Rewrite the given equation in slope intercept form, y=mx+c. Where the slope is m and the y-intercept is c.
Rewrite the given equation as follows:
[tex]\begin{gathered} 9y-6x+8=0 \\ \text{Take x term and the constant to the right side and change their sign} \\ 9y=6x-8 \\ \text{Divide each term by 9:} \\ \frac{9y}{9}=\frac{6x}{9}-\frac{8}{9} \end{gathered}[/tex]Simplify the equation:
[tex]y=\frac{6}{9}x-\frac{8}{9}[/tex]Compare to the equation y=mx+c, to get:
[tex]\begin{gathered} m=\frac{6}{9} \\ c=-\frac{8}{9} \end{gathered}[/tex]Hence, the slope is 6/9 and the y-intercept is -8/9.
You can also write the y-intercept as an ordered pair (0,-8/9) since the x-value at the y-intercept is zero.
Please thank you :(Use the functions f(x) = x ^ 2 - 1 and g(x) = x + 11 to answer parts (a) - (g)
Answer:
(a) {-1, 1)
(b) {-11}
(c) {-3, 4}
***(d) { x < -1 or x > 1, I am not sure how else to put it, try {-1, 1} if you are not allowed to put in > or < signs
(e) (-∞, -11] or x ≤ -11
(f) {-3, 4}
(g) ( -√2, √2)
***I know the correct solution sets but I am not sure how to represent all of them given the one box you have in your solution for (a). Maybe the solution boxes for the other parts are different. Without knowing that I am only able to provide what is the correct expression
Step-by-step explanation:
We have
f(x) = x² - 1
g(x) = x + 11
(a) f(x) = 0
=> x² - 1 =
=> x² = 1
x = ± 1
Answer (a): The solution set is {-1, 1}
(b)
g(x) = 0
=> x + 11 = 0
=> x = -11
Answer (b): Solution set: {-11}
(c)
f(x) = g(x)
=> x² - 1 = x + 11
=> x² -x -12 = 0
This is a quadratic equation which can be solved by factoring:
=> (x - 4)(x+3) = 0
=> x = 4, x = -3
{-3, 4} Answer
(d) f(x) > 0
=> x² - 1 > 0
Add 1 to both sides
x² > 1
x < -1 or x > 1
[tex]\left(-\infty \:,\:-1\right)\cup \left(1,\:\infty \:\right)[/tex]
(e) g(x) ≤ 0
=> x + 11 ≤ 0
=> x ≤ -11
{-∞, -11}
(f)f(x) > g(x)
=> x²-1 > x +11
=> x² -x - 12 > 0
=> (x + 3)(x +4) > 0
=> x + 3 >0 and x - 4 > 0
=> x > -3 and x < 4
{-3, 4}
(g) f(x) ≥ 1
=> x² - 1 ≥ 1
=> x² ≥ 2
=> x ≥ ± √2
=> x ≤ -√2 or x ≥ √2
=> { -√2, √2}
In the above derivations note that if x² ≥ 1 then two possibilities are
x < - 1 or x > 1
If x and y vary directly and y is 120 when x is 15, find y when x is 6.
Based on the direct variation between x and y, the value of y is 48
How to determine the value of y when the value of x is 6?The given statements are:
If x and y vary directlyy is 120 when x is 6From the above points, we understand that:
The variation is a direct variation
A direct variation is represented as
y = kx
Where k represents the constant of variation
The above equation is a linear equation
As a general rule, linear equations are equations that have constant average rates of change.
So, we have
y = kx
y is 120 when x is 15
This means that
120 = 15k
Divide by 15
k = 8
So, we have
y = 8x
The value of y when x is 6 is
y = 8 x 6
Evaluate
y = 48
Hence, the value of y when the value of x is 6 is 42
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7. (01.03 LC) A craft store marks up all sewing machines 45%. What is the selling price of a sewing machine that costs $155.00 before the markup? (1 point) $169.75 $224.75 $245.50 O $278.25
The selling price is $224.75.
What is Percent?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Cost price= $155
Cost marks up = 45%
Then the selling price is
=155 + 155 x 45/100
= 155 + 155 x 0.45
=155 + 69.75
= $224.75
Hence, The selling price is $224.75.
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3x – 2 ( 6x – 3 ) = 42
Answer:
x=-4Step-by-step explanation:
3x−(12x−6)−42=0
−9x+6−42=0
(−9)⋅x+(−36)=0
x=−(−36)/−9
x=-4
Which angle is NOT congruent to 4
The angle not congruent to the angle 4 in the options is angle 7(∠7)
How to find congruent angles?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.
Therefore, corresponding angles are equal, alternate angles are equal and vertically opposite angles are equal.
Therefore,
∠4≅∠6(vertically opposite angles)
∠4≅∠2(corresponding angles)
∠4≅∠8(alternate exterior angles)
Therefore the angle not congruent to ∠4 among the option is ∠7
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2. Franklin jogs before and after school each day. He jogs 0.65 miles before school and 1.5 miles after school. What is the total number of miles Franklin jogs? Franklin jogs a total of # miles.
Let's summarize the given information:
iles before school: 0.65
Miles after school: 1.5
o find the total mnumber of miles that Franklin jogs we need to add the miles he jogs before and after school:
[tex]0.65+1.5[/tex]The result of the addition is:
[tex]2.15\text{ miles}[/tex]He jogs 2.15 miles.
nswer: 2.15 miles
Find the equation of the line connecting the points (2, 0) and (3, 15).
Answer:
y = 15x - 30
Hope this helps!
Step-by-step explanation:
The slope can be found with the equation [tex]\frac{y_{2} -y_{1} }{x_{2} - x_{1} }[/tex].
Add in the numbers from the two points to get [tex]\frac{15-0}{3-2}[/tex] which is [tex]\frac{15}{1}[/tex] : 15.
That means slope is 15. To get the other numbers, you can do y = 15x and then plug in one of the points, for example (0) = 15(2), which is 0 = 30. To make this equation true, you need to minus 30 so it would be 0 = 30 - 30 and this is true, so putting it all together would get y = 15x - 30.
Find the inverse and determine if it is true or false.
Statement : Obtuse angles are not right angles.
The inverse statement is If an angle is not obtuse, then it is a right angle False. Option C
What is an inverse statement?An inverse statement can be defined as a type of conditional sentence having a prompt or immediate inference made from original statement.
It carries the negation of both the hypothesis and conclusion from the
It states the opposite of the original statement given.
The statement is formed by negating the hypothesis and conclusion of a given conditional statement.
An inverse statement is expressed the form:
Original statement: If p, then q
Inverse statement: If not p, not q
Given the statement as;
Obtuse angles are not right angles
The inverse statement is:
If an angle is not obtuse, then it is a right angle
Hence, the inverse statement is False. Option C
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A rectangular dog pen is constructed using a barn wall as one side and 120m of fencing for the other three sides. a) give a sketch of the situation. b) express the area in terms of x. c) sketch the graph. d) find the value of x that gives the greatest area. e) find the dimensions of the pen. f) state the domain.
Answer:
see the attachments for the sketch and the graphA = x(120 -2x)x = 30 maximizes the areadimensions: 30 m by 60 mdomain of x: [0, 60]Step-by-step explanation:
You want an expression for area, maximum area, and dimensions of a rectangular pen fenced on three sides with a total of 120 m of fencing.
a) SketchThe first attachment shows a sketch of the pen with x defined as the dimension the pen extends from the barn wall. The total length of fence is 120 m, so the side parallel to the barn will be (120 -2x) m in length.
b) AreaThe area is the product of the length and width of the rectangle:
A = (x)(120 -2x)
c) GraphThe second attachment shows a graph of the area as a function of x.
d) Greatest areaThe value of x that gives the greatest area is the x-coordinate of the vertex of the parabola. It is halfway between the zeros at x=0 and x=60. The maximum area will be had when x=30.
e) DimensionsThe dimensions of the pen are ...
x = 30
120 -2x = 120 -2(30) = 60
The pen is 30 m by 60 m, with the 60 m dimension parallel to the barn wall.
f) DomainThe area function only makes sense for values of x between 0 and 60 meters.
The domain of x is 0 ≤ x ≤ 60.
Can somebody please help me
We were given the following details:
Car registration = $90
Car Insurance (annual) = $520
Home Insurance = $1020
Since we are to calculate for the monthly amount to budget for Car Insurance, we have:
[tex]\begin{gathered} CarInsurance(monthly)=\frac{CarInsurance\mleft(annual\mright)}{No\mathrm{}of\mathrm{}months} \\ CarInsurance(monthly)=\frac{520}{12}43.33\approx43.00 \\ CarInsurance(monthly)=\text{\$}43.00 \end{gathered}[/tex]herefore, the correct nanswer is A. ($43.00 per month)
A square has a perimeter of 120 cm what is the length of one side of the square
Identifying each relation, decide wether or not it is a function
For the following relations, using the condition for a relation to represent a function, we have that:
Relation 1 is not a function.Relation 2 is a function.When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
The input may also be called domain, while the output may also be called range.
For a point in the standard format (x,y), we have that:
x is the input or domain.y is the output or range.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.Hence, in the context of this problem, we have that:
Relation 1 is not a function, as the domain of f is mapped to different ranges of f and g.Relation 2 is a function, as each domain is mapped to only one range.More can be learned about relations and functions at https://brainly.com/question/12463448
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The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
The water pressure on a submerged object is given by P = 64d, then the
a. The answer to the subject of the formula, "d," is d = P/64.
b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.
What is a function?A function can be defined as an expression, law or rule that shows the relationship between two variables.
These variables are namely;
Independent variableDependent variablegiven the role as;
P = 64d
Where;
P stands for pounds per square foot of pressure.
d represents the object's depth in feet.
Let's now make the variable "d" the focus of the formula.
The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.
We get,
P/64 = 64d/64
d = P/ 64
P equals 672 pounds per square foot if there is pressure.
When the variable's value is substituted into the formula, we get;
d = P/64
Then,
d = 672/64
Discover the quotient.
d = 10. 5 ft.
The value is 10.5 feet.
Therefore,
a. The answer to the subject of the formula, "d," is d = P/64.
b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.
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Which set of ordered pairs does not represent a function?
O {(-6, 9), (-7, 1), (-4,-2), (-4,5)}
O {(-6,-8), (-9, 8), (6, 9), (5,8)}
O {(3,-8), (-4,0), -9,-1), (8,0)}
O {(6,4), (-1,-9), (-9, 1), (-2,-1)}
Answer:
The top set does not represent a function because -4 corresponds to two y-values.
a brigde connecting 2 cities separted by lakes has a lenght of 5927.61 find lenght of bridge in miles round to nearest tenth
The length of the bridge that connect the two cities separated by the lake is 3.4 miles.
What is the length of the bridge?The mathematical operation that would be used to convert yards to miles is division. Division is the process of putting a number into equal groups using another number. For example, when 6 is divided by 3, 3 divides 6 into 2 equal groups.
In order to convert yards to miles, divide the given length in yards by 1760.
1 yard = 1 / 1760 miles
5927.61 / 1760 = 3.36796 miles
= 3.4 miles
To round off to the nearest tenth, since the hundredth digit is greater than 5, 1 is added to the tenth digit and the digits less than the tenth digit is replaced with zero.
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please help me with this question anyone
Write the numbers in the blanks that make this equation true.
( 2 + 1 ) + 3 = 2 + ( _ + _ )
A’ (,)
B, (,)
C’ (,)
Please answer I give brainliest
The image's coordinates are:
A = (-2,5),
B = (3,-3),
C = (-4,-1).
What is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair od numerical coordinates, that are the signed distances from two lines that are fixedly perpendicular to the point and are measured in the same length.
How do you find coordinates on a plane?The reverse is done in order to determine a point's coordinates in a coordinate system. Start at the point and move along a vertical line either up or down to the x-axis. Your x-coordinate is located there. To get the y-coordinate, repeat the previous steps while following a horizontal line.
According to the given data:The graph's coordinates are as follows:
A = (-2,5)
B = (3, -3)
C = (-4,-1)
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Juan is a teacher who has an annual salary of $65,798. He has to pay state income tax of 5%. What is the amount that Juan pays in state income tax?
Responses
Answer:
$3,289.90
Step-by-step explanation:
65,798 times 5%
Ava's pin code is a 4-digit number.The some of the four digits is 22.Reading from left to right,the first and second digits are the same.The second digit is twice the third digit.The first digit is four times the fourth digit.What is Ava's pin code?
From the provided information we get that Ava's Pin code is 8842.
Ava's pin code is a 4-digit number.
Let the first digit = x equation 1
Reading from left to right, the first and second digits are the same. So,
Second digit = x equation 2
Let, third digit = y
The second digit is twice the third digit. So,
x = 2y
⇒ y = x/2
Third digit = x/2 equation 3
Let, fourth digit = z
The first digit is four times the fourth digit. So,
x = 4z
⇒ z = x/4
Fourth digit = x/4 equation 4
Sum of the four digits is 22. So, using equation 1 , equation 2 , equation 3 and equation 4 , we can write
x + x + (x/2) + (x/4) = 22
2x + (x/2) + (x/4) = 22
Multiplying both sides by 4 , we get
8x + 2x + x = 88
11x = 88
x = 8
First digit = x = 8
Second digit = x = 8
Third digit = x/2 = 8/2 = 4
Fourth digit = x/4 = 8/4 = 2
So, we can conclude that the Ava's Pin code is 8842.
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Find the distance between (-12, 1) and (12, -1).
If the coordinates of two points are (x_1,y_1) and (x_2,y_2), the distance between them is given by the formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute for the coordinates: (-12,1) and (12,-1):
[tex]\begin{gathered} d=\sqrt[]{(12-(-12))^2+(-1-1)^2} \\ =\sqrt[]{(12+12)^2+(-2)^2} \\ =\sqrt[]{(24)^2+4} \\ =\sqrt[]{576+4} \\ =\sqrt[]{580} \\ =2\cdot\sqrt[]{145} \\ \approx24.08318916\ldots \end{gathered}[/tex]Therefore, the distance between (-12,1) and (12,-1) is approximately 24.08.
Write an equation of the line passing through the point (9, 6) that is parallel to the
line y = -6x - 6.
⇒Parallel line have the same gradient if the gradient of the given equation is m=-6 it means that the gradient of the new equation is also m=-6
The general equation of a straight line is y=mx+c
⇒plug in the points and find the value of the unknown c
[tex]6=-6(9)+c\\6=-54+c\\c=6+54\\c=60[/tex]
⇒This means that the new equation parallel to the given equation is⇒
[tex]y=-6x+60[/tex]
Here are two right circular cylnders. The radius of the smaller cylinder on the left is 4 cm, and its height is 8 cm. The radius of the larger cylinder on the right is 16 cm, and its height is 8 cm. The volume of the larger cylinder is how many times as large as that of the smaller cylinder?
The larger cylinder is 16 times as large as the smaller cylinder.
Volume of cylinderThe formula for calculating the volume of cylinder is expressed according to the equation;
V = πr²h
where:
r is the radius
h is the height.
Determine the volume of the smaller cylinder;
V = π(4)²(8)
V = 128π cm^3
Determine the volume of the larger cylinder;
V = π(16)²(8)
V = 2048π cm^3
Determine the ratio
Ratio = 2048π/ 128π
Large/Small = 16
Large = 16 Small
This shows that the volume of the large cylinder is 16 times greater than that of smaller cylinder.
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a bank features a savings account that has an annual percentage rate of 4.7% with interest compounded monthly.Sean deposits $3500 into the account. How much money will sean have in the account in 1 year
Based on the interest compounded by the bank monthly, and the amount deposited by Sean in the account, the amount of money that will be in that account in a year is $3,668.09
How to find the amount saved?First, find the monthly rate because the interest is compounded monthly:
= 4.7% / 12
= 4.7/12 %
The number of periods would be:
= 1 x 12 months a year
= 12 periods
The amount that Sean will have in a year can be found by the formula:
= Amount invested x (1 + periodic rate) ^ number of periods
Solving for the amount in the account after 1 year gives:
= 3,500 x (1 + 4.7%/12) ^ 12
= 3,500 x 1.0480257937581146250656044647993
= $3,668.09
In conclusion, the amount that Sean will have after saving for a year in the account would be $3,668.09
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The Royal Fruit Company produces two types of fruit drinks. The first type is 40% pure fruit juice, and the second type is 65% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 70 pints of a mixture that is 55% pure fruit juice?
By using the concept of weighted averages, 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice are needed to produce 70 pints of 55 % pure fruit juice.
How to produce a quantity of a given concentration from two quantities of different concentrations?
The situation describes a mixing process with two fruit juices of different concentrations. All pure fruit percentages are known and we are asked to determine the numbers of pints of 40 % pure fruit juice and 65 % pure fruit juice to produce 70 pints of 55 % pure fruit juice. This can be determined by means of the concept of weighted average:
(55 / 100) · 70 = (40 / 100) · x + (65 / 100) · (70 - x)
38.5 = 0.4 · x + 45.5 - 0.65 · x
0.15 · x = 7
x = 46.667
We need 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice to produce 70 pints of 55 % pure fruit juice.
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A company charges $120 for an accident policy. If the person is injured by a vehicle, the company will pay $500. If the person is injured on the job, the company will pay $800. It has been found that five out of 900 claims are filed for vehicular injury and seven out of 900 claims are for an on the job accident. What is the expected annual profit for this policy for the company? Answer:
Assuming that the total number of people that pay the $120 are the 900 that claim the policy, and assuming that out of the 900 cases only the vehicular and job related policies are covered, then the profit for this policy will be:
[tex]p=900(120)-5(500)-7(800)\Rightarrow p=99900[/tex]So, under those assumptions, the profit would be $99 900.
Graph the following features: Y-intercept = -4 slope is -1/3
The equation of the line is y = -1/3x - 4
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the equation of the line?The given parameters are
Slope, m = -1/3
y-intercept, c = -4
A linear equation is represented as
y = slope * x + y-intercept
i.e.
y = mx + c
So, we have
y = -1/3x - 4
Hence. the linear equation is y = -1/3x - 4
See attachment for the graph
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X+ 2y = 166 -7x-3y = 24
We are asked to solve the following system of equations using the elimination method:
x + 2 y = 16
-7 x- 3 y = 24
so we select to multiply the first equation by "7", that way we will be able to eliminate the term in "x" by simple combining term by term the two equations:
7 (x + 2 y) = 7*16
7 x + 14 y = 112
now we combine this new expression term by term with the second equation:
7 x + 14 y = 112
-7 x - 3 y = 24
_____________
0 + 11 y = 136
solve for y by dividing both sides by 11:
y = 136/11
Now we use this value to solve for x in the first equation:
x + 2 (136/11) = 16
x +
Please help I’ll mark you as brainliest if correct!!
Answer: 3
Step-by-step explanation:
1. 2 packs of 6
2. 6 packs of 2
3. 3 packs of 2 and one pack of 6
How can you use the Product of Powers, Power of a Product, and Power of a Power Laws to evaluate and write equivalent numerical expressions with whole-number exponents?
The product of powers, power of a product, and power of a power laws can be used to evaluate the equivalent numerical expressions such as:
2² × 2³ = 2^5 = using product of Powers2² × 3² = (2×3)² = 6² = using power of a Product(2²)³ = 2^6 = using power of a powerHow to illustrate the information?According to the Power of a Product Property, you can distribute the exponent to each factor if a term is raised to one.
According to the rule of a power, when a base is raised to a power and then raised to another power, the exponents are multiplied while the base is left unchanged.
According to the product of powers rule, you can multiply two words with the same base by simply adding their exponents to get the result.
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