Answer:
14
Step-by-step explanation:
Answer:
Im Sure there is 10 different combinations.
Step-by-step explanation:
Two princesses, Nat and Kat, are gifted with a savings account from their royal parents, Matt and Pat, when they turn 5 years old. The royal parents put a specific amount into each account annually such that Nat’s account follows a linear model. Nat’s savings account has an initial balance of when it is opened and each year on her birthday, Nat’s parents put a constant amount into the account and never remove any money. Her account has $6200 when she is 7 and when Nat is 12, she has $21200 in her account.
a. Write a linear function N(t) for the amount of money, N, that Nat has in her account ‘t’ years after her 5th birthday.
b. Kat’s account doesn’t follow a linear model, but rather a quadratic model. On her 5th birthday, her parents open the account and then add money annually just like with Nat. Kat’s parents plan is to add money so that her account maxes out at $44100 on her 25th birthday. At the age of 14, she has $32000. Write a quadratic function K(t) for the amount of money, K, in Kat’s account ‘t’ years after her 5th birthday.
c. What age will both Nat and Kat have the same amount in their account?
Answers and Step-by-step explanations:
(a) We want to find the slope-intercept equation (y = mx + b), where m is the slope and b is the y-intercept. We already have two points: (2, 6200) and (7, 21200). The slope is change in y over change in x so:
m = (21200 - 6200) / (7 - 2) = 3000
Now, we have y = 3000x + b. Plug in 6200 for y and 2 for x to solve for b:
y = 3000x + b
6200 = 3000 * 2 + b
b = 200
Nat's equation is y = 3000t + 200.
(b) We want a quadratic formula in vertex form because the problem says that Kat's account maxes out at 44100 on her 25th birthday, indicating that's the vertex. Our vertex point is (20, 44100); note that it's 20 and not 25 because she starts the account at age 5, not age 0. The generic vertex form of a quadratic is:
y = a(x - h)² + k, where (h, k) is the vertex
Plug in our vertex:
y = a(x - 20)² + 44100
We also have the point (9, 32000), so put that in to find a:
32000 = a(9 - 20)² + 44100
-12100 = a * 121
a = -100
So Kat's equation is y = -100(t - 20)² + 44100.
(c) In order to find the age when they have the same amount, we set the two equations equal:
3000t + 200 = -100(t - 20)² + 44100
-100(t² - 40t + 400) + 44100 = 3000t + 200
-100t² + 4000t - 40000 + 44100 - 3000t - 200 = 0
-100t² + 1000t + 3900 = 0
t² - 10t - 39 = 0
(t - 13)(t + 3) = 0
t = 13 or t = -3 -- obviously, years can't be negative, so t = 13.
Note, however, that t is the number of years after Kat and Nat are 5, so we need to add 13 to 5:
13 + 5 = 18
The age is 18.
A: [tex]N(t) = 3000t +200[/tex]
B: [tex]y = -100(x-20)^2+44100[/tex]
C: When they turn 18.
A. Write a linear function N(t) for the amount of money, N, that Nat has in her account ‘t’ years after her 5th birthday:
You can determine a linear equation using the two coordinates provided:
(2, 6200) and (5, 21200).
To do this, first find the slope of the graph. You can do this by using the expression
[tex]\frac{y2-y1}{x2-x1}[/tex], where the coordinate (2, 6200) is 1 and (7, 21200) is 2:
[tex]\frac{21200-6200}{12-7}\\\\\frac{15000}{5}[/tex]
The slope is equal to 3000. Now, you need to find the y-intercept. Plug in 2 for x and see what the y intercept would need to be to equal 6200:
6200 = 3000 * 2 + b
6200 = 6000 + b
b = 200
Thus, your equation for Nat's bank account is [tex]N(t) = 3000t + 200[/tex]
B: Kat’s account doesn’t follow a linear model, but rather a quadratic model. On her 5th birthday, her parents open the account and then add money annually just like with Nat. Kat’s parents plan is to add money so that her account maxes out at $44100 on her 25th birthday. At the age of 14, she has $32000. Write a quadratic function K(t) for the amount of money, K, in Kat’s account ‘t’ years after her 5th birthday:
The question supplies you with the vertex to the parabola, (20, 44100). This is the point at which the maximum value of the function is reached.
It also supplies you with a point on the parabola, (9, 32000).
You can use the vertex form of the quadratic equation to find the formula for Kat's bank account:
[tex]y=a(x-h)^2+k[/tex], where (h, k) is the vertex.
Substituting the vertex in for that equation, we get:
[tex]y=a(x-20)^2+44100[/tex]
Now, you can substitute the point (14, 32000) in for x and y to solve for a:
[tex]32000=a(9-20)^2+44100\\\\-12100 = 121a\\a = -100[/tex]
Thus, the equation is [tex]y = -100(x-20)^2+44100[/tex].
C. What age will both Nat and Kat have the same amount in their account? 18 years old.
To find what age each account will be equal, set the equations equal to each other:
[tex]-100(x-20)^2+44100 = 3000x +200[/tex]
Then, you can solve for x:
[tex]-100(x-13)(x+3)=0[/tex]
Solving for x, we notice that the accounts equal each other when Nat and Kat are -3 or 13. However, Nat's function is only specified to begin after she turns 5, so add 5 to 13 to get 18.
They will both have the same money in their accounts when they turn 18.
help me in geometry!!
Answer:
30.
Step-by-step explanation:
To find the area of a rectangle, you need to multiply length x width.
A = L x W
6 x 5 = 30.
Feel free to let me know if you need more help. :)
What is the probability of spinning green on the first spinner and blue on the second spinner?
The probability of spinning 'green' on the first spinner and 'blue' on the second spinner can be calculated by multiplying the individual probabilities assuming that they are independent events.
Explanation:The probability of getting 'green' on the first spinner and 'blue' on the second spinner can be calculated by multiplying the individual probabilities if the two events are independent. If the first spinner has 'g' green out of 't' total possible outcomes and the second spinner has 'b' blue out of 's' total outcomes, the first probability would be 'g/t' and the second one 'b/s'. Hence, the probability of spinning 'green' on the first and 'blue' on the second would be (g/t) * (b/s).
For instance, if the first spinner has 2 green areas out of 10 total (2/10=0.2) and the second spinner has 3 blue areas out of 10 (3/10=0.3), then the probability of spinning 'green' first and 'blue' second would be 0.2*0.3=0.06 or 6%. Remember that the aforementioned explanation assumes that the outcomes from the two spinners are independent, that is, the result from the first does not affect the result from the second.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
The probability of spinning green on the first spinner and blue on the second spinner is 1/9.
To calculate the probability of independent events, we need to multiply the probabilities of each event occurring separately.
Assume the first spinner has equal sections for each color: red, blue, and green.
Thus, the probability of spinning green is 1/3.
Similarly, assume the second spinner has equal sections for each color: red, blue, and green.
Thus, the probability of spinning blue is 1/3.
Since the spins are independent events, the overall probability is calculated by multiplying these probabilities:
P(Green on first) * P(Blue on second) = 1/3 * 1/3 = 1/9
FIRST PERSON TO HELP GETS MARKED BRAINIEST !
(You have to actually help)
Answer: d = 13 inches.
Step-by-step explanation: The total surface area = 674 in²
Given the value of rectangular prism are 9 and 10 in respectively.
Area of rectangular prism = 2(lw+ wh+ lh)
2(d10 + 10×9+d9) = 2(19d+90) = 38d+180 = 674
38d = 674-180 = 494
d = 494/38 = 13in
∴ d = 13in
Which expressions are equivalent
to 1/81 ? check all that apply.
picture provided
[tex] {8}^{ - 1} = \frac{1}{8} [/tex]
8-¹ ❌
[tex] {9}^{ - 2} = \frac{1}{ {9}^{2} } = \frac{1}{81} [/tex]
9-² ✔️
[tex] \frac{ {9}^{8} }{ {9}^{4} } = {9}^{8 - 4} = {9}^{8} [/tex]
9^8/9^4 ❌
[tex] \frac{9 {}^{8} }{ {9}^{10} } = {9}^{8 - 10} = {9}^{ - 2} = \frac{1}{9 {}^{2} } = \frac{1}{81} [/tex]
9^8/9^10 ✔️
[tex] {9}^{ - 6} \times {9}^{3} = {9}^{ - 6 + 3} = {9}^{ - 3} = \frac{1}{9 {}^{3} } = \frac{1}{729} [/tex]
9^-6 . 9³ ❌
[tex] {9}^{5} . \: { 9}^{ - 7} = {9}^{5 - 7} = 9 {}^{ - 2} = \frac{1}{ {9}^{2} } = \frac{1}{81} [/tex]
9^5 . 9^-7 ✔️
Which other expression has the same value as (-14) - 8?
An expression that has the same value as (-14) - 8 is (-14) + (-8), both of which equal -22.
Explanation:The question is about finding an expression that is equivalent to (-14) - 8. When we subtract a positive number from a negative number, we move further to the left on the number line, making the number more negative. Therefore, (-14) - 8 is the same as adding the opposite of 8, which is -8, to -14, giving us -22. Another way to see it is moving 8 units to the left from -14 on a number line.
Thus, an equivalent expression might be the subtraction of the negative of 8, which is (-14) + (-8). We add the two negative numbers together following the rule that adding two negative numbers results in a negative sum. In this case, (-14) + (-8) is also -22.
- 3x + 2 - 5(2x -1) simplified
Answer:
-13x + 7
Step-by-step explanation:
trust me
Help plz the value of x and y
Answer:
ANSWER IS A ...........
A reindeer runs 20 1/4
miles in 3 hours. At that rate, how many miles does it run in 1 hour?
Answer:
6 3/4 or 6.75 mph
Step-by-step explanation:
Take the rate of miles per 3 hours, 20 1/4, and divide it by 3.
That equals 6.75 or 6 3/4 mph
Hope this helps!
Answer:
6 3/4Step-by-step explanation:
Lets take the rate of miles per 3 hours So, we have 20 1/4 so now if we divide it by 3 That will equal 6.75 in decimal if you were asked to write it in fraction write it like this 6 3/4.
Decimal= 6.75 Fraction= 6 3/4
Hope this helps you!!
Find the area of the rectangle polynomial
hello,
[tex]Area =(2x + 4) \times ( 4x - 2) \\ Area =8 {x}^{2} - 4x + 16x - 8 \\ Area = {8x}^{2} + 12x - 8[/tex]
[tex]\boxed{crsjr}[/tex]
Answer:
[tex]\Longrightarrow: \boxed{\sf{8x^2+12x-8}}[/tex]
Step-by-step explanation:
Using the distributive property, you multiply by the area to find the area of the rectangle polynomial.
[tex]: \Longrightarrow \sf{(Area)= (2x+4)*(4x-2)}[/tex]
Solve.
(2x+4)*(4x-2)Multiply by expand.
Use the distributive property.
Distributive property:⇒ A(B+C)=AB+ACUse the FOIL method.
FOIL method:
[tex]\Longrightarrow: \sf{\left(A+B\right)\left(C+D\right)=AC+AD+BC+BD}[/tex]
[tex]\Longrightarrow: \sf{2x\cdot \:4x+2x\left(-2\right)+4\cdot \:4x+4\left(-2\right)}[/tex]
[tex]\Longrightarrow: \boxed{\sf{=8x^2+12x-8}}[/tex]
Therefore, the correct answer is 8x²+12x-8.I hope this helps! Let me know if you have any questions.
What is the factorization of 12164 - 49?
O (11b - 7)(11b - 7)
O (11b + 7)(11b - 7)
O (1162 - 7)(1162 - 7)
O (1162 + 7)(1162 - 7)
The factorization of 12164 - 49 is,
⇒ (110.3 - 7) (110.3 + 7)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The number is,
⇒ 12164 - 49
Now, We can factor as;
⇒ 12164 - 49
⇒ 110.3² - 7²
⇒ (110.3 - 7) (110.3 + 7)
Thus, The factorization of 12164 - 49 is,
⇒ (110.3 - 7) (110.3 + 7)
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
Determine the equation for the given line in
slope-intercept form.
y=-5/3x-1
Y=5/3x+1
Y=3/5x+1 Y=-3/5x-1
Answer:
Y= -3/5 - 1
Step-by-step explanation:
if you start on the y intercept an go down once (-1)
then go down three times (-3)
positive 5 so go right 5 times it lands on the point :)
im not a teacher and i took this last year so sorry if my explanation isn't the best
The equation for the given line in slope-intercept form is y = (-3/5)x - 1.
Option D is the correct answer.
We have,
The slope-intercept form of a linear equation,
y = mx + b
where m represents the slope of the line and b represents the y-intercept.
The slope (m) of the line using the two given points (0, -1) and (5, -4):
m = (y₂ - y₁) / (x₂ - x₁)
m = (-4 - (-1)) / (5 - 0)
m = (-4 + 1) / 5
m = -3 / 5
Substitute it into the slope-intercept form, along with one of the given points (0, -1), to find the value of b:
-1 = (-3/5)(0) + b
-1 = b
The y-intercept (b) is -1.
The equation of the line using the slope-intercept form:
y = (-3/5)x - 1
Thus,
The equation for the given line in slope-intercept form is y = (-3/5)x - 1.
Learn more about the equation of a line here:
https://brainly.com/question/23087740
#SPJ4
The city plans a roadway to have trees every 1/6 mile. If the path is 5 1/2 miles long, how many trees will the city need?
Answer: The city will need 33 trees.
Step-by-step explanation:
Hi, to answer this question we simply have to divide the length of the path (5 1/2 miles) distance between trees (1/6).
Mathematically speaking:
5 1/2 ÷ 1/6 = (5x2+1) /2 ÷1/6 = 11/2 ÷1/6 = (11x6) /(2x1) = 66/2 =33 trees
The city will need 33 trees.
Feel free to ask for more if needed or if you did not understand something.
Final answer:
To determine the number of trees needed for a roadway with trees spaced every 1/6 mile along a 5 1/2-mile path, divide the total distance by the spacing distance to find 33 trees required.
Explanation:
Roadway:
To find the number of trees needed, we first calculate the distance between trees: 1/6 mile. The total length of the road is 5 1/2 miles, so we divide the total length by the distance between trees to find the number of trees needed:
5 1/2 miles ÷ 1/6 mile = 5.5 ÷ 1/6 = 5.5 * 6 = 33 trees
clara read 2/3 of a book. which fraction is equivalent to what clara read?
Answer:
1/3 of the book she needs to read
Step-by-step explanation:
(5x+2)(2x-3) legit idk what to do xD
Answer:
make it polynomial eqution and than solve it for x
Step-by-step explanation:
hope this will help you
Answer:
10x² - 11x - 6
Step-by-step explanation:
(5x+2)(2x-3)
10x² + 4x - 15x - 6
10x² - 11x - 6
What are the vertices of the hyperbola whose equation is (x+3)^2/4-(y-5)^2/16=1
Answer:
(-5,5) and (-1,5)
Step-by-step explanation:
second option on edge
Answer:
Provided below. Hope this helps:))
Step-by-step explanation:
Use the values given in the table and the functions to
determine the missing values. Help please
Answer:
1/4
1
4
Step-by-step explanation:
The function is g(x) = 4^((1/2)*x)
For A, the value is -2. Plug this into the equation.
g(-2) = 4^((1/2)*-2)
g(-2) = 4^(-1)
g(-2) = 1/4
For B, the value is 0. Plug it into the equaiton.
g(0) = 4^((1/2)*0)
g(0) = 4^(0)
g(0) = 1
For C, the value is 2. Plug it into the equation.
g(2) = 4^((1/2)*2)
g(2) = 4^1
g(2) = 4
A function is a relationship between inputs where each input is related to exactly one output.
The value of A is 1/4.
The value of B is 1.
The value of C is 4.
What is a function?
A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = [tex]4^x[/tex]
g(x) = [tex]4^{\frac{1}{2}x[/tex]
For x = -2
A = [tex]4^{\frac{1}{2}\times-2[/tex]
A = 1/4
For x = 0
B = [tex]4^0[/tex]
B = 1
For x = 2
C = [tex]4^1[/tex]
C = 4
Thus,
The value of A is 1/4.
The value of B is 1.
The value of C is 4.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ5
Owen follows the rule "divide by 2" to write the pattern below. He will write two
more numbers to complete the pattern. Which statement is true?
800, 400, 200, 100, O, O
1) Every number in the pattern will have a 0 in its ones place.
)) Every number in the pattern will have a 0 or a 5 in its tens place.
) Every number in the pattern will have a 0 or a 5 in its ones place.
)) Every number in the pattern will have a 0 in its tens place.
Answer:
C)
Step-by-step explanation:
100/2 = 50 goes in the fifth position of the list
50/2 = 25 goes in the sixth position of the list
And the complete pattern is: 800, 400, 200, 100, 50, 25
Then, every number in the pattern will have a 0 or a 5 in its ones place.
What is the volume of the prism?
An oblique prism has a square base and height of 3
centimeters.
30 cm
O 45 cm
60 cm
75 cm
Answer:
75 cm³
Step-by-step explanation:
Edge 2020
The volume of the given prism is equivalent to V = a².
What is volume?Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -
V = ∫∫∫ F(x, y, z) dx dy dz
Given is to find the volume of the prism that has a square base and height of 3 centimeters.
The volume of a square pyramid is -
V = a²h/3
Now, the base edge length is not given. Assume it to be {a} units. So, we can write -
V = 3a²/3
V = a²
Therefore, the volume of the given prism is equivalent to V = a².
To solve more questions on Prisms, visit the link-
https://brainly.com/question/22147194
#SPJ7
Consider the diagram below. GA and FA are radii and DG and FD are tangent to circle A. Determine the value of x.
Answer:102
Step-by-step explanation:
180-36=144
x+42=144
x=102
The measure of x from the circle is x = 102
What is Central Angle?The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.
The central angle of a circle formula is as follows.
Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
r is the radius of the circle
Central Angle = 2 x Angle in other segment
Given data ,
Let the measure of the external angle ∠GDF = 36°
Now , Central Angle = 2 x Angle in other segment
And , the measure of ∠GAF = ( x + 42 )°
On simplifying , we get
( x + 42 )° = 180° - 36°
x + 42 = 144
Subtracting 42 on both sides , we get
x = 102
Hence , the measure of x of circle is 102
To learn more about central angle click :
https://brainly.com/question/11877137
#SPJ2
The dot plot shows the number of magazines sold. Determine the median of the data set.
A) 17
B) 19
C) 20
D) 23
Answer:
C) 20
Step-by-step explanation:
The median is the middle most number of the dataset.
17 18 18 19 20 20 20 20 20 23 23 23 24 25 25
20 is the middle most number. The median is 20.
Answer:
20
Step-by-step explanation:
Median is the middle value
Median position: (15+1)/2 = 16/2
= 8th value
Read in ascending or descending order, 8th value is 20
Solve 2x = 3.
Round to the nearest ten-thousandth.
divide by 2 on both sides.
3/2
x=1.5
Answer:
1.5850
Step-by-step explanation:
It was simple really
A skating rink charges a group rate of $9 plus a fee to rent each pair of skates. A family rents 7 pairs of skates and pays a total of $30. What does "X" represent?
In the problem, 'X' denotes the cost to rent each pair of skates. Setting up and solving the equation, 9 + 7X = 30, we find 'X', the cost per pair, is $3.
Explanation:In this problem, 'X' represents the cost to rent each pair of skates. The problem refers to a situation where a skating rink charges $9 for a group rate and an additional fee for every pair of skates rented. According to the provided information, a family who rents 7 pairs of skates pays a total of $30. We can set up an equation to solve for 'X.'
The equation is 9 + 7X = 30, where X is the cost per pair of skates.
To solve this equation, you have to subtract 9 from both sides, getting 7X = 21. Afterward, you divide both sides by 7, and you get X = 3. Therefore, 'X' corresponds to $3, the cost per pair of skates.
Learn more about Variables in Math here:https://brainly.com/question/34153333
#SPJ12
*ANSWER CORRECTLY TO BE COUNTED AS BRAINLIEAT*
Answer:
mean = 6.4
median = 6.5
range = 9
Step-by-step explanation:
hope this helps!!
Answer:
Step-by-step explanation:
Mean = Sum of scores/number of games
[tex]=\frac{4+10+7+9+2+11+4+9+2+6}{10}\\\\=\frac{64}{10}\\\\[/tex]
Mean = 6.4
4,10,7,9,2,11,4,9,2,6
Ascending order: 2,2,4,4,6,7,9,9,10,11
Median is the middle term. As number of terms is even number (10),
We have to find the mean of middle terms. ie median of 5th and 6th term
[tex]Median=\frac{6+7}{2}\\\\=\frac{13}{2}[/tex]
Median = 6.5
Range = Maximum score - minimum score
= 11 - 2
Range = 9
What is the value of x?
12x+34=9
Answer:
B. 16 1/2
Step-by-step explanation:
1/2x+3/4=9
multiply both sides by 4
4(1/2x+3/4)=9x4
2x+3=36
2x=36-3
2x=33
x=33/2
x=16 1/2
Answer:
2.1
Step-by-step explanation:
you start with 12x+34=9 so do inverse operations
12x+34=9
-34 -34
12x=-25
12x/12=-25/12
x=-2.083333ect.
or 2.1
Please help me with the problem attached.
Answer:
c
Step-by-step explanation:
Which label on the cone below represents the radius?
A
В
С
D
D
The answer for the label on the cone below that represents the radius is A
Step-by-step explanation:
the answer should be B cause the radius is the line that goes threw the middle
If 2c + 1 = 11, what is the value of 2c?
A. 4
B. 5
C. 10
D. 12
Answer:
2c =10
Explanation:
2c+1-1=11-1 - Subtract 1 from both sides
2c=10 - Simplify
If you want the value of x you would divide 2 on both sides and you would get 5. But you asked for 2c that's why I gave you 2c.
Hoped this helped! :)
Answer:
2c =10
Step-by-step explanation:
~Inosuke Hashibria~
What is the equation of the vertical line through (2, 3)?
Answer:
x=2 or y=3
Step-by-step explanation:
x=2 is a vertical line at the x-value of 2
y=3 is a horizontal line at the y-value of 3
multiply write the result in scientific notation (9.10^4)(8.10^6) help please
To multiply numbers in scientific notation, multiply the coefficients and add the exponents. The final answer is 7.2 x 10^11.
Explanation:To multiply numbers in scientific notation, you need to multiply the coefficients and add the exponents.
In this case, (9.104) multiplied by (8.106) gives you (9 * 8) multiplied by (104+6).
So the result is 72 multiplied by 1010, which can be written in scientific notation as 7.2 x 1011.