All categories

3 years ago

A and B are complementary angles. If m_A = (6x + 29) and m

Mathematics

2 answers:

Liono4ka [1.6K]3 years ago

6 0

Answer:

m∠ $A=77$ °

Step-by-step explanation:

Complementary angles are a pair of angles whose measures have a sum of $90$ °. Since m∠ $A$ = $6x+29$ and m∠ $B$ = $x+5$ , we can write the following equation to solve for $x$ :

$6x+29+x+5=90$

Solving for $x$ , we get:

$6x+29+x+5=90$

$7x+34=90$ (Simplify LHS)

$7x+34-34=90-34$ (Subtract $34$ from both sides of the equation to isolate $x$ )

$7x=56$ (Simplify)

$\frac{7x}{7}=\frac{56}{7}$ (Divide both sides of the equation by $7$ to get rid of $x$ 's coefficient)

$x=8$

Therefore, m∠ $A=6x+29=6(8)+29=48+29=77$ °. Hope this helps!

almond37 [142]3 years ago

6 0

Answer:

The measurement of angle A is: 77°

Step-by-step explanation:

First of all, let us define complementary angles

The angles whose sum is 90° are called complementary angles.

Given angles are:

m∠A = 6x+29

m∠B = x+5

With respect to the definition, the sum of both angles will be 90°

Writing this mathematically we get

$A+B = 90\\6x+29+x+5 = 90\\7x+34=90\\7x = 90-34\\7x = 56\\\frac{7x}{7} = \frac{56}{7}\\x = 8$

Putting the value of x in the expression for angle A

$A = 6x+ 29 = 6(8)+29 =48+29\\A = 77$

Hence,

The measurement of angle A is: 77°

You might be interested in

Evaluate the integral e^xy w region d xy=1, xy=4, x/y=1, x/y=2

LUCKY_DIMON [66]

Make a change of coordinates:

$u(x,y)=xy$
$v(x,y)=\dfrac xy$

The Jacobian for this transformation is

$\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}$

and has a determinant of

$\det\mathbf J=-\dfrac{2x}y$

Note that we need to use the Jacobian in the other direction; that is, we've computed

$\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}$

but we need the Jacobian determinant for the reverse transformation (from $(x,y)$ to $(u,v)$ . To do this, notice that

$\dfrac{\partial(x,y)}{\partial(u,v)}=\dfrac1{\dfrac{\partial(u,v)}{\partial(x,y)}}=\dfrac1{\mathbf J}$

we need to take the reciprocal of the Jacobian above.

The integral then changes to

$\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv$
$=\displaystyle\frac12\int_{v=}^{v=}\int_{u=}^{u=}\frac{e^u}v\,\mathrm du\,\mathrm dv=\frac{(e^4-e)\ln2}2$

8 0

3 years ago

During a company's first full year in business, the price of oil increased $50. In the second year of business, the price of oil

Nonamiya [84]

Answer:

Step-by-step explanation:

Um 150 x 2 divided by 4 i believe

6 0

3 years ago

Solve for b 15=3b<br> Please I need help

IgorLugansk [536]

15=3b
15/3 = 3b/b
5= b

Isolate the variable by diving 3 on both sides

6 0

2 years ago

Latoya drives 8 miles to work in 13 minutes. What is her average rate, in miles per hour, when rounded to the nearest wholes num

Mama L [17]

Answer:

37 miles per hour

Step-by-step explanation:

To find the average rate (average speed) of Latoya in miles per hour, you would divide the distance traveled (in miles) by the time taken to travel (in hours).

So we know that Latoya traveled 8 miles in 13 minutes. We cannot divide 8 by 13, because 13 is in minutes, not hours. We must convert 13 minutes to hours before dividing.

There are 60 minutes in one hour, so to covert minutes into hours, we would divide the minutes (13) by 60. Doing this would give you 13/60. You cannot simplify the fraction 13/60, because 13 is a prime number. It would be best to just leave it as it is for now. So Latoya traveled for 13/60 hours.

Now, to find her average rate in miles per hour, you divide the distance traveled in miles (8 miles) by the time it took to travel in hours (13/60):

8 ÷ 13/60

Remember, a ÷ b/c = a × c/b. Using this:

8 ÷ 13/60 = 8 × 60/13 = 480/13 ≈ 37 rounded to the nearest whole number.

Latoya had an average rate of about 37 miles per hour.

I hope this helps. :)

6 0

2 years ago

Mary is going for a walk. She walks 12.5 miles in 5 hours. What is her speed

xz_007 [3.2K]

To find her speed, divide the total distance by the total time:

12.5 miles / 5 hours = 2.5 miles per hour.

3 0

3 years ago