Answer:
3
Step-by-step explanation:
so you set up an equation because the sides are equal
10+x=4x+1
then you solve
10=3x+1
9=3x
x=3
10)
M
p
By which rule are these triangles congruent?
A)
AAS
B)
ASA
SAS
D
SSS
Answer:
B)
ASA
Step-by-step explanation:
Angle K, Side KN, Angle N
In a 30-60-90 triangle, the length of the side that is opposite from the 30° angle is 11 inches. What is the length of the hypotenuse in
inches?
Answer:
22 inches
Step-by-step explanation:
Hello!
We are given a 30-60-90 triangle. The angles of the triangle are 30°, 60°, and 90°
The triangle is a right triangle, since one of the angles is 90° (it is a right angle)
We are also given the length of the side opposite from the 30° angle as 11 inches, and we want to find the length of the hypotenuse (the side OPPOSITE of the right angle)
In a right triangle, if we know the length of the side opposite from an angle measuring 30°, then we know that the length of the hypotenuse is TWICE the length of the side opposite to 30°
In other words, if the length of the side opposite to the 30° angle is a, then the length of the hypotenuse is 2a
In this case, a would be 11, and since the length of the hypotenuse is 2a, if we plug 11 as a, it would be 2×11, which would mean the hypotenuse is 22 inches long
Hope this helps!
What algebraic expression could represent the average of 2x, x + 3, and 6x?
Answer:
3x+1
Step-by-step explanation:
(2x+x+3+6x)/3
9x+3/3
3x+1
The final result is a simplified algebraic expression 3x + 1 that represents the average of 2x, x + 3, and 6x.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The average of 2x, x + 3, and 6x can be represented by the algebraic expression (2x + (x + 3) + 6x)/3.
This expression takes the sum of 2x, x + 3, and 6x, and then divides that sum by 3, which is the number of terms being averaged.
Alternatively, the average can be represented by (2x + x + 6x + 3) / 3 = (9x + 3) / 3 = 3x + 1.
In either case, the final result is a simplified algebraic expression that represents the average of 2x, x + 3, and 6x.
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in a correlational study on the relationship between caffeine consumption and heart disease in police officers, the fact that the officers could not be randomly assigned to high and low caffeine groups suggests the results may be due to:
Confounding variables can affect the relationship between caffeine consumption and heart disease in a correlational study of police officers. Controlling for these variables is necessary to accurately assess the relationship.
The fact that the officers in the study could not be randomly assigned to high and low caffeine groups suggests that the results of the study may be due to confounding variables. A confounding variable is a third variable that is correlated with both the independent variable (in this case, caffeine consumption) and the dependent variable (in this case, heart disease). If a confounding variable is present, it can make it difficult to determine the true relationship between the independent and dependent variables.
For example, if the officers who consume more caffeine also have other unhealthy habits (such as smoking or eating unhealthy diets) that increase their risk of heart disease, it may be difficult to determine the true effect of caffeine on heart disease. In this case, the unhealthy habits would be the confounding variable, and controlling for these variables would be necessary to accurately assess the relationship between caffeine consumption and heart disease.
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find the area of the triangle
Answer:
88.28
Step-by-step explanation:
applying formula of area of triangle, 1/2 X base X height.
given.= base= 16.9 height=10.4
so keeping value in formula.
1/2 X 16.9 X 10.4
on solving it will be 88.28
Answer:
The Correct Answer Is 87.88
Step-by-step explanation:
10.4*16.9=175.76
175.76/2=87.88
Do not round ft² = 87.88
Hope this helps everyone using Acellus program!
AB has endpoints A(-2, 5) and B(1, -1). If AB is reflected in the y-axis and rotated 90° counterclockwise about the origin, what are the coordinates of the
endpoints of the image. A"B"?
A"
and B"
The coordinates of the endpoints of the image A''B'', following the rotation and reflection transformation are are;
A''(-5, 2), and B''(1, -1)
What is a reflection transformation?A reflection transformation is a type of transformation that takes each point on a figure and flips or reflects it across a line known as the line of reflection to create a mirror image.
What is a rotation transformation?
A rotation transformation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees about a specified point.
The transformations in the question are a reflection and a rotation
The coordinates of the point (x, y) on the coordinate plane, following a reflection across the y-axis is; (-x, y)
The coordinate of the point (x, y) following a rotation of 90° counterclockwise about the origin is; (-y, x)
Therefore, the coordinates of the image of points A and B following a reflection across the y-axis are;
A(-2, 5) → A'(2, 5)
B(1, -1) → B'(-1, -1)
The coordinates of the image of points A' and B' following a rotation of 90° counterclockwise about the origin are;
A'(2, 5) → A''(-5, 2)
B'(-1, -1) → B''(1, -1)
The coordinates of the endpoints of the image, A''B'' are therefore;
A''(-5, 2) and B''(1, -1)
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What is the code in python to remove ' at the beginning and at the end and also remove the item at index 12?
To remove the single quotation marks ('') at the beginning and end of a string and remove the item at index 12, you can use Python's string manipulation methods and list slicing. First, you can use the strip() method to remove the surrounding single quotation marks. Then, you can convert the string into a list using the list() function, remove the item at index 12 using list slicing, and finally convert the list back into a string using the join() method.
To remove the single quotation marks at the beginning and end of a string, you can use the strip() method. This method removes any leading and trailing characters specified in the argument. In this case, you can pass the single quotation mark ('') as the argument to strip().
Here's an example:
string = "'example string'"
stripped_string = string.strip("'")
After executing this code, the value of stripped_string will be 'example string' without the surrounding single quotation marks.
To remove the item at index 12 from the string, you need to convert it into a list. You can use the list() function for this conversion. Then, you can use list slicing to remove the item at index 12 by excluding it from the list. Finally, you can convert the modified list back into a string using the join() method.
Here's an example:
string_list = list(stripped_string)
string_list.pop(12)
result_string = ''.join(string_list)
After executing this code, the value of result_string will be the modified string with the item at index 12 removed.
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Which of the following is the solution set of the
problem?
O (-∞, -3)
(-∞, -3]
O
[-3,00)
O (-3,00)
DONE
The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;
(-∞, -3]How can the solution set of an inequality be found?A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;
2•x + 3 ≤ -3Solving the above inequality, we have;
2•x + 3 ≤ -3
2•x ≤ -3 - 3 = -6
2•x ≤ -6
Therefore;
x ≤ -6 ÷ 2 = -3
x ≤ -3
Which gives;
-∞ < x ≤ -3-∞ < x ≤ -3 in interval notation is (-∞, -3]
The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;
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I really need help ASAP ILL GIVE BRAINLY
Answer: D.
Step-by-step explanation:
You can start out with the form AX = B and solve for matrix X that would yield the answer
Then X = (A^-1)(B)
A = [1 -1]
[1 1]
A^-1 = (1/(1 - (1)(-1)))*[1 1]
[-1 1]
which can be written as (1/2) * [1 1]
[-1 1]
B = [26]
[6]
(A^-1)(B) = (1/2)*[1 1] [6]
[-1 1] [26]
= (1/2)*[32]
[20]
= [16]
[10]
please answer this for me!!
Answer:
x = 40
y = 8
Step-by-step explanation:
3x-9 = 2x+31
3x-2x = 31+9
x = 40
4y+5 = 2y+21
4y-2y = 21-5
2y=16
y=8
Choose a process that you are comfortable describing or that you have an understanding of. for example, you might describe how to cook a family recipe, maintain a bicycle, beat a challenging video game level, create an app, code a game, sew something, craft something, build something, repair something, draw or paint something, or execute a skilled athletic maneuver. step 2: research the process you chose. a) identify methods for completing the process. b) take notes on important details. step 3: create an outline. outline the process step by step. include specific details to support each step of the process.
To make homemade pizza: Gather ingredients/tools, prepare dough, preheat oven, shape dough, assemble with sauce, cheese, and toppings, bake at 475°F for 12-15 mins, remove, slice, and serve hot. Customize as desired.
Process: How to make a homemade pizza
Gather Ingredients and Tools
Pizza dough (store-bought or homemade)
Tomato sauce
Cheese (mozzarella or your preferred type)
Toppings of choice (e.g., pepperoni, mushrooms, bell peppers, etc.)
Olive oil
Salt
Flour (for dusting)
Rolling pin
Baking sheet or pizza stone
Oven
Prepare the Dough
If using store-bought dough, follow the instructions on the package. If making homemade dough:
a) Combine flour, yeast, salt, and water in a mixing bowl.
b) Knead the dough until it becomes smooth and elastic.
c) Place the dough in a greased bowl, cover it, and let it rise until it doubles in size (usually around 1-2 hours).
Preheat the Oven
Set the oven temperature to 475°F (245°C) and allow it to preheat.
Shape the Dough
Sprinkle flour on a clean surface and place the dough on it.
Roll out the dough with a rolling pin, creating a round or rectangular shape according to your preference.
If you prefer a thinner crust, roll it out more; for a thicker crust, keep it slightly thicker.
Assemble the Pizza
Transfer the shaped dough to a greased baking sheet or pizza stone.
Brush olive oil over the surface of the dough to prevent it from getting soggy.
Spread a layer of tomato sauce evenly over the dough, leaving a small border for the crust.
Sprinkle a generous amount of cheese over the sauce.
Add your desired toppings on top of the cheese.
Bake the Pizza
Place the baking sheet or pizza stone with the assembled pizza in the preheated oven.
Bake for approximately 12-15 minutes or until the crust is golden brown and the cheese is bubbly and melted.
Remove and Serve
Carefully remove the pizza from the oven using oven mitts.
Let it cool for a few minutes before slicing it into desired portions.
Serve hot and enjoy!
Remember to customize the process based on personal preferences and dietary restrictions. Experiment with different toppings and techniques to create your perfect homemade pizza.
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one day, the weather forecast expects a storm may have rainfall at the rate of 1cm per hour. on this rate, how long will the pond be filled
To calculate how long it will take for the pond to be filled with rainfall at a rate of 1cm per hour, we need to know the volume of the pond. This answer seems impractical as it equates to approximately 17,917 years. Therefore, we can conclude that the pond will never fill up with rainfall at a rate of 1cm per hour.
Let's assume the pond is a circular shape with a diameter of 10 meters and a depth of 2 meters. To find the volume, we need to use the formula for the volume of a cylinder, which is πr^2h, where π is approximately 3.14, r is the radius of the pond (5 meters), and h is the depth (2 meters).
So, the volume of the pond is approximately 157 cubic meters (3.14 x 5^2 x 2). Now, we need to convert this volume into centimeters, as the rainfall rate is given in cm/hr. One cubic meter is equal to 100 x 100 x 100 cubic centimeters, which equals 1,000,000 cubic centimeters. Therefore, the pond's volume is 157 x 1,000,000 = 157,000,000 cubic centimeters.
Now, we can calculate how long it will take to fill the pond with rainfall at a rate of 1cm per hour. We divide the volume of the pond by the rate of rainfall, which gives us 157,000,000 / 1 = 157,000,000 hours.
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Please help me with this :
The value for x in the given triangle ABC is 8.The solution is obtained by using the mid-segment theorem.
What is the mid-segment theorem?
A midpoint segment is a portion of a line that connects the midpoints of two triangle sides. According to the theorem, a line segment drawn from the intersection of any two triangle sides will be parallel to the third side and precisely half its length.
In the question, we are given a triangle ABC and we are told that line segment DE is the mid-segment.
Mid segment divides a line into two equal parts.
Since, DE is the mid-segment, so, line segment BC has two parts i.e. BE and EC
BE = EC
We are given EC = 8
So, BE = 8
Hence, the value for x is 8.
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Since there are multiple questions so, the question answered above is attached below
How do you solve : 3x^4 - 11x^3 -x^2 + 19x + 6
You can't use long division in this equation.
Step-by-step explanation:
This is a polynomial so we can use rational roots Theorem to solve the equation.
The rational roots simply states that the roots of a polynomial, in the form of
\(p{x}^{n} + ax {}^{n - 1} + bx {}^{n - 2} .....r {}^{0} \)
The possible roots of the polynomial are the factors of
p/r.
We say r^0 to represent the constant and p to represent the leading coeffceint.
So the rational roots states the possible roots of a polynomial is
the factors of leading coeffceint/ the factors of the constant.
In this case, the polynomial leading coeffecient is 3 and its constant is 6 so we do the factors of 3 divided by the factors of 6.
The factors of 3, are plus or minus 1 and 3. divided by factors of 6 which are plus or minus 1,2,3,6. So our possible roots are
positive or negative (1,1/2, 1/3,1/6, 3, 3/2).
Now, we see which of the following roots will that the polynomial, P will equal zero.
It seems that -1 can work so by definition, (x+1) is the a factor of the polynomial. So now we use synetheic or long division to cancel out that factor.
So our factored version of the polynomial is
\((x + 1)(3x {}^{3} - 14 {x}^{2} + 13x + 6)\)
Now can we continue and factor the right side of the factors.
3 also works so x-3 is a factor as well so
\((3 {x}^{2} - 5x - 2)(x + 1)(x - 3)\)
Now factor the quadratic using factoring by grouping
\(3 {x}^{2} - 5x - 2 = 3 {x}^{2} - 6x + x - 2 = 3x(x - 2) + 1(x - 2) \)
So our factor are
\((3x + 1)(x - 2)\)
So in conclusion our factors are
\((3x + 1)(x - 2)(x + 1)(x - 3)\)
And our x values are -1/3, 2, -1, and 3.
676 x 122 - 45 + 69
Brainliest to whoever answers first
Answer:
82.358
Step-by-step explanation:
You have to use PEMDAS to solve this question. Since M is the first one we have to multiply since M stands for multiplication.
676 • 122 - 45 + 69
82,472 - 45 + 69
Then you add because A is next.
82,472 - 114
Then finish it
82,358
Your answer would be = 82,358
I hope it helps! Have a great day!
Muffin ^^
5 and 4 sevenths times negative 2 and 2 fifths
Answer:
3/2
Step-by-step explanation:
ugygv
Determine the maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD. D=100k,L=140k assume L<100psf,Lr=40k,W=+160k or −100k,E=+180k or −125k
The maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD is 434 kips.
The maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD,
where
D = 100k,
L = 140k, L < 100psf,
Lr = 40k,
W = +160k or −100k, and
E = +180k or −125k is given below:
Design load = 1.2D + 1.6(Lr or S or R) + 0.5(L + Lr or R) + (W or E)
Here, D is the weight of dead load, L is the weight of live load, Lr is the weight of the roof live load, W is the weight of wind load and E is the weight of earthquake load.
Therefore, for the given loads,
D = 100k
L = 140k
Lr = 40k
W = +160k or −100k
E = +180k or −125k
Max load = 1.2D + 1.6(Lr) + 0.5(L + Lr) + W
= 1.2 (100) + 1.6 (40) + 0.5 (140 + 40) + 160
= 120 + 64 + 90 + 160
= 434 kips
Therefore, the maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD is 434 kips.
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consist a right angled triangle PQR right angled at P such that PQ is 6 cm and PR is 8 cm measure PR
Answer:
10
Step-by-step explanation:
by Pythagoras theorem,
PR^2=PQ^2+PR^2
Therefore,PR=√(PQ^2+PR^2)
=√(6^2+8^2)
=√100
=10
The weight of corn chips dispensed into a 12-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 12.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 12-ounce bags contain more than the advertised 12 ounces of chips
The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.
The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips can be determined by finding the area under the normal distribution curve to the right of the mean.
To find this proportion, we can use the z-score formula:
z = (x - mean) / standard deviation
In this case, we want to find the proportion of bags that contain more than 12 ounces, so x = 12 ounces.
z = (12 - 12.5) / 0.2
z = -2.5 / 0.2
z = -12.5
Next, we need to find the cumulative probability associated with the z-score. We can use a standard normal distribution table or a calculator to find this probability.
Looking up the z-score of -12.5 in the table or using a calculator, we find that the cumulative probability is approximately 0.
Therefore, the proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.
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Some doctors believe that a person can lose five pounds, on average, in a month by reducing his or her fat intake and by consistently exercising. Suppose weight loss has a normal distribution. Let X = the amount of weight lost, in pounds, by a person in a month. Use a standard deviation of two pounds. X ~ N(5, 2). Fill in the blanks.
a. Suppose a person lost 10 pounds in a month. The z-score when x = 10 pounds is z = 2.5 (verify). This z-score tells you that x = 10 is ________ standard deviations to the ________ (right or left) of the mean _____ (What is the mean?).
Suppose a person lost 10 pounds in a month. This z-score tells you that x = 10 is 2.5 standard deviations to the right of the mean 5 pounds.
To verify that the z-score when x = 10 pounds is z = 2.5, we can use the formula:
z = (x - μ) / σ
where x is the value of the random variable, μ is the mean, and σ is the standard deviation.
Plugging in the given values, we have:
z = (10 - 5) / 2 = 2.5
This confirms that the z-score when x = 10 pounds is z = 2.5.
To determine what the z-score tells us about the location of x = 10 pounds relative to the mean, we can use the definition of a z-score:
z = (x - μ) / σ
Rearranging the formula, we have:
x = μ + zσ
So, when z = 2.5 and σ = 2, we have:
x = μ + 2.5(2) = μ + 5
This tells us that x = 10 pounds is 5 pounds above the mean. Since the z-score is positive, x = 10 pounds is to the right of the mean.
Therefore, the z-score tells us that x = 10 is 2.5 standard deviations to the right of the mean of 5 pounds.
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What is the solution to the linear equation?
2 + p = 7/3 + 30
O p= 1
Op=2
O p = 8
O p = 10
The equation 2 + p = 7/3 + 30 is a linear equation, the solution to the linear equation is p = 91/3
How to determine the solution to the equation?The equation is given as:
2 + p = 7/3 + 30
Subtract 2 from both sides
p = 7/3 + 30 - 2
Evaluate the difference
p = 7/3 + 28
Evaluate the sum
\(p = \frac{7 + 28 * 3}3\)
Evaluate the sum
p = 91/3
Hence, the solution to the linear equation is p = 91/3
None of the options is correct
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Identify the location of the values square root of 11, square root of 8, and twenty two ninths on the number line.
Number line with points plotted at two and four tenths labeled Point A, two and eight tenths labeled Point B, and three and three tenths labeled Point C.
Point A is square root of 11, point B is square root of 8, and point C is twenty-two ninths.
Point A is twenty-two ninths, point B is square root of 8, and point C is square root of 11.
Point A is twenty-two ninths, point B is square root of 11, and point C is square root of 8.
Point A is square root of 11, point B is twenty-two ninths, and point C is square root of 8.
The location of the values square root of 11, square root of 8, and twenty two ninths on the number line is illustrated below.
What is a number line?It should be noted that a number line simply means a straight line that serves as an abstraction for real numbers.
It should be noted that square root of 11 will be 3.316. The square root of 8 is 2.83 and twenty two ninths on the number line will be around 20.22.
This is important to know the place where each falls on the number line.
Note that an overview was given.
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The restaurant in a large commercial building provides coffee for the occupants in the building. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of .6. A new tenant of the building intends to have a total of 125 new mployees. What is the probability that the new employees will consume more than 240 cups per day?
To solve this problem, we can use the concept of the sampling distribution of the sample mean. The mean number of cups of coffee consumed in a day by all occupants is 2.0 with a standard deviation of 0.6. Since the sample size is large (125 employees) and the population standard deviation is known, we can approximate the sampling distribution of the sample mean as a normal distribution.
The mean of the sampling distribution is equal to the population mean, which is 2.0 cups per day Now, we need to calculate the z-score for the value of 240 cups per day using the formula:
z = (x - μ) / σ,
where x is the desired value (240 cups per day), μ is the mean of the sampling distribution (2.0 cups per day), and σ is the standard deviation of the sampling distribution (0.6 / sqrt(125)).
Plugging in the values, we have:
z = (240 - 2) / (0.6 / sqrt(125)) ≈ 58.01.
Finally, we can use a standard normal distribution table or a calculator to find the probability of obtaining a z-score greater than 58.01. However, since this z-score is extremely large, the probability will be very close to zero.
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what would you have to know about the solution set of a homogeneous system of 18 linear equations in 20 variables in order to know that every associated nonhomogeneous equation has a solution
The solution set of a homogeneous system of 18 linear equations in 20 variables lies in the null space of the coefficient matrix.
To know that every associated nonhomogeneous equation has a solution, we need to ensure that the homogeneous system has a nontrivial solution.
This means that we need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, i.e., whether there exist free variables.
If the rank is less than the number of variables, then there are infinitely many solutions to the homogeneous system, and thus every associated nonhomogeneous equation has a solution.
However,
We also need to ensure that the particular solution to the nonhomogeneous equation does not lie in the null space of the coefficient matrix.
This is equivalent to checking whether the null space of the coefficient matrix is orthogonal to the vector on the right-hand side of the nonhomogeneous equation.
If it is, then the nonhomogeneous equation has a solution.
So, in summary, to know that every associated nonhomogeneous equation has a solution.
We need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, and we need to check whether the particular solution lies in the null space of the coefficient matrix.
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Question is in the picture.
Answer:it should be #2
Step-by-step explanation:
g The two general approaches to forecasting are: historical and associative. qualitative and quantitative. judgmental and qualitative. precise and approximation. mathematical and statistical.
The two general approaches are qualitative and quantitative.
What is Forecasting?Forecasting is a technique that uses past data as inputs to make future predictions by determining the direction of trends in the future.
What is Qualitative forecasting?It is an estimation methodology that uses judgment, other than numerical analysis. This type of forecasting depends upon the knowledge of most experienced employees and consultants to provide predictions for future outcomes.
What is Quantitative forecasting?It is a data-based math process that teams use to understand performance and predict future based revenue on the data and the patterns. Forecasting results gives businesses the ability to make informed decisions on strategies and processes to ensure continuous success
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answer to one out of every seven mathematicians is a philosopher, and one out of every nine philosophers is a mathematician. are there more philosophers or mathematicians?
Based on the information that has been provided, it is not possible to conclude whether there are a greater number of philosophers or mathematicians.
The statement only provides information regarding the proportion of mathematicians to philosophers and vice versa; it does not provide information regarding the total number of people working in either subject. It is possible that there are a greater number of philosophers, a greater number of mathematicians, or an equal number of both. We would need further information, such as the overall number of people in the fields, in order to accurately establish the number of persons who are present in each field specifically.
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help me with this problem offering alot!
Answer:
The surface area of the toy box is 300 cm².
Step-by-step explanation:
The formula for the area of a rectangle is the product of its width and length:
Area = width × lengthThe surface area of the open top rectangular prism is made up of:
One base rectangle 15 cm x 6 cm.Two congruent side rectangles 6 cm x 5 cm.Two congruent side rectangles 15 cm x 5 cm.Therefore, the surface area of the toy box is:
\(\begin{aligned}\textsf{Total S.A.}&=15 \times 6+2(6 \times 5)+2(15 \times 5)\\&=90+2(30)+2(75)\\&=90+60+150\\&=150+150\\&=300\; \sf cm^2\end{aligned}\)
Total Surface Area
2(LB+BH+LH)-15×62(6×5+5×15+15×6)-902(30+75+90)-90390-90300cm²\( \underline{ \underline{ \text{question}}} : \)
In the given figure , AP = BP = PC. Prove that \( \angle\)ABC = 1 rt.angle.
~Thanks in advance ! ♡
Answer:
See Below.
Step-by-step explanation:
In the given figure, AP = BP = PC.
And we want to prove that ∠ABC is a right angle.
Since AP = BP and BP = PC, we can create two isosceles triangles: ΔAPB and ΔCPB.
By the definition of isosceles triangles, in ΔAPB, ∠PAB and ∠PBA are equivalent. Let the measure of each of them be x°.
Likewise, in ΔCPB, ∠PCB and ∠PBC are equivalent.
And since AP = BP = PC, each of the angles∠PCB and ∠PBC will also be equivalent to x°.
And since the sum of the interior angles of a triangle total 180°, we acquire:
\(\angle PAB+\angle PBA+\angle PCB+\angle PBC=180\)
Since they are all equivalent:
\(4x=180\)
Hence:
\(x=45^\circ\)
∠ABC is the sum of ∠PBA and ∠PBC, each of which measures 45°. Hence:
\(\angle ABC=\angle PBA+\angle PBC=45+45=90^\circ\)
Answer:
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The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function f(x) = 10(0.5). What
is the multiplicative rate of change of the function?
The multiplicative rate of change of the exponential function is 0.5.
How to analyze an exponential function
In this problem we have three that are part of a exponential function, whose form is shown below:
\(y = a\cdot r^{x}\) (1)
Where:
a - Initial valuer - Rate of changeWe notice that for Δx = 1, the value of y is halved. Hence, the multiplicative rate of change of the exponential function is 0.5.
To learn more on exponential functions: https://brainly.com/question/14355665
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