One quarter of the difference of a number and 3 is -1. find the number
The number, based on the fact that one quarter of the difference between the number and 3, is - 1, is - 1
How to find the number?The number can be denoted as x in which case, the formula of the situation would be:
1 / 4 ( x - 3 ) = - 1
The number can then be solved for by looking for the value of x with the quarter constraint :
1 / 4 ( x - 3 ) = - 1
x - 3 = - 1 / ( 1 / 4)
x = -4 + 3
x = - 1
The number is therefore -1
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Which two cases can be solved using the Law of Sines? (Select all that apply.)
AAS
SSS
SAS
SSA
SSS and SAS are the two cases can be solved using the Law of Sines.
What is trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
here, we have,
To use the law of sines we need to know two angles and one side or two sides and one angle which should be opposite to one of known sides.
SSS - unable to solve as no angle is known
AAS - two angles and non-included side, able to find the missing angle solve the rest
ASA - two angles and the included side, able to find the missing angle solve the rest
SAS- two sides and the included angle, unable to solve
SSA - two sides and non-included angle, able to find the other angles and solve fully
Hence, SSS and SAS are the two cases can be solved using the Law of Sines.
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Which number is a rational number?
a :2–√
b: π
c: 0.7¯
d: 5–√
If ()={ 2-x if x <= 2 , x if x >2 then A) f'(2)=−1 B) '(2)=1 X) not differentiable at =2 D) All are true
f'(2) is not differentiable at =2 .
What is differentiability?In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain
here, we have,
given that,
f(x)={ 2-x if x <= 2 ,
{ x if x >2
at, x=2,
f(2)= 0
so, f'(2) is not differentiable at =2 .
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Arianna is a stylist at a salon. She earns a different amount of money each day depending on what task she does. She earns $95 for the day if she is answering the phone. She earns e dollars per hour cutting hair. The table shows Arianna's work schedule this week. Which expression represents the total amount of money Arianna earns this week? 3+2+95c 3c+ 2c + 95 3c + 2c + 95c 3+2+95 Arianna's Work Schedule 3 hours cutting hair 2 hours cutting hair Answering phones Monday Tuesday Wednesday
The expression that represents the total amount of money Arianna earns this week is 3c + 2c + 95.
What is an algebraic expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. The variables in the expression represent unknown values, and the numbers and operations determine how the variables are related.
The expression that represents the total amount of money Arianna earns this week is:
3c + 2c + 95
Where,
c represents the amount of money Arianna earns per hour cutting hair.
This expression represents the total amount of money Arianna earns from cutting hair (3c + 2c) and the amount of money she earns from answering phones (95).
The other expressions listed in the options do not correctly represent Arianna's earnings.
Hence, the expression that represents the total amount of money Arianna earns this week is 3c + 2c + 95.
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If the apothem of a regular hexagon is 12 cm and the side length is 8 cm, then find the area of the hexagon
576 in^2
244 in^2
36 in^2
The area of the hexagon will be 288 cm².
What is a polygon?In geometry, a polygon can be defined as a flat or plane, two -dimensional closed shape bounded with straight sides. It does not have curved sides.A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges, faces or facets of the object.Given is that the apothem of a regular hexagon is 12 cm and the side length is 8 cm.
An apothem of a regular polygon will always be a radius of the inscribed circle.The apothem a can be used to find the area of any regular n - sided polygon of side length {a} - A = apothem x 1/2{P}.The perimeter is given by : {P} = n x a.We can write -
A = apothem x 1/2{na}
A = 12 x 1/2{6 x 8}
A = 12 x 24
A = 288 cm²
Therefore, the area of the hexagon will be 288 cm².
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During a sale, a store offered a 30% discount on a couch that originally sold for $870. After the sale, the discounted price of the couch was marked up by 30%. What was the price of the couch after the markup? Round to the nearest cent.
The price of the couch after the markup gotten during a sale, a store offered a 30% discount on a couch that originally sold for $870 is $791.70.
How can the price of the couch after the markup be calaculated?The concept that will be used here is the discounted price . The discount is represented in the advertisement as a percentage off the list price. As a result, a sale price of $70 will be achieved with a 30% discount on a $100 list price. Another way to understand the phrase is to say that it simply refers to the selling price of an item.
The price of the couch after the markup can be determine as :
$870 * (1 + 30% ) * (1 - 30% )
Then this can be simplifIed as :
= $870 *1.3 * 0.7
=$ 791.7
Then Rounding up to the nearest cent will give $ 791.70
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A rectangular prism has a length of 14 centimeters, a height of 4 1 2 centimeters, and a volume of 756 cubic centimeters. What is the width of the prism? Write your answer as a whole number, proper fraction, or mixed number.
The width of the prism is, 12 centimeter.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
A rectangular prism has a length of 14 centimeters, a height of 4 1/2 centimeters, and a volume of 756 cubic centimeters.
Let the width of the prism = x
Now, We know that;
⇒ Volume of prism = Length × Width × Height
Substitute all the given values, we get;
⇒ 756 = 14 × x × 4 1/2
⇒ 756 = 14 × 9/2 × x
⇒ 756 = 63x
⇒ x = 756 / 63
⇒ x = 12 centimeter
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Need help with this equation
Answer:
AC = 19
Step-by-step explanation:
ignore the other work on the paper
Challenge Word Problems
1. A 747 Airplane la 762 Inohos tall. How fall to it in foot?
2. The river raft ride at the amusement park oan hold 12 riders at a
time. There are 527 people in line. How many times will the ride need
to run in order to get all 527 people through the ride?
3. One school bus can hold 46 students. There are 24 students in each
of the 5 fifth grade classes. How many buses will they need in order to
transport everyone to the zoo for a field trip?
4. Write and solve a word problem that requires long division AND has a
remainder.
02014 Tedoning Wittra Mountain View
ඉල ම
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A) A 747 Airplane is 762 inches tall. 762 inches is equal to 63.5 feet, so the airplane is 63.5 feet tall.
What is airplane?An airplane is a type of aircraft that is heavier than air and propelled by one or more jet engines. It is used for transport across long distances, typically carrying passengers and cargo.
The river raft ride at the amusement park can hold 12 riders at a time. 527 people divided by 12 riders per ride is 44.75. This means the ride will need to run 44 times in order to get all 527 people through the ride.
One school bus can hold 46 students. There are 24 students in each of the 5 fifth grade classes. 24 students times 5 classes is 120 students, so they will need 3 buses in order to transport everyone to the zoo for a field trip.
Write and solve a word problem that requires long division AND has a remainder.
Samantha has 192 lollipops. She wants to evenly divide them into bags of 10. How many bags will she need and how many lollipops will be left over?
192 divided by 10 is 19 with a remainder of 2. Samantha will need 19 bags and will have 2 lollipops left over.
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Please someone help me
Solving the question provided, we can say that cos(x) = 12/15 in trigonometry. So the value of tan(2x) according to the given equation is 38.07588924.
What is Trigonometry?The mathematical branch of trigonometry examines the relationship between the side lengths and angles of a triangle. The area first appeared in the Hellenistic period around the 3rd century BC. From the use of geometry in the study of astronomy. The branch of mathematics known as exact methods deals with certain trigonometric functions and how they can be used in calculations. There are six common trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecane are their respective names and acronyms (csc). The study of the properties of triangles, especially right triangles, is called trigonometry. However, the study of geometry is characteristic of all geometric figures.
To find tan(2x) you can use the identity.
[tex]tan(2x) = (2tanx) / (1 - (tan^2)x)[/tex]
To find tan x, we can use the identity.
tanx = sinx / cosx
Since cos(x) = 12/25 in quadrant I, we can use the following procedure:
find sinx with sin(x) = [tex]sqrt(1 - (cos^2)x)[/tex] = [tex]sqrt(1 - (12/25)^2)[/tex] = [tex]sqrt(1 - 144/625)[/tex] = [tex]sqrt(481/625)[/tex]
Find tanx with tanx = sinx / cosx =
sqrt(481/625) / (12/25)
Substitute this tanx value into the first ID to find tan(2x).
Sunburn (2x) =
[tex]tan(2x) = (2 * sqrt(481/625) / (12/25)) / (1 - (481/625))\\ = (2 * sqrt(481) / (3 * 5)) / (144/625) \\=(2 * sqrt(481)) / (144/125)[/tex]
According to the given formula, the value of tan(2x) is 38.07588924.
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After a 75% reduction, you purchase a new clothes dryer on sale for $140.
What was the original price of the clothes dryer?
The original price was?
Answer:
245
Step-by-step explanation:
140 x 1.75 = 245
A video game store sells 218 video games for $54 each. Which is the best estimate of the total sales for the video games?
A $10,000
B $10,500
C $12,000
D $12,500
Answer:
C $12,000
Step-by-step explanation:
$54 × 218 = 11,772
11,772 - 10,500 = 1772
12,000 - 11,772 = 228
Therefore,
12 000 is the nearest number for total sales
convert 7/6 in a mixed number
Answer:
1 1/6
Step-by-step explanation:
Answer:
The answer is 1 1/6
Step-by-step explanation:
The reason why this answer is 1 1/6 is that you're dividing the numbers 7 and 6 which equals 1.16. So, 1 is the quotient and the other 1 is the remainder, and 6(denominator) stays in the fraction as the denominator. One goes into a whole number and the other one goes into the numerator, while the six stays in the denominator (1 1/6).
16x² + 4x² - 2x-12x² + 4x simplified
Answer: 8x^2 + 2x
Step-by-step explanation:
Group like terms: 16x²+4x²-12x²-2x+4x
Add similar elements: 16x²+4x²-12x²=8x²
=8x²-2x+4x
Add similar elements: -2x+4x=2x
=8x²+2x
The angles to right are complementary angles determine the measure of
The measure of the given angles are -
m∠1 = 80°
m∠2 = 10°
What are complementary angles?Two angles are called complementary when their measures add to 90 degrees.
Given is a complementary angles pair as shown.
We can write -
∠1 + ∠2 = 90
x + (11x - 30) = 90
12x - 30 = 90
12x = 120
x = 10
m∠1 = 11x - 30 = 11 x 10 - 30 = 110 - 30 = 80°.
m∠1 = 80°
m∠2 = x = 10°.
m∠2 = 10°
Therefore, the measure of the given angles are -
m∠1 = 80°
m∠2 = 10°
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An item is regularly priced at $75 . it is on sale for 95% off the regular price. how much (in dollars) is discounted from the regular price?
Answer:
3.75
Step-by-step explanation:
All of the following are equivalent except _____.
1.) -2^4
2.) (-2)^4
3.) (-2)(-2)(-2)(-2)
4.) 2^4
So, on solving the provided question we can say that the equation = -2^4 is different
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here,
the equation -
-2^4
(-2)^4
(-2)(-2)(-2)(-2)
2^4
in these -2^4 is different
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Given the radical equation equation reads square root of quantity six times m plus nineteen end quantity minus two equals m , complete each part.
Part A: Solve the equation for the variable m. Be sure to show all your steps in solving to receive full credit.
Part B: Check each solution found in Part A in the original equation. Be sure to show all your steps to receive full credit.
Part C: Using complete sentences, explain if each solution is extraneous or non-extraneous. Be sure to use complete sentences in each explanation.
The value of the variable are -3 and 5.
In this case, -3 is an extraneous solution and 5 is a non- extraneous solution.
How to explain the equation?From the information, the radical equation reads square root of quantity six times m plus nineteen end quantity minus two equals m.
To solve for m goes thus:
✓[6m + 19] - 2 = m
6m + 19 = (m + 2)²
Opening the parentheses
m² - 2m - 15 = 0
(m + 3)(m - 5)
m = -3 and 5
Here, it should be noted that -3 is an extraneous solution and 5 is a non- extraneous solution.
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What is 6/6 as a mixed number
6/6 can't be a mixed number.. it's simply just 1.
Parallel to the graph of x + y = 6 and passing through the point at (4, 3)
The equation of line that passes through (4,3) and is parallel to x + y = 6 is y = -x + 7.
What is the equation of line that passes through the given point and is parallel to x + y = 6?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line
x + y = 6
y = -x + 6
Using the slope intercept, slope m is -1
The equation of a parallel line to y = -x + 6 must have a slope similar to the original slope.
Slope of parallel line = -1
Plug the slope m = -1 and point (4,3) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
( y - 3 ) = -1( x - 4 )
y - 3 = -x + 4
y = -x + 4 + 3
y = -x + 7
Therefore, the equation of the parallel line is y = -x + 7.
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The figure above shows a right triangle with dimensions in inches. Solve for c to the nearest inch.
Answer:
Step-by-step explanation:
We can use trigonometry for this.
Cos x = Adjacent/ Hypotenuse
cos 27° = 15/c
c = 15/cos 27 = 16.835 inch ≈ 17 inches
Please help me find the area of the decagon.
Each side measures 9.15 cm
From the center of the shape to the midpoint of each side of the polygon, it is 14.26 cm
The area of the decagon is approximately 312.2 cm2. This can be calculated using the formula A = (1/2) × 10 × 14.26^2 × sin (36°).
Find the area of the decagon?To find the area of the decagon, we need to use the formula A = (1/2) * ap * p, where ap is the apothem (the distance from the center of the decagon to the midpoint of a side) and p is the perimeter (the sum of all the sides).A = (1/2) * 14.26 cm * (9.15 cm * 10)
A = (1/2) * 14.26 cm * 91.5 cm
A = 654.71 cm^2
To find the area of a decagon, you must use the formula A = 1/2 × ap × s, where a is the apothem, p is the perimeter, and s is the length of each side. The apothem is the distance from the center of the shape to the midpoint of each side. The perimeter is the sum of the lengths of all the sides.First, calculate the apothem. The distance from the center of the decagon to the midpoint of each side is 14.26 cm. Therefore, the apothem is 14.26 cm.Next, calculate the perimeter. The length of each side is 9.15 cm, so the perimeter is 9.15 cm × 10, or 91.5 cm.Finally, plug the apothem and perimeter into the area formula and solve. A = 1/2 × 14.26 cm × 91.5 cm = 654.9 cm2. Therefore, the area of the decagon is 654.9 cm2.To learn more about the area of the decagon refer to:
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In the town of Centralburg (Figure 1), which is laid out in a uniform block grid, the grocery store is three blocks East and four blocks North of the post office. Which of the following is a correct equation for the quantities represented in this scenario?
Answer:
tan(θ)= dn/de
θ=arctan(dn/de)
Step-by-step explanation:
Madelyn wants to buy a charm bracelet. Oxford Fine Jewelry charges $12 per charm, plus $40 for the bracelet. Espinoza Jewelers, in contrast, charges $14 per charm and $30 for the bracelet. If Madelyn wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. How many charms would that be?
Using a system of equations, for Madelyn to add a certain number of charms to her bracelet, where the cost will be the same at either jewelry shop, the number of chams would be 5.
What is a system of equations?When two or more equations are solved concurrently, they are described as a system of equations.
Another description of a system of equations is simultaneous equations.
Oxford Fine Espinoza
Unit cost per charm $12 $14
The cost of the bracelet $40 $30
Let the number of charms = c
Equations:Equation 1: (Costs at Oxford Fine) 12c + 40
Equation 2: (Costs at Espinoza) 14c + 30
For the cost to be the same at either jewelry shop, Equation 1 must equal Equation 2:
12c + 40 = 14c + 30
-2c = -10
c = 5
Check:
12c + 40
12(5) + 40 = $100
14c + 30
14(5) + 30 = $100
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K
The table shows the fraction of the population in selected countries that used cell phones in a recent year. Complete
the table by writing each fraction as an equivalent fraction with a denominator of 100.
Country
Country A
Country B
Country C
Country D
Country E
Country F
Country G
Country H
Country I
Country J
Fraction of
Equivalent Fraction
Population Using Cell with a Denominator of
Phones
100
87
100
9
10
23
25
23
25
17
25
91
100
4
5
67
100
2
25
...
7
10
The solution is given below.
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
here, we have,
from the given chart we get,
the solution is attached below.
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Which property is used in the following calculation?
2(5⋅33)
(2⋅5)⋅33
10(33)
330
Associative Property of Multiplication
Identity Property of Multiplication
Distributive Property
Commutative Property of Multiplication
None of these
The property used here is the associative property of Multiplication.
What is the Associative Property?According to the Associative property, when 3 or more numbers are added or multiplied, the result (sum or the product) remains the same even if the numbers are grouped in a different way. Here, grouping is done with the help of brackets. This can be expressed as, a × (b × c) = (a × b) × c and a + (b + c) = (a + b) + c.
Given here: 2(5⋅33)=(2⋅5)⋅33
=10(33)
=330
Clearly the property a × (b × c) = (a × b) × c is used here
Hence, The property used here is the associative property of Multiplication.
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How is two 55 degrees related
A recipe calls for 2 cup of brown sugar for every 6 cups of white sugar. How many cups of brown sugar are required for every 12 cups of white sugar?
(PLEASE HELP!!)
There are 4 cups of brown sugar are required for every 12 cups of white sugar.
A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:
2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar
To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:
2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar
24 cups brown sugar = 6x cups brown sugar
x = 24/6
x = 4
So, 4 cups of brown sugar are required for every 12 cups of white sugar.
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HEELPPP YALLLL PLEASE
The number line can be represented by the equation option D: -6 + 5 =- 1.
What is a number line?
A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.
The number line is given in the image.
It shows that the arrow is moving from positive to negative side.
The units for which the arrow is moving is = -6
Five units are left before the arrow on the left hand side.
Therefore, the equation is -6 + 5 = -1
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