A sequence is represented by the explicit formula
The 40th term of the sequence aₙ = - 24 - 3n is - 144.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, A sequence is represented by the explicit formula aₙ = - 24 - 3n.
We know, Substitution in mathematics is when we replace some specific numerical values to variables according to our wants or given in the problem.
Therefore, To find a₄₀, we'll simply replace n with 40.
So, a₄₀ = - 24 - 3(40).
a₄₀ = - 24 - 120.
a₄₀ = - 144.
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Jaime went to have a haircut that cost $40. She wanted to tip the hair stylist 20% and tax is 6.25%. How much did she spend total for the haircut?
How many triangles are there in the following figure 18 17 16 15?
There are 15 triangles in the given figure. Each of the four shapes in the figure can be divided into four triangles.
The figure contains four triangles, each with three sides. To calculate the total number of triangles in the figure, we can multiply the number of sides of each triangle by the number of triangles. Therefore, the total number of triangles in the figure is 3 x 4 = 12.
However, the figure also contains two additional triangles that are formed when three of the triangles intersect. To calculate the total number of triangles, we must add the two additional triangles to the 12 triangles we calculated earlier. Thus, the total number of triangles in the figure is 12 + 2 = 14.
Since the figure also has three more sides, it can be divided into one more triangle. Therefore, the total number of triangles in the figure is 14 + 1 = 15.
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Find the surface area of a square pyramid with side length 6 cm and slant height 7 cm.
120
Step-by-step explanation:Over all plan:This is a square pyramid so you know that all four triangular sides are congruent. This means that to solve this problem, which is asking you to find the surface area, you need to find the area of one of these triangles, and multiply that by 4. Next you need to find the area of the square and add it to the areas of the triangles.
Detailed Steps:
You know the formula to finding the area of the triangle is [tex]\frac{bh}{2}[/tex] where b is the base length and h is the height. We are given b = 6 and h = 7 in your question.Plug in the values into the formula. You get: [tex]\frac{6\cdot7}{2}[/tex]Simplify. You get: [tex]\frac{42}{2} = 21[/tex]Next Multiply this by 4 to find out the total area of all the triangular faces.21 x 4 = 84Now find the area of the square. The formula for the area of a square is [tex]s^2[/tex] where s is the given value of a side.Plug in your value, [tex]6^2=36[/tex]
36+84=120.
120 is your final answer.
hope this helped
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is y = x proportional
Answer:
yes
Step-by-step explanation:
What is the value of x if the points A 4 3 and B x 5 are on the circle with Centre O 2 3?
The value of x with points A ( 4, 3 ) and B ( x ,5 ) on the circle and O(2,3) as centre is equal to 2.
As given in the question,
Points A(4,3 ) and B ( x, 5 ) are on the circle.
Centre of the circle is represented by O( 2,3)
OA and OB represents the radius of the circle.
This implies
OA = OB
Using distance formula we get,
√ ( 2 - 4 )² + ( 3 - 3 )² = √ ( 2 - x )² + ( 3 - 5 )²
⇒ √ 4 + 0 = √ 4 - 4x + x² + 4
⇒4 = 4 - 4x + x² + 4
⇒4 - 4x + x² = 0
⇒ ( x - 2 )² = 0
⇒ x - 2 = 0
⇒ x = 2
Therefore, the value of x for the given point of the circle is equal to 2.
The above question is incomplete , the complete question is :
What is the value of x , if the points A(4, 3) & B(x, 5) are on the circles with Centre O(2, 3), find the value of x.
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You fill a 13 1/2 gallon tub 1/9 full of water. How many gallons of water are in the tub?
Answer:
2
Step-by-step explanation:
The average weekly salary of two employees is $5350. One makes $250 more than the other. Find their salaries.
One employee makes $
and the other makes $?
Answer:
g
Step-by-step explanation:
g
What does Y=3x + 15 look like on a graph
Answer:
Step-by-step explanation:
y = 3x + 15 represents a straight line whose y-intercept is (0, 15) and which has the steep positive slope m = 3.
Answer:
it looks like that
Step-by-step explanation:
1. Choose your answer inside the box.
vertex
face
net
solid figures
sphere
cone
edge
rectangular prism
cube
square
pentagonal prism
pyramid
cylinder
rectangle
1. Flat parts of the solid figure.
2. The line where two faces meet.
3. The point where three edges meet.
4. Closed figure that can be folded into a closed 3-dimensional figure. It is a pattern
you can form into solid figures.
5. A polyhedron whose bases are congruent polygons and whose lateral faces are
parallelograms.
6. A polyhedron whose base is a polygon. The lateral faces are triangles
7. A solid figure with a curved surface of points that are all of the same distance from
the other
8. A solid figure with curved surfaces and one circular base
9. A solid figure with curved surfaces and that has two circular bases that are
congruent and parallel
10. A polygon with four equal sides and angles.
Answer:
I AM sure u will find answers in googl
let me go check
Step-by-step explanation:
FaceEdgeVertexNetPrism PiramidSphereConeCylinder Square40% of Damien‘s marbles are blue. Damien has three marbles how many of the marbles are not blue
40% of Damien’s marbles are 6/5 or 1.2.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Damien has three marbles.
40% of Damien’s marbles are blue.
That means,
40% of 3 blue marbles.
So, using the percentage formula,
40% of 3,
= 40 x 3/100
= 120/100
= 12/10
= 6/5
= 1.2
Therefore, 1.2 marbles are blue.
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What is the sum of all the positive two-digit integers where one of the digits is three times the other
The sum of all the positive two-digit integers where one of the digits is three times the other is 630.
To arrive at this result, the numbers can be broken down into two groups. The first group consists of numbers with 3 as the first digit, and the second group consists of numbers with 3 as the second digit.
For the first group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9. This gives a sum of 3+6+9+12+15+18+21+24+27 = 135.
For the second group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9 and then reversing the digits. This gives a sum of 30+60+90+12+51+81+21+42+72 = 495.
The total sum of all the positive two-digit integers where one of the digits is three times the other is 135+495 = 630.
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Suppose Johnny applied for a job at companies A and B.
Through extensive research, Johnny determined he has a 60% chance of getting a job offer from company A, a 50%
chance of getting a job offer from company B, and a 30% chance of getting a job offer from both companies A and B.
What is the probability of Johnny not getting a job offer from either company?
The probability of Johnny not getting a job offer from either company is 0.8
Suppose Johnny applied for a job at companies A and B.
Through extensive research, Johnny determined he has a 60% chance of getting a job offer from company A,
A = 0.6
a 50% chance of getting a job offer from company B,
B = 0.5
and a 30% chance of getting a job offer from both companies A and B.
What is the probability of Johnny not getting a job offer from either company?
Suppose, probability of an event A occurring is P(A)
and that of is B IS P(B)
P(A) = 0.6
and
P(B)= 0.5
probability of either or P(AUB)=0.3
Now we need to find the probability of neither nor, which is
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∩B) = P(A) + P(B) -P(A∪B)
= 0.6 + 0.5 - 0.3
= 0.8
Now the events are mutually exclusive, so
Therefore, the probability of neither nor is 0.8
The probability of Johnny not getting a job offer from either company is 0.8
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SOMEONE PLS TELL ME IF IM RIGHT ILL MARK BRAINLIEST
Answer:
u r correct
look at the picture I sent
Answer:
Its actually 5 you were about 4 away
Find BC. AB=25 AC=25 BD=3x+4 DC=4x-5
Answer:
b
Step-by-step explanation:
Since AB = AC = 25, then the triangle is isosceles
Segment AD bisects BC at right angles , then
CD = BD, that is
4x - 5 = 3x + 4 ( subtract 3x from both sides )
x - 5 = 4 ( add 5 to both sides )
x = 9
Then
BC = 3x + 4 + 4x - 5 = 7x - 1 = 7(9) - 1 = 63 - 1 = 62
Answer:
3x+4=4x-5
3x‐(4x)=-5+-4
x=9
plug in 9 for x on both sides and add them together to find BC
each side is 31,
answer is 62.
Find the value of X.
Answer:
im not sure but I think its 8.3
What is the factor of the dilation?
The scale factor of dilation explains how the size of the figure has changed. An expansion has a scale factor of x > 1 (greater than 1).
A reduction is a scale factor that is 0 <1 (higher than 0 but less than 1).
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A dilatation that results in a reduction (imagine shrinking) or an expansion (think stretching) produces a smaller or bigger picture, respectively.
The picture is reduced if the scale factor is between 0 and 1.
The picture is an enlargement if the scale factor is larger than 1.
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The 7th term of a geometric progression is 48 the 8th term is -16 find the common ratio
Answer:
48 = 768* (r)^2
thus, r = 0.25
solving for a(7)
a(7) = 768 * (0.25)^(5)
a(7) = 0.75
Step-by-step explanation:
Answer:
r = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The common ratio r is calculated as
r = [tex]\frac{a_{8} }{a_{7} }[/tex] = [tex]\frac{-16}{48}[/tex] = - [tex]\frac{1}{3}[/tex]
what can 18 and 6 both be divided by
Answer:
6
Step-by-step explanation:
they can both be divided by 6
Answer:
they can both be divided by 6
Step-by-step explanation:
18÷6=3
6÷6=1
Find the range, mean, median and mode for the scores. Round to the nearest tenth when necessary.a.40; 75.5; 75; 75c.40; 74.5; 75; 100b.35; 75.5; 75; 75d.40; 74.5; 75; 75
6x + y = 20
x - 4y = -5
The value of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]2[/tex]
The given equations are
[tex]6x+y=20\\x-4y=-5[/tex]
We need to find the value of [tex]x[/tex] and [tex]y[/tex]
First let's take equation [tex]2[/tex] and we can simplify it
[tex]x-4y=-5\\x=-5+4y[/tex]
Now, let's substitute the value of [tex]x[/tex] in equation [tex]1[/tex], that is
[tex]6x+y=20\\6(-5+4y)+y=20[/tex]
We can open the bracket and simplify
[tex]=-30+24y+y=20\\=-30+25y=20\\=25y=20+30\\=25y=50\\=y=\frac{50}{25} \\y=2[/tex]
Now we can substitute the value of [tex]y[/tex] in equation [tex]x-4y=-5[/tex]
[tex]x-4(2)=-5\\x-8=-5\\x=-5+8\\x=3[/tex]
The complete question is find the value of [tex]x[/tex] and [tex]y[/tex] from the given equations.
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Do isosceles triangles have 3 congruent angles?
Yes, isosceles triangles have three congruent angles.
An isosceles triangle is a triangle with at least two congruent sides and two congruent angles. The two congruent sides and two congruent angles form an isosceles triangle. The two congruent angles are known as the base angles, and they are opposite to the two congruent sides. The third angle in an isosceles triangle must also be congruent to the two base angles in order for the triangle to be true. This is because the angles of a triangle must always sum up to 180 degrees. Therefore, isosceles triangles have three congruent angles. These angles are all equal in measure and have the same shape. The angles of each isosceles triangle can be different from other isosceles triangles, but the angles are still congruent to each other. Therefore, isosceles triangles have three congruent angles.
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help me on this one bro I hate math
The initial amount of the investment is $800, the investment grows at the rate of 10% each year, and the value of the investment after 12 years is $1760.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates from the graph.
(0, 800), (1, 880), (2, 968)
x-coordinate is the number of years and the y-coordinate denotes the Value.
Now,
The initial amount of the investment is when x = 0.
= 800
Now,
Rate of change of the value each year.
=(880 - 800) / (1 - 0)
= $80
Rate of percentage.
= 80/800 x 100
= 10%
Now,
The value of the investment after 12 years.
= 800 + 12 x 80
= 800 + 960
= $1760
Thus,
The initial amount of the investment is $800.
The investment grows at the rate of 10% each year.
The value of the investment after 12 years is $1760.
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The total number of laps anitia swims, d, is proportional to the total timethat she swims, t, at constant pace, r. Which of the following equations best represents this situation.?
Tiles with the numbers 1 through 9 are placed in a bag. What is the probability of choosing an even number that is greater than or equal to 4?
have anyone figured it out yet? pleaseee i need answer
The probability of choosing an even number that is greater than or equal to 4 is 0.3333 or 33.33%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Tiles with the numbers 1 through 9 are placed in a bag.
The total outcomes will be
Total outcome = 9 {1, 2, 3, 4, 5, 6, 7, 8, 9}
The probability of choosing an even number that is greater than or equal to 4 will be
Favorable event = 3 {4, 6, 8}
Then the probability will be
[tex]\rm P = \dfrac{3}{9}\\\\P = 0.3333\\\\P = 33.33 \%[/tex]
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1. Find the value of the expressions using the correct order of operations.
a. -8 +5 (-3))
b. 5. (
29)
- 8+ -15 = -23
c. -57-4-3
0
d. 4+ (-5). 5-6
e. 3.-5. (-5)
f. (-5 + 4) 8
-8
21
8.
P: -64.-16 -
2
-5
i. -8
4
2. Find the value of the expressions when x = -2 and y - 5.
a. x(y + 1) -2 (5+1)
b. xy + 1
c. -2(x + y)
Can somebody help me with this question?
Answer:
answer is 6 btw does ~ means congruent
A museum has scale models representing different time periods in history. A scale in which one inch in the model represents two feet is used to construct the models. The museum's sculptor wants to build a model of an 18-foot-tall tree for one of the exhibits. How tall should she make the model of the tree?
Answer:
9 inStep-by-step explanation:
Use ratios:
1 in ⇔ 2 ftx in ⇔ 18 ftSolve by cross-multiplication:
1/2 = x/ 182x = 18x = 9 inCan you help me with this
a) The ordered pair so that the set still remains the function is (-5, 17)
b) The ordered pair so that the set does not remain the function is (-26, 15).
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
A Relation is said to be a function if the input value or the x- value is unique and have their corresponding output.
But if the input value repeats then it may no longer be a function.
First, Add a ordered pair so that the set still remains the function as
(-5, 17)
and, Add a ordered pair so that the set does not remain the function as
(-26, 15).
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50PTS 50PTS don’t explain just answer.
Answer:
[tex] \sf \: x = 7[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of x.
Forming the equation,
→ 2x + 5 = 3x - 2
Then the value of x will be,
→ 2x + 5 = 3x - 2
→ 2x - 3x = -2 - 5
→ -x = -7
→ [ x = 7 ]
Hence, the value of x is 7.