Answer:
To solve this problem, we need to use the following two facts:
1) If a quadratic equation has integer coefficients only, and if one of the roots is a + √b (where a and b are integers), then a - √b is also a root of the equation.
2) If r and s are roots of a quadratic equation, then the equation is of the form x^2 – (r +s)x + rs = 0.
Since we know that 1 - √2 is a root of the quadratic equation, we can let:
r = 1 + √2
and
s = 1 - √2
Thus, r + s = (1 + √2) + (1 - √2) = 2 and rs = (1 + √2)(1 - √2) = 1 – 2 = -1.
Therefore, the quadratic equation must be x^2 – 2x – 1 = 0.
Answer: D
Step-by-step explanation:
Efectúa las siguientes operaciones, aplicando la propiedad distributiva de la multiplicación. De ser posible simplifique los resultados
e) 3√2 (2√6-√4-5√6-6)
f) -5√2 (√9+√8-3√4-1)
Answer:
Step-by-step explanation:
e) 3√2 (-3√6 -2 -6)
3√2 (-3√6 - 8)
-9√12 - 24√2
-9√(2^2 * 3) - 24√2
-18√3 - 24√2
or
6(-3√3 - 4√2)
f) -5√2 (3 + 2√2 - 6 - 1)
-5√2(-4 + 2√2)
20√2 - 20
or
20(√2 - 1)
Which transformations are needed to change the parent sine function to the sine function below? On a coordinate plane, a curve crosses the y-axis at y = 1.5. It has a minimum at y = 0.5 and a maximum at y = 1.5. It goes through one cycle at 4 pi. Vertical compression of One-half, horizontal stretch to a period of 4 pi, vertical shift of 1 unit up, phase shift of Pi units left vertical stretch of 2, horizontal compression to a period of 4 pi, vertical shift of 2 units up, phase shift of Pi units left vertical stretch of One-half, horizontal compression to a period of 2 pi, vertical shift of 1 unit up, phase shift of Pi units left vertical compression of One-half, horizontal stretch to a period of 2 pi, vertical shift of 1 unit down, phase shift of Pi units left
Answer:
Vertical compression of One-half, horizontal stretch to a period of 4 pi, vertical shift of 1 unit up and a phase shift of pi units left
Step-by-step explanation:
The parameters of the sine function are;
The point the curve crosses the y-axis (at x = 0) = 1.5
The minimum of the curve is y = 0.5
The maximum is y = 1.5
The time it goes through one cycle = 4 pi
The general form of the sine function is presented as follows;
y = A·sin(B·(x - C)) + D
From the given information, we have;
A = 0.5
The period = 4·π = 2·π/B
∴ B = 1/2
At x = 0, y = max, therefore, B·(x - C) = (1/2)·(0 - C) = π/2
∴ C = -π
D = 1
Therefore, the given sine function can be presented as follows;
y = 0.5·sin((1/2)·(x - π)) + 1
Therefore, the transformation needed to change the parent sine function to the given sine function are
Vertical compression of One-half, horizontal stretch to a period of 4 pi, vertical shift of 1 unit up and a phase shift of pi units left
Answer:
The answer is A
Step-by-step explanation:
Neeedddd answweerrrr plaeeessee
9514 1404 393
Answer:
B. log_b(a) - log_b(d)
Step-by-step explanation:
The applicable rule of logarithms is ...
log(a/b) = log(a) -log(b)
All the logs need to have the same base.
__
Here, the base is 'b', but the rule still applies:
[tex]\log_b{\dfrac{a}{d}}=\log_b{(a)}-\log_b{(d)}[/tex]
The mass of the moon is 7.343 × 10^19 tonnes. The Earth has a mass of 81 times bigger than that of the moon. Work out the mass of the Earth.
Answer:
= 7. 343 × 10^19 ×81
= 1.377 × 10^21
(6/11) to the power 2 answer pls
Step-by-step explanation:
in fraction it comes 36/121
and in decimal.it comes 0.3
Answer:
Step-by-step explanation:
6/11^2 = 6/11 * 6/11 = 36 / 121.
You cannot simplify 36/121
A circle has a central angle of 6 rad that intersects an arc of length 14 inches. Which equation find the length of the radius, R, of the circle?
Answer:
Step-by-step explanation:
θ=l/r
where θ is central angle in degrees.
l=length of arc.
r=radius of circle.
6=14/r
6r=14
r=14/6=7/3 =2 1/3 inches.
What is the answer of this question?
Answer:
2 ( Option A )
Step-by-step explanation:
The given integral to us is ,
[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]
Here 5 is a constant so it can come out . So that,
[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]
Now we can write √x as ,
[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]
Simplify ,
[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]
By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,
[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]
On simplifying we will get ,
[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]
Guys please help me if you don’t mind
Step-by-step explanation:
Step 1: The factors of -60 that add up to -11 are -15 and 4.
Step 2:
[tex]( 6{x}^{2} - 15x)( 4x - 10)[/tex]
Step 3:
[tex]3x(2x - 5) + 2(2x - 5)[/tex]
[tex](3x + 2)(2x - 5) [/tex]
A restaurant owner is planning to have a courtyard area sodded. The sod comes in rolls that are 3 feet long by 1 foot wide. If the courtyard measures 60 feet by 50 feet, which of the following expressions represents the number of rolls of sod needed?
Answer:
[tex](60\times 50)\div 3[/tex]
Step-by-step explanation:
We are given that
Length of roll of sod, l=3 feet
Width of roll of sod, b=1 feet
Length of courtyard, L=60 feet
Breadth of courtyard, B=50 feet
Area of rectangle=[tex]Length\times breadth[/tex]
Using the formula
Area of roll of sod=[tex]3\times 1 feet^2[/tex]
Area of roll of sod=3 square feet
Area of courtyard=[tex]60\times 50[/tex] square feet
Number of rolls of sod needed=[tex]\frac{Area\;of\;courtyard}{area\;of\;roll\;of\;sod}[/tex]
Using the formula
Number of rolls of sod needed=[tex]\frac{60\times 50}{3}[/tex]
Number of rolls of sod needed=[tex](60\times 50)\div 3[/tex]
This is required expression which represents the number of rolls of sod needed.
Kylie has only quarters and
nickels in a jar. The total value in
the jar is $2.00. If there are a total
of 20 coins, how many of each
type of coin are in the jar?
? Quarters. ? Nickels
Se conoce que 6 jarras cuestan lo mismo que 5 cubiertos y que 3 cubiertos cuestan S/. 7.20, ¿Cuánto costarán 7 jarras? (2 PUNTOS)
Answer:
7 jarras costarán 14 $
Step-by-step explanation:
Si 3 cubiertos cuestan 7.20 $
1 cubierto cuesta 7.20/3 = 2.40 $
y 5 cubiertos cuestan 5* 2.40 = 12 $
que también cuestan 6 jarras = 12 $
Luego 1 jarra cuesta 12/6 = 2 $
Por lo que 7 jarras costarán: 7 * 2 = 14 $
Mr. Lord borrowed $100,000 from a bank at a rate of 8% per annum for 3 years. Calculate the amount accruing for the loan
Answer: [tex]\$125,971.2[/tex]
Step-by-step explanation:
Given
Principal amount [tex]P=\$100,000[/tex]
Rate of interest [tex]r=8\%[/tex]
Time period [tex]t=3\ yr[/tex]
Amount in compound interest is given by
[tex]\Rightarrow A=P\left(1+r\%\right)^t\\\Rightarrow A=100,000(1+0.08)^3\\\Rightarrow A=\$125,971.2[/tex]
Thus, the amount accruing for loan is [tex]\$125,971.2[/tex]
Choose the correct answer from the given four options:In an AP if a = –7.2, d = 3.6, an = 7.2, then n
2
4
3
5
Answer:
n=5
Step-by-step explanation:
by using
n=(an-a)/a+1
substituting values
n= 7.2-(-7.2)/3.6 +1
n=5
STREAM WALLS BY LOUIS TOMLINSON
Answer:
OMG I LOVE LOUIS SO MUCH HE IS SO PERFECT
Step-by-step explanation:
Can someone help me with this math homework please!
Answer:
Check off both of the boxes
Step-by-step explanation:
In your reponse you included that most ancient societies didn't have symbols for math operations and didn't have symbols for variables/unknown quantities.
Hope it helps (●'◡'●)
On a coordinate plane, a line goes through (negative 3, negative 4) and (3, 0).
What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept?
The slope is Negative three-halves and contains the point (0, 2).
The slope is Negative two-thirds and contains the point (0, −2).
The slope is Three-halves and contains the point (0, 2).
The slope is Negative three-halves and contains the point (0, −2
Answer:
The slope is Negative three-halves and contains the point (0, 2).
Step-by-step explanation:
(-3,-4)(3,0)
M= -4/-6 = 2/3
⊥M = -3/2
0 = 2/3(3) + B
B=2
Simplity the expression.
3(2y - 8) - 2y(5 - y)
Answer:
2y² - 4y - 24
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
3(2y - 8) - 2y(5 - y)
Step 2: Simplify
[Distributive Property] Distribute 3 and -2y: 6y - 24 - 10y + 2y²Combine like terms: 2y² - 4y - 24If the price of a gallon of gas was $0.89 in 1984 and was $3.59 in 2014, what was the average rate of change in the price per gallon of gas?
Answer:
0.09
Step-by-step explanation:
avg rate of change is: change in y/ change in x
so it´d be 3.59 - 0.89 / 2014 - 1984
= 2.7/ 30
= 0.09
note:
The slope formula and the average rate of change formula are the same, just written a bit different, so you could also use:
y2 - y1 / x2 - x1
What is the value of x?
Hello,
The sum of the angles of a triangle is equal to 180°.
So :
x = 180 - 40 - 55 = 85°
Have a nice day :)
Find the domain in the given ordered pairs.
{(2, 3), (3, 5), (6, 7), (8, 9)}
Answer:
saaad
Step-by-step explanation:
Answer:
Domain = {-5,2,4,6,8,9), range = (-3,-1,0,4,6,7}
Step-by-step explanation:
{(2,4), (8,-3), (-5,-1), (4,6), (6,7), (9,0)}
The domain is the input and the range is the output
domain is { 2,8,-5,4,6,9} and the range is {4,-3,-1,6,7,0}
We put the numbers in order from smallest to largest
Domain = {-5,2,4,6,8,9), range = (-3,-1,0,4,6,7}
The white triangle drawn on the road sign in the picture has a helght of 8" and a base of 5". The red rim around the edge adds another Inch to each dimension making the base of the larger triangle 12 inches. Ignoring the white edge around the very outside, what is the area of the red border? (Hint: find the area of the whole triangle and subtract the area of the smaller triangle inside it.
Answer:
The answer would be
Step-by-step explanation:
you multiple 8 and 5 then you multiple 12 (inches) then subtract the inch that makes up 12 let me know if you need help
¿Cuál es el capital que necesito, si quiero obtener una ganancia de $9745 en 5 meses aplicando una tasa del 6,3?
Answer:
The capital is $ 309365.
Step-by-step explanation:
What is the capital that I need, if I want to obtain a profit of $ 9745 in 5 months applying a rate of 6.3?
Let the capital is P.
Simple interest, I =$ 9745
Rate, R = 6.3 %
Time, T = 5 months
Use the formula of the simple interest.
[tex]9745=\frac{P\times 6.3\times 5}{1200}\\\\P = 309365[/tex]
A lighthouse casts a 128-ft shadow. A nearby lamppost that measures 5
feet casts an 8-foot shadow. What is the height of the light house, rounded
to the nearest foot? *
Answer: 80 feet
Step-by-step explanation:
We can write these as fractions and do cross multiplication with the numerator being the height of the object while the denominator being the length of the shadow:
5 * 128 = 8x
640 = 8x
80 = x
Thus, the height of the lighthouse is 80 feet tall.
What is the value of x in the equation 4 . 10 X+52 3 +35x+1 5 ?
:)
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
Given:
[tex]4\frac{3}{10}-(2\frac{2}{5}x+5\frac{1}{2})=\frac{1}{2}(-3\frac{3}{5}x+1\frac{1}{5})[/tex]
Distribute to remove parentheses:
[tex]4\frac{3}{10}-2\frac{2}{5}x-5\frac{1}{2}=-\frac{18}{10}x+\frac{6}{10}[/tex]
For simplification and clarity, reduce all mixed numbers to simplified common fractions:
[tex]\frac{43}{10}-\frac{12}{5}x-\frac{11}{2}=-\frac{9}{5}x+\frac{3}{5}[/tex]
Combine like terms:
[tex]-\frac{12}{5}x-\frac{6}{5}=-\frac{9}{5}x+\frac{3}{5}[/tex]
Add 6/5 to both sides, then add 9/5x to both sides:
[tex]-\frac{3}{5}x=\frac{9}{5}[/tex]
Divide both sides by -3/5 to isolate x (recall dividing by a number is equal to multiplying by its reciprocal):
[tex]x=\frac{9}{5}\cdot -\frac{5}{3}, \\x=\frac{-9}{3},\\x=\boxed{-3}[/tex]
Type the correct answer in the box. Simplify this expression: -2x + 3 – (5 – 6x).
Answer:
4x - 2
Step-by-step explanation:
Given
- 2x + 3 - (5 - 6x) ← distribute parenthesis by - 1
= - 2x + 3 - 5 + 6x ← collect like terms
= 4x - 2
The expression -2x + 3 – (5 – 6x) simplifies to 4x - 2.
What is the correct way of simplifying an expression ?The correct way of simplifying expressions is first solving what are inside the brackets.Then solving divisions then multiplications then additions and last subtractions.This way of solving order has a short name which is BODMAS order.
According to the given question we have to simplify the expression
-2x + 3 – (5 – 6x).
First we'll solve what are inside the brackets.
-2x + 3 - 5 + 6x. (negative sign distributed to get a positive).
= 4x - 2.
= 2(2x - 1).
learn more about simplifying expressions here :
https://brainly.com/question/16738857
#SPJ2
Factor 2x^2 +15x +25 = 0
Answer:
Step-by-step explanation:
(2x + 5)(x + 5) = 0
2x + 5 = 0
2x = - 5
x = -5/2
x + 5 = 0
x = -5
For the inverse variation equation P= 8/v , what is the value of V when p = 4?
1/8
1/2
2
32
Answer:
V = 2
Step-by-step explanation:
P = 8/v
4 = 8/v
8/4 = 2
v = 2
Answer:
v=2
Step-by-step explanation:
p=8/v
When p = 4, 4=8/v
We multiply both sides by v, we get:
4v=8
Now we divide both sides by 4,
v=2
if x/y=(3/5)^3÷(6/5)^0'find the value of (x/y)^2
Answer:
729/15625
Step-by-step explanation:
1. Evaluate the power
( (27/125) ÷ 1 )^2
2. divide
( 27/125 )^2
evaluate the power
( 27^2 / 125^2 )
729/15625
which statements are true about the target function? Check all that apply.
tan(PAB) = y/x
tan(APB) = x/y
tan(PAB) = sin(PAB)/cos(PAB)
tan(PAB) = cos(PAB)/sin(PAB)
tan(PAB) = PB/AB
Answer:
A, B, C, E.
Step-by-step explanation:
.
Express sin U as a fraction in simplest terms
Answer:
4/5
SOH-CAH-TOA
sin = opposite / hypotenuse
Hypotenuse = sqrt(18^2 + 24^2) = 30
sin 24/30 = 4/5
Step-by-step explanation:
