The unknow angle of the triangle is as follows:
m∠C = 46.2°
How to find the angle of a triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
In simpler term, a triangle is a kind of polygon that 3 sides and 3 angles.
Therefore, the sum of angles in a triangle is equals to 180 degrees.
Hence, the sum of angles in ΔABC is 180 degrees.
Therefore,
m∠A + m∠B + m∠C = 180°
m∠A = 32.1°
m∠B = 101.7°
m∠C = x
32.1 + 101.7 + x = 180
x + 133.8 = 180
x = 180 - 133.8
x = 46.2 degrees.
Therefore, the unknow angle of the triangle is as follows:
m∠C = 46.2°
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Answer: 46.2
Step-by-step explanation:
Let f(x)=3 x-2 and g(x)=x²+1 . Perform each function operation.
f(x)+g(x)
The value of f(x)+g(x)= x²+ 3x - 1
a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
f(x) is the value of the function.
there is an x in the function f, it is replaced with the function g(x).
f(x)=3 x-2
g(x)=x²+1 .
(f+g)(x) = x²+1 + 3 x-2
f(x)+g(x)= x²+ 3x - 1
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In the figure below, m angle 4=62 degrees, find m angle 1, m angle 2, and m angle 3
Answer:
Angle 1 = 118°
Angle 2 = 62°
Angle 3 = 118°
Angle 4 = 62°
Step-by-step explanation:
Given : Angle 4 = 62°
Here ,
=> Angle 4 + Angle 1 = 180° { linear pair }
=> 62 + Angle 1 = 180
=> Angle 1 = 180 - 62
=> Angle 1 = 118°
Angle 4 = Angle 2 { vertically opposite angle }
Angle 1 = Angle 3 { vertically opposite angles }
I JUST NEED HELPPP YOU CAN TAKE ALL MY POINTS
Answer:
2
Step-by-step explanation:
Assuming a linear relationship, find the missing value in the table below.
y
x
1
2
3
4
5
4
7
10
13
Assuming a linear relationship, the missing value in the table above is equal to 3.
What is a linear equation?A linear equation can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
By critically observing the values in the table above, we can logically deduce that there exist a linear relationship between the data set. Therefore, the value of x increases by 1 while the value of y increases by 3.
Also, we can determine the slope of the given data set as follows:
Slope = Δy/Δx
Slope = (7 - 4)/(2 - 1)
Slope = 3/1
Slope = 3.
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Laura borrowed a total of $18,000 from two different banks to start a business. One bank charged the equivalent of 6% simple
Interest, and the other charged 7.5% interest. If the total interest after 3 years was $3330, determine the amount borrowed from
each bank.
Part: 0/4
Part 1 of 4
Let x represent the principal on the business loan at 6%.
Then,
is the remaining amount borrowed at 7.5%.
Step-by-step explanation:
Let x be the amount invested at 6% so that 18000-x is the amount invested at 7.5% both in dollars.
The total interest in 3 years is $3330 so we can write: 0.06x(3)+0.075(18000-x)(3)=3330
Solve for x:
0.06x(3)+0.075(18000−x)(3)=3330
Step 1: Simplify both sides of the equation.
0.06x(3)+0.075(18000−x)(3)=3330
0.06x(3)+−0.225x+4050=3330(Distribute)
0.18x+−0.225x+4050=3330
(0.18x+−0.225x)+(4050)=3330(Combine Like Terms)
−0.045x+4050=3330
−0.045x+4050=3330
Step 2: Subtract 4050 from both sides.
−0.045x+4050−4050=3330−4050
−0.045x=−720
Step 3: Divide both sides by -0.045.
−0.045x/−0.045=−720/−0.045
x=16000
x=16000
So, the amounts borrowed are:
Bank at 6% = 16000
Bank at 7.5% = 2000
Tickets to a Broadway show cost $50 for adults and $10 for children. The total receipts for 1440 tickets at one performance were $54,000. How many adult and how many child tickets were sold?
The number of adult tickets sold for $50 is 990 and the number of children tickets sold for $10 is 450
How do we represent adult tickets and children's tickets?
The adult tickets can be represented by x whereas the children's tickets are represented by y, hence, the sum of x and y gives 1440 tickets
x+y=1440.......... equation 1
50x+10y=54000........ equation 2
solve for x in equation 1
x=1440-y
substitute for x in equation 2
50(1440-y)+10y=54000
72000-50y+10y=54000
72000-54000=50y-10y
18000=40y
y=18000/40
y=450
x+y=1440
x+450=1440
x=1440-450
x=990
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its easy but its confusing because it leads me to the finish is this a error or what?
Answer:
I think it's an error it should be correct and in the right spot or whatever it an error
Is 6/5 greater than one?
Yes it is because 6/5 is the same as saying 1 and 1/5.
What’s the answer to the I l i really need help
Please help, it then ask CPI would be in both 2014 & 2015
Answer: 2014 was a great year for my family
Step-by-step explanation:
2014; my family came together that year
2015; my family fell apart that year
Divide.Rationalize all denominators 2+√5 / √5
The value of the expression [tex]\frac{2+\sqrt{5} }{\sqrt{5} }[/tex] after rationalizing the denominator is [tex]\frac{2\sqrt{5}+5 }{5}[/tex].
A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Rationalizing the denominator is the process of shifting a root, such as a square root or a cube root, from the fraction's denominator to its numerator (numerator).
The numerator is the part of a fraction that comes before the vinculum.
The denominator of a fraction is the phrase that comes before the vinculum.
Consider the expression,
[tex]\frac{2+\sqrt{5} }{\sqrt{5} }[/tex]
Now, let [tex]y=\frac{2+\sqrt{5} }{\sqrt{5} }[/tex]
To rationalize the denominator we multiply and divide the expression by √5.
[tex]y=\frac{2+\sqrt{5} }{\sqrt{5} } \times \frac{\sqrt{5} }{\sqrt{5} }[/tex]
[tex]y=\frac{2\sqrt{5}+(\sqrt{5} )^{2} }{(\sqrt{5} )^{2}}[/tex]
[tex]y=\frac{2\sqrt{5}+5 }{5}[/tex]
The value of the expression when rationalized [tex]\frac{2+\sqrt{5} }{\sqrt{5} }[/tex] is [tex]\frac{2\sqrt{5}+5 }{5}[/tex].
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I need help please-
(30 Points)
Answer:
I believe b but not 100%
Step-by-step explanation:
xoxo
Let u=(-1,3), v=( 2,4) , and w= (2,-5) . Find the component forms of the following vectors. -4 \mathrm{w}
Applying the rules of addition and scalar multiplication of vectors, –4w = (–8, 20) and –4u + w = (6, –7)
In the 2D coordinate system, vectors can be split into x-component and y-component.
we can write, for example, a vector r = (2,–6), which means:
x-component = 2
y-component = –6
Addition / subtraction of vectors: Just add or subtract the corresponding components.In the given problem:
u = (-1,3), v = ( 2,4) , and w = (2,-5)
Then,
–4w = –4(2, –5)
= (–4 . 2, –4. (–5)) = (–8, 20)
–4u + w = –4(-1,3) + (2, –5)
= (–4.(–1), –4 . 3) +(2, –5)
=(4, –12) + (2, –5)
= (4+2, –12–(–5)) = (6, –7)
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dose 2x+6=4x+4 have any solutions
Answer:
X=1
Search it up on a calculator next time
Answer:
solution:
x=1
Step-by-step explanation:
2x + 6=4x+4
2x -4x +6-4=0
-2x +2 =0
-2x = -2
x = -2/-2
× = 1
A salaried employee will always have a(n)
profit-sharing plan.
employment contract.
dental and vision insurance.
option to buy company stock.
A salaried employee will always have a(n) employment contract.
Who is a salaried employee?
A salaried employee is an individual who is said to often receives a fixed amount of money (salary), regardless of the number of hours they work each week.
It is one that is referred to as a salaried employee because they often get compensated for 40 hours of work per week and it is one that is based on the use of an employment contract.
Since the employment contract is seen as a legally binding form of an agreement between an employer and that of their employee, A salaried employee will always have a(n) employment contract.
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A. find the common ratio of the ff. G.S
1) 2, 6, 18, 54, ... r = __
2) 7, -7, 7, -7, ... r = __
3) 1, 1/2, 1/4, 1/8, ... r = __
4) 200, -100, 50, ... r = __
5) 5, 15, 45, ... r= __
Answer: 3, -1, 1/2, -1/2, 3
Step-by-step explanation:
The common ratio is the number you must multiply the preceding term by to get the next term.
Children's tickets to the zoo cost $9 each, and adult tickets cost $16 each. On Monday, the zoo sold a total of 95 tickets and made $1,380 on ticket sales. Which of the following systems of equations could be used to find out how many of each ticket type was sold? Let a equal the number of adult tickets, and let c equal the number of child tickets.
(A) a+c=1,380, 9c+16a=95
(B) a+c=95, 9a+16c = 1,380
(C) a+c=95, 9c+16a = 1,380
(D) a+c=1,380, 9a+16c = 95
Answer:
B
Step-by-step explanation:
the total number of adult/ children tickets sold was 95 , then
a + c = 95
the ticket sales totalled $1380 , then
9a + 16c = 1380
the system of equations is
a + c = 95 , 9a + 16c = 1380
A rectangular hotel room is 5 meters by 7 meters. The owner of the hotel wants to recarpet
the room with carpet that costs $47.00 per square meter. How much will it cost to recarpet
the room?
Answer:
It will cost $1,645 to recarpet the room
Step-by-step explanation:
room 5 meters by 7 meters is 35 m^2
Therefore, 35*47.00 = $1,645
Determine the probability that the first child of clara and charles will be a boy with hemophilia. express your answer as a fraction (example 1/8).
The probability that the first child of Clara and Charles will be a boy with hemophilia is 1/4.
How to calculate the probability?It shouldbe noted the dominant and recessive alleles is given as H and h. It should be noted that A and a also represent the tyrosinase alleles.
The father of Clara had hemophilia.
Therefore, the probability that the first child of Clara and Charles will be a boy with hemophilia will be:
= 1/2 × 1/2
= 1/4.
Therefore, the probability is 1/4.
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In humans, hemophilia (OMIM 306700) is an X-linked recessive disorder. The dominant and recessive alleles represented by H and h . Albinism is an autosomal recessive condition . A and a represent the tyrosinase alleles. A healthy woman named Clara (II-2), whose father (I-1) has hemophilia and whose brother (II-1) has albinism, is married to a healthy man named Charles (II-3), whose parents are healthy. Charles's brother (II-5) has hemophilia, and his sister (II-4) has albinism. The pedigree is shown.
Determine the probability that the first child of clara and charles will be a boy with hemophilia.
can u solve inequality and graph please on a number line
|x|<3
Answer:
−3<x<3
hope this helps
find the minimum value of the function f(x)=1.8x^2-6.2x+2.5 to the nearest hundredth
Answer:
Below in bold.
Step-by-step explanation:
f(x)=1.8x^2-6.2x+2.5
As the coefficient of x^2 is positive this has a minimum value.
Find the derivative:
f'(x) = 3.6x - 6.2
This = 0 for a minimum value of f(x):
3.6x - 6.2 = 0
x = 6.2/3.6 = 1.722
This is the value of x when f(x) is a minimum.
So, the minimum value of f(x)
= 1.8(1.722)^2 - 6.2*1.722 + 2.5
= -2.838......
= -2.84 to nearest hundredth.
An online music store is having a promotion. Customers receive a $ 5 rebate if they buy any regular priced CD at $ 13 each. They can also recelve 15 % off if they register as a store member.
a. What functions model the two discounts?
The functions that model the two discounts will be given as R (x) = 5 x and M (y) = 0.15 y.
We are given that:
Rebate a customer receives if he buys a regular priced CD at $ 13 each = $ 5.
If a customer registers for the store member, he get a discount = 15 %.
Now, let the regular priced CD purchased be x and the application for store member be y.
So, the functions will become:
For rebate:
R (x) = 5 x
For discount:
M (y) = 15 % of x
M (y) = 0.15 x
Therefore, we get that, the functions that model the two discounts will be given as R (x) = 5 x and M (y) = 0.15 y.
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Is investing $ 2000 in an account that pays 5% annual interest compounded continuously the same as investing $ 1000 at 4 % and $ 1000 at 6% , each compounded continuously? Explain.
No , investing $ 2000 in an account that pays 5% annual interest compounded continuously is not same as investing $ 1000 at 4 % and $ 1000 at 6% .
Compound interest is interest calculated on the principal and the interest accrued in previous periods. Compound interest is interest based on principal and interest accumulated over a period of time.If we specifically state that the quantity in question is "continuously composed", we must use the continuous constitutive formula which is given by [tex]A=Pe^{rt}[/tex] ..... (1) where, P = initial amount , A = final amount , r = interest rate , t = time , e is a mathematical constant with e ≈ 2.7183.
It is given that principal is $2000 , annual interest rate is 5 % , time is 1 years
Putting [tex]P=\$2000 , \ r= 5\% , \ t=1 \ year[/tex] in equation (1) , we get
[tex]A=2000\times 2.71^{0.5 \times 1}\\A=2000\times 2.71^{0.5}\\ \ A=2000\times1.64872 \\A =\$3297.44[/tex]
It is given that principal is $1000 , annual interest rate is 4 % , time is 1 years
Putting [tex]P=\$1000 , \ r= 4\% , \ t=1 \ year[/tex] in equation (1) , we get
[tex]A=1000\times 2.71^{0.4 \times 1}\\A=1000\times 2.71^{0.4}\\ \ A=1000\times1.49182 \\A =\$1491.82[/tex]
It is given that principal is $1000 , annual interest rate is 6 % , time is 1 years
Putting [tex]P=\$1000 , \ r= 6\% , \ t=1 \ year[/tex] in equation (1) , we get
[tex]A=1000\times 2.71^{0.6 \times 1}\\A=1000\times 2.71^{0.6}\\ \ A=1000\times1.82211 \\A =\$1822.11[/tex]
Adding the above amounts , we get
[tex]A=1491.82+1822.11=\$3313.93\neq 3297.44[/tex]
which is not equal to amount investing $ 2000 in an account that pays 5% annual interest compounded continuously .
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Pavani collects 20.3 pounds of metal to take to a recycling center. The recycling center pays her for 18.4 pounds of the metal, and refuses the rest of it.
How much of Pavani's collection was refused, in pounds?
1.9 pounds of metal was refused of her collection.
Given that
Pavani collects 20.3 pounds of metal to take to a recycling center. The recycling center pays her for 18.4 pounds of the metal, and refuses the rest of it.To find
How much metal of Pavani's collection was refused, in poundsSo according to the question
We have,
Total collection by her = 20.3 pounds of metalThe recycling center pays her = 18.4 pounds of the metal.For finding the remaining metal of her collection, we have to subtract the metal buy by recycling center from her total collection
So, we can say that
remaining metal = her total collection - he metal buy by recycling center
Now, putting the values from question
remaining metal = 20.3 - 18.4
= 1.9 pounds of metal.
Answer:
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what extra step do you need to take when using the Multiplication Property of Inequality and the Division Property of Inequality when the coefficient of the variable term is negative? Give an example to illustrate your reasoning. Algebra 1... I need this before tomorrow pls help
Answer:
Step-by-step explanation:
a five number summary for hours studied in a week for a statistics class were 5, 8, 13, 17, and 20. problem 1 what is the value such that 50% or more of the students studied longer than that value? problem 2 what was the longest number of hours studied by anyone? problem 3 what was the shortest number of hours studied by anyone? problem 4 what is the value such that 75% or more of the students studied longer than that value? *hint* draw it out! problem 5 what is the value such that 25% or more of the students studied longer than that value? *hint* draw it out!
The 50% value is 13.
The longest hours studied is 20.
The shortest hours studied is 5.
The 75% number is 17.
What is the five number summary?The five number summary is the summary of a dataset that contains information on the minimum number, the 25th percentile, the median, the 75th percentile and the maximum number.
The median is the number at the center of the dataset. The median is 13. The maximum number provides information on the longest number of hours studies. The minimum number is the shortest number studied by anyone. The minimum number is 5. The 75th percentile is 17.
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Find the area and perimeter.
The figure shows a triangle. One side is given by 4 x minus 3 units. The second side is given by x plus 9 units. The third side is equal to 8 units. The height from the third side is given by 3 x units.
Hint: The height of a non-right triangle is the length of the segment of a line that is perpendicular to the base and that contains the opposite vertex.
A) 24x; 5x + 14
B) 12x; 5x + 14
C) 24x; 10x + 8
D) 12x; 7x + 3
The area and perimeter of the triangle are:
B. 12x; 5x + 14
How to Find the Area the Triangle?The area of the triangle in the image is calculated using the formula, area = 1/2(b)(h), where:
Base (b) = 8 unitsHeight (h) = 3x unitsSubstitute
Area of the triangle = 1/2(8)(3x)
Area of the triangle = 4(3x)
Area of the triangle = 12x units²
How to Find the Perimeter of the Triangle?The perimeter of the triangle in the image is calculated by adding the length of all three sides of the triangle, which is:
Perimeter = (x + 9) + 8 + (4x - 3)
Perimeter = x + 9 + 8 + 4x - 3
Combine like terms
Perimeter = 5x + 14 units
In conclusion: the area and perimeter of the triangle are:
B. 12x; 5x + 14
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Expand each logarithm.
log√x²-4 / (x+3)²
Expanded form of logarithm log√x²-4 / (x+3)² is 1/2log(x²-4)-2log (x+3).
By considering the given logarithm function
log√x²-4 / (x+3)²
log√x²-4 -log (x+3)²
1/2log(x²-4)-2log (x+3)
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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Solve the inequality
Answer:
Step-by-step explanation:
Simplify each complex fraction
(2/a) / (1/b)
Answer:
[tex] \frac{2b}{a} [/tex]
Step-by-step explanation:
[tex] \frac{2}{a} \div \frac{1}{b} [/tex]
[tex]\frac{2}{a} \: \times \:b[/tex]
[tex] \frac{2b}{a} [/tex]