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emmainna [20.7K]
3 years ago
9

Write the equation of the parallel line - x + 2y = 12 that goes through the

Mathematics
1 answer:
Oxana [17]3 years ago
6 0

Answer:

Step-by-step explanation:

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If AFGH<br> AQRS, find the measure of Q.
irakobra [83]

Answer:

D. 28°

Step-by-step explanation:

Since ∆FGH is congruent to ∆QRS, it follows that:

m\angle F = m\angle Q

Thus:

2x + 10 = 3x + 1 (Substitution)

Collect like terms

2x - 3x = -10 + 1

-x = -9

Divide both sides by -1

x = 9

\angle Q = 3x + 1

Plug in the value of x

\angle Q = 3(9) + 1

\angle Q = 28 degrees

7 0
3 years ago
9. A ladder of length 23 feet leans against the side of a building. The angle of elevation of the ladder is 76. Find the distanc
irakobra [83]

<h3><u>Answer:</u></h3>

  • B) 22.32 feet

\quad\rule{300pt}{1pt}

<h3><u>Solution</u><u>:</u></h3>

we are given that , a ladder is placed against a side of building , which forms a right angled triangle . We wre given one side of a right angled triangle ( hypotenuse ) as 23 feet and the angle of elevation as 76 ° . We can find the Perpendicular distance from the top of the ladder go to the ground by using the trigonometric identity:

\qquad\quad\bull ~{\boxed{\bf{ Sin\theta =\dfrac{Perpendicular}{Hypotenuse}}} }~\bull

Here,

  • hypotenuse = 23 feet
  • \theta = 76°
  • Value of Sin\theta = 0.97
  • Perpendicular = ?

\quad\dashrightarrow\quad \sf { sin\theta =\dfrac{P}{H}}

\quad\dashrightarrow\quad \sf { sin76° =\dfrac{P}{23}}

\quad\dashrightarrow\quad \sf { 0.97=\dfrac{P}{23}}

\quad\dashrightarrow\quad \sf {P = 0.97 \times 23 }

\quad\dashrightarrow\quad \sf { P = 22.32}

‎ㅤ‎ㅤ‎ㅤ~<u>H</u><u>e</u><u>n</u><u>c</u><u>e</u><u>,</u><u> </u><u>the </u><u>distance </u><u>from </u><u>the </u><u>top </u><u>of </u><u>the </u><u>ladder </u><u>to </u><u>the </u><u>ground </u><u>is </u><u>2</u><u>2</u><u>.</u><u>3</u><u>2</u><u> </u><u>feet </u><u>!</u>

\rule{300pt}{2pt}

4 0
2 years ago
Ben simplified this expression (2x^-4y^7 / 3x^3y^2)^3 Analyze bens work. did he simplify the expression correctly? If not, what
katovenus [111]

-c

No , he needed to apply the exponents to all factors in the product in the second step .

6 0
3 years ago
Will mark brainliest if right and you show your work!
Anna007 [38]

Answer:

(x - 5)(x + 8)

Step-by-step explanation:

Your equation is: x² + 3x - 40

1. Factor the quadratic

(a) Find two numbers that multiply to give -40 and add to give 3.

List the positive factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

One of the numbers must be negative. Start with the numbers near the middle of the list.

By trial and error, you will find that +8 and -5 work:

-5 × 8 = -40 and -5+8 = 3

(b) Rewrite 3x as -5x + 8x

x² - 5x + 8x - 40

(c) Factor the first two and the last two terms

x(x - 5) + 8(x - 5)

(d) Separate the common factor

x² + 3x - 40  = (x - 5)(x + 8)

2. Using Desmos

You can plot the equation with Desmos.

You get a parabola with x-intercepts at x = -8 and x = 5.

These are the solutions to

x + 8 =0 and x - 5 = 0, so

x² + 3x - 40 =  (x+ 8)(x - 5)

6 0
3 years ago
What is the range of f(x) = 4x?
antoniya [11.8K]
Range is all positive real numbers

answer is D. last one
8 0
3 years ago
Read 2 more answers
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