Find the measure of the third angle of a triangle given that the first two angles are 44º and 72º.
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[tex]5x + 3x -4 = 10\\8x=14\\x=\dfrac{14}{8}=\dfrac{7}{4}[/tex]

one

Answer:0ne

Step-by-step explanation:

Answer:

the angle Ф is 63.9 degrees.

Step-by-step explanation:

A right triangle describes this situation.  The height of the triangle is 45 ft and the base is 22 ft.  The ratio height / base is the tangent of the angle of elevation and is tan Ф.  We want to find the angle Ф:

                opp

tan Ф = ---------- = 45 / 22 = 2.045.  

               adj

Using the inverse tangent function on a calculator, we find that the angle Ф is 63.9 degrees.

Answer:

Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes

Step-by-step explanation:

Let

x ------> amount of clothing bag that Jenny collected

y ------> amount of clothing bag that Hanan collected

we know that

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

[tex]x=\frac{3}{4}[/tex] -----> equation B

Substitute equation B in equation A

[tex]y=\frac{1}{2}(\frac{3}{4})[/tex]

[tex]y=\frac{3}{8}[/tex]

therefore

Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes

Answer:

A.  s = 3/10 m.

Step-by-step explanation:

s = km  where k is a constant , s = the length of the string and m = the mass of the object.

Substituting m = 30 and s = 9:

9 = k * 30

k =  9/30 = 3/10

So the equation is s = 3/10 m.

Answer:

Option C and E are correct.

Step-by-step explanation:

We need to solve the following equation

(2x+3)^2=10

taking square root on both sides

[tex]\sqrt{(2x+3)^2}=\sqrt{10}\\2x+3=\pm\sqrt{10}[/tex]

Now solving:

[tex]2x+3=\sqrt{10} \,\,and\,\,2x+3=-\sqrt{10}\\2x=\sqrt{10}-3 \,\,and\,\,2x=-\sqrt{10}-3\\x=\frac{ \sqrt{10}-3}{2} \,\,and\,\,x=\frac{-\sqrt{10}-3}{2}[/tex]

So, Option C and E are correct.

Answer: E .√10 - 3 / 2 or

c. -√10 - 3 / 2

Step-by-step explanation:

(2x + 3)^2 = 10

take the square root of bothside

√(2x + 3)^2 = ±√10

2x + 3 = ±√10

subtract 3 from bothside

2x = ±√10 - 3

Divide bothside by 2

x = ±√10 - 3 / 2

Either x = √10 - 3 / 2 or

x = -√10 - 3 / 2

5(x - 2) - 3x + 7.

First use the distributive property:

5(x-2) = 5x-10

Now you have:

5x - 10 - 3x +7

Now combine like terms to get:

2x - 3

Answer:

2x -3

Step-by-step explanation:

5(x - 2) - 3x + 7

Distribute the 5

5x -10 -3x+7

Combine like terms

5x-3x   -10 +7

2x -3

Answer:

It would be 7/2s, however if you want to solve it completely, you do 7 ÷ 2. It would give you 3.5 so, s = 3.5.

Answer:

- [tex]\frac{27}{7}[/tex]

Step-by-step explanation:

Given

f(x) = [tex]\frac{3}{x+2}[/tex] - [tex]\sqrt{x-3}[/tex]

Evaluate f(19) by substituting x = 19 into f(x)

f(19) = [tex]\frac{3}{19+2}[/tex] - [tex]\sqrt{19-3}[/tex]

       = [tex]\frac{3}{21}[/tex] - [tex]\sqrt{16}[/tex]

       = [tex]\frac{1}{7}[/tex] - 4

       = [tex]\frac{1}{7}[/tex] - [tex]\frac{28}{7}[/tex] = - [tex]\frac{27}{7}[/tex]

Answer:

B. 3

Step-by-step explanation:

First of all we will define rotational symmetry.

Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.

The order of rotational symmetry is how many times it matches the original shape during the rotation.

So, for the given shape the rotated shape will match the original shape three times so the order for symmetry for the given shape is 3.

Hence,

the correct answer is B. 3 ..

Answer:

60 different votes.

Step-by-step explanation:

This is a permutations question. There are a total of 5 bands to be voted for, and Rafeal has to vote only for 3 of the bands. It is also mentioned that the voting has to be done for the favorite, the second favorite, and the third favorite bands from the list. This means that the order of selection is important. This means that permutations will be used. Thus, 3 bands out of 5 have to be selected in an order. This implies:

5P3 = 5*4*3 = 60 possibilities.

There are 60 different votes!!!

Answer: 60 different votes are possible

Step-by-step explanation:

We have a list of 5 bands and we must choose 3 of them. In this case, the order of the election is important. Therefore this is a problem that is solved using permutations.

The formula for permutations is:

[tex]nPr=\frac{n!}{(n-r)!}[/tex]

Where n is the number of bands you can choose and you choose 3 of them.

Then we calculate:

[tex]5P3 =\frac{5!}{(5-3)!}\\\\5P3=\frac{5!}{2!}\\\\5P3 = 60[/tex]

Finally, the number of possible votes is 60

Answer:

asa only because the two triangles are facing each other like a reflection making them congruent

ΔWZV and ΔWZY are congruent by AAS congruency

Considering    ΔWZV         and        ΔWZY

                      ∠WVZ            =            ∠WYZ  (given)

                        ∠WZV           =           ∠WZY   ( both angles are 90° since it is given that WZ is perpendicular to VY)

                           WZ is common side

So  ΔWZV and ΔWZY are congruent (AAS congruency)

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Answer:

67.972 ÷ 10 = 6.7972

679.72 ÷ 10 = 67.972

6797.2 ÷ 10 = 679.72

6797200 ÷ 10 = 679720

Answer: 1

Step-by-step explanation:

A formula for the slope of a line is rise/run.

First let’s find the ‘rise’

To find the rise, we must look at the difference between the elevation of the points. We can find the rise by subtracting y1 from y2. 7-3=4, so the rise is 4

Run is the same concept. We must subtract x2 - x1.

2-(-2)=2+2=4

So the rise is 4 and the run is 4. There for rise/run = 4/4 =1

The slope of the line is 1

Answer:

C) 1287 cubic feet

Step-by-step explanation:

To find the volume of a rectangular prism the formula is length time width times height. That means area=9*11*13 which is 1287 or C.

Answer:

Oops I went too far.

The other point is (9,4).

The average rate of change is 1/5.

Step-by-step explanation:

So I think your function is [tex]f(x)=\sqrt{x}+1[/tex]. Please correct me if I'm wrong.

You want to find the slope of the line going through your curve at the points (4,f(4)) and (9,f(9)).

All f(4) means is the y-coordinate that corresponds to x=4 and f(9) means the y-coordinate that corresponds to x=9.

So if [tex]f(x)=\sqrt{x}+1[/tex], then

[tex]f(4)=\sqrt{4}+1=2+1=3[/tex] and

[tex]f(9)=\sqrt{9}+1=3+1=4[/tex].

So your question now is find the slope of the line going through (4,3) and (9,4).

You can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] but I really like to just line up the points vertically and subtract then put 2nd difference over 1st difference. Like this:

( 9  ,   4)

-( 4  ,   3)

-------------

 5         1

So the slope is 1/5.

The average rate of change of the function f on the interval [4,9] is 1/5.

A function describes the relationship between related variables.

Given that:

[tex]f(x) = \sqrt x + 1,\ 4 \le x \le 9[/tex]

The average rate of change (m) is calculated as:

[tex]m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]

[tex]m = \frac{f(9) - f(4)}{9 - 4}\\[/tex]

So, we have:

[tex]m = \frac{f(9) - f(4)}{5}[/tex]

Calculate f(4)

[tex]f(x) = \sqrt x + 1[/tex]

[tex]f(4) = \sqrt 4 + 1[/tex]

[tex]f(4) = 2 + 1[/tex]

[tex]f(4) = 3[/tex]

Calculate f(9)

[tex]f(x) = \sqrt x + 1[/tex]

[tex]f(9) = \sqrt 9 + 1[/tex]

[tex]f(9) = 3 + 1[/tex]

[tex]f(9) = 4[/tex]

So, we have:

[tex]m = \frac{f(9) - f(4)}{5}[/tex]

[tex]m = \frac{4 - 3}{5}[/tex]

[tex]m = \frac{1}{5}[/tex]

Recall that:

[tex]f(4) = 3[/tex] --- this represents the coordinate of the start interval

[tex]f(9) = 4[/tex] --- this represents the coordinate of the end interval

Hence, the coordinates of the end interval is (9,4)

Read more about average rates of change at:

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Area of a full circle is PI x r^2

Area = 3.14 x 8^2 = 200.96

Area of a sector is area *  central angle / full circle

Area = 200.96 x 5PI/3 / 2PI = 160PI/3

Answer is C.

Answer:[tex]\frac{160\pi }{3} units^2[/tex]

Step-by-step explanation:

Given

Angle subtended by sector is[tex]\frac{5\pi }{3}[/tex]

radius =8 units

[tex]Area of sector=\frac{\theta }{2\pi }\pi r^2 [/tex]

[tex]A=\frac{20\times 8\pi }{3}[/tex]

[tex]A=\frac{160\pi }{3}[/tex]

Answer:

where is rectangle???

Answer:

10

Step-by-step explanation:

The length of AB is 10 and the length of BC is 13. CD is parallel to AB so its 10.

Megan can have 7 different values of A for the number of 25c coins she possesses.

Given:

Megan has 25c coins and 10c coins with a total value of $1.95.

To find:

Number of different values of A (number of 25c coins) Megan can have.

Step-by-step solution:

Therefore, Megan can have 7 different values of A for the number of 25c coins she possesses.

Answer:

57 children

54 adults

Step-by-step explanation:

Let's call x the number of children admitted and call z the number of adults admitted.

Then we know that:

[tex]x + z = 111[/tex]

We also know that:

[tex]3.25x + 4z = 401.25[/tex]

We want to find the value of x and z. Then we solve the system of equations:

-Multiplay the first equation by -4 and add it to the second equation:

[tex]-4x - 4z = -444[/tex]

[tex]3.25x + 4z = 401.25[/tex]

----------------------------------

[tex]-0.75x = -42.75[/tex]

[tex]x =\frac{-42.75}{-0.75}\\\\x=57[/tex]

Now we substitute the value of x in the first equation and solve for the variable z

[tex]57 + z = 111[/tex]

[tex]z = 111-57[/tex]

[tex]z = 54[/tex]

Answer:

Number of children=57

Number of adults=54

Step-by-step explanation:

We can start by forming simultaneous equations from the information provided.

Let the number of children be x and adults be y, then the the sum of the amount collected from both children and adults=3.25x+4y=401.25

The total number of people in attendance x+y=111

Let us solve these equations simultaneously.

3.25x+4y=401.25

x+y=111

Using substitution method.

y=111-x

3.25x+4(111-x)=401.25

3.25x+444-4x=401.25

-0.75cx=-42.75

x=57

Number of children=57

Adults=111-57

=54

Answer:

The correct answer is 6-4i

Answer:

6 - 4i .

Step-by-step explanation:

I will assume that (10 - 51) is ( 10 - 5i) since the other number is a complex number.

You add the real parts and the imaginary parts separately.

(-4 + i) + (10 - 5i)

= (-4 + 10) + (i - 5i)

= 6 - 4i .

Answer:

[tex]\large\boxed{\dfrac{x^2-1}{x^2-x}=\dfrac{x+1}{x}=1+\dfrac{1}{x}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x^2-1}{x^2-x}=\dfrac{x^2-1^2}{x(x-1)}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{(x-1)(x+1)}{x(x-1)}\qquad\text{cancel}\ (x-1)\\\\=\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}[/tex]

Answer:

its b on edge 2021

Step-by-step explanation:

Answer:

First draw two axes x and y. Then mark all points for which x=4, this is a vertical line. Do the same for the other sides and you will find a square with side length 8.

Answer:

220 glasses.

Step-by-step explanation:

Quantity of fruit juice = 13 liters 200 ml

Number of glasses of each capacilty 60ml can be filled = ?

The quantity of fruit juice has 2 units. one is liter and the other is milliliter.

So we will convert liter into milliliter.

We have the quantity 13 liters 200 ml:

We know that:

1 liter = 1000 ml

Hence we have 13 liters so 13 will be multiplied by 1000 to convert it into milliliter.

13 * 1000 = 13000 ml

Now we have 13000 ml 200ml

Notice that we have two milliliters, so we will add both the quantities to make it one.

(13000+200)ml = 13200ml

Total quantity of fruit juice = 13200ml

Now divide the total quantity by the capacity of 60ml

=13200ml/60ml

= 220 glasses

It means that 220 glasses can be filled....

Answer:

.333333... can be expressed as 1/3.

Step-by-step explanation:

A rational number is defined as:

any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

aka, any number that you can express as a fraction.

Any person who has spent enough time in math should be familiar with the fact that the thirds (aka 1/3, 2/3) are repeating decimals, but are rational numbers as they can be written as whole number fractions.

If you didn't know this, don't worry. You'll get it soon enough.

Hope this helped!

Answer:

The foci are located at [tex](0,\pm \sqrt{5})[/tex]

Step-by-step explanation:

The standard equation of an ellipse with a vertical major axis is [tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex] where [tex]a^2\:>\:b^2[/tex].

The given equation is [tex]9x^2+4y^2=36[/tex].

To obtain the standard form, we must divide through by 36.

[tex]\frac{9x^2}{36}+\frac{4y^2}{36}=\frac{36}{36}[/tex]

We simplify by canceling out the common factors to obtain;

[tex]\frac{x^2}{4} +\frac{y^2}{9}=1[/tex]

By comparing this equation to

[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]

We have [tex]a^2=9,b^2=4[/tex].

To find the foci, we use the relation: [tex]a^2-b^2=c^2[/tex]

This implies that:

[tex]9-4=c^2[/tex]

[tex]c^2=5[/tex]

[tex]c=\pm\sqrt{5}[/tex]

The foci are located at [tex](0,\pm c)[/tex]

Therefore the foci are [tex](0,\pm \sqrt{5})[/tex]

Or

[tex](0,-\sqrt{5})[/tex] and [tex](0,\sqrt{5})[/tex]

The probability of guessing a 3-digit pin correctly on the first attempt, when repetition of digits is allowed, is 1 out of 1000, or 0.001.

The subject under scrutiny is related to the concept of probability in mathematics. To solve this, we need to consider that there are 10 possible digits (0 to 9) on the keypad for each of the 3 input spots in the pin. Since a digit can be repeated, each spot has 10 possibilities. The total number of possible pin combinations is thus 10*10*10 = 1000.

The probability of guessing the pin correctly on the first attempt would be 1 (since there's only one correct pin) divided by the total number of possibilities, which is 1000. Therefore, the probability of this happening is 1/1000 or 0.001.

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The probability of a correct guess on the first try is 1/729.

In this scenario, the thief must randomly guess the correct three-digit pin code from a 9-key keypad where repetition of digits is allowed. To determine the probability of a correct guess on the first try, we need to calculate the ratio of favorable outcomes to total outcomes.

There are 9 possible digits to choose from, and repetition is allowed. Therefore, the number of outcomes is 9 raised to the power of 3 (since the thief needs to guess a three-digit pin code). This gives us 729 total outcomes. There is only one favorable outcome in this case, which is the correct pin code. Therefore, the probability of a correct guess on the first try is 1/729.

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Answer:

2y = 3x

Step-by-step explanation:

general formula for a straight line is given as

y = mx + b

Given 2 points (2,3) and (4,6), we can use the attached formula to calculate the slope, m of the line which connects the 2 points

m = (6-3) / (4-2) = 3/2

hence the general formula becomes

y = (3/2) x + b

Substitute  one of the given points into this equation to find b.

We pick point (2,3)

3 = (3/2) (2) + b

b = 0

hence the equation is

y = (3/2)x

2y = 3x  (answer)

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) :( 3,2)\\(x_ {2}, y_ {2}): (- 2,3)[/tex]

Substituting we have:

[tex]m = \frac {3-2} {- 2-3} = \frac {1} {- 5} = - \frac {1} {5}[/tex]

Finally, the slope is:

[tex]m = - \frac {1} {5}[/tex]

Answer:

[tex]m = - \frac {1} {5}[/tex]

(4 - 7n) – (20+5)

Simplify:

(4 -7n) - 25

Remove parenthesis:

4 - 7n -25

Combine like terms:

4-25 = -21

Now you have:  -21-7n

The term with the variable is usually rearranged to be in front, so it becomes:  -7n-21

Answer:

83 square inches

Step-by-step explanation:

Let's find the answer, you can see the attached file for clarity.

Because we have a rectangle measuring 8 inches by 5 inches, we can use the area of the rectangle as follows:

A1=base*height=(8 inches)*(5 inches)=40 square inches

Now, because we have a triangle over the square side of 8 inches long, we can divide the triangle into 2 rectangle triangles, each of them with a base of 4 inches and a height of 7 inches, obtaining:

A2=2*(base*height/2)=2*(4 inches)*(7 inches)/2=28 square inches

Doing the same for the other triangle we get 2 triangles with a base of 2.5 inches and a height of 6 inches, obtaining:

A3=2*(base*height/2)=2*(2.5 inches)*(6 inches)/2=15 square inches

The addition of all areas is:

A=A1+A2+A3=40 square inches + 28 square inches + 15 square inches

A=83 square inches.

In conclusion we have an area of 83 square inches.

Answer:

83

Step-by-step explanation: