Using a calculator we can approximate this to be A ≈ 568.89 cm^2.
What is regular decagon?A regular decagon is a two-dimensional geometric shape with ten sides of equal length and ten interior angles of equal measure. It is a polygon, which is a two-dimensional shape made up of line segments (straight sides).
The approximate area of a regular decagon can be calculated using the formula A = (5/2) * a^2 * tan(π/5), where a is the length of each side. Since the radius of the decagon is 8 cm, the length of each side can be calculated using the formula a = 2r * sin(π/10) where r is the radius.
Plugging these values into the formula we get A = (5/2) * (2 * 8 * sin(π/10))^2 * tan(π/5) which simplifies to A = 320 * sin^2(π/10) * tan(π/5).
Using a calculator we can approximate this to be A ≈ 568.89 cm^2.
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Select all of the true statements below.
1.) 8u+3v+5 is written as a sum of three terms.
2.)8u is a coefficient.
3.)8u and 5 are like terms.
4.)5 is a constant.
5.) 8u is a factor.
6.)None of these are true.
the true statements for 8u + 5 + 3v are:
1.) 8u+3v+5 is written as a sum of three terms.
4.)5 is a constant.
What is constant?The word "constant" in mathematics has several different connotations. When used as a noun, it can have either of the following two meanings: Non-variance (i.e., not changing in relation to some other value) or Variance.
an unchanging number or other non-changing mathematical object that is fixed and well-defined. Sometimes, to distinguish between these two meanings, the terms mathematical constant or physical constant are used.
a function with a constant value (i.e., a constant function).
These constants are frequently represented by a variable that is independent of the main variable or variables in question.
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Customary American Units of Capacity
1 cup = 8 ounces
1 pint = 2 cups or 16 ounces
1 quart = 2 pints, 4 cups, or 32 ounces
1 gallon = 4 quarts, 8 pints, 16 cups, or 128 ounces
9 cups = ___ pints ____ cups
20.945649350649 c = 9 dry pt, Four pints equal nine cups. The metric system uses the litre and millilitre as the units of capacity. By dividing by 11000, we may convert millilitres into litres.
What is the US customary unit for capacity?In the United States, ounces, cups, pints, quarts, and gallons are the commonly used measurement units for capacity or volume. Cups, pints, quarts, and gallons are some of the volume or capacity measuring units used in the United States. 8 fluid ounces are the equivalent of 1 cup. There are 2 cups in a pint. 1 quart equals 2 pints.
The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. Every liquid has this property. The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. For all liquids, this is true. 4 pints are equal to 9 cups.
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A moving company wants to buy a new type of truck and needs to know the volume of the storage compartment before they can decide if they should purchase the truck. What’s is the volume of the storage compartment
Answer: jump off a cliff and shatter your bones
Step-by-step explanation:
What is the domain of the function below?
A) x < 2
B) x ≤ 3
C) x ≥ 2
D) All Real Numbers
Answer:
I would say (option A)
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
We see that our x-values can be any number. Therefore, we have all real numbers as our domain:
→ A) x < 2.
Hope this helps!
kjs is a right triangle formed by the placement of 3 squares. what is the area of the shaded square?
area of small square = 87 in
side of big square = 18 in
The area of the square having the same length of the base of the triangle is 7245 square inches.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
From the given figure as the base of the triangle is an equal length of the side of a square we can obtain the area of the square by first applying Pythagoras on the right angle triangle having a height of 87 inches and a hypotenuse of 18 inches.
So,
Base = {√(87² - 18²)}.
Base = √(7245) inches.
Base = 85.11 inches.
Now, We also know that the area of a square is (side)².
Therefore it is (87.11)² which is the same as 7245 sq inches.
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Triangle JKL has vertices J(6, -1), K(10,-2), and L(5, -3). Determine the
coordinates of the vertices of the image after a translation along (0,4)
and a reflection in the y-axis.
J''(-6, 3) , K''(-10, 2) , and L''(-5, 1) those exists the vertices after the transformations.
What is meant by coordinates of the vertices?[tex](x_1,y_1), (x_2,y_2),[/tex] and [tex](x_3,y_3)[/tex] are the coordinates of a triangle's vertices [tex](x_3,y_3)[/tex]. The line connecting the first two is divided in the proportion l:k, and the line connecting this point of division to the opposing angular point is divided in the proportion m:k+l.
When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point. Some kids might be instructed to remember this by saying "along the corridor, up the stairs," which means they should follow the x axis first and then the y axis.
First do the first transformation, the translation.
J (6, -1 + 4), K (10, -2 + 4), and L (5, -3 + 4).
After adding, we get J'(6, 3) , K'(10, 2) , and L'(5, 1).
We Utilize those new coordinates to do the reflection in the y axis.
J''(6(-1), 3) , K''(10(-1), 2) , and L''(5(-1), 1).
After multiplying, we get J''(-6, 3) , K''(-10, 2) , and L''(-5, 1).
Those exists the vertices after the transformations.
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J''(-6, 3) , K''(-10, 2) , and L''(-5, 1) those exists the vertices after the transformations.
What is meant by coordinates of the vertices?[tex](x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3})[/tex] are the coordinates of a triangle's vertices . The line connecting the first two is divided in the proportion l:k, and the line connecting this point of division to the opposing angular point is divided in the proportion m:k+l.
When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point. Some kids might be instructed to remember this by saying "along the corridor, up the stairs," which means they should follow the x axis first and then the y axis.
First do the first transformation, the translation.
J (6, -1 + 4), K (10, -2 + 4), and L (5, -3 + 4).
After adding, we get J'(6, 3) , K'(10, 2) , and L'(5, 1).
We Utilize those new coordinates to do the reflection in the y axis.
J''(6(-1), 3) , K''(10(-1), 2) , and L''(5(-1), 1).
After multiplying, we get J''(-6, 3) , K''(-10, 2) , and L''(-5, 1).
Those exists the vertices after the transformations.
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show that x^4-1=0 has four solutions
Step-by-step explanation:
Why can't I plus x² to each side of the inequality x²+4x > -x² ?
(Note: one adds things; one does not plus them.)
You can easily add x² to both sides here:
(x² + 4x) + x² > (-x²) + x², or
2x² + 4x > 0, or
x² + 2x > 0, or
x(x + 2) > 0.
For this to be true, x > 0 and x+2 > 0; or else x < 0 and x+2 < 0.
Case 1: x > 0 and x+2 > 0.
Rewrite this as x > 0 and x > -2.
This is true for all x > 0.
Case 2: x < 0 and x+2 < 0.
Rewrite this as x < 0 and x < -2.
This is true for all x < -2.
The solution set for the inequality, in interval notation, is then (-∞,-2) ∪ (0,∞).
done its a good question btw ....
Graph the solution to this inequality on the number line.
The
Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers.
How do you identify inequalities?By drawing a straight line and designating the end points with either an open circle or a closed circle, we can depict inequalities on a number line by illustrating the range of integers. An open circle indicates that it excludes the value. A closed circle indicates that it does contain the value.
Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.
With regard to the inequality expression
-3m + 5 > 14
5 from each side is subtracted.
-3m + 5 - 5 > 14 - 5
-3m > 9
Subtract -3 from both sides.
-3m/-3 < 9/-3
m < -3
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Select all the correct answers. A farmer wants to build two fenced-off sections within his field, one in the shape of a rectangle and the other in the shape of a square. The side of the square must be equal to the width of the rectangle, x feet. The length of the rectangle must be 50 feet longer than its width. The field the farmer wants to build the two fenced sections in has an area of y square feet. The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet. In addition, the sum of the fenced areas must be less than the area of the field. This is the system of inequalities that represents this situation. Which points represent viable solutions?
(20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that the side of the square must be equal to the width of the rectangle, x feet.
The length of the rectangle must be 50 feet longer than its width
The field the farmer wants to build the two fenced sections in has an area of y square feet.
The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet
the sum of the fenced areas must be less than the area of the field.
y≥x²+1000
y>2x²+50x
(20, 2,200) and (5, 3,000) are the viable solutions
Hence, (20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.
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Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas. If Lydia uses the same recipe to make 1 pizza, how much cheese is needed?
Answer: Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas, which means that she used 1/3 / 3 = 1/9 pound of peppers and 1/10 / 3 = 1/30 pound of cheese per pizza.
If Lydia uses the same recipe to make 1 pizza, she will need 1/9 pound of peppers and 1/30 pound of cheese. Therefore, the amount of cheese needed is 1/30 pound.
Step-by-step explanation:
Pls help me I beg u I need help with the red ones
Answer:
see below
Step-by-step explanation:
You want the ingredient quantities for several different multiples of the basic recipe.
Table ValuesTo fill the table, consider what the column heading is as a multiple of the recipe for 12 people. Use that multiplier for the rest of the numbers in the column.
[tex]\begin{array}{ccccc}\text{12 people}&\times2&\times3&\times\dfrac{1}{3}&\times\dfrac{1}{2\vphantom{g_g}}\\\cline{1-5}1\text{ cup}&2&3&\dfrac{1\vphantom{b^b}}{3\vphantom{g_g}}&\dfrac{1}{2}\\3\text{ cups}&6&9&1&1\dfrac{1}{2}\\2\text{ cups}&4&6&\dfrac{2}{3\vphantom{_g}}&1\\\dfrac{1}{2}\text{ cup}&1&1\dfrac{1}{2}&\dfrac{1}{6}&\dfrac{1\vphantom{^b}}{4\vphantom{_g}}\\1\dfrac{\vphantom{^b}1}{3}&2\dfrac{2}{3}&4&\dfrac{4}{9}&\dfrac{2}{3}\end{array}[/tex]
If a new video game costs the store $25 and they sell it for 37.50, what was the percent markup?
The percent markup of the supplied statement is equal to 50% after the problem is solved.
How much of a markup should I use?There isn't a predetermined "optimal" markup percentage, however most companies set their markup at 50%. A 50% markup, also referred to as "keystone," denotes a price that is 50% greater than the cost of the commodity or service.
Exactly how is markup determined?The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.
According to the given information:Cost price of game=$25
Selling price of game=$37.50
Profit = selling price - cost price
Profit = 37.50 - 25
Profit / markup percentage = (profit /cost price ) * 100
= (12.50/25) * 100
= 50%
The percent markup of the supplied statement is equal to 50% after the problem is solved.
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Find the inverse of y=3/(x+1) -2
The inverse of the function is y = 3/(x + 2) - 1
How to determine the inverse of the functionFrom the question, we have the following parameters that can be used in our computation:
y=3/(x+1) -2
Rewrite as
y = 3/(x + 1) - 2
Swap the positions of x and y
So, we have the following representation
x = 3/(y + 1) - 2
Next, we make y the subject of the formula
This gives
3/(y + 1) = x + 2
Take the inverse of both sides
(y + 1)/3 = 1/(x + 2_
So, we have
y = 3/(x + 2) - 1
Hence, the inverse is y = 3/(x + 2) - 1
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Michael bakes a soft pretzel and a loaf of bread. Use the system of equations to find c, the amount of flour, in cups, needed for the soft pretzel, and b, the amount of flour, in cups, needed for the loaf of bread. Show your work.
b = 24c
(1/4)b + 4c = 5/4
The amount of flour needed for soft pretzel is c = 1/8 and the amount of flour needed for the loaf of bread is b = 3.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given system of equations,
b = 24 c and
[tex]\frac{1}{4}[/tex] b + 4c = [tex]\frac{5}{4}[/tex]
Substitute b = 24 c in the second equation.
[tex]\frac{1}{4}[/tex] (24 c) + 4c = [tex]\frac{5}{4}[/tex]
6c + 4c = [tex]\frac{5}{4}[/tex]
10 c = [tex]\frac{5}{4}[/tex]
c = [tex]\frac{5}{4}[/tex] × [tex]\frac{1}{10}[/tex] = [tex]\frac{1}{8}[/tex]
b = 24c = 24 / 8 = 3
Hence c = 1/8 and b = 3 in cups.
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3 3/10 minus 2 1/5 as improper fraction
Answer:
11/10
Step-by-step explanation:
33/10 - 22/10
Kiara invested some money into a savings account that earns 2.7% annual simple interest. At the end of 5 years, she earned $6.62 in interest. How much money did she put into the account initially? Round to the nearest dollar.
The initial amount that was invested in the account was $49.
What is the principal?We know that we can be able to obtain the principal by the use of the formula for the simple interest and by that formula we would now have that;
I = PRT/100
I = interest
P = principal
R = rate
T = time
Then we are going to have that;
R = 2.7
P = ?
I = 6.62
T = 5
Then;
6.62 = P * 2.7 * 5/100
6.62 * 100 = P * 2.7 * 5
P = 6.62 * 100/2.7 * 5
P = 662/13.5
P = 49
Thus we have but in at the beginning about $49
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Which property is illustrated by the statement below? 4(3+2)=4(3)+4(2)
Distributive property is illustrated by the statement given as 4[3+2]=4[3]+4[2]
What is distributive property?The distributive property is defined as an expression of the form A(B + C). This property is known by distributive law and applies to subtraction also. This can be solved by a multiplication over addition operation that is written as:
A(B + C) = AB + AC
Distributive property is the sum of two numbers times a third number is equal to the sum of each add end times the third number.
Since the general rule is that:
a(b + c) = ab + ac
Then, 4[3+2]=4[3]+4[2]
Therefore, the given statement elaborates the Distributive property.
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Find the range of values of k for which the equation 4x² + 12x + k = 0 has no real roots.
Hello there!
Answer:
[tex](9, +\infty)[/tex]
Step-by-step explanation:
It has no real roots only if
[tex] \sqrt{b {}^{2} - 4ac } [/tex]
has no roots. That means that b² - 4ac is smaller than 0:
[tex]b {}^{2} - 4ac < 0 \\ 12 {}^{2} - 4 \times 4 \times k < 0 \\ 144 - 16k < 0 \\ 144 - 144 - 16k < - 144 \\ - 16k < - 144 \\ k > 9 \\ k \: \: \: in \: \: \: (9, +\infty)[/tex]
we can approach this from the standpoint of the discriminant, if the discriminant is negative then we only get complex roots or namely "imaginary" solutions or values, well, let's check before that happens, when the discriminant is 0.
[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+k} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]
[tex]0=(12)^2 - 4(4)(k)\implies 0=144-16k\implies 16k=144 \\\\\\ k=\cfrac{144}{16}\implies k=9\hspace{5em} \stackrel{if~k > 9\textit{, then we land on negative territory}}{{\Large \begin{array}{llll} k > 9 \end{array}}}[/tex]
In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other. Because acids and bases are usually colorless (as are the water and salt produced in the neutralization reaction), pH is measured to monitor the reaction. Suppose that the equivalence point is reached after approximately 100 mL of a NaOH solution have been added (enough to react with all the acetic acid present) but that replicates are equally likely to indicate from 95 to 104 mL to the nearest mL. Assume that volumes are measured to the nearest mL and describe the sample space. (a) What is the probability that equivalence is indicated at 100 mL? (b) What is the probability that equivalence is indicated at less than 100 mL? (c) What is the probability that equivalence is indicated between 98 and 102 mL (inclusive)?
Neglecting the fractional points and taking the whole number values for volume, the probability of getting equivalence point at 100 ml is 1/10. The probability of getting less than 100 ml is 1/2.
What is probability?The probability is the measurement of the chance of an event to happen. It is determined based on the total possibilities and criteria.
Given that the experiment trials got the values from 95 to 104. From 95 to 104, there are 10 numbers. Thus, the volume of the acid can be any of these 10.
Thus, total possibility = 10.
probability of getting 100 = 1/10
There are 5 volumes which are less than 100 here, [95, 99]. Thus, the probability = 5/10 = 1/2.
There are 5 values between 98 and 102 including these two values.
Hence, probability of getting these range = 5/10 = 1/2.
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1/3m = 12-m
Please explain step by step to get marked as brainliest.
Step-by-step explanation:
cross multiply
12-m(3m)= 1
12-3m²-1=0
multiply by -1
3m²+1-12=0
3m²= 11
m²= 11/3
m=√11/3.
You have a budget of $1,900 per week for employees. Employees are paid $11 per hour and work 40 hours per week. Ignore overhead, how many employees can you hire?
You can hire around 173 employees. Here's the calculation: $1,900 / ($11/hour * 40 hours/week) = 173.333..., which rounds down to 173.
Ms. Sharon bought 84 litre of cooking oil. She used 1/3 of it on Monday and another 20 litre
of it on Tuesday.
a) How much oil she used on Monday?
b) How much cooking oil did she use altogether?
c) How much cooking oil was left with her?
d) Write the fraction of cooking oil left with her
Find the measure of angle A,
The value of the Angle A is 74.3°.
What is Relation between angle and Side of a triangle?The longest side is in opposition to the longest angle, and the shortest side is in opposition to the smallest angle, respectively.
The opposite of the longest side is the greatest angle, while the opposite of the shortest side is the smallest angle. According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.
The comparable sides are proportionate and the angles are same. The sides that are opposite the same angle are the corresponding sides. For instance, if two triangles have a 90-degree angle on each side, Triangle A's opposing side will match Triangle B's opposite side.
We know:-AB/sin(c)=AC/sin(a)=BC/sin(b)
8/sin(a)=5/Sin37°
Angle= 74.3°.
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Use the drop-down boxes to show a function in the form y = mx + b for the line that contains the points (–6.4, –2.6) and (5.2, 9).
The equation in the slope-intercept form is y = x + 3.8
What is a slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
A line that contains the points (–6.4, –2.6) and (5.2, 9).
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
So, the equation,
y + 2.6 = {(9 + 2.6)/(5.2 + 6.4)} (x + 6.4)
y + 2.6 = x + 6.4
y = x + 6.4 - 2.6
y = x + 3.8
Therefore, the equation y = x + 3.8 is in the slope-intercept form.
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What is the value of 7/8+ (-2/3) - (-4)?
The value of fraction will be;
⇒ 101/24
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The expression is,
⇒ 7/8+ (-2/3) - (-4)
Now,
Since, The expression is,
⇒ 7/8+ (-2/3) - (-4)
Simplify as;
⇒ 7/8 - 2/3 + 4
⇒ (21 - 16)/24 + 4
⇒ 5/24 + 4
⇒ (5 + 96) / 24
⇒ 101/24
Thus, The solution is,
⇒ 101/24
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What are the main things I need to know when doing variables on both sides of the equation?
Answer:
Make sure to keep track of the signs of the variables. If you add or subtract a variable on one side of the equation, you must do the same to the other side.
Don't forget to distribute if you have a variable inside parentheses. For example, if you have 3x + 2(x + 4) = 7, you would need to distribute the 2 to get 3x + 2x + 8 = 7.
When solving for a variable, make sure to perform the same operation on both sides of the equation to isolate the variable. For example, if you want to solve for x in the equation 3x + 2 = 7, you would need to subtract 2 from both sides to get 3x = 5.
please help me thank you so much
the number of geusts,g, coming for dinner is not 8
The number of guests, g, coming for dinner is not 8, is g ≠ 8.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
The expression,
the number of guests, g, coming for dinner is not 8.
That means,
Let the number is g.
According to the question,
the number is not equals to 8.
That means,
the expression in the numerator form,
g ≠ 8.
Therefore, the term in the mathematical form g ≠ 8.
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A ball is launched from a 25.48-meter tall platform. The equation
for the ball's height h at time t seconds after launch is h (t) =
-4.9t² + 2.94t + 25.48, where his in meters. When does the object
strike the ground?
Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.
Define equation.Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.
Here,
Given : -4.9t² + 2.94t + 25.48
Then,
To find the When does the object strike the ground :
We get :
=> -4.9t² + 2.94t + 25.48 = 0
Using discriminant formula
We find the value of t:
=> t = -19.6 ±[tex]\sqrt{19.6^{2} - 4 (-4.9)(25.48)}[/tex] / 2(-4.9)
=> t =-2 or 6
So we neglect -2
So solution for t = 6 seconds
Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.
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what is the value of q³?!
Answer:
-6
Step-by-step explanation:
You seem to want the value of q₃ in the matrix Q⁻¹.
Matrix inverseThe inverse matrix, Q⁻¹, is the transpose of the cofactor matrix, divided by the determinant. That makes q₃ = -q₂₁/det(Q):
q₃ = -(-2/3)/((-1(-1/9) -(-2/3)(-1/3))
q₃ = (2/3)/(1/9 -2/9) = (6/9)/(-1/9)
q₃ = -6
__
Additional comment
The transpose of the cofactor matrix of a 2×2 matrix is the original with the diagonal terms swapped, and the off-diagonal terms negated. Basically, the only math involved in computing the inverse is finding the determinant, and dividing by it.