Since all coefficients are integers, we can apply the rational zeros theorem.
The trailing coefficient is -6 with the following factors (possible values for p):
[tex]p\colon\pm1,\pm2,\pm3,\pm6[/tex]The leading coefficient is 1, with factors:
[tex]q=\pm1[/tex]Therefore, all the possible values of p/q are:
[tex]\frac{p}{q}\colon\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{3}{1},\pm\frac{6}{1}[/tex]Simplifying, the possible rational roots are:
[tex]\pm1,\pm2,\pm3,\pm6[/tex]Next, we have to check if they are roots of the polynomials by synthetic division, in which the remainder should be equal to 0.
0. Dividing ,f (x), by ,x−1,. Remainder = ,-8, ,+1, is ,NOT ,a root.
,1. Dividing ,f (x), by x+,1,. Remainder = 0, ,-1, ,IS ,a root.
,2. Dividing ,f (x), by x-2. Remainder = 0, ,+2, ,IS ,a root.
,3. Dividing ,f (x), by ,x+2,. Remainder = ,4, ,-2, is ,NOT ,a root.
,4. Dividing ,f (x), by ,x−3,. Remainder = 24,, ,+3, is ,NOT ,a root.
,5. Dividing ,f (x), by ,x+3,. Remainder = 0,, ,-3, IS ,a root.
,6. Dividing ,f (x), by ,x−6,. Remainder = 252,, ,+6, is ,NOT ,a root.
,7. Dividing ,f (x), by ,x+6,. Remainder = -120,, ,-6, is ,NOT ,a root.
Actual rational roots: A. -3, -1, 2; f(x) = (x + 3)(x + 1)(x - 2)
Which expression allows us to find the discount amount of ANY price thatis discounted 25%?*
the expression of the discount amount is
[tex]discountamount=x\times\frac{25}{100}[/tex]here x is the price
and the discount is 25%
f(x) = 3x² + 9x – 16
Find f(-8)
Answer: 104
Step-by-step explanation:
[tex]f(-8)[/tex] represents [tex]f(x)[/tex] evaluated at [tex]x=-8[/tex].
[tex]f(-8)=3(-8)^2 +9(-8)-16\\\\=192-72-16\\\\=120-16\\\\=104[/tex]
A. Side a is 24 inches longand side bis 21 inches longB. Side a is 63 inches long and side bis 54 inches long.C. Side a is 18 inches long and side bis 15 inches long.D. Side a is 7 inches long and side bis 6 inches long.
Since both drawings are similar and have a scale factor, we can say that all sides keep the same scamle factor, if the scale drawing is in a proportion of 3:1 means that all of its sides is 3 times the real objects sides.
write this as equations
[tex]\begin{gathered} 3\cdot a=21in \\ 3\cdot b=18in \end{gathered}[/tex]to find the respetive values for a and b we divide the sides by 3
[tex]\begin{gathered} a=\frac{21in}{3}=7in \\ b=\frac{18in}{3}=6in \end{gathered}[/tex]The correct answer is D.
Find the volume of the figure round to the nearest 10th if needed
Given: A triangular prism with base 6ft,height of triangle is 8 ft and height of prism is 12ft
Find : the volume of the prism.
Explanation: the volume of the triangular prism is equal to area of the base triangle times height of the prism.
[tex]\begin{gathered} =\frac{(8\times6)\times12}{2} \\ =288\text{ ft}^3 \end{gathered}[/tex]final answer: the volume of the rectangular prism is
[tex]288ft^3[/tex]how many term has G.p whose 2nd term is 1/2 and common ratio and the last term are 1/4and1/128respestively
The geometric progression has the form:
[tex]\mleft\lbrace a,ar,ar^2,ar^3,\ldots,ar^n\mright\rbrace[/tex]We have the information about the second term, a*r:
[tex]ar=\frac{1}{2}[/tex]We know that the common ratio is
[tex]r=\frac{1}{4}[/tex]So from this information we can get the coefficient a:
[tex]\begin{gathered} ar=\frac{1}{2} \\ a\cdot\frac{1}{4}=\frac{1}{2} \\ a=\frac{4}{2}=2 \end{gathered}[/tex]And we also know that the last term is 1/128, that is
[tex]ar^n=\frac{1}{128}[/tex]From this one we can find n:
[tex]\begin{gathered} 2\cdot(\frac{1}{4})^n=\frac{1}{128} \\ (\frac{1}{4})^n=\frac{1}{128\cdot2} \end{gathered}[/tex]We can apply the property of the logarithm of power to get n:
[tex]\begin{gathered} \log ((\frac{1}{4})^n)=\log (\frac{1}{256}) \\ n\cdot\log (\frac{1}{4})^{}=\log (\frac{1}{256}) \\ n=\frac{\log (\frac{1}{256})}{\log (\frac{1}{4})} \\ n=4 \end{gathered}[/tex]Be careful, because n is not the number of terms. The number of terms is n+1, so the G.P. has 5 terms
create a model for (x + 7)(2x - 6). What is the product
What is the volume of this cone round to the nearest hundreth
We have to calculate the volume of the cone.
The volume of the cone is 1/3 of the area of the base times the height.
As the base has diameter D = 16 yd, we can calculate the area of the base as:
[tex]\begin{gathered} A_b=\frac{\pi D^2}{4} \\ A_b\approx\frac{3.14*16^2}{4} \\ A_b\approx\frac{3.14*256}{4} \\ A_b\approx200.96 \end{gathered}[/tex]Knowing the height is h = 14 yd, we then can calculate the volume as:
[tex]\begin{gathered} V=\frac{1}{3}A_bh \\ V=\frac{1}{3}*200.96*14 \\ V\approx937.81 \end{gathered}[/tex]Answer: the volume is 937.81 cubic yards.
x - 5 = 2(4x-3) - 5 = 7x - 6 1/7= xx - 5 = 8x - 6-5 + 6 = 7x-6+6 1 = 7x x-x-5 = 8x - x - 6 1/7 = 7x/7Original equationCombine like terms. Solution Distributive PropertyAddition Property of EqualityCombine like terms.Subtraction Property of EqualityDivision Property of Equality What is the order to do this equation.
We have to solve the equation:
[tex]\begin{gathered} x-5=2(4x-3) \\ x-5=8x-6 \\ x-x-5=8x-x-6 \\ -5+6=7x-6+6 \\ 1=7x \\ \frac{1}{7}=\frac{7}{7}x \\ \frac{1}{7}=x \end{gathered}[/tex]The steps are:
1. Original equation
2. Distributive property
3. Substraction property of equality
4. Addition property of equality
5. Combine all terms
6. Division property of equality
7. Solution
Elijah is snorkeling above a shipwreck. The ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation. What is Elijah's elevation?
Elijah's elevation when Elijah is snorkeling above a shipwreck is -14.
What is elevation?Elevation simply has to do with the height above sea level.
In this case, Elijah is snorkeling above a shipwreck and the ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation.
Elijah's elevation will be:
= Fraction of his snorkeling × Ship's elevation
= 2/15 × (-105)
= -14
This shows the elevation of Elijah.
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Gabrielle is 8 years older than Mikhail. The sum of their ages is 104. What is Mikhail's age?
Let x represent Mikhail's age.
Since Gabrielle is 8 years older than Mikhail, it means that Gabrielle's age is
x + 8
If the sum of their ages is 104, it means that
x + x + 8 = 104
2x = 104 - 8
2x = 96
x = 96/2
x = 48
Mikhail's age is 48
The coordinates of point F are (8,4) and the coordinates of point G are (-4,9). What is the slope of the line that is perpendicular to line FG. Enter the answer as a simplified fraction.
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for finding slope is
m = (y2 - y1)/(x2 - x1)
y2 and y1 are the final and initial values of y
x2 and x1 are the final and initial values of x
From the given points ,
x1 = 8, y1 = 4
x2 = - 4, y2 = 9
m = (9 - 4)/(- 4 - 8) = 5/- 12 = - 5/12
Recall, if two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. The negative reciprocal of - 5/12 is 12/5
Thus, the slope of the perpendicular to line FG is 12/5
David is laying tiles on his kitchen floor. His kitchen measures 16 feet by 20 feet Each tile is a square that measures 2 feet by 2 feet (a) What is the area of his kitchen floor? (b) How many tiles will David need to purchase to cover the floor? One Tile 2 ft 2 ft
(a) To find the area of the kitchen floor, we just have to multiply
[tex]A=16ft\times20ft=320ft^2[/tex](b) To find the number of tiles needed, we have to find the area of each tile, which is
[tex]A_{\text{tile}}=2ft^{}\times2ft^{}=4ft^2[/tex]Then, we divide the total area of the kitchen floor by the area of each tile.
[tex]n=\frac{320ft^2}{4ft^2}=80[/tex]Hence, David will need 80 tiles to cover the floor.
Find f.Write your answer in simplest radical form. ___ units
Answer:
The value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]Explanation:
Given the triangle in the attached image.
Recall that;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]from the given figure;
[tex]\begin{gathered} \theta=30^{\circ} \\ \text{opposite}=f \\ \text{adjacent}=3\sqrt[]{6} \end{gathered}[/tex]substituting the values;
[tex]\begin{gathered} \tan 30=\frac{f}{3\sqrt[]{6}} \\ f=3\sqrt[]{6}\tan 30 \\ f=3\sqrt[]{6}(\frac{\sqrt[]{3}}{3}) \\ f=3\sqrt[]{2} \end{gathered}[/tex]Therefore, the value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]The perimeter of a rectangle is 48 centimeters. The relationship between the length, the width, and the perimeter of the rectangle can be described with the equation 2⋅length+2⋅width=48. Find the length, in centimeters, if the width is w centimeters
Using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.
Recall:
Perimeter of a rectangle (P) = 2(L + W) (relationship between the width, length and perimeter)
Given:
Width (W) = 3.6 cm
Perimeter (P) = 48 cm
Length (L) = ?
Using the relationship between the dimension of a rectangle and its perimeter, the following equation would be derived:
48 = 2(L + 3.6)
Solve for the value of L
48 = 2L + 7.2
Subtract 7.2 from each side
48 - 7.2 = 2L
40.8 = 2L
Divide both sides by 2
20.4 = L
L = 20.4 cm
Therefore, using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.
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14|x + 14| + 13 =-69
Solve for x
Answer: No real solutions
Step-by-step explanation:
[tex]14|x+14|+13=-69\\\\14|x+14|=-82\\\\|x+14|=-82/14[/tex]
Since absolute value is always non-negative, there are no real solutions.
The oil tank in your car is leaking at a rate of 1.2 oz per mile driven you drove 15 miles how many cups of oil did your car leak
we know that
The unit rate is equal to
1.2 oz per mile
so
To obtain the number of ounces
multiply the unit rate by the number of miles driven
1.2*(15)=18 oz
step 2
Convert ounces to cups
Remember that
1 oz=0.125 cups
so
18 oz=18*0.125=2.25 cups
therefo
The difference between two numbers is 28. The sum of the two numbers is 56. Let x be the larger number and y be the smaller number. Which system of equations represents this proble O y - x = 28 I + y = 56 O x=y= 28 x + y = 56 Oy - 2 = 56 x + y = 28 - y = 56
Since x is the larger number and y is the smaller number
Since their sum is 56
That means add x and y then equate them by 56
[tex]x+y=56(1)[/tex]Since the difference between them is 28
That means subtract y from x and equate the answer by 28
[tex]x-y=28(2)[/tex]Look at the answer to find the correct answer
It is B
x - y = 28 and x + y = 56
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.
[tex]x^2+y^2=400[/tex]
a) find dy/dt given x=16, y=12 and dy/dt=7
b) find dx/dt given x=16, y=12, and dy/dt =-3
For the given equation: x² + y² = 400, the required values of dy/dt and dx/dt are [(-28)/3] and 4 respectively.
What are differentiable functions?
If the derivative f '(a) exists at each point in its domain, then f(x) is said to be differentiable at the point x = a. Given two functions g and h, where y = g(u) and u = h(x). A function is referred to as a composite function if its definition is y = g [h (x)] or goh(x). Therefore, fog is also differentiable and (fog)'(x) = f'(g(x) if g (x) and h (x) are two differentiable functions. g’(x).
Given, the equation for x and y is: x² + y² = 400
Differentiating the equation above with respect to t using chain rule, we have: (2x)(dx/dt) + (2y)(dy/dt) = 0 -(i)
Rearranging (i) for dy/dt, we have: dy/dt = (-x/y)(dx/dt) - (ii)
Again, rearranging (i) for dx/dt, we have: dx/dt = (-y/x)(dy/dt) - (iii)
For (a), x = 16, y = 12 and dx/dt = 7, thus dy/dt using (ii) can be written as:
dy/dt = (-x/y)(dx/dt) = (-16/12)*7 = (-4/3)*7 = (-28)/3
For (b), x = 16, y = 12 and dy/dt = -3, thus dx/dt using (iii) can be written as:
dx/dt = (-y/x)(dy/dt) = (-12/16)*(-3) = (4/(-3))*(-3) = 4
Therefore, for the given equation: x² + y² = 400, the required values of dy/dt and dx/dt are [(-28)/3] and 4 respectively.
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Cisco Enterprises in Ontario purchased the following in a single month all-inclusive of taxes:
16,000 units of network routers at $79.25 each
Answer:
1268000
Step-by-step explanation:
16000x79.25=1268000
giving that -3+20=5x-4 write 3 more equations that you know are true
Answer:
Step-by-step explanation:
ft7654
Find the mean of the set of data. Round to the nearest tenth if necessary 6.4,6,8, 8.1,5.4, 11.1,6.7 The mean is
Given a set of data:
6.4,6,8, 8.1,5.4, 11.1,6.7
The sum of the given data =
[tex]6.4+6.8+8.1+5.4+11.1+6.7=44.5[/tex]The number of the data = 6
so, the mean =
[tex]\frac{44.5}{6}=7.4166667[/tex]Rounding to the nearest tenth, so, the answer will be:
Mean = 7.4
What is the probability that a student does not play on a sports team?
Answer:
P = 0.5
Explanation:
The probability can be calculated as the division of the number of students that does not play on sports team by the total number of students.
Taking into account the table, there is a total of 20 students and from those 10 does not play on a sports team. Therefore, the probability is:
P = 10/20 = 0.5
In a cricket match, you have a squad of 15 players and you need to select 11 for a game. The two opening batsmans are fixed and the rest of the players are flexible. How many batting orders are possible for the game?
The number of batting orders that are possible for the game is 1365 orders.
What are combination?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!
n = the number of items.
r = how many items are taken at a time.
This will be:
15! / 11! (15 - 11)!
= 15! / 11! 4!
= 15 × 14 × 13 × 12 / 4 × 3 × 2
= 1365 orders
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Given right triangle ABC, with altitude CD intersecting AB at point D. If AD = 5 and DB = 8, find the length of CD, in simplest radical form. In your video include whether you would use SAAS or HYLLS to solve (and WHY), the proportion you would set up, how you would solve for the missing side, and how you know your answer is in simplest radical form.
First we dra a triangle:
To prove that the triangles are similar we have to do the following:
Considet triangles ABC and ACD, in this case we notice that angles ACB and ADC are equal to 90°, hence they are congruent. Furthermore angles CAD and CAB are also congruent, this means that the remaining angle in both triangles will also be congruent, therefore by the AA postulate for similarity we conclude that:
[tex]\Delta ABC\approx\Delta ACD[/tex]Now consider triangles ABC and BCD, in this case we notice that angles ACB and BDC are congruent since they are both equal to 90°. Furthermore angles ABC and DBC are also congruent, this means that the remaining angle in both triangles will, once again, be congruent. Hence by the AA postulate we conclude that:
[tex]\Delta ABC\approx\Delta BCD[/tex]With this we conclude that traingles BCD and ACD are both similar to triangle ABC, and by the transitivity property of similarity we conclude that:
[tex]\Delta ACD\approx BCD[/tex]Now that we know that both triangles are similar we can use the following proportion:
[tex]\frac{h}{x}=\frac{y}{h}[/tex]this comes from the fact that the ratios should be the same in similar triangles.
From this equation we can find h:
[tex]\begin{gathered} \frac{h}{x}=\frac{y}{h} \\ h^2=xy \\ h=\sqrt[]{xy} \end{gathered}[/tex]Plugging the values we have for x and y we have that h (that is the segment CD) has length:
[tex]\begin{gathered} h=\sqrt[]{8\cdot5} \\ =\sqrt[]{40} \\ =\sqrt[]{4\cdot10} \\ =2\sqrt[]{10} \end{gathered}[/tex]Therefore, the length of segment CD is:
[tex]CD=2\sqrt[]{10}[/tex]Write expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
Solution
Note: Laws Of Logarithm To Use
[tex]\begin{gathered} (1).\text{ }log_a(M)-log_a(N)=log_a(\frac{M}{N}) \\ \\ (2).\text{ }log_a(b^n)=nlog_a(b) \end{gathered}[/tex]From the question, we have
[tex]\begin{gathered} log_3(18)-log_3(2) \\ \\ log_3(\frac{18}{2}) \\ \\ log_3(9)\text{ } \\ \\ The\text{ above expression is single logarithm} \end{gathered}[/tex]To evaluate, we have
[tex]\begin{gathered} log_3(9)=log_3(3^2) \\ \\ log_3(9)=2log_3(3) \\ \\ log_3(9)=2(1) \\ \\ log_3(9)=2 \end{gathered}[/tex]The answer is
[tex]2[/tex]which ordered pair is a solution of the equation 7x−5=4y−6?PLEASE HURRY THIS IS DUE NOW A. only (2,4)B. only (3,6)C. both A and BD. neither A or B
To answer this question, we can take the coordinates (2, 4), and (3, 6) and substitute each of them in the given equation. Then, we can determine which of these ordered pairs is a solution of the equation 7x - 5 = 4y - 6. Then, we have:
1. Case: Ordered pair (2, 4):
[tex]7\cdot(2)-5=4\cdot(4)-6\Rightarrow14-5=16-6\Rightarrow9\ne10[/tex]This ordered pair is NOT a solution.
2. Case: Ordered pair (3, 6):
[tex]7\cdot(3)-5=4\cdot(6)-6\Rightarrow21-5=24-6\Rightarrow16\ne18[/tex]This ordered pair is NOT a solution.
Therefore, neither the ordered pair (2, 4) nor (3, 6) are solutions to the given equation (Option D).
Question 3 4.5 pts At the honor roll party, students had the choice of cheese or pepperoni pizza and coke or sprite. Of the 125 students that made the honor roll 64% had cheese pizza. There were 48 students that had cheese pizza and a coke. 5 more students chose to have a Coke rather than Sprite. Complete the table below.
The table would look like this;
We are told that Of the 125 students that made the honor roll 64% had cheese pizza.
64% of 125 is 80 students, therefore, 80 students in total had cheese pizza.
Let's fill that in.
We now know that those who had pepperoni pizza are 125 - 80 = 45 in number.
There were 48 students that had cheese pizza and a coke, let's fill that in too, we have.
This means that the number of students that had a cheese and sprite is 80 - 48 = 32 students.
We are also told that 5 more students chose to have a coke than a sprite.
Let the total number that chose coke be x.
Then the total who chose sprite would be x - 5.
But these total must add up to 125.
So;
[tex]\begin{gathered} x+x-5=125 \\ 2x-5=125 \\ 2x=130 \\ x=\frac{130}{2}=65 \\ x-5\text{ = 60} \end{gathered}[/tex]Therefore, 65 students took coke in total and 60 took sprite, let's fill that in too.
We can now fill in the pepperoni column.
For pepperoni and coke, we subtract 48 from 65 to obtain 17
For pepperoni and sprite, we subtract 32 from 60 to obtain 28
ii. The joint relative frequency of the students who had a sprite and pepperoni pizza.
From the table, the joint relative frequency of those who had a sprite and a pepperoni pizza is
[tex]\begin{gathered} \frac{28}{45} \\ \end{gathered}[/tex]i.e 28/45 or 0.6 of those who had pepperoni pizza, took sprite.
A bank features a savings account that has an annual percentage rate of 4.8 % with interest compounded monthly. Umbrosia deposits $6,500 into the account.
How much money will Umbrosia have in the account in 1 year?
What is the annual percentage yield (APY) for the savings account?
S(8)=3500(1+(.047/4))^32
S(8)=$5086.40 in the account after 8 years.
a)The relative growth rate is .25, or 25%
b)at t=0, the population is 955e^.25(0)=955
c)at t=5; the population is 955*e^.25(5)=955*3.49=3333.28 bacterium.
The circle graph shows the results of a survey by a bakery on which of their new products 105 customerspreferred most. How many customers preferred cake? Round your answer to the nearest whole number.
If 105 customers were the total, and 35% prefers cake, we must calculate 35% of 105, then we must do 105 multiplied by 35%, we can doit transforming the 35% in the fraction notation:
[tex]35\%=\frac{35}{100}[/tex]And the multiplication
[tex]105\cdot\frac{35}{100}=36.75[/tex]Therefore, if we round it to the nearest whole number, the number of customers that prefer cake is 37.
37 customers prefer cake.
x-y=3x+y=5unit 7 systems of linear equations
then
[tex]\begin{gathered} x+y=5 \\ 3+y+y=5 \\ 3+2y=5 \\ 3+2y-3=5-3 \\ 2y=2 \\ \frac{2y}{2}=\frac{2}{2} \\ y=1 \end{gathered}[/tex]solve for x
[tex]\begin{gathered} x=3+y \\ x=3+1 \\ x=4 \end{gathered}[/tex]answer: C. (4,1)