Answer:
[tex]a_n=-8n-7[/tex] is the closed linear form of the given sequence.Step-by-step explanation:
Given that [tex]a_1=-15[/tex] and [tex]a_{n+1}=a_n-8[/tex]
To find the closed linear form for this given sequence :So each of the successive term of the given sequence is decreases by 8
Therefore the common difference is -8
The given sequence is a arithmetic sequence.
The general form is [tex]a_n=a_1+(n-1)d[/tex]
Substitute [tex]a_1=-15[/tex] and d=-8 in [tex]a_n=a_1+(n-1)d[/tex] we get
[tex]a_n=-15+(n-1)(-8)[/tex]
[tex]=-15-8n+8[/tex]
[tex]a_n=-8n-7[/tex]
Therefore [tex]a_n=-8n-7[/tex] is the closed linear form of the given sequence.Answer:
c) an=-7+8n
Step-by-step explanation:
i got it wrong and it told me the right answer so ill make sure you guys don't get it wrong :3
21, 28, and 36 units is a triangle
Answer:
Yes, it could be a triangle.
Step-by-step explanation:
If the Pythagorean Theorem is satisfied, then these three side lengths represent a right triangle:
21^2 + 28^2 = 36^2 => 1225 = 1296 FALSE; we don't have a right triangle here.
However, the sum 21 + 28 is greater than 36, so we could indeed construct a triangle from these 3 side lengths. It just wouldn't be a right triangle.
If a tennis ball has a diameter of 14, What is the volume of the tennis ball? Use 3.14 for pi.
Answer:
1436
Step-by-step explanation:
Write an equation in slope intercept form for the line that has a slope of 12 and passes through the point (3,20)
Answer:
y= 12x-16
Step-by-step explanation:
Given that you have a slope of 12 and a point of (3, 20), you are most obligated to using the Slope-Intercept form, or y=mx+b.
What this allows you to find is the y-intercept if your line has one. You take your point, (3,20), and you insert the values at the appropriate places. You should now have 20=12(3)+b. You will then solve for b by multiplying 12 and 3 to get 36 and subtract that from both sides of the equal sign. You should have 20-36=b. 20-36 is -16, which is your y-intercept.
Now you know all your needed values, you would write the Slope-Intercept form without the values for y and x, to represent your equation.
Since 12 is your slope, it will be 'm' and -16 will be 'b'.
You will end with y = 12x - 16.
Given:
Line passing through,
[tex](x_1,y_1) = (3, 20)[/tex]Slope,
[tex]m = 12[/tex]The equation will be:
→ [tex]y - y_1 = m(x-x_1)[/tex]
By substituting the values,
→ [tex]y-20=12(x-3)[/tex]
→ [tex]y-20=12x-36[/tex]
[tex]y = 12x-16[/tex]
Thus the above answer is right.
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Please help me with this problem, The answer is 192 but how do you solve it??
Answer:
192
Step-by-step explanation:
You can form a rectangle from sides 15 and 3, another rectangle with dimensions 10 and 9, another rectangle with dimensions 6 and 5, and a triangle with sides 9 and 6 (all formed by extending lines inside the figure, don't want to go into detail). Add all the areas and the answer would be 192:
15*3 =45
10*9=90
6*5=30
0.5*9*6=27;
45 + 90 +30 + 27 = 192 units squared
What is 8.40 in word form
Answer:
Step-by-step explanation:
8.40 ×10°
Answer:
eight and four tenths
Step-by-step explanation:
Solve the equation:
12/x = 3/2
Hence the value of x is 8
Answer:
8
Step-by-step explanation:
12/x = 3/2
(x)(12/x)=3/2x
12=3/2x
(12)(2/3)=x
8=x
Find x and y on a 30 60 90 triangle number 9
Answer:
x=12, y=[tex]12 \sqrt{3} [/tex]
Step-by-step explanation:
Please see attached picture for full solution.
sinθ= opp/hyp
cosθ= adj/hyp
=
Write an equation in slope-intercept form for the line with y-intercept 5 and slope -1/4
Equation is y = -1/4x + 5
Step-by-step explanation:
Step 1: Given slope, m = -1/4 and y-intercept, b = 5. Write the equation in slope intercept form which is y = mx + b⇒ y = -1/4x + 5
Angie has saved $2.50 of her allowance every week for the past 12 weeks. If she continues saving the same amount each week, how many more weeks will it take her to save a total of $50
Answer:
20
Step-by-step explanation:
$2.50 x 12 equals 30
2.50 x 20 equals 50
x10= 2.50 x 20 =$50
Helppppppppppppppppppppp
Answer:
see below
Step-by-step explanation:
Use the distributive property:
(y^2 +3y +7)(8y^2 +y +1)
= y^2(8y^2 +y +1) +3y(8y^2 +y +1) +7(8y^2 +y +1)
= 8y^4 +y^3 +y^2 + 24y^3 +3y^2 +3y + 56y^2 +7y +7
= 8y^4 +y^3(1 +24) +y^2(1 +3 +56) +y(3 +7) +7
= 8y^4 +25y^3 +60y^2 +10y +7 . . . . . matches the last choice
HELP ME PLEASE BE QUICK
Answer:
Radius is 5/2 or 2.5 inches
Step-by-step explanation:
C = 2πr
5π/2π = 2πr/2π
5/2 = r
Answer: Radius is 5/2 or 2.5 inches
Find the square root of 60 accurate to one decimal place (and two decimal places)
The specific answer is
7.74596669241
Sammy opens a bag of
skittles and counts all the
green skittles. There are
13 green skittles in a bag
with 65 skittles. What is the
ratio of green to total
skittles?
Final answer:
To find the ratio of green to total skittles, divide the number of green skittles by the total number of skittles and simplify the fraction. The ratio of green to total skittles is 1:5.
Explanation:
To find the ratio of green to total skittles, we need to divide the number of green skittles by the total number of skittles and simplify the fraction.
Ratio = Number of green skittles / Total number of skittles
Ratio = 13 / 65
Since 13 and 65 are both divisible by 13, we can simplify the fraction to:
Ratio = 1 / 5
Therefore, the ratio of green to total skittles is 1:5.
Which number is most likely an irrational number?
Kris is staining 30 wooden rectangular fence pieces. The fence pieces are different sizes, and Kris wants
to determine the approximate number of square feet of paint she will need. She decides to take a sample
of 4 fence pieces and calculate the mean of the areas instead of calculating the area of each fence piece.
Which is a true statement about this problem?
A. The sample size is 30,
B. The population is the 4 fence pieces
C. The mean area of the 4 fence pieces is a parameter
D. The mean area of the 4 fence pieces multiplied by 30 would be similar to the total area.
Answer:
D
Step-by-step explanation:
A line that comes closest to data in the coordinate plane is called the line of
That would be the line of best fit.
The line of best fit is a straight line that best represents the data on a scatter plot.
Hope that helps, :)
In △ABC , line AB is extended up to point E and line BC is extended up to D . The measure of some of the angles is given as; ∠BAC=70° and ∠EBC=120° .
Answer:
[tex]\angle ACD = 130 ^\circ[/tex].
Step-by-step explanation:
[tex]\angle ABC[/tex] and [tex]\angle EBC[/tex] are supplementary angles. Their sum should be [tex]180^\circ[/tex]. [tex]\angle EBC = 120^\circ[/tex] [tex]\implies \angle ABC = 180^\circ - \angle EBC = 180^\circ - 120^\circ = 60^\circ[/tex].
The sum of the three angles in triangle [tex]\triangle ABC[/tex]: [tex](\angle ABC + \angle BAC + \angle ACB)[/tex] should be equal to [tex]180^\circ[/tex].
[tex]\angle ABC = 60^\circ[/tex] and [tex]\angle BAC = 70^\circ[/tex] [tex]\implies \angle ACB = 180^\circ - \angle ABC - \angle ACB = 180^\circ - 70^\circ - 60^\circ = 50^\circ[/tex].
[tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] form another pair of supplementary angles. Their sum should also be [tex]180^\circ[/tex]. [tex]\angle ACB = 50^\circ[/tex] [tex]\implies \angle ACD = 180^\circ - \angle ACB = 180^\circ - 50^\circ = 130^\circ[/tex].
Answer:
sum should also be . .
Step-by-step explanation:
The reference angle for 305
Answer:
55°
Step-by-step explanation:
The angle 305° is in the fourth quadrant
To find the related acute angle ( the reference angle ) subtract from 360°
reference angle = 360° - 305° = 55°
will your balance increase on your credit card from month to month if you have a balance, but no new charges?why?
Answer:
yes (if no payments are made)
Step-by-step explanation:
If you have no new charges and you make no payments, you will incur interest costs every month.
Hence yes, you balance will increase by amount of interest owed.
Sarah and Kaylee go to the movie theater and purchase refreshments for their friends.
Sarah spends a total of $47.00 on 12 drinks and 1 bag of popcorn.
Kaylee spends a total of $81.75 on 3 drinks and 9 bags of popcorn.
Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.
Using these equations, determine and state the price of a drink, to the nearest cent.
Each drink costs $3.25 and each popcorn costs $8.
Step-by-step explanation:
Step 1:
Assume each drink costs x dollars and each popcorn costs y dollars.
From the given data, we can write the following equations;
[tex]12x + y = 47[/tex], take this as equation 1,
[tex]3x+9y=81.75[/tex], take this as equation 2.
Step 2:
We multiply equation 2 with 4 so we can cancel out the variable x in both equations. By doing this we get
[tex]3x+9y = 81.75[/tex], take this as equation 3. When we subtract 3 from 1, the x variable is canceled out and y can be calculated.
[tex]-35y = -280, y = \frac{280}{35} = 8[/tex]
Step 3:
Substituting this value of y in any of the previous equations we will get x's value.
Here this value of y is substituted in equation 1.
[tex]12x+8 = 47, 12x= 39[/tex],
[tex]x=\frac{39}{12} = 3.25[/tex]
So we have x = $3.25 and y = $8. So each drink costs $3.25 and each popcorn costs $8.
Janet researcher compares the math placement scores of college applicants who have, or have not taken a special college preparation program.
Independent Variable (IV):
How will you describe the IV?:
Dependent variables (DV): ]
How will you measure the DV?:
Hypothesis:
Answer:
Step-by-step explanation:
Independent Variable (IV): Special college preparation program
How will you describe the IV: Independent variable or known as manipulated variable is a variable where the researcher purposely manipulate the variable to see how it affect the results of the experiment.
Dependent variables (DV): Math placement scores of college applicants
How will you measure the DV: DV can be measured by recording the math placement scores of each applicants who have or have not taken the special college preparation program.
Explanation: In this case, the researcher wants to see how taking special college preparation program (IV) can affect the math placement scores of the applicants (DV). Explanation: In this case, the researcher wants to see how taking special college preparation program (IV) can affect the math placement scores of the applicants (DV).
Hypothesis:
If the applicants take the special college preparation program, the applicants will have higher math placement scores compared to the one who have do not take the program.
Final answer:
The independent variable in the study is whether college applicants have taken a special college preparation program or not, with the dependent variable being the math placement scores. A potential hypothesis could be that applicants who took the program will achieve higher math scores.
Explanation:
Independent Variable (IV): The independent variable in this study is whether college applicants have taken a special college preparation program or not.
Dependent Variable (DV): The dependent variable is the math placement scores of the college applicants.
Hypothesis: A possible hypothesis could be 'College applicants who have taken a special college preparation program will have higher math placement scores compared to those who have not taken the program.'
Michelle opened a savings account for her emergency fund. She deposited $2000 into her account, which earns 2.10% interest, compounded monthly. How much will she have in the account after one year?
Michelle will have $28200 in account after one year.
Step-by-step explanation:
Given ,
P ( Principle amount )= $2000
r ( rate of interest)= 2.10% per month
n (number of times rate of interest is applied) = 12
t ( time period ) = 1 years
Compound Interest = P ( 1 + r/n ) * n*t
⇒ [tex]2000 (1+2.10/12) * 12*1[/tex]
⇒ [tex]2000*12*1.175[/tex]
⇒ 28200
Michelle will have $28200 in account after one year.
The first layer of a rectangle prism is packed with 25 unit cubes. There are no spaces or gaps between the cubes. The prism is 7 unit cubes tall. Which expression represents the volume of the rectangular prism?
Answer:
So, the answer is 175 but in an expression it is 25x where x would be the height in this situation it is 7.
Step-by-step explanation:
So basicly if there is 25 units and there are 7 layers of that 25 units you would multiply 7 by 25 to get 175.
Hence, in an expression it would be 25x where x would be 7
A survey was conducted on 37 people so find out the colours that they like. It was found that 20 people like red, 22 people like blue and 17 people like green. It was also found that 7 people like blue and red, 12 people like blue and green, and 9 people like red and green. Assuming that x persons like three colours, find the value of x
A) 2
B) 4
C) 6
D) 8
Kate bought $23.40 worth of two types of bird seed. Thistle bird seed sells for $1.60 per pound
and wild bird seed sells for $0.95 per pound. If she bought 12 pounds of wild bird seed, write
and solve a linear equation to find the amount of thistle bird seed she purchased
Answer:
The amount of thistle bird seed she purchased was 7.5 pounds
Step-by-step explanation:
Let
x ----> the amount in pounds of thistle bird seed she purchased
x ----> the amount in pounds of wild bird seed she purchased
we know that
Kate bought $23.40 worth of two types of bird seed.
so
[tex]1.60x+0.95y=23.40[/tex] ----> equation A
She bought 12 pounds of wild bird seed
so
[tex]y=12\ pounds[/tex]
substitute the value of y in the equation A
[tex]1.60x+0.95(12)=23.40[/tex]
solve for x
[tex]1.60x=23.40-11.40\\1.60x=12\\x=7.5\ pounds[/tex]
therefore
The amount of thistle bird seed she purchased was 7.5 pounds
Kate bought 7.5 pounds of thistle bird seed.
Since Kate bought $ 23.40 worth of two types of bird seed, thistle bird seed sells for $ 1.60 per pound and wild bird seed sells for $ 0.95 per pound, if she bought 12 pounds of wild bird seed, to find the amount of thistle bird seed she purchased, the following calculation must be performed, through a linear function:
(12 x 0.95) + 1.60X = 23.40 11.40 + 1.60X = 23.40 1.60X = 23.4 - 11.4 X = 12 / 1.60 X = 7.5
Therefore, Kate bought 7.5 pounds of thistle bird seed.
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ANSWER ASAP PLEASE :)
Answer:
20%
Step-by-step explanation:
If 10 goes to 12, that means there was an increase of 2. 2/10 is, in decimal form, 0.2. To change a decimal into a percentage, you multiply it by 100, giving you 20.
True or false: f(x) is a function.
f(x)
Answer:
yes it is
Step-by-step explanation:
f(x) or g(x) are functions
Answer:
It is False
Step-by-step explanation:
I tried true and got it wrong
Hey! Some easy points people. Is this a polygon and what shapes would be a polygon and why?
A store that sells merchandise on a college campus is restocking their inventory of sweatshirts and t-shirts. They order a total of 934 items. Each sweatshirt costs $8.00 and each t-shirt costs $5.00. They spend a total of $5,933.00.
A system of equations is written to represent this scenario, where s represents the number of sweatshirts ordered and t represents the number of t-shirts ordered.
{s+t=934
{8s+5+=5933
The solution to the system is (421, 513). Interpret this solution in the context of the situation.
A. The store ordered 513 sweatshirts and 421 t-shirts.
B. The store ordered 421 sweatshirts and 513 t-shirts.
C. The store spent $513.00 on sweatshirts and $421.00 on t-shirts.
D. The store spent $421.00 on sweatshirts and $513.00 on t-shirts.
Answer:
Option B.
Step-by-step explanation:
A system of equations is written to represent this scenario, where s represents the number of sweatshirts ordered and t represents the number of t-shirts ordered.
s + t = 934
8s + 5t = 5,933
The solution to the system is (421, 513).
So, The number of sweatshirts = 421
And the number of t-shirts = 513
Because 8 * 421 + 5 * 513 = $5,933
We will check the options:
A. The store ordered 513 sweatshirts and 421 t-shirts. ⇒Wrong
B. The store ordered 421 sweatshirts and 513 t-shirts. ⇒True
C. The store spent $513.00 on sweatshirts and $421.00 on t-shirts. ⇒Wrong
Because the solution represents the number of sweatshirts and t-shirts.
D. The store spent $421.00 on sweatshirts and $513.00 on t-shirts. ⇒Wrong
Because the solution represents the number of sweatshirts and t-shirts.
So, the answer is option B.
Factor: 25 m 6 −16 25m6−16 (5m3 + 8)(5m3 – 8) (5m3 – 8)2 (5m3 – 4)2 (5m3 + 4)(5m3 – 4)
Answer:
(5m^3+4)(5m^3-4)
Step-by-step explanation:
(*) A^2 - B^2 =(A+B) (A-B)
25m^6-16=
(5m^3)^2 - 4^2=(*)
(5m^3+4)(5m^3-4)