Answer:
10,26,74,218,650
Explanation:
Each number is 4 less then 3 times than previous number.
The list of number is bounded by a set of rules that guide the creation of the set of numbers. The first 5 terms are: 10, 26, 74, 218, 650
Represent the number of terms with n.
So, the nth term is: [tex]T_n[/tex]
The start of the build is 10 means:
[tex]T_1 = 10[/tex]
The rule to generate the next terms is:
[tex]T_{n+1} = 3 \times T_n - 4[/tex] ---- i.e. 4 less than 3 times the previous term
So, the next terms till the 5th are:
[tex]T_{2} = 3 \times 10 - 4 = 26[/tex]
[tex]T_{3} = 3 \times 26- 4 = 74[/tex]
[tex]T_{4} = 3 \times 74- 4 = 218[/tex]
[tex]T_{5} = 3 \times 218- 4 = 650[/tex]
So, the first 5 terms are: 10, 26, 74, 218, 650
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Point F lies on line EG and point M lies on line EN. If F, E, and M are collinear, what must be true of these rays?
Answer:
Step-by-step explanation:
Some options would have definitely helped in answering this question. i am answering this question based on my knowledge. If F,E, and M are collinear, then EG and EN will form a line. Some options would have definitely helped in answering this question. i am answering this question based on my knowledge. If F,E, and M are collinear, then EG and EN will form a line.
When three is added to four times a number, the result is 15
(a) Write an equation to represent the above information.
Answer
(b) Solve your equation in (a)
Answer:
A. 4y + 3 = 15
B. y = 3
Step-by-step explanation:
Three is added to four times a number, the result is 15
A. Equation to represent the above information:
Let the unknown number= y
4 * y + 3 = 15
4y + 3 = 15
B. Solve your equation in (a)
4y + 3 = 15
Collect like terms
4y = 15 - 3
4y = 12
Divide both sides by 4
4y / 4 = 12 /4
y = 3
Therefore, the unknown number is 3
Practice Writing Composite Functions Given: f(x) = x - 7 and h(x) = 2x + 3 Write the rule for h(f(x)).
Answer:
h(f(x)) = 2x - 11Step-by-step explanation:
f(x) = x - 7
h(x) = 2x + 3
To find h(f(x)) substitute f(x) into h(x) that's replace every x in h(x) by f(x)
That's
h(f(x)) = 2(x - 7) + 3
h(f(x)) = 2x - 14 + 3
We have the final answer as
h(f(x)) = 2x - 11Hope this helps you
A
Find the value of x. Your answer must be exact.
30
9
Answer:
x = 9√3Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use tan
tan∅ = opposite/ adjacent
From the question
The opposite is 9
The adjacent is x
Substitute the values into the above formula
That's
[tex] \tan(30) = \frac{9}{x} [/tex]
[tex]x \tan(30) = 9[/tex]
Divide both sides by tan 30
[tex]x = \frac{9}{ \tan(30) } [/tex]
We have the final answer as
x = 9√3Hope this helps you
Find the area of the shape shown below.
9.0
3.5
2
5
2.
units
Answer:
[tex] \boxed{42.5 \: {units}^{2} }[/tex]Step-by-step explanation:
The shape could be divided into a rectangle and a trapezoid ( bottom part )
Let's find the area of the given shape:
Area of the given shape = [tex] \mathsf{ (l \times b) + \frac{1}{2} (b1 + b2)h}[/tex]
plug the values
[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 +9 - (5 + 2) \times 2}[/tex]
[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 + 2)(2)}[/tex]
[tex] \mathsf{ = 31.5 + \frac{1}{2} \times 11 \times 2}[/tex]
[tex] \mathsf{ = 31.5 + 11}[/tex]
[tex] \mathsf{ = 42.5 \: {units}^{2} }[/tex]
Hope I helped!
Best regards!
Combine your expressions from part E (x+2) and part F (y+ (-4) to give the pair of coordinates of any point after a translation two yards East and four yards south.
Answer:
A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)
Step-by-step explanation:
A transformation is the movement of a point from its initial position to a final position. If an object is transformed all its points are also transformed. Types of transformation are reflection, rotation, translation and dilation.
If a point O(x, y) is translated left by h unit, the new coordinate is O'(x-h, y) while if O(x, y) is translated right by h unit the new coordinate is O'(x+h, y)
If a point O(x, y) is translated up by h unit, the new coordinate is O'(x, y+h) while if O(x, y) is translated down by h unit the new coordinate is O'(x, y-h)
The location of the shape as shown in the diagram is:
A(3, 6), B(3, 3), C(4, 3), D(4, 6)
If the points are translated two yards East and four yards south, it means it is translated 2 unit right and 4 unit down i.e. (x+2, y-4). The new coordinates are:
A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)
Answer:
ombining the expressions from parts E and F, for any given initial point (x, y), the coordinates of the new point after a translation of two yards east and four yards south are (x + 2, y + (-4)).
Step-by-step explanation:
this is more simple
Evaluate the expression 5^3
Answer: Five to the power of three (5*5*5) is equal to 125.
Hope this helps!
Answer:
125
Step-by-step explanation:
[tex]5^3=\\\\5*5*5=\\\\25*5=\\\\\boxed{125}[/tex]
3 x 19 x 14 + 18 ÷ 2
Answer:
807Step-by-step explanation:
[tex]3 \times 19 \times 14 + 18 \div 2 \\ PEDMAS \\ (3 \times 19 \times 14 )+ 9 \\ = 798 + 9 \\ [/tex]
[tex] = 807[/tex]
Answer:
408
Step-by-step explanation:
3x19= 57
57x14= 798
798 + 18= 816
816/ 2= 408
What is x
I dont get it
Answer:
x = 35
Step-by-step explanation:
The angles of a triangle add to 180 degrees
103+ 42 + BCA = 180
BCA = 180 -103 -42
BCA =35
BCA and x are corresponding angles and corresponding angles are equal if the lines are parallel
If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse?
Answer:
8.94~9.0
Step-by-step explanation:
If A squared plus B squared equals C squared. Then you can used this formula and find that 4 squared plus 8 squared equals 80. then square root 80 to find 8.94 or rounded to 9. This would equal C or the hypotenuse. Hope this helps!
The required length of the hypotenuse of the triangle is 16√5.
Given that,
If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse is to be determined.
In a right-angled triangle, its side, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.
Here,
Applying the Pythagorean theorem,
Hypotenuse² = perpendicula² + base²
Hypotenuse² = 8² + 4²
Hypotenuse² = 64 + 16
Hypotenuse² = 80
Hypotenuse = √80
Hypotenuse = 16√5
Thus, the required length of the hypotenuse of the triangle is 16√5.
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|10-11| = simplify the expression
Answer:
1
Step-by-step explanation:
Let's ignore the absolute value signs for a moment.
We have the expression [tex]10-11[/tex]. We know that if we subtract 10 from 10 we get 0, so if we subtract 11 from 10 we must get -1.
However, there is an absolute value sign. This means that whatever number is inside it has to be converted to a positive number.
-1 as a positive number is +1, or just 1.
Hope this helped!
Determine whether or not the given pair of triangles is similar and state how you know.
Is ΔGHI ~ ΔJKI?
Mark all that apply.
Answer:
by SAS. YesStep-by-step explanation:
∠HIG and ∠JIK are vertical angles, so:
m∠HIG = m∠JIK
[tex]\dfrac{GI}{IJ}=\dfrac{7.5}3=2.5\\\\\dfrac{HI}{IK}=\dfrac{2.5}1=2.5[/tex]
[tex]\left\{\dfrac{GI}{IJ}=\dfrac{HI}{IK}\quad\ \wedge\quad m\angle HIG=m\angle JIK\right\}\implies \triangle HIG\sim\triangle JIK\ \ by\ SAS[/tex]
Use the concept of slope to find t such that the three points are collinear. (-8,5) (0,t) (2,-1)
Answer:
t = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Since the points are collinear they lie on the same line.
Thus the slopes between any of the 3 points are equal.
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 8, 5) and (x₂, y₂ ) = (2, - 1)
m = [tex]\frac{-1-5}{2+8}[/tex] = [tex]\frac{-6}{10}[/tex] = - [tex]\frac{3}{5}[/tex]
Repeat using
(x₁, y₁ ) = (- 8, 5 ) and (x₂, y₂ ) = (0, t) and equate to previous m
m = [tex]\frac{t-5}{0+8}[/tex] = [tex]\frac{t-5}{8}[/tex] = - [tex]\frac{3}{5}[/tex] ( cross- multiply )
5(t - 5) = - 24 , that is
5t - 25 = - 24 ( add 25 to both sides )
5t = 1 ( divide both sides by 5 )
t = [tex]\frac{1}{5}[/tex]
Simplify 18 - 2[x + (x - 5)].
A) 13 - x
B) 13 - 4x
C) 8 - 4x
D) 28 - 4x
Answer:
Well the correct answer is −4x+28... But I don't
see that as one of your options. :/
Simplify:
18−2(x+x−5)
Distribute:
=18+(−2)(x)+(−2)(x)+(−2)(−5)
=18+−2x+−2x+10
Combine Like Terms:
=18+−2x+−2x+10
=(−2x+−2x)+(18+10)
=−4x+28
Answer:
−4x+28
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{28 - 4x}}}}}[/tex]Option D is the correct option.
Step-by-step explanation:
18 - 2 [ x + ( x - 5 ) ]
Remove the unnecessary Parentheses
⇒18 - 2 [ x + x - 5 ]
Collect like terms
⇒18 - 2 [ 2x - 5 ]
Distribute 2 through the parentheses
⇒18 - 4x + 10
Add the numbers
⇒28 - 4x
Hope I helped!
Best regards!!
Solve for f.
-f + 2 + 4f = 8 - 3
f=
Answer:
1
Step-by-step explanation:
-f + 2 + 4f = 8 - 3
3f = 6 - 3
3f = 3
f = 1
Answer:
f=1
Step-by-step explanation:
-f+2+4f=8-3
First what you want to do i that you want to simplify as best as you can.
-f+2+4f=8-3 becomes 3f+2=8-3 because you add the 4f to the -1f.
Then, just subtract 2 from both sides to get 3f=8-5
Now, simplify even more
3f=8-5 becomes 3f=3
It should be easy now, but if you still need help, divide
f=1
Malia measures the longer side of a dollar bill using a ruler at school. Which of the following is most likely the quantity she measured?
Answer:
Step-by-step explanation:
The most likely quantity is centimetres.
The second option can be inches.
Hope this helps
plz mark it as brainliest!!!!!!!!!
Here are the ages (in years) of 10 professors at a college. , 47, 44, 48, 43, 35, 65, 56, 37, 7351 What is the percentage of these professors who are younger than 50?
Answer:
50%
Step-by-step explanation:
We are given this set of data: Age of professors in years
47, 44, 48, 43, 35, 65, 56, 37, 73,51
We can firstly rearrange the years properly in ascending order.
Hence we have:
35, 37, 43, 44, 48, 51, 53 56, 65, 73
The number of the professor given = 10 professors
The number of professors younger 50 years = 5
Therefore, the percentage of these professors who are younger than 50
Is:
5/10 × 100 = 50%
Therefore, 50% of the professors are younger than 50
what is the length of DI? A 1.4 B 4.4 C 5.6 D 17.6
[tex]\dfrac{DI}{DR}=\dfrac{DE}{DZ}\\\\\dfrac{DI}{6+2.8}=\dfrac{3}{6}\\\\6DI=26,4\\DI=4,4[/tex]
Part 1: You work 4 hours and earn $36. What is your earning rate (dollars per hour)?
Answer:
9 dollars per hour
Step-by-step explanation:
36/4=9
Answer:
9
Step-by-step explanation:
4 hours : $36
1 hour : $ x
we need to find x so,
4 hours ÷ 4 = 1 hour
1 : $
since we have divided 4 by 4,
we need to do that to 36 aswell
36 ÷ 4 = 9
1 hour : $9
Jon wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor
is
oft by 3 1 ft. Find the area the carpet needs to cover. •!
12
4
5
tiled floor
Entar
Answer:
321/8 ft^2
Step-by-step explanation:
The whole area is 49/4 × 5 = 245/4 ft^2
The area of tiled floor is 13/2 × 13/4 = 169/8
245/4 - 169/8 we need to equalise the bottom of fraction to subtract so
2/2 × 245/4 = 490/8
490/8 - 169/8 = 321/8 ft^2
equation y = (2x)/(x-1), how do I get -0.5 as the x intercept ???
Answer:
( 0,0) is the x intercept
Step-by-step explanation:
y = (2x)/(x-1),
To find the x intercept set y = 0 and solve for x
0 = (2x)/(x-1)
Multiply by x-1 on each side assuming x does not equal 1
0 = 2x
x = 0
The x intercept is 0
( 0,0) is the x intercept
PLEASE HELP
Arrange the functions for which the result is a non-infinite value and the limit exists in ascending order of their limit values as x tends to infinity.
Answer:
h,k,i,m,g,l
Step-by-step explanation:
I did all the work and i(x) limt should = -.25 and k(x) =0 but it said it was wrong. f(x) and j(x) cant be used, so my guess is to switch i(x) and k(x)
The answer is given in the image below.
Do all functions have limits?One of the fundamental standards of calculus is limits (limits of a function); it offers the fee of a function at a particular factor called limit. Limits are used to calculate the exact vital of the function. Not all functions include limits. A few functions no longer have any restrictions as the variable has a tendency to infinity.
What are examples of nonfunctions?The equations y = ± x and x 2 + y 2 = 9 are examples of non-function due to the fact there is at least one -price with or greater -values.
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a man bought a car for 8500 GH cedis and he later sold it at for 9500. find his percentage gain
Answer:
11.7647059 % gain
Step-by-step explanation:
To find the gain, take the new amount and subtract the original amount
9500-8500 = 1000
Divide by the original amount
1000/8500=.117647059
Multiply by 100% to get in percent form
11.7647059 % gain
solve for x 3x - 4 = 3x - 10
Answer:
no solution
Step-by-step explanation:
3x - 4 = 3x - 10
Subtract 3x from each side
3x-3x - 4 = 3x-3x - 10
-4 = -10
This is never true so there is no solution
Answer:
Step-by-step explanation:
I think you might have copied down the problem incorrectly.
If you try and solve this problem by moving the variables onto one side and the constants onto the other, you get:
3x-4=3x-10
+10 +10
3x+6=3x
-3x -3x
6=0 (which is FALSE)
Hope this helps!
P.S. Please give me brainliest. Thanks :)
How many bicycles and how many skateboards are in the shop? Show your work.
Answer:75
Step-by-step explanation:54+21
Answer:
15 bicycles, 6 skateboards
Step-by-step explanation:
We are looking for the number of skateboards and the number of bicycles. Those two numbers are our unknowns.
We define variables for those two numbers.
Let s = number of skateboards.
Let b = number of bicycles.
A skateboard has 4 wheels. s number of skateboards have 4s wheels.
A bicycle has 2 wheels. b bicycles have 2b wheels.
The total number of wheels is 4s + 2b.
The total number of wheels is 54, so our first equation is
4s + 2b = 54
The total number of skateboards and bicycles combined is s + b.
We are told the total number of skateboards and bicycles combined is 21.
The second equation is
s + b = 21
We have a system of two equations in two unknowns.
4s + 2b = 54
s + b = 21
We can solve it by the elimination method.
Rewrite the first equation below.
Multiply both sides of the second equation by 2 and write it below that. Then add the equations.
4s + 2b = 54
(+) -2s - 2b = -42
-----------------------------
2s = 12
s = 6
There are 6 skateboards.
Now we substitute 6 for s in the second original equation and solve for b.
s + b = 21
6 + b = 21
b = 15
There are 15 bicycles.
Answer: 15 bicycles, 6 skateboards
3-2y-1+5x^2-7y+7+4x^2
Answer: Hi!
The only thing we can do to simplify the equation is combine like terms.
5x^2 + 4x^2 = 9x^2
-2y - 7y = -9y
3 - 1 + 7 = 9
Our equation now looks like this:
9x^2 - 9y + 9
We have nothing left to simplify, so we're done!
Hope this helps!
What is the volume of the rectangular prism 3 1/2, 5 1/4,4 in
Answer:
73.5in³
Step-by-step explanation:
You multiply the three numbers.
3.5x5.25x4=73.5in³
What property is 21+(36+19)
Answer:
76
Step-by-step explanation:
21+(36+19)
21+(55)
21+55
=76
Answer:
The identity property
Step-by-step explanation:
I took it on Egd.
what is the prime factorization of 430
Answer:
[tex]\huge \boxed{430=2 \times 5 \times 43}[/tex]
Step-by-step explanation:
Using factor tree,
Answer:
[tex]\large\boxed{2, 5, 43}[/tex]
Step-by-step explanation:
430
/ \
215 2
The 2 cannot be factorized anymore, so I will put a small box around it.
430
/ \
215 [tex]\boxed{2}[/tex]
/ \
43 5
5 and 43 cannot be factorized any smaller.
430
/ \
215 [tex]\boxed{2}[/tex]
/ \
[tex]\boxed{43}[/tex] [tex]\boxed{5}[/tex]
The prime factorization is the numbers in the boxes, which are 2, 5, and 43.
[tex]\large\boxed{2, 5, 43}[/tex]
Hope this helps :)
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If the formatting is not showing up correctly, please refer to the images of my answer below instead.
PLEASE help me with this question. This is really URGENT
Answer:
c. p(10)=26,327(1+0.024)^10
Step-by-step explanation:
its just the answer
Answer:
[tex]\boxed{\sf Option \ 3}[/tex]
Step-by-step explanation:
The problem is exponential growth.
[tex]a(1+r)^t[/tex]
[tex]a = \sf initial \ amount[/tex]
[tex]r = \sf rate[/tex]
[tex]t= \sf time[/tex]
The third option is right.
[tex]P(10)=26237(1+2.4\%)^{10}[/tex]
[tex]P(10)=26237(1+0.024)^{10}[/tex]
