Answer:
1. x=3/2-y-3z/2
2.x=-y/2-17/3
3.x=3-5y/2-z/2
Step-by-step explanation:
i gusse
The position vector of p (relative to the origin) is op = (x, y). if the magnitude of op is 5 units, find the set of all possible values of (x, y), with x, y E z
Answer:
S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }
Step-by-step explanation:
Remember that the distance between two points (a, b) and (c, d) is given by:
[tex]distance = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
So, here we have that the distance between the point (x, y) and the origin, (0, 0) must have a magnitude of 5 units, then we want to solve:
[tex]5 = \sqrt{(x - 0)^2 + (y - 0)^2} \\5 = \sqrt{x^2 + y^2}[/tex]
If we square both sides, we get
[tex]5^2 = (\sqrt{x^2 + y^2} )^2\\25 = x^2 + y^2[/tex]
Now we want to find all the points (x, y) that meet this condition, suc that:
x ∈ Z
y ∈ Z
So both x and y must be integers.
So here we can just play with different values of x and y.
For example, if we define:
x = 0 we get:
25 = 0^2 + y^2
25 = y^2
√25 = y
Then we can have y = 5 or y = -5
from this we got two points:
(0, 5) and (0, - 5)
if x = 1 we have:
25 = 1^2 + y^2
25 - 1 = y^2
24 = y^2
There is no integer such that its square is equal to 24, so we can stop here.
if x = 2 or - 2, we have:
25 = 2^2 + y^2
25 = 4 + y^2
25 -4 = 21 = y^2
Again, there is no integer such that its square is equal to 21, so we can stop here.
if x = +3 or -3, we have:
25 = 3^2 + y^2
25 = 9 + y^2
25 - 9 = 16 = y^2
√16 = y
then we can have y = 4 or y = -4
from this we got four points:
(3, 4)
(-3, 4)
(3, -4)
(-3, -4)
And for symmetry, if x = 4 or -4 we have the points:
(-4, 3)
(4, 3)
(-4, -3)
(4, -3)
finally, again for symmetry, if we take x = 5 or x = -5 we have the points:
(5,0)
(-5, 0)
Concluding, the set of all possible values (x, y) is:
S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }
Each column of the matrix represents a vertex of a triangle. If Rosa scales the triangle by finding 3T, what are the vertices of the scaled triangle?
(3, 3), (3, 9), (9, 3)
(0, 0), (0, 6), (6, 0)
(3, 3), (0, 9), (9, 0)
(0, 0), (0, 9), (9, 0)
Answer:
(0,0), (0,9), (9,0)
Step-by-step explanation:
The matrix corresponding vertices are:
(0,0)
(0,3)
(3,0)
Rosa scales by 3T, so we need to multiply each point by 3.
(3*0, 3*0)
(0*3, 3*3)
(3*3, 0*3)
=
(0,0)
(0,9)
(9,0)
last answer choice is right.
pls mark me brainly
The vertices of the scaled triangle, 3T is, (0, 0), (0, 9), (9, 0).
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, A matrix [tex]T=\begin{bmatrix}0 & 0 & 3\\0 & 3 & 0\end{bmatrix}[/tex] represents the vertices of a triangle.
Let, ABC be the triangle,
So, A(0, 0), B(0, 3), C(3, 0).
Now, If [tex]T=\begin{bmatrix}0 & 0 & 3\\0 & 3 & 0\end{bmatrix}[/tex], Then [tex]3T=3\begin{bmatrix}0 & 0 & 3\\0 & 3 & 0\end{bmatrix}[/tex].
Therefore, [tex]3T=\begin{bmatrix}0 & 0 & 9\\0 & 9 & 0\end{bmatrix}[/tex].
Hence, The new vertices are, (0, 0), (0, 9), (9, 0).
learn more about matrices here :
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Students are asked to estimate the number of gumballs in a jar. Sam says there are 228 gumballs. In actuality, there are 240 gumballs. What is the percent error
Answer:
5%
Step-by-step explanation:
Percent error = (actual - estimated) / actual x 100
(240 - 228) / 240 x 100 = 5%
if you horizontally shift the square root parent function f(x)=√x left two units what is the equation of the new function
Answer:
[tex] \sqrt{x + 2} [/tex]
If you horizontally shift the square root parent function f(x)=√x left two units the equation of the new function is: g(x) = √(x + 2).
What is horizontal shift?A horizontal shift is a function transformation that shifts a graph to the left or right without changing its shape.
If we want to shift the square root parent function f(x) = √x two units to the left, we must replace the argument x with (x + 2), because a positive value of x + 2 gives us the same x value two units to the left.
So the equation of the new function is:
g(x) = √(x + 2)
This new function is the square root function shifted two units to the left. For any given input value of x, we add 2 to it before taking the square root. This causes the graph to shift horizontally to the left by two units.
Thus, g(x) = √(x + 2) will be the new function.
For more details regarding horizontal shift, visit:
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(5x)/7 - x/14 = 9/7 solve for the unknown value this is a linear equation
Step-by-step explanation:
[tex]\longmapsto \rm \dfrac{5x}{7} - \dfrac{x}{14} = \dfrac{9}{7} \\ [/tex]
[tex]\longmapsto \rm \dfrac{10x + x}{14} = \dfrac{9}{7} \\ [/tex]
[tex]\longmapsto \rm \dfrac{11x}{14} = \dfrac{9}{7} \\ [/tex]
→ 11x(7) = 14(9)
→ 77x = 126
→ x = 126 ÷ 77
→ x = 1.63
Can I plsss get some helpp
True or False: The following lengths form a right triangle:
a = 8 units
b = 6 units
C = 10 units
10
op
6
O True
O False
Answer:
True is the correct answer
Answer:
I believe the answer is true
Problem 2 : Using in the pattern in the image below, how many dots would be in Step 4
Answer:
20
Step-by-step explanation:
One pattern is that we are adding one row and one column for each step.
The first step has 1 row and 2 columns,
the second one has 2 rows and 3 columns,
and the third has 3 rows and 4 columns.
Thus, it would make sense for the fourth step to have 4 rows and 5 columns. This makes a rectangle with a length and a width, with the area of the rectangle being length * width. 4 * 5 = 20 as our number of dots
The lengths of the sides of a rectangle are in a ratio of 4:7. If the length is 31.5 in, find the width, perimeter, and area of this rectangle.
Answer:
L = 31.5 w = (4/7)31.5 = 18 p = 2 * 31.5 + 2 * 18 A = 31.5 * 18
Step-by-step explanation:
what is energy efficiency
Answer:
The goal to reduce the amount of energy used to provide products and services; saving the earth vibes.
What is the common ratio for this sequence: 4, -16, 64, -256, ...
A. R = - 2
B. R = - 4
C. R = 2
D. R = 4
Answer:
The answer is D I think :)))
The original price of a computer was reduced by 225 dollars. The new discounter price is 1274 dollars.
Answer:
1499
Step-by-step explanation:
Given that :
New discounted price = 1274
Let original price = p
Reduction in original price = 225
Original price is the sum of the reduction and the new discounted price
The Original price = Reduction in original price + new discounted price
P = 225 + 1274
P = 1499
The scatter plot below represents the amount of dog food a brand recommends
based on the weight of the dog.
Amount of Food per Day cups
20
40
60
No
100
Weight of Dog (b)
Which best describes the type of association shown in this scatter plot?
A
No association
B Nonlinear association
C Positive linear association
D Negative linear association
Answer:
positive linear association
Step-by-step explanation:
the slope is positive so the linear association is also positive and linear mean generaly in a line not on a curve like a nonlinear assciation.
can somebody help me with this question please!
fig 3 would take 18 triangle
fig 4 would take 30 small triangles
if its wrong i am sorry
Answer:
the answer is 33the answer is 18Given that y is directly proportional to x. If y = 30 and x= 5, write an equation that connects y with x.
Given:
y is directly proportional to x.
[tex]y=30[/tex] when [tex]x=5[/tex]
To find:
The equation that connects y with x.
Solution:
It is given that, y is directly proportional to x. So,
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is the constant of proportionality.
We have, [tex]y=30[/tex] when [tex]x=5[/tex]. Substituting these values in (i), we get
[tex]30=k(5)[/tex]
Divide both sides by 5.
[tex]\dfrac{30}{5}=k[/tex]
[tex]6=k[/tex]
Substituting [tex]k=6[/tex] in (i), we get
[tex]y=6x[/tex]
Therefore, the required equation is [tex]y=6x[/tex].
PLS HELP ASAAPPPP!! will mark brainliest if i can !!
Answer:
2nd option
Step-by-step explanation:
The discriminant b² - 4ac tells us about the nature of the roots
• If b² - 4ac > 0 then 2 real and distinct roots
• If b² - 4ac = 0 then 2 real and equal roots
• If b² - 4ac < 0 then the roots are not real
Here b² - 4ac = 15 > 0
Then there are 2 real and distinct roots
x = 2 and x = - 3 are possible solutions to the equation
Answer:
option b) x = 2 and x = -3
Step-by-step explanation:
If discriminant is greater than zero, then the quadratic equation will have two solutions.
If discriminant is equal to zero, then the quadratic equation will have only one solution.
If discriminant is less than zero no solution
Here the discriminant is 15 , which is greater than zero.
Therefore we will have to solutions.
There is only one option with two solutions for x.
So option b is the answer.
Mr yates owns a smoothie shop. To mix a batch of his famous orange punch smoothies, he uses 18 ounces of freshly squeezed orange juice. Each day he squeezes 560 ounces of fresh orange juice. How many batches of orange punch smoothies can he make in a day?
Answer:
31 batches
Step-by-step explanation:
Find how many batches of orange punch smoothies he can make by dividing 560 by 18:
560/18
= 31.11
Since we can only have a whole number answer, round down.
So, he can make 31 batches of orange punch smoothies.
Graph 8x-2y=1 and 4x+y=3
Answer:
no thanks i dont feel like doing all that work to help u. i apologize my dear friend bahahahahahahahahahahhahaha
Step-by-step explanation:
can someone help me I forget how to do this.
Answer:
If i recall Maria collected 34 cicadas
Answer:
17 Cicadas
Step-by-step explanation:
62 - 28 divided by two will give us the amount Maria collected.
62 - 28 = 34
34/2 = 17
Maria had 17 cicadas.
How to verify:
17 + 28 + 17 Should equal 62
34 + 28 = 62
plz help me I will give u branist and like u back plz help me I will also follow u
Answer:
hi, the answer is Nu5000
250×20=5000
I’ve never understood this, please help!
Answer:
-80
Step-by-step explanation:
So basically what we need to do is find the value of x that satisfies the equation.
When I mean satisfy, I basically mean a value of x that makes one side of the equals sign equal to the other side of the equals sign.
So in this case, we need -6 = -6.
To find this lets solve the equaion step by step:
-6=x/8+4
So first off, you always want to get the variable on one side, and the number on the other.
This means you want to subtract the 4 from both sides, leaving x/8:
-6=x/8+4
-4 -4
-10=x/8
Whenever x is not 1x, you have to divide or multiply to get it equal to 1x.
If this is a bit confusing, here is an example:
100=10x
We need 1x, but above is 10x. The reason why we want 1x is because it is the lowest ratio, and most accurate x value.
You can think of it like a 1 dollar bill. Its easier and better to use than per say a 3 dollar bill.
So in the example above you would divide by 10, since 10x/10 would equal 1x.
Remember the rule however, that what you do on one side you must do on the other. This emans you would divide both sides by 10:
100/10 =10x/10
=
10=1x
We have in our equation:
-10=x/8
Our x is lower than 1. It x/8. Whenever we have a value of x greater than 1, we divide, like we did in the example. However here, it is below x. So we multiply.
In this case we multiply by 8, since its x/8:
-10 * 8 = x/8 * 8
=
-80=x
So x is equal to -80.
I hope you understand it better now :D
Please help me solve my problem!!!
Answer:
The answer is E.
Step-by-step explanation:
A quadrilateral that has only one pair of parallel sides is called a Trapezoid.
Gretchen make a paper cone to hold a gift for a friend the paper cone was 10 inches high and had a radius of 4 inches find the volume of the paper cone to the nearest tenth use 3.14 for pi
Answer: [tex]167.5\ in.^3[/tex]
Step-by-step explanation:
Given
Height of paper cone [tex]h=10\ in.[/tex]
Radius of cone [tex]r=4\ in.[/tex]
The volume of the cone is given by
[tex]\Rightarrow V=\dfrac{1}{3}\pi r^2h[/tex]
Insert the values
[tex]\Rightarrow V=\dfrac{1}{3}\times 3.14\times 4^2\times 10\\\\\Rightarrow V=167.5\ in.^3[/tex]
Thus, the volume of the cone is [tex]167.5\ in.^3[/tex]
Which expression can be used to convert 100 USD to Japanese?
Answer:The expression that can be used to convert 100 USD to Japanese Yen is 100 USD = 100/Y Japanese Yen.
Step-by-step explanation:
What is the equation of the line that is perpendicular to the given line and passes through the point (5, 3)?
A.) 4x - 5y = 5
B.) 5x + 4y = 37
C.) 4x + 5y = 5
D.) 5x - 4y = 8
Answer: A , 4x - 5y = 5
Step-by-step explanation:
i just did it , duhhh
Answer:
a
Step-by-step explanation:
peter collects antique marbles. he has these two boxes full of marbles
Answer:
3 marbles
Step-by-step explanation:
and they have died inside too
Hydro Sunday in a right triangle the sum of the squares of the leg length is equal to the square of the high-profile tenseness length
Answer: hello your question is vague hence i will provide a more general answer
Area of a right angled triangle = 1/2 * b * h
Step-by-step explanation:
For a right- angled triangle; the sum of squares of the opposite and adjacent sides = square of the longest side ( i.e. hypothenuse )
hence the Area of a right angled triangle = 1/2 * b * h
where : b = adjacent , h = opposite side
PLZZ HELPPP!!!!!!!!!!
Answer:
$375.32
Step-by-step explanation:
100% - 40% = 80%
80/100 = 0.8 (multiplier)
521.28 x 0.8 = 417.024
417.024 to 417.02 (2 d.p.)
100 - 10 = (ans)/100 = 0.9
417.02 x 0.9 = 375.318
$375.32
Step 1: Find the sales price
The surfboard was marked down 40% of its original price, $521.28.
0.40(521.28) = 208.512
521.28 - 208.512 = 312.768
Step 2: Find the final price
We add the tax on the sales price, not the original price. The tax is 10% in this case.
0.10(312.768) = 31.2768
312.768 + 31.2768 = 344.0448
Final price = $344.04
---I did not round until the end in this case, but rounding at every step leads to an answer of $344.05
Hope this helps!
[tex]{(\frac{4}{3}) ^{-1} - (\frac{1}{4} )^{-1})}^{-1}[/tex]
Pls include steps
Step-by-step explanation:
(4/3)–1 = 3/4 and (1/4)–1 = 4/1
now we have,
(3/4 - 4)–1 = (-13/4)–1
= -4/13
Let f(x)=2(4)x+1−2. The graph of f(x) is translated 7 units to the left to form the graph of g(x).
in isosceles Triangle RST below what is the value of y
Answer:
second option
Step-by-step explanation:
y + y + 38 = 180 degree ( sum of interior angle of a triangle is 180 degree)
2y = 180 - 38
y = 142/2
y = 71 degree
Answer:
71 degrees
Step-by-step explanation:
Hi there!
All the interior angles of a triangle add up to 180 degrees.
Knowing this, we can construct the following equation:
[tex]180=y+y+38\\180=2y+38[/tex]
Subtract 38 from both sides
[tex]180-38=2y+38-38\\142=2y\\71=y[/tex]
I hope this helps!