Joseph and Molly each have coin collections. Joseph starts with 15 coins in his collection and adds 25 coins each month. Molly starts with 25 coins in her collection and adds 25 coins each month. How many coins would Joseph have after 3 months?

Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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Answer:

36

Step-by-step explanation:

nine times 4 is 36 making it 36 options to choose from

hope this helps! :)

If Santiago has been approved for a mortgage up to $195,000 and the conventional loan requires a 20% down payment, then his down payment will be:

Down payment = 20% * $195,000

Down payment = $39,000

Therefore, if Santiago buys a house for the maximum amount he has been approved for, he will need to make a down payment of $39,000.

To calculate how much house Santiago can afford, we need to subtract the down payment from the total amount he has been approved for:

Maximum home price = Total mortgage amount - Down payment

Maximum home price = $195,000 - $39,000

Maximum home price = $156,000

Therefore, Santiago can afford a home up to a maximum price of $156,000.

To summarize:

Santiago's down payment will be $39,000.

Santiago can spend up to $156,000 on a house.

I'm sorry to disturb but can you please mark me BRAINLEIST if this ans is helpfull

Step-by-step explanation:

speed=distance÷time

A.V.S=440÷11=40m/s

hope it helps.. Please mark brainliest.

Answer:

40 m/s

Step-by-step explanation:

Find:

We are asked to find the unit rate, How many meters per 1 second?

Know:

440 meters in 11 seconds

Solve:

440 meters in 11 seconds

  ? meters in 1 second

   440/11  = 40 meters per second

Answer:

The average speed of the person is 40 m/s

Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:

y ≤ -11/7x - 4

This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.

Step-by-step explanation: .

Answer:

eywgw6 the car is in the car is in the car is in

Step-by-step explanation:

Wu and I will be in the car is in the car is in the car is in the car is here and we can 4

Answer:

Safe fund = $24,000

Risky fund = $6,000

Step-by-step explanation:

Definition of variables:

Given information:

Convert the percentages into decimal form:

\(\implies 2.5\%=\dfrac{2.5}{100}=0.025\)

\(\implies 8\%=\dfrac{8}{100}=0.08\)

Create a system of equations from the given information and defined variables:

\(\begin{cases}0.025x+0.08y=1080\\x=4y\end{cases}\)

Substitute the second equation into the first equation and solve for y:

\(\implies 0.025(4y)+0.08y=1080\)

\(\implies 0.1y+0.08y=1080\)

\(\implies 0.18y=1080\)

\(\implies \dfrac{0.18y}{0.18}=\dfrac{1080}{0.18}\)

\(\implies y=6000\)

Substitute the found value of y into the second equation and solve for x:

\(\implies x=4(6000)\)

\(\implies x=24000\)

Therefore, the amount invested in each fund was:

Answer:

where's the x in the equation?

Answer:

25/12 Therefore, this equation is true: 25/12 = 25/12 If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction. 25/12 = 2 1/12. Simplify Fractions.

Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

Answer:

Step-by-step explanation:

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Answer:

- 9/2

Step-by-step explanation:

got this question right

Answer:

\(\boxed {\boxed {\sf 74}}\)

Step-by-step explanation:

The nth term of an arithmetic sequence can be found using the following formula.

\(a_n=a_1+(n-1)d\)

Where n is the term, a₁ is the first term, and d is the common difference.

We want to find the 21st term, we know the first term is -6, and the common difference is 4.

\(n= 21\\a_1= -6 \\d=4\)

Substitute the values into the formula.

\(a_{21}=-6+(21-1)4\)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Solve inside the parentheses.

\(a_{21}=-6+(20)4\)

Multiply 20 and 4.

\(a_{21}= -6+80 \\\)

Add -6 and 80.

\(a_{21}=74\)

The 21st term of the sequence is 74

Answer:

Here we will use the formula

\( \tt \: a_n \: = a_1 +( n - 1)\: \times d\)

\( \tt\: a_{21} = −6+(21−1)4\)

By using PEMDAS

\( \tt \: a_{21} = - 6 + (20)4\)

\( \tt \: a_{21} \: = - 6 + 80 = 74\)

\( \huge \tt \bigodot \: \: 74\)

Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

Answer:

The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.

So the answer is f(x) = 2x2

Thank you and please rate me as brainliest as it will help me

The function f(x) = 2x² is the quadratic function while the other functions are not the quadratic function. The first option is the correct one.

A quadratic function is a polynomial with degree 4.

f(x) = 2x² is a quadratic function as the degree of the function is 2.

g(x) = 5x³ is a cubic function as the degree of the function is 3.

k(x) = -x is a linear function as the degree of the function is 1.

\(b(x) = -9x^4\) is a quartic function as the degree of the function is 4.

So, among all options, f(x) = 2x² is the quadratic function. The correct option is the first one.

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6 x 15 = 90

6 and 15 are factors of 90

Answer:

The slopes of A⁢B↔ and the parallel line through point C are equal.

Step-by-step explanation:

Edmentum

Answer:

The slopes of the parallel AB lines through point C  are equal.

Step-by-step explanation:

9514 1404 393

Answer:

  dy/dx = 2x +1

Step-by-step explanation:

The power rule can be used.

  d/dx(x^n) = n·x^(n-1)

Then the derivative of x² is 2x¹ = 2x, and the derivative of x = 1x⁰ = 1.

The derivative of the function is ...

  dy/dx = 2x +1

x=6

d=12

7x+12 or 7x+d

7(6) + 12 or (7x6) + 12 = 54

78-12 = 66

66/6 = 11

11x + 12 =78.

Answer:

please look at detailed answers below

Step-by-step explanation:

example 1 is correct.

example 2:

x = (12 sin 15) / sin 75 = 3.22.

example 3:

x/sin 90 = 19/sin (180 - 90 -36)

x = (19 sin 90) / sin 54

= 23.5

example 4:

x/sin 53 = 7/sin (180 -90 - 53)

x = (7 sin 53)/ sin

= 9.29

Answer:

x=1

Step-by-step explanation:

Hi there!

We are given that a line is perpendicular to y = -6 and passes through the point (1, 3)

We want to write the equation of this line in slope-intercept form

Slope-intercept form is y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name

First, we need to find the slope (m) of the line

Remember that we were given that the line is perpendicular to y = -6

Perpendicular lines have slopes that multiply to get -1

The slope of y = -6 is 0; therefore, to find the slope of this line, we can do the following equation

0m=1

Divide both sides by 0

m = 1/0

This answer is undefined - therefore, the line has an undefined slope

If this is the case, then it means the line is a vertical line

A vertical line is written as x=k, where k is the value of x at the x intercept. It can't be written in slope-intercept form.

This value is also the value of x at every point that lies on such line - in this case, as given by the point (1, 3) , this value is 1

So substitute 1 as k.

x = 1

This is the line of the equation.

Hope this helps!

Answer:

49

Step-by-step explanation:

Answer:

y = 29

Step-by-step explanation:

Since it is a vertical angle, both angles represented by the equations are equal. Meaning we can set them equal to each other and find y by simplifying.

4y-8 = 79+y

-79     -79

4y-87 = y

-4y       -4y

-87 = -3y

Divided by -3

29 = y

When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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