We have the following information:
The perimeter (adding up all the sides) of a rectangular piece of land is 228 feet. The length of the land can be shown by x and its width can be shown by (2x + 6).
We know that the perimeter of rectangle is given by the following formula:
2(length+width)
2(x+2x+6) = 228
2(3x+6) = 228
Dividing by 2 on both the sides:
3x+6 = 228/2
3x+6 = 114
Subtracting 6 from both the sides:
3x = 114-6
3x = 108
x = 108/3
x = 36 feet
Now, the length of the rectangle = 36 feet
Width = 2x+6
Width = 2*36+6
Width = 72+6
Width = 78 feet
Hence, the value of x is 36 feet and the length of the rectangle is 36 feet and the width is 78 feet.
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If x= 4-5 and y = -4 - 7i, what is x + y?
The value of x + y is -12i.
What are complex numbers?
Real numbers and imaginary numbers combine to form complex numbers, which have two components. Complex numbers serve as the foundation for more complex math, including algebra. They have numerous practical applications, particularly in the fields of electronics and electromagnetism.
Here, we have
Given x = 4 - 5i and
y = -4 - 7i
Now we have to find the value of x+y.
We will add both complex numbers and we get
x + y = 4 - 5i + (-4 -7i)
x + y = - 12i
Hence, the value of x + y is 12i.
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