Find the values of the variables and the measures of the angles

Answer:

KM = 15

Step-by-step explanation:

From the diagram, ΔJKL and ΔJKM are similar to each other because they share the same angle J and they are both right angle triangle. Therefore they are similar by AA property.

Since JL=25 and JM=5, JM = JL + JM= 25 + 5 = 30

Since ΔJKL and ΔJKM are similar to each other, therefore:

[tex]\frac{JK}{JL}=\frac{JM}{JK}\\ Substituting:\\\frac{JK}{30}=\frac{5}{JK}\\JK^2=150\\JK=\sqrt{150}\\ \\From\ hypotenuse:\\JK^2=JM^2+KM^2\\Substituting:\\(\sqrt{150} )^2=5^2+KM^2\\150=25+KM^2\\KM^2=150-25=125\\KM=\sqrt{125}\\ KM=15[/tex]

Answer: Associative Property: (40+(12+18)+27. Evaluate: 97

Answer:

{3/2, 4}

Step-by-step explanation:

Set x - 4 = 0 and solve for x:  x = 4 is a solution.

Seet 2x - 3 = 0 and solve for x:  3/2 is another solution.

Answer:

using identity (a+b)(a-b) = a^2 -b^2

Answer:

FGH and BCD

it's obvious.

no common lines between them

Answer:

53

Step-by-step explanation:

We know the first term and common difference so we can write the explicit formula. The formula is:

aₙ = a₁ + (n - 1)d

aₙ = 8 + (n - 1) * 3

aₙ = 3n + 5

This means that a₁₆ = 3 * 16 + 5 = 53

by using the formula for arithmetic sequence, the 16th term of the progression can be obtained. Given A1 = 8 and d = 3,

A16=A1 + (n-1) d

A16=8 + (16-1) (3)

A16 = 53

I hope I helped! Be safe!

Answer

Part 1

Step-by-step explanation:

T2=3(5)-12=3

T3=-3

T4=-21

T5=-75

Answer:

[tex]\boxed{105}[/tex]

Step-by-step explanation:

∠DAB = ∠BAC = 105 degrees

This is because opposite angles of a parallelogram are congruent.

Answer:

105

Step-by-step explanation:

∠DAB = ∠BAC = 105

Answer:

(5, -3)

Step-by-step explanation:

(-16+x)/2 = -5.5 => x=5

(4+y)/2 = 0.5 => y=-3

Answer: about 5 hours and 3 min

Step-by-step explanation:

Answer:

about 8 hours and 7 minutes

Step-by-step explanation:

have 60 minutes divided by 20.3 minutes to find the correct ratio to find themph if the speed remained constant. It is about 2.95567 and using this number multiply to 21 to get the miles per hour. the speed is about 62.069 mph. then divide the 504 miles by the mph of the car to find how long it will take to get there. It is about 8 hours 7 minutes and 20 seconds give or take, or 8.12 hours.

Hey there! :)

Answer:

[tex]\frac{121}{9}[/tex]

Step-by-step explanation:

We can solve this by first converting -3 2/3 to an improper fraction:

[tex]-3\frac{2}{3} = \frac{-11}{3}[/tex]

Square the fraction:

[tex](\frac{-11}{3})^{2} = (\frac{-11}{3}) * (\frac{-11}{3}) = \frac{121}{9}[/tex]

Answer:

Step-by-step explanation:

1) We would determine the cube root of 27 and find its square.

Cube root of 27 = 3

3² = 9

Solution = 9

2) 36³ = 46656

√36³ = √46656 = 216

3) we would find the 5th roof of - 243 and find its cube

5th root of - 243 = - 3

- 3³ = - 27

Solution = - 27

4) Looking at the expression, 40⅔, we can see that

a = 2

b = 3

c = 40

Answer: 1) We would determine the cube root of 27 and find its square.Cube root of 27 = 33² = 9Solution = 92) 36³ = 46656√36³ = √46656 = 2163) we would find the 5th roof of - 243 and find its cube5th root of - 243 = - 3- 3³ = - 27Solution = - 274) Looking at the expression, 40⅔, we can see that a = 2b = 3c = 40

Step-by-step explanation:

Answer:

the base???

Step-by-step explanation:

Answer:

Exponent

Step-by-step explanation:

An exponent is a shorthand notation which tells how many times a number (or expression) is multiplied by itself.

Work Shown:

908 rounds to 900. This is because 908 is closer to 900, than it is to 1000.

While 67 rounds to 100, for similar reasoning as above.

Multiplying those rounded values gives 900*100 = 90,000. This is the number 90 thousand.

Note that 9*1 = 9 and its followed by four zeros (two each from 900 and 100). This is a quick way to mentally multiply things like this.

Using a calculator, we see that 908*67 = 60,836 which is fairly off from what we estimated. This is to be expected as estimates only give us a rough idea of how big a number is.

Answer:

[tex]f^{-1}[/tex] (x) = [tex]\frac{x-1}{2}[/tex]

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

[tex]\frac{y-1}{2}[/tex] = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , so

[tex]f^{-1}[/tex] (x) = [tex]\frac{x-1}{2}[/tex]

Answer:  " f⁻¹(x) = (x-1)/2  ";  or, write as:

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              " f⁻¹(x) = (x/2) - (1/2) " .

___________________________________

Step-by-step explanation:

___________________________________

Given:   f(x) = 2x + 1 ;  Find the inverse:

___________________________________

1)  Rewrite as y = 2x + 1 ;

2) Replace the "x" with "y" ; and the "y" with "x" ; and rewrite:

         x = 2y + 1 ;

3)  Now, "solve"; with "y" standing alone as a single, isolated variable on the left side of the equation, with an "equals" sign following the "y" :

         x = 2y + 1 :

Subtract "1" from each side of the equation:

         x - 1 = 2y + 1 - 1 ;

to get:

         x - 1 = 2y ;

___________________________________

↔  Rewrite as :

2y = x - 1 ;

Now, divide each side of the equation by "2" ;

  to isolate "y" on the left-hand side of the equation;

  & to solve in terms of "y":

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2y / 2 = (x-1)/2 ;

___________________________________

to get:

y = (x-1)/2 ;

or; write as:  y = (x/2) - (1/2);

___________________________________

Now, rewrite; by replacing the "y" with "f⁻¹(x) "; as follows (to indicate that this is the "inverse function"):

___________________________________

f⁻¹(x) = (x-1)/2 ;  or, write as:

___________________________________

f⁻¹(x) = (x/2) - (1/2) .

___________________________________

Hope this is helpful to you!

 Best wishes!

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Well for the activity we can do a game.

In a game you start with 50 coins and everytime you kill a monster "x" you get 2 more coins.You need 100 coins to level up.

We can make the following inequality,

2x + 50 ≥ 100

So to find x we single it out,

2x + 50 ≥ 100

-50 to both sides

2x ≥ 50

Divide 2 by both sides

x ≥ 25

For the number line look at the image below ↓

The solution in the number line is the number of monsters killed in order to level up.

Hope this helps :)

Answer:

The chemical element loses 4% of its weight everyday

Step-by-step explanation:

Here, we are interested in knowing the percentage weight loss of the chemical each day.

The key to answering this is looking at the expression inside the bracket.

We can express M(t) = 169•(0.96)^t as

M(t) = 169•(1-0.04)^t

So what this means is that we need to find the percentage value corresponding to 0.04 since it is a constant term here

Mathematically, 0.04 is same as 4/100, so we can clearly say that the constant percentage loss is 4%

Answer:

0.96

Step-by-step explanation:

The exponential function modeling the mass of the sample is of the form M(t)=A⋅Bt. Therefore, AAA determines the initial mass of the sample (when Clemence began studying it) and BBB determines the daily change in the mass of the sample.

The mass of the sample is multiplied by \it{0.96}0.960, point, 96 every day. Since 0.96<10.96<10, point, 96, is less than, 1, the mass of the sample shrinks by a factor of 0.960.960, point, 96 every day.

Every day, the mass of the sample shrinks by a factor of 0.960.960, point, 96.

Answer:

864

Step-by-step explanation:

512÷8=64

108÷8=13.5

64×13.5=864

Answer:

b) 864 squares

Step-by-step explanation:

A(rectangle) = 512cm x 108cm = 55296 cm²

A(square) = 8cm x 8cm = 64 cm²

Ar/As = 55296cm²/64cm² = 864 squares

Answer: 18 animals

Step-by-step explanation:

3 out of 20 pet owners get their pet from a breeder.

To find how many animals have been bought from a breeder, you need to find 3/20 of the 122 animals.

3/20 = 0.15

122 * 0.15 = 18.3

18.3 rounds down to 18

There are 18 animals who have been bought from a breeder.

.

this is answer ok? ok :) leleelellelelelelelelel

Answer:

B.  y ≤ 1/2x + 3

Step-by-step explanation:

Well we can start by finding the y-intercept which is the point on the line that touches the y-axis in this case it’s 3.

And by looking at the shade it is facing down and the line is solid so the inequality starts with y ≤,

So we can cross out answer choices C. and D.

And the slope is 1/2 because that’s how far away each points are from each other.

So the inequality is y ≤ 1/2x + 3

Look at the image below.

Answer:

Area of sphere = 576 pi ft^2

Volume of sphere = 2,304 pi ft^3

Step-by-step explanation:

Radius of great circles are the same as radius of the sphere

So let’s calculate the radius of the sphere from the area given;

Mathematically;

pi * r^2 = 144pi

r^2 = 144

r = square root of 144

r = 12 ft

Volume of sphere = 4/3 * pi * r^3

= 4/3 * pi * 12^3 = 2,304 pi ft^3

Area of sphere = 4 * pi * r^2 = 4 * pi * 12^2 = 4 * 144 * pi = 576 pi ft^2

Answer:

D.   22.5 sq. un.

Step-by-step explanation:

W divides BU so that there is a ratio of 1;2 meaning that there are 3 parts.

That means that 3 parts is BUV; we know that one of those parts is 4.5 sq. un. so 4.5*3=13.5 sq. un.  - Also 4.5*2=9 to get WUV

V is the midpoint of the line BS so that means that BUV and UVS are equal

we know that BUV is 13.5 so we multiply that by 2 to get the whole triangle

=27

The last step is to get rid of BVW which we know is 4.5

27-4.5=22.5

Answer:

  [tex]\dfrac{2xy+x}{3y+2}[/tex]

Step-by-step explanation:

Factor numerator and denominator and cancel common factors.

  [tex]\dfrac{3x-12xy^2}{6-3y-18y^2}=\dfrac{-3x(4y^2-1)}{-3(6y^2+y-2)}=\dfrac{x(2y-1)(2y+1)}{(2y-1)(3y+2)}\\\\=\boxed{\dfrac{2xy+x}{3y+2}}[/tex]

Answer:

The correct answer is B. 880

Step-by-step explanation:

220%=2.2

2.2(400)=880

Answer:

B. 880

Step-by-step explanation:

220% × 400

= 220/100 × 400

= 88000/100

= 880

Answer:35 cars in 7 hours.

Step-by-step explanation:15/3=5 per hour. 5x7=35.

Answer:

35 cars in 7 hrs

Step-by-step explanation:

Steve's rate of work is (15 cars) / (3 hrs), or 5 cars/hr.

In 7 hrs he can wash

5 cars

---------- * 7 hrs = 35 cars in 7 hrs

   hr

Answer:

It's (B)

Step-by-step explanation:

Answer:

x=45

Step-by-step explanation:

the sum of straight angle=180

2x+45+x=180

3x=180-45

3x=135

x=135/3=45

Answer:

45 degree

Step-by-step explanation:

Since it is an straight line it means all of the added angles together equal 180

2x+45+x=180

3x+45=180

3x=135

x=135/3

x=45

Answer:

67

Step - Step - Explanation