The vertex form of the equation of a parabola is X=(y-3)^2+41. What is the standard form of the equation?

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

Answer:

2 2/3

Step-by-step explanation:

AB

BD

=  

AC

CE

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

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:

[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]

Modern presidents are more powerful than their predecessors due to access to advanced technologies, executive actions, and media influence.

Presidents today are more powerful than they were in the past due to various factors. Firstly, modern presidents have access to advanced technologies such as television, the internet, and social media, which allow them to shape public opinion and build support for their policies. Secondly, they have a greater ability to use executive action, including executive orders and signing statements, to bypass Congress and enact their own policies. Finally, modern presidents can use their popularity and media attention to increase pressure on Congress and influence policy change.

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The Correct answer is Option C) is correct: "Yes, because the bike order meets the restrictions of [tex]4c+6a\leq 120[/tex] and [tex]4c+4a\leq 100[/tex]."

To determine whether the company can build [tex]10[/tex] child bikes (c) and [tex]12[/tex]adult bikes (a) within the given time constraints, we need to check if the total building time and testing time for both types of bikes do not exceed the limits.

Each child bike requires [tex]4[/tex] hours to build and [tex]4[/tex] hours to test, while each adult bike requires [tex]6[/tex] hours to build and [tex]4[/tex] hours to test.

So, the total building time [tex](4c+6a)[/tex] and the total testing time [tex](4c+4a)[/tex]for the given number of bikes should not exceed the maximum limits of [tex]120[/tex] hours and [tex]100[/tex] hours, respectively.

Therefore, the system of inequalities that best represents this scenario is:

[tex]4c+6a\leq 120\\4c+4a\leq 100[/tex]

Option 3) is correct: "Yes, because the bike order meets the restrictions of [tex]4c+6a\leq 120[/tex] and [tex]4c+4a\leq 100[/tex]."

COMPLETE QUESTION:

A bicycle manufacturing company makes a particular type of bike. Each child bike requires [tex]4[/tex] hours to build and [tex]4[/tex] hours to test. Each adult bike requires [tex]6[/tex] hours to build and [tex]4[/tex] hours to test. With the number of workers, the company is able to have up to [tex]120[/tex] hours of building time and [tex]100[/tex] hours of testing time for a week. If [tex]c[/tex] represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build [tex]10[/tex] child bikes and [tex]12[/tex] adult bikes in the week.

A) No, because the bike order does not meet the restrictions of [tex]4c + 6a \leq 120[/tex] and [tex]4c + 4a \leq 100[/tex]

B) No, because the bike order does not meet the restrictions of [tex]4c + 4a \leq 120[/tex] and [tex]6c + 4a \leq 100[/tex]

C) Yes, because the bike order meets the restrictions of [tex]4c + 6a \leq 120[/tex]and [tex]4c + 4a \leq 100[/tex]

D) Yes, because the bike order meets the restrictions of [tex]4c + 4a \leq 120[/tex]and [tex]6c + 4a \leq 100[/tex]

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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:

3. I depends on P, R, and T.

Step-by-step explanation:

We have been given the simple interest formula [tex]I=PRT[/tex], where,

I = Amount of simple interest,

P = Principal amount,

T = Time in years,

R= Interest rate.

The bigger principal amount and higher interest rate for a long period of time will result in big amount of interest, while small principal amount at a smaller interest rate and for a small period of time will result in small amount of interest.

Since amount of interest depends on principal amount, rate and time, therefore, 3rd option is the correct choice.

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.

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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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:

4.3

Step-by-step explanation:

We are given that an expression

[tex]14.3-2\times 5^2\div 5[/tex]

We have to find the value of given expression.

DMAS rule:

D=Divided first

M=Multiply

A=Addition

S=Subtraction

Using DMAS rule ,

We  solve  first divide operation

[tex]14.3-2\times 5^{2-1}[/tex]

Using property: [tex]a^x\div a^y=a^{x-y}[/tex]

Then, we get

[tex]14.3-2\times 5[/tex]

Now, we solve multiply operation

[tex]14.3-10[/tex]

Now, we solve subtraction operation

[tex]4.3[/tex]

Hence, [tex]14.3-2\times 5^2\div 5=4.3[/tex]

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.

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]

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

Answer:

X in 1st

Step-by-step explanation:

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.

Tom divided the rectangle into 8 equal parts, and each part represents 1/8 of the total area. This fraction is derived from the fact that division of an area into equal parts means each part is one of those parts as a fraction of the whole.

Tom divided the rectangle into 8 equal parts. If we are to find the fraction that represents the area of one of these parts, we simply consider that each part should be an equal division of the whole. Hence, one part out of eight equal parts is represented by the fraction 1/8. This is because division by 8 is equivalent to multiplication by its reciprocal, which is 1/8. This is the same as dividing the rectangle into smaller, more manageable areas, such as rectangles, and determining the area of one such rectangular area.

It's important to understand that in a rectangle divided evenly into parts, any single part represents a fraction of the whole, with the denominator reflecting the total number of parts. In this case, since there are 8 parts, each individual part is 1/8 of the total area. This provides us with a simple way to address problems involving finding fractions of areas, particularly when the total area is partitioned into equally-sized segments.