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frosja888 [35]
3 years ago
9

(03.01 MC)

Mathematics
1 answer:
vekshin13 years ago
6 0

Answer:

Option (1) will be the answer.

Step-by-step explanation:

Coordinates of the points A and B lying on the line f are (0, 2) and (2, 0) respectively.

Slope of the line f,

m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

m_{1}=\frac{2-0}{0-2}

m_{1}=-1

After dilation of line f by a scale factor of 2, coordinates of A' and B' will be,

Rule for dilation,

(x, y) → (kx, ky)

Where k = scale factor

A(0, 2) → A'(0, 4)

B(2, 0) → B'(4, 0)

Slope of line f',

m_{2}=\frac{0-4}{4-0}

m_{2}=-1

Since, m_{1}=m_{2}=-1

Therefore, both the lines f and f' will be parallel.

Option (1) will be the answer.

You might be interested in
10. RECREATION In a game of kickball, Rickie has to kick the
wel

Answer:

The angle Rick must kick the ball to score is an angle between the lines BX and BZY which is less than or equal to 32°

Step-by-step explanation:

The given measures of the of the angle formed by the tangent to the given circle at X and the secant passing through the circle at Z and Y are;

m\widehat{XZ}  = 58^{\circ}

m\widehat{XY}  = 122^{\circ}

The direction Rick must kick the ball to score is therefore, between the lines BX and BXY

The angle between the lines BX and BXY = ∠XBZ = ∠XBY

The goal is an angle between m\widehat{XY}

Let 'θ' represent the angle Rick must kick the ball to score

Therefore the angle Rick must kick the ball to score is an angle less than or equal to ∠XBZ = ∠XBY

By the Angle Outside the Circle Theorem, we have;

The angle formed outside the circle = (1/2) × The difference of the arcs intercepted by the tangent and the secant

\therefore \angle XBZ = \dfrac{1}{2} \times \left (m\widehat{XY}  -m\widehat{XZ} \right)

We get;

∠XBZ = (1/2) × (122° - 58°) = 32°

The angle Rick must kick the ball to score, θ = ∠XBZ ≤ 32°

4 0
2 years ago
can someone help me with this? this is algebra 2 question and please show me all work (orderd pair, vertex, graph ect..)
Andrews [41]
To find the maximum height you need to find the vertex:(h,k)  
Your equation is in vertex form a(x-h)+k and the vertex is (h,k) where k is the maximum height and the h is the distance it went to reach the maximum height.
k=6 so the kangaroo's maximum height is 6 feet.

To find how long is the kangaroo's jump, take a look at the graph. You will notice that the parabola ends at the distance the kangaroo jumped. You will also see that it is the one of the x-intercepts. 

 
 -.03(x-14)^2+6=0
-.03(x-14)^2+6-6=0-6
-.03(x-14)^2=-6
-.03/-.03(x-14)=-6/-.03
(x-14)^2=200
[(x-14)^2]^.5=200^.5
x-14=(200)^.5
x-14+14=(200)^.5+14
x≈28.14 feet
The kangaroo jumped a distance of 28.14 feet.

You will notice that the square root of a number gives you two solutions a positive and a negative one. The other solution is -.14, which we know distance is not negative so we do not use that solution. Also, I used the ^.5 instead of using the square root. It is the same. 


8 0
3 years ago
Consider the following sets of matrices: M2(R) is the set of all 2 x 2 real matrices; GL2(R) is the subset of M2(R) with non-zer
defon

Answer:

Step-by-step explanation:

REcall the following definition of induced operation.

Let * be a binary operation over a set S and H a subset of S. If for every a,b elements in H it happens that a*b is also in H, then the binary operation that is obtained by restricting * to H is called the induced operation.

So, according to this definition, we must show that given two matrices of the specific subset, the product is also in the subset.

For this problem, recall this property of the determinant. Given A,B matrices in Mn(R) then det(AB) = det(A)*det(B).

Case SL2(R):

Let A,B matrices in SL2(R). Then, det(A) and det(B) is different from zero. So

\text{det(AB)} = \text{det}(A)\text{det}(B)\neq 0.

So AB is also in SL2(R).

Case GL2(R):

Let A,B matrices in GL2(R). Then, det(A)= det(B)=1 is different from zero. So

\text{det(AB)} = \text{det}(A)\text{det}(B)=1\cdot 1 = 1.

So AB is also in GL2(R).

With these, we have proved that the matrix multiplication over SL2(R) and GL2(R) is an induced operation from the matrix multiplication over M2(R).

7 0
3 years ago
How would I show 2/5 as a division problem? Please explain using complete sentences.
dangina [55]

Answer:

There are many ways to show it like-

Step-by-step explanation:

2/5 as it’s already shown, or you can use 2 divide by 5, many people use 2[5] that’s the ways they showed my in my school idk if its different for you

5 0
3 years ago
Read 2 more answers
3x-9x+6=20-3x+4x Please answer.
fomenos
I gotchu.
<span>3x-9x+6=20-3x+4x
Combine like terms.
-6x+6=20+x
Bring x over to the left side.
-x            -x
-7x+6=20
bring 6 to the right side.
     -6   -6
-7x=14
Divide -7 on both sides to isolate x.
x= -2

CHECK
</span><span>3x-9x+6=20-3x+4x
-6(-2)+6=20+(-2)
18=18 
ANSWER: x= -2</span>
6 0
3 years ago
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