Add or subtract. Simplify where possible. 7/2 c - 2 / c²

Answer:

Step-by-step explanation:

How many solutions does each of the following equations have?

10+5(x+2)=5x-20

10+5x+10=5x-20

10 + 10 = -20

20 = -20

this equation has no solution

Answer:

Step-by-step explanation:

10+5(x+2)=5x-20

10+5x+10=5x-20

5x-5x=-20-10-10

x = -40

The total amount subtracted from her account after 6 months of having the membership is −6|20| = −$120. option C

Given:

Cost of membership

Cost per month for a car wash membership = $20

Number of months = 6 months

Total amount subtracted from her account = Number of months × Cost per month for a car wash membership

= 6 (-20)

= -120

Therefore, the total amount subtracted from her account after 4 months of having the membership is −6|20| = −$120.

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Answer:

Step-by-step explanation:

F = 9/5 C + 32 is the correct formula.

9/5 C = F - 32

C = 5/9(F - 32)

So, 68 degrees Fahrenheit

= 5/9(68 - 32)

= 5/9 * 36

= 20 degrees C.

The difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).

Difference of two squares is a particular case of a second order polynomial whose form is the following:

a² - b² = (a + b) · (a - b)

Now we proceed to demostrate the equivalence between the two expressions:

a² - b² → (a + b) · (a - b)

a² - b²                             Given

(a² - b²) + 0                     Modulative property

(a² - b²) + a · b - a · b      Existence of additive inverse

(a² + a · b) + (- b² - a · b) Associative property

a · (a + b) - b · (a + b)      Definition of power / Distributive property / (- a) · b = - a · b

(a + b) · (a - b)                 Commutative and distributive property /  

(a + b) · (a - b) → a² - b²

(a + b) · (a - b)                 Given

(a + b) · a + (a + b) · (- b) Distributive property

a² + a · b - a · b - b²        Distributive property / (- a) · b = - a · b / Definition of power

(a² - b²) + (a · b - a · b)    Associative property

a² - b²                             Existence of the additive inverse / Modulative property / Result

Hence, the difference of squares is a quadratic polynomial of the form is a² - b² = (a + b) · (a - b).

The statement is incomplete. The complete form is: What is a difference of two squares?

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The slope of the line containing (6,-2) and (-3,-5) is  (3/8).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -5 , [tex]y_{1}[/tex] = -2 , [tex]x_{2}[/tex] = -3 , and [tex]x_{1}[/tex] = 6 .

On substituting the values of variables in equation1, we will get

m = ( (-5)-(-2) ) / ( (-3)-(6) ) = (-3/(-8)) = (3/8).

As the slope of a line is (3/8), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing  (6,-2) and (-3,-5) is  (3/8).

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After solving the equation, the value of y = x/4 for the equation 12 y=3 x.

⇒ 12 y=3 x

⇒ y = 3x/12

⇒ y = x/4

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

a) [tex]\sqrt{3}[/tex]

b) 2

Step-by-step explanation:

a) tan 30 = opposite side / adjacent side 1/[tex]\sqrt{3}[/tex] so AC is [tex]\sqrt{3}[/tex]

b)3

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]1^{2}[/tex] +[tex]\sqrt{3} ^{2}[/tex] = [tex]c^{2}[/tex]

1 + 3 = [tex]c^{2}[/tex]

4 = [tex]c^{2}[/tex]

[tex]\sqrt{4}[/tex] =[tex]\sqrt{c^{2} }[/tex]

2 = c

The length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The right-angled triangle ABC has an angle BAC of 30º.

The length of BC  be one unit

We have to find the length of AC

tan (30)= opposite side/ adjacent side

1/√3 = opposite side/ adjacent side

The adjacent side is √3  which is length of AC

Now let us find the length of AB by using pythagoras theorem

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

AB² = AC² + BC²

AB²=√3² + 1²

AB²= 4

AB = 2 units

Hence, the length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem

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Answer:

[tex] \sf{49}[/tex]

Step-by-step explanation:

Given that,

m => 4

p => 7

Let us solve the given expression by using the given values.

[tex] \sf \: {p}^{2} m \div 4 \: \: \: \: \: \\ \sf{(7)}^{2} \times 4 \div 4 \\ \sf 49 \times 4 \div 4 \\ \sf196 \div 4 \: \: \: \: \: \: \\ \sf49 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

An octagon is known to be a type of polygon that is said to have up to 8 sides the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane then the measure of arc NPQ is 180°.

An inscribed angle of a circle is an angle whose vertex is a point A on the circle and whose sides are line segments (called chords) from A to two other points on the circle.

An octagon is known to be a type of polygon that is said to have up to 8 sides the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane. A regular octagon will have all its sides equal in length.

The surface area of a regular octagon encircled by a circle of radius one unit. Divide the octagon into eight congruent triangles. We can find the area of one triangle and multiply it by 8 to get the area of the entire octagon.

The complete question is:

A stop sign in the shape of a regular octagon is inscribed in a circle.

What is the measure of arc NPQ?

A. 45°

B. 90°

C. 135°

D. 180°

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The equation of the parabola in vertex form is

P is -[tex]\frac{1}{2}[/tex]

(0,-[tex]\frac{1}{2}[/tex])

y=[tex]\frac{-1}{2}[/tex][tex]x^{2}[/tex] -[tex]\frac{1}{2}[/tex]

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a variety of seemingly unrelated mathematical descriptions, all of which may be shown to define the same curves.

One definition of a parabola includes a line and some extent  (the focus) (the directrix). The directrix isn't the main focus. The locus of points therein plane that is equally spaced apart from the directrix and the focus is known as the parabola. A right circular conical surface and a plane parallel to a different plane that is tangential to the conical surface intersect to form a parabola, which is additionally known as a conic section.

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The street can be represented in slope intercept form as follows:

y = x + 4

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Parallel lines have the same slope.

The street goes by the name y = x + 17.

The slope of the street is 1.

Therefore, the street parallel to that one should have the same slope.

The street can be represented in slope intercept form is as follows:

y = x + 4

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The area of the parallelogram is 42 units².

The area of a parallelogram can be calculated by finding the product of its base with the altitude. The base and altitude of a parallelogram are always perpendicular to each other.

i.e., The area of a parallelogram = base × height.

To find the perimeter of a parallelogram, add the lengths of the sides. Opposite sides of a parallelogram are equivalent.

Given:

base= 7 units

height = 6 units.

Now, area of a parallelogram,

= 7 × 6

= 42 units²

Hence, area of the parallelogram is 42 units².

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Answer:

f^-1 (x)= -6x+24

Step-by-step explanation:

the inverse function would be negative six (x) plus 24

the correct option is D, the inverse relation is only a function if it passes the vertical line test.

A relation maps elements from one set (called the domain) into elements of another set (called the range).

A relation is a function only if each element in the domain is mapped into only one element of the range. So, there is something called the vertical line test.

It says that if at any part of the graph of the relation you can draw a vertical line that intercepts the graph of the relation more than once, then it is not a function. Passing the vertical line test means that no vertical line intercepts the graph more than once.

Then the correct option is D, the inverse relation is only a function if it passes the vertical line test.

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Answer:

Slope of a perpendicular line:
[tex]\boldsymbol{\dfrac{1}{9}}[/tex]

Slope of a parallel line:
[tex]\boldsymbol{-9}[/tex]

Step-by-step explanation:

A line perpendicular to a line y = mx + b will have its slope as[tex]-\dfrac{1}{m}[/tex]
Here slope of given line = -9
[tex]\displaystyle \mathrm {reciprocal\; of\;} -9 = -\dfrac{1}{9}[/tex]

[tex]\mathrm {negative\; of \;reciprocal\;}= -\left(-\dfrac{1}{9}\right) = \dfrac{1}{9}\\[/tex]

parallel lines have the same slope so a parallel line will have slope = -9

The latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m

Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks and He must arrive at his friend’s house by 7:00 p.m.

The time it takes Lyle to drive to his friend's house is given by t = d/v where

Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, we have that

Substituting the values of the variables into t, we have

t = d/v

= 720 km/80 km/h

= 9 h

So, it takes Lyle 9 hours to drive.

Now, since Lyle takes an hour for Lunch and two 15 minutes breakes, this extra time is t' = 1 h + 2 × 15 min

= 1 h + 30 min

= 1 h + 30 min/60 min × 1h

= 1 h + 0.5 h

= 1.5 h

So, the total time Lyle takes to reach his friend's house is T = t + t'

= 9 h + 1.5 h

= 10.5 h

Since Lyle must reach his friend's place no later than 7:00 pm, 10.5 hrs from 7:00 pm is 8:30 am.

So, Lyle must leave no later than 8:30 a.m

So, the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m

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Answer:

Step-by-step explanation:

History(H),Economics(E),Literature(L)

1a).To find History(H) only is

H only =H-HE-HL+HEL

H only =60-30-16+10=24

b).E only=50-30-22+10=8

c). L only=48-22-16+10=20

2).no of candidates who sat for the exam is 24+8+20=52

Answer:

AC is the longest side

Step-by-step explanation:

• the longest side is side opposite largest angle in the triangle

• the shortest side is opposite the smallest angle in the triangle

the largest angle is ∠ B = 68°

the longest side is then AC

Answer:

c) 7.3 m/s

Step-by-step explanation:

We know that 87 is the total and 12 is the time do you take the total divided by the time so 87/12=7.25. 7.25 rounded is 7.3.

Using the digits 1 to 9 at most one time each to make the largest quotient is 98 ÷ 12 .

According to the question we have to use digits 1 to 9 at most one time each to make the largest quotient.

Now we know that the number that is being divided is known as the dividend and the number by which we divide is known as the divisor.

Now dividend should be greater than the divisor.

So tot make the largest quotient the dividend and the divisor will be

98 and 12 respectively.

That is,     98 ÷ 12 = 8.2 which is the largest quotient.

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The equation of the circle (x - 3)^2 + (y + 1)^2 = 36 has a radius of 6 and a center located at (3 , -1).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, (x - 3)^2 + (y + 1)^2 = 36, is in standard form, then

h = 3

k = -1

r = 6

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  The value of the geometric mean of the numbers 36 and 24 is.

Gm ( 36, 24) = 12√6

     The definition of geometric mean is a calculation that is performed on a set of numbers which consists of calculating the square root of the product between them, the equation is as follows:

Gm (a,b) = √ab

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

Gm (36, 24) = √ab = √36×24

Gm (36, 24) = √864

Gm (36, 24) = √6×144

Gm ( 36, 24) = 12√6

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Answer:

No, Dell does not have enough soil to fill the planter.

Step-by-step explanation:

The sequence 23,27,31,35,39, . . . . is arithmetic and the tenth term is: 59

We can determine that the sequence is arithmetic, because two consecutive terms differ by "d".

To solve this exercise we are going to apply the formula of the arithmetic sequence:

Where:

Information about the problem:

Calculating the "d" term, we have:

d = aₙ₊₁ - aₙ

d = 27 - 23

d = 4

Calculating the tenth term, we get:

aₙ= a + (n-1) * d

a₁₀= 23 + (10-1) * 4

a₁₀= 23 + (9) * 4

a₁₀= 23 + 36

a₁₀= 59

It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.

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Answer:

1. 68.1

2. 61.983

Step-by-step explanation:

nearest tenth is one digit after the decimal. nearest thousandth is three digits after the decimal. since 4 is less than 5, the 1 remains the same. in the second problem, the fourth digit is 6 which is greater than 5 so you change the 2 to a 3.

The value of the other angles

∠1 = 180 - 82°

∠2 = ∠1 = 98°

∠3 = ∠ = 98°

∠4 = ∠5 = 82°

According to the given data,

m∠5=82° given

∠5 = ∠7 = ∠4 = ∠8 = ∠6 = ∠12

∠1 = ∠10 = ∠2 = ∠11 = ∠3 = ∠ 12 = 180° - ∠5

we get, measures of other angles

∠1 = 180 - 82°

∠2 = ∠1 = 98°

∠3 = ∠ = 98 °

∠4 = ∠5 = 82°

A transversal is a line that intersects two coplanar lines at two different points. In the figure,

line t is a transversal. The table summarizes the names of angle pairs formed by a transversal.

Corresponding angles lie on the same side of the transversal and on the same

sides of the intersected lines. ∠1 and ∠5

Same-side interior angles lie on the same side of the transversal and between

the intersected lines. ∠3 and ∠6

Alternate interior angles are nonadjacent angles that lie on opposite sides of

the transversal between the intersected lines. ∠3 and ∠5

Alternate exterior angles lie on opposite sides of the transversal and outside

the intersected lines. ∠1 and ∠7

Same-Side Interior Angles Postulate

If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure.

Corresponding Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of corresponding angles have the same measure.

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The quadratic equation of the form ax² + bx + c = 0.

The value of x = 4 and x = -3

No solution

No real-valued solution

The quadratic equation of the form

ax² + bx + c = 0.

The form is called the standard form of the quadratic equation.

Let the given equation be x² = x + 12

By using quadratic equation, ax² + bx + c = 0

ax² + bx + 12 = 0

x² = x + 12

⇒ x² - x - 12 = 0

Let the quadratic equation be

[tex]$x=\frac{\left(-b\right)\pm \sqrt{\left(b)^2-4\cdot \:a\cdot \left(c)}}{2\cdot \:a}[/tex]

a = 1, b = -1 and c = -12

Substitute the values in the above equation, we get

[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-12\right)}}{2\cdot \:1}[/tex]

simplifying the above equation, we get

[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \:7}{2\cdot \:1}[/tex] and

[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a++ \:7}{2\cdot \:1}[/tex]

[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a+- \:7}{2\cdot \:1}[/tex]

x = 4 and x = -3

Therefore, the value of x = 4 and x = -3

No solution

No real-valued solution

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