A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?

A.
-3x + 4y = 3

B.
-1.5x − 3.5y = -31.5

C.
2x + y = 20

D.
-2.25x + y = -9.75

Answer:

The circumference of the circle = 26π unit.

Step-by-step explanation:

Given:

Radius of the circle, r = "x+6"

Diameter of the circle, d = "3(x)+5"

We have to find the circumference of the circle in terms of pi.

Formula to be used:

Circumference of a circle = 2πr or πd

As we know that:

Radius = Half of diameter

So,

⇒ [tex]radius=\frac{diameter}{2}[/tex]

⇒ [tex]x+6=\frac{3x+5}{2}[/tex]

⇒ [tex]2\times (x+6)=\frac{3x+5}{2}\times 2[/tex]

⇒ [tex]2x+12=3x+5[/tex]

⇒ [tex]12-5=3x-2x[/tex]  ...Arranging variables and constants.

⇒ [tex]7=x[/tex]

Plugging x = 7 we will find the radius and the diameter.

⇒ Radius = "x+6" = "7+6" = 13

⇒ Diameter = "3(x)+5" = 3(7)+5 =26

Lets find the circumference of the circle.

⇒ Circumference = [tex]2\pi r= 2\pi (13) = 26 \pi[/tex]        Or

⇒ Circumference = [tex]\pi d=\pi (26)=26\pi[/tex]

The circumference of the circle = 26π unit.

Given:

To find out:

If it runs into a wall what force will be exerted by the cat?

Formula used:

Force = mass × acceleration

Solution:

Force = mass × acceleration

Now, Putting these values of m and a in the above equation.

we get:

F = 10 × 10

= 100 N

Thus, the force will be exerted by the cat is 100 N.

The force exerted by the cat when it runs into a wall can be calculated using Newton's Second Law of Motion, resulting in a force of 100 Newtons.

The subject of this question pertains to the concept of Newton's Second Law of Motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. Here, the cat is considered the object in motion. The cat's mass is 10kg, and its acceleration is given as 10 m/s².

By substituting these values into Newton's second law (Force = mass x acceleration), we can calculate the force exerted by the cat as it runs against a wall: Force = 10kg x 10 m/s² = 100 N (Newtons). Therefore, the cat will exert a force of 100 Newtons when it runs into the wall.

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Answer:

x^3 - 3x^2 + 5x - 15

x^2(x-3) +5(x-3)

(x^2 + 5)(x - 3) <==Answer

Step-by-step explanation:

Answer:

that is the solution to the question

Final answer:

To calculate the principal with an interest of $119.88, an interest rate of 3.6%, and a time of 3 years, use the simple interest formula. By rearranging the formula and doing the math, the principal amount is found to be $1,110.

Explanation:

To find the principal amount when you know the interest earned, the interest rate, and the time, you can use the formula for simple interest which is Interest = Principal × rate × time. Our goal is to rearrange the formula to solve for the principal.

Given that the Interest earned is $119.88, the interest rate is 3.6% (or 0.036 when converted to a decimal), and the time is 3 years, we can plug these values into the formula:

Interest = Principal × rate × time
$119.88 = Principal × 0.036 × 3
$119.88 = Principal × 0.108

To find the Principal, divide the interest earned by the product of the rate and time:

Principal = $119.88 / 0.108
Principal = $1,110

The principal amount is $1,110.

Answer:

520

Step-by-step explanation:

If you pay for a half an hour lesson that is 20 dollars.

So if you do that for a total of 26 weeks you would multiply 20 dollars by 26 weeks.

20*26=520

Therefore she spends 520 dollars for half hour lessons that cost 20 for 26 weeks

Answer: [tex]32009355.90cm^3[/tex]

Step-by-step explanation:

Formula: [tex]V=Bh\\[/tex]

Since the base is a circumference, we can replace B for the area of a circumference formula.

[tex]V=\pi r^2h[/tex]

What we have here is 12 ft as the diameter of the circumference. A diameter is twice the radius, therefore we can conclude that if we take the diameter and divide it by 2, it will give us the radius.

[tex]12/2=6ft[/tex] this is the radius.

Now plug all this information into your formula.

[tex]V=(3.14)(6ft)^2(10ft)\\V=(3.14)(36ft^2)(10ft)\\V=1130.40ft^3[/tex]

Our values are in feet but the question requires cm. Let's convert from [tex]ft^3[/tex] to [tex]cm^3[/tex].

Normally, our conversion factors are raised to the power of 1, but in this case it's raised to the power of 3. So, first let's see how many cm are 1 ft.

[tex]1ft=30.48cm[/tex]

Here is where magic comes. We can raise both to the power of 3, in order to find the cubic ft and cm that we need as our conversion factors.

[tex](1ft)^3=(30.48cm)^3\\1ft^3=28316.8cm^3[/tex]

Now we have our conversion factors.

[tex]1130.40ft^3(\frac{28316.84cm^3}{1ft^3})=32009355.90cm^3[/tex]

Answer:

slow hiker rate= 1.1mph and fast hiker rate= 5.5 mph

Step-by-step explanation:

lets consider the Speed of the slow hiker =x

Then Speed of fast hiker =x+4.4

As we know that distance is the product of speed and time

therefore,

Distance covered by slow hiker in 5 hours = 5x km

Distance covered by fast hiker in 5 hours=5 (x+4.4)=5x+22 km

As they are are 33 miles apart , therefore

5x + 5x+22 = 33

10x = 33-22

10x = 11

x =11/10 => 1.1

Rate of slow hiker is x i.e 1.1mph

Rate of fast hiker = x+4.4 => 5.5 mph

Answer:

slower hiker's speed = 1.1 mph

faster hiker's speed = 5.5 mph

Step-by-step explanation:

Extracting the key information from the question:

*** Two hikers are 33 miles apart and are walking towards each other.

*** One of them walks 4.4 mph faster than the other and later met themselves in 5 hours.

*** We are required to find the speed of each of the hikers.

  Speed = distance/time

 Let us use "x" to represent the slower speed. Since one of the hikers was 4.4 mph faster than the other hiker, we can represent the faster speed with x+4. Now, if they met themselves in 5 hours, even though they were 33 miles apart initially, then we can represent the situation with the given equation:-

  (x mph × 5hours) + [(x+4.4)×5] = 33 miles

5x  +  (5x + 22) = 33

5x + 5x + 22= 33

10x + 22 = 33

 10x = 33-22

  10x = 11

    x = 11/10

    x = 1.1mph (speed of slower hiker)

 The speed of the faster hiker = x + 4.4

 = 1.1 + 4.5

 = 5.5mph

Answer:

166 2/13 deg

Step-by-step explanation:

The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).

A hexagon has 6 sides, so n = 6.

sum of measures of angles = 180(n - 2) = 180(6 - 2) = 180(4) = 720

4x + 5x + 6x + 7x + 8x + 9x = 720

39x = 720

x = 720/39

x = 240/13

The largest angle has measure 9x.

9x = 9 * 240/13 = 2160/13

2160/13 = 166 2/13

Answer: 166 2/13 deg

the size of largest angle is  [tex]166\frac{2}{13}[/tex] degree

Hexagon is a two-dimensional geometrical shape that is made of six sides, having the same or different dimensions of length. Some real-life examples of the hexagon shape are a hexagonal floor tile, pencil cross-section, clock, a honeycomb, etc. It can be either regular (with 6 equal side lengths and equal angles) or irregular (with 6 unequal side lengths and angles).

According to the question,

The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).

A hexagon has 6 sides, so n = 6.

sum of measures of angles = 180(n - 2)

                                             = 180(6 - 2)

                                             = 180 × 4

                                             = 720

4x + 5x + 6x + 7x + 8x + 9x = 720

39x = 720

x = 720/39

x = 240/13

The largest angle has measure 9x.

9x = 9 × 240/13 = 2160/13

[tex]\frac{2160}{13}[/tex]  = [tex]166\frac{2}{13}[/tex]

Hence, the size of largest angle is  [tex]166\frac{2}{13}[/tex] degree

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Answer:

It will hold 200 Litres  of water

Step-by-step explanation:

To find the number of litres of water the fish tank can hold, we will follow the steps below;

Write down the formula for calculating its volume

V = l×w×h

where v = volume of the tank

w=width of the tank  

l = length of the tank

From the question given;

w= 50 cm = 0.5 m

height h = 20 cm = 0.2 m

l = 2 m

V= l×w×h

  =  2×0.5×0.2

  =0.2 m³

we can now change it to liters

V = 0.2 m³ × 1000 = 200 L

It will hold 200 Litres  of water

Answer:

  4.8 or 4 4/5

Step-by-step explanation:

Put the given value into the equation and solve for the missing one.

  (3/5)(6) -(1/3)y = 2

  3.6 -y/3 = 2 . . . simplify to decimal form

  -y/3 = -1.6 . . . . subtract 3.6

  y = 4.8 . . . . . . . multiply by -3

The missing number is ...

  4.8 = 4 4/5

_____

The coefficients are given as fractions, so the answer may be expected in mixed-number form.

Steps to solve:

-3x - 8 = 10

~Add 8 to both sides

-3x - 8 + 8 = 10 + 8

~Simplify

-3x = 18

~Divide -3 to both sides

-3x/-3 = 18/-3

~Simplify

x = -6

Best of Luck!

The solution of the equation -3x - 8 = 10 is,

⇒ x = -6

The given algebraic equation is,

-3x - 8 = 10

Now since its degree is 1

Therefore it is nothing but a linear equation.

By simple operation we can solve it

Now to solve it proceed the following steps:

Add 8 both sides, we get

⇒ -3x - 8 + 8 = 10 + 8

⇒            -3x  = 18

Divide by -3 both sides we get

⇒            x  = 18/-3

⇒            x  = 6

Hence,

The solution is x = -6

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Answer:

(-8, -1)

Step-by-step explanation:

The problem tell us that y = -1.  Plug in this y-value to wherever you see a y in the first equation.  You should be able to solve from there.  Your solution will be (-8,-1).

-2x - 3(-1) = 19

-2x + 3 = 19

-2x = 16

x = -8

For this particular problem, you could have also looked at the answer choices and seen that there was only one answer with the correct y-value.

Answer:

L = 9

Step-by-step explanation:

Translating this into symbols, we get L = W + 1 and A = 72 = W * L.

Substituting W + 1 for L in the latter equation, we get:

72 = W(W + 1), or:

W^2 + 1W - 72 = 0

This factors into (W + 9)(W - 8) = 0, so that W must be either -9 or +8.

Since W represents width, a physical measurement, we eliminate the negative result and conclude that W = 8 units.  Then L = W + 1 = 9 units.

Note that (8)(9) = 72, as we already know.

The length of the rectangle is: [tex]\[ {9} \] units.[/tex]

Let's denote the width of the rectangle as \( w \) and the length of the rectangle as \( l \).

According to the problem, the length \( l \) is given by:
[tex]\[ l = w + 1 \][/tex]

The area of the rectangle is given by:
[tex]\[ \text{Area} = l \times w = 72 \][/tex]

Substituting the expression for \( l \) into the area formula:
[tex]\[ (w + 1) \times w = 72 \][/tex]

This can be rewritten as:
[tex]\[ w^2 + w - 72 = 0 \][/tex]

We now have a quadratic equation. To solve this, we can use the quadratic formula:
[tex]\[ w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\where \( a = 1 \), \( b = 1 \), and \( c = -72 \).\\[/tex]
Plugging in these values:
[tex]\[ w = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot (-72)}}{2 \cdot 1} \]\[ w = \frac{-1 \pm \sqrt{1 + 288}}{2} \]\[ w = \frac{-1 \pm \sqrt{289}}{2} \]\[ w = \frac{-1 \pm 17}{2} \][/tex]

This gives us two potential solutions for \( w \):
[tex]\[ w = \frac{16}{2} = 8 \]\[ w = \frac{-18}{2} = -9 \][/tex]

Since a width cannot be negative, we discard \( w = -9 \) and take \( w = 8 \).

Therefore, the width \( w \) is 8 units. Using the relationship \( l = w + 1 \), we find:
[tex]\[ l = 8 + 1 = 9 \][/tex]

So, the length of the rectangle is: [tex]\[ {9} \] units.[/tex]

Answer:

The volume of this pyramid is 56 millimeters³

Step-by-step explanation:

The volume for a triangular pyramid is given by the following formula:

volume = (1/3)*(base area)*h

In order to solve this problem we must take the given data for the pyramid and apply it to the formula above. We have:

volume = (1/3)*42*4

volume = 14*4

volume = 56 millimeters³

The volume of this pyramid is 56 millimeters³

Answer: B. 2.5 in

Step-by-step explanation:

From the given right angle triangle,

the hypotenuse of the right angle triangle is the unknown side.

With m∠32 as the reference angle,

the adjacent side of the right angle triangle is 4 in

the opposite side of the right angle triangle is w

To determine w, we would apply

the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side. Therefore,

Tan 32 = w/4

w = 4tan32 = 4 × 0.625

w = 2.5 in

Answer:

There is an average of approximately 1 sheep per square mile.

Step-by-step explanation:

Given there are 9.54 sheep spread across 18.52 square miles of land.

The average number of sheep per square mile is given as

A = 9.54/18.52

Without using a calculator, this is by inspection, about 9/18 = 0.5.

Using a calculator, we have

A = 9.54/18.52 = 0.51511879

Approximately 1 sheep per square mile.

Answer:|−3 4 | > |0.5| > |− 2 5 | > |0.35|

Hope this is helpful!

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. Here are two key characteristics of the polar coordinate system:

1. Radial Distance (Radius): In the polar coordinate system, the location of a point is determined first by its distance from a fixed point, called the pole, analogous to the origin in the Cartesian coordinate system. This distance is often denoted as \( r \), and it can be thought of as the radius of a circle centered at the pole, with the point lying on the circumference of this circle.

2. Angular Coordinate (Angle): The second characteristic of a point's location in the polar coordinate system is the angle [tex]\( \theta \)[/tex] (theta), which is measured from a fixed direction, typically the positive x-axis of the corresponding Cartesian coordinate system. This angle, usually measured in degrees or radians, determines the direction of the line from the pole to the point.

These two values, [tex]\( r \)[/tex] and [tex]\( \theta \)[/tex], are called polar coordinates, and they provide an alternative to the Cartesian (rectangular) coordinate system for representing points on a plane, particularly useful in scenarios where the geometry or the nature of the problem is radially symmetric, such as in the cases of circular motion or fields (gravitational, electric, etc.).

Answer: 24 miles

Step-by-step explanation: 12 mph is two times as fast as 6 mph so 6 hours round trip is 2 hours for bike and 4 hours for jogging. You can either plug 2 for 12 (bike) or 4 for 6 (jog) either way you get 24

Answer:

24 miles

Step-by-step explanation:

The correct option is Class A had the higher median score. Class A scored better on the test.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two whiskers that represents the maximum and minimum numbers.

On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.

The median of class A = 9

The median of class B = 8.2

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Answer:

p=3

Step-by-step explanation:

16-3p=2/3p+5

16=3 2/3p+5

11=3 2/3p

3=p

Answer:

p = -33/7

Step-by-step explanation:

We first re-organize the equation.

3p - 2/3p = 5 - 16

9-2/3p = -11

7p/3 = -11

Then we cross multiply-

7p = -33

p = -33/7

Im sorry but why are you putting this on here?

Answers:

They probably bump their heads against humans because they want someone to pet them or they like humans.

Explanation:hope I get brainliest!:D

Answer:

$11.88

Step-by-step explanation:

Given that Kelly would get one box of cereal half off if she buys one, then we must take that into account.

Box 1: $4.75

Box 2: $4.75 ÷ 2 = $2.38

Box 3: $4.75

Now we simply add the totals:

4.75 + 2.38 + 4.75 = $11.88

Answer:false

Step-by-step explanation: Then you would get rid of the x

Answer:

[tex]P(x)=-0.3x^2+56x-14[/tex]  

Step-by-step explanation:

The given functions are

[tex]R(x)=59x-0.3x^2[/tex]

[tex]C(x)=3x+14[/tex]

It is given that

[tex]P(x)=R(x)-C(x)[/tex]

Substitute the values of given functions in the above equation.

[tex]P(x)=59x-0.3x^2-(3x+14)[/tex]

[tex]P(x)=59x-0.3x^2-3x-14[/tex]

Combine like terms.

[tex]P(x)=-0.3x^2+(59x-3x)-14[/tex]

[tex]P(x)=-0.3x^2+56x-14[/tex]  

Therefore, the required function is [tex]P(x)=-0.3x^2+56x-14[/tex]   .

0.8‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

Answer:

o.8

Step-by-step explanation:

trust me im doing it

Answer:

One centimeter is equal to 10 millimeters. It is also equal to 0.1 decimeter and 0.01 meter. One kilometer contains 100,000 centimeters.

Step-by-step explanation:

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Answer: 100x centimeters

Step-by-step explanation:

We know that 100 centimeters are in every meter. To find the number of centimeters in X amount of meters, we multiply X by 100. Take for example 4 meters. 4 times 100 equals 400. We then know that there are 400 centimeters in 4 meters.

Answer:

a:x=-3

c:x=1

Step-by-step explanation:

The zeros of a function are the values of x for which the value of the function f(x) becomes zero.

In this problem, we have the following function:

[tex]f(x)=\frac{1}{2}(x-1)(x+3)[/tex]

Here we want to find the zeros of the function, i.e. the values of x for which

[tex]f(x)=0[/tex]

In order to make f(x) equal to zero, either one of the factors [tex](x-1)[/tex] or [tex](x+3)[/tex] must be equal to zero.

Therefore, the two zeros can be found by requiring that:

1)

[tex]x-1=0\\\rightarrow x=+1[/tex]

2)

[tex]x+3=0\\\rightarrow x=-3[/tex]

So the correct options are

a:x=-3

c:x=1