To find the absolute value of -1 1/2 +5 you make the addition:
You can write the mixed number also as -3/2 (because -1 is equal to -2/2 and -2/2 and 1/2 is -3/2).
You add fractions as follow:
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}[/tex]You can write the 5 as 5/1:
[tex]-\frac{3}{2}+\frac{5}{1}=\frac{-3\cdot1+5\cdot2}{2\cdot1}=\frac{-3+10}{2}=\frac{7}{2}[/tex]As the addition of the given numbers is 7/2, the absolute value or the distance is:
[tex]\lvert\pm a\rvert=a[/tex][tex]\lvert-1\frac{1}{2}+5\rvert=\lvert\frac{7}{2}\rvert=\frac{7}{2}[/tex]Then, the distance is 7/2Third-degree, with zeros of -3,-1, and 2 and passes through the point (3,6)
Since the polynomial must have zeroes at x=-3, x=-1, x=2, then, we can write it as a combination of the factors (x+3), (x+1), (x-2):
[tex]p(x)=k(x+3)(x+1)(x-2)[/tex]The constant k will help us to adjust the value of the polynomial when x=3:
[tex]\begin{gathered} p(3)=k(3+3)(3+1)(3-2) \\ =k(6)(4)(1) \\ =24k \end{gathered}[/tex]Since p(3) must be equal to 6, then:
[tex]\begin{gathered} 24k=6 \\ \Rightarrow k=\frac{6}{24} \\ \Rightarrow k=\frac{1}{4} \end{gathered}[/tex]Therefore, the following polynomial function has zeroes at -3, -1 and 2, and passes through the point (3,6):
[tex]p(x)=\frac{1}{4}(x+3)(x+1)(x-2)[/tex]Write an equation for the line that contains (-32, -12) and is perpendicularto the graph -8x + 10y = 40Can anyone that KNOWS the answer help?
The first step is finding the slope of the equation -8x + 10y = 40.
To do so, let's put this equation in the slope-intercept form: y = mx + b, where m is the slope.
So we have:
[tex]\begin{gathered} -8x+10y=40 \\ -4x+5y=20 \\ 5y=4x+20 \\ y=\frac{4}{5}x+4 \end{gathered}[/tex]Then, since the line we want is perpendicular to this given line, their slopes have the following relation:
[tex]m_2=-\frac{1}{m_1}[/tex]So, calculating the slope of the line, we have:
[tex]m_2=-\frac{1}{\frac{4}{5}}=-\frac{5}{4}[/tex]Finally, our equation has the point (-32, -12) as a solution, so we have:
[tex]\begin{gathered} y=mx+b \\ y=-\frac{5}{4}x+b \\ -12=-\frac{5}{4}\cdot(-32)+b \\ -12=-5\cdot(-8)+b \\ -12=40+b \\ b=-12-40 \\ b=-52 \end{gathered}[/tex]So our equation is y = (-5/4)x - 52
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]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]Which 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]The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).8,20,50,...Find the 10th term.
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
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
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]Which of the following statements about the Real Number System is always true?A Rational numbers include irrational numbers.B A number that is an integer is also a whole number and a natural number.C A number that is a whole number is also an integer and a rational Fimber.Tmber.D A number that is a whole numbers is also a natural number.
C
1) Let's draw a sketch to better understand this:
2) So, based on that we can say that
A number that is a Whole number is also an integer and a Rational Number.
Whole numbers are counting number with the 0 included
Integers numbers are whole numbers and the negative numbers
Rational numbers are any number that can be written as a ratio like 2, (2/1), 3/2, 5, 6/7, etc.
So whole numbers are integer numbers and rational ones simultaneously.
For example 2, 3, etc.
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]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]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
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]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 :)
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.
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
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 385.13Part A: Show all work to solve the quadratic equation x2 − 12x + 35 = 0 by factoring.Part B: Using complete sentences, explain what the solutions from Part A represent on the graph.
Answer:
A) Notice that:
[tex]\begin{gathered} x^2-12x+35=x^2+(-5-7)x+(-5)(-7) \\ =x^2-5x-7x+(-5)(-7)=x(x-5)-7(x-5) \\ =(x-7)(x-5)\text{.} \end{gathered}[/tex]Therefore:
[tex]x^2-12x+35=0\text{ if and only if x=7 or x=5.}[/tex]B) The solutions from part A represent the x-coordinates of the x-intercepts of the graph of the function
[tex]f(x)=x^2-12x+35.[/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
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]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
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.
What is the volume of this rectangular prism? 5/3 cm 1/4 cm 3/2 cm
The volume of the prism can be determined as,
[tex]\begin{gathered} V=\frac{5}{3}cm\times\frac{1}{4}cm\times\frac{3}{2}cm \\ V=\frac{5}{8}cm^3 \end{gathered}[/tex]Thus, the required volume is 5/8 cubic centimeters.
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]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
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]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.
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.
To learn more about liability visit: https://brainly.com/question/18484315
#SPJ1
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]