The second and fifth term for the given sequence are 6 and 48 respectively and a₆ > 50.
What is an inequality expression?An inequality expression refers to the relation between an algebraic expression to some known value that contains inequality sign. Unlike an equation it can have a range of values inside an interval.
The given problem can be solved as,
(a) The nth term of the sequence is given as aₙ = 3n²/2
Then, substitute n = 2 to get second term as below,
a₂ = (3 × 2²)/2 = 6
(b) The fifth term is obtained as,
a₅ = (3 × 2⁵)/2 = 48.
(c) The inequality expression for the given case can be written as,
3n²/2 > 50
⇒ 3n² > 100
⇒ n² > 33.33
This is possible only for n = 6.
Hence, the second and fifth terms are 6 and 48 respectively. And, the 6th term will be the first to be greater than 50.
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Evaluate the expression for
m = -3.
-4 |5+m |
Answer: the correct answer is -8
Step-by-step explanation:
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
What is the first step in evaluating an expression?The first step in evaluating an expression is to substitute the given value of a variable into the expression. Then you can finish evaluating the expression using arithmetic.
What is an example of evaluating expressions?A variable is a letter, for example, x, y, or z, that represents an unspecified number. To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.
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Please help its not working
Answer:
[tex]33\%[/tex]
Step-by-step explanation:
To work out the percentage of the circle shaded blue, we first must work out the area of the whole circle.
Area of the whole circle = [tex]\pi r^2[/tex]
[tex]r=4+3+3\\\pi * (4+3+3)^2=\pi*10^2=100\pi[/tex]
Now we need to work out the area of the blue 2d torus, by finding out the area of the blue circle, then subtracting the area of the innermost white circle.
Blue shaded area = [tex]\pi(r_{0}{^2}-r_{1}{^2})[/tex]
[tex]r_0=4+3\\r_1 = 4\\\pi ((4+3)^2-(4)^2)= \pi (7^2-4^2)=33 \pi[/tex]
Now we have the total areas of each, we can work out the fraction of blue to non blue by dividing the blue area by the total area, and then working out the percentage by multiplying by 100.
[tex]\frac{33\pi}{100\pi}*100=\frac{33\pi}{\pi}=33\%[/tex]
Jaylen and Michael are making a pizza with a 16 inch diameter. They want to put three cheese blend on 5 of the 45° slices (including the crusts). Each handful of cheese covers 21 square inches, Calculate the area of the pizza slices that they want to put cheese on.
Answer:
125.66 in2
Step-by-step explanation:
The area of the pizza is given by the formula:
Area = pi * radius^2
The radius of the pizza is half the diameter, so radius = 16/2 = 8 inches
Then, the total area is:
Area = pi * 8^2 = 64pi in2
They will put cheese in 5 of the 45° slices, so the total angle covered is 5 * 45° = 225°.
If the full area of the pizza is 360°, we can find the area covered by cheese using a rule of three:
360° -> 64pi in2
225° -> x in2
x = (225/360) * 64pi
x = 125.66 in2
The triangles are congruent by SSS and HL. Triangles R S T and V W X are shown. Triangle R S T can be rotated about point S and then shifted down and to the left to form triangle V W X. Which transformation(s) can be used to map △RST onto △VWX? reflection only translation only reflection, then translation rotation, then translation
Answer:
rotation then translation
Based on the information given regarding the triangle, the transformations that can be used to map △RST onto △VWX is D. rotation, then translation.
What is a congruent triangle?It should be noted that a congruent triangle simply means when two triangles have the same sides and the same angles.
Since Triangle RST can be rotated about point S and then shifted down and to the left to form triangle VWX, the transformations that can be used to map △RST onto △VWX is rotation, then translation.
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Maths Help Asap
The question is given below
Answer only if sure and give explanation
Answer:
40 pages
Step-by-step explanation:
240/12 = 20 = pages read in 1 hour
20 x 2 = 40 = pages read in 2 hours
When multiplying two negative integers, what is the sign of the product?
positive
negative
zero
one
Mark this and return
Save and Exit
y Next
Sul
Answer:
positive
Step-by-step explanation:
negative and negative = positive
positive and positive = positive
positive and negative = negative
negative and positive = negative
hope u got what u needed
Answer:
The correct answer is positive
Step-by-step explanation:
Negitive x Negitive = Positive
Positive x Positive = Positive
Negitive x Postive = Negitive
Positive x Negitive = Negitive
This should help you for next time you have a question like this.
I hope this helps.
Someone tell me answer!!!
Answer:
X=70
Step-by-step explanation:
180-120=60
60 + 50=110
180-110=70
Answer:70°
Step-by-step explanation:
missing angle- 180°-120°= 60
a total triangle= 180°
so x = 180-(50+60)
=180-110
x=70°
There are 130 people in a sport centre.
76 people use the gym.
60 people use the swimming pool.
32 people use the track.
23 people use the gym and the pool.
8 people use the pool and the track.
20 people use the gym and the track.
6 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
Answer:
7/130Step-by-step explanation:
Using set notation to answer the question. let:
n(U) be the total people in a sport centre =130
n(G) be number of people that use the gym. = 76
n(P) be number of people that use the swimming pool. = 60
n(T) be number of people that use the track = 32
n(G∩P) be number of people that uses the gym and the pool = 23
n(P∩T) be number of people that uses the pool and the track = 8
n(G∩T) be number of people that uses the gym and the track = 320
n(G∩P∩T) be number of people that uses all three facilities = 6
Using the relationship below;
n(U)= n(GUPUT)+n(GUPUT)'
where n(GUPUT)' is the number of people that doesn't use any facility.
Before we can get that, we need to know n(GUPUT) using the formula;
n(GUPUT) = n(G) + n(P)+n(T)-n(G∩P)-n(P∩T)-n(G∩T)+n(G∩P∩T)
n(GUPUT) = 76+60+32-23-8-20+6
n(GUPUT) = 123
n(GUPUT)' = n(U)- n(GUPUT)
n(GUPUT)' = 130 - 123
n(GUPUT)' = 7
This means that 7 person doesn't use any facility.
Probability that a person selected at random doesn't use any facility = n(GUPUT)' /n(U) = 7/130
Workers in an office of 90 staff where asked there favourite type of takeaway. The results are summarised in the table. Work out the size of each angle to draw a pie chart.
Step-by-step explanation:
just draw out according to a graph chart or pie chart
the one who answered it first will be marked brainliest and with correct sollutio and working
Answer:
2.375m
Step-by-step explanation:
Length of box = 8 m
Width of box = 3 m
Height of box = 2.4 m
It initially contains water of volume 37 m³. 20 m³ of water is added to it.
So, New volume = 37+20 = 57 cubic m
Volume of water = Length \times Width \times Height = 8 \times 3 \times Height
So, 8 x 3 x height = 57
Height = 57/ 8x3
Height =2.375 m
hence the depth of the water in the through after 20 m³ of water is added to it is 2.375m
PLEASE HELP ANSWER WILL GET BRAINLIEST!! What is the value of x in the equation
Answer:
[tex]-3\frac{2}{3}[/tex]
Step-by-step explanation:
A store displays the sign shown. You want to buy a belt that costs &8 and a pair of jeans. You have $18. Write and solve an inequality to find the original prices you can afford
Answer: P ≤ $10
Step-by-step explanation:
You have $18
You want to buy a belt that cost $8, so the money that you have tou buy a pair of jeans is $18 - $8 = $10
This means that we the range of prices P that you can afford is:
P ≤ $10
This means that the price of the jeans can be, at maximum, 10 dollars.
FAST ANSWER PLEASE THANKS
Answer:
Option (1).
Step-by-step explanation:
Given functions are f(x) = [tex]\frac{1}{x}[/tex] and g(x) = x - 2
(fog)(x) = f[g(x)]
By substituting g(x) in place of x in the function f(x),
f[g(x)] = [tex]\frac{1}{(x-2)}[/tex]
Graph of the function f[g(x)] will have,
Vertical asymptotes : x = 2
Horizontal asymptotes : y = 0
And no oblique asymptotes.
Out of four options graph number (1) matches the given characteristics of the function.
Therefore, graph (1) will be the answer.
An inspector checks 98 cell phones and finds 2 of them not working. If a company
has 850 of the phones, how many are likely to not be working?
Answer:
17
Step-by-step explanation:
Use ratio method
98:2
850:x
so, x = (850 x 2) divided by 98 = 17.3469388
Round it to nearest whole number = 17
Find the surface area of the polyhedra
pls!! show how you got the surface area
Answer:
The surface area of the lower rectangle is 20cm x 4cm= 80 square cm
the surface area of the two triangles is 12 square centimetres
the surface area of one of the top rectangular faces is 20×5= 100 square centimetres
the surface area of the other is 20×3= 60 square centimetres
80+12+60+100=252 square centimetres is the surface area of the polyhydron
Are you an expert? then answer this.
Answer:
a) n = 3
b) every 9 cm represents 175,000 km
Step-by-step explanation:
a) 20 min : 1 hour
Let's convert it into same units
⇒20 min : 60 min
÷ 20 ÷ 20
⇒ 1 : 3
So n = 3
b) 1 : 25,000
Which means every 1 cm on the map represents 25,000 km
And,
1 cm = 25,000 km
So,
9 cm = 25,000 × 9
9 cm = 175,000 km
So every 9 cm represents 175,000 km
Answer:
a) 3
b) 2.25 km
Step-by-step explanation:
a) 20 min : 1 hour = 1 : n
20 min : 60 min= 1 :3
n=3
b) 1: 25000 scale
1 mm : 25000 mm
9 cm = 90 mm
90 mm : 90*25000 mm
9 cm : 2250000 mm
9 cm : 2.25 km
what is the discriminant of the equation 2x^2-4x+1=0
Answer:
8 i think
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
2x^2-4x+1=0
This is written in the form
ax^2 +bx+c =0
a=2 b = -4 c =1
The discriminant is
b^2 -4ac
(-4)^2 -4(2)(1)
16 - 8
8
The discriminant is 8
Write 150 as a product of primes. Use index notation where appropriate.
Answer:
150=2x5x5x3, or 150=2x5^2x3
Step-by-step explanation:
150=50x3
50=5x10
10=2x5
150=2x5x5x3
Find the slope of the line that passes through (4, 18) and (7, 10).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
The right answer is -8/3
please see the attached picture for full solution
hope it helps
Answer:
[tex]slope = \frac{8}{ - 3} [/tex]
Step-by-step explanation:
[tex](4 \: \: \: ,\: \: 18) = > (x1 \: \: ,\: \: y1) \\ (7 \: , \: \: \: \: \: 10) = > (x2 \: \: \: ,\: \: y2)[/tex]
[tex]slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{18 - 10}{4 - 7} \\ = \frac{8}{ - 3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
what is the scale factor of polygon qrstu to poligon defgh
Answer:
A
Step-by-step explanation:
Since the two polygons are similar, corresponding sides will have a constant ratio. So, the ratio between ST and FG will be the same as the scale factor between the two shapes.
[tex]\dfrac{FG}{ST}=\dfrac{15}{36}=\dfrac{5}{12}[/tex]
Therefore, the correct answer is choice A. Hope this helps!
solve a²b³-(ab)² if a=-2 and b=3
Answer:
The answer is 72.
Step-by-step explanation:
You have to put in the values of a and b into the expressions :
[tex] {a}^{2} {b}^{3} - {(ab)}^{2} [/tex]
[tex]let \: a \: = - 2 \\ let \: b = 3[/tex]
[tex] {( - 2)}^{2} \times {(3)}^{3} - {( - 2 \times 3)}^{2} [/tex]
[tex] = 4 \times 27 - { (- 6)}^{2} [/tex]
[tex] = 108 - 36[/tex]
[tex] = 72[/tex]
What’s 30x8+5 divided by 8% =
Answer:
302.5
Step-by-step explanation:
30 x 8
5/8
I hope this helps I'm like 90 percent sure this is right. There is no other answer I could think of so I hope Hope helpa
What is (n^2)(n^3)^-2?
At a clothing store, 15% of the dresses are blue. Which decimal is equivalent to 15%?
Answer:
0.15
Step-by-step explanation:
15% = 0.15
__________________________________
Solution,
15%
=15/100
=0.15
So, 0.15 decimal is equivalent to 15%
Hope this helps
Good luck on your assignment
_______________________________
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.
MY LAST 3 QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
1. If the conditional statement “If my dog gets out, he will run away,” is true, which other statement must also be true?
A) If my dog did not run away, he did not get out.
B) If my dog did not get out, he did not run away.
C) None must be true.
2. If a conditional statement is written in the form “If p then q”, how is the converse of the conditional statement is written?
A) If not q then p
B) If not p then not q
C) If q then p
3. The statement “If I do not ask permission, I will get in trouble” is the contrapositive of the conditional statement
A) If I do not get in trouble, I asked permission.
B) If I get in trouble, I did not ask permission.
C) If I get in trouble, I asked permission.
D) If I ask permission, I will not get in trouble.
Answer:
The answer to 1 is: A
The answer to 2 is: C
The answer to 3 is: A
Step-by-step explanation:
A conditional statement is one that has the form "If P then Q," where P and Q are sentences. The correct option for the first, second, and third questions are A, C, and A respectively.
What are Conditional statements?A conditional statement is one that has the form "If P then Q," where P and Q are sentences. P is referred to as the hypothesis in this conditional statement, while Q is referred to as the conclusion. "If P then Q" implies that Q must be true whenever P is true.
1.) If the conditional statement “If my dog gets out, he will run away,” is true, then the statement "If my dog did not run away, he did not get out." must also be true.
Hence, the correct option is A.
2.) If a conditional statement is written in the form “If p then q”, then the converse of the conditional statement is written as "If q then p".
Hence, the correct option is C.
3.) The statement “If I do not ask permission, I will get in trouble” is the contrapositive of the conditional statement "If I do not get in trouble, I asked permission."
Hence, the correct option is A.
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It’s the math question please help
Answer:
-22, 4, -27, 2
Step-by-step explanation:
-10 + (-12) = -10 - 12 = -22
-3 + 7 = 4
-11 - 16 = -27
-13 - (-15) = -13 + 15 = 2
Answer:
-22 4 -27 2
Step-by-step explanation:
-10 + (-12) = -22
-3 + 7 = 4
-11 - 16 = -27
-13 -(-15) = 2
Which of the following is most likely the next step in the series?
A.
B.
C.
D.
Answer: A. Triangle
Step-by-step explanation: Its A because its in order of number of sides starting from the left side. It goes 6 sides, 5 sides, 4 sides, then next should be 3 sides.
Answer:
A
I think A is the correct answer and this can only be true if we are following the sequence because the first shape has 6 sides followed by 5 and 4 so probably 3 should be the next.
SOLVE FOR 20 pls hurry
Answer:
4(-2) + 8(4) / 7 - (-2)²
-8 + 32 / 7 - 4
24 / 3
= 8
Step-by-step explanation:
In a cookie mix, we find oatmeal cookies,
raisin cookies, and butter cookies in a ratio
of 5:1:3. If a bag of the mix contains 60
butter cookies, how many cookies in total
are there?
Answer:
100 : 20 : 60 Making the total number of cookies 180
Step-by-step explanation:
Looking at the basic information given we know:
If there are 5 oatmeal cookies, there will be: 1 raisin cookie and 3 butter cookies. This is a base value.
So, we have equations like this:
[tex]r = 1/3b[/tex] and [tex]o = 5/3b[/tex]
So, if we plug in 60 for butter cookies we will have something like this:
[tex]o : r : 60[/tex] or [tex](5/3b) : (1/3b) : b[/tex] where b=60
Solving:
[tex](5/3b) : (1/3b) : b[/tex]
[tex](5/3b) : (1/3b) : 60\\100 : 20 : 60[/tex]
Then add the amounts of together to get 180.
I hope this helps! It's a bit difficult to explain, where I do most of this in my head, but I hope this will be able to provide some understanding to you.
