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love history [14]
3 years ago
14

Translate the triangle. Then enter the new coordinates. A(-3, 4) A'([?], [?]) B'([ ], [ ] C([],[]) B(0, 1) C(-4,1)

Mathematics
1 answer:
Sedbober [7]3 years ago
7 0

Answer:

The new coordinates are A'(x,y) = (3, 0), B'(x,y) = (6, -3) and C'(x,y) = (2, -3).

Step-by-step explanation:

Vectorially speaking, the translation of a point can be defined by the following expression:

V'(x,y) = V(x,y) + T(x,y) (1)

Where:

V(x,y) - Original point.

V'(x,y) - Translated point.

T(x,y) - Translation vector.

If we know that A(x,y) = (-3,4), B(x,y) = (0,1), C(x,y) = (-4,1) and T(x,y) = (6, -4), then the resulting points are:

A'(x,y) = (-3, 4) + (6, -4)

A'(x,y) = (3, 0)

B'(x,y) = (0,1) + (6, -4)

B'(x,y) = (6, -3)

C'(x,y) = (-4, 1) + (6, -4)

C'(x,y) = (2, -3)

The new coordinates are A'(x,y) = (3, 0), B'(x,y) = (6, -3) and C'(x,y) = (2, -3).

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The Prize Place has 252 toys to be divided equally among 6 piñatas.How many toys will go into each piñata?
Mumz [18]
This is an example of division. 252/6=42. So 42 toys will go into each pinata.
8 0
3 years ago
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Gelneren [198K]

Answer:

4

Step-by-step explanation:

Hurley drank between 4 and 5 liters of water for 8 different days and drank between 1 or 2 liters of water on 4 different days. To find the answer we have to use the following equation.

# of days Hurley drank (4-5 L) - # of days Hurley drank (1-2 L) = # of more days

8 - 4 = 4

4 0
3 years ago
For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4
Elina [12.6K]

Answer:

<em>C.</em> (5-\frac{1}{2})^6

Step-by-step explanation:

Given

15(5)^2(-\frac{1}{2})^4

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

Sum = 2 + 4

Sum = 6

Each term of a binomial expansion are always of the form:

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

Where n = the sum above

n = 6

Compare 15(5)^2(-\frac{1}{2})^4 to the above general form of binomial expansion

(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......

Substitute 6 for n

(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......

[Next is to solve for a and b]

<em>From the above expression, the power of (5) is 2</em>

<em>Express 2 as 6 - 4</em>

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

By direct comparison of

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

and

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

We have;

^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4

Further comparison gives

^nC_r = 15

a^{n-r} =(5)^{6-4}

b^r= (-\frac{1}{2})^4

[Solving for a]

By direct comparison of a^{n-r} =(5)^{6-4}

a = 5

n = 6

r = 4

[Solving for b]

By direct comparison of b^r= (-\frac{1}{2})^4

r = 4

b = \frac{-1}{2}

Substitute values for a, b, n and r in

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

Solve for ^6C_4

(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......

<em>Check the list of options for the expression on the left hand side</em>

<em>The correct answer is </em>(5-\frac{1}{2})^6<em />

3 0
3 years ago
-2(3x+9)=-54<br><br> AND 2(3x+4) -3x=35 <br><br> SHOW WORK PLEASE
Naily [24]

Answer:

1. x=6

2. x=9

Step-by-step explanation:

1.

-2(3x+9)=-54\\-6x-18=-54\\+18 +18\\-6x=-36\\\frac{-6x}{-6} = \frac{-36}{-6}\\x=6

2.

2(3x+4)-3x=35\\6x+8-3x=35\\3x+8=35\\-8 -8\\3x=27\\\frac{3x}{3} =\frac{27}{3} \\x=9

<u>Written Explanation: </u>

1.

-2x(3x+9)=-54

-6x-`8=54 (Distributive property)

Add 18 to both sides

-6x=-36

Divide both sides by -6 (negative divided by a negative equals a positive)

x=6

2.

2(3x+4)-3x=35

6x+8-3x=35 (distributive property)

3x+8=35 (combine Iike terms and then subtract them 6x-3x=3x)

Subtract 8 from both sides

3x=27

Divide both sides by 3

x=9

5 0
3 years ago
At 10:00 a.m., Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han runs
Dominik [7]

Answer:

2.5 miles, 5 miles, no

Step-by-step explanation:

3 0
2 years ago
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