Answer:
see explanation
Step-by-step explanation:
the sequence is linear, that is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₈ = 18 and a₁₂ = 26 , then
a₁ + 7d = 18 → (1)
a₁ + 11d = 26 → (2)
subtract (1) from (2) term by term to eliminate a₁
4d = 8 ( divide both sides by 4 )
d = 2
substitute d = 2 into (1) and solve for a₁
a₁ + 7(2) = 18
a₁ + 14 = 18 ( subtract 14 from both sides )
a₁ = 4
then
a₂₀ = 4 + (19 × 2) = 4 + 38 = 42
Please help .!!!!!!!!!
Answer:
-60 = x
Step-by-step explanation:
(-1/4)x - 12 = x + 3
(-1/4)x = x + 15
-0.25x = x + 15
-60 = x
If
5sin 2x +4 = 10 sin ²x, show
that tanx = 2 or tan x =-1/3
[tex]~~~~~5\sin 2x +4 =10 \sin^2 x\\\\\implies 5\cdot 2\sin x \cos x+4 =10 \sin^2 x\\\\\implies 10 \sin x \cos x +4 = 10\sin^2 x\\\\\implies 10\tan x + 4\sec^2 x = 10\tan^2 x~~~~~;[\text{Divide both sides by}~ \cos^2 x]\\\\\implies 10\tan^2 x -10 \tan x -4(1+ \tan^2 x)=0\\\\\implies 10\tan^2 x -10 \tan x -4 -4\tan^2 x =0\\\\\implies 6 \tan^2 x -10 \tan x -4 =0\\\\\implies 3 \tan^2 x -5 \tan x -2 =0~~~~~;[\text{Divide both sides by 2}]\\\\\implies 3\tan^2 x - 6\tan x +\tan x -2 =0\\\\[/tex]
[tex]\implies 3 \tan x( \tan x -2) + (\tan x -2) = 0\\\\\implies (\tan x -2) ( 3 \tan x +1) = 0\\\\\implies \tan x = 2 ~~ \text{or}~~ \tan x = - \dfrac 13\\\\\text{Showed.}[/tex]PLEASE HELP!!!! CUMULATIVE EXAM!!!! 50 POINTS
Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x
How many classes would Gina need to take for the total cost to be the same at both dance studios?
10
15
100
150
Answer:
10
Step-by-step explanation:
My guy just plug in the number for x it's not that hard
At Shannon's Pancake House there are 228 dirty coffee mugs and 247 clean coffee mugs. What percentage of the coffee mugs at the pancake house are dirty? Write your answer using a percent sign
Answer:
48%
Step-by-step explanation:
First, we need to add the amounts together to be able to see what percent of all the cups are dirty. (228 + 247 = 475). Now we can find one percent of 475 we can do this by moving the decimal point two to the left. (4.75). so If 4.75 is 1% we can multiply 4.75 until we get 228.
4.75 x 20 = 95.
4.75 x 40 = 190
4.75 x 45 = 213.75
4.75 x 50 = 237.5
4.75 x 48 = 228
Since every time we multiplied by 1 more we went up 1%. We multiplied by 48 so 48%.
this is what i need help with
Answer:
It's B
Step-by-step explanation:
All you're doing is adding 1.5 each time
Hope this helps :)
Solve the following equation. Then place the correct number in the box provided.
6(x - 1) = 4(x - 2)
Answer:
x = -1
Step-by-step explanation:
First we expand both sides :
Let's start with the right side:
6(x-1) = 6x-6
Now we do the left side:
4(x-2) = 4x-8
Now we add 6 to both sides:
(6x-6)+6 = (4x-8)+6
Simplify:
6x = 4x -2
Subtract 4x from both sides:
6x - 4x = (4x-2) - 4x
Simplify:
2x = -2
Divide both sides by 2:
2x÷2 = -2÷2
Simplify:
x = -1
I dont see a box so can't do the second part.
Hope this helps and brainliest please
An elevation of-89ft.is 89 feet_______
See level.
Answer:
- sign indicates the fact that it's Below sea level
help please. this doesn't make sense
Answer:
a = 39.2650873379cm
b = 11.5529459767cm
Step-by-step explanation:
a - Use the area of a triangle equation - 1/2 * a * b * Sin(C)
1/2 * 8 * 10 * Sin(79) = 39.2650873379cm
b - Use the cosine rule - c^2 = a^2 + b^2 - (2 * a * b * Sin(C)
64 + 100 - (2 * 8 * 10 * Cos(79)) = 133.4705607398
c = square root of 6.9396506484 = 11.5529459767cm
Put to however many significant figures / decimal places required.
:)
need help with this asap
Answer:
they are three I will explain
Step-by-step explanation:
x+4/3÷6/x
this 3 expressions are equivalent to the equation above
1. x+4/3{x/6}
2. {x/6}x+4/3
3. x^2 + 4x /18
How many meters are in 360in?
Answer:
9.411
Step-by-step explanation:
Answer:9.144
Step-by-step explanation:
Pls help i need this so I can pass
Answer:
i cant see the photo, but i would love to help
Step-by-step explanation:
Make it quick please!
What are the coordinates of the hole in the graph of the function f(x)?
f(x)=x2−9/x−3
Factor out the numerator first
y=x²-9/x-3y=x²-3²/x-3y=(x+3)(x-3)/(x-3)y=x+3The hole is at x-3=0 i.e x=3
And
y=3+3=6The hole is at (3,6)
Our basketball team won 60 percent of their games. If they lost 8 games, how many games did they play altogether?
Answer:
they played 20 games together
Step-by-step explanation:
use percentages
Let x be the number of total games.
If 60% is won games then 40% is lost games.
(8/x)*100 = 40
8/x = 4/10
80 = 4x
X = 80/4
Therefore the number of games is 20
A right triangle has one angle that measures 48°. What is the measure of the other acute angle?
Answer:
minus 48 to 90 then divide the answer by 2
Answer:
42°
Step-by-step explanation:
The 2 acute angles in a right triangle add up to 90°
90° - 48° = 42°
Hope this helps
The image shows a circle with center (4,6) and radius 10 units.
A circle is a curve sketched out by a point moving in a plane. The point that lies on the circle is (-4, 12), (-6, 6), and (4, 16).
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The simple way to do such questions is to make the given circle and plot the points on the graph. As shown below.
The other way to do the question is to find the distance between the centre point of the circle and the point if it is equal to the radius of the circle, the point will lie on the circle, otherwise not.
The formula to find the distance between the two points on a graph is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence, the point that lies on the circle is (-4, 12), (-6, 6), and (4, 16).
Learn more about Circle:
https://brainly.com/question/11833983
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What is the slope of the line that passes through the points (-1, 6) and (14, 3)? Write your answer in simplest form.
the slope is m= -1/5.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
y_2 - y₁ = m(x₂ - x₁).
here, we have,
the slope of the line that passes through the points (-1, 6) and (14, 3)
Slope: m= y_2 - y₁/(x₂ - x₁).
= 3-6/14+1
= -1/5.
hence, the slope is m= -1/5.
To learn more on slope click:
https://brainly.com/question/3605446
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the probability of a certain hockey player making a goal after hitting a slap shot is 1/5. How many successful slapshots would you expect her to make after 120 attempts?
Ally surveyed 5 classrooms. She wanted to know the number of students in each class who love painting. The data she collected from the 5 classrooms is below.
10, 7, 9, 11, 8
The value that could be the best measure of the center of this data is__.
Answer:
45 im not to shur
Step-by-step explanation:
10 + 7 + 9 + 11 + 8 = ?
? = 45
Write the missing number to make these equivalent fractions correct
?/20=2/5
Answer:
8
Step-by-step explanation:
From 5 to get to 20 it would be (X4), so we would do the same for the 2, and 2 times 4 would be 8. The answer is 8.
Alex is 6 years older than Frank. The sum of their ages is 50. Find Alex's age and
Frank's age.
HELP
Answer: Alex 28
Frank 22
Step-by-step explanation: Age difference is 6. Addition is 50
Which of the following is a geometric series? 6 13 20 27 7 21 35 45 14 21 28 35 2 14 98 686
The geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.
What is geometric series?In mathematics, a geometric series is the sum of an infinite number of terms that have a constant or common ratio between successive terms
A. 6 + 13 + 20 + 27 .
the difference between two terms are 13-6 = 7 , 20-13= 7
The terms are increasing by 7. So it is not geometric
B. 7 + 21 + 35 + 45
the difference between two terms are 21-6 = 14 , 35-21= 14
The terms are increasing by 14. So it is not geometric
C. 14 + 21 + 28 + 35
the difference between two terms are 21-14 = 7 , 28-21= 7
The terms are increasing by 7. So it is not geometric
D. 2 + 14 + 98 + 686
Here the difference is not same, so we find the ratio
14/2= 7
98/14= 7
686/98= 7
So common ratio is 7
When the common ratio is same then it is Geometric series
Hence the geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.
To know more about geometric progression follow
https://brainly.com/question/24643676
Answer:
D
Step-by-step explanation:
multiplied by 7 each time
What is the value of 4(x−2)(x−3)+7(x−2)(x−5)−6(x−3)(x−5) when x=5? Type the answer in the box below.
Answer:
24
Step-by-step explanation:
when x = 5,
4(5-2)(5-3) + 7(5-2)(5-5) - 6(5-3)(5-5)
= 4(3)(2) + 7(3)(0) - 6(2)(0)
= 24
The store pays 120 for a bike the store is going out of business and is selling all of the bikes at a 30% discount what is the sil price of the bicycle
I need some help please
Answer:
24
Step-by-step explanation:
The way you calculate the volume of a shape is length x width x height. 4 x 3 x 2 = 24.
1. What is( - 1/2 + 2)
2. 4( 1/2+5/4) + (-5)
(please answer, I will mark brainliest)
:)
1)
[tex]\longrightarrow (-\dfrac{1}{2} +2)[/tex]
[tex]\longrightarrow (-\dfrac{1}{2} +\dfrac{4}{2} )[/tex]
[tex]\longrightarrow \dfrac{-1+4}{2}[/tex]
[tex]\longrightarrow \dfrac{3}{2}[/tex]
[tex]\sf \bold{\longrightarrow 1\dfrac{1}{2}}[/tex] (final answer)
2)
[tex]\longrightarrow \sf 4(\dfrac{1}{2} +\dfrac{5}{4} ) + (-5)[/tex]
[tex]\longrightarrow \sf 4(\dfrac{2}{4} +\dfrac{5}{4} ) + (-5)[/tex]
[tex]\longrightarrow \sf 4(\dfrac{7}{4} ) + (-5)[/tex]
[tex]\longrightarrow \sf 7-5[/tex]
[tex]\longrightarrow \bold{\sf 2}[/tex] (final answer)
pls help me with this
Answer:
7 with a remainder of 2
Step-by-step explanation:
i just did the math rn
What is the Volume of the square pyramid? (Round to the nearest tenth as needed)
base= 25 mm
height= 28 mm
to find:the volume of the square pyramid.
solution:[tex]volume = {a}^{2} \frac{h}{3} [/tex]
[tex]v = {25}^{2} \frac{28}{3} [/tex]
[tex]v = 5833.33333 {mm}^{3} [/tex]
[tex]v = 5833.3 {mm}^{3} [/tex]
help plese will markbrainliest
Your answer is 53
Yw :D
A tank is being filled with water at a rate of 5.5 gallons per
minute. Write the first five terms of the arithmetic sequence
being represented after each minute if the tank started with
10 gallons of water.
Arithmetic sqaure: a + (n-1) * d
where "a" is the first term, "d" is the common difference
Here given:
a = 10 gallons
d = 5.5 gallons
nth term: 10 + (n-1) * 5.5Solve for first 5 terms:
10 + (1-1) * 5.5 = 10
10 + (2-1) * 5.5 = 15.5
10 + (3-1) * 5.5 = 21
10 + (4-1) * 5.5 = 26.5
10 + (5-1) * 5.5 = 32
first five terms: 10, 15.5, 21, 26.5, 32
General formula
a_n=a+(n-1)da_n=10+(n-1)5.5So
a_1=10a_2=10+5.5=15.5a_3=10+11=21a_4=10+16.5=26.5a_5=10+22=32a_6=10+27.5=37.5A triangle has sides with lengths of 13ft, 82ft, and 83ft. Is it a right triangle
Answer:
NOT a right triangle
Step-by-step explanation:
IF it is a right triangle, then the Pythagorean theorem would apply
13^2 + 82^2 = 83^2 ?????
169 + 6724 = 6889
6893 = 6889 ? No...it is NOT a right triangle