Answer:
Step-by-step explanation:
The distance between two points (-6, 3) and (3, -9) is 10.81 units.
We have a graph a right triangle with the two points A(-6,3) and B(3, -9) forming the hypotenuse.
We have find the distance between the two points using only the sides of the right triangle.
What is the formula to find the distance between the two points on Cartesian plane ?The distance between two points -
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
According to the question, we have -
Coordinates of Point A = (- 6, 3)
Coordinates of Point C = (3, -9)
Now -
Coordinates of Point B will be (- 6, -9) [formed by the intersection of sides].
Distance AB -[tex]AB = \sqrt {\left( {-6 - (-6) } \right)^2 + \left( {3 - (-9 } \right)^2 }[/tex] = 6 units
Distance BC -[tex]BC = \sqrt {\left( {-6 - 3 } \right)^2 + \left( {-9 - (-9 } \right)^2 }[/tex] = 9 units
Using the Pythagoras theorem -
[tex](AC)^{2} =(AB)^{2} +(BC)^{2}[/tex]
[tex](AC)^{2} =[/tex] 36 + 81
AC = [tex]\sqrt{117}[/tex] = 10.81
Hence, the distance between two points (-6, 3) and (3, -9) is 10.81 units.
To solve more questions on Distance formula, visit the link below -
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solve for x and explain the steps:
3x-6=4(2-3x)-8x
Answer: x = 14/23
Step-by-step explanation:
3x-6=4(2-3x)-8x
3x-6=8-12x-8x --> Expand 4(2-3x)
3x-6=8-20x --> Collect like terms
3x-6+6=8-20x+6 --> Add 6 to both sides, to remove it from the right side
3x=-20x+14
3x+20x=-20x+14+20x --> Add 20x to both sides, to remove it from the left side
23x=14
[tex]\frac{23x}{23}=\frac{14}{23}[/tex] --> Divide both sides by 23
x = 14/23
Perform the operation. (-4x^2-2x-6)-(-7x^2-2x-2)
Answer:
3x²-4
Step-by-step explanation:
1 distribute
(-4x²-2x-6)+7x²+2x+2
2 eliminate redudant parentheses
-4x² -2x - 6+7x² +2x+2
3 Add the numbers
-4x²-2x-4+7x²+2x
4 Combine like terms
3x²-2x-4+2x
5 Combine like terms
3x²-4
Answer:
[tex]3x^{2} -4[/tex]
Step-by-step explanation:
Before solving this you have to know that,
( - ) × ( - ) = ( + )
( + ) × ( + ) = ( + )
( - ) × ( + ) = ( - )
Let us solve now.
[tex](-4x^2-2x-6)-(-7x^2-2x-2)[/tex]
[tex](-4x^2-2x-6)+7x^{2} +2x+2[/tex]
[tex]-4x^2-2x-6+7x^{2} +2x+2[/tex]
Now combine like terms
[tex]-4x^{2}+7x^{2} -2x+2x-6+2[/tex]
[tex]3x^{2} -4[/tex]
Hope this helps you .
Let me know if you have any other questions :-)
A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times as long
the banner and the poster have perimeters 24 inches. What are the lengths and of widths of the poster and the banner?
Rectangular Poster:
Length = 9
Width = 3
Rectangular Banner:
Length = 10
Width = 2
Hope this is helpful!
What is the slope of this graph?
0.3
-3
los
1
3
3
1
2 3 4 5
Answer:
A
Step-by-step explanation:
Use the formula rise/run. The rise, in this case, was 3 and the run was 1. There for it would be 3/1 which is simplified to 3.
benny uses 2/5 grams (G) of toothpaste each time he brushes his teeth. If benny buys 30-g tube, how many times will be able to brush his teeth?
Answer:
75
Step-by-step explanation:
First divide 2/5 to get 0.4. Then divide 30 by 0.4 to get the answer. A simple way to think about it is how many 0.4 grams are in 30 gram tube.
Find the slope of the line that passes through the points given in the first column and match them with the appropriate result. (10,7) and (1,2)\left(10,7\right)\ and\ \left(1,2\right)(10,7) and (1,2)
Answer:
Step-by-step explanation:
1) The slope of line with the coordinate points (10, 7) and (1, 2) is [tex]\frac{5}{9}[/tex].
2) The slope of line with the coordinate points (9, 9) and (1, 16) is [tex]-\frac{7}{8}[/tex].
3) The slope of line with the coordinate points (9, 3) and (2, 1) is [tex]\frac{2}{7}[/tex].
4) The slope of line with the coordinate points (8, 8) and (1, 2) is [tex]\frac{6}{7}[/tex].
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
From the given table, we have
1) The coordinate points are (10, 7) and (1, 2)
Here, slope [tex]=\frac{(2-7)}{(1-10)}[/tex]
[tex]=\frac{5}{9}[/tex]
2) The coordinate points are (9, 9) and (1, 16)
Here, slope [tex]=\frac{(16-9)}{(1-9)}[/tex]
[tex]=-\frac{7}{8}[/tex]
3) The coordinate points are (9, 3) and (2, 1)
Here, slope [tex]=\frac{(1-3)}{(2-9)}[/tex]
[tex]=\frac{2}{7}[/tex]
4) The coordinate points are (8, 8) and (1, 2)
Here, slope [tex]=\frac{(2-8)}{(1-8)}[/tex]
[tex]=\frac{6}{7}[/tex]
Therefore,
1) The slope of line with the coordinate points (10, 7) and (1, 2) is [tex]\frac{5}{9}[/tex].
2) The slope of line with the coordinate points (9, 9) and (1, 16) is [tex]-\frac{7}{8}[/tex].
3) The slope of line with the coordinate points (9, 3) and (2, 1) is [tex]\frac{2}{7}[/tex].
4) The slope of line with the coordinate points (8, 8) and (1, 2) is [tex]\frac{6}{7}[/tex].
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Simplify (y²z⁴)³ and explain answer
Answer:
y^6 z^12
Step-by-step explanation:
When the bases are the same that means that the powers on the inside can be multiplied by whatever is outside.
Hope this helps :)
What is -7w-4-5w+13 simplified?
Given f(x) = 3x+5x and g(x) = sqrt x+ 4
find f(g(12))
Answer:
Below in bold.
Step-by-step explanation:
g(12) = √12 + 4
so f(g(12))
= 3(√12 + 4) + 5(√12 + 4)
= 8(√12 + 4)
= 59.71 to nearest hundredth.
#3: Classify the number below. Select all that apply.
-8
A. Real Number
B. Irrational
C. Rational
D. Integer
E. Whole
F. Natural
On Tuesday, it snowed 15 inches in 6 hours. On Friday, it snowed 30 inches in 8 hours. On which day did it snow at a greater rate each hour? How much more per hour? please answer asap
Answer: Friday, 1.25 more per hour
Step-by-step explanation: if we take the inches it snowed and divide it by the hours, we get the rate of snowfall for one hour. 15/6=2.5 and 30/8=3.75
To get how much more we take the bigger snowfall per hour minus the smaller snowfall per hour 3.75-2.5=1.25
Pls help! Will mark Branliest!! 50 points for whoever answers!!!!!!
Answer: See below
Step-by-step explanation:
Isolate x for x-2y+2z=9
3x=9+2y
[tex]x=\frac{9+2y}{3}[/tex]....(1)
Substitute (1) into the 2nd equation
[tex]\begin{bmatrix}-\frac{9+2y}{3}+3y=-4\\ 2\cdot \frac{9+2y}{3}-5y+3z=16\end{bmatrix}[/tex]
[tex]\frac{3\left(-9+7y\right)}{3}=3\left(-4\right)[/tex]
7y=-3
y=-3/7
Substitute y=-3/7
[tex]\begin{bmatrix}3z+\frac{18-11\left(-\frac{3}{7}\right)}{3}=16\end{bmatrix}[/tex]
[tex]\begin{bmatrix}3z+\frac{53}{7}=16\end{bmatrix}[/tex]
Isolate z by substituting it
[tex]3z+\frac{53}{7}=16[/tex]
[tex]\frac{3z}{3}=\frac{\frac{59}{7}}{3}[/tex]
[tex]z=\frac{59}{21}[/tex]
For x =9+2y/3 substitute z=59/21 and y=-3/7
[tex]x=\frac{9+2\left(-\frac{3}{7}\right)}{3}[/tex]
[tex]x=\frac{19}{7}[/tex]
[tex]x=\frac{19}{7},\:z=\frac{59}{21},\:y=-\frac{3}{7}[/tex]
Answer:
(1, - 1, 3 )
Step-by-step explanation:
x - 2y + 2z = 9 → (1)
- x + 3y = - 4 → (2)
2x - 5y + 3z = 16 → (3)
Add (1) and (2) term by term to eliminate x
y + 2z = 5 → (4)
Multiply (2) by 2
- 2x + 6y = - 8 → (5)
Add (3) and (5) term by term to eliminate x
y + 3z = 8 → (6)
Subtract (6) from (4) term by term to eliminate y
- z = - 3 ( multiply both sides by - 1 )
z = 3
Substitute z = 3 into (4)
y + 2(3) = 5
y + 6 = 5 ( subtract 6 from both sides )
y = - 1
Substitute y = - 1, z = 3 into (1) and solve for x
x - 2(- 1) + 2(3) = 9
x + 2 + 6 = 9
x + 8 = 9 ( subtract 8 from both sides )
x = 1
solution is (1, - 1, 3 )
ANSWER PLZZ NO LINKS PORFA
How many miles longer is Trail A than Trail B?
round 0.006772 to 1 significant figure
Answer:
0.007
Step-by-step explanation:
0's before other numbers are non-significant. Then you just round your number.
Hope that helps
WHAT DOES AN ANIMAL BREEDER DO?????????
I LITERALLY NEED HELP ON THIS ONE!!
Some school commercial thingy.
Answer:
Breeders cross animals of the same species with desirable traits to create desirable offspring.
Step-by-step explanation:
Lester has 2 toy cars. Ivan has t times as many toy cars as Lester. Write an expression that shows how many toy cars Ivan has
Answer:
I=2t
Step-by-step explanation:
ivan has 2 times t
Solve the following quadratic equation for all values of x in simplest form.
2(5x + 9)2 + 10 = 28
Step-by-step explanation:
x = 2/5 or x = 0 Hope that will help
PLS HELP MEE :((
Write an equation representing the area Felicia covered, y, in terms of the number of tiles she used, x.
y =
Answer:
Check the picture below
Step-by-step explanation:
Please help will mark brainliest 12 x 12 - 44
Answer:
(12 x 12) - 44 = 100
Step-by-step explanation:
= 3 and 1/2 × 3 and 1/2
Step-by-step explanation:
please mark me as brainlest
Solve for x the equation 6cos^2 x+4sin^2 x=5.Forex 2 question 6 cos square x + 4 sin square x is equal to 5
Step-by-step explanation:
[tex]6 \cos {}^{2} (x) + 4 \sin {}^{2} (x) = 5[/tex]
[tex]6(1 - sin {}^{2} x) + 4 \sin {}^{2} (x) = 5[/tex]
[tex]6 - 6 \sin {}^{2} (x) + 4 \sin {}^{2} (x) = 5[/tex]
[tex]6 - 2 \sin { }^{2} (x) = 5[/tex]
[tex] - 2 \sin {}^{2} (x) = - 1[/tex]
[tex] \sin {}^{2} (x) = \frac{1}{2} [/tex]
[tex] \sin(x) = \frac{1}{ \sqrt{2} } [/tex]
Take the arc Sine of the function
[tex]arcsin( \frac{1}{ \sqrt{2} } ) = \frac{\pi}{4} [/tex]
Finally, Sine is a periodic function so it has two answers within the interval (0, 2 pi)
Use the identity
[tex] \sin(x) = \sin(x + \pi) [/tex]
We know that
[tex] \sin( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} } [/tex]
so using the identity
[tex] \sin( \frac{\pi}{4} + \pi ) = \sin( \frac{5\pi}{4} ) [/tex]
So we have two answers.
[tex]( \frac{\pi}{4} )[/tex]
[tex]( \frac{5\pi}{4} )[/tex]
Help me with this pleassssseeeedeeeeeeee..
Luis has $4.00 from his allowance. He visits an arcade where soda costs $0.75 and video games cost $0.25. Which of the following expressions represents the amount of money Luis will have left if he buys one soda and plays "g" video games? *
5 points
4.00 - 0.25 - 0.75g
4.00 + 0.75 + 0.25g
4.00 - 0.75 - 0.25g
4.00 - 0.25 + 0.75g
Answer: c
Step-by-step explanation:
1) Find the probability of rolling a
number greater than 3 on a standard
number cube.
Answer:
50%
Step-by-step explanation:
5(x-2)-3= 5x-13
help me plz
Can someone help me with these 2 problems I’ve been stuck on them for a very long time :’) tysm!!
Answer:
Christmas How many pouds this proportion to solve
I need help on this question
x = -7
hope this helps!
Help plz im on a timer at school
Answer:
it is reduction so the answer is B.
Step-by-step explanation:
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
[tex]\huge \bf༆ Answer ༄[/tex]
Let's solve this using unitary method ~
[tex] \sf3 \: seconds = 63 \: meters[/tex][tex] \sf1\: second= 63 \div 3 \: meters[/tex][tex] \sf1\: second= 21 \: meters[/tex][tex] \sf5\: seconds= 21 \times 5 \: meters[/tex][tex] \sf5\: seconds= 105 \: meters[/tex]Therefore , the ostrich will run 105 meters in 5 seconds.
Which geometric series converges? StartFraction 1 Over 81 EndFraction StartFraction 1 Over 27 EndFraction one-ninth one-third ellipsis 1 one-half one-fourth one-eighth ellipsis Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1 Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1.
The geometric series that converges from the listed option is [tex]1+\frac{1}{2} + \frac{1}{4} +\frac{1}{8} ,...[/tex] Option B is correct.
The nth term of a geometric sequence is expressed as;
[tex]a_n=ar^{n-1}[/tex]
a is the first term of the sequencer is the common ration is the number of terms.For a geometric sequence to converge, the modulus of its common ratio must be less than 1 (|r| < 1), otherwise, it diverges.
For the first series given as [tex]\frac{1}{81} + \frac{1}{27} +\frac{1}{9} +\frac{1}{3}+ ,...[/tex]
[tex]r = \frac{1}{27} \div \frac{1}{81}\\r=\frac{1}{27} \times 81\\r=\frac{81}{27} \\r=3 > 1[/tex]
Since the common ratio of the sequence is greater than 1, hence the series diverges.
For the series [tex]1+\frac{1}{2} + \frac{1}{4} +\frac{1}{8} ,...[/tex]
[tex]r=\frac{1/2}{1} =\frac{1/4}{1/2} = \frac{1}{2}[/tex]
Since the common ratio of the sequence is less than 1, hence the series converges.
Learn more on convergence of series here: https://brainly.com/question/14294471