You have to find the greatest common factor first.
To do so, do as follows:
[tex]6x^4-42x^3+12x^2[/tex]Factors of 6 are: 1, 2, 3, 6
Factors of 12 are: 1, 2, 3, 4, 6, 12
Factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The greates common factor is the greatest common factor shared by all values, in this case is 6
Now to factor it out you have to divide each term of the equation by it.
[tex](\frac{6x^4}{6})=x^4[/tex][tex](\frac{42x^3}{6})=7x^3[/tex][tex](\frac{12x^2}{6})=2x^2[/tex]The expression with the GCF factorized is then:
[tex]6(x^4-7x^3+2x^2)[/tex]Evaluate: 6+ [8x(5-1)]
6+ [8x(5-1)]
First, solve the parenthesis:
6+ [8x4]
Then the brackets:
6+ 32
Finally, add both numbers.
38
What is the difference between 3xg and gº? .
EXPLANATION
The difference is that 3*g is a multiplication that give us a Real number and g° is a degree number.
Find two points on the line to graph the function Any lines orCurves will be drawn once all required points are plotted
ANSWER:
A: (4, 9)
B: (-1, -3)
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]q(x)=4x-\frac{(3+8x)}{5}[/tex]We determine the two points when x = 4 and when x = -1, like this:
[tex]\begin{gathered} q(4)=4\cdot4-\frac{\left(3+8\cdot4\right)}{5}\: \\ \\ q(4)=16-\frac{3+32}{5}=16-7 \\ \\ q(4)=9 \\ \\ A=(4,9) \\ \\ q(-1)=4\cdot\left(-1\right)-\frac{\left(3+8\cdot(-1)\right)}{5}\: \\ \\ q(-1)=-4-\frac{3-8}{5} \\ \\ q(-1)=-4-(-1)=-4+1 \\ \\ q(-1)=-3 \\ \\ B=(-1,-3) \end{gathered}[/tex]Therefore point A is (4, 9) and point B is (-1, -3)
Solve the compound an equality. Write the solution in interval notation.
Step 1: Write the two inequalities equations
[tex]4u\text{ + 1 }\leq\text{ -3 -2u }\ge\text{ 10}[/tex]Step 2: Solve the two inequalities separately
[tex]\begin{gathered} 4u\text{ + 1 }\leq\text{ -3} \\ 4u\text{ }\leq\text{ -3 -1 } \\ 4u\text{ }\leq\text{ -4} \\ u\text{ }\leq\text{ }\frac{-4}{4} \\ u\text{ }\leq\text{ -1} \end{gathered}[/tex][tex]\begin{gathered} -2u\text{ }\ge\text{ 10} \\ \text{When you divide inequalities by -2, the sign will change} \\ \frac{-2u}{-2}\text{ }\leq\text{ }\frac{10}{-2} \\ u\text{ }\leq\text{ -5} \end{gathered}[/tex]
Final answer
[tex](-\infty,\text{ -5\rbrack}[/tex]Or
[tex]\lbrack\text{ x }\leq\text{ -5\rbrack or ( -}\infty,\text{ -5)}[/tex]Calculate the sum of interior angles of a 6 sided polygon
The sum of interior angles of a polygon can be calculated using the formula below.
[tex]\begin{gathered} S\text{ = }(n-2)\times180^0 \\ \text{Where; } \\ S\text{ = sum of interior angles of the polygon } \\ n\text{ = number of sides of the polygon} \end{gathered}[/tex]For the given question the polygon is 6 sided, so;
[tex]n\text{ = 6}[/tex]Substituting the value of n into the formula, we have;
[tex]\begin{gathered} S\text{ = (6-2)}\times180^0 \\ S\text{ = 4}\times180^0 \\ S=720^0 \end{gathered}[/tex]Therefore, the sum of interior angles of a 6 sided polygon is 720 degree
[tex]S=720^0[/tex]I don't understandDescribe in words and by using function notation
f(x) = 2(x +3)^2 + 1
1. Scale f(x) by 1/2 ==> (1/2) f(x) = (x + 3)^2 + 1
2. Reflect f(x) through x axis ==> -(x+3)^2 + 1
3. Shirt f(x) to the right by 5 units ==> -(x + 3)^2 - 4
4. Shift f(x) down by 5 units ==> -(x - 2) - 4 = g(x)
Given that tan A= 5/12 and tan B= -4/3 such that A is an acute angle and B is an obtuse angle find the value of,a) tan (A-45°)b) tan (B+360°)
Solve for tan(A-45°).
Recall that tan(45°) = 1
[tex]\begin{gathered} \tan (A-45\degree)=\frac{\tan A-\tan B}{1+\tan A\tan B} \\ \tan (A-45\degree)=\frac{\frac{5}{12}-1}{1+(\frac{5}{12})(1)} \\ \tan (A-45\degree)=\frac{-\frac{7}{12}}{1+\frac{5}{12}} \\ \tan (A-45\degree)=\frac{-\frac{7}{12}}{\frac{17}{12}} \\ \tan (A-45\degree)=-\frac{7}{17} \end{gathered}[/tex]Therefore, tan(A-45°) = -7/17.
Solve for tan(B+360°)
Recall that tan(360°) = 0
[tex]\begin{gathered} \tan (B+360\degree)=\frac{\tan A+\tan B}{1-\tan A\tan B} \\ \tan (B+360\degree)=\frac{\frac{5}{12}+0}{1-(\frac{5}{12})(0)} \\ \tan (B+360\degree)=\frac{\frac{5}{12}}{1-\frac{5}{12}} \\ \tan (B+360\degree)=\frac{\frac{5}{12}}{\frac{7}{12}} \\ \tan (B+360\degree)=\frac{5}{7} \end{gathered}[/tex]Therefore, tan(B+360°) = 5/7.
Match the appropriate graph to each equation. t(x)= 1/x+3t(x) = -1/x +3
The graph of the function is attached below.
[tex]t(x)=\frac{1}{x+3}[/tex]This matches with the 3rd graph.
Part B
The graph of the function is attached below
[tex]t(x)=-\frac{1}{x}+3[/tex]This matches with the 2nd graph.
Determine whether the ordered pair is a solution of linear equation.Y = x - 1/2, ( -5, -2 ) A- yes it is a solution B- no it is not a solution
The ordered pair is (- 5, - 2)
This means that when x = - 5, y = - 2
To determine if the ordered pair is a solution of the linear equation, We would substitute the values into the equation. If we substitute x = - 5 into the equation and y gives us - 2, then it is a solution.
Therefore,
y = - 5 - 1/2 = - 5 - 0.5
y = - 5.5
Since it is not - 2, then the answer is B
B- no it is not a solution
ed pai
Nine hundred people who attended a movie were asked whether they enjoyed it. The table shows the results.Did Not EnjoyTotalChildrenAdultsTotalEnjoyed461277738114162900How many more children were surveyed than adults? Enter a numerical answer only
Given:
Total number of people that attended = 900
The total number of adults that attended = 277 + 114 = 391
Total number of children that attended = Total number of people - number of adults
= 900 - 391 = 509
To find how many more children were surveyed than adults, subtract the number of adults from the number of children.
Thus, we have:
Number of children surveyed than adults = 509 - 391 = 118
Therefore, 118 more children were surveyed more than adults.
Let's complete the table below:
ENJOYED DID NOT ENJOY TOTAL
CHILDREN 461
Need help. The ps5 cost 610 dollars And Be gets 100 dollars every week
Let x be the number of weeks after Mohammed started to save up. Since he receives $100 every week, then, after x weeks, he would receive 100x dollars.
Since he already had $50 at the beginning, then, the total amount of money y that he has saved after x weeks, is:
[tex]y=100x+50[/tex]Since the cost of the PS5 is $610, then, set y=610 and solve for x to find the number of weeks that he will need to save money:
[tex]\begin{gathered} y=610 \\ \Rightarrow610=100x+50 \\ \Rightarrow610-50=100x \\ \Rightarrow560=100x \\ \Rightarrow\frac{560}{100}=x \\ \Rightarrow x=5.6 \end{gathered}[/tex]He will need to save for at least 5.6 weeks. Nevertheless, he only receives money once a week and 5 weeks won't be enough for buying the PS5. Then, he needs to save for 6 weeks.
Which statement describes a key feature of the function g if g(x) =f(x)-7
The graph of the function f(x)=e^x is given.
To determine the function g(x),
g(x)=f(x)-7.
Then the graph of function g(x) is
Then from the graph above , the horizontal asymptote is y=-7.
Hence the correct option is D.
please help me please please please please please please please please please please please please please please
EXPLANATION
The Area of a square shape is:
Area= side*side = s^2
If we have that:
Area = 121 yd^2, then:
121=s^2
Isolating s:
[tex]s=\sqrt[]{121}=11\text{ ---> The answer is 11}[/tex]Solve for y:2x – 3y = 5
y = (2x-5)/3
Explanation:
[tex]\begin{gathered} 2x\text{ - 3y = 5} \\ To\text{ solve for y, we need to make y the subject of formula} \end{gathered}[/tex][tex]\begin{gathered} \text{Let's take every other thing not attached to y to the right side of the equation:} \\ -3y\text{ = 5 - 2x} \\ To\text{ make y stand alone, we will divide through by -3} \\ \frac{-3y}{-3}=\text{ }\frac{5-2x}{-3} \\ y\text{ = }\frac{-(5-2x)}{3}\text{ or }\frac{-5\text{ +2x}}{3}\text{ } \\ y\text{ = }\frac{2x\text{ -5}}{3} \end{gathered}[/tex]What is the area of this figure?5 in5 in12 in23 in18 in17 in
The area of the figure is 331 square inches
Explanation:The area of the shape can be obtained by:
Treating the shape as a rectangle with side lengths 23 in and 17 in
Finding the area of the rectangle
Finding the area of the small portion cut, which is a rectangle with side lengths 5 in and 12 in.
Subtracting the area of the small portion from the area of the big rectangle.
Area of the big rectangle = 23 * 17 = 391 in^2
Area of the small portion = 5 * 12 = 60 in^2
Area of the shape = 391 - 60 = 331 in^2
Identify the parent function of f(x) = -×^2+2
The given function is
[tex]f(x)=-x^2+2[/tex]The parent function refers to the simplest function possible.
Hence, the parent function is[tex]f(x)=x^2[/tex]Consider the following functions.Step 3 of 4: Find (f g)(-1). Simplify your answer.Answerf(x) = x² + 6 and g(x) = -x +5(-2)-1)=
Solving for (f•g)(-1)
[tex]\begin{gathered} (f\cdot g)(x)=f(x)\cdot g(x) \\ (f\cdot g)(x)=(x^2+6)\cdot(-x+5) \\ (f\operatorname{\cdot}g)(-1)=((-1)^2+6)\operatorname{\cdot}(-(-1)+5) \\ (f\operatorname{\cdot}g)(-1)=(1+6)\cdot(1+5) \\ (f\operatorname{\cdot}g)(-1)=7\cdot6 \\ \\ \text{Therefore, }(f\operatorname{\cdot}g)(-1)=42 \end{gathered}[/tex]In 2018 the scores of students on the May SAT had a normal distribution with mean u = 1450 and a standard deviation of o = 120.a. What is the probability that a single student randomly chosen from all those taking the test scores 1500 or higher?b. If a sample of 50 students is taken from the population, what is the probability that the sample mean score of these students is 1470 or higher?
From the question,
[tex]\begin{gathered} \mu\text{ = 1450, } \\ \sigma\text{ = 120} \end{gathered}[/tex]a. We are to find the probability that a single student randomly chosen from all those taking the test scores 1500 or higher?
we will do this using
[tex]\begin{gathered} P(x<\text{ z) such that } \\ z\text{ = }\frac{x\text{ -}\mu}{\sigma} \end{gathered}[/tex]From the question, x = 1500.
Therefore
[tex]\begin{gathered} z\text{ =}\frac{1500\text{ - 1450}}{120} \\ z\text{ = }\frac{50}{120} \\ z\text{ = 0.417} \end{gathered}[/tex]applying z - test
[tex]\begin{gathered} P(xThus, the probability that a single student is randomly chosen from all those taking the test scores 1500 or higher is approximately 34%b. From the question
[tex]\begin{gathered} n\text{ = 50, }^{}\text{ }\mu\text{ = 1450} \\ \bar{x}\text{ = 1470},\text{ }\sigma\text{ = 120} \end{gathered}[/tex]we will be using
[tex]\begin{gathered} z\text{ = }\frac{\bar{x}\text{ - }\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ \end{gathered}[/tex]inserting values
[tex]\begin{gathered} z\text{ = }\frac{1470\text{ - 1450}}{\frac{120}{\sqrt[]{50}}} \\ z\text{ = }20\text{ }\times\frac{\sqrt[]{50}}{120} \\ z\text{ = }\frac{\sqrt[]{50}}{6} \\ z\text{ = 1.18} \end{gathered}[/tex]Applying z-test
[tex]\begin{gathered} P(xHence,
The probability that the sample mean score of these students is 1470 or higher is approximately 12%
More and more people are purchasing food from farmers' markets. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 5% each year. If there are 7,700 farmers' markets this year, how many will there be in 5 years?
Given:
A market researcher predicts that the number of farmers' markets will increase by 5% each year
There are 7,700 farmers' markets this year
we will the number of farmers' markets after 5 years
So, we will use the following formula:
[tex]A=P\cdot(1+r)^t[/tex]We will calculate (A) when P = 7700, r = 5% and t = 5
so,
[tex]A=7700\cdot(1+\frac{5}{100})^5=7700\cdot1.05^5=9827.368[/tex]Rounding to the nearest whole number
so, the answer will be 9827
I need help with this question please! I have options to choose from also. Also the graph below the wording is just option A
The correct option is D
Explanation:Given the function:
[tex]f(x)=x^2-5x+6[/tex]This may be written as:
[tex]y=x^2-5x+6[/tex]For x = -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
we need to find the corresponding values for y.
For x = -5
y = (-5)^2 - 5(-5) + 6
= 56
For x = -4
y = (-4)^2 - 5(-4) + 6
= 42
For x = -3
y = (-3)^2 - 5(-3) + 6
= 30
For x = -2
y = (-3)^2 - 5(-2) + 6
= 20
For x = -1
y = (-1)^2 - 5(-1) + 6
= 12
For x = 0
y = (0)^2 - 5(0) + 6
= 6
For x = 1
y = (1)^2 - 5(1) + 6
= 2
For x = 2
y = (2)^2 - 5(2) + 6
= 0
For x = 3
y = 3^2 - 5(3) + 6
= 0
For x = 4
y = 4^2 - 5(4) + 6
= 2
For x = 5
y = 5^2 - 5(5) + 6
= 6
By inspection, we see that the correct option is D
Suppose z varies directly with x and inversely with the square of y. If z = 18 when I = 6 and y = 2, what is z when I 7 and y = 7? Z =
It is given that z varies directly with x and inversely with the square of y so it follows:
[tex]z=k\frac{x}{y^2}[/tex]It is also given that z=18 when x=6 and y=2 so it follows:
[tex]\begin{gathered} 18=k\frac{6}{2^2} \\ k=\frac{18\times4}{6} \\ k=12 \end{gathered}[/tex]So the equation of variation becomes:
[tex]z=12\frac{x}{y^2}[/tex]Therefore the value of z when x=7 and y=7 is given by:
[tex]\begin{gathered} z=\frac{12\times7}{7^2} \\ z=\frac{12}{7} \\ z\approx1.7143 \end{gathered}[/tex]Hence the value of z is 12/7 or 1.7143.
this composed figure is made up of three similar shapes what is the area of the figure
Given data:
The given figure is shown.
The area of the composite figure is,
[tex]\begin{gathered} A=(10\text{ cm)}\times(5\text{ cm)+}(3\text{ cm)(6 cm)+}\frac{1}{2}(3\text{ cm)(4 cm)} \\ =50cm^2+18cm^2+6cm^2 \\ =74cm^2 \end{gathered}[/tex]Thus, the area of the composite figure is 74 square-cm.
Read the following conjectures and decide if they are true or false: • Angles that are adjacent angles share a vertex. • All right angles are supplementary angles. • The square of all odd numbers is an odd number • The product of an even number and odd number is even Counterexamples:
1) Angles that are adjacent share a common vertex = True
Points to know about adjacent angles:
They have a side in common
They have a common vertex
They do not overlap
2) All right angles are supplementary angles = False
Right angles = 90 degrees (they are complementary)
3) The square of all odd numbers is an odd number = True
All odd numbers take the form 2n + 1 (notice the offshoot of 1)
The square of odd numbers will be :
(2n + 1) ² = 4n ² + 4n + 1 (this also has an offshoot of 1)
This means that both an odd number and its square are odd
4) The product of an even number and an odd number is even = True
I have a calculus question about linear approximation. It is a doozie. High school, 12th grade senior AP Calculus. Math, not physics.
To get the linear approximation, we follow the equation below:
[tex]y=f(a)+f^{\prime}(a)(x-a)[/tex]where "a" is the given value of x and f'(a) is the slope of the function at a given value of "a".
In the given equation, the given value of "a" or x is 5.
Let's now solve for the linear approximation. Here are the steps:
1. Solve for f(a) by replacing the x-variable in the given function with 5.
[tex]f(5)=5^5[/tex][tex]f(a)=3125[/tex]The value of f(a) is 3125.
2. Solve for the first derivative of f(x) using the power rule.
[tex]f(x)=x^5\Rightarrow f^{\prime}(x)=5x^4[/tex]The first derivative is equal to 5x⁴.
3. Replace the "x" variable in the first derivative with 5 and solve.
[tex]f^{\prime}(5)=5(5)^4[/tex][tex]f^{\prime}(5)=5(625)[/tex][tex]f^{\prime}(5)=3125[/tex]The value of the first derivative at x = 5 is also 3,125.
4. Using the linear approximation formula above, let's now replace f(a) with 3125 and f'(a) with 3125 as well since those are the calculated value in steps 1 and 3. Replace "a' with 5 too.
[tex]y=3125+3125(x-5)[/tex][tex]y=3125+3125(x-5)[/tex]5. Simplify the equation above.
[tex]y=3125+3125x-15625[/tex][tex]y=3125x-12500[/tex]Hence, the equation of the tangent line to f(x) at x = 5 is y = 3,125x - 12500 where the slope m is 3,125 and the y-intercept b is -12,500.
Now, to find our approximation for 4.7⁵, replace the "x" variable in the equation of the tangent line with 4.7 and solve.
[tex]y=3,125x-12,500[/tex][tex]y=3,125(4.7)-12,500[/tex][tex]y=14,687.5-12,500[/tex][tex]y=2187.5[/tex]
Using the approximated linear equation, the approximated value of 4.7^5 is 2, 187.5.
A door to playhouse is 50 inches tall.Which of the following is another measure eaqual to the height?A.4 ft 2 in.B.4 ft 1 in.C.4 ft 1/2 in.D.5 ft
Dereo, this is the solution:
All we need to do is to convert inches to feet, as follows:
Let's recall that:
12 inches = 1 feet
In consequence,
50 inches = 50/12 feet
50 inches = 4 feet + 2 inches
The correct answer is A.
The school that Imani goes to is selling tickets to a spring musical. On the first day of ticketsales the school sold 6 senior citizen tickets and 8 child tickets for a total of $122. The schooltook in $167 on the second day by selling 9 senior citizen tickets and 8 child tickets. WriteaSOE and solve it to find the price of a senior citizen ticket and the price of a child ticket
Define the system of equations to solve the problem
Take x as the price of a senior citizen ticket and y as the price of a child ticket
[tex]\begin{gathered} 6x+8y=122 \\ 9x+8y=167 \end{gathered}[/tex]Solve the system
[tex]\begin{gathered} 6x+8y=122 \\ 8y=122-6x \\ 9x+8y=167 \\ 8y=167-9x \end{gathered}[/tex][tex]\begin{gathered} 122-6x=167-9x \\ 9x-6x=167-122 \\ 3x=45 \\ x=\frac{45}{3} \\ x=15 \end{gathered}[/tex][tex]\begin{gathered} 8y=122-6x \\ y=\frac{122-6x}{8} \\ y=\frac{122-6\cdot15}{8} \\ y=\frac{122-90}{8} \\ y=\frac{32}{8} \\ y=4 \end{gathered}[/tex]The price of a senior citizen ticket is $15 and for child is $4
One canned juice drink is 20% orange juice, another is 10% orange juice. How many liters of each should be mixed together in order to get 10L that is 11% orangeNice?
Let:
x = Liters of 20% orange juice
y = Liters of 10% orange juice
z = Liters of 11% orange juice
so:
[tex]0.2x+0.1y=10\cdot0.11[/tex]so:
[tex]\begin{gathered} 0.2x+0.1y=1.1 \\ y=10-x \\ so\colon \\ 0.2x+0.1(10-x)=1.1 \\ 0.2x+1-0.1x=1.1 \\ 0.1x=0.1 \\ x=\frac{0.1}{0.1} \\ x=1 \\ so\colon \\ y=10-1=9 \end{gathered}[/tex]Answer:
1 liters of 20% orange juice
9 liters of 10% orange juice
Over 12 hours, the water in Julia's pool drained a total of 534.72 liters. It drained the same number of liters each hour. Write an equation to represent the change in the number of liters of water in Julia's pool each hour.
Answer:
the pool lost 44.56 liters per hour
Step-by-step explanation:
find the following numbers
We have the numbers 5, 11, 8, 8 7, 4, 10, 9, 7, 7, 6 and we have to calculate its mean.
To calculate the mean of a group of numbers we have to sum them all and then divide by the number of items we have added.
In this case we have 11 elements, so the mean can be calculated as:
[tex]M=\frac{5+11+8+8+7+4+10+9+7+7+6}{11}=\frac{82}{11}\approx7.45[/tex]The mean of this group of numbers is 7.45 periodic.
15h - 13h - h + 3= 7
Answer:
[tex]h=4[/tex]Explanation: We need to solve for h in the given equation, which is:
[tex]15h-13h-h+3=7[/tex]Isolating unknowns and constants:
[tex]\begin{gathered} 15h-13h-h+3=7\rightarrow15h-14h+3=7 \\ \therefore\rightarrow \\ 15h-14h=7-3=4 \\ \therefore\rightarrow \\ 15h-14h=4 \end{gathered}[/tex]Simplifying gives:
[tex]\begin{gathered} 15h-14h=4 \\ \therefore\rightarrow \\ h=4 \end{gathered}[/tex]