A sample of 40 11th graders were asked to select a favorite pattern out of 6
choices. The following display shows what their favorite color patterns were.
The counts have been recorded in the accompanying table according to
pattern and the number of students who selected that pattern. What is the
missing value in the table?
NEN
OA. 12
OB. 10
O C. 11
D. 13
Color Pattern
Blue on gray
Green
Pink polka dots
Purple
Red and orange
stripes
Yellow
Frequency
6
7
8
7
3

Solving the given equations we get,

If the quadratic equation is [tex]ax^2+bx+c=0[/tex] then the solutions of this are given by,

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here in the problem given that,

The first quadratic equation is [tex]9x^2-25=-12-10x[/tex]

Converting it into standard form of quadratic equation we get,

[tex]9x^2-25=-12-10x\\9x^2-25+12+10x=0\\9x^2+10x-13=0[/tex]

So here a=9,b=10,c=-13

The solutions of the equation is given by,

[tex]x=\frac{-10\pm\sqrt{10^2-4\times9\times(-13)}}{2\times9}=\frac{-10\pm\sqrt{100+468}}{18}\approx\frac{-10\pm23.83}{18}[/tex]

So either,

[tex]x=\frac{-10+23.83}{18}=\frac{13.83}{18}\approx0.77[/tex]

Or,

[tex]x=\frac{-10-23.83}{18}\approx-1.88[/tex]

So the solutions are given by x=0.77 and -1.88

Second quadratic equation is [tex]4n^2-1=12n+3n^2+11[/tex]

Converting the equation in its standard form we get,

[tex]4n^2-1=12n+3n^2+11\\4n^2-1-12n-3n^2-11=0\\n^2-12n-12=0[/tex]

so here a=1,b=-12,c=-12

Solutions are given by,

[tex]n=\frac{-(-12)\pm\sqrt{(-12)^2-4\times1\times(-12)}}{2\times1}=\frac{12\pm\sqrt{144+48}}{2}\approx\frac{12\pm13.86}{2}[/tex]

So either

[tex]n=\frac{12+13.86}{2}=12.93[/tex]

Or,

[tex]n=\frac{12-13.86}{2}=-0.93[/tex]

Solutions are given by n = 12.93 and -0.93

Hence the solutions are x=0.77 and -1.88 for first equation and n=12.93 and -0.93 for second equation.

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Answer:

[tex]\rm slope: -\dfrac{7}{6}[/tex]

[tex]\rm Distance: 2\sqrt{85} \ units[/tex]

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y }{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here given points are: (6, -6), (-6, 8)

Insert the values:

[tex]\sf \rightarrow slope: \dfrac{8-(-6)}{-6-6}[/tex]

[tex]\sf \rightarrow slope: \dfrac{8+ 6}{-12}[/tex]

[tex]\sf \rightarrow slope: \dfrac{14}{-12}[/tex]

[tex]\sf \rightarrow slope: -\dfrac{7}{6}[/tex]

[tex]\sf Distance \ between \ points : \sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Using the formula,

[tex]\sf d = \sqrt{(-6 - 6)^2 + (8-(-6))^2}[/tex]

[tex]\sf d = \sqrt{(-12)^2 + (14)^2}[/tex]

[tex]\sf d = \sqrt{144 +196}[/tex]

[tex]\sf d = \sqrt{340}[/tex]

[tex]\sf d = \sqrt{85 \times 4}[/tex]

[tex]\sf d = 2\sqrt{85}[/tex]

Hence, the distance is 2√85 units.

Hii!

___________________________________________________________

[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]

Slope =

Distance =

[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}[/tex]

[tex]\bullet[/tex] Let's work out the slope

[tex]\twoheadrightarrow\sf \cfrac{y2-y1}{x2-x1}[/tex]

[tex]\bullet[/tex] Stickin the values

[tex]\twoheadrightarrow\sf \cfrac{8-(-6)}{-6-6}[/tex]

[tex]\bullet[/tex] Simplify

[tex]\twoheadrightarrow\sf \cfrac{8+6}{-12}[/tex]

[tex]\bullet[/tex] Finish simplifying

[tex]\twoheadrightarrow\sf \cfrac{14}{-12}[/tex]

[tex]\bullet[/tex] Reduce the fraction

[tex]\twoheadrightarrow\sf \cfrac{7}{-6}[/tex]

[tex]\bullet[/tex] Work out the distance

[tex]\twoheadrightarrow\sf \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

[tex]\bullet[/tex] Stick in the values

[tex]\twoheadrightarrow\sf \sqrt{(-6-6)^2+(8-(-6)^2}[/tex]

[tex]\bullet[/tex] Simplify the radical expression

[tex]\twoheadrightarrow\sf \sqrt{(-12)^2+14^2}\\\\\twoheadrightarrow\sf \sqrt{144+169} \\\\\twoheadrightarrow\sf \sqrt{340}\\\\\twoheadrightarrow\sf \sqrt{85\cdot4} \quad (simplifying\,the\,surd)[/tex]

[tex]\ddagger[/tex] [tex]\boldsymbol{DISTANCE=2\sqrt{85} \,Units}[/tex] [tex]\ddagger[/tex]

--

Hope that this helped! Best wishes.

--

Answer:

-3(-4-4) would work giving you 24

Step-by-step explanation:

im sorry that qustion doesnt make sense, if you mean higher then 21, less than 30 than -3(-4-4) would work giving you 24

If both pipes are opened. Then the number of hours to fill up the tank fully is 100 hours.

The complete question is attached below.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Let t be the filling time.

Then we have

Time is inversely proportional to rate of filling tank.

1/20 – 1/25 = 1/t

0.05 - 0.04 = 1/t

          0.01 = 1/t

                t = 1/0.01

                t = 100 hours

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Answer:

D. 2

E. -2

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

You should have this in mind , one raise to the power of any number is one and also any number with the power zero is 1.

{(1)¹⁰⁰ + (−1)¹⁰¹+(2500)⁰} x2³

= 1 - 1 + 1 × 8

= 1 - 1 + 8

= 1 +7

= 8

Answer:

1st set of equations - parallel

2nd set - perpendicular

3rd set - neither

Step-by-step explanation:

First set:

simplify the equation for line 1  by dividing by -4: y = 0.5x + 1

simplify the equation for line 1  by dividing by -6: y = 0.5x - 1.5

Both have the same slope: 0.5 so the lines are parallel.

Second set:

simplify the equation for line 1  by dividing by 3: y = -2/3x + 4

simplify the equation for line 1  by dividing by -4: y = 3/2x - 7/4

-2/3 * 3/2 = -1, so the lines are perpendicular

Third set

simplify the equation for line 1  by dividing by 1/2: y = -2x+4

simplify the equation for line 1  by dividing by 2: y = -1/4x +2

-2x+4=-0.25x+2

-2x+0.25x=2-4

-1.75x=-2

x=1.14

y=-2(1.14)+4 = 1.7143. So there is an intersection point

The pair of lines 2x - 4y = -4 & 3x - 6y = 9, 2x + 3y = 12 & and 6x - 4y = 7, and x + (1/2)y = 2 & (1/2)x + 2y = 4 will be parallel lines, perpendicular lines, and neither parallel nor perpendicular, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The pair of lines is given as,

2x - 4y = -4     ⇒        y = (1/2)x + 1

3x - 6y = 9      ⇒        y = (1/2)x - 3/2

The pair of lines are parallel to each other because the slope is equal.

2x + 3y = 12     ⇒        y = -(2/3)x + 4

6x - 4y = 7       ⇒        y = (3/2) x - 7/4

The pair of lines are parallel to each other because the product of slopes is -1.

x + (1/2)y = 2        ⇒        2x + y = 4

(1/2)x + 2y = 4      ⇒        2x + 4y = 8

The pair of lines are neither parallel nor perpendicular to each other.

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Answer:

G(-6) = -29

Step-by-step explanation:

plug -6 into the equation

G(-6) = 5(-6) +1

multiply

G(-6) = -30+1

add

G(-6) = -29

Answer:

See below

Step-by-step explanation:

When you multiply or divide both sides of an inquality equation by a NEGATIVE number , it reverses the symbol to see this in action:

- 4n >36       Instead of dividing by -4   let's ADD - 4n to both sides

0 > 36 + 4n    now SUBTRACT 36 from both sides

-36 > 4n       re-arrange just a little

4n < -36       <======== see how the symbol has reversed ???

n < -9        

Hii!

___________________________________________________________

Answer:

'Cause both sides were divided by a negative number! ^^

Step-by-step explanation:

The sign of the inequality was flipped because you divided both sides of the inequality by -4, which is a negative number.

When we divide, or multiply, both sides of an inequality by a negative number, we flip the inequality sign.

--

Hope that this helped! Best wishes.

--

Answer:

-38,994

Step-by-step explanation:

-291*134

=-38,994

Answer:

-38,994

Step-by-step explanation:

(-291) × 134

Apply PEMDAS.

Remember,

Solution:

Evaluating,we obtain

The range of y = sin(x) is [-1,1]

The function is given as:

y = sin(x)

The above function is the parent function of a sine function.

A sine function has a minimum of -1 and a maximum of 1.

This is represented by the interval [-1,1]

Hence, the range of y = sin(x) is [-1,1]

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A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

As 106.7 out of 100 gives 106.7% calculated below:

Percentage formula = (Obtained value/total value) x 100.......eq(1)

Putting values:

= (106.7/100) x 100

= 106.7%

Now finding 106.7% of 4:

Putting values in eq (1):

106.7% = (Obtained value/4) x 100

106.7/100= (Obtained value/4)    

1.067= (Obtained value/4)

4 x 1.067 = Obtained value

4.268 = Obtained value

Then 106.7% of 4 will be equal to 1.067 x 4  = 4.268

A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.

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The members of a possible set C are {6, 9, 12}

The universal set is the set that contains all other sets. Given the following sets

ξ = {x:x is an integer, 2 ≤ x ≤ 14}

B = {x:x is a prime number}

A = {x:x is a multiple of 3}

The sets B and A are:

B = {2, 3, 5, 7, 11}

A = {3, 6, 9, 12}

If C is a subset of A with a cardinality of 3, hence the required set will be {6, 9, 12}. Note that 3 is excluded since B n C must be an empty set.

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A binomial expression is a two-term algebraic statement with variables, coefficients, exponents, and a constant. The various terms that are possible are a⁷b, b⁸, a⁶b², and a⁸.

A binomial expression is a two-term algebraic statement with variables, coefficients, exponents, and a constant. x² + 4x is an example of a binomial polynomial.

The variable terms that are possible in the expansion of (3a + 4b)⁸ are terms whose sum of powers is equal to 8.

Hence, the various terms that are possible are a⁷b, b⁸, a⁶b², and a⁸.

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Using the cosine rule, BC = √(115² + 80² - 2(115)(80)(cos 72) ≈ 118.1 m (1 decimal place).

If we are given a triangle with two known sides and an included angle, the cosine rule that can be used to find the side opposite to the given angle is: a = √(b² + c² - 2bc(cos A)

We are given the following:

Plug in the values

BC = √(115² + 80² - 2(115)(80)(cos 72)

BC ≈ 118.1 m (1 decimal place)

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Answer:

(-5, -7) and the x-axis

Step-by-step explanation:

when looking for a point that is 7 points away, we are looking for a difference of 7 in either the x-value or the y-value.

[remember: a point is written as (x, y) ]

We know that the x-value is -7, meaning that it is 7 units under the x-axis (meaning that it is 7 units away)

We know that our point, (2 , -7) has the same y-value as (-5, -7), so we are looking for a change in x. The difference (which is the change) between:

-5 and 2 is 7

(2 - (-5) = 2 + 5 = 7)

so, both the x-axis and the point (-5, -7) are 7 units away from (2, -7)

(the other point (-7, 7) is not near (2 , -7) at all--they have a larger difference on both the y-values, the x-values, and the length of if you made a diagonal line)

(I've attached an image to help you visualize what we're doing)

hope this helps!!

Answer:

d because the point satisfied both

Answer:

D

Step-by-step explanation:

Answer:

h^24

Step-by-step explanation:

hope that helpssndbfbsb

Answer: -24

Step-by-step explanation:

I am assuming you want the value of (f × g)(-2)

[tex]f(-2)=(-2)^2+4\\f(-2) = 4+4\\f(-2)=8[/tex]

[tex]g(-2)=2(-2)+1\\g(-2)=-4+1\\g(-2)=-3[/tex]

8 × -3 = -24

Answer:

56cmsquared

Step-by-step explanation:

if you look clearly at that question that diagram which has the coloured part out of that small square comes a quarter circle.

now take that quarter circle and get its area .

then put a dotted line such that they'll be formation of a triangle in that quarter circle.

then get the area of that quarter triangle in minus it from the area of the quarter circle.

and you'll get the area of 1 shaded part because you had subdivided those shaded parts by the dotted line you had kept earlier in order to emerge with a triangles

after that what multiply what you got by two to get the whole shaded part then finalize by multiplying by two because two shapes were shaded.

good day

Answer:

False

Step-by-step explanation:

these lines are unable to form a triangle, the longest line (BA) is 15. The other small lines (AC and CB) if added together, need to be longer than 15, otherwise if you were trying to form a triangle, they would not be able to connect completely with eachother while creating a triangle shape

The factors of the given polynomial will be ( x + 2 ), ( x + 5 ) and ( x + 3 ).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given expression will be solved as:-

f(x) = x³ + 10x² + 31x + 30

f(x) = ( x³ + 7x² + 10x + 3x² + 21x + 30

f(x) = ( x² + 7x + 10 ) ( (x + 3 )

f(x) = ( x²+ 5x + 2x + 10 ) ( x + 3 )

f(x) =[ x ( x+ 5 ) +2 ( x+ 5) ] ( x + 3 )

f(x) = ( x + 5 ) ( x + 2 ) ( x + 3 )

Therefore factors of the given polynomial will be ( x + 2 ), ( x + 5 ) and ( x + 3 ).

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Body design, muscular power and steadiness, flexibility and cardio-respiratory endurance are the components of fitness. Fitness is a major component of a healthy lifestyle.

While performing tasks during gymnastics she needs balance so that she can maintain and control a particular position.

Body design, muscular power and steadiness, flexibility and cardio-respiratory endurance are the components of fitness. Fitness is a major component of a healthy lifestyle.

Balances are of two types dynamic and static. Balance used while moving and performing the task is dynamic balance while performing in a standing position is static balance.

Gymnasts require balancing as the main component cause they use poles and beams to perform their tasks.

Therefore, balance is the skill mainly required in gymnastics.

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Answer:

m<1 OR m>7

Step-by-step explanation:

3m<5-2

3m<3

m<1

m+1>8

m>8-1

m>7

Answer:

m<1 or m>7

Step-by-step explanation:

3m + 2 < 5

3m + 2-2 < 5-2

3m < 3

[tex]\frac{3m}{3}[/tex] < [tex]\frac{3}{3}[/tex]

m < 1

[tex]\frac{m+1}{2}[/tex] > 4

[tex]\frac{m+1}{2}[/tex]*2 > 4*2

m +1 > 8

m +1 -1 > 8 -1

m > 7

9.7 to one significant figure is 10

We have:

9.7

To approximate to one significant figure, we have to estimate the number such that it is represented by a non zero digit.

When 9.7 is approximated, we have:

10

Hence, 9.7 to one significant figure is 10

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The perimeter of the figure above is [tex]43\frac{22}{40} = 43\frac{11}{20}[/tex]

The perimeter of a shape is the sum of the whole sides.

Therefore, perimeter of the figure is the addition of the whole length.

Hence,

perimeter = [tex]14\frac{3}{4}+4\frac{1}{2}+8\frac{1}{2}+10\frac{2}{5}+10\frac{2}{5}+12\frac{4}{5}[/tex]

let's convert to improper fraction for easy calculation.

Hence,

perimeter = [tex]\frac{59}{4}+\frac{9}{2}+\frac{17}{2}+\frac{52}{5}+\frac{52}{5}+\frac{64}{5}[/tex]

perimeter = [tex]\frac{590+180+340+60+60+512}{40} =\frac{1742}{40} = 43\frac{22}{40}[/tex]

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Answer:

X1 2/7

Step-by-step explanation:

Step-by-step explanation:

We can write it in radical form, and the denominator of the exponent became the power of the radical. That is

And

We can also write it as

And that's the simplified form of the given exponential form .

Answer:

x-intercept: [tex](\frac{7}{2},0)[/tex]

y-intercept: [tex](0,-7)[/tex]

Step-by-step explanation:

to find the x intercept set y = 0 and solve

0 = 2x - 7

2x = 7

x = 7/2

to find the y intercept set x = 0 and solve

y = 2(0) - 7

y = -7