Answer:
5 sqrt(6) = x
Step-by-step explanation:
The pythagorean theorem states
a^2 + b^2 = c^2
Where a and b are the legs and c is the hypotenuse
7^2 + (sqrt(101))^2 = x^2
49+101 = x^2
150 = x^2
Take the square root of each side
sqrt(150) = sqrt(x^2)
sqrt(25*6) = x
5 sqrt(6) = x
What is the range of f?
O -15≤x≤35
Oy > 15
Oy> 35
O all real numbers
The possible values for the range of f(x) are given by:
y > 15.y > 35.all real numbers.What is the range of a function f(x)?The range of a function f(x) is the set that contains all possible output values for the function. Looking at the graph of the function, the range is composed by the values of y.
In this problem, the function is not given, so I can't give you an exact answer, but since the range is composed by the values of y, the first option is not possible, and the possible values for the range of f(x) are given by:
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Use the expression 4•(12) What is the value of the expression
Answer:
48
Step-by-step explanation:
12 x 4 = ?
Can I get a crown?
simplify 15a^2 * 4c * 5ab
Answer: 300a^3cb
Step-by-step explanation:
\($$Simplify the following:$$15 \times 4 \times 5 a^{2} c a b$$$$\begin{aligned}&15 a^{2} \times 4 c \times 5 a b=15 a^{2+1} \times 4 c \times 5 b: \\ \\&15 \times 4 \times 5 a^{2+1} c b\end{aligned}$$$$\begin{aligned}&2+1=3 \\ \\&15 \times 4 \times 5 a^{3} c b \end{aligned}$$$$\begin{aligned}&15 \times 4=60 \\ \\&60 \times 5 a^{3} c b\end{aligned}$$$$60 \times 5=300$$Answer:$$300 a^{3} c b$$\)
Write an equation that solves this table.
4
5
6
7
12
0
2
4
6
Answer:
y=2x-8 x=12 y=16
Step-by-step explanation:
the function is y=2x-8
if x=12
y= 2 (12)-8=16
A standard number cube is rolled. Calculate: P(rolling 1 or 3)
Answer:
the probability is:
P(A) 2/6 =1/3
Now let's take rolling a prime number:
A prime number is a natural number greater than 1 which can only be divided without a remainder by 1 and itself. So from the numbers on the cube prime numbers are:
2, 3 and 5. The probability of getting a prime number in a single roll is:
P(B) =3/6=1/2
Now to calculate the probability of A and B
you have to multiply both probabilities:
P(A-B)=P(A) . P(B) = 1/3 . 1/2 = 1/6
Step-by-step explanation:)
What is the formula for calculating the surface area of a sphere?
Answer:
Please give brainliest
Step-by-step explanation:
c
A wedding tent is built in the shape of a right rectangular prism topped with a rectangular pyramid. The dimensions of the prism are 32 ft by 35 ft by 9 ft, and the height of the pyramid is 4 ft. Find the total volume of the tent. Round your answer to the nearest tenth if necessary. (Note: diagram is not drawn to scale.)
The total volume of the wedding tent is 14560 ft³.
To find the total volume of the wedding tent, we need to calculate the volume of both the rectangular prism and the rectangular pyramid, and then add them together.
The volume of a rectangular prism is given by the formula:
Volume_prism = length * width * height
In this case, the dimensions of the prism are 32 ft by 35 ft by 9 ft, so the volume of the prism is:
Volume_prism = 32 ft * 35 ft * 9 ft = 10080 ft³
The volume of a rectangular pyramid is given by the formula:
Volume_pyramid = (length * width * height) / 3
The dimensions of the top of the pyramid are the same as the base of the prism, so the length and width of the pyramid are both 32 ft. The height of the pyramid is 4 ft. Using these values, we can calculate the volume of the pyramid:
Volume_pyramid = (32 ft * 35 ft * 4 ft) / 3 = 4480 ft³
To find the total volume of the tent, we add the volume of the prism and the volume of the pyramid:
Total_volume = Volume_prism + Volume_pyramid
Total_volume = 10080 ft³ + 4480 ft³ = 14560 ft³
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HELP ME QUICKLY!!!!!!!!!!!!!!!It takes Luis 15
minutes to read 3
pages. How long
Will it take him to
read 90 pages?
Answer:
450 min hope this helps!
Step-by-step explanation:
Answer
It will take him 450 minutes to read 90 pages.
Explanation
Luis can read 3 pages every 15 minutes.
You are trying to find how long it will take him to read 90 pages.
Set up this ratio.
\(\frac{15}{3} =\frac{x}{90}\)
To get from 3 to 90, you multiply by 30. Do the same thing to 15.
15 times 30 is 450.
It will take Luis 450 minutes to read 90 pages.
If the volume of the pyramid is 12 cubic inches,
what is the height of the pyramid, in inches?
Answer:
6
Step-by-step explanation:
h=3(12/6)
simplify 15a+21b-6a-4
Answer:
9a+21b-4
Step-by-step explanation:
first of all combine the like terms
15a + 21b - 6a - 4
= 9a + 21b - 4 Ans.
The simplified expression of 15a+21b-6a-4 is 9a+21b-4
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 15a+21b-6a-4
Fifteen times of a plus twenty one times of b minus six times of a minus four.
a and b are the variables and plus, minus are the operators
Add the like terms in the expression
15a-6a+21b-4
Fifteen times of a and minus six times of a are the like terms.
So add these like terms.
When 15 and -6 are added we get 9
So the expression becomes as Nine times of a plus twenty one times of b minus four.
9a+21b-4
Hence, the simplified expression of 15a+21b-6a-4 is 9a+21b-4
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Factor the following two matrices into A = XΛX^−1:
We may compute XX-1 and compare it to A to ensure that this factor ization is accurate: X * * inv (X)
How are matrices solved?We must determine A's eigenvalues and eigenvectors in order to factor A into XX1.
A = [1 2; 0 3] is the initial matrix, therefore let's start there.
Det(A - I) = (1-)(3-) - 0*2 = 2 - 4 + 3 is the characteristic polynomial of A.
The eigenvalues of the characteristic polynomial are 1 = 1 and 2 = 3, which are determined by finding its roots.
We solve the system of linear equations (A - I)x = 0 for each eigenvalue in order to determine the eigenvectors. 1 = 1 results in the equation:
(A - λ1I)x = (1-1) (1-1) 2; 0 (3-1)x = 0
which is equivalent to:
[0 2; 0 2]x = 0
x1 = [1; 0] is an eigenvector for the number 1. 2 = 3 results in the equation:
(A - λ2I)x = (1-3) (1-3) 2; 0 (3-3)x = 0
which is equivalent to:
[-2 2; 0 0]x = 0
x2 = [1; 1] is one of the eigenvectors for 2.
As a result, A can be expressed as A = XX-1, where X = [1 1; 0 1].
Λ = [1 0; 0 3]
We may compute XX-1 and compare it to A to ensure that this factorization is accurate: X * * inv (X)
We should now have access to the original matrix A.
A = [1 1; 3 3] is the second matrix, therefore let's factor it now:
Det(A - I) = (1-)(3-) - 3*1 = 2 - 4 is the characteristic polynomial of A.
The eigenvalues of the characteristic polynomial are 1 = 0 and 2 = 4, which are determined by finding its roots.
We solve the system of linear equations (A - I)x = 0 for each eigenvalue in order to determine the eigenvectors.
We get the equation: for 1 = 0.
(A - λ2I)x = (1-4) (1-4) 1; 3 (3-4)x = 0
which is equivalent to:
[-3 1; 3 -1]x = 0
x2 = [1; 3] is an eigenvector for the number 2.
As a result, A can be expressed as A = XX-1, where X = [-1 1; 1 3].
Λ = [0 0; 0 4]
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please help me :)
i will give your answer a brainiest if it’s correct!
Answer:
a) 6ab
b) c⁶
c) 10y⁷
d) 12g⁴h⁵
30 points for the answer
Answer:
1. James encourage Dan and Andy to work together
2. James encourage Dan and Andy to offer a solution.
3. James let's Dan and Andy express their individual opinion in an open manner
4. James discuss........
Answer: I got drip
Step-by-step explanation: drip drip drip
what is the prime factorization of 90
Answer:So, the prime factors of 90 are 2 × 3 × 3 × 5 or 2 × 32 × 5, where 2, 3 and 5 are the prime numbers.
Step-by-step explanation:
Max and Molly plan to put down all-weather carpeting on their porch. The length of the porch is 9 ft longer than twice the width, and the perimeter is 138 ft.
Answer:
Step-by-step explanation:
What
is an arithmetic sequence with a common difference of −2?
Answer:
An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.
To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.
Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is
20,18,16,14,12
In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.
The instructor noted the following scores on the last quiz of the semester for 8 students. Find the range of this data set 59,61,83,67,81,80,81,100
answer: the range is 41.
to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.
then we subtract the minimum from the maximum.
59 - 100 = 41.
Can anyone help me with this question please
Answer:
1 = 130° , 2 =50° , 3 = 85°, 4=45°
Step-by-step explanation:
1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}
2 = 180 - 1 { angles on a straight line equals 180}
= 180 -130 = 50°
4 = 180 - 135 = 45° { angles on a straight line equals 180}
3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}
3 = 135-50 = 85°
Note : sum of opposite interior angles equals external exterior angle, let's prove it:
If we look at the triangle at the bottom left, we have :
85, 45 and r { let's denote r as the missing angle}
So 85 + 45 + r = 180° { sum of angles of a triangle}
By simple arithmetic
r = 180 - ( 85+45) = 180 - 130 = 50°
but r + 4 = 180° { sum of angles in a straight line equals 180°}
4 = 180 - 50 = 130°
So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Create a factorable polynomial with a GCF of 6. Rewrite that polynomial in two
other equivalent forms. Explain how each form was created. (10 points)
Polynomial: 6x^3 + 12x^2 - 18x
Form 1: 6(x^3 + 2x^2 - 3x)
Explanation: This form was created by factoring out the GCF of 6 from each term in the polynomial.
Form 2: 6x(x^2 + 2x - 3)
Explanation: This form was created by factoring out the GCF of 6x from each term in the polynomial.
In both forms, the GCF of 6 allows us to factor out common factors and simplify the polynomial expression while preserving its original meaning.
To create a factorable polynomial with a greatest common factor (GCF) of 6, we can start by considering the common factors of the terms. Let's construct a polynomial:
Polynomial: 6x^3 + 12x^2 - 18x
To rewrite this polynomial in two other equivalent forms, we can factor out the GCF from each term and simplify.
Form 1: 6(x^3 + 2x^2 - 3x)
In this form, we factored out the GCF of 6 from each term: 6x^3/6 = x^3, 12x^2/6 = 2x^2, and -18x/6 = -3x.
Form 2: 6x(x^2 + 2x - 3)
In this form, we factored out the GCF of 6x from each term: 6x^3/6x = x^2, 12x^2/6x = 2x, and -18x/6x = -3.
We created each form by identifying the common factors in the polynomial and factoring them out. This process allows us to rewrite the polynomial in equivalent forms that emphasize different aspects.
In Form 1, we factored out the GCF of 6, leaving the remaining polynomial inside the parentheses. This form highlights the fact that the polynomial can be written as the product of the GCF and the remaining terms.
In Form 2, we factored out the GCF of 6x, again leaving the remaining polynomial inside the parentheses. This form emphasizes the fact that the polynomial can be written as the product of the GCF and another factor, in this case, x.
By rewriting the polynomial in these two forms, we have created equivalent expressions that emphasize the presence of the GCF and demonstrate the polynomial's factorability.
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Caleb has 12 grams of tea. He bought 5/4 of that amount for his mom. How many grams did Cameron get his mom?
Answer: Caleb bought 15 grams for his mom
Step-by-step explanation:
5/4 is equal to 1.25, so Caleb bought 1.25 x 12 grams.
1.25 x 12 = 15 grams.
What is the slant height x of this square pyramid?
What is an equivalent function to f(x)=(x-2)^3
Answer:
x^3-6x^2-4x-8
Step-by-step explanation:
First you would multiply (x-2) by itself (x-2) to get
x^2-2x-2x+4
then you would combine like terms
x^2-4x+4
Then you would multiply that by x-2
(x^2-4x+4)(x-2)
x^3-2x^2-4x^2-8x+4x-8
then you combine like terms
x^3-6x^2-4x-8
Find the domain of the inverse function w-1 (x) . Express your answer as in inequality
Answer:
ANSWER
Step-by-step explanation:
Without knowing the specific function w(x), it is impossible to determine the domain of the inverse function w^-1(x). However, in general, the domain of an inverse function is the range of the original function, and vice versa.
If we assume that w(x) is a one-to-one function (which is necessary for it to have an inverse function), we can determine the range of w(x) and use it to find the domain of w^-1(x).
For example, if we know that w(x) is a function that takes all real numbers except x=2, then the range of w(x) is (-∞,2) U (2,∞). The domain of w^-1(x) is then the same as the range of w(x), which is (-∞,2) U (2,∞). Therefore, the domain of w^-1(x) is x ≠ 2.
Without more information about w(x), we cannot determine the domain of w^-1(x) more precisely.
A teacher wants to know students post-graduation plans. He surveys his homeroom class and learns that most students plan to become soldiers. The inference is valid or not valid
Based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid.
The teacher surveyed his homeroom class about their post-graduation plans. He found out that most of his students plan to become soldiers.
An inference is a conclusion that can be drawn from a given set of data. In this case, the inference that can be made is that a significant number of students in the homeroom class plan to become soldiers.Therefore, the inference is valid based on the data provided.
However, it is essential to keep in mind that the sample size in the homeroom class is relatively small and may not be representative of the entire population. If the teacher had surveyed a more extensive and diverse population, the results might have been different.
In conclusion, based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid. However, this may not apply to the entire population, and it is crucial to consider the sample size when drawing inferences.
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SOMEONE PLEASE HELP ASAPP I NEED HELP
Answer:
11
Step-by-step explanation:
A weather forecaster predicts that the May rainfall in a local area will be between 2 and 8 inches but has no idea where within the interval the amount will be. Let x be the amount of May rainfall in the local area, and assume that x is uniformly distributed over the interval 2 to 8 inches.
(a) Calculate the expected May rainfall. (Round your answer to 1 decimal place.) μx
(b) What is the probability that the observed May rainfall will fall within two standard deviations of the mean?
Within one standard deviation of the mean? (Round all intermediate and final answers to 4 decimal places.)
Probability of May rainfall will fall within two SD Probability of May rainfall will fall within one SD
a) The expected May rainfall is 5.0 inches.
b) The probability of May rainfall falling within one standard deviation of the mean is 0.6827, and within two standard deviations is 0.9545.
(a) To calculate the expected May rainfall, we need to find the mean (μx) of the uniform distribution. The mean of a uniform distribution can be found using the formula:
μx = (a + b) / 2
where a and b are the lower and upper limits of the distribution, respectively. In this case, a = 2 and b = 8. So,
μx = (2 + 8) / 2
μx = 10 / 2
μx = 5
(b) To find the probability that the observed May rainfall will fall within one and two standard deviations of the mean, we first need to calculate the standard deviation (σx) of the uniform distribution. The formula for the standard deviation of a uniform distribution is:
\(σx = √((b - a)^2 / 12)\)
Using the values of a and b from before, we have:
\(σx = √((8 - 2)^2 / 12)\)
σx = √(36 / 12)
σx = √3
For a uniform distribution, the probabilities of falling within one and two standard deviations of the mean are as follows:
- Within one standard deviation (±1σx): 68.27% or 0.6827
- Within two standard deviations (±2σx): 95.45% or 0.9545
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Q2: Write in descriptive form a. A=10, 20, 30 --------- Ans
The descriptive form A=10, 20, 30...... is A = {x : x is a multiple of 10}
How to write the descriptive form?The set is given as:
A=10, 20, 30......
Notice that the numbers 10, 20 and 30 are all multiples of 10.
This means that the set A contains the multiples of 10.
Hence, the descriptive form A=10, 20, 30...... is A = {x : x is a multiple of 10}
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Consider the function f(x)=x^2+bx−21, where b is a constant. If the function has an axis of symmetry at x=2, what is the value of b?
Answer:
2x+b
Step-by-step explanation:
f(x)=x
2
+bx−21
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax
n
is nax
n−1
.
2x
2−1
+bx
1−1
Subtract 1 from 2.
2x
1
+bx
1−1
Subtract 1 from 1.
2x
1
+bx
0
For any term t, t
1
=t.
2x+bx
0
For any term t except 0, t
0
=1.
2x+b×1
For any term t, t×1=t and 1t=t.
2x+b
Please give me width and height, no links
Answer:
I believe the answer is 341 hope this helps