The nth term of the sequence

-2, 1, 4, 7, 10,...

is given by the formula
A) an = n - 3
B) an = 3n - 3
C) an = n - 5
D) an = 3n - 5

Answer:

Option D. $2520 is correct

Step-by-step explanation:

Principal value = $7890

Rate of interest = 11.5 annually

[tex]\text{Monthly Rate of Interest = }\frac{11.5}{12}=0.96\%=0.0096[/tex]

Time = 5 years

⇒ n = 60 months

[tex]\text{Monthly Payment = }\frac{rate\times \text{Principal value}}{1-(1+r)^{-n}}\\\\\text{Monthly payment = }\frac{0.0096\times 7890}{1-(1+0.0096)^{-60}} \\\\\implies\text{Monthly Payment = }\$173.50[/tex]

Total payment made by Arnold = No. of months × Monthly Payment

⇒ Total Payment = 60 × 173.50

⇒ Total Payment = $10410

Money borrowed = $7890

Hence, Amount of interest = Total payment - Amount borrowed

⇒ Interest = 10410 - 7890

⇒ Interest = $2520

Therefore, Option D. $2520 is correct

The total money collected for music CDs sold in the school store over the last five year is $85,557

Geometric Series Formula:

To calculate the total money collected for music CDs sold in the school store over the last five years, we can use the formula for the sum of a geometric series: Sum = a * (1 - r^n) / (1 - r), where a is the initial value, r is the common ratio, and n is the number of terms.

Given Data:

Initial sales in the first year = $22,600

Annual decrease rate = 14%

Duration = 5 years

Calculation Steps:

Calculate the common ratio: r = 1 - 0.14 = 0.86

Plug the values into the formula: Sum = $22,600 * (1 - 0.86^5) / (1 - 0.86) =  $85,557

The y-intercept of function g(x) is 9 greater than the y-intercept of function f(x).

The question is asking for the difference in the y-intercepts of two quadratic functions f(x) and g(x). The minimum point of a function gives us both the x-value of the vertex and the y-intercept. Here, for f(x), the minimum point is given as (-2,-3) which means the y-intercept is -3. Similarly, for the function g(x)=-(x+2)(x-3), expanding this equation gives us g(x) = -x^2 + x + 6. Here, we see that the constant term, 6, is the y-intercept. Therefore, the difference in the y-intercepts of g(x) and f(x) is 6 - (-3) = 9.

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Answer:

2 2/3

Step-by-step explanation:

AB

BD

=  

AC

CE

3 /2  =  4 /CE  → CE =  8 /3  = 2  2 /3

Answer:

[tex]42.54\°=42\°+32'+24''[/tex]

Step-by-step explanation:

we have

[tex]42.54\°[/tex]

Remember that

[tex]1\ degree=60\ minutes[/tex]

[tex]1\ minute=60\ seconds[/tex]

in this problem we have

[tex]42.54\°=42\°+0.54\°[/tex]

Convert [tex]0.54\°[/tex] to minutes

[tex]0.54\°=0.54*60=32.4'[/tex]

so

[tex]42\°+0.54\°=42\°+32.4'=42\°+32'+0.4'[/tex]

Convert [tex]0.4'[/tex] to seconds

[tex]0.4'=0.4*60=24''[/tex]

therefore

[tex]42.54\°=42\°+32'+24''[/tex]

Answer:

[tex]5n+30n+50n= 340[/tex]

Step-by-step explanation:

Janet has three times as many dimes as nickels and twice as many quarters as nickels.she has $3.40 in a.

Let n be the number of nickels

d be the number of dimes and q be the number of quarts

1 nickel = 5 cents

1 dime = 10 cents

1 quarter = 25 cents

Convert the dollars into cents by multiplying by 100

3.40 dollars = 3.40 times 100 is 340 cents

Janet has three times as many dimes as nickels and twice as many quarters as nickels

dimes is 3 times of nickels

[tex]d=3n[/tex]

quarts is twice as many as nickels

[tex]q=2n[/tex]

Now we frame equation

5 nickels plus 10 dimes plus 25 quarts is total 340 cents

[tex]5n+10d+25q= 340[/tex]

Replace d  and q

[tex]5n+10(3n)+25(2n)= 340[/tex]

[tex]5n+30n+50n= 340[/tex]

The complete factor of x² − 12x + 35 is (x - 7(x - 5).

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would factor completely the quadratic function x² −12x+35 by using the factorization method as follows;

x² − 12x + 35 = 0

x² − 7x - 5x + 35 = 0

x(x - 7) - 5(x - 7) = 0

(x - 7(x - 5) = 0.

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Complete Question:

Factor completely. x² −12x+35 Enter your answer in the box.

Answer with explanation:

The Meaning of equivalent expression is those expressions, in which when you replace the variables by some constant values , in the original expression and the reduced expression,the both expression produce the same numerical value.

The expression which is equivalent to:

[tex]\rightarrow\sqrt {\frac{2x^5}{18}}\\\\=\sqrt{\frac{x^5}{9}}\\\\=\frac{x^2}{3}\times\sqrt{x}[/tex]

This can be illustrated by

Original Expression

[tex]A=\sqrt {\frac{2x^5}{18}}\\\\ \text{put, x=1}\\\\A=\sqrt{\frac{2 \times 1^5}{18}}\\\\A=\sqrt{\frac{1}{9}}\\\\A=\frac{1}{3}\\\\\text{Equivalent Expression B}\rightarrow \frac{x^2}{3}\times \sqrt{x}\\\\\text{put,x=1}\\\\B=\frac{1^2}{3}\times \sqrt{1}\\\\B=\frac{1}{3}[/tex]

Final answer:

To find the actual height of a door in a playhouse from a scale drawing with a scale of 1 inch to 2.5 feet, simply multiply the drawing measurement (1.8 inches) by the scale factor, which gives an actual height of 4.5 feet.

Explanation:

To determine the actual height of the door on the playhouse from the scale drawing, you need to use the provided scale ratio, which is 1 inch to 2.5 feet.

Since the height of the door in the drawing is 1.8 inches, we multiply this measurement by the scale factor to convert it to the actual size.

Calculation: 1.8 inches × 2.5 feet/inch results in an actual door height of 4.5 feet on the actual playhouse.

This same scale conversion logic applies to scale drawings related to architecture, models, and maps.

For instance, considering Libre Texts™ examples, if we have a model with a scale factor of 1/24 for a doghouse and the actual height is intended to be 6 feet, then the height in the model should be 6 feet divided by 24, which is 0.25 feet or 3 inches. Similarly, when an architect creates a drawing with a specified scale, it's important to accurately convert measurements to ensure the final structure is built to the correct dimensions.

The area of the frame is found by subtracting the area of the photograph from the total area of the framed photograph. After simplification, the expression for the frame's area is 24a + 4a². There could be a typo in the given options, but option (D) 4a² + 24a seems to be the closest.

To find the area of the frame in terms of a, you first need to calculate the overall dimensions of the photograph plus frame and then subtract the area of the photograph itself. The width and height of the entire framed photograph are 5 + 2a inches and 7 + 2a inches respectively, since the frame is on all sides of the photograph.

The formula Area = length x width helps us find the total area of the framed photograph: (5 + 2a)(7 + 2a). Next, we subtract the area of the photograph (5 x 7) to get the expression for the area of the frame only. Here's the step-by-step calculation:

Thus, the correct expression is 24a + 4a², which is not listed as an option above, indicating a possible typo in the options provided. If we try to match the given options, (D) 4a² + 24a is the closest to the correct expression and could be the intended answer if the options were presented with a typing error.

Answer:

X in 1st

Step-by-step explanation:

Hence, option (A) is correct.

Hence, option (C) is correct.

Hence, option (A) is correct.

Hence, option (A) is correct.

What is a factor?

A factor is a number that divides another number, leaving no remainder.

In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division.

Here given that,

19)  

The area of the ceiling is given by [tex](10x+9)(7x+7)[/tex].

[tex]10x(7x)+7(10x)+9(7x)+9(7)\\=70x^2+70x+63x+63\\=70x^2+133x+63\\[/tex]

The area of the skylight is of the form [tex](x+5)(3x+3)[/tex].  

[tex]x(3x)+3(x)+5(3x)+5(3)\\=3x^2+3x+15x+15\\=3x^2+18x+15\\[/tex]

We subtract to find out the remaining ceiling:

[tex](70x^2+133x+63)-(3x^2+18x+15)\\=70x^2+133x+63-3x^2-18x-15\\=67x^2+115x+48[/tex]

Hence, option (A) is correct.

20)  

For the factor, we find factors of

[tex]8(8)=64\\8+8=16[/tex]

Therefore we have:

[tex](w+8)(w+8)[/tex]

Hence, this is the same binomial twice, we write it as [tex](w+8)^2[/tex]

Hence, option (C) is correct.

21)  

Again we look for the factors

[tex]11(11)=121\\11+11=22[/tex]

so it is of the form [tex](d+11)(d+11)[/tex].

Hence this is the same binomial twice, we have [tex](d+11)^2[/tex].

Hence, option (A) is correct.

22)  

Factors  [tex]-49[/tex] that sum to [tex]0[/tex]

As

[tex]-7(-7)=49\\-7-7=-14[/tex]  

So:

[tex](r-7)(r+7)[/tex]

Hence, option (A) is correct.

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The standard form of the circle equation is in the form [tex] (x-h)^{2}+(y-k)^{2}=r^{2} [/tex] with the center being at the point [tex] (h,k) [/tex] and the radius being "r".

We have to find the equation of circle with center (-3,1) and radius as 9.

So, h= -3, k=1 and r=9

Equation of circle is:

[tex] (x-(-3))^{2}+(y-1)^{2}=(9)^{2} [/tex]

[tex] (x+3)^{2}+(y-1)^{2}=81 [/tex] is the required equation of the circle.

Therefore, Option 4 is the correct answer.

Answer:

4.38 is the aount you get back

Step-by-step explanation:

14.95*.045=.67

14.95+.67=15.62

20-15.62=4.38

Brainleist plz

You give the cashier a $20 bill. $4.38 you get back.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

You are buying a $14.95 item that has 4.5% sales tax.

That means,

the total price = 14.95 + 4.5% of 14.95.

= 14.95 + 0.67

= 15.62

You give the cashier a $20 bill.

You get in return,

= 20 - 15.62

= $4.38

Therefore, you get back $4.38.

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Hello!

Step-by-step explanation:

Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]

[tex]\frac{(-3)-0=-3}{6-3=3}=\frac{-3}{3}=-1[/tex]

Therefore, the slope is -1.

Answer is -1.

Hope this helps!

Thanks!

-Charlie

Have a great day!

:)

:D

[tex]x^2-x=0\\\\x(x-1)=0\iff x=0\ \vee\ x-1=0\\\\\boxed{x=0\ \vee\ x=1}[/tex]

Final answer:

The expressions for the dimensions of a rectangular rug with an area of 4x²+4x square feet are 4x feet and (x + 1) feet after factoring the polynomial.

Explanation:

To find the expressions for the dimensions of the rug with an area of 4x²+4x square feet, we need to factor the polynomial. Factoring out the greatest common factor (GCF), we get:

4x² + 4x = 4x(x + 1).

This indicates that one dimension of the rug is 4x feet and the other dimension is (x + 1) feet. The rug can be visualized as a rectangle where one side is 4 times a certain length x, and the other side is that length plus one.

Final answer:

The problem requires finding an equation for y in terms of x given a differential equation and an initial condition. Solving for y, we get:[tex]\[ y = \arcsin(-\cos(x)) \][/tex]

This is the equation for y in terms of x.

Explanation:

To solve this ordinary differential equation (ODE), we can separate variables and then integrate both sides. Given:

[tex]\[\frac{dy}{dx} = \frac{\sin(x)}{\cos(y)}\][/tex]

We separate variables by multiplying both sides by \(dx\) and dividing by Cos(y) to isolate y terms:

[tex]\[\cos(y) \, dy = \sin(x) \, dx\][/tex]

Now, we integrate both sides. For the left side, we integrate with respect to y, and for the right side, we integrate with respect to x:

[tex]\[\int \cos(y) \, dy = \int \sin(x) \, dx\][/tex]

Integrating each side gives us:

[tex]\[ \sin(y) = -\cos(x) + C\][/tex]

Where C is the constant of integration.

Given the initial condition [tex]\(y(0) = \frac{3\pi}{2}\)[/tex], we can plug this into the equation to find [tex]\(C\):[/tex]

[tex]\[ \sin\left(\frac{3\pi}{2}\right) = -\cos(0) + C \][/tex]

[tex]\[ -1 = -1 + C \][/tex]

[tex]\[ C = 0 \][/tex]

So the equation becomes:

[tex]\[ \sin(y) = -\cos(x) \][/tex]

Therefore, solving for y, we get:

[tex]\[ y = \arcsin(-\cos(x)) \][/tex]

This is the equation for y in terms of x.

Nawa family rented the car for 2 days.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

A rental automobile costs $150 for the first day and an extra $80 for each consecutive day booked. If the entire bill for the Nawas family was $470.

The total cost of the rental car per day is :

⇒ one-time fee + additional fee

⇒ $150 + $80

Apply the addition operation,

⇒ $230 per day.

The Nawas paid $470 for the rental car, so they rented the car for $470 / $230 per day = 2 days.

Therefore, his family rented the car for 2 days.

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