ANSWER :
f(x) = (3x-2)(x-3)(x-4)(x-2)^3
EXPLANATION :
A polynomial with a degree of 6 has 6 factors.
f(x) = (x - a)(x - b)(x - c)(x - d)(x - e)(x - f) with 6 roots or x-intercepts.
But the problems states that it has 4 x-intercepts, so we will reduced the number of roots but maintaining the number of factors.
f(x) = (x - a)(x - b)(x - c)(x - d)(x - a)(x - a).
From here, we still have 6 factors but only 4 x-intercepts, the last two factors (x - a) is the same as the first factor.
So we can rewrite this as :
[tex]f(x)=(x-a)^3(x-b)(x-c)(x-d)[/tex]Next is to have a y-intercept of 64, y-intercept is the value of f(x) when x = 0
Substitute 0 to the function.
[tex]\begin{gathered} f(0)=(0-a)^3(0-b)(0-c)(0-d) \\ f(0)=a^3(b)(c)(d) \end{gathered}[/tex]Now we have f(0) = a^3bcd and f(0) = 64 as the definition from above.
We need to find the factors of 64,
64 = 8 x 4 x 3 x 2/3
And we can rewrite the equation as :
[tex]\begin{gathered} f(0)=a^3bcd \\ 64=a^3bcd \\ 8\times4\times3\times\frac{2}{3}=a^3bcd \end{gathered}[/tex]From here, we can observe that,
a^3 = 8 ⇒ a = 2
b = 4
c = 3
d = 2/3
So the function will be :
[tex]\begin{gathered} f(x)=(x-2)^3(x-4)(x-3)(x-\frac{2}{3}) \\ f(x)=(x-2)^3(x-4)(x-3)(3x-2) \end{gathered}[/tex]Explanation in 2/3
Since we only need 4 distinct factors of 64.
8 x 4 x 3 x 2/3
8 x 4 = 32
The product of the 3rd and 4th factor should be 2, in order to get 64.
Since from the first
The top needs to know what type of triangle like sas ssa or the other types
From the parameters given, the triangle could be as shown below
a) From the above figures, the triangle can either be an acute triangle or a reflex triangle .
b) There are thus, 2 solutions
Suppose the Rocky Mountains have 72 centimeters of snow. Warmer weather is melting the snow at a rate of
5.8 centimeters a day. If the snow continues to melt at this rate, after seven days of warm weather, how much
snow will be left?
Answer:
31.4 cm
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The y-intercept is the y-value when x is zero, so the initial value.
If the initial amount of snow is 72 cm, the y-intercept is 72.
The slope is the rate of change.
If the snow is melting at a rate of 5.8 cm per day, then the rate of change is -5.8.
Therefore, the equation that models the given word problem is:
[tex]\boxed{\begin{minipage}{5.4 cm}\phantom{w}\\$y=-5.8x+72$\\\\where:\\ \phantom{ww}$\bullet$ $y$ is height of the snow in cm. \\ \phantom{ww}$\bullet$ $x$ is the time in days.\\\end{minipage}}[/tex]
To find how much snow is left after 7 days, substitute x = 7 into the found equation:
[tex]\implies y=-5.8(7)+72[/tex]
[tex]\implies y=-40.6+72[/tex]
[tex]\implies y=31.4[/tex]
Therefore, there will be 31.4 cm of snow left after seven days of warm weather.
An item on sale costs 40% of the original price if the original price was $25 what is the sale price
Answer: $10
Step-by-step explanation:
original price = 25
40% = 0.4
25 * 0.4= 10
Which answer choice identifies the relevant information in the problem?
Sarah left the house at 12:15 p.m. to go to the store. She spent $42.20 on 2 books for her children and she spent $5.67 on a toys for her dog, Rover. Sarah arrived home at 1:00 p.m. How much did Sarah spend on each book?
Answer:
$18.26
Step-by-step explanation:
The total price is $42.20
We want to know how much 1 of those books cost
We know that $5.67 were for her dog
So we are gonna subtract that from $42.20
$42.20-$5.67=36.53
Now your gonna divide that by 2 because she got 2 books
So 36.53/2=$18.26
1 book=$18.26
I call a selling books for $12 each she wants to make more than $180 in books sellers the inequality 12b>180 can be used to detain the numbers of books ,b, she must sell in order to meet her goal which number line best represents the solution of the inequality
solve for b:
Divide both sides by 12:
[tex]\begin{gathered} \frac{12}{12}b>\frac{180}{12} \\ b>15 \end{gathered}[/tex]The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h(t)=−6t2+24t . Re-write h(t) in the form h(t)=a(t-h)^2+k and determine the maximum height of the projectile. Show all work.
We are given the following function:
[tex]h(t)=-6t^2+24t[/tex]We will take "-6" as a common factor:
[tex]h(t)=-6(t^2-4t)[/tex]Now, we will complete the square in the expression inside the parenthesis by adding and subtracting the following term:
[tex]undefined[/tex]The instructor’s friend also plans to rent an apartment in the same complex. Use the graph to identify the y-intercept and the slope used to write the equation in slope intercept form.
y-intercept =
Slope =
Linear equation =
The y-intercept of the graph is: 3,000
The slope is: -2.75
The linear equation of the graph is: y = -2.75x + 3,000.
What is the Linear Equation of a Graph?The linear equation that represents a linear graph shows the slope (m) and y-intercept (b) of the graph and is expressed in slope-intercept form as, y = mx + b.
In the given graph:
The y-intercept (b) is the starting value, which is the point on the y-axis where the line intercepts, and it is equal to: 3,000.
Using two points on the graph, (0, 3,000) and (2, 2,450), the slope of the graph = change in y / change in x = (3,000 - 2,450)/(0 - 2) = 550/-2 = -2.75.
To write the linear equation, substitute m = -2.75 and b = 3,000 into y = mx + b:
y = -2.75x + 3,000.
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1. Given the following table and graph, write the equation to representthe exponential function.уy43-1-4210-2-4-20х1-12-0.5
In order to find the equation of this exponential function, let's use this model for an exponential equation:
[tex]y=a\cdot b^x[/tex]Now, using some of the points given, we can find the values of the coefficients 'a' and 'b':
[tex]\begin{gathered} x=0,y=-2 \\ -2=a\cdot b^0 \\ a=-2 \\ \\ x=1,y=-1 \\ -1=-2\cdot b^1 \\ b=\frac{-1}{-2}=0.5 \end{gathered}[/tex]So our function is:
[tex]y=-2\cdot0.5^x[/tex]Write the correct expression for the following statement.
x six times
Use / for division
do not put any spaces
For each expression, select all equivalent from the list.
(a) 9x-5x+8x
(b) 9(1+7y)
Answer:
a)12x
b)9+63y
goodluck
A group of 175 college students who took math last term were interviewed. They were asked whether they passed their math course and whether they live on campus. Their responses are summarized in the following table. Passed math Failed math Live on campus 49 21 Live off campus 28 77 Х x $ ? (a) What percentage of the students passed math? [% (b) What percentage of the students live on campus? % (C) What percentage of the students who live on campus passed math? []% (d) Is there evidence that students who live on campus tend to pass math more often than average? O No, because the percentage found in part (c) is about the same as the percentage found in part (a). O No, because the percentage found in part (c) is about the same as the percentage found in part (b). ○Yes, because the percentage found in part (C) is much greater than the percentage found in part (a).○yes because the percentage found in part C is much greater than the percent is found in Part B
Given the group of 175 college students who took math last term:
(a) You can identify in the table that the total number of students that passed math is:
[tex]49+28=77[/tex]Therefore, knowing the total number of students that were interviewed, you can determine that the percentage of the students who passed math is:
[tex]\frac{77}{175}\cdot100=44\text{ \%}[/tex](b) Based on the data shown in the table, the total number of students who live on campus is:
[tex]49+21=70[/tex]Therefore, you can determine that the percentage of the students who live on campus is:
[tex]\frac{70}{175}\cdot100=40\text{ \%}[/tex](c) You can identify that 49 students live on campus and passed math. Therefore, the percentage of the students who live on campus and passed math is:
[tex]\frac{49}{49+28}\cdot100\approx63.6\text{ \%}[/tex](d) Knowing that 63.6% of the students who live on campus passed math, 40% of the student who live on campus, and 44% of the students interviewed passed math, you can identify that students who live on campus tend to pass math more often than average, because:
[tex]63.6\text{ \%}>40\text{ \%}[/tex]Hence, the answers are:
(a)
[tex]44\text{ \%}[/tex](b)
[tex]40\text{ \%}[/tex](c)
[tex]63.6\text{ \%}[/tex](d) Last option.
How do you use the z- tables for continuous normal distribution
The z-score table can be used by starting on the left side of the table, going down to 1.0, and then moving up to 0.00 (which corresponds to the value of 1.0 +.00 = 1.00). A mathematical table for the values of, which are the values of the cumulative distribution function of the normal distribution, is known as a standard normal table.
What is a continuous normal distribution?Continuous probability distribution with a bell-shaped probability density function is known as a normal (or Gaussian) distribution. In terms of statistics, it is the most prominent probability distribution.
The z-score table can be used by starting on the left side of the table, going down to 1.0, and then moving up to 0.00 (which corresponds to the value of 1.0 +.00 = 1.00). The probability is represented by the value. 8413 in the table.
A z-table, also known as the standard normal table, is a mathematical table that enables us to determine the proportion of values in a standard normal distribution that fall below (to the left) a given z-score (SND).
A mathematical table for the values of, which are the values of the cumulative distribution function of the normal distribution, is known as a standard normal table. It is also known as the unit normal table or the Z table.
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Select the GCF for each pair of numbers. 9,15 12,18 15,27 30,54
The Greatest common factors for each pair of numbers are;
1, ( 9 , 15 ) = 3
2. ( 12 , 18 ) = 6
3. ( 15 , 27 ) = 3
4. (30, 54) = 6
What is Greatest common factors?
The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The pairs of numbers are;
1, ( 9 , 15 )
2. ( 12 , 18 )
3. ( 15 , 27 )
4. (30, 54)
Now,
Find the Greatest common factors of the pairs of the numbers as;
1, ( 9 , 15 )
LCM of 9 = 3 x 3
LCM of 15 = 3 x 5
So, GCF of 9 and 15 = 3
2. ( 12 , 18 )
LCM of 12 = 2 x 3 x 2
LCM of 18 = 3 x 3 x 2
So, GCF of 12 and 18 = 3 x 2 = 6
3. ( 15 , 27 )
LCM of 15 = 3 x 5
LCM of 27 = 3 x 3 x 3
So, GCF of 15 and 27 = 3
4. (30, 54)
LCM of 30 = 2 x 3 x 5
LCM of 18 = 3 x 3 x 2
So, GCF of 30 and 54 = 3 x 2 = 6
Thus, The Greatest common factors for each pair of numbers are;
1, ( 9 , 15 ) = 3
2. ( 12 , 18 ) = 6
3. ( 15 , 27 ) = 3
4. (30, 54) = 6
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Clarissa's division test was a 60% the first six weeks and a 72% the second six weeks. find the percent change. also, label it as increase or decrease.
The percentage change of the division test is 12%.
There is a percentage increase.
How to find percentage change?Percentage change is the difference in values and the percent change from the original value to the new value.
In other words, percentage change can be defined as a percentage change in value due to changes in the old number and new number, and the values can either increase or decrease.
Percentage change is all about comparing old to new values.
The division test was 60% in the first six week.
The division test was 72% in the second six week.
Therefore,
percentage change = 72% - 60%
percentage change = 12%
Therefore, there is a percentage increase by 12%.
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Let f (2) = x? and g(2) r” and g(2) = 77 - 2. What is (fog)(x)? What is (fog)(0)?
This is function composition, so:
[tex]\begin{gathered} f(x)=x^2,g(x)=\sqrt[]{7-x}\text{ } \\ (f\circ g)(x)=f(g(x))=g(x)^2=(\sqrt[]{7-x})^2 \\ (f\circ g)(x)=(\sqrt[]{7-x})^2 \end{gathered}[/tex]And (f o g)(0) is:
[tex]\begin{gathered} (f\circ g)(0)=(\sqrt[]{7-0})^2 \\ (f\circ g)(0)=(\sqrt[]{7})^2=7^{} \end{gathered}[/tex]The answer is (f o g)(0) = 7
HELP!
For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.
m∠Y = 22°
m∠Y = 43°
m∠Y = 99°
m∠Y = 158°
The value of m∠Y in triangle XYZ is 99°
How to solve an equationAn equation is used to show the relationship between two or more numbers and variables.
In triangle XYZ, the angles are angle x, y and z. Hence:
∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)
Substituting:
38 + (5x -11) + (4x -45) = 180
Collecting like terms:
9x - 18 = 180
9x = 198
x = 22
m∠Y = 5(22) - 11 = 99°
m∠Y is 99°
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An item on sale costs 40% of the original price if the original price was $45 what is the sale price
Answer:
$18
Step-by-step explanation:
Finding 40% of something is the same as multiplying it by 0.4.
If we do this to 45 we get:
45 x 0.4 = 18
So, the sale price would be $18.
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she dropped 37.5 feet. How many feet had she been below sea level, if she was 80.7 feet below sea level after she dropped?
Answer:1234567.00 feet
Step-by-step explanation: feet are yummy
find the X and the Y intercepts of the graph of the equation below 8x + 2y equals negative 16
The expresion is:
[tex]8x+2y=-16[/tex]to find the intercepts with the x axis we have to rplace in the equation y = 0, so:
[tex]\begin{gathered} 8x+2(0)=-16 \\ 8x=-16 \end{gathered}[/tex]and we solve for x
[tex]x=-\frac{16}{8}=-2[/tex]the intersection with the x axis is -2
And for the itercepts with the y axis we replace x = 0
[tex]\begin{gathered} 8(0)+2y=-16 \\ 2y=-16 \end{gathered}[/tex]and we solve for y
[tex]y=-\frac{16}{2}=-8[/tex]This means that the intersepts with the y axis is -8
What are the values of X where f(x)=g(x)Round to the nearest hundredth’s place if necessary.select all that apply
Given:
The functions
[tex]\begin{gathered} f(x)=2Cos(x) \\ g(x)=(x+0.5)^2+1 \end{gathered}[/tex]Required:
What are the values of x where f(x)=g(x).
Explanation:
From graph we can see that function equals at x value (-0.934) and (0.412)
Answer:
The x values are (-0.93) and (0.41)
based off of this table, what would be the best guess for the domain and range of the composition?? i cant figure this out. PLEASE HELP
The composite function is:
[tex]y=\lvert-x^2\rvert[/tex]The domain (D) is:
The domain is the set of all possible x values. Since there are no limitations for the x-values, the domain is all real numbers.
D = (-∞, ∞).
The Range (R) is:
The range is the set of all possible y values (output values). As you can see in your table, there are no negative output values. So, the range is the positive real numbers and the zero.
R = [0, ∞).
simply the (3x^2y^2)^2
Answer:
9x^4y^4
Step-by-step explanation:
Attachment below. :D
Recite pi - First 1000 decimal places
Pi (π) is an irrational number that can be found by dividing the radius of a circumference by its diameter.
The digits of π considering the first 1,000 digital places are:
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989
If the area of a parallelogram is 36 cm^2 and has a height of 4 cm, what is the basea cm
Given, the area of the parallelogram, A=36 cm^2.
The height of the parallelogram, h=4 cm.
The area of a parallelogram is,
[tex]A=bh[/tex]Here, b is the base length and h is the height of the parallelogram.
Put values of A and h in the above equation to find base b.
[tex]\begin{gathered} 36=b\times4 \\ \frac{36}{4}=b \\ 9cm=b \end{gathered}[/tex]Therefore, the base of the parallelogram is 9 cm.
Circle A has center (0, 0) and radius 3. Circle B has center (-5, 0) and radius 1. What sequence of transformations could be used to show that Circle A is similar to Circle B?
A translation of T(x, y) = (- 5, 2) and a dilation with center (- 5, 2) with a scale factor of 1 / 3 are necessary to transform circle A into circle B. (Correct choice: D)
What sequence of rigid transformations can be done on a circle
In this problem we must determine the sequence of transformations require to transform circle A into circle B. From analytical geometry we know that the equation of the circle in standard form is:
(x - h)² + (y - k)² = r²
Where:
(h, k) - Coordinates of the center.r - Radius of the circle.Then, we need to apply the following rigid transformations:
Translation
f(x, y) → f(x - h, y - k), where (h, k) is the translation vector.
Dilation with center at the center of the circle
r → k · r, where k is the scale factor.
The circle A is represented by x² + y² = 3, then we derive the expression for the circle B:
f(x, y) → f(x + 5, y - 2)
(x + 5)² + (y - 2)² = 9
r → k · r
(x + 5)² + (y - 2)² = (1 / 3)² · 9
(x + 5)² + (y - 2)² = 1
Then, a translation of T(x, y) = (- 5, 2) and a dilation with center (- 5, 2) are necessary to transform circle A into circle B.
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The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
The range of the graph is 0 <= M <= 5.5
How to find the range of the function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the domain and the range?The domain
On the graph of the function, we can see that:
The x values start from 0 and it ends at 7.5
This means that the domain is 0 <= x <= 7.5
The range
On the graph of the function, we can see that:
The x values start from 0 and it ends at 5.5
This means that the range is 0 <= M <= 5.5
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Answer:
0 <= M <= 5.5
Step-by-step explanation:
Is 5 ft, 6 ft, 11 ft a right triangle
Answer:
No, not right or a triangle lol
Step-by-step explanation:
This is not a triangle.
5+6=11, it has to be greater :)
your triangle is a straight line.
:]
What is the result when 4x3 19x2 + 19x + 13 is divided by 4x + 1? If there is a remainder, express the result in the form q(x) + 6(2):
Answer:
[tex]\frac{4x^3-19x^2+19x+13}{4x+1}=(x^2-5x+6)+7[/tex]1. Write the other side of this equation so that this equation is true for all values of u.2. Write the other side of this equation so that this equation is true for no values of u6(u-2)+2
SOLUTION
Given the question in the question tab, the following are the solution steps for the answer
Step 1: Write out the equation
[tex]6(u-2)+2[/tex]Step 2
write the next three terms of the arithmetic sequence. 4, 3 3/4, 3 1/2, 3 1/4.
In an arithmetic sequence, the consecutive terms differ by a common difference. This means that the second term minus the first term would be equal to the third term minus the second term. The pattern continues.
Looking at the sequence, the common difference is
3 3/4 - 4 = 3 1/2 - 33/4 3 1/4 - 3 1/2 = - 1/4
The next term after 3 1/4 would be 3 1/4 + - 1/4 = 3 1/4 - 1/4 = 3
The next term after 3 would be 3 + -