All categories

3 years ago

Will give brainleist please help ASAP

Mathematics

1 answer:

LenKa [72]3 years ago

3 0

Answer:

x = 14

Step-by-step explanation:

(5x - 19)° and (9x + 3)° are the measures of the interior angles on the same side of the transversal.

Therefore,

(5x - 19)° + (9x + 3)° = 180°

(5x - 19 + 9x + 3)° = 180°

(14x - 16)° = 180°

14x - 16 = 180

14x = 180 + 16

14x = 196

x = 196/14

x = 14

You might be interested in

How to graph y=3x+44

Andre45 [30]

This is in slope intercept form, which tells us directly where the y-intercept is, and what the slope is.

y=mx + b

m = slope

b = y-intercept

So, the y intercept is (0, 44)

And the slope is 3, or 3/1

7 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y =

miss Akunina [59]

Answer:

381.18 cubic units

Step-by-step explanation:

Graph the region:

desmos.com/calculator/iwvreqjz2m

The region is a trapezoid. When we rotate it about x = 1, we get a hollow cylinder shape. We can either use washer method or shell method to find the volume.

If we find the volume using washer method, we'll have to use two integrals, one for the triangular part of the trapezoid and one for rectangular part. If we use shell method, we only need one integral. So let's use shell method.

Cut a thin, vertical slice of the region. The width of this slice is dx. The height of the slice is y₂ − y₁ = x − 0 = x. The radius of the shell is x − 1.

The volume of the shell is:

dV = 2π (x − 1) (x) dx

dV = 2π (x² − x) dx

The total volume is the sum of all the shells from x=5 to x=7.

V = ∫ dV

V = ∫₅⁷ 2π (x² − x) dx

V = 2π ∫₅⁷ (x² − x) dx

V = 2π (⅓ x³ − ½ x² + C) |₅⁷

V = 2π [(⅓ 7³ − ½ 7² + C) − (⅓ 5³ − ½ 5² + C)]

V = 2π [⅓ 7³ − ½ 7² − ⅓ 5³ + ½ 5²]

V = 2π [⅓ (7³ − 5³) + ½ (5² − 7²)]

V = 2π [⅓ (218) + ½ (-24)]

V = 2π (72⅔ − 12)

V = 121⅓ π

V ≈ 381.18

The volume is approximately 381.18 cubic units.

6 0

2 years ago

The top of angies ladder is resting against the side of her house 22 feet above the ground.If the base of the ladder is 5 feet f

Andrews [41]

Answer:

Step-by-step explanation:

The attached diagram shows the triangle ABC formed by the ladder with the wall of the house.

Triangle ABC is a right angle triangle. It has a 90 degree angle. The length of the ladder forms the hypotenuse(AC)of the triangle. This length can be determined by applying Pythagoras theorem

Hypotenuse^2 = opposite ^2 + adjacent^2

AC^2 = 22^2 + 5^2

AC^2 = 484 + 25 = 509

AC = √509

AC = 22.56

The slope of the ladder is

(change in y)/(change in x)

Slope = 22/5 = 4.4

3 0

3 years ago

A playground is in the shape of a square with each side equal to 109 yards. It has skating rinks in the shape of the quadrants o

I am Lyosha [343]

Answer:

radius = 30 yd , cost of cement = $7065

Step-by-step explanation:

First we will find the area of the circular sectors. From that we can find the cost of cement and their radius.

The area of the playground is ...

playground area = (109 yd)^2 = 11,881 yd^2

Then the area of the skating rinks is:

rink area = playground area - remaining field

rink area = 11,881 yd^2 - 9,055 yd^2 = 2,826 yd^2

Then the cost of cement for the rink area is ...

(2826 yd^2)($2.50 yd^2) = $7065

The four quarter-circle skating rinks add to a total area of a full circle. That area is given by ...

A = πr^2

Put the values in the formula:

2826 = 3.14r^2

Divide both sides by 3.14

900 = r^2

By taking square root at both sides we get,

30 = r

The radius of each quadrant is 30 yards....

6 0

3 years ago

2/3 gas tank cuts 3 lawns how many does 1 gas tank cut

postnew [5]

(2/3) / 3 = 1/x...2/3 to 3 lawns = 1 to x lawns
cross multiply
(2/3)(x) = (3)(1)
2/3x = 3
x = 3 * 3/2
x = 9/2 or 4 1/2 lawns can be cut with a full tank of gas

8 0

2 years ago