On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 2 3/4 when a = -2 3/4 . Which equation represents this direct variation between a and b?

A) 22°

∡DBG = (360° - BD - BG)/2

= (360° - 170° - 146°)/2

= 44°/2

= 22°

Let A, B, and C denote the sets of students that have taken calculus, sociology, and Spanish, respectively.

We're given that [tex]A\cup B\cup C[/tex] consists of 187 students.

We want to find the size of [tex]A\cap B\cap C[/tex], given that

• A has 61 students;

• B has 78;

• C has 72;

• [tex]A\cap B[/tex] has 15;

• [tex]A\cap C[/tex] has 20; and

• [tex]B\cap C[/tex] has 13.

Using the inclusion/exclusion principle, we have

[tex]|A\cup B\cup C|=|A|+|B|+|C|-(|A\cap B|+|A\cap C|+|B\cap C|)+|A\cap B\cap C|[/tex]

where |X| denotes the size of the set X. Plug in all the known sizes:

[tex]187=61+78+72-(15+20+13)+|A\cap B\cap C|[/tex]

[tex]\implies|A\cap B\cap C|=24[/tex]

so 24 students have taken all three classes.

Answer:

3 1/3 km or 3.33 km (to the hundredth)

Step-by-step explanation:

Using the given formula,

estimated distance = v.t  = velocity * time,

velocity = 5 km/h

time = 40 minutes = [tex]\frac{40}{60}[/tex] hours = [tex]\frac{2}{3}[/tex]  hours

Therefore

distance = 5 km/h * [tex] \frac{2}{3} [/tex]  hours = 10/3 km

= 3.33 km approximately

Answer:

[tex]\boxed{Distance = 3.33\ km}[/tex]

Step-by-step explanation:

Given:

Time = t = 40 min = 40/60 = 0.67 hours

Speed = v = 5 km/hr

Required:

Distance = S = ?

Formula:

Distance = Speed × Time

Solution:

Distance = 5 × 0.67

Distance = 3.33 km

Answer:

Step-by-step explanation:

[tex]x \times 2 + 1 = 10[/tex]

[tex]2x + 1 = 10[/tex]

Move constant to R.H.S and change its sign

[tex]2x = 10 - 1[/tex]

Subtract the numbers

[tex]2x = 9[/tex]

Divide both sides of the equation by 2

[tex] \frac{2x}{2} = \frac{9}{2} [/tex]

Calculate

[tex]x = 4.5[/tex]

Hope this helps..

Best regards!!

Answer:

8 more unit of tiles

Step-by-step explanation:

The function is given as;

f(x) = x² - 6x + 1

Now, we want to add more unit tiles to complete the square.

The given function(f(x)) is of the order 2 due to the highest power of 2 attached to x, but the side of the square will be of the order 1.

Now, Let's make a general order 1 expression ax + b to be the side of the square.

From the function forming the square after adding some p unit tiles, we have;

f(x) + p = (side of square)²

Thus;

x² - 6x + 1 + p = (ax + b)²

x² - 6x + 1 + p = a²x² + 2abx + b²

Comparing both sides of the equation, we have;

a² = 1

2ab = 6

b² = 1 + p

From a² = 1, a = 1

From 2ab = 6,putting 1 for a, we have;

2(1)b = 6

b = 6/2

b = 3

From b² = 1 + p

Putting 3 for b, we have;

3² = 1 + p

9 = 1 + p

9 - 1 = p

p = 8

Thus, 8 more unit of tiles are required to complete the square.

Answer:

The amount spent on shower water by Trevor's family in the past month is $86.4

Step-by-step explanation:

The given information are;

The number of people in Trevor's family house are 6

The volume of water each person showered with during the month = 72 litres

The water costs = $0.20 per litre

The total volume of water used for shower by the 6 people = 72 × 6 = 432 litres

The amount spent on shower water by Trevor's family in the past month = The total volume of water used for shower × The cost per litre of water

The amount spent on shower water by Trevor's family in the past month = 432 × 0.2 = $86.4.

Answer:

$86.4

Step-by-step explanation:

Answer:

The axis of symmetry, vertex, degree of polynomial and x and y intercepts

Step-by-step explanation:

When we talk of a polynomial function, we refer to a function that involves only non-negative integer(whole number) powers of the independent variable (x in most cases). Thus, popular examples of polynomial functions include quadratic, cubic and triatic functions.

Kindly note that once a function includes a non negative power, it is not a polynomial any longer. That is why although x^2 + 2x is a polynomial function, x^2 + 2x^-1 is not a polynomial function.

Now, there are some key features that are necessary in sketching a polynomial function.

These are the vertex, axis of symmetry, x and y intercepts and the degree of the polynomial

These properties are needed to successfully make a sketch of a polynomial function.

The vertex of a polynomial function refers to that point on the curve of the function where it changes direction. For example, quadratic polynomial functions are known to have a parabolic sketch. That point in which there is a change in direction of the parabolic curve is known as the vertex of the polynomial function. A knowledge of this would ensure a proper sketch of the polynomial function curve. It helps in showcasing the concavity of the function.

The axis of symmetry applies to polynomials with even degrees. A polynomial function with an axis of symmetry will have mirror images on each side of a line that directly cuts through the polynomial.

The x and y intercepts talks about the points at which the function touches the axes of the plot

The degree of the polynomial helps to find the end behavior of the polynomial. The degree of a polynomial refers to the highest power to which the independent variable is raised. It is an important factor in determining if a polynomial function sketch will possess an axis of symmetry.

Answer:

I have:

33 - 3N/44   marbles

N = marbles of Nicole

Step-by-step explanation:

Nicole + me = 44 marbles

m = 44 - N

m = me

N = Nicole

if i lose 1/4 of my marbles

4/4 - 1/4 = 3/4

i have left:

3/4 of my marbles

then:

m = 3(44-N)/4

m = 3*44/4 + 3*-N/44

m = 33 - 3N/44

I have finally:

33 - 3N/44

Answer:

[tex]\frac{9}{4}/\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]-2\frac{1}{4}[/tex] is equilavalent to [tex]-\frac{9}{4\\}[/tex].

[tex]-\frac{2}{3}[/tex] can stay put.

The equation is division so neither answers #2 and #3 are the correct ones because when dividing fractions the second fraction has to be flipped in order to continue multiplying instead.

In addition, when two negatives are put together the answer must always be positive.  

Hence the answer is [tex]\frac{9}{4}/\frac{3}{2}[/tex].

Answer:

C. 18.5

Step-by-step explanation:

1/2(11 + 26) = 18.5

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{x^2}{x^4+1}=\dfrac{1}{7} \ \ }[/tex]

Step-by-step explanation:

Hello,

We know that (let's assume that x is different from 0 as we cannot divide by 0)

   [tex]x+\dfrac{1}{x}=3[/tex]

and we want to estimate

   [tex]\dfrac{x^2}{x^4+1}[/tex]

Let's take the square.

[tex]9=3^2=(x+\dfrac{1}{x})^2=x^2+2\cdot x \cdot \dfrac{1}{x}+\dfrac{1}{x^2}=x^2+2+\dfrac{1}{x^2}=\dfrac{x^4+1}{x^2}+2[/tex]

So, we can write

[tex]\dfrac{x^4+1}{x^2}=9-2=7 \\ \\\\\text{*** let's take the inverse ***} \\ \\\dfrac{x^2}{x^4+1}=\dfrac{1}{7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Type I error

Step-by-step explanation:

Here, we are interested in knowing the type of error that stems from the hypotheses set up

in the question.

From the suggestion of the sample, we know that the food is actually safe but was wrongly labeled as being unsafe.

So in this case, the type of error committed is the type 1 error since the food is actually safe but there was a wrong suggestion of being generally unsafe by the sample

Answer:

A. Yes

B. Yes

C. No

Step-by-step explanation:

We can substitute each value in to the equation and see if the sides match up. Let's start with a.

[tex]4\cdot(2)-3 = -2\cdot(2)+9\\8-3 = -4+9\\5 = 5[/tex]

So, n = 2 works for equation a. Let's try B.

[tex]9\cdot(\frac{10}{3}) - 19 = 3\cdot(\frac{10}{3}) + 1\\\\\\\frac{90}{3} -19 = \frac{30}{3} + 1 \\ 30 - 19 = 10 + 1\\11 = 11[/tex]

So, m = [tex]\frac{10}{3}[/tex] works for B. Now let's try C.

[tex]3(30+8) = 2\cdot(30)-6\\3(38) = 60-6\\114 \neq 54[/tex]

So y = 30 doesn't work for C.

Hope this helped!

Answer:

D.  y + 6 = -3(x - 2)

Step-by-step explanation:

To find the equation in point-slope form, you need to use the slope and a point from that line.  The slope is -3 and the point given is (2, -6).

Point-slope form is y - y₁ = m(x - x₁).  Plug in the slope and point.

y - (-6) = -3(x - 2)

y + 6 = -3(x - 2)

Answer:

D. [tex]y - 2 = -3(x+6 )[/tex]

Step-by-step explanation:

Well point slope form is,

[tex]y - y_{1} = m(x-x_{1} )[/tex]

So we already have slope meaning we can plug that in for m.

[tex]y - y_{1} = -3(x-x_{1} )[/tex]

And with the given point (2,-6),

we can create point slope form.

[tex]y - 2 = -3(x+6 )[/tex]

Therefore,

the answer is d. [tex]y - 2 = -3(x+6 )[/tex].

Hope this helps :)

Answer:

Reflection

Step-by-step explanation:

Just took the test got a 100%

edg 2021

Answer:

A: Reflection

Step-by-step explanation:

Let's be honest, no one hardly ever pays attiontion to the explanation.

<3

Answer:

  x = 5 is the solution

Step-by-step explanation:

See the attachment for table values.

  f(x) = g(x) for x = 5

The solution to the equation ...

  2.5x -10.5 = 64(0.5^x)

is x = 5.

Answer: D

Step-by-step explanation:

D makes a lot more sense because if you are someone who watches TV a lot then your more likely to score less on a given test.

Negative correlation means that as the x values increases the y value decrease.

So in this case hours will be on the x coordinate and y will be your test score.

Answer:

about 37% chance or, rounding to the nearest tenth, 36.5% chance

Step-by-step explanation:

since there are only 6 black face cards out of 52 cards, so the fraction is 6/52

there are also 13 spade cards out of 52 cards, so the fraction is 13/52

to find the percent you have to add the two fractions becuase all you want to do is draw a black face card or a spade card. when you add them you get 19/52

then dividing the fraction gives you .3653846154 on my calculator :)

Answer:

Step-by-step explanation:

Given the sequence that represents the diameter of a circle

2.5 cm, 3.1 cm, 3.7 cm and 4.3 cm. This sequence forms an arithmetic progression with a common difference.

nth term of an arithmetic progression is expressed as [tex]T_n = a+(n-1)d[/tex]

a is the first term of the sequence

n is the number of terms

d is the common difference.

From the sequence above, the first term a = 2.5

common difference = 3.1-2.5 = 3.7-3.1 = 4.3-3.7 = 0.6

Substituting this given values into the formula above will give;

[tex]T_n = 2.5+(n-1)*0.6\\\\T_n = 2.5+0.6n-0.6\\\\T_n = 2.5-0.6+0.6n\\\\T_n = 1.9+0.6n[/tex]

If f(n) represent diameter in centimetres and n the term number in the sequence, the equation that represents the sequence of diameters is

f(n) = 1.9+0.6n

Answer:

f(n) = 0.6n + 1.9

Step-by-step explanation:

Answer:

25x  ²−49y ²

Step-by-step explanation:

We need to find product of (5x+7)(5x−7y)

By using identity (a+b)(a−b)=a −b  ²

We have a=5x,b=7y

Thus (5x+7y)(5x−7y)=(5x)  ²−(7y)  

let me know if it was helpful

25x² - 49y²

Step-by-step explanation:

To Find:

The product of (5x - 7y)(5 x + 7)

How to solve:

Just need to use the formula of a² - b² = (a+b)(a-b)

let's assume a = 5x and b = 7x

Solution:

(5x - 7y)(5 x + 7) = (5x)² - (7y)²

= 25x² - 49y²

Hence required answer is 25x² - 49y².

Answer:

The answer is below

Step-by-step explanation:

The shape of the figure attached is the shape of a sector with an angle of 90° (quarter of a circle).

From the sector, AB = AC = radius of the sector (r) = 12. Therefore:

[tex]Area\ of\ sector=\frac{\theta}{360}*\pi r^2 = \frac{90}{360}*\pi * (12)^2 = 0.25 * \pi * 144=36\pi\\\\Area\ of\ triangle\ ABC=\frac{1}{2}*base *height= \frac{1}{2}*AB*BC=\frac{1}{2}*12*12=72\\\\Area \of\ shaded\ region = Area\ of\ sector-Area\ of\ triangle=36\pi-72\\\\Area \of\ shaded\ region =36\pi-72[/tex]

From the triangle: AC² = AB² + BC²

AC² = 12² + 12² = 144 + 144

AC² = 288

AC=√288 = 12√2

[tex]Perimeter\ of\ sector=\frac{\theta}{360}*2\pi r = \frac{90}{360}*2\pi * (12) = 0.25 * 2\pi * 12=6\pi\\\\Perimeter \of\ shaded\ region = Perimeter\ of\ sector+AC=6\pi + 12\sqrt{2}[/tex]

Answer:

Trapezoid

Step-by-step explanation:

Got it right on quiz

The following that best classifies a quadrilateral with coordinates is :

A) Trapezoid

Thus, the correct answer is A.

Find out more information:

https://brainly.com/question/24200218referrer=searchResults

Answer:

The pupils who are not participating in sports games are 82

Step-by-step explanation:

According to the given data we have the following:

2/31 participate in athletics

1/9 in volleyball games

Total participants=98

Therefore, pupils participate in athletics= 98*2/31

pupils participate in athletics=6

pupils participate in volleyball games=98*1/9

pupils participate in volleyball games=10

Therefore, pupils are not participating in sports games=98-16

pupils are not participating in sports games=82

The pupils who are not participating in sports games are 82

Answer:

yes

Step-by-step explanation: i agree its 3

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{4}[/tex] x + 4 ← is in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

Parallel lines have equal slopes, thus this is slope of parallel line.

The line crosses the y- axis at (0, 2) ⇒ c = 2

y = [tex]\frac{3}{4}[/tex] x + 2 → C

Answer:

[see below]

Step-by-step explanation:

Geo has 3/8 of a pizza. His sister has 7/9 of another pizza.

Add the values:

[tex]\frac{3}{8}+\frac{7}{9}\\\\ \text{The LCM of the denominators is 72.}\\\\\frac{3*9}{8*9}=\frac{27}{72}\\\\\frac{7*8}{8*9}=\frac{56}{72}\\\\\frac{27+56}{72}=\frac{83}{72}\\\\\frac{83}{72}=1\frac{11}{72}\\\\\boxed{\frac{3}{8}+\frac{7}{9} = 1\frac{11}{72}}[/tex]

Answer:

x = 1

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, thus

AE = CE , substitute values

11x - 3 = 12 - 4x ( add 4x to both sides )

15x - 3 = 12 ( add 3 to both sides )

15x = 15 ( divide both sides by 15 )

x = 1

Answer:

[tex]x = 17[/tex]

Step-by-step explanation:

According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.

That is, [tex]x + 4 = 21[/tex]

Solve for x

[tex]x + 4 = 21[/tex]

Subtract 4 from both sides

[tex]x + 4 - 4 = 21 - 4[/tex]

[tex]x = 17[/tex]

Answer:

x = 6

Step-by-step explanation:

The x-intercept of the equation is where the graph crosses the x-axis when y = 0. So, we simply plug in 0 for y:

2(0) - x = -6

0 - x = -6

-x = -6

x = 6

Alternatively, you can graph the equation into a graphing calc and analyze where the graph crosses the x-axis.

Answer:

SAS Postulate

Step-by-step explanation:

In EDG & ADC ,

1) AD = ED ( given )

2)angle( EDG ) = angle ( ADC )................ [ Vertical Opposite Angles are equal ]

3) GD = CD ( D is the mid - point of CG )

So triangles EDG & ADC are congruent by SAS postulate....