The measure of the third angle = 105°.
What is angles?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The sum of the angles in a triangle is :
A° + B° + C° = 180°
Where A, B and C are the three angles in a triangle.
Hence, if two of the angles are given as : 55° and 20°
The measure of the third angle will be :
Let the measure of the third angle = C
(55 + 25 + C) = 180°
180° - (55° + 20°)
180° - 75° = 105°
The measure of the third angle = 105°
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A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $400 and the daily rate for each partner is $1000. The law firm assigned a total of 16 lawyers to the case and was able to charge the client $11800 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system of equations.
Using system of linear equations, the law firm employed 7 associate and 9 partners
System of Linear EquationThe system of linear equations can be defined as a set of two or more linear equations that have the same variables. Linear equations can be said as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
In this question, we have to write out two equations and solve for the unknown variable.
let;
x = associatey = partnerx + y = 16 ...eq(i)
400x + 1000y = 11800 ...eq(ii)
From equation 1
x = 16 - y ...eq(iii)
Put eq(iii) into equation (ii)
400(16 - y) + 1000y = 11800
6400 - 400y + 1000y = 11800
6400 + 600y = 11800
600y = 11800 - 6400
600y = 5400
y = 5400 / 600
y = 9
Put y = 9 in equation (i)
x + 9 = 16
x = 16 - 9
x = 7
The firm has 7 associate and 9 partners
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Select all of the equations that are true.
823÷418=2110
1112÷834=11135
256÷314=319
1223÷614=2275
123÷112=1
There are no equations that 's suitable.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
823÷418=2
1112÷834=1.333333333
Hence, There are no equations that 's suitable.
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What is the measure of c and b
Answer:
Step-by-step explanation:
im not 100% sure but probly 135
Answer:
angle c and b are 137 degrees both
Step-by-step explanation:
given angle is 43° and when subtracted from 180°
we have 137°.
using the alternative angle property the angle b is also 137°.
Help with this real fast
It is growing exponentially so this is non linear function of squares of given negative numbers.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element. A relation between a domain and range is called a function when each value in the domain only has one value in the range.
Here,
0²=0
-1²=1
-2²=4
-3²=9
Hence, It is a nonlinear function of the squares of the given negative numbers because it is growing exponentially.
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what's the GCF of 3a+5a
The common factor, in this case, is a, so the GCF is still a.
What is the greatest common factor (GCF)?
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.
To find the greatest common factor (GCF) of two or more terms, we need to factor each term and then identify the factors that are common to both terms.
In this case, we have the terms 3a and 5a. To find the GCF, we can factor each term as follows:
3a = 3a
5a = 5a
The only common factor between the two terms is a, so the GCF of 3a and 5a is a.
Alternatively, we could have written the terms as:
3a = 3 * a
5a = 5 * a
Hence, The common factor, in this case, is a, so the GCF is still a.
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Amy is considering visiting her new friend at one of his beach houses in Florida. She really loves the warm weather, so she would like to choose to go somewhere with a high median temperature, anda small interquartile Which place should she choose to visit? Ft. Meyers Jacksonville Beach Destin Pensacola Beach 70 75 80 85 90 95 100 70 75 80 85 90 95 100 A) Ft. Meyers B Jacksonville Beach C Destin (D Pensacola Beach
Amy is considering visiting her new friend at one of his beach houses she chooses to visit Destin and 85.
Amy is considering visiting her new friend at one of his beach houses in Florida.
She really loves the warm weather,
So she would like to choose to go somewhere with a high median temperature, and a small interquartile range.
We have to determine the place should she choose to visit.
Interquartile range :
The interquartile range is a measure of where the middle fifty is in a data set.
Destin HI 70 75 80 85.
Here She can choose the 4th position and which is 85.
The only one that passes 85.
Amy is considering visiting her new friend at one of his beach houses she chooses to visit Destin and 85.
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How many full cae and additional item are needed to fulfill the order?
80 item ordered item per cae
In linear equation,2 is the number of cases and the number of additional units.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
13 cases of 6 units each = 78
Additional units = 2
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The complete question is -
80 units needed, 6 units per case. What is the number of cases and the number of additional units?
Comparing Guy montage and Harrion Bergeon and eeing how they are different, imilar and the negative reult of their dytopian world and their contrating fate
Montag serves as a metaphor for free thought in Fahrenheit 451. Guy doesn't fit in with society as Beatty or Mildred do.
In what ways is Harrison Bergeron's society like to our own?Although the parallels are subtle, there are some similarities between the modern world and the setting of "Harrison Bergeron" in the narrative. Egality is a topic that both of them address and that has issues and effects. Another resemblance is the conflict that results from competition and attempts to stop it from happening, both of which cause issues.
Which aspects of society are Harrison Bergeron's writings critical of?The manipulative and desensitizing impact of the mass media is one political practice in American culture that the short story "Harrison Bergeron" might be seen as an oblique indictment of. overregulation of some human actions. restricting freedom of speech
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Divide negative 3 and one-sixth ÷ negative 8 and two-fifths.
252 over 95
95 over 252
51 over 30
30 over 51
The value of the expression divide negative 3 and one-sixth ÷ negative 8 and two-fifths is 95 over 252. Option B
What is a fraction?A fraction can be defined as the part of a whole item, number or element.
The several types of fractions are;
Simple fractionsProper fractionsImproper fractionsMixed fractionsComplex fractionsFrom the information given, we have that;
-3 1/ 6 ÷ - 8 2/ 5
Turn into improper fractions
-19/ 6 ÷ 42/ 5
Take the inverse of the divisor and multiply
- 19/ 6 × 5/ 42
95/252
Hence, the value is 95/252
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Please help need an answer by tonight :(
Rewrite x^2+4x−20=−8
in the form (x−p)2=q
Step-by-step explanation:
then we do the multiplications and compare :
(x - p)² = q
x² - 2px + p² = q
x² - 2px + p² - q = 0
our target is
x² + 4x - 20 = -8
x² + 4x - 12 = 0
now we compare the variable expression with the target.
x² = x² check
4x = -2px
4 = -2p
p = -2
-12 = p² - q = 4 - q
-16 = -q
q = 16
so, we have
(x - -2)² = 16
(x + 2)² = 16
What kind of function best models each situation?
Cate started with $0 in her account. After one week Cate saved $1; after two weeks she saved $4; after three
weeks she saved $9; and after four weeks she saved $16.
The function representing the given situation will be f(x) = x², where x is the number of week.
What is function?A function is defined as a relation between a set of inputs having one output each.
Given that, Cate started with $0 in her account. After one week, Cate saved $1; after two weeks she saved $4; after three weeks she saved $9; and after four weeks she saved $16.
As we see,
In 1 week the amount is $1
In 2 week the amount is $4
In 3 week the amount is $9
Which is showing that the amount is square of the week.
Hence, we can write the function as f(x) = x², where x is the number of week.
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If you deposit $3,000 at 2.5% compounded continuously, what would your ending balance after 4 years?
You will have $3276.44 after 4 years if you deposit $3,000 at an annual interest rate of 2.5%, compounded continuously.
What is continuous compound interest?
In theory, continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.
The formula for continuously compounded interest is:
[tex]A = P * e^{rt}[/tex]
where:
A is the ending balance (the amount you will have after 4 years)
P is the principal (the initial amount you deposited, in this case $3,000)
r is the interest rate (2.5% per year, or 0.025)
t is the time in years (4 years)
Plugging these values into the formula, we get:
[tex]A = $3,000 * e^{(0.025 * 4)}[/tex]
Calculating this gives us an ending balance of $3,276.44.
Hence, you will have $3276.44 after 4 years if you deposit $3,000 at an annual interest rate of 2.5%, compounded continuously.
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Write [tex]$\frac{2^{2010} + 2^{2008}}{2^{2005} - 2^{2003}}$[/tex] in the simplest form.
Answer:
160/3
Step-by-step explanation:
[tex]\frac{2^{2010}+2^{2008}}{2^{2005}-2^{2003}} \\ \\ =\frac{2^7 + 2^5}{2^2 - 1} \\ \\ =\frac{128+32}{4-1} \\ \\ =\frac{160}{3}[/tex]
You have a recipe that indicates to use 7 parts of sugar for every 4 parts of milk. You use 28 cups of sugar how much milk do you need
You'll need 16 parts of milk and sugar.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
Hence, You'll need 16 parts of milk and sugar.
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help with both questions please
The solution of the compound inequality are
-2x ≤ 4 and 10 ≥ -2x
x ≥ -2 and -5 ≤ x10 < 3x - 2 OR -3x - 2 > 14
3 < x OR x < -5How to solve the compound inequalityA sentence or equation having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality.
To solve the compound inequality each of them is solved individually
-2x ≤ 4 and 10 ≥ -2x
-2x ≤ 4 10 ≥ -2x
dividing by a negative sign reverses the inequality
x ≥ -2 -5 ≤ x
plot attached
The solution of the inequality is x ≥ -2 and -5 ≤ x
10 < 3x - 2 OR -3x - 2 > 14
10 + 2 < 3x -3x > 14 + 2
12 < 3x -3x > 16
3 < x x < -5.333
3 < x x < -5
plot attached
The solution of the inequality is 3 < x OR x < -5
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Solve for a:(8^(-1))/(4^(-1))-a^(-1)=1.
The value of the a is 2.
What is the fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when used in conversational English.
We have,
8⁻¹ / 4⁻¹ - a⁻¹ = 1
By simplifying the given equation we get,
8⁻¹ - a⁻¹ = 1 * 4⁻¹
By further calculating the equation,
1/8 - 1/a = 1/4
4(1/8 - 1/a) = 1
4/8 - 4/a = 1
1/2 - 4/a = 1
4/a = 1/2
1/a = 4/2
a = 2/4
a = 2
Hence, the value of the a is 2.
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PLEASE HELP!! WILL GIVE BRAINLIEST AND 13 POINTS!!
Solve for x
A. 10
B. 100
C. 64
Answer: 10
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]6^2 + 8^2=x^2\\\\36+64=x^2\\\\100=x^2\\ \\ x=10[/tex]
y=x+3
x-2y=-1
find x and y
[tex]y=x+3[/tex] for x
Flip the equation:
[tex]x+3=y[/tex]
Add -3 to both sides:
[tex]x+3+-3=y+-3[/tex]
[tex]\fbox{x = y - 3}[/tex]
__________________________________________________________
[tex]x-2y=-1[/tex] for y
Add -x to both sides:
[tex]x-2y+-x=-1+-x[/tex]
[tex]-2y=-x-1[/tex]
Divide both sides by -2:
[tex]\dfrac{-2y}{-2} =\dfrac{-x-1}{-2}[/tex]
[tex]\fbox{y = $\dfrac{1}{2}x+ \dfrac{1}{2} $}[/tex]
solve for u. u/4-8=20
Answer:
u = 112
Step-by-step explanation:
u/4-8=20
u/4 - 8 + 8 = 20 + 8 ==> add 8 on both sides to isolate u
u/4 = 28
4 * u/4 = 4 * 28 ==> multiply by 4 on both sides to isolate u
u = 112
Pls help I inserted a picture and have one last chance ALSO IT HAS TO BE IN A INEQUALITY
Eli brings 6 3/5 pizzas to a party. His friends eat 5 7/10 pizzas. Peng shows up with 2 3/4 pizzas. How many pizzas are there now?
A. 2 13/20
B. 2 15/20
C. 3 13/20
D. 3 18/20
The number of pizzas there now will be 3 ¹⁷/₂₀. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Eli brings 6 3/5 pizzas to a party. His companions eat 5 7/10 pizzas. Peng appears with 2 3/4 pizzas.
⇒ (6 + 3/5) - (2 + 3/4)
⇒ (33 / 5) - (11 / 4)
⇒ (132 - 55) / 20
⇒ 77 / 20
⇒ 3 ¹⁷/₂₀
The number of pizzas there now will be 3 ¹⁷/₂₀. Then the correct option is D.
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Option D in the correct form is given below.
D. 3 17/20
A stalk of wheat grows at a rate of 4 inches every month. Emerson planted A stalk of wheat when it was initially only 6 inches tall. > Create an explicit formula for this situation.
Answer: 4x+6
Step-by-step explanation:
We know that the growth rate is 4 inches every month, so let x represent the number of months, so we have 4x.
We know that it was originally 6 inches, so we have +6
So the equation is 4x+6
If you can, please give me a Brainliest, I only need 2 more to become an Ace, thank you!
he
2
2
63
Paula is standing on a bridge that is 110 above
the water below. She throws a pebble over
the edge of the bridge, and it hits the top of a
24 foot high bridge guard. The quadratic
equation that models the path of the pebble is:
p(t) = -16t² + 48t + 110
such that t is the time in seconds and p is
the height of the pebble.
What is the maximum height of the
pebble?
A) 2 feet
(B) 146 feet
C110 feet
D) 210 feet
Answer:
(B) 146 feet
Step-by-step explanation:
You want to know the maximum height of a pebble whose height is described by p(t) = -16t² + 48t + 110.
Vertex formWe can write the equation in vertex form as follows:
p(t) = -16(t² -3t) +110
p(t) = -16(t² -3t +2.25) +110 +16(2.25)
p(t) = -16(t -1.5)² +146
This shows the vertex of the quadratic curve to be (1.5, 146).
The maximum height of the pebble is 146 feet.
Find the sale price: Sergio bought a belt that was discounted 43% from an original price of $543.
Answer: $309.51
Step-by-step explanation:
100% - 43% = 57%
543 times 0.57 = $309.51
I NEED HELP PLEASE!!!!!!
What is the classification of each system?
Drag the answers into the boxes to match each system.
{x+5y=−2x+5y=4
{y=3x+4−2x+y=4
{3x+y=4−6x−2y=−8
Consistent Independent Consistent Dependent Inconsistent
Inequality classifications
x + 5y = −2 and x + 5y = 4 Inconsistent
y = 3x + 4 and −2x + y = 4 consistent and independent
3x + y = 4 and −6x − 2y = −8 consistent and dependent
What are inconsistent equations?A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.
x + 5y = −2
x + 5y = 4
subtracting gives
0 = -6 no solution
What are consistent and independent equations?A system is deemed consistent if it has at least one solution.
A consistent system is independent if it only has one solution.
-3x + y = 4
−2x + y = 4
subtracting gives
-x = 0
x = 0
substituting x to get y
-3 * 0 + y = 4
y = 4
What are consistent and dependent equations?A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them.
3x + y = 4
−6x − 2y = −8
subtracting gives
9x + 3y = 12 - none cancels out meaning infinite number of possible solutions
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I NEED HELP ASAP
FIRST TI ANSWER GET BRAINLEST
Answer:
2nd Option
Step-by-step explanation:
m=6
y=-3
so from equation
y=mx+c
y=6x-3
is the req ...... equation..
Answer: 2nd Option is the answer for this
Step-by-step explanation:
Pls help due today!!!!! -
Answer:
-3<2-y<-1
Step-by-step explanation:
1/5 1/y and 1/3 y is
a ball is dropped from a height of 20 feet. each time it drops h feet, it rebounds 0.89h feet. find the total distance traveled by the ball. (round your answer to two decimal places.)
a ball is dropped from a height of 20 feet. each time it drops h feet, it rebounds 0.89h feet, 343.63 feet the total distance traveled by the ball.
What is distance?The length of the line connecting any two places is known as their distance from one another. Subtracting the different coordinates will reveal the distance if the two locations are on the same horizontal or vertical line.
h₁ = 20 feet = h
h₂ = 0.89h
h₃ = 0.89²h
h₄ = 0.89³h
...........................
h(n) = 0.89ⁿh
Therefore, total distance travelled = 20 + 2 (0.89h + 0.89²h + 0.89³h +.....)
= 20 + 2h (0.89 + 0.89² + 0.89³ +.....)
Sum of (h.p)∞ = a/ (1-r)
Where, a = first term = 0.89
r = common ratio = 0.89
total distance travelled = 20 + 2 × 20 ×(0.89) × [1/(1 - 0.89)]
= 343.63 ft.
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Explain step-by-step how to simplify -5(2x - 3y + 6Z - 10)
Answer:
-10x + 15y - 30z + 50
Step-by-step explanation:
apply the distributive property
-10x + 15y - 30z + 50
Can someone help me with this, I understand nothing and I’m so confused. Been trying to work in this all weekend but I’m stumped.
Answer:
Try Doing Like this.
If u still need to understand, watch organic chemistry tutor guide or ask tr until u understand.