Part (a)
The radius is r = 42 because OA = 42.
The circumference, aka distance around the circle, is
C = 2*pi*r
C = 2*(22/7)*42
C = 264
We're told that arc AB is 110 mm which is 110/264 = 5/12 of the full distance around the circle.
So we'll apply 5/12 to the full rotation 360 to get (5/12)*360 = 150
Answer: 150 degrees==============================================================
Part (b)
Compute the area of the full circle
A = pi*r^2
A = (22/7)*(42)^2
A = 5544
Then take 5/12 of this because we only want 5/12 of the full circle area (to get the area of the shaded pizza slice)
(5/12)*(5544) = 2310
Answer: 2310 square mm==============================================================
Side note: Both answers are approximate because pi = 22/7 is approximate.
HELP ME WITH THIS PROBLEM PLEASE!!
Answer:
w ≈ 33.9 in
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
w² + w² = 48²
2w² = 2304 ( divide both sides by 2 )
w² = 1152 ( take the square root of both sides )
w = [tex]\sqrt{1152}[/tex] ≈ 33.9 in ( to the nearest tenth )
pls help me solve this multiplication fractions. (show work)
Answer:
32:3/4
33:4/3
34:40
35:48
Please help, explain too and I will give brainliest :)
Answer:
c
Step-by-step explanation:
Answer:
C. 37 degrees
Step-by-step explanation:
27, 36, 45 is just a larger 3, 4, 5 triangle. The smallest angle is across from the smallest side. With those in mind, we have 37, 53, and 90 degrees as the angles for a 3, 4, 5 triangle. We pair the 27, (the three when we reduce) with the smallest angle, the 37.
I'm sure you can do it with an actual formula, but i can't recall. Cheers
Can someone please help me out with a small explanation thank you :)
Step-by-step explanation:
1 . when we collect like terms we only focus on the variables and the power of the variable I f exist so in this question the answer is 8x^2 because both have the same variable and same power or exponent.
2. one term is monomial
two terms is binomial
3. b
4. -9
5. c
which algebraic expression represents this word description?
the product of two and the difference between eleven and a number
a. 2(11-x)
b. 11-2x
c. 2x-11
d. 2(x-11)
Step-by-step explanation:
c. 2x-11 this is the answer
hope this helps you
have a nice day:)
A group of 40 workers can do a construction in 16 days. When has elapsed 4 days, 10 workers retired. How many days of delay the construction will be delivered?
Answer:
4 days
Step-by-step explanation:
The time it would take the group of 40 workers to deliver the work, [tex]t_{estimated}[/tex] = 16 days
The number of workers that retired after 4 days = 10 workers
Therefore, the number of workers remaining = 40 - 10 = 30 workers
The time it would take 1 worker to do the work = The number of work days in the construction = 40 × 16 = 640 work days
The amount of work done in 4 days = 40 × 4 = 160 work days
The amount of work remaining after the elapsed 4 days = (640 - 160) work days = 480 work days
The number of days, n, it would take the remaining 30 workers to do the remaining work, is given as follows;
n = 480 work days/(30 workers) = 16 days
The actual total number of work days it took for the work to be delivered, [tex]t_{actual}[/tex] = 4 days + 16 days = 20 days
The number of days delay the construction will be delivered, [tex]t_{delay}[/tex], is given as follows = [tex]t_{actual}[/tex]
[tex]t_{delay}[/tex] = [tex]t_{actual}[/tex] - [tex]t_{estimated}[/tex]
∴ [tex]t_{delay}[/tex] = 20 days - 16 days = 4 days
The number of days delay the construction will be delivered, [tex]t_{delay}[/tex] = 4 days
need help with this question ! :(
Which of the following is the value of y that solves the system of equations shown below?
2x + 3y = -14
x - y = 3
———————————————
(1) -4
(2) -2
(3) 7
(4) 4
thank you to anyone who answers this i appreciate it :))
Answer:
-4
Step-by-step explanation:
2x + 3y = -14
x - y = 3
Multiply the second equation by -2 to eliminate x
2x + 3y = -14
-2x +2 y = -6
-----------------------
5y = -20
Divide by 5
5y/5 = -20/5
y = -4
Answer:
Step-by-step explanation:
What is [tex]\pi r^2[/tex] ?
Answer:
The formula to determine the area of the circle.
Step-by-step explanation:
↔
see screenshot below
Answer:
A&D
Step-by-step explanation:
we want to solve the following equation for x:
[tex] \displaystyle ( {2}^{x} - 3) ({2}^{x} - 4) = 0[/tex]
to do so let [tex]2^x[/tex] be u and transform the equation:
[tex] \displaystyle (u - 3) (u - 4) = 0[/tex]
By Zero product property we obtain:
[tex] \displaystyle \begin{cases}u - 3 = 0\\ u - 4= 0 \end{cases}[/tex]
Solve the equation for u which yields:
[tex] \displaystyle \begin{cases}u = 3\\ u = 4 \end{cases}[/tex]
substitute back:
[tex] \displaystyle \begin{cases} {2}^{x} = 3\\ {2}^{x} = 4 \end{cases}[/tex]
take logarithm of Base 2 in both sides of the both equations:
[tex] \displaystyle \begin{cases} \log_{2} {2}^{x} = \log_{2} 3\\ \log_{2} {2}^{x} = \log_{2} 4 \end{cases}[/tex]
hence,
[tex] \displaystyle \begin{cases} x_{1} = \log_{2} 3\\ x_{2} = 2 \end{cases}[/tex]
Answer:
( A ) and ( D )
Step-by-step explanation:
( 2^x -3 ) ( [tex]2^x -4[/tex] ) = 0
When the the product of factors equals 0, atleast one factor is 0.[tex]2^x [/tex]- 3 = 0
2^x - 4 = 0
Solve for x.[tex]2^x [/tex]- 3 = 0 , [tex]2^x -4[/tex]
x = [tex]log_2[/tex] (3) , x = 2
The equation has two solutions;
[tex]x_1[/tex] = [tex]log_2[/tex] (3) , [tex]x_2[/tex] = 2.
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
x – 4
x – 2
x + 2
x + 4
Hellllllllp plsss!! Due in very soon maths
Answer: 23, 27,29
Those im absolutely positive about.
Im not sure abt the rest
Step-by-step explanation:
what would be the u to usub and what would be the steps to solving this integral?
Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).
Then substituting u = ln(x) and du = dx/x gives
[tex]\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}[/tex]
What is the surface area of the cone?
Answer: C
Step-by-step explanation:
To find the surface area of a cone, you use the formula [tex]A=\pi r(r+\sqrt{h^2+r^2} )[/tex]. Since we are already given the height and radius, all we have to do is plug in the values and solve.
[tex]A=9\pi (9+\sqrt{41^2+9^2} )[/tex] [solve inside of square root]
[tex]A=9\pi (9+\sqrt{1762} )[/tex] [parenthesis]
[tex]A=9\pi (50.976 )[/tex] [multiply]
[tex]A=458[/tex]
Therefore, the closest answer is C.
The answer for (a) is 28 and the answer for (b) is 13 but I don’t know how to get the answer
Answer:
Step-by-step explanation:
If Quan had 15 and Kaden had 3 times as much, then Kaden had 15(3) = 45. If he spent 10 then he had 35 left. The amount of money Quan had after his mom gave him some was 4/5 the amount of Kaden's 35 (let x = the amount of money Quan has after his mom gives him some):
[tex]x=\frac{4}{5}(35)[/tex] 35 divides by the 5 in the denominator 7 times, and 7 times 4 is 28. That's how you get your 28 in part a.
For part b., he started with 15 and ended with 28, so his mom gave him 28-15=13. That's how you get the 13.
what would be the answer?
Answer:
A
Step-by-step explanation:
As two angles are same which means 3rd also is equal which means aaa axiom
Rewrite as a simplified fraction please! Btw please be aware of the repeating symbol on the 8!
If x = 0.888…, then 10x = 8.888… and
10x - x = 9x = 8 ==> x = 8/9
Solve 7x + 1 < 4(x - 2).
A. {x | x > 3}
B. {x | x > -3}
C. {x | x < -3}
D. {x | x < 3}
Given:- 7x + 1 < 4(x - 2)
Solving It:-7x + 1 < 4(x - 2)
7x + 1 < 4x - 8
7x - 4x < -8 -1
3x < -9
x < -9/3
x < -3
So Correct Solution Set Will BeC. {x | x < -3}Hope This Helps Youi need help A S A P!
Answer:
ewfwefwfewfwfwe
Step-by-step explanation:
Please solve this question 3(n+4)=5n?
Answer:
6=n
Step-by-step explanation:
Hi there!
We are given this equation:
3(n+4)=5n
And we need to solve it for n
To do that, we need to isolate n on one side
But we need to open up the parentheses on the left side by doing the distributive property
Multiply both n and 4 by 3
3n+12=5n
Now subtract 3n from both sides to remove it from the left side
12=2n
Divide both sides by 2 to change the coefficient on n from 2 to 1
6=n
n is now isolated on one side
Hope this helps!
Answer:
n=6
Step-by-step explanation:
Using the distributive property, we distribute 3 to n and 4. In case if you don't know what that means, it means we multiply 3 to the variables inside the parentheses. So we get (3×n)+(3×4)=5n, and we simplify it so we get 3n+12=5n. Now, we can subtract 3n from both sides and get 12=2n, and divide 2 from both sides and get n=6.
what is the account balance of an investment of 7,500after 25 years in an account earning 8% interest compounded continuously
Mario invested $6,000 in an account that pays 5% annual interest compounded annually. Using the formula A = P(1 + r)t, what is the approximate value of the account after 2.5 years?
Answer:
$6778.36
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]
P is principle amountr is raten is compounded ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 6000
r = 5% = 0.05
n = 1
t = 2.5
Step 2: Find Interest
Substitute in variables [Compounded Interest Rate Formula]: [tex]\displaystyle A = 6000(1 + \frac{0.05}{1})^{1 \cdot 2.5}[/tex]Simplify: [tex]\displaystyle A = 6000(1.05)^{2.5}[/tex]Evaluate: [tex]\displaystyle A = 6778.36[/tex]c. Suppose you are given the functa. If f(x) = 10x − 1, the value of f(−2) is __________. b. If g(x) = −5x + 13, the value of g(1) is __________. c. If h(x) = x2 − x − 12, the value of h(3) is __________.ion h(x) = −2x + 3 and asked for h(4). This is the same as asking for the value of the function at x = __________.
Answer:
c. f(-2)= -21
b. g(x)=8
c. h(3)= -19
h(4)= -5
Step-by-step explanation:
1. Resuelve las ecuaciones:
a. x2 + 12x + 32 = 0
b. 9x2 +6x + 1 = 0
2. Resuelve las ecuaciones:
a. 2x2 +5x = 0
b. 2x2 -32 = 0
3. Calcula el valor de m para que la ecuación x2 + mx + 9 = 0 tenga solución doble.
4. Resuelve las ecuaciones:
a. x4 - 25x2 + 144 = 0
b. x4 + 9x2 - 162 = 0
AYUDA ;v
Answer:
1. a) x1 = -8 y x2 = -4
b) x1 = -1/3
2. a) x1 = 0 y x2 = -5
b) x1 = 4 y x2 = -4
3. m debe ser 6. Asi tendriamos (x+3)²=0
4. a) x1 = 4, x2 = -4, x3 = 3 y x3 = -3
b) x1 = 3, x2 = -3 las otras dos raices son complejas.
Step-by-step explanation:
1. a) [tex]x^{2}+12x+32=0[/tex]
Factorizando:
[tex](x+8)(x+4)=0[/tex]
Entonces: x1 = -8 y x2 = -4
4. a) x1 = 4, x2 = -4, x3 = 3 y x3 = -3
b) [tex]9x^{2}+6x+1=0[/tex]
Factorizando:
[tex](3x+1)(3x+1)=0[/tex]
[tex](3x+1)^{2}=0[/tex]
Entonces: x1 = -1/3
2. a) [tex]2x^{2}+5x=0[/tex]
Aplicando factor comun:
[tex]x(x+5)=0[/tex]
Entonces: x1 = 0 y x2 = -5
b) [tex]2x^{2}-32=0[/tex]
Despejamos x.
[tex]2x^{2}=32[/tex]
[tex]x^{2}=16[/tex]
Entonces: x1 = 4 y x2 = -4
3. m debe ser 6. Asi tendriamos (x+3)²=0
4. a) [tex]x^{4}-25x^{2}+144=0[/tex]
Hacemos cambio de variable: [tex]w=x^{2}[/tex]
[tex]w^{2}-25w+144=0[/tex]
Ahara podemos factorizar:
[tex](w-16)(w-9)=0[/tex]
Usando el cambio de variable nuevamente.
[tex](x^{2}-16)(x^{2}-9)=0[/tex]
Entonces los valores de x son: x1 = 4, x2 = -4, x3 = 3 y x3 = -3
b) [tex]x^{4}+9x^{2}-162=0[/tex]
Hacemos cambio de variable: [tex]z=x^{2}[/tex]
[tex]z^{2}+9z-162=0[/tex]
Ahara podemos factorizar:
[tex](z-9)(z+18)=0[/tex]
Usando el cambio de variable nuevamente.
[tex](x^{2}-9)(x^{2}+18)=0[/tex]
Entonces los valores de x son: x1 = 3, x2 = -3 las otras dos raices son complejas.
Espero ye haya servido!
Ah(t)
1800-
A ball is dropped from a height of 1296 ft. Its height h,
in feet, after t seconds is given by h(t) = 1296 - 1612.
After how long will the ball reach the ground?
0 0
1296
0-
0
12
The ball will reach the ground in seconds.
(Type an integer or a simplified fraction.)
Find the volume
Help me please
Answer:
54piecm^3
Step-by-step explanation:
pie x radius ^2 x h
= v
pie x 9
= 9pie x 6
= 54pie
Given a circle with centre O and radius 2.4cm. P is a point such that the lenght of the tengent from Q to the circle is 4.5cm. Find the lenght of OP
Answer:
5.1 cm
Step-by-step explanation:
(Probable) Question;
Given a circle with center O and radius 2.4 cm. P is a point on the tangent that touches the circle at point Q, such that the length of the tangent from P to Q is 4.5 cm. Find the length of OP
The given parameters are;
The radius of the circle with enter at O, [tex]\overline{OQ}[/tex] = 2.4 cm
The length of the tangent from P to the circle at point Q, [tex]\overline{PQ}[/tex] = 4.5 cm
The length of OP = Required
By Pythagoras's theorem, we have;
[tex]\overline{OP}[/tex]² = [tex]\overline{OQ}[/tex]² + [tex]\overline{PQ}[/tex]²
∴ [tex]\overline{OP}[/tex]² = 2.4² + 4.5² = 26.01
[tex]\overline{OP}[/tex] = √26.01 = 5.1
The length of OP = 5.1 cm
What is -2.53 rounded to the nearest hundredth
Answer:
-2.50
Step-by-step explanation:
3 is closer to 0then 10
Answer:
-2.53
Step-by-step explanation:
Already rounded to the nearest Hundredth
PLEASE HURRY PLEASSEEEE i need help
Answer:
5
Step-by-step explanation:
We cannot repeat an x value for the relation to be a function
Since x=3 ,4, 7 are already used
We must let x=5
What is the standard form of the ellipse equation
25x2 - 150x + 9y2 = 0?
O
(x - 3)2
32
y
1
+
52
0 (x - 5)
1
y2
22
(y - 3)2
22
0x2
+
14
1
O
x2
32
(y - 3)2
22
= 1
Answer: The correct answer is in the first option.
Step-by-step explanation:
Equation of an Ellipse
[tex]\dfrac{x^{2} }{a^{2} } +\dfrac{y^{2} }{b^{2} } =1\\\\25x^{2} - 150x + 9y^{2} = 0\\\\\text {Let's \: perform \: the \: transformations:}\\\\\dfrac{25x^{2} }{25 \cdot 9} -\dfrac{150x}{25 \cdot 9} +\dfrac{9y^{2} }{25 \cdot 9} =0\\\\\dfrac{x^{2} }{3^{2} } -\dfrac{6x}{3^{2} } +\dfrac{y^{2} }{5^{2} } =0\\\\\dfrac{x^{2} -6x}{3^{2} } +\dfrac{y^{2} }{5^{2} } +\dfrac{3^{2} }{3^{2} } -\dfrac{3^{2} }{3^{2} } =0\\\\\dfrac{x^{2} -6x+3^{2} }{3^{2} } +\dfrac{y^{2} }{5^{2} } =\dfrac{3^{2} }{3^{2} }[/tex]
[tex]\dfrac{(x-3)^{2} }{3^{2} } +\dfrac{y^{2} }{5^{2} } =1[/tex]
f(x) = 3x + 5
Work out a if f(a)= -13
Answer:
a = - 6
Step-by-step explanation:
Given
f(x) = 3x + 5 , then
f(a) = 3a + 5 and f(a) = - 13 , then equating the right sides
3a + 5 = - 13 ( subtract 5 from both sides )
3a = - 18 ( divide both sides by 3 )
a = - 6
Answer:
a = -6
Step-by-step explanation:
see, x has been replaced by a.
so f(a) = 3a + 5 . . . . . . . (i)
a displaces x from it's every position in the equation.
and it's given that f(a) = -13
putting f(a) = -13 in equation (i) :-
3a + 5 = -13
taking like terms to one side3a = -18
dividing the equation by 3[tex] \blue{ \implies}\mathfrak { \red { \underline{ \: a = - 6 } } } [/tex]