The value of the variable 'x' is calculated by solving equation of the line by using slope value is: x = 3
What is slope of a line?
The slope of a line explain the steepness of the line segment. It is ration of the coordinates of the y-axis and the vertical coordinates of the x-axis. Depending upon the slope value, it is classified as whether lines are parallel or perpendicular.
According to the question, the given parameters for the line segment is as written below:
Slope of a line = (-4) and the coordinate points = (-1, 7)(x,-9): (x1 = -1; y1 = 7)
Now, by using standard equation for the line segment: y = mx + c
where, 'm' is the slope; c is the y-intercept; (x, y) are coordinates
Substituting given values that is slope and y-intercept in the standard equation, we get:
y = mx + c
⇒ 7 = (-4)(-1) + c
⇒ c = 7 - 4 = 3
Therefore, the value of the y-intercept is: c = (3)
Equation of the line by substituting the value of the y-intercept as well as slope value in another equation whose coordinates are (x, -9):
-9 = (-4)x + (3) ⇒ -12 = -4x ⇒ x =3
Hence, the value of the variable 'x' is calculated by solving equation of the line by using slope value is: x = 3
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find the derivative of [tex]\sqrt({x^{2}*6^x})^9[/tex]
Answer: [tex]9x^8 6^{9x/2}+\ln(6^{4.5}) \cdot 6^{4.5x}[/tex]
Step-by-step explanation:
[tex]w=\sqrt{(x^2 6^x)^9}=(x^2 6^x)^{9/2}=x^9 6^{9x/2}\\\\[/tex]
Using the product rule,
[tex]\frac{dw}{dx}=6^{9x/2}\frac{d}{dx} (x^9)+x^9 \frac{d}{dx}(6^{9x/2})\\\\=9x^8 6^{9x/2}+\ln(6^{4.5}) \cdot 6^{4.5x}[/tex]
Find y when x = 1, if y = 3 when x = 2. a. y = x; y =  b. y = –x; y = – c. y = x; y =  d. y = x; y = 1
ANSWER
y = 1.5 or 3/2
EXPLANATION
We are given that:
y = 3 when x = 2
From the question, we know that y and x have a proportional relationship.
This means that y and x change at the same rate:
=> y = kx
where k = constant of proportionality
y is 3 when x is 2:
3 = k * 2
=> k = 3/2 = 1.5
Therefore, when x = 1:
y = 1.5 * 1
y = 1.5 or 3/2
find the domain of f(x)=ln(cosx)
x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z
The domain of f(x)=ln(cosx) = x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z
Solution:The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f (x). A function's range is the set of values that the function can take.Given function,
f(x)=ln(cosx)
When cos(x) is positive, the domain is.
(cos(x)) > 0
since,
cos0 = 1
cos π/2 = 0
cos π = -1
cos 3π/2 = 0
cos 2π = 1
cos 3π/2 = 0
The values of cos(x) are then between -1 and 1.
That is domain of f(x)=ln(cos x)
= cos x ∈ (0;1] -> x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z
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which equation would be used to find three consecutive even integers whose sum is 78
Let n be the smallest integer of the 3, then since all the numbers have to be even numbers, the other two numbers are of the form:
[tex]\begin{gathered} n+2, \\ n+4. \end{gathered}[/tex]Since the sum of the numbers has to be 78, we can set the following equation:
[tex]n+n+2+n+4=78.[/tex]Simplifying the above equation we get:
[tex]3n+6=78.[/tex]Answer:
[tex]3n+6=78.[/tex]
The sum of a number and five more than the number is 17.
The number is 6.
What is a number?
A number is a mathematical entity that may be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.
Let the number be n.
Then according to que, n + (5+n) = 17
or, 2n = 17 - 5
or, n = 12/2 = 6
Hence the number is 6.
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Kristin has to pick up her children, who all attend different schools. She is at home (H) and needs to go to children First Pre-School (C), Braden Rivera Elementary (B) and stephen middle school (S). Kristin estimates the distance among these locations as follows. H to C is 5 miles. H to B is 8 miles. H to S is 15 miles. C to B is 11 miles, C to S is 17 and B to S is 10 miles..What is the minimum distance Kristin can travel?
In order to find the minimum distance, first let's write a map with all positions and distances:
Now, let's write the total distance for the paths she can choose:
[tex]\begin{gathered} HBCS=8+11+17=36 \\ HBSC=8+10+17=35 \\ HCBS=5+11+10=26 \\ HCSB=5+17+10=32 \\ HSBC=15+10+11=36 \\ HSCB=15+17+11=43 \end{gathered}[/tex]Therefore the minimum distance is 26 miles.
Which function in vertex form is equivalent to f(x) = x² + x +1?
Answer:
f(x) = (x + 1/2)² + 3/4
===============================
Vertex form of quadratic equation:
f(x) = a(x - h)² + kConvert the given expression into vertex form by completing the square:
f(x) = x² + x + 1 = x² + 2*(1/2)x + (1/2)² + 1 - (1/2)² = (x + 1/2)² + 1 - 1/4 = (x + 1/2)² + 3/4Answer:
[tex]f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
To find the vertex form of the given function, complete the square.
Given function:
[tex]f(x)=x^2+x+1[/tex]
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=x^2+x+\left(\dfrac{1}{2}\right)^2+1-\left(\dfrac{1}{2}\right)^2[/tex]
[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+1-\dfrac{1}{4}[/tex]
[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+\dfrac{3}{4}[/tex]
Factor the perfect square trinomial formed by the first three terms:
[tex]\implies f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
In the lab, Jane has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B. Solution A is 12% alcohol and Solution B is 20% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 176 milliliters of pure alcohol?
Answer:
700 ml of Solution B was used
Step-by-step explanation:
Whenever we have unknowns the first thing to do is to represent the unknowns using variables, set up equations using given information and solve equations for the unknowns
Here the unknowns are volume of solution A and volume of solution B
Set up our variables as follows
Let x = volume of solution A used for mixing in ml
Let y = volume of solution B used for mixing in ml
We are given that volume of A used is 400 ml less than volume of B used
In math terms this can be represented as
y - x = 400
Or,
- x + y = 400 [1]
We are given the percentages of alcohol in A and B respectively
Since A contains 12% alcohol, the actual volume of alcohol in A
= 12% of x ml
= 0.12x (12% = 12/100 = 0.12)
Similarly alcohol by volume in B
= 0.20x
Total alcohol by volume if x of A and y of B are mixed is
0.12x + 0.20y
and we are given that this quantity is 176 ml
So we set up our second equation as
0.12x + 0.20y = 176 [2]
Using both equations we eliminate either the x or y terms to arrive at an equation involving only the other term.
Since the question asks us to determine only the volume of Solution B used, we should eliminate x term from both equations to get a single equation involving only the y term
Let's review the equations:
- x + y = 400 [1]
0.12x + 0.20y = 176 [2]
Make the coefficients of x the same :
Multiply [1] by 0.12
=> -0.12x + 0.12y = = 0.12 x 400
=> 0.12x + 0.12y = 48 [3]
Add [2] and [3] to eliminate the x term
0.12x + 0.20y = 176
+
-0.12x + 0.12y = 48
-----------------------------------------
0x + 0.32 y = 224
=> 0,32y = 224
Divide both sides by 0.32
==> 0.32y/0.32 = 224/0.32
==> y = 700
So 700 ml of Solution B was used
If we wanted to find volume of solution A used, subtract 400 from 700 to get 300 ml of A
(One-Step Inequalities MC) Write the inequality for the statement: the difference between a number and four sevenths is no more than negative nine elevenths f minus 4 over 7 is less than or equal to 9 over 11 f minus 4 over 7 is less than negative 9 over 11 f plus 4 over 7 is less than or equal to negative 9 over 11 f minus 4 over 7 is less than or equal to negative 9 over 11
The inequality for the given statement is [tex]f-\frac{4}{7} \leq -\frac{9}{11}[/tex] .
By definition, any monotonically growing function can be applied to both sides of an inequality without destroying the relationship between the two (provided that both expressions are in the domain of that function).
However, the inequality relation would be reversed if a monotonically declining function were applied to both sides of an inequality. Examples of using a monotonically declining function are the rules for the additive inverse and the multiplicative inverse for positive numbers.The inequality stays strict if the function is strictly monotonic and the inequality is strict (a b, a > b). The resulting inequality is non-strict if only one of these requirements is met. In fact, applying a strictly monotonically declining function is demonstrated by the criteria for both additive and multiplicative inverses.The inequality for the given statement is [tex]f-\frac{4}{7} \leq -\frac{9}{11}[/tex] .
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Answer:
the answer is D.
For right triangle ABC, find the sine ratio of angle θ.Opition - three fifthsthree fourthsfour fifthsfour thirds
For any given angle in a right triangle that is not the 90° angle its sine is given by the quotient between its opposite side and the hypotenuse. For triangle ABC the hypotenuse is BC and the opposite side to theta is AB. Then the sine of this angle is given by the following equation:
[tex]\sin\theta=\frac{AB}{BC}=\frac{4}{5}[/tex]AnswerThen the answer is the third option, 4/5.
find z and y..no decimals just exact answers
Triangle is a right triangle because has a 90° angle
then we can use trigonometric ratios to find sides
if I use sine
[tex]\sin (\alpha)=\frac{O}{H}[/tex]whre alpha is the reference angle, O the opposite side to the angle and h the hypotenuse of the triangle
using 60° as reference angle
[tex]\sin (60)=\frac{x}{4\sqrt[]{3}}[/tex]then solve for x
[tex]\begin{gathered} x=4\sqrt[]{3}\sin (60) \\ \\ x=6 \end{gathered}[/tex]the value of side x is 6 units
If I use cosine
[tex]\cos (\alpha)=\frac{A}{H}[/tex]where alpha is the reference angle, a the adjacent side to the references angle and H the hypotenyse of the triangle
using 60° as reference angle
[tex]\cos (60)=\frac{y}{4\sqrt[]{3}}[/tex]then solve for y
[tex]\begin{gathered} y=4\sqrt[]{3}\cos (60) \\ \\ y=2\sqrt[]{3} \end{gathered}[/tex]the value of side x is 2root3 units
Name three real-world applications of polynomials and why they impact society.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
polynomials
Step 02:
applications of polynomials:
The polynomials can be represented graphically, and are used in many economics and engineering problems. In economics they appear, for example, to model markets, showing how prices vary over time; how raising or lowering the price of a product affects its sales; or also in the calculation of taxes.
In forestry engineering, for example, we need geometry to calculate areas, but also polynomials in problems such as calculating how many trees we need to replant after having cut down an area of a forest.
Other uses of polynomials are the calculation of the trajectory of projectiles (they are parabolic trajectories), or in the calculation of orbits of satellites or rockets.
That is the full solution.
how many minutes does it take Julian to ride School
Given data:
The time taken by Amy is A=30 min.
The expression for the time taken by Julian is,
[tex]\begin{gathered} J=A+\frac{60}{100}A \\ =(1.6)A \end{gathered}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} J=1.6(30\text{ min)} \\ =48\text{ min} \end{gathered}[/tex]Thus, the time taken by Julian is 48 minutes.
What is the value of x? S *+559 W 2x–71° X-30
As shown in the figure :
The sum of the central angles = 360
so,
[tex](x+55)+(2x-71)+(x-3)+55=360[/tex]Solve the equation for x :
[tex]\begin{gathered} x+55+2x-71+x-3+55=360 \\ 4x+36=360 \\ 4x=360-36 \\ 4x=324 \\ \\ x=\frac{324}{4}=81 \end{gathered}[/tex]So, the answer is : x = 81
1. You will receive $100 per year for 10 years. The discount rate is 10%. What is the
present value of this stream?
Answer:
100 ×10 =1000
Step-by-step explanation:
10% of 1000 is 100 that's the final answer if am wrong let me know
Lin needs to mix paint ratio 3 cups yellow to 2 cups red.how many cups of red and yellow do you need to get 20 total cups of paint
Mix of paintings to obtain 20 cups of paint
there are 3X cups of yellow
there are 2Y cups of red
then find X and Y such that
3X + 2Y = 20
One possible solution is X = 2 Y= 7
2 cups yellow, and 7 cups red
Isaac wants to play miniature golf. Go Golf charges $2.50 for ball and club rental and $4.25 per game. Golf Games charges $3.25 for ball and club rental and $8.50 for two games. For how many games would the cost be the same? Write and solve an equation to determine the number of games for which the cost would be the same.
NEED FAST RESPONSE EQUATION AND SOLUTION
The equation is 6.75x = 5.875y
The price will be the same for 47 Go Golf games and 54 Golf Games
Go Golf charges for the ball and club rental = $2.50
Go Golf charges per game = $4.25
Total charges for Go Golf for one game = $6.75
Golf Games charges for the ball and club rental = $3.25
Golf Games charges for two games = $8.50
Total charges for Golf Game for two games = $11.75
Per game charges = $11.75/2 = $5.875
Let x be the number of games for Go Golf and y be the number of games for Golf Games
Formulating the equation we get:
6.75x = 5.875y
Converting into fractions we get:
675/100x = 5875/1000y
27/4x = 47/8y
After cross multiplication
x/y = 57/48
x = 57 and y = 48
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Using Euler's formula, howmany edges does a polyhedronwith 7 faces and 10 verticeshave?[?] edgesEuler's Formula: F + V = E + 2
Given: The following
[tex]\begin{gathered} N_{umber\text{ of faces}}=7 \\ N_{umber\text{ of vertices}}=10 \end{gathered}[/tex]To Determine: The number of edges
Solution:
The Euler's formula is given as
F + V = E + 2,
where F is the number of faces,
V the number of vertices, and
E the number of edges.
Substitute the given into the formula
[tex]\begin{gathered} F=7 \\ V=10 \\ E=? \end{gathered}[/tex][tex]\begin{gathered} F+V=E+2 \\ E=F+V-2 \\ E=7+10-2 \\ E=17-2 \\ E=15 \end{gathered}[/tex]Hence, the number of edges possessed by the polyhedron is 15
A fuelling vehicle finished filling a plane with 12.40 tons of fuelat 10:35. If the fuelling rate is 0.20 ton of fuel per min, at whattime did the fuelling start? Give your answer in a 12-hour clockformat, such as 9:00.Enter the answer
Let's define,
X := Total minutes it takes to fill the plane (with fuel)
Then,
[tex]X\cdot0.20=12.40[/tex]Solving it for X, we get
[tex]X=\frac{12.40}{0.20}=62\text{ min}[/tex]This means that the vehicle takes 1 h 2 min to fill the plane. If the fuelling finished at 10:35, it began at
[tex]10-1\colon35-2=9\colon33[/tex]9:33.
Write a mixed number and an improper fraction for the model below.
The mixed fraction can be 3 2/3 and the improper fraction would be 11/3 for the same mixed fraction.
What is mixed fraction?A mixed fraction is one that is represented by its quotient and remainder. 2 1/3, for example, is a mixed fraction in which 2 is the quotient and 1 is the remainder. A mixed fraction is thus the product of a whole number and a proper fraction.
What is improper fraction?An improper fraction is one in which the numerator (top number) exceeds or equals the denominator (bottom number). Fractions like 651/14 are "incorrect." They are simply another way to write a mixed number.
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PLEASE HELP ME ASAP
What is the slope of the line passing through (0, 5) an d(-12, 2) ?
Enter your answer in the box.
Answer:
Slope = 0.25
Step-by-step explanation:
m= -3 / -12 = -1 / -4 = 0.25
distance between x's = 12
distance between y's = 3
hope this helped thank you!
Jessica is a software saleswoman. Her base salary is $1900, and she makes an additional $50 for every copy of History is Fun she sells.
Let P represent her total pay (in dollars), and let N represent the number of copies of History is Fun she sells. Write an equation relating P to N. Then use this equation to find her total pay if she sells 28 copies of History is Fun.
Equation:
Total pay if Jessica sells 28 copies:
The equation which represents Jessica's income is 1900+50n.
Jessica's total income after selling 28 copies of History is Fun is $3300
Base salary of Jessica = $1900
The additional income per copy of History is Fun = $50
Let p represent her total pay (in dollars), and let n represent the number of copies of History is Fun she sells:
Formulating the equation we get the following:
Jessica's total pay = Base salary + Additional income per copy of History is Fun*Number of copies sold by Jessica
= 1900 + 50*n
Income, when she sells 28 copies of History, is Fun:
= 1900 + 50*28
= 1900 + 1400
= $3300
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please help. I don't understand this
The answer of the expression is 3 -4 and the sum is -1
Given,
In the figure, given a number line.
And, write an addition expression represented by number line. Then find the sum.
Now, According to the question:
To solve for an expression is:
Calculate the principle based on the number line .
We can figure out the formula .
= 3 - 4
[Moving to the right is positive and moving to the left is negative ]
To find the sum:
3 - 4 = -1
According to the figure , the end point of the movement is -1 and the answer is correct.
Hence, The answer of the expression is 3 -4 and the sum is -1
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Whats the answer I DONT het how to do this At all
Given that the radius r of a circle is written as a function of the area A with the following equation:
[tex]r=\sqrt[]{\frac{A}{\pi}}[/tex]The domain of the above function is the area A of the circle.
This is because, in this context, the area is an independent and unique variable.
A is the input value.
How many solutions can be found for the linear equation? 3(x+4)=3x+7
Answer:
there is no solution because there aren't any nubmer of X to get linear equation
3X-3X= 12-7
0=5
there aren't solutions so it will be 0
An electronics store has portable CD players on sale for $54.95.If the local sales tax is 6.5%, what is the total cost of a CD player?
The total cost of a CD player is $58.52
If 8 - x = 17, then find the value
of 6x - 22
Answer: -25
Step-by-step explanation: 8 - x = 17 ~ x=-9 6*(-9)-22=-25
Find a polynomial function of degree 4 with - 1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
The polynomial function in expanded form is f(x) = _
(Use 1 for the leading coefficient.)
Answer: [tex]f(x)=x^4 +3x^3 +3x^2 +x[/tex]
Step-by-step explanation:
[tex]f(x)=x(x+1)^3 \\\\=x(x^3 +3x^2 +3x+1)\\\\=x^4 +3x^3 +3x^2 +x[/tex]
Connor deposited $84 into his checking account. If his new balance is $51. what was his balance before the deposit?'
Answer: -33
Step-by-step explanation: I guess he had like debt to pay lol but he would've had to have -33 dollars and added $84 to get a total of $51