Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (2,2) with x-intercept 5
The total amount of candy sold at Cassandra's Candy Corner can be represented by the function C(x) = 4x3 + 10x2 + 54x + 520, where x represents the number of years since the store opened. The amount of types of candy can be modeled by the linear function T(x) = 2x + 10. Which expression represents the amount of candy sold each year per type at Cassandra's Candy Corner?
2x^2 – 5x + 52
2x^2 + 5x + 52
4x^3 + 10x^2 + 52x + 510
4x^3 + 10x^2 + 56x + 530
Using polynomial division, it is found that the expression that represents the amount of candy sold each year per type at Cassandra's Candy Corner is:
[tex]2x^2 - 5x + 52[/tex]
The amount of candy sold per type is given by the following division:
[tex]\frac{C(x)}{T(x)} = \frac{4x^3 + 10x^2 + 54x + 520}{2x + 10}[/tex]
The denominator can be written as:
[tex]2x + 10 = 2(x + 5)[/tex]
At the numerator, to see if we can simplify, we verify if x = -5 is a factor:
[tex]C(-5) = 4(-5)^3 + 10(-5)^2 + 54(-5) + 520 = 0[/tex]
Since C(-5) = 0, it is a factor of the numerator, and thus, since the numerator is of the 3rd degree, it can be written as a 3 - 1 = 2nd degree polynomial multiplying x + 5:
[tex](ax^2 + bx + c)(x + 5) = 4x^3 + 10x^2 + 54x + 520[/tex]
[tex]ax^3 + (5a + b)x^2 + (5b + c)x + 5c = 4x^3 + 10x^2 + 54x + 520[/tex]
Equaling both sides:
[tex]a = 4[/tex]
[tex]b = 10 - 5a = -10[/tex]
[tex]5c = 520 \rightarrow c = 104[/tex]
Thus:
[tex]C(x) = (4x^2 - 10x + 104)(x + 5)[/tex]
And:
[tex]\frac{C(x)}{T(x)} = \frac{(4x^2 - 10x + 104)(x + 5)}{2(x + 5)} = 2x^2 - 5x + 52[/tex]
Thus, the expression is:
[tex]2x^2 - 5x + 52[/tex]
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What’s the answer to number 7?
Answer/Step-by-step explanation:
The statement of question 7 is, "There are not 7 days in a week and Halloween is not on October 31st."
We know both of these statements are incorrect, therefore the truth value is False.
1) Choose the best answer.
To solve an equation, you must
which means you must perform
whatever operations are necessary so that the variable appears by itself on one side of
the equation but not on the other side.
A.use substitution
B.isolate the variable
C.check your answer
D.apply the Symmetric Property of Equality
The process of isolating the variable is the primary step involved in solving an equation.
Thus, option (B) is correct.
A) Substitution refers to the act of replacing a variable with a known value in an equation, which can be a useful strategy in some cases but is not a fundamental step in solving equations.
B) To solve an equation, it is necessary to perform operations that isolate the variable on one side of the equation and keep the other side free of the variable.
C)To verify if the obtained solution satisfies the original equation, but it is not a step required to solve the equation.
D) It states that if a = b, then b = a.
It is a property that allows us to interchange the positions of two equal expressions in an equation but is not directly related to solving equations.
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Graph the equation,
y = 5x - 5
Answer:
Step-by-step explanation:
there are 2 ways to graph equations. I'll teach u the faster way.
step 1) graph the y-intercept.
so the slop-intercept form of a line is y=mx+b. b represents the y-intercept and m represents the slope. u need two points to graph a line, the first point will be the y intercept. in this case, the y-intercept is -5. so this is what you should do: (the underlined star represents a point. also, the underlined star is on point -5.)
| y
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------------------------------------------------------------x
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*
|
step 2) graph the second point using the slope.
slope equals rise over run. (m=rise/run.) in this case, the slope is 5/1. To graph the second point, u should RISE up by 5 and RUN to the right by one: (the underlined star is on point 1.)
| y
|
|
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-----------------------*-------------------------------------x
|
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*
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now draw a line through those two points.
still confused? watch the first video that pops up after searching: how to graph a line
i couldnt insert the link to the vid for whatever reason but that vid helped me learn
Evaluate and reduce:
-12/16+(11/12)
Adding and subtracting
Answer:
The answer is 1/6
Step-by-step explanation:
-12/16 + (11/12)
-3/4 + 11/12
Take LCM
-3 × 6/4 × 6 + 11 × 2/12 × 2
-18/24 + 22/24
-18 + 22/24
4/24 = 1/6
Thus, The answer is 1/6
-TheUnknownScientist 72
What is the expected value for the spinner shown below? Enter your answer as a
decimal rounded to the thousandths place,
6
-5
2
-2
Anser: rely hard for me sry
explennatien:
i dont no the anser im only 6 year old
y = (x - 5) (x + 2) , when x=3
Answer:
-10
Step-by-step explanation:
y = (x - 5) (x + 2)
y = (3 - 5) (3 + 2)
y= (-2) (5)
y= -2 x 5
y= -10
John lives 27 miles from school. Steven lives 9 more miles from school
than John.
How many miles does Steven live from
school?
Answer: 36
Step-by-step explanation:
27+9=36
Answer:
36
Step-by-step explanation:
27+9=36
I steven lives 9 more miles than john we are adding.
Can somebody help me anyone
Which statements about opposites are true? HELLP ME ASAP PLS!!!
Select each correct answer.
The opposite of a number is 1 divided by that number.
The opposite of the opposite of a number is the number itself.
A non-zero number and its opposite are located on opposite sides of zero on a number line.
The opposite of a number is always a negative number.
i need help fast please
its too long and if you want someone to do it fast it takes a long time
coeffitiant of 3x-y+4
Answer:
3
Step-by-step explanation:
....,.................
NO LINKS OR ASSESSMENT!!!
Part 2: State the Domain and Range of each graph in BOTH inequality and interval notation
Domain = set of input value
Range = set of output values
#1Domain: -2 < x ≤ 2 or (-2, 2]Range: -4 < y ≤ 4 or (-4, 4]#2Domain: -5 ≤ x ≤ 1 or [-5, 1]Range: -1 ≤ y ≤ 5 or [-1, 5]#3Domain: -4 < x < 4 or (-4, 4)Range: -1 ≤ y < 3 or [-1, 3)Indicate which property is illustrated in step 1
Answer:
Step-by-step explanation:
communicative because you moved the three to the other side
Please help me on my homework
the correct answer is $948
show that x2-8x+20 can be writtern in the form (x-a)2 +a where a is an interger
and explain how you know x2-8x+20 is always positive
Answer:
The answer is . (x-4)²-11.Step-by-step explanation:
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True or false? Pqr is a right triangle.
PQR is a right triangle - TRUE .
Answer:
I think it's true
Step-by-step explanation:
PQR is a right triangle. Hope this helps you!
[tex]SilentNature\\(GraceRosalia)[/tex]
0.4 decimal to a fraction
2/5
Step-by-step explanation:
0.4
= 4/10 → divided by 2
= 2/5
What is the value of this expression?
4(610−15)+0.4
Answer:
Work the bracket first
610 - 15 = 595
multiply by 4
595 x 4 = 2380
add 0.4
final answer is 2380.4
Draw a model to represent 42/7
Here is a model I have made (I'm not a great artist). There are 42 circles in total, placed in 7 columns. Each column has 6 circles. This model represents 42/7 by splitting 42 into 7 parts, which are the columns, and showing that each column has 6 circles, which is the answer to 42/7.
The model to represent 42/7 is shown in the image attached,
What is the modelA "model" is a representation or abstraction of a system, concept, process, or phenomenon that helps us understand, predict, or explain how things work or interact.
In this image representation, each number represents one-seventh of the whole. One can shade in six of them to represent 42/7. In a more technical context, precise methods of representing fractions, such as using mathematical notation or diagrams is used.
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Ryan is making biscuits. The recipe call for 0.25 quart of milk and 2.5 cups of flour. He has 1/5 quart of milk and 9/4 cups of flour. Explain his error
Ryan's error lies in not utilizing the right units for measurement. He used inadequate milk and wrong flour measurement, influencing the recipe's proportion and result.
How to explain Ryans' errorRyan's error lies in not utilizing the right units for measurement. The formula calls for 0.25 quart of drain and 2.5 glasses of flour. Ryan utilized 1/5 quart of drain (which is less than 0.25 quart), and rather than utilizing glasses for flour, he utilized 9/4 mugs (which is identical to 2.25 mugs, not 2.5 glasses).
This bungle of units and wrong measurements might lead to the rolls having the off-base consistency and taste due to the awkwardness of fixings. It's imperative to use the desired units and estimations in formulas to realize the expected result.
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How to solve the slope of this line?
Answer:
4/5
Step-by-step explanation:
the equation for the slope of a line is
[tex]y=\frac{y_{2 - y_{1} } }{x_{2}-x_{1} }[/tex]
we can find the two points (-2,0) and (3,4) on the graph
plugging the points into the equation, we get (4-0)/(3-(-2)
= 4/5
5/9 divided by 8/5 the lesson is called dividing fractions
Answer: It can sometimes be difficult to divide fractions, such as 5/9 divided by 8/5. But it's no problem! We have displayed the answer below: 5/9 ÷ 8/5 = 25/72
Step-by-step explanation: Hope this help u bru
Intro to Solving Literal Equations and Formulas
Picture Below:
Answer:
f/2 is the answers for the question
Step-by-step explanation:
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Question 8 of 10
Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark (/) as the fraction bar if necessary.
Help please
Answer:
no
Step-by-step explanation:
no
The solution is, the slope of the line below is 1/2.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
from the given graph, we get,
the line is passing through the points (-2, -3 ) and, (2, -1 )
now , we know that,
We can find the slope of a line given two points by using the following:
m = ( y2-y1)/(x2-x1)
so, substituting the values of the coordinates of the points,
we get,
m = -1 + 3 / 2 + 2
= 2 / 4
= 1/2
Hence, The solution is, the slope of the line below is 1/2.
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Consider the functions f(x) = 6x - 5 and g(x) = 6x + 3. Which statement compares the
relationship between the graphs of the two functions?
A) The graph of g(x) is the same as the graph of f(x) translated down 2 units.
B) The graph of g(x) is the same as the graph of f(x) translated up 8 units.
C) The graph of g(x) is the same as the graph of f(x) translated up 2 units.
D) The graph of g(x) is the same as the graph of f(x) translated down 8 units.
Answer:
D
Step-by-step explanation:
since we have -5 and 3, in order to translate f(g) into f(x), we subtract 8 from f(g)
The graph of g(x) is the same as the graph of f(x) translated up 8 units. Therefore, option B is the correct answer.
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
Given that, f(x)= 6x-5 and g(x)= 6x+3.
When the shape is moved up by k units, then replace y with y + k.
Here, g(x)=6x-5+8
g(x)= 6x+3
The graph of g(x) is the same as the graph of f(x) translated up 8 units. Therefore, option B is the correct answer.
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Can somebody help me as soon as possible if can !
At a local bodega, the cost of a bag of chips at the corner store is $1.35, and the cost of a bottle of soda is $0.85. What would it cost to get 5 bags of chips and 7 bottles of soda? What would it cost to get xx bags of chips and y bottles of soda?
Using a system of equation to represent the scenario described, the cost is purchase made is $12.70
Cost per bag of chip = $1.35 Cost per bottle of soda = $0.85Cost of 5 bags of chips and 7 bottles of soda :
5(1.35) + 7(0.85) = $12.70
The cost of x bags of Chips and x bottles of soda can be expressed thus :
1.35x + 0.85yTherefore, the cost of x and y bags of Chips and soda respectively is 1.35x + 0.85y
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CAN SOMEONE HELP PLSSSS ITS THE LAST QUESTION
Answer:
1
Step-by-step explanation:
by equality of triangles
13x-12=7x-6
13x-7x=12-6
6x=6
x=1