You have the following two points:
(2,1)
(-1,3)
In order to determine what is the distance between the previous points, you use the following formula:
[tex]d=\sqrt[]{(x_1-x_2)^2-(y_1-y_2_{}^{})^2}[/tex]where (x1,y1) and (x2,y2) are the points with a distance between them of d.
You use the given points to replace them into the formula for d:
[tex]\begin{gathered} d=\sqrt[]{(1-3)^2-(2-(-1))^2} \\ d=\sqrt[]{(-2)^2+(3)^2} \\ d=\sqrt[]{4+9} \\ d=\sqrt[]{13} \end{gathered}[/tex]hence, the distance between the given points is √13
Which of the following is the equation of the perpendicular bisector of the line segment joining the points X(2,4) and B(8,-2)?
step 1
Find out the slope of segment XB
m=(-2-4)/(8-2)
m=-6/6
m=-1
Remember that, if two lines are perpendicular, then their slopes are negative reciprocal
that means
the slope of the perpendicular bisector is
m=1
step 2
Find out the midpoint segment XB
[tex]\begin{gathered} M(\frac{2+8}{2},\frac{4-2}{2}) \\ M(5,1) \end{gathered}[/tex]step 3
Find out the equation of the perpendicular bisector
y=mx+b
we have
m=1
point M(5,1)
substitute and solve for b
1=(1)(5)+b
1=5+b
b=1-5
b=-4
therefore
the equation is
y=x-4Help me find the numbers for the “Image” I already have them for pre-image
If the point (x, y) is dilated around the origin by a scale factor m, then its image is
(mx, my)
That means multiplying each coordinate by the scale factor of the point to get its image
Since the scale factor of dilation is 2
Since S = (-3, 3), then
S' = (-6, 6)
Since U = (-1, 4), then
U' = (-2, 8)
Since N = (-2, -1), then
N' = (-4, -2)
Faustine was hired in 2010 with a gross monthly salary of 1600€. every year her employer increases her gross monthly salary by 40€.what was Faustina's monthly net salary in 2010? 2020?
Step-by-step explanation:
I think there is a typo.
we have no information about her deductions. so, we can only calculate her gross monthly salary and not her net monthly salary.
every year it is increased by €40.
x = number of years after 2010.
salary(x) = 40x + 1600
so, 2010 is 0 years after 2010
salary(0) = 40×0 + 1600 = $1600
2020 is 10 years after 2010
salary(10) = 40×10 + 1600 = 400 + 1600 = $2000
I need help understanding these concepts I know that the degree is 9 but don’t remember how to do the rest
Given:
[tex]P(x)=x^9+2x^5-7x^3-x+2[/tex]b) The polynomial of degree n has a total n linear factor.
The degree of the given polynomial is 9.
So, the linear factors are 9.
c) The number of real solutions is,
The positive real root
[tex]\begin{gathered} P(x)=x^9+2x^5-7x^3-x+2 \\ \text{Changes the sign 2 times } \\ \text{from }+2x^5\text{ to }-7x\text{ and from }-x\text{ to }+2 \end{gathered}[/tex]So, 2 positive real roots.
The negative real root,
[tex]\begin{gathered} P(-x)=(-x)^9+2(-x)^5-7(-x)^3-(-x)+2 \\ =-x^9-2x^5+7x^3+x+2 \\ \text{Chnages the sign 1 times} \\ \text{from }-2x^5\text{ to }+7x^3 \end{gathered}[/tex]So, 1 negative rel root.
Hence the number of real solutions is 3.
d) As the total number of real solutions is 3. it means the polynomial can have 6 ( 9-3=6 ) or 0 number of complex solutions.
e) The fundamental theorem of algebra can be used to determine the complex solutions of the polynomial.
f) To check x = 2 is the solution of the given polynomial or not.
[tex]\begin{gathered} P(x)=x^9+2x^5-7x^3-x+2 \\ \text{for x=2} \\ P(2)=2^9+2(2)^5-7(2)^3-2+2=520\ne0 \\ \Rightarrow x=2\text{ is not the solution of the given polynomial} \end{gathered}[/tex]x=2 is not the solution of the given polynomial as it does not satisfy f(2)=0.
A(-1, 4), B(2, -5), M(-3, 2), N(3,0). A(-4, -8), B(4, -6), M(-3, 5), N-1, -3)are they parallel or perpendicular
A = (-1, 4), B = (2, -5)
M = (-3, 2), N = (3, 0)
If AB and MN have the same slope, then they are parallel
If the product of the slope of AB and MN is -1, then AB and MN are perpendicular
Let us find their slope and decide they are what
The slope = change of y/change of x
Change of y = yB - yA = -5 - 4 = -9
Change of x = xB - xA = 2 - (-1) = 2 + 1 = 3
The slope of AB = -9/3 = -3
Let us do the same with M and N
Change of y = yN - yM = 0 - 2 = -2
Change of x = xN - xM = 3 - (-3) = 3 + 3 = 6
The slope of MN = -2/6 = -1/3
Since -3 not equal -1/3
AB and MN are not parallel
Since -3 * -1/3 = 1
11 1 point Find the trig ratio for tan(B)? 5 1 B 2 O 3 4 10.9
Notice that the triangle △ABC is a right triangle. The side AB is the hypotenuse of the triangle, since it is opposed to the right angle C.
The tangent of the angle B is given by the ratio of the lengths of the side opposite to it and the side adjacent to it. Then:
[tex]\tan (B)=\frac{AC}{BC}[/tex]From the Pythagorean Theorem, we know that:
[tex]AC^2+BC^2=AB^2[/tex]Substitute the values AC=5 and AB=12 and solve for BC:
[tex]\begin{gathered} 5^2+BC^2=12^2 \\ \Rightarrow BC^2=12^2-5^2 \\ \Rightarrow BC^2=144-25 \\ \Rightarrow BC^2=119 \\ \Rightarrow BC=\sqrt[]{119} \end{gathered}[/tex]Once we know the value of BC, substitute the lengths of AC and BC to find the tangent of B:
[tex]\tan (B)=\frac{5}{\sqrt[]{119}}[/tex]Since the square root of 119 is approximately 10.9, then:
[tex]\tan (B)=\frac{5}{10.9}[/tex]9. MP YOU BE THE TEACHERBVDescartes says a fraction equivalentto 3 has a 3 in the denominator anda 1 in the numerator. Is Descartescorrect? Explain.
Answer:
[tex]No,\text{ Descartes is incorrect}[/tex]Explanation:
Here, we want to check if Descartes is right
From what he said, the fraction has 3 in the denominator and 1 in the numerator
This can be expressed as:
[tex]\frac{1}{3}[/tex]It is mathematically impossible for 3 to be equal to 1/3 and as such, what Descartes said is incorrect
Dee invested a total 10,125 in two accounts pay 9.5% and 4% simple interest. if a total return at the end of the two years was 1580, how much did she invest in each account?
Suppose Dee invests "x" dollars in 9.5% interest paying account and "y" dollars in 4% interest paying account.
Total Invested = $ 10,125
Thus, we can write:
[tex]x+y=10125[/tex]Simple Interest earned is given by the formula
[tex]i=\text{Prt}[/tex]Where
i is the interest earned,
P is the amount invested in the account,
r is the rate of interest in decimal
t is the time in years
• For 9.5% account, we can say that the interest earned is:
[tex]\begin{gathered} i=\text{Prt} \\ i=(x)(0.095)(2) \\ i=0.19x \end{gathered}[/tex]• For 4% account, we can say that the interest earned is:
[tex]\begin{gathered} i=\text{Prt} \\ i=(y)(0.04)(2) \\ i=0.08y \end{gathered}[/tex]The total interest earned is 1580, thus we can form the second equation:
[tex]0.19x+0.08y=1580[/tex]Solving the first equation for x gives us:
[tex]\begin{gathered} x+y=10125 \\ x=10125-y \end{gathered}[/tex]Now, we substitute this into the second equation and solve for y first:
[tex]\begin{gathered} 0.19x+0.08y=1580 \\ 0.19(10125-y)+0.08y=1580 \\ 1923.75-0.19y+0.08y=1580 \\ 0.19y-0.08y=1923.75-1580 \\ 0.11y=343.75 \\ y=3125 \end{gathered}[/tex]Using this value of y, we can easily figure out the value of x.
[tex]\begin{gathered} x=10125-y \\ x=10125-3125 \\ x=7000 \end{gathered}[/tex]So,
Dee invested $7000 in 9.5% account and $3125 in 4% account.
8students 16, 6, 10, 7, 20, 11, 9, 16 mean and median round to nearest tenth
The mean is 11.9 while the median is 10.5
Here, we want to calculate the mean and the median
Mathematically, the mean is the average of the numbers
We proceed as follows to find the mean;
[tex]\begin{gathered} \operatorname{mean}\text{ = }\frac{16+6+10+7+20+11+9+16}{8} \\ \\ \operatorname{mean}\text{ = }\frac{95}{8}\text{ = 11.875} \\ \\ \text{which is 11.9 to the nearest tenth} \end{gathered}[/tex]To get the median, we simply re-arrange the values in the data set from the lowest to the highest
That will be;
6,7,9,10,11,16,16,20
The median term refers to the middle number
Since the number of terms here is even, then the median would be the average of the two 4th terms counting from both ends
Thus, the median is;
[tex]\frac{10+11}{2}\text{ = }\frac{21}{2}\text{ = 10.5}[/tex]The median is 10.5
two fish tanks are being filled.Below the equation and the graph represent the volume of water in two different fish tanks.Graph the equation on the grid.v=4t+8
The graph of the equation is the line in red
Yo
we can calculate the equation of the black line
V=2t+8
solving using elimination 5x+ 6 y = -19 5 x + 5 y = -20
We have to solve this system of equations by elimination.
We can substract the second equation directly from the first equation in order to cancel x.
Then, we can solve for y:
[tex]\begin{gathered} (5x+6y)-(5x+5y)=-19-(-20) \\ 5x-5x+6y-5y=-19+20 \\ 0x+1y=1 \\ y=1 \end{gathered}[/tex]With the value of y, we can solve for x:
[tex]\begin{gathered} 5x+5y=-20 \\ 5x+5\cdot1=-20 \\ 5x+5=-20 \\ 5x=-20-5 \\ 5x=-25 \\ x=-\frac{25}{5} \\ x=-5 \end{gathered}[/tex]Answer: x=-5 and y=1
À certain wall is 13 ft by 9 ft. A can of paint willcover 50ft? Will one paint can be enough?Draw a picture:a
To answer this question, we need to calculate the area of the given wall first to know the area to be painted, and we have the following information:
• We have that the dimensions of the wall are 13ft by 9ft.
,• A can of paint will cover 50ft² (50 square feet).
Then we have:
1. Find the area of the wall:
[tex]\begin{gathered} A_{wall}=13ft*9ft \\ A_{wall}=117ft^2 \end{gathered}[/tex]2. Therefore, we have that a can of paint can cover only 50ft², then it can paint only:
[tex]\frac{50ft^2}{117ft^2}\approx0.42735042735\approx0.43\text{ \lparen Or about 43\% of the wall\rparen}[/tex]3. Therefore, we can say that the paint can cover about 43% of the wall.
Then we have:
Will one can of paint be enough?No, one can of paint will not be enough since it can cover, approximately, 43% of the area of the given wall.
99999÷9999 pls help me
99999 ÷ 9999
using the calculator the answer will be 10.0009
Write the equation 3x + 2 = 4x² in standard form.
Answer:
−4x^2+3x+2=0
Step-by-step explanation:
what is the area of the castle Elliot built from wooden blocks ?.
The total Area is then 160 square units.
The ordered pair (1, 4) is a solution to the equation x + y = 5 because 1 + 4 = 5 is a true statement. Which of the following ordered pairs is also a solution to the equation x + y = 5 ?(- 3, - 2)(2, 3)o (- 4, 1) (0, - 5)
Given
The ordered pair (1, 4) is a solution to the equation x + y = 5 because 1 + 4 = 5 is a true statement. Which of the following ordered pairs is also a solution to the equation x + y = 5
Solution
[tex]\begin{gathered} x+y=5 \\ \text{The ordered pair (1,4)} \\ \therefore x=1\text{ and y = 4} \\ 1+4=5 \\ \\ \text{NOW } \\ (2,3)\text{ Which is (x,y)} \\ x+y=5 \\ 2+3=5 \end{gathered}[/tex]The final answer
[tex](2,3)[/tex]when you multiply two terms by two terms, you should get four terms but the result is only three terms because we combine the middle linear terms. For example, when we multiply( x + 3) (x - 4)we getx^2 - 12Give an example of multiplying two terms that will result in only two terms in your final expression
The multiplication of two terms result in only two terms after multiplication, if middle terms cancels each other.
Consider an example of (x + 3)(x - 3).
Evaluate the product of (x + 3)(x - 3).
[tex]\begin{gathered} (x+3)(x-3)=x^2+3x-3x-3\cdot3 \\ =x^2-9 \end{gathered}[/tex]So possible example of two terms which results in only terms in multiplication is (x + 3)(x - 3).
Which statements are true regarding the diagram?GNH and HNJ are complementary.JNK and KNL are supplementary.KNL and LNM are complementary.Om HNK + m_KNL = 180°m_MNG + m_GNH = 90°
A right angle = 90 degrees ( complementary )
a straight angle = 180 degrees ( supplementary )
Hence, GNH + HNT = 90 ( YES )
JNK + KNL = 180 ( NO )
KNL + LNM = 90 ( YES )
< HNK + < KNL = 180 ( YES )
< MNG + < GNH = 90 ( NO )
What’s the answer to c and d
Part c: -3x + 5 + 5x - 1 = 0; x = 2 is incorrect.
Part d: -(x -1) = 4x -5 - 3x ; x = 3 is correct.
What is defined as the word equation?A linear equation can have multiple variables. A linear equation is one in which the variable's highest power is always 1. A one-degree equation is another name for it.For the given equations,
Part c: -3x + 5 + 5x - 1 = 0.
Simplify the equation.
-3x + 5 + 5x - 1 = 0
2x + 4 = 0
x = -4/2
x = -2
Thus, the given value x = 2 is incorrect.
Part d: -(x -1) = 4x -5 - 3x
Simplify the equation.
-(x -1) = 4x -5 - 3x
-x + 1 = x - 5
2x = 6
x= 3
Thus, the given value x = 3 is correct.
Thus, the given conditions for the equation is found.
To know more about the equations, here
https://brainly.com/question/2972832
#SPJ1
Does anyone know how to solve this?
Answer:
x = 124 degrees, y = 56 degrees
Step-by-step explanation:
triangle = 180 degrees
y + 34 + 90 = 180
y + 124 = 180
y = 56
straight line = 180 degrees
x + 56 = 180
x = 124
can you give me the answer to this , i need help and yeah thank you .
In the right triangle of the figure
K and H are the legs (perpendicular sides)
and M is the hypotenuse (greater side)
so
the answer is the hypotenuseIf we reduce the number of vertices of a convex polygon P by 20%, the number of its diagonals decreases by 37.5%. How many vertices does P have?
Answer:
35 vertices
Explanation:
Given a convex polygon with n-vertices, the number of diagonals in the polygon is given by the formula:
[tex]\frac{n(n-3)}{2}[/tex]If n is reduced by 20%, the new value of n will be:
[tex](100-20)\%\text{ of n}=\frac{80}{100}n=0.8n[/tex]Replace n in the formula above with 0.8n:
Next, we are told that the number of its diagonals decreases by 37.5%. Using the original formula for the number of diagonals, we have:
[tex]\begin{gathered} (1-0.375)\times\frac{n(n-3)}{2} \\ =\frac{0.625n(n-3)}{2}\cdots(2) \end{gathered}[/tex]Equate (1) and (2):
[tex]\frac{0.8n(0.8n-3)}{2}=\frac{0.625n(n-3)}{2}[/tex]We solve the equation for n:
[tex]\begin{gathered} 0.8n(0.8n-3)=0.625n(n-3) \\ 0.64n^2-2.4n=0.625n^2-1.875n \\ 0.64n^2-0.625n^2=2.4n-1.875n \\ 0.015n^2=0.525n \\ \text{ Divide both sides by 0.015n} \\ \frac{0.015n^2}{0.015n}=\frac{0.525n}{0.015n} \\ n=35 \end{gathered}[/tex]The polygon P has 35 vertices.
Helppppppppppppppppppp
We have the following line equation:
y = -x+7
Remember that the canonical form of the line equation is
y = mx + b
where m is the slope of the line. In our case we have
y = -x+ 7
that is
y = (-1) x + 7
then the slope of the above line is (-1) , therefore the slope of the line perpendicular to this line is the negative reciprocal of -1 , that is - 1/(-1), that is 1.
7 Given APHS = ACNF, find the values of x, y, and z.F(3y - 1)H (6x - 290°S36°Р115°fc(4z - 32)N
Here, we have two congruent triangles
Since they are congruent, they have similar and equal angles.
From the diagram, we can see that;
6x - 29 = 115 (They are both topmost angles of both triangles)
Solving this, we have;
6x = 115 + 29
6x = 144
divide both sides by 6
x = 144/6
x = 24°
Furthermore, we can see that;
4z - 32 = 36
4z = 36 + 32
4z = 68
z = 68/4
z = 17°
And lastly;
(3y-1) + 115 + (4z-32) = 180 ( sum of angles in a triangle)
Since z = 17, 4z - 32 will be 4(17)-32 = 68 - 32 = 36
Thus;
3y - 1 + 115 + 36 = 180
3y + 150 = 180
3y = 180 -150
3y = 30
divide both sides by 3
y = 30/3
y = 10°
x = 24° , y = 10° and z = 17°
Convert 0.0042 ns --> Gs
0.0042
to convert this to standard form
there are 4 figures after the decimal points
this indicate ten of thoudsandth which is 1/10000
the actual figure after the zeros is 42
therefore, 42 x 10^-4
4.2 x 10^1 x 10^-4
4.2 x 10^1-4
4.2 x 10^-3
The answer is 4.2 x 10^-3
The function (x) is a transformation of the square root parent function,f(x) = V. What function is h(x)?5h(x)Fix-55-5
The parent function is root of x.
we have to subtract 5 to the function.
Hence the transformed function is
[tex]h(x)=\sqrt[]{x}-5[/tex]Mark As CompleteTry It!C) 6. a. If mZNOP = 31 and mZNOQ = 114, what is mZROQ?toN0ICHECK ANSWERAw
A store display shows one red shirt, three blue shirts, and four shirtswith red and white stripes. The display also shows three pairs of bluejeans, two pairs of white pants, and three pairs of red shorts. What isthe probability of randomly selecting an item with white or red on it?TiAtt11O 3/8O 5/8O 1/4ionO 3/4DraliauNout
Let's get the total number of the items=1+3+4+3+2+3=16items
Let us get the probability of items wit
Step 1
No of items with white or red colour = 4 = No of required items
Step 2'
Find the probability of choosing items with red or white colour
[tex]\frac{4}{16}=\frac{1}{4}[/tex]Evaluate the following limits. lim n -> ∞ sum i = 1 to n ((i ^ 2)/(n ^ 2)) * (1/n) (Picture of equation for clarification)
Given:
Required:
To find the limit value of the given function.
Explanation:
[tex]\begin{gathered} =\lim_{n\to\infty}[\frac{1^2}{n^3}+\frac{2^2}{n^3}+........+\frac{n^2}{n^3}] \\ =\lim_{n\to\infty}\frac{1^2+2^2+3^2+.........+n^2}{n^3} \\ =\operatorname{\lim}_{n\to\infty}\frac{\sum_^n^2}{n^3} \\ =\operatorname{\lim}_{n\to\infty}\frac{1}{n^3}\times\frac{n(n+1)(2n+1)}{6} \\ =\operatorname{\lim}_{n\to\infty}\frac{n^3(1+\frac{1}{n})(2+\frac{1}{n})}{6n^3} \end{gathered}[/tex]Cancel out the same terms from the numerator and denominator.
[tex]=\lim_{n\to\infty}\frac{(1+\frac{1}{n})(2+\frac{1}{n})}{6}[/tex]Now apply the limit.
[tex]\begin{gathered} =\frac{(1+\frac{1}{\hat{\infty}})(2+\frac{1}{\infty})}{6} \\ =\frac{(1+0)(2+0)}{6} \\ =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}[/tex]Final Answer:
The limit value of the given function is
[tex]\frac{1{}}{3}[/tex][tex]\frac{1{}}{3}[/tex]Solve the statistics question shown in the picture provided, complete A, B, and C, thanks.
a) The variable of interest is X: the price of a home of a certain city.
The distribution of the home prices of the city is strongly skewed right, with mean μ=420 thousand dollars, and standard deviation σ= 180 thousand dollars.
There was a sample of n=60 houses for sale taken, to determine the shape of the sampling distribution you have to apply the Central Limit Theorem, which states:
As a rule, a sample size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation. So, by applying the CLT you can approximate the sampling distribution to normal:
[tex]X\lbrack bar\rbrack\approx N(\mu,\frac{\sigma^2}{n})[/tex]For this example, the distribution is:
[tex]\begin{gathered} X\lbrack bar\rbrack\approx N(420;\frac{32400}{60}) \\ X\lbrack bar\rbrack\approx N(420;540) \end{gathered}[/tex]b) You have to determine the approximate probability that the mean price of the homes for the sample taken is more than 450 thousand dollars.
To determine this probability you have to work with the approximation of the standard normal distribution, derived from the approximation of the sampling distribution:
[tex]Z=\frac{X\lbrack bar\rbrack-\mu}{\frac{\sigma}{\sqrt[]{n}}}\approx N(0,1)[/tex]You can symbolize the probability as follows:
[tex]P(X\lbrack bar\rbrack>450)=1-P(X\lbrack bar\rbrack\leq450)[/tex]First step is to determine the Z-value corresponding to X[bar]≤450
[tex]\begin{gathered} Z=\frac{X\lbrack bar\rbrack-\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ Z=\frac{450-420}{\frac{180}{\sqrt[]{60}}} \\ Z=\frac{30}{6\sqrt[]{15}} \\ Z=1.29 \end{gathered}[/tex]Using the tables of the standard normal distribution you can determine the probability for values less than or equal to Z=1.29
[tex]P(Z\leq1.29)=0.9010[/tex]Now you can determine the probability:
[tex]\begin{gathered} P(X\lbrack bar\rbrack>450)=1-P(X\lbrack bar\rbrack\leq450) \\ P(Z>1.29)=1-P(Z\leq1.29)=1-0.9010=0.090 \end{gathered}[/tex]The probability that the mean value of the homes is more than 450 thousand dollars is 0.09 or 9%
c) The probability of obtaining a mean price greater than 450 thousand dollars is 9%, this probability is low, which means that the mean price is an uncommon value.