The total area of the patio will be 20 * 40 = 800 square feet.
What is area of the scale model?The proportionate relationship between a linear dimension of a feature on a model, map, or drawing of an object and the same feature on the genuine thing. A scale model is a physical representation of an object that is geometrically equivalent (known as the prototype).
Since the scale drawing is 3 inches : 10 feet, this means that every 3 inches on the drawing represents 10 feet in real life. Hence, 1 inch on the drawing represents 10/3 = 3.33 feet in real life.
So the patio measures 6 inches by 12 inches on the drawing, which corresponds to 6 * 3.33 feet by 12 * 3.33 feet in real life, or 20 feet by 40 feet.
Therefore, the total area of the patio will be 20 * 40 = 800 square feet.
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Find the total surface area for the triangular prism. The prism shown is 5 inches long, 3 inches wide
and the height of the triangular face is 2.5 inches.
Therefore , the solution of the given problem of surface area comes out to be 46.80909 inch square.
Defining surface areaThe amount of space it occupies on the surface is a decent indication of its overall size. The complete surroundings is taken into account when calculating the area of a tri shape. Something's total size is determined by its surface area. The volume of water inside a cuboid is equal to the total of the volumes on each and every six of its rectangular sides. To calculate the box's measurements, use the formula below: In 2lh, 2lw, and 2hw, the region is identical (SA). The surface area of the multipurpose shape represents the region.
Here,
Given :
Length = 5 inches
Width = 3 inches
and
height = 2.5 inche
To find the total surface area for triangular prism
=>A=ah+bh+ch+1/2 √﹣a⁴ +2(ab)² +2(ac)²﹣b⁴+2(bc)² c⁴
=> 5·2.5+3·2.5+5·2.5+1/2√﹣5⁴+2·(5·3)²+2·(5·5)²﹣34+2·(3·5)²54
=> 46.80909 inch square
Therefore , the solution of the given problem of surface area comes out to be 46.80909 inch square.
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The sum of the Atlantic
Ocean’s average depth (in feet) and
its greatest depth is 43,126. Use the
information in the graph to write and
solve an equation to find the average
depth of the Atlantic Ocean. Show
that your answer is reasonable.
The average depth of the Atlantic Ocean is given by the equation
A = 12,880 feet
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Let the average depth of the Atlantic ocean be A
From the graph the sum of the Atlantic Ocean’s average depth (in feet) and its greatest depth is 43,126 feet
The greatest depth of the Atlantic ocean is D = 30,246 feet
So , the equation will be
A + D = 43,126 feet be equation (1)
Substituting the values in the equation , we get
A + 30,246 = 43,126
On simplifying the equation , we get
Subtracting 30,246 on both sides of the equation , we get
A = 43,126 - 30,246
A = 12,880 feet
Therefore , the value of A is 12,880 feet
Hence , the average depth is 12,880 feet
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Valentina is being careful with her spending so she can later purchase a house. She has allocated no more than $320 each month for both travel expenses and eating out. On average, every time she eats out it costs $16, and every travel journey costs $5.
Let x be the number of times she eats out and y represent the number of travel journeys each month.
Write an inequality representing the relationship between x and y, with y as the subject.
On solving the provided question we cans say that the inequality is 16x+5y320
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
Firm the question, the amount she spends on food every month is 16x and the amount he spends on travel every month is 5y.
Therefore, the total amount she spends every month is 16x+5y.
Since she can't spend more than $320 each month, the inequality is
16x+5y320.
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What is the solution to 9|x + 8| > 45?
x < –3 or x > 13
–3 < x < 13
x < –13 or x > –3
–13 < x < –3
Answer:
x<-13 or x>-3
Step-by-step explanation:
solve 9 abs(x + 8)>45 = x<-13 or x>-3
Morgan buys 4 1/3 crates of apples for 39$. How much does 1 carton of apples cost?
Answer:
$9
Step-by-step explanation:
because we would take the total which is $39 so we divide 39/ 4 1/3 = to 9 so for one crate it is going to be $9 a crate
hope this helps
PLEASE HELP
if f(x)=8x-2/2x what is f (I) equeal to?
A.3
b. 5
c.6
d.8
The value of f(1) is equal to 7
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here f(x)=8x-2/2x putting x=1 we get
f(1)= 8-2/2
= 7
Hence f(1) is equal to 7
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Solve 3x 1 = 15 for x using the change of base formula log base b of y equals log y over log b. −0.594316 1.405684 1.464973 3.469743
Using the change of base formula log base b of y equals log y over log b x = 4.69743.
To solve 3x + 1 = 15 for x, we can use the change of base formula, which states that log base b of y equals log y over log b. In this case, we can use log base 3 on both sides of the equation to solve for x.
First, we take the log base 3 of both sides of the equation:
log base 3 (15) = log base 3 (3x + 1)
Next, we can use the property of logarithms, which states that log base b (xy) = log base b (x) + log base b (y):
log base 3 (15) = log base 3 (3) + log base 3 (x + 1/3)
We can solve for x by subtracting log base 3 (3) from both sides of the equation:
log base 3 (15) - log base 3 (3) = log base 3 (x + 1/3)
We can then use the change of base formula to solve for x:
log 15/3 = log x + 1/3 over log 3
We can then solve for x by taking the antilog of both sides of the equation:
15/3 = x + 1/3
We can then solve for x by subtracting 1/3 from both sides of the equation:
15/3 - 1/3 = x
Finally, we can solve for x by dividing both sides of the equation by 3:
x = (15/3 - 1/3) / 3
Therefore, x = 4.69743.
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A carousel spins at a rate 2 miles in 7 minutes
What is the speed in miles per minute
Answer:
0.29 miles per minute.
Step-by-step explanation:
Speed, s, is defined by the distance, d, divided by the time, t ⇒ [tex]s = \frac{d}{t}[/tex].The distance the carousel travels is 2 miles.The time it takes for the carousel to travel the total distance is 7 minutes.Therefore, [tex]Speed = \frac{2 miles}{7 minutes}[/tex].Speed is equal to 0.285 or 0.29 miles per minute. A common mistake would be to divide the amount of time by the distance, resulting in an incorrect answer.Please let me know if this helped!!!
Adam bought granola bars at the store. The
expression 6p + 5n gives the number of bars
in p boxes of plain granola bars and n boxes of
granola bars with nuts. What are the terms of
the expression?
given h(x)=-9x+5 find h(8)
Help me Evaluate the expression n4 for n = 0.3
Answer:
0.0081
Step-by-step explanation:
n^4
n = 0.3
We just need to put 0.3 in for n and solve
(0.3)^4 = 0.3 x 0.3 x 0.3 x 0.3 = 0.0081
What is the rule for the reflection?
ryx(x, y)-(-y, -x)
ryx(x, y)-(-y, -x)
ryx(x, y) (y,x)
ryx(x, y) → (V, x)
While reflecting about the line y=x, option (c) [tex]r_{y=x}(x,y) = (y,x)[/tex] is correct and while reflecting about the line y= -x, option (b) [tex]r_{y=-x}(x,y) = (-y,-x)[/tex] is correct.
What is the rules of reflection in coordinate geometry?The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed). The line y = x is the point of reflection of the point (x,y) across (y, x).
Firstly, the rule for reflecting a point about the line y=x is:
[tex]r_{y=x}(x,y) = (y,x)[/tex]
While reflecting about the line y=x, we get the reflected points by swapping the coordinates.
So, Option 3 is correct.
Now, the rule for reflecting a point about the line y= -x is:
[tex]r_{y=-x}(x,y) = (-y,-x)[/tex]
While reflecting about the line y= -x, we get the reflected points by multiplying '-1' with the swapped coordinates.
So, Option 2 is correct.
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How many square kilometers are in 1,750,000
square meters?
Answer:1.75
Step-by-step explanation:
what is 64 divided by 48000
and I need work please
need help with finding solving for X
Answer:
15
Step-by-step explanation:
Since the sum of all angles in a triangle is 180, we can make an equation
111 + 44 + 2x - 5 = 180
2x - 5 = 25
2x = 30
x = 15
I’m literally tired of this, math is literally riddles
Answer:
JM is the answer
Step-by-step explanation:
i was going to explain but my brain is in shambles right now
Is z =9 a solution to 3z+8=25
Answer:
No, z =9 isn't a solution to 3z+8=25
Step-by-step explanation:
Let's see if it is...
[tex]\sf 3z+8=25[/tex]
Subtract 8 from both sides:-
[tex]\sf 3z+8-8=25-8[/tex]
[tex]\sf 3z=17[/tex]
Divide both sides by 3:-
[tex]\sf \cfrac{3z}{3}=\cfrac{17}{3}[/tex]
[tex]\sf z=\cfrac{17}{3}\;\; or \;\; z=5.6666....[/tex]
Therefore, no z = 9 isn't a solution to 3z+8=25.
____________________
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Have a great day!
What is logarithm and what are the properties of logarithm?
Logarithm is a mathematical operation that is the inverse of exponentiation. It is denoted by log b (x), which means the logarithm of x to base b.
For example, log2 8 = 3, since 23 = 8. Logarithm is useful in solving equations that involve exponential terms.
The properties of logarithm are:
1. log b 1 = 0: This property states that the logarithm of 1 is zero for any base b.
2. log b b = 1: This property states that the logarithm of any base b is 1.
3. log b (xy) = log b (x) + log b (y): This property states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers. For example, log2 (8x32) = log2 8 + log2 32 = 3 + 5 = 8.
4. log b (x/y) = log b (x) - log b (y): This property states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the two numbers. For example, log2 (8/32) = log2 8 - log2 32 = 3 - 5 = -2.
5. log b c = clog b (c): This property states that the logarithm of a number c to the base b is equal to c times the logarithm of b. For example, log2 32 = 32log2 2 = 5.
These properties of logarithm are very useful in solving mathematical problems involving exponential terms.
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How do you find the absolute value of a complex number in polar form?
The absolute value of the complex number z = 2∠45° is therefore equal to 2.
What is value?Value can be defined as the worth of something, which may be monetary, social, or personal. It is an intangible concept that is based on individual beliefs and opinions. Value can be determined by considering the utility, quality, scarcity, desirability, and other factors associated with an item. Values can be measured in terms of tangible goods, such as money, or in terms of intangible goods, such as love or honor.
The absolute value of a complex number in polar form is the magnitude of the complex number. It is also referred to as the modulus of the complex number. To find the absolute value of a complex number in polar form, we need to use the following equation:
Absolute Value = r = |z| = √(a² + b²)
Where 'r' is the absolute value of the complex number, 'z' is the complex number, and 'a' and 'b' are the real and imaginary parts of the complex number respectively.
For example, if we have a complex number in polar form, such as z = 2∠45°, then the absolute value of the complex number is calculated by taking the square root of the sum of the squares of the real and imaginary parts:
Absolute Value = r = |2∠45°| = √(2² + 0²) = 2
The absolute value of the complex number z = 2∠45° is therefore equal to 2.
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Solve for x.
6x = 18
Enter your answer in the box.
x =
Answer:
x = 3
Step-by-step explanation:
6x = 18
Divided both sides by 6
x = 3
Let's check
6(3) = 18
18 = 18
So, x = 3 is the correct answer.
Answer:
x = 3
Step-by-step explanation:
1) 6x = 18
2) Divide by 6.
6x = 18
6 6
x = 3
(Two-Step Linear Inequalities MC) Which graph represents the solution to the inequality 2(b + 2) > 24? number line with open point at 10 with arrow pointing left number line with closed point at 10 with arrow pointing left number line with closed point at 10 with arrow pointing right number line with open point at 10 with arrow pointing right
The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left
What is a graph?You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal. The graph is a diagram that illustrates the statement.
The given inequality is 2(b + 2) > 24
Opening the brackets to get
2b+4≥24
2b≥24-4
This implies that 2b≥20
Making b the subject
b≥20/2
b≥10
Therefore, the graph is a number line with closed point at 10 with arrow pointing left
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Find the measure of angle “x” in degrees. Round to two decimals places as necessary!! HELPP PLS
Answer:
x ≈ 50.06°
Step-by-step explanation:
using the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{23}{30}[/tex] , then
x = [tex]sin^{-1}[/tex] ( [tex]\frac{23}{30}[/tex] ) ≈ 50.06° ( to 2 decimal places )
whats colder? -0.9 or -1.2
assuming they are the same unit, -1.2 is colder
when a number is negative, the further the number is from zero the less (colder) it is
For my higher grade and i dint get this problem
Answer:
y = 9
Step-by-step explanation:
[tex]\frac{2}{6}[/tex] = [tex]\frac{y}{27}[/tex] ( cross- multiply )
6y = 2 × 27 = 54 ( divide both sides by 6 )
y = 9
Answer:
Step-by-step explanation: From the question 2/6 = y/ 27
Cross multiply
It becomes 2 * 27 = 6 * y
54 = 6y
Make y the subject
y = 54/ 6
y = 9
Question 1 (5 points)
The notation "f(x)" (f of x) is another way of representing y-values in a function
True
False
The given statement "The notation "f(x)" (f of x) is another way of representing y-values in a function" is true because it represents the range or output values.
What is a function?In Mathematics, a function is a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.
This ultimately implies that, a function typically indicates the relationship between input values (domain or x-values) and output values (range or y-values) of a data set, including the ways in which the elements in a table are uniquely mapped (paired).
In conclusion, we can reasonably infer and logically deduce that the output values (range or y-values) of a function are plotted on the y-coordinate of a graph and they are primarily denoted by either the notation f(x) or y.
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Find the value of X and Y. Write your radical in simplest form. Exact answers only.
to
28
Answer:
X = 45, Y = 14√2
Step-by-step explanation:
We are given that the diagram is a square, and is cut in half using the length that is 28. Therefore x = 45
Now for y, we know that we have a 45 45 90 triangle with hypotenuse of 28, and the formula for that is the legs have length of x, and hypotenuse of x√2
y = x
=> 28 = x√2
x = 14√2
=> y = 14√2
Nine years ago, Katie was twice as old as Elena was then. Elena realizes, "In four years, I'll be as old as Katie is now!" Elena writes these equations to help make sense of the situation: k - 9 = 2(e - 9)
e + 4 = k
If Elena is currently e years old and Katie is k years old, how old is Katie now?
Answer: Katie is 9 years old now. ✅
Step-by-step explanation:
By using the second equation, we can find that k = e+4,
then we can substitute k = e+4 into the first equation
k-9 = 2(e-9)
e+4-9 = 2(e-9)
e-5 = 2e-18
5 = e
so k = e + 4 = 5 + 4 = 9
Therefore, Katie is 9 years old now.
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Can the line segments 1.5 cm 2 cm 2.5 cm be the sides of a right angled triangle?
It is possible to construct a triangle whose sides are 1.5 cm 2 cm and 2.5 cm because the sum of two sides are greater than three sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 1.5 cm 2 cm and 2.5 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 1.5 and 2
1.5 + 2 > 2.5
3.5 > 2.5
Now we add 2.5 and 2
2.5 + 2 > 1.5
4.5 > 1.5
Now we add 1.5 and 2.5
1.5 + 2.5 > 2
4 > 2
It is possible to construct a triangle whose sides are 1.5 cm 2 cm and 2.5 cm because the sum of two sides are greater than third sides.
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How do you find the ratio of area of two circles?
The ratio of the area of two circles can be found by dividing the area of one circle by the area of the other.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. To calculate the ratio of the areas of two circles, take the area of one circle and divide it by the area of the other:
Ratio of area of two circles = A1/A2 = (πr1^2)/(πr2^2)
For example, if the radius of one circle is 3 and the radius of the other is 5, then the area of the first circle is 28.27 and the area of the second circle is 78.54. The ratio of the areas of these two circles is then 28.27/78.54, which is 0.36.
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What is the solution Y=x-5
The solution of the expression for x is y+ 5.
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 expression is y = x - 5. The solution of the expression for x will be,
y = x - 5
x = y + 5
Therefore, the solution of the expression for the value of x will be x = y + 5.
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