Solve for x.
x = [?]
4x - 16
2x + 16,
,
If the 3rd term of an arithmetic sequence is 2 and the 17th term is -40, find the 7th term
Answer:
-10
Step-by-step explanation:
t3 = a1 + (n - 1)*d
t3 = a1 + (3 -1)*d
2 = a1 + 2d
t17 = a1 + (n - 1)*d
-40 = a1 + 16d Put the first condition underneath and subtract
2 = a1 + 2d
-42 = 14 d
d = - 3
2 = a1 + 2*(-3)
2 = a1 - 6 Add 6 to both sides
2 + 6 = a1
a1 = 8
Now you want the 7th term
t7 = a1 + (n - 1)*d
t7 = 8 + (7 - 1)*d
t7 = 8 + 6*(-3)
t7 = 8 - 18
t7 = - 10
Factorize the expression, 10ab (a − 2b)³ +24ab² (3a − 6b)²
Answer:
226a³b² - 824ab³ + 984b⁴
Step-by-step explanation:
We can factorize the given expression by expanding the two binomials and then combining like terms.
First, expand the two binomials:
10ab (a − 2b)³ +24ab² (3a − 6b)² = 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)
Then, combine like terms:
= 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)
= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)
= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)
= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)
= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)
= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)
= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)
= 226a³b² - 824ab³ + 984b⁴
Find the volume of the pyramid. 5 ft 2 ft 2 ft
Answer:
v=6.6667
Step-by-step explanation:
[tex]V=L*W*H/3[/tex]
[tex]V=20/3[/tex]
[tex]V=6.6667[/tex]
Hope this helps :)
Can anyone help me with this question please thank you
Giving brainliest correct answer please
Answer:
1/216
Step-by-step explanation:
These are independent events because of probability of first event is not affecting the probability of another event .
probability of getting 4 on first try is 1 / 6
probability of getting six on second try is also 1 / 6 and then probability of getting more 6 on next try is again 1/6
so combined probability is 1/6 ×1/6 ×1/6= 1/216
How do you write 0.00000000090 in scientific notation?
Answer:
Step-by-step explanation:
9.0 × 10-10 I think.....
State whether the equation represents exponential growth, exponential decay, or neither.
y = 11.1.07%
Answer:
Neither
Step-by-step explanation:
This questions only states
[tex]y = 11.1.07\%[/tex]
This is not a fucntion because there is no variable.
This is not a valid statement, because 11.1.07% is non-sensical.
The equation x + c = k has a solution of x = 2. Both cand k are rational numbers.
Select all the statements that must be true in all cases.
cis 2 greater than k.
cand k must be whole numbers.
The solution x = 2 is the only solution.
If c is a whole number, k is also a whole number.
I need help ASAP PLEASE
Answer:
The solution x = 2 is the only solution
If c is a whole number, k is also a whole number.
Sue ate one sweetie one day, and each afterward she ate one sweetie more than she did the day before. How many sweeties did she eat during her first week?
on solving the provided question we can say that - by unitary method we have 12 days.
What is unitary method ?
The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Sue ate one sweetie one day,
Sue ate 12 sweetie 12 day,
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
find the value of x in the following figure
Answer:
x = 172
Step-by-step explanation:
A circle is 360 degrees
The angles will add to 360 degrees
x/2 + 59 + x/4 + x = 360
Subtract 59 from each side
x/2 + x/4 +x +59-59 = 360 -59
x/2+x/4+x = 301
Combine like terms
2x/4 +x/4 +4x/4 = 301
7/4x = 301
Multiply each side by 4/7 to isolate x
4/7 * 7/4 x = 301 *4/7
x =172
Samantha walks a total of 2/3 mile to get to and from school each day . Find the total number of miles that Samantha walked to and from school over 5 days
Answer:
3 1/3 miles
Step-by-step explanation:
If Samantha walks 2/3 miles everyday and they are asking for 5 days
2/3miles · 5days = 3 1/3 or 10/3 miles
Determine whether the linear transformation T is invertible by considering its matrix with respect to the standard bases.
T : P_2 → P_2 defined by
T(p(x)) = p(x) + p'(x)
If T is invertible, use the theorem below to find the inverse of T (attached).
Answer:
it is invertible
Step-by-step explanation:
The length of an arc of a circle is one-eighth the circumference of the circle.Find the angle subtended by this arc at the centre if the radius of the circle is 14cm
Given:
The radius of the circle is 14 cm.
The length of an arc of a circle is one-eighth the circumference of the circle.
To find:
The angle subtended by this arc at the center.
Solution:
Formula for arc length is:
[tex]s=2\pi r\times \dfrac{\theta }{360^\circ}[/tex] ...(i)
Where, r is the radius and [tex]\theta [/tex] is the central angle.
The length of an arc of a circle is one-eighth the circumference of the circle.
[tex]s=\dfrac{1}{8}(2\pi r)[/tex] ...(ii)
Where, [tex]2\pi r[/tex] is the circumference of the circle.
Using (i) and (ii), we get
[tex]2\pi r\times \dfrac{\theta }{360^\circ}=\dfrac{1}{8}(2\pi r)[/tex]
[tex]\dfrac{\theta }{360^\circ}=\dfrac{1}{8}[/tex]
[tex]\theta =\dfrac{360^\circ}{8}[/tex]
[tex]\theta =45^\circ[/tex]
Therefore, the central angle is 45 degrees.
Center: (2, 8) radius: 3
how do I write the equation of the circle in standard form?
We are given:
Coordinates of center: (2,8)
Radius of circle: 3 units
Finding equation of the circle:
We know that the general form of a circle is:
(x-h)² + (y-k)² = (radius)²
where h is the x-coordinate of the center and k is the y-coordinate
replacing with the given values, we get:
(x-2)² + (y-8)² = (3)²
HELP ASAP I will give 20 points
Solve 2 < n +1| ≤ 7. Explain your reasoning and graph
the solution set.
Let n = the number
The solution set is {x | x > 10}. 2. 5 ≥ 7 + y.
What is the value of N?It's used to refer to the collection of all natural numbers. Positive whole numbers that are not zero make up the natural numbers. N = 1 , 2 , 3 , 4 . By multiplying the integers from 1 to n, the factorial of n is calculated and denoted by the symbol n!. n! = n (n - 1)! is the formula for n factorial. Example: What is9! if8, which is40,320, is?The sample size, or n, is the number of data points. described in Chapter 2 here. in a probability experiment using a binomial model, the total number of trials.Instead of the product n n, which is typically pronounced"n squared," the equivalent exponentiation n2 is used to represent a number's square.To learn more about exponentiation refer to:
https://brainly.com/question/13669161
#SPJ1
A committee must be formed with 3 teachers and 3 students. If there are 10 teachers to choose from, and 9 students, how many different ways could the committee be made?
Answer:
10080 ways
Step-by-step explanation:
First we find the amount of combinations of teachers who can be chosen, which is denoted by 10 choose 3 (10 nCr 3), shown below:
10! / (3! * 7!) --> 120
Next to find the amount of combinations of students, you evaluate 9 choose 3(9 nCr 3), shown below:
9! / (3! * 6!) --> 84
To find the total number of combinations, you multiply the teachers combinations by the students combinations:
120 * 84 = 10080
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown
O 10 units
O 24 units
O 36 units
O 64 unitsl
Answer: 24 units.
Step-by-step explanation: To find the perimeter of a triangle, you need to add the length, width, and hypotenuse. The length and width are provided, but we need to find the hypotenuse of the triangle. To do this, we need to use the Pythagorean Theorem.
The Pythagorean Theorem is basically a^2 + b^2 = c^2 where a and b are the legs of the triangle and c is the hypotenuse (also known as the triangle's longest side). However, whatever answer you get needs to be square-rooted, which is your complete answer. Let's say that the side that's 6 units is leg a and the side that's 8 units is leg b.
6^2 + 8^2 = c^2
36 + 64 = 100
√100 = 10.
Now that we know the hypotenuse, we can add it to our other two sides.
6 + 8 + 10 = 24.
Therefore, 24 is your answer.
Let me know if this is right! :)
Victoria invests $200 into an account with a 2.6% interest rate that is compounded semiannually.
How much money will she have in this account if she keeps it for 10 years?
Round your answer to the nearest dollar,
Answer:
A = $258.95
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 2.6/100
r = 0.026 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 200.00(1 + 0.026/2)(2)(10)
A = 200.00(1 + 0.013)(20)
A = $258.95
Need help finding missing answers
Check the picture below.
so let's start with 34, well a centroid is the point where all "medians" meet, well a median is half of the segment, the heck does that mean? well, it means that CG = GD, and since CD is 34, that means that GD = 17.
let's keep in mind that a centroid cuts all medians in a 2 : 1 ratio, meaning one cut-side is twice as along as the other, that said
[tex]\stackrel{\textit{keeping in mind that BG=57}}{\cfrac{BH}{HG}=\cfrac{2}{1}\implies \cfrac{BH}{HG}=\cfrac{2\cdot \frac{57}{2+1}}{1\cdot \frac{57}{2+1}}}\hspace{10em} \cfrac{BH=38}{HG=19} \\\\\\ \cfrac{HD}{EH}=\cfrac{2}{1}\implies \cfrac{HD}{15}=\cfrac{2}{1}\implies HD=30\hspace{5em}\stackrel{15~~ + ~~30}{ED=45} \\\\\\ \stackrel{\textit{keeping in mind that CF=39}}{\cfrac{CH}{HF}=\cfrac{2}{1}\implies \cfrac{CH}{HF}=\cfrac{2\cdot \frac{39}{2+1}}{1\cdot \frac{39}{2+1}}}\hspace{10em}\cfrac{CH=26}{HF=13}[/tex]
A shopper buys cat food in bags of 33 lbs. Her cat eats \frac{3}{4}
4
3
lb each week. How many weeks does one bag last?
Total of 44 weeks does one bag last.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator
Total amount of cat food = 33 lbs in one bag
Amount of food cat eats each week = 3/4 lb = 0.75 lb
Number of weeks one bag of cat food last = 33 / 0.75
= 44
Hence one bag of cat food will last for 44 weeks.
To learn more about Fractions, click on the link :
https://brainly.com/question/10354322
#SPJ1
If your annual salary is $37,350 and your housing budget is 24%, How much is your yearly housing cost?
Answer:
$8964Step-by-step explanation:
Annual salary is $37350
Housing budget is 24%
Housing cost:
$37350*24/100 = $8964Answer:
$8,964
Step-by-step explanation:
Given:
Annual salary = $37,350Housing budget = 24%To find the yearly housing cost, calculate 24% of the annual salary:
[tex]\begin{aligned}\implies \sf Yearly\:housing\:cost & = \sf 24\% \:of\:37350 \\\\& = \sf \dfrac{24}{100} \cdot 37350\\\\& = \sf \dfrac{24 \cdot 37350}{100}\\\\& = \sf \dfrac{896400}{100}\\\\& = \sf 8964\end{aligned}[/tex]
Therefore, the yearly housing cost is $8,964.
Learn more about percentages here:
https://brainly.com/question/27998542
https://brainly.com/question/27975347
how do i get the answer on pc"?
Answer:
I. D. K. what is the question
Step-by-step explanation:
write a real-life word problem that involves one-variable equation. Discuss how you would go about solving this problem.
help pls
Answer:
A waiter at a restaurant earns 10 dollars per hour. How much money is earned in 4 hours?
Equation: m = 10h
m = money earned
h = hours worked
Plug in 4 for (h)
m = 10(4)
m = 40 dollars
The waiter earns 40 dollars in 4 hours.
Step-by-step explanation:
What are 3 prime numbers that add up to 55?
Answer and Step-by-step explanation:
Prime numbers are numbered that can't be divided by whole numbers other than itself and 1.
7, 11, and 37 are prime numbers that add up to 55.
7 + 11 + 37 = 55
7 + 48 = 55
55 = 55
#teamtrees #PAW (Plant And Water)
Answer:
37+17+1
Step-by-step explanation:
I think
A prime number always has 2 factors:-)
1 and itself are its factors
I hope it helps
PLEASE HELP FIND THE SOLUTION IN SLOPE INTERCEPT FORM
Answer: y= -3/4x+8
Step-by-step explanation:
What is the ?
Please help I need it quick
Mississipi has the lowest income at 40.6 thousand dollars.Mississippi also has about 207 bacherlors degree per 1000 people what does the linear model estimate for that number of bachelors degrees per 1000 per person for Mississippi based on the median income? How good is this estimate?
Answer: A linear model is a type of mathematical equation that describes the relationship between two variables, such as median income and the number of bachelor's degrees per 1000 people. In order to estimate the number of bachelor's degrees per 1000 people for Mississippi based on the median income, you would need a linear equation that describes that relationship.
Without that equation, it's not possible to estimate the number of bachelor's degrees per 1000 people for Mississippi based on the median income.
Additionally, without more information about the data that the model was trained on, the correlation between median income and the number of bachelor's degrees per 1000 people and how accurate and reliable the model is, it's difficult to determine the goodness of this estimate. However, in general, a linear model may provide only a rough estimate, especially if the relationship between the variables is complex or non-linear.
Step-by-step explanation:
Wendy Wilson planned to bake a triple recipe of chocolate chip cookies for her office party. If the recipe calls for 2 3/4 cups of flour, how many cups will she need? Need answer now!
Answer: 8 1/4 cups
Step-by-step explanation: All you must do is multiply 2.75 (which is 2 3/4 in decimal form) by 3 since Wendy is baking a TRIPLE recipe. So, the work will look like this: 2.75x3=8.25 or 8 1/4 cups of flour.
5 lbs. of organic red potatoes cost
$6.00. What is the price per lb?
Answer:
0.83333333333
Step-by-step explanation:
5 lbs. of organic red potatoes cost $6.00. The price per pound of organic red potatoes is $1.20.
To find the price per pound of organic red potatoes, we can divide the total cost by the weight in pounds.
Price refers to the monetary value or amount that is assigned or charged for a product, service, or commodity. It represents the cost or value that a buyer is required to pay in exchange for obtaining or acquiring something.
Given that 5 lbs. of organic red potatoes cost $6.00, we can set up the following equation:
Price per pound = Total cost / Weight in pounds
Price per pound = $6.00 / 5 lbs.
Dividing $6.00 by 5 pounds gives us:
Price per pound = $1.20
Therefore, the price per pound of organic red potatoes is $1.20.
To know more about price here
https://brainly.com/question/26075805
#SPJ2