Answer: x = -3/4 can not be a rational zero of the polynomial.
Step-by-step explanation:
We have the polynomial:
6x^5 + ax^3 -bx -12 = 0.
The theorem says that:
If P(x) is a polynomial with integer coefficients, and p/q is a zero of P(x) then p is a factor of the constant term (in this case the constant term is -12) and q is a factor of the leading coefficient (in this case the leading coefficient is 6.).
The factors of -12 (different than itself) are (independent of the sign).
1, 2, 3, 4 and 6.
So p can be: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6.
The factors of 6 are:
1, 2 and 3, so q can be 1, -1, 2, -2, 3, -3.
Then the option that can not be a zero of the polynomial is
x = -3/4
because the number in the denominator must be a factor of the leading coefficient, and 4 is not a factor of six.
Eldrick is using the dot plots to compare two sets of data. Both plots use the same number line. What is the difference between the mean of each data set?
Answer:
15
Step-by-step explanation:
mean means add all the numbers and divide them by how many there are
plot 1: 63 divided by 9 equals 7
plot 2: 330 divided by 15 equals 22
so now we need to subtract 22 minus 7 equals 15
hope this helps
Answer:
15
Step-by-step explanation: you have to add all of the numbers and then divide the answer by the number of numers you added
What is the value of this expression when g=-3.5?
8-12g-51
Step-by-step explanation:
If g=3.5 what about 12g
12g×3.5=42
8_42_51=_85
Given 1 ABCD and 2D = 1459, what is the measure of C?
A. 1450
B. 900
C. 105°
D. 35°
E. 80°
F. Cannot be determined
Answer:
D
Step-by-step explanation:
Assuming the figure to be a parallelogram, then
The consecutive angles are supplementary, that is
∠ D + ∠ C = 180°
145° + ∠ C = 180° ( subtract 145° from both sides )
∠ C = 35° → D
Please answer this question now
Answer:
m < S = 55°
Step-by-step explanation:
Based on tangent theorem, a tangent line is said to be perpendicular to a radius of a circle when they intercept. The point at which they meet is said to be at 90°.
Therefore, in the ∆PQS, given, m < P = 90°.
m < Q = 35°
m < S = 180° - (90° + 35°) (sum of the angles in a triangle)
m < S = 180° - 125°
m < S = 55°
I am being timed pls asap
Answer:
Writing it in matrix form
- 2 - 4 - 5 - 155
1 1 6 101
2 2 - 3 37
I hope this helps you
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number. Also, If the tens digit is x, then the equation is: ___?
The Goodsmell perfume producing company has a new line of perfume and is designing a new bottle for it. Because of the expense of the glass required to make the bottle, the surface area must be less than 150 cm2. The company also wants the bottle to hold at least 100mL of perfume. The design under consideration is in the shape of a cylinder. Determine the maximum volume possible for a cylindrical bottle that has a total surface area of less than 150 cm2. Determine the volume to the nearest 10mL. Report the dimensions of the bottle and he corresponding surface are and volume.
Answer:
Dimensions of the bottle
x (radius of the base ) = 3,99 cm
h (heigh of the bottle ) = 3,99 cm
Surface area = 149,99 cm²
Volume of the bottle = 199,45 cm³
Step-by-step explanation:
The bottle volume must be V(b) = 100 ml or V(b) = 100 cm³
The shape of the bottle is cylindrical
Surface area of bottle is
S = surface area of the base + lateral area
Area of the base = π*x ² where x is radius of circle
Lateral area is 2*π*x*h where h is the heigh of the bottle
V(b) = π* x²*h (1)
π*x² + 2*π*x*h < 150 cm² we work with the limit 150
π*x² + 2*π*x*h = 150
h = (150 - π*x²) /2*x*π
Plugging that value in equation (1)
V(x) = π*x² * (150 - π*x²) /2*x*π ⇒ V(x) = 150*π*x²/2*x*π - π²*x⁴/2*x*π
V(x) = 75*x - π*x³/2
Taking derivatives on both sides of the equation
V´(x) = 75 - 3*π*x²/2
V´(x) = 0 75 - 3*π*x² /2 = 0
x² = 75*2 /3*π ⇒ x² = 15,92 ⇒ x = 3,99 cm
And h = ( 150 -π*x² )/2*π*x
h = ( 150 - 49,98 )/25,05
h = 3,99 cm
Dimensions of the bottle
x (radius of the base ) = 3,99 cm
h (heigh of the bottle ) = 3,99 cm
Surface area = 149,99 cm²
Volume of the bottle = 199,45 cm³
how do u find rate of change on a graph
Step-by-step explanation:
The correct answer is the vertical change divided by the horizontal change between two points on a line. We can find the slope of a line on a graph by counting off the rise and the run between two points. If a line rises 4 units for every 1 unit that it runs, the slope is 4 divided by 1, or 4.
Answer:
Calculate the rise over the run/the change in y over the change in x
Step-by-step explanation:
In order to find the rate of change on a graph from a slope, you need to look at how many units up and how many units to the right. Find a solid point on the graph for both the x and y directions. Count how many units go up and how many go right. Divide how many units go up by how many go to the right and that is the rate of change on the graph.
A windshield wiper blade is 18 inches long. To the nearest square
inch, what is the area covered by the blade as it rotates through an
angle of 122 degrees? (Enter just a number for your answer.)
the answer is 22 degrees
The area covered by the blade as it rotates through an angle of 122 degrees is approximately 346 square inches.
We have,
The area of a sector can be calculated using the formula:
Area = (θ/360) * π * r²
where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the sector.
The central angle is 122 degrees, and the radius of the wiper blade is 18 inches.
Substituting the values into the formula:
Area = (122/360) * π * (18²)
Area = (0.3389) * 3.14159 * 324
Area ≈ 344.77 square inches
Area = 345 square inches
Therefore,
The area covered by the blade as it rotates through an angle of 122 degrees is approximately 346 square inches.
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Anya graphed the line (y−2)=3(x−1) on the coordinate grid. A coordinate plane with a line passing through the points, (negative 2, negative 7), (0, negative 1), and (1, 2). What is the slope of Anya’s line? −3 −1 1 3
Answer:
Slope of Anya's line is m = 3
Step-by-step explanation:
Explanation:-
Given Anya graphed the line
(y−2)=3(x−1)
we know that slope intercept form is
y = mx +c
now given Anya line
y−2=3(x−1)
⇒ y - 2 = 3x - 3
⇒ y = 3x - 3 + 2
⇒ y = 3 x - 1
Comparing slope -intercept form
y = mx +c
slope of Anya's line is m = 3 and y-intercept C = -1
Answer:
M=3
Step-by-step explanation:
Hope this helps!
I need help on this question fast!!
Answer: y=235x+15
Step-by-step explanation:
Plug in 4 for x
Y= 235(4)+15
Y= 955
Find the approximate side lengths and perimeter of quadrilateral WXYZ. If necessary, round your answers to the nearest hundredth.
The approximate length of segment WX is
[tex]\left[\begin{array}{ccc}2\\4.12\\4.47\\5\end{array}\right][/tex]
The approximate length of segment XY is
[tex]\left[\begin{array}{ccc}2\\4.12\\4.47\\5\end{array}\right][/tex]
The approximate length of segment YZ is
[tex]\left[\begin{array}{ccc}2\\4.12\\4.47\\5\end{array}\right][/tex]
The approximate perimeter of quadrilateral WXYZ is [tex]\left[\begin{array}{ccc}14\\14.47\\15\\15.59\end{array}\right][/tex]
Answer:
The answer is given below
Step-by-step explanation:
Given that the location of the points are W = (3, 1) , X = (7, -1), Y = (7, -3) and Z = (3,-3)
The distance between two points A(x1, y1) and B(x2, y2) is given by the formula:
[tex]|AB|=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Therefore, the side length of the quadrilaterals are:
[tex]|WX|=\sqrt{(-1-1)^2+(7-3)^2}=\sqrt{20} =4.47[/tex]
[tex]|XY|=\sqrt{(-3-(-1))^2+(7-7)^2}=\sqrt{20} =2\\\\|YZ|=\sqrt{(-3-(-3))^2+(3-7)^2}=\sqrt{20} =4\\\\|ZW|=\sqrt{(-3-1)^2+(3-3)^2}=\sqrt{20} =4[/tex]
The Perimeter of the quadrilateral = |WX| + |XY| + |YZ| + |ZX| = 4.47 + 2 + 4 + 4 = 14.47 units
Answer:
4.47,
2
4
14.47
Step-by-step explanation:
Orion is working with a data set that compares the outside temperature, in degrees Celsius, to the number of gallons of ice cream sold per day at a local grocery store.
The data has a line of best fit modeled by the function f(x) = 3x + 4 . Orion determines that when the temperature is 25∘C, the store should sell about 79 gallons of ice cream. The correlation coefficient of the data is 0.39.
Explain how accurate Orion expects the prediction to be.
Answer: kindly check Explanation.
Step-by-step explanation:
The function f(x) = 3x + 4 is a linear regression model. Orion's prediction was obtained by Substituting 25 for x to obtain the predicted variable
f(25) = 3(25) + 4 = 75 + 4 = 79.
However, with a correlation Coefficient of 0.39, which is a numerical value of range - 1 to +1 and is used to measure the statistical relationship between the dependent variable (number of gallons of ice-cream sold per day) and the independent variable (temperature).
The closer the correlation Coefficient (r) value is to +1 or - 1, the stronger the degree of correlation. Positive r values depicts positive relationship while negative r values depicts negative relationship. The closer the r value is to 0. The weaker the relationship and a r value of means there is no Relationship exists between the two variables.
With a correlation Coefficient of 0.39, we can Infer that that only a moderate positive relationship exists between temperature and gallons of ice cream sold per day.
What is the surface area of a sphere with a diameter of 16 cm?
Answer:
804.25 cm² (corrected to 2 decimal places)
Step-by-step explanation:
Radius = diameter / 2
= 16/ 2
=8 cm
Surface area of sphere = 4πr²
= 4π8²
=804.25 cm² (corrected to 2 decimal places)
any number that divisible by 3 is also divisible by 6 . Find a counterexample to show that the conjecture is false
Answer:
Counterexample: 21 which is divisible by 3 but not by 6.
Step-by-step explanation:
Use for example the number 21 which is divisible by 3 rendering 7, but not divisible by 6.
You can find any number with at least a factor of "3", but no factor "2" in it, so any odd number divisible by 3 would work as counterexample.
Given: x + 2y=-6.
Solve for y
Oy=x-6/2
Oy=-x+6/2
Oy=-x-6/2
Answer:
y = (-x - 6)/2
Step-by-step explanation:
x + 2y = -6
2y = -x - 6
y = (-x - 6)/2
HELP ASAP, PLEASE!!!!
Answer:
Fraction = 5/10 = 1/2
Decimal = 0.5
Step-by-step explanation:
Answer:
fraction-5/10 decimal-0.5
plz give brainiest
Step-by-step explanation:
Q3. Ishah spins a fair 5-sided spinner. She then throws a fair coin.
(i) List all the possible outcomes she could get. The first one has been done for you.
(1, H)
(ii) Ishah spins the spinner and tosses the coin.
Work out the probability that she will get a 2 and a head.
Answer:
see below
Step-by-step explanation:
1.
1, H - 2, H - 3, H - 4, H - 5, H
1, T - 2, T - 3, T - 4, T - 5, T
2.
2,H is one out of 10 possible outcomes, so the probability is 1/10
THIS IS A WHOLE PAGE ITS FOR 40 points MIDDLE SCHOOL PLEASE HELP
Answer:
the leanth of the track is 1/2 miles long.
Step-by-step explanation:
Im sorry that i couldn't complete all the questions, I had a family thing to go to so sorry.
The diagram shows an incomplete polygon. How do I determine whether it is a regular polygon or not? How should I write my reasoning?
Answer:
see explanations below.
Step-by-step explanation:
The shown sides are all equal.
If it is a regular polygon, it must have all interior angles equal, and all sides equal.
IF
all sides are equal and all angles are equal,
THEN
it is a regular polygon, with 12 sides, because in regular polygons, all exterior angles are equal, and add up to 360 degrees.
No. of sides = 360/(180-150) = 360/30 = 12 sides.
How many ways are possible to choose 3 days out of February? NOTE: Use 28 days for the number of days in February. A) 3276 B) 378 C) 20475 D) 2925
Answer:
A) 3,276 ways.
Step-by-step explanation:
In this case, choosing February 1, February 12, and February 20 would be the same thing as choosing February 12, February 1, and February 20. So, since order does not matter, we will use a combination to solve the question.
The formula for combinations is...
n! / [r!(n - r)!], where n = the number of days in February (28) and r = the number of days you are choosing (3).
28! / [3! * (28 - 3)!]
= 28! / (6 * 25!)
= (28 * 27 * 26) / 6
= (14 * 9 * 26) / 1
= 14 * 9 * 26
= 126 * 26
= A) 3,276.
Hope this helps!
The perimeter (distance around the triangle) of a triangular lot is 73 meters with Sides A, B, and C. Side A is 16 meters, Side B is twice the length of Side C. Find the length of Side C.
Answer:
Brainliest please
Step-by-step explanation:
perimeter is to add all sides
73m= 16+B+C
{ use algebra}
C is a, B is twice C, hence 2a
a+2a(+16)=73
3a=73-16= 57
3a=57, divide
a= 19
B=19×2= 38m
C=19m
C is 19m
Answer:
C = 19 m
Step-by-step explanation:
Side B is twice the length of Side C.
B = 2C -----------(I)
Perimeter = 73 m
A + B + C = 73
A + 2C + C = 73 {from (I)}
16 + 3C = 73
3C = 73 - 16
3C = 57
C = 57/3
C = 19 m
What is the equation of the following line written in slope-intercept form?
(1,5)
Oy=-5x
Oy= 5x
Oy=5/x
Answer:
y = 5x
Step-by-step explanation:
The y intercept is 0 since it crosses the y axis at 0
The slope is rise over run
From (0,0) we go up 5 and to the right 1
5/1 = 5
Slope = 5
The slope intercept equation is
y = mx+b where m is the slope and b is the y intercept
y = 5x+0
y = 5x
Answer:
y=5x
Step-by-step explanation:
Work out the mean for the data set below: 3004, 3007
Answer:
Hey!
Your answer would be 3,005.5!
Step-by-step explanation:
How did we get this?
Well to find the mean of a data set we...
ADD ALL THE VALUES UP and DIVIDE BY THE AMOUNT OF NUMBERS PRESENT...
So in this case...
WE DO: 3,004 + 3,007 = 6,011
NOW: DIVIDE BY 2...6,011 / 2
YOUR ANSWER IS 3005.5!
Hope this helps!
The mean for the data set given 3004, 3007 is, 3005.5
What is mean?In one of the branches of mathematics called statistics, We use one term known as mean; it generally tells us what is the central tendency of the data set.
Generally, we use three terms for measurement of central tendency like, mean, median, mode.
In simple words, mean is an average of all the dataset.
formula;
Mean = Sum of all the dataset/Total number of dataset
Given data set,
3004 & 3007
Mean = X₁+X₂/2
Mean = (3004+3007)/2
Mean = 3005.5
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A $86 ,000 trust is to be invested in bonds paying 9% , CDs paying 6% , and mortgages paying 10% . The bond and CD investment together must equal the mortgage investment. To earn a $7180 annual income from the investments, how much should the bank invest in bonds?
Answer:
to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.
Step-by-step explanation:
Let the mortgage investment be X
The Bond to be Y
and the CDs to be Z
Thus;
X+Y+Z = 86000 ------- (1)
Y + Z = X ------------(2)
10X + 9Y + 6Z = 7180 × 100 ------ (3)
So;we now have:
X+Y+Z = 86000 ------- (1)
Y + Z = X ------------(2)
10X + 9Y + 6Z = 718000 ------ (3)
Let ; replace X with Y+Z in equation (1) and (3)
Y+Z + Y+Z = 86000
2Y + 2Z = 86000
Divide both sides by 2
Y+Z = 43000 ------ (4)
From equation (3)
10X + 9Y + 6Z = 718000
10(Y+Z) + 9Y + 6Z = 718000
10Y +10Z + 9Y +6Z = 718000
19Y + 16Z = 718000 -----(5)
Y+Z = 43000 ------ (4)
19Y + 16Z = 718000 -----(5)
Using elimination method; multiply (-16) with equation (4) and (5) ; so, we have:
-16 Y -16 Z = -688000
19Y + 16Z = 718000
3Y + 0 = 30000
3Y = 30000
Y = 30000/3
Y = 10000
From (4);
Y+Z = 43000
So; replace Y with 10000; we have:
10000 + Z = 43000
Z = 43000 - 10000
Z = 33000
From (1) ;
X+Y+Z = 86000
X + 10000 + 33000 = 86000
X + 43000 = 86000
X = 86000 - 43000
X = 43000
Since we assume the bond to be Y and Y = $10000;
Thus; to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.
Gassim bought 2L of colour paints to paint a wall of a villa. He already had 0.75L of colour paint. If he uses 2/5 of colour paints , find the amount of colour paints left?
THNXX for answering : )
Answer:
0.45 litres
Step-by-step explanation:
2/5 multiplied by 2 = 0.8
0.8+0.75= 1.55
2-1.55 = 0.45
If f(x) =x/2+8, what is f(x) when x=10
Answer:
f(10) =13
Step-by-step explanation:
f(x) =x/2+8,
Let x = 10
f(10) =10/2+8,
= 5+8
= 13
PLEASE HELP IMMEDIATELY
Find x when[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]
[tex] - \frac{23}{4} [/tex]
[tex] - \frac{19}{4} [/tex]
[tex] \frac{19}{4} [/tex]
[tex] \frac{23}{4} [/tex]
Answer:
[tex]x = - \frac{19}{4} [/tex]Option B is the correct option.
Step-by-step explanation:
[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]
Move constant to R.H.S and change its sign:
[tex]x = - \frac{21}{4} + \frac{1}{2} [/tex]
Take the L.C.M
[tex]x = \frac{ - 21 + 1 \times 2}{4} [/tex]
[tex]x = \frac{ - 21 + 2}{4} [/tex]
Calculate
[tex]x = - \frac{19}{4} [/tex]
Hope this helps...
Good luck on your assignment..
Step-by-step explanation:
-19/4 is the correct answer for your question
The tables for f(x) and g(x) are shown below.
х
f(x)
-11
-5
-2
1
1
13
5
29
х
-5
g(x)
-7
-1
-2
1
5
5
13
What is the value of (f-9)(5)?
Answer:
16
Step-by-step explanation:
(f - g)(5) = f(5) -g(5)
From the tables, ...
f(5) = 29
g(5) = 13
Your desired function is ...
f(5) -g(5) = 29 -13 = 16
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