find the slope of the line on the graph write your answer as a fraction or a whole number

Step-by-step explanation:

(π * r²) will give you are of entire circle

the multiply by 60/360 , to give the shaded part

Answer:

A ≈ 25.7 cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{60}{360}[/tex]

   = π × 7² × [tex]\frac{1}{6}[/tex]

   = [tex]\frac{49\pi }{6}[/tex]

   ≈ 25.7 cm² ( to the nearest tenth )

The values of b and c are -4 and 4 respectively

The function is given as:

f(x) = x^2 + bx + c

Differentiate f(x)

f'(x) = 2x + b

Set to 0

2x + b = 0

Solve for b

b = -2x

The minimum is (2, 0).

So, we have:

b = -2 * 2

b = -4

Substitute b = -4 in f(x) = x^2 + bx + c

f(x) = x^2 - 4x + c

Substitute (2, 0)

0 = (2)^2 - 4(2) + c

This gives

0 = 4 - 8 + c

Evaluate

c = 4

Hence, the values of b and c are -4 and 4 respectively

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Answer:

7/15

Step-by-step explanation:

To find the probability the student is a senior

P( senior) = number of seniors / total students

                = 14 / ( 14+7+4+5)

               = 14/30

               = 7/15

Answer:

14/30 or 7/15

Step-by-step explanation:

probability = no. of senior students / total no. of students

probability = 14 / (14+7+4+5)

probability = 14/30

This can be simplified to 7/15.

Hope this helps!

Answer:

[tex]\sf Equation: \quad \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]

The number is 2.

Step-by-step explanation:

The reciprocal of a number is simply 1 divided by the number.

The reciprocal of a fraction is where the numerator and denominator are swapped (so the fraction is turned upside down).

Let x be the positive number.

The reciprocal of the positive number x:

[tex]\sf \implies \dfrac{1}{x}[/tex]

The reciprocal of 3 more than the number x:

[tex]\sf \implies \dfrac{1}{x+3}[/tex]

The sum of the reciprocal of a positive number and the reciprocal of 3 more than the number is 7/10:

[tex]\implies \sf \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]

To solve, make the denominators of the two fractions on the left side the same by multiplying them.

Multiply the numerator of the first fraction by the denominator of the second fraction to get the new numerator of the first fraction.

Multiply the numerator of the second fraction by the denominator of the first fraction to get the new numerator of the second fraction.

[tex]\implies \sf \dfrac{1(x+3)}{x(x+3)}+\dfrac{1(x)}{(x+3)(x)}=\dfrac{7}{10}[/tex]

[tex]\implies \sf \dfrac{x+3}{x(x+3)}+\dfrac{x}{x(x+3)}=\dfrac{7}{10}[/tex]

Add the numerators and keep the denominator so that there is now one fraction:

[tex]\implies \sf \dfrac{2x+3}{x(x+3)}=\dfrac{7}{10}[/tex]

Cross multiply:

[tex]\implies \sf 10(2x+3)=7x(x+3)[/tex]

Expand:

[tex]\implies \sf 20x+30=7x^2+21x[/tex]

Rearrange so the equation is equal to zero:

[tex]\implies \sf 7x^2+x-30=0[/tex]

Split the middle term:

[tex]\implies \sf 7x^2+15x-14x-30=0[/tex]

Factor the first two terms and last two terms separately:

[tex]\implies \sf x(7x+15)-2(7x+15)=0[/tex]

Factor out the common term (7x + 15):

[tex]\implies \sf (x-2)(7x+15)=0[/tex]

Apply the zero product property:

[tex]\sf (x-2)=0 \implies x=2[/tex]

[tex]\sf (7x+15)=0 \implies x=-\dfrac{15}{7}[/tex]

As x is a positive number, x = 2.

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The angle of m∠5 is 116 degrees.

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line m and n are parallel lines cut by the a transversal.

Hence,

m∠2 = 64 degrees

Therefore,

m∠5 = m∠4 (alternate angles)

Therefore,

m∠5  + m∠2 = 180

m∠5  = 180 - 64

m∠5  = 116 degrees.

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The degree measure of the angle labelled 5; m<5 = 116°.

The angle measure of the angle labelled 5 as in the complete task content in the attached image can be determined as follows;

It follows from the complete task content that; that the measure of angle 2 is; 64°.

On this note, it follows from the sum of angle measures on a straight line theorem that; m<4 = 180° - 64° = 116°.

Additionally, it follows from the congruence of alternate angles theorem that <4 and <5 are congruent and hence, their measures are equal.

Therefore, m<5 = 116°.

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Answer:

6

Step-by-step explanation:

The arc length is (2)(pi)(27)(40/360)=6pi.

So, k=6.

Answer: B. [tex]12log(x)-4log(y)[/tex]

Step-by-step explanation:

Properties of logs:

[tex]log_{a} (\frac{B}{C} )=log_{A}B-log_{A} C[/tex]

[tex]logA^B = BlogA[/tex]

So, [tex]log\frac{x^{12} }{y^4} =logx^{12} -logy^4 =12log(x)-4log(y)[/tex]

It would be 12 log x - 4 log y (B)

Answer:

last answer:

h(x) = 1/4 x

Step-by-step explanation:

First, change f(x) to y.

f(x) = 4x

y = 4x

Then switch the x and y.

y = 4x

x = 4y

Last, solve for y.

x = 4y

x/4 = 4y/4

x/4 = y

y = x/4

This is the same as:

y = 1/4 x

h(x) = 1/4 x

Part A - Tara cuts [tex]12[/tex] pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] feet of rope.

Part B - The quotient means the amount of foot pieces so it is [tex]12[/tex] foot pieces.

How can we find the foot pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex]  rope. ?

from part A

we solve the fraction

[tex]4\frac{4}{5} =24/5[/tex] rope

And Tara needs to pieces of [tex]2/5[/tex] foot

So we need to divide

[tex]\frac{24/5}{2/5} \\=\frac{24}{5} *\frac{5}{2} \\=\frac{24}{2} \\=12[/tex]

For part B

When we using the information from part A we decide that the quotient means the amount of foot pieces Tara can cut from the [tex]4\frac{4}{5}[/tex] feet of rope.

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The y-intercept which is the point at which x = 0 is; A: -10

The general form of an equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given the slope;

m = -4

Now, the line passes through the point 0, -10. Thus;

(y - y1)/(x - x1) = -4

(y + 10)/(x - 0) = -4

y + 10 = -4x

y = -4x - 10

Thus, the y-intercept which is the point at which x = 0 is; y = -10

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r = 3 + 3cos(θ) polar equation would best match the desired audible range of the microphone.

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Answer:

D

Step-by-step explanation:

Answer:

3x +8 = -5x

3x + 5x = -8

8x = -8x

x = -8 /8

x = -1

Hope it helps...

Please contact me for further explanation....

Answer:

Step-by-step explanation:

      the answer is on the graph

Answer:

The area of the square is 121mm

Step-by-step explanation:

To solve this we need two basic formulas:

P = 4s

A = [tex]s^{2}[/tex]

P = perimeter

s = the length of the side

Since the shape is a square all the sides are the same length. To get the value of 's' we need to isolate:

P = 4s

44 = 4s

44 / 4 = 4s / 4

11 = s

Now plug in the answer for 's' to get the area:

A = [tex]s^{2}[/tex]

A = [tex]11^{2}[/tex]

A = 121

Hope this helps.

The seventh term of the sequence is 364.5

From the question, we are to determine the seventh term of the sequence

Using the formula,

[tex]a_{n} = ar^{n-1}[/tex]

Where [tex]a_{n}[/tex] is the nth term

a is the first term

and r is the common ratio

From the given information,

a = 1/2

r = 3

Thus,

[tex]a_{7} = (\frac{1}{2}) 3^{7-1}[/tex]

[tex]a_{7} = (\frac{1}{2}) 3^{6}[/tex]

[tex]a_{7} = \frac{1}{2} \times 729[/tex]

[tex]a_{7} = 364\frac{1}{2} \ OR \ 364.5[/tex]

Hence, the seventh term of the sequence is 364.5

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The solutions to the given system of equations are x = 6 and y = -5

From the question, we are to solve the given system of equations

The given system of equation is

4x+5y=-1

-5x-8y=10

Multiply the first equation by 5 and the second equation by 4

5× (4x+5y=-1)

4× (-5x-8y=10)

20x + 25y = -5

-20x - 32y = 40

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

0x + (-7y) = 35

-7y = 35

y = 35/-7

y = -5

Substitute the value of y into the first equation to find x

4x + 5y = -1

4x + 5(-5) = -1

4x -25 = -1

4x = -1 +25

4x = 24

x = 24/4

x = 6

Hence, the solutions to the given system of equations are x = 6 and y = -5

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Answer:

28.5 ft²

Step-by-step explanation:

shaded area = area of triangle minus area of rectangle

shaded area = (1/2)bh - LW

base of triangle = 5 ft + 4 ft = 9 ft

height of triangle = 3 ft + 6 ft = 9 ft

shaded area = (1/2)(9 ft)(9 ft) - (4 ft)(3 ft)

shaded area = 40.5 ft² - 12 ft²

shaded area = 28.5 ft²

The number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.

In this question,

Positive integers are 0,1,2,3,4,5,6,7,8,9

Total number of integers = 10

This can be solved by permutation concepts.

Case 1: 4-digit positive integers with no repeated digits,

First digit, cannot be zero. So remaining 9 digits.

Second digit, can be any digit other than the first digit. So 9 digits.

Third digit, can be any digits other than first and second. So 8 digits.

Fourth digit, can be any digits other than first, second, third digit. So 7 digits.

Thus, Number of ways of 4-digit positive integers with no repeated digits ⇒ (9)(9)(8)(7)

⇒ 4536 ways.

Case 2:  4-digit positive integers, there may be repeated digits, but all digits are odd

Odd integers are 1,3,5,7,9

Number of digits = 5

In this case, we can repeat the digits. So all places can have 5 possibilities.

Thus number of ways of 4-digit positive integers with repeated digits, but all digits are odd = (5)(5)(5)(5)

⇒ 625 ways.

Hence we can conclude that the number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.

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Applying exponential properties, the simplified base for the function is given as follows:

[tex]f(x) = 2(3)^{2x}[/tex]

The function is represented by the following definition:

[tex]f(x) = 2\sqrt[3]{27^{2x}}[/tex]

As an exponent, the function is given by:

[tex]f(x) = 2(27)^{\frac{2x}{3}}[/tex]

27 can be simplified as follows:

27 = 3 x 3 x 3 = 3³

Hence:

[tex]f(x) = 2(3^3)^{\frac{2x}{3}}[/tex]

Then, the 3 at the exponent multiplies 2x and can be simplified with the 3 of the root, hence:

[tex]f(x) = 2(3)^{\frac{3 \times 2x}{3}} = 2(3)^{2x}[/tex]

Hence the simplified base for the function is given as follows:

[tex]f(x) = 2(3)^{2x}[/tex]

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Answer:

Question 6) Neither (Not an inverse variation)

Question 7) Inverse variation

Question 8) Inverse variation

Step-by-step explanation:

These are the two formulas we need to know prior to solving the question.

Direct variation: c times x

Inverse variation: c times 1/x --> c/x

- Here, c is the constant

6. y = x + 7

This is neither. It is not in the form of a direct, or inverse variation, so it does not belong in any category.

7. 14 = xy

This equation is an inverse variation.

xy = 14

y = 14/x

14 is the constant, and the format is the same as for an inverse variation.

8. x = -8/y

This equation is an inverse variation.

yx = -8

y = -8/x

-8 is the constant, and the format is the same as for an inverse variation.

So we can conclude that questions 7 and 8 is an inverse variations, while question 6 isn't.

General forms

Direct

Inverse

so

#6

Not inverse and direct also as 7 is present

#7

Yes

#8

Yes

Answer:

slope = - 2

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (- 4, - 5 ) and (x₂, y₂ ) = (- 2, - 9 )

m = [tex]\frac{-9-(-5)}{-2-(-4)}[/tex] = [tex]\frac{-9+5}{-2+4}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

Answer:

16

Step-by-step explanation:

You replace m with 14. 2 + 14 = 16.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Assuming equation:}[/tex]

[tex]\mathsf{\dfrac{m}{2} + m}[/tex]

[tex]\huge\textsf{If so, let's solve for your equation:}[/tex]

[tex]\mathsf{\dfrac{m}{2} + m}[/tex]

[tex]\mathsf{= \dfrac{14}{2} + 14}[/tex]

[tex]\mathsf{= 7 + 14}[/tex]

[tex]\mathsf{= 21}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{21}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Here, given

sides of polygon= a(3,7)b(3,3)c(7,3)d(7,7)

Let, 3 = x1 & 7= y1   , 3= x2  & 7= y2   , 7= x3  & 3= y3   ,  7=  x4  & 7= y4

[tex]\frac{1}{2}[/tex] [det.(9-21)+det.(9-21)+det.(49-21)+det.(49-21)] {we took determinants of all the given sides}

[tex]\frac{1}{2}[/tex] (32)

16cm^2

Hence, the area of the polygon is 16cm2.

The formula for calculating the area of ​​a regular polygon is: area = (number of sides x 1 side length x apothem distance) / 2, where the value of the apothem is the formula apothem = [(1) Length side). / {2 × (tan (180 / number of sides))}].

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The measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

A triangle with two sides and angles of equal length and degrees is an isosceles triangle.

Acute Triangle:-

A triangle whose all angels are greater than and less than 90° i.e., all angels are acute is called an acute triangle.

Therefore, all the three angles are less than 90 degrees and two angles are equal.

If one angle is 36 degrees, the other two angles will be 72 degrees each.

If the two angles are 36 degrees each, the last angle will be 108 degrees. 108 degrees is greater than 90 degrees..

Therefore, the angles will be 36°, 36° and 72°.

Hence, the measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

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Answer: Option 4

Step-by-step explanation:

[tex]m\angle 20=62^{\circ}[/tex] (linear pair)

[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)

[tex]m\angle 12=110^{\circ}[/tex] (linear pair)

The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.

According to the statement

we have given Following are the pairs of the complex number:

(1+2i)(8i),

(1 + 2i)(2 – 5i)

(1+2i)(1-2i) and (1+2i)(4i)

We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".

So, For this purpose

we have to multiply these pairs with each other.

So,

(1+2i)(8i) = 8i +16(i)^2

And

(1 + 2i)(2 – 5i) = 2 +4i - 5i +10(i)^2

And

(1+2i)(1-2i) = 1 -4(i)^2 -2i +2i = 1+4 = 5

And

(1+2i)(4i) = 4i + 6(i)^2

From these multiplication we found that the third pair have a real number product.

So, The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.

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Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at  B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C  which is at D(1, 5).

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

Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at  B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C  which is at D(1, 5).

The location of point A, B, C and D is located on the graph.

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VARIABLE is a symbol which is used for representation in a  math.

According to the statement

we have to explain about the what is a variable.

So, VARIABLE is a symbol which is used for representation in a  math.

It represent the so many things like Algebra, Matrix,Vector etc. and also so many things.

A variable may also be called a data item.

It is used to represent a data like country name, name, age, date of birth etc.

we know that the every thing is changeable. So, like ther things variables are also changeable.

The changing of variable parameters is called as variation. In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value.

So, VARIABLE is a symbol which is used for representation in a  math.

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Answer:

8(5) + 8(2)

Step-by-step explanation:

8 (5 + 2) is 8 (7) or 56

If I distribute the 8 through the problem, I will get the same answer

8(5) + 8(2)

40 + 16

56

The area of the rectangle is 108 square centimeters.

Given Information

The following information has been given in the question,

Length of the diagonal of the rectangle, l = 15 cm

Length of one of the sides of the rectangle, a = 9 cm

Let the other side of the rectangle be b.

Finding the Other Side of the Rectangle

According to Pythagoras Theorem,

(hypotenuse)² = (base)² + (perpendicular)²

Applying this theorem in the right-angle triangle formed by the diagonal and 9cm side of the rectangle, we get,

l² = a² + b²  [∵ The diagonal makes the hypotenuse]

(15)² = (9)² + b²

b² = (15)² - (9)²

b² = 225 - 81

b² = 144

b = √144

b = 12 cm

Calculating the Area of the Rectangle

Area of the rectangle, A = a × b

A = 9 × 12

A = 108 cm²

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