Answer:
54
Step-by-step explanation:
We are given the sequence or function:—
[tex]\displaystyle \large{a(n) = 3(2)^n}[/tex]
To find the sum of 1st term and 4th term, first we must find the first term and the fourth term which can be done by substituting n = 1 and n = 4.
[tex]\displaystyle \large{a(1)=3(2)^1}\\\displaystyle \large{a(1)=3 \cdot 2}\\\displaystyle \large{a(1)=6}[/tex]
Then when n = 4.
[tex]\displaystyle \large{a(4) = 3(2)^4}\\\displaystyle \large{a(4) = 3 \cdot 16}\\\displaystyle \large{a(4) = 48}[/tex]
Therefore, the sum of 1st term and 4th term is:—
[tex]\displaystyle \large{a(1)+a(4) = 6+48}\\\displaystyle \large{a(1)+a(4)=54}[/tex]
The length and the breadth of a rectangle are 40 m and 30 m respectively. If its perimeter = perimeter of a square. Find the side of the square
Answer:
above is the solution to the question
[tex]\frac{x^{2} -1}{16x} X \frac{4x^{2} }{5x + 5}[/tex]
Answer:
x^2-x / 20
Step-by-step explanation:
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{x^{2} -1}{16x} \times \frac{4x^{2} }{5x + 5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{\cancel{(x+1)}(x-1)}{16x} \times \frac{4x^{2} }{5\cancel{(x + 1)}} \quad\quad(a^2-b^2 = (a+b)(a-b))\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{x-1}{\cancel{16x}} \times \frac{\cancel4x^{\cancel2} }{5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{(x -1)(x)}{4\times 5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{x^2-x}{20} \\\end{gathered} [/tex]
More Identities:-[tex]\begin{gathered}\boxed{\sf{ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf{ {(a - b)}^{2} = {a}^{2} + {b}^{2} -2ab \: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf{ {x}^{2} - {y}^{2} = (x + y)(x - y) \: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf {(a + b)² = (a - b)² + 4ab\: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf {(a - b)² = (a + b)² - 4ab\: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf {(a + b)² + (a - b)² = 2(a² + b²)\: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf{ (a + b)³ = a³ + b³ + 3ab(a + b)\: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf {(a - b)³ = a³ - b³ - 3ab(a - b)\: }} \\ \end{gathered}[/tex]
Josephine is constructing a circle circumscribed about triangle XYZ. She uses the following sequence of steps to construct the circle.
1. She constructs the perpendicular bisectors of two sides.
2. She finds their point of intersection, P.
3. She uses a compass, with the fixed end on X, to draw a circle passing through point P.
Did Josephine make any errors while constructing the circle?
OA. Yes, she should have placed the compass with the fixed end on P and drawn a circle through point x.
OB. No, she did not make any errors.
OC.
Yes, she should have constructed the angle bisectors.
ज
OD.
Yes, she should have found the perpendicular bisectors of all 3 sides.
Answer:
A
Step-by-step explanation:
there is not much more to say.
the point where actually all 3 line bisectors intersect, is also called the "circumcenter". I guess you understand what that means : it is the center of the circle circumscribing the whole triangle (passing through all 3 corners/vertices).
once you find that point with 2 line bisectors, there is no need to construct the third - it WILL intersect the others at the same point.
Answer:
A
Step-by-step explanation:
10 y + 4 = 0
A) x - y=0
C) -y=-4
B) y=-4
D) x + y = 0
Answer:
B) y = -4
Step-by-step explanation:
When rearranging an equation we divide, multiply, subsract, add the same things to both sides of the equation.
So here we would - 4 from both sides to give:
y + 4 - 4 = 0 - 4
This would simplify to:
y = -4
Please help with this question (I will mark brainliest) Thank u >u<
A turtle population that started at 368 has begun to decrease by 7 percent each month. Which equation below could be used to model this situation?
Answer:
Im Not 100% but, I will give you the best answer.
I think it might be Option 3
If not, (give me 1 star)
I tried
Step-by-step explanation:
Worth 10 points please help me
Answer:
x = 100°
Step-by-step explanation:
40 + 40, the bottom two angles, = 80. a triangle has 180 degrees in total. 180 - 80 = 100. the missing angle of the bottom triangle is 100. since the bottom 100 is a vertical angle to the x, x must equal 100 degrees
What is the value of m in the equation {m-in
-n = 16, whеn n = 8?
o20
032
оооо
44
48
Answer:
m = 24
Step-by-step explanation:
if i'm wrong sorry not that good with math
circle A has a diameter of 9 cm. Circle b has a radius of 5 cm
Which circle has the larger circumference ?explain your reasoning
About how many centimeters larger is it?explain your reasoning
Answer:
Circle B has a larger circumference.
Step-by-step explanation:
Circumference of a circle is the diameter times pi.
C = pi•d
Circle B has radius 5, so its diameter is 10. Circle A has diameter of 9. A larger diameter will give a larger circumference.
C_circle A = 9pi
~= 28
While,
C_circle B = 10pi
~= 31
Circle B's circumference is about 3 cm larger. More accurately it's 1pi larger.
e
Which describes the horizontal cross section of
the given right rectangular prism?
A. A rectangle with dimensions of 15 inches and 16
inches.
B. A rectangle with dimensions of 15 inches and 7
inches.
C. A rectangle with dimensions of 9 inches and 15
inches.
D. A rectangle with dimensions of 9 inches and 7
inches.
The horizontal cross section of a rectangular prism would have the same shape and size as the rectangular base.
What is a prism?A prism is a three dimensional shape with two parallel bases of the same shape and the other faces which are quadrilateral.
A rectangular prism has the shape of a cuboid. The horizontal cross section of a rectangular prism would have the same shape and size as the rectangular base.
Find out more on prism at: https://brainly.com/question/23963432
Olive flipped a coin and rolled a number cube with the
numbers 1-6 on it. What is the probability that she flipped
heads and rolled an even number?
1
al
2
3
4
5
6
н
H1
H2
H3
H4
H5
16
T
T1
T2
T3
T4
T5
T6
3
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!
(07.06) y ≤ 27. Which of the following statements is the best way to describe the value of y? The value of y is less than 27. The value of y is greater than 27. The value of y is at most 27. The value of y is at least 27.
Solve the following:
(i)20 ÷7
(ii) 22÷7
Answer: i) 2.85714285714, ii) 3.14285714286
Step-by-step explanation:
i) 20/7 = 2.85714285714
ii) 22/7 : This is an approximation for pi. it comes to: 3.14285714286
Answer what the picture is asking.
Answer:
Step-by-step explanation:
-17x+44=180
-17x=136
x=-8
Top right angle = -4(-8)+5=37
Bottom Left angle=-13(-8)+39=143
Three sisters, whose average age is 10, all have different ages. When they get together in pairs, the average ages of two such pairs are 11 and 12. What is the age of the eldest sister?
The age of the eldest sister is 16 years.
What is an equation?An equation is used to show the relationship between two or more variables and numbers.
Let x represent the age of the older sister and y, z represent the other sisters ages.
Three sisters, whose average age is 10, all have different ages. Hence:
(x + y + z)/3 = 10 (1)
Also, When they get together in pairs, the average ages of two such pairs are 11 and 12, hence:
(x + y)/2 = 11 (2)
(x + z)/2 = 12 (3)
From equation 1, 2 and 3:
x = 16, y = 6, z = 8
The age of the eldest sister is 16 years.
Find out more on equation at: https://brainly.com/question/18176080
Which expression shows a sum of five terms? (3 points)
5(x + 5)
5x
x5
5 + x + 5 + x + x
5.
Answer:
5 + x + 5 + x + x
Step-by-step explanation:
We are given 4 expressions and we have to determine which expressions shows a sum of five terms.
We use the process of elimination:
5(x + 5)
=5x+25 (distributing 5)
This contains sum of only two terms, eliminate.
5x
It contains only 1 term, eliminate.
5 + x + 5 + x + x
It contains 5 terms 5,x,5,x and x, KEEP!
5.
Only contains 1 term, eliminate.
With this said, were left with:
5 + x + 5 + x + x
Which is the correct answer! :)
I just need help with this pls
Answer:
Option D
Step-by-step explanation:
Hello!
Recall the quadratic equation: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Remember that a quadratic equation is written in the form [tex]ax^2 + bx + c\\[/tex]
So:
a = 2b = 5c = -1Plug the values in and solve:
[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-5\pm\sqrt{5^2 - 4(2)(-1)}}{2(2)}$\\\\x = $\frac{-5\pm\sqrt{25 +8}}{2(2)}$\\\\x = $\frac{-5\pm\sqrt{33}}{4}[/tex]
This would be [tex]\boxed{\text{Option D}}[/tex]
A deck of cards have suits spade, diamonds, clubs, and hearts. There are 13 of each suit Ace, 2,3,4,5,6,7,8,9,10, jack, queen, and king. What is the probabililty of choosing a King from a standard deck?
Answer:
1 out of 13
Step-by-step explanation:
Judy and Amna are on a safari. They are standing 20 feet apart when they spot a snake. Judy and Amna run in opposite directions at speeds of 180 feet per minute and 120 feet per minute, respectively. In how many minutes will they be 2420 ft apart?
Using proportions, it is found that Judy and Amna will be 2420 ft apart after 8 minutes.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
They run in opposite directions, at speeds of 180 feet per minute and 120 feet per minute, respectively, hence each minute they get 180 + 120 = 300 feet apart.
They already are 20 feet apart, so they will need to get more 2420 - 20 = 2400 ft apart. Hence:
1 minute - 300 ft apart.
x minutes - 2400 ft apart.
Applying cross multiplication:
300x = 2400
x = 8.
Judy and Amna will be 2420 ft apart after 8 minutes.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ2
In the basketball game, Rachel scored 6 points less than twice the number of points Trina scored. Trina scored 9 points. How may points did Rachel score.
Answer:
Rachel scored 12 points in total
Explanation:
You must first multiply 9x2 which equals 18. Now you'll need to subtract 18-6 which equals 12. Therefore, Rachel scored 12 points in total.
I hope this helps! ^-^
Find the area of trapezoid ABCD by decomposing it into a rectangle and triangle.
A)80 cm^2
B)96 cm^2
C)104 cm^2
D)112 cm^2
Answer:
c) 104
Step-by-step explanation:
The angles in a triangle are in the ratio 1:2:3.
a) Show that the triangle is a right-angled triangle.
Answer:
Step-by-step explanation:
Remark
The angles can measure
x + 2x + 3x
The total must be 180 degrees because all triangles have 180 degrees
Equation
x + 2x + 3x = 180 Combine
6x = 180 Divide by 6
6x/6 = 180/6
x = 30
1x = 30
2x = 60
3x = 3*30 = 90
A right angle triangle has 90 degrees.
If x = 8 and y = -3, evaluate the following expression: 20 - 5y + 2x
Answer:
51
Step-by-step explanation:
Given the following question:
[tex]20-5y+2x[/tex]
[tex]x=8[/tex]
[tex]y=-3[/tex]
Substitute and solve using PEMDAS:
[tex]20-5y+2x[/tex]
[tex]20-5(-3)+2(8)[/tex]
[tex]5\times-3=-15[/tex]
[tex]20--15+2(8)[/tex]
[tex]2\times8=16[/tex]
[tex]20-(-15)+16[/tex]
[tex]20--15=35[/tex]
[tex]35+16=51[/tex]
[tex]=51[/tex]
Your answer is "51."
Hope this helps.
Find y so that (1/4) ^-3 × (4)^8 = (1/4)^ -4y.. help me please. I will mark brainliest
please mark me as brainlest
PLEASE HELP ASAP
What is 7/8 expressed as a percent? Enter your answer as a decimal in the box.
Answer:
87.5
Step-by-step explanation:
A box contains 5 red, 3 white, and 2 blue marbles. A sample of six marbles is drawn with replacement; that is, each marble is replaced before the next marble is drawn. Find the probability that: (a) 3 are red, 2 are white, 1 is blue, (b) 2 are red, 3 are white, 1 is blue, (e) 2 of each color appear
Answer:
i dont know but i'll try
Step-by-step explanation:
10-6=4
2 each color
i think because if you divide 4 divided by 2 is 2.
SO i thought wait oh no dont copy this rate it as bad as you want but im just a ---- grader
Calculate the simple interest earned as a amount R1400 at an annual interest rate 6.5% over 3 years?
Answer:
principle (p)=Rs1400
Rate(R)=6.5
time(T)=3
we know that
I=P×I×T/100
=1400×6.5×3/100
=273
therefore the simple interest earned is Rs273
I am trying Find the surface area of a prism or cube and it only has 3.5
if danielle still drove 24 miles on the eight day how many miles would tim need to drive to make the median amount of miles that tim and danielle drove the same?
Answer:
the answer would be she would drive 192 miles
Which number is not in scientific notation? (1 point)
0.2 • 10^3
3 • 10^28
1.03 • 10^–2
1.5 • 10^–6
Answer:
Hi I'm always here to help!!!
_______________________
Ah welp that was wrong it was A
Sorry that I was wrong
_______________________
Have a great day!!!!
Answer:
Your answer would be:
A.) 0.2 x 10^3
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
please help find the point of intersection (ordered pair)
x + 2y=3
2x - 4y = -20
Answer:
Check out Tiger algebra
it gave me
Slope=-2.000/2.000=-1.000
x - intercept = 3/1 = 3.00000
y - intercept = 3/2 = 1.50000
and
Slope=1.000/2.000=0.500
x - intercept = 10/1 = 10.00000
y - intercept = 10/2 = 5
It requires nothing.