If < A and < B are vertical angles, and < A = 5x - 1 degrees, and < B = 4x + 4 degrees, find x.
Select one:
a. 5 / 9
b. - 3
c. 5
d. 11

Answer:

1. about 11.18

2. about 8.66

Step-by-step explanation:

1. 5^2 + 10^2= 125

square root of 125 equals about 11.18

2. 10^2-5^2=75

square root of 75 equals about 8.66

Answer:

a=2

b=-3

c=2

d=0

Step-by-step explanation:

3a+b=3......1

3c-d=6.......2

a-b=5....... 3

a+b+d=2d-1

a+b=2d-d-1

a+b=d-1......4

taking equation 1 and 3 we get,

3a+b =3....... 1

a-b=5

a=5+b

substitute the value of a in equation 1 we get,

3*(5+b)+b=3

15+3b+b=3

4b=3-15

4b=-12

b=-12/4

b=-3

now putting the value of b in equation 3 we get,

a-b=5

a+3=5

a=5-3

a=2

substitute the value of a and b in equation 4 we get,

a+b=d-1

2-3=d-1

-1=d-1

d=-1+1

d=0

substitute the value of d in equation 2 we get,

3c-d=6

3c-0=6

3c=6

c=6/3

c=2

[tex]\\ \sf\longmapsto \left[{3a+b\atop a-b}\:\:\:{3c-d\atop a+b+d}\right]=\left[{3\atop 5}\:\:\;{6\atop 2d-1}\right][/tex]

Now constructing equations

[tex]\\ \sf\longmapsto 3a+b=3\dots(1)[/tex]

[tex]\\ \sf\longmapsto a-b=5\dots(2)[/tex]

[tex]\\ \sf\longmapsto 3c-d=6\dots(3)[/tex]

[tex]\\ \sf\longmapsto a+b+d=2d-1\dots(4)[/tex]

Adding eq(1) and (2)

[tex]\\ \sf\longmapsto 4a=8[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{8}{4}[/tex]

[tex]\\ \bf\longmapsto a=2[/tex]

Put the value in eq(2)

[tex]\\ \sf\longmapsto a-b=5[/tex]

[tex]\\ \sf\longmapsto b=a-5[/tex]

[tex]\\ \sf\longmapsto b=2-5[/tex]

[tex]\\ \bf\longmapsto b=-3[/tex]

put the values in eq(4)

[tex]\\ \sf\longmapsto a+b+d=2d-1[/tex]

[tex]\\ \sf\longmapsto 2+(-3)+d=2d-1[/tex]

[tex]\\ \sf\longmapsto d-1=2d-1[/tex]

[tex]\\ \sf\longmapsto d-2d=-1+1[/tex]

[tex]\\ \sf\longmapsto -d=0[/tex]

[tex]\\ \bf\longmapsto d=0[/tex]

Put the value in eq(3)

[tex]\\ \sf\longmapsto 3c-d=6[/tex]

[tex]\\ \sf\longmapsto 3c-0=6[/tex]

[tex]\\ \sf\longmapsto 3c=6+0[/tex]

[tex]\\ \sf\longmapsto 3c=6[/tex]

[tex]\\ \sf\longmapsto c=\dfrac{6}{3}[/tex]

[tex]\\ \sf\longmapsto c=2[/tex]

Answer:

5^3

Step-by-step explanation:

5^1 x 5^2

indices rules when multiplying you add the powers to 1+2=3

5^3

Answer:

always

Step-by-step explanation:

Zero is always greater than any negative integer.

Answer:

14 yards shorter

Step-by-step explanation:

Use Pythagoras' Theorem

a²+b²=c²

16²+63²=4225

√4225= 65yd

The diagonal line (c) is 65 yards long

16 + 63 = 79 yd

It would be 14 yards shorter (79-65)

Answer:

The height is 12 cm

Step-by-step explanation:

Hi there!

We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).

This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.  

One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.

Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:

a=15

b=20

c=25  

Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle

15²+20²=25²

225+400=625

625=625

So we can safely say that the triangle is a right triangle

This makes the problem way easier, as there are 2 ways to find the area of a right triangle:

The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2

The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2

First, we need to figure out which sides are the legs, and which side is the hypotenuse

By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs

So let's find the area of the triangle using the legs

A=[tex]\frac{15*20}{2}[/tex]=[tex]\frac{300}{2}[/tex]=150

So the area of the triangle is 150 cm²

However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2

Which means that the area is also:

A=[tex]\frac{25x}{2}[/tex] cm²

As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)

[tex]\frac{25x}{2}=150[/tex]

Multiply both sides by 2

25x=300

Divide both sides by 25

x=12 cm

So the height of the triangle is 12 cm

Hope this helps!

Answer:

x + 3

Step-by-step explanation:

Image below

Answer:

b

Step-by-step explanation:

Answer:

(AB) is longer than (AC)

Step-by-step explanation:

1. Approach

Use the distance formula to find the length of the segments (AC) and (AB); substitute their endpoints into the distance formula and simplifying to solve for the length. After finding the length of each segment, compare their lengths to find out which of the statements is true. The distance formula is as follows:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where ([tex](x_1,y_1)[/tex]) and ([tex](x_2,y_2)[/tex]) are the endpoints of the segment.

2. Find the length of (AC)

Coordinates of point (A): [tex](-1,1)[/tex]

Coordinates of point (C): [tex](-4,4)[/tex]

Substitute these points into the distance formula,

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]D=\sqrt{((-1)-(-4))^2+((1)-(4))^2}[/tex]

Simplify,

[tex]D=\sqrt{((-1)-(-4))^2+((1)-(4))^2}[/tex]

[tex]D=\sqrt{(-1+4)^2+(1-4)^2}[/tex]

[tex]D=\sqrt{(3)^2+(-3)^2}[/tex]

[tex]D=\sqrt{9+9}[/tex]

[tex]D=\sqrt{18}[/tex]

3. Find the length of (AB)

Coordinates of point (A): [tex](-1,1)[/tex]

Coordinates of point (B): [tex](0,-4)[/tex]

Substitute these points into the distance formula,

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]D=\sqrt{((-1)-(0))^2+((1)-(-4))^2}[/tex]

Simplify,

[tex]D=\sqrt{((-1)-(0))^2+((1)-(-4))^2}[/tex]

[tex]D=\sqrt{(-1-0)^2+(1+4)^2}[/tex]

[tex]D=\sqrt{(-1)^2+(5)^2}[/tex]

[tex]D=\sqrt{1+25}[/tex]

[tex]D=\sqrt{26}[/tex]

4. Find the correct statement

(AB) is longer than (AC)

This statement is true for the following reason:

[tex]\sqrt{18}>\sqrt{26}[/tex]

Answer:

24units

Step-by-step explanation:

From the parallelogram given, we can see that the line FH bisects EG at V. Hence;

GE = 2GV.

Given that

GV = 12

GE = 2(12)

GE = 24

Hence the measure of the length GE is 24units

Answer:

keep the pic clearly

Step-by-step explanation:

keep the pic clearly

From eq(1)

[tex]\\ \sf\longmapsto x+y=4[/tex]

[tex]\\ \sf\longmapsto x=4-y\dots(3)[/tex]

[tex]\\ \sf\longmapsto 2x-y=5[/tex]

[tex]\\ \sf\longmapsto 2(4-y)-y=5[/tex]

[tex]\\ \sf\longmapsto 8-2y-y=5[/tex]

[tex]\\ \sf\longmapsto 8-3y=5[/tex]

[tex]\\ \sf\longmapsto 8-5=3y[/tex]

[tex]\\ \sf\longmapsto 3y=3[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{3}{3}[/tex]

[tex]\\ \sf\longmapsto y=1[/tex]

Put value in eq(3)

[tex]\\ \sf\longmapsto x=4-y[/tex]

[tex]\\ \sf\longmapsto x=4-1[/tex]

[tex]\\ \sf\longmapsto x=3[/tex]

Answer:

1 mile = 5280 feet, then

Find 1000 feet in miles:

[tex]\\ \sf\longmapsto 1feet= \dfrac{1}{5280}miles[/tex]

Now

[tex]\\ \sf\longmapsto 1000feet[/tex]

[tex]\\ \sf\longmapsto 1000\times \dfrac{1}{5280}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1000\times 1}{5280}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1000}{5280}[/tex]

[tex]\\ \sf\longmapsto 0.18miles[/tex]

Let x = 3.191919…. Then 100x = 319.191919…, and we have

100x - x = 319.191919… - 3.191919…

99x = 316

x = 316/99

Next, we have

316 = 297 + 19 = 3 × 99 + 19

so

316/99 = (3 × 99 + 19)/99 = 3 + 19/99

Answer:

a) 7085g

b) 6346g

c) 5342g

Step-by-step explanation:

1kg = 1000g

Answer: 111.1 m

Step-by-step explanation:

(30*2)/60 = 1 km ( the tunnel length is 1 Km.)

1 Km = 1000 m.

1000/9 = 111.1 m.

Answer:

13/45

Step-by-step explanation:

x = .2888888888

100(x + .2888888)

100x + 28.8888

 10x + 2.88888

90x = 26

x = 26/90 = 13/45

Answer:

D

Step-by-step explanation:

graph it

Answer:

RS, RT, ST

Step-by-step explanation:

We require the third angle in the triangle

∠ T = 180° - (92 + 71)° = 180° - 163° = 17°

The shortest side is opposite the smallest angle

∠ T = 17° → opposite side RS

The longest side is opposite the largest angle

∠ R = 92° → opposite side ST

Then sides from shortest to longest is

RS, RT, ST

Answer: 2, acute equilateral

Step-by-step explanation:

the image shows a triangle with all 3 sides congruent and 3 acute angles

Answer:  [tex](x-3)^2 + (y-2)^2 = 16[/tex]

Explanation:

The center of this circle is point A(3,2). These coordinates are the (h,k) values.

The radius is r = 4

Plug those three items into the template [tex](x-h)^2 + (y-k)^2 = r^2[/tex] to arrive at the final answer shown above.

Answer:

it should be 90 I could be wrong

I think the answer is 240

Answer:

12/20 = 60%

Step-by-step explanation:

The probability that the candy Roger selected was NOT a gummy worm;

P(Not a gummy worm) = 0.6

Miniature peanut butter cups = 5

Dark Chocolate bars = 7

Gummy worms = 8

Total number of candy bars = 5 + 7 + 8

Total number of candy bars = 20

Probability is found as; number of possible outcomes/number of events.

P(randomly selected is a gummy worm) = 8/20

P(randomly selected is a gummy worm) = 0.4

Probability that it was not a gummy worm = 0.6

Read more at; https://brainly.com/question/13160116

Answer: C . 147π / 4 mi²

Concept:

The sector is the part of a circle is enclosed by two radii of a circle and their intercepted arc.

A = (θ / 360) πr²

θ = angle of the sector

π = constant

r = radius

Solve:

Given variable

θ = 270°

r = 7 mi

Given formula

A = (θ / 360) πr²

Substitute values into the formula

A = (270 / 360) π (7)²

Simplify exponents

A = (270 / 360) π 49

Simplify by multiplication

A = (147 / 4) π

A = 147π / 4

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x=50

Step-by-step explanation:

Let's look at the red angle. if a flat line makes the angle 180, and the outer angle is 120, subtract 120 from 180. This will give you 60. Now every angle of a triangle added together will give you the sum of 180. So you already have 60 and 70, which make 130 all together. Subract 130 from 180 - (180-130) - and you'll get the result of 50.

The solution is :  the measure of the missing angle X is x=50.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given diagram, we get,

Let's look at the red angle.

if a flat line makes the angle 180, and the outer angle is 120,

subtract 120 from 180.

This will give you 60.

Now every angle of a triangle added together will give you the sum of 180.

So you already have 60 and 70,

which make 130 all together.

Subtract 130 from 180

i.e. (180-130) = 50

and we get the result of 50.

Hence, The solution is :  the measure of the missing angle X is x=50.

To learn more on angle click:

brainly.com/question/28451077

#SPJ2

Answer:

10

Step-by-step explanation:

2000/ 2x = 10

Multiply each side by 2x

2000/ 2x = 10 *2x

2000 = 20x

Divide by 20

2000/20 = 20x/20

100 = x

Take the square root of each side

sqrt(100) = sqrt(x)

10 = sqrt(x)

Parameterize C by

r(t) = 〈x(t), y(t)〉 = 〈cos(t), sin(t)〉

with 0 ≤ t ≤ π. Then the line integral is

[tex]\displaystyle \int_C (2+x^2y)\,\mathrm ds = \int_0^\pi (2+\cos^2(t)\sin(t))\left\|\mathbf r'(t)\right\|\,\mathrm dt \\\\ = \int_0^\pi (2+\cos^2(t)\sin(t)) \,\mathrm dt = \boxed{\frac23+2\pi}[/tex]

Answer:

12

Step-by-step explanation:

The first number they will both say = L.C.M of (6,4)

=> L.C.M of (6,4) is 12

The first number they will both say is 12

Answer:

Step-by-step explanation:

θ=l/r

θ=6/11 radians

≈0.555... radians