Answer:
The first six terms of the sequence are -3, 3, 21, 74, 234 and 714
Step-by-step explanation:
Given the initial value a0 = -5 and the general form of the sequence given as An = 3an-1 + 12
To get the first six terms of the sequence, we will substitute for n=1 up to n= 6 in the general equation.
when n=1
A1 = 3a(1-1)+12
A1 = 3a0+12
A1 = 3(-5)+12
A1 = -15+12
A1 = -3
when n=2;
[tex]A2 = 3a(2-1)+12\\A2 = 3a1+12\\A2 = 3(-3)+12\\A2= -9+12\\A2= 3\\\\A3= 3a(3-1)+12\\A3= 3a2+12\\A3 = 3(3)+12\\A3= 9+12\\A3= 21\\\\A4= 3a(4-1)+12\\A4 = 3a3+12\\A4= 3(21)+12\\A4= 63+12\\A4 = 74\\\\A5= 3a(5-1)+12\\A5 = 3a4+12\\A5= 3(74)+12\\A5= 222+12\\A5 = 234\\\\\\A6= 3a(6-1)+12\\A6 = 3a5+12\\A6= 3(234)+12\\A6= 702+12\\A6 = 714\\[/tex]
The first six terms of the sequence are -3, 3, 21, 74, 234 and 714
The first side of a triangle measures 5 in. less than the second side, the third side is 3 in, more than the first side, and the
perimeter is 17 in. How long is the third side?
If s represents the length of the second side, which of the following represents the length of the third side?
A. s - 5
B. s-2
C. s+3
Final answer:
The third side of the triangle is determined by the expression 's - 2 inches', where s represents the length of the second side of the triangle.
Explanation:
To find the length of the third side of the triangle, we can first define the lengths of the other two sides in terms of s, the length of the second side. The first side is s - 5 inches, according to the problem statement. Since the third side is 3 inches more than the first side, its length would be (s - 5) + 3, which simplifies to s - 2 inches.
Now, knowing that the perimeter of the triangle is 17 inches, we can set up an equation to include all three sides: s + (s - 5) + (s - 2) = 17 inches. Solving this equation for s will give us the length of the second side and consequently the length of the third side using s - 2 inches.
What does it mean for an equation to be a radical equation?
Answer:
In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a 'square root' symbol, and many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher.
Step-by-step explanation:
Write this in word form.
a ≤ 20 and a ≥ 25
Answer:
ok so for a ≤ 20 it is A is less than or equal to 20
a ≥ 25 is A is greater than or equal to 25
Step-by-step explanation:
whenever you have a symbol like ≥, where it has a line under it, it means it could be equal to. And when the symbol is like a<20 (where < is the alligator it eats the bigger number so 20 is larger) And this means a is less than but since there is ≥ then its Equal to as well. :) sorry if this is confusing i will be willing to further explain if needed.
Please help! i couldnt copy and paste it into here so i decided to just screenshot it :)
Based on the data set shown, which of the following is a true statement?
-1, -1, 0, 1, 1, 1, 1, 2, 2, 2, 3
mean = mode
mean < median
mode < median
Answer:
mean = mode
Step-by-step explanation:
To make this easier, let's find the mean, median, and mode.
Mean: Sum of a set of numbers divided by number of terms
Median: Middle number of data when data is in numerical order
Mode: Number that occurs most often in data
To find the mean, add all the values together. -1 - 1 + 0 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 = 11. Now, divide by the number of terms, which is 11. 11/11 = 1. The mean is 1.
To find the median, look at the number in the middle of the data. -1, -1, 0, 1, 1, 1, 1, 2, 2, 2, 3. The median is 1.
To find the mode, look at the number that occurs most often. There are 4 1's, so the mode is 1.
Since all numbers are equal, the only possible answer is the first option.
The mean, median, and mode are all equal; thus, a.) mean = mode is true.
Sum of all values: (-1) + (-1) + 0 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 = 11
Number of values: 11
Mean = Total sum / Number of values = 11 / 11 = 1
Arrange the values in ascending order: -1, -1, 0, 1, 1, 1, 1, 2, 2, 2, 3
The middle value (6th value) is 1
Median = 1
The value that appears most frequently is 1 (occurs 4 times)
Mode = 1
Comparing these values:
Mean = 1
Median = 1
Mode = 1
The product of 2 and the sqrt of 3 and 3 and the sqrt of 12 in simplified form is _______? (your supposed to answer the stupid question yourself. your meant to simplify 2 and the sqrt of 3 and 3 and the sqrt of 12 to get your answer so don't report it for being incomplete)
Answer:
[tex](2 \sqrt{3} )(3 \sqrt{12}) = 6 \sqrt{36} = 6(6) = 36[/tex]
Which rays form the sides of WXY?
ロロロロロロ
D. XW
E. Ws
Answer:
XY and XW
Step-by-step explanation:
plzzz help I need help with this question will give you brainliest!!!!!
Zero softballs with a diameter of 3.8 inches will fit into the container as length of the container is less the diameter of the softball.
Zero softballs can fit in length and zero softballs will fit in width.
Why-
Length of the square base in rectangular pyramid = s
Breadth of the square base in rectangular pyramid = s
Height of the square base in rectangular pyramid, l = 11 inches
Volume of the square base in rectangular pyramid, V=
Volume of the cuboid = l × b × w
V= s × s × l
s = 3 inches
Softballs with a diameter of 3.8 inches.
1. Find the next three terms of the arithmetic sequence.
12, 9, 6, 3, ___ ,___ ,___
2. Find the next three terms of the arithmetic sequence.
-2, 2, 6, 10, ___, ___, ___
3. Write an equation to the nth term of the arithmetic sequence. (write the equation for the sequence)
15, 13, 11, 9
Answer: of the first one 0 , -3, -6. Second 14, 18, 22
Step-by-step explanation:
Work out the perimiter of a semi circle with radius of 3
Give your answer in term of pi
Answer:
15.425 cm is it without terms of pie
Step-by-step explanation:
you need to put it into terms of pie
Answer:
3pi + 6 units.
Step-by-step explanation:
The perimeter = the diameter + curved part.
Radius = 3 so the diameter = 2*3 = 6.
Length of the curved part = 1/2 * circumference of the circle = 1/2 * pi * diameter.
Perimeter = 6 + 1/2 pi * 6
= 3pi + 6 units.
PLEASE ANSWER QUICKLY!
Frank is 6 inches taller than his young brother, Pete. Pete's height is p . Write an algebraic expression to represent Frank's height.
Answer:
P + 6
Step-by-step explanation:
Louise sold 340 soft pretzels. If she sold them in groups of 17 soft pretzels, how many groups did she sell? A. 22 B. 20 C. 19 D. 21
Answer:
she sold 20 pretzels 340/17 =20
Step-by-step explanation:
Which expressions are equivalent to -90 – 60w?
Answer:
-30 (2w + 3) is the only one I can figure out.
I hope this helped tho!! :]
Last night the temperature in New York City went down t 4 degrees F. In Antarctica, the temperature went down to -20 degrees F. What is the difference between the two temperatures?
Answer:
The answer is -16
Step-by-step explanation:
2x^2-19x+9=0 quadratic formula or zero product property. Which ever is easier?
Answer:
9
Step-by-step explanation:
x=9
The most popular pizza at Pizza Parlor is a large pizza with a 12- inch radius. which of the following best represents the circumference of this pizza?
Answer:
75.3982236862
Step-by-step explanation:
Answer:
I believe the answer is 75.36
Plz plzplzplzplz help me plz
Answer:
ok
Step-by-step explanation:
The diagram below shows a 20-foot ladder leaning against a wall. The bottom of the ladder is 10 feet from the
base of the wall.
20 ft.
Wall
2-
101. -
Based on the dimensions in the diagram, what is the value of x?
The value of ∠x is 30⁰. Option B is correct.
How to determine the ratio value of ∠x in the figure.
From the given figure,
The triangle formed by ladder is right angled triangle
∠x⁰ is opposite to the horizontal distance between the foot of the and the point where the ladder touches the ground.
The ladder form the hypotenuse of the triangle.
Therefore,
sinθ = opposite/hypotenuse
θ is the angle opposite to distance between the wall foot and the ladder.
θ = x⁰
opposite = 10 ft
hypotenuse = 20 ft
so,
Sin(x) = 10/20
sin(x) = 1/2
find the sine inverse of (0.5)
x = sin⁻¹(0.5)
x = 30⁰
The value of ∠x is 30⁰. Option B is correct.
Select the correct answer.
Which relation does not represent a function?
A. {(3, 0), (0, 3)}
B. {(6, -2), (5, -2)}
C. {(3, 4), (3, 5)}
D. {(5, 5), (-5, -5)}
E. {(1, -2), (-2, 1)}
Relation C: {(3,4), (3,5)} does not represent a function because it has the same first component with different outputs.
Explanation:In Mathematics, a relation is defined as a set of ordered pairs. A relation is considered as a function if for each input (x value), there is exactly one output (y value). In other words, no two distinct ordered pairs in the function have the same first component. Looking at the options given:
A. {(3, 0), (0, 3)}B. {(6, -2), (5, -2)}C. {(3, 4), (3, 5)}D. {(5, 5), (-5, -5)}E. {(1, -2), (-2, 1)}The relation C. {(3,4), (3,5)} does not represent a function because there are two distinct ordered pairs with the same first component (or x-value) which is 3, but with two different y-values which are 4 and 5. Therefore, this relation violates the definition of a function.
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Final answer:
The relation that does not represent a function is Option C: {(3, 4), (3, 5)} because the number 3 in the domain is paired with two different values in the range, contradicting the definition of a function.
Explanation:
The relation that does not represent a function is Option C: {(3, 4), (3, 5)}. This is because a function is defined as a set of ordered pairs where each element of the domain (the first value in each pair) must correspond to exactly one element in the range (the second value in each pair). Option C depicts the number 3 in the domain being paired with both 4 and 5 in the range, which violates this rule. Therefore, Option C does not satisfy the definition of a function.
Option A, B, D, and E each show that every element of the domain is matched with only one unique value in the range, indicating they are all functions.
3(c+5) = 12
so what does c= ?
Answer: 4
Step-by-step explanation:
12 - 5 = 7,
7 - 3 = 4.
The answer to this is 4.
20 BRAINLY POINTS!!!!!!!!!!!!!!!
Answer:
is A , D , C
maybe b not sure
A bag contains 140 marbles, some white some blue. The ratio of white marbles to blue ones is 5:2. How many blue marbles are there?
Answer:
40
Step-by-step explanation:
5 + 2 = 7
140 div by 7 = 20
2 times 20 = 40
You have $90 in your bank account. Each week you plan to deposit $8 from your allowance and $15 from your paycheck. The equation bequals90plus(15plus8)w gives the amount b in your account after w weeks. How many weeks from now will you have $200 in your bank account?
A cylinder has a height of 19 feet and a radius of 6 feet. What is the volume. Use 3.14 as pi and round the answer to the nearest hundredth
ANSWER:V≈2148.85.I hope this helps!!
Which of the following theorems verifies that DEF - XZY?
Answer:
AA
Step-by-step explanation:
The question is about the congruency of two triangles DEF and XZY. A Congruence Theorem (SSS, SAS, ASA, or AAS) would demonstrate their congruence, but without specific measurements, we can't identify which theorem applies.
Explanation:The subject area of this question is Geometry, more specifically, the concepts concerning triangles. The given notation, DEF - XZY, suggests that the student wants to establish the congruency between the two triangles DEF and XZY.
Based on the information provided, the student is likely referring to a Congruence Theorem, which is one of the primary methods to determine if two given triangles are congruent. The main Congruence Theorems are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side).
Without any additional specification, it's impossible to definitively say which theorem supports DEF - XZY. The student would need to provide specific measurements related to the triangles DEF and XZY, such as the lengths of the sides or the measures of the angles, to determine which Congruence Theorem applies.
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what condition must be true for 2 nonintersecting lines?
-they have different slopes
-they have the same slope
-they have different y-intercepts
-they have the same y-intercepts
Answer:
they have the same slope.
The diameter of a circle measures 17 mm. What is the measure of its radius ?
Answer:
the radius is 8.5 mm
Find the sum. Enter your answer in lowest terms in the box below as a
fraction, using the slash mark ( 7 ) for the fraction bar.
7/20
3/9
Answer here
Answer:
41/60
Step-by-step explanation:
7
20
+
3
9
Cancel the common factor of
3
and
9
.
Tap for more steps...
7
20
+
1
3
To write
7
20
as a fraction with a common denominator, multiply by
3
3
.
7
20
⋅
3
3
+
1
3
To write
1
3
as a fraction with a common denominator, multiply by
20
20
.
7
20
⋅
3
3
+
1
3
⋅
20
20
Write each expression with a common denominator of
60
, by multiplying each by an appropriate factor of
1
.
Tap for more steps...
7
⋅
3
60
+
20
60
Combine the numerators over the common denominator.
7
⋅
3
+
20
60
Simplify the numerator.
Tap for more steps...
41
60
The result can be shown in multiple forms.
Exact Form:
41
60
Decimal Form:
0.68
¯
3
The steps in solving 5b-6=24 are
A. Add 6 to both sides and divide both sides by 5
B. Add 6 to both sides and multiply both sides by 5
C. Subtract 6 from both sides then multiply both sides by 5
D. Subtract 6 from both sides then divide both sides by 5
I need the answer
Answer:
the answer is A.
Step-by-step explanation:
5b-6=24
add 6 to both sides
5b=30
divide 5 to both sides
b=6
hope this helps
(mark as brainliest)
The steps in solving 5b-6=24 are adding 6 to both sides and dividing both sides by 5, the value of b is 6.
What is the linear equation?The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable.
The given equation is;
5b-6=24
The steps are used to solve the problem given below.
Add 6 to both sides
5b-6=24
5b - 6+6 = 24 +6
5b =30
Divide both sides by 5
5b/5 = 30/5
b= 6
Hence, the steps in solving 5b-6=24 are adding 6 to both sides and dividing both sides by 5, the value of b is 6.
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A circle with a radius of 8 centimeters. Use the diagram to complete each statement. Use 3.14 for π, when necessary. The radius of the circle is cm. The circumference of the circle is about cm. The area of the circle is about cm2.
Answer: 200.96 cm area
Step-by-step explanation:
Area=3.14(r^2)
Area=3.14(64)
Area=200.96
Answer:
8
50.24
200.96
Step-by-step explanation: