Answer:
a.
f(1)=6; f(n)=6+d(n-1), n>0
Step-by-step explanation:
We are given that
First layer has squares, a=6
Second layer has squares, a2=12
We have to find an arithmetic explicit formula to determine the number of squares in each layer.
[tex]d=a_2-a_1=12-6[/tex]
nth term of an A.P
[tex]a_n=a+(n-1)d[/tex]
Substitute the value of a
Now, we get
[tex]a_n=6+(n-1)d[/tex]
f(1)=a=6
[tex]a_n=f(n)=6+d(n-1)[/tex]
Hence, option a is correct.
a.
f(1)=6; f(n)=6+d(n-1), n>0
Answer:
f(1) = 6; f(n) = 6 + d(n − 1), n > 0
Step-by-step explanation:
I took the test on flvs and got it right.
100% Guaranteed Correct :)
, Hope this helps
Have a great day!!
if x=3√8, find the value of 1/x
plz its urgent
Answer:
[tex]\frac{1}{x} =\frac{1}{3\sqrt{8} } =\frac{1(\sqrt{8})}{3\sqrt{8}(\sqrt{8})} =\frac{\sqrt{8}}{3*8} =\frac{\sqrt{8}}{24} =\frac{\sqrt{(2)(2)(2)}}{24}=\frac{2\sqrt{2} }{2(12)} =\frac{\sqrt{2} }{12}[/tex]
Find the discernment and the numbers of the number of real roots for this equation.
x^2+3x+8=0
Answer: 2 distinct complex solutions (ie non real solutions).
Work Shown:
The given equation is in the form ax^2+bx+c = 0, so
a = 1, b = 3, c = 8
Plug those into the formula below to find the discriminant
D = b^2 - 4ac
D = 3^2 - 4(1)(8)
D = -23
The discriminant is negative, so we get two nonreal solutions. The two solutions are complex numbers in the form a+bi, where a & b are real numbers and [tex]i = \sqrt{-1}[/tex]. The two solutions are different from one another.
Answer:
Discriminant: -23
Number of real roots: 0
Step-by-step explanation:
For a quadratic in standard form [tex]ax^2+bx+c[/tex], the discriminant is given by [tex]b^2-4ac[/tex].
In [tex]x^2+3x+8[/tex], assign:
[tex]a\implies 1[/tex] [tex]b\implies 3[/tex] [tex]c\implies 8[/tex]The discriminant is therefore:
[tex]3^2-4(1)(8)=9-32=\boxed{-23}[/tex]
For any quadratic:
If the discriminant is greater than 0, the quadratic has two real rootsIf the discriminant is equal to 0, the quadratic has one real rootIf the discriminant is less than 0, the quadratic as no real rootsSince the quadratic in the question has a discriminant less than 0, there are no real solutions to this quadratic.
Find the line’s slope and a point on the line
Y-4=-3/4(x+5)
Answer:
The slope is -3/4 and a point on the line is (-5,4)
Step-by-step explanation:
This equation is in point slope form
y -y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
Y-4=-3/4(x+5)
Y-4=-3/4(x - -5)
The slope is -3/4 and a point on the line is (-5,4)
A car travelling at v kilometers per hour will need a stopping distance, d, in meters without skidding that can be modelled by the function d=0.0067v2+0.15v. Determine the speed at which a car can be travelling to be able to stop within 37m.
I’m need of serious help!
Answer:
v = 14 km/h
Step-by-step explanation:
d = 0.0067[tex]v^{2}[/tex] + 0.15v
differentiate the function with respect to v to have;
d = 0.0134v - 0.15
given that the distance without skidding = 37 m (0.037 km) , then;
0.037 = 0.0134v - 0.15
0.0134v = 0.037 + 0.15
= 0.187
v = [tex]\frac{0.187}{0.0134}[/tex]
= 13.9552
v = 14 km/h
The speed of the car travelling would be 14 km/h to be able to stop within 37m.
I’m stuck on this one help anyone?
Answer:
just add a small amount to the 2.8 and square the result
Step-by-step explanation:
x x^2
2.8 7.84
2.81 7.8961
2.82 7.9524
2.83 8.0089
2.84 8.0656
2.85 8.1225
2.86 8.1796
2.87 8.2369
In a shipment of airplane parts, 6% are known to be defective. If 42 parts are found to be defective, how many parts are in the shipment?
Answer:
700 parts
Step-by-step explanation:
To find the total amount of parts in the shipment, all we need to do is divide.
6% = 0.06
42 / 0.06 = 700
Best of Luck!
Si un proyectil asciende verticalmente, y después de 3 segundos alcanza su altura máxima, calcule la velocidad que lleva a la mitad de su trayectoria descendente
Answer:
The speed is 20.8 m/s
Step-by-step explanation:
If a projectile ascends vertically, and after 3 seconds it reaches its maximum height, calculate the velocity that it carries to the middle of its downward trajectory
Let the maximum height is h and initial velocity is u.
From first equation of motion
v = u + at
0 = u - g x 3
u = 3 g.....(1)
Use third equation of motion
[tex]v^2 = u^2 - 2 gh \\\\0 = 9 g^2 - 2 gh \\\\h = 4.5 g[/tex]
Let the speed at half the height is v'.
[tex]v^2 = u^2 + 2 gh \\\\v'^2 = 0 + 2 g\times 2.25 g\\\\v'^2 = 4.5\times 9.8\times9.8\\\\v' = 20.8 m/s[/tex]
Mr. Mancuso plants tomatoes on 1/3 acre of land, corn on 3/4 acre, and carrots on 1/2 acre. On how many acres of land total did he plant?
1 acres
1 acres
1 acres
2 acres
Answer:
1 7/12 acres of land
Step-by-step explanation:
Tomatoes = 1/3 acre of land
Corn = 3/4 acre of land
Carrots = 1/2 acre of land
Total acres of land he planted = tomatoes + corn + carrots
= 1/3 + 3/4 + 1/2
= (4+9+6) / 12
= 19/12 acres
= 1 7/12 acres of land
Or
= 1.5833333333333 acres
Total acres of land he planted = 1 7/12 acres of land
None of the given options is correct
Which pair shows equivalent expressions?
O 2x+10=-2(x-5)
O-2(x+5)=2x-10
0 -2x-10=-2(x+5)
O -2(x-5)=-2x-10
Answer:
O-2(x+5)=2x-10
Explanation
O-2(x+5)=2x-10
SOLUTION
-2x(x)= -2x
-2x+5 = -10
Jessica ate 7 /10 of her orange before lunch and 1/10 of her orange after lunch. How much of her orange did she eat?
Answer:
8/10
Step-by-step explanation:
Find the value of x.
A. 99
B. 9
C. 90
D. 11
ILL GIVE BRAINLIEST
Answer:
B) 9
Step-by-step explanation:
Because there's a square between the 2 angles, that means these angles are complementary (angles that add up to 90°). So:
5x - 9 + 6x = 90
11x - 9 = 90
11x = 90 + 9
11x = 99
x = 9
Answer:
B.9
Step-by-step explanation:
The way to solve this is by noticing that these angles are complementary(they add up to 90 degrees). So you add the equations together and equal them to 90. 5x-9+6x=90.Then you solve to find that x=9.
3c + 2 = -22
whats c?
3c+ 2= -22
⇔3c = -22 -2
⇔3c = -24
⇔c= -24/3
⇔c=- 8
Answer:
3c= -22-2
3c= -24
c= -24/3
c= -8
Step-by-step explanation:
The square root of 0.25 is 0.5 which is a greater number. Give another number whose square root is larger than the number and explain why.
Answer:
Another example of a number who's square root is greater than the number is [tex]\sqrt{0.49}[/tex] which is 0.7
Step-by-step explanation:
This square root is larger than the number because it is a decimal. When you multiply a decimal by a decimal, the decimal point becomes greater. For example: 0.7 multiplied by 0.7 equals 0.49 which has 2 decimal places, while 0.7 only has one.
2. En una división el dividendo es 445, el divisor es 32, el cociente es 14 y el resto es 7. ¿Está bien hecha? Compruébalo de dos maneras diferentes
Respuesta:
El cálculo no está bien hecho.
el cociente es 13
El resto es 29
Explicación paso a paso:
Dividendo = 445
Divisor = 32
Cociente = 14
Resto = 7
445/32 = 13,90625
El cociente = 13
Resto = (13.90625 - 13) * 32
Resto = 0.90625 * 32
Resto = 29
Por lo tanto, el cálculo no se realiza correctamente ya que el cociente es 13 y el resto es 29
Choose the correct description of the graph of the inequality X - 3 greater than or equal to 25
A. Open circle on 8, shading to the left
B. Closed circle on 8, shading to the left.
C. Open circle on 8, shading to the right.
D. Closed circle on 8, shading to the right.
I’m pretty sure it’s D
Answer:
D. Closed circle on 8, shading to the right.
How much money invested at 3% compounded monthly for 3 years will yield $520?
$179.42
$475.30
$358.84
$148.78
Answer:
Step-by-step explanation:
Use this formula:
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex] where A(t) is the amount after the compounding is done, P is the initial investment (our unknown), r is the interest rate in decimal form, n is the number of compoundings per year, and t is the time in years. Filling in:
[tex]520=P(1+\frac{.03}{12})^{(12)(3)}[/tex] and simplifying that a bit:
[tex]520=P(1+.0025)^{36[/tex] and a bit more:
[tex]520=P(1.0025)^{36[/tex] and even bit more:
520 = P(1.094551401) and divide to get
P = $475.30
40 points Please help!!!
What is the volume of this regular prism?
48.55 cubic inches
55.8 cubic inches
9.7 cubic inches
24.28 cubic inches
Answer:
V = 24.28 in ^3
Step-by-step explanation:
The area of the base is
A =5/2 × s × a where s is the side length and a is the apothem
A = 5/2 ( 2.13) * .87
A = 4.63275
The volume is
V = Bh where B is the area of the base and h is the height
V = 4.63275 ( 5.24)
V =24.27561 in^3
Rounding to the hundredth
V = 24.28 in ^3
plsssssssssss helppppppppp i want it right now pls
Answer:
hope this helps you
have a great day
Solve EFD. Round the answers to the nearest hundredth.
A. m F ≈ 26, m D ≈ 64.01, FD = 7,921
B. m F ≈ 26, m D ≈ 64.01, FD = 89
C. m F ≈ 64.01, m D ≈ 26, FD = 89
D. m F ≈ 64.01, m D ≈ 26, FD = 7,921
Answer:
Option B
<F = 26°
<D = 64.01°
FD = 89
Answered by GAUTHMATH
For right triangle EFD, m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89
The correct answer is an option (B)
What is hypotenuse?It is the longest side of the right triangle.
What is Pythagoras theorem?For a right triangle,
[tex]a^{2}+ b^{2} = c^{2}[/tex], where c is hypotenuse and a, b area other two sides of the right triangle
For given example,
We have been given a right triangle EFD with hypotenuse FD.
Also, EF = 80, ED = 39
Using the Pythagoras theorem,
[tex]\Rightarrow FD^{2}= EF^{2} + ED^{2}\\\\ \Rightarrow FD^{2}= 80^{2} + 39^{2}\\\\ \Rightarrow FD^2 = 6400 + 1521\\\\ \Rightarrow FD^2 = 7921\\\\\Rightarrow FD = 89[/tex]
Consider, sin(F)
[tex]\Rightarrow sin(F)=\frac{ED}{FD} \\\\\Rightarrow sin(F)=\frac{39}{89}\\\\ \Rightarrow sin(F)=0.4382\\\\\Rightarrow \angle F=sin^{-1}(0.4382)\\\\\Rightarrow \angle F=25.98^{\circ}\\\\\Rightarrow \angle F\approx 26^{\circ}[/tex]
Now, consider sin(D)
[tex]\Rightarrow sin(D)=\frac{FE}{FD}\\\\ \Rightarrow sin(D)=\frac{80}{89}\\\\ \Rightarrow \angle D = sin^{-1}(0.8988)\\\\\Rightarrow \angle D = 64.009^{\circ}\\\\\Rightarrow \angle D \approx 64.01^{\circ}[/tex]
Therefore, for right triangle EFD, m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89
The correct answer is an option (B)
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
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I need to verify this function is symmetric with respect to the y-axis. How would I go about doing that?
h(x)=x^4-5x^2+3
Answer:
Yes, the function is symmetric about y-axis.
Step-by-step explanation:
To check whether the function is symmetric with respect to y-axis, replace each x as -x and simplify.
If h(x) = h(-x) then it is symmetric about y-axis.
Let's find h(-x) now.
h(-x)= [tex](-x)^4} -5(-x)^{2} +3[/tex]
Let's simplify it
h(-x)=[tex]x^{4}-5x^{2} +3[/tex]
Here, h(x) = h(-x). The function is symmetric about y-axis.
A bus has less than 42 seats. If 36 seats are already occupied, write an
inequality representing the possible number of passengers that can be
added to the bus.
A.) x - 36 < 42
B.) x + 36 < 42
C.) x - 36 > 42
D.) x + 36 > 57
Answer:
B
Step-by-step explanation:
A x - 36 <42 is wrong because its saying how many can be added
B x +36 < 42 this one is most likely correct because its displays x as how many can be added
C x - 36 > 42 this is wrong because the bus has less than 42 seats
D x + 36 >57 like i said cant be over 42
The inequality representing the possible number of passengers that can be added to the bus is Option(B) x + 36 < 42.
What is inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. Inequality is used most often to compare two numbers on the number line by their size. There is always a definite equation to represent it.
How to form the given inequality equation ?Let x be the number of passengers that can be added to the bus.
It is given that the bus has less than 42 seats and 36 seats are already occupied.
The sum of the remaining seats which are to be filled by the passenger and the 36 seats which are filled, must be less than the total seats that is 42.
Therefore the inequality equation becomes,
x + 36 < 42.
Thus, the inequality representing the possible number of passengers that can be added to the bus is Option(B) x + 36 < 42.
To learn more about inequality equation, refer -
https://brainly.com/question/17448505
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What is the equation of a circle with its center at (−6,−3) and a radius of 12?
Answer:
(x+6)^2 + ( y +3)^2 = 144
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 +(y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x- -6)^2 + ( y - -3)^2 = 12^2
(x+6)^2 + ( y +3)^2 = 144
Answer:
x² + y² + 12x +6y - 99 = 0
Step-by-step explanation:
Given :
Centre = (-6,-3) Radius = 12 ,Using the Standard equation of circle ,
( x - h)² + (y-k)² = r² ( x +6)² + (y+3)² = 12² x² + 36 + 12x + y² + 9 + 6y = 144 x² + y² + 12x + 6y +45-144 = 0 x² + y² + 12x +6y - 99 = 0Let j=+5 - 5+ |-5 x 1/5
What is the value of+J?
Answer:
j=|x|
Step-by-step explanation:
What is “8 - 4(-x + 5)” equivalent too?
Answer:
4x -12
Step-by-step explanation:
8 - 4(-x + 5)
Distribute
8 -4(-x) -4(5)
8 +4x -20
4x -12
answer 4( - 3 + x)
factor expression 4(2 - ( - x + 5)4(2 + x - 5)answer
[tex]4( - 3 + x)[/tex]
simplify the expression[tex]8 - 4( - x + 5)[/tex]
answer
[tex] - 12 + 4x[/tex]
How many tacos could you buy on a Wednesday with 20 dollars and tacos cost 50. cents
Answer:
40 tacos
Step-by-step explanation:
Step 1: Determine how many tacos you can buy
Cost of one taco: $0.50
Money in wallet: $20
So for every $1 you can buy 2 tacos. Therefore, 20 * 2 = 40 tacos
Answer: 40 tacos
Answer:40 tacos
Step-by-step explanation: because yeah
Help Please Now!!!
Find the volume Of The Rectangle Prism
Answer:
180m cubed
Step-by-step explanation:
Multiply the length, width, and height together: 6×6×5=180
Answer:
Formula of a rectangular prism:
L x W x H
Now we place in the numbers and solve:
5 x 6 x 6 = 180 m3
Lines c and d are parallel lines cut by transversal p.
Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8.
Which must be true by the corresponding angles theorem?
A. ∠1 ≅ ∠7
B. ∠2 ≅ ∠6
C. ∠3 ≅ ∠5
D. ∠5 ≅ ∠7
Answer:
Option (B).
Step-by-step explanation:
Here there are two parallel lines c and d cuts by a transversal p.
The angles are formed as shown in diagram.
Here,
[tex]\angle 1 = \angle 7 (alternate)\\\\\angle 2 = \angle 6 (corresponding)\\\\\angle 3 = \angle 5 (alternate)\\\\\angle 5 = \angle 7 (alternate)[/tex]
So, the option (B) is correct.
help me out (geometry)
Answer:
⊥
Step-by-step explanation:
d and b meet at a 90 degree angle ( as shown by the box)
The lines are perpendicular (⊥)
Please help me Find PA.
PLEASE HELP, AND FAST! I WILL GIVE BRAINLIEST!!
Given the expression: 6x10 − 96x2
Part A: Rewrite the expression by factoring out the greatest common factor.
Part B: Factor the entire expression completely. SHOW THE STEPS OF YOUR WORK.
Answer:
Step-by-step explanation:
factor the numerical coefficients (6 and 96)
HCF 6 and 96 is 6
HCF x^10 and x^2 = x^2
HCF: 6x^2
(6* x^8*x^2 - 16*6 x^2) Take out the highest common factor
6x^2 (x^8 - 16)
