Answer:
x=55°, y=35°
Step-by-step explanation:
The angle between x and 35° is a right angle.
A right angle equals 90°.
Therefore. 90=x+35
x=55°
Now that x is known, we can find y.
The angle made between the x and y axis is 90°.
Therefore, 90=x+y
90=55+y
y=35°
Answer:
X=55° and Y=35° ................................
what is the nearest 5 of 562817
The nearest 5 integers of 562817 are:
562815, 562816, 562817, 562818, 5628179
Explain about the integers?An integer comprises a whole number which can be positive, negative, and zero and is not a fraction. Integer examples include: -5, 1, 25, 18, 97, as well as 3,043. 1.43, 21 3/4, 3.84, and other numbers that don't constitute integers are some examples.
Positive, negative, and zero are all examples of integers. As a result, integers include numbers like 0, 1, 2, 3, in addition to -1, -2, and 3. There are no additional parts, such as fractions or decimals, in integers. As a result, fractional values like 3 1/2 and decimal numbers like -7.5 are Really not integers.Thus,
The nearest 5 integers of 562817 are obtained by subtracting and adding the smallest integer that is 1 from the given number.
562815, 562816, 562817, 562818, 5628179
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What is the area of this complex figure?
A) 179 m^2
B) 128 m^2
C) 30 m^2
D) 20 m^2
The area of the complex figure is 178 m². Option A
How to determine the area of the complex figureThe formula for calculating the area of a rectangle is expressed as;
Area = lw
Given that;
l is the length of the rectanglew is the width of the rectangleFor the bigger rectangle
Area = 16(8)
Multiply
Area = 128m²
For the smaller rectangle
Area = 6(5)
Area = 30m²
For the triangle
Area = 1/ 2× base × height
Area = 1/2 × 8 × 5
Area = 20m²
Add the areas of the three figures
Total area = 128 + 20 + 30
Total area = 178 m²
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assume that y=C(a)^x is an exponential function. Why can a not equal zero?
The function eˣ is considered as a function of real numbers has domain (−∞,∞) and have value between 0 to ∞ . That is the reason why "a" cannot be zero.
Reason why any function of form eˣ cannot be zero:Considered as a function of real numbers, the function ex has domain (−∞,∞) and range (0,∞). Therefore, only strictly positive values can be assumed. Considering ex as a function of complex numbers, we know that there is a domain C and a range C\{0}. In other words, the only value eˣ cannot have is 0.
Thus, the base cannot be equal to 0.
What are functions in mathematics?A formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable). Functions are ubiquitous in mathematics and essential in the natural sciences for formulating physical relationships.
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a cannot be equal to zero in an exponential function because a must be greater than 0 in order for the equation to work, and because the base of an exponential function must be a positive number for it to be an exponential function.
What is an exponential function?An exponential function is a type of mathematical function that increases or decreases by a consistent rate over time. It is usually expressed in the form of y = abx, where a and b are constants and x is the independent variable. The graph of an exponential function is a curved line that starts off flat and then increases or decreases in a curved manner. The rate of change of the function is determined by the value of b, with higher values of b resulting in a steeper curve.
In this situation, a must be greater than 0 because an exponential function cannot have a base of 0. This is because any number raised to the power of 0 is equal to 1, so if the base of the exponential function is 0, then the entire equation would be equal to C1, which is simply C. Therefore, the only way to make the equation work is to make sure that a is greater than 0.
Therefore, a cannot be equal to zero in an exponential function. This is because a must be greater than 0 in order for the equation to work, and because the base of an exponential function must be a positive number in order for it to be an exponential function.
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In the figure, each small cube has edges that are 1/3 yd long. Which expression can you use to find the volume of the rectangular prism is cubic yards?
The expressiοn (B) 2 × 4 × 5 × 1/3 × 1/3 × 1/3 can be used tο find the vοlume οf the rectangular prism is cubic yards.
What is equatiοn?A mathematical equatiοn links twο statements and utilises the equals sign (=) tο indicate equality. In algebra, an equatiοn is a mathematical assertiοn that prοves the equality οf twο mathematical expressiοns. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical fοrmula may be used tο determine hοw the twο sentences οn either side οf a letter relate tο οne anοther. The lοgο and the particular piece οf sοftware are usually identical. like, fοr instance, 2x - 4 = 2.
Vοlume is calculated using the fοrmula LWH
Here each cube has side 1/3 yd
Sο vοlume = (2 × 1/3) × (4 × 1/3) × (5 × 1/3)
It can be written as 2 × 4 × 5 × 1/3 × 1/3 × 1/3
Thus, οptiοn B is cοrrect.
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Complete question:
The matrix \[ A=\left[\begin{array}{cccc} -3 & 0 & -4 & 0 \\ 7.5 & 0 & 10 & 0 \\ 3 & 0 & 4 & 0 \end{array}\right] \] is a matrix of a linear transformation \( T: \mathbb{R}^{k} \rightarrow \mathbb{R}^
The matrix A represents the linear transformation T that maps vectors from a k-dimensional vector space to a 3-dimensional vector space and can be used to find the image of a vector under the linear transformation is:
[tex]T=\left[\begin{array}{c} -15 \\ 37.5 \\ 15 \end{array}\right][/tex]
What is linear transformation?A linear transformation is a function that maps vectors from one vector space to another and preserves the operations of vector addition and scalar multiplication. In this case, the matrix A represents the linear transformation T that maps vectors from a k-dimensional vector space to a 3-dimensional vector space.
The matrix [tex]\[ A=\left[\begin{array}{cccc} -3 & 0 & -4 & 0 \\ 7.5 & 0 & 10 & 0 \\ 3 & 0 & 4 & 0 \end{array}\right] \][/tex]
is a matrix of a linear transformation [tex]\( T: \mathbb{R}^{k} \rightarrow \mathbb{R}^{3} \).[/tex]
The matrix A can be used to find the image of a vector under the linear transformation T. For a vector [tex]\( \mathbf{x} \in \mathbb{R}^{k} \)[/tex], the image of the vector under the linear transformation T is given by the matrix-vector product [tex]\( A\mathbf{x} \).[/tex]
For example, if [tex]\( \mathbf{x} = \left[\begin{array}{c} 1 \\ 2 \\ 3 \\ 4 \end{array}\right] \)[/tex]
Then the image of the vector under the linear transformation T is given by
[tex]\[ A\mathbf{x} = \left[\begin{array}{cccc} -3 & 0 & -4 & 0 \\ 7.5 & 0 & 10 & 0 \\ 3 & 0 & 4 & 0 \end{array}\right] \left[\begin{array}{c} 1 \\ 2 \\ 3 \\ 4 \end{array}\right] = \left[\begin{array}{c} -15 \\ 37.5 \\ 15 \end{array}\right] \][/tex]
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a closet in the shape of a rectangular prism measures x+3 ft. wide, x-5.5 ft. depth and x ft height. the volume is 220 ft^3. what is the height of the closet?
The height οf the clοset is x ft = 8 ft.
What is the vοlume οf a rectangular prism?The vοlume οf a rectangular prism is the amοunt οf space οccupied by the three-dimensiοnal οbject. It is calculated by multiplying the length, width, and height οf the prism.
In this prοblem, we are given that the clοset has a vοlume οf 220 ft^3 and its dimensiοns are x+3 ft. wide, x-5.5 ft. deep, and x ft. high. Sο, we can write the equatiοn:
V = (x+3)(x-5.5)(x)
where V is the vοlume οf the clοset.
Tο sοlve fοr x, we can simplify the equatiοn by multiplying the factοrs:
[tex]V = (x^2 - 2.5x - 16.5)(x) = x^3 - 2.5x^2 - 16.5x[/tex]
Nοw, we can substitute the given value οf V and sοlve fοr x:
[tex]220 = x^3 - 2.5x^2 - 16.5x[/tex]
We can rearrange this equatiοn tο get:
[tex]x^3 - 2.5x^2 - 16.5x - 220 = 0[/tex]
This is a cubic equatiοn that can be sοlved by factοring οr using numerical methοds. By using numerical methοds, we can find that οne sοlutiοn οf this equatiοn is x = 8.
Therefore, the height of the closet is x ft = 8 ft.
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[tex]\sqrt{x} 150\\[/tex]
If √x = 150, then the value of x will be 22,500.
What is the value of x in the root function?
If √x = 150, then we can find the value of x by squaring both sides of the equation:
(√x)² = (150)²
Simplifying the left side of the equation:
x = (150)²
x = 150 x 150
x = 22,500
Therefore, the value of x for the given root function is determined as 22,500.
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The complete question is below:
If √x = 150, find the value of x
YO PLEASE HELP IVE BEEN DOING OVER DUES FOR SIX HOURS AND THIS IS MY LAST MATH ONE What is the volume of this figure PLEASE THANK YOU GUYS
Answer:
144
Step-by-step explanation:
A rectangle has the area of 54x8y6
square inches and a length of 9x3y4
. Which expression represents the width of the rectangle?
Responses
The expression that represents the width of the rectangle is 6x^5y^2
Which expression represents the width of the rectangle?We know that the area of a rectangle is given by the formula:
Area = Length x Width
We can rearrange the formula for the area to solve for the width:
Width = Area / Length
From the question, we have the following parameters that can be used in our computation:
Area = 54x^8y^6
Length = 9x^3y^4
Substituting the given values, we get:
Width = (54x^8y^6) / (9x^3y^4)
Evaluate the quotient expression
Width = 6x^5y^2
Hence, the width expression is 6x^5y^2.
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Find the missing side of the triangle (h).
Wse the Law of Cosines to determine the indicated angle e0. (Assume \( a=69.01, b=39.28 \), and \( c=42.65 \), Round your answer to two decimal places.) \[ d= \] Neod Help?
The final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.
To determine the indicated angle, we can use the Law of Cosines, which states that: \[ c^2 = a^2 + b^2 - 2ab\cos(C) \]We can rearrange this equation to solve for the cosine of the indicated angle: \[ \cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \]Plugging in the given values for a, b, and c, we get: \[ \cos(C) = \frac{69.01^2 + 39.28^2 - 42.65^2}{2(69.01)(39.28)} \]Simplifying the expression, we get: \[ \cos(C) = 0.7664 \]Now, we can use the inverse cosine function to find the indicated angle: \[ C = \cos^{-1}(0.7664) \]This gives us an angle of 40.32 degrees. However, the question asks us to round our answer to two decimal places, so the final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.
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3randon Vasquez percent More or Less (Formula ) L^(1) reb 21, 8:52:44 PM Watch help video What is the result when the number 72 is decreased by 50% ? Answer: Submit Answer
The result when the number 72 is decreased by 50% is 36.
We can use the formula:
Result = Original Number - (Original Number x Percent Decreased)
In this case, the original number is 72 and the percent decreased is 50%.
So, we can plug in the values into the formula:
Result = 72 - (72 x 0.50)
Result = 72 - 36
Result = 36
Therefore, the result when the number 72 is decreased by 50% is 36.
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Triangle T was dilated to form triangle T prime.
Triangle T has side lengths of 36 and 18. Triangle T prime has side lengths of 20 and 10
Triangle T prime is similar to triangle T with a scale factor of 5/9.
What is the scale factor?
In mathematics, a scale factor is a number that scales, or multiplies, a quantity or geometric figure. In other words, it is the ratio of any two corresponding lengths in two similar figures.
To determine the scale factor of the dilation, we can compare the corresponding side lengths of the two triangles.
For example, we can compare the longest sides of each triangle (also known as the "hypotenuse" in a right triangle):
scale factor = length of corresponding side in T prime / length of corresponding side in T
scale factor = 20 / 36
scale factor = 5/9
This means that triangle T prime is a reduction (since the scale factor is less than 1) of triangle T by a factor of 5/9. In other words, the side lengths of triangle T prime are 5/9 times the corresponding side lengths of triangle T. Therefore, we can find the lengths of the other sides of triangle T prime by multiplying the corresponding side lengths of triangle T by the scale factor:
10 = 18 * 5/9
20 = 36 * 5/9
So, the side lengths of triangle T prime are 20, 10, and (36*5/9) = 20.
Therefore, triangle T prime is similar to triangle T with a scale factor of 5/9.
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A central angle of a circle measures 37°. the arc intercepted by this central angle measures 16 inches. which value best approximates the radius of the circle? responses 24.78 in. 24.78 in. 25.38 in. 25.38 in. 46.44 in. 46.44 in. 50.76 in.
The value that best approximates the radius of the circle is 25.38 inches.
The measure of the central angle in degrees is related to the length of the arc intercepted by the central angle and the radius of the circle by the formula:
Arc length = (Central angle measure / 360°) x (2πr)
where r denotes the circle's radius.
Substituting the given values, we have:
16 inches = (37° / 360°) x (2πr)
Simplifying and solving for r, we get:
r = 16 inches / [(37/360) x (2π)]
r ≈ 25.38 inches (rounded to two decimal places)
Therefore, the value that best approximates the radius of the circle is 25.38 inches.
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I don’t understand how to solve this when one number is missing! Pls help
Given:
5yd
To find:
The area of the hexagon
Solution:
[tex]area \: of \: hexagon = 6s[/tex]let the area of hexagon here be x. [tex] = 5 \times 6 \\ = 30yd[/tex]Learn more about area and perimeter:https://brainly.ph/question/14127685using a table of values what is an approximate solution to the equation f(x)=g(x) to the nearest quarter of a unit
The desired solution is to the nearest quarter of a unit, the approximate solution is x=2.25.
What is a quarter?A quarter is a fraction that represents one-fourth of a whole number or quantity. It can be written as a ratio, a decimal, or a percentage. A quarter is one of the simplest fractions, and it can be used to divide an object or number into four equal parts. It is also used to calculate percentages and proportions.
A table of values is a great way to approximate a solution to an equation. To approximate a solution to the equation f(x)=g(x) to the nearest quarter of a unit, the table of values must contain the x-values and the corresponding f(x) and g(x) values.
For example, if the equation was f(x)=2x+3 and g(x)=x+2, the table of values would look like this:
x f(x) g(x)
0 3 2
1 5 3
2 7 4
3 9 5
4 11 6
To find the approximate solution to f(x)=g(x), the table must be examined for the first x-value where the f(x) and g(x) values are equal. In this case, the x-value is 2 and the corresponding f(x) and g(x) values are both 7. Since the desired solution is to the nearest quarter of a unit, the approximate solution is x=2.25.
This method of using a table of values to approximate a solution to an equation is very simple and quick. It is a great way to get a rough answer to an equation without having to solve it. It is also a useful tool for double-checking the exact solution to an equation.
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please someone complete this ive never struggled so bad
Answer:
Step-by-step explanation:
Im not really sure what the heck you doing because im only in 8th grade but right now im in central and i'm kind of good at math but i'll try. Lets see........ I think they would all just be $11.50, but like i said im only in 8th grade and not that good at this kind of math so before you answer it please check with someone else to see if i got it right for you, cause i don't want to give you the wrong answer and you fail it.
Mario has 1 gallon of milk. He pours 4 cups of milk for him and his 3 siblings to have with their breakfast. How much milk is left ? Simplify your answer .
1 gallon of milk is equal to 16 cups of milk (1 gallon = 4 quarts = 16 cups).
Mario poured 4 cups of milk for each of the 4 people, which is a total of 16 cups of milk.
So the amount of milk left is:
16 cups (total) - 16 cups (poured) = 0 cups
Therefore, there is no milk left.
alaska ranks as the 48th states when comparing populations. In 1980, the population wa 410,851 and in 2017 the population was 739818. Which equation models the population of alska t years after 1980. If the population of Alaska continues to grow at the same rate, predict the population of Alaska in 2040
Therefore, the predicted population of Alaska in 2040 is approximately 1,038,428.
Given by the question.
P₀ = 410,851
P = 739,818
t = 2017 - 1980 = 37
r = ln (739818/410851) / 37
r ≈ 0.0136
Therefore, the equation that models the population of Alaska t years after 1980 is:
P(t) = 410,851 * [tex]e^{(0.0136*t)}[/tex]
To predict the population of Alaska in 2040, we need to find the value of P (60), since 2040 is 60 years after 1980:
P (60) = 410,851 * [tex]e^{(0.0136*60)}[/tex]
P (60) ≈ 1,038,428
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At a county fair, 60% of the entries are livestock. Of those entries, 70% are sold at the auction. If
130 entries of livestock are sold at the auction, how many total entries were there at the fair?
Answer:
Let's start by using algebra to solve the problem.
Let x be the total number of entries at the fair.
Given that 60% of the entries are livestock, we can write:
0.6x = number of livestock entries
Of those livestock entries, 70% are sold at the auction, which means:
0.7(0.6x) = 130
Simplifying the second equation, we get:
0.42x = 130
Solving for x, we can divide both sides by 0.42:
x = 309.52
Since we can't have a fractional number of entries, we can round up to the nearest whole number, giving us:
x = 310
Therefore, there were a total of 310 entries at the fair.
Step-by-step explanation:
With a partner, you are going to research recipes and find examples of fractional
amounts of spices and/or seasonings. Use cookbooks, recipe cards, or on-line sources to find recipes of your favorite foods. You
can even interview a chef or cook! Find 3 recipes that have at least one ingredient that
uses a fractional amount of some of the ingredients. Choose one of the ingredients that is a fractional amount. If you were to double
the recipe, how much of the ingredient would you use? Talk to an adult about what
operation you would use to double the amount. Practice doubling some of the fractional
amounts with the 3 recipes you chose. Create a recipe with fractional amounts of several ingredients. Then have another
student double your recipe
There are three recipes provided to mention the fractional amounts of ingredients:
Recipe for Chicken Curry:
2 teaspoons of turmeric
1/2 teaspoon of cumin
1/4 spoon of any type of pepper
If you were to double this recipe, you would use:
4 teaspoons of turmeric
1 teaspoon of cumin
1/2 teaspoon of pepper
To double the amount of the ingredients, you would multiply each fraction by 2.
Chocolate chip cookies:
1/4 teaspoon of baking soda
1/2 teaspoon of salt
double the quantities if u want to make more or huge quantities
Tomato soup recipe
half a spoonful of dried basil
1/4 teaspoon of dried thyme
for this recipe, we will need
1 spoon of basil
1/2 teaspoon of dried thyme
Recipe for Pasta Salad:
fourth cup of Olive oil
1/3 cup of red wine vinegar
1/2 teaspoon of dried oregano
1/4 teaspoon of salt
1/8 teaspoon of black pepper
We can multiply by 2 if we increase the quantity.
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What are the original equations to these 2 transformed
equations?
Equation 1: y= 3sin 2x-2
Equation 2: y=4sin(x-1)+3
The original equations for these two transformed equations can be found by reversing the transformations that have been applied to the standard sine function y = sin(x).
For Equation 1: [tex]y = 3sin(2x-2)[/tex], the original equation is y = sin(x). The transformations that have been applied are a vertical stretch by a factor of 3, a horizontal compression by a factor of 2, and a horizontal shift to the right by 2 units. To reverse these transformations, we would divide the y-values by 3, divide the x-values by 2, and shift the graph to the left by 2 units.
For Equation 2: [tex]y = 4sin(x-1)+3[/tex], the original equation is also y = sin(x). The transformations that have been applied are a vertical stretch by a factor of 4, a horizontal shift to the right by 1 unit, and a vertical shift up by 3 units. To reverse these transformations, we would divide the y-values by 4, shift the graph to the left by 1 unit, and shift the graph down by 3 units.
Therefore, the original equations for these two transformed equations are both y = sin(x).
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Find the volume of a cone with a diameter of 12m and height of 9m ? A.108 m3 B.1296 m3 C. 324 m4 D.108 m3
The closest choice is A. 108 which is the right response if the cone's real height is 4.5m rather than 9m.
what is volume ?The amount of space a three-dimensional object takes up is measured by its volume. It is a numerical assessment of an object's three-dimensional physical dimensions—length, breadth, and height. Cubic units, such as cubic meters, cubic feet, cubic centimeters, or cubic inches, are used to indicate volume. Mathematical equations can be used to determine the formula for calculating the volume of many geometric shapes, including a cube, rectangular prism, sphere, or cylinder.
given
Finding the cone's radius, which is equal to half of its diameter, is the first stage.
radius: (12 m / 2) = 6 m
The capacity of a cone is calculated as follows:
V = (1/3)π[tex]r^2[/tex]h
In place of the ideals we hold:
V = (1/3)π([tex]6m^2[/tex])(9m) (9m)
V = (1/3)π([tex]36^2[/tex])(9m) (9m)
V = (1/3)π(324[tex]m^3[/tex])
V = 108π [tex]m^3[/tex]
With the aid of a computer, we can roughly convert to 3.14:
V ≈ 108 x 3.14 [tex]m^3[/tex]
V ≈ 339.12 [tex]m^3[/tex]
As a consequence, the cone, which has a 12 m diameter and a 9 m height, has a capacity of about 339.12 m3.
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Nathan's orchestra has 18 string
musicians, 9 percussion musicians,
15 brass musicians, and 12 woodwind
musicians. Six of the musicians cannot
play in the next performance. If the
remaining musicians plan to sit in rows
of 6 chairs, how many rows of chairs
are needed?
Rows of chairs that are needed to make 48 musicians sit is 8 rows.
What is division?The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers.
Given,
Number of musicians in orchestra
18 string musicians, 9 percussion musicians,
15 brass musicians, and 12 woodwind musicians
Total number of musicians
= 18 + 9 + 15 + 12
= 54
Six of the musicians cannot play in the next performance
Number of musicians playing in next performance
= 54 - 6
= 48
48 musicians will sit on 48 chairs
Number of chairs in one row = 6
Number of rows for 48 chairs = 48/6 = 8
Hence, 8 rows of chairs are needed to make 48 musicians sit.
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An open-topped box is constructed from a rectangular piece of cardboard that is twice as long as it is wide by removing a square of size 3 inches from each corner and turning up the edges.
If the box is to hold 1,620 in3, how big should the originial piece of cardboard be?
The original piece of cardboard should be approximately 32.86 inches by 16.43 inches.
To find the size of the original piece of cardboard, we can use the formula for the volume of the box, which is V = l × w × h. Since the box is open-topped, the height will be the size of the square that was removed from each corner, which is 3 inches. Also, given that the length of the original piece of cardboard is twice the width, we can substitute l = 2w in the formula. Therefore, the formula becomes:
V = (2w) × w × 3
Now, we can plug in the given volume of 1,620 in3 and solve for w:
1,620 = (2w) × w × 3
540 = 2w^2
270 = w^2
w = √270
w ≈ 16.43 inches
Now, we can use the value of w to find the length of the original piece of cardboard:
l = 2w = 2(16.43) = 32.86 inches
Therefore, the original piece of cardboard should be approximately 32.86 inches by 16.43 inches.
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Find the length of the missing side.
Answer:
8
Step-by-step explanation:
Let's call the unknown side [tex]c[/tex].
The Pythagorean Theorem states that in any right triangle, [tex]a^{2} + b^2 = c^2[/tex]
Now plug in the known values.
[tex]6^2 + (2\sqrt 7)^2 = c^2\\36 + 4(7) = c^2\\36 + 28 = c^2\\64 = c^2\\c = \sqrt{64} = 8[/tex]
they also needed red fabric. each yard of red fabric costs $2. if they buy 6 1/2 or red fabric, how much will it cost
The amount of cost for the fabric is given by A = $ 13
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the total cost of red fabric be represented as A
Now , the amount of red fabric be = 6 1/2 yards
And , the cost of red fabric per yard = $ 2
So , the total cost of red fabric A = amount of red fabric x cost of red fabric per yard
On simplifying the equation , we get
The total cost of red fabric A = ( 6 1/2 ) x 2
The total cost of red fabric A = ( 13/2 ) x 2
The total cost of red fabric A = $ 13
Therefore , the value of A is $ 13
Hence , the total cost of red fabric is $ 13
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Jacques needs 5/8 kg of flour to make a loaf of bread
he tips 2/5 Kg of white flour onto a weighing scale
how much more flour does he need to add?
9/40 more flour does he need to add.
What is Fraction?A fraction represents a part of a whole.
Given that Jacques needs 5/8 kg of flour to make a loaf of bread, he tips 2/5 Kg of white flour onto a weighing scale.
We need to find amount of flour he still need to make a loaf of bread.
2/5 + x =5/8
Subtract 2/5 from both sides
x = 5/8 -2/5
LCM of 8 and 5 is 40.
=25-16/40
=9/40
Hence, 9/40 more flour does he need to add.
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Solving Trigonometric Functions 6. a. Solve the following equations using algebra. You must show your algebra steps for full marks. You may use desmos to verify, but the marks will be allocated to the process not just the solution.
i. 2 sin^2 θ = 1, 0 < θ < 2π
ii. sin 1/2 θ = 1, - π < θ < 2π
iii. 4 cos(θ-45º) + 7 = 10, 0 < θ < 360 º
The solutions to the given trigonometric equations are:
i. θ = π/4, 3π/4, 5π/4, 7π/4
ii. θ = π/2, 3π/2
iii. θ ≈ 76.96º, 13.04º
To solve the given trigonometric equations using algebra, we need to rearrange the equations and use trigonometric identities to find the values of θ that satisfy the equations.
i. 2 sin^2 θ = 1, 0 < θ < 2π
First, we rearrange the equation to isolate sin^2 θ:
sin^2 θ = 1/2
Next, we take the square root of both sides:
sin θ = ±√(1/2)
Using the identity sin θ = cos (π/2 - θ), we can find the values of θ that satisfy the equation:
θ = π/4, 3π/4, 5π/4, 7π/4
ii. sin 1/2 θ = 1, - π < θ < 2π
First, we rearrange the equation to isolate θ:
sin θ = 2
Next, we use the identity sin θ = 1/csc θ to find the values of θ that satisfy the equation:
θ = π/2, 3π/2
iii. 4 cos(θ-45º) + 7 = 10, 0 < θ < 360 º
First, we rearrange the equation to isolate cos(θ-45º):
4 cos(θ-45º) = 3
cos(θ-45º) = 3/4
Next, we use the identity cos θ = sin (π/2 - θ) to find the values of θ that satisfy the equation:
θ = 45º + cos^-1(3/4), 45º - cos^-1(3/4)
Using desmos, we can verify our solutions and find the approximate values of θ:
θ ≈ 76.96º, 13.04º
Therefore, the solutions to the given trigonometric equations are:
i. θ = π/4, 3π/4, 5π/4, 7π/4
ii. θ = π/2, 3π/2
iii. θ ≈ 76.96º, 13.04º
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PLEASE I REALLY NEED HELP ASAP
[5 points] Draw a picture of each size of tile below. Label the side lengths and then find the area of each tile. Use x and/or y to represent different unknown side lengths.
If the length of the tile is x and the breadth of the tile is y then the area of each tile is equal to xy units.
How to calculate the areaGiven that we can assume the length of tile be x and breadth of tile be y. We are required to find the area of the each tile and draw a figure showing the tile whose length is x and the breadth is y.
Tile is in the shape of the rectangle because the length and breadth are different and we know that the area of the rectangle is equal to product of the length and breadth of that rectangle.
If the length of tile is x and the breadth of tile is y then the area of the tile is equal to x*y which is xy units. Figure is attached with the solution.
Hence if the length of the tile is x and the breadth of the tile is y then the area of each tile is equal to xy units.
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