Which is an equation of the line graphed below?
A. y=2x-3
B. y=1/2x-3
C. y= -1/2x-3
D. y= -2x-3
Evaluate the expression 14.3 minus 2 times 5 to the 2nd power divided by 5
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]
PLEASE HELP ASAP
EXTRA POINTS
Sheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.
The photograph is positioned so that the matting is twice as wide at the top and bottom as the sides.
Write an equation for the area of the photo in terms of x.
The simple interest on a principal amount, P, borrowed for T years at R% annual interest is given by the following formula. Which of the following describes the relationship between the variables of the simple interest formula?
1.P depends on R and T
2.R depends on P and T
3.I depends on P, R, and T
4.R depends on I
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.
if dy/dx= sin x/ cos y and y(0) = 3pi/2, find an equation for y in terms of x
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.
Tom separated the rectangle shown below into 8 equal parts what fraction shows the area of one of the parts
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.
rank from highest to lowest in order of decresing mass
1 Gg, 100 g, 1 kg, 50 cg, 1 cg, 1 dg, 50 million ng,
PLEASE HELP ASAP!
Volume of rectangular prism
Area of a parallelogram
Circumference of a circle
Area of a circle
Area of a triangle
Area of a trapezoid
Perimeter of a quadrilateral
-
Item bank:
2L + 2W
πd
πr2
bh
lwh
1/2(b1 + b2)h
1/2 bh
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:
Volume of a rectangular prism is given by the formula V = lwh (length × width × height).Area of a parallelogram is found using A = bh (base × height).Circumference of a circle requires the formula C = πd or C = 2πr where d is diameter and r is radius.Area of a circle is calculated by A = πr² (pi times radius squared).Area of a triangle can be computed using A = 1/2 bh (half the base times the height).Area of a trapezoid is found with A = 1/2(b1 + b2)h where b1 and b2 are the bases and h is the height.Perimeter of a quadrilateral is the sum of the lengths of all four sides, often expressed as P = 2L + 2W for rectangles, with L being length and W being width.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.
Please help!!! Fast
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
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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Ashley has 100 books that she wants to give away at the rate of n books per week. Write a recursive function that represents the number of books Ashley has at any time. The recursive function that gives the number of books Ashley has at any time is = , starting at
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.
if you were to solve the following system by substitution what would be the best variable to solve and from what equation? 2x+8y=12 3x-8y=11
Answer:
X in 1st
Step-by-step explanation:
PLZZ HELP AND PLZZ HURRY
What other information is needed to prove that △FGE ~ △IJH by the SAS similarity theorem?
A. ∠F ≅ ∠J
B. ∠I ≅ ∠F
C. ∠E ≅ ∠H
D. ∠G ≅ ∠I
Answer:
I think the answer is B. ∠I ≅ ∠F.
Step-by-step explanation:
Which is a solution of x2 – x – = 0?
[tex]x^2-x=0\\\\x(x-1)=0\iff x=0\ \vee\ x-1=0\\\\\boxed{x=0\ \vee\ x=1}[/tex]
What is the slope of the line that passes through the points E(3, 0) and F (6, -3)?
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!
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please help I will mark brainlist if correct
PLEASE HELP!!!
Use a calculator to find the approximate value of arccos(0.63).
a) 39.05 degrees
b) 50.95 degrees
c) 78.1 degrees
d) 32.21 degrees
Please explain how you achieved this answer. Thanks!
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.
Consider the function f(x)=−23x+5 . What is f(52) ? Enter your answer, as a simplified fraction, in the box.
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
f(52) = -1191.Arnold borrowed $7890 at 11.5 percent for five years. How much did Arnold Pay in interest?
A.$2,199
B.$2,300
C.$1,150
D.$2.520
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
You have been really sick, so you went to the doctor. The culture taken shows you have 400,000 bacteria. Your doctor prescribes a strong antibiotic which makes the bacteria decrease by a half every 4 hours. How many bacteria will be left after a day?
Why did you delete my answer?
In what ways do you think presidents today are more powerful than they were in the past?
Modern presidents are more powerful than their predecessors due to access to advanced technologies, executive actions, and media influence.
Explanation: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.
Learn more about Power of modern presidents here:https://brainly.com/question/29360176
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How do u do question 27 and 29. Find the measure of angle x?
Factor completely. x2−12x+35 Enter your answer in the box.
The complete factor of x² − 12x + 35 is (x - 7(x - 5).
What is the general form of a quadratic function?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:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.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
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Complete Question:
Factor completely. x² −12x+35 Enter your answer in the box.
The center of a circle is at (−3, 1) and its radius is 9.
What is the equation of the circle?
(x+3)2+(y−1)2=18
(x−3)2+(y+1)2=18
(x−3)2+(y+1)2=81
(x+3)2+(y−1)2=81
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.
Which graph is defined by f(x) = |x2 − x − 2|?
The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring. What is the constant of the quadratic function in this equation?
How do you know a radical expression is in simplest form?
(a - b)(a 2 + ab + b 2) HELP
What is the distance between point l (3,5) and point m (9,−7)?
Janet has three times as many dimes as nickels and twice as many quarters as nickels. If she has $3.40 in all, how many nickels, dimes, and quarters does she have?
If n represents the number of nickels Janet has, which of the following equations could be used to solve the problem?
5n + 10n + 25n = 340
n + 3n + 2n = 340
5n + 30n + 50n = 340
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]