In the diagram, Find y.

We can solve for angle HKG by using supplementary angles. The angle next to it and itself will add up to 180 degrees, as they are on a straight line.

[tex]120 + ?=180[/tex]

[tex]?=60[/tex]

Angle HKG is 60 degrees.

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Now, we also know that in triangles, the angles are 180 degrees. We can add up all the angles and find x:

[tex]60+(6x-10)+(2x+10)=180[/tex]

Remove parenthesis:

[tex]60+6x-10+2x+10=180[/tex]

Add like terms:

[tex]8x+60=180[/tex]

Subtract 60 from both sides:

[tex]8x=120[/tex]

Divide both sides by 8:

[tex]x=15[/tex]

We have more supplementary angles. We can find angle JHG:

[tex]?+72=180[/tex]

[tex]?=108[/tex]

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Now add up the interior angles of the triangle:

[tex]4x-2+3x+4+108=180[/tex]

Add like terms:

[tex]7x+110=180[/tex]

Subtract 110 from both sides:

[tex]7x=70[/tex]

Divide both sides by 7:

[tex]x=10[/tex]

We have more supplementary angles. We can find angle BDC:

[tex]?+111=180[/tex]

[tex]?=69[/tex]

---

Now add up the interior angles of the triangle:

[tex]69+7x+5+8x-14=180[/tex]

Add like terms:

[tex]60+15x=180[/tex]

Subtract 60 from both sides:

[tex]15x=120[/tex]

Divide both sides by 15:

[tex]x=8[/tex]

Answer:

170 is the difference between 120 & -50 on a number line

Step-by-step explanation:

so - 50 to 0 is 50

than 0 to 120

so, |-50| + 120 = 170

Answer:

x = 9

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Here the exterior angles has a measure of 10x + 58° while its opposite interior angles have measures of 6x + 56° and 38°

If an exterior angle of a triangle is equal to the sum of the opposite interior angles then 10x + 58 = 6x + 56 + 38  

we now solve for x

10x + 58 = 6x + 56 + 38  

==> combine like terms

10x + 58 = 6x + 94

==> subtract 58 from both sides

10x = 6x + 36

==> subtract 6x from both sides

4x = 36

==> divide both sides by 4

x = 9

and we are done! :)

Answer:

x = 9

Step-by-step explanation:

The sum of all the interior angles of a triangle = 180 degrees

one of the angles of the triangle's interior is blank, so to find it we can subtract the exterior angle measure next to it from 180 degrees (a straight line)

38 + (6x + 56) + (180 - (10x + 58)) = 180

Now, we can do our best to simplify and combine like terms:

[38 + 56 + (180 - 58)] + [6x - 10x] = 180

216 - 4x = 180

Now we can subtract 180 from both sides...

36 - 4x = 0

And then add 4x to both sides...

36 = 4x

Now we've manged to isolate x, all that's left is to divide both sides by 4

9 = x

Or

x = 9

Hope this explanation helped! Feel free to ask questions if anything didn't fully make sense!

Answer:

9 hours

Step-by-step explanation:

4 times 3 is 12. Simple multiplication. 3 times 3 is 9. WOW

Answer:

9 hours

The average rate of snowfall here is 4 inches per/hour, so that means we have to multiply the amount of hours by itself to get the answer.

3 × 3 = 9(with 12 inches of snow fell total, equaling 1 foot)

Answer:

7662247+20728678=28290925+33807580=620985505

Answer:

Step-by-step explanation:

Answer:

z = 7/3 is extraneous.

Step-by-step explanation:

√(z^2+8) = 1 - 2z

z^2 + 8 = (1 - 2z)^2

z^2 + 8 = 1 -4z + 4z^2

3z^2 - 4z - 7 = 0

3z^2 + 3z - 7z - 7 = 0

3z(z + 1) - 7(z + 1) = 0

(3z - 7)(z + 1) = 0

3z = 7, z = -1

z = 7/3, -1.

One of these might be extraneous.

Checking:

√(z^2+8) = 1 - 2z, if z = -1:

√(1 + 8) = 3, -3

1 - 2(-1) = 3.    So its not z = -1

if z = 7/3

√((7/3)^2 + 8) = 13.44

1 - 2(7/3) = -3.66

So its z = 7/3

Answer:

[tex]z=\dfrac{7}{3}[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt{z^2+8}=1-2z[/tex]

Square both sides:

[tex]\implies (\sqrt{z^2+8})^2=(1-2z)^2[/tex]

[tex]\implies z^2+8=1-4z+4z^2[/tex]

Subtract [tex]z^2[/tex] from both sides:

[tex]\implies 8=1-4z+3z^2[/tex]

Subtract 8 from both sides:

[tex]\implies 0=-7-4z+3z^2[/tex]

[tex]\implies 3z^2-4z-7=0[/tex]

Rewrite the middle term:

[tex]\implies 3z^2+3z-7z-7=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 3z(z+1)-7(z+1)=0[/tex]

Factor out the common term [tex](z+1)[/tex]:

[tex]\implies (3z-7)(z+1)=0[/tex]

Therefore:

[tex]\implies (z+1)=0 \implies z=-1[/tex]

[tex]\implies (3z-7)=0 \implies z=\dfrac{7}{3}[/tex]

To find the extraneous solution (the root that is not a root of the original equation), enter the two found values of z into the original equation:

[tex]\begin{aligned}z=-1\implies \sqrt{(-1)^2+8}&=1-2(-1)\\\implies 3&=3\implies \textsf{true}\\\end{aligned}[/tex]

[tex]\begin{aligned}z=\dfrac{7}{3} \implies \sqrt{\left(\frac{7}{3}\right)^2+8}&=1-2\left(\frac{7}{3}\right)\\\implies \dfrac{11}{3} &=-\dfrac{11}{3}\implies \textsf{false}\end{aligned}[/tex]

[tex]\textsf{As}\: \dfrac{11}{3} \neq -\dfrac{11}{3}\:\textsf{then}\: z=\dfrac{7}{3}\:\textsf{is the extraneous solution}[/tex]

Answer:

d.45 sq.ft

Step-by-step explanation:

Surface are i.e. Total surface area of square pyramid = a^2 + 2al

where a^2 is area of base

a is side of base

l is slant height

by the figure

a=3ft

a^2 = a×a

=3×3

=9ft

l=6ft

Surface area = a^2+2al

=9+2×3×6

=9+36

=45 sq.ft

Answer:

x = 30

Step-by-step explanation:

Answer:

Біологічні відносини є результатом взаємодії організмів один з одним. У природі немає організмів, які ізольовані від оточуючого середовища.

Missing: Проект ‎призи ‎нація (

Answer:

the ans is c

Step-by-step explanation:ive done it b4

Answer:

379 (Rounded to nearest whole)

A = a² + 2a [tex]\sqrt{\frac{a^2}{4} + h^2}[/tex]

    = 10² + 2 × 10 × [tex]\sqrt{\frac{10^2}{4} + 13^2 }[/tex] ≈ 378.57

Answer:

43.43

Step-by-step explanation:

Convert 25 minutes to decimal degrees by 25/60 = 0.416...=0.42

Convert 36 seconds to decimal degrees by 36/3600 (There are 3600 seconds in a degree) = 0.01

Now you have:

43 degrees, 0.42 degrees. and 0.01 degrees.

Add them all to get 43.43

Rina Take home pay is $457.20

The basic salary divided by the Gross salary is multiplied by 100. The result is the percentage of gross salary.

Given that:

gross salary = $624

14% income tax = 624* 0.14 = $87.36

group health plan = $4.25

Company retirement = 624 * 0.060 =$37.44

Social Security = 624 * 0.0605 = $37.752

Home pay= 624 - 87.36 - 4.25 - 37.44- 37.752

= 457.198

Her take home pay is $457.198

if she gets a $35 raise per pay period,

So, new gross salary would be,

= $624 + $35

= $659.

Again, we have

14% Income tax = 659 * 0.14 = $92.26

Group health plan = $4.25

Company retirement = 659 * 0.060 = $39.54

Social Security = 695* 0.0605  = $39.8695

Home take pay,

=659-39.8695 - 45.825 - 39.54-92.26

=441.5055

Her take home pay is $441.5055

learn more about calculation of salary percentage here:

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Using sampling concepts, it is found that the population and the sample are given by:

Population: all the chicken meat; Sample: three random places in the chicken.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population.

In this problem, a group of 3 chicken meat is taken from all the chicken meat, which is the population, hence the correct option is given by:

Population: all the chicken meat; Sample: three random places in the chicken.

More can be learned about sampling concepts at https://brainly.com/question/25122507

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Answer:

n >= -1/4

Step-by-step explanation:

Divide both sides by the same factor, and flip the relation because the factor is negative

-28n/-28 >= 7/-28

Simplify,

Cancel terms that are in both the numerator and denominator.

n >= 7/-28

Divide the numbers.

n >= 7/-28 = n >= -1/4

The answer is n >= -1/4

Hope this helps!

Answer:

248

Step-by-step explanation:

Consecutive angles of a parallelogram are supplementary.

56 + y = 180

y = 180-56

y =124

The opposite angles of a parallelogram are equal.

x = y = 124

x+y = 124+124

      =248

Answer:

x + y = 248

Step-by-step explanation:

consecutive angles in a parallelogram sum to 180°

opposite angles are congruent

x + 56° = 180° ( subtract 56° from both sides )

x = 124°

then

y = x = 124 , so

x + y = 124 + 124 = 248

Answer:

784.3

Step-by-step explanation:
3.14(15.8)^2 = 784.3

hope this helped :>

Answer:

C) All squares are rhombuses. Rhombeses have 4 sides that are the same length. Therefore, all squares have 4 sides that are the same length.

Step-by-step explanation:

Answer:

[tex]2\sqrt{14}[/tex]

Step-by-step explanation:

To find, do 9^2-5^2=[tex]\sqrt{x\\}[/tex], so 81-25=56 which is 2[tex]\sqrt{14}[/tex]

Answer:

[tex]2\sqrt{14}[/tex]

Step-by-step explanation:

The missing side must be [tex]2\sqrt{14}[/tex] for the Pythagorean Theorem to be true.

Hope it helps, have a fantastic day.

Answer:

x = [tex]\frac{c-ab}{a}[/tex]

Step-by-step explanation:

a(x + b) = c ← distribute parenthesis on left side

ax + ab = c ( subtract ab from both sides )

ax = c - ab ( divide both sides by a )

x = [tex]\frac{c-ab}{a}[/tex]

Answer:

Just expand and solve for x :)

According to "Black Hole Beginnings," the destruction of some stars results in an an intense gravitational pull.

To answer the question, we need to know what Black Holes are.

Blackholes are regions of space in which no matter can escape

So, when black holes are formed, some stars are destroyed and collapse due to intense gravitational forces.

So, according to "Black Hole Beginnings," the destruction of some stars results in an an intense gravitational pull.

Learn more about black holes here:

https://brainly.com/question/6037502

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For the function: y = x² + 4

For the function: x² - 4

For the function: 1 - x²

Conclusion:

green line = x² + 4;  blue line = x² - 4; black line = 1 -x²

Answer:

See below ~

Step-by-step explanation:

Equation of Graph A :

Equation of Graph B :

Equation of Graph C :

Answer:

80

Step-by-step explanation:

Look at the box plot and look at each line.

The first line that is all the way to the left, that is the Quartile 1.

The last line all the way to the right, that is Quartile 3.

Now lets look at the box part.

The beggining of the box is the minimum.

The ending of the box is the maximum.

The middle line is the median.

How I remember it is Median=Middle

Hopw this hels :D

Answer:

Given:

Solution:

Let's assume Width of rectangle be x and Length of rectangle be x + 7 respectively.

Using formula

[tex] \\ \: \: \: \: \pink{ \dashrightarrow \: \: \: \: \sf { \underbrace{Area_{(Rectangle)} = Length × Width }}} \\ \\ [/tex]

On Substituting the required values, we get;

[tex]\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x)(x + 7) = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 31x - 24x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x(x + 31) - 24 (x + 31) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x + 31)(x - 24) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x = 24 \: or \: - 31 \\ \\ [/tex]

As we know that width of the rectangle can't be negative. So x = 24

Hence,

[tex] \therefore[/tex]Length of rectangle is 31 yards and Width is 24 yards.

Answer:

Two right angles = 180 degrees

Step-by-step explanation:

A right angle = 90 degrees

The sum of the interior angles of a triangle = 180 degrees

Two right angles (2 * 90) = 180

180 = 180

Therefore, the sum of the interior angles of  any triangle is equal to two right angles.