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2 years ago

M <N=...the scale factor is 2

Mathematics

1 answer:

aivan3 [116]2 years ago

7 0

We know that the sum of the internal angles in each triangle is 180°.

Therefore we have the equation:

$m\angle C+m\angle D+m\angle E=180^o$

substitute and solve:

$79+(6x+11)+(7x-14)=180\\(6x+7x)+(79+11-14)=180\\13x+76=180\ \ \ |-76\\13x=104\ \ \ |:13\\x=8$

We have

$m\angle N=3x+18$

substitute the value of x to the expression:

$m\angle N=3(8)+18=24+18=42$

Answer: m∠N = 42 degrees

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Is -2/3(12b - 6 + 9b - 18) equivalent to 2b(b + 8)? Show your work.

AURORKA [14]

Answer:

No, they are not equivalent

Step-by-step explanation:

$\frac{-2}{3}(12b - 6 + 9b - 18) = \frac{-2}{3}(12b + 9b - 6 - 18)\\\\=\frac{-2}{3}(21b - 24)\\\\ = \frac{-2}{3}*21b -24*\frac{-2}{3}\\\\= -2*7b + 8*2\\\\= 2( -7b + 8)$

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3 years ago

Read 2 more answers

Find the value of x which satisfies the following equation. log2(x−1)+log2(x+5)=4

weqwewe [10]

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \: x = 3$

____________________________________

$\large \tt Solution \: :$

$\qquad \tt \rightarrow \: log_{2}(x - 1) log_{2}(x + 5) = 4$

$\qquad \tt \rightarrow \: log_{2} \{(x - 1)(x + 5) \} = 4$

[ log (x) + log (y) = log (xy) ]

$\qquad \tt \rightarrow \: ( x - 1)(x + 5) = {2}^{4}$

$\qquad \tt \rightarrow \: {x}^{2} + 5x - x - 5 = 16$

$\qquad \tt \rightarrow \: {x}^{2} + 4x - 5 - 16 = 0$

$\qquad \tt \rightarrow \: {x}^{2} + 4x -21 = 0$

$\qquad \tt \rightarrow \: {x}^{2} + 7x - 3x - 21 = 0$

$\qquad \tt \rightarrow \: x(x + 7) - 3(x + 7) = 0$

$\qquad \tt \rightarrow \: (x + 7)(x - 3) = 0$

$\qquad \tt \rightarrow \: x = - 7 \: \: or \: \: x = 3$

The only possible value of x is 3, since we can't operate logarithm with a negative integer in it.

$\qquad \tt \rightarrow \: x = 3$

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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2 years ago

Sketch a quadratic function with the given characteristics.

xeze [42]

Answer:

See photo below

Add arrows to the two ends of the parabola.

Step-by-step explanation:

To sketch this quadratic function, we to connect three dots: the two roots and a vertex.

The given roots are -1 and 1.

Draw two dots at the x-intercepts, which are (-1, 0) and (1, 0).

Vertex dot: V (x, y)

The vertex x-coordinate always in the middle of the two roots. The middle of -1 and 1 is 0. That's the same as the y-axis.

V (0, y)

Since the function increases when x < 0, the parabola will open up.

We read from left to right. The greater numbers are towards the top of the page.

You can put the vertex anywhere on the y-axis that is below the x-axis.

7 0

2 years ago

Simplify if x = 5 and y = 4.

Oxana [17]

9 = 20 = 100 = 10 = -8 =
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3 0

2 years ago

Dhanraj spent $204.20 purchasing volleyballs and basketballs.

Lemur [1.5K]

Answer:

Number of volleyballs bought = 8

Number of basketballs bought = 11

Step-by-step explanation:

Given that:

Total amount spent = $204.20

Let,

x be the number of volleyballs

y be the number of basketballs

According to given statement;

y = x+3 Eqn 1

8.20x+12.60y=204.20 Eqn 2

Putting value of y from Eqn 1 in Eqn 2

8.20x + 12.60(x+3) = 204.20

8.20x + 12.60x + 37.80 = 204.20

20.80x = 204.20 - 37.80

20.80x = 166.40

Dividing both sides by 20.80

$\frac{20.80x}{20.80}=\frac{166.40}{20.80}\\x=8$

Putting x=8 in Eqn 1

y = 8+3 = 11

Hence,

Number of volleyballs bought = 8

Number of basketballs bought = 11

6 0

2 years ago