Answers
What is the solution of the equation [tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1[/tex] ?
x=4
How is the given equation solved?
[tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1\\\\\frac{2}{3} x-\frac{2}{3} -\frac{2}{5} x+\frac{3}{5}=1\\\\\frac{2}{3} x-\frac{2}{5}x =1+\frac{2}{3}- \frac{3}{5}\\\\\text{Taking LCM},\\\\\frac{10x-6x}{15} =\frac{15+10-9}{15} \\\\4x= 16\\\\x=4[/tex]
What is solving an equation?
Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics.Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.To learn more about equation solving, refer:
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Related Questions
Solve the system algebraically. Make sure that any points you name satisfy both equations.
Answers
Write out the two equations given
[tex]\begin{gathered} y=-x^2+5=====(\text{equation 1)} \\ -x+y=3======(\text{equation 2)} \end{gathered}[/tex]Make y the subject of equation 2
[tex]\begin{gathered} -x+y=3 \\ y=3+x====(\text{equation 3)} \end{gathered}[/tex]Since y is equal to y, then equations 1 and 3 are equal
[tex]\begin{gathered} y=-x^2+5 \\ y=3+x \\ y=y \\ -x^2+5=3+x \\ x^2+x+3-5=0 \\ x^2+x-2=0 \end{gathered}[/tex][tex]\begin{gathered} x^2-x+2x-2=0 \\ x(x-1)+2(x-1)=0 \\ (x-1)(x+2)=0 \\ x-1=0,x=1 \\ \text{or} \\ x+2=0,x=-2 \end{gathered}[/tex]Substitute x into equation 3
[tex]\begin{gathered} y=3+x \\ \text{when x=1} \\ y=3+1=4(1,4) \\ \text{when x=-2} \\ y=3+(-2) \\ y=3-2=1(-2,1) \end{gathered}[/tex]Hence, the coordinates of the solution are (1,4) (-2,1)
which of the following are point-slope equations of the line going through (-2,-2) and (2,1) check all that apply
Answers
The Point-Slope form of the equation of a line is:
[tex]y_{}-y_1=m(x-x_1)_{}[/tex]Where "m" is the slope of the line and this is a point on the line:
[tex](x_1,y_1)[/tex]You can find the slope of a line using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, knowing that this line passes through these points:
[tex](-2,-2);\mleft(2,1\mright)[/tex]You can set up that:
[tex]\begin{gathered} y_2=-2 \\ y_1=1 \\ x_2=-2 \\ x_1=2 \end{gathered}[/tex]Substituting values into the formula and evaluating, you get:
[tex]m=\frac{-2-1}{-2-2}=\frac{-3}{-4}=\frac{3}{4}[/tex]Knowing the slope and coordinates of two points on the line, you can set up these two equations for this line:
1. First equation:
[tex]\begin{gathered} y-(-2)=\frac{3}{4}(x-(-2)) \\ \\ y+2=\frac{3}{4}(x+2) \end{gathered}[/tex]2. Second equation:
[tex]y-1=\frac{3}{4}(x-2)[/tex]The answers are: Option A and Option B.
On a map, a museum is located at (15, 17). A library is located at (15, -2). How many units away museum from the libraryA. 2 unitsB. 13 unitsC. 17 unitsD. 19 units
Answers
Let's look at the locations of the library and museum in a coordinate plane:
The museum is "17" units above the x-axis.
The library is "2" units below the x-axis.
The total units between the museum and library is 17 + 2 = 19 units
Thus, the distance between the museum and library is 19 units.
Correct Answer:
D
for any numbers x,y [x=0 in(4) and y = 0 in (5)] and any positive integers m,n, the following holds:x^m · x^n=x^m+nProve number 1
Answers
Proved
Explanation:
To prove x^m · x^n=x^m+n, let's assign numbers to x, m and n
let x = 2
m = 3, n = 4
x^m · x^n = 2^3 . 2^4
x^m+n = 2^(3+4)
Solve each of the above seperately and comparew the answer:
[tex]\begin{gathered} x^m\times x^n=2^3\times2^4 \\ =\text{ (2}\times2\times2)\times(2\times2\times2\times2) \\ =\text{ 8}\times16 \\ =\text{ }128 \end{gathered}[/tex][tex]\begin{gathered} x^{m+n}=2^{3+4} \\ =2^7\text{ = 2}\times2\times2\times2\times2\times2\times2 \\ =\text{ 128} \end{gathered}[/tex][tex]\begin{gathered} sincex^m\times x^n\text{ = 128} \\ \text{and x}^{m+n}\text{ = 128} \\ \text{Therefore, }x^m\times x^n\text{ = x}^{m+n} \end{gathered}[/tex]This expression x^m · x^n=x^m+n has been proved to be equal
Danielle owes $13.80 for text messaging in the month of March. If her text messaging plan costs $9 forthe first 550 messages and 20¢ for each additional text message, how many text messages did shesend that month?AnswerKeypadKeyboard Shortcutstext messages
Answers
Given
Danielle owes $13.80 for text messaging in the month of March.
If her text messaging plan costs $9 for the first 550 messages and 20¢ for each additional text message.
To find the number of text messages did she send that month.
Now,
Let x be the number of text messages she send that month.
Then, from the given data,
[tex]x=550+\frac{13.8-9}{0.20}[/tex]Since 20cents is $0.20.
Then,
[tex]\begin{gathered} x=550+\frac{13.8-9}{20}\times100 \\ =550+\frac{4.8\times100}{20} \\ =550+4.8\times5 \\ =550+24 \\ =574 \end{gathered}[/tex]Hence, the number of text messages send by her is 574.
I need some help finding slope from an equation-4y = 12+2x
Answers
Given the equation:
[tex]-4y=12+2x[/tex]To find the slope of the equation, solve the equation for (y)
It is required to make the equation like the slope-intercept form
[tex]y=mx+b[/tex]So, for the given equation, divide all terms by (-4)
So,
[tex]\begin{gathered} \frac{-4y}{-4}=\frac{12}{-4}+\frac{2x}{-4} \\ \\ y=-3-\frac{1}{2}x \\ \\ y=-\frac{1}{2}x-3 \end{gathered}[/tex]compare the last result with the slope-intercept form
So, the slope = m = -1/2
So, the answer will be:
[tex]\text{slope}=-\frac{1}{2}[/tex]pair of shoes $80 find the total paid if taxes 6%
Answers
The first step is to find the value of the tax, you do it by multiplying the price of the shoes by the tax (in decimal form), this way:
[tex]t=80\cdot0.06=4.8[/tex]Now, add this value to the price of the shoes:
[tex]80.00+4.8=84.80[/tex]The total paid is $84.80.
Kurt bought a vacant lot in a development that was 85% completed. When he started
working with the builder to lay out where the house and driveway would lie, it was
determined that he would need an easement because his driveway would spill over onto
the adjacent lot by a few feet. What type of easement is this?
Easement appurtenant
Easement by necessity
Easement by prescription
Easement in gross
Answers
This is a case of easement appurtenant
What is easement?
An easement is a nonpossessory right to use and/or enter another's real property without owning it. It is "best shown by a right of way that one landowner, A, may have over the land of another, B." In most countries, an easement is a property right and sort of incorporeal property in and of itself. Real covenants and equitable servitudes are analogous to easements. The Restatement (Third) of Property in the United States attempts to integrate these notions as servitudes. Easements are useful for allowing persons to access other properties or resources by granting access across two [further explanation needed] or more pieces of property.
This is a case of easement appurtenant
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please help me (question “e”)
Answers
Answer:
42 - 6 ÷ (6 - 3) = 40
Step-by-step explanation:
BODMAS
The BODMAS rule is an acronym representing the order of operations in math:
BracketsOrders (Powers and Square Roots, etc.)Division and Multiplication (from left to right)Addition and Subtraction (from left to right)Given calculation:
42 - 6 ÷ 6 - 3 = 40
Following the order of operations, where division comes before subtraction, the current calculation is:
⇒ 42 - 6 ÷ 6 - 3
⇒ 42 - 1 - 3
⇒ 41 - 3
⇒ 38
Therefore, brackets should be added around (6 - 3) to make the calculation correct:
⇒ 42 - 6 ÷ (6 - 3)
⇒ 42 - 6 ÷ 3
⇒ 42 - 2
⇒ 40
If g(x) = 5(x²+1) + 16, what is the value of g(11) ?
Answers
Answer:
626
Step-by-step explanation:
11^2= 121
121+1=122
122x5=610
610+16=626
hope this helped
Joan attended school for 2 weeks longer than 3/4 of the year. How long did Joan attend school? (Assume 52 weeks in a year.)
Answers
The duration Joan attended school is 41 weeks.
How to find how long she attend school?Joan attended school for 2 weeks longer than 3/4 of the year.
The time she attended school can be calculated as follows:
52 weeks = 1 year
3 / 4 of 52 = 156 / 4
3 / 4 of 52 = 39 weeks
Therefore, 3 / 4 of a year is 39 weeks.
She attended school 2 weeks longer than 3 /4 of the year(39 weeks).
Hence,
the duration she attended school = 39 + 2
the duration she attended school = 41 weeks
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3.1 x 10^3 in scientific notation
Answers
Answer:3100
Step-by-step explanation:
If 3.1 x 10^3 is because you count the first number and then you use what is less in the power like you have 3 and u used 1 for the number 1 so you left with 2 those 2 will be zeros 3100.
I hope this helped pls put it as brainliest
Answer: 3.1 × 103
Step-by-step explanation:
y=tan(x/8) Find the period, x intercepts, and vertical asymptotes
Answers
Given:
[tex]y=\tan(\frac{x}{8})[/tex]Find-: Period, x-intercepts, and vertical asymptotes.
Sol:
Graph of function is:
The period of the function is:
[tex]\text{ Period}=8\pi[/tex]The x-intercept of function is:
For the x-intercept value of "y" is zero so,
[tex]\begin{gathered} y=\tan(\frac{x}{8}) \\ \\ \tan(\frac{x}{8})=0 \\ \\ \frac{x}{8}=\tan^{-1}(0) \\ \\ x=8\tan^{-1}(0) \\ \\ x=-8\pi,0,8\pi,16\pi...... \end{gathered}[/tex]Vertical asymptotes are:
For the function can't find vertical asymptotes.
Based on the density graph below, what is the probability of a value in thesample space being anywhere from 15 to 20?
Answers
Given
Density graph
Find
Probability of the value in the sample space being anywhere from 15 to 20
Explanation
from density graph , we cna get the distribution is uniform.
so , the probability of the value in the sample space being anywhere from 15 to 20 will be
[tex]\begin{gathered} p=\frac{20-15}{25-0} \\ \\ p=\frac{5}{25} \\ \\ p=0.2\approx20\% \end{gathered}[/tex]Final Answer
Hence , the correct option is D
Which equation below would produce thefollowing graph?A) f(2)=-(2+4)(3-1)(-5)B) f(z) = (2+4)(z-1)(-5)C) f(3) = (2-4)(2+1)(2+5)D) f(3) = -(2-4)(2+1)(2+5)
Answers
If we take the first option of the question, we have the following zeros or points passing through the x-axis:
[tex]f(x)=-(x+4)\cdot(x-1)\cdot(x-5)=0[/tex][tex]x+4=0,x-1=0,x-5=0[/tex]We then have:
[tex]x=-4,x=1,x=5[/tex]These points coincide with the ones in the graph.
The expansion of this equation is:
[tex]f(x)=-x^3+2x^2+19x-20_{}[/tex]If we give some points to the equation at points x = -6, x = -3, x = 0, x = 3, x = 6, we have:
f(-6) = 154
f(-3) = -32
f(0) = -20
f(3) = 28
f(6) = -50
And all these values adjust to the proposed graph.
Therefore, the equation for option A would produce the proposed graph.
This is a way to solve this question. We can also make use of the derivatives of the first or of the second-order to find if this equation produces this graph.
The function f(x)= -200x+1000 represents the altitude (in feet) of a paraglider x minutes from the time the paraglider begins a descent to a landing site located 100 feet above sea level. Identify the slope, domain, and range.
Answers
The slope of the Function is -200, the domain of the function is any real value of x and the range of the function is [1000,∞).
The provided function is,
f(x) = -200x+1000
This function is representing the altitude of a paraglider and time from where the paraglider descent. Here, x is representing time in minutes.
The landing site is located at the depth of 1000 feet.
we can write the function as,
y = -200x + 1000
Here, y is the range of the function.
As we observes the function, it is an equation of line,
So, the slope is equal to the coefficient of x.
So the slope is -200.
The domain is any value of x for which the function is defined,
as this it an equation of line,
The domain would be any real value of x.
The range is the output that we get after putting value of x.
Here,
Put x = 0.
y = -200(0)+1000
y = 1000
Now. putting x = -1,
y = -200(-1) + 1000
y = 1200.
Putting any negative value of x will make y positive,
So, the range will be [1000,∞)
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Indicate whether the following statements are True (T) or False (F). 1. The product of two real numbers is always a real number. 2. The quotient of two real numbers is always a real number (provided the denominator is non-zero). 3. The ratio of two real numbers is never zero. 4. The difference of two real numbers is always a real number. 5. The sum of two real numbers is always a real number. 6. The quotient of two real numbers is always a rational number (provided the denominator is non-zero). 7. The difference of two real numbers is always an irrational number.
Answers
The required answer is true, false, true, false, true, true, and false for statements 1, 2, 3, 4, 5, 6, and 7 respectively.
The product of two real numbers is always a real number is true.
The quotient of two real numbers is always a real number (provided the denominator is non-zero) is false because when you divide, you get the quotient, and when you divide, you might get decimals.
The ratio of two real numbers is never zero is true.
The difference of two real numbers is always a real number is false because it could be a decimal.
The sum of two real numbers is always a real number is true.
The quotient of two real numbers is always a rational number (provided the denominator is non-zero) is true.
The difference of two real numbers is always an irrational number is false.
Therefore, the required answer is true, false, true, false, true, true, and false for statements 1, 2, 3, 4, 5, 6, and 7 respectively.
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Find the area using A = 1 * W. Mr. Janacek's class is doing an art projec with different-colored squares. How many 1-inch squares can be cut from an 18-inch by 24-inch piece of construction paper?
Answers
We have the following:
The area is
[tex]A=L\cdot W[/tex]L (long) is 24 inch and W (wide) is 18 inch, replacing:
[tex]\begin{gathered} A=24\cdot18 \\ A=432 \end{gathered}[/tex]The area is 432 squares inch, therefore:
[tex]\frac{432}{1}=432[/tex]Therefore a total of 432 1-inch squares can be cut
Please help (There are two parts to this question you have to graph and then find the slope)
Answers
From the given graph,
The line representing the rise and the line representing the run on the given graph can be seen below
To find the slope, m, of a straight line, the formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Taking points from the graph
A company claims that each bag of pretzels weighs 11.3 oz. A sample of 37 bags was weighed. The mean weight of these bags was 11.05 oz, with a standard deviation of 1.35 oz Test the hypothesis at a 5% level of significance.A. Reject the null hypothesis. There is enough evidence to oppose the company's claim.B. Fail to reject the null hypothesis. There is enough evidence to oppose the company's claim.C. Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.D. Reject the null hypothesis. There is not enough evidence to oppose the company's claim.
Answers
Solution
[tex]\begin{gathered} H_0\colon\mu=11.03 \\ \\ H_1\colon\mu=11.05 \\ \\ z=\frac{11.03-11.05}{1.35} \\ \\ Z_{\text{score}}=0.98803>0.05 \end{gathered}[/tex]C. Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
If you had half a dollar, three quarters, eight dimes, six nickels, and nine pennies, how much money would you have altogether?
Answers
If we have half a dollar, three quarters, eight dimes, six nickels, and nine pennies , then we altogether have $2.44 .
In the question ,
it is given that
we have half a dollar ,
which means half a dollar = $0.50
we have , three quarters means
we have 75 cents
and 75 cents = $0.75
we have 8 dimes ,
we know that 1 dime [tex]=[/tex] 10 cents
so , 8 dimes = 80 cents
and 80 cents = $0.80
we have six nickels,
we know that 20 nickels = $1
so , 1 nickel = $1/20
and 6 nickel = $ 6/20 = $0.30
we have nine pennies ,
we know that 100 pennies = $1
So ,1 Pennie = $1/100
and 9 pennies = $ 9/100 = $0.09
Combining all together we get
total money = half a dollar + three quarters + 8 dimes + six nickels + nine pennies .
Substituting the values , we get
total money = $0.50 + $0.75 + $0.80 + $0.30 + $0.09
= $2.44
Therefore , if we have half a dollar, three quarters, eight dimes, six nickels, and nine pennies , then we altogether have $2.44 .
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what are three consecutive integers that add to 40
Answers
Answer:
12 1/3 + 13 1/3 + 14 1/3 = 40
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 40. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 40. Therefore, you can write the equation as follows:
Identify the variables, coefficients, and constants of the following equations.
3x = 12
y = 1/2x - 6
Answers
Answer:
Variables are the letters that represent a number. So, it would be the ones bolded here: 3x=12 and y=1/2x-6
The coefficients are next to the variables-the ones being multiplied with the variable. They are bolded here: 3x= 12 and y= 1/2x-6
The constants are the numbers that aren't coefficients or variables. So they are bolded here: 3x=12 and y=1/2x-6
During second period, Anita completed a grammar worksheet. Of the 18 questions, Anita got 50% right. How many questions did Anita get right?
Answers
Answer:
Anita answered nine questions correctly.
Step-by-step explanation:
50% is 1/2 and 1/2 of 18 is 9.
Sorry for bad English, love from Vanuatu!
Josh wants to make the lamp purple.
He will use dye to make the plastic purple.
Josh will mix red dye with green dye and blue dye in the ratio 9:3:15 to make
purple dye.
Josh uses 30 litres of green dye.
(b) How many litres of purple dye will Josh make with the 30 litres of green dye?
Show a check of your working.
(5)
Answers
Answer:
Step-by-step explanation:
since 30 liters is ten times 3 liters, you must mulitply all of the amounts of dye liters (not green because we know its 30) by 10. this would make a ratio of 90:30:150. Now, add them all up to equal 270 liters of purple dye in total.
an item is regularly priced at $33. it is now priced at a discount of 85% off the regular price
Answers
Answer: The item should now cost $4.95 if that is the question
Step-by-step explanation:
15% of 33 is 4.95 giving you the answer of 4.95 hope this helps
Suppose that the function f is defined, for all real numbers, as follows.1--x' +4 if x13f(x) = 24if x=1Find f(-4).f(1), and f(3).1(-4) = 0음f(1) = 0X Х?f(3) =
Answers
Answer:
[tex]\begin{gathered} f(-4)=-\frac{4}{3} \\ f(1)=4 \\ f(3)=1 \end{gathered}[/tex]Step-by-step explanation:
These types of functions are called Piecewise-defined functions since it use a different formula for different parts of its domain because it has a point of discontinuity.
We have the following function:
[tex]f(x)=\begin{cases}-\frac{1}{3}x^2+4\rightarrow ifx\ne1^{} \\ \text{ 4 if x=1}\end{cases}[/tex]So, to find f(-4), we need to substitute x=-4 into the function for x≠1.
[tex]\begin{gathered} f(-4)=\frac{-1}{3}(-4)^2+4 \\ f(-4)=-\frac{1}{3}(16)+4 \\ f(-4)=-\frac{16}{3}+4 \\ f(-4)=-\frac{4}{3} \end{gathered}[/tex]Now, for f(1) we know that the outcome is 4.
[tex]f(1)=4[/tex]Then, for f(3), substitute x=3 into the function for x≠1.
[tex]\begin{gathered} f(3)=-\frac{1}{3}(3)^2+4 \\ f(3)=-\frac{1}{3}(9)+4 \\ f(3)=1 \end{gathered}[/tex]A family has 5 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 5 girls if it is known that the family's first child is a girl.
Answers
The required probability is 1/31 that the family has 5 girls if it is known that the family's first child is a girl.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Let us express every possible set of 5 children as a 5-letter word made up of the letters G or B. (G for a girl and B for a boy).
In all, 2⁵ = 32 such words are outcomes, with two options for each of the five slots.
The constraint "if it is known that the family contains at least one female" suggests that we would evaluate the reduced space of all such words, except the word (BBBBB).
This reduced event space is made up of 32-1 = 31 elements.
There is just one such term in the favorable collection of events (GGGGG).
As a result, the probability for the question is P = 1/31.
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Liz bought seven liters of orange juice for a party. About how many quarts of juice did she buy?
Answers
Let's make a conversion:
[tex]7l\times\frac{1.05669qt}{1l}=7.39683qt\approx7.40qt[/tex]She bought about 7.39683qt
Liz bought 7.396817 quarts of orange juice for a party.
What are Quarts?The liquid quart in the United States is a measure of fluid volume equal to one-fourth of a gallon, two pints, or four cups. The liquid quart is not to be confused with the dry quart (US) or the imperial quart, which are two distinct units.
Multiply the volume by the conversion ratio to transform a liter measurement into a quart measurement.
Since each liter equals 1.056688 quarts, you may use the following easy formula to convert:
quarts = liters × 1.056688
The volume in quarts is equal to the liters multiplied by 1.056688.
We have been given that Liz bought seven liters of orange juice for a party.
We have to convert 7 liters to quarts using the formula above.
7 L = (7 × 1.056688) = 7.396817 qt
Thus, she bought 7.396817 quarts of orange juice for a party.
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(d) Find the domain of function R. Choose the correct domain below.
Answers
Answer:
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.