Answer:
[tex]\rm slope: -\dfrac{7}{6}[/tex]
[tex]\rm Distance: 2\sqrt{85} \ units[/tex]
Part A[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y }{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here given points are: (6, -6), (-6, 8)
Insert the values:
[tex]\sf \rightarrow slope: \dfrac{8-(-6)}{-6-6}[/tex]
[tex]\sf \rightarrow slope: \dfrac{8+ 6}{-12}[/tex]
[tex]\sf \rightarrow slope: \dfrac{14}{-12}[/tex]
[tex]\sf \rightarrow slope: -\dfrac{7}{6}[/tex]
Part B[tex]\sf Distance \ between \ points : \sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Using the formula,
[tex]\sf d = \sqrt{(-6 - 6)^2 + (8-(-6))^2}[/tex]
[tex]\sf d = \sqrt{(-12)^2 + (14)^2}[/tex]
[tex]\sf d = \sqrt{144 +196}[/tex]
[tex]\sf d = \sqrt{340}[/tex]
[tex]\sf d = \sqrt{85 \times 4}[/tex]
[tex]\sf d = 2\sqrt{85}[/tex]
Hence, the distance is 2√85 units.
Hii!
___________________________________________________________
[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]
Slope =
Distance =
[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}[/tex]
[tex]\bullet[/tex] Let's work out the slope
[tex]\twoheadrightarrow\sf \cfrac{y2-y1}{x2-x1}[/tex]
[tex]\bullet[/tex] Stickin the values
[tex]\twoheadrightarrow\sf \cfrac{8-(-6)}{-6-6}[/tex]
[tex]\bullet[/tex] Simplify
[tex]\twoheadrightarrow\sf \cfrac{8+6}{-12}[/tex]
[tex]\bullet[/tex] Finish simplifying
[tex]\twoheadrightarrow\sf \cfrac{14}{-12}[/tex]
[tex]\bullet[/tex] Reduce the fraction
[tex]\twoheadrightarrow\sf \cfrac{7}{-6}[/tex]
____________________________________[tex]\bullet[/tex] Work out the distance
[tex]\twoheadrightarrow\sf \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf \sqrt{(-6-6)^2+(8-(-6)^2}[/tex]
[tex]\bullet[/tex] Simplify the radical expression
[tex]\twoheadrightarrow\sf \sqrt{(-12)^2+14^2}\\\\\twoheadrightarrow\sf \sqrt{144+169} \\\\\twoheadrightarrow\sf \sqrt{340}\\\\\twoheadrightarrow\sf \sqrt{85\cdot4} \quad (simplifying\,the\,surd)[/tex]
[tex]\ddagger[/tex] [tex]\boldsymbol{DISTANCE=2\sqrt{85} \,Units}[/tex] [tex]\ddagger[/tex]
--
Hope that this helped! Best wishes.
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A water wheel is designed in the shape of a regular octagon. What is the perimeter of the water wheel?
The graph shows an eight-sided polygon. Some major points are (0, 4), (3, 3), (4, 0), (3, minus 3), (0, minus 4), (minus 3, minus 3), (minus 4, 0), and (minus 3, 3).
A.
B.
C.
D.
Perimeter is the sum of the length of the sides used to make the given figure. The perimeter of the regular octagon is 8√58 units.
What is the perimeter?Perimeter is the sum of the length of the sides used to make the given figure.
For a regular octagon, the length of each side of the octagon is the same. Therefore, the length of a single side of the octagon is,
Length of the side of the octagon = √[(-4-3)² + (0 + 3)²] = √58
Now, the perimeter of the octagon is 8 times of√58.
Perimeter = 8 ×√58 = 8√58
Hence, the perimeter of the regular octagon is 8√58 units.
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Translate each English phrase in the following problem into an algebraic expression and set up the related equation. Let z be the unknown number. The difference between a number and −23 − 23 is equal to the product of the number and 13 13 . Step 2 of 3 : Translate "the product of the number and 13 13 ".
The English phrase of the obtained equation is 12 times z subtracted by 3. The obtained equation after solving is 12z -23
What exactly is simplification?Simplifying means making something easier to do or comprehend, as well as making something less difficult.
Given data;
z be the unknown number
Given conditions;
1. The difference between a number and −23.
2.−23 is equal to the product of the number and 13.
The mathematical form of the given phrase is;
⇒ z - (-23) = z × 13
⇒z+23 = 13z
⇒12z -23
The English phrase of the obtained equation is 12 times z subtracted by 3.
Hence the simplification of the given expressions is 12z -23.
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(-3,-2) (x,6) m=-8/5 solve for x
Answer:
-8
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
-8/5=(6-(-2))/(x-(-3))
-8/5=(6+2)/(x+3)
-8/5=8/(x+3)
5=-(x+3)
5=-x-3
-x=5+3
-x=8
x=-8
In Triangle XYZ, XZ = XY and m∠Y=57°. The longest side of the triangle is ______.
YZ
XZ
XY
Both XZ and XY
Answer:
I think YZ 'cause the triangle is iscoceles triangle. As the two sides XY and XZ are equal the longest side is YZ.
Simplify x^2+2x+1 divided by x+1
The quotient is x+1.
What Long division method?Long division is a method for dividing one large multi digit number into another large multi digit number.
Given:
f(x)= x²+2x+1
g(x)= x+1
The steps to divide the polynomial is :
Divide the leading term of the dividend by the leading term of the divisor: x²/x=x.Multiply it by the divisor: x(x+1)=x²+x.Subtract the dividend from the obtained result: (x²+2x+1)−(x²+x)=x+1.Divide the leading term of the obtained remainder by the leading term of the divisor: x/x=1.Multiply it by the divisor: 1(x+1)=x+1.Subtract the remainder from the obtained result: (x+1)−(x+1)Learn more about long division method here:
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Given that the slope is 4 and (4, 6) is on the line. Write the equation of the line
in the slope-intercept
form
Answer:
y= 4x - 10
Step-by-step explanation:
y-6 = 4(x - 4)
y - 6 = 4x -16
+6. +6
y= 4x - 10
How do I solve this problem? It’s been awhile since I’ve done math
C=(2+y)h
solve for y
Answer:
y = C/h - 2
Step-by-step explanation:
Equation
C = (2 + y)*h
Solution
C = (2 + y)*h Divide by h
C/h = (2 + y)*h/h
C/h = 2 + y Subtract 2 from both sides
C/h-2 = 2-2+ y Combine
C/h - 2 = y
Question 4: 11 pts
Elena wants to earn at least $180 a week to help her parents with bills. She determines that
she can charge $15 an hour to babysit and can earn $10 an hour bagging groceries. She can
only work 13 hours per week. Write and graph a system of linear inequalities that shows the
number of hours she can work so she can help her parents. Use x for the number of hours
babysitting and y for the number of hours bagging groceries.
our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph can be seen at the end.
How to get the system of inequalities?Here we have the variables:
x = number of hours babysitting.y = number of hours bagging groceries.We know that she can only work 13 hours per week, then we have:
x + y ≤ 13.
And she wants to earn at least $180 per week, then:
x*$15 + y*$10 ≥ $180.
So our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph of the system can be seen below. The solution set is defined by the zone where the two shaded regions intersect (where we also should add the restrictions x >0, y > 0).
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From this diagram, select the
pair of lines that must be
parallel if angle 2 is congruent to angle 6. If there is no pair of lines, select none
Answer:
A). O is parallel to qif angle 2 is congruent to 6 them the slope of line o and q is equal
that is line o is parallel to q
can someone please help me?!? 25 points
please write wether each one is a function or a growth rate!!!
Answer:
See below
Step-by-step explanation:
There are 52 weeks in a year, so divide t by 52
= 120 (1.016)^(t/52)
then the % for one week = 1.016^1/52 = 1.0003 = .03%
Describe the end behavior for the graph of y=-x³- ax + 3, if a is a constant.
Answer: Choice C
As [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]
As [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]
Check out the diagram below.
========================================================
Explanation:
The leading term is the term with the largest exponent. That would be the term of [tex]-\text{x}^3[/tex]. The leading term directly determines the end behavior. The other terms will not play a role.
What this means is that the end behavior of [tex]\text{y} = -\text{x}^3 - \text{ax} + 3[/tex] is the exact same as the end behavior of [tex]\text{y} = -\text{x}^3[/tex]
As x gets really big in the positive direction, we'll have [tex]-\text{x}^3[/tex] get really small in the negative direction. For instance, x = 10 leads to [tex]-\text{x}^3 = -10^3 = -1000[/tex] and x = 100 leads to [tex]-\text{x}^3 = -100^3 = -1,000,000[/tex]
Therefore, as [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]
Visually the graph goes forever downward when we move to the right. We can consider this as "falls to the right".
--------------------------------
The graph "rises to the left" because as [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]
Here's a small table to give numeric examples:
[tex]\begin{array}{|c|c|} \cline{1-2}x & y\\\cline{1-2}-1 & 1\\\cline{1-2}-10 & 1000\\\cline{1-2}-100 & 1,000,000\\\cline{1-2}\end{array}[/tex]
As x gets more negative, y becomes more positive. We have this opposite nature going on similar to the previous section.
This graph goes uphill when moving to the left.
Check out the graph below. In the diagram I used a = 2, but you could use any value of 'a' you want to get the same end behavior.
Of the following fractions3/7, 5/8, 7/13, and 11/19 Which is the largest
Answer:
5/8
Step-by-step explanation:
5/8=0.6.25
0.625> all the other numbers
5. Dan is making the perfect shade of purple paint for his Nana. The perfect shade of purple mixes red and blue paint at a
ratio of 4 to 5. Accidently Dan mixed five cups of red and four cups of blue, using up all his red paint. How much blue must
he add to fix his mistake?
Answer:
2 and 1/4 cups
Step-by-step explanation:
4 cups-5 cups
5 cups-?
(5×5)÷4=6 cups and 1/4
6 and 1/4-4=2 cups and 1/4
calculate the median for: 5, 10, 12, 4, 6, 11, 13, 5r
Step-by-step explanation:
please mark me as brainlest
Answer:
8
Step-by-step explanation:
We need to sort your set into Least-to-Greatest order.
4, 5, 5, 6, 10, 11, 12, 13
That is your set in least to greatest order.
Which 2 numbers are in the middle?
They are 6 and 10.
Now, we find the mean of 6 and 10.
(6+10)/2 = 8
8 is your median
Which statement describes how the y-intercept of the graph of f(x) = |2x − 1| compares to the y-intercept of the graph of g(x) = |2x − 5|? A. The y-intercept of g is 4 units above the y-intercept of f. B. The y-intercept of g is 4 units below the y-intercept of f. C. The y-intercept of g is 4 units to the right of the y-intercept of f. D. The y-intercept of g is 4 units to the left of the y-intercept of f.
The statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.
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.
We have two functions:
f(x) = |2x - 1| and
g(x) = |2x - 5|
After plotting on a coordinate plane.
The y-intercept of f(x) is 1
The y-intercept of g(X) is 5
Or plug x = 0 to find the y-intercept.
The y-intercept of g is 4 units above the y-intercept of f
Thus, the statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.
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Cai drove 189 miles in 7 hours. If he continued at the same rate, how far would he
travel in 12 hours?
I need this answered fast pleasee
Suppose you and your friends form a band and you want to record a demo. Studio A rents for $75 plus $75 an hour and Studio B rents for $150 and $50 an hour. Let t = the number of hours and c = cost.
Part A Write a system of equations to represent the cost at each studio.
Part B Solve the system of equations from Part A. Explain your method.
Part C Explain what the solution to the system means in terms of where your band will rent a studio.
The descriptive answer of different part is described below.
What is Linear Equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.
Here, Studio A rents for $75 plus $75 an hour .
Studio B rents for $150 and $50 an hour.
Let t = the number of hours and c = cost.
Part A
Studio A: c = 75 +75·t
Studio B: c = 150 +50·t
Part B
We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.
150 +50·t = 75 +75·t, subtract 75 and 50t from both sides
150 -75 = 75t -50t, combine likes terms
75 = 25t, divide both sides by 25
3 = t
Now we know that t = 3 so we find c by substituting t with 3 in the second equation.
c = 150 +50·t
c = 150 +50·3
c = 300
The solution of the system of equations is c = 300 and t = 3
Part C:
The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.
The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.
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A city has a population of 1300. If the city’s population grows 30%, what is its new population?
Answer:
1699
Step-by-step explanation:
30/100*13000
Then add answer with 1300
eg 1300+399
I hope this explanation helps you.Also You can follow me.
The power 3 Superscript negative 3 equals StartFraction 1 Over 27 EndFraction . Which expression is equivalent to 3 Superscript negative 3?
Applying the negative exponent, it is found that the equivalent expression to [tex]3^{-3}[/tex] is [tex]\frac{1}{27}[/tex].
How to deal with a negative exponent?When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator, as follows:
[tex]a^{-b} = \frac{1}{a^b}[/tex]
Hence, in this problem, the equivalent expression is:
[tex]3^{-3} = \frac{1}{3^3} = \frac{1}{27}[/tex]
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Question 4tiple Choice Worth 5 points)
(07.03 MC)
Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. What steps will help show that circle A is similar to circle B?
O Translate circle A using the rule (x+4y+3)
O Rotate circle A 45" about the center
O Dilate circle A by a scale factor of 4
O Reflect circle A about the origin
Answer:
Dilate circle A by a scale factor of 4.
Step-by-step explanation:
To show that two circles are similar, use transformations to map one to the other.
Step 1
Translate circle A so that its center is the same as circle B.
Center of circle A = (6, 7)Center of circle B = (2, 4)Translate circle A using the rule (x - 4, y - 3)
Step 2
Find the scale factor needed to dilate circle A to the size of circle B using the radii of the circles.
Radius of circle A = 4Radius of circle B = 16⇒ scale factor = 16 ÷ 4 = 4
Dilate circle A by a scale factor of 4.
Therefore, the only answer option that is correct is:
Dilate circle A by a scale factor of 4.
Identify parallel and perpendicular lines
Parallel lines are those on a plane that do not intersect while perpendicular lines are those that intersect at an angle of 90°.
How are parallel and perpendicular lines different?Parallel lines will never intersect with each other and will maintain the same distance from each other for as long as they are on the same plane.
Perpendicular lines on the other hand will intersect each other and will do so at a 90° angle. An example of such a line is the steps on a ladder which intersect the beam at a 90° angle.
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Solve the inequality
correct function combinations to x2-7x-18
The factors of the function after factorization f(x)=[tex]x^{2} -7x-18[/tex] is (x+2) and (x-9)
Given Function f(x)=[tex]x^{2} -7x-18[/tex] and we have to find the factors of the given function.
The function whose factors are to be found is f(x)=[tex]x^{2} -7x-18[/tex]
Factorization means finding various expressions which when together multiplied will give the function itself. Correct combination can only be found by finding the factors of the function. Without finding factors no one can find the solution of an equation or expression also.
f(x)=[tex]x^{2} -9x+2x-18[/tex]
=x(x-9)+2(x-9)
=(x+2)(x-9)
Hence the factors which when combine together gives function f(x)=[tex]x^{2} -7x-18[/tex] are (x+2)(x-9).
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A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours. Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the rebuilding times are normally distributed, what percentage of sample means are greater than 8.8 hours? Express your answer as a percent rounded to hundredths of a percent.
Answer:
40.9 %
Step-by-step explanation:
8.8 is .4 hours above the mean this is .4/1.77 = .226 standard deviations above the mean
Using z-score table this corresponds to ~ .5910 (59.10%)
this percentage is LESS than 8.8 hours
the percentage ABOVE this is 40.9%
(Not asked, but this is 40.9 (40 ) = ~ 16 of the 40 mechanics sampled)
Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
1. Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)
2. Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)
The margin of error will be 20 and 10 respectively.
How to calculate the margin of error?The margin of error for Robert will be:
= 1.96 × 50/✓25
= 1.96 × (50/5)
= 1.96 × 10
= 20 approximately
The margin of error for Val will be:
= 1.96 × 50/✓100
= 1.96 × 50/10
= 1.96 × 5
= 10 approximately
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Find the surface area of the composite figure
4 cm
13 cm
3 cm
4 cm
12 cm
SA = [?] cm²
5 cm
3 cm. Pls help
Please help!!
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation
(-4,5) y=1/3x +6
Answer:
The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Multiplication of slope of two perpendicular lines is = -1
first line is y= [tex]\frac{1}{3}[/tex]x +6
slope of this line is [tex]\frac{1}{3}[/tex]
So the slope of the second line is : [tex]\frac{-1}{3}[/tex]
Equation of line would be written by using :
(y - y1) = m(x - x1)
here the line passing through (-4,5)
put the values in equation
y -5 =[tex]\frac{-1}{3}[/tex][x - (-4)]
3y - 15 = -x -4
3y = -x +11
y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
So The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
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Add. State the sum in simplest form.
Answer:
[tex] \frac{ {3x}^{2} }{x + 5} + \frac{15x}{x + 5} [/tex]
[tex] \frac{3 {x}^{2} + 15x}{x + 5 } [/tex]
3x ( x + 5) /( x + 5).
3x, X is not equal to (-5)
Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][-2, 3)[/tex]Range: [tex](-5, 4][/tex]Is the relation a function? - YesStep-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A relation is a function if each value of x maps onto no more than one value of y.
On Friday, a local hamburger shop sold a combined total of 396 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number
of hamburgers sold. How many hamburgers were sold on Friday?
Answer:792
Step-by-step explanation:
