The equation that represents the length of the square dining room in feet is (1/4)x - 5/6.
What are the dimensions of a square?The area of a square is a product of it's any two sides or a product of diagonals divided by two. If a side has a length 'a' then the diagonal is a√2.
The perimeter of a square is the sum of the lengths of all the sides.
We know the perimeter of a square is 4×side.
We also know that 1 foot is equal 12 inches.
Given, A square dining room table has a perimeter of (12x - 40)".
Now if we factor out a 4 we'll have the side inside the bracket which is,
4(3x - 10)'', This is in inches to convert it to feet we have to divide what is inside the bracket by 12 which is,
= (3/12)x - 10/12 feet.
= (1/4)x - 5/6 feet.
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What do () mean in math?
Parentheses are employed to indicate changes to the usual order of operations.
Define round brackets.The well-known () symbols, often known as "round brackets," are used in pairs to group things together or designate the order of operations in an equation. You will frequently need to employ brackets in math when forming or resolving equations. They support number grouping and operation definition.
Mention other brackets as well.{}, [] are other type of brackets.
In mathematical expressions, parentheses are employed to indicate changes to the usual order of operations (precedence rules). In an expression like, the portion of the expression enclosed in parentheses,, is first assessed, and the outcome is then incorporated into the remaining portions of the expression.
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How do you find out if a triangle is acute obtuse or right?
The steepness of a ramp is graphed using the points (0,3) and (36,0). The steepness of a second ramp is represented by the function g(x)= -1/4x+2. What is the slope of the ramp?
The slope of a line is a measure of its steepness and can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the points (0,3) and (36,0) represent the coordinates of two points on the ramp. To find the slope of the ramp, we can plug these values into the formula:
slope = (0 - 3) / (36 - 0) = -3 / 36 = -1/12
The slope of the ramp is -1/12. This indicates that the ramp is relatively flat, as a negative slope means that the line is sloping downward.
To find the slope of the second ramp, represented by the function g(x) = -1/4x + 2, we can take the derivative of the function. The derivative of a function represents the slope of the function at any given point, and it is calculated using the formula:
derivative = f(x) = -1/4
The derivative of the function g(x) is a constant value of -1/4, which means that the slope of the second ramp is also -1/4. This is a steeper slope than the first ramp, as the value of the derivative is larger in magnitude.
The function f open argument x close argument varies inversely with x and f open argument x close argument equals 0.5 when x
The value of function f(x), when x=2.4 is f(x)=0.00625.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
If the function f(x) varies inversely with x, then this function is of the form -
f(x)=a/x
where a is unknown number.
Since f(x)=0.5 when x =0.3, then -
0.5 = a/0.3
a = 0.5 × 0.3
a = 0.15
So, the function now becomes -
f(x) = 0.15/x
Substituting for x = 2.4 -
f(2.4) = 0.15 / 2.4
= 15/240
= 1/16
= 0.00625
Therefore, f(x) value is obtained as 0.00625.
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The function f(x) varies inversely with x and f(x)=0.5 when x =0.3. what is f(x) when x=2.4?
The sides of a triangle are 68, 61, and 46. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
Answer: Acute
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex]. A and b are legs while c is hypotenuse. Hypotenuse is also the longest side. Let's plug them in and see if they are equal to each other.
[tex]46^2+61^2=68^2[/tex] [exponent]
[tex]2116+3721=4624[/tex] [add]
[tex]5837\neq4624[/tex]
Since they are not equal, then it is not a right triangle.
To tell is a triangle is acute, if the sum of the two shorter sides squared is greater than the longest side squared, then the triangle is acute.
At the end of the Pythagorean Theorem, we got 5837≠4624. 5837>4624, so that tells us that the triangle is acute.
Han earns 33.00 for babysitting 4 hours at this rate how much will he earn if the babysitter for 7 hours explain your reasoning
Han will make $57.75 for 7 hours of babysitting.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is that Han earns $33 for babysitting 4 hours.
Han made $33 for 4 hours of work.
Then, he will make $(33/4) in 1 hour of work.
Then, he will make $(33/4 x 7) in 7 hours of work.
$(33/4 x 7)
$(33/4 x 7)
$(231/4)
$57.75
Therefore, Han will make $57.75 for 7 hours of babysitting.
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A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200
A: If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?
B: If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?
C: If the car spends no time going 35 miles per hour, how long would the trip take? Explain your reasoning.
Answer:
A. The car spends 2.05 hours going 55 miles per hour
B. The car spends 1 hour going 35 miles per hour
C. The trip takes 3.6 hour
Step-by-step explanation:
The equation is
55x+35y=200
Let's solve A
We know the car spends 2.5 hours going 35 miles per hour on the trip, so we put 2.5 in for y and solve for x
55x+35(2.5) = 200
55x + 87.5 = 200
55x = 112.8
x = 2.05 hours going 55 miles per hour
So, the car spends 2.05 hours going 55 miles per hour
Let's solve B
55(3)+35y=200
165 + 35y = 200
35y = 35
y = 1 hour
So, the car spends 1 hour going 35 miles per hour
Let's solve C
We know the car spends no time going 35 miles per hour, so we put 0 in for y and solve for x
55x+35(0)=200
55x = 200
x = 3.6 hours
So, the trip takes 3.6 hour
What is the value of 2 by 7 and 3 by 7?
the value of 2 by 7 and 3 by 7 is: 5/7. This can be solved using the concept of fraction of addition.
What is the fraction?A fraction is a piece of the entire. The number is stated in arithmetic as a quotient, which signifies the numerator divided by the denominator. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction is a fraction. A suitable fraction has a numerator that is smaller than its denominator.
Three main fractional kinds exist. They come in three varieties: appropriate fractions, incorrect fractions, and mixed fractions. The numerator and denominator words are known as fractions. We define its kinds in light of these two words.
the value of 2 by 7 and 3 by 7 is:
= (2/7) + (3/7)
= 5/7
When adding the fractions 2/7 and 3/7 we get 5/7, as the denominator is same.
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Find values of a and b that make the following equality into identity:
(2x+5)/(x-8)(2x+1)=a/(x-8) + b/(2x+1)
Giving 30+ points!
The values of a and b in the fraction are 21/17 and -8/17
How to determine the values of a and bFrom the question, we have the following parameters that can be used in our computation:
(2x+5)/(x-8)(2x+1)=a/(x-8) + b/(2x+1)
Take the LCM
So, the expression can be expressed as
(2x+5)/(x-8)(2x+1)=a(2x+1) + b(x-8)/(x-8)(2x+1)
Multiply both sides by (x-8)(2x+1)
(2x+5) = a(2x+1) + b(x-8)
Open the brackets
2x + 5 = 2ax + a + bx - 8b
By comparison, we have
2a + b = 2
a - 8b = 5
Make a, the subject in a - 8b = 5
a = 5 + 8b
Substitute a = 5 + 8b in 2a + b = 2
10 + 16b + b = 2
Evaluate the like terms
17b = -8
Divide by 17
b = -8/17
Substitute b = -8/17 in a = 5 + 8b
a = 5 + 8 * -8/17
Evaluate
a = 5 - 64/17
So, we have
a = 21/17
Hence, the values are 21/17 and -8/17
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What are the solutions of the equation 9x4 minus 2x2 7 0?
The solution of the equations are x = √1 = ± 1
Now, According to the question:
The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]
Using the substitution rule we put [tex]x^{2}[/tex] = u .
The given equation now changes to
[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)
Equation(1) is a simple quadratic equation which can be solved by factorization as follows:
[tex]9u^2 - 2u - 7 = 0[/tex]
(9u + 7)(u - 1) = 0
Therefore
9u + 7 = 0 → u = -7/9
u -1 = 0→ u = 1
Since u = [tex]x^{2}[/tex] implies
x = √-7/9 = ± i√7/9
x = √1 = ± 1
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The complete question is this:
What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.
Work out the value of (6.31 x 10^5)+(2.6 x 10^4)
Give your answer in standard form
The answer in standard form is given by 65.7 ×10⁴
What is the Standard Form of a Number?A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.
Given here: (6.31 x 10⁵)+(2.6 x 10⁴)
Simplifying the equation further we get
(6.31 x 10⁵)+(2.6 x 10⁴)= 63.1×10⁴+2.6×10⁴
=65.7×10⁴
Hence, The answer in standard form is given by 65.7 ×10⁴
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Find y for 0.5y-2 2/5=1/2y+2.4
To solve this equation for y, you can follow these steps:
First, get all the terms with y on one side of the equation and all the other terms on the other side. To do this, you can add 2/5 to both sides to get rid of the 2/5 on the left side:
0.5y - 2 2/5 + 2/5 = 1/2y + 2.4 + 2/5
Simplify the left side of the equation:
0.5y - 2 + 2/5 = 1/2y + 2.4 + 2/5
0.5y - 2 + 2/5 + 2/5 = 1/2y + 2.4 + 2/5 + 2/5
0.5y - 2 + 4/5 = 1/2y + 2.4 + 4/5
Combine like terms on each side:
(0.5y + 4/5) - 2 = (1/2y + 2.4) + 4/5
Simplify:
0.5y + 4/5 - 2 = 1/2y + 2.4 + 4/5
0.5y - 2 + 4/5 = 1/2y + 2.4 + 4/5
Combine like terms on each side:
(0.5y + 4/5) = (1/2y + 2.4) + 4/5
Simplify:
0.5y + 4/5 = 1/2y + 2.4 + 4/5
Combine like terms on each side:
0.5y = 1/2y + 2.4
Subtract 1/2y from both sides:
0.5y - 1/2y = 1/2y - 1/2y + 2.4
0 = 2.4
Solve for y:
0 = 2.4
This equation has no solution, so there is no value of y that satisfies the given equation.
Answer:
Step-by-step explanation:nosoulution
If a temperature at 9pm i one third the temperature at midnight then what i the anwer ?
-4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.
What is temperature ?The physical concept of temperature indicates in numerical form how hot or cold something is.
A thermometer is used to determine temperature.
Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and thermometric substances.
The most popular scales are the Celsius scale, sometimes known as centigrade, with the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).
The lowest point on the thermodynamic temperature scale is absolute zero, or zero kelvin, or 273.15 °C. It can be very closely approximated experimentally but never actually reached, as stated in the third rule of thermodynamics.
Hence, -4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.
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What is the formula of polynomial?
The general formula of a polynomial is:
P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0
A polynomial is a mathematical expression consisting of variables (such as x), coefficients, and exponents. The general formula of a polynomial is P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0. Here, a_n, a_(n-1), ... , a_2, a_1, and a_0 are coefficients, and n is the degree of the polynomial. The highest exponent in the polynomial is the degree of the polynomial. For example, in the polynomial 3x^2 + 5x – 8, x^2 is the highest exponent, so the degree of the polynomial is 2. The coefficient of the highest exponent is known as the leading coefficient. In the example above, 3 is the leading coefficient. Polynomials can be used to represent a variety of functions, from simple linear equations to complex curves.
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YG and h are parallel. what is the value of n
Answer:
139⁰
Step-by-step explanation:
since g and h are parallel
then n= 139⁰ (corresponding angles)
What does log2 mean on a calculator?
The log base 2 calculator quickly computes the value of the logarithm function with base two, i.e., log₂(x) for arbitrary (positive) x
What do we mean by an expression?
An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent rules.
To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.
To find which expression is equivalent to log₅32:
Law of logarithms:
The law of logarithms states that: log(a) b = log(10)b/log(10)a
Given the log function, which is written as log₅32
a = 5
b = 32
Substitute as: log₅32 = log32/log5
Therefore, the given expression log₅32 is equivalent to the expression log32/log5.
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Please help- thank you!!
Answer: u = -3
Step-by-step explanation:
To solve the equation, we will isolate the u variable by simplifying and using inverse operations.
Given:
4(3u + 5) = 2(2u - 2)
Distribute the 4 and the 2:
12y + 20 = 4u - 4
Subtract 20 from both sides of the equation:
12y = 4u - 24
Subtract 4u from both sides of the equation:
8u = -24
Divide both sides of the equation by 8:
u = -3
In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm find the radiu of the circumcircle
In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm then the radiu of the circumcircle is 39
A chord is the line segment joining two points of the circumference of a circle as shown in the image attached.
If the chord is passing through the center of the circle then it will become diameter which means the diameter is the longest possible chord inside a circle.
A chord is always within the circumference because it is inside the circle.
Whats the definition of a circumference?
a line that goes around or encloses a circle. : the outer boundary of a figure or area. 3. : the distance around something. the circumference of the earth at the equator.
since ABC is an equilateral triangle
therefore SD bisects BC
BD= BC/2
BD= 36
IN Triangle ABC
since angle BDS = 90 degree
Therefore
BS = 39
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James made 7 identical bags using 5 yards of fabric. How much fabric did James use for each bag?
Answer:
James used 5 yards of fabric to make 7 identical bags, so he used 5/7 yards of fabric per bag.
Step-by-step explanation:
Is 4x² 3x 7 a polynomial?
As all the exponents of x are whole numbers, the expression 4x² – 3x + 7 is a polynomial in one variable.
What is exponents?The exponent of a number shows how many times the original value of the number has been multiplied. For example, the number 34 indicates that we have multiplied three by four. 3 × 3 × 3 × 3 × 3 is its expanded form. Exponent is another term for a number's power. It might be a decimal, a fraction, a negative number, or a whole number.
Exponents are important because without them, writing the product when a number was repeated many times on its own would be very difficult. For example, it is much easier to write 57 than it is to write 5 × 5 × 5 × 5 × 5.
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Find the missing angle. 60° 75° 75° ?
Answer:
65?
Step-by-step explanation:
im not to sure but maybe 65
2. 15 - |-4a|
It says evaluate the expression.
If a = 2
Answer:
7
Step-by-step explanation:
So first you substitute A in
15-|-4(2)|
Then you multiply first because of GEMDAS or PEMDAS
15-|-8|
And because absolute value means how far away it is from 0, -8 is 8 away from 0 , thus |-8| is 8. So we simplify the equation
15-8
=7
A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made
After the modification, the maximum amount of medical costs in the sample must have stayed the same.
After the wrongly recorded medical expense was repaired, the adjusted amount remained more than or equal to every other medical expense in the sample. This suggests that the sample statistic linked to the highest value must have remained unchanged after the modification.
The highest value, also known as the maximum or largest value, of the medical expenses in the sample, had to have remained constant. Even though the real quantity was mistakenly recorded as being 10 times its value, the rectified amount still had the highest value in the sample.
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4 Siobhan and Ralph shared £700 in the
ratio 2:3.
Siobhan gave a quarter of her share to Karen.
Ralph gave a fifth of his share to Karen.
What fraction of the £700 did Karen receive?
Therefore ,the solution to the given problem of proportion comes out to be karen got £70.
What is a proportion?The rule of three is used to link the measures because a proportion is a fraction of a total amount. It is possible to construct equation or relations between variables that are either direct (when both rise or decrease) or inverse proportional (when one increases and the other declines, or vice versa) in order to determine the necessary measures in the situation.
Here,
Given :
Siobhan and Ralph shared £700 in the
ratio 2:3.
Thus,
280 / 420 = 2/3
Thus,
Siobhan and Ralph has £280 and £420 respectively.
and Siobhan gave a share of quarter to karen :
So,
280/4 =70
Therefore ,the solution to the given problem of proportion comes out to be karen got £70.
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I do not understand this problem pls help thank you
The value of x in the triangle LMO is 38°
What is an equation?An equation shows how two or more numbers and variables are related to each other.
∠KLO + ∠OLM = 180° (sum of angle in straight line)
134 + ∠OLM = 180°
∠OLM = 46°
∠OML + ∠OMN = 180° (sum of angle in straight line)
∠OML + 84 = 180°
∠OML = 96°
∠OLM + ∠OML + ∠LOM = 180° (angle in a triangle)
46 + 96 + x = 180
x = 38°
The value of x is 38°
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What is the first step for solving 2x 3 7?
the question is of set of equations and the solution is as follows,
the equation is 2x -3 = 7,
First, add 3 to each side to get
2x - 3 + 3 = 7 +3
2x = 10
x = 10/2
x =5.
equations
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For Example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
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d. -(y² - 2) = y²-5-2y², solve for y
Answer:
No solution
Step-by-step explanation:
-(y² - 2) = y²-5-2y²
= y^2 - 5 - 2y^2 = - (y^2 - 2)
= -y^2 - 5 = - (y^2 - 2)
= −(y^2 − 2)
= -y^2 - 5 = -y^2 + 2
-5 = 2
We know that -5 is not equal to 2
So, there is no solution
Answer:
2
Step-by-step explanation:
You have a circle-shaped mirror in your bedroom. To figure out where to hang it, you must find the diameter of the circle. You know the radius is 34 centimeters. How long is the diameter in inches? (Diameter = 2xradius) ( 1in = 2.54cm)
A. 26.8 inches
B. 86.4 inches
C. 172.7 inches
D. 13.4 inches
The diameter of a given circle, measured in inches, is 26.8 inches, according to the solution.
The correct option is A.
What makes it called a circle?A circle is a circular shape that can be created by tracing a moving point in a plane so that its distance from thea specified point remains constant. From the Greek word kirks, which means hoop or ring, comes the term circle.
How can a circle be so strong?Circular shapes give us a feeling of completion, assurance, and harmony from a psychological perspective. They stand for the concepts of oneness, integration, and wholeness. In addition to lacking angles, they also lack a beginning and an end. Because of this, a circle is a strong, yet secure, kind, and benign element.
According to the given information:Given,
Radius of circle= 34cm=13.36 inches
Diameter= 2x radius
Diameter = 26.8 inches
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Find the volume of the pyramid.
7 m
12 m
The volume is
16 m
cubic meters.
The value of volume of pyramids is 448 cubic meter.
How to calculate volume of pyramid?A triangular pyramid's volume can be calculated using the formula Volume= 1/3 Base area Height. The side, height, and slant height of a triangular pyramid are the three parameters needed to calculate its surface area.
The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."
Given,
Length=12m
Width=7m
height=16m
volume =l * w * h / 3
= 12*7*16/3
= 448 cubic meter
Therefore volume of pyramid is 448 cubic meter .
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Please graph the question in the image.
Answer:
I used desmos to make the graph
Step-by-step explanation:
Hopefully this helps!