Combine like terms. What is a simpler form of the expression?
-3(-4y + 3) + 7y
Question 4 options:
-19y + 3
19y - 9
10y
-19y - 9
the perimeter of Jared's property is 56 yards. how many feet of fence will Jared need if he wants to enclose the whole property?
Steve is turning half of his backyard into a chicken pen. His backyard is a 24 meter by 45 meter rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How many meters of fencing will Steve need?
A grasshopper jumps off a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function shown below. After how many seconds will the grasshopper land on the ground? Round to the nearest tenth.
h(t) = -t^2 + 4/3t + 1/4
A. -0.2 seconds
B. 0.5 seconds
C. 1.5 seconds
D. 0.7 seconds
The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function , which is
[tex] h(t) =-t^2+\frac{4}{3}t+ \frac{1}{4} [/tex]
When the grasshopper land on the ground,
[tex] h(t)=0 [/tex]
that is,
[tex] -t^2+\frac{4}{3}t+ \frac{1}{4}=0 [/tex]
Multiplying whole equation by 12 to get rid of denominators 3 and 4
[tex] -12t^2+16t +3=0 [/tex]
[tex] (3-2t)(6t+1)=0
\\
3-2t=0 , 6t+1=0
\\
t= \frac{3}{2} , \frac{-1}{6} [/tex]
And time cant be negative, so the correct option is
[tex] t = \frac{3}{2}=1.5 seconds [/tex]
Correct option is C .
The correct option is (D) 0.7 seconds.To determine when the grasshopper lands on the ground based on its height function, solve the quadratic equation and round to the nearest tenth for the time in seconds.
The height of the grasshopper above the ground is given by the function h(t) = -t² + 4/3t + 1/4. To find when the grasshopper lands on the ground, set h(t) = 0 and solve for t.
By setting -t² + 4/3t + 1/4 = 0 and solving the quadratic equation, you'll find the solutions for t. Round to the nearest tenth to get the time when the grasshopper lands.
The correct answer is 0.7 seconds (D).
the main difference between secured and unsecured loans is that the secured loan ___.
A) has a higher interest rate
B) requires a cosigner
C) offers protection against identity theft
D) includes a pledge of collateral
Apex.
It includes a pledge of collateral.
John is adding a curved edge to the landscaping in front of the high school. The curve is an arc of a circle with a radius of 1600 feet. The central angle that intercepts the curve measures π/8 radians. The length of the curve to the nearest foot is _____ feet.
The length of the curve to the nearest foot is 628 feet.
To find the length of the curved edge, which is an arc of a circle, one can use the formula for the arc length [tex]\( L \)[/tex] of a circle, given by the product of the radius [tex]\( r \)[/tex] and the radian measure [tex]\( \theta \)[/tex] of the central angle that intercepts the arc:
[tex]\[ L = r \cdot \theta \][/tex]
In this case, the radius [tex]\( r \)[/tex] is given as 1600 feet, and the central angle [tex]\( \theta \)[/tex] is given as [tex]\( \frac{\pi}{8} \)[/tex] radians.
Plugging in the values, we get:
[tex]\[ L = 1600 \text{ feet} \cdot \frac{\pi}{8} \text{ radians} \][/tex]
To find the numerical value, we use the approximation [tex]\( \pi \approx 3.14159 \)[/tex]:
[tex]\[ L \approx 1600 \cdot \frac{3.14159}{8} \] \[ L \approx 1600 \cdot 0.39269906 \] \[ L \approx 628.3185 \][/tex]
Since we are asked to round to the nearest foot, we consider the value 628.3185 feet. Rounding this to the nearest whole number, we get:
[tex]\[ L \approx 628 \text{ feet} \][/tex]
Therefore, the length of the curve to the nearest foot is 628 feet.
The area of a rectangle is 56 cm. The length is 2cm more than x and the width is 5 cm less than twice x.Solve for x
If cos theta = 1/4 and 0 degrees, find tan theta
Final answer:
To find tan theta when cos theta = 1/4, use the Pythagorean identity to find sin theta and then divide sin theta by cos theta to get tan theta, which is (sqrt(15)).
Explanation:
To find tan theta when given that cos theta = 1/4 and knowing that theta is between 0 and 90 degrees, we can use the Pythagorean identity for trigonometric functions, which states that sin^2 theta + cos^2 theta = 1. Since we have cos theta, we can solve for sin theta.
First, square cos theta to get cos^2 theta:
cos^2 theta = (1/4)^2 = 1/16
Now, apply the identity:
sin^2 theta = 1 - cos^2 theta = 1 - 1/16 = 15/16
Take the square root to find sin theta (choosing the positive root since theta is between 0 and 90 degrees):
sin theta = √(15/16) = √15/4
Finally, use the definition of tan, which is sin theta / cos theta:
tan theta = sin theta / cos theta = (√15/4) / (1/4) = √15
The sum of a student's three score is 246. if the first is 14 points more than the second, and the sum of the first two is 6 more than twice the third, what was the first score?
Help Please...
So, I'm doing a blueprint assignment for my school. I have to determine a scale factor. Right now, the house is in feet, its measurements 20 by 40. I want to do a blue print using centimeters as my scale. What I want to do is scale factor it so it's not too small but at the same time doesn't take up the whole graph paper. If anyone has a idea on what scale factor I should use, please answer.
A holding pen for cattle must be square and have a diagonal length of 84 84 meters.
a. find the length of a side of the pen.
b. find the area of the pen.
To find the length of a side of the pen, we can use the Pythagorean Theorem. The area of the pen can be calculated by multiplying the length of a side by itself.
Explanation:To find the length of a side of the pen, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the diagonal of the pen acts as the hypotenuse.
Let's let s represent the length of a side of the pen. Using the Pythagorean Theorem, we have:
s^2 + s^2 = 84^2
Simplifying the equation, we get:
2s^2 = 7056
Dividing both sides of the equation by 2, we get:
s^2 = 3528
Taking the square root of both sides, we get:
s ≈ 59.46 meters
To find the area of the pen, we can multiply the length of a side by itself. So, the area is:
s * s = 59.46 * 59.46 = 3536.8516 square meters
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Which choice is the common difference between the terms of this arithmetic sequence?4x + 7y, 8x + 2y, 12x + -3y, 16x - 8y, 20x - 13y, ...
A.4x - 5y
B.-5x - 4y
C.4x + 5y
D.5x + 4y
E.5x - 4y
Simplify. x-2/(x^2+4x-12)
A company is looking to design a new cover for their smartphone. The scale drawing of the design is shown below. The coordinates of the actual cover are: R' (12, 0); S' (0, 0); T' (0, 16); U' (12, 16). Is the design of the cover similar to the actual cover?
Rectangle RSTU is shown. Point R is at 3,0. S is at 0,0. T is at 0,4. U is at 3,4.
Yes; the corresponding sides are proportional.
No; the corresponding sides are not proportional.
Yes; the corresponding angles are proportional.
No; the corresponding angles are not proportional.
6x – 2y = 10 2x + 3y = 51 Solving the first equation above for y gives
Answer with Step-by-step explanation:
6x – 2y = 10
2x + 3y = 51
Solving the first equation above for y:
6x-2y=10
⇒ 2y=6x-10
dividing both sides by 2
y=3x-5
Putting value of y in second equation
2x + 3(3x-5) = 51
2x+9x-15=51
11x=51+15
11x=66
⇒ x=6
y=3×6-5
=18-5
= 13
Hence, solution is: x=6 and y=13
and Solving the first equation above for y gives: y=3x-5
Need help on this question
7,24,25. 7 , 23,24 7, 25,26
Which of the following will form a right triangle
Answer:
7, 24, 25
Step-by-step explanation:
7^2=49
24^2 = 576
25^2 = 625
576 + 49 = 625.
therefore, its a right angle
Four baskets contain scented soaps. the baskets contain 9, 9, 11, and 15 soaps. if the soaps are divided evenly among the baskets, how many soaps will go in each basket?
Answer:
The answer is C on EDGEN.
Step-by-step explanation:
C. 11
Does anyone else agree that the answer for this family of curves question is E, dy/dx = x + y?
Observe the two functions on the graph.
Match each function with a type of function.
f(x): Cubic
Linear
Exponential
Quadratic
g(x): Cubic
Linear
Exponential
Quadratic
James has 16 balloons.1/4 of his balloons are red.How many red balloons does he have?
TIMED, need the answer
Determine whether the graph of the quadratic function y = –x2 – 10x + 1 opens upward or downward. Explain.
a. Because a > 0, the parabola opens downward.
b. Because a < 0, the parabola opens upward.
c. Because a < 0, the parabola opens downward.
d. Because a > 0, the parabola opens upward.
When a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards and from the given equation a < 0 that is why the graph of the quadratic equation is a parabola that opens downward.
Given :
Quadratic Function --- [tex]y = -x^2-10x + 1[/tex]
The graph of the quadratic equation is in the shape of the parabola. The generalized quadratic equation is given by:
[tex]ax^2 + bx +c = 0[/tex]
Now, compare the given equation ([tex]y = -x^2-10x + 1[/tex]) with the generalized quadratic equation which is given above.
[tex]a = -2[/tex]
b = -10
c = 1
According to the rules of the graph, when a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards.
Therefore, the correct option is c).
For more information, refer to the link given below:
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I dont inderstand this at all
What is the volume of the cylinder below?
Answer:
C) 288π units³
Step-by-step explanation:
When the height of an oblique cylinder is given, the formula for volume is
V = π×r²×h
Our radius is 6 and our height is 8:
V = π(6²)(8) = π(36)(8) = 288π
The volume of the cylinder is [tex]\boxed{288\pi {\text{ unit}}{{\text{s}}^3}}[/tex].Option (C) is correct.
Further explanation:
Given:
Theheight of the cylinder is [tex]{\text{8 units}}[/tex] and the radius of the cylinder is [tex]{\text{6 units}}.[/tex]
The options of the volume are given as follows.
A. [tex]{\text{216}}\pi {\text{uni}}{{\text{t}}^3}[/tex]
B. [tex]324\pi {\text{uni}}{{\text{t}}^3}[/tex]
C. [tex]288\pi {\text{uni}}{{\text{t}}^3}[/tex]
D. [tex]432\pi {\text{uni}}{{\text{t}}^3}[/tex]
Explanation:
The formula for the volume of the cylinder can be expressed as,
[tex]\boxed{{\text{Volume}} = \pi {r^2}h}[/tex]
‘r” is the radius of the cylinder and “h” is the height of the cylinder.
The volume of the right cylinder can be obtained as follows,
[tex]\begin{aligned}{\text{Volume}} &= \pi {r^2}h\\&= \pi\times {\left( 6 \right)^2} \times 8\\&= \pi\times 36 \times 8\\&=288\pi \\\end{aligned}[/tex]
The volume of the cylinder is [tex]36\pi {\text{ unit}}{{\text{s}}^3}.[/tex]
The volume of the cylinder is [tex]\boxed{288\pi {\text{ unit}}{{\text{s}}^3}}[/tex].Option (C) is correct.
Learn more:
Learn more about inverse of the functionhttps://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497Answer details:
Grade: High School
Subject: Mathematics
Chapter: Mensuration
Keywords: Cylinder, surface area of the cylinder, volume of the cylinder, right cylinder, height, radius depth.
In each round of a game show, a contestant answers a multiple-choice question that has three answer choices. The contestant advances to the next round by answering the question correctly. What is the probability of advancing to the seventh round if the contestant randomly guesses the answer to each question? Write your answer as a fraction in simplest form.
The probability of advancing to the seventh round by randomly guessing on a game show with three answer choices per question is 1/729.
The probability of advancing to the seventh round if the contestant randomly guesses the answer to each multiple-choice question with three answer choices is calculated by raising the probability of guessing one question correctly to the power of six, since the contestant needs to guess correctly six times in a row to reach the seventh round.
The probability of guessing one question correctly is 1/3, as there are three possible choices and only one correct answer. Thus, the probability of guessing six questions correctly in a row is (1/3)⁶.
Simplifying this, we get:
(1/3)⁶ = 1/729.
Therefore, the probability is 1/729.
HELP ME PLEASE
Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.
an = 8(1/2)n − 1; average rate of change is −3
an = 10(1/2)n − 1; average rate of change is 3
an = 8(1/2)n − 1; average rate of change is 3
an = 10(1/2)n − 1; average rate of change is −3
Answer:
Option A
Step-by-step explanation:
To find nth term we use the given options.
[tex]a_n= 8(\frac{1}{2})^{n-1}[/tex]
Lets pick any point from the graph and plug it in the given option
LEts pick (1,8) and (2,4)
[tex]a_n= 8(\frac{1}{2})^{n-1}[/tex], n=1, an=8
[tex]8= 8(\frac{1}{2})^{1-1}[/tex]
[tex]8= 8(\frac{1}{2})^{0}[/tex]
8=8 True
LEts check with (2,4), n=2 and an=4
[tex]4= 8(\frac{1}{2})^{2-1}[/tex]
4=4 True
Average rate of change from n=1 to n=3= [tex]\frac{a_3-a_1}{3-1} =\frac{2-8}{2} =-3[/tex]
Average rate of change from n=1 to n=3 is -3
multiply and /or divide the following polynomials
Answer:
D) 4x - 17
E) -b - 6a
F) -2(7x + 34)
Explanation:
For question D, we divide each term in the first binomial by 3x and simplify:
(12x² / 3x) - (51xy / 3x)
12 / 3 = 4, x² / x = x 51 / 3 = 17, x / x = 1, y / 1 = y
4x - 17(1)y
4x - 17y is left as a quotient
For question E, we do distribute -3a to the binomial in the numerator and do the same, divide each term in the binomial by -6a and simplify:
-3a(-2b - 12a) = -3a(-2b) - 3a(-12a) = 6ab + 36a²
(6ab + 36a²) / -6a =
(6ab / -6a) + (36a² / -6a)
6 / -6 = -1, a / a = 1, b / 1 = b 36 / -6 = -6, a² / a = a
-1(1)(b) + (-6)(a)
-b - 6a is left as a quotient
For question F, we distribute the 4 and 3x to their respective binomials and then combine like terms where applicable:
4(x² - 8x) + 3x(-6x - 12)
4(x²) + 4(-8x) + 3x(-6x) + 3x(-12)
4x² - 32x - 18x² - 36x
4x² - 18x² - 32x - 36x
-14x² - 68x, both terms have a greatest common factor (GCF) of -2 which can be divide out of them to further simplify:
-2(7x + 34)
A man has 14 coins in his pocket, all of which are dimes and quarters. if the total value of his change is $2.60, how many dimes and how many quarters does he have?
How is commission calculated?
Commission is typically a percentage of sales paid to an agent or employee, and it can be calculated by multiplying the percentage rate by the sale amount. Real estate agencies and stock brokers have different structures for commission, which can significantly affect agents' earnings and motivation. Properly designed sales commission structures balance salary and commissions for optimum sales and customer satisfaction.
Commission is a fee paid to an employee or agent for conducting a transaction or service, typically a percentage of the sale made. Real estate agencies often pay agents a combination of salary and commission, with the intent to motivate them to achieve higher sales and provide satisfactory service to clients. For instance, agencies like RE/MAX pay almost 100% commission, attracting agents who are confident in their sales abilities and prefer a high-reward structure, though this may come at a cost to agency-wide cooperation.
The calculation of commission generally involves multiplying the sale amount by the commission percentage agreed upon. If a real estate agent sells a house for $200,000 and has a commission rate of 5%, their commission would be $200,000 * 0.05 = $10,000. While most agencies operate on average commission rates of about 50%, RE/MAX's near-100% commission structure can be very lucrative for highly skilled agents.
In the stock market, since May 1, 1975, when the SEC abolished fixed commissions, commission rates have been competitive and are typically lower for 'round lots' (buying or selling 100 shares) compared to 'odd lots'. It is also a common practice for firms to add a flat brokerage charge to the transaction.
To design an effective compensation plan incorporating commission along with a fixed salary, companies must carefully balance the two to ensure that they achieve an optimum balance between sales volume, profitability, and customer satisfaction. This balance is critical to attract and retain talented agents and salespeople who are motivated to perform well.