Answer:
166.59 cm³ (approx.)
Step-by-step explanation:
A University has three student residences which are located at points (−6, 12) (0,0) (3,9). The University wants to build a tennis court an equal distance from all three residences. Determine the coordinates of the tennis court. What is the distance from a residence to the court to the nearest 10th of a metre? (1unit=40m).
Answer:
a. (-3, 6)
b. 268.3 m
Step-by-step explanation:
a. Determine the coordinates of the tennis court.
Let (x,y) be the coordinates of the tennis court. Since we have equal distances from the tennis court to each residence, we have using the equation for distance between two points (x₁,y₁) and (x₂,y₂), d = √[(y₂ - y₁)² + (x₂ - x₁)²]. Using the first two residences, (-6, 12) and (0,0) as (x₂,y₂) and (x, y) = (x₁,y₁), So,
d = √[(12 - y)² + (-6 - x)²]
d = √[(12 - y)² + (6 + x)²]
d = √[(144 - 24y + y² + 36 + 12x + x²]
d = √x² + y² + 12x - 24y + 180
d² = x² + y² + 12x - 24y + 180 (1)
Also, with (x₂, y₂) = (0,0) we have
d = √[(0 - y)² + (0 - x)²]
d = √[( - y)² + (- x)²]
d = √[y² + x²]
d = √[x² + y²]
d² = x² + y² (2)
Also, with (x₂, y₂) = (3,9) we have
d = √[(9 - y)² + (3 - x)²]
d = √[(81 - 18y + y² + 9 - 6x + x²]
d = √(x² + y² - 6x - 18y + 90)
d² = x² + y² - 6x - 18y + 90 (3)
Substituting (2) into (1), we have
d² = x² + y² + 12x - 24y + 180 (1)
d² = d² + 12x - 24y + 180 (1)
d² - d² = 12x - 24y + 180
12x - 24y + 180 = 0
12x - 24y = -180
dividing through by 12, we have
x - 2y = -15 (4)
Substituting (2) into (3), we have
d² = x² + y² - 6x - 18y + 90 (3)
d² = d² - 6x - 18y + 90 (3)
d² - d² = - 6x - 18y + 90
- 6x - 18y + 90 = 0
- 6x - 18y = -90
dividing through by -6, we have
x + 3y = 15 (5)
Subtracting (5) from (4), we have
x - 2y = -15 (4)
-
x + 3y = 15 (5)
-5y = -30
y = -30/-5
y = 6
substituting y = 6 into (4), we have
x - 2y = -15
x - 2(6) = -15
x - 12 = -15
x = 12 - 15
x = -3
So, the coordinates of the tennis court is (-3, 6)
b. What is the distance from a residence to the court to the nearest 10th of a metre? (1unit=40m).
Using equation (2),
d² = x² + y² (2) where x and y are the coordinates of the tennis court, and x = -3 and y = 6
So,
d² = x² + y²
d² = (-3)² + (6)²
d² = 9 + 36
d² = 45
d = √45 units
Since 1 unit = 40 m,
d = √45 × 40 m
d = 6.708 × 40 m
d = 268.33 m
d ≅ 268.3 m to the nearest tenth of a metre
gavin and play a game with 20 numbered balls. The 20 balls are numbered from 1 to 20. Write down the probability that the score is a multiple of 3.
Step-by-step explanation:
6/20
3/10 (simplified)
do you want the percentage?
Answer:
[tex]\frac{3}{10}[/tex]
Step-by-step explanation:
The multiplies of 3 from 1-20 are:
3, 6, 9, 12, 15, 18
Since there are [tex]20-1+1=20[/tex] numbers from 1-20 inclusive, the probability that a ball is a multiple of 3 is [tex]\frac{6}{20}=\boxed{\frac{3}{10}}[/tex]
Dahlia is simplifying (3 t) Superscript 4 using these steps:
(3 t) Superscript 4 = 3 t times 3 t times 3 t times 3 t = 3 times 3 times 3 times 3 times t times t times t times t
Although Dahlia is correct so far, which step could she have used instead to simplify the expression (3 t) Superscript 4?
(3 t) Superscript 4 = 3 t Superscript 4
3 Superscript 4 Baseline t = 81 t
4 (3 t) = 12 t
3 Superscript 4 Baseline t Superscript 4 Baseline = 81 t Superscript 4
Answer:
D would be the answer
Step-by-step explanation:
Took the test got it correct <33 good luck
Leo will create a mural consisting of five
vertical stripes of different colors. If Leo has
eight different colors from which to choose,
and the order of the stripes matter, in how
many ways can he complete his mural?
Answer:
he got 8 different colors to choose from for the first stripe. he has to choose from 7 for the second (one choose less bc he alrdy took one color)
that alone makes 56 different ways for just two stripes.
he will use 5 stripes in total, so the calculation is:
8*7*6*5*4 = 6720
(8!-3! would also work with the calculator 8! uses all the naturalnumbersfrom 1 to 8 and multiplies them)
A 4.5 m long pipe rests against a 2 m high
tank. One end of the pipe is on the ground
3 m from the base of the tank. How much
of the pipe overhangs the tank?
4.5 m
Bm
3 m
help me please lol
Answer:
0.89 m is the answer
Step-by-step explanation:
the wall, the ground and portion of pipe form a right angle triangle with pipe portion being the hypotenuse.
for a right triangle
[tex]{hypotenuse}^{2} = {base}^{2} + {height}^{2} [/tex]
here we have base = 3m and height = 2m.
thus
[tex] {h}^{2} = {3}^{2} + {2 }^{2} \\ = 9 + 4 \\ = 13 \\ h = \sqrt{13} [/tex]
portion of pipe overhanging = 4.5 - sqrt (13)
= 4.5 - 3.61
= 0.89 m
What is the volume of a cube with a side length of 3tunits?
Cube V = 93
Answer:
The volume 27.
The volume of a cube:
Volume = side³
The volume of a cube with side 3 units is 27 cubic units.
What is a cube?It is a polygon having six faces.
The volume of a cube:
Volume = side³
Example:
The volume of a cub with a side length of 2 cm is 8 cubic cm.
We have,
Side = 3 units
Volume = Side³
Volume:
= 3³
= 3 x 3 x 3
= 27 cubic units
Thus,
The volume of a cube with side 3 units is 27 cubic units.
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Tilly and her mom made a rectangular dog run. They used 26 one-yard long pieces of fencing. They put 6 pieces of fencing on one side. How many pieces did they put on the next side?
Tell whether the triangle with the given side lengths is a right triangle.
65, 72,97
The answer is yes or no
Answer:
yes
Step-by-step explanation:
when I add 65+72 and the answer gave me and I find the square root of that number
A 21-inch rope is to be cut into two pleces so that one piece is 8 inches longer than twice the other. How long is each piece, if a=2, b= 8, and I=21
smaller plece
in
larger plece
Answer:
4 1/3 inches Smaller piece
16 2/3 inches Larger piece
Step-by-step explanation:
x + (2x + 8) = 21
3x + 8 = 21
3x = 13
x = 13/3
x = 4 1/3 inches Smaller piece
2x + 8 = 8 2/3 + 8
2x + 8 = 16 2/3 inches Larger piece
Lisa uses 2 pieces of copper wire, each 9 feet long, for
each robot she builds. If she started with a 500-yard roll
of copper wire, which of the following represents the
number of yards of wire left on the roll after 'Lisa built r
robots? (3 feet = 1 yard)
Answer:
yards of wire left on the roll = 500 - r(3)
Step-by-step explanation:
9 feet = 3 yards we need to find how much wire is left on the roll after she builds a certain amount of robots. she uses 9 feet or 3 yards per robot so we have to multiply the amount of robots (r) by 3 yards and subtract that from 500 yards or the total amount of wire she has and that gives us the total amount of wire she has left. Hope this helps.
CAN SOMEONE HELP ME ASAP????
Find the gradient of the line 2y = -10x + 1
Answer:
Gradient = -5
Step-by-step explanation:
The gradient of a line is the slope of the line.
The standard form of the line equation is y = mx + b
where m is the slope ( or gradient) b is the y - intercept.
Given :
2y = -10x + 1
[tex]y = -\frac{10}{2} x + \frac{1}{2}\\\\y = -5x + \frac{1}{2}\\\\Therefore , \ gradient \ is \ -5[/tex]
The gradient of the line whose equation is 2y=-10x+1 is -5.
What is gradient?Gradient could be a measure of how steep a slope or a line is.
How to calculate the gradient of the line?The equation of the road is 2y=-10x+1
y=-5x+1/2
Therefore the gradient of the line is that the coefficient of x which is -5.
Hence the gradient of the line is -5.
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For which equations does the fraction 13 make the equation true? A 6x __=3 B 6x__=2 C 7x__=7/21 D 8x__=3 1/3
Answer:
B. 6 x 1/3 = 2
Step-by-step explanation:
2 is 1/3 of 6
So multiplying 6/1 (6) bu 1/3 :
6/1 * 1/3 = 6 / 3 = 2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
i keep getting this Q wrong can someone help me solve it :)
Answer:
Can I have your points because you stole it
my precious points
your answer is helpless
If j + m=5, what is the value of 50j + m)?
Answer:250
Step-by-step explanation:
j+m=5
50(j+m)=50x5=250
Answer:
If you mean 5(j + m) and j + m = 5 then you answer is 6j + 6m = 5.
If you mean 50j + m and j + m = 5 then there is no solution.
Step-by-step explanation:
j + m = 5
5(j + m)
5(j + m) + j + m = 5
5j + 5m + j + m
6j + 6m = 5
Simplify the expression below. (x^5)(x^2)
A. x^2
B. x^5
C. x^7
D. x^10
[tex]\longrightarrow{\green{C.\: {x}^{7}}}[/tex]
Step-by-step explanation:
[tex]( {x}^{5} )( {x}^{2} ) \\\\ = {x}^{5 + 2} \\\\ = {x}^{7} \\\\ (∵ {a}^{m} \times {a}^{n} = {a}^{m + n} )[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Point J is the image of point A. Which translation describes the transformation?
A.(x-10, y+10)
B.(x+5, y-10)
C.(x-5, y+10)
D.(x+10, y-5)
Write a function to describe the following scenario.
The temperature of a hot steak starts at 140° F and decreases at 5° F per minute. What will the temperature be of this steak after a certain number of minutes?
y= ? - ?x
Answer:
Below.
Step-by-step explanation:
Temperature after 1 minute = 140 - 5(1)
Temperature after 2 minutes = 140 - 5(2)
Temperature after 3 minutes = 140 - 5(3),
- and so on.
So the function is
y = 140 - 5x.
The temperature of the steak after a certain number of minutes can be described as the function
y = 140 - 5x
What is a linear equation?A linear equation with one variable has the standard form Cx + D = 0. In this case, the variable is x and C are coefficient, while D is a constant.
How to solve this problem?Let the certain number of minute is x.
Since the temperature decreases at 5° F per minute, then after x minutes, it will decrease 5x.
Initial temperature = 140° F
Then the present temperature, y = 140 - 5x.
Therefore, the temperature of the steak after a certain number of minutes can be described as the function
y = 140 - 5x
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The isosceles triangle has a perimeter of 7.5 m.
Which equation can be used to find the value of x if the
shortest side, y, measures 2.1 m?
y
O 2x-2.1 = 7.5
O 4.2 + y = 7.5
X
O y-4.2 = 7.5
0 2.1 + 2 x = 7.5
Mart this and return
Save and Exit
Next
Submit
Answer:
Option d) 2.1 + 2x = 7.5
Step-by-step explanation:
An isosceles triangle is a triangle with two equal sides.
Perimeter of a triangle is some of all the 3 sides.
Let the equal sides be x
Let the third side be y
Therefore,
Perimeter = x + x + y
7.5 = 2x + y
7.5 = 2x + 2.1 [ given shortest side, y = 2.1m ]
tina works 15 hours a week (monday to friday). last week she worked 3 1/2 hours on monday, 4 hours on tuesday, 2 1/6 hours on wednesday and 1 1/2 on thursday. how many hours did she works on fridays
Answer:
Tina worked [tex]3 \frac{5}{6}[/tex] hours on Friday.
Step-by-step explanation:
To solve for how many hours Tina worked on Friday you have to add up all the hours worked then subtract that from 15 hours to get the remainder.
Step 1 : Add up all the hours worked so far.
[tex]3\frac{1}{2}[/tex] + 4 + [tex]2\frac{1}{6}[/tex] + [tex]1\frac{1}{2}[/tex] = ?
We need to turn these mixed numbers into improper fractions first so we can add. Let's turn them all into sixths.
[tex]3 \frac{3}{6}[/tex] + 4 + [tex]2\frac{1}{6}[/tex] + [tex]1 \frac{3}{6}[/tex] = [tex]11\frac{1}{6}[/tex]
Allright, so now we know that Tina already worked 11 and 1/6 hours already, so we subtract that from 15 to find how many hours she worked on Friday.
Step 2 : Subtract [tex]11\frac{1}{6}[/tex] from 15.
15 - [tex]11\frac{1}{6}[/tex] = [tex]3 \frac{5}{6}[/tex]
Therefore Tina worked [tex]3 \frac{5}{6}[/tex] hours on Friday.
Hope this helps, please mark brainliest if possible. Have a great day.
Deborah buys a book for 30% less than the regular price of $14.50.
Which is the amount of Deborah's discount?
Answer:
$4.35
Step-by-step explanation:
Find the distance between the line segment with end points (-3,5) and (1,5)
Answer:
[tex]\displaystyle d = 4[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (-3, 5)
Point (1, 5)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(1- -3)^2+(5- 5)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{4^2+0^2}[/tex][√Radical] Simplify: [tex]\displaystyle d = \sqrt{4^2}[/tex][√Radical] Evaluate: [tex]\displaystyle d = 4[/tex]17 x 8 = (10 + 7) + 8
17 * 8 = (10 ~ 8) + (
Answer:
ur mom kid
Step-by-step explanation:fotnite
What is the solution to the equation 3(x - 1) – 2(2x + 1) = 8(x - 1)?
Which function represents the graph below?
Answer:
answer is A. you can see each intervals slowly to know this
Please help me with my maths
Answer:
Step-by-step explanation:
x² + 5x³ +2x + 4 - 3x⁴
1) -3x⁴ + 5x³ + x² + 2x + 4
2) Coefficient of x⁴ term = -3
3) Index (Exponent) of term x = 1
4) Degree of the expression : Highest power/exponent/ index is the degree.
Degree of the expression = 4
5) Constant term : 4
6) There are 5 terms in the expression
7) x = 2
-3(2)⁴ +5(2)³ + 2² + 2*2 + 4 = -3*16 + 5*8 + 4 + 4 + 4
= -48 + 40 +4 + 4 + 4
= 4
The triangles below are similar. Find the measure of ∠B and ∠F
Answer:
∠ B = 45°, ∠ F = 22°
Step-by-step explanation:
Since the triangles are similar then corresponding angles are congruent, so
∠ B = ∠ E = 45°
∠ F = ∠ C = 22°
PLEASE HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
M1=44 M2=136 M3=44 M4=136
Step-by-step explanation:
M3= 44 so M1=44 due to opposite angles being equal
then if two of the angles add to 88
360-88= 272
divide 272 by 2 as M2 and M4 are equal
272/2=136
Answer:
m∠1 = 44°
m∠2 = 136°
m∠4 = 136°
Step-by-step explanation:
m∠1 explanation:
I got it from m∠3 since they're both congruent
m∠2 explanation:
Since we already have the measure of 3 and 1, we can easily add both of the measures (44 + 44 = 88°) then subtract it from 360° (total) = 272°
Then since both measures (2 and 4) are congruent (measuring the exact same length and angle) we can divide 272° ÷ 2 = 136°
m∠4 explanation:
I got it from m∠2 since they're both congruent
Steven earns extra money babysitting. He charges $31.25 for 5 hours and $43.75 for 7 hours.
.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and
y represent the amount he charges.
The equation is y =?
Given:
Steven charges $31.25 for 5 hours and $43.75 for 7 hours.
To find:
The equation that represents the relationship.
Solution:
Let x represent the number of hours Steven babysits and y represent the amount he charges.
Then the two points on the function are (5,31.25) and (7,43.75). So, the equation of the line that passes through these two points is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-31.25=\dfrac{43.75-31.25}{7-5}(x-5)[/tex]
[tex]y-31.25=\dfrac{12.5}{2}(x-5)[/tex]
[tex]y-31.25=6.25(x-5)[/tex]
On further simplification, we get
[tex]y-31.25=6.25(x)-6.25(5)[/tex]
[tex]y-31.25=6.25x-31.25[/tex]
[tex]y=6.25x-31.25+31.25[/tex]
[tex]y=6.25x[/tex]
Therefore, the required equation for the given situation is [tex]y=6.25x[/tex].
if x:y=5:3 then (8x-5y): (8x+5y)=?
A triangle has base 8 3/8 feet and height 6 3/4 feet. Find the area of the triangle as a mixed number.
Answer:
First you convert the mixed numbers into improper fraction
[tex]8\frac{3}{8} = \frac{67}{8} \\\\6 \frac{3}{4} = \frac{27}{4}[/tex]
Solution
[tex]A=\frac{\frac{27}{4} + \frac{67}{8} }{2}[/tex]
[tex]A=\frac{\frac{54 + 67}{8} }{2}[/tex]
[tex]A\frac{\frac{121}{8} }{2}[/tex]
[tex]A=\frac{121}{8}[/tex] * [tex]\frac{1}{2}[/tex]
[tex]A= \frac{121}{16}[/tex]
[tex]A= 7 \frac{9}{16}[/tex]
Step-by-step explanation: