A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
We know that a square has 4 sides of the same length, meaning that the length and the width are the same length. You can solve for the area of the first three rooms with a length of 13 feet using an equation like this:
(13 × 13) × 3
Now, for the other two rooms with the length of 15 feet:
(15 × 15) × 2
Simply add them together.
([13 × 13] × 3) + ([15 × 15] × 2)
Simplified, the expression would look like this:
(169 × 3) + (225 × 2) = 957
Therefore, the expression that shows the total area of these five rooms would look like this: ([13 × 13] × 3) + ([15 × 15] × 2), or it being simplified would look like this: (169 × 3) + (225 × 2) = 957
What is the equation in slope-intercept form of a line whose slope is 9 and whose y-intercept is -3?
The equation in slope-intercept form of a line whose slope is 9 and whose y-intercept is -3 is y = 9x - 3
How to determine the equation of the lineThe general formula used to represent the equation of a given line of graph is expressed mathematically as;
y = mx + c
Given that the parameters are;
m is the slope of the given line of the graphy is the point on the y - axis represented by the graphx is the point on the x - axis represented by the graphc is the intercept on the y- axis by the line of the graphFrom the information given, we have that;
y = -3
m = 9
Now, substitute these values into the general formula for the equation of a line of graph, we have;
y = 9x +(-3)
expand the bracket
y = 9x - 3
Hence, the equation is y = 9x - 3
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Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ACDE=AOPQ?
Check all that apply.
A. SAS
B. AAS
C. HA
D. ASA
E. LL
F. HL
On solving the provided question, we can say that by AAS property both triangles are congruent.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
in this triangle
one sides are equal
and two angles are equal.
so by AAS property they are congruent/
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URGENT PLEASE HELP
f(x) = √x + 7. Find the inverse of f(x) and its domain.
Answer: B
Step-by-step explanation: The inverse is f^-1(x)=x^2-7 and the domain is x>7
Problem #3
Ngozi earns $24,000 in salary in the first year she works as an interpreter. Each year, she earns a
3.5% raise.
Write a function that gives Ngozi's salary S(t), in dollars, t years after she starts to work as an
interpreter.
Do not enter commas in your answer.
S(t)
=
oblem #4
The exponential function f. whose graph is given below, can be written as f(a)=a-b.
The function that gives Ngozi's salary is S(t) = 24,000(1.035)^t. Where t is the number of years after she starts to work.
What is an exponential function?
A mathematical function of form f (x) = a^x is an exponential function. where x is a variable and an is a constant known as the function's base. The transcendental number e, which is approximately 2.71828, is the most commonly encountered exponential-function base.
Given that the starting salary is $24,000.
Each year, she earns a 3.5% raise.
The increase of salary follows a compound.
The formula of compound is
A =P(1+r)^t.
Here P= 24,000, r = 3.5% = 0.035.
After t year, the salary will be:
S(t) = 24,000(1+0.035)^t
S(t) = 24,000(1.035)^t.
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Solve the Simulataneous equations 2x + 4y=1
2 x + 4 y = 1 has the simultaneous equation [tex]x=\frac{1-4 y}{2}[/tex] .Eliminate a variable by using the elimination procedure.
What do you meant by Simulataneous equations?for x, solve, [tex]2 x+4 y=1 \quad: \quad x=\frac{1-4 y}{2}[/tex]
2 x + 4 y=1
4 y in the correct direction
2 x = 1 - 4 y
multiply both sides by two.
[tex]\frac{2 x}{2}=\frac{1}{2}-\frac{4 y}{2}[/tex]
Simplify
[tex]x=\frac{1-4 y}{2}[/tex]
You can find answers to both unknowns in two separate equations that have the same two unknowns in each. The three most popular approaches to solving are addition/subtraction, substitution, and graphing. simultaneous problems Equations: Elimination, Substitution, Graphical, and Matrix Methods | Vivax Solutions.
Steps for Solving Multiple Equations at Once Using the Elimination Method. Selecting a variable to remove is step one. Find the LCM of the variable's coefficients in step two. Step 3: Multiply the equations' two sides to create the coefficient of the variable you want to remove from the LCM.
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For a ride on a rental scooter, Abdul paid a $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill for Abdul's ride was $20.71 . For how many minutes did Abdul ride the scooter?
Answer:
6min and 39sec
Step-by-step explanation:
$3+11cents=$3.11
1min=$3.11
?min=$20.71
$20.71÷$3.11
=6min and 39secs
A waitress received a $2.25 tip for serving a dinner that cost $15.
What percent of the cost of the dinner was the tip?
O 20%
O 15%
O 18%
O 12%
On a dinner of cost $2.25, you want to add 15% to the bill. As a result, your lunch will cost more money overall $2.59.
How to find the calculation?In order to perform a computation, first change the 15% to an actual value. To do this with percentages, just divide the percentage (in this case, 15%) by 100. In terms of a precise mathematical value, the colloquial word "15%" thus becomes 15% / 100% = 0.15.You should next calculate the 15% portion of your $2.25 meal's cost.Always multiply 0.15 by $2.25 to arrive at this figure.
0.15 x $2.25=$0.34.
Your planned tip is $0.34, so that is how much you will give.As a result, your lunch will cost more money overall (to write on your charge slip or other payment)$2.25 + $0.34 = $2.59.
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What are the first five terms in the recursive sequence defined by the following?
a_1= 150
a_n= 0.85a_n-1
The first five terms in the recursive sequence defined by a_1 = 150 and a_n = 0.85a_n-1 are:
a_1 = 150
a_2 = 0.85150 = 127.5
a_3 = 0.85127.5 = 108.375
a_4 = 0.85108.375 = 91.8125
a_5 = 0.8591.8125 = 77.853125
What is a recursive sequence?A recursive sequence is a sequence of numbers where each successive term is determined by the value of previous terms, typically by applying a mathematical operation to those terms.
Therefore, the first five terms in the recursive sequence are 150, 127.5, 108.375, 91.8125, and 77.853125.
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Kadeem has $50,000 in an account that compounds interest sem-annually at a rate of 1.8%. He withdraws $5,000 semiannually from the account
Will his money last:
4.5 years (yes or no), 5 years (yes or no), 5.5 years (yes or no), 6 years (yes or no)
The time taken will be; 5.3 years.
What is Compound Interest?Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.
Compound interest is when you receive interest on both your interest income and your savings.
Given that P = 50, 000
W= 5000
r= 1.8%= 0.018
n= 2
Now we know that , P = W (1- (1+ r/n)^{-nt}) / (r/n)
Putting all the values we get;
P = W (1- (1+ r/n)^{-nt}) / (r/n)
50000 = 5000 (1- (1+0.018/2)^{-2t}) / (0.018/2)
10 = (1- (1+0.009)^{-2t}) / (0.009)
0.09 = 1 - (1.009)^{-2t
(1.009)^{-2t = 0.91
Taking log on both side;
-2t log 1.009 = log 0.91
t= log 0.91/ (log 0.091) / (-20
t= 5.3
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Last year a team lost 20% of its games. If the team won 24 goes, and had no tied games, how many games did it play?
The total no : of game=20
How many games did it play?team lost=20%
team won=24
assume no: of games played=100x
no: of games lost=20
actual no: of game lost=420x=4
x=1/5
the total no: of game played=100*(1/5)=20
so the total no : of game=20
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For a given input value xxx, the function fff outputs a value yyy to satisfy the following equation.
-5x-4y=-8
Write a formula for f(x)
The formula for the function f(x) is given as -
f(x) = - (5/4)x + 2.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the function as follows -
- 5x - 4y = - 8
In mathematics, 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.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
The given expression is -
- 5x - 4y = - 8
- 4y = 5x - 8
y = - (5/4)x + 2 = f(x)
Therefore, the formula for the function f(x) is given as -
f(x) = - (5/4)x + 2.
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Help on this calculus question please!
The given piecewise function value of k is [tex]\frac{1}{6}[/tex].
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). The definition of a function is a relationship between a set of inputs and each output. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Here the given function is h(x)=[tex]\left \{ {{\frac{x-3}{x^2-9} for -3,3} \atop {k} for x=3 } \right.[/tex]
Here h(x) = [tex]\frac{x-3}{(x-3)(x+3)}[/tex] = [tex]\frac{1}{x+3}[/tex] for x≠3,-3
The given function h is continuous at x=3 then
[tex]\lim_{x \to \3} h(x)= \lim_{n \to \3} h(x) = h(3)[/tex]
=> [tex]\lim_{x \to \3} \frac{1}{x+3} = \lim_{x \to \2} k = k\\[/tex]
=> k = [tex]\frac{1}{3+3} = \frac{1}{6}[/tex]
Hence the value of k is [tex]\frac{1}{6}[/tex].
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Solve for x.
89(54x−36)+2=−34(−40+16x)+90x
The value of x for the equation is 0.35.
What is simplification?Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
Given equation,
89 (54x − 36) + 2 = -34( −40 + 16x) + 90x
using PEMDAS
solving Parentheses first,
89(54x) - 36(89) + 2 = -34(-40) + 16x(-34) +90x
4806x - 3204 +2 = -1360 - 544x + 90x
4806x + 544x - 90x = -1360 + 3204 -2
5260x = 1842
x = 0.35
Hence the value of x is 0.35.
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report (3,000 words), and begs Monica to type it for her. If Monica agrees, how long will it
take her?
If Monica agrees to type the report for her manager, she will take 40 minutes, based on the unit rate.
What is the unit rate coefficient?The unit rate refers to the coefficient of proportionality between two proportional quantities.
The unit rate is computed as the quotient of the total number and the typing speed or rate per minute.
In this situation, we are given the total words of the report and Monica's typing speed. Based on this, we can compute the time for her to complete the typing by dividing the total words by the typing speed.
The total number of words in the report = 3,000 words
Monica's typing rate per minute = 75 words per minute
The time for Monica to complete typing the 3,000-word report = 40 minutes (3,000/75).
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Question Completion:A report contains 3,000 words and the manager begs Monica to type it for her. If Monica agrees, how long will it take her, assuming Monica's typing speed per minute is 75 wpm?
9x +11y = 2
3x + 4у = 4
Answer: (-12, 10)
Step-by-step explanation:
I will assume that you want to solve for x and y
9x + 11y = 2 (1)
3x + 4y = 4 (2)
Multiply (2) by 3:
9x + 12y = 12 (3)
Do (3) - (1):
y = 10
x = -12
(x, y) = (-12, 10)
The expression below was simplified using two properties of operations. 3(10n +2+14n)
Answer:
Associative property, then distributive property
Step-by-step explanation:
Temperature in degrees Celsius maybe change 2°F by using the formula F equals 1.8 C +32° find the temperature in degrees Fahrenheit in C equals 25°.
Answer:
A. 77 degrees Celsius
Step-by-step explanation:
(25°C × 9/5) + 32 = 77°F
3 · {(300 - 70 ÷ 5) - [3 · 23 - (8 - 2 · 3)]}
Answer:
(657)
Step-by-step explanation:
Simplify the following:
3 (300 - 70/5 - (3×23 - (8 - 2×3)))
The gcd of -70 and 5 is 5, so (-70)/5 = (5 (-14))/(5×1) = 5/5×-14 = -14:
3 (300 + -14 - (3×23 - (8 - 2×3)))
-2×3 = -6:
3 (300 - 14 - (3×23 - (-6 + 8)))
8 - 6 = 2:
3 (300 - 14 - (3×23 - 2))
3×23 = 69:
3 (300 - 14 - (69 - 2))
| 6 | 9
- | | 2
| 6 | 7:
3 (300 - 14 - 67)
300 - 14 - 67 = 300 - (14 + 67):
3 ((300 - (14 + 67)))
| 1 |
| 6 | 7
+ | 1 | 4
| 8 | 1:
3 (300 - 81)
| | 9 |
| 2 | | 10
| | |
- | | 8 | 1
| 2 | 1 | 9:
3 (219)
3 (219) = (3×219):
(3×219)
3×219 = 657:
Answer: (657)
Using the Law of Sines to find a triangle with one obtuse angle if
After using law of sine the measure of triangle ∠B=50° , ∠C= 85° and
c= 36.4.
What is sine law?
According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides. The sine rule is another name for it.
Here the given triangle measures are , ∠A = 45° , a = 26 and b=28.
Now using sine law then
=> [tex]\frac{a}{sin A} = \frac{b}{sin B}[/tex]
=> [tex]\frac{26}{sin 45} = \frac{28}{sin B}[/tex]
=> sin B = [tex]\frac{28\times sin 45}{26}[/tex]
=> sin B =0.7615
=> ∠B= 49.60° ≅ 50°
Now we know that sum of all angles in triangle is add upto 180°.
=> ∠A+∠B+∠C = 180°
=> 45°+50°+∠C = 180°
=> ∠C = 180°-95° = 85°
Now again using sine law then
=> [tex]\frac{b}{sin B} = \frac{c}{sin C}[/tex]
=> [tex]\frac{28}{sin 50}=\frac{c}{ sin85}[/tex]
=> c = [tex]\frac{28\times sin 85}{sin 50}[/tex]
=> c = 36.4
Hence the answers are ∠B=50° , ∠C= 85° and c= 36.4
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A. Explain the different strategies that Nicky and
Tavon used, and the advantages or **
disadvantages of each.
The different strategies are: Nicky collected the similar terms together, took the LCM and then solved for x. Tavon multiplied both sides of the equation by the lowest common denominator and then solved for x.
What is LCM?Finding the smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple.
Nicky collected the similar terms together, took the LCM and then solved for x. This method is quick but can result in wrong answer if the fractions are solved incorrectly.
Tavon on the other hand multiplied both sides of the equation by the lowest common denominator and then solved for x. The method is time consuming, yet it simplifies the equation significantly.
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Suppose that an individual has a body fat percentage of 15.7% and weighs 166 pounds. How many pounds of his weight is made up of fat? Round
your answer to the nearest tenth.
pounds
The individual' weight made up of fat is 26.27 pounds.
What portion of his weight—in pounds—is made up of fat?The individual's body fat percentage is 15.7%, which means that 15.7% of their total weight is fat.To calculate the amount of fat in pounds, we simply need to calculate 15.7% of 166 pounds.To do this, we can use the formula:Percentage X Total amount = AmountSo, in this case, we can plug in our values:15.7% X 166 = 25.922Therefore, the individual has 25.922 pounds of fat. To convert this to a whole number, we can round up to 26 pounds.So the individual has 26 pounds of fat in their body, out of a total weight of 166 pounds. It's important to note that a healthy body fat percentage is generally considered to be between 18-24% for men, and 25-31% for women.So, while this individual has a lower than average body fat percentage, they should still work on maintaining a balanced diet and regular exercise to stay healthy.To learn more about The body fat percentage method refer to:
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3. A cylinder is shown. What is the approximate surface area, using 3.14 for π? Use the formula for surface area of a cylinder, А 2πr² + 2πrh. PLEASE HELP THANK SM EASY!!
.
The approximate surface area, using 3.14 for π is 866.64m^2
How to find the lateral surface area of a cylinder?The lateral surface area of a cylinder is also called the curved surface area of the cylinder.
Suppose that:
Radius of the considered cylinder = 'r' units
Height of the considered cylinder = 'h' units
The area of upper and lower circle of cylinder=[tex]2\pi r^{2}[/tex]
Then, the surface area of that cylinder is;
[tex]S_L = 2\pi r h \: \rm unit^2[/tex] + [tex]2\pi r^{2}[/tex]
Given;
The value of [tex]\pi[/tex] =3.14
Radius of cylinder= 6m
Height of cylinder= 17m
Area of cylinder= 2πr² + 2πrh
=2(3.14) x6^2 + 2(3.14)x6x17
=226.08+640.56
=866.64m^2
Therefore, the surface area will be 866.64m^2
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Solve for x.
I NEED HELP IN THIS ONE PLEASE
Step-by-step explanation:
the case of 2 secants starting at the same point (L).
the product of the circle outer part with its total length (to the far circle arc) is constant for all secants from the same point.
so,
10(10 + 42) = 13(13 + x)
520 = 169 + 13x
351 = 13x
x = 351/13 = 27
Please help me I need these done lol
Answer: 216!
Step-by-step explanation:
216 because 6 times 6 times 6 =216
**sorry if my english is bad i dont speak it**
During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?
If during a baseball game, a player hits a ball while a bird is flying across the field. The intersection points of the equations represent: C the time when the height of the ball and the bird are the same.
What is intersection points?Intersection points can be defined as the points in which two lines meet or equate.
Height of the baseball over time = h = –16t2 + 65t
Height of a bird over time = h = 8t + 20
Where:
t represent the time in seconds
h represent the height in feet
–16t² + 65t = 8t + 20
-16t² +57t -20 =0
So,
t = -57 ±√57² -4×(-16) × (-20) / 2× (-16)
t = -57±√3249 -1280/ -32
t = -57 ±√1969 /-32
t = -57 + 44.373 / -32
t = -12.627 /-32
t =.395
t = -57 - 44.373 / -32
t = -101.373 /-32
t =3.168
Based on the above the time when the height of the ball and the bird are the same are the intersection points.
Therefore the correct option is C.
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The complete question is:
During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?
the height of the bird and the ball when the ball and the bird are the same distance from the player
the height of the bird and the ball when the player hits the ball
the time when the height of the ball and the bird are the same
the time when the ball and the bird hit the ground
I need help with 1 and 3
Diagram C does not depict a function, according to the idea of function.
What is meant by function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.Therefore,
Each input value of a function can be connected to a single output value.Only one line can exit the diagram from each value entered in the input.Diagrams A, B, and D are functions since each input value has a single corresponding value on the output for each of these three diagrams.Diagram C's input 7 is mapped to outputs 8 and 12, i.e., one input is mapped to two outputs, indicating that the diagram is not a function.To learn more about function, refer to:
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6. In the expression –¼x + 3,
Gianna factored the expression and wrote: –(¼x – 3)
Hannah factored the expression and wrote: –1(¼x – 3)
Both Gianna and Hannah claim to be correct. Do you agree? Why or why not?
Both Gianna and Hannah are correct, as the lone difference is that Gianna kept the one hidden while Hannah did not.
How to factor the expression?The expression for this problem is given as follows:
y = -x/4 + 3.
Gianna's factoring is given as follows:
-(x/4 - 3).
The negative represents the distributive property, meaning that it changes the signal of each term inside the expression, hence:
-(x/4 - 3) = -x/4 + 3.
Which is correct.
Hanna's factoring is given as follows:
–1(¼x – 3)
Which is the same as Gianna's, as -(x/4 - 3) and -1(x/4 - 3) is the same expression, just for the first the one is hidden.
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Que es *Clasificación de polígonos por el numero de sus lados
Triángulo: 3 lados. Cuadrilátero: 4 lados. Pentágono: 5 lados. Hexágono: 6 lados.
The ratio of yellow peeps to blue peeps is 7 to 4. What is the maximum number of total peeps when the number is less than 130
Thus there can be no more than 8 total peeps when the number is less than 130.
what is proportionality ?Relationships that have the same ratio over time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear relationship between two numbers or variables. When the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases.
When two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities stays the same at all values. As an example, consider the diameter and circumference of a circle.
given
total peeps when the number is less than 130
ratio = 7:4
Thus there can be no more than 8 total peeps when the number is less than 130.
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Help!! Have no clue where to start due tomorrow morning
Hi! So you need CE. CD + DE = CE, and the values are 14 + 2x + 3. That's 17 + 2x. Is there any more given information? I don't see what's available. Otherwise that may be the only way you can simplify it.