Answer:
[tex]x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2} [/tex]
Step-by-step explanation:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 3 + - \sqrt{9 + 24} }{2} \\ x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2} [/tex]
if 2 is added to denominator and nemerator it becomes 9/10 and 3 is substracted from nemerator and denominator it becomes 4/5 find the fraction
Answer:
9-2 /10-2
7/8
4+3/5+3
7/8
fraction is 7/8
Could anyone help me out with this?
Answer: they are abt the same its all abt percentage now- Pitcher A
Step-by-step explanation: more water lessens the strength
Write an expression for each statement: A truck has a total of a pounds of fruit which were packed in n boxes. How many pounds of fruit are in each box?
Answer:
The answer is "[tex]\text{Total number of boxes} =\frac{a}{n \ boxes}[/tex]"
Step-by-step explanation:
Total pounds carried by the vehicle are "a" pounds.
This will be spread into many boxes, each containing "n" pounds.
It implies that:
[tex]\text{Total pounds = box number} \times \text{amount of pounds from every box} \\\\a = \text{box number} \times n\\\\\text{Box number} = \frac{a}{n \ boxes}[/tex]
If the measure of < A is 99 ° and the measure of < B is 81 ° , then < A and < B are _____.
Select one:
a. complementary angles
b. adjacent angles
c. vertical angles
d. supplementary angles
Answer:
D.supplementary angles
Step-by-step explanation:
81+99=180
(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.
(b) Prove that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational.
Answer:
(a) [tex]x\³ - 6x - 6[/tex]
(b) Proved
Step-by-step explanation:
Given
[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root
Solving (a): The polynomial
A cubic function is represented as:
[tex]f = (a + b)^3[/tex]
Expand
[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]
Rewrite as:
[tex]f = a^3 + 3ab(a + b) + b^3[/tex]
The root is represented as:
[tex]r=a+b[/tex]
By comparison:
[tex]a = $\sqrt[3]{2}[/tex]
[tex]b = \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]
Expand
[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
Evaluate like terms
[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]
Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = 6 + 6r[/tex]
Equate to 0
[tex]f - 6 - 6r = 0[/tex]
Rewrite as:
[tex]f - 6r - 6 = 0[/tex]
Express as a cubic function
[tex]x^3 - 6x - 6 = 0[/tex]
Hence, the cubic polynomial is:
[tex]f(x) = x^3 - 6x - 6[/tex]
Solving (b): Prove that r is irrational
The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6
The divisors of -6 are: -6,-3,-2,-1,1,2,3,6
Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values
[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]
[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]
[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]
[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]
[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]
[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]
[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]
[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]
For r to be rational;
The divisors of -6 must divide f(x) without remainder
i.e. Any of the above values must equal 0
Since none equals 0, then r is irrational
I NEED HELP ASAP HEELP
Answer:
S > 2kg
Step-by-step explanation:
It took Sarah 4 days to write a paper, she wrote 12 pages on day 1, 15 pages on day 2 and 9 pages on day 3. If she wrote 12 pages per day , how many pages did she write on the fourth day ?
Answer:
Option A
Step-by-step explanation:
Sarah took 4 days to write a paper.
She wrote 12 pages per day, so total number of pages she wrote in 4 days = 12 × 4
= 48 pages
On day 1, she wrote number of pages = 12
On day 2, she wrote number of pages = 15
On day 3, she wrote number of pages = 9
On day 4, she wrote number of pages = P
She wrote total number pages in 4 days = 12 + 15 + 9 + P
= 36 + P
Therefore, P + 36 = 48
P = 48 - 36
P = 12
She wrote 12 pages on day 4.
Option A is the answer.
The area of a duck enclosure is 300 square feet, with 100 square feet occupied by a pond. Each duck in the enclosure needs more than 20 square feet of space on dry land. If x ducks can be put in the enclosure, which is the simplest inequality that represents this situation?
Answer: x = 100 duck
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
What expression represents the product of b and 34
Answer:
b + 24
Step-by-step explanation:
b and 24 would be b + 24
Solve for x. Round your answer to the nearest tenth if necessary.
Answer:
12.6
Step-by-step explanation:
[tex]\frac{84}{87}[/tex] = [tex]\frac{x}{13}[/tex]
cross multiply
87x = 1092
x = 12.6 rounded
sharon is planning a holiday for 4 people for 7 days
just multiply the numbers together, and it gives you 28, which is what she did thought everything
a right triangle is 18 inches long and a hypotenuse that is 30 inches long. what is the perimeter, in inches, of this triangle?
Answer:
The perimeter is 72 inches
Step-by-step explanation:
using the pythagorean theorem we can solve for the missing leg by plugging in the values we know.
[tex]a^{2} + b^{2} = c^{2} \\18^{2} + b^{2} = 30^{2} \\324 + b^{2} = 900\\ b^{2} = 900-324\\b^{2} = \sqrt{576} \\b= 24[/tex]
now you just add the values, 30 + 24 + 18
A condition statement is logically equivalent to a biconditional statement. true or false
Answer:
true
Step-by-step explanation:
Because a logically equivalent is the same as biconditional statement
Step-by-step explanation:
hello the answer is true, you can check but it's obviously true
I have no idea how to do this, it is due in two days. Hopefully someone sees this before then.
Hello,
[tex]m\ \widehat{ABC}=x\\m\ \widehat{BAC}=2*x\\\\So:\\ x+2x=90^o\\x=30^o\\[/tex]
[tex]cos(30^o)=\dfrac{\sqrt{3} }{2} \\[/tex]
In the triangle ABC,
[tex]cos(30^o)=\frac{BC}{BA} \\\\BA=\dfrac{cos(30^o)}{BC} \\\\BA=\frac{\dfrac{\sqrt{3} }{2} }{24} =16*\sqrt{3} \\\\[/tex]
[tex]sin(30^o)=\dfrac{1 }{2} =\dfrac{AC}{AB} \\\\AC=\dfrac{1}{2} *16\sqrt{3} =8\sqrt{3}[/tex]
In the triangle ACB,
[tex]cos(30^o)=\dfrac{AC}{AL} \\\\AL=\dfrac{8\sqrt{3} *2}{\sqrt{3} } =16\\[/tex]
How much will it cost for a customer to travel:
2 miles
6 miles
How far did a customer travel if they paid £3.50
Answer:
2miles = $3
6 miles = $5
3 miles
Step-by-step explanation:
By observation of the graph, the lines match up from 2 miles to $3
Answer:
offcourse it will be 2 miles .
Solve for x. Round to the nearest tenth of a degree, if necessary.
Sin (angle) = opposite leg / hypotenuse
Sin(x) = 2.1/4
x = arcsin(21./4)
x = 31.7 degrees
Solve the equation and enter the value of x below. 4(x + 1) = 64
Answer:
15
Step-by-step explanation:
Use the distributive property
4x+4=64, then subtract
4x=60, then divide
x=15
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]4(x + 1) = 64 \\ 4x + 4 = 64 \\ 4x = 64 - 4 \\ 4x = 60 \\ x = \frac{60}{4} \\ x = 15[/tex]
=> The answer is 15.
what is 9.7 as a fraction ?
Answer:
Step-by-step explanation:
9.7 = [tex]\frac{97}{10}[/tex]
Count the number of places in the decimal number after the decimal point.
Here , there is only one place.
So, multiply and divide by 10. 9.7 *10/1*10 = 97/10
Please help me solve this problem I’m really struggling
Answer:
x × 3 + 5[tex]x^{2}[/tex] - x- 5
reorder the terms
3x + 5[tex]x^{2}[/tex] - x - 5
collect like terms
2x + 5[tex]x^{2}[/tex] - 5
reorder the terms
Solution
5[tex]x^{2}[/tex] + 2x -5
Answer:
[tex] {x}^{3} + 5 {x}^{2} - x - 5 \\ {x}^{2} (x + 5) - 1(x + 5) \\ (x + 5)(x - 1) \\ \\ (x + 5)( {x}^{2} - {1}^{2} ) \\ (x + 5)(x - 1)(x + 1) \\ [/tex]
URGENT HELP NOW PLEASE QUICKK!!!!
Answer:
(2,-2)
Step-by-step explanation:
Its just (-7+9 , 1-3)
Answer:
P' = (2,-2)
Step-by-step explanation:
P = (-7,1)
T(x,y) = (x + 9, y - 3)
(-7 + 9,1 - 3) = (2,-2)
help leee plzzzzzzzbbbnbbbb
15< 4 + x
O A. x>11
O B. X> 19
O C. x< 19
O D. x< 11
Answer:
A. x>11
Step-by-step explanation:
15 < 4 + x
take 4 to the LHS this becomes 15 - 4 < x
•°• 11 < x
< means less than
Therefore x is greater than 11
x > 11
Record the length of these
segments
PC =
PC' =
units
units
There's all the lengths so you don't have to search them all up
?
Which graph contains the points of intersection
satisfying this linear-quadratic system of equations?
x2 + y2 = 20
x-y + 2 = 0
Answer:
Step-by-step explanation:
Find the distance between A (2,0,-1) and B (3,1,4) and find the mid-point of line segment AB."
Step-by-step explanation:
To Find :-
Distance between the two points .Solution :-
Using Distance Formula ,
> d = √{ ( 2-3)² + (0-1)² + (-1-4)² }
> d = √{ (-1)² + (-1)² + (-5)² }
> d = √{ 1 + 1 + 25 }
> d = √26 .
Using midpoint formula ,
> m = ( 2+3/2 , 0+1/2 , -1+4/3 )
> m = ( 5/2 , 1/2 , -3/3 )
> m = ( 2.5 , 0.5 , -1 )
Someone pls help me ill give out brainliest pls don’t answer if you don’t know
Answer:
i dont know
Step-by-step explanation:
figure it out yourself
The sum of two numbers is 3000. If 8% of one number is equal to 12% of the other, find the numbers.
one is 1800 and another is 1200
Step-by-step explanation:
let no's be A and B
so, A+B =3000
given, 8% = 8/100 = 2/25
12%= 12/100 = 3/25
As per question 8% of A is = 12% of B
so, (2/25)*A = (3/25)*B
now, multiply cross wise
then we get, (A/B) = 3:2
thus two numbers are in the ratio of 3:2
so, let A =3x, B=2x
cause sum of these is 3000 so, A+B =3000
3x+2x =3000
5x = 3000
x= 3000/5
.: x = 600
so, first no is 3x =3*600=1800
2nd no is 2x= 2*600= 1200
Hope this helps you
Can someone help me with this math homework please!
Answer:
(B) h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.
Step-by-step explanation:
You've probably seen this function notation format before, most likely f(x). Other common ones are g(x) and p(x). The f, g, and p are just function names, like the h in this question.
The t in the parentheses is the input, because it's the same as the t in 210 - 15t.
Together, h(t) is the output, which is the exact same as y if you used the formula y = mx + b.
Hope it helps (●'◡'●)
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
Answer:
these points lie INSIDE THE CIRCLE
Hope it helps
have a nice day
question in picture | Math
Answer:
Y=4/-2
Step-by-step explanation:
