these two triangles are similar. find x
first triangle 8 , 6 second triangle 12 , x
The value of x is obtained as follows:
x = 9.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Considering the equivalent side lengths, the proportional relationship for this problem is given as follows:
8/6 = 12/x.
Applying cross multiplication, the value of x is obtained as follows:
8x = 72
x = 72/8
x = 9.
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Tommy had equal sized pieces of wood that measured 3.5 inches on each side. He glued the pieces of wood on top of each other until they reached a height of 7 feet. How many pieces of wood did Tommy glue together to reach a height of 7 feet?
He will need 2 wood in order to reach a height of 7 feet
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Tommy had equal-sized pieces of wood that measured 3.5 inches on each side.
He glued the pieces of wood on top of each other until they reached a height of 7 feet.
One is glued above another so the wood add up in the stack.
To make 7 ft in total he need2*3.5 = 7ft
Hence He will need 2 wood in order to reach a height of 7 feet
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Given the grid on your work template, plot the points A(4,5) and B(-7,7). Calculate the distance between the 2 points, and find the midpoint.
distance=
u (rounded to hundredths place)
Answer:
distance = 11.1803 units
midpoint : (-1.5, 6).
Step-by-step explanation:
To plot the points A(4, 5) and B(-7, 7) on the grid, we locate the points at the coordinates (4, 5) and (-7, 7) respectively.
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values for A and B, we get:
d = √((-7 - 4)^2 + (7 - 5)^2)
d = √(11^2 + 2^2)
d = √(121 + 4)
d = √125
d = 11.1803 (rounded to hundredths place)
The midpoint of two points (x1, y1) and (x2, y2) can be calculated as follows:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
The midpoint of A and B is:
x = (4 - 7) / 2 = -1.5
y = (5 + 7) / 2 = 6
So the midpoint of A and B is approximately (-1.5, 6).
Ava draws a circle with a radius of 4cm. Elliana draws a circle with a diameter of 6 cm. without calculating, whose circle has the greater area? explain.
Answer:
Elliana's circle with a radius 4 has a greater area
Step-by-step explanation:
The area of a circle is given by πr²
Area is directly proportional to the square of the radius
A ∝ r²
So the greater the radius, the greater the area
Hence, Elliana's circle has a greater area
At a specific spot along the coast of North Carolina, the continental shelf extends out from the shoreline into the ocean. At that point, the depth of the water is . From there, the ocean floor slopes down to the oceanic crust which begins from the shoreline at a depth of . Find the slope of the ocean floor connecting the edge of the continental shelf and the beginning of the oceanic crust. That section of the ocean floor is called the continental slope.
The slope formula to calculate the slope of the ocean floor would be
[tex]slope = \frac{y}{x}[/tex].
What is slope?
The slope of a line characterizes its direction.
To find the slope of the ocean floor, we need to calculate the rise (change in depth) and the run (distance along the ocean floor) between the edge of the continental shelf and the beginning of the oceanic crust.
Let's call the depth of the water at the edge of the continental shelf "d1" and the depth of the water at the beginning of the oceanic crust "d2". Then, the rise is:
rise = d2 - d1
We don't have the actual values for d1 and d2, so let's call the rise "y" and the run "x". Then, the slope of the ocean floor is given by:
[tex]slope =\frac{rise}{run} \\\\slope = \frac{y}{x}[/tex]
So, we can use the slope formula to calculate the slope of the ocean floor.
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in investigation 2, if you were to double the length of the paper strip you dropped through the tape timer, would the number of dots on the paper also double?
Yes, when the length of the paper strip doubles, so will the number of dots on it.
Yes, when the length of the paper strip doubles, so will the number of dots on it. This is the case because the dots are uniformly spaced apart, and the total number of spaces between the dots doubles as the length of the strip does. As a result, to occupy the same number of spaces as the strip's length, the number of dots must also double. The same rule holds true for every paper strip of any length; increasing the strip's length will result in doubling the number of dots on it. The quantity of dots on the paper strip is therefore directly proportional to the length.
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Simplify the expression. Explain each step. (12+x)+2
Answer:
Step-by-step explanation:
The answer is x + 14. If just adding 2 to (x + 12), the parenthesis can be disregarded.
The ________ means that none of the points in the line will satisfy the inequality.
Answer: dotted/dashed line
To create the design shown, shade the triangle formed by the three midsegments of the triangle. Then repeat the process for each unshaded triangle.
a. What is the perimeter of the shaded triangle in Stage 1?
b. What is the total perimeter of all the shaded triangles in Stage 2?
c. What is the total perimeter of all the shaded triangles in Stage 3?
The total perimeter of all the shaded triangles in Stage 3 is 114 units.
What is midpoint theorem?The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the length of the third side.
a) The shaded triangle in stage 1 is formed by the three midsegments of the triangle in stage 0 whose side is 16.
As the mid-segment theorem says the mid-segment is parallel and half in length to the third side of the triangle.
Apply the midsegment theorem, the side of the shaded triangle in stage 1 will be half of the side of the triangle in stage 0 i.e.,
16/2 =8
So, the perimeter is 3×8= 24 units
b) Perimeter = Perimeter of small triangle + Perimeter of 3 smaller triangles
= 24+3×3×4
= 60 units
c) Perimeter = Perimeter of small triangle + Perimeter of 3 smaller triangles + Perimeter of 9 smallest triangles
= 24+3×3×4+9×3×2
= 114 units
Therefore, the total perimeter of all the shaded triangles in Stage 3 is 114 units.
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Calculate the tax for each of the taxable incomes of the head of household taxpayer
The tax for a head-of-household taxpayer with a taxable income of $27,811 is $3,103.
What do you mean by tax?Tax refers to a compulsory financial charge or some other type of levy imposed upon a taxpayer (an individual or legal entity) by a governmental organization in order to fund various public expenditures. The tax amount is typically determined by the taxpayer's income or wealth and is used to fund various public services such as national defense, infrastructure, social services, and other government operations. Taxes can be direct, such as income tax, or indirect, such as sales tax. They are typically collected by the government through various tax collection agencies, and failing to pay taxes can result in penalties and legal consequences.
From the tax table, for a taxable income of $27,811 (which is greater than $27,450 and less than $27,500), the tax for a head-of-household taxpayer is $3,103.
Therefore, the tax for a head-of-household taxpayer with a taxable income of $27,811 is $3,103.
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in a positively skewed distribution, the peak of the distribution corresponds to which measurement(s)? a. the median only b. the mean only c. the mode, mean, and median d. the mode only
The correct answer is option d. the mode only.
Positively skewed distribution:
A positively skewed distribution, also known as a right-skewed distribution, is a type of distribution in statistics in which most values are centered around the left tail and the right tail is longer. The distribution that is positively skewed is the exact opposite of one that is negatively skewed.
Positively skewed data differ from normally distributed data. The following inequality can be used to represent the general relationship between the central tendency measurements in a positively skewed distribution:
Mean > Median > Mode
Here
The peak of the distribution corresponds to the mode only
Therefore,
The correct answer is option d. the mode only.
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neck size, in inches, and number of teeth of 18 randomly selected puppies are compared. which significance test should be used to see if neck size and number of teeth have a linear relationship? assume all test conditions are met.
The appropriate test to see if neck size and number of teeth have a linear relationship in 18 randomly selected puppies is the t-test for slope of regression line.
A regression line is a line that best fits the data by minimizing the sum of the squared differences between the observed and predicted values. A t-test for slope of regression line tests the null hypothesis that the slope of the regression line is equal to zero, which would indicate that there is no linear relationship between the variables.
In this case, neck size and number of teeth are two continuous variables and we want to test if there is a linear relationship between them. A t-test for slope of regression line would provide information on the significance of the relationship and the direction of the relationship (positive or negative).
It is important to note that the test conditions such as independence, normality, and homoscedasticity must be met before conducting the test. If these conditions are not met, the results of the test may be biased and should be interpreted with caution.
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Complete Question: Comparing the neck circumference (in inches) and tooth count of 18 puppies chosen at random. Which statistical analysis should be performed to determine whether there is a linear relationship between neck size and tooth count? Assume that every test requirement is satisfied.
a. Z-test with two samples
b. T-test with two samples
c. Test of two proportions
d. T-Test for Regression Line Slope
e. Z-test for one proportion
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Answer: 12.2
Step-by-step explanation: I did 8 times 6.3= 50.4
Then 8 times 4.4=35.2.
50.4-35.2=15.2 then minus the 3 is 12.2
A 2 pound bag of broccoli costs $1.92. What is the price per ounce.
The cost of broccoli per ounce is $0.06.
What is unit conversion?The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.
Given 2 pound bag of broccoli costs $1.92,
to find the cost per ounce
we know,
1 pound = 16 ounces
2 pound = 2*16 ounces
2 pound = 32 ounces
cost of 32 ounces = $1.92
cost per ounce = $1.92/32
cost per ounce = $0.06 per ounce
Hence per ounce, the cost is $0.06.
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The Price per ounce is $0.06.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A 2 pound bag of broccoli costs $1.92.
As, 1 pound = 16 ounce
So, the cost of 32 ounce of broccoli is 1.92.
Then, the price per ounce
= 1.92/ 32
= 0.06
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what happens to the power of a study if a statistician decides to decrease the overall alpha level from 0.10 to 0.05
The power of a study refers to the ability of a statistical test to correctly detect a difference or association in the population when it actually exists. Decreasing the overall alpha level from 0.10 to 0.05 would increase the power of the study.
The alpha level, also known as the significance level, is the probability of making a Type I error in a statistical test, which is rejecting the null hypothesis when it is actually true. By decreasing the alpha level, the statistical test becomes more stringent, and the likelihood of making a Type I error decreases.
For example, if the alpha level is 0.10, a statistically significant result would be achieved if the p-value (the probability of observing the test statistic under the null hypothesis) is less than or equal to 0.10. If the alpha level is decreased to 0.05, the p-value must now be less than or equal to 0.05 for the result to be considered statistically significant.
In general, decreasing the alpha level makes the test more conservative and increases the power of the study. However, this comes at the cost of increased likelihood of Type II error, which is failing to reject the null hypothesis when it is actually false.
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Use a graphing tool to solve the system.
1.5x−y3=182x−3y=43
Enter the coordinates of the solution in the boxes. Round each coordinate to the nearest hundredth.
The solution is, x= 50 & y= 19.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
given that,
1.5x−y3=18
2x−3y=43
solving the equations in graph , we get,
x= 50
y= 19
Hence, The solution is, x= 50 & y= 19.
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What is the answer? i need help
The area of the base of the triangular prism is 3 inches square.
How to find the area of a figure?The figure above is a triangular prism. Therefore, the base of the triangular prism is a triangle.
Therefore, let's find the area of the base.
Hence,
area of the base = 1 / 2 bh
where
base of the triangleh = height of the triangleTherefore,
b = 5 inches
height = 1.2 inches
Hence,
area of the base = 1 / 2 × 5 × 1.2
area of the base = 6 / 2
Therefore,
area of the base = 3 inches²
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21.A man borrowed Rs. 50,000 for 3 years at the rate of 12% simple interest but he could pay only Rs. 25,000 at the end of 3 years and
agreed to clear his debt at the end of next two years at the rate of 10 %
annual compound interest. Find how much should he pay to clear his
debt? Also find the amount of interest he paid altogether.
What is the order from coolest to warmest? 34 degrees Fahrenheit,100 degrees Fahrenheit,185 degrees Fahrenheit,0 degrees Celsius,37 degrees Celsius, and 100 degrees Celsius
The order from coolest to warmest is 0 degrees Celsius, 37 degrees Celsius, 34 degrees Fahrenheit, 100 degrees Celsius, 100 degrees Fahrenheit, and 185 degrees Fahrenheit.
0 degrees Celsius is the coolest temperature of the given options, followed by 37 degrees Celsius.
34 degrees Fahrenheit is the next coolest temperature.
100 degrees Celsius and 100 degrees Fahrenheit are the next warmest temperatures.
185 degrees Fahrenheit is the next warmest temperature.
100 degrees Celsius is the next warmest temperature.
The warmest temperature of the given options is 185 degrees Fahrenheit.
Therefore, the order from coolest to warmest is 0 degrees Celsius, 37 degrees Celsius, 34 degrees Fahrenheit, 100 degrees Celsius, 100 degrees Fahrenheit, and 185 degrees Fahrenheit.
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Consider the function g(x)=−(x−1)^3−2. Which ordered pair lies on the inverse of the function?
(62,−3)
(−4, 123)
(3, 1)
(3,−6)
The ordered pair lie on the inverse of the function is (62,−3).
Option A is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = -(x - 1)³ - 2
The inverse of f(x).
y = -(x - 1)³ - 2
interchange x and y and solve for y.
x = -(y - 1)3 - 2
(y - 1)³ = -2 - x
(y - 1)³ = -(2 + x)
Cuberoot on both sides.
y - 1 = ∛-(2 + x)
y = ∛-(2 + x) + 1
Now,
Substitute in the inverse of g(x).
(62, -3) = (x, y)
(−4, 123) = (x, y)
(3, 1) = (x, y)
(3,−6) = (x, y)
So,
y = ∛-(2 + x) + 1
y = ∛-(2 + 62) + 1
∛-1 = -1
y = -1∛64 + 1
y = -1 x 4 + 1
y = -4 + 1
y = -3
So,
(62, -3) ______(1)
And,
y = ∛-(2 + x) + 1
y = ∛-(2 - 4) + 1
∛-1 = -1
y = ∛(-2 + 4) + 1
y = ∛2 + 1
y = 1.26 + 1
y = 2.26
So,
(-4, 2.26) _______(2)
And,
y = ∛-(2 + x) + 1
y = ∛-(2 + 3) + 1
∛-1 = -1
y = -1∛5 + 1
y = -1 x 1.71 + 1
y = -1.71 + 1
y = -0.71
So,
(3, -0.71) _______(3)
And,
y = ∛-(2 + x) + 1
y = ∛-(2 + 3) + 1
∛-1 = -1
y = -1∛5 + 1
y = -1 x 1.71 + 1
y = -1.71 + 1
y = -0.71
So,
(3, -0.71) ______(4)
Thus,
From (1), (2), (3), (4) we see that,
(62, -3) is the solution to the inverse of g(x).
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find the total cost a) The radius of a circular field is 63 m. Find the perimeter of the field. Also, find the length of wire required to fence it with 5 rounds. =
The perimeter of the circle is 395.64 m, and the length of wire needed to fence it with 5 rounds is 1,978m
How to find the perimeter?We kow that for a circle, the perimeter is equal to its circumference, and the circumference of a circle of radius R is:
C = 2*pi*R
Where pi = 3.14
Then the perimeter of a circle of radius of 63m is:
Perimeter = 2*3.14*63m = 395.64 m
And the length of wire needed to fence it with 5 rounds is 5 times that, so we will get:
total length = 5*395.64 m = 1,978m
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The distance from two golf balls to the hole is 8 feet and 13 feet, respectively. If both balls are hit directly into the hole, the angle formed by their pathways is 64. Find the distance between the golf balls
The distance between the golf balls is determined to be 14 feet.
Let's call the distance between the two golf balls "d".
Using the law of cosines, we can find the value of d by using the angles and the two distances to the hole:
d² = 8² + 13² - 2 * 8 * 13 * cos(64)
d² = 64 + 169 - 104 * cos(64)
d² = 233 - 104 * cos(64)
Next, we'll use a calculator to find the value of cos(64):
cos(64) = 0.37
So,
d² = 233 - 104 * 0.37 = 233 - 38.48
d² = 194.52
Finally, we'll take the square root of both sides to find the value of d:
d = √(194.52) = 14.0
So the distance between the golf balls is 14 feet.
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1
32^1/25 × 2^x = 8^1/4
Work out the exact value of x
Answer:
Step-by-step explanation:
0.267
Find the coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2
The coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2 is (6/ 5 , 0).
What is section formula?The line segment is divided into two pieces by a point, which may or may not be equal. If we know the coordinates of the point, we may calculate the ratio by which the supplied line segment is divided. Additionally, if we are aware of the ratio that the line segment connecting two places has produced, we can locate the point of division. The two can be accomplished using a section formula from coordinate geometry.
The coordinates of the points on the line are:
M = (-3, -3)
N = (4, 2)
m= 3
n = 2
Using the section formula we have:
M(x, y) = (mx2 + nx1 / m+n , my2 + ny1 /m + n)
M(x, y) = ((3)(4) + (2)(-3)) / (3 + 2) , (3)(2) + (2)(-3) / (3 + 2))
M (x, y) = (12 - 6 / 5 , 6. -6 / 5)
M (x, y) = (6/ 5 , 0)
Hence, the coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2 is (6/ 5 , 0).
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How much of the circle is shaded write your answer as a fraction in simplest form one for 1/4 2/7
Step-by-step explanation:
The circle as a whole is one.
So to find the shaded area find a common denominators for both first
1/4 = 7/28
2/7= 8/28
Add the two together
7/28 + 8/28 = 15/28
This is the area taken up the the white fractions areas
Now because the circle is one
28/28 - 15/28 = 13/28
So the area of the blue is
13/28
Hope this helped :)
A father wishes to distribute his 2 hectare field equally among his 4 sons. How many ares will each son's plot measure?
Answer:
50 ares
Step-by-step explanation:
You want the area each of 4 sons will receive if a 2 hectare plot is divided equally among them.
HectareA hectare is 100 ares, so 2 hectares is 200 ares. One quarter of that area is ...
(200 ares)/4 = 50 ares
Each son's plot will be 50 ares.
Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 6 hours. How long will it take them to do the job
working together?
Answer: 4 hours
Step-by-step explanation: the difference (6-2) = 4
The combined rate at which they complete the job is the sum of their individual rates, so their combined rate is 2 + 6 = 8 hours per job.
Therefore, they will do the job in 1/8 of the time it would take either of them working alone, so it will take them 1/8 of 2 hours = 15 minutes to do the job together.
Simplify.
3√27t^27
hi i need steps to simplify the equation for this question!
Bonjour j'ai besoin d'aide.
Merci de votre aide.
Answer: en fait je ne sais pas désolé
Step-by-step explanation: désole.
Given ABCD is a parallelogram.From B draw a line meets CD at M ; from D draw a line meets BC at N such that BM = DN . Intersection of DN and BM is point I. Prove that IA is a bisector of ∠BID
ABCD is a parallelogram and ∠ BID is equal to ∠ BAI, which means that IA is a bisector of ∠BID.
An angle's bisector divides the angle into two identical segments. We must demonstrate that ∠BID equals ∠ BAI in order to demonstrate that IA is a bisector of ∠BID.
Since ABCD is a parallelogram, we have:
AB || CD, which means that ∠ABD is equal to ∠ADC.
BC || AD, which means that ∠ ABC is equal to ∠ DAC.
Adding these equal angles, we have:
∠ABD + ∠ ABC = ∠ ADC + ∠ DAC
∠BDA = ∠CDA
Also, since BM = DN, we have:
∠DBM = ∠ DNM (by vertical angles)
Adding these equal angles, we have:
∠ BDA + ∠ DBM = ∠CDA + ∠ DNM
∠ BID = ∠ BAI
Therefore, we have shown that ∠ BID is equal to ∠BAI, which means that IA is a bisector of ∠BID.
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