Answer:
Slope: -2/3
Step-by-step explanation:
In order to solve this we first have to clear the equation for Y:
[tex]2x+ 3y= -12\\3y=-12-2x\\y=\frac{-12-2x}{3}\\ y=-4-\frac{2}{3} x[/tex]
Remember that the equation in the form of Y is represented in this way:
y=mx+c
Where M is the slope and C is the constant, so the slope is the number that is multiplying x, in the equation, in this case -2/3 is the number that is multiplying x, sot eh slope of the equation is -2/3
The table of values below represents a linear function and shows the height of a tree since it was transplanted. What was the height of the tree when it was transplanted?
The height of the tree when it was transplanted was:
4 feet
Step-by-step explanation:As we could observe that the given table represents a linear function.
The table is given as follows:
Year since it was 4 4.5 5
transplanted
Height (Feet) 12 13 14
We will find the linear function.
Let y denotes height and x denote year since it was transplanted.
We know that any linear function passing through two points (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here let (a,b)=(4,12) and (c,d)=(5,14)
Hence, the linear function is calculated as follows:
[tex]y-12=\dfrac{14-12}{5-4}\times (x-4)\\\\\\y-12=2(x-4)\\\\\\y-12=2x-8\\\\\\y=2x-8+12\\\\\\y=2x+4[/tex]
Now the height of tree when it was transplanted is the value of y when x=0
Hence, when x=0 we have:
y=4
Hence, the height was:
4 feet
Express the Set -4x-6<2x+6 using interval notation
Use the premises and conclusion to answer the questions. Premises: If an angle measure is less than 90°, then the angle is an acute angle. The measure of angle ∠B is 48°. Conclusion: ∠B is an acute angle. Is the argument valid? Why or why not? The argument is not valid because the conclusion does not follow from the premises. The argument is not valid because the premises are not true. The argument is valid by the law of syllogism. The argument is valid by the law of detachment.
Find the area of the following circle. Use = 3.14
r = 5 yd.
A salesperson's commission rate is 5 %. What is the commission from the sale of $ 44,000 worth of furnaces? Use pencil and paper. Suppose sales would double. What would be true about the commission? Explain without using any calculations.
a. The commission from the sale of $ 44,000 worth of furnaces is $1,800
b. Commission would double as well.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
We are given that salesperson's commission rate is 5 %
Then Commission paid on $36,000 worth of furnaces with a rate of 5% is:
= Amount of sales x commission rate
= 36,000 x 5%
= $1,800
If the sales were to double, the commission would be based on double the amount so it would double;
= 36,000 x 2
= $72,000
Commission = 72,000 x 5%
= $3,600
therefore Commission is doubled.
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Barb’s class has 18 bikes .tim’s class has some rows of bikes with 5 bikes in each row. Tim’s class has more bikes than barb’s class. How many rows of bikes could tim’s class have?
Casey has a job doing valet parking. Casey makes an hourly rate of $4.55 per hour plus tips. Last week Casey worked 26 hours and made $898.55. How much in tips did Casey earn last week?
a. $34.56
b. $118.30
c. $157.25
d. $780.25
Please select the best answer from the choices provided
A
B
C
D
Casey earned $780.25 in tips last week. This was calculated by first finding out her earnings from her hourly wage, and then subtracting this from her total earnings.
Explanation:First, we need to calculate how much Casey earns from the hourly rate alone. Given that Casey's hourly rate is $4.55 per hour and she worked for 26 hours last week, we multiply the two to get her earnings from the hourly wage, which is $4.55 * 26 = $118.30.
Then we need to find out how much Casey made in tips. Casey's total earnings last week were $898.55. We subtract the earnings from her hourly rate from her total earnings to find out how much she made in tips. So, $898.55 - $118.30 = $780.25.
Therefore, Casey earned $780.25 in tips last week, which corresponds to option D.
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help!! me asap!! please!!
A customer pays $3.27 for oranges and $4.76 for pears. How many pounds of fruit does the customer buy?
A total of 7 pounds of fruit does the customer buy.
Given that, a customer pays $3.27 for oranges and $4.76 for pears.
The cost of 1 pound orages=$1.09 and the cost of 1 pound pears=$1.19
What is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, the number of pounds of oranges =3.27/1.09=3 pounds
The number of pounds of pears =4.76/1.19=4 pounds
Total weight=3+4=7 pounds
Therefore, a total of 7 pounds of fruit does the customer buy.
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The gas tank in the car holds 20 gallons of gasoline. You used up 4 gallons and 1 quart on your trip. How much gasoline is left in the tank?
The correct answer is:
Total capacity of tank in quarts:
20 gallons = 20 × 4 = 80 quarts
Gasoline used in quarts:
4 gallons 1 quart = (4 × 4) + 1 = 17 quarts
Gasoline left in the tank in quarts:
80 − 17 = 63 quarts
Gasoline left in the tank in gallons and quarts:
63 quarts = 63 ÷ 4 = 15 remainder 3 = 15 gallons 3 quarts
The perimeter of a square is 26.46 inches. What is the side length of the square?
The side length of a square whose perimeter is 26.46 inches can be calculated by dividing the given perimeter by 4 (the number of sides in a square), resulting in a side length of approximately 6.615 inches.
Explanation:The subject of this question is Mathematics, with the specific topic being measurement and geometry. This question is applicable to Middle School grade levels. The student seeks to determine the side length of a square, knowing the perimeter is 26.46 inches.
To find the side length, we need to recall the formula for the perimeter of a square: P = 4s, where P represents the perimeter and s represents the length of a side. The student's square has a perimeter of 26.46 inches, so the equation would be 26.46 = 4s.
To isolate the value of s, we divide both sides of the equation by 4. This gives us: s = 26.46/4. Upon doing the division, we find that each side of the square is approximately 6.615 inches.
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spiders can walk on walls write the statement in if then form
(01.02) Choose the best definition for the following term: variable
x = 0
y = 1 + 2x Substitute x = 0
y = 1 + 2(0) Any number times 0 is 0
y = 1 + 0 Simplify
y = 1
I hope this could help.
The length of a rectangle is four times its width. If the area is 400 cm squared, find its perimeter
The perimeter of the rectangle with four times longer in length than its width and an area of 400 cm2 is 100 cm.
To solve this, let's assume the width of the rectangle is w centimeters. This would make the length 4w centimeters. Since the area of a rectangle is given by the product of its length and width, we have:
w x 4w = 400
Solving for w, we find that w2 = 100, so w = 10 cm.
Hence, the length is 4 x 10 = 40 cm.
The perimeter of a rectangle is given by the formula 2l + 2w, so substituting in our values:
Perimeter = 2(40) + 2(10) = 80 + 20 = 100 cm.
Therefore, the perimeter of the rectangle is 100 cm.
Given that P = (-4, 11) and Q = (-5, 8), find the component form and magnitude of vector QP
Answer:
<1, 3>, square root of ten
Step-by-step explanation:
find the next three terms in the geometric sequence: 4, -12, 36, -108
10 x 6 tens-unit form and standard form
Answer:
Standard form: 600
Unit form: 6 hundreds.
Step-by-step explanation:
We have been given a number [tex]10\times 6[/tex]-tens. We are asked to write our given number in unit form and standard form.
To write our given number in standard form, we will expand our given number as shown below:
6-tens [tex]6\times 10=60[/tex]
[tex]10\times 6[/tex]-tens would be [tex]10\times 60=600[/tex]
Therefore, our given number in standard form would be 600.
We know that unit form is writing a number using place value units.
We can see that our given number has 0 ones, 0 tens and 6 hundreds.
Therefore, our given number in unit form would be 6 hundreds.
We have that the Tens unit form of 10 x 6 and Standard form is mathematically
[tex]6*10^1[/tex]
6tens
From the question we are told that
10 x 6
10 x 6=60
Standard form is a number, between 1 and 10 multiplied by a power of 10
Generally the equation for the Standard form is mathematically given as
x*10^y
Therefore
the Standard form of 10 x 6 is mathematically given as
[tex]6*10^1[/tex]
And
Generally the equation for the Tens unit form of 10 x 6 is mathematically given as
x*tens(10)
Tens-unit form is mathematically given as
6tens
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Find the vertex of the parabola whose equation is y = x2 - 4x + 6.
How many kilometers could the red car travel in 12 hours?
A rectangle has its base on the x axis and its upper two vertices on the parabola y = 9 − x2. (a) Draw a graph of this problem. (b) Label the upper right vertex of the rectangle (x,y) and indicate the lengths of the sides of the rectangle. (c) Express the area A as a function of x and state the domain of A. (d) Calculate the derviative of A and solve for the critical values. (e) What is the largest area the rectangle can have?
Answer:
(a) see attached(b) width: 2x; height: y = 9-x²(c) A=2x(9-x²) . . . 0 ≤ x ≤ 3(d) dA/dx = -6x² +18; x=±√3(e) 12√3 units²Step-by-step explanation:
(a) The attachment shows the graph of the parabola in blue. It also shows an inscribed rectangle in black.
(b) The upper right point of the rectangle is shown in the attachment as (x, y). The dimension y is the height of the rectangle. The x-dimension is half the width of the rectangle, which is symmetrical about the y-axis. Hence the width is 2x.
(c) As with any rectangle, the area is the product of length and width:
... A = (2x)(9 -x²) . . . . . the attachment shows a graph of this
... A = -2x³ +18x . . . . . expanded form suitable for differentiation
A suitable domain for A is where both x and A are non-negative: 0 ≤ x ≤ 3.
(d) The derivative of A with respect to x is ...
... A' = -6x² +18
This is defined everywhere, so the critical values will be where A' = 0.
... 0 = -6x² +18
... 3 = x² . . . . . . . divide by -6, add 3
... √3 = x . . . . . . . -√3 is also a solution, but is not in the domain of A
(e) The rectangle will have its largest area where x=√3. That area is ...
... A = 2x(9 -x²) = 2√3(9 -(√3)²) = 2√3(6)
... A = 12√3 . . . . square units . . . . ≈ 20.785 units²
The parabola y = 9 - x^2 is graphed, and a rectangle's vertices and area calculations are superimposed on it. The derivative of the area function gives critical values, determining the maximum area is 18 square units.
Explanation:To solve this problem, we must utilize quadratic equations, Two-Dimensional (x-y) Graphing, and calculus.
(a) To begin, we need to draw a graph of the parabolic equation y = 9 - x^2. The vertex of the parabola is at the point (0,9) since the x-coordinate of the vertex is -b/2a in a general quadratic equation of the form y = ax^2 + bx + c, and here a = -1 and b = 0.
(b) For the rectangle, the upper right vertex is at point (x, y=(9 - x^2)), with base length 2x and height (9 - x^2).
(c) The area (A=base * height) of the rectangle is then given by A = 2x * (9 - x^2). The domain of A is specified by the values of x for which A is defined. Here A is defined for all x ∈ (-∞, ∞).
(d) The derivative of A with respect to x is A’ = 2(9 - 3x^2), which can be set equal to zero, the solution of which gives critical values x = ±√3.
(e) By the second derivative test or comparing values at the endpoints and critical points, you can determine that the largest area is 18 square units when x = √3.
Therefore,
b) The upper right vertex is at point (x, y=(9 - x^2)), with base length 2x and height (9 - x^2).
c) Here, A is defined for all x ∈ (-∞, ∞).
d) The solution of which gives critical values x = ±√3.
e) The largest area is 18 square units.
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Given the values of the derivative f′(x) in the table and that f(0)=150, find or estimate f(x) for x=0,2,4,6.
To find or estimate f(x) for x=0,2,4,6, integrate the given derivative f'(x) with respect to x to find the constant term. Then, add each value of f'(x) in the table to the constant term to obtain the values of f(x) for x=0,2,4,6.
Explanation:To find or estimate f(x) for x=0,2,4,6, we need to use the values of the derivative f'(x) given in the table. Since f'(x) represents the rate of change of f(x) at different values of x, we can use the derivative to find or estimate the values of f(x). Given that f(0) = 150, we can start by finding the constant term of the function using this initial condition.
To find the constant term, we need to integrate the derivative f'(x) with respect to x. This will give us the original function f(x).Integrating f'(x) gives us f(x) = 150 + C, where C is the constant term we need to find.Next, we can use the given values of f'(x) in the table to find or estimate the corresponding values of f(x) for x=0,2,4,6.Let's assume that the third column in the table represents the values of f'(x) at different values of x. We can add each value to the constant term C to obtain the values of f(x) for x=0,2,4,6.Therefore, by integrating f'(x) and adding the constant term, we can find or estimate the values of f(x) for x=0,2,4,6.
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What percentage of 3000 is 330
Answer:
11
Step-by-step explanation:
Carol ate 2/5 of the cake. Dima ate 3/5 of the REMAINING CAKE, mom ate the rest.
How many times more did Carol eat compared to Dima? PLEASE EXPLAIN, GIVING BRAINLIEST, PLEASE HELP.
Cody filled a container with 7 3/16 quarts of iced tea. how many 1/4 quart glasses can be served from the container
how to round 254 to the nearest hundred
382 & 3/10 - 191 & 87/100= WHAT?
The formula s= sa/6 gives the length of the side, s, of a cube with the surface area, sa. How much longer is the side of the cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters ?
Answer with explanation:
Side of cube = S
Surface Area of Cube = S.A
Relation between Side of a cube and surface area
[tex]S=\frac{S.A}{6}[/tex]
→If surface area of cube =180 Square meters
Side of cube (S)
[tex]S_{1}=\frac{180}{6}\\\\=30[/tex] meters
→ If surface area of cube =120 Square meters
Side of cube (S)
[tex]S_{2}=\frac{120}{6}\\\\=20[/tex] meters
[tex]S_{1}-S_{2}=30 -20=10\\\\S_{1}=S_{2}+10[/tex]
Side of cubic having surface area 180 square meters is greater by 10 meters, than a cube with the surface area of 120 square meters.
Solve for x.y = mx+b
Solve the system 2x-2y=10 4x-5y=17
There are 24 student's in a science class. Mr. Sato will give each pair of student's 3 magnets. So far, Mr. Sato has given 9 pairs of students their 3 magnets. How many more magnets does Mr. Sato need zo.that each pair of student's habe exactly 3 magnets?