What is the value of x in the proportion StartFraction 2 x plus 7 over 3 x minus 4 EndFraction equals 11 over 2?
A. 2
B. 58
C. eleven-twenty-ninths
D. two-fifths

Answer:

I think the answer is B. ∠I ≅ ∠F.

Step-by-step explanation:

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.

Let's assume

Randy's speed =x mph

we have

Andy’s speed was slower than Randy’s by 15 miles per hour

so,

Andy's speed =x-15

Randy drove 540 miles

so, we can find time taken by Randy

time = distance / speed

so, we get

[tex]t_R=\frac{540}{x}[/tex]

we can find time taken by Andy

time = distance / speed

so, we get

[tex]t_A=\frac{135}{x-15}[/tex]

Randy drove 540 miles in three times the time it took Andy to travel 135 miles

so,

[tex]t_R=3t_A[/tex]

we can plug it

[tex]\frac{540}{x}=3*\frac{135}{x-15}[/tex]

now, we can solve for x

[tex]540\left(x-15\right)=405x[/tex]

[tex]135x=8100[/tex]

[tex]x=60[/tex]

so,

Calculation of rate:

Randy's speed is 60 mph

Andy's speed =x-15

Andy's speed =60-15=45mph

Calculation of time:

Randy's time is

[tex]t_R=\frac{540}{x}[/tex]

[tex]t_R=\frac{540}{60}[/tex]

[tex]t_R=9 hours[/tex]

Andy's time is

[tex]t_A=\frac{135}{x-15}[/tex]

[tex]t_A=\frac{135}{60-15}[/tex]

[tex]t_A=3 hours [/tex]

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 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]

Unlocked badge showing an astronaut’s boot touching down on the moon

See what the community says and unlock a badge.

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.

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]

Final answer:

Clear geometry formulas for calculating volume, area, and perimeter include V = lwh for rectangular prisms, A = bh for parallelograms, and C = πd for the circumference of a circle, among others.

Explanation:

Understanding Geometry, Area, and Volume

To help with remembering formulas from geometry, it's essential to understand the relationships between shapes and their dimensions. Here are the correct formulas for each of the items listed:

To solve problems in geometry effectively, it's helpful to visualize the shapes and understand how to derive their area and volume using standard formulas. This also applies when dealing with more complex objects, such as spheres and cylinders. In trigonometry, understanding the relationships within a right triangle can be crucial for solving spatial problems.

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.

To find the approximate value of arccos(0.63), input 0.63 into the calculator and use the inverse cosine function to find the answer, which is approximately 50.95 degrees. So correct answer is option B.

The approximate value of arccos(0.63) can be found using a calculator.

To find arccos(0.63), you need to input 0.63 into the calculator and then find the inverse cosine or cos^-1 function. On most calculators, this is represented as cos^-1 or arccos.

When you calculate arccos(0.63), you will get approximately 50.95 degrees as the correct answer.

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.

Read more on quadratic functions here: brainly.com/question/29499209

#SPJ6

Complete Question:

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

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

Final answer:

To describe Ashley's book giveaway scenario with a recursive function, define the base case as her starting with 100 books and the recursive step reflecting the weekly giveaway of n books, allowing the calculation of remaining books at any week.

Explanation:

Ashley's scenario of giving away books can be described using a recursive function. If she starts with 100 books and plans to give away n books per week, we can denote the total number of books she has after x weeks as f(x). The recursive function that represents this situation can be written as:

f(0) = 100 - This is our base case, where Ashley starts with 100 books before any are given away.

f(x) = f(x-1) - n - This is the recursive step, indicating that the total number of books Ashley has after x weeks is the number she had the week before, minus n, the number of books given away weekly.

This recursive formula allows you to calculate the number of books Ashley will have after any given number of weeks, as long as n is a known constant number of books she gives away each week.

Why did you delete my answer?

Final answer:

Intellectual property rights such as patents and copyrights incentivize creative work by providing creators a temporary monopoly, allowing them to recover development costs and potentially make a profit without immediate competition.

Explanation:

Two intellectual property rights are patents and copyrights. A patent gives the inventor the exclusive legal right to make, use, or sell an invention for a limited time, usually for 20 years, and a copyright provides the author exclusive legal rights over their creative works.

Intellectual property rights offer creators monopoly profits during this protected period, acting as significant incentives for the production of creative work.

This exclusive period allows researchers and companies to recover the costs associated with research and development. Without these protections, there would be little to no incentive to invest in creating new works if they could quickly be replicated without any benefit to the creator.

Answer:

X in 1st

Step-by-step explanation:

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]

Step-by-step explanation:

Given function f(x)=−23x+5

We need to find f(52).

In order to find the value of f(52), we need to plug x= 52 in the given above linear function f(x) = -23x+5.

Plugging x= 52, we get

f(52) = -23(52) +5

On multiplying -23 and 52 we get -1196.

Therefore,

f(52) = -1196 +5

And

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.

https://brainly.com/question/29360176

#SPJ3