Answer:
n=10
Step-by-step explanation:
The given equation is
[tex]10+12+14+...+2n=90[/tex] ...(1)
Let nth term is 2n.
We need to find the values of n.
It is clear that [tex]S_n=10+12+14+...+2n[/tex] is sum of A.P., whose first term is 10 and common difference is 2.
Sum of A.P. is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
where, a is first term and d is common difference.
Substitute a=10 and d=2 in the above formula.
[tex]S_n=\dfrac{n}{2}[2(10)+(n-1)2][/tex]
[tex]10+12+14+...+2n=n[10+n-1][/tex]
[tex]10+12+14+...+2n=n[9+n][/tex] ...(2)
From (1) and (2), we get
[tex]n(9+n)=90[/tex]
[tex]n^2+9n-90=0[/tex]
Splitting middle term, we get
[tex]n^2+15n-6n-90=0[/tex]
[tex]n(n+15)-6(n+15)=0[/tex]
[tex](n+15)(n-6)=0[/tex]
[tex]n=-15,6[/tex]
Since, n represents the number of terms so n cannot be a negative number, therefore number of term is 6.
Note: nth term and variable n both are different.
[tex]a_n=a+(n-1)d[/tex]
[tex]a_6=10+(6-1)2=10+10=20[/tex]
Sixth term is 20. So,
[tex]2n=20[/tex]
[tex]n=10[/tex]
Therefore, the value of n is 10.
Please answer correctly !!!!!!!! Will mark brianliest !!!!!!!!!!!!!
Answer:
So since the ball is at x=0 at the end.
We plug in it.
h(x) = 16 if you simplify it
Points 2
Triangle ABC is translated 3 units left and 4 units up. Find the coordinates of
the new triangle
Answer:
a = -1,6 b = 1,11 c = 4,11 .
De los siguientes datos:2;2;4;4;5;6;6;7;7;8, si se cambian los numeros 4 por 5, ¿cuál de las siguientes medidas cambia?
1: moda
2: mediana.
3: media aritmética
A) solo 2
B) solo 3
C) solo 1 y 2
D) solo 1 y 3
E) 1,2,3
Answer:
what is the question I do not understand
Melanie is walking a path around a circular path to view all of the artwork painted on the cement edge. The circular fountain has a radius of 30 feet. If Melanie only walked around the fountain once, how far did she travel?
In triangle ABC, Aat the top of the triangle, B at 90° and C at the third end, angle C = 21°, the hypotenus = 15m,find BC = y the unknown side
Answer
Step-by-step explanation:
Law of sines: SinB/15 = SinA/BC
B = 90
A = 180-90-21=69°
BC= (15*SinA)/SinB = (15*sin69)/1 ≈ 14m
2x - 15
x+9
For what value of x would the expression be undefined
Answer:
Undefined when x = -9
Step-by-step explanation:
(2x-15)/ (x+9)
This would be undefined when the denominator is 0
x+9 =0
x = -9
What is the value of x in the equation −6 + x = −1? (5 points)
a
−5
b
−7
c
7
d
5
Answer:
5
Step-by-step explanation:
Add 6 to both sides. The answer is 5.
Answer:
5
Step-by-step explanation
since we are looking for the value of x,we have to make it the subject of the formula(stand alone).
Therefore,-6 would cross over the equality sign and it would become =6.
NOTE:when a negative number crosses the equality sign,it becomes a positive number.
This implies that x= -1+6
NOTE:when you come across - + +(minus plus plus),u would have to minus.
and to know the sign that would be at the front of the answer,just take a look at the sign the bigger number holds.At this point it is plus.
Therefore,x= -1 +6
x=5(u could have stated it was +5 but it isnt necessary since there is an invisible plus sign at the front of a number as long as minus is not there
In December, Sara's Sodas produced 4.0 million liters of the beverage. Manufacturing overhead was $1,435,000 and the cost per liter was $0.47. Labor costs were 25 percent of materials cost. Required: a. Calculate the materials cost for December.
Answer:
The material cost for December = $356,000
Step-by-step explanation:
The manufacturing overhead is the sum of the indirect costs that come from the manufacturing process except labor and materials
Hence, whereby the cost per liter = $0.47, we have;
Total volume produced = 4.0 million liters
Manufacturing overhead = $1,435,000
Total cost = Cost per liter × Total volume produced
∴ Total cost = 4 × 10⁶ × $0.47 = $1,880,000
Hence the cost of labor + materials = Total cost - Manufacturing overhead
the cost of labor + materials = $1,880,000 - $1,435,000 = $445,000
Labor cost = 25% material cost = 0.25 × material cost
∴ 0.25 × material cost + material cost = $445,000
1.25 × material cost = $445,000
material cost = $445,000/1.25 = $356,000
Which gives labor cost = 0.25 × $356,000 = $89,000
The material cost for December = $356,000.
Which could be the side length of a 30°-60°-90° triangle?
*
A. 2,3, V2
B. V3, 2V3,3
C. 3,3,3V2
D. 3, 3V3 ,6V3
Given that D is the midpoint of AB and B is the midpoint of AC, which statement must be true? A line has points A, D, B, K, C. AD = One-thirdAC AC = 4DB AB + DC = AC BK = KC
Answer:
AC = 4DB
Step-by-step explanation:
see attachment
Given that B is the midpoint of AC, this means that AB≅BC.
Also, D is the midpoint of AB, therefore AD≅DB.
This shows that AD is 1/4 of the length of AC, since it is 1/2 of the length (1/2 x 1/2 = 1/4). DB is the same length, since it is congruent to AD.
Thus, AC = 4DB.
Answer:
B. AC = 4DB
May I have brainliest please? :)
I need help ASAP!! A, B, C, D
Answer:
C. Both f(x) and its inverse function intersect at point (2, 2).
Step-by-step explanation:
First of all, let's begin defining f(x) = y.
Since the linear function f(x) intersects at
• 6 on the y-axis; and
• 3 on the x-axis;
we can deduce the following equation:
6x + 3y = 6(3)
6x + 3y = 18
3y = -6x + 18
y = -6x/3 + 18/3
y = -2x + 6
f(x) = -2x + 6
Then, we'd want to find the inverse of f(x), which is f`¹(x).
f(x) = -2x + 6
y = -2x + 6
Interchange the variable y to x and vice versa.
x = -2y + 6
2y = -x + 6
y = (-1/2)x + 3
f`¹(x) = (-1/2)x + 3
Since both f(x) and its inverse function are equal to y, set them both as equal.
f(x) = f`¹(x)
-2x + 6 = (-1/2)x + 3
-2x + (1/2)x = 3 - 6
(-3/2)x = -3
x = 2
Substitute x = 2 into y = -2x + 6.
y = -2(2) + 6
y = -4 + 6
y = 2
Now that we know x = 2 and y = 2, then the intersection point of (x, y) must be (2, 2).
I hope this helps! Sorry if my English didn't really help with giving a clearer explanation.
Have a great wonderful fantastic amazingggg dayyyy!!!
Answer: 176m^2
Step-by-step explanation:
The smaller rectangle is taking up space among the larger one. So in order to find the area of this shaded region, you need to subtract that smaller one from the larger one.
12 x 15 = 180
1 x 4 = 4
180 - 4 = 176m^2
Answer:
44
Step-by-step explanation:
To start you have to calculate the perimeter of the white box. 1 times 2 is 2. 4 times two is 8. 8 plus 2 is 10. Then you have to find the perimeter of the purple box. 12 times 2 is 24. 15 times 2 is 30. 24 plus 30 is 54. After that you have to subtract to get the final answer. 54 minus 10 in 44. 44 is the final answer.
WY is the perpendicular bisector of XZ. Y =
(I attached an image) Please help! Thank you!
Answer:
y=5
Step-by-step explanation:
Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
WY is the perpendicular bisector of XZ.
2x + 3 = 3x - 5
x = 8
5y - 2y = 7 + 8
y = 5
The value of y is 5
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
WY is the perpendicular bisector of XZ.
We see that,
2x + 3 = 3x - 5
3x - 2x = 3 + 5
x = 8
Now,
We have two right triangles.
∠WXY
WY² = WX² + XY² _____(1)
∠WYZ
WY² = WZ² + YZ² ______(2)
From (1) and (2) we get,
WX² + XY² = WZ² + YZ²
(2y + 7)² + (2x + 3)² = (5y - 8)² + (2x + 3)²
(2y + 7)² = (5y - 8)²
2y + 7 = 5y - 8
5y - 2y = 7 + 8
3y = 15
y = 5
Thus,
The value of y is 5
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ5
(15 POINTS AND BRAINLIEST)
A health club has a one time membership fee of $99, then charges $15 per month for members.
a) Write an equation in slope-intercept form for the cost y of joining the club
for x months.
b) How much has Muscular Marty paid if he has been a member for one year?
Answer:
a) The line will be y = 15x + 99 because the 99 is a one time purchase.
b) After 1 year, x will be 12 so Muscular Marty will pay 15 * 12 + 99 = $279.
Answer:
a) y = 99 + 15x
b) 279
Step-by-step explanation:
b) 1 yr = 12 months
thus x is 12
y = 99 + 15(12) = 99 + 180 = 279
when f(x)=-3, what is x
Answer:
0
Step-by-step explanation:
Basically the function has no "x" value so it is 0. X could be anything but in the function "x" is not even present so probably 0
Answer:
The answer would be 1 1/5
48/40 = 1 8/40
1 8/40 Simplify to 1 1/5
Hope this helps!
Step-by-step explanation:
Not sure but I think it is!
What two whole, positive numbers that have a one-digit answer when multiplied and a two-digit answer when added?
Answer:
1 & 9
Step-by-step explanation:
I believe that the numbers 1 and 9 fit the statement- as they would be 1 x 9= 9 and 1 + 9=10.
Hope this helped!! Please mark as Brainliest and/or give a rating !! Thank You :)
82.8cm measured to the nearest tenth of a cm
Answer:
The answer is already 82.8
Step-by-step explanation:
The .8 is already to the tenth so it is 82.8
Answer: 83.0
Step-by-step explanation:
This is the answer because if you round it to a tenth it is 83.0 and it is closest to a cm
Explain the meaning of “net” drawing. Provide an example.
The net of a 3D figure is the 2D surface area all laid out flat. One example would be that you have a box and you unwrapped the wrapping paper, placing it all flat on the table. By "placing it flat", I mean there are no portions that overlap. A 2D net is useful to help see that surface area is really just area. Specifically, surface area is the total area of each face of the 3D polyhedron.
Given that f(x) = x^2? + 9x + 18 and g(x) = x + 3, find (f ÷ g) (x) and express the result in standard form.
Answer:
x + 6
Step-by-step explanation:
(f ÷ g)(x)
= [tex]\frac{x^2+9x+18}{x+3}[/tex] factorise the numerator
= [tex]\frac{(x+3)(x+6)}{x+3}[/tex] ← cancel the factor (x + 3) on numerator/ denominator
= x + 6
HELP. THIS IS ABOUT DILATION EXPLANATION NEEDED
Answer:
(16,14)
Step-by-step explanation:
Dilation is increasing/decreasing something by a factor. The shape remains the same; it's just bigger or smaller.
This shape is a square, so all lines are the same length. Find the distance between C and D (it can honestly be any adjacent points). The distance is 6. You can usually use the distance formula, but since C and D have the same y-coordinate, you can just do |x2-x1|. Since you're multiplying by 2, the new distance should be 12. Since the y-coordinate of A' is 14, the y-coordinate of B is also 14. The x-coordinate should be 12 units away from the new A' (which is (4,14)). B is (16, 14)
Answer:
To dilate from the origin, you would need to multiply each coordinate by 2. For example, for A(2*2,7*2). After you do that to each coordinate, plot the points on a graph(by hand or using Desmos). Then, since it is a square determine point B by counting a certain number of units away from another point. A square has four congruent sides.
A. - 8/5
B. 5/8
C. - 5/8
D. 8/5
Answer:
5/8
Step-by-step explanation:
To find the slope, use the formula
m = (y2-y1)/(x2-x1)
= (2 - -3)/(6 - -2)
= (2+3)/(6+2)
= 5/8
Answer:
B
Step-by-step explanation:
Four college roommates rented an apartment together. When they
moved out, they were charged $1500 for damages to the carpet
and walls. The roommates agreed to equally share the cost.
What integer represents how much each person will have to pay?
Answer:
Step-by-step explanation:
What we do is to divide 1500 by 4 = $1500/4 = $375
Answer:375
Step-by-step explanation:
1500/4=375
i only need help with B
Answer:
it will take 3 sticks to make pattern n
_
| |
find the permimter of the quadrilateral if x=2 the perimiter is in inches the perimiters are (4x2+8x) (31 ) (7x+30) (3x2-5x+20)
Answer:
115
Step-by-step explanation:
4*2+8(2) = 24
31
7(2)+30 = 44
3*2-5(2)+20 = 6-10+20 = -4+20 = 16
24+31+44+16
115
Q 1. The area of a certain rectangle is 1 m².What is the area of a triangle that was cut off from that rectangle along a line connecting the midpoints of two adjacent sides?
Answer:
0.125 m²
Step-by-step explanation:
The area of a rectangle is the product of its length and breadth. Therefore:
area of the rectangle = length (l) × breadth (b) = 1 m².
l × b = 1
A triangle is cut off from that rectangle along a line connecting the midpoints of two adjacent sides, therefore the base of the triangle = length of rectangle/2 and the height of triangle = breadth of rectangle/2.
Area of triangle = 1/2(base × height) = [tex]\frac{1}{2}*\frac{l}{2}*\frac{b}{2}=\frac{1}{8}lb[/tex]
since lb = 1:
Area of triangle = [tex]\frac{1}{8}*1=0.125m^2[/tex]
i suck at geo please help
Answer:
It's B
Step-by-step explanation:
Because you see a reflection would show the traingle flipped translation would mean the traingle is in a totally different space and rotation would mean the shape is rotated and so B is left and so B is the correct answer.
CAN SOMEONE HELP ON MY LAST QUESTION PLZZZ
Which question are you talking about? I mean that why is there no attachment / image of your question? How do we know what is the question?So could you pls complete your question? :)
Answer:
(1, - 12 )
Step-by-step explanation:
Given the graph of f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Thus f(x) - 4 represents a shift down of 4 units, that is
(1, - -8 ) → (1, - 8 - 4 ) → (1, - 12 )
What is the common denominator of 13/24 + 7/12?
Answer:
The common denominator of 13/24 and 7/12 would be 12.
Step-by-step explanation:
The least common factor of 24 and 12 is 12.
Select all of the equations for which x = -1 *
1 point
x + 1 = 0
3x = -3
x - 9 = -8
5x = -5
Find the number missing from the following equivalent fractions:4/11= ?/66
Answer:
24
Step-by-step explanation:
whatever you add or divide to the numerator, you do to the denominator. the same occurs the other way round,too.
If 11 is multiplied by 6 to give 66.
then, 4 should also be multiplied by 6, for the equivalent fraction. This gives you 24.
Hope this helps. Good Luck
The missing number is 24.
please see the attached picture for full solution
Hope this helps..
Good luck on your assignment..
