Answer:
[tex]\boxed{\sf \boxed{\sf x=\frac{1}{3}}\; or\;\boxed{\sf x=0.333...}}[/tex]
Step-by-step explanation:
[tex]\sf 3x-5=2-6[/tex]
Subtract numbers:-
[tex]\sf 2-6=\bf -4[/tex]
[tex]\sf 3x-5=-4[/tex]
Add 5 to both sides:-
[tex]\sf 3x-5+5=-4+5[/tex]
Simplify:-
[tex]\sf 3x=1[/tex]
Divide both sides by 3:-
[tex]\sf \cfrac{3x}{3}=\cfrac{1}{3}[/tex]
Simplify:-
[tex]\sf x=\cfrac{1}{3}[/tex]
__________________
Hope this helps!
Have a great day! :)
Answer:
x = 7/9
Step-by-step explanation:
Given equation,
→ 3x - 5 = 2 - 6x
Now the value of x will be,
→ 3x - 5 = 2 - 6x
→ 3x + 6x = 2 + 5
→ 9x = 7
→ [ x = 7/9 ]
Hence, value of x is 7/9.
a map has a scale on it which 3in represents 50 miles use information to match each map distance on the left to the number of miles to distant represent on the right
It is given that the scale used in the map is,
[tex]3\text{ in}\equiv50\text{ miles}[/tex]For 9 inches,
[tex]9\text{ inches=3}\times(\text{3 inches)}\equiv\text{3}\times(\text{50 miles)}=150\text{ miles}[/tex]Thus, a distance of 9 inches on the map corresponds to 150 miles in actual.
For 15 inches,
[tex]15\text{ inches=5}\times(\text{3 inches)}\equiv5\times(\text{50 miles)}=250\text{ miles}[/tex]Thus, a distance of 15 inches on the map corresponds to 250 miles in actual.
For 21 inches,
[tex]21\text{ inches=7}\times(\text{3 inches)}\equiv7\times(\text{50 miles)}=350\text{ miles}[/tex]Thus, a distance of 21 inches on the map corresponds to 350 miles in actual.
If PR = 10 and PQ = 4, then QR =
PR = 10 and PQ = 4 QR
QR is the difference between PR and PQ . Hence
QR = 10 - 4
= 6
I need to solve the following system of equations and enter my answers as an ordered pair the equations are 3x + y equals -10 and 2y + 8 equals -4x
Using the graph of the function g(x) = log2 (x – 2), what are the x-intercept and asymptote of g(x)?A. The x-intercept is –3, and the asymptote is located at x = 4.B. The x-intercept is –2, and the asymptote is located at y = 3.C. The x-intercept 3, and the asymptote is located at x = 2.D. The x-intercept is 4, and the asymptote is located at y = 2.
Solution
step 1
Step 2
X Intercepts = 3
or (3, 0)
Step 3
Vertical asymptote = 2
Final answer
C. The x-intercept 3, and the asymptote is located at x = 2.
how do i isolate F in the equation C= 5 over 9 (F - 32)
According to the given data we have the following:
[tex]C=\frac{5}{9}(f-32)[/tex]In order to isolate F in the equation we would make the following:
First we would have the following property:
[tex]\frac{a}{b}=\frac{m}{n}=a\cdot n=b\cdot m[/tex]Therefore 9C=5f-160
9C+160=5f
So:
[tex]\begin{gathered} \frac{9C\text{ + 160}}{5}=f \\ \frac{9}{5}C+32=f \end{gathered}[/tex]enter the ratio as a fraction in lowest terms 4ft to 82in
Answer
(4 ft/82 in) = (24/41)
Explanation
To answer this, we first need to note that
1 foot = 12 inches
So,
4 feet = 4 × 12 = 48 inches
So,
4 ft to 82 inches
= 48 inches to 82 inches
Dividing both sides by 2, we have
48 inches to 82 inches
= 24 inches to 41 inches.
In fraction form,
(4 ft/82 in) = (24/41)
Hope this Helps!!!
Find the percent increase for the given original and new quantities in parts a through c.a. Original quantity: 100 New quantity: 106b. Original quantity: 10 New quantity: 16c. Original quantity: 50 New quantity: 56
We can find the percent of increase by means of this formula:
Increase in percent = 100 * (new quantity - original quantity) /original quantity
By replacing the given values into the above formula, we get:
a.
Increase in percent = 100 * (106 - 100) / 100 = 100 * 6 / 100 = 600/100 = 6
Then, the percent of increase equals 6%
b.
Increase in percent = 100 * (16 - 10) / 100 = 100 * 6 / 10 = 600/10 = 60
Then, the percent of increase equals 60%
c.
Increase in percent = 100 * (56- 50) / 50 = 100 * 6 / 50 = 600/50 = 12
Then, the percent of increase equals 12%
2. Write an expression for the perimeter of a rectangle with a length of(3x2 + x + 2) and a width of (-22 – 5x + 1).O 4248x 7.60 4224x + 34x28x + 6O 2x24x + 3
You have that the perimeter of the rectangle is given by the following formula:
[tex]P=2l\text{ + 2w}[/tex]l: length of the rectangle
w: width of the rectangle
[tex]\begin{gathered} l=3x^2+x+2 \\ w=-x^2-5x+1 \end{gathered}[/tex]Then, you replace the pevious expression for l and w in the formula for the perimeter, just as follow:
[tex]\begin{gathered} P=2(3x^2+x+2)+2(-x^2-5x+1) \\ P=2(3x^2)+2(x)+2(2)+2(-x^2)+2(-5x)+2(1) \\ P=6x^2+2x+4-2x^2-10x+2 \\ P=4x^2-8x+6 \end{gathered}[/tex]Hence, the perimeter of the rectangle is P = 4x2 - 8x + 6
Jotham needs 12 liters of a 20% alcohol solution. He has a 10% and a 50% solution available. How many liters of the 10% and how many liters of the 50% solutions should he mix to make the 20% solution?
Given:
There are given that the Jotham needs 12 litters of 20% alcohol solution.
Explanation:
Let x be the volume of the 50% solution needed
Then,
The volume of the 10% solution to mix is:
[tex](12-x)[/tex]Then,
The equation to find x is:
[tex]0.50x+0.10\times(12-x)=0.20\times12[/tex]That means,
It say that the volume of the pure alcohol in ingredients is equal to the volume of pure alcohol.
Then,
From the above equation, calculate the value of x
So,
[tex]\begin{gathered} 0.50x+0.10\times(12-x)=0.20\times12 \\ 0.50x+0.10\cdot12-0.10x=0.20\cdot12 \\ 0.40x+0.10\cdot12=0.20\cdot12 \\ 0.40x=0.20\cdot12-0.10\cdot12 \\ x=\frac{12(0.1)}{0.40} \\ x=3 \end{gathered}[/tex]Final answer:
For the 50%, there are 3 litters solution and for the 10%,
[tex]\begin{gathered} 12-x=12-3 \\ =9 \end{gathered}[/tex]Hence, 3 liters of the 50% solution and 9 liters of the 10% solution.
Name three real-world applications of polynomials and thoroughly explain why they impact our society.
Polynomials are algebraic expressions with several terms, in which each of them is the mutiplication of some constant by some variable raised to some non negative intger. Polynomials have applications in many problems in the real world, let's discuss some of them.
Polynomials to determine how much we need to pay.
Think of this situation: You go shopping and you would like to buy some jeans, some shirts and some shoes. Suppose the price tag is nowhere around but you'd like to take the things you choose with you so you have the correct size on the way out. Since you don't know the prices yet you can asign a variable to the price of each time you choose, let's say x for the jeans, y fot the shirst and z for the shoes. Let's assume you picked 4 jeans, 5 shirst and 2 pairs of shoes, then the cost for all of them will be represented by the polynomial:
[tex]4x+5y+2z[/tex]Once you know the price of each item you can plug them in the expression to determine the total price of them.
Polynomials in physics.
In physics the polynomials are a common ocurrence, for example, the distance and object falls from a certaing height h is given by the equation:
[tex]y=h-\frac{1}{2}at^2[/tex]Notice how the right side of the equation is a polynomial since the height h and the accelaration a are constants; then the expression that determines the distance the object has fallen is a polynomial of second degree in t.
Another example in physics of a polynomial is the total mechanical energy of an object with mass m, this is given by the polynomial:
[tex]mgh+\frac{1}{2}mv^2[/tex]Since the mass of the object m, and the acceleration of the gravity g are constants this is a polynomial of the variables h (the height of the object) and the velocity v. Once we know this we can determine the total mechanical energy of the object and this will helps us to predict the future motion given some conditions.
Polynomials in economics.
Usually we can express the cost of producing an amount x of certain item with a polynomial on x. Also we can express the revenue also as a polynomial on x.
If we would
I would like you to help me with both A and B.
Let
x -----> ordered sandwiches
y ----> extra sandwiches
Part a
we have
x=20
y=3
ratio=x/y
substitute
ratio=20/3Part b
we have
x+y=184 -----> x=184-y ----> equation 1
x/y=20/3 -----> x=(20/3)y ----> equation 2
equate equation 1 and equation 2
184-y=(20/3)y
solve for y
(20/3)y+y=184
(23/3)y=184
y=184*3/23
y=24
Find out the value of x
x=184-24
x=160
therefore
number of sandwiches is 160Solve the following system of equations by finding when they are equal to each othery = -6x + 7 y= 13 - 8x The equations are equal to each other when x = and y=
ANSWER
x = 3, y = -11
EXPLANATION
We want to find the solution to the system of equations by finding when they are equal to one another.
The equations are:
y = -6x + 7
y = 13 - 8x
Now, we equate both of them:
-6x + 7 = 13 - 8x
Collect like terms:
-6x + 8x = 13 - 7
2x = 6
Divide through by 2:
x = 6 / 2
x = 3
From the first equation:
y = -6x + 7
Put the known value of x into the equation:
y = -6(3) + 7
y = -18 + 7
y = -11
Therefore, the equations are equal to each other when x = 3 and y = -11.
A person invested $7, 900 in an account growing at a rate allowing the money todouble every 8 years. How much money would be in the account after 5 years, to thenearest dollar?
Given,
The principal amount is $7900.
The time period is 8 years.
The amount of the investment is double of the principal.
Required:
The money would be in the account after 5 years, to the nearest dollar.
The Amount is calculated as:
[tex]\begin{gathered} Amount\text{ = }\frac{Principal\times rate\times time}{100}+principal \\ Amount=(\frac{\text{rate}\times\text{t}\imaginaryI\text{me}}{\text{100}}\text{+1\rparen pr}\imaginaryI\text{nc}\imaginaryI\text{pal} \end{gathered}[/tex]Substituting the value in the above formula then,
[tex]\begin{gathered} 15800=(\frac{\text{rate}\times8}{\text{100}}\text{+1\rparen7900} \\ 2=\frac{rate\times8}{100}+1 \\ 1=rate\times\frac{8}{100} \\ rate=\frac{100}{8} \\ Rate=12.5\text{ \%} \end{gathered}[/tex]The amount in the account after 5 years is:
[tex]\begin{gathered} Amount\text{ =7900\lparen}\frac{5\times12.5}{100}+1) \\ =7900\times\frac{162.5}{100} \\ =12837.5 \end{gathered}[/tex]Hence, money would be in the account after 5 years is $12837.5
Is the inequality always, sometimes, or never true?5x - 6<5(x - 5)Choose the correct answer below.Sometimes trueNever trueAlways true
In order to avaliate the inequatily, let's first expand the parenthesis in the right side:
[tex]5x-6<5x-25[/tex]We can subtract 5x from both sides of the inequality:
[tex]-6<-25[/tex]-6 is not lesser than -25, and any value of x we use will not change the final inequality, so this inequality is NEVER TRUE.
use the graph of y=-x/3 -1 determine which of the ordered pairs of the solution to the equation select all correct answers
Given:
[tex]y=-\frac{x}{3}-1[/tex]We have the graph below:
To determine the correct ordered pairs, let's solve for each of them.
a) (x, y) ==> (0, -1)
From the equation, substitute 0 for x and -1 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -1=-\frac{0}{3}-1 \\ \\ -1=0-1 \\ \\ -1=-1 \\ \\ \text{Therefore (0, -1) is a solution} \end{gathered}[/tex]b) (x, y) ==> (3, -2)
Substitute 3 for x and -2 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -2=-\frac{3}{3}-1 \\ \\ -2=-1-1 \\ \\ -2=-2 \\ \\ (3,\text{ -2) is a solution} \end{gathered}[/tex]c) (x, y) ==> (3, -5)
Substitute 3 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{3}{3}-1 \\ \\ -5=-1-1 \\ \\ -5=-2 \\ \\ (3,\text{ -5) is not a solution} \end{gathered}[/tex]d) (0, -5)
Substitute 0 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{0}{3}-1 \\ \\ -5=0-1 \\ \\ -5=-1 \\ \\ (0,\text{ -5) is not a solution} \end{gathered}[/tex]e) (x, y) ==> (-3, 0)
Substitute -3 for x and 0 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ 0=-\frac{-3}{3}-1 \\ \\ 0=1-1 \\ \\ 0=0 \\ \\ \text{The ordered pair (-3, 0) is a solution} \end{gathered}[/tex]ANSWER:
(0, -1)
(3, -2)
(-3, 0)
HELP PLEASE In the table above, what is the constant of proportionality for width tolength?
A teacher asks her students to use the Multiplication Property ofX-4.4 = 3.4. Courtney writes x = 4.100 = 3.100. Have bothEquality to write an equation equivalent to x 4 = 3. Alondra writesstudents followed the teacher's instructions? Explain your reasoning.
we have the equation
[tex]\frac{x}{4}=3[/tex]Alondra
Multiply by 4 both sides (property equality of multiplication)
so
[tex]\begin{gathered} \frac{x}{4}\cdot4=3\cdot4 \\ x=12 \end{gathered}[/tex]Courtney
Multiply by 100 both sides (property equality of multiplication)
[tex]\begin{gathered} \frac{x}{4}\cdot100=3\cdot100 \\ 25x=300 \end{gathered}[/tex]therefore
Both followed the teacher's guidelines, but by multiplying by 4, Alondra was able to solve the equation, while Courtney had to apply additional steps.
which square root is a whole number ?
Let's find the square root of all to find which is a whole number
√254 = 15.937
√255 =15.967
√256 =16
Hence √256 is a whole number
The correct option is C.
so im working on mixed properties homeworkand i just need help on it. so one question is determine the algebraic property shown so i need to know the property of 7*2 and 2*7
Recall that we are given the numbers 2*7 and 7*2. By a fact, we have that
[tex]7\cdot2\text{ =2}\cdot7[/tex]Note that in both cases, we are multiplying numbers 2 and 7, but what is changed it the order in which we do so. On the expression on the left we are multiplying 7 times 2, and on the expression on the expression on the right we are multiplying 2 times 7. This two expressions are equal due to the conmutative property of the multiplication of integers.
36. Let f(x) = x2 + x-6 and g(x) = x2 – 2x – 15. Find f(x) 1g(x)
The numerator is
[tex]f\mleft(x\mright)=x^2+x-6[/tex]The denominator is
[tex]g(x)=x^2-2x-15[/tex]The solution is 1 + the remainder divided the denominator:
[tex]1+\frac{3x+9}{x^2-2x-15}[/tex]None of the options is correct
Will give brainliest if someone helps with this question
Answer:
y=-3x-6
Step-by-step explanation:
go down 3
over 1
rise over run 3/1
it's already on -6
Anna is using a 6 1/2 pound bag of salt to Pour on snow. After using the salt 2/5 of the bag remains. How many pounds of salt did Anna use to pour on snow
If after using the salt, 2/5 of the salt remains, it means that Anna used 3/5 of the salt in the bag.
A bag contains 6 1/2 pounds of salt, convert this to a fractional number:
[tex]6\frac{1}{2}=6+\frac{1}{2}=\frac{13}{2}[/tex]To find how many pounds of salt she used, multiply 3/5 by the total amount of salt in the bag, this is:
[tex]\frac{3}{5}\cdot\frac{13}{2}=\frac{39}{10}[/tex]She used 39/10 pounds of salt.
Find the output global maximum and global minimum values of the function f(x) = x^3- 9x^2 - 32x + 10(A) Interval = -5, 0Global maximum = (B) Interval = 0,9 Global minimum = (C) Interval =-5, 9.Global maximum =Global minimum =
Given the function f:
We want to find its output global maximum and global minimum values.
To do this, we need to find the deritative of the function first:
Now, we're going to set it equal to zero:
Finally, replace the values x=-5, x=0, and the solutions of the previous equation in the original function. The highest value will be the maximum and the lowest value will be the minimum:
The output global maximum at the interval -5,0 is 34.43.
1) write each mixed number as a decimal 2 2/52) write each decimal as a fraction in simplest form: 0.5
1) 2.4 2) 1/2
First, let's rewrite:
[tex]2\frac{2}{5}[/tex]We would convert the fraction to decimal and add the outcome to the whole number:
[tex]\begin{gathered} \frac{2}{5}\text{ = 0.4} \\ \text{whole number = 2} \\ 2\frac{2}{5}\text{ = 2 + }\frac{2}{5} \\ =\text{ 2 + 0.4} \\ =\text{ 2.4} \end{gathered}[/tex]Answer = 2.4
2) 0.5 = 5/10
In its simplest form, we need to divide with a number that is common to both the numerator and the denominator. The number is 5
0.5 as a fraction in its simplest form = 1/2
Tom wants to buy a pool table thatmeasures 3 foot by 7 foot. The cost of the table is $14.50 per square foot. How much will it cost Tom to buy the pool table he wants?
ANSWER :
$304.50
EXPLANATION :
From the problem, we have a pool table with dimensions of 3 foot by 7 foot.
The area of the table is :
[tex]3ft\times7ft=21ft^2[/tex]The cost of the table is $14.50 per square foot.
So the cost of the table will be :
[tex]21\cancel{ft^2}\times\frac{\$14.50}{1\cancel{ft^2}}=\$304.50[/tex]i need help my other tutor literally left
To determine the total area of a Pyramid you have to use the following formula:
[tex]TA=A_{\text{base}}+\frac{1}{2}(P_{\text{base}}\cdot s)[/tex]Where
A_base refers to the area of the base, in this case, it would be the area of the hexagon
P_base refers to the perimeter of the base, in this case, the perimeter of the hexagon
s indicates the slant height of the pyramid
Before you can determine the total area of the pyramid, you have to calculate the area and perimeter of the regular hexagon.
The perimeter of the hexagon
To determine the perimeter of any shape, you have to add the length of its sides, in this case, the hexagon is regular which means that all sides are equal, so the perimeter is equal to 6 times the side length (a):
For a=4
[tex]\begin{gathered} P_{\text{base}}=6a \\ P_{\text{base}}=6\cdot4 \\ P_{\text{base}}=24\text{units} \end{gathered}[/tex]The area of the hexagon
To determine this area you have to use the following formula:
[tex]A_{\text{base}}=\frac{3\sqrt[]{3}a^2}{2}[/tex]Where "a" represents the side length
For a=4, the area of the base is:
[tex]\begin{gathered} A_{\text{base}}=\frac{3\sqrt[]{3\cdot}4^2}{2} \\ A_{\text{base}}=\frac{3\sqrt[]{3}\cdot16}{2} \\ A_{\text{base}}=24\sqrt[]{3}\text{units}^2 \end{gathered}[/tex]Total area of the pyramid
Now that we determined the area and perimeter of the base, given that the slant height of the pyramid is s=6, we can calculate the total area as follows:
[tex]\begin{gathered} TA=A_{\text{base}}+\frac{1}{2}(P_{\text{base}}\cdot s) \\ TA=24\sqrt[]{3}+\frac{1}{2}(24\cdot6) \\ TA=24\sqrt[]{3}+\frac{1}{2}\cdot144 \\ TA=24\sqrt[]{3}+72 \end{gathered}[/tex]The total area of the hexagonal pyramid is 72+24√3 units²
Can I Plss get some help on my homework I got stuck es
Hello there. To solve this question, we'll have to remember some properties about mean and standard deviation.
Given the table with the calories of each pizza type.
We have to determine why the standard deviation is 87.6 and understand what does it mean in context.
First, the mean of the values were calculated in question 8, that is the arithmetic mean of the values.
Adding all calories and dividing it by the number of values, we get
[tex]\dfrac{168+181+165+177+321+380+309+313+157}{9}=\frac{2171}{9}\approx241.2[/tex]Okay. Now, we find the variance of the set by using the formula:
[tex]Var(x)=\sum_{i=1}^n\dfrac{(x_i-\mu)^2}{n}[/tex]In which we get
[tex]Var(x)=\dfrac{(168-241.2)^2+(181-241.2)^2+\cdots+(157-241.2)^2}{9}=7673.2[/tex]And the standard deviation is the square root of the variance, hence
[tex]\sigma=\sqrt{Var(x)}=\sqrt{7673.2}\approx87.6[/tex]In statistics, the standard deviation is a measure of how are the values getting away from the meanO, that is the point in the middle of the distribution:
This is the answer we're looking for.
For number eleven, suppose the new pizza has x calories.
We'll have a change in the mean, now being
[tex]\mu=\dfrac{2171+x}{10}[/tex]And the variance will be
[tex]Var(x)=\sum_{i=1}^n\dfrac{(x_i-\mu)^2}{10}=\dfrac{\left(168-\dfrac{2171+x}{10}\right)^2+\left(181-\dfrac{2171+x}{10}\right)^2+\left(177-\dfrac{2171+x}{10}\right)^2+\left(157-\dfrac{2171+x}{10}\right)^2+\left(321-\dfrac{2171+x}{10}\right)^2+\left(309-\dfrac{2171+x}{10}\right)^2+\left(380-\dfrac{2171+x}{10}\right)^2+\left(313-\dfrac{2171+x}{10}\right)^2+\left(165-\dfrac{2171+x}{10}\right)^2+\left(x-\dfrac{2171+x}{10}\right)^2}{10}[/tex]Consider taking x to be closer to the mean, that is
[tex]x\approx241.2[/tex]So the mean would be
[tex]\dfrac{2171+241.2}{10}\approx241.2[/tex]Won't change at all
And the difference between the value would be identically zero
Hence the variance will become smaller, making the standard deviation (the square root of it), smaller as well = 82.58
5. If AKLJ - AVWU, find the value of x.
The triangles are similar according to the question. Therefore, the following ratio can be formed
[tex]\begin{gathered} \frac{25}{20}=\frac{4x-23}{2x+2} \\ \text{cross multiply} \\ 25(2x+2)=20(4x-23) \\ 50x+50=80x-460 \\ 50x-80x=-460-50 \\ -30x=-510 \\ x=\frac{-510}{-30} \\ x=17 \end{gathered}[/tex]we have to simplify it im not sure the right answer
(3x +2)(2x - 5)
To simplify this expression, you have to apply distributive property, as follows:
3x(2x) + 3x(-5) + 2(2x) + 2(-5) =
= 6x² - 15x + 4x - 10 =
= 6x² - 11x - 10
Translate the following statement into probability notation news X as the random variable
Let be x the random variable
a)
If we need the probability of x when it is not more than a, we can write it using inequalities as below
[tex]x\le a[/tex]Notice that x can be equal to a but no more than a
And the probability is then
[tex]P(x\le a)[/tex]So, the answer to question a) is the 4th option
b) 'x being at least a' can be written using inequalities in this way:
[tex]x\ge a[/tex]Notice that x can be equal to a, but not less than a
Therefore, the probability is given by the expression
[tex]P(x\ge a)[/tex]So, the answer to question b) is the last option