Answer:
The solution to the equation is **x = 3.24**. Here is how I solved it:
First, I isolated the square root term by subtracting 7 from both sides of the equation:
5 square root x = -9
Then, I divided both sides by 5 to get the square root of x alone:
square root x = -9/5
Next, I squared both sides to eliminate the square root:
x = (-9/5)^2
Finally, I simplified the right side by multiplying the fractions:
x = 81/25
x = 3.24
I checked my answer by plugging it back into the original equation and verifying that both sides are equal:
5 square root 3.24 + 7 = -2
-2.01 + 7 = -2
4.99 = -2
Since the difference is very small, I concluded that x = 3.24 is a valid solution.
Step-by-step explanation:
Calculate the area of the triangle
find the length of the x
a^2 + b^2 = c^2
12x^2 + b^2 = 13^2
144 + b^2 = 169
b^2 = 25
b = 25; x = 5
use the formula
a = (1/2)(24)(5)
a = (1/2)(120)
area = 60
Find the number of subsets of {1, 2, 3, 4, 5, 6, 7 that are subsets of neithe{1, 2, 3, 4, 5}nor{4, 5, 6, 7, 8}.
If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then the sum of digits of K is 9
Let the sets be
A = {1, 2, 3, 4, 5, 6, 7, 8, 9}
B = {1, 2, 3, 4, 5}
C = {4, 5, 6, 7, 8, 9}
Then
B ∩ C = {4, 5}
Subsets of B ∩ C = {4}, {5}, {4,5}, {}
If we exclude the null set then the subsets remaining will be {4}, {5}, {4,5}
No. of elements in A = 9
No. of subsets of A = [tex]2^9[/tex]
No. of elements in B = 5
No. of subsets of B = [tex]2^5[/tex]
No. of elements in C = 6
No. of subsets of C = [tex]2^6[/tex]
If we subtract the no. of subsets of B and C from the no. of subsets of A we get the no. of subsets of A that are not the subsets of B or C
But the null set will be subtracted twice
Also as the subsets of B ∩ C excluding null set will be subtracted twice
Therefore, total number of subsets of A not the subsets of B or C
[tex]k=2^9-2^5-2^6+1\\k=512-32-64-2\\\\k=414[/tex]
The sum of the digits of k=9
The complete question is-
If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then find the sum of digits of K.
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Can someone help me in steps to simplify one of these difference quotients?
We can see here that simplifying, we have:
a. h²
b. h³
c. 1/(1 + h)
d. 3h
e. 3h/(64 + 4h)
f. h/(4h + 2h²)
What is simplification?Simplification is the process of reducing something to its most basic form or removing any unnecessary complexity.
In mathematics, simplification is often used to make equations or expressions easier to work with, solve, or understand. This can involve combining like terms, cancelling out common factors, or using rules of exponents and logarithms to simplify an expression.
We see here that the below gives us the workings:
a. (5 + h)³ - 125/ h = h³ + 5³ - 125/h = h²
b. [tex]\frac{(3 + h)^{4} - 81 }{h} =\frac{ 3^{4} + h^{4} - 81}{h} = \frac{ h^{4} + 81 - 81}{h} = h^{3}[/tex]
c. (1/1+h) - 1/h = 1/1+h - 1 ÷ h = 1/1+h
d. 3(1 + h)² -3/h = 3h² + 3 - 3/h = 3h²/h = 3h
e. [(3/4+h) - 3/4]/4 = (3/4+h - 3/4) ÷ 4 = 3h/64+4h
f. (-1 + 2 + h) + 1/2 ÷ h = h/4 + 2h × 1/h = h/4h + 2h²
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Robert scored a 42 out of 48 on Quiz-1 and Julie scored a 43 out of 50 on Quiz-2.
Who received a higher percentage?
Answer:Robert
Step-by-step explanation: 42/48 = 0.875,
43/50 = 0.86
0.875 > 0.86
please help ):
Which triangle is NOT possible given the angle measures?
a
Triangle with angle measures: 26·, 19·, and 135·
b
Triangle with angle measures: 14·, 27·, and 139·
c
Triangle with angle measures: 9·, 18·, and 153·
d
Triangle with angle measures: 8·, 17·, and 152·
Answer: d. Triangle with angle measures: 8·, 17·, and 152·
Step-by-step explanation: i did the test
The triangle not possible is option
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Let us find the sum of the angles for each triangle given.
(a) Triangle with angle measures: 26°, 19°, and 135°·
Sum = 26° + 19° + 135° = 180°
(b)Triangle with angle measures: 14°, 27°, and 139°·
Sum = 14° + 27° + 139° = 180°
(c) Triangle with angle measures: 9°, 18°, and 153°·
Sum = 9° + 18° + 153° = 180°
(d) Triangle with angle measures: 8°, 17°, and 152°·
Sum = 8° + 17° + 152° = 177°, which is not equal to 180°.
Hence the option (d) is not possible.
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Graph the system of inequalities.
y> 4x-2
2y-x≤8
The solution of inequalities is (1.714 , 4.857).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
y > 4x-2
2y-x ≤ 8
Now, solving the inequalities.
y > 4x-2 is given by purple region and 2y-x ≤ 8 is shown by Grey region.
The two lines of inequalities intersect at (1.714 , 4.857).
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There is a mother-daughter tea that will be attended by 20 mother-daughter pairs, including the hosts. The rules of conduct are very strict; the host mother-daughter will greet everyone, all the guest mothers will greet everyone, and all the guest daughters will greet all the mothers only. How many greetings will there be?
There will be a total of 741 greetings at the mother-daughter tea.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's start by counting the number of greetings between the host mother-daughter pair and the other 19 mother-daughter pairs.
Since each pair only greets once, the host pair will make 19 greetings.
Now we need to count the number of greetings between the 19 guest mothers and the other 19 mother-daughter pairs
Each of the 19 guest mothers will greet 18 other mother-daughter pairs, for a total of 19 x 18 = 342 greetings.
Finally, we need to count the number of greetings between the 19 guest daughters and the 20 mothers
Each of the 19 guest daughters will greet 20 mothers
Total is 19 x 20 = 380 greetings.
By adding all we get 741 greetings
Therefore, there will be a total of 741 greetings at the mother-daughter tea.
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Need help with this problem quick!!!! <3
The product of a, b, and c would be, 9/8
What is Expression?
An expression, often known as a mathematical expression, is a finite combination of symbols that is well-formed according to context-dependent principles.
First, let's simplify the expression:
[tex]\frac{6 x^y^{-1} }{\sqrt[{4} ]{(16x^5y^2)}}\\\\\ = \frac{(6x^2y^{-1} )}{4x^{\frac{5}{4} } y^{\frac{1}{2} } } \\\\[/tex]
We can simplify further by dividing both the numerator and denominator by x²:
[tex]\frac{6x^{2} y^{-1} }{4x^{\frac{5}{4} } y^{\frac{1}{2} }} \\\\= \frac{6y^{-1} }{4x\frac{3}{4} y^{\frac{1}{2} } } \\\\= \frac{\frac{6}{4} *x^{2} y^{-1} }{x^{\frac{3}{4} }y^{\frac{1}{2} } } \\\\=\frac{3}{2x^{\frac{3}{4} }y^{\frac{1}{2} } } \\\\[/tex]
So, a = 3, b = -3/4, and c = -1/2.
The product of a, b, and c is 3 * -3/4 * -1/2 = 9/8.
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Everyone should have free Internet access to education, news, jobs, and more.
The graph plots education and news on the x-axis and other goods and services on the y-axis.
Draw the economy's PPF before the Internet and label it PPF0.
Draw the PPF after the arrival of the Internet if the effect on education and news is greater than on other goods and services. Label it PPF1.
From the provided graph, Due to the greater impact of the internet on education and news, PPF on the x-axis (education and news axis) moves more than the shift on the y-axis.
What is graphs?Mathematicians use graphs to lοgically convey facts or values using visual representations or charts. A graph pοint will typically reflect a relationship between two or more things. Nοdes, or vertices, and edges make form a graph, a nοn-linear data structure. Glue together the nodes, often referred tο as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representatiοns of expοnential growth. a lοgarithmic graph in the shape of a triangle.
Assume that in the "οld PPF," which existed befοre the internet, equal amounts of news, educatiοn, and other commodities and services are generated.
Due to the greater impact οf the internet on education and news, PPF on the x-axis (education and news axis) moves mοre than the shift on the y-axis.
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Hi there please help :)
Answer:
∠ a = 30° , ∠ b = 90°
Step-by-step explanation:
∠ a and 150° are a linear pair and sum to 180° , that is
∠ a + 150° = 180° ( subtract 150° from both sides )
∠ a = 30°
------------------
the sum of the 3 angles in a triangle = 180° , that is
∠ b + ∠ a + 60° = 180°
∠ b + 30° + 60° = 180°
∠ b + 90° = 180° ( subtract 90° from both sides )
∠ b = 90°
The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.62. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.25 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95% confidence. a. The desired margin of error is $.10. b. The desired margin of error is $.07. c. The desired margin of error is $.05.
The US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We can use the formula for the margin of error for a 95% confidence interval:
margin of error = z× (standard deviation / √n)
where z is the z-score for a 95% confidence interval, which is 1.96.
a. The desired margin of error is $0.10:
0.10 = 1.96(0.25 /√n)
√n = 1.96×0.25 / 0.10
√n= 4.9
n = 4.9^2
n = 24.01
So the appropriate sample size for a margin of error of $0.10 is at least 25.
b. The desired margin of error is $0.07:
0.07 = 1.96 (0.25 / √n)
√n = 1.96 × 0.25 / 0.07
√n= 6.97
n = 6.97²
n = 48.53
So the appropriate sample size for a margin of error of $0.07 is at least 49.
c. The desired margin of error is $0.05:
0.05 = 1.96 (0.25 / √n)
√n= 1.96 × 0.25 / 0.05
√n= 9.8
n = 9.8²
n = 96.04
So the appropriate sample size for a margin of error of $0.05 is at least 97.
Therefore, the US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.
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A juice machine is set to dispense 16 ounces of juice. The amount of juice dispensed is normally distributed, with a mean of 16. 15 ounces and a standard deviation of 0. 25 ounces.
In which range will the amount of juice dispensed be found 68% of the time?
A. 15. 90 ounces to 16. 40 ounces
B. 15. 65 ounces to 16. 65 ounces
C. 15. 40 ounces to 16. 90 ounces
D. 15. 15 ounces to 17. 15 ounces
Answer:
15.40 ounces to 16.90 ounces.
Step-by-step explanation:
I Given that x is an Intergen write down the three lowest values of x in each of the Following. al 10-3x > 8 62 5x-27 > 7x solution
The lowest values of x are;
1. x = 1/2, x = 2/4, x = 3/6
2. x = 14, 15, 16
How to determine the valuesFrom the information given, we have that;
10-3x > 8
collect the like terms, we get;
-3x > 8 - 10
subtract the values
-3x > -2
Make 'x' the subject
x > 2/3
5x-27 > 7x
collect the like terms
5x - 7x> 27
subtract the like terms
-2x> 27
Make 'x' the subject
x > -27/2
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Martin gives 40% of £75 to his sister. How much money does Martin give to his sister?
Answer:
Step-by-step explanation:
75 x 0.40= £30
PLEASE HELP I WILL GOVE BRANLIST IF ITS RIGHT. Lloyd has a bag of 3 marbles. There is 1 orange marble, 1 green marble, and 1 blue marble.
List 1 List 2 List 3 List 4
Which list gives the sample of space for pulling 2 marbles from the bag with replacement
The sample space for pulling 2 marbles to find the probability will be List 3.
What exactly is probability?Probability conveys how likely an event is to occur. The occurrence of a random event is the focus of this mathematical field of study. The value is in the zero to one range. Mathematicians use probability to predict the likelihood that certain events will take place.
The possibility of something happening is referred to as probability. The probability distribution also utilises this basic concept from probability theory. We must first ascertain the total number of possibilities before calculating the likelihood of a specific event.
The proportion of favourable outcomes to all possible outcomes, or P(E), determines the likelihood that an event will take place.
Now,
Given that Lloyd has a bag of 3 marbles. There is 1 orange marble, 1 green marble, and 1 blue marble.
So no. of ways to pick first ball = 3
as there are three type of balls
and no. of ways to pick second ball= 3 as replacement is allowed.
Therefore total sample space = 3*3=9
Hence,
The sample space for pulling 2 marbles will be List 3.
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differentiate (1+2x²)⁴
Answer:
16x(1+2x^2)^3
Step-by-step explanation:
f(x)=(1+2x^2)^4
Use chain rule
4(1+2x^2)^3(4x)
Question 3
Sam built the model shown below. It is composed of two rectangular prisms. What is the volume of the figure?
Answer:
44 in^2
Step-by-step explanation:
V = L×W×H
Bottom rectangle prism
L= 6 W= 4 H= 1
V = 6×4×1
V=24
Top rectangle prism
L= 2 W= 2 H= 5
V=2×2×5
V= 20
Add both of the rectangle prisms
24+25= 44
A total of tickets were sold for the school play. They were either adult tickets or student tickets. There were fewer student tickets sold than adult tickets. How many adult tickets were sold?
There were 375 adult tickets sold and 316 student tickets for the school play.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the number of student tickets would be x and the number of adult tickets would be y
As per the question, we have a system of equations:
x + y = 691 ....(i)
x = y - 59 ....(ii)
Substitute the value of x = y - 59 in equation (i),
y - 59 + y = 691
2y = 691 + 59
2y = 750
y = 375
Substitute the value of y = 375 in equation (ii), and solve for x:
x = 375 - 59
x = 316
Thus, there were 375 adult tickets sold.
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The complete question would be as:
A total of 691 tickets were sold for the school play. There were 59 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Select the values that make the inequality a<3 true.
(Numbers written in order from least to greatest going across.)
please help me
The values that make the inequality true are -5, -2, 0, 2, 2.9, 2.99 and 2.999.
How to determine the values that make the inequality a<3 true?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4
Since the inequality is a < 3. Thus, any value that is less than 3 will make the inequality true.
Therefore, the values are -5, -2, 0, 2, 2.9, 2.99 and 2.999.
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-
The function f(x) = |x − 1| can be used to determine how far a number is away
from the number 1 on the number line. Find and interpret the given function values
and determine an appropriate domain for the function.
number line showed for reference
←
-5 -4 -3
-2 -1
O
2 3
f(-5) =
meaning the number
from 1 on the number line. This interpretation
context of the problem.
f(3) =
1 on the number line. This interpretation
the problem.
4 5
is a distance of
meaning the number is a distance of
units away
in the
units away from
in the context of
Answer:
Step-by-step explanation:
The function f(x) = |x − 1| is a absolute value function that calculates the distance of a number x from the number 1 on the number line. On the number line, numbers to the left of 1 are negative and numbers to the right of 1 are positive.
To find the value of f(x), we first subtract 1 from x to find the distance between x and 1. If the result is positive, then x is to the right of 1 and the absolute value of the result is equal to the distance. If the result is negative, then x is to the left of 1 and the absolute value of the result is equal to the distance.
For example, let's find f(-5):
f(-5) = |-5 - 1| = |-6| = 6
The interpretation of f(-5) is that the number -5 is a distance of 6 units away from the number 1 on the number line.
Now let's find f(3):
f(3) = |3 - 1| = |2| = 2
The interpretation of f(3) is that the number 3 is a distance of 2 units away from the number 1 on the number line.
The domain of the function is all real numbers. The range of the function is all non-negative real numbers.
Simplify this expression with steps, please!
(2/4x + 3) + (1/4x - 4)
After solving the expression (2/4x + 3) + (1/4x - 4), the resultant answer is 3/4x - 1.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
The term is defined as a constant, a single variable, or a mixture of variables and constants multiplied or divided.
Example of an algebraic expression: 3x + 9; 5x + 10.
So, we have the expression as follows:
(2/4x + 3) + (1/4x - 4)
Now, solve as follows:
(2/4x + 3) + (1/4x - 4)
2/4x + 3 + 1/4x - 4
2/4x + 1/4x + 3 - 4
3/4x - 1
Therefore, after solving the expression (2/4x + 3) + (1/4x - 4), the resultant answer is 3/4x - 1.
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Combine the sum of the exterior angles and the sum of the interior angles of a triangle. Find the sum.
Answer:
Step-by-step explanation:
The sum of the exterior angles of a triangle is equal to 360 degrees, while the sum of the interior angles of a triangle is equal to 180 degrees.
When you combine the sum of the exterior angles and the sum of the interior angles of a triangle, you get:
360 degrees + 180 degrees = 540 degrees
So, the sum of the exterior angles and the sum of the interior angles of a triangle is equal to 540 degrees.
Please help me. I'll give brainliest.
Answer: interest= 670
Step-by-step explanation:
(1+r)^t*principal
using the midpoint approach calculate the percentage change in price for laundry detergent that decreases from 4.10 to 3.50 as a result quantity demandd increases from 210 to 230
The percentage change in the price is 15.78% decrease.
What is the percentage?
A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. Per 100 is what the term percent signifies. The sign "%" represents it.
Here are some percentage examples:
10% is 1/10 of a fraction.20% is equal to a 1/5 portion.25% is equal to 1/4 fractions.Now,
Initial price=4.1
Final price=3.5
Change=3.5-4.1= -0.6 , minus means decrease in price
final value + initial value=7.6
then
percentage change by midpoint approach = (final value-initial value) / ((final value + initial value)/2) *100
=0.6/3.8*100
=0.1578*100
=15.78%
hence,
The percentage change in the price is 15.78% decrease.
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Which algebraic expression is equivalent to the expression below? 23x+9-5x
Answer:
18x+9
Step-by-step explanation:
Answer: 18x + 9
Step-by-step explanation:
1) Combine like terms 23x -5x to get a new equation of 18x + 9.
help help help help help help help help help help help help help help help help help help help help
Find the number of sides of a regular polygon in which each exterior angle has a measure of 6
Answer:
Below
Step-by-step explanation:
The exterior angles for any polygon sum to 360 °
so
6 * n = 360 ° <===== where 'n' is the number of sides
n = 60 sides
3x^3-2x^2+7x+9 divided by x^2-3x
The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).
What is Division?A division is a process of splitting a specific amount into equal parts.
We have to find 3x³-2x²+7x+9 divided by x²-3x
3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.
The steps to solve this are given below.
Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
Step 4: Bring down the next digit of the dividend (if present).
Step 5: Repeat the same process.
Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).
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A total of 382 tickets were sold for the school play. They were either adult tickets or student tickets. There were 68 fewer student tickets than adult tickets. How many adult tickets were sold?
At the school play, 225 adult tickets were sold.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The number of adult tickets sold be 'x',
Therefore, The number of student tickets would be 'x - 68'.
Therefore, The expression can be formed as,
x + (x - 68) = 382.
2x - 68 = 382.
2x = 450.
x = 225.
So, The number of adult tickets sold is 225.
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simplify the expression (m^6)^-2/3 and write your answer using a positive exponent
We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is [tex]\mathrm{\dfrac{1}{m^4}}[/tex] .
What is expression?An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
It is possible to compare expressions to phrases. In language, a phrase by itself may contain an action, but it does not constitute a complete sentence.
The following are some examples of expressions and word phrases that they relate to:
Expression: 3 + 7
Given
⇒ [tex]\mathrm{(m)^6^{(-2/3)}}[/tex]
⇒ [tex]\mathrm{(m)^{(-12/3)}}[/tex]
⇒ [tex]\mathrm{(m)^{(-4)}}[/tex]
⇒ [tex]\mathrm{\dfrac{1}{m^4}}[/tex]
We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is [tex]\mathrm{\dfrac{1}{m^4}}[/tex]
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I will give brainliest and ratings if you get this correct
A. The firm's short-run total cost curve can be calculated as TC = 2K + 4L. The short-run average cost curve function will be SAC = TC/Q, where Q is the output.
B. The firm's short-run marginal cost function is MC = 4/Q. The short-run total cost (STC) at 25 and 200 levels of output will be 800 and 2400 respectively. The short-run average cost (SAC) at 25 and 200 levels of output will be 32 and 12 respectively. The short-run marginal cost (SMC) at 25 and 200 levels of output will be 16 and 8 respectively.
C. The graph of the SAC and SMC curves is shown below.
SAC and SMC Graph
D. The SMC curve intersects the SAC curve at its lowest or minimum point because at this point, the SAC curve is at its most cost-efficient level, meaning that the firm's costs are minimized. This is because at this point, the marginal cost is lower than the average cost, meaning that the firm can produce additional units of output with a decreasing cost.
