The missing term when using the square root method is the discriminant. The discriminant is a number that is calculated from the coefficients of a quadratic equation.
What is quadratic equation?A quadratic equation is a type of mathematical equation that can be written in the form of ax² + bx + c = 0, where a, b, and c are real numbers, a cannot equal 0. It is called a quadratic equation because it has a second-order term, which is the x² term. This type of equation has two solutions, which are referred to as the roots. These roots can be found by using the quadratic formula, which is x = -b ± √(b² - 4ac) / 2a. This equation can be used to solve a wide variety of problems, including finding the length of a side in a right triangle, calculating the area of a circle, finding the maximum or minimum of a function, and solving systems of linear equations.
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what is 4+4 tell me pls :)
Answer:
8
Step-by-step explanation:
It would be best if you put in the calculator. Have a good day.
Bally Manufacturing sent Intel Corporation an invoice for machinery with a $14,000 list price. Bally dated the invoice July 23 with 2/10 EOM terms. Intel receives a 40% trade discount. Intel pays the invoice on August 5. What does Intel pay Bally?
The amount of money Intel pay Bally is given by the equation A = $ 8,232
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount be represented as A
Now , the equation will be
The total invoice amount = $ 14,000
The trade discount given by Intel = 40 %
So , the amount of discount = trade discount x total invoice amount
Substituting the values in the equation , we get
The amount of discount = ( 40/100 ) x 14000
The amount of discount = 0.4 x 14000
The amount of discount = $ 5600
So , the amount after 40 % discount = total invoice amount - amount of discount
Substituting the values in the equation , we get
The amount after 40 % discount = 14,000 - 5,600
The amount after 40 % discount = $ 8,400
And , 2/10 means 2%discount if the amount received within 10 days
So , the amount after 2 % discount = amount after 40 % discount - ( 2/100 ) x amount after 40 % discount
Substituting the values in the equation , we get
The amount after 2 % discount A = 8400 - 0.02 x 8400
The amount after 2 % discount A = $ 8400 - $ 168
The amount after 2 % discount A = $ 8,232
Hence , the amount is $ 8,232
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Triangle ABC is defined in the coordinate plane by the points A(1, 2), B(4, 3), and C(4, 0).
Under which transformations will the image of triangle ABC be similar to the preimage?
select all that apply
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What’s dilation?The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.
According to the figure AB=1. AC=4
A'B' = 3, A'C' = 12
FAB'=3AB [A'C' = BAC
So, the scale factor is 3
Dilation is a method for producing comparable numbers. By increasing distances by the scale factor, each point is extended outwards from the center point D. (If the scale factor is more than one, go outwards.)
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Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What’s dilation?The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.
A. [tex]$T(x, y) \rightarrow(-x, -y)$[/tex]
This is a reflection to the origin that does not preserve angles or aspect proportions. Therefore, triangle ABC under this transformation does not resemble that image.
Example: [tex]$T(x, y) \rightarrow(x, x-y+1)$[/tex]
This is a shear transformation that does not preserve angles or aspect ratio. Therefore, triangle ABC under this transformation does not resemble that image.
C. [tex]$T(x, y) \rightarrow(x+3, y)$[/tex]
This is a translation that preserves angles and aspect ratio. So the triangle ABC under this transformation resembles that image.
D. [tex]$T(x, y) \rightarrow(0.2x, 4y)$[/tex]
This stretches by a factor of 0.2 in the x direction and 4 in the y direction, preserving angle and horizontal proportions. So the triangle ABC under this transformation resembles that image.
E. [tex]$T(x, y) \rightarrow(2x, 2y)$[/tex]
This is a stretch by a factor of 2 in both the x and y directions, preserving the proportions of the angles and sides. So the triangle ABC under this transformation resembles that image.
F. [tex]$T(x, y) \rightarrow(3x, 4y)$[/tex]
This stretches by a factor of 3 in the x direction and 4 times in the y direction, preserving the proportions of angles and sides. So the triangle ABC under this transformation resembles that image.
Therefore, the similarity-preserving transformations between triangle ABC and its image are C, D, E, and F.
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find the area of the parallelogram with vertices p(3, 3, 2), q(5, 6, 4), r(9, 10, 12), and s(7, 7, 10).
The area of the parallelogram with vertices p(3, 3, 2), q(5, 6, 4), r(9, 10, 12), and s(7, 7, 10) is √336≈18.34 units.
A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram.
Calculate the length of PQ → Position vector of Q - Position vector P
PQ→ (5-3)i + (6-3)j + (4-2)k
PQ→ 2i + 3j + 2k
Calculate the length of PS →Position vector of S - Position vector P
PQ→ (7-3)i + (7-3)j + (10-2)k
PQ→ 4i + 4j + 8k
Area of parralelogram = [tex]\left[\begin{array}{ccc}i&j&k\\2&3&2\\4&4&8\end{array}\right][/tex]
= √16² + 8² + 4²
=√336
=18.34 units
The area of a parallelogram is the region bounded by the parallelogram's four sides. It is measured in square units like cm2, m2, and inch2 and can be computed if we know the size of the parallelogram's base and height.
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find the perimeter, in feet, of the parallelogram. a parallelogram is 17 feet wide, 27 feet long, and 24 feet high.
The perimeter of a parallelogram P=102mm.
The perimeter of a parallelogram is defined as the total length of the boundaries, surrounding it. The sum of all the sides of a parallelogram is known as the perimeter of a parallelogram.
The formula for the perimeter of a parallelogram:
P=2(a+b).
There are some properties of a parallelogram:
The pair of opposite sides and angles of a parallelogram are parallel and equal to each other.Diagonals of a parallelogram bisect each otherPairs of adjacent angles are supplementary, the sum of all interior angles is equal to 360 degreesThe given information is slant height is 17, height is 24 and breadth is 27.
substitute the given values in the above formula.
P=2*(24+27)
P=2*(51)
P=102.
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if cot theta equals -root3 then what does tan theta equal
Answer:
The tangent of theta is -1/3.
Explation step-by-Step
The tangent of theta is -1/3. This is calculated as follows:
cot theta = -√3
cot theta = 1/tan theta
-√3 = 1/tan theta
-1/3 = tan theta
If algebra tiles have the dimensions shown here, what would you call this tile collection?
In other words, what is the total area of all of the pieces?
Ignore the 3rd Question
The total area of all of the pieces is;
Total Area = 4x + 4y + 3xy + 6x² + y²
What is Area?Area is the amount of space occupied by a 2-dimensional figure. It is the quantity that measures the number of unit squares that cover the surface of a closed figure. The word 'area' means a vacant surface. The area of a shape is calculated with the help of its length and width. Length is unidimensional and measured in units such as feet (ft), yards (yd), inches (in), etc.
From the diagrams, we have the following shapes;
Rectangle (x,1) = 4 x X x 1
Rectangle (y,1) = 4 x y x 1
Rectangle (x,y) = 3 x x x y
Square (x,x) = 6 x X x X
Square (y,y) = 1 x y x y
Total Area = 4x + 4y + 3xy + 6x² + y²
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Question 3
A set of data include 2000 observations. How many classes would you suggest to construct a frequency
distribution?
A total of 11 classes should be suggested to construct a frequency distribution.
What is frequency?A value's frequency is the number of times it occurs or takes place. In a frequency table, a list of objects is presented together with the frequency of each item.
The quantity of observations that take place during a specific predetermined timeframe is the frequency of a class interval. Therefore, if 20 individuals between the ages of 5 and 9 are found in the data from our study, the frequency for the 5–9 age range is 20.
The frequencies of each category are represented individually in a frequency graph; the frequencies of each category are shown cumulatively.
By doing so, we are able to analyze the data's distribution in greater detail than we could have done by using a frequency polygon and performing statistics.
If k is the number of classes and n is the number of observations, then for number of classes we should select the smallest k such that
[tex]2^k > n[/tex] ( 2 to k rule)
In our case, the no. of observations is 2000
i.e.
2¹⁰ = 1024 < 2000
With this,
2¹¹ = 2048 > 2000
Thus, A total of 11 classes should be suggested to construct a frequency distribution.
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i need to add this fraction i need to know the explantion and answer Add: 3 38
+ 7 34
The addition of the given fraction numbers 3(3/8) and 7(3/4) is, 89/8
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
Two fraction numbers,
3(3/8) and 7(3/4)
The addition of two fraction number is,
⇒ 3(3/8) + 7(3/4)
In simple form it can be written as,
⇒ 24+3/8 + 28+3/4
⇒ 27/8 + 31/4
LCM Of 8 & 4
= 8
⇒ 27/8 + 31×2/4×2
⇒ 27/8 + 62/8
⇒ (27 + 62)/8
⇒ 89/8
Hence, the result is 89/8
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Derive an exact closed form bound in terms of n on the number of times function F called in each code segment. Use floor/ceilings as needed. Clearly explain your answer and show your work. (a) 1: function COUNT1 (n) 2: for i = 1 to 2n ^ 2 do for 1 to i do 3: k = 1 4: 5: while k <= n do 6: k = k + 8 7: F(i, j) (b) 1: function COUNT2(n) 23 for i = 1 ton do for j = 1 to i do 4: 6: for k = j ton do 5: 2966 F(i, j) F(j, k) 7: F(k, i) (c) The initial call is F(n ^ 2) 1: function F(i) 2: if i < 4 then 3: return 4: while i > 1 do 5: i leftarrow i / 4 6: F(i)
In order to calculate the exact closed form bound of the number of times function F is called in each code segment, we need to consider the number of times F is called in each line of code.
For COUNT1, line 3 calls F once, line 5 calls F n times, and line 7 calls F once more, for a total of n+2 calls.For COUNT2, line 4 calls F once, line 6 calls F n(n+1)/2 times, and line 7 calls F n(n-1)/2 times, for a total of n*(2n+1)/2 calls.For the initial call of F(n^2), the number of times F is called depends on the value of n. To calculate the exact number of calls for any value of n, we can use a recursive approach, starting from the top line of code and working our way down.
For example, for n=4, the initial call of F(16) will call F(4), which will then call F(1) four times, for a total of 5 calls. For n=8, the initial call of F(64) will call F(16), which will call F(4) four times and F(1) sixteen times, for a total of 20 calls.
Thus, for any value of n, the exact closed form bound of the number of times function F is called is given by the formula [1]:
F(n^2) + 4 * F(n/4) + 16 * F(n/16) + …Where the number of terms in the summation is equal to the number of times n is divided by 4 before it reaches 1.
For example, for n=16, the summation will have four terms (n=16, n=4, n=1), and for n=32, the summation will have five terms (n=32, n=8, n=2, n=1).
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bgrvfecdwxsafecdwxstcrefdxwsza
The value of x in the triangle is 23.83
How to determine the value of x in the triangleFrom the question, we have the following parameters that can be used in our computation:
A right triangle
The value of x can be calculated using the following tangent equation
tan(40) = 20/x
Make x the subject of the equation
x = 20/tan(40)
Evaluate
x = 23.83
Hence, the value of x is 23.83
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I have added a screenshot.
The value for n(A ∩ [tex]B^c[/tex]) is {3}
Option D is the correct answer.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
Set A = {1, 3}
Set B = {1, 7}
U = {1, 3, 5, 7}
[tex]B^c[/tex] = U - B = {3, 5}
A ∩ [tex]B^c[/tex].
= Numbers that are common to both A and [tex]B^c[/tex].
= {3}
Thus,
n(A ∩ [tex]B^c[/tex]) = {3}
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You might need: Calculator
The expression 1.08s +1.02b predicts the end-of-year value of a financial portfolio where s is
the value of stocks and b is the value of bonds in the portfolio at the beginning of the year.
What is the predicted end-of-year value of a portfolio that begins the year with $200 in stocks
and $100 in bonds?
Show Calculator
The predicted end-of-year value of the portfolio can be calculated as follows:
What is a mathematical expression?
A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities. The expression structure is as follows: Expression: Math Operator, Number/Variable, Math Operator
s = $200
b = $100
1.08s = 1.08 * $200 = $216
1.02b = 1.02 * $100 = $102
Therefore, the predicted end-of-year value of the portfolio is $216 + $102 = $318.
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None of the students taking literature are taking physics, but several of the students taking physics are taking art. In addition, none of the students taking rhetoric are taking physics.
Which one of the following statements follows logically from the statements above?
A. There are students who are taking art but not literature.
B. None of the students taking literature are taking art.
C. There are students who are taking rhetoric but not literature.
D. None of the students taking rhetoric are taking literature.
E. There are students who are taking both art and literature.
The correct option is (A).
The following statements follows logically from the statements is there are students who are taking art but not literature.
"None of the students taking literature are taking physics."
So: if you are student taking literature, then you are not taking physics.
⇒TL=Taking Literature
⇒TP=Taking Physics
⇒TA=Taking Art
⇒TR=Taking Rhetoric
P1: TL ==> not TP
TP ==> not TL
"but several of the students taking physics are taking art."
So: some of the students taking physics are also taking art.
Q1: TP-some-TA
TA-some-TP
"In addition, none of the students taking rhetoric are taking physics."
So: if you are a student taking rhetoric, then you are not taking physics.
P2: TR ==> not TP
TP ==> not TR
Answer choice (A) states: "There are students who are taking art but not literature."
So: some students who are taking art are not taking literature.
(A): TA-some-not TL
not TL-some-TA
Can we logically infer this from the statements above? Yes.
Remember we can combine a quantifier statement with a Sufficient & Necessary statement if the right-hand side variable of the quantifier statement is the same as the sufficient condition of the Sufficient & Necessary statement. We have that with P1 and Q1.
So, we can combine Q1 to P1 like so: TA-some-TP ==> not TL to infer: TA-some-not TL, so the correct option is (A).There are students who are taking art but not literature.
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A water tank is being filled with water. Before water is pumped in, the water level in the tank is 14 inches high. After 20 minutes, the water level is 52 inches high.If t represents the time in minutes and h represents the water level, which of the following equations can be used to model this situation?A. h= 39+13tB. h=1.95t-13C. h=1.95t+13
The equation which can be used to model this situation is equals to the h = 1.9t + 14 , where h represents the water level , t represents the time in minutes.
We have, A water tank which is filled with water. Before pumping the water,
The level i.e., high of water in water tank
= 14 inches
After 20 minutes, the level of water in tank = 52 inches
We have to determine the equation to model this situation in form of time "t" in minutes. Let "h" be level of water increases from initial point/ level in t minutes. As the change in water level from initial to after 20 minutes = 52 inches - 14 inches = 38 inches
That is, water level increased 38 inches in 20 minutes. Then rate of increase in level = 38/20 = 1.9 inches per minutes
Now, the for time 't' the equation is formed by multiplying the rate of chenge of water level with 't' and adding initial water level.
=> h = 1.9t + 14
which is linear equation in two variables,i.e., h and t . Hence,the required equation model is h = 1.9t + 14 .
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Please help, I am trying to get this question answered.
They are similar by the property of SAS and the factor by which the triangle grows is 1.25
A scientist studies a sample that weighs 1 ounce, which is about 28 grams. About how many grams would be in a 48-ounce sample?
Step-by-step explanation:
1 ounce = 28 grams
48 ounce = 1344 grams
So, 1344 grams would be in a 48-ounce sample.
1. Explain the difference between a discrete variable and a continuous variable. Choose the correct answer below.
2. Give an example of each type. Choose the correct answer below.
1. A discrete variable has possible values that are separate numbers, while a continuous variable has possible values that form an interval.
2. The number of children in a family is a discrete variable, while the time it takes to run a marathon is a continuous variable.
what is a discrete variable and example?
Discretized variables require a certain amount of time to count. Consider counting the coins in your pocket as an example. Your bank account's funds can be counted. The balances in each person's bank accounts might also be added up. Even if it may take some time to count the last thing, it is still a countable item.
what is a Continuous Variable and example?
Counting continuous variables would literally take an eternity. In actuality, you would reach "forever" and never reach the end of the list. Consider age as an example. Age cannot be measured. why not Considering that it would take an eternity? For instance,
Twenty-five years, ten months, two days, five hours, four seconds, four milliseconds, eight nanoseconds, 99, and so on.
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The full question would be just part 1.
Explain the difference between a discrete variable and a continuous variable.
a high school sells students tickets for $5 as well as general admission tickets for $7 to attend thier football games. The school needs to bring in at least $1500 per game in order to maintain the costs of the football team
The cost of students ticket is $37.5and the cost of general admission is $187.5.
What is system of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
Assume s be the students tickets cost and g be the general admission cost.
From the given information,
⇒ s + g = 225 ..(1)
5s + 7g = 1500 ..(2)
From equation (1),
s = 225 - g
Plug the value of s in equation (2)
5(225 - g) + 7g = 1500
1125 - 5g + 7g = 1500
2g = 1500 - 1125
2g = 375
g = 187.5
Plug g = 125 in equation (1),
s + 187.5= 225
s = 225 - 187.5
s = 37.5
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a raised flower bed is 25 feet long 8 feet wide and 1.5 feet deep. find the volume of soil that it holds in cubic yards round to 1 decimal place. please explain
The volume of the soil that it holds in cubic yards is 11.1.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
Given:
A raised flower bed is 25 feet long 8 feet wide and 1.5 feet deep.
In yards,
a raised flower bed is 8.33 yards long, 2.67 yards wide, and 0.5 yards deep.
The volume of the soil that it holds,
= 8.33 x 2.67 x 0.5
= 11.10 cubic yards.
Therefore, the volume is 11.1 cubic yards.
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Please help me with this question.
The area of the given region that is enclosed by a cardiod r = 20+20sinθ, is 600π
What are definite integrals?A definite integral is a formal calculation of area beneath a function, using infinitesimal slivers or stripes of the region.
Given that, we need to find an area for region that is enclosed by a cardiod
r = 20+20sinθ
Using definite integral,
[tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(20+20\sin \left(\theta\right)\right)^2d\theta[/tex]
= [tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(400+400\sin^2 \left(\theta\right)+800sin\theta\right)d\theta[/tex]
= [tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(400+400(\frac{1-cos2\theta}{2})+800sin\theta\right)d\theta[/tex]
= [tex]\frac{1}{2}\cdot \int _0^{2\pi }\left(600+200cos2\theta}+800sin\theta\right)d\theta[/tex]
= [tex]\frac{1}{2}\cdot \:1200\pi[/tex]
= [tex]600\pi[/tex]
Hence, the area of the given region that is enclosed by a cardiod
r = 20+20sinθ, is 600π
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Recently many airlines have had cancel flight in a single day republic airlines had to cancel 416 flights representing 15.1% of the airlines scheduled flights. How many flights were originally scheduled?
The number 2755 flights were scheduled.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Recently many airlines have had to cancel flights in a single day.
Republic airlines had to cancel 416 flights representing 15.1% of the airlines' scheduled flights.
The number of flights scheduled,
= 416 x 100/ 15.1
= 41600/15.1
= 2754.96
≈ 2755
Therefore, 2755 flights were scheduled.
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Subtract: (9x^3-4x^2+2x) - (2x^+6x^2-3x)
Answer:
7x^3 + 2x^2 - x
Step-by-step explanation:
To subtract the two expressions (9x^3-4x^2+2x) and (2x^+6x^2-3x), we will need to line up the terms with the same exponent and subtract them.
(9x^3-4x^2+2x) - (2x^+6x^2-3x)
= (9x^3 - 2x^3) + (-4x^2 + 6x^2) + (2x - 3x)
= 7x^3 + 2x^2 - x
So the result of the subtraction is 7x^3 + 2x^2 - x
Please note that if you want to simplify the result further, you can combine like terms.
Please help me with this question.
The value of the sin(2θ) is given as follows:
-24/25.
How to obtain the sine of twice the angle?We are given the cosine of the angle, hence the following identity must be considered:
sin²(θ) + cos²(θ) = 1.
Considering the value of the cosine, the value of the sine is obtained as follows:
sin²(θ) + (3/5)² = 1
sin²(θ) = 16/25
sin(θ) = -4/5 -> apply the square root, angle in the fourth quadrant is negative.
Then the sine of twice the angle is obtained as follows:
sin(2θ) = 2sin(θ)cos(θ)
Hence:
sin(2θ) = 2 x (-4/5) x (3/5) = -24/25.
Meaning that the correct option is the third option.
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In a poker hand consisting of 5 cards, find the probability of holding a. 3 kings b. 4 hearts and 1 diamonds Expert's answer A poker hand consists of 5 cards. The sample space has (52/5) possible outcomes. a. Choose 3 kings from 4 kings. From the remaining 52−4=48cards choose 2 non-kings to make a five-card poker hand P(3 kings)=(43)(52−45−3)(525)=P(3 kings)=(552)(34)(5−352−4)= =4!3!(4−3)!⋅48!2!(48−2)!52!5!(52−5)!==5!(52−5)!52!3!(4−3)!4!⋅2!(48−2)!48!= =2(48)(47)(120)52(51)(50)(49)(48)=9454145≈0.001736=52(51)(50)(49)(48)2(48)(47)(120)=5414594≈0.001736 b. There are total 13 hearts and 13 diamonds. Choose 4 hearts from 13 hearts (134)(413) Choose 1 diamonds from 13 diamonds (131)(113) P(4 hearts and 1 diamonds)=(134)(131)(525)=P(4 hearts and 1 diamonds)=(552)(413)(113)= =13!4!(13−4)!⋅13!1!(13−1)!52!5!(52−5)!==5!(52−5)!52!4!(13−4)!13!⋅1!(13−1)!13!= =13(12)(11)(10)(5)(13)52(51)(50)(49)(48)=14339984≈0.003576=52(51)(50)(49)(48)13(12)(11)(10)(5)(13)=39984143≈0.003576
In a poker hand consisting of 5 cards, the probability of holding 3 kings is 0.0009 .
The probability of holding 3 kings in a poker hand of 5 cards can be calculated as follows:
The number of ways to choose 3 kings from a deck of 4 kings is= ⁴C₃ = 4.
The number of ways to choose 2 other cards from the remaining 48 cards is = ⁴⁸C₂ = 1128.
The total number of 5-card hands from a standard deck of 52 cards is = ⁵²C₅ = 2598960.
So , the probability of holding 3 kings in a 5 card hand is
⇒ (4 × 1128)/2598960
⇒ 4512/2598960 .
⇒ 0.00085148 .
Therefore , probability of holding 3 kings in a 5card hand is approximately 0.0009 .
The given question is incomplete , the complete question is
In a poker hand consisting of 5 cards, find the probability of holding 3 kings .
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Find the equation of the line that contains the given point and is perpendicular to the given line. Write the equation in slope-intercept form, if possible. (6,2); 3x−2y=7 please help me with this, it’s due tomorrow!!?
The equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8
What is slope-intercept form?The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point
Given that, a line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7, we need to find the equation of the line,
The line is
3x-2y = 7
Converting into slope-intercept form,
3x-2y = 7
2y = 3x - 7
y = 3x/2 - 7/2
We know that, the slopes of two perpendicular lines are negative reciprocal of each other,
Therefore, the slope of the asked line = -2/3
Therefore, the equation of the asked line is, y = -2x/3 + c....(I)
Put x = 6 and y = 2 in equation to find c,
2 = -4 + c
c = 8
Therefore, put c = 8 in equation (i)
y = -2x/3 + 8
Hence, the equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8
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A storm system is in the Central Texas area and moving in a straight line through Austin. The Weather Service Office forecasts that t hours after 12 noon the storm will be a distance of s(t) = 5 + 14t – 3t2 miles from Austin. How fast will the storm be moving at 4:00 pm and in what direction will it be moving? storm moving 1. storm speed = 12 mph, away from Austin. storm moving 2. storm speed = 10 mph, toward Austin. 3. storm speed = -12 mph, storm moving toward Austin. storm moving 4. storm speed = 12 mph, toward Austin. storm moving 5. storm speed = 10 mph, away from Austin. 6. storm speed = –10 mph, storm moving toward Austin.
Storm moving toward austin at speed of -10 mph.
To find the speed of the storm at 4:00 PM, we need to find the rate of change of the distance of the storm from Austin at that time. To do this, we can use the derivative of the function s(t) = 5 + 14t - 3t^2, which represents the distance of the storm from Austin.
s'(t) = 14 - 6t
At t = 4 hours, or 4:00 PM, the speed of the storm is given by:
s'(4) = 14 - 6 * 4
s'(4) = 14 - 24
s'(4) = -10 mph
So, the storm will be moving at 10 mph towards Austin at 4:00 PM.
Therefore, the answer is: 6. storm speed = -10 mph, storm moving toward Austin.
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A town's population is currently 6,595. If the population doubles every 29 years, what will the population be 145 years from now?
Answer:
Below
Step-by-step explanation:
145 yr / 29 yr/double = 5 doubles
6595 x 2 ^5 = 211 040 ppl
Victoria scored a total of 9 points
The expression that represents the total number of points Victoria scored in the basketball games for the whole season is,
5x + 9.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
Victoria scored a total of 9 points in the first basketball game of the season.
She scored 5 points per game in each of the other x basketball games she played that season.
That means, 5x is the score.
The expression that represents the total number of points Victoria scored in the basketball games for the whole season is,
5x + 9.
Therefore, the expression is 5x + 9.
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The complete question:
Victoria scored a total of 9 points in the first basketball game of the season. She scored 5 points per game in
each of the other x basketball games she played that season.
Which of the following expressions represents the total number of points Victoria scored in the basketball games for the whole season?
A debate team consists of 5 freshmen and 4 sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so at least two of the sophomores are standing next to each other, and at least two of the freshmen are at the ends of the line?
The number of ways that at least two of the freshmen are at the ends of the line and at least two of the sophomores are standing next to each other will be 9.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A debate team consists of 5 freshmen and 4 sophomores. (Everyone is distinguishable.)
⇒ (3 x 3)
⇒ 9
The number of ways that at least two of the freshmen are at the ends of the line and at least two of the sophomores are standing next to each other will be 9.
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