Answer:
[tex]\large \boxed{\sf \ \ \ -1, \ -5, \ -\dfrac{1}{4} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
Let's determine the possible rational zeros of this polynomial function using the rational zeros theorem:
[tex]P(x) = 4x^4 + 13x^3-49x^2-73x-15[/tex]
First of all, what is the rational zeroes theorem?
If P(x) is a polynomial with integer coefficients
and if (p and q being integer)
[tex]\dfrac{p}{q}[/tex]
is a zero of P(x), meaning
[tex]P(\dfrac{p}{q})=0[/tex]
then p is a factor of the constant term of P(x) and
q is a factor of the leading coefficient of P(x).
How to apply it here?
The constant term of P(x) is -15
The leading coefficient of P(x) is 4
so p is a factor of -15
q is a factor of 4
15 = 1 * 5 * 3
4 = 2 * 2 * 1
q can be 1, 2, 4
-p can be 1, 3, 5, 15
so it gives the following potential solutions
-1, -3, -5, -15
[tex]\dfrac{-1}{2}, \dfrac{-3}{2}, \dfrac{-5}{2}, \dfrac{-15}{2}[/tex]
[tex]\dfrac{-1}{4}, \dfrac{-3}{4}, \dfrac{-5}{4}, \dfrac{-15}{4}[/tex]
Let's compute P(x) for x in this list of potential solutions
x P(x)
-1 0
-3 -264
-5 0
-15 148680
-0.5 7.875
-1.5 -39.375
-2.5 -185.625
-7.5 4948.125
-0.25 0
-0.75 7.96875
-1.25 -15.9375
-3.75 -324.84375
It gives -1, -5 and -0.25
Conclusion
The possible rational zeroes of P(x) are
-1
-5
[tex]\dfrac{-1}{4}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $52 and then they charge her $8 per hour. She has $144 Available to spend on a car rental. What is the greatest number of hours for which she can rent the car?
Answer:
11 hours
Step-by-step explanation:
First, you have to subtract 144-52= 92. After the initial fee, she has 92 dollars to spend on the car. Then, you divide 92 by 8 because it costs 8 dollars an hour. And this gets you 11.5 which you would have round down because she can't pay for the extra hour. She does not have enough money.
in which table does y vary inversely with x?
Answer:
Table B
Step-by-step explanation:
Note that for y to vary inversely as x, an increase in x will cause a decrease in y. Therefore, by careful observation of tables A, B, C, and D, we would notice the following:
In table C:
As x increases from 1 to 2 to 3, y also increases from 26 to 52 to 78. Which means that an increase in x causes an increase in y. This is not an inverse variation.
In table D:
As x increases from 1 to 2 to 3, y also increases from -7 to -1 to 6. Which means that an increase in x causes an increase in y. This is also not an inverse variation.
We are left with options A and B
If y varies inversely as x, the following relationship must hold:
[tex]y \alpha \frac{1}{x}\\y = \frac{k}{x}[/tex]
Where k is a constant of proportionality
considering option B:
When x = 1, y = 36
36 = k/1
k = 36 * 1
k = 36
when x = 2, y = 36/2
y = 18
when x = 3, y = 36/3
y = 12
These tally with all that is indicated in the table. Option B is an inverse variation
Now that you know the total skid distance (3.8 ft), use the skid-distance formula to find how fast the car was going before it started skidding. How fast was the car traveling before it started skidding? s= sqrt (30 * drag factor * skid distance * braking efficiency)
s= speed
drag factor= 0.90
skid distance= 3.8
braking efficiency= 80% or 0.80
Answer:
9.1 mph
Step-by-step explanation:
Put the numbers in the formula and do the arithmetic.
s = √(30×drag factor×skid distance×braking efficiency)
s = √(30×0.90×3.8×0.80) = √82.08 ≈ 9.06
The car was traveling about 9.1 mph before it started skidding.
To make a chocolate sponge cake for 8 people you need:
300g flour
100g cocoa
400g sugar
350g butter
1 egg
a) How much of each ingredient do you need to make a cake for 10 people?
b) if you only had 60g of cocoa,how much of each ingredient would you now need?
Answer:
this is som A sorry if you can't read it
Calculate the perimeter of this trapezoid
Answer:
31 cm
Step-by-step explanation:
The perimeter is the sum of the sides so the answer is 8 + 10.5 + 9 + 3.5 = 31 cm.
Two tangents. find x. angle measures and segment lengths. Acellus. PLEASE HELP!!!
Answer:
x=60
Step-by-step explanation:
x=1/2(240-120)
x=60
I need someone to answer this immediately please. ... The area of a piece of land is 50cm square. Fi d the value of x, if the length
and breadth are given as (x+2) and (x-3)m respectively
options. A. 3
B. 5
C. 7
D. 8
Answer:
x=8
Step-by-step explanation:
Area is equal to
A = l * w
50 = ( x+2) ( x-3)
FOIL
50 = x^2 -3x+2x -6
Combine like terms
50 = x^2 -x -6
Subtract 50 from each side
0 = x^2 -x -56
Factor
What two numbers multiply to -56 and add to -1
-8*7 = -56
-8+7 = -1
0 = ( x-8) ( x+7)
Using the zero product property
x-8 =0 x+7 =0
x = 8 x=-7
Since the length cannot be negative x cannot be negative
x=8
Answer:
8
Step-by-step explanation:
put the 50 under area and continue with like that
Answer:
????
Step-by-step explanation:
Where is the question????
plz help me x+y=7
x=3-y
Answer:
no solution
Step-by-step explanation:
x+y=7
x=3-y
Substitute the second equation into the first
(3-y) +y = 7
Combine like terms
3 = 7
This is never true so there is no solution
Answer:
[tex]\boxed{\mathrm{No \: solution}}[/tex]
Step-by-step explanation:
x + y = 7
Plug x = 3 - y
3 - y + y = 7
Combine like terms.
3 = 7
No solution.
expand the following (x+3)(x-3)
Answer:
x² - 9
Step-by-step explanation:
Given
(x + 3)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) + 3(x - 3) ← distribute both parenthesis
= x² - 3x + 3x - 9 ← collect like terms
= x² - 9
Answer:
x² - 9Step-by-step explanation:
[tex](x + 3)(x - 3)[/tex]
Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )
[tex]x(x - 3) + 3(x - 3)[/tex]
Calculate the product
[tex] {x}^{2} - 3x + 3x - 3 \times 3[/tex]
Multiply the numbers
[tex] {x}^{2} - 3x + 3x - 9[/tex]
Since two opposites add up to zero, remove them from the expression
[tex] {x}^{2} - 9[/tex]
Hope this helps..
Best regards!!
Find the m∠CDE rjrsjrsrjr
Answer:
m∠CDE = 60°
Step-by-step explanation:
Given that the arc at the center = 2 times the arc at the circumference, we have;
Angle at the center = arc CE = 120°
Whereby the angle at the circumference is given as m∠CDE and it is opposite the circle arc CE
We note that m∠CDE is the acute angle between chord DC and DE
Therefore, we have;
Angle at the center = 120° = 2 times the arc at the circumference = 2 × m∠CDE
120° = 2 × m∠CDE
m∠CDE = 120/2 = 60°
Therefore the angle of m∠CDE is equal to 60°.
How is the graph of y=(x+1)^2-9 transformed from the graph of y=x^2? a shifted 1 unit left and 9 units up b shifted 1 unit right and 9 units up c shifted 1 unit left and 9 units down d shifted 1 unit right and 9 units down
Answer:
Step-by-step explanation:
Due to the '+1', the graoph of x^2 is shifted 1 unit to the left. The '+9' results in the entire graph being shifted downward 9 units.
Please answer it now in two minutes
Answer:
901.1 km²
Step-by-step explanation:
The area of ∆WXY can be found using the formula, ½*a*b*sin(θ),
Where a and b, are two known sides of the triangle, and θ is the angle between both sides.
To find the area of ∆WXY, follow the steps below:
Step 1: Find XY using the law of sines.
m < W = 180 - (65 + 48) (sum of angles in a ∆)
W = 180 - (113) = 67°
X = 65°
WY = 49 km
XY = ?
[tex] \frac{XY}{sin(W)} = \frac{WY}{sin(X)} [/tex]
[tex] \frac{XY}{sin(67)} = \frac{49}{sin(65)} [/tex]
[tex] \frac{XY}{0.92} = \frac{49}{0.91} [/tex]
Cross multiply
[tex] XY*0.91 = 49*0.92[/tex]
Divide both sides by 0.91
[tex] \frac{XY*0.91}{0.91} = \frac{49*0.92}{0.91} [/tex]
[tex] XY = 49.54 [/tex]
XY ≈ 49.5
Step 2: find the area
Area = ½*WY*XY*sin(Y)
Area = ½*49*49.5*sin(48)
Area = ½*49*49.5*0.743
Area = 901.07325
Area = 901.1 km² (nearest tenth)
Molly was curious if quadrilaterals ABCDABCDA, B, C, D and EFGHEFGHE, F, G, H were congruent, so she tried to map one figure onto the other using transformations
Answer:
The answer is below
Step-by-step explanation:
A transformation of a point is the movement of an point from an initial position to a new position. If an object is transformed, all the point of an object is transformed. Two figures are said to be congruent if they have the same shape and the measure of each of their sides are the same.
An object is congruent to another object if the object can be mapped to the other object when transformed.
Answer:
The answer is c
Step-by-step explanation:
It is the correct solution because you are able to map circle m onto m
What is the volume of the pyramid in cubic inches?
9in.
6 in.
8 in.
Answer: C) 144
Step-by-step explanation:
The area of a pyramid can be found via lwh/3
(9*8*6)/3 = area
72*6/3 = area
432/3 = area
144 = area
Hope it helps <3
express each of the following decimal number in the p/q form (1)0.5 (2)3.8
Answer:
see explanation
Step-by-step explanation:
(1)
0.5 = [tex]\frac{5}{10}[/tex] = [tex]\frac{1}{2}[/tex]
(2)
3.8 = 3 [tex]\frac{8}{10}[/tex] = [tex]\frac{10(3)+8}{10}[/tex] = [tex]\frac{30+8}{10}[/tex] = [tex]\frac{38}{10}[/tex] = [tex]\frac{19}{5}[/tex]
(i) The third and the seventh terms of an A.P. are 20 and 36 respectively. Find the first
term and the common difference,
Answer:
The first term is 12. The common difference is 4.
Step-by-step explanation:
[tex] a_n = a_1 + d(n - 1) [/tex]
The difference between the third and seventh terms is
36 - 20 = 16
The 7th term is the 4th term after the 3rd term, so the common difference is
16/4 = 4
[tex] a_3 = a_1 + 4(3 - 1) [/tex]
[tex] 20 = a_1 + 4(3 - 1) [/tex]
[tex] 20 = a_1 + 8 [/tex]
[tex] a_1 = 12 [/tex]
Answer: The first term is 12. The common difference is 4.
Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister. Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Answer:
volume 1 =763 cm3
volume 2 = 6,104 cm3
Second volume is 8 times greater than the first volume.
Surface area 1 = 466 cm2
surface area 2 =1,865 cm2
second surface area is 4 times greater than the first surface area .
Step-by-step explanation:
Volume of a cylinder: π radius^2 x height
Radius = diameter /2 = 9/2 = 4.5
V = 3.14 x 4.5^2 x 12 = 763 cm3
Surface area: (3.14 r^2)2 + 2(π x radius x height)
Sa = (3.14 x 4.5^2 )2 + 2(3.14 x 4.5 x 12 )=466 cm2
Since the second canister is double the size:
Radius = 4.5 x 2 = 9
Height = 12 x 2 =24
V = 3.14 x 9^2 x 24 = 6,104 cm3
Sa = (3.14 x 9^2 )2 + 2(3.14 x 9 x 24 )=1,865 cm2
Dividing the second volume by the first one:
6,104/ 763 = 8
Second volume is 8 times greater than the first volume.
Dividing the second surface area by the first one:
1865/466 = 4
second surface area is 4 times greater than the first surface area .
Helpppp urgently ❤️❤️❤️❤️
Answer:
d. (x + 5)
Step-by-step explanation:
The factorization of 2x^2 - 4x - 70 is (x + 5)(2x - 14)
Answer:
2( x + 5 ) × ( x - 7 )
Step-by-step explanation:
2x² - 4x - 70
2( x² - 2x - 35)
2( x² + 5x - 7x - 35)
2(x × (x + 5) -7 (x + 5))
2(x + 5 ) × (x - 7)
Can someone tell me the answer it would really help 3(x−2)+1 =
Step-by-step explanation:
3(x-2)+1
= 3x-6+1
= 3x-5
Answer:
Step-by-step explanation:
3(x-2)+1=
Then distribute, and now you get:
3x-6+1=
Now combine like terms, and now you get:
3x-5=
There is nothing much to do because there isn't a answer for it
How many 5 digit numbers have five distinct digits?
Answer:3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each
person showered for an average of 480 minutes and used an average 72 liters of shower water (over the
entire month). Water costs 0.20 dollars per liter.
How much did Trevor's family pay per minute on shower water?
Answer:
0.03
Step-by-step explanation:
Khan
The amount of money the Trevor's family pay per minute on shower water is $0.03
How to find cost of water per minuteTotal number of people in Trevor's house = 6Number of bathrooms = 3Time each person spent bathing = 480 minutesWater used by each person per month = 72 liters Cost of water per liter = $0.20Cost of water used per minute = Water used by each person per month / Time each person spent bathing × Cost of water per liter
= 72 / 480 × 0.20
= 0.15 × 0.20
= $0.03
Learn more about cost:
https://brainly.com/question/19104371
Which list is in order from least to greatest
The correct answer to this question is A. 9.4 x [tex]10^{-8}[/tex], 9.25 x [tex]10^{-6}[/tex], 2.5 x [tex]10^{3}[/tex], 7 x
Explanation:
These numbers are written in scientific notation. In this system, the exponent shows the number of spaces the period has been moved to make the number shorter. Additionally, a positive exponent shows the number has a certain number of digits to the right, while a negative exponent shows the number has digits to the left. In this way, the numbers presented can be converted as:
9.4 x [tex]10^{-8}[/tex] = 0.000000094 (Exponent indicates eight spaces to the left)
9.25 x [tex]10^{-6}[/tex] = 0.00000925 (Exponent indicates six spaces to the left)
2.5 x [tex]10^{3}[/tex] = 2500 (Exponent indicates three spaces to the right)
7 x [tex]10^{3}[/tex] = 7000 (Exponent indicates three spaces to the right)
Maya is interning at a law firm over the summer and is paid by the hour. If her hourly wage is $52, which equation represents the proportional relationship between the wages she earns (w) and the number of hours (h)?
Answer: w= 52h
Step-by-step explanation:
Given: Maya is interning at a law firm over the summer and is paid by the hour.
Her hourly pay = $52
i.e. She is paid $52 per hour.
Let the wages she earns is denoted by 'w' and the number of hours is denoted by 'h'.
Now, (Total wages earned) = (hourly pay) x (Number of hours)
w = (52) (h)
⇒ w= 52h
Hence, the equation represents the proportional relationship between the wages she earns (w) and the number of hours (h): w= 52h
Answer:52h
Step-by-step explanation: tried got it right
The hourly revenue of a certain clothes manufacturer is represented by the function f(x) = -0.082x2 + 7.3x + 3.6 for the domain [0, 89]. According to this model, what is the maximum revenue this clothes manufacturer can have in an hour?
Answer:
166.07
Step-by-step explanation:
since the domain is [0,89] means the maximum amount is when x=89
vertex is where it reached the maximum amount:(44.512,166.07)
Figure ABCD is a parallelogram. Parallelogram A B C D is shown. Angle A is (4 p + 12) degrees and angle C is 36 degrees. What is the value of p? 6
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
i checked on edge
Xavier buys a two-quart bottle of juice for $5.12. What is the unit rate of the cost of the juice per fluid ounce?
Answer:
The cost is $.08 per ounce or 8 cents per ounce
Step-by-step explanation:
1 quart = 32 ounces
2 quarts = 64 pints
2 quarts costs 5.12
Take the cost and divide by the number of ounces
5.12 / 64
.08 per ounce
The cost is $.08 per ounce or 8 cents per ounce
=================================================
Explanation:
1 quart = 32 fluid ounces
2 quarts = 64 fluid ounces (multiply both sides by 2)
He paid 5.12 dollars for 64 fluid ounces, so the unit rate is 5.12/64 = 0.08 dollars per fluid ounce, or 8 cents per fluid ounce.
---------
We can think of it this way in terms of an equation
5.12 dollars = 64 fluid ounces
5.12/64 dollars = 64/64 fluid ounces ... divide both sides by 64
0.08 dollars = 1 fluid ounce
We divided both sides by 64 to turn "64 fluid ounces" into "1 fluid ounce", due to how the term "unit rate" is set up. The term "unit" means "one". Basically we're finding the cost per 1 unit, or per 1 fluid ounce.
2^2(3-8)÷5-1 please help
Answer:
-5
Step-by-step explanation:
2^2*(3-8)÷5-1
4*(-5)÷4
-20÷4
=-5
Answer:
-5
Step-by-step explanation:
Firstly 2^2=4, 4(3-8)=4*(-5)= -20, -20/5 -1= -4-1= -5
find the coordinates of the point satisfying lying on x axis at a distance of 5 units to the right of x axis lying on y axis at a distance of 3 units below the orgin
Answer:
(5, -3)
Step-by-step explanation:
Coordinates are located on Cartesian planes (more like locating a point on a graph). Cartesian coordinates can be two dimensional or three dimensional in nature depending on the number of axis we are considering. For the question, the dimension of the required coordinate is 2-dimensional i.e (x,y).
On the Cartesian plane, we have the x axis along the horizontal plane and y axis along the vertical.
Note that positive values lies towards the right of the x-axis and also up the y-axis. The negative values lies towards the left of the x-axis and also down the y-axis.
According to the question, if a point is lying on x axis at a distance of 5 units to the right of x axis, then the value of x will be +5 i.e x = +5
Also, if a point lies on the y axis at a distance of 3 units below the origin, then the value of y will be -3 i.e y = -3.
Hence, the coordinates satisfying this points (x,y) is (5, -3)
In square units, what is the area of the sector that is not shaded?
Answer:
[tex] A = 350\pi \approx 1100 [/tex]
Step-by-step explanation:
The shaded area is a sector with a central angle of 45 deg.
The total measure of the central angle of a full circle is 360 deg.
The central angle of the unshaded sector is
360 deg - 45 deg = 315 deg
The area of a sector of a circle with a central angle of n degrees and a radius r is
[tex] A = \dfrac{n}{360}\pi r^2 [/tex]
[tex] A = \dfrac{315}{360}\pi \times 20^2 [/tex]
[tex] A = 350\pi \approx 1100 [/tex]