The solution of the equation is x =3.33.
What is a solution?A solution is a value assignment to an unknown variable that makes the equality of the equation true. In other words, a solution is a value or set of values (one for each unknown) that becomes an equation when the equation is replaced by the unknown. In mathematics, solving an equation means finding its solution, which is a value (number, function, set, etc.) that satisfies the conditions specified by the equation, usually two equations separated by an equal sign. Connected. When looking for a solution, one or more variables are called unknowns. A solution is a value assignment to an unknown variable that makes the equality of the equation true.In other words, a solution is a value or set of values (one for each unknown) that becomes an equation when the equation is replaced by the unknown.Solutions of equations are often called roots of equations and are not specifically limited to polynomial equations. The set of all solutions of an equation is the solution set.3 = 4 - 5³ × √x⁸
3 = 4 - 125 × x⁴
124 = x⁴
x = 3.33
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The solution of the equation is x =3.33.
What is a solution?A solution is a value assigned to an unknown variable that makes the equality of the equation true.In other words, a solution is a value or set of values (one for each unknown) that becomes an equation when the equation is replaced by the unknown.In mathematics, solving an equation means finding its solution, which is a value (number, function, set, etc.) that satisfies the conditions specified by the equation, usually two equations separated by an equal sign.A solution is a value assigned to an unknown variable that makes the equality of the equation true.Solutions of equations are often called roots of equations and are not specifically limited to polynomial equations.The set of all solutions of an equation is the solution set:
3 = 4 - 5³ × √x⁸3 = 4 - 125 × x⁴124 = x⁴x = 3.33Therefore, the solution of the equation is x =3.33.
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a/5 + 8<13 please help
We have the inequality
[tex]\frac{a}{5}+8<13[/tex]solving for a, we have
[tex]\begin{gathered} \frac{a}{5}+8<13 \\ \frac{a}{5}<13-8 \\ \frac{a}{5}<5 \\ a<5\cdot5 \\ a<25 \end{gathered}[/tex]Then a has to be less than 25. Written the solution in interval form we have:
[tex](-\infty,25)[/tex]You invest $3,150.00 in a stock plan. The first year, it loses 5% of its value. The second year, it gains 9% of its value. What is the difference between the value of your stocks at the end of the second year and your initial investment?
Given:
The investment is $3,150.00.
The loss percent for the first year is 5 %.
The gain percent for the second year is 9 %.
Required:
We need to find the investment amount at end of the second year.
Explanation:
The investment amount at the end of the first year is
[tex]=3150(1-\frac{5}{100})[/tex][tex]=3150(1-0.05)[/tex][tex]=2992.5[/tex]The investment amount at the end of the first year is $2992.5.
The investment amount at the end of the second year is
[tex]=2992.5(1+\frac{9}{100})[/tex][tex]=2992.5(1+0.09)[/tex][tex]=3261.825[/tex][tex]=3261.83[/tex]The investment amount at the end of the second year is $3261.83.
Final answer:
The investment amount at the end of the second year is $3261.83.
Find the greatest common factor of the following terms. 20x^5,80x^6, and 30x
Answer:
10x
Explanation:
Given the terms: 20x⁵, 80x⁶, and 30x
In order to find the greatest common factor, express each of the terms as a product of its factors.
[tex]\begin{gathered} 20x^5=10x\times2x^4 \\ 80x^6=10x\times8x^5 \\ 30x=10x\times3 \end{gathered}[/tex]Observing the three products, 10x is the only common factor,
Therefore, the greatest common factor is 10x.
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).8,20,50,...Find the 10th term.
NO -6 -10 Use the graph to complete the function table. Input Output -7 1 5 Submit
In order to complete the function table, we just need to locate the input values in the x-axis and then find the corresponding values of y in the line.
For x = -7, we have y = 9
For x = 1, we have y = -3
For x = 5, we have y = -9
So the output values for the table are
The principal is trying to come up with a playground policy to protect students from the risk of getting heatstroke on especially hot and humid days. If that's her goal, at which temperature should students stop being allowed outside for recess?A 80 degrees B 90 degrees C 105 degreesD 130 degrees
The temperature should be the following:
*Temperatures greater than 80° on hot or humid days should be the temperature limit.
Solve the following logarithmic equation. Express all solutions in exact form.√log x-3 =log x-3
Square both side of equation and simplify the equation.
[tex]\begin{gathered} (\sqrt[]{\log x-3})^2=(\log x-3)^2 \\ \log x-3=(\log x)^2-6\log x+9 \\ (\log x)^2-6\log x-\log x+9+3=0 \\ (\log x)^2-7\log x+12=0 \end{gathered}[/tex]Assume log x = y. So equation is,
[tex]y^2-7y+12=0[/tex]Simplify the equation to obtain the value of y.
[tex]\begin{gathered} y^2-7y+12=0 \\ y^2-4y-3y+12=0 \\ y(y-4)-3(y-4)=0 \\ (y-3)(y-4)=0 \\ y=3,4 \end{gathered}[/tex]So the value of y is 3 or 4,
[tex]\begin{gathered} \log x=3 \\ x=e^3 \end{gathered}[/tex]Or
[tex]\begin{gathered} \log x=4 \\ x=e^4 \end{gathered}[/tex]10c - 6(2c - 1) = -2( c- 3) Your answer
10c - 6(2c - 1) = -2( c- 3)
[tex]10c-6\left(2c-1\right)=-2\left(c-3\right)[/tex]in this case, we have a equation with an unknown value (c9
Step 1
operate to eliminate ()
[tex]\begin{gathered} 10c-(6\cdot2c)-(6)(-1)=-2c+6 \\ 10c-12c+6=-2c+6 \\ 10c-12c+2c=6-6 \\ 12c-12c=0 \\ 0=0 \end{gathered}[/tex]it means, that for any value of x, it will work
this equation has infinite solutions
I am in alternative school I am a 12th grader I dropped out Beginning 10th grade then came back to school 12th grade I have applied math I have no clue what I'm doing I'm scared for my finals in May I need help
we have the expression
4÷5×6+7×55
Remember that
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
so
step 1
Multiplication and Division (left-to-right)
5x6=30
7x55=385
substitute in the given expression
4÷30+385
step 2
Multiplication and Division (left-to-right)
4÷30=0.13
substitute
0.13+385
step 3
Addition and Subtraction (left-to-right)
0.13+385=385.13
therefore
the answer is 385.13Which of the following functions best describes this graph?O A. y=x2- 8x+15O B. y=x+8x+15O c. y = x + x - 12O D. y=x2-5x+6
We will investigate how to best represent a parabolic graph using a function description.
All parabolas are denoted as either a " U " or inverted " U ". There are two principal parameters of a parabola. The vertex i.e the maximum or minimum point attained by the parabola. The line of symmetry or focus point: The line of symmetry can either be vertical or horizontal but it always passes through the focus point.
We are given a graph of a parabola that has two zeros which can be read off from the plot.
We will locate these zeros and write them down:
[tex]\begin{gathered} x\text{ = 3} \\ x\text{ = 5} \end{gathered}[/tex]All parabolas are expressed by a quadratic polynomial function. The quadratic polynomial can be expressed in factorized form as follows:
[tex](\text{ x - }\alpha\text{ )}\cdot(x\text{ - }\beta\text{ )}[/tex]Where,
[tex]\begin{gathered} \alpha\text{ = 3 ( First Zero )} \\ \beta\text{ = 5 , ( Second Zero )} \end{gathered}[/tex]We will express our located zeros in the factorized quadratic expressed above:
[tex](\text{ x - 3 )}\cdot(x\text{ - 5 )}[/tex]Then we will try to solve the parenthesis and expand the factorized form as follows:
[tex]\begin{gathered} -5\cdot(x\text{ - 3 ) + x}\cdot(x\text{ - 3 )} \\ -5x+15+x^2\text{ - 3x} \end{gathered}[/tex]Group the similar terms and simplify:
[tex]x^2\text{ - 8x + 15 }[/tex]Therefore the function that best describes the given plot is:
[tex]y=x^2\text{ -8x + 15 }\ldots\text{ Option A}[/tex]Evaluate each expression using the graphs of y=f(x) and y = g(x) shown below.(a) (gof)(-1) (b) (gof)(0) (c) (fog) - 1) (d) (fog)(4)
Answer:
a) 5
b) 6
c) -2
d) -3
Explanation:
Given:
a) From the graph, we can see that f(-1) = 1 and g(1) = 5, so we'll have that;
[tex](g\circ f)(-1)=g(f(-1))=g(1)=5[/tex]b) From the graph, we can notice that f(0) = 0, g(0) = 6, so we'll have that;
[tex](g\circ f)(0)=g(f(0))=g(0)=6[/tex]c) From the graph, we can notice that g(-1) = 4 and f(4) = -2, so we'll have that;
[tex](f\circ g)(-1)=f(g(-1))=f(4)=-2[/tex]d) From the graph, we can see that g(4) = 3 and f(3) = -3, so we'll have that;
[tex](f\circ g)(4)=f(g(4))=f(4)=-3[/tex]I can’t figure this out. Getting different answer than listed. Please help with attached pic.
Solution
We are required to use synthetic division to rewrite the expression
[tex](x^3+6x^2-5)\div(x+2)[/tex]The synthetic division is shown below
Re-write the result in polynomial form
[tex]=x^2+4x-8+\frac{11}{x+2}[/tex]The answer is
[tex]=x^2+4x-8+\frac{11}{x+2}[/tex]I have 2 sets of numbers and need to calculate the percentage between them.
It is 0.696% for Part A, and 0.634% for Part B
Male students are more represented in Part A.
Explanation:Given that there are 19100 students.
For Part A, the percentage of male students is part A is:
[tex]\begin{gathered} \frac{\text{Sum of male students in part A}}{\text{Total male students}} \\ \\ =\frac{133}{19100}\times100 \\ \\ =0.696 \end{gathered}[/tex]For Part A, the percentage of male students is part B is:
[tex]\begin{gathered} \frac{121}{19100}\times100 \\ \\ =0.634 \end{gathered}[/tex]the sum of 2 numbers is 30. the sum of the squares of the two numbers is 468 what is the product of the two numbers
Take x and y as the 2 numbers
Define the equation that represents each situation
The sum of 2 numbers is 30
[tex]x+y=30[/tex]The sum of the squares of the numbers is 468
[tex]x^2+y^2=468[/tex]Complete the square in the second equation (don't forget to write
Consider the sequence below:-2,1,6,13,22, ....What explicit expression can be used to find the nth term of this sequence?
Answer:
f(n)=n²-3
Explanation:
In the sequence:
[tex]-2,1,6,13,22,...[/tex]First, we find the difference between the terms.
[tex]\begin{gathered} 1-(-2)=3 \\ 6-1=5 \\ 13-6=7 \\ 22-13=9 \end{gathered}[/tex]It is observed that the difference between successive terms is the addition of consecutive odd numbers.
This is an example of a quadratic sequence.
The general form of a quadratic sequence is:
[tex]\begin{gathered} f(n)=an^2+bn+c \\ f(1)=-2 \\ \implies a+b+c=-2 \\ f(2)=1 \\ \implies4a+2b+c=1 \\ f(3)=6 \\ \implies9a+3b+c=6 \end{gathered}[/tex]If we solve the system of equations:
[tex]\begin{gathered} a+b+c=-2 \\ 4a+2b+c=1 \\ 9a+3b+c=6 \\ a=1,b=0,c=-3 \end{gathered}[/tex]The explicit expression for this sequence is:
[tex]f(n)=n^2-3[/tex]HEL LE Maria has 36 episodes of Grey's Anatomy to watch with her friends. They watch 3 episodes each day. Which of the following equations represents the number days, d, it took for them to have 21 episodes left? 0210 - 3 = 36 O 21 - 3d = 36 36 - 3d = 21 36 + 3d = 21 LE
Total episodes: 36
Episodes watched per day: 3
Number of days: d
To represents the number of days, d, it will take for them to have 21 episodes left:
Subtract the episodes watched per day (3d) to the total episodes (36), and that expression must be equal to 21:
36-3d=21
Which equation could be used to find how many soft drink refills Ryan ordered
Solution
We are given
Restaurant charge = $16.99
Soft drink refill charge each = $1.75
Ryan paid = C
Let x denotes the number of soft drink refill Ryan ordered, so we have
[tex]16.99+1.75x=C[/tex]Therefore, the answer is
[tex]1.75x+16.99=C[/tex]Find the product. 1. 9 х 10 4 2 10 5. 2 1 X 12 12
First, convert into an improper fraction, then operate and simplify:
[tex]\begin{gathered} 3\frac{2}{8}\cdot\frac{9}{10}\rightarrow\frac{3\cdot8+2}{8}\cdot\frac{9}{10}\rightarrow\frac{26}{8}\cdot\frac{9}{10}\rightarrow\frac{13}{4}\cdot\frac{9}{10}\rightarrow\frac{117}{40} \\ \\ 2\frac{4}{10}\cdot\frac{4}{5}\rightarrow\frac{2\cdot10+4}{10}\cdot\frac{4}{5}\rightarrow\frac{24}{10}\cdot\frac{4}{5}\rightarrow\frac{12}{5}\cdot\frac{4}{5}\rightarrow\frac{48}{25} \\ \\ 1\frac{4}{12}\cdot\frac{2}{12}\rightarrow\frac{12+4}{12}\cdot\frac{2}{12}\rightarrow\frac{16}{12}\cdot\frac{2}{12}\rightarrow\frac{4}{3}\cdot\frac{1}{6}\rightarrow\frac{4}{18}\rightarrow\frac{2}{9} \\ \\ 3\frac{2}{3}\cdot\frac{2}{8}\rightarrow\frac{3\cdot3+2}{3}\cdot\frac{2}{8}\rightarrow\frac{11}{3}\cdot\frac{1}{4}\rightarrow\frac{11}{12} \end{gathered}[/tex]Convert Following expression in radical form into an exponential expression in rational form, multiply and simplify then divide you do not need to evaluate just put in simplest form
9.
[tex]\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}[/tex]Using the following properties:
[tex]\begin{gathered} x^a\cdot x^b=x^{a+b} \\ a^{-x}=\frac{1}{a^x} \\ \sqrt[z]{x^y}=x^{\frac{y}{z}} \end{gathered}[/tex][tex]\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}=5^{\frac{7}{2}}\cdot5^{\frac{6}{2}}\cdot5^{-\frac{3}{5}}=5^{\frac{7}{2}+\frac{6}{2}-\frac{3}{5}}=5^{\frac{59}{10}}[/tex]Answer:
5 7/5
Step-by-step explanation:
As you can see there is a divisions sign so you will start there.
The square root of 5^6 will turn into 5 6/2 divided by 5 3/5.
You want to find the LCD for the denominator. That will be 10, 6 divided by 3 equals 2 so you will have 5 7/2 times 5 2/10. You then change the two to a 10 and multiply the 7 and 2 which will become 5 14/10.
Once simplified the answer is 5 7/5.
Hope this helps :)
how many marriage licenses were issued in 2006 ? round answer to the nearest hundred
To solve the exercise we have to replace the value requested on the equation given to model the problem as above
[tex]y=3.4905(2006)^2-17674(2006)+21533000=124853.658[/tex]As we see and approximating the result to the options, we get that the correct answer is the second one (124900)
A) Find the points of intersection between the curve y = x(x - 1) (x - 2) and x-axis.
To find the intersection of the curve
[tex]y=x(x-1)(x-2)[/tex]And the x-axis, we first have to notice that the x-axis is the same as the line:
[tex]y=0[/tex]Now, we have a system of two equations.
If we substitute y = 0 into the first, we have:
[tex]x(x-1)(x-2)=0[/tex]Now, for this equation to be true, one of the factors, "x", "(x-1)" or "(x-2)" has to be zero.
So, we will have three solutions:
[tex]\begin{gathered} x=0 \\ x-1=0\leftrightarrow x=1 \\ x-2=0\leftrightarrow x=2 \end{gathered}[/tex]And since these are on the x-axis, we already know that the y values for them are all y = 0.
Thus, the points of intersections are:
[tex]\begin{gathered} (0,0) \\ (0,1) \\ (0,2) \end{gathered}[/tex]An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Lisphenotype codes where 1 = smooth-yellow, 2 = smooth-green, 3 = wrinkled-yellow, and 4 = wrinkled-green. Do the results make1 1 3 2 1 2. 4 2 3 1 3 3 3 3A. The mode phenotype code is(Use a comma to separate answers as needed.)Help me solve thisView an exampleGet more help210SongOLD
Step 1
The mode is the value that occurs most often. The mode is the only average that can have no value, one value or more than one value. When finding the mode, it helps to order the numbers first.
For this qustion , the number code that occurs most are/is;
[tex]3[/tex]The mode phenotype code = 3 and this represents wrinkled yellow
Triangles RTS and XYZ are similar. Match each given side of triangle XYZ with the corresponding side on triangle RTS. R À À S TY YZ XY 111 XZ :: RS :: RT :: TS hp
we know that
if the triangles are similar, thrn itcs corresponding sides are proportional
so
In this problem
the corresponding sides are
YZ and TS
XY and RT
XZ and RS
two segments are interesting outside the circle, choose the correct equation to set up before having to solve for y
Option (C)
Given:
Two segments are interesting outside the circle.
The objective is to find the correct equation.
Since the two lines drawn from a point outside the circle passes through two points in a circle, the line is call secant line.
Consider the given figure as,
If two secant line is drawn from a point outside the circle, the equation wil be,
[tex]a(a+b)=c(c+d)[/tex]Now, substitute the given values in the above formula,
[tex]\begin{gathered} 4(4+6)=2(2+y) \\ 4(10)=2(2+y) \end{gathered}[/tex]Hence, option (C) is the correct answer.
PLEASE HELP!!!
As part of a major renovation at the beginning of the year, Atiase Pharmaceuticals, Incorporated, sold shelving units (recorded as Equipment) that were 10 years old for $800 cash. The shelves originally cost $6,400 and had been depreciated on a straight-line basis over an estimated useful life of 10 years with an estimated residual value of $400.
1. Complete the table below, indicating the account, amount, and direction of the effect on disposal. Assume that depreciation has been recorded to the date of sale. (Enter any decreases to Assets, Liabilities, or Stockholders' Equity with a minus sign. Do not round intermediate calculations.)
ASSETS = LIABILITIES + STOCKHOLDERS' EQUITY
The total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.
Given that,
Aliases Pharmaceuticals, Incorporated sold shelving units (recorded as Equipment) that were ten years old for $800 cash as part of a significant upgrade at the beginning of the year. The shelves had a $6,400 initial cost that had been straight-line depreciated over a 10-year anticipated useful life, leaving a $400 estimated residual value.
What is Accounting equation?It is the relationship among the assets, liabilities and stockholders’ equity. Total liabilities, as well as stockholders' equity, equal total assets. This equation states that an increase in assets will result in an increase in either liabilities or owners' equity. The accounting equation is solved using the formula below.
Assets = Liabilities +Stockholders equity
Calculate accumulated depreciation for 10 years.
Accumulated depreciation for 10 years=[(Original cost of the equipment-Residual value) / Useful life] ×10 years
=[($6400-$400)/10 years]×10 years
=$600×10 years
=$6000
Calculate book value of equipment.
Book value equipment=Original cost of the equipment-Accumulated depreciation for 10 years
=$6400-$6000
=$400
Calculate gain on sale of equipment.
Gain on equipment sale equals selling price minus book value of equipment
=$800-$400
=$400
Therefore, the total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.
The table we can see in the picture.
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A 20% tip on a $26.00 dinner bill ishow much money?
Mela, this is the solution:
Dinner bill = $ 26
Tip = 20% or 0.2
Tip = 26 * 0.2
Tip = $ 5.20
Sec 0=9/4, 0 in quadrant 4. Find tan 0. Show your work
Determine the value of angle theta.
[tex]\begin{gathered} \sec \theta=\frac{9}{4} \\ \theta=\sec ^{-1}(\frac{9}{4}) \\ =296.3878\text{ (As }\theta\text{ lie in fourth quadrant)} \end{gathered}[/tex]Determine the value of tan theta.
[tex]undefined[/tex]What are all of the answers for these questions? Use 3 for pi. Please do not use a file to answer, I cannot read it.Question 8.
To calculate the area of the doughnut, we need to calculate the area of the larger circle and substract the area of the smaller circle.
The area of a circle can be calculated using its radius:
[tex]A=\pi r^2[/tex]The diameter of the larger circle is 6cm which meand that its radius is half as large, so the radius is 3 cm and the area of the larger circle is:
[tex]A_L=\pi3^2=9\pi[/tex]Area of 9π cm².
The smaller one have a diameter of 2 cm, so its radius is half as large, radius of 1 cm.
So, the area of the smaller circle is:
[tex]A_S=\pi1^2=\pi[/tex]Area of π cm².
The total shaded area is, then, the area of the larger minus the area of the smaller.
So, the shaded area is:
[tex]\begin{gathered} A=A_L-A_S \\ A=(9\pi-\pi)cm^2 \\ A=8\pi cm^2 \\ A\approx(9\cdot3)cm^2 \\ A\approx27cm^2 \end{gathered}[/tex]The area of the entire figure below is 111 square unit.The area of the entire figure below is 111 square unit.
Looking at the image, the width of the rectangle is 7 small rectangles and the length is 9 small rectangles, therefore the area of 1 square unit is equal to 9 * 7 = 63 small rectangles.
From these small rectangles, an area of 5 * 4 = 20 small rectangles is shaded.
Therefore the shaded area is calculated as:
[tex]\frac{20}{63}\cdot1\text{ square unit}=\frac{20}{63}\text{ of a square unit}[/tex]Use the Law of Sines to find the indicated side x. (Assume a = 400. Round your answer to two decimal places.)
The law of sines is given by:
a/sinA = b/sinB = c/sinC
Take into account that in the given problem you need to know what is the measure of angle C, to be able to use the law of sines.
Consider that the sum of the interioiro angles of a triangle is 180°. Then, you have:
m∠C + 98.4° + 24.6° = 180°
m∠C + 123° = 180°
m∠C = 180° - 123°
m∠C = 57°
Next, use the law of sines with sides a and x, angle A and C:
a/sinA = x/sinC solve for x
(a/sinA)(sinC) = x
x = (a/sinA)(sinC) replace the values of known parameters (a = 400)
x = (400/sin98.4°)(sin57°)
x = 339.106
Hence, the length of side x is x = 339.106