Answer:
x=3
Step-by-step explanation:
-(x-10)=7
-x+10=7
-x=-3
x=3
-(3-10)=7
Christian is planning a vacation and finds an airplane ticket that cost 180$. He found a promo code offering 17% off. Write a single algebraic expression that can be used to find the cost of Christian’s ticket after the discount.
Answer:
83/100 x 180
Step-by-step explanation:
We have to find the cost of the ticket after the discount.
100% - 17%= 83%
83% of the total percentage of the original price that he needs to pay.
So we do:
83/100 x 180
So, this would be the expression.
Hope this helps!:)
Solve the following equations: e^−x^−e^x =3
We have to find the value of x for the given equation e^(−x^)−e^x =3. Here we can use a small trick to get the solution. We know that e^-x is the reciprocal of e^x. So we can replace e^-x with 1/e^x. Now we have the equation e^(−x^)−e^x =3 in the form e^x - 1/e^x = 3.
This is a quadratic equation in the form ax^2 + bx + c = 0. Here a = 1, b = 0, c = -3. We can solve this quadratic equation to get the value of x.
Given equation is e^(−x^)−e^x =3.We can replace e^-x with 1/e^x.Now the equation is e^(x) - 1/e^(x) = 3.
Let's take e^x as a variable and solve the equation:e^x - 1/e^x = 3Multiplying both sides by e^x, we get e^x * e^x - 1 = 3e^xNow e^(2x) - 3e^x - 1 = 0.
This is a quadratic equation in the form ax^2 + bx + c = 0. Here a = 1, b = -3, c = -1.
We can solve this quadratic equation using the quadratic formula which is given as:x = [-b ± sqrt(b^2-4ac)]/2a.
Substituting the values, we get:x = [-(-3) ± sqrt((-3)^2-4(1)(-1))]/2(1)x = [3 ± sqrt(13)]/2Hence the value of x is x = [3 ± sqrt(13)]/2.
We can solve the given equation e^(−x^)−e^x =3 using a small trick. We know that e^-x is the reciprocal of e^x. So we can replace e^-x with 1/e^x. Now we have the equation e^(−x^)−e^x =3 in the form e^x - 1/e^x = 3. This is a quadratic equation in the form ax^2 + bx + c = 0.
Here a = 1, b = 0, c = -3. We can solve this quadratic equation to get the value of x.We have, e^x - 1/e^x = 3Multiplying both sides by e^x, we get e^x * e^x - 1 = 3e^xNow e^(2x) - 3e^x - 1 = 0This is a quadratic equation in the form ax^2 + bx + c = 0. Here a = 1, b = -3, c = -1.
We can solve this quadratic equation using the quadratic formula which is given as:x = [-b ± sqrt(b^2-4ac)]/2aSubstituting the values, we get:
\(x = [-(-3) ± sqrt((-3)^2-4(1)(-1))]/2(1)x = [3 ± sqrt(13)]/2So the value of x is x = [3 ± sqrt(13)]/2.\)
Hence the solution of the equation e^(−x^)−e^x =3 is x = [3 ± sqrt(13)]/2.
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Most elements exist as components of compounds rather than in a free state. Explain why?
Most elements exist as components of compounds rather than in a free state because of their tendency to form chemical bonds with other elements.
Elements in their free state have a higher energy state and are typically more reactive. By forming compounds, elements can achieve a more stable configuration and lower their energy level.
Compounds are formed when elements chemically combine with each other through sharing, gaining, or losing electrons. This process allows the elements to achieve a full outer electron shell, which is the most stable electron configuration. This stability is achieved by following the octet rule, which states that elements tend to gain, lose, or share electrons to have eight electrons in their outermost shell (except for hydrogen and helium, which require only two electrons).
Additionally, compounds often have different properties and characteristics compared to the individual elements. This is because the chemical bonds between the elements in a compound create new structures and arrangements of atoms, resulting in unique properties. These properties make compounds valuable for various purposes, such as in medicine, technology, and industry.
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Give the name (monomial, binomial,
trinomial, etc.) and the degree of the
polynomial.
-5x7
Name??
Degree?
Answer:
Name? : Monomial
Degree? : 7
Step-by-step explanation:
Terms for identifying a polynomial Monomial - A polynomial with 1 termBinomial - A polynomial with 2 termsTrinomial - A polynomial with 3 termsThe given polynomial, -5x^7 has only 1 term meaning that it is a monomial.
The degree of a polynomial is the sum of the exponents.
Here, there is only 1 exponent, which is 7, therefore the degree of the polynomial is simply 7
The name of the polynomial is monomial.
The degree of the polynomial is 7.
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Consider the curve in R2 defined by the parametric equations x=t^2,y=−1/4t t>0. (a) Determine the points on the curve, if there are any, at which the tangent line is parallel to the line y=x. (Hint: Vectors parallel to y=x are ones whose components are equal.) (b) Determine the points on the curve at which it intersects the hyperbola xy=1.
(a) The curve defined by the parametric equations x = t^2, y = -1/4t (t > 0) represents a parabolic trajectory, the point of intersection between the curve and the hyperbola is (4∛2, -1/(4∛2)).
To find the points on the curve where the tangent line is parallel to the line y = x, we need to determine when the slope of the tangent line is equal to 1.
The slope of the tangent line is given by dy/dx. Using the chain rule, we can calculate dy/dt and dx/dt as follows:
dy/dt = d/dt(-1/4t) = -1/4
dx/dt = d/dt(\(t^2\)) = 2t
To find when the slope is equal to 1, we equate dy/dt and dx/dt:
-1/4 = 2t
t = -1/8
However, since t > 0 in this case, there are no points on the curve where the tangent line is parallel to y = x.
(b) To determine the points on the curve where it intersects the hyperbola xy = 1, we can substitute the parametric equations into the equation of the hyperbola:
\((t^2)(-1/4t) = 1 \\-1/4t^3 = 1\\t^3 = -4\\\)
Taking the cube root of both sides, we find that t = -∛4. Substituting this value back into the parametric equations, we get:
x = (-∛4)^2 = 4∛2
y = -1/(4∛2)
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A sprinkler that sprays water in a circular area can spray up to a radius of 22ft what is the maximum area of lawn that can be watered by the sprinkler use 3.14 to approximate date for Pie enter your answer as a decimal rounded to the nearest tenth in the Box
[ ] ft^2
To find the maximum area of the lawn that can be watered by the sprinkler, we can use the formula for the area of a circle:
A = πr^2
Given that the radius of the sprinkler's spray is 22ft, we can substitute this value into the formula:
A = 3.14 * (22)^2
A ≈ 3.14 * 484
A ≈ 1519.76
Rounded to the nearest tenth, the maximum area of the lawn that can be watered by the sprinkler is approximately 1519.8 ft^2.\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}\)
The total revenue for a company in billions of dollars) can be approximated by the function f(x)=4190.00, where x = 7 corresponds to the year 2007 (a) What was the total revenue in 2012? (b) What was the first full year in which revenue exceeded $134 bilion? (a) The total revenue in 2012 was approximately $billion (Type an integer or decimal rounded to the nearest hundredth as needed.) (b) The first full year in which revenue exceeded $134 billion was
(a) Total revenue in 2012, we substitute x = 2012 into the given function f(x) = 4190.00, where x = 7 corresponds to the year 2007.
(b) The value of x, when rounded up, will represent the first full year.
(a) To find the total revenue in 2012, we substitute x = 2012 into the given function f(x) = 4190.00.
f(2012) = 4190.00
Therefore, the total revenue in 2012 was approximately $4190 billion.
(b) To determine the first full year in which revenue exceeded $134 billion, we set the function f(x) = 134 and solve for x.
4190.00 = 134
This equation is not possible since 4190.00 is significantly larger than 134.
However, let's consider the correct equation:
134 = 4190.00
By solving this equation, we find:
x ≈ 0.03198
This means that the first full year in which revenue exceeded $134 billion was approximately 0.032 years after the year 2007.
To convert this to a full year, we can round up to the nearest whole number. Therefore, the first full year in which revenue exceeded $134 billion would be 2007 + 1 = 2008.
Therefore, the first full year in which revenue exceeded $134 billion was 2008.
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William is thinking of 2 numbers. The larger number is four less than two times the smaller
number. The sum of the numbers is 104. What are William's numbers? Please write your
answer in a sentence.
Answer:
The numbers are 36 and 68.
Step-by-step explanation:
Let the smaller number be x.
"The larger number is four less than two times the smaller
number."
The larger number is
2x - 4
The sum of the numbers is x + 2x - 4, or 3x - 4.
"The sum of the numbers is 104."
3x - 4 = 104
3x = 108
x = 36
The smaller number is 36.
The larger number is 2x - 4, or
2x - 4 = 2(36) - 4 = 72 - 4 = 68
The larger number is 68.
Answer: The numbers are 36 and 68.
Consider the linear optimization model
Minimize xx−3yy
Subject to 6xx− yy ≥18
3xx+ 2yy ≤24
xx, yy ≥0
(a) Graph the constraints and identify the feasible region.
(b) Choose a value and draw a line representing all combinations of x and y that make the objective
function equal to that value.
(c) Find the optimal solution. If the optimal solution is at the intersection point of two constraints,
find the intersection point by solving the corresponding system of two equations.
(d) Label the optimal solution(s) on your graph.
(e) Calculate the optimal value of the objective function.
Recall the Sonoma Apple Products Company’s problem from Assignment #2.
(a) Enter the model in Excel and use Solver to find the optimal solution. Submit your
Excel file (not a screen capture).
(b) How many jars of applesauce and bottles of apple juice should they produce?
(c) How much should they spend on advertising for applesauce and apple juice?
(d) What will their profit be?
(a) To graph the constraints, we can rewrite them in slope-intercept form:
1) 6xx - yy ≥ 18
-yy ≥ -6xx + 18
yy ≤ 6xx - 18
2) 3xx + 2yy ≤ 24
2yy ≤ -3xx + 24
yy ≤ (-3/2)xx + 12
The feasible region is the area that satisfies both inequalities. To graph it, we can plot the lines 6xx - 18 and (-3/2)xx + 12 and shade the region below both lines.
(b) To draw a line representing all combinations of x and y that make the objective function equal to a specific value, we can choose a value for the objective function and rearrange the equation to solve for y in terms of x. Then we can plot the line using the resulting equation.
(c) To find the optimal solution, we need to find the point(s) within the feasible region that minimize the objective function. If the optimal solution is at the intersection point of two constraints, we can solve the corresponding system of equations to find the coordinates of the intersection point.
(d) After finding the optimal solution(s), we can label them on the graph by plotting the point(s) where the objective function is minimized.
(e) To calculate the optimal value of the objective function, we substitute the coordinates of the optimal solution(s) into the objective function and evaluate it to obtain the minimum value.
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Write an equation is point slope form of a line given that the slope is 2/3 and that the line goes through the point (5,-2)
Answer:
\((y+2)=\frac{2}{3} (x-5)\)
Step-by-step explanation:
Point slope form is shown below:
\((y-y_1)=m(x-x_1)\)
We are given the slope m = 2/3 and the point x1 = 5, y1 = -2
Simply plug in these numbers into the above equation.
\((y--2)=\frac{2}{3} (x-5)\)
Simplify:
\((y+2)=\frac{2}{3} (x-5)\)
the correlation between two variables related to the same sample is a scaled quantitative measure. what is used to scale this measurement?
The correct option is the standard deviations of the variables.
What is correlation?
Any statistical relationship between two random variables or bivariate data, whether causal or not, is referred to in statistics as correlation or dependence.
Correlation is a term used to describe the linear relationship between two entities. When using a correlation tool, the variables must be present in quantities of two or more to test their relationship (degree of association).
In order to scale the measurement between two variables connected to a similar sample, the standard deviation measures dispersion.
The variables' standard deviations are the best choice as a result.
Option involving the standard errors of the variables is incorrect because standard error, which stands for standard deviation, determines the relationship between dependent and independent variables.
Option involving the coefficients of variation of two variables is incorrect because the coefficient expressing standard deviation and mean ratio determines how much variation there is.
Option The means of the variables are incorrect because they are not a scale for determining the correlation between two variables.
Hence, the correct option is the standard deviations of the variables.
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Complete question:
The correlation between two variables related to the same sample is a scaled quantitative measure. What is used to scale this measurement?
- the standard deviations of the variables
- the standard errors of the variables
- the coefficients of variation of the two variables
- the means of the variables
Can U pls help me on this question
Answer:
25
Step-by-step explanation:
they are alternative exterior angles meaning they are equal.so you can solve by doing
7x-40=5x+10
isolate the terms by adding like terms. ( add 40 from the left side of the equation to the right.)
so it would look like this.
7x=5x+10+40. (the 40 was negative on the left side so you have to do the inverse to move it) do the same with the 5x.
now you have
2x=50. divide 50 by 2 to get your final answer .
Solve: 2 3/4 ÷ 1 4/7=
Help?
Answer:
\( \frac{11}{7} \)
Step-by-step explanation:
\(2 \frac{3}{4} \div 1\frac{4}{7} \)
\( = 2 \frac{3}{4} \times \frac{4}{7} \)
\( = \frac{11}{4} \times \frac{4}{7} \)
\( = 11 \times \frac{1}{7} \)
\( = \frac{11}{1} \times \frac{1}{7} \)
\( = \frac{11 \times 7}{1 \times 7} \)
\( = \frac{11}{1 \times 7} \)
\( = \frac{11}{7} \)
2
Given the function r(x) = -x +4, find each value.
3
S
1. r(-6) =
T
Answer:
Step-by-step explanation:
\(r(-6)=-(-6)+4=6+4=10\)
A gadget company randomly selects 10 toys per hour to inspect. The number of defective toys in the last six samples is shown in the table.
Sample Defective Toys
123456 / 021120
Based on this information, how many toys are likely to be defective in a sample of 500?
1
5
50
300
Answer:
50
Step-by-step explanation:
I copied it from someone
Answer: 5
Step-by-step explanation:
guess
What is the value of x+y in this question and what’s the equation?
Answer:
Step-by-step explanation:x
v+19= 36
----------------
Answer:
17
Step-by-step explanation:
v+19=36
v=36-19
v=17
3x+6y=3y-7. Find the equation of the line which passes through the point (13,-9) and is perpendicular to the given line. Express your answer in slope -intercept form. Simplify your answer.
The equation of the line passing through (13, -9) and perpendicular to the given line is y = 3x - 48 in slope-intercept form.
To find the equation of a line perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line 3x + 6y = 3y - 7 can be simplified to 3x + 3y = -7y - 7 and further to y = -x/3 - 7/3 in slope-intercept form, where the coefficient of x represents the slope.
The slope of the given line is -1/3. To find the slope of a line perpendicular to this, we take the negative reciprocal of -1/3, which gives us 3. So, the slope of the line we are looking for is 3.
Next, we use the slope-intercept form of a line, y = mx + b, and substitute the values of the given point (13, -9) and the slope 3 to solve for the y-intercept, b. By substituting these values into the equation, we get -9 = 3(13) + b, which simplifies to -9 = 39 + b. Solving for b, we find b = -48.
Therefore, the equation of the line passing through (13, -9) and perpendicular to the given line is y = 3x - 48 in slope-intercept form.
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2/3 + r =-4/9
What’s the value of r
Answer:
-10/9
Step-by-step explanation:
I made it so that 2/3 a -4/9 had the same denominator which turned 2/3 into 6/9
then I solved normally
Help! To solve this system of equations by elimination, what operatfon could be used to eliminate the x-variable and find the value of y?
6x + 5y = 2
4x + 2y = 8
es )
A)
subtract 2 times the second equation from 3 times the first equation
B)
subtract 3 times the second equation from 2 times the first equation
9
subtract 5 times the second equation from 2 times the first equation
D)
subtract 2 times the second equation from 5 times the first equation
Answer:
c)
subtract 5 times the second equation from 2 times the first equation
Step-by-step explanation:
subtract 5 times the second equation from 2 times the first equation
This will make the coefficient of the y variable 10
for both equations
10y - 10y = 0
leaving only x
Write the expression c · d · c · c · d · b · c · d · d · b · d · d · d · d using exponents. Write the variables in alphabetical order.
Answer:
b^2 * c^4 * d^6
Step-by-step explanation:
i think this is right
what is the x-intercept of the line 5x-2y=10
a.5
b.0
c.2
d.-10
d) A company increased the monthly salary of its employees by 20%. If an employee
gets Rs 6000 now, find his previous salary.
Can someone help me with this question ?
Answer:
f(x)= -2x+3
Step-by-step explanation:
You wish to test the following claim ( H a ) at a significance level of α = 0.001 . H o : μ = 82.4 H a : μ ≠ 82.4 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=305 with mean M=83.6 and a standard deviation of SD=14.9.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
The p-value is...
less than (or equal to) α
greater than α
This test statistic leads to a decision to...
reject the null
accept the null
fail to reject the null
As such, the final conclusion is that...
There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 82.4.
There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 82.4.
The sample data support the claim that the population mean is not equal to 82.4.
There is not sufficient sample evidence to support the claim that the population mean is not equal to 82.4.
The test statistic for this sample and the p-value for this sample is t = 0.467.
Given:
sample of size n=305
M=83.6
SD=14.9.
Significance level of α = 0.001 . H o : μ = 82.4 H a : μ ≠ 82.4
To find the Test statistic
\(test=\frac{\bar x-\mu}{\frac{s.t}{\sqrt{n} } }\)
\(=\frac{82.4.6-83.6}{\frac{14.9}{\sqrt{305} } }\)
\(0.467\)
P-value:
With t = 0.467.
p-value = (1 - 0.467)
0.533 > 0.001
So, fail to reject H₀
Therefore, the failing to reject the Null Hypothesis.
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MULTIPLE CHOICE QUESTION
What is the biggest square number that goes
into 52?
A. 13
B. 1
C. 4
D. 16
Answer: C. 4
Step-by-step explanation:
First, we can prime factorize 52.
52 = 2^2 * 13
13 is not a square number, but 4 is a square number because it equals 2 squared.
Therefore, the correct answer is C. 4
who is kay floxk i so confused so help me wit this
Do you mean Kay Flock? Because they are a rapper.
https://en.m.wikipedia.org/wiki/Kay_Flock
What is the value of x in the figure below? In this diagram, ΔABD ~ ΔCAD.
Answer:
D
Step-by-step explanation:
The triangles CDA and ADB are similar, thus the ratios of corresponding sides are equal, that is
\(\frac{CD}{AD}\) = \(\frac{DA}{DB}\) , substitute values
\(\frac{13}{x}\) = \(\frac{x}{3}\) ( cross- multiply )
x² = 39 ( take square root of both sides )
x = \(\sqrt{39}\) → D
Answer:
D is the answer
Step-by-step explanation:
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. it crosses the y-axis at (0, 4). what is the initial value of the exponential function shown on the graph? 0 1 2 4
Answer:
its 4
Step-by-step explanation:
trust me bro im a geinus
The initial value of the exponential function shown on the graph should be 4.
What is an exponential function?The exponential function represents a dependency relationship. In this type of mathematical operation there is a variable in the exponent and the real number in the base.
In this case, the exponential function is:
F(X)=Y
Knowing that the given points correspond to X=0 and Y= 4, when placing in the formula of the function, one finds:
F(0)=4
F(4)=0
So, the initial value of the exponential function shown on the graph should be 4.
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Determine the vertical asymptotes and holes for the graph of the equation below.
y=x+1/x^2-6x-7
Vertical asymptote x=7; Hole x=0
Vertical asymptote x=7; Hole x = -1
Vertical asymptote x=1; Hole x = 7
Vertical asymptote x= -1; Hole x = -7
The equation y = (x + 1) / (\(x^2\) - 6x - 7) has vertical asymptotes at x = 7 and x = -1, and it has a hole at x = -7.
To determine the vertical asymptotes and holes of the given equation, we need to analyze the behavior of the denominator.
First, we factor the denominator, \(x^2\) - 6x - 7, as (x - 7)(x + 1). This tells us that the denominator is equal to zero when x = 7 and x = -1.
Vertical asymptotes occur when the denominator approaches zero but the numerator does not. Therefore, we have vertical asymptotes at x = 7 and x = -1.
To identify holes, we look for common factors between the numerator and the denominator. In this case, there is no common factor other than 1. However, we observe that the equation has a discontinuity at x = -7. This means that the function has a hole at x = -7.
In conclusion, the equation y = (x + 1) / (\(x^2\)- 6x - 7) has vertical asymptotes at x = 7 and x = -1, and it has a hole at x = -7.
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