The equation that passes through the given point 2x-3y=0.
Let the point which they pass be the origin (0,0).
From the given equation we get [tex]y= 2/3x + 19[/tex]
On comparing this with the general equation that is [tex]y= mx+c[/tex]
We get [tex]m= 2/3[/tex]
Thus as we know the equation of line is [tex]y-y1 = x-x1[/tex]
Substituting the values in this equation we get;
[tex]y-0= 2/3(x-0)[/tex]
On cross multiplying we get
[tex]3y=2x[/tex] or [tex]2x-3y=0[/tex]
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The volume of this cylinder is 6480π cm3.
Find the length of the radius,
The sides are equal to 180cm.
Answer:
The length of the radius is 10.7cm
Step-by-step explanation:
[tex]v = \pi {r}^{2} h[/tex]
6480=(22r*180)/7
6480*7=3960r
r=
[tex]r = \sqrt{45360 \div 396} [/tex]
radius=10.7tell wheter the lines through the given points are parallel, perpendicular or neither.
a. Line 1: (2,-3), (-4, -6)
Line 2: (-3, 2), (2, -8)
b. Line 1: (-4, -5), (4, 1)
Line 2: ( 6, 10), (-3, -2)
c. Line 1: (0, -4), (-2, -8)
Line 2: (-1, 5), (1, 9)
Help I need this by tomorrow :c
Answer:
a. Perpendicular
Make sure to read the step-by-step explanation to figure out how to do the other 2.
Step-by-step explanation:
I will not be providing answers to all three, but I will answer the first one (this is, so you don't depend on people to solve this for you).
Parallel lines have one thing in common, their slope. Two lines that have the same slope never intersect because they are both facing the same direction and moving the same distance. So, you can find the slope of two lines by using the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{-6-(-3)}{-4-2}=\frac{-3}{-6}=\frac{1}{2}\\m_2=\frac{-8-2}{2-(-3)}=\frac{-10}{5}=-2[/tex]
This is evidence that the two lines are not parallel. But, by finding the slope, we can conclude that it is perpendicular.
This brings me to how to identify perpendicular lines. The slope of perpendicular lines is negative reciprocals. A reciprocal is just a fraction that is flipped, and it's negative. For example, [tex]\frac{-2}{3}[/tex]'s negative reciprocal would be [tex]\frac{3}{2}[/tex]. The negative of -2/3 is a positive, and the reciprocal of 2/3 is 3/2. So, the negative reciprocal is 3/2.
How does this apply to what I said earlier?Well, [tex]-2[/tex] is the negative reciprocal of [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2, and the negative of 2 is -2. So, simply, lines 1 and 2 are perpendicular.
Use this method to solve the other questions. If they don't have the same slope and aren't negative reciprocals, then they are neither.
Answer:
Step-by-step explanation:
To solve this problem, we use the following formula:
[tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
a) (2,-3) (-4,-6)
[tex]x_1=2\ \ \ \ x_2=-4\ \ \ \ y_1=-3\ \ \ \ y_2=-6[/tex]
[tex]\displaystyle\\\frac{x-2}{-4-2} =\frac{y-(-3)}{-6-(-3)} \\\\\frac{x-2}{-6}=\frac{y+3}{-6+3} \\\\\frac{x-2}{-6} =\frac{y+3}{-3}[/tex]
Multiply both parts of the equation by -3:
[tex]\displaystyle\\\frac{x-2}{2}=y+3\\\\0.5x-1=y+3\\\\0.5x-1-3=y+3-3\\\\0.5x-4=y\\[/tex]
⇔ Line 1: y=0.5x-4 m₁=0.5
(-3,2) (2,-8)
[tex]\displaystyle\\\frac{x-(-3)}{2-(-3)}=\frac{y-2}{-8-2} \\\\\frac{x+3}{2+3} =\frac{y-2}{-10} \\\\\frac{x+3}{5} =\frac{y-2}{-10} \\\\[/tex]
Multiply both parts of the equation by -10:
[tex]-2(x+3)=y-2\\-2x-6=y-2\\-2x-6+2=y-2+2\\-2x-4=y[/tex]
⇔ Line:y=-2x-4 m₂=-2
[tex]\displaystyle\\m_1=-\frac{1}{m_2}[/tex]
⇒ The given lines are perpendicular
b)
(-4,-5) (4,1)
[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+4}{4+4}=\frac{y+5}{1+5} \\\\\frac{x+4}{8} =\frac{y+5}{6} \\[/tex]
Multiply both parts of the equation by 6:
[tex]\displaystyle\\\frac{6(x+4)}{8} =y+5\\\\\frac{3}{4} x+3=y+5\\\\\frac{3}{4} x+3-5=y+5-5\\\\\frac{3}{4} x-2=y\\[/tex]
⇔ Line 1: y=(3/4)x-2 m=3/4
(6,10) (-3,-2)
[tex]\displaystyle\\\frac{x-6}{-3-6} =\frac{y-10}{-2-10} \\\\\frac{x-6}{-9} =\frac{y-10}{-12} \\\\[/tex]
Multiply both parts of the equation by -12:
[tex]\displaystyle\\\frac{-12(x-6)}{-9} =y-10\\\\\frac{4}{3}x-8=y-10 \\\\\frac{4}{3}x-8+10=y-10+10\\\\\frac{4}{3}x+2=y[/tex]
⇔ Line 2: y=(4/3)x+2 m=4/3
⇒ The given lines are neither perpendicular and neither parallel
c)
(0,-4) (-2,-8)
[tex]\displaystyle\\\frac{x-0}{-2-0} =\frac{y-(-4)}{-8-(-4)} \\\frac{x}{-2}=\frac{y+4}{-8+4} \\\\\frac{x}{-2}=\frac{y+4}{-4}[/tex]
Multiply both parts of the equation by -4:
[tex]2x=y+4\\2x-4=y+4-4\\2x-4=y[/tex]
⇔ Line 1: y=2x-4 m₁=2
(-1,5) (1,9)
[tex]\displaystyle\\\frac{x-(-1)}{1-(-1)} =\frac{y-5}{9-5} \\\\\frac{x+1}{1+1} =\frac{y-5}{4}\\\\\frac{x+1}{2} } =\frac{y-5}{4} \\[/tex]
Multiply both parts of the equation by 4:
[tex]2(x+1)=y-5\\2x+2=y-5\\2x+2+5=y-5+5\\2x+7=y[/tex]
⇔ Line 2: y=2x+7 m₂=2
m₁=m₂
⇒ The given lines are parallel
b) A different pattern is made using 20 straight lines
and 14 arcs.
The straight lines and arcs are made from metal.
20 straight lines cost £12
cost of one straight line: cost of one arc = 2:3
Work out the total cost of metal in the pattern.
26.4
total cost of metal in the pattern is £24.6
What is ratio and proportion ?To compare two values is to use a ratio. A proportion is formed when two ratios have the same value. Choose whether the ratio is part-to-part or part-to-whole before you write it.
Calculation20 straight line cost £12
12 ÷ 20 = 0.6 per straight line
straight line : cost of one arc = 2:3
arc = 0.6 x (3/2) = 0.9
total = 12 + 14 x 0.9
= 12 + 12.6
= 24.6
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UGH I HATE MATH HELP
Hello!
What is the slope-intercept form:
[tex]y = mx + b[/tex]
m: is the slope[tex]m = \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-4}{0--2} =\dfrac{-5}{2}[/tex]
⇒ where (x₂,y₂) and (x₁,y₁) are random points on the line
b: y-intercept or the point that has an x-coordinate value of '0'⇒ thus our y-intercept is '-1'
Thus our line's equation in slope-intercept form:
[tex]y= -\dfrac{5}{2}x -1[/tex]
Hope that helps!
A bowl is used to serve punch for a party.
Which figure would be best to use to estimate the volume of the punch bowl?
C
Semicircle is the best figure to use to estimate the volume of the punch bowl.
What is meant by volume?Every three-dimensional object requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object within the boundaries of three-dimensional space. It is also known as the object's capacity. The liquid state has a definite volume but no definite shape. A solid state has a definite volume and a definite shape. Even if the containers are changed, the solid's shape and volume remain constant. Volume is a measurement of an object's capacity. For example, the volume of a cup is 100 ml if it can hold 100 ml of water up to the brim.To learn more about volume, refer to:
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Show your work. Please help I really need!
a. Expression for length L in terms of x is L = 1040 - 2x
b. Expression for the area of the pasture in terms of L and x, A = Lx
c. Expression for the area of the pasture in terms of x only = x (1040 - 2x)
d. The area of the pasture will enclose greater than or equal to 60 square feet
How to find the area in terms of the given dimensionsGiven data
length of fence = 1040 ft
length if the pasture = L
width of the pasture = x
Expression for length L in terms of x
from the figure we can see that the fenced part is 3 sides which include 2 widths and 1 length. So we represent this with the expression below
L + x + x = 1040
L + 2x = 1040
L = 1040 - 2x
Expression for the area of the pasture in terms of L and x
Area of the pasture, A = L * x
A = Lx
Expression for the area of the pasture in terms of x only
= L * x
and L = 1040 - 2x
= x (1040 - 2x)
A sentence that makes the area to enclose at least 60 000 square feet.
from A = Lx
we have
A = Lx ≥ 60
The area of the pasture will enclose greater than or equal to 60 square feet
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Which of the following are rational numbers?
5.48
78.541
97
42.111...
Answer:
5.48, 78.541 and 97
Step-by-step explanation:
A rational number by definition refers to a number that is in the form of k/m and in which k and m are integers and m is not equal to 0.
Let me give you some examples:
1/32/41/59/3From our question,
5.48 = 137/25 hence rational number78.541 = 78541/1000; rational 97 = 97/1; rational 42.111..... = 4211111*/100000: irrational number. It is recurring hence not a rational number.Therefore 5.48, 78.541 and 97 are rational numbers
Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
The minimum number of sets of knives Kaj should buy if the restaurant needs at least 736 knives is 48. 4 sets of knives
How to find the minimum number of sets of knives Kaj should buy?Number of knives needed by the restaurant = at least 736 knivesNumber of knives currently available at the restaurant = 155 knivesEach set of knives = 12Number of sets of knives needed to buy = x155 + 12x ≥ 736
substract 155 from both sides12x ≥ 736 - 155
12x ≥ 581
divide both sides by 12x ≥ 581 / 12
x ≥ 48.41666666666666
Approximately,
x ≥ 48. 4 sets of knives
In conclusion, the sets of knives kaj needs to buy more is 48. 4 sets of knives
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PLS Heeeeeeelp!!!!!!!!!!
Answer 9 3/7
Step-by-step explanation:
[tex] \frac{30}{7} \times \frac{11}{5} \\ = \frac{330}{35} \\ = 9 \frac{15}{35} [/tex]
SIMPLIFIED WE GET:
[tex]9 \frac{3}{7} [/tex]
THE LAST OPTION IS THE ANSWER
Help quick!! I need someone to answer this for me.
Use the digits 1, 2, 3 and 4 to fill in each rectangle in order to
create the sum closest to 50. Each digit may only be used once.
+
Manewering the Middle 110
The sum will be 46 which is the nearest combinational value that could be deduced from the digits 1, 2, 3, and 4.
Let's check all the combinations which can be possibly used,
34 + 21 = 46, which is 4 numbers less than 50 so far the nearest.
43 + 12 = 55, which is 5 numbers more than 50.
32 + 41 = 73, which is 23 numbers more than 50.
32 + 14 = 46, which is 4 numbers less than 50 so far the nearest.
23 + 41 = 64, which is 14 numbers more than 50.
So the two combinations are deduced after permutation and a combination of numbers that are 3 and 4 + 2 and 1 and another is 3 and 2 + 1 and 4.
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The integer 6 makes which of the following equations false?
−6(t − 8) = 12
5m + 3 = 3m
t + 5 = 11
9 = 2x − 3
Answer:
5m+3 =3m
Step-by-step explanation:
−6(t − 8) = 12
-6((6) -8) =12
5m+3=3m
5m-3m=3
2m=3
2(6)≠3
t + 5 = 11
(6) + 5 = 11
9 = 2x − 3
2x = 9+3
2(6) = 12
Amari bought three chicken wings for $4.80 if Morris spent $27.20 how many chicken wings did she buy
Answer:
24 wings
Step-by-step explanation:
Answer:
17 wings
Step-by-step explanation:
1. first we multiply 3 by 27.20 you get 81.6
2. then we divide 81.6 by 4.80 and we get 17
17 wings
(EASY POINTS)
Solve for x in this figure.
x=
Answer:
x = 132°
Step-by-step explanation:
Sum of interior angles = (n - 2) x 180, where n is number of sides of the polygon.
Sum = (6 - 2) x 180 = 720°
sum = 160 +75 + 132 + 113 + 108 + x
sum = 588 + x
720 = 588 + x
x = 720 - 588
x = 132°
:)
John held a garage sale. He priced all the items at a dime or a quarter. His sales totaled
less than $5. Write an linear inequality that describes this situation.
John held a garage sale. He priced all the items at a dime or a quarter, his sales totaled less than $5, the solution is shaded region in quadrant I.
What is a slope?In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent the slope; reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of equation for a straight line as "y = mx + b" and "y = mx + c," respectively.
He priced all items at a dime or a quarter. His sales totaled less than $5
Since dime =$ 0.10=$0.10 and the quarter =$0.25=$0.25
Let x=x= the number of the items sold for a dime
Let y=y= the number of the items sold for a quarter
0.10x+0.25y<5
0.10x+0.25y<5
Inequality in the slope-intercept form
0.10x+0.25y Subtract 0.10x from both sides
0.25y<-0.10x+5 Divide both sides by 0.25
Subtract 0.10x from both sides
[tex]y= -\frac{2}{5}x+20\\[/tex]
The slope is, [tex]-\frac{2}{5}[/tex] and the y- intercept is 20
Since inequality sign is << so, draw a dashed line
Test point (0,0)(0,0)
Substituting the values 0 for x and 0 for y,
[tex]y < -\frac{2}{5}x+20\\\\0 < -\frac{2}{5}(0)+20\\\\0 < +20[/tex]
Since inequality is true
So, (0,0)(0,0) is solution of the inequality
Shade region containing (0,0)(0,0).
The graph below shows all possible solutions
Since boundary line is dashed and the number of items is always positive
The solution is shaded region in quadrant I
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The black triangle in the first quadrant is the original figure. Label each other triangle with its
transformation.
A. Translation of 6 to the left
B. Translation of 6 to the left and down 4
C. X-axis reflection
D. Y-axis reflection
E. Translation of 3 to the left and down 6
City carpet advertises that they can instal 1,200 square feet of carpet in 2 1/2 hours They charge $40 per hour for a special install of 1,920 squares free how much will they charge
Total charge for 1,920 squares feet is $160.
What is basic algebra ?The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including trigonometry, calculus, and coordinate geometry. 2x + 4 = 8 is a straightforward algebraic expression.In algebra, symbols are used, and operators are used to connect the symbols to one another. It is more than just a mathematical idea; it is a skill that we all utilize on a regular basis without even being aware of it.
Given that :City carpet advertises that they can instal 1,200 square feet of carpet in 2 1/2 hours They charge $40 per hour.
City carpet can install 1,200 square feet of carpet in 2.5 hours
In 1 hour they can install [tex]\frac{1200}{2.5} =480 squares feet[/tex]
In 4 hour they can install 1920 squares feet carpet
They charge $40 per hour
So total charges for 1920 square feet will be 4 ×40
= $160
Total charge for 1,920 squares feet is $160.
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An angle measures 27.8° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
∠1 = 103.9° ; ∠2 = 27.8°
Step-by-step explanation:
Supplementary angles = 180°
So, Let the angles be 'x'
Then, x + x -27.8° = 180°
2x - 27.8° = 180°
2x = 180° + 27.8°
2x = 207.8°
x = 207.8°/2
x = 103.9°
Therefore ∠1 = 103.9° ; ∠2 = 27.8°
I hope the answer is correct and has helped you!!!
Given: -3(4x + 1) = 21
Prove: x = -2
Answer:
-3(4x + 1) = 21 given
4x + 1 = -7 Division Property of Equality
4x = -8 Subtraction Property of Equality
x = -2 Division Property of Equality
Answer:
see explanation
Step-by-step explanation:
prove by solving the equation
- 3(4x + 1) = 21 ( divide both sides by - 3 )
4x + 1 = - 7 ( subtract 1 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
thus solution is x = - 2
a 100 gram chocolate bar is shared equally between 5 students while a separate 100 gram chocolate bar is shared equally between 20 students. which group of students receives the larger amount of chocolate per student?
Answer:
The 5 students receive the larger amount.
100:5= 20 gram per student
100÷20= 5 gram per student
Step-by-step explanation:
prove me wrong
a shorter solution that probably will get full pts :
Because each group has the same mass of the chocolate bar, whichever group has less students will get a larger amount of chocolate per student (as there are less people receiving)
and here's if you think it is kinda not too detailed :
The first group has each student receiving 100 : 5 = 20 grams of chocolate per student
The second group has each student receiving 100 : 20 = 5 grams of chocolate per student
Both solutions give us a conclusion of : The group with 5 students have each of the receiving a larger amount of chocolate.
Which transformation
of y = f(x) moves the graph
7 units to the left and 3 units down?
1) y=(x+7)-3
2) y=f(x+7)+3
3) y=f(x-7)-3
4) y=f(x-7)+3
what is the value of cos 360
Write the negation of the following statement: No one has a pet water buffalo.
SOMEONE HAS A PET WATER BUFFALO.
THE GIVEN STATEMENT IS INDICATING THAT NOT EVEN ONE PERSON HAS A PET WATER BUFFALLO SO THE NEGATION SHOULD INDICATE THERE IS SOMEONE WHO DOES HAVE A PET WATER BUFALLO.
HOPE THIS HELPS
Lisa walked 10,560 feet in 30 minutes. She walked at a constant rate.
At what rate did Lisa walk in miles per hour
convert feet to miles;
10,560 = 2 miles
30 minutes to miles;
2; therefore,
in 1hr she walked 4 miles
4 miles/hour
Answer:
Step-by-step explanation:
Please answer the two questions in the photo ( will mark brainliest if correct )
Answer: The rhombus below has two lines of symmetry, and the shape below has two lines of symmetry.
Step-by-step explanation:
Symmetry is when we split an object in half, in which both sides are equivalent. This definition must explain how the rhombus was most plausibly split, as well as the letter "H".
What is the slope-intercept form of the equation of the line that contains the points (1, 4)and (0, 1)?
Answer:
3
Step-by-step explanation:
m=y2-y1÷x2-x1
4-1÷1-0=3÷1=3
Given ΔRST is similar to ΔUVW with RT = 9 inches, UW = 5.4 inches, and RS = 6 inches.
Which is the length of UV¯¯¯¯¯¯¯¯
?
Responses
3.6 inches
3.6 inches
2.4 inches
Because triangle SRT and VUW are similar, all sides of triangle SRF are scaled up by an amount.
We calculate the scale factor : 9/5.4 = 5/3
-> The corresponding side of SR (UV) is scaled down 5/3 times from the length of SR
-> UV = 6 : 5/3 = 3.6 (inches).
If T is the midpoint of SU,find x. ( ST=14x-6 and TU= 12x+5). What is the value of x?
the numerical value of x in fraction and decimal form are 11/2 and 5.5 respectively.
What is the numerical values of x?A midpoint is simply a point that divides a line segment into two equal halves.
Given the data in the question;
T is the midpoint of SUSegment ST = 14x - 6Segment TU = 12x + 5Numerical value of x = ?Since that T is the midpoint of segment SU, segment ST and segment TU are two equal halves of of segment SU.
Segment ST = Segment TU
Plug in the given values and solve for x
14x - 6 = 12x + 5
14x - 12x = 5 + 6
2x = 11
x = 11/2
x = 5.5
Therefore, 11/2 or 5.5 is the numerical value of x.
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Find the midpoint of each line segment
1) (4, 8)
2) (4, 8)
The midpoints are already given to you.
Answers:
(-1, 26) for problem 1(14, 12) for problem 2=======================================================
Explanation:
A = (9, -10)
B = (4,8)
C = (x,y)
A and C are the endpoints. B is the midpoint of segment AC.
The x coordinates of A and C are 9 and x respectively. Add them up and divide in half to get (9+x)/2. This is set equal to the x coordinate of point B and we solve for x.
(9+x)/2 = 4
9+x = 2*4
9+x = 8
x = 8-9
x = -1
The x coordinate of point C is -1.
Use the same idea for the y coordinates.
(-10+y)/2 = 8
-10+y = 2*8
-10+y = 16
y = 16+10
y = 26
Point C is located at (-1, 26)
The midpoint between (9, -10) and (-1, 26) is (4, 8)
Use the midpoint formula to confirm this.
------------------------
The steps for the second problem are going to follow the same outline.
A = (-6,4)
B = (4,8)
C = (x,y)
(-6+x)/2 = 4 solves to x = 14
(4+y)/2 = 8 solves to y = 12
Point C is located at (14, 12)
The midpoint between (-6, 4) and (14, 12) is (4, 8)
Name the property used in the given expression −33/ 57 × −7/ 28 = −7/ 28 × −33/ 57 . With steps and solution pls
Step-by-step explanation:
as the other answer said, if is the commutative property of multiplication (the same as for addition, as multiplication is just a shortcut form of special additions) :
a × b = b × a
you need a solution ? you mean, you need this multiplication done and simplified, right ?
you know that
a/b × c/d = (a×c)/(b×d)
so,
-33/57 × -7/28 = -33/57 × -7/(4×7) =
= -33/57 × -1/4 = (-33×-1)/(57×4) =
= 33/228