Answer:
=−42.875x6+0.24
Step-by-step explanation:
−58.8
−245
+(−3.5x2)3
=0.24+−42.875x6
Perform the indicated operation(s). Where possible, reduce the answer to lowest terms.
{1/2 + 1/3} / {1/2 +{1/6}
5/7
11/6
4/3
8/5
the lowest term for the given expression will be 5/4.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
The given fractions division is
{1/2 + 1/3} / {1/2 +{1/6}
={5/6}/{4/6}
={5/6}*{6/4}
=5/4
Hence the lowest term for the given expression will be 5/4.
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A soccer field is 115 yards (yd) long by 70 yd wide.
What is the length of the diagonal of a soccer field? Round your answer to the nearest tenth.
Answer:
135.3 yd
Step-by-step explanation:
The length of the diagonal of a rectangle can be found using the Pythagorean theorem, which states that the square of the length of the diagonal (c) is equal to the sum of the squares of the length (a) and the width (b) of the rectangle. So the formula is c = √(a^2 + b^2)
Given the length of the soccer field is 115 yd and the width is 70 yd, we can use the formula:
c = √(115^2 + 70^2)
c = √(13225 + 4900)
c = √(18125)
c = 135.3 yd
Rounding the answer to the nearest tenth we get 135.3 yd
Therefore, the length of the diagonal of a soccer field is 135.3 yd.
A house has decreased in value by 24% since it was purchased. If the current value is $209,000, what was the value when it was purchased?
Answer:
A house has decreased in value by 24% since it was purchased, that means the current value is 24% less than the value when it was purchased.
To find the original value, we can use the following formula:
Original Value = Current Value / (1 - (Decrease % / 100))
where the decrease is expressed as a decimal, thus 24% is 0.24
Original Value = $209,000 / (1 - 0.24)
Original Value = $209,000 / 0.76
Original Value = $275,000
So the original value when it was purchased is $275,000
Ibrahim owns a rectangular shaped property having a width of 1.9 miles and length of 3.6 miles. Once a week, Ibrahim walks around the perimeter of his property at a pace of 4.2 miles per hour. How many hours does it take Ibrahim to walk around the perimeter of his property once?
Answer:
about 2.62 hours
Step-by-step explanation:
add 1.9 and 3.6 twice
11
divide the parameter by 4.2
A pizzeria sells three sizes of pizza: small, medium, and large. The pizzas sell for $6
, $9
, and $10
, respectively. One evening they sold 37
pizzas and received $321
. If they sold 9
more large than medium pizzas, how many of each size did they sell?
Use the Gaussian elimination method with back substitution to solve the given word problem.
which graph represents the solutions to this system of inequalities? x=5y≤10
The graph that represents the inequality 5y≤10 is plotted below.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The given inequality is 5y≤10.
In a graph of an inequality, the symbols (<,>) are represented using a dotted line and the symbols (≤,≥) are represented using a straight line.
So, the graph of inequality 5y≤10 will have a straight line.
Now, writing the inequality 5y≤10 in slope-intercept form y = mx + b -
5y = 10
5y = 0x + 10
Substituting the values of x and y with origin (0,0) -
5(0) = 0(0) + 10
0 = 10
Putting the inequality symbol back -
0 ≤ 10
Since, 0 ≤ 10 is true hence the shaded region of graph will cover the origin.
On solving 5y = 10 -
y = 2
Hence the points of the inequality will be (0,2).
Therefore, the graph for the inequality 5y≤10 is plotted.
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function f(x) is shown on the graph. On a coordinate plane, a curved line with 3 arcs, labeled f of x, crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (3, 0), and the y-axis at (0, negative 6). What is f(0)? 0 only –6 only –2, –1, 1, and 3 only –6, –2, –1, 1, and 3 only
The described graph crossing the y-axis at (0, negative 6) has f(0) at
A. only –6How to find the y - interceptThe y - intercept is calculated by substituting the value of x as zero.
For a graph, when the curve passes through the y axis, the point is the y intercept.
On a coordinate axis the points are represented using ordered pairs of the form (x, y). For an equation, this is represented as f(x) = y
Because of this, the points (negative 2, 0), (negative 1, 0), (1, 0), and (3, 0) are f(-2) = 0, f(-1) = 0, f(1) = 0, and f(3) = 0, are the x intercepts
The y intercept in the problem is (0, negative 6), represented in equation form as
f(0) = -6
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5f-9c=160 solve for f
Step-by-step explanation:
5f = 160+9c
f = {160+9c} ÷ 5
EASY POINTS!
Winter has just begun. After one week, the temperature decreased by 46.8° with a
percent change of 72%. What was the temperature at the beginning of the week and
what is the temperature now?
The temperature at the beginning of the week was = 65
and, the temperature now = 18.2
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
After one week, the temperature decreased by 46.8° with a
percent change of 72%.
let,
the temperature at the beginning of the week = x
so, we get,
x= 46.8/72*100
=65
i.e. the temperature at the beginning of the week was = 65
and, the temperature now = 18.2
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I genuinely need help, please answer quickly
P.S the answer is not
[tex]x \leqslant - 5[/tex]
that is a step to getting the answer.
The solution to the compound inequality as a single inequality will be → x ≤ -3.
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.f(x) < g(x), means that expression f(x) is less than g(x) {for given (x)}.f(x) > g(x), means that expression f(x) is greater than g(x) {for given (x)}.f(x) = g(x), means that expression f(x) is equal to g(x) {for given (x)}.Given is the compound inequality as -
(x/3) ≤ -1
- 6 ≥ (x - 1)
The given inequalities are -
(x/3) ≤ -1 → x ≤ -3
-6 ≥ (x - 1) → x ≤ -5
The solution to the compound inequality as a single inequality will be -
x ≤ -3
Therefore, the solution to the compound inequality as a single inequality will be → x ≤ -3.
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Which of the following is the solution to 3 |x-1/2 12?
Therefore , the solution of the given problem of equation comes out to be x>5 .
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula.
Here,
Given :
we have equation 3|x - 1| > 12
So , to find the value of x :
=> 3x-3 >12
=> 3x>15
=> x>5
thus , x value is x>5 ,
So , it can be 6,7 and so on.
Therefore , the solution of the given problem of function comes out to be x>5 .
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How to solve the problem of equivalent fractions
1/2=1/2=1/2.is the value for the given equivalent fraction, by putting the value 3.4 in the numerators respectively
What is Equivalent Fraction?The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
1/2 = /6 = /8.
a. Multiply numerator and denominator by 3 for equivalenting the equation /6
Therefore,
3*3/6*3
=9/18
=1/2
therefore:1/2=1/2.
b. Multiply numerator by 4
Therefore,
4/8
=1/2.
Therefore:
1/2=1/2.
1/2=1/2=1/2.
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Graph h(x)=7sinx .
Use 3.14 for π .
Answer:
To graph h(x) = 7sin(x), we need to plot a set of points that satisfy the equation. To do this, we can pick several values of x, substitute them into the equation and find the corresponding y values.
We can use the fact that h(x) = 7sin(x) = 7sin(x + 2π) = 7sin(x + 4π) = .... = 7sin(x + 2nπ) , for any integer n.
The graph of h(x) = 7sin(x) is a sine function with an amplitude of 7 and a period of 2π.
It oscillates between -7 and 7 and the graph will look like a wave that oscillates between y = -7 and y = 7.
It has a horizontal shift of 2π to the right.
It is not possible to graph the function here but you can easily plot it using a graphing calculator or a program like Desmos.
Step-by-step explanation:
The length of a rectangle is 11 ft less than three times the width and the area of the rectangle is 70ft ^2
The length of the rectangle is 10ft and width of the rectangle is 7ft.
What is area of rectangle?
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.
According to the question
Length = 3(width)-11
=> l = 3w-11.
Now area of rectangle = lw
=> 70 = (3w-11)(w)
=> [tex]3w^2-11w=70[/tex]
=> [tex]3w^2-11w-70=0[/tex]
=> [tex]3w^2+10w-21w-70=0[/tex]
=> (3w+10)(w-7)=0
=> w= 7 ft
Then length l = 3(7)-11=21-11 = 10 ft.
Hence the length of the rectangle is 10ft and width of the rectangle is 7ft.
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K After a 75% reduction, you purchase a new sofa on sale for $135. What was the original price of the sofa? The original price was $ ***
The original price of the sofa is $540.
What is percentage?
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Here the Cost price of sofa after reduction = $135.
Now here reduction percentage is 75%.
Let us take original price percentage of sofa is 100%. Then
Here 100%-75%=25% is the cost price after reduction .
=> 25% of original price = 135
=> 25% of x = 135
=> [tex]\frac{25}{100}x =135[/tex]
=> [tex]\frac{135\times 100}{25}[/tex] = 135×4 = $540.
Hence the original price of the sofa is $540.
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Which expression is equivalent to 2^8? A) 8^2 B) 2•8 C) 2^4 • 1^4 D) 2^4 • 2^2 E) 2^4 • 2^4
Answer:
E) [tex]2^{4} * 2^{4}[/tex]
Step-by-step explanation:
By properties of exponents, when multiplying two numbers that have the same base, you can add the exponents. Therefore:
[tex]2^{8}=2^{4} * 2^{4}\\2^{8}=2^{(4+4)}\\2^{8}=2^{8}[/tex]
REINFORCE Suppose “triangle”DOG congruent to “triangle ”CAT. If m of the angle D = 30° and m of the angle A = 50°, find m of the angle T. Explain your
solution.
Pretty sure it'd be 100°.
Since the triangles are congruent, measurement D = measurement C. This means measurement C = 30°. Also, they give us measurement A, which is 50°. Of triangle CAT, we already know two of its angles. We can add them to see the last measurement of angle T. 30° + 50° = 80°. There is 180° in a triangle, so 180° - 80° = 100°, which gives us our last measurement, T.
PLEASE HELP ASAP!!!
Which sequence shows the numbers in order from least to greatest?
A.
B.
C.
D.
Order of numbers from least to greatest is -2.14<|-2.8|<3.2. Therefore, the option D is the correct answer.
What is the order of an integers?Numerical order is a way of arranging a sequence of numbers. This could be in ascending or descending order.
Ascending order: Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.
The given numbers are -2.14, √10, |-2.8|.
Here, √10=3.2
Order of numbers from least to greatest is
-2.14<|-2.8|<3.2
Therefore, the option D is the correct answer.
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer.
Part B: Write a function to represent the data. Show your work.
Part C: Determine the average rate of change between station 2 and station 4. Show your work.
Answer:
She will need a time of 1024 units to complete the 10th station.
Step-by-step explanation:
A. As the quotient between consecutive terms is the same, the data is a geometric sequence.
B. The recursive formula is:
C. She will need a time of 1024 units to complete the 10th station.
In a sequence, if the difference between consecutive terms is the same, the sequence is arithmetic.
If the quotient between consecutive terms is the same, the sequence is geometric.
Item a:
When x increases by 1, y is multiplied by 2, hence, as the quotient between consecutive terms is the same, the data is a geometric sequence.
A room has its floor dimensions as 8m by 6m. The floor is to be covered with carpet
which is sold by the metre from a roll 1 1/2 metres wide. How many metres of the carpet will be required to cover the floor completely without wastage?
The room floor has a rectangular dimensions with an area of 48 square metres and it will take 32 metres of the carpet to cover the floor completely without wastage.
How to calculate for the required metre of carpetThe floor has rectangular dimensions 8 m by 6 m such that:
area of the floor = 8 m × 6 m
area of the floor = 48 m²
Since the carpet roll is 1.5 metres wide;
48 m²/ 1.5 m = 32 m
Therefore, it will take 32 meters of the carpet to cover the rectangular floor with 8m by 6m dimensions completely without wastage.
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Please help me find the perimeter
The perimeter of one of the equilateral triangles in the window is equal to 12 feet.
How to evaluate for the perimeter of the equilateral triangleAn interior angle of an equilateral triangle measures 60°, hence by considering the right triangle LNX and the sine of angle X = 60°, we will derive one of the side lengths of the equilateral triangle as follows:
sin 60° = 2/XL {opposite/hypotenuse}
1/2 = 2/XL {sin 60° = 1/2}
XL = 2 × 2 {cross multiplication}
XL = 4 feet
All side length of an equilateral triangle are equal so;
one of the triangles perimeter = 3 × 4 feet
one of the triangles perimeter = 12 feet
Therefore, the perimeter of one of the equilateral triangles in the window is equal to 12 feet.
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Martin Luther King, Jr. Day was first celebrated in 1986, three years after it was signed into law. However, it was not until 2000 that all 50 states began to officially observe the holiday.
How many years has it been since MLK Day first signed into law??
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I BEEN STRUGGLING FOR 30min NOW
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ANSWER ASAP PLEASE I WILL GIVE 50 POINTS
Which of the following tables represents a linear relationship that is also proportional?
x −1 0 1
y −3 −2 −1
x −2 0 2
y −3 0 3
x −2 0 2
y 0 2 3
x −2 0 2
y 2 4 6
A table which represents a linear relationship that is also proportional include the following:
B. x −2 0 2
y −3 0 3
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables.k represents the constant of proportionality.In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = -3/-2 = 3/2
Constant of proportionality (k) = 3/2.
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Answer: The answer is B
Step-by-step explanation: I took the test and got it right
After 5 hours of flight, how much farther would the fastest bird have traveled than the slowest bird?
Answer: The crow would have traveled 40 miles per hour faster than the seagull after 5 hours of flight
Step-by-step explanation: (crow) 24 times 5 is 120 (seagull) 16 times 5 is 80, so it’s 120 - 80 which is 40
A strategy from learning science for retaining material is to write a summary of things you have learned and to note how this new information relates to previous concepts. Take a few moments to answer the following questions or write a summary of what you have learned from this section. a. How can you recognize a quadratic equation? b. What methods can you use to solve a quadratic equation? Explain each method. c. How many solutions can a quadratic equation have? d. What is the discriminant of a quadratic equation, and what does it determine? e. Write the formulas that you can use to solve application problems. f. How can you connect the concepts in this section to previous topics you have learned?
The information related to the quadratic equation is given below.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
A polynomial with degree 2 is called a quadratic equation.
It is in the form of ax² + bx + c
So,
We can recognize a quadratic equation if the highest power of the equation is two.
Now,
The methods that can be used to solve are:
Middle-term factorization.
Example:
x² + 2x + 1
x² + (1 + 1)x + 1
x² + x + x + 1
x(x + 1) + 1(x + 1)
(x + 1) (x + 1)
Using the determinant formula.
ax² + bx + c
x = [-b ± √(b² - 4ac)] / 2a
Now,
The number of solutions is equal to the degree of the quadratic equation.
Now,
The discriminant of a quadratic equation is [-b ± √(b² - 4ac)] / 2a.
Where ax² + bx + c is the equation.
The discriminant determines the solutions.
Thus,
The information related to the quadratic equation is given above.
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Whis one is warmer ; -5°C or -7°C?
the stingray tank contains 6 inches of water. the Shark tank is empty. each hour, 4 inches of water are added to the stingray tank and 6 inches are added to the shark tank. will the water in the shark tank ever be as deep as the water in the stingray tank
Yes, after 3 hours the level of water in both tanks will be equal.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the stingray tank contains 6 inches of water. the Shark tank is empty. each hour, 4 inches of water are added to the stingray tank and 6 inches are added to the shark tank.
The time at which both the tanks will have the same level will be calculated as;-
4x + 6 = 6x
6x - 4x = 6
2x = 6
x = 3 hours
Level = 6x = 6 x 3 = 18 inches
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Simplify -9 + (-y) + 6-y
Answer:
-3+(-2y)
Step-by-step explanation:
Combine the like terms
(-9+6) + (-y-y)
-9+6= -3 -y-y= -y+ -y= -2y
-3+-2y
Select the classification that best identifies 0
A) integer, rational number, real number
B) integer, whole number, rational number, real number
C) integer, natural number, whole number, rational number, real number
D) irrational number, real number
Answer: either b or c
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
m/ABD is a straight angle.
m/CBD = 8x+16°
m/ABC = 6x - 60°
Find m/ABC:
Answer:
Solution in attached photo.
Step-by-step explanation:
SolutionThe solution is attached as a photo. This Question tests on the concept of Angle Properties.
Properties required:
1) Angles in a straight line sums up to 180°.