Answer:
a=3 and b=-2
Step-by-step explanation:
We are given that five terms of a quadratic sequence are
1 8, 21, 40, 65.
The nth term of this sequence
=[tex]an^2+bn[/tex]
We have to find the value of a and b where a and b are integers.
For n=1
[tex]a+b=1[/tex] ......(1)
For n=2
[tex](2)^2a+2b=8[/tex]
[tex]4a+2b=8[/tex]
[tex]2a+b=4[/tex] .....(2)
Subtract equation (1) from (2) we get
[tex]2a-a=4-1=3[/tex]
[tex]a=3[/tex]
Using the value of a=3 in equation (1)
[tex]3+b=1[/tex]
[tex]b=1-3=-2[/tex]
Hence, the value of
a=3 and b=-2
Sophia pays £222 for a plane ticket.
She also pays 100 euros airport tax.
The exchange rate is £1 = 1.38 euros.
What percentage of the total cost of the ticket and the airport tax does Sophia pay
for the
airport tax?
Give your answer correct to 1 decimal place.
9514 1404 393
Answer:
24.6%
Step-by-step explanation:
The cost of the ticket in euros is ...
£222 × €1.38/(£1) = €306.36
Then the ratio of the tax to the to the total cost is ...
€100/(€306.36 +100) = 100/406.36 ≈ 24.6%
Someone help me please
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Explanation:
The table says that
5 students got an A10 students got a B15 students got a CThat's 5+10+15 = 30 students out of 35 total.
The probability is therefore 30/35 = 0.8571 approximately which rounds to 0.86
There's roughly an 86% chance of picking someone who got an A, B or C.
Find the value of x for the right triangle.
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
#SPJ2
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
Determining if a Relationship Is a Function
Which represents a function?
Answer:
only the first one...
a "FUNCTION" has a UNIQUE relation between each input and output...
notice the middle one the -2 goes to BOTH th2 10 & -7 that makes it NOT a FUNCTION
Step-by-step explanation:
What is sin 28°?
62
8
17
90
15
28
A.
Sooden
O c.
O
Answer:
the sin of 28 degree is 28
Step-by-step explanation:
it's the same degree in radians I hope this help
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]
Solve the equation 15x + 22 = 7x +62
Answer:
hope it helps you........
Answer:
x = 5
Step-by-step explanation:
1. Subtract 22 from both sides.
15x = 7x + 62 - 22
2. Simplify 7x + 62 - 22 to 7x + 40.
15x = 7x + 40
3. Subtract 7x from both sides.
15x - 7x = 40
4. Simplify 15x - 7x to 8x.
8x = 40
5. Divide both sides by 8.
x = [tex]\frac{40}{8}[/tex]
6. Simplify [tex]\frac{40}{8}[/tex] to 5.
x = 5
Examine circle O, where chords AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ are congruent.
Point P lies on AB¯¯¯¯¯¯¯¯ and point Q lies on CD¯¯¯¯¯¯¯¯.
Angles APO and DQO are right angles.
The diagram as described in the problem.
Which congruence statement is true?
CD≅AP
QD≅QO
OP≅OQ
OP≅AB
In a company of 35 employees, four-sevenths work in sales. How many of the employees work in sales ?
Answer:
20
Step-by-step explanation:
Multiply 4/7 with 35, this will get you 140/7, which simplifies to 20 employees
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!
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.
A football was kicked through the air and it followed the path h\left(s\right)=-3s^2+75h(s)=−3s 2 +75 . Let h\left(s\right)h(s) represent the height of the soccer ball after, s, seconds.
Complete question is;
A soccer ball was kicked through the air and it followed the path. Let h(s) = −3s² +75 represent the height of the soccer ball after s seconds.
Find the time at which the soccer ball hits the ground.
Answer:
s = 5 seconds.
Step-by-step explanation:
We are given the function;
h(s) = −3s² +75
Where;
h(s) is height at time s
s is the time taken
Now, the time at which the time at which the soccer ball hits the ground would be at h(s) = 0 since height is at 0 point.
Thus;
−3s² +75 = 0
−3s² = -75
s² = 75/3
s² = 25
s = √25
s = 5 seconds.
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
Seventy of Myra’s classmates are traveling by bus to a football game in another town. They hired 2 buses, but there were only 64 seats. The remaining 6 students had to travel in a separate van.
The equation 2b + 6 = 70 represents the given scenario. What does b represent?
Answer:
seats in each bus
Step-by-step explanation:
total no.of seats = 64
so, the no.of seats in each bus = 64/2 =32
therefore , b denotes the no.of seats in each bus
PLEASE MARK ME AS BRAINLIEST .
shanika has a lamp that she wants to send to her sister in baltimore.the lamp is in the shape of a rectangular prism.it measures 14 high, 9 wide, and 3 long.she wants to buy a box so that there is 1 all around the lamp for bubble wrap
Consider we need to find the dimensions and volume of the box.
Given:
The shape of the lamp is a rectangular prism.
It measures 14 high, 9 wide, and 3 long.
There is 1 all around the lamp for bubble wrap
To find:
The dimensions and volume of the box.
Solution:
Length of the box is:
[tex]3+2=5[/tex]
Width of the box is:
[tex]9+2=11[/tex]
Height of the box is:
[tex]14+2=16[/tex]
Therefore, the dimensions of the box are 5 by 11 by 16 units.
The volume of the box is:
[tex]V=l\times w\times h[/tex]
Where, l is length, w is width and h is height.
Putting [tex]l=5, w=11, h=16[/tex], we get
[tex]V=5\times 11\times 16[/tex]
[tex]V=880[/tex]
Therefore, the volume of the box is 880 cubic units.
Somebody give the answer to the question attached please
A photo printer is on sale for $195.50. The regular price is $230. What is the percent of the discount on the photo
printer?
Select the correct answer.
Function h is a transformation of the parent exponential function, f(x) = 2^x.
.h(x)=-3.2^x
-
Which statement is true?
A record club has found that the marginal profit,
Upper P prime (x ), in cents, is given by
Upper P prime (x )equals negative 0.0008 x cubed plus 0.20 x squared plus 46.8 x for x less than or equals 200,
where x is the number of members currently enrolled in the club. Approximate the total profit when 120 members are enrolled by computing the sum
Summation from i equals 1 to 6 Upper P prime (x Subscript i Baseline )Upper Delta x with Upper Delta x equals 20.
Solution :
Given :
[tex]$P'(x) = -0.0008x^3+0.20x^2+46.8x,$[/tex] for x ≤ 200
Total profit when 120 members are enrolled is :
[tex]$\sum_{i=1}^6P'(x_i) \Delta x$[/tex] with [tex]\Delta x = 20[/tex]
Using the left end points, we get,
The values of [tex]x_i[/tex] are : { 0, 20, 40, 60, 80, 100}
Therefore,
[tex]$P'(x_1) = P'(0)=-(0.0008)(0)^3+(0.20)(0)^2+(46.8)(0)$[/tex]
= 0
[tex]$P'(x_2) = P'(20)=-(0.0008)(20)^3+(0.20)(20)^2+(46.8)(20)$[/tex]
= 1009.6
[tex]$P'(x_3) = P'(40)=-(0.0008)(40)^3+(0.20)(40)^2+(46.8)(40)$[/tex]
= 2140.8
[tex]$P'(x_4) = P'(60)=-(0.0008)(60)^3+(0.20)(60)^2+(46.8)(60)$[/tex]
= 3355.2
[tex]$P'(x_5) = P'(80)=-(0.0008)(80)^3+(0.20)(80)^2+(46.8)(80)$[/tex]
= 4614.4
[tex]$P'(x_6) = P'(100)=-(0.0008)(100)^3+(0.20)(100)^2+(46.8)(100)$[/tex]
= 5880
[tex]$\sum_{i=1}^6P'(x_i) \Delta x = P'(x_1)\Delta x + P'(x_2)\Delta x + P'(x_3)\Delta x + P'(x_4)\Delta x + P'(x_5)\Delta x + P'(x_6)\Delta x $[/tex]
= (0)(20) + (1009.6)(20) + (2140.8)(20) + (3355.2)(20) + (4614.4)(20) + (5880)(20)
= (20)( 0 + 1009.6 + 2140.8 + 3355.2 + 4614.4 + 5880)
= (20)(17,000)
= 340,000 cents
[tex]$=\frac{340000}{100} \ \text{dollars}$[/tex]
= 3400 dollars
Hence, the required total profit is 3400 dollars.
Which graph shows the solution set of
Let j=+5 - 5+ |-5 x 1/5
What is the value of+J?
Answer:
j=|x|
Step-by-step explanation:
An amusement park charges and admission fee of 30 dollars for each person. Let C be the cost (in dollars) of admission for P people. Write an equation relating C to P.
Answer:
14
Step-by-step explanation: B is the midpoint of AC, in other words it is the halfway point.
So A to B should be equal to B to C
Our expression is:
2x + 9 = 37
Subtract 9
2x = 28
Divide by 2
x = 14
Someone help me pls ..
Answer:
because they are both in the circle
Step-by-step explanation:
help me in this plz....
Answer:
70. 8x⁴
71. 3n - 10
72. a/5 + 12
Step-by-step explanation:
70. a number "x" raised to the fourth = x⁴
Product of 8 and x⁴ = 8 × x⁴
= 8x⁴
71. 3 times a number "n" = 3 × n = 3n
3n decreased by 10 = 3n - 10
72. Quotient of a number "a" and 5 = a/5
12 more than a/5 = a/5 + 12
Two legs of a right triangle measure 23 inches and 38 inches. What is the length of the hypotenuse, to the nearest
inch?
Answer:
hypotenuse ≈ 44 inches
Step-by-step explanation:
Using Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other two sides.
let the hypotenuse be h , then
h² = 23² + 38² = 529 + 1444 = 1973 ( take square root of both sides )
h = [tex]\sqrt{1973}[/tex] ≈ 44 inches ( to the nearest inch )
Please hurry I will mark you brainliest
What is the equation in standard form for the line with slope 3 and y-intercept -4?
Answer: -3x+y=-4
Step-by-step explanation:
Standard form is Ax+By=C. In y=Mx+b form, it would be y=3x-4. To put it into standard form you subtract 3x from both sides. So then you have -3x+y=-4.
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
Find the value of x.
B
X+2
3
D
E
х
2
А
x = [?]
Answer:
x = 4
Step-by-step explanation:
The line DE is parallel to AC and divides the sides proportionally, that is
[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BE}{CE}[/tex] , substitute values
[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
3x = 2(x + 2) = 2x + 4 ( subtract 2x from both sides )
x = 4
