Find the distance between P(2, 8) and Q(5, 3).
Answer:
The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((X2-X1)2+(Y2-Y1)2)
d = √ (5-2)2+(3-8)2
d = √ ((3)2+(-5)2)
d = √ (9+25)
d = √ 34
The distance between the points is 5.8309518948453
The midpoint of two points is given by the formula
Midpoint= ((X1+X2)/2,(Y1+Y2)/2)
Find the x value of the midpoint
Xm=(X1+X2)/2
Xm=(2+5)/2=3.5
Find the Y value of the midpoint
Ym=(Y1+Y2)/2
Ym=(8+3)/2=5.5
The midpoint is: (3.5,5.5)
Graphing the two points, midpoint and distance
P1 (2,8)
P2 (5,3)
Midpoint (3.5,5.5)
The length of the black line is the distance between the points (5.8309518948453)
Find the slope of the line connecting the two points
Slope = (Y2-Y1) = (3-8) = (-5) = -1.66666666666667
(X2-X1) (5-2) (3)
Find the equation of the line passing through the two points
The general equation for a straight line is
y = mx + b
Where m represents the slope of the line which we found in the previous step to be -1.66666666666667
y = -1.67x + b
We substitute x and y for the values from one of our points (2,8)
8 = -1.67×2 + b
8 = -3.33 + b
8--3.33 = b
11.33 = b
Knowing both b and m, we can contruct the equation of the line
y= -1.67x+ 11.33
X and Y intercepts
The x-intercept is a point on the graph where y is zero
Using the equation we found in the previous step and substituting zero for y
y= -1.67x+ 11.33
0= -1.67x+ 11.33
1.67x= 11.33
x= 11.33/1.67 = 6.80
The x intercept for this straight line is 6.80
The y-intercept is a point on the graph where x is zero
Using the equation we found in the previous step and substituting zero for x
y= -1.67×0+ 11.33
y= 11.33
The y intercept for this straight line is 6.80
References
refernce image showing the distance between two points on the xy plane
Step-by-step explanation:
The distance between the two points will be √34. The correct option is c
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
The distance (d) between two points (x₁,y₁) and (x₂,y₂) is given by the formula:-
d = √ ((X₂-X₁)²+(Y₂-Y₁)²)
d = √ (5-2)²+(3-8)²
d = √ ((3)²+(-5)²)
d = √ (9+25)
d = √ 34
Therefore, the distance between the two points will be √34. The correct option is c
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If h(x) = 6 - X, what is the value of (10)
Answer:
-4 = h(x)
Step-by-step explanation:
[tex]6 - 10 = -4[/tex]
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points -3,2 rotated 90 clockwise
its a maze i need help o thank u
Answer:
(2,3)
Step-by-step explanation:
Rotation through 90 clockwise gives the expression
( x , y )___ ( y ,- x )
so when you put the points -3 ,2 in the relation , it becomes
( -3 , 2 ) ___ ( 2, - -3 )
= ( x, y ) __ ( 2, 3 ). meaning when you rotate -3,2 through 90 clockwise you will get the image ( 2 ,3 )
I also need some help on this part of the geometry homework.please help me if you can.
Answer:
They are mirrored
Step-by-step explanation:
When you cut it in half horizontally you can see both sides are mirrored so the lines have the same length
what is equivalent to the square root of -98
Answer:
7√2 i
Step-by-step explanation:
√(-98)
=√{(-1) .98}
=√(-1 . 2 . 7²)
=√-1 .√2 . √7²
= i . √2 . 7 [∵√-1 = i ]
=7√2 i
Answer:
[tex]\large\boxed{\sqrt{-98}=7\sqrt2\ i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-98}=\sqrt{(-1)(49)(2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{-1}\cdot\sqrt{49}\cdot\sqrt2\qquad\text{use}\ \sqrt{-1}=i\ -\text{an imaginary unit}\\\\=i\cdot7\cdot\sqrt2\qquad\sqrt{49}=7\ \text{because}\ 7^2=49\\\\=7\sqrt2\ i[/tex]
evaluate the problem below -4 1/6 + 5 2/3
Answer:
3/2 (or 1 1/2)
Step-by-step explanation:
-4 1/6 + 5 2/3 (express as improper fractions)
= -25/6 + 17/3 (convert fractions common denominator i.e 6)
= -25/6 + (17/3)(2/2)
= -25/6 + (17 x 2)/6
= -25/6 + 34/6
= 9/6
= 3/2
=1 1/2
Which equation is equivalent to Vx+11 = 15?
x + 11 = 225
x + 121 = 225
x = 15+11
x = 15-11
The equation which is equivalent to √x + 11 = 15 is: C. √x = 15 - 11.
Given the following equation:
√x + 11 = 15.To evaluate the given mathematical equation:
How to evaluate an equation.In this exercise, you're required to evaluate the given mathematical equation. Thus, we would make x the subject of formula in the equation and then simplify as follows:
√x = 15 - 11 (equivalent)
√x = 4
Taking the square of both sides, we have:
x = 4²
x = 16.
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Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
<-1, -1>, square root of two
<1, 1>, square root of two
<1, 1>, 2
<-1, -1>, 2
Answer:
<1 ,1>..., square root of two
Step-by-step explanation:
Component of vector PQ...,
; Q - P...where you subtract the x coordinate of Q by the x coordinate of P and the same for the y coordinate
; <(6-5),(9-8)>
; < 1,1 >
And the magnitude of PQ...,
;square root of( 1^2 + 1^2 )
;square root of 2
Final answer:
The component form of vector PQ is <1, 1>, and the magnitude is the square root of 2, thus the correct answer is <1, 1>, square root of 2.
Explanation:
To find the component form and magnitude of vector PQ, we calculate the difference in the x-coordinates and the y-coordinates of points P and Q. The component form of a vector is obtained by subtracting the coordinates of the initial point from the coordinates of the terminal point. In this case, the initial point is P(5, 8) and the terminal point is Q(6, 9).
The component form of vector PQ is therefore:
Vector PQ = (Qx - Px, Qy - Py)
Vector PQ = (6 - 5, 9 - 8)
Vector PQ = <1, 1>
Next, to find the magnitude of vector PQ, we use the Pythagorean theorem, which is the square root of the sum of the squares of the components:
Magnitude of PQ = √(1^2 + 1^2)
Magnitude of PQ = √(2)
Magnitude of PQ = √2
Therefore, the correct answer is <1, 1>, √2.
A bus has 40 seats . There are as many adults as children riding the bus so there are
Answer:
20 children and 20 adults
Step-by-step explanation:
20 + 20 = 40
Answer:
20 adults 20 children
Step-by-step explanation:
if theres the same amount of children and adults just do 40/2
The height of a cone is twice the radius of its base. What expression represents the volume of the cone, in cubic units?
A)2/3πx^3
B) 4/3πx^2
C) 2πx^3
D) 4πx^3
Answer:
A
Step-by-step explanation:
The general formula for the volume of a right cone is as follows (also see attached):
V = (1/3) π r² h; where r = radius of base and h = height
In this case, it is given that r = x
also given :
height = 2 (base radius)
or
h = 2x.
Hence the formula becomes:
V = (1/3) π r² h
V = (1/3) π x² (2x)
V = (2/3) π x³ (answer A)
look at the attached file.
please show your work on how you got the answer
Answer:
D
Step-by-step explanation:
[tex]\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{2x+4}{2x^2+4x}[/tex]
Factor out 2 on the numerator and 2x on the denominator.
= [tex]\frac{2(x+2)}{2x(x+2)}[/tex]
Cancel the factor (x + 2) on the numerator/ denominator
= [tex]\frac{2}{2x}[/tex] ← cancel the 2 on numerator/ denominator
= [tex]\frac{1}{x}[/tex] : x ≠ 0
S = 2lw + 2wh + 2lh; solve for l
Answer:
l = (S - 2wh)/(2w + 2h)
Step-by-step explanation:
S = 2lw + 2wh + 2hl
S - 2wh = 2lw + 2hl
S - 2wh = l (2w + 2h)
(S - 2wh)/(2w + 2h) = l
The equation S = 2lw + 2wh + 2lh the value of l is given by l = S / (2w + 2h + 2wh)
To solve for l in the equation S = 2lw + 2wh + 2lh, we'll isolate l on one side of the equation. Here are the steps to do that:
Step 1: Start with the given equation:
S = 2lw + 2wh + 2lh
Step 2: Factor out l from the terms that contain it:
S = l( 2w + 2h + 2wh )
Step 3: Divide both sides of the equation by (2w + 2h + 2wh) to solve for l:
S / ( 2w + 2h + 2wh ) = l
So, the value of l is given by:
l = S / ( 2w + 2h + 2wh )
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Write an equation of the line that passes through (−3,7) and is perpendicular to the line y=−2x−5.
Answer:
Step-by-step explanation:
an equation is : Use the point-slope formula.
y - y_1 = m(x - x_1) ; m : the slope when : x_1 = -3 and y_1 = 7
- 2 ×m = - 1 because this line is perpendicular to the line y= -2x-5 when the slope is -2
so : m= 1/2
an equation is : y - 7 =(1/2)(x+3)
Answer:
The desired equation is
y = (1/2)x + 17/2
Step-by-step explanation:
The slope of the perpendicular line is the negative reciprocal of -2: m = 1/2.
Start with y = mx + b.
Substituting 7 for y, 1/2 for m and -3 for x, we get:
7 = (1/2)(-3) + b. Then 7 = -3/2 + b, so that b = 17/2.
The desired equation is
y = (1/2)x + 17/2
[tex] \sqrt[3]{216} [/tex]
reduce the index of the radical and exponent with 3, rhen you get your answer, 6
ANSWER PLS ITS URGENT NEED DONE IN ONE MIN BUS IS COMING!!!! pls dont let me fail!!!!! (will mark as brainliest)
(answer the circled ones) its quadratic equation factoring
Answer:
8.) x = 5, x=-12
9.)x = 5, x = -8
10.)x = -1/5, x = -2
Hope I helped :)
Answer:
10. -2, -⅕ = x
9. -8, 5 = x
8. -12, 5 = x
7. -5, 6 = x
Step-by-step explanation:
10. [tex]5{x}^{2} + 11x + 2 = 0 \\ \\ (5{x}^{2} + x) + (10x + 2) = 0 \\ x(5x + 1) + 2(5x + 1) \\ \\ (x + 2)(5x + 1) = 0 \\ \\ -2, \: - \frac{1}{5} = x[/tex]
9.
[tex]2{x}^{2} + 6x - 80 = 0 \\ \\ (2{x}^{2} + 16x) - (10x - 80) = 0 \\ 2x(x + 8) -10(x + 8) = 0 \\ \\ (x + 8)(2x - 10) = 0 \\ \\ -8, \: 5 = x[/tex]
8.
[tex] {x}^{2} + 8x - 65 = x - 5 \:→ {x}^{2} + 7x - 60 \\ \\ ({x}^{2} - 5x) + (12x - 60) \\ x(x - 5) + 12(x - 5) \\ \\ (x + 12)(x - 5) = 0 \\ \\ 5, \: -12 = x[/tex]
7.
[tex] {x}^{2} = x + 30 → - {x}^{2} + x + 30 \\ \\ (-{x}^{2} - 5x) + (6x + 30) \\ -x(x + 5) + 6(x + 5) \\ \\ -(x - 6)(x + 5) = 0 \\ \\ -5, \: 6 = x[/tex]
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simplify 20+3xy-3+4y^2+10-2y^2
Patty needs a total of $80 to buy a bicycle. She has already saved $35. If she saves $10 a week from her earnings, what is the least number of weeks she must work to have enough money to buy the bicycle?
F.3
G.4
H.5
J.8
Answer:
h
Step-by-step explanation:
80-35=45
4days x10=40
leaving 5 dollars left so u need another week to save 5 dollars more
in total of 5 weeks
The answer is She has to work at least for 4.5 to be able to buy the bicycle i.e x≥4.5
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: price of the bicycle is $80 and she has $35 in hand
If she earns $10 in a week then let x weeks be the minimum number of weeks she has to work then we have
x= 45/10
=4.5 weeks
Hence, She has to work at least for 4.5 to be able to buy the bicycle
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31. The bus fare in a city is $1.25. People who use the bus
have the option of purchasing a monthly discount pass for
$15.00. With the discount pass, the fare is reduced to $0.75.
Determine the number of times in a month the bus must
be used so that the total monthly cost without the discount
pass is the same as the total monthly cost with the discount pass.
The bus must be used 30 times in a month for the total monthly cost without the discount pass to be the same as the total monthly cost with the discount pass.
Explanation:The mathematical problem deals with determining the number of times one must take a bus ride for a monthly discount pass to be as cost-effective as individual fare payments. To solve it, we must set up an equation based on the cost of bus rides. Let's denote the number of bus rides as 'n'.
Without the pass, each ride is $1.25, so n rides would cost 1.25n dollars.
With the pass, each ride is $0.75 and you also need to pay $15 for the monthly pass, so n rides would cost 0.75n + 15 dollars.
To find out the break-even point, we set these two expressions for the total cost equal to each other:
1.25n = 0.75n + 15
Solving this equation gives us:
0.5n = 15, n = 15/0.5 = 30.
Therefore, the bus must be used 30 times in a month for the total monthly cost without the discount pass to be the same as the total monthly cost with the discount pass.
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Which lines are parallel? Check all that apply.
89.5°
91.51
88.5°
89.5°
90.5°
The lines that are parallel to each other are as follows;
b║fc║eHow to know lines that are parallel from the angles?When parallel lines are cut by a transversal, angles relationship are formed.
This angle relationship includes corresponding angles, alternate angles, vertical angles and many more.
Therefore, the lines that are parallel are as follows;
b║f : If you use alternate angle theorem you will notices line b and f are parallelc║e: using alternate and corresponding angle theorem you will notice both line c and e are parallel.learn more on parallel lines here: https://brainly.com/question/10652739
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Marco has a piece of wood that measures 9 x 1/10 + 6 x 1/100 + 4 x 1/1000 how can this measurement be written as a decimal? you miss ONE DAY OF SCHOOL
Answer:
The decimal number is 0.964
Step-by-step explanation:
we have
[tex]9(\frac{1}{10})+ 6(\frac{1}{100})+4(\frac{1}{1,000})[/tex]
step 1
Multiply each fraction by the whole number
[tex](\frac{9}{10})+ (\frac{6}{100})+(\frac{4}{1,000})[/tex]
step 2
Convert each fraction in a decimal number
Remember
Move the decimal point to the left as many places as there are zeros in the factor.
Move the decimal point one step to the left (10 has one zero).
Move the decimal point two steps to the left (100 has two zeros)
Move the decimal point three steps to the left (1000 has three zeros)
[tex]0.9+0.06+0.004[/tex]
step 3
Adds the number
[tex]0.964[/tex]
Lainey bought a set of 20 markers for $6
Final answer:
To find the unit price of markers in a set, divide the total cost by the number of markers to find that each marker costs $0.30 when 20 are purchased for $6.
Explanation:
Lainey's purchase of a set of 20 markers for $6 can be used to illustrate a simple mathematical concept known as unit price, which is the cost per individual item when items are sold in a set or batch. To calculate the unit price, you divide the total cost by the number of items in the set. Here's how you can do this calculation:
Determine the total cost of the set of markers, which is $6.
Count the number of markers in the set, which is 20.
Divide the total cost by the number of markers to find the unit price: $6 ÷ 20 = $0.30 per marker.
Therefore, the cost of each individual marker from the set is $0.30. Starting small, such as with markers, pencils, sharpeners, and erasers, and gradually adding other items like construction paper or magnets, are good practices in both purchasing supplies and understanding incremental costs in financial literacy.
Chandresh has several fishing rods that she would like to pack in boxes. One box is shown below.
Which fishing rod will fit in the box shown?
A. 17-inch fishing rod
B. 24-inch fishing rod
C. 27-inch fishing rod
D. 32-inch fishing rod
Answer: A, 17 inch
The box is 21 inches long, anything longer and it won't fit. 17 inch is the only thing shorter than 21.
Answer:
the green means its right at the top
Step-by-step explanation:
257
What names apply to this number
Answer:
Step-by-step explanation:
Whole, integer, rational, real
Which graph of ordered pairs shows a proportional relationship?
Answer:
c
Step-by-step explanation:
Graph C of ordered pairs shows a proportional relationship.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other.
What is a proportional relationship on a graph?A proportional relationship is one where there is multiplying or dividing between the two numbers. A linear relationship can be a proportional one (for example y=3x is proportional), but usually, a linear equation has a proportional component plus some constant number (for example y=3x +4).
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What is the GCF of 36, 48, and 60?
Answer:
12
Step-by-step explanation:
HELP! PLEASE SHOW WORK.
Answer:
2⅖
Step-by-step explanation:
Set this up as a proportion:
⅘ ? [parts of the necklace]
__ = __
⅓ 1 [hours]
Divide four-fifths by one-third to get 2⅖.
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** ⅓ hour = 20 minutes
Suppose karl uses 5 cups of tomatoes how many salqds can he make? Write a division equation and multiplication equation
Assuming one salad requires 1 cup of tomatoes, Karl can make 5 salads as shown by the division equation 5 cups / 1 salad = 5 salads. The multiplication equation 5 salads x 1 cup = 5 cups demonstrates the amount of tomatoes needed for 5 salads.
Explanation:To properly answer this question, we first need to know the number of cups of tomatoes required to make one salad. However, if we suppose that one salad requires 1 cup of tomatoes, then the division equation is 5 cups / 1 salad = 5 salads. This equation illustrates that Karl can make 5 salads with the amount of tomatoes he has.
On the other hand, the multiplication equation would be 5 salads x 1 cup = 5 cups. This equation pertains to how many cups of tomatoes are needed to make 5 salads. Please note that these equations assume that 1 cup of tomatoes is needed for a single salad, but the proportions may vary depending on the actual recipe.
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Karl can make 5 salads using 5 cups of tomatoes.
Assuming Karl makes salads that require 1 cup of tomatoes each, we can determine the number of salads he can make using division:
Number of salads = Total tomatoes (cups) / Tomatoes per salad (cups)
Number of salads = 5 cups / 1 cup/salad
Therefore, Karl can make 5 salads using 5 cups of tomatoes.
A multiplication equation can be used to express the relationship between the number of salads, the number of tomatoes per salad, and the total number of tomatoes:
Total tomatoes (cups) = Number of salads × Tomatoes per salad (cups)
5 cups = 5 salads × 1 cup/salad
Both equations demonstrate the same relationship between the number of salads, the number of tomatoes per salad, and the total number of tomatoes.
As lucia fills her fish tank, she notices that it fills 8 cubic centimeters of water in 4 minutes. How many cubic centimeters of water does it fill in 1 minute?
Answer:
2 cubic centimeters per minute
Step-by-step explanation:
8 cubic centimeters filled per 4 minutes
divide 8 by 4 = 2
2 cubic centimeters per minute
Answer: 2 cubic centimeters
Step-by-step explanation:
Given : As lucia fills her fish tank, she notices that it fills 8 cubic centimeters of water in 4 minutes.
i.e. Time taken to fills 8 cubic centimeters of water = 4 minutes
By UNITARY METHOD, we have
Amount of water it fills in 1 minute (i.e. Unit rate) = [tex]\dfrac{\text{8 cubic centimeters }}{\text{4 minutes}}[/tex]
= [tex]\dfrac{8}{4}=2[/tex] cubic centimeters
Therefore, it fills 2 cubic centimeters in 1 minute.
Hence, the correct answer is 2 cubic centimeters.
The subject of the formula below is y.
y = x + a-b
Rearrange the formula to make x the subject.
Pls help
Answer:
x = y + b - a
Step-by-step explanation:
Given
y = x + a - b ( add b to both sides )
y + b = x + a ( isolate x by subtracting a from both sides )
y + b - a = x
-2 (5) + 4 help plzzz
Answer:
-6
Step-by-step explanation:
-2 * 5 = -10
-10 + 4 = -6
Answer is -6
-2(5)+4
You multiply '-2' to '(5)' which equals to '-10' then you add '4' and the correct answer is '-14'
Hope this helped, my dude