Given: ΔABC

Prove: m∠ZAB = m∠ACB + m∠CBA

Triangle A C B is shown with its exterior angles. Line A B extends through point X. Line A C extends through point Y. Line C A extends through point X.

We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.

We know that m∠ZAB + m∠CAB = 180° by the

.

We also know m∠CAB + m∠ACB + m∠CBA = 180° because

.

Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.

Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the
.

Answer:

Larger percentage of kids

Step-by-step explanation:

Kids: 32/40 = 4/5

Adults: 25/32 = 5/8

4/5 > 5/8

Answer:

volume of cone = 1/3 volume of cylinder

according to the question, volume of cylinder =

V =

[tex]\pi \times (r) {}^{2} h[/tex]

diameter = 3 inches

radius = 3/2 inches

height = 8 inches

V = 22.7 * (3/2)²* 8

V = 22.7 * 9/4 * 8

V = 22.7 * 18

maximum volume a cone can have = 1/3 of cylinder

Volume of cone = 1/3 * 22.7 * 18

= 22.7 * 6

= 132.6

I'm assuming that the diagonals intersect at E. Since diagonals of a parallelogram bisect each other, BE=ED.

As distance must be positive, we reject the negative case, so x=8.

Thus, BE=ED=54.

Answer: A=9x^4

Step-by-step explanation:

Hii, do you need to find the area of a square with a side length of 3x^2? Let me help you out! (:

To find the area of a square, you need to square its side length.

Sounds strange, right?

The formula is shown below.

[tex]\LARGE\boldsymbol{A=a^2}[/tex]

Here "A' (capital A) denotes the area

"a" (lower-case a) denotes the side length

The 2 above the a tells us that we need to multiply the side length times itself.

Alright, now it's just a matter of sticking in the known values...

[tex]\sf A=(3x^2)^2[/tex]

Simplify

[tex]\sf A=9x^4[/tex]

Voila! There's our answer, cheers! (;

Hope I helped! Best wishes! (:

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

Step-by-step explanation:

f(x) = y = 64x³ - 1

y + 1 = 64x³

(y + 1)/64 = x³

[tex]x = \sqrt[3]{(y + 1) \div 64} [/tex]

[tex]x = \sqrt[3]{y + 1} \div 4[/tex]

that is the actual inverse function to calculate the original x value for a given y value of the original function.

but to make it a "normal" function, we need to rename the variables (x to y, y to x) :

[tex]y = \sqrt[3]{x + 1} \div 4[/tex]

this is now f^-1(x)

but careful, don't get confused, if dealing together with the original function, this "x" is actually standing for the "y" of the original function ...

When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

Firstly, ∠1 and ∠7 are alternate exterior angles as shown in the image, now to prove if these two angles will be congruent we can use the below proof.

First Method:

∠1  + ∠2 = 180° {Supplementary angles because both lies on the line q}

∠2 = (180° - ∠1)

Similarly, ∠2 = ∠6 = (180° - ∠1), corresponding angles are equal,

∠6 + ∠7 = 180° {Supplementary angles because both lies on the line r}

∠7 = 180° - ∠6

∠7 = 180° - (180° - ∠1)

∠7 = 180° - 180° + ∠1

∠7 = ∠1

OR

Second Method:

∠1 = ∠3 {Vertical angles formed by intersecting lines q and r}

∠3 = ∠5 {Alternate Interior angles}

∠5 = ∠7 {Vertical angles formed by intersecting lines s and r}

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Answer:

20°

Step-by-step explanation:

Measure of QR is 180 - 108 = 72°

 then using     intercepted arc - external angle theorem:

angle RPQ then equals  1/2 ( 108 - 72) = 20 °

Answer:

y= x +4

Step-by-step explanation:

The slope-intercept form of an equation is given by y= mx +c, where m is the slope and c is the y-intercept.

Start by finding the slope of the line.

[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]

Slope

[tex]=\frac{5-3}{1-(-1)}[/tex]

[tex]=\frac{2}{1+1}[/tex]

[tex]=\frac{2}{2}[/tex]

= 1

Substitute m= 1:

y= x+c

Finally, find c by substituting a pair of coordinates.

When x= 1, y= 5,

5= 1 +c

c= 5 -1

c= 4

Thus, the equation of the line is y= x +4.

Additional:

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If points d and f are on side ab and points e ang g are on side ac then line segment de and fg are parallel.

Given There is a triangle abc.

Parallel lines are those lines that do not meet at any point. If we draw a triangle abc and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle.

Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.

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Answer:D-E is parallel to FG which is parallel to B-C meaning all three are parallel

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

Answer:

24 gallons

Step-by-step explanation:

Since the 2 gallons of gas increased the fill ratio from 1/6 to 1/4, we can find how much of the tank the 2 gallons filled by solving the equation 1/4 - 1/6 = 1/12. This means that each gallon of gas is 1/24th of the tank.

Thus, the tank has a fuel capacity of 24 gallons.

Answer:

24

Step-by-step explanation:

Let x be the total fuel capacity of the tank, in gallons.

Then from the given information

x/6 + 2 = x/4,

Multiplying both sides by 12 to remove the fractions, we get

2x + 24 = 3x so x = 24. 

Therefore, the total fuel capacity of the tank is 24 gallons.

The location of point B that partitions A(3, 4) and C(5, 11) in the ratio 2:3 is (3.8, 6.8).

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let b = (x, y) represent the location of the point B, hence:

x = (2 / (2 + 3))(5 - 3) + 3 = 3.8

y = (2 / (2 + 3))(11 - 4) + 4 = 6.8

The location of point B that partitions A(3, 4) and C(5, 11) in the ratio 2:3 is (3.8, 6.8).

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By using the given graph, we will see that:

Here we have a graph of function G(x), and we want to evaluate it in different values of x.

To do that, we need to look at the interval where the lines are defined. An open dot means that the endpoint does not belong to the interval, while the closed dot means that the endpoint belongs.

First, G(0).

If you look at the graph, when x = 0 we have a closed dot on the bottom line. That is the line that we need to look to do this evaluation, there we can see that when x = 0, we have G(0) = -5.

Then we have x = 2.999.

Notice that x < 3.

And the second line (the one at y = -3) is on the interval (0, 3].

Then x = 2.999 is included on that interval, it means that:

G(2.999) = -3.

Now we have x = 0.0001

Again, notice that the second line is on the interval (0, 3]

Because 3 > 0.0001 > 0, then:

0.0001 ∈ (0, 3]

From that, we conclude that:

G(0.0001) = -3

Finally:

G(3).

Again, 3 belongs to the interval (0, 3]

Then we use the second line again.

G(3) = -3

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Answer:

G(0) = -5

G(0.0001) = -3

G(2.999) = -3

G(3) = -3

Step-by-step explanation:

Answer:

c2

Step-by-step explanation:

Answer:

Step-by-step explanation:

784-263=521

784+521=1305

answer=1305

The last  equation h(x) = 2x+4/x+1.

The pictorial representation of quantities and how the increase or decrease in one affects the other.

Analysis:

The graph cuts the x-axis and y-axis at (-2, 0) and(0, -4) respectively.

gradient of the curve = y2 - y1/x2 - x1 = -4-0/0--2 = -4/2 = -2.

The equation with a gradient equal to -2 is, h(x) = 2x+4/x+1

differentiating the equation by quotient rule,

u = 2x+4, du/dx = 2, v = x+1 dv/dx = 1

dy/dx = [tex]\frac{(x+1)(2) - (2x+4)(1)}{(x+1)^{2} }[/tex] = [tex]\frac{-2}{(x+1)^{2} }[/tex]

When x = -2, dy/dx = -2

In conclusion, 2x+4/x+1 is the equation for the curve above.

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The correct statement regarding the box plot of the data-set is given by:

The box plot will have its right tail longer than the left tail because a few exceptionally high prices make the distribution skewed to the right.

It shows:

In this problem, we have two unusually high values, $28 and $30, hence the right tail is longer than the left tail, hence the box plot is right-skewed, and the correct statement is:

The box plot will have its right tail longer than the left tail because a few exceptionally high prices make the distribution skewed to the right.

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Answer:

$2

Step by Step:

Four quarters is one dollar

Four quarters is 8 pennies

Multiply 8 by 25 (25 being the value of the quarters)

25 cents is times four is one dollar

.25x4=1, 25x4=100, 100x.25=25

2x4=8 8x25=200

A pound of pennies is worth $12.5.

In mathematics, multiplication is one of the basic operations where one number is multiplied or added repeatedly to itself as times as that of the other number. Multiplication of two numbers a and b is represented as "a × b", read as a multiplied to b or a times b.

For example 2 multiplied to 4 implies that 2 is added to itself like 4 times (2+2+2+2) or 4 is added to itself 2 times (4+4).

We have from the question,

1 quarter = 2 pennies

Also, it is given that,

A pound of quarters = $25

Since 1 quarters = 2 pennies, we have,

A pound of 2 pennies = $25

A pound of 1 penny = 25 / 2

                                 = 12.5

Hence we have a pound of pennies worth $12.5.

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By the distributive property, 5(x+3) is equal to 5x + 15.

The equation of the line will be y = [tex]\dfrac{1}{5}x + \dfrac{12}{5}[/tex]

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

First, we need to find the equation of the line that is given:

We can use the formula,

[tex]m = \dfrac{y_1 - y_2}{x_1-x_2}[/tex]

[tex]m=\dfrac{-3-(-4)}{0-(-5)}=\dfrac{1}{5}[/tex]

So the equation for this line is  

y = (1/5) x - 3

This means that the equation for the line we are trying to find has a slope of as well

Let's put the points in the equation and try to find the y-intercept:

2 = [tex]\dfrac{1}{5}[/tex] ( -2 ) + b

[tex]\dfrac{15}{5} = b[/tex]

So the final equation for the line we are trying to find is y = [tex]\dfrac{1}{5}x + \dfrac{12}{5}[/tex]

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This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality. The value of y can be found as shown below.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

 p∝ q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

1.) The relation can be written as,

y ∝ x

y = kx

27 = k × 3

k = 9

Value of y, when x=4 is,

y = 9 × 4 = 36

2.)  The relation can be written as,

y ∝ x²

y = k x²

160 = k × 4²

160 = k × 16

k = 10

Value of y, when x=6 is,

y = 10 × 36 = 360

3.) The relation can be written as,

y ∝ (1/x)

y = k/x

16 = k × (1/2)

k = 32

Value of y, when x=17 is,

y = 32 × (1/17) = 1.8823

4.)  The relation can be written as,

y ∝ (1/x²)

y = k(1/x²)

64 = k × (1/4²)

64 = k × (1/16)

k = 1024

Value of y, when x=7 is,

y = 1024 × (1/49) = 20.8979

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Answer:

4/8 = y/14

Step-by-step explanation:

These triangles are similar (see 1 sign of similarity of triangles)
Let's rotate the 2nd triangle, we'll see that the ratio of y to 14 is 4/8

Answer:

48 and 37

Step-by-step explanation:

The 2 square numbers are 16 (4 squared) and 64 (8 squared)

So the difference between these 2 numbers: 64 - 16=48

The 2 cube numbers are 27 (3 cubed) and 64 (4 cubed)

64-27=37

answer:

48 and 37

step explanation:

The 2 square numbers are 16 (4 squared) and 64 (8 squared)

So the difference between these 2 numbers: 64 - 16=48

The 2 cube numbers are 27 (3 cubed) and 64 (4 cubed)

64-27=37

Delete the commas if necessary.

============================================================

Explanation:

There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.

Plug n = 6 and r = 2 into the nCr combination formula below

[tex]n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\[/tex]

This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.

Repeat those steps for the other grade levels.

n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.

You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.

Similarly, 8C4 = 70 is the number of ways to pick the juniors.

Lastly, 14C3 = 364 is the number of ways to pick the seniors.

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

To recap, we have...

Multiply out those values to get to the final answer.

15*1287*70*364 = 491,891,400

This massive number is a little under 492 million.

The diameter of the cell model according to the taks content is; 14in.

Volume of paint = 615.44 square inches

π = 3.14

Volume of a sphere = 4πr²

615.44 = 4 × 3.14 × r²

615.44 = 12.56/r²

r² = 615.44 ÷ 12.56

r² = 49

r = 7

Hence, the diameter of the cell is; 2 × r = 2 × 7 = 14in.

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Answer:

The second and third equations are correct.  

Step-by-step explanation:

Note that the equations are all the same, with the exception of the math operation (=,>,<,[tex]\leq[/tex], etc.).  Let's do one calculation and then decide which of the statements is true.

The components may be simplified by separating the numbers from the exponents and doing the calculations separately:

(2.06x10^-2)(1.88x10^-1)  becomes (2.06*1.88)*(10^-2 * 10^-1)

Left Side:

(2.06*1.88) = 3.91

(10^-2 * 10^-1) = 10^-3  [The exponents add when multiplying]

(2.06x10^-2)(1.88x10^-1) = 3.91x10^-3

Right side:

(7.69/2.3) = 3.343

(10^-2)/(10^-5) = 10^3  [The bottom exponent is subtracted from the top. ( -2 - (-5)) = 3   ]

(7.69x10^-2)/(2.3x10^-5) = 3.343x10^3

For all equations:

LEFT                    RIGHT

3.91x10^-3       3.343x10^3

We can now answer the question.  Is the left side (3.91x10^-3 )      

A.  <

B.  =>

C.  >, or

D.  =

to the right side (3.343x10^3)

We can drop the 10^-3 to make the comparison simpler, since it is the same on both sides.  Think of it as dividing both sides by 10^3.

                                             Correct?

A.    3.91   <   3.34                NO

B.     3.91 =>  3.34                YES  

C.    3.91  >    3.34, or          YES

D.    3.91  =    3.34                NO

The number of possible license plates that can be issued using this system is 67600000.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.

Here, number plate contains 5 numbers and 2 letters

Total possible number (0-9) = 10

Total possible letters (A-Z) = 26

Possible number plates which contains 5 numbers and 2 letters are

          ¹⁰C₁ X  ¹⁰C₁ X  ¹⁰C₁ X  ¹⁰C₁ X  ¹⁰C₁ X ²⁶C₁ X ²⁶C₁

             10 X 10 X 10 X 10 X 10 X 26 X 26

                 10⁵ X 26²

                   676 X 10⁵

                 67600000

Thus, the number of possible license plates that can be issued using this system is 67600000.

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