the scale of a map is 1:500000 the actual distance between two town is 172 km calculate the distance, in centimeters, between two towns on the map. ​

Answer:

f(-7)=0.

f(2)=-9/5.

f(3) doesn't exist because 3 isn't in the domain of the function.

Step-by-step explanation:

[tex]f(x)=\frac{x+7}{x^2-9}[/tex] is the given function.

We are asked to find:

[tex]f(-7)[/tex]

[tex]f(2)[/tex]

[tex]f(3)[/tex].

f(-7) means to replace x in the expression called f with -7:

Evaluate [tex]\frac{x+7}{x^2-9}[/tex] at [tex]x=-7[/tex]

[tex]\frac{(-7)+7}{(-7)^2-9}[/tex]

[tex]\frac{0}{49-9}[/tex]

[tex]\frac{0}{40}[/tex]

[tex]0[/tex]

So f(-7)=0.

f(2) means to replace x in the expression called f with 2:

Evaluate [tex]\frac{x+7}{x^2-9}[/tex] at [tex]x=2[/tex]

[tex]\frac{2+7}{2^2-9}[/tex]

[tex]\frac{9}{4-9}[/tex]

[tex]\frac{9}{-5}[/tex]

[tex]\frac{-9}{5}[/tex]

So f(2)=-9/5

f(3) means to replace x in the expression called f with 3:

Evaluate [tex]\frac{x+7}{x^2-9}[/tex] at [tex]x=3[/tex]

[tex]\frac{3+7}{3^2-9}[/tex]

[tex]\frac{10}{9-9}[/tex]

[tex]\frac{10}{0}[/tex]

Division by 0 is not allowed so 3 is not in the domain of our function.

Answer:

[tex]\large\boxed{y=\dfrac{2}{5}x+\dfrac{24}{5}}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the slope [tex]m=\dfrac{2}{5}[/tex] and the point (-2, 4).

Put them in the equation of a line:

[tex]4=\dfrac{2}{5}(-2)+b[/tex]

[tex]4=-\dfrac{4}{5}+b[/tex]       add 4/5 to both sides

[tex]4\dfrac{4}{5}=b\to b=\dfrac{24}{5}[/tex]

Answer:

I think that the answer is C

Answer:

So, Option A is correct.

Step-by-step explanation:

If the triangles are similar, then the sides are proportional

If triangle ABC is similar to triangle PQR

then sides

AB/PQ = BC/QR = AC/PR

We need to find PQ

We are given AB = 6, BC =8 and QR=24

AB/PQ = BC/QR

Putting values:

6/PQ = 8/24

Cross multiplying:

6*24 = 8*PQ

144/8 = PQ

=> PQ = 18

So, Option A is correct.

Answer: Option A

[tex]PQ=18[/tex]

Step-by-step explanation:

Two triangles are similar if the length of their sides is proportional.

In this case we have the triangle ∆ABC and ∆PQR so for the sides of the triangles they are proportional it must be fulfilled that:

[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]

In this case we know that:

[tex]BC=8[/tex]

[tex]QR=24[/tex]

[tex]AB=6[/tex]

Therefore

[tex]\frac{BC}{QR}=\frac{AB}{PQ}[/tex]

[tex]\frac{8}{24}=\frac{6}{PQ}[/tex]

[tex]PQ=6*\frac{24}{8}[/tex]

[tex]PQ=18[/tex]

Answer:

(27,000 - 22,900)/27,000 = 0.1519 or 15.19% decrease in price.

Step-by-step explanation:

For this case, we propose a rule for three:

27,000 -----------> 100%

22,900 -----------> x

Where "x" represents the percentage associated with 22,900.

[tex]x = \frac {22,900 * 100} {27,000}\\x = 84.8148148148[/tex]

Now we look for the percentage of decrease:

100% -84.8148148148% = 15.1851851852%

Rounding off we have:

15.19%

Answer:

15.19%

Answer: 1.6 or 8/5

Step-by-step explanation: If you want to simplify it, the answer would be 8/5 because each number can be divided by 3. If you need the decimal, it would be 1.6.

Step-by-step explanation:

[tex]\dfrac{24}{15}=\dfrac{24:3}{15:3}=\dfrac{8}{5}\\\\\\\dfrac{8}{5}=\dfrac{5+3}{5}=1\dfrac{3}{5}\\\\\\1\dfrac{3}{5}=1\dfrac{3\cdot2}{5\cdot2}=1\dfrac{6}{10}=1.6[/tex]

Answer:

So the solution is -2<x<4 with it's graph is

       O~~~~~~O

------(-2)--------(4)-----------

Step-by-step explanation:

The intersection symbol means it has to be included in both sets.

We have that x<4 and x>-2.

If we graph this, where do we see both shadings:

~~~~~~~~~~~~~~~0                   x<4

         O~~~~~~~~~~~~~~~~~    x>-2

-------(-2)-------------(4)------------

Both shadings happen between -2 and 4 (and not outside that area).

So the solution is -2<x<4

It's graph is

       O~~~~~~O

------(-2)--------(4)-----------

Disclaimer:

I didn't see any equal signs in your problem.

You know the [tex]\ge[/tex] or the [tex]\le[/tex] so we didn't have any closed dots.

The graph is, °←--------------------→°

                   -2____0_________4

The intersection of two sets is the set of all those elements which are common to both of the sets.

Here, given that, {x | x < 4} ∩ {x | x > -2}

It indicates that, x is less than 4, i.e. x= 3,2,1,0,-1,-2,-3,......

Again, x is greater than -2, i.e. x = -1,0,1,2,3,4,....................

Now, as it is intersection of this two sets

So, we have, x= -1,0,1,2,3.

Hence, the required graph is,

       °←------------------------------------→°

_(-2)__________0____________4_____

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Answer:

y = [tex]\frac{30-3x}{5}[/tex]

Step-by-step explanation:

Given

3x + 5y = 30

Isolate the term in y by subtracting 3x from both sides

5y = 30 - 3x ( divide both sides by 5 )

y = [tex]\frac{30-3x}{5}[/tex]

Answer:

[tex]y=\frac{-3}{5}x+6[/tex]

Step-by-step explanation:

3x+5y=30 is the given equation.

We are asked to isolate y.

The term that contains y is 5y. I'm going to first isolate 5y.

To isolate 5y we see that we have +3x with it.  To undo addition of 3x we will need to subtract 3x on both sides.

3x+5y=30

-3x          -3x

     5y=-3x+30

We now have 5y by itself.  There is actually one step left to get the y by itself.

The last step is undo this multiplication between 5 and y.

To undo multiplication you divide.

So we will be dividing 5 on both sides. This gives us:

3x+5y=30

-3x        -3x

     5y=-3x+30

     --     ---------

     5          5

So the whole reason we did that is because 5y/5 is just y.  I'm going to separate that fraction on the right hand side.  This gives me:

     y=-3/5  x   +  30/5

I'm going to simplify the 30/5 to 6.

    y=-3/5   x          +6

Answer:

Measure of arc PQR is 190°

Step-by-step explanation:

First have a sketch of the quadrilateral PQRS inside a circle

You should notice that the intercepted angle is ∠PSR

You should remember that the intercepted arc PQR is twice the intercepted angle ∠PSR

Find the intercepted angle ∠PSR

Remember that in a quadrilateral opposite angles add up to 180°

Hence;

∠PQR+∠PSR=180°

85 + ∠PSR=180°

∠PSR=180°-85°=95°

Find arc PQR

Arc PQR =2×∠PSR

Arc PQR=2×95°

=190°

Answer:

x = - 5, x = 4

Step-by-step explanation:

Given

f(x) = x² + x - 20

To find the zeros equate f(x) to zero, that is

x² + x - 20 = 0

Consider the factors of the constant term ( - 20) which sum to give the coefficient of the x- term ( + 1)

The factors are + 5 and - 4, since

5 × - 4 = - 20 and + 5 - 4 = + 1, hence

(x + 5)x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 4 = 0 ⇒ x = 4

Answer:

The zeroes are {-5, 4}.

Step-by-step explanation:

f(x)  =  x^2 + x - 20 = 0

To factor this function we need 2 numbers whose sum is + 1 ( x = 1x) and whose product is -20. They are 5 and - 4 so we have:

(x + 5)(x - 4) = 0

x + 5 = 0 gives x = -5

and x - 4 = 0 gives x =  4.

Answer:

Her oven will cool to 75°F in 100 minutes, or 1 hour 40 minutes.

Step-by-step explanation:

Let T(t) represent the oven temperature, and t the time in minutes.

Then:

T(t) = 400°F - (3.25°F/min)t

Find the time, t, at which T(t) will = 75°F:

400°F - (3.25°F/min)t = 75°F

Subtracting 75°F from both sides, we get:

(3.25°F/min)t = 325°F.

Dividing both sides by (3.25°F/min) yields:

t = 100 minutes.

Her oven will cool to 75°F in 100 minutes, or 1 hour 40 minutes.

It will take 100 minutes for Laura's oven to cool down from 400°F to 75°F at a cooling rate of 3.25°F per minute.

The temperature must drop from 400°F to 75°F, so the temperature difference: 400°F - 75°F = 325°F.

325°F / 3.25°F per minute = 100 minutes.

Answer:

[tex]y=\frac{3}{5} x+1[/tex] and [tex]5y=3x-2[/tex] are parallel.

[tex]10x-6y=-4[/tex] is neither parallel nor perpendicular.

Step-by-step explanation:

First, you have to simplify each equation in terms of y.

[tex]y=\frac{3}{5} x+1\\5y=3x-2\\10x-6y=-4[/tex]

Your first equation is already in terms of x, so simplify your second equation.

[tex]5y=3x-2\\y=\frac{3}{5} x-\frac{2}{5}[/tex]

Now you can simplify your third equation.

[tex]10x-6y=-4\\-6y=-10x-4\\y=\frac{5}{3} x+\frac{2}{3}[/tex]

These are your three equations in terms of y:

[tex]y=\frac{3}{5} x+1\\\\y=\frac{3}{5} x-\frac{2}{5} \\\\y=\frac{5}{3} x+\frac{2}{3}[/tex]

Now, all you have to know is how to tell using your slope if a line is parallel or perpendicular to another.

Two parallel lines will have the exact same slope.

Two perpendicular lines will have slopes which are opposite reciprocals. For example, a line with a slope of 2 is perpendicular to a line with a slope of [tex]-\frac{1}{2}[/tex], as they have opposite signs and are reciprocal (2/1 versus 1/2) to each other.

Your first two equations have the same slope and are therefore parallel.

Your third equation is a reciprocal, but it is not opposite, and is therefore not parallel nor perpendicular.

The first and the second lines are parallel as they both have a slope of 3/5. None of the lines is perpendicular to the others.

In geometry and algebra, lines can be either parallel, perpendicular, or neither. To determine this, we need to look at the slope of each line. The slope of a line is the value of 'm' in the equation of the line, y = mx + c.

The equations you have provided are:

When two lines have the same slope, they are parallel. When two lines have slopes that are negative reciprocals of each other (meaning their product is -1), they are perpendicular. In this case, the first and the second line are parallel (both have a slope of 3/5), and none of these lines is perpendicular to the others.

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Supplementary angles are 2 angles that have the sum of 180 degrees. Therefore, the requirement of supplementary angles is to have the 2 angles to equal 180 degrees.

Hope this helps!

Answer:

the sum of angles must be 180 degrees

Step-by-step explanation:

The definition of supplementary angles is

"Two angles are supplementary angles if their sum is 180 degrees".

For example, if x and y are supplementary angles then

x + y = 180

Therefore, we can conclude that the requirement of supplementary angles is " the sum of angles must be 180 degrees".

Answer:

[tex]1.02 \times 10^{13}[/tex]

Step-by-step explanation:

Speed of the sound = [tex]3.4 \times 10^{2}[/tex] meters per second

Time to calculate the distance traveled = [tex]3 \times 10^{10}[/tex] seconds

Since,

Distance = Speed x Time

Using the values we get:

[tex]Distance=3.4 \times 10^{2} \times 3 \times 10^{10}\\\\ = 3.4 \times 3 \times 10^{(2+10)}\\\\ = 10.2 \times 10^{12}[/tex]

Since the calculators show the final answer is scientific notation, the above answer in scientific notation would be:

Distance = [tex]1.02 \times 10^{13}[/tex]

Answer:

1.02 E 13

Step-by-step explanation:

The Answer is 1.02 E 13 because E means "time 10 to the power of". So 1.02 E 13 is basically just 1.02 time 10 to the power of 13.

Answer:

Step-by-step explanation:

√(6-a)^2+(-2-a)^2+(0-a)^2 = 10

36-12a+a^2+4+4a+a^2+a^2 =100

3a^2 -8a -60=0

(3a+10)(a-6)=0

a= -3/10 or 6

Answer:

A

Step-by-step explanation:

The definition of a parabola.

Any point on the parabola (x, y) is equidistant from a point ( the focus ) and a line ( the directrix ).

Parabola is best describe by:

"Parabola is defined as the set of all the points in a plane that are equidistant from a fixed point known as focus and a fixed line called directrix."

According to the question,

A. The set of all points in a plane that are equidistant from a single

point and a single line.

It represents the parabola.

Option(A) is the correct answer.

B. The set of all points in a plane that are equidistant from two points.

It represents the line.

Option (B) is not the correct answer.

C. The set of all points in a plane at a given distance from a given

point.

It represents the circle.

Option (C) is not the correct answer.

D. The set of all points in a plane that are equidistant from two points

     and a single line.

It represents the perpendicular bisector.

Option (D) is not the correct answer.

Hence, Option(A) is the correct answer.

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Answer:

L ≅ P

Step-by-step explanation:

To prove congruence through ASA, we need the measures of two angles that are adjacent to a given side. If we are given that two angles are congruent to other angles in another triangle respectively and both of those angles are adjacent to one side (in which each side of each triangle is congruent) then the triangles are congruent through ASA.

To prove congruence using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal. The additional information needed is that angle NM is congruent.

To prove that the triangles are congruent using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal.

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Answer: 9 points

Step-by-step explanation:

The coefficient of determination is a number between 0 and 1 used to measure the level of precision with which the regression model  created fits the data. A measure of [tex]R ^ 2 = 1[/tex]   means that the model explains the entire variation between the two variables without error.

Therefore, in this case if [tex]R ^ 2 =1[/tex] means that the 9 points are on the line

Answer:

9 points

Step-by-step explanation:

Answer:

The domain is {x : x ∈ R} or (-∞ , ∞)

Step-by-step explanation:

* Lets explain how to find the domain

- The domain of the function is the values of x which make the

  function defined

- The quantity under the square root must be ≥ 0 because there is

  no square root for negative value

* Lets solve the problem

∵ f(x) = √(x² - x + 6)

∴ The value of (x² - x + 6) must be greater than or equal zero because  

   there is no square root for negative value

- Graph the function to know which values of x make the quantity

  under the root is negative that means the values of x which make

  the graph under the x-axis

∵ The graph doesn't intersect the x-axis at any point

∵ All the graph is above the x-axis

∴ There is no value of x make f(x) < 0

∴ x can be any real number

∴ The domain of f(x) is all real numbers

∴ The domain is {x : x ∈ R} or (-∞ , ∞)

Answer:

Step-by-step explanation:

A cube has 6 faces and faces are square in shape. Thus to find the surface area of a cube, first we will find the area of one face. To find the area of a face we will simply multiply the side length twice.

20*20=400

Thus the area of one face = 400 units square.

Now to find the surface area  of a cube we will simply multiply the area of one face by the number of total faces of a cube.

400*6 = 2400

Therefore the net folded to form a cube has a surface area of 2400 units square....

Answer:

The answer is 3/5x^6y^6

Step-by-step explanation:

The given expression is:

-9x^-1 y^-9/-15x^5 y^-3

It can be written as:

= -9/-15 * x^-1/x^5 * y^-9/y^-3

As we know that [x^m/x^n = x^m-n]

= 3/5 * x^-1-5 * y^-9+3

= 3/5 * x^-6 * y^-6

= 3/5 * 1/x^6 * 1/y^6

= 3/5x^6y^6

The answer is  3/5x^6y^6....

The expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

(-9x^-1 y^-9)/(-15x^5 y^-3)

This can be written as

[tex](-9x^{-1}y^{-9} )\div (-15x^{5}y^{-3})[/tex]
[tex](-9\times \frac{1}{x} \times \frac{1}{y^{9} } )\div (-15 \times x^{5} \times \frac{1}{y^{3} } )[/tex]

[tex](\frac{-9}{xy^{9} } )\div (\frac{-15x^{5} }{y^{3} } )[/tex]

This becomes

[tex](\frac{-9}{xy^{9} } )\times (\frac{y^{3} }{-15x^{5} } )[/tex]

[tex]\frac{-9}{-15 } \times \frac{y^{3} }{xy^{9}\times x^{5} }[/tex]

[tex]\frac{3}{5 } \times \frac{1 }{y^{6}\times x^{6} }[/tex]

= [tex]\frac{3}{5x^{6}y^{6} }[/tex]

= [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]

Hence, the expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]

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Answer:

1) 32

2) 8 yards

Step-by-step explanation:

1. We must first subtract the base area of the pyramid from the total surface area to get the lateral surface area:

[tex]LA=2225-25^2=1600[/tex]

The lateral surface area is 4 times the area of one the congruent triangles.

[tex]LA=4\cdot \frac{1}{2}\cdot 25\cdot x[/tex]

[tex]\implies 1600=50x[/tex]

[tex]\implies \frac{1600}{50}=\frac{50x}{50}[/tex]

[tex]32=x[/tex]

Therefore the height of the slant surface is 32 yards

2) The surface area of a cone is [tex]S.A =\pi r^2+\pi r l[/tex], where l is the slant height.

We substitute the surface area S.A=151.58 and [tex]\pi=3.14,r=4[/tex] to obtain:

[tex]151.58=3.14\cdot 4^2+3.14\cdot 4 l[/tex]

[tex]151.58=50.24+12.56l[/tex]

[tex]101.34=12.56l[/tex]

[tex]\frac{101.34}{12.56}=l[/tex]

l=8.06

To the nearest whole number, the slant height is 8 yards

[tex]\bf \stackrel{\textit{number divided by 4}}{(x\div 4)}\qquad \stackrel{\textit{then added to 17}}{+17}\qquad \stackrel{\textit{the result is}}{=}\qquad 25\implies \cfrac{x}{4}+17=25 \\\\\\ \cfrac{x}{4}=25-17\implies \cfrac{x}{4}=8\implies x=(4)8\implies x=32[/tex]

Answer:

Option B is correct.

Step-by-step explanation:

we are given [tex]f(x) = \frac{x}{2}-3[/tex]

and [tex]g(x) = 3x^2+x-6[/tex]

We need to find (f+g)(x)

We just need to add f(x) and g(x)

(f+g)x = f(x) + g(x)

[tex](f+g)(x)=(\frac{x}{2}-3)+(3x^2+x-6)\\(f+g)(x)=\frac{x}{2}-3+3x^2+x-6\\(f+g)(x)=3x^2+\frac{x}{2}+x-3-6\\(f+g)(x)=3x^2+\frac{3x}{2}-9\\[/tex]

So, Option B is correct.

For this case we have the following functions:

[tex]f (x) = \frac {x} {2} -3\\g (x) = 3x ^ 2 + x-6[/tex]

We must find [tex](f + g) (x).[/tex] By definition, we have to:

[tex](f + g) (x) = f (x) + g (x)[/tex]

So:

[tex](f + g) (x) = \frac {x} {2} -3+ (3x ^ 2 + x-6)\\(f + g) (x) = \frac {x} {2} -3 + 3x ^ 2 + x-6\\(f + g) (x) = + 3x ^ 2 + x + \frac {x} {2} -3-6\\(f + g) (x) = + 3x ^ 2 + \frac {2x + x} {2} -9\\(f + g) (x) = + 3x ^ 2 + \frac {3x} {2} -9[/tex]

Answer:

Option B

Answer:

7

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 = 8x + 7 ← is in slope- intercept form

with y- intercept c = 7

Answer:

3 packages

Step-by-step explanation:

To find how many packages you can buy for $9, you have to divide 9 by 3.

Since each package costs $3.

So, 9/3 = 3

So you can buy 3 packages of blueberries.

Answer:

3 packages

Step-by-step explanation:

Since you can buy a package for $3, and you only have $9, how many $3 can you fit? Only 3. In conclusion, you can only buy 3 packages.

Answer:

y ≤ 3x - 2  and  4x + y ≥2

Step-by-step explanation:

We can easily solve this problem by using a plotting tool or any graphing calculator.

We test each case, until we arrive to the correct option

Case 1

y ≤ 3x - 2  and  4x + y ≥2

Correct Option.

Please see attached image for graph

Answer:

Please see attached image.

Step-by-step explanation:

When you multiply a function by -1 you are basically reflecting the values of the function over the x-axis.

The values that were negative become positive and the positive values become negative.

Please, take a look at the attached graph below, where there are examples with two functions.

Answer:

The side length is 7 yds

Step-by-step explanation:

We know the formula for area of a square is

A = s^2 where s is the side length

49 = s^2

Take the square root of each side

sqrt(49) = sqrt(s^2)

7 =s

The side length is 7 yds

Final answer:

To find the side length of a square given its area, calculate the square root of the area. In this case, the side length of the square is 7 yards.

Explanation:

A square has an area of 49yd². To find the side length of each side, you need to take the square root of the area. In this case, the side length of each side would be 7 yards.

Answer:

{f + c < 12

{7c + 4f < 100

-5⅓ < f

7⅓ > c

Step-by-step explanation:

The keyphrase is no more than, which tells you that the inequality symbol has to be less than.

I am joyous to assist you anytime.

Answer:

The measure of arc x is 70°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

and

The inscribed angle is half that of the arc it comprises.

so

The arc that comprises the inscribed angle of 15 degrees is equal to

15(2)=30 degrees

The outer angle of 20 degrees is equal to

20°=(1/2)[x-30°]

40°=[x-30°]

x=40°+30°=70°