What is the midpoint of AB

Answer:

The estimate size of the crowd is 52800 people

Step-by-step explanation:

The given information are;

The number of people that fit comfortably in a 2 by 2 foot area = 5

Therefore, we have;

The area occupied by the 5 people = 2 × 2

The crowd ratio = 5/(2 × 2) = 5/4

The area occupied by the crowd = 4 feet deep, and 1 mile long on both sides of the street

By conversion factors, 1 mile = 5,280 feet

Therefore, the area occupied by the crowd = 4 × 5280 × 2 = 42240 ft²

The number of people in the crowd = Crowd ratio × The area occupied by the crowd

The number of people in the crowd = 5/4 × 42240 = 52800 people

Therefore, The estimated size of the crowd = 52800 people.

You need to find the GCF (greatest common factor) of 96 and 36. The GCF of 96 and 36 is 12.

12 times what gets you 36?

12 times 3 gets you 36.

12 times what gets you 96?

12 times 8 gets you 96.

So the third answer has 12 as the GCF.

The answer is 12(8+3) = 96+36 = 132

♡ Hope this helped! ♡

❀ 0ranges ❀

Answer:  see both proofs below

Step-by-step explanation:

Use Difference Identity: tan (A - B) = (tan A - tan B)/(1 + tanA · tanB)

Use Unit Circle to evaluate: tan (π/4) = 1

Use Tangent Identity: tanA = (sinA)/(cosA)

Use Half-Angle Identities:

[tex]\cos \dfrac{A}{2}=\sqrt{\dfrac{1+\cos A}{2}}\\\\\\\sin \dfrac{A}{2}=\sqrt{\dfrac{1-\cos A}{2}}[/tex]

Part 1   Proof LHS → Middle

LHS:                                [tex]\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)[/tex]

Difference Identity:        [tex]\dfrac{\tan (\frac{\pi}{4})-\tan(\frac{A}{2})}{1+\tan(\frac{\pi}{4})\cdot \tan(\frac{A}{2})}[/tex]

Unit Circle:                      [tex]\dfrac{1-\tan(\frac{A}{2})}{1+ \tan(\frac{A}{2})}[/tex]

[tex]\text{Tangent Identity:}\qquad \qquad \dfrac{\frac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}}}{\frac{\cos\frac{A}{2}+\sin\frac{A}{2}}{\cos\frac{A}{2}}}[/tex]

Simplify:                             [tex]\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}[/tex]

LHS = Middle:  [tex]\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}=\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}\qquad \checkmark[/tex]

Part 2   Proof  Middle → RHS

Middle:                                     [tex]\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}[/tex]

[tex]\text{Half-Angle Identity:}\qquad \qquad \dfrac{\sqrt{\frac{1+\cos A}{2}}-\sqrt{\frac{1-\cos A}{2}}}{\sqrt{\frac{1+\cos A}{2}}+\sqrt{\frac{1-\cos A}{2}}}[/tex]

Simplify:                               [tex]\dfrac{\sqrt{1+\cos A}-\sqrt{1-\cos A}}{\sqrt{1+\cos A}+\sqrt{1-\cos A}}[/tex]

Rationalize Denominator:  [tex]\dfrac{\sqrt{1+\cos A}-\sqrt{1-\cos A}}{\sqrt{1+\cos A}+\sqrt{1-\cos A}}\bigg(\dfrac{\sqrt{1+\cos A}-\sqrt{1-\cos A}}{\sqrt{1+\cos A}-\sqrt{1-\cos A}}\bigg)[/tex]

                                          [tex]=\dfrac{1+\cos A-2\sqrt{1-\cos^2 A}+1-\cos A}{1+\cos A-(1-\cos A)}[/tex]

Simplify:                                [tex]\dfrac{2-2\sqrt{1-\cos^2 A}}{2\cos A}[/tex]

                                         [tex]=\dfrac{2-2\sqrt{sin^2 A}}{2\cos A}[/tex]

                                         [tex]= \dfrac{2-2\sin A}{2\cos A}[/tex]

Factor:                                   [tex]\dfrac{2(1-\sin A)}{2(\cos A)}[/tex]

Simplify:                               [tex]\dfrac{1-\sin A}{\cos A}[/tex]

Expand:                                [tex]\dfrac{1-\sin A}{\cos A}\bigg(\dfrac{1+\sin A}{1+\sin A}\bigg)[/tex]

                                          [tex]=\dfrac{1-\sin^2 A}{\cos A(1+\sin A)}[/tex]

Simplify:                                 [tex]\dfrac{\cos^2 A}{\cos A(1+\sin A)}[/tex]

                                          [tex]=\dfrac{\cos A}{1+\sin A}[/tex]      

Middle = RHS:   [tex]\dfrac{\cos A}{1+\sin A}=\dfrac{\cos A}{1+\sin A}\qquad \checkmark[/tex]            

Answer:

Step-by-step explanation:

Function means that for each x we get y, and no no x gives two different y-es

{(−5,−7),(−5,4),(−2,−8),(3,5)}  for x = -5 we have two different y-es therefore its not function

Answer:

97%

Step-by-step explanation:

89%+98%+96%+?=95×4

283+?=380

?=380-283

?=97%

The lowest score Olivia can get on her fourth test is 97%.

The average score can be determined by dividing the sum of the four scores by the total number of tests taken.

The first step is to determine the sum of the three scores Olivia already has.

Sum of scores = 89 + 98 + 96 = 283%

The second step is to multiply 95 x 4. 95% x 4 = 380%

The third step is to subtract 283% by 380%. 380% - 283% = 97%

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Answer:

Last given option is the correct answer:

"The product of complex conjugates is a sum of two squares and is always a real number."

Step-by-step explanation:

The product of two conjugates can be described and solved like this:

[tex](a + b\,i) \,(a - b\,i)= a^2-a\,b\.i+a\,b\,i-b^2\,i^2=a^2+0-b^2\,(-1)= a^2+b^2[/tex]

so, no matter what the values for the real values a and b are, the product is always a real number and the sum of two squares.

Answer:

(a + bi)(a – bi) = a2 – (bi)2 = a2 + b2

The product of a complex number and its complex conjugate is

✔ always

a real number.

Answer:

[tex]\Huge \boxed{\mathrm{C. \ 129 }}[/tex]

Step-by-step explanation:

Apply : Angles of Intersecting Chords Theorem

m∠x is half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

m∠x = 1/2(54+204)

Add numbers in brackets.

m∠x = 1/2(258)

Expand brackets.

m∠x = 129

Answer:

she would have 21 dollars left

Step-by-step explanation:

44.50-11

33.50-12.50

Answer:

[tex]\Huge \boxed{\$ \ 21}[/tex]

Step-by-step explanation:

She had $-11 initially and gained $44.50.

-11 + 44.5 = 33.5

She has $33.5 in her account.

She buys two tickets for $6.25 each.

33.5 - (2)6.25 = 21

She has $21 left in her account.

Answer:

8

Step-by-step explanation:

We know Joshua has 11 baskets of apples with a total of 88 apple, it can be written down to something like this:

88 ÷ 11

We know that 88 divided by 11 is 8, therefore, there are 8 apples in each basket.

Don't believe me? Checked work:

11 x 8 = 88

8 apples per basket

Answer:

The correct options are;

[tex]4\dfrac{2}{3} - \dfrac{\sqrt{4} }{8}[/tex]

[tex]4\dfrac{2}{3} \div \dfrac{\sqrt{4} }{8}[/tex]

Step-by-step explanation:

We note that a rational number is one that can be expressed as a ratio of two integers a and b

An irrational number is one that cannot be expressed as a ratio of two integers. Example of an irrational number is √3

Also an irrational number divided by a rational number is an irrational number, therefore, we have, the expressions without irrational numbers, which are;

[tex]4\dfrac{2}{3} - \dfrac{\sqrt{4} }{8}[/tex] = [tex]\dfrac{53}{12}[/tex]

and

[tex]4\dfrac{2}{3} \div \dfrac{\sqrt{4} }{8}[/tex]

Answer:

A.-8

Step-by-step explanation:

The greater the slope the steeper the line.

In order to determine which line is closer to vertical, we have to consider the absolute values, because the slope can be positive or negative.

Therefore, the steepest is -8.

Answer:

[tex]\Huge \boxed{\mathrm{52\°}}[/tex]

Step-by-step explanation:

Complementary angles add up to 90 degrees.

There are two angles in this case.

Let the first angle be x.

Let the second angle be x+14.

The sum of these two angles is 90.

x + x + 14 = 90

Combine like terms.

2x + 14 = 90

Subtract 14 from both sides.

2x = 76

Divide both sides by 2.

x = 38

Let x = 38 for the second angle.

38 + 14 = 52

The two angles are 52 degrees and 38 degrees.

52 degrees is 14 degrees more than complementary angle.

Answer:

[tex]\huge\boxed{ Angle = 52\ degrees}[/tex]

Step-by-step explanation:

Complementary angles add up to 90 degrees

So, Let the first angle be x then the second angle will be x + 14

Given condition is:

x + x + 14 = 90

2x + 14 = 90

Subtracting 14 to both sides

2x = 90 - 14

2x = 76

Dividing both sides by 2

x = 38

So, the second angle that is 14 degrees more than 38

=> Second Angle = 38 + 14

=> Second Angle = 52 degrees

We have that in teach number system to someone who had never seen numbers before you have to give a clear and understand explanation on numbers and number systems to in a language they can understand.

Firstly we have to understand what number are

Numbers

A number or numbers are just words or expressions or drawings or even symbols use to represent(Represent being a key word) a particular quantity or used to calculate.

With the definition above every one must have come across number but in a different way from other

Therefore

its just left for you to open their eyes to what the have already encountered

In conclusion

You have to give a clear and understand explanation on numbers and number systems to in a language they can understand

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A number system is a mathematical system for representing numbers, that is, quantities.

Thus, the numbers are writing symbols that allow a mental representation of a certain quantity, as well as the different mathematical operations that arise from said quantities.

Otherwise, that is, if the numbers did not exist, the representation of quantities would be very limited.

It also would only abstain from the existence or nonexistence of a certain thing or situation.

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Answer:

The graph of a proportional relationship has the same unit rate, is a straight line, and starts at the origin.

Step-by-step explanation:

this the answer

The graph of a proportional relationship is a straight line.

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

We have a graph of Molly’s garden.

Since, the graph is not given, i will write the condition for proportional relationship. The graph of a proportional relationship is a straight line whose equation is given by -

y = mx + c

Therefore, the graph of a proportional relationship is a straight line.

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Answer:

u= -3

Step-by-step explanation:Solve for

u by simplifying both sides of the equation, then isolating the variable.

Answer : 5u– 5(1–u)=u+8

5u - 5+ 5u = u+ 8

10u -5 = u+ 8

9u = 13

u = 1.44

Answer:

Hey! I think I can help.

Parallel lines are lines that can't meet.Perpendicular lines are lines that can meet.

e.)Since the line at 12 and the line at 9 meets then it is a perpendicular line.

c.)Perpendicular line.

a.)Perpendicular line.

b.)Parallel line.

d.)Depending on how they are faced if the ends of the telephone wire meets the second one then it is perpendicular but if not then it is parallel that's if they are in different directions which they can not meet.Thank you for the question

Answer:

2*x^4*z^3

Step-by-step explanation:

To answer this kind of question, you first start rearranging the terms in the numerator and denominator, so you don't get confused.

3x^3 * 4x^3 * z^4 / 2x * x * 3z

Now you multiply like parts in the numerator and denominator to keep it simple.

(3x^3 * 4x^3) * z^4 / (2x * x) * 3z

3x^3 * 4x^3 = 12x^6

2x * x = 2x^2

12x^6 * z^4 / 2x^2 * 3z

Now divide like terms that are in the numerator and denominator so multiplying later will be easier.

12x^6 / 2x ^ 2 * z^4 / 3z

12x^6 / 2x^2 = 6x^4

z^4/3z = z^3 / 3

Now you multiply both terms,

6x^4 * z^3/3

2*x^4*z^3

Answer:

P = 26

Step-by-step explanation:

see attached

to get the side 5,

sqrt((10-7)² + 4²)

side = 5

P = 4 + 7 + 5 + 10

P = 26

Answer:

A y C  → complementarios

A Y B → suplementarios

D Y E  → suplementarios

El complemento de un ángulo de 39°, mide  51°

La amplitud de m, como suplemento es de 36°

Si lo tomamos como ángulo conjugado, es de 217°

Step-by-step explanation:

Ángulos completarios → Aquellos que sumados, me dan 90°

Ángulos complementarios → Aquellos que sumados, me dan 180°

Angulos complementarios entonces, son:

A y C (sumados, dan 90° → 25 + 65)

Angulos suplementarios entonces, son:

A y B (sumados, dan 180° → 25 + 155)

D y E (sumados, dan 180° → 30 + 150)

Complemento de un ángulo de 39° → Ya vimos que su suma debe dar 90°, por lo que el complemento mide: 90 - 39 = 51°

Si la amplitud del ángulo R es 143°, la del ángulo m, será 37°. Sería el ángulo suplementario a R.

No podríamos tener un complemento porque estamos en valores a 90°, pero también se podría obtener otro ángulo cuya amplitud sea de 217°, en este caso ambos ángulos suman 360°, se los llama angulos conjugados.

Answer:

1/7

Step-by-step explanation:

From the above question, we have the following values:

White socks = 2

Brown socks = 4

Black socks = 2

Total number of socks = 8

We are told in the question that:

You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot.

From above question, we can see that this is a probability with dependent events. This means have a white sock on your left foot and brown sock on your right are events that depend on each other, hence, the probability will occur with replacement.

The probability ( having a white sock on your left foot and brown sock on right) =

2/8 × 4/7

= 8/56

= 1/7

Therefore, the probability of this occuring is 1/7

Answer:

All (a,b) that satisfy a.b < 0 will make that statement false

Step-by-step explanation:

It is only right when:

|a-b| = |a| - |b|

<=> ( |a-b| ) ^ 2 = ( |a| - |b| ) ^ 2

<=> a^2 - 2ab + b^2 = a^2 - 2.|ab| + b^2

<=> ab = |ab|

<=> ab ≥ 0

So, when ab < 0, it's wrong

Answer:

if you round the 13 to fifteen and the 49 to 50, your best estimate answer would be 750. Hope this is what you were looking for and that it helps!

Step-by-step explanation:

The best estimate of the product of 13 and 49 is 600.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

The two given numbers are 13 and 49.

The product of 13 and 49 is

13×49 =637

So, 637 is estimated to 600

Therefore, the best estimate of the product of 13 and 49 is 600.

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Answer:

59°

Step-by-step explanation:

From the question given, we obtained the following:

C + (3x + 16) = 180 (sum of angle on a straight line)

5x – 54 = 3x + 16 (Altanate angles are equal)

Next, we shall determine the value of x.

This can be obtained as follow:

5x – 54 = 3x + 16

Collect like terms

5x – 3x = 16 + 54

2x = 70

Divide both side by the coefficient of x i.e 2

x = 70/2

x = 35

Finally, we shall determine the value of C as shown below:

C + 3x + 16 = 180

But, x = 35

C + 3(35) + 16 = 180

C + 105 + 16 = 180

C + 121 = 180

Collect like terms

C = 180 – 121

C = 59°

Therefore, the value of C is 59°

Answer:

0

Step-by-step explanation:

The y's are the same so they do not go up or down so the slope is 0.

The slope of the line passes through points (10, 3) and (2, 3) is 0.

Given that,
The slope of the line that passes through points (10, 3) and (2,3) is to be determined.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,
The slope of the line passes through the point (10, 3) and (2, 3).
Now, put the point in the equation of the slope,

m =(y₂ - y₁) /  (x₂ - x₁)
m = 3 - 3 / (2 - 10)
m = 0 / -8
m = 0

Thus, the slope of the line passes through the points (10, 3) and (2, 3) is 0.

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1.

[tex](3^3+5x^2+3x-7)+(8x-6x^2+6)=\\\\=27\ \underline{+\,5x^2}\ \underline{ \underline{+\,3x}}-7\ \underline{\underline{\,+8x}}\ \underline{-\,6x^2}+6=\\\\=-x^2+11x+26[/tex]

or if you mean (3x^3+5x^2+3x-7)+(8x-6x^2+6):

[tex](3x^3+5x^2+3x-7)+(8x-6x^2+6)=\\\\=3x^3\ \underline{+\,5x^2}\ \underline{ \underline{+\,3x}}-7\ \underline{\underline{\,+8x}}\ \underline{-\,6x^2}+6=\\\\=3x^3-x^2+11x-1[/tex]

2.

[tex](8x-4x^2+3)-(x^3+7x^2+3x-8)=\\\\=\underline{8x}\ \underline{\underline{-\ 4x^2}}+3-x^3\ \underline{\underline{-\,7x^2}}\ \underline{-\,3x}+8=\\\\=-x^3-11x^2+5x+10[/tex]

Answer:

-1

Step-by-step explanation:

Since the denominators are the same, then we add the numerators

-6+-5/11

-11/11

-1

Step-by-step explanation:

-6/11 - 5/11 = -11/11

1. The fraction of -5/11 stays negative because -*+ = -. So the fraction stays negative.

2. Then, you can add the two fractions because they are both the same sign and also have the same denomination.

The answer is -1 or -11/11.

Hope this helped,

Kavitha

Answer:

3

Step-by-step explanation:

2a + C

Let a = 2 and c = -1

2* 2 + -1

4 -1

3

Answer:

Step-by-step explanation:

[tex]a = 2\\ b = -3\\c = -1\\ d = 4\\\\2a+c =?\\2(2) +(-1)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:2\left(2\right)\::\quad 4\\=4+\left(-1\right)\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:4+\left(-1\right)\:\\:\quad 3[/tex]