Answer:
Recursive formula is: [tex]a_1=-1 ; \ \ a_n=a_{n-1}+7[/tex]
Explicit formula is: [tex]a_n=7n-8[/tex]
Step-by-step explanation:
We need to find recursive formula and explicit formula for arithmetic sequence -1,6,13,20,27
In the given sequence First term a₁= -1
Common difference d = 7
Finding Recursive Formula
The recursive formula is of type:[tex]a_1= First \ term[/tex] and [tex]a_n=a_{n-1}+d[/tex]
Since the First term a₁ is -1 and common difference d is 7 so, the recursive formula for given arithmetic sequence will be:
[tex]a_1=-1 ; \ \ a_n=a_{n-1}+7[/tex]
Finding Explicit Formula
The explicit formula is of type: [tex]a_n=a_1+(n-1)d[/tex]
We have
First term a₁= -1
Common difference d = 7
So, explicit formula will be:
[tex]a_n=-1+(n-1)7\\a_n=-1+7n-7\\a_n=7n-8[/tex]
So, explicit formula is: [tex]a_n=7n-8[/tex]
△ABC is a right triangle with right angle C. Side AC¯¯¯¯¯¯¯¯ is 6 units longer than side BC¯¯¯¯¯¯¯¯. If the hypotenuse has length 217−−√ units, find the length of AC¯¯¯¯¯¯¯¯.
Given:
In △ABC is a right angle triangle.
AC is 6 units longer than side BC.
[tex]Hypotenuse=2\sqrt{17}[/tex]
To find:
The length of AC.
Solution:
Let the length of BC be x.
So, Length of AC = x+6
According to the Pythagoras theorem, in a right angle triangle
[tex]Hypotenuse^2=Base^2+Perpendicualar^2[/tex]
△ABC is a right angle triangle and AC is hypotenuse, so
[tex](2\sqrt{17})^2=(x)^2+(x+6)^2[/tex]
[tex]68=x^2+x^2+12x+36[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
Subtract 68 from both sides.
[tex]0=2x^2+12x+36-68[/tex]
[tex]0=2x^2+12x-32[/tex]
[tex]0=2(x^2+6x-16)[/tex]
Divide both sides by 2.
[tex]x^2+6x-16=0[/tex]
Splitting the middle term, we get
[tex]x^2+8x-2x-16=0[/tex]
[tex]x(x+8)-2(x+8)=0[/tex]
[tex](x+8)(x-2)=0[/tex]
[tex]x=-8,2[/tex]
Side cannot be negative, so x=2 only.
Now,
[tex]AC=x+6[/tex]
[tex]AC=2+6[/tex]
[tex]AC=8[/tex]
Therefore, the length of AC is 8 units.
HURRY PLEASE!! I NEED TO TURN THIS IN TODAY!!
I WILL GIVE YOU BRAINLIEST!
i need the equation you solved it with too.
Answer:
I cant tell you the answer but multiply 3x1 then 137 by 2 then add the 3x1 and the 137 x 2 all together and you get the answer
Identify the like terms in the expression below: 6w2+11w+8w2−15w
Answer:
14w 2 − 4w
Step-by-step explanation:
Which equation represents Which equation represents the vertical line passing through (1,-9)?
A.
x = -9
B.
x= 1
C.
y=-9
D. y=1
Equation x = 1 represents the vertical line passing through (1 ,-9).
What is equation of line ?" Equation of a line is defined as an algebraic expression which is represented by linear equation in two variables with highest degree 1. Minimum two coordinates required to draw a line."
According to the question,
Coordinates in the plane represented by (x, y)
We have
Line passing through the point = (1 ,-9)
x = 1 for different values of y represents a line perpendicular to x-axis.
Therefore,
Vertical line passing through (1, -9) is equals x = 1.
Hence, Option(B) is the correct answer.
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1. Determine whether line KM and line ST are Parallel, Pers
Line KM has a slope of 5/8
Line ST has a slope of -8/5
Answer:
Since the slope of KM and ST are different, they are not parallel
Step-by-step explanation:
Slope of line KM = [tex]\frac{5}{8}[/tex]
Slope of ST = [tex]-\frac{8}{5}[/tex]
Determine whether the lines are perpendicular;
Solution:
We can use the slope of a line to determine whether they are perpendicular or parallel to one another.
Parallel lines do not meet one another
Perpendicular lines cross one another at an angle of 90°
Two lines are parallel if their slopes are the same;
Since the slope of KM and ST are different, they are not parallel
The manufacturer of a certain brand of lightbulbs claims that the variance of the lives of these bulbs is 4100 square hours. A consumer agency took a random sample of 26 such bulbs and tested them. The variance of the lives of these bulbs was found to be 5900 square hours. Assume that the lives of all such bulbs are (approximately) normally distributed. Test at the 20% significance level whether the variance of such bulbs is different from 4100 square hours. a)The value of the test statistic x is 15.743; we fail to reject the null hypothesis. b)The value of the test statistic x is 32.859; we fail to reject the null hypothesis. c)The value of the test statistic y is 32.859; we reject the null hypothesis. d)The value of the test statistic is 35.976; we fail to reject the null hypothesis. e)The value of the test statistic is 15.743; we reject the null hypothesis. f)The value of the test statistic x is 35.976; we reject the null hypothesis.
Answer:
124345
Step-by-step explanation:
HONORS INLY:
5. Find the measurements of the angles
marked with x, y and z.
(Isosceles triangle theorem
Answer:
x = 55°
y = 70°
z = 125°
Step-by-step explanation:
Based on the Isosceles triangle theorem, since two sides of the triangle are congruent, therefore, the angles opposite to each of the equal sides are congruent.
Thus:
x = 180° - 125° (angles on a straight line/linear pair)
x = 55°
If x = 55°, the other base angle will also be 55°.
Therefore,
y = 180° - (55° + 55°) (sum of ∆)
y = 70°.
z = x + y (exterior angle of a ∆ theorem)
z = 55° + 70° (substitution)
z = 125°
A football team loses 2 yards every 5 minutes. How many yards did the team lose after 15 minutes?
Suppose that the amount of snowfall per storm in Lincoln is normally distributed with µ = 4.2 inches and standard deviation µ = 2.3 inches (totally made up data). If the mayor decides that only the top 5% of storms should have school cancelled, what is the cutoff snowfall for school to be cancelled?
Answer:
7.9835
Step-by-step explanation:
Given that :
Mean snowfall per storm (µ) = 4.2 inches standard deviation (s) = 2.3 inches
Only the top 5% of storm should result in school being canceled :
Cut off snowfall for school to be canceled '
P(Z ≥ 5%) ; p(Z ≥ 0.05) = 1.645
Using the z relation :
Z = (x - m) / s
1.645 = (x - 4.2) /2.3
x - 4.2 = 2.3 * 1.645
x - 4.2 = 3.7835
x = 3.7835 + 4.2
x = 7.9835
Cut off snowfall for school to be canceled 7.9835
Answer:
hopes this photo helps
Here is a list of numbers 5 -17 -3 17 -6 -17 19 -14 -20 state the median.
Answer:
the answer is -6
Step-by-step explanation:
the median is the number that is directly in the middle of a sequence of numbers
6 3/4 plus 2 1/4 divided by 7/8
Answer: 72 over 7
Step-by-step explanation: Hoped this helped you
Answer:
[tex]6 \frac{3}{4} + 2 \frac{1}{4}[/tex] × [tex]\frac{8}{7}[/tex]
Decimal Form: 9.32
Step-by-step explanation
A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be five times the amount of vinegar. How much of each ingredient is needed in order to make 15 oz of furniture polish?
Answer:
Missing Information.
Multiply 8674 x 678 is what
Answer:
5880972
hope it helps..
Father to his first biological son true or false?
Answer:
True
Step-by-step explanation:
have a great day!
PLEASE ITS EASY I FOGOT HOW TO DO IT
Answer:
x> -1
Step-by-step explanation:
Open circle means > or <
Step 1:Choose the lowest common denominator
Find the sum of 1/5 and 7/10
The expression written in equation from with common denominator is______
The sum is___
Answer:
-6/8 +5/8 and -1/8
Step-by-step explanation:
just got done doing it.
Please help its important!!
Triangle ABC in the figure above represents the area serviced by a shipping company that plans to build a distribution center at the incenter of the triangle located at point E. A circle is constructed to represent the location of the center. The diameter of the circle is 28 miles. The existing road is perpendicular to the incenter and the company is looking to build 2 more perpendicular roads but connecting the other 2 sides of the triangle. How many more miles of road will be needed?
Select one:
A. 28
B. 34
C. 43
D. 56
Answer:
A. 28
Step-by-step explanation:
A. 28
step 1.
We know that the diameter of the circle inscribed within the triangle is 28 miles, and we know that E is the incenter of triangle ABC.
step 2.
Next, we learned that the perpendicular legs from the incenter to the sides of the triangle are congruent, and we know that the radius of a circle is 1/2 of the diameter of the circle.
step 3.
Since the diameter of the circle is 28, we know the distance of segment DE is 14. Next, we know the perpendicular legs are equal to segment DE. Thus, we can solve for the amount of additional miles of road by writing 14 + 14 = 28.
Is the following relation a function?
Yes
or
No
Answer:
no
Step-by-step explanation:
Answer:
I think that it is yes but not sure
I NEED HELP ASAP PLZ!!!!
A bag is filled with small and large marbles. The ratio of small to large marbles is 1:3.
There are eight more large marbles than small marbles. How many total marbles are in the bag? [Type your answer as a number.]
Answer:
There would be four small marbles and twelve large marbles so your answer should be sixteen marbles in total
Step-by-step explanation:
I'll brainlist!!
Plant A is 18 inches tall after one week, 36 inches tall after two weeks, 56 inches tall after three weeks. Plant B is 18 inches tall after one week, 36 inches tall after two weeks, 54 inches tall after three weeks. Which situation represents a proportional relationship between the plants?
Height and number of weeks?
Answer:
There are 2 given situations:
Plant A and Plant B growing in 3 weeks. Find which plant grows proportional
Plant A
=> 1st week = 18 inches
=> 2nd week = 36 inches
=> 3rd week = 56 inches
=> 18 + 18 = 36 + 20 = 56
Thus, this is not proportional
Plant B
=> 1st week = 18 inches
=> 2nd week = 36 inches
=> 3rd week = 54 inches
=> 18 + 18 = 36 + 18 = 54 inches
thus, the growth of this plant is proportional
Helpppppp pleaseeeee
Save me from this questionnnnn
Every triangle must have an acute angle. True or false?
Answer:
This is true every triangle has to have 1 acute angle.
Step-by-step explanation:
18 divided by 4
Please help
Answer:
Step-by-step explanation: 4.5
Answer:
4.5
Step-by-step explanation:
18/4=4.5
hope this helps :3
if it did pls mark brainliest
Why is it important for mathematicians to graph functions? Select all that apply.
A. For them to determine if a function can be inverted.
B. For them to visualize the function.
C. For them to extrapolate beyond the known data.
D. For them to determine if the function can be graphed.
E. For them to determine characteristics of the function.
Answer:
e
Step-by-step explanation:
s
Use Newton's method to approximate the given number correct to eight decimal places. 4√73
Answer:34.17601498.
Step-by-step explanation:
Newton's method of approximation is used to approximate values.
The value of [tex]\mathbf{4\sqrt{73}}[/tex] is 34.17601498
Let the number be x.
So, we have:
[tex]\mathbf{x = 4\sqrt{73}}[/tex]
Square both sides
[tex]\mathbf{x^2 = 1168}[/tex]
Subtract 1168 from both sides
[tex]\mathbf{x^2 - 1168 = 0}[/tex]
Express as a function
[tex]\mathbf{f(x) = x^2 - 1168 }[/tex]
Set x1 to 73/2.
So, we have:
[tex]\mathbf{x_1 = \frac{73}{2} = 36.5}[/tex]
Where:
[tex]\mathbf{x_{n+1} = x_n- \frac{x_n^2-1168}{2x_n}}[/tex]
So, we have:
[tex]\mathbf{x_{1+1} = x_1- \frac{x_1^2-1168}{2x_1}}[/tex]
[tex]\mathbf{x_{2} = x_1- \frac{x_1^2-1168}{2x_1}}[/tex]
This gives
[tex]\mathbf{x_{2} = 36.5- \frac{36.5^2-1168}{2 \times 36.5}}[/tex]
[tex]\mathbf{x_{2} = 34.25}[/tex]
[tex]\mathbf{x_{3} = x_2- \frac{x_2^2-1168}{2x_2}}[/tex]
[tex]\mathbf{x_{3} = 34.25- \frac{34.25^2-1168}{2 \times 34.25}}[/tex]
[tex]\mathbf{x_{3} = 34.1760948905}[/tex]
[tex]\mathbf{x_{4} = x_3- \frac{x_3^2-1168}{2x_3}}[/tex]
[tex]\mathbf{x_{4} = 34.1760948905- \frac{34.1760948905^2-1168}{2\times 34.1760948905}}[/tex]
[tex]\mathbf{x_{4} = 34.1760149814}[/tex]
[tex]\mathbf{x_{5} = x_4- \frac{x_4^2-1168}{2x_4}}[/tex]
[tex]\mathbf{x_{5} = 34.1760149814- \frac{34.1760149814^2-1168}{2\times 34.1760149814}}[/tex]
[tex]\mathbf{x_{5} = 34.1760149813}[/tex]
The values of x4 and x5 are the same up till the 8th decimal place.
Hence, the value of [tex]\mathbf{4\sqrt{73}}[/tex] is 34.17601498
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y = 3x. How do you graph it???
Answer:
If you go to desmos.com, select the graphing calculator, and enter in y = 3x you should be able to see how it's graphed! Hope this helps!
Answer:
(0, 0) and (1, 3)
happy to help!
fill in the blanks thanks
Answer:
Um threre is no blanks or there is no question.
Step-by-step explanation:
help please I’m struggling badly because Im sooo bad at math
Answer:
40˚ degrees
Step-by-step explanation:
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Multiply: 1/ 3 × 2 /5 To find the product, the numerators and the denominators. The product is . Divide: 2/ 5 ÷ 3/ 5 To divide, multiply by the . The quotient is .
Multiply: 1
3
× 2
5
To find the product,
✔ multiply
the numerators and
✔ multiply
the denominators.
The product is
✔ 2/15
.
Divide: 2
5
÷ 3
5
To divide, multiply by the
✔ reciprocal
.
The quotient is
✔ 2/3
.
Edg 2020 :)))))))
The multiplication result to 2/15 and division result to 2/3.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
1/ 3 × 2 /5
Now, to multiply we have multiply numerator and denominator.
1/ 3 × 2 /5
=(1 x 2)/ ( 3 x 5)
= 2 /15
Now, 2/ 5 ÷ 3/ 5
We have to divide the fraction.
Fraction does not support division.
So,2/ 5 ÷ 3/ 5
= 2/5 x 5/3
= 2/3.
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Chloe is remodeling her living room and wants to put down new wood floors. The wood floors cost $8.50 per square foot to buy and install. If her living room has an area of 156.5 square feet, how much will the new floors cost?
Answer:
1 330,25
Step-by-step explanation:
8.50x156,6=1330,25
