Replace x by 5 and y by 2 on both equations, and check if the equalities remain:
2x-3y=4
2(5)-3(2) =4
10-6= 4
4=4 EQUAL
2x+8y= 11
2(5) + 8(2)=11
10 + 16 = 11
26=11
26 is not equal to 11
The ordered pair is NOT a solution to the system of equations.
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
What is the entire set of people for a study?
census
population
sample
survey
Answer: The population
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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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°
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
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
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
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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A B C D Given that ABCD and AD - CB, how can you prove that A ABD ACDB? (G.6)(1 point) O A. Side-Side-Angle (SSA) O B. Angle-Side-Angle (ASA) C. Side-Side-Side (SSS) O D. Side-Angle-Side (SAS)
Answer
Option C is correct.
Side-Side-Side (SSS)
Explanation
The key to proving that two triangles are similar or congruent is to prove that three of either side lengths or angles are congrunet, similar or the same.
For the figure given, we have already been told that
Side AB = Side CD
Side AD = Side CB
Since the two triangles share a similar side in BD, we can complete this by saying
Side BD = Side BD
Side AB = Side CD
Side AD = Side CB
Side BD = Side BD
So, three of the sides of the triangles are equal or congruent.
Hope this Helps!!!
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]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]
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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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!
Blood types: The blood type O negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person.
Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type O negative blood. For this
reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U.S. residents
have type O negative blood. Assume that a blood bank has recruited 19 donors. Round the answers to four decimal places.
a) what is the probability that three or more of them have type O negative blood?
b) what is the probability that fewer than four of them have type O negative blood?
c) It (would/wouldn’t) be unusual if none of the donors had type O negative blood since the probability is __?
a) It is 0.1275 times more probability that fewer than five of them have type o negative blood.
b) The probability that less than five of them are type o negative blood types is 0.9933.
c) 0.2708 probability that there are no donors who have type O negative blood. It would not be odd to have no type o negative donors because this likelihood is higher than 0.05.
There are only two outcomes that can occur for any individual. Type o negative blood is either present or absent. Any other person has no effect on a person's likelihood of having type O negative blood. To answer this question, we thus employ the binomial probability distribution.
Binomial probability distributionThe probability of precisely x successes on n repeated trials is known as a binomial probability, and X can only have two possible outcomes.
P(X=x)= [tex]C_{n,x.P^{x}.(1-P)^{n-x} }[/tex]
Additionally, p is the probability that X will occur.
A whopping 7% of Americans have type o negative blood.This means that P=0.07
18 donors.This mean that n = 18
the probability that three or more of them have type o negative bloodEither less than three have, or at least three do. The sum of the probabilities of these events is 1. So
P(X<3) + P(X≥3)=1
We want P(X≥3)
So,
P(X≥3) = 1-P(X<3)
In which
P(X< 3)= P(X = 0)+P(X = 1)+P(X = 2) = 0.2708 + 0.3669 +0.2348 = 0.8725
P(X≥3) = 1-P(X<3) = 1- 0.8725=0.1275
It's 0.1275 times more likely that fewer than five of them have type O negative blood.
The probability that fewer than five of them have type o negative bloodP ( x < 5 )= P(X=0)+P(X=1)+P(X=3)+P(X=3)+P(X=4)
P(X=x)= [tex]C_{n,x.P^{x}.(1-P)^{n-x} }[/tex]
P(X=0)= [tex]C_{18,0(0.07)^{0}.(0.93)^{18} }= 0.2708[/tex]
P(X=1)= [tex]C_{18,1(0.07)^{1}.(0.93)^{17} }= 0.3669[/tex]
P(X=2)= [tex]C_{18,2(0.07)^{2}.(0.93)^{16} }= 0.2348[/tex]
P(X=3)= [tex]C_{18,3(0.07)^{3}.(0.93)^{15} }= 0.0942[/tex]
P(X=4))= [tex]C_{18,4(0.07)^{4}.(0.93)^{14} }= 0.0266[/tex]
P(X < 5)=P(X=0)+P(X=1)+P(X=3)+P(X=3)+P(X=4)
0.2708+0.3669+0.2348+0.0942+0.0266=0.9933
Would it be unusual f none of the donors had type o negative bloodP(X=0)= [tex]C_{18,0(0.07)^{0}.(0.93)^{18} }= 0.2708[/tex]
Probability of having no type O negative blood donors is 0.2708. It would not be odd to have no type o negative donors because this likelihood is higher than 0.05.
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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]What are the solutions to x2 + 8x + 7 = 0?
x = –8 and x = –7
x = –7 and x = –1
x = 1 and x = 7
x = 7 and x = 8
The solutions for the quadratic equation x² + 8x + 7 = 0 is option B x = -7 and x = -1
Given,
The quadratic equation : x² + 8x + 7 = 0
We have to find the solutions for this quadratic equation using the quadratic formula.
Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = 1, b = 8 and c = 7
Now,
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
= [tex]\frac{-8(+-)\sqrt{8^{2} -4(1)(7)} }{2(1)}[/tex]
= [tex]\frac{-8(+-)\sqrt{64-28} }{2}[/tex]
= (-8±√36)/2
= (-8±6)/2
Now,
Solve for
(-8 + 6) / 2 = -2/2 = -1
Solve for
(-8 - 6) / 2 = -14/2 = -7
That is,
The solutions for the quadratic equation x² + 8x + 7 = 0 is x = -1 and x = -7
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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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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]
can somebody help me with this problem in mathematics.
Answer:
Hachem saves $875.
Step-by-step explanation:
$2,500 - 35% = $1,625
$2,500 - $1,625 = $875
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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◆ Rewrite the fractions as sixths. 1/2 + 1/3= _/6 + _/6
Answer: 1/2 + 1/3 = 3/6 + 2/6
Step-by-step explanation: you multiply 1/2 by 3/3 (1 x 3 and 2 x 3), which gives you 3/6, and then multiply 1/3 by 2/2 (1 x 2 and 3 x 2), which gives you 2/6.
hope this helps! :)
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.
The perimeter of the triangle below is 68 units. Find the value of y
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)
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
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°.
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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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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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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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]