The value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
using the trigonometric ratio of tan 45°
{recall that tan 45° = 1}
tan 45° = QR/RT {opposite/adjacent}
tan 45° = x/2√3
x = tan 45 × 2√3 {cross multiplication}
x = 1 × 2√3
x = 2√3
Therefore, the value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.
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Write your answer as a two column proof.
Since opposite angles are equal, this means that GHJK is a parallelogram, because opposite sides are parallel.
Describe Parallelogram?Additionally, each pair of opposite sides of a parallelogram are congruent (of equal length), and the opposite angles of a parallelogram are also congruent (of equal measure). These properties make parallelograms useful in various fields such as engineering, architecture, and geometry.
There are different types of parallelograms, including rectangles, rhombuses, and squares, which have additional properties such as perpendicular sides, equal sides, or right angles. A rectangle is a type of parallelogram with four right angles, while a rhombus has four sides of equal length, and a square has both equal sides and right angles.
To prove that GHJK is a parallelogram, we need to show that opposite sides are parallel.
Since GK is parallel to HJ, we have:
∠LGK + ∠KHL = 180° (because GK // HJ)
But we are given that:
∠LGK = ∠LKL (given)
Therefore:
∠LKL + ∠KHL = 180°
This means that ∠KHL is a supplementary angle to ∠LKL.
Similarly, we can show that ∠KJH is a supplementary angle to ∠JKL:
∠JKL + ∠KJL = 180° (because GK // HJ)
But we are given that:
∠LGK = ∠LKL
Therefore:
∠LGK + ∠KJL = 180°
This means that ∠KJL is a supplementary angle to ∠LGK.
Now, we can use the fact that the opposite angles of a parallelogram are equal to show that GHJK is a parallelogram:
∠LKL = ∠JKL (alternate interior angles)
∠KHL = ∠KJH (alternate interior angles)
Since opposite angles are equal, this means that GHJK is a parallelogram, because opposite sides are parallel.
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100 POINTS YALL BETTER ANSWER ISTG
PICTURE BELOW ZOOM IN
The answer of this question is in every 5 hour 6 m water height increase in tank. So we have to learn about proportional.
What is Proportional?Proportional is the right amount, size , degree or quantity compared with something else. We can simply say that it is comparison between one object or thing with another object or thing.
Their are two types of proportional properties:
a. Directly Proportional, In this when amount , size or degree of any object increases than the amount ,size, or degree of another object are also increases with same ratio.
b. Indirectly Proportional, In this when amount , size or degree of any object increases than the amount , size or degree of another object is decreases in same ratio.
Let Solve this question, in this the first property used.
[tex]\frac{1}{4} = \frac{3}{10} , we\ get\ 5 = 6[/tex]
[tex]\frac{1}{2} = \frac{3}{5}\ we\ get\ 5 = 6[/tex]
[tex]\frac{3}{4} =\frac{9}{10} \ we\ get\ 5 =6[/tex]
So, In every 5 hour 6 m water height increase in tank.
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Please Help
20 Points
Show you're work please..
Answer:
(a) 512 ft² , (b) 720 ft²
Step-by-step explanation:
the area of a rectangle is calculated as
area = length × width
(a)
area of pool = 32 × 16 = 512 ft²
(b)
the area of the deck is calculated as
area of outer rectangle - area of pool
area of outer rectangle = 44 × 28 = 1232 ft²
area of deck = 1232 - 512 = 720 ft²
An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.10 worth of electricity, $0.10 and worth of steel; the electric industry needs $0.03 worth of coal, $0.03 worth of electricity, and $0.04 worth of steel; and the steel industry needs $0.20 worth of coal and $0.01 worth of steel. The sales demand is estimated to be $4 billion for coal, $3 billion for electricity, and $3 billion for steel. Suppose that the demand for electricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand?
The steel industry should use 1.7 billion dollars worth of coal and 0.035 billion dollars worth of steel.
What is amount?Amount is a term used to refer to the total of a certain quantity or sum. It is often used to describe the value of something, such as a financial transaction, or the size of a collection of objects. Amounts are usually expressed in units of measurement such as dollars, kilograms, or liters. Amounts can also be expressed as a percentage or fraction.
The coal industry should produce 8 billion dollars worth of output, the electric industry should produce 9 billion dollars worth of output, and the steel industry should produce 3.5 billion dollars worth of output. The coal industry should use 0.08 billion dollars worth of coal, 0.8 billion dollars worth of electricity, and 0.8 billion dollars worth of steel. The electric industry should use 0.06 billion dollars worth of coal, 0.9 billion dollars worth of electricity, and 1.2 billion dollars worth of steel. The steel industry should use 1.7 billion dollars worth of coal and 0.035 billion dollars worth of steel.
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need help with This Math
The value of XS in the perpendicular lines is 16 units.
How to find length of line segment?The line VU is perpendicular to the line XS. Perpendicular lines are defined as two lines that meet or intersect each other at right angles.
Therefore, perpendicular bisector is a line that divides a given line segment exactly into two halves forming 90 degrees angle at the intersection point.
Hence,
b + 5 = 3b - 1
b - 3b = -1 - 5
-2b = -6
divide both sides by -2
b = -6 / -2
b = 3
Therefore, let's find XS as follows:
XS = b + 5 + 3b - 1
XS = 4b + 4
XS = 4(3) + 4
XS = 12 + 4
XS = 16 units
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Four identical cubes are joined to make a new shape.
What is the new shape’s surface area?
The surface area of the shape which was formed when four identical cubes were joined, is 882 yd ².
How to find the surface area ?The surface area of a cube can be found by the formula :
= Number of faces x Length of a side ²
When four identical cubes were joined, this leads to the creation of 18 faces which means that the surface area of the cube would then be :
= 18 x 7 x 7
= 18 x 49
= 882 yd ²
In conclusion, the area is 882 yd ².
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conaider a regular 96-sided polygon exlain how to found your anser in orlder to get full credit
To make a regular polygon with 96 sides we can take a circle as a starting point and divide it into 96 equal sides.
How to create a regular polygon with 96 sides?To create a regular polygon with 96 sides, we must take into account that all its sides must be equal, so we can take a circumference as a starting point. In this case, the circumference has 360°, so we must divide this into 96 parts and the result would be the distance between the edges of the polygon.
360° / 96 = 3.75In this case, we must make a circle with a protractor and mark every 3.75°, when we have completed this procedure in the entire circumference we will have a regular polygon with 96 sides.
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thier sum is -7 thier diffrence is 14
HELP
Using algebraic expressions, x = 7/2 and y = -21/2.
An algebraic expression might be made up of a single word or a group of words.
An algebraic expression can be any number, variable, or set of operations, whereas an equation is two different algebraic expressions connected together with an equal sign.
x = 7/2 and y = -21/2
Let x and y be those numbers.
In response to your query
x + y = -7
x - y =14
both equations added
2x = 7
or x = 7/2
the equivalent x value in either equation
y = -21/2
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Complete question -
What are the two numbers if their sum is −7 and their difference is 14?
A cylinder has a volume of 1 and one third in3 and a radius of one third in. What is the height of a cylinder? Approximate using pi equals 22 over 7.
42 over 6 inches
42 over 9 inches
42 over 11 inches
42 over 22 inches
The height of the cylinder is approximately 42/11 inches. The answer is option C.
What is the formula for the volume of the cylinder?
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cylinder is 1 and one-third in^3 and the radius is one-third in. Substituting these values into the formula, we get:
1 and one-third = 4/3
V = π(1/3)²h = 4/3
Simplifying the equation, we get:
h = (4/3) / (π(1/3)²) = (4/3) / (π/9) = (4/3) * (9/π) = 12/π
Approximating π as 22/7, we get:
h ≈ (12/π) ≈ (12/(22/7)) = 42/11 inches
Therefore, the height of the cylinder is approximately 42/11 inches. The answer is option C.
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Roberto bought a $340,000 house, paying 20% down, and financing the rest at 5% interest for 30 years. Her
monthly payments are $1460.15. How much will he really pay for her $340,000 house?
Roberto will pay a total of $
for the house.
Answer:
Therefore, Roberto will pay a total of $593,654 for his $340,000 house, including $253,654 in interest over the 30-year period.
Step-by-step explanation:
Roberto paid 20% down on a $340,000 house, which is 0.20 x $340,000 = $68,000.
So, the amount he financed is $340,000 - $68,000 = $272,000.
Roberto financed the $272,000 at 5% interest for 30 years, making monthly payments of $1460.15.
To find the total amount he will pay for the house, we need to calculate the total amount he will pay over the 30-year period.
First, we can calculate the total number of payments he will make over the 30 years by multiplying the number of years by the number of payments per year:
30 years x 12 months/year = 360 payments
The total amount Roberto will pay is the sum of all the monthly payments he makes over the 30 years:
Total amount = 360 x $1460.15 = $525,654
However, this includes both the principal amount of $272,000 and the interest he will pay over the 30 years. To find out how much he will pay in interest, we can subtract the principal from the total amount:
Total interest = $525,654 - $272,000 = $253,654
Therefore, Roberto will pay a total of $593,654 for his $340,000 house, including $253,654 in interest over the 30-year period.
if n square- 1 over m is equal to 4
Express n in terms of m
find n when m is 12
Answer:
n=√(4m+1) , 7
Step-by-step explanation:
According to statement
( n²-1 )÷m=4
∴n²-1=4m
⇒n²=4m+1
⇒n=√(4m+1)… … … … 1
If m=12
put the value of m in 1 equation
n=√(4×12+1)
=√49=7
what is a bisection
Answer:
this is the intersecting of lines
Answer:
gogel chrome. will answer faster than this app
PLEASE HELP ME!!! ASAP.
Enter your answer and show all the steps that you used to solve this problem in the space provided.
(Click imagine for the table)
X. 3, 9, 13, 20.
Y. 9, 27, 39, 60
State weather the relationship between the variables in the table is a direct variation, an inverse variation, or neither.
if it direct, write a function and model it.
The relationship between the variables in the table is a direct variation.
A function that models the relationship is y = 3x.
What is a direct variation?In Mathematics, a direct variation is also referred to as direct proportion and it can be modeled by using the following mathematical expression or function:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.Under direct variation, the value of x represent an independent variable while the value of y represents the dependent variable. Therefore, the constant of proportionality (variation) can be calculated as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 9/3 = 27/9 = 39/13 = 60/20
Constant of proportionality (k) = 3.
Therefore, the required function is given by;
y = kx
y = 3x
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The correct options are: [tex]x^{2}[/tex] - 4 = 0 and 4[tex]x^{2}[/tex] = 16
What is Linear equation ?
A linear equation is an algebraic equation in which each term is either a constant or a product of a constant and a variable raised to the first power, also called a linear term.
A linear equation can be written in the form of:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope or gradient of the line, and b is the y-intercept (the point where the line crosses the y-axis).
The equations that are true for x = -2 and x = 2 are:
[tex]x^{2}[/tex] - 4 = 0, which is true for x = -2 but not for x = 2
4[tex]x^{2}[/tex] = 16, which is true for x = 2 but not for x = -2
Therefore, the correct options are: [tex]x^{2}[/tex] - 4 = 0 and 4[tex]x^{2}[/tex] = 16
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5 questions 15 points please help with these math questions
From the given scatter plot, point L is an outlier. The association is negative linear association. The line is not the best fit accurate. Graph shows a negative linear association. As the number of weeks increases, the number of tickets sold decreases
What is scatter plot?
A scatter plot is a type of data visualization that displays the relationship between two numerical variables. It is a graph with points plotted on it that represent the values of two different variables.
1. In a scatter plot, an outlier is a data point that lies far away from the other data points in the plot, and is not in line with the overall pattern or trend that the other data points display.
2. The scatter plot for this data is likely to show a negative linear association between the number of people in a group and the zoo ticket price per person. As the number of people in a group increases, the zoo ticket price per person decreases.
The rate of change of Zoo Ticket Price with respect to the the number of persons:
[tex]m=14.50-1500/2-1=-0.5[/tex]
3. No because the line should touch every point. When we draw a line passing through the origin, it passes through the data points (2,3), (4,3), and (4,5), but it does not pass through the other data points (6,5), (6,6), and (8,7).
This indicates that the line of best fit may not accurately represent the overall trend of the data.
4. The given data points are (1,5), (2,4), (3,3), (4,2), (5,1), and (6,0). When we plot these points on a graph with x-axis representing variable x and y-axis representing variable y, we get a downward sloping straight line passing through all the points.
This pattern suggests a negative linear association between the variables x and y. As the value of x increases, the value of y decreases at a constant rate.
Therefore, the graph shows a negative linear association between x and y.
5. The answer is option (a) "As the number of weeks increases, the number of tickets sold decreases".
As per the given data points and the line passing through (1,100) and (6,35), we can observe that the number of tickets sold decreases as the number of weeks a movie has been in theaters increases. Therefore, the statement "As the number of weeks increases, the number of tickets sold decreases" best describes the relationship between the number of weeks a movie has been in theaters and the number of tickets sold.
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I need help with this please
Answer:
First statement is true.
Second statement is false--there are some 3d shapes that unit cubes cannot be used to find the volume of. Examples are cylinders and cones.
The rectangle shown has a perimeter of 180 cm and the given area. Its length is 5 more than four times its width. Write and solve a system of equations to find the dimesions of the rectangle.
The dimensions of the rectangle are, length = 73 cm and width = 17 cm.
What do system of equations depict?Finding the values of the variables employed in a system of equations entails solving the set of equations. By keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the provided equations true is the primary goal when solving an equation system. A given system of equations may have a variety of solutions.
Let us suppose the width of the rectangle = w.
Given that, length is 5 more than four times its width.
Thus,
l = 5 + 4w
Now, the perimeter of the rectangle is given as:
P = 2(l + w)
Substitute the value of P = 180:
180 = 2l + 2w
The system of equations is:
l = 5 + 4w
180 = 2l + 2w
Substitute the value of l from equation 1 into equation 2:
180 = 2(5 + 4w) + 2w
180 = 10 + 8w + 2w
180 - 10 = 10w
170 = 10w
w = 17
Substitute the value of w = 17 in the first equation:
l = 5 + 4w
l = 5 + 4(17)
l = 73
Hence, the dimensions of the rectangle are, length = 73 cm and width = 17 cm.
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Factorise 3-6x I don’t know how to do it
Answer:
Step-by-step explanation:
-3(2x-1)
Suppose the demand and supply of tea are modeled by the two following functions:
Q = 34P + 53
Q = -25P + 177
What is the equilibrium price of tea? Round your answer to two places after the decimal point (0.01).
Answering the question, we may state that So the equilibrium price of equation tea is $2.10 per unit.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
To find the equilibrium price of tea, we need to set the quantity demanded equal to the quantity supplied:
[tex]34P + 53 = -25P + 177\\59P + 53 = 177\\59P = 124\\P = 2.10[/tex]
So the equilibrium price of tea is $2.10 per unit.
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List the first 5 elements of set A
The first 5 elements of set A are: {-1, -2, 1, -3, 2}.
What is the set of elements?
The objects in a set are called the elements (or members ) of the set; the elements are said to belong to the set (or to be in the set), and the set is said to contain the elements. Usually, the elements of a set are other mathematical objects, such as numbers, variables, or geometric points.
Set A is defined as:
A = {x | x = k(-1)ⁿ where k ∈ Z* and n ∈ N}
To find the first 5 elements of A, we can substitute different values of k and n:
For k = 1 and n = 1, x = 1(-1)¹ = -1
For k = 2 and n = 1, x = 2(-1)¹ = -2
For k = 1 and n = 2, x = 1(-1)² = 1
For k = 3 and n = 1, x = 3(-1)¹ = -3
For k = 2 and n = 2, x = 2(-1)² = 2
Therefore, the first 5 elements of set A are: {-1, -2, 1, -3, 2}.
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When $0.58 tax was added to the price of a book, the total bill came to $7.05. What was the price of the book?
Step 1 of 2: Describe the above situation as a linear equation, using "x" or "y" as variable names to describe the unknown quantity
Answer:
Let's use "x" to represent the price of the book before tax.
After the tax is added, the total price becomes:
x + 0.58
We know that the total bill came to $7.05, so we can set up an equation:
x + 0.58 = 7.05
This equation represents the situation described.
Step-by-step explanation:
Answer:
I believe the answer would be $6.47
Step-by-step explanation:
In how many ways can the letters A, B, C, D, E, F, G, H be arranged?
Answer:
40,320
Step-by-step explanation:
There are 8 letters in total:
So, in the first place we can put all 8 letters
In the 2nd place we can put 7 (all except the letter in the first place and so on...)
Let's multiply the options (the order is important):
8! or 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320 (8 places for letters in total)
Find the area of this composite shape. 10 cm, 5 cm, 8 cm, and 4 cm.
new grill costs $550 discount = 15% off what is the final bill?
A loan of $12,000 with interest at 14% compounded annually is to be amortized by equal payments at the end of each year for six years. What will the balance outstanding be after second year?
Draw a dialation with center at the Irgun of the triangle with the vertices (2,0) ,(4-4), (6,2) scale factor of k =1.5
The sides of the dilated triangle are parallel to the sides of the original triangle, but their lengths are multiplied by the scale factor k.
What is triangle?A triangle is a closed two-dimensional figure with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many different areas of mathematics, science, and everyday life. A triangle is defined by its three vertices (or corners), which are the points where the sides of the triangle intersect. The three sides of the triangle are the line segments connecting the vertices. The three angles of the triangle are the angles formed by the intersection of two sides.
Here,
To dilate a triangle with a center at the origin, we need to multiply the coordinates of each vertex by the scale factor k. However, in this case, the center of dilation is not at the origin, but at the point Irgun. To perform the dilation, we can follow these steps:
Plot the original triangle with vertices (2,0), (4,-4), and (6,2).
Draw a line segment from the center of dilation Irgun to each vertex of the triangle.
Measure the distance from Irgun to each vertex, and multiply it by the scale factor k = 1.5 to find the new distance.
Use the new distances to construct the dilated triangle by drawing line segments from Irgun to points that are 1.5 times farther away from Irgun than the corresponding vertices of the original triangle.
The resulting dilation of the triangle with center at Irgun and scale factor k = 1.5 is shown below:
In this image, the original triangle is shown in black, and the dilated triangle is shown in blue. The center of dilation Irgun is marked with a red dot. Note that the new vertices of the dilated triangle are (0.5,0), (3,-6), and (7.5,3), which are 1.5 times farther away from Irgun than the corresponding vertices of the original triangle.
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A local bank has determined that the daily balances of the checking accounts of its customers are normally distributed with an average of $280 and a standard deviation of $20.
a. What percentage of its customers has daily balances of more than $275?
b. What percentage of its customers has daily balances less than $243?
c. What percentage of its customers' balances is between $241 and $301.60?
Answer:
Step-by-step explanation:
Need a z-score with all of these, which essentially makes the table needed a standard normal table with mean 0 and sd 1
z=(x-mean)/sd
a. (275-280)/20=-0.25
want the probability of z <-0.25, and that is 0.4013 or 40.13%
b.(243-280)/20=-1.85, and probability of z < -1.85 is 0.0322 or 3.22%
c. this is z of -39/20 or -1.95 and z of 21.60/20 or 1.08. This has a probability of 0.8343 or 83.43%
Use 2nd VARS 2 for normal cdf and put in the numbers, with at least -6 or +6 for minus or plus infinity. 1E99 is fine but isn't really necessary.
Enter the volume, in cubic feet of the cone. Round your answer to the nearest hundredth.
HELP!
Answer: 565.49ft^3/ 565.49ft cubed
Hopefully it is correct!
if you borrow $2,500 when you open up account the loan was for 2 years and the amount of the loan interest was $155 what were you charge when you open up the account for the loan
Answer:
the charge for opening up the account was $155.
Step-by-step explanation:
To find the charge for opening up the account, we need to subtract the interest from the total amount borrowed.
The total amount repaid at the end of the loan period is the sum of the amount borrowed and the interest charged. In this case, the total amount repaid is:
$2,500 + $155 = $2,655
The interest charged on the loan is the difference between the total amount repaid and the amount borrowed. Therefore, the amount charged for opening up the account is:
$2,655 - $2,500 = $155
So the charge for opening up the account was $155.
You have the following data set: 10, 14, 12, 16, 13, 14, 16, 10, 12, and 10. For the given data set, which values would be included on the relative frequency for a value of 10?
The relative frequency οf value οf 10 is 0.3.
What is relative frequency?The relative frequency is calculated as the prοduct οf the number οf times a given value οf the data appears in the set οf all οutcοmes divided by the tοtal number οf οutcοmes.
Here the given data set is 10, 14, 12, 16, 13, 14, 16, 10, 12, and 10.
Fοr value οf 10, the number οf times 10 οccured is 3 and tοtal number οf data set is 10.
Relative frequency,
=> Number οf times οf value οf 10/ Tοtal number οf data set
=> 3/10
=> 0.3.
Hence the relative frequency οf value οf 10 is 0.3.
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Answer:
Step-by-step explanation: