[tex]\large\underline{\sf{Solution-}}[/tex]
Given that:
[tex]\sf p(y) = 2y^3+my^2+11y+m+3 [/tex]
We are also given that, p(y) is divisible by 2y - 1.
So, 2y - 1 is a factor of p(y).
[tex]\sf\longmapsto 2y-1=0[/tex]
[tex]\sf\longmapsto y=\dfrac{1}{2}[/tex]
So, 1/2 is a zero of p(y).
[tex]\sf\longmapsto p(1/2) =0 [/tex]
[tex]\sf\longmapsto p(y) = 2y^3+my^2+11y+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{2}\right)^3+m\left(\dfrac{1}{2}\right)^2+11\left(\dfrac{1}{2}\right)+m+3 [/tex]
So,
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{8}\right)+m\left(\dfrac{1}{4}\right)+11\left(\dfrac{1}{2}\right)+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = \dfrac{1}{4}+\dfrac{m}{4}+\dfrac{11}{2}+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) =\dfrac{1}{4}+\dfrac{m}{4}+\dfrac{22}{4}+\dfrac{4m}{4}+\dfrac{12}{4} [/tex]
[tex]\sf\longmapsto 0 =\dfrac{1+m+22+4m+12}{4} [/tex]
[tex]\sf\longmapsto 0 =\dfrac{5m+35}{4}[/tex]
[tex]\sf\longmapsto 5(m+7)=4\times0[/tex]
[tex]\sf\longmapsto 5(m+7)=0[/tex]
[tex]\sf\longmapsto m+7=0[/tex]
[tex]\longmapsto\bf m=-7[/tex]
Therefore, the value of m is -7.
I'm not sure how I can find my answer, any help?
Answer:
The next number would be 3
Step-by-step explanation:
As you can see its a repeating pattern of "1739"
Answer:
3
Step-by-step explanation:
1 7 3 9 1 7 3 9 1 7 3 9 1 7 3 9 ...
What does 2-for-1 split mean
Answer:
you two shares for every one share of a company you own
Step-by-step explanation:
hi could someone explain this??
im thinking it is J=50(15)^t???
Answer:
J=15t+50
Step-by-step explanation:
The equation to represent this situation will be in the form J=mt+b where b is the starting value of love units, m represents the "love units" that are multiplied by the number of week, t is the number of weeks, and J represents Jack's love at that specific week.
The equation becomes: J=15t+50
To check, the equation should equal 50 when t=0, 65 when t=1, and 80 when t=2.
Checking t=0:
J=15(0)+50=0+50=50
Checking t=1:
J=15(1)+50=15+50=65
Checking t=2:
J=15(2)+50=30+50=80
The equation J=15t+50 does model the behavior of Jack's love at any week t based on the given data. Note that the equation used was based on slope intercept form (y=mx+b) due to the given data having a linear relationship.
5x + 2 = 3x + 4(2x - 1)
show steps
Answer:
x=1
Step-by-step explanation:
5x+2=3x+4(2x-1)
5x+2=3x+8x-4
5x+2=11x-4
5x-11x=-4-2
-6x=-6
6x=6
x=1
What methods do you know that can be used to solve a quadratic equation?
Answer: If the quadratic equation has real, rational solutions, the quickest way to solve it is often to factorise into the form (px + q)(mx + n), where m, n, p and q are integers. This is especially true where the coefficient of x2 is 1.
Example 1 - Solve x2+7x+12=0
Step-by-step explanation:
that's the only one I remember
Answer:
factoring, using the square roots, completing the square and the quadratic formula.
Step-by-step explanation:
please help me with this sum
Step-by-step explanation:
2667
1884
1953
782
2046
3105
8559
5368
963
3367
Answer:
381 x 7 = 2667
471 x 4 = 1884
651 x 3 = 1971
391 x 3 = 1173
341 x 6 = 2046
Hope its help full
Find the unit price in dollars per ounce).
A 24-ounce can of pineapple for $1.08
PLS PLS HELPME ASAP
Answer:
$0.05 per ounce
Step-by-step explanation:
To find the price in dollars per ounce, divide the price by the number of ounces.
[tex]\frac{1.08}{24}[/tex] = $0.045 per ounce = $0.05 per ounce
Which statement is true about the expressions below?
Evaluate.
plz help
12⋅(14+13)2+23
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
52
Step-by-step explanation:
14+13= 27+2=29+23=52
The value of the numerical expression 12 ⋅ (14 + 13)² + 23 will be 8771.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The expression is given below.
⇒ 12 ⋅ (14 + 13)² + 23
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To answer the problem properly and accurately, this rule must be followed.
⇒ 12 ⋅ (14 + 13)² + 23
⇒ 12 ⋅ (27)² + 23
⇒ 12 ⋅ 729 + 23
⇒ 8748 + 23
⇒ 8771
The value of the numerical expression 12 ⋅ (14 + 13)² + 23 will be 8771.
More about the value of the expression link is given below.
brainly.com/question/23671908
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What is the slope of the line shown on the grid?
Answer:
Answer is last option, -3.
Step-by-step explanation:
We know it's going to be a negative slope because the line is going down to the right, so it can't be eighther option 1 or 3.
Next it appears the line is going 3 units down and 1 unit to the right. So it will be written as -3/1 because of rise/run.
Hope this helps/makes sense :)
what is the length of segment XZ?
192
12
8
144
Answer:
12 is the length of XZStep-by-step explanation:
Pythagorean Theorem Formula: a² + b² = hypotenuse²
x² + 5² = 13²
x² + 25 = 169
x² + 25 - 25 = 169 - 25 (subtract 25 in both sides)
x² = 169 - 25
√x² = √144
x = 12
Can I get help with 1C please?
Answer:
14
Step-by-step explanation:
If f(x)=3x-2 and g(x)=2x+1, find (f+g)(x)
A. 5x - 3
B. x - 3
C. x - 1
D. 5x - 1
brainliest for help!!
Answer:
D. 5x - 1
Step-by-step explanation:
To solve this, you need to add together f(x) and g(x)
f(x) + g(x) = (3x - 2) + (2x + 1)
3x + 2x = 5x
-2 + 1 = -1
The answer is 5x - 1
When a 3-digit number is rounded to the nearest ten and the nearest hundred, the difference is 50. What is the number?
Answer: 150?
Step-by-step explanation:
150 -> 200 200-150=50
150-> 150 200-150=50
A cylinder with a radius of 10ft has a volume of 2, 198.0013
What is the height of the cylinder
Answer:
~7 ft
Step-by-step explanation:
2,198.0013 = pi × 10^2 × h
h = 2198.0013 / (3.1416 × 100)
h = 6.996 ft ~ 7 ft
the sum of three consecutive even integers if the largest number is y
Answer:
y
Step-by-step explanation:
4y=6 sorry thats all i know
Plz help me with math well mark brainliest!
Answer:
15 is divided by a number
Consider the functions p(x) = 5x3 + 6x2 + 4x and qx) = 5640.
-
1. Use graphing technology to find a value of that makes p(x) = q() true.
On Mrs. Sean's desk,
there are pink and yellow
markers. The ratio of pink
markers to total markers
is 1:3. If there are 16
yellow markers, then how
many markershare pink?
Since the ratio of pink markers to total markers is 1:3, then there are 8 pink markers.
Number of yellow markers given = 16
Based on the information given, therefore, the pink markers will be half of the yellow markers. This will be:
= 1/2 × 16
= 8 markers
Therefore, the total markers will be:
= 8 + 16 = 24
In conclusion, pink markers will be 8/24 = 1/3. Therefore, the number of pink markers is 8.
Read related link on:
https://brainly.com/question/25265419
what should she do next?
Answer:
(-2) *6 = -12
Step-by-step explanation:
4 + (2-4) *6 , solve the subtraction in parenthesis
4 + (-2)*6, solve the multiplication of (-2) *6
4 - 12, solve the subtraction
-8
-12 1/2 + 4 1/2
I need the work
Answer:
-4
Step-by-step explanation:
1/2 of -12 is -6. 1/2 of 4 is 2.
-6 + 2 is -4.
Write the equation of the line containing the points (3, 6) and (7, - 2) in standard form.
Answer:
[tex]y = mx + c \\ 6 = 3m + c...(1) \\ - 2 = 7m + c...(2) \\ subtract \: (2) - (1) \\ 4m = - 8 \\ \therefore \: m = - 2 \: sub \: in \: (1) \\ 6 = 3( - 2) + c \\ \therefore \: c = 12 \\ \boxed{y = - 2x + 12}[/tex]
Answer:
y=-2x+12
Step-by-step explanation:
[tex] \sqrt{5.29} = [/tex]
a) 2.3
b) 2.4
c) 2.5
d) 2.6
Answer:
2.3
Step-by-step explanation:
In this case we are going to use the 'Babylonian Method' to get the square root of any positive number.
We must set an error for the final result. Say, smaller than 0.01. In other words we will try to find the square root value with at least 1 correct decimal places.
Step 1:
Divide the number (5.29) by 2 to get the first guess for the square root .
First guess = 5.29/2 = 2.645.
Step 2:
Divide 5.29 by the previous result. d = 5.29/2.645 = 2.
Average this value (d) with that of step 1: (2 + 2.645)/2 = 2.3225 (new guess).
Error = new guess - previous value = 2.645 - 2.3225 = 0.3225.
0.3225 > 0.01. As error > accuracy, we repeat this step again.
Step 3:
Divide 5.29 by the previous result. d = 5.29/2.3225 = 2.2777179763.
Average this value (d) with that of step 2: (2.2777179763 + 2.3225)/2 = 2.3001089882 (new guess).
Error = new guess - previous value = 2.3225 - 2.3001089882 = 0.0223910118.
0.0223910118 > 0.01. As error > accuracy, we repeat this step again.
Step 4:
Divide 5.29 by the previous result. d = 5.29/2.3001089882 = 2.299891017.
Average this value (d) with that of step 3: (2.299891017 + 2.3001089882)/2 = 2.3000000026 (new guess).
Error = new guess - previous value = 2.3001089882 - 2.3000000026 = 0.0001089856.
0.0001089856 <= 0.01. As error <= accuracy, we stop the iterations and use 2.3000000026 as the square root.
So, we can say that the square root of 5.29 is 2.3 with an error smaller than 0.01 (in fact the error is 0.0001089856). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(5.29)' is 2.3.
Note: There are other ways to calculate square roots. This is only one of them.
Normal:
The square root of 5.29 is defined as the only positive real number such that, multiplied by itself, it is equal to 2.3.
The square root of 5.29 can be written as (5.29)1/2. So,
(5.29)1/2 = (2.3 × 2.3)1/2
(5.29)1/2 = [(2.3)2]1/2
(5.29)1/2 = (2.3)2/2
(5.29)1/2 = (2.3)1
Thus,
√5.29 = 2.3
pls help i am in k12
Refer to the equation 2x − 6y = 12.
Write the equation in Slope Intercept Form.
Find the x-intercept and the y-intercept?
Create a table of values for 4 points. You can include the intercepts. Show your work.
X
Y
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y yand solve for x . To find the y-intercept, substitute in 0 for x and solve for y .
x-intercept(s): ( 6 , 0 )
y-intercept(s): ( 0 , − 2 )
Use the slope-intercept form y = m x + b to find the slope m and y-intercept b .
Slope: [tex]\frac{1}{3}[/tex]
graph in pic
(Credit: M a t h w a y)
How much of the circle is shaded? Write your answer as a fraction in simplest form.
Answer:
3/8\
Step-by-step explanation:
you do one half minus one eight and you get 3/8
rewrite 5% as a decimal number
Answer:
5% as a decimal number is 0.05.
Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
The required area of the figure is 100.75 units².
What is area?Area of an object shows that how much space it can cover.
Given is figure, made by scooping out a semicircle from a rectangle of length 14 units and width 10 units,
We need to find the area of the figure,
To find the same, we will find the area of whole rectangle and then subtract the area of the semicircle from it,
Area of a rectangle = length × width = 14 × 10 = 140 units²
Area of a semicircle = π × radius² / 2
Here the diameter of the semicircle will be the width of the rectangle,
So,
Diameter = 10
Radius = 5
Area of a semicircle = 3.14 × 25/2 = 39.25 units²
Now,
The area of the figure = 140 - 39.25 = 100.75 units²
Hence, the required area of the figure is 100.75 units².
Learn more about areas, click;
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Find the square roots of the number: 25
Answer:
square root of 25 is 5
Step-by-step explanation:
when you take the numbers that multiply together to make 25 which in this case is 5 5*5=25
please help me with this sum
Answers:
781 × 8 = 6248
231 × 7 = 1617
421 × 6 = 2526
531 × 5 = 2655
681 × 2 = 1362
951 × 4 = 3804
741 × 3 = 2223
361 × 3 = 1083
931 × 7 = 6517
821 × 2 = 1642
Cookies are on sale! Today each cookie costs $0.75 less than the normal price, Right now if you buy 7 of
them it will only cost you $2.80
Write an equation to determine the normal price of each cookie (c),
Find the normal price of each cookie,
Answer:
2.80$ dived by 7 to get 40 cents each on sale. add 75 sents to each cookie. 40 plus 75 in cents. your left with 1.15$ per cookie. 1.15 times 7 is 8.05
Step-by-step explanation:
Answer:
The normal price of each cookie is n = c = $1.15.
Step-by-step explanation:
Represent the normal cookie price by n.
Then the sale price today is n - $0.75 each, and so 7 cookies will cost you 7(n - $0.75), or $2.80, or, as an equation, 7(n - $0.75), or $2.80.
We simplify this equation by dividing both sides by 7, which results in:
n - $0.75n = $0.40.
Combining like terms, we get
n = $1.15
The normal price of each cookie is n = c = $1.15.