Answer: 13
Step-by-step explanation: The number goes up by three each time, so it would be 13.
Answer:
The nᵗʰ term of the sequence is 3n - 2.
Step-by-step explanation:
GIVEN :↝ First-term a₁ = 1↝ Second-term a₂ = 4↝ Third-term a₃ = 7↝ Fourth term a₄ = 10TO FIND :↝ nth term of the sequence USING FORMULA :[tex]\longrightarrow{\sf{a_n = a + (n - 1)d}}[/tex]
where :
» aₙ = nth term» a = first term» n = number of terms» d = common difference SOLUTION :Here we can see that the difference between two terms is 3.
Thus, finding the nth term of the sequence by substituting all the given values in the formula :
[tex]\longrightarrow{\sf{a_n = a + (n - 1)d}}[/tex]
[tex]\longrightarrow{\sf{a_n = 1 + (n - 1)3}}[/tex]
[tex]\longrightarrow{\sf{a_n = 1 + (n \times 3 - 1 \times 3)}}[/tex]
[tex]\longrightarrow{\sf{a_n = 1 +(3n - 3)}}[/tex]
[tex]\longrightarrow{\sf{a_n = 1 +3n - 3}}[/tex]
[tex]\longrightarrow{\sf{\underline{\underline{a_n = 3n - 2}}}}[/tex]
Hence, the nth term of the sequence is 3n - 2.
—————————————————find the slope of this line
What is the standard form equation of an ellipse that has vertices (18,1) and (−10,1) and co-vertices (4,14) and (4,−12)?
Answer: [tex]\frac{(x-4)^2}{196} +\frac{(y-1)^1}{169} =1[/tex]
Step-by-step explanation:
You first need to determine if the ellipse is horizontal or vertical, which can be found by the length of the major axis.
The vertices are at (18,1) and (-10,1). The distance is 28 units. (horiz)
The co-vertices are at (4,14) and (4,-12) The distance 26 units (vert)
The major axis is horizontal, so the standard form of the ellipse is
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex] where (h,k) are the coordinates of the center.
To find the center, find the midpoint of the major axis [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]
The center is at (4,1)
Since the major axis is 2a, a would be 28 divided by 2=14 squared : 196
The minor axis is 2b, so b would e 26/2=13 squared: 169
Inserting the center and a,b values into the standard form eq:
[tex]\frac{(x-4)^2}{196} +\frac{(y-1)^1}{169} =1[/tex]
hope this helps.
Which of the following is true about horizontal asymptotes?
a.) A function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ .
b.) All horizontal asymptotes describe what happens when x gets close to 0 .
c.) All rational functions have at least one horizontal asymptote.
d.) All horizontal asymptotes describe what happens when the denominator's value gets close to 0.
A function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ is the correct statement about horizontal asymptotes. Option A
What are horizontal asymptotes?A horizontal asymptote of a graph can be defined as a horizontal line at y = b where the graph tend to approach the line as an inputs approach to infinity ( ∞ or –∞).
A slant asymptote of a graph is known as a slanted line y = mx + b where the graph approaches the line as the inputs approach the positive infinity ∞ or to the infinity –∞.
Thus, a function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ is the correct statement about horizontal asymptotes. Option A
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To what power must 10 be raised to give 10
The answer is 1
10¹ = 10
i hope it was helpful
Triangle PQR is rotated, translated, and dilated to obtain triangle P'Q'R' as shown. An Image of triangle PQR and PQR prime are displayed. The Triangle PQR intersects P at (minus 2, 0.5), R at (minus 2, minus 2.5) and Q at (0, minus 1.5). Similarly P, R, Q prime at (1.5,minus 1.5), (1.5,3), and (minus 1.5,1.5). Which statement about the two figures is correct? A. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. B. The two figures are similar because each angle measure of the image is times the corresponding angle measure of the preimage and all the pairs of corresponding sides are congruent. C. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent. D. The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.
The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.
How to determine the true statements?The transformations are given as:
RotationTranslationDilationRotation and translation would preserve the lengths and the angles of the triangles. Because they are rigid transformations.
Dilation would only preserve the angle of the triangles. Because it is a nonrigid transformation.
The above means that the angles of triangle PQR and triangle P'Q'R' are congruent
Hence, the true statement is (d)
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How to solve for X in the triangle
Answer:
22.6
Step-by-step explanation:
a^2+b^2=c^2
8^2+b^2=24^2
b^2=512
b=22.6
Answer:
[tex]x = 16\sqrt{2}[/tex]
Step-by-step explanation:
we are given a right triangle.
then
In order to determine x we need to use
the Pythagorean theorem:
[tex]x^{2}+8^{2}=24^{2}[/tex]
⇔ x² + 64 = 576
⇔ x² = 576 - 64
⇔ x² = 512
⇔ x² = 2⁹
⇔ x² = 2 × 2⁸
[tex]\Longleftrightarrow x=\sqrt{2\times 2^{8}} =\sqrt{2\times \left( 2^{4}\right)^{2} }[/tex]
[tex]\Longleftrightarrow x= \sqrt{\left( 16\right)^{2} } \times \sqrt{2[/tex]
[tex]\Longleftrightarrow x = 16\sqrt{2}[/tex]
You are building a ramp for your grandparent’s house. The ramp will replace the steps that go to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the front door. How long will the ramp need to be?
Answer:
10.4403 or the square root of 109
Step-by-step explanation:
We do this by finding the height (3) and squaring it then the base (10) and squaring that, this sets up the Pythagorean theorem which is A^2+B^2=C^2 then you square C to find it's value
Select all the correct answers.
Exponential function fis represented by the table.
2
X
0
0
-12
B
-4
Function gis represented by the equation.
9 (2) = -12 (3)
Which statements are true about the two functions?
0
3
2
4
3
Both functions are increasing on all intervals of x.
Both functions approach the same value as x approaches ...
The functions have the same x-intercept.
Both functions approach - as x approaches -...
The functions have the same y-intercept.
The true statements are
(d) they have the same y-intercept(e) they approach negative infinity as x approaches negative infinityHow to determine true statements?The function g(x) is given as:
[tex]g(x) = -12(\frac 13)^x[/tex]
Set x = 0, to determine the y-intercept
[tex]g(0) = -12(\frac 13)^0[/tex]
g(0) = -12
From the table, we y-intercept of f(x) is
f(0) = -12
This means that they have the same y-intercept
Because the functions have negative initial values, they would approach negative infinity as x approaches negative infinity
Hence, the true statements are (d) and (e)
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A square lawn has area 98 ft². A sprinkler placed at the center of the lawn sprays water in a circular pattern as
shown in the figure. What is the radius of the circle?
The radius of the circle exists approximately 4.95 feet.
How to estimate the radius of the circle?Given the area of the square as A = 98 ft²
The side length of the square choice is equivalent to the diameter of the circle.
First, we must obtain the length of the square.
Area of a square [tex]= L^2[/tex]
98 = L²
L = √98
L = 9.89 ft
Thus the diameter of the circle exists at 9.89 ft
radius = diameter/2
radius = 9.89/2
radius ≈ 4.95 feet
Therefore the radius of the circle exists approximately 4.95 feet.
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An equestrian club orders magazine subscriptions for new members.
Last year they had 32 new members and spent $624 on subscriptions.
Use the equation 32m = 624 to find the cost of each subscription.
Answer:
19.50
Step-by-step explanation:
32m = 624
m = 19.50
need more words
Find the indicated real nth root(s) of a.
n=3, a = - 216
Answer:
-6
Step-by-step explanation:
A suitable calculator can find this for you directly.
Odd root of a negative number-1 raised to an odd power is -1. That means an odd-index root of a negative number will be the opposite of the corresponding root of its absolute value:
∛(-216) = -∛216 = -6
__
Additional comment
Many calculators and spreadsheets do not respond well to requests for roots of negative numbers. A calculator with built-in support for complex numbers is the best choice for this sort of problem.
The second attachment shows a calculator capable of finding the complex roots as well as the real one.
Adult tickets to the fall play cost $8
and student tickets cost $4. The drama class
sold 20 more adult tickets than student tickets
to the fall play. If the class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution is
Solving a system of equations we will see that they sold 80 adult tickets.
how many adult tickets were sold?
To solve this, we need to solve a system of equations. To define said systems of equations, we first need to define the variables, we will use:
x = adult tickets sold.y = student tickets sold.They sold 20 more adult tickets than student tickets, then:
x = y + 20
And they collected a total of $880, then:
x*$8 + y*$4 = $880
The the system of equations is:
x = y + 20
x*$8 + y*$4 = $880
Isolating y on the first equation we get:
y = x - 20
Replacing that on the other equation we get:
x*$8 + (x - 20)*$4 = $880
Now let's solve that for x.
x*$12 - $80 = $880
x*$12 = $880 + $80 = $960
x = $960/$12 = 80
They sold 80 adult tickets.
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What are the exact values of a and b?
Right triangle A B C is shown with labeled sides and one labeled angle. Side A B is the hypotenuse and it is labeled 10. Side B C is the height and it is labeled a. Side C A is the base and it is labeled b. The angle opposite side B C is 30 degrees.
Answer:
a = 5b = 5√3Step-by-step explanation:
A right triangle with one acute angle measuring 30° is the 30°-60°-90° "special" triangle. The ratios of its side lengths are well known to be ...
1 : √3 : 2
Side lengthsIn the given triangle, the longest side is labeled 10, so is 5 times the measure of the longest side in the ratios given above. Multiplying those ratio values by 5, we have side lengths ...
a : b : c = 5 : 5√3 : 10
That is ...
a = 5
b = 5√3
__
Additional comment
If you want to figure the side lengths using trigonometry, you have ...
a = c·sin(30°) = 10·(1/2) = 5
b = c·cos(30°) = 10·(√3/2) = 5√3
Find a Cartesian equation for the curve.
r = 3 sec(θ)
Identify the curve.
▢ ellipse
▢ line
▢ hyperbola
▢ limaçon
▢ circle
[tex]r = 3sec( \alpha ) \\ r = \frac{3}{cos( \alpha )} [/tex]
[tex]x = rcos( \alpha ) \: \: \: \: \: \: \: cos( \alpha ) = \frac{x}{r} [/tex]
[tex]r = \frac{3}{ \frac{x}{r} } \\ r = \frac{3r}{x} \: \: \: \: \: \: x = 3 \\ line[/tex]
what is 3495 x 30595
Multiplication of 3495 by 30595 is: 106,929,525.
MultiplicationMultiplication can be defined as the way of multiplying a number by another name.
Using a calculator to multiply 3495 by 30595.
Hence:
Multiplication= 3495×30595
Multiplication= 106,929,525
Therefore Multiplication of 3495 by 30595 is: 106,929,525.
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Which mixed number is equivalent to the improper fraction 42/5?
4 2/5
7 4/5
8 2/5
9 3/5
40 points if answer is right
Answer:
8 2/5
Step-by-step explanation:
42/5
to find the improper fraction, divide the numerator by the denominator
and then find the remainder
42 / 5 = 8 ( 5*8) the remainder is 42-40 = 2
Put the remainder over the denominator
8 2/5
Hey there!
Question reads….
Which mixed number is equivalent to the improper fraction 42/5?
EQUATION:
42/5
The one that is equivalent to the fraction is:
8 2/5
Reason:
8 2/5
= 8 * 5 + 2 / 5
= 40 + 2 / 5
= 42 / 5
Therefore, your answer should be:
Option C. 8 2/5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Solve for d
d+13 = 40
Answer:
d=27
Step-by-step explanation:
d+13=40
-13 -13 Subtract 13 from both sides to leave by itself
d=27
Hope it helps:)
Please help me with this problem. Seriously desperate again !!
Answer: 17 inches by 7 inches
Step-by-step explanation:
119 = 1 x 119 & 7 x 17
7 x 17 is the more likely answer, so let's test it
7 x 2 + 3 = 17
Therefore, the dimensions are 17 by 7.
Dan & Alex measure themselves against a tree in their backyard. The tree is 80% taller than Dan and 20% taller than Alex. Which of the following statements is true?
A. Alex is 50% taller than Dan.
B. Dan is 60% taller than Alex.
C. Dan is 40% taller than Alex.
D. Alex is 40% taller than Dan.
The true statement is that Alex is 50% taller than Dan.
How to solve percentage questions?They both measured themselves against a tree in their backyard.
Therefore, the tree is 80% taller than Dan and 20% taller than Alex.
Hence,
let
Dan height = x
Tree's height = x + 0.8x
Tree's height = 1.8x
let
Alex height = y
Tree's height = y + 0.2y
Tree's height = 1.2y
Therefore, if we use Dan height as 100, the height of the tree will be 180.
Then,
180 = 1.2y
y = 150
This means Alex is 50 percent taller than Dan.
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How much would you need to deposit in an account now in order to have $4000 in the account in 15 years? Assume the account earns 4% interest compounded monthly. Round to the nearest cent
Answer:
$2500
Step-by-step explanation:
CA=p(1+MR÷1200)
4000=p(1+180×4÷1200) 15 yrs =15×12=180 month
4000=1.6p
p=4000÷1.6
p=2500
please give me brainliest
Type the correct answer In each box. Round your answers to the nearest tenth.
A ladder is placed 30 Inches from a wall. It touches the wall at a helght of 50 inches from the ground.
The angle made by the ladder with the ground is
(blank) degrees, and the ength of the ladder Is (blank)
Inches.
Answer:
Angle = 59.03 degrees
Length = 58.3 inches
Step-by-step explanation:
Find the standard deviation for the set of data. (17,26,28,9,30, 29,6,21,23}
Using it's concept, the standard deviation for the given data-set is of 8.22.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The mean for this problem is:
M = (17 + 26 + 28 + 9 + 30 + 29 + 6 + 21 + 23)/9 = 21
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(17-21)^2 + (26-21)^2 + (28-21)^2 + \cdots + (21-21)^2 + (23-21)^2}{9}} = 8.22[/tex]
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A committee of 6 members is to be selected from 8 senior and 10 junior. find how many ways can this be done if there is no restriction
Answer:
18564 ways
Step-by-step explanation:
The number of committees is equal to the number of combinations of 6 members that we can form out of 18 person :
then
This can be done in [tex]C^{6}_{18}[/tex] ways.
[tex]C^{6}_{18}=\frac{18!}{6!\left(18-6 \right)! } = 18564[/tex]
find x and the length of each segment
s
13
T
6
U
2x-18
y
4x-29
Answer:
x = 15, UV = 12, SV = 31
Step-by-step explanation:
13 + 6 + (2x - 18) = 4x - 29
2x + 1 = 4x - 29
2x = 30
x = 15
UV = 2x - 18 = 2*15 - 18 = 30 - 18 = 12
SV = 4x - 29 = 4*15 - 29 = 60 - 29 = 31
give at least five problems solving about area of a sector of a circle.
five example of arc length
fixe example or arc of a circle
See below for the examples of sectors and arcs of a circle
Area of sector of a circleThe area of a sector is calculated as:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex] ---- when the angle is in degrees
[tex]A = \frac{\theta}{2} *r^2[/tex] ---- when the angle is in radians
Take for instance, we have the following problems involving sector areas
Calculate the area of a sector where the radius of the circle is 7, and
The central angle is 30 degreesThe central angle is π/12 radThe central angle is 90 degreesThe central angle is π/4 radThe central angle is 180 degreesUsing the above formulas, the sector areas are:
1. [tex]A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83[/tex]
2. [tex]A = \frac{\pi}{12} * 7^2 = 12.83[/tex]
3. [tex]A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5[/tex]
4. [tex]A = \frac{\pi}{2} * 7^2 = 38.5[/tex]
5. [tex]A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77[/tex]
Examples of arc lengthThe length of an arc is calculated as:
[tex]L= \frac{\theta}{360} * 2\pi r[/tex] ---- when the angle is in degrees
[tex]L = r\theta[/tex] ---- when the angle is in radians
Take for instance, we have the following problems involving arc lengths
Calculate the length of an arc where the radius of the circle is 7, and
The central angle is 30 degreesThe central angle is π/12 radThe central angle is 90 degreesThe central angle is π/4 radThe central angle is 180 degreesUsing the above formulas, the arc lengths are:
1. [tex]L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7[/tex]
2. [tex]L = \frac{\pi}{12} * 7 = 3.7[/tex]
3. [tex]L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0[/tex]
4. [tex]L = \frac{\pi}{4} * 7 = 11[/tex]
5. [tex]L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22[/tex]
Examples of the arcs of a circleThe examples include:
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To convert grams to kilograms, you can use the ratio
OA. True
B. False
1,000 grams
1 kilogrami
Answer:
A. True
Step-by-step explanation:
The ratio 1000 grams=1kilogram is correct.
Pls hellp
A small bowl of candy has a piece of chocolate, cinnamon, and butterscotch candy. Over the course of a few days, the three candies were eaten. Determine the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order.
Please show work.
Using the arrangements formula, the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order is:
[tex]\frac{1}{6}[/tex].
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, there are 3 candies, hence the number of ways they can be eaten is:
[tex]A_3 = 3! = 6[/tex]
The desired order is only one, hence the probability is:
[tex]\frac{1}{6}[/tex].
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An 8ft length of 4 inch wide crown molding cost $13. How much it cost to buy 88ft of crow molding
The amount it costs to buy 88ft of crow molding is; $143.
How much does it cost to buy 88ft if crow molding?It follows from the task content that the cost for 8ft length of a specific width crown molding is; $13.
On this note, it follows that the cost of buying 88ft of the same kind of crow molding can be estimated as;
88 × ($13/8)
= $143.
Therefore, the cost of 88ft of crow molding is; $143.
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f(x) =4x2 + 8x -5 factor completely
The factors of 4x^2 +8x-5 are (2x-1) and (2x+5)
How do i convert the follwing Powers Of Ten into standard numbers?
i need help w/ this fast!
[tex]10^{7}[/tex]
[tex]10^{5}[/tex]
[tex]10^{8}[/tex]
[tex]10^{12}[/tex]
[tex]10^{6}[/tex]
The given numbers written in standard forms are
1.0 × 10⁷
1.0 × 10⁵
1.0 × 10⁸
1.0 × 10¹²
1.0 × 10⁶
respectively
Standard form of a numberFrom the question, we are to write the given numbers in standard form
To write the given numbers in standard form,
Multiply each of the numbers by 1.0
Then,
10⁷ in standard form is 1.0 × 10⁷
10⁵ in standard form is 1.0 × 10⁵
10⁸ in standard form is 1.0 × 10⁸
10¹² in standard form is 1.0 × 10¹²
10⁶ in standard form is 1.0 × 10⁶
Hence, the given numbers written in standard forms are
1.0 × 10⁷
1.0 × 10⁵
1.0 × 10⁸
1.0 × 10¹²
1.0 × 10⁶
respectively
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