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By applying the point-slope formula, the linear function y = -x/3 - 4 has a slope of - 1/3 and passes through the point (-3, -3) seen on Cartesian plane.
How to determine the line equation by knowing its slope and a point
According to analytical geometry, we could know the equation of the line by means of the point-slope equation:
y - y₁ = m · (x - x₁) (1)
Where:
x - Independent variabley - Dependent variable(x₁, y₁) - Known pointm - SlopeIf we know that m = -1/3 and (x₁, y₁) = (-3, -3), then the line equation is:
y + 3 = -(1/3) · (x + 3)
y + 3 = -x/3 -1
y = -x/3 - 4
Lastly we proceed to graph the function by a graphing tool (i. e. Desmos).
By applying the point-slope formula, the linear function y = -x/3 - 4 has a slope of - 1/3 and passes through the point (-3, -3) seen on Cartesian plane.
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Related Questions
Write 14 16 in lowest terms.
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By applying algebra properties for simplifying rational numbers, we conclude that the rational number 14/16 is equivalent to the rational number 7/8.
How to simplify a rational number
Rational numbers are real numbers of the form n/m, where n, m ∈ [tex]\mathbb{Z}[/tex] and n ≠ 0. Rational numbers are in lowest terms whether they cannot be reduced. A rational number is simplified by applying the following property:
[tex]\frac{a\cdot c}{b\cdot c} = \frac{a}{b}[/tex] (1)
Where c is the common multiplier.
Now we proceed to simplify the given rational number, whose common multiplier is 2:
[tex]\frac{14}{16} = \frac{7}{8}[/tex]
By applying algebra properties for simplifying rational numbers, we conclude that the rational number 14/16 is equivalent to the rational number 7/8.
RemarkThe statement is poorly formatted: Write 14/16 in lowest terms.
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What should I write for this?
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Answer:
a. Solve the System of Equations. Show your work
Write down the coordinates of point A.
( ……… , ………)
b) The line L is shown on the grid. Find the equation of line L in the form of y = mx + c.
..............................
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The coordinates of point A is: (-2, 5)
The equation of line L, in slope-intercept form, is: y = 1/2x + 2
What is the Equation of a Line?In slope-intercept form, the equation of a straight line is given as, y = mx + b, where:
b is the y-intercept, which is where the line cuts the y-axism is the slope = change in y / change in x.The coordinates of point A is: (-2, 5)
Slope (m) of line L = 2/4 = 1/2.
y-intercept (b) = 2
The equation of line L will be:
y = 1/2x + 2.
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A special-edition model of a smart watch is sold in gold, green, blue, or red. ernie's electronics sold 234 of these smart watches last week. they sold twice as many red watches as gold watches. they sold 3 times as many green watches as gold watches. they sold the same number of blue watches as green watches. how many green smart watches did the store sell last week?
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The number of green watches that were sold is 78
How to determine the number of green watches?The given parameters are:
Total =234Red = 2 * GoldGreen = 3* GoldBlue = GreenThe number of watches can be represented as
Gold + Green + Blue + Red = 234
Substitute Blue = Green
Gold + Green + Green + Red = 234
Gold + 2 * Green + Red = 234
Substitute Red = 2 * Gold
Gold + 2 * Green + 2 * Gold = 234
Evaluate the like terms
2 * Green + 3 * Gold = 234
Make Gold the subject in Green = 3* Gold
Gold = Green/3
Substitute Gold = Green/3 in 2 * Green + 3 * Gold = 234
2 * Green + 3 * Green/3 = 234
Evaluate the product
2 * Green + Green = 234
Evaluate the sum
3 * Green = 234
Divide both sides by 3
Green = 78
Hence, The number of green watches that were sold is 78
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I need help on this please
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Answer:
Volume of a cone = (1/3) πr³
r = radius = d/2 = 2/2 = 1 ft
Volume = (1/3) * π * 1³
volume = 1.04 cubic ft
A complete graph of the polynomial function f is provided. Use your knowledge of the domain, range, behavior at each x intercept, end behavior, symmetry, local and global extreme values, and intervals of increasing and decreasing to select the best choice of the polynomial function, f.
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The graph represents a polynomial graph, and the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²
How to determine the equation?From the graph, we have the following observations:
The graph has a turning point at x = 2The graph changes the factor of its direction at x = -5This means that the graph has a multiplicity of 2 at x = 2 and a multiplicity of 3 at x = -5
So, we have:
f(x) = a(x + 5)³(x - 2)²
The curve is inverted,
This means that a < 0
Assume a = -1.
Then, we have:
f(x) = -(x + 5)³(x - 2)²
Hence, the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²
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PLEASE HELP ME I RELLY NEED IT
Answers
In rectangle , opposite sides are equal so the value of KL is 45.6
Answer:
[tex]KL=45.6[/tex]
Step-by-step explanation:
Property of a Rectangle: Opposite sides are equal.
This means:
[tex]KL = JM \text{ where JM = 45.6}[/tex]
[tex]KL = 45.6[/tex]
Question 1 (Multiple Choice Worth 1 points)
(03.01 MC)
Solve 7/3+2V9 and explain whether the answer is rational or irrational.
O The answer 9/12 is rational because the sum of a rational number and irrational number is a rational number.
The answer 9/12 is irrational because the sum of a rational number and irrational number is an irrational number.
The answer 773 +6 is rational because the sum of a rational number and irrational number is a rational number.
The answer 713+6 is irrational because the sum of a rational number and irrational number is an irrational number.
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Answer:
The answer 7|3+6 is irrational because the sum of a rational number and irrational number is an irrational number.
The left windshield wiper on a Chevrolet Traverse cleans an area of 500.3in ^2.when in motion it has a cleaning pattern that arcs 98 degree . What is the length of the windshield wiper? Approximate the length to the nearest inch.
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The length of the windshield wiper to the nearest inch is 24 inches
How to calculate the area of a sectorThe formula for calculating the area of a sector is given as:
A = r²β/2
r is the length of the wiper
β is the subtended angle
Given the following
A = 500.3 square in
β = 98 degrees = 98pi/180 = 49pi/90
Substitute
500.3 = r²49pi/180
500.3 = 153.86r²/180
153.86r² = 90054
r² = 585.298
r = 24.19
Hence the length of the windshield wiper to the nearest inch is 24 inches
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Write the following fraction as a decimal number. 4/3/100 4.003 4.03 4.33 4.34
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Answer:
133.3 <-- goes on forever
I think the rest are in decimal form.
give answer in simplest form with working out pls
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Answer:
5 x 5+3/5= 25+3/5=28/5÷8/3
28/5 x8/3= 224/15 =14.93
Please help! Im a bit confused, offering 25 points! This mix and match!
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Addition:
Increased by, greater than, more than, sum
Subtraction:
Decreased by, decrease, less than, difference
Multiplication:
Times, equal groups, __ times as many, product
Division:
Quotient, divided by, goes into, split equally
Type the missing number in this sequence:
6, 8, 11, 15, 20,____,33
Answers
Answer: 26
Step-by-step explanation: the pattern is +2, +3, +4, +5. +6, +7
6+2 = 8
8+3 = 11
11+4 = 15
15+5 = 20
20+6 = 26
26+7 = 33
Answer:
26
Step-by-step explanation:
In this, the addition of numbers is starting from 2 and continue. Such as 6+2=8,then 8+3=11. Similarly the addition of numbers is continuing
Round your answers to the nearest cent.
f(0) =
meaning the cost of buying
gallons of paint would be
in the context of the problem.
f(10)
, meaning the cost of buying
gallons of paint would be
in the context of the problem.
f(67.5)
meaning the cost of buying
gallons of paint would be
This interpretation
in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the
function is
=
This interpretation
=
This interpretation
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The interpretations of the function values are: the cost of buying 0, 10 and 67.5 gallons of paint would be 0, 28.5 and 73.9, respectively
How to interpret the function values?The equation of the function is given as:
f(x) = 9√x
When x = 0, 10 and 67.5, we have:
f(0) = 9√0 = 0
f(10) = 9√10 = 28.5
f(67.5) = 9√67.5 = 73.9
Hence, the interpretations of the function values are:
The cost of buying 0, 10 and 67.5 gallons of paint would be 0, 28.5 and 73.9, respectively
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A Panel in a stained-glass window in the shape of a parallelogram has the dimensions shown. Find the area of the panel.
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Answer: 20 sq ft
Step-by-step explanation: The base is AB = 5 ft because AB = CD. Recall that opposite sides in a parallelogram are congruent and parallel.
area of parallelogram = base * height = 5*4 = 20
note: the base is always perpendicular to the height
A quantity y varies inversely with the square of x. if y=8 when x=3, find y when x is 4.
Answers
I think 7/2 im not definate
Which number sentence is represented by this model?
Answers
Answer:
Correct answer is B. -3 • 5 = - 15
PLEASE HELP ME WITH THIS QUESTION!!!
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9x²+3x-1=0
D=b²-4ac
= 3²-4×9×-1
=9+36
=45
x1= (-b+VD)/2a
= (-3+V45)/2×9
= (-3+3V5)/18
=(-1+V5)/6
x2=(-b-VD)/2a
=(-3-3V5)/18
=(-1-V5)/6
What is f(4) for the function f(x) = 5x + 3?
Answers
how to solve x-3y=1 4x+5y=4 using elimination
Answers
Answer:
X=1, Y=0
Step-by-step explanation:
Solve for X and Y using a2 +b2 = c2
Carpet costs $8.30 per square foot. How much will it cost to carpet the room? Show your work.
The area is 812ft
Answers
Answer:
about 98 dollars to cover the whole room in carpet
Step-by-step explanation:
The Carpet costs $8.30 per square foot, so 812 ÷ 8.30 = 97 with remainder. Therefore 98 as a rounded total ✅
The first number in a pattern is 208. The pattern follows the rule subtract 18. What are the next three numbers? (3 points)
a
195, 183, 172
b
190, 183, 176
c
190, 181, 172
d
190, 172, 154
Answers
Answer:
d) 190,172,154
Step-by-step explanation:
208-18=190
190-18=172
172-18=154
4. Find (f◦g)(x) and (g◦f)(x) and the domain of each.
f(x)=x+3, g(x)=
Answers
Answers:
[tex](f \circ g)(x) = 2x^2-5x\\\\(g \circ f)(x) = 2x^2+7x\\\\[/tex]
The domain is "all real numbers" which you could type in (-infinity, infinity) or [tex](-\infty, \infty)[/tex] when doing interval notation. This applies to both.
=========================================================
Explanation:
See the attached image for the steps of each.
The domain is the set of all real numbers because each result is a polynomial. We don't have to worry about dividing by zero, taking a square root of a negative number etc. There are no restrictions on x. Any real number can replace x to get some real number result for y. This applies to both composite functions.
what is an event in which the outcome does impact the probability of the next event?
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Answer:
Dependent Event
Step-by-step explanation:
Dependent Events: Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.
Jackie has a choice of 3 pairs of shoes, 3 pants, and 4 shirts that can make an outfit for today. Each pair of shoes has a different heel height, each pair of pants is made from a different fabric, and each shirt is a different color.
Jackie randomly picks some clothes.
What is the probability that she chooses an outfit consisting of the flat heel or spike heel shoes, the twill or the denim pants, and the white or black shirt?
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Answer:
2/9
Step-by-step explanation:
i just took a test with this exact question, and the answer was 2/9
youre welcome future learners ;)
Please help me, I need an answer as soon as possible.
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Answer:
[tex]\huge\boxed{\sf x = \pm \sqrt{7} }[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2-7[/tex]
We can also write it as:
[tex]y =x^2-7[/tex]
x-intercept is the point where y = 0
Put y = 0 in the above equation
[tex]0=x^2-7\\\\Add \ 7 \ to \ both\ sides\\\\7 = x^2\\\\Take \ sqrt \ on \ both \ sides\\\\\pm \sqrt{7} =x\\\\x = \pm \sqrt{7} \\\\\rule[225]{225}{2}[/tex]
Please help help …….. pls
…..
Answers
Answer:
1) 1/2or 50%
2) 38/50 or 76%
3) 38/60 or 63%
4) not sure tbh
Step-by-step explanation:
Does anybody understand this? QSRT is a Rectangle and SQR=55
Answers
Answer:
90°; 55°; 35°; 110°; 70°
Step-by-step explanation:
A rectangle has corner angles that are 90°. When the corner angle is divided into two parts, the total of the parts is 90°.
Each of the triangles is isosceles. The figure is symmetrical about its center.
An exterior angle to a triangle is equal to the sum of the remote interior angles.
__
∠SRT = 90° . . . . a corner angle
∠STR = 55° . . . . symmetrical to the given angle
∠QRS = 180° -55° -90° = 35° . . . . sum of angles in ΔQRS is 180°
∠QPT = 2×55° = 110° . . . . exterior angle to ΔQPS; ∠QSP =∠SQP
∠TPR = 180° -110° = 70° . . . . forms a linear pair with ∠QPT
_____
There are numerous ways to figure any or all of these angles. They come down to the fundamentals: angles in a triangle total 180°; angles that form a line total 180°; corner angles of a rectangle are 90°. Base angles of an isosceles triangle are congruent.
The exterior angle rule derives from the sum of angles in a triangle and on a line both being 180°.
PLEASE HELP WILL GIVE BRAINLEST! Which trigonometric function does the graph below represent?
Answers
Answer:
Answer In this Picture.
find the volume of a rectangular prism with a length of 4 inches and a width of 7 inches and a height of 11 inches
Answers
Answer:308
Step-by-step explanation:Multiply 4*7*11