Answer:
3
Step-by-step explanation:
let unknown point (x, -2)
-2(x)+4=-2
-2x=-6
x=3
is it f(2)=10 ? I don’t get number 2.
10
Step-by-step explanation:
f(2)=
3(2)+4
3x2+4
using PEMDAS multiplication comes first
6+4
=10
Answer:
f(2) = 10 and f(3) = 13
Step-by-step explanation:
In this context f(2) means "what is y when x equals 2?" How about when x = 3? So we plug the values into the equation and solve for f(x) - which is basically what we called "y" in algebra.
5. Each term in the second row is deter- mined by the function y=2x-1. 2 4 5 3 7 9 What number belongs in the shaded box? X y 1 1 3 5 12
Answer:
23
Step-by-step explanation:
12 * 2= 24
24-1= 23
Simplify to the fullest;
[tex]{ \rm{ \frac{dy}{dx} + 2x + 1 = 2 }}[/tex]
Answer:
[tex]{ \tt{ \frac{dy}{dx} + 2x + 1 = 2 }} \\ \\ { \tt{ \frac{dy}{dx} = - 2x + 1 }} \\ \\ { \tt{dy = ( - 2x + 1) \: dx}} \\ \\ { \tt{ \int dy = \int( - 2x + 1) \: dx}} \\ \\ { \tt{y = - {x}^{2} + x + c}} \\ \\ { \tt{y = - x(x + 1) + c}}[/tex]
Answer:
[tex]y=-x^2+x+\text{C}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{\text{d}y}{\text{d}x}+2x+1=2[/tex]
[tex]\text{Isolate $\dfrac{\text{d}y}{\text{d}x}$}:[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}+2x+1-2x-1=2-2x-1[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-2x+1[/tex]
Multiply both sides by dx to get all the terms containing y on the left side, and all the terms containing x on the right side:
[tex]\implies \text{d}y=(-2x+1)\;\text{d}x[/tex]
Integrate both sides:
[tex]\implies \displaystyle \int 1\;\text{d}y=\int(-2x+1)\;\text{d}x[/tex]
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Integrate each term separately:
[tex]\implies \displaystyle \int 1\;\text{d}y=\int -2x\;\text{d}x+\int 1\;\text{d}x[/tex]
Take the constant outside the integral:
[tex]\implies \displaystyle \int 1\;\text{d}y=-2\int x\;\text{d}x+\int 1\;\text{d}x[/tex]
Integrate, using the rules given below:
[tex]\implies y=-2 \cdot \dfrac{1}{1+1}x^{(1+1)}+x+\text{C}[/tex]
[tex]\implies y=-x^2+x+\text{C}[/tex]
Integration rules:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]
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What value of n makes the equation true?
(2x9y") (4x²,10)-8x^11,20
=
In the equation [tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex] value of n = 10
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.
[tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex]
exponents multiplied with the same base: am * an = a{m + n}
On the powers of x, use the Rule of Multiplying Exponents.
⇒ x⁹ * x² = x⁹⁺² = x¹¹
The powers of y operate similarly.
⇒ [tex]y^{n} * y^{10} = y^{n + 10} = y^{20}[/tex]
Since y¹⁰⁺¹⁰ = y²⁰
Therefore in the given equation, the value of n = 10
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Solve each step of this problem
The cost is given as
[tex]10+0.5x[/tex]Where x is the number of hours
The y-intercept is obtained from the graph as shown below
The value of the y-intercept is obtained to be 10
The y-intercept represents the value represents the fixed cost.
The slope of the cost is obtained from the cost function to be 0.5.
The slope represents the change in cost with respresent to time (hour).
Hence,
lank 1: 10
Blank 2: The fixed cost
Blank 3: 0.5
Blank 4: Change in cost or charge with respect to time used in hours
Blank 5:
[tex]C=10+0.5h[/tex]Answer:
donde están lo calisado los continentes
The measure of the vertex angle of an isosceles triangle is three times the measure of a base angle. Find the number of degrees in the measure of the vertex angle.
We will label the base angles of the triangle as "x".
[tex]\text{Base angle=x}[/tex]Since the vertex angle is 3 times the measure of the base angle, the vertex angle will be equal to 3x:
[tex]\text{Vertex angle =3x}[/tex]The following image represent the angles in the isosceles triangle:
Now we use the following property of triangles:
The sum of all of the internal angles in a triangle must be equal to 180°.
Thus, we add the angles and equal them to 180°
[tex]3x+x+x=180[/tex]We combine the terms on the left:
[tex]5x=180[/tex]And divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{180}{5} \\ x=36 \end{gathered}[/tex]And since x=36, the vertex angle will be:
[tex]\text{vertex angle = 3x = 3(36)=108\degree}[/tex]answer: 108°
Find a formula for the exponential function passing through the points (-1,5/4) and (3,320).
[tex]{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=-1\\ y=\frac{5}{4} \end{cases}\implies \cfrac{5}{4}=ab^{-1}\implies \cfrac{5}{4}=\cfrac{a}{b} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} x=3\\ y = 320 \end{cases}\implies 320=ab^3\implies 320=ab^{4-1}\implies 320=ab^4 b^{-1} \\\\\\ 320=ab^4\cdot \cfrac{1}{b}\implies \stackrel{\textit{substituting from the previous equation}}{320=\cfrac{a}{b}b^4\implies 320=\cfrac{5}{4}b^4}\implies 320\cdot \cfrac{4}{5}=b^4 \\\\\\ 256=b^4\implies \sqrt[4]{256}=b\implies \boxed{4=b} \\\\\\ \cfrac{5}{4}=\cfrac{a}{b}\implies \cfrac{5}{4}=\cfrac{a}{4}\implies \boxed{5=a}~\hfill {\Large \begin{array}{llll} y =5(4)^x \end{array}}[/tex]
in what quadrant l ll lll lv does the point 8,-9 lie?
The point lie in Quadrant IV (8 , -9).
Quadrant in coordinate geometry is divided into four parts which is called Quadrants.
Quadrants I (x, y)Quadrants II (-x, y)Quadrants III (-x, -y)Quadrants IV (x, -y)And, To find the in which quadrant does point (8, -9) lie ?
Now According to the above explanation is that:
We have, Point is (8, -9)
Thus, we can clearly see that
This point is lie in Quadrant IV (8 , -9).
Hence, The point lie in Quadrant IV (8 , -9).
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The perimeter of the triangle below is 68 units. Find the value of y
1 2 3 5 9 Find a number between and 10 Write your answer as an improper fraction and as a mixed number
In finding a number between 9/8 and 10/8, we can use the average of these two.
We can ensure that this number lies between this two.
[tex]Ave=\frac{1}{2}(a+b)[/tex]where a and b are the two numbers
So we have :
[tex]\begin{gathered} Ave=\frac{1}{2}\times(\frac{9}{8}+\frac{10}{8}) \\ =\frac{9}{16}+\frac{10}{16} \\ =\frac{19}{16} \end{gathered}[/tex]Therefore, one number that lies between 9/8 and 10/8 is :
[tex]\begin{gathered} \frac{19}{16} \\ or \\ 1\frac{3}{16} \end{gathered}[/tex]Suppose the top of the minute hand of a clock is 2 in. From the center of the clock. For the duration, determine the distance traveled by the tip of the minute hand (30 minutes)
yes
yes
yes
yes
yes
yes
no
For the function f(x)=x2−9, find
(a) f(x+h),
(b) f(x+h)−f(x), and
(c) f(x+h)−f(x) h
(a) f(x+h)=
The value of f(x+h) is x² + 2xh + h² - 9, the value of f(x+h)−f(x) is 2xh + h², and the value of (f(x+h)−f(x))/h is 2x + h.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The function:
f(x) = x² - 9
(a) f(x + h)
f(x + h) = (x + h)² - 9
f(x + h) = x² + 2xh + h² - 9
(b) f(x+h)−f(x)
= x² + 2xh + h² - 9 - (x² - 9)
f(x+h)−f(x) = 2xh + h²
(c) (f(x+h)−f(x))/h
= (2xh + h²)/h
= 2x + h
Thus, the value of f(x+h) is x² + 2xh + h² - 9, the value of f(x+h)−f(x) is 2xh + h², and the value of (f(x+h)−f(x))/h is 2x + h.
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Enter values to complete the table below.
The slope of the equation, represented by the value of y/x for the given values of x and y, is 3/1, 3/1, 3.
What does slope in mathematics mean?The slope of a line can be used to gauge how steep it is. Slope is theoretically determined as "rise over run" (change in y divided by change in x).
The slope is the ratio of the rise in height between two points to the fall in elevation between those same two points.
The x and y values are provided.
The equation's slope is shown by the ratio y/x.
if y = -3 and x = -1,
y/x = 3/1
if y = 3 and x = 1
y/x = 3/1
if y = 6 and x = 2
y/x = 6/2 = 3
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HURRY On a coordinate plane, a curve goes through (negative 6, 0), has a maximum at (negative 5, 500), decreases to (negative 2.5, negative 450), increases through (0, negative 50), increases again through (1, 0), and then goes through (2, 400).
The real solutions to the equation 3x5 + 25x4 + 26x3 – 82x2 + 76x = 48 are shown on the graph. What are the nonreal solutions?
StartFraction 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus i StartRoot 5 EndRoot Over 3 EndFraction.
StartFraction negative 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus i StartRoot 5 EndRoot Over 3 EndFraction.
StartFraction negative 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
StartFraction 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
The non-real solutions of the polynomial expression are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x5 + 25x4 + 26x3 – 82x2 + 76x = 48
Rewrite the equation as
3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0
The points on the graph are given as
(-6, 0), (-5, 500), (-2.5, -450), (0, - 50), (1, 0), (2, 400).
Write out the x-intercepts
(-6, 0) and (1, 0)
This means that
Real solution = -6
Real solution = 1
Rewrite the above as
x = -6 and x = 1
So, we have
x + 6 = 0 and x - 1 = 0
Multiply
(x + 6)(x - 1) = 0
The next step is to divide the polynomial equation 3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0 by (x + 6)(x - 1) = 0
This is represented as
3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1)
Using a graphing calculator, we have
3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1) = 3x^3 + 10x^2 - 6x + 8
So, we have
3x^3 + 10x^2 - 6x + 8
Factorize
(x + 4)(3x^2 - 2x + 2)
Next, we determine the solution of the quadratic expression 3x^2 - 2x + 2 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (2 ± √((-2)² - 4 * 3 * 2))/2 * 3
So, we have
x = (2 ± √-20)/6
This gives
x = (2 ± 4√-5)/6
Divide
x = (1 ± 2√-5)/3
Split
x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3
So, the conclusion is that
Using the polynomial expression, the non-real solutions are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3
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Hello? Can someone help me with this please?The coffee preferences of 100 people were recorded in a survey.What proportion of the circle (in degrees) is represented by the espresso segment?
Recall that a whole circle is equal to 360°.
Espresso accounts for 5 out of 100 people surveyed.
Therefore,
[tex]\begin{gathered} 360\degree\times\frac{5}{100} \\ =360\degree\times0.05 \\ =18\degree \end{gathered}[/tex]The proportion of the circle that is represented by the espresso segment is 18°.
state where the function is continuous, discontuous and the type of discontinuity for each
For x = 2
[tex]\lim _{x->2^-}(\frac{x}{x-2})=-\infty[/tex][tex]\begin{gathered} \lim _{x->2^+}(6)=6 \\ \end{gathered}[/tex]Since:
[tex]\lim _{x->2^+}f(x)\ne\lim _{x->2^-}f(x)[/tex]The function is discontinuous at x = 2. Besides since the function has a vertical asymptote on one of the sides, we can conclude it is a infinite discontinuity.
For x = 6:
[tex]\lim _{x->6^-}6=6[/tex][tex]\lim _{x->6^+}\frac{x-2}{x^2-6x+8}=\lim _{x->6^+}\frac{x-2}{(x-2)(x-4)}=\lim _{x->6^+}\frac{1}{x-4}=\frac{1}{2}[/tex]Since:
[tex]\lim _{x->6^+}f(x)\ne\lim _{x->6^-}f(x)[/tex]The function is discontinuous at x = 6, at this point the function has a jump discontinuity
Lorena solved the equation 5k – 3(2k – ) – 9 = 0. Her steps are below.
5k – 6k + 2 – 9 = 0
–k – 7 = 0
–k = 7
k = 1/7
Analyze Lorena’s work to determine which statements are correct. Check all that apply.
Answer: K= -9
Step-by-step explanation:
5k−3(2k)−9=0
Multiply 3 and 2 to get 6.
5k−6k−9=0
Combine 5k and −6k to get −k.
−k−9=0
Add 9 to both sides. Anything plus zero gives itself.
−k=9
Multiply both sides by −1.
k=−9
(Hope this helps)
Use the graph below which shows the profit y in thousands of dollars of a company in a given year t where t represents the number of years since 1980 find the linear function y where y depends on t the number of years since 1980 Y=_
First we need to find the slope by using two points
(15,190)=(t1,y1)
(25,170)=(t2,y2)
[tex]m=\frac{y_2-y_1}{t_2-t_1}=\frac{170-190}{25-15}=\frac{-20}{10}=-2[/tex]Then we calculate the y-intercept
[tex]190=-2(15)+b[/tex]we isolate the b
[tex]b=190+30=220[/tex]The equation is
[tex]y=-2t+220[/tex]11) BUSINESS Julian makes and sells wallets. He estimates that his income can be modeled by
y = 16x130, where x is the number of wallets he sells. He estimates that his costs to make
the wallets can be modeled by y = 8x + 150. How many wallets does Julian need to make in
order to break even?
The number of wallets does Julian need to make in order to break even are 35.
What are linear equation?X 1, ldots, and x n are the variables, and display style b, a 1, ldots, and a n are the coefficients. In mathematics, a linear equation is an equation that can be written as x 1, ldots, and x n + a n + b = 0. Ax + By = C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y). frequently actual numbers. The first-degree equations are linear equations. The following is the equation for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.
In order to "break even," his earnings and expenses have to be equal. The number of wallets (x) is represented in both equations. Simply put, you have to work out the equations in the system.
Both the given equation are equal to y
So,
16x - 130 = 8x + 150
16x - 8x = 150 + 130
x = 280/8
x = 35
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Evaluate the expression,g(m - 9) +5 if g = -4 and m = 3
To find the answer you substitute in the expression the g by -4 and the m by 3, as follow:
[tex]-4(3-9)+5[/tex]To evaluate:
1. Make operations in parenthesis:
[tex]=-4(-6)+5[/tex]2. Multiplication
[tex]=24+5[/tex]3. Addition:
[tex]=29[/tex]18x-3y=-15
-6x+y=5
Solve by substitution
Answer:
consistent system with equation [tex]y=6x+5[/tex]
Step-by-step explanation:
[tex]18x-3y=-15[/tex], [tex]-6x+y=5[/tex]
To solve by substitution, we have to isolate a variable in one of the equations. I will isolate y in the second equation.
[tex]-6x+y=5[/tex]
+6x +6x
[tex]y=6x+5[/tex]
Next, substitute this y value for y in the first equation:
[tex]18x-3y=-15[/tex]
[tex]18x-3(6x+5)=-15[/tex]
and distribute.
[tex]18x-18x-15=-15[/tex]
[tex]-15=-15[/tex]
We are left with an equality of constants. This means that the system of equations is actually just one equation, meaning it has an infinite number of solvable points (this is sometimes called consistent). And, its equation is just what we solved for in the first step:
[tex]y=6x+5[/tex]
x + y = 12 x - y = 2
Answer:
x = 7
y = 5
(7, 5)
Step-by-step explanation:
From the way, this question looks I'm going to assume substitution.
x + y = 12
x - y = 2
------------------
2x = 14
÷2 ÷2
-------------
x = 7
x + y = 12
7 + y = 12
-7 -7
-------------------
y = 5
I hope this helps!
Given: f (x) = 2x² − 3x+5 and g(x)=x-4, find (f+g)(x) * help
The value of (f+g)(x) is c(x) = 2x² + (-2)x + 1.
How can we add linear functions?
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as
c(x) = a(x) + b(x) = (a+b)(x) – (i)
Domain of a quadratic equation:
The domain of a quadratic function f(x) is the set of x-values for which the function is defined, and the range is the set of all the output values, as is the case with any function (values of f). Any x is a valid input for quadratic functions because their domain is typically the entire real line. Generally, for a quadratic equation the domain goes from (-∞ ,∞ ).
Given, f(x)= 2x² - 3x + 5 and g(x)= x - 4
Let, y = c(x) denote the value of the function (f+g)(x).
Here, following available literature,
c(x) = (f+g)(x) = f(x) + g(x) [Using (i)]
c(x) = (2x² - 3x + 5)+(x - 4) = 2x² - 3x + 5 + x - 4 = 2x² + (-2)x + 1
Therefore, y = c(x) = 2x² + (-2)x + 1 is the value of (f+g)(x).
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Rectangle ABCD is transformed into rectangle EFGH. Choose all the correct statements about the transformation below. CHOOSE ALL STATEMENTS THAT ARE CORRECT.
A. Rectangle ABCD is similar to rectangle EFGH
B. The scale factor of the dilation is 0.4
C. Rectangle ABCD is congruent to rectangle EFGH
D. The dilation is an enlargement
E. The dilation is a reduction
F. The scale factor of the dilation is 2.5
The correct options are,
A. Rectangle ABCD is similar to rectangle EFGH.
D. The dilation is an enlargement.
F. The scale factor of the dilation is 2.5.
The similarity criteria of rectangles are that their corresponding sides should be proportional to each other. The ratio of their corresponding length is equal to L = 25÷10, which gives L=2.5, and the ratio of their corresponding width is equal to W = 15÷6, which gives w = 2.5. Hence, both rectangles are similar.
The dilation is an enlargement because the size of the rectangle is increased by a scale factor of 2.5.
The scale factor of the dilation is the ratio of the sides, which is equal to 2.5.
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identify the maxima and minima and intervals on which the function is decreasing and increasing
Solution
From the given graph,
The maxima is
[tex](1,-1)[/tex]The minima isThe inetrev
[tex](7,-19)[/tex]aterval inwh which the function is increasing is
[tex](-\infty,1)\cup(7,\infty)[/tex]dec
[tex](1,7)[/tex]The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 2400 pounds on Planet A, find the elephant's weight on Planet B.
The weight of the elephant on planet B given the ratio of the weights on planet A an B is 72 pounds.
What is the weight of the elephant on Planet B?Ratio is used to compare two or more quantities together. It shows the number of times that one quantity is contained in another quantity. In this question, the weight of the elephant on Planet B is 100/3 times that of Planet A.
In order to determine the weight of the elephant on Planet B, multiply the ratio of the weight in planet B by the weight in Planet A and divide by the ratio of weight in planet A.
Weight in Planet B = (3 x 2400) / 100 = 72 pounds
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Please tell me the answer and how you got the answer (AKA How you solved it) And the first person to give me the correct answer gets marked (Due In 3.5 Minutes)
• Thanks
Step-by-step explanation:
the range is the interval or set of all valid y (functional result) values.
we see that y goes continuously through every value between +5 (we see no y values bigger than that) and -5 (we see no y values lower than that).
the filled dots also tell us that the end points would be included (if this would be a necessary information - it is not, because the curve reaches +5 and -5 also in between).
so, the range is
-5 <= y <= +5
a figure is dilated by a scale factor of 3, if the origin is the center of dilation, what is the new vertex, a', if the old vertex was located. at A(3,4)?
A figure is dilated by a scale factor of 3 if the origin is the center of dilation, What is the new vertex, a', if the old vertex was located. at A(3,4)?
_______________________________________
Please, give me some minutes to take over your question
__________________________________________
Please help I’ll mark you as brainliest if correct !
For the given 14 digit credit card, the value of first letter A is found as 4.
What is defined as the arithmetic progression?An arithmetic progression (AP) is a succession in which the differences between each successive term are the same. In this type of progression, it is possible to derive a formula for the AP's nth term.For the given question;
The formula for finding the sun of nth terms of the AP are-
Sn = n/2(a + l)
Where, Sn is the sum of all termsn is the total number of AP.a is the initial term.l is the last term.From the given 14 digits credit card, consider initial 3 letters.
A,_, 8
The sum of three consecutive numbers is 18.
Thus, applying Sum formula of AP
Sn = n/2(a + l)
n = 3Sn = 18a = Al = 3Put the values;
18 = 3/2(A + 8)
Simplifying;
3A + 24 = 36
A = 12/3
A = 4
Thus, the value of the first digit of the credit card is found as 4.
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I need help I’m confused and stuck
Answer:
Step-by-step explanation:
x = -A x 2/7 + 10
Answer:
-3.5 (or -3.50); each cup of coffee is $3.50
Step-by-step explanation:
the slope of the function is what is in front of the x
that is
-3.50 or just -3.5
this means that each cup of coffee is $3.50