22. “n is less than 15 and greater than or equal to 3”

Complete the following steps to receive full credit for this question:

• The inequality translated in numerical form
• The solution graphed on a number line
• The solution in interval form

Answer:

(x + 3)² + (y + 1)² = 100

Step-by-step explanation:

Equation of a circle is:

(x − h)² + (y − k)² = r²

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

The center is on the line x − 4y = 1, so:

h − 4k = 1

h = 1 + 4k

(x − 1 − 4k)² + (y − k)² = r²

Two points on the line are (3, 7) and (5, 5), so:

(3 − 1 − 4k)² + (7 − k)² = r²

(5 − 1 − 4k)² + (5 − k)² = r²

Set the equations equal:

(3 − 1 − 4k)² + (7 − k)² = (5 − 1 − 4k)² + (5 − k)²

(2 − 4k)² + (7 − k)² = (4 − 4k)² + (5 − k)²

4 − 16k + 16k² + 49 − 14k + k² = 16 − 32k + 16k² + 25 − 10k + k²

4 − 16k + 49 − 14k = 16 − 32k + 25 − 10k

53 − 30k = 41 − 42k

12k = -12

k = -1

h = 1 + 4k

h = -3

(3 − 1 − 4k)² + (7 − k)² = r²

(3 − 1 + 4)² + (7 + 1)² = r²

6² + 8² = r²

r = 10

Therefore, the equation of the circle is:

(x + 3)² + (y + 1)² = 10²

Answer:

Step-by-step explanation:

Answer:

Third term=4

Step-by-step explanation:

Given:

C(n)=4/9(-3)^n-1

Find the third term

Let n=3

Substitute n=3 into the equation

C(n)=4/9(-3)^n-1

C(3)=4/9(-3)^3-1

Step 1: evaluate the power 3-1

C(3) = 4/9(-3)^2

Step 2: evaluate (-3)^2

C(3) = 4/9(9)

It can be rewritten as

C(3) = 4/9*9

9 numerator will strike 9 denominator out leaving 4

C(3)=4

Therefore, the third term=4

C(3)=4

Answer:

3x-18x^2+1

Step-by-step explanation:

(6x+1)(1-3x)

6x-18x^2+1-3x

6x-3x-18x^2+1

3x-18x^2+1

Hope this helps :)

Answer:

[tex]-18x^2+3x+1[/tex]

Step-by-step explanation:

[tex]6x *1=6x\\6x*-3x=-18x^2\\1*1=1\\1*-3x=-3x\\[/tex]

Add all the like terms

[tex]-9x^2+3x+1[/tex]

Answer:

(10, 17)

Step-by-step explanation:

It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.

Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)

From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.

y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.

The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.

x: 4+6 = 10

y: 8+9=17

The fruit market is at point (10,17)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates

[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]

[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]

Tia is at P(4, 8) and Lei is at Q(12, 20).

The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1

So,

[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]

Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.

Learn more about graph here:

brainly.com/question/16608196

#SPJ5

Answer:

9.42

pi x radius x radius x (height / 3) = volume

1 x 1 = 1 and 9/3 = 3

pi x 1 x 3 = volume

pi x 3 = volume

3.14 x 3 = 9.42

Hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find an equation of a line given two points first find the slope / gradient

Slope of the line using points (-1,4) and (-2,2) is

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

So the equation of the line using point (-1,4) is

Hope this helps you

Answer:

We have the system:

y > 2*x

y > 3

Now, let's find the limits:

taking y > 3, we can see the limit y = 3.

Now we replace it in the first inequality:

3 > 2*x

3/2 > x.

Then we have that:

y > 3

x < 3/2

Those two inequalities define our system.

So any ordered pair where x is smaller than 3/2 and y is larger than 3, is a solution.

or example:

(1, 3.5) is a solution.

Answer:

(1,5)

Step-by-step explanation:

the other options make the system of equations wrong..

Answer:

Again the domain consists of the pre-images and the range the images.

When we are looking for the f(x) we just look at the number it is pointing to in the range (when we have a diagram), and when we are looking for x when f(x)=y we look at the number that has a line pointed to y.

So the f(4)=

f(x)=4 when x is 8

Answer:

25 students

Step-by-step explanation:

What we need to do here is to do some tracing. We simply need to go to the point on the concert band where we have the value 35.

After sighting this value, we then make a tracing to the line of best fit. Then from this line of best fit, we trace the point on the matching band that correlated with the value 35.

If properly traced, we would arrive at a value of 25 on the marching band

Answer:

24 cm

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

2304 pi = 4/3 pi r^3

Divide each side by pi

2304 = 4/3 r^3

Multiply each side 3/4

2304 * 3/4 = 4/3 r^3 * 3/4

1728 = r^3

Take the cube root of each side

1728 ^ 1/3 = r^3 ^ 1/3

12 = r

We want the diameter

d = 2*r

d = 2*12

d = 24

Answer:

24 centimeters

Step-by-step explanation:

A basketball is a sphere. The volume of a sphere can be found using the following formula:

V= 4/3 π r^3

We know that the volume is 2304 π cm^3, therefore we can substitute 2304π in for V.

2304π = 4/3 π r^3

We want to find out what r is. Therefore, we must get r by itself. First, divide both sides by pi.

2304π/π=4/3πr^3/π

2304π/π=4/3r^3

2304=4/3r^3

Next, divide both sides by 4/3, or multiply by the reciprocal of 4/3. The reciprocal of 4/3 is 3/4 (flip the numerator and denominator).

2304*3/4=4/3r^3*3/4

2304*3/4=r^3

1728=r^3

Now, take the cube root of both sides.

∛1728=∛r^3

∛1728=r

12=r

r= 12 cm

The radius is 12 centimeters, but the question asks us to find the diameter. The diameter is twice the radius.

d= 2r

d= 2* 12 cm

d= 24 cm

The diameter of the basketball is 24 centimeters.

Answer:

A right scalene triangle would have a 90 degree angle and 3 non congruent sides

Step-by-step explanation:

Answer:

it May be SAS postulate

Answer:

Let's put the chart into ordered pairs:

(x, y)

(2,1)

(3,4)

(3,3)

(4,2)

(5,5)

In bold, we see that there are two y-values at x=3. This means that this relation fails the vertical line test (two points on the same verticle line). This is not a function. 

The answer options may be mis-written. 

The answer is no, because one x value corresponds to more than one y-value. 

Answer:

a = -6

Step-by-step explanation:

-5a-9+a=15

Combine like terms

-5a+a  -9 = 15

-4a  -9 = 15

Add 9 to each side

-4a -9+9 = 15+9

-4a = 24

Divide by -4

-4a/-4 = 24/-4

a = -6

Answer:

a = -6

Step-by-step explanation:

1. Combine like terms: -4a – 9 = 15

2. Use the additive property of equality to add 9 to both sides: -4a = 24

3. Use division property of equality to divide -4 on both sides: a = -6

Answer:

42

Step-by-step explanation:

P(left) = 0.10

Expected number of lefties among high school grads of 424

= 424 * 0.10

= 42 (to the nearest person)

Answer:

you do 20% of 424

1 0% of 424 =42.4

you could round it to 42

Answer:

d is 5 units

Step-by-step explanation:

Answer:

Answer:

True

Step-by-step explanation:

trust me, i remember this question

In order to solve this problem, we will need a little more information, for example, we need to know what the functions are. Let's say the problem looks like this:

Use the drawing tool(s) to form the correct answer on the provided number line. Consider the functions below.

[tex]f(x)=|3x|-3[/tex]

and

[tex]g(x)=-x^{2}+8x-5[/tex]

Represent the interval where both functions are increasing on the number line provided.

Answer:

See attached picture

Step-by-step explanation:

Since this problem is posted on the algebra section of Brainly, I assume we will need to make use of an algebraic approach to solve this. Basically, the idea is to graph the functions and find the x-values for which both functions increas. In order to graph the functions, we will need to build a table with points for each of the functions. In order to graph the functions you need to pick the x-values you wish and evaluate them in the given functions. (See attached pictures)

Once you got the desired points, you can plot them in the coordinate axis and find the x-values for which both graphs will be increasing. If we take a close look at the graphs we can see the f(x) graph increases in the interval:

(0,∞)

and the g(x) graph increases in the interval:

(-∞,4)

so the interval in which both graphs are increasing will be the region where both intervals cross each other, which will be (0,4)

so that's the interval we draw on our number line. (see attached picture.

Answer:

see photos

Step-by-step explanation:

Plato/Edmentum

Answer:

(5, 7.5)

Step-by-step explanation:

Each day the movie is late adds $1.50 for late fees.Then, after 5 days of past due, the total late fee would be: 5 * $1.50 = $7.50

Then the coordinate pair representing this would be: (5, 7.5)

[tex]-4(8+y)=90\implies8+y=-22.5\implies y=-30.5[/tex].

Hope this helps.

Answer:

-30.5.

Step-by-step explanation:

-4(8 + Y) = 90

-32 - 4Y = 90

-4Y = 122

Y = -30.5.

Hope this helps!

Answer:

49 cupboards

Step-by-step explanation:

See the steps below, it is self-explanatory:

As 14*14/4= 49, the answer is 49 cupboards

Answer:

( x+3) ^2 + ( y-4) ^2 = 9

Step-by-step explanation:

The equation of a circle can be written as

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

Where ( h,k) is the center and r is the radius

( x--3) ^2 + ( y-4) ^2 = 3^2

( x+3) ^2 + ( y-4) ^2 = 9

Answer:

[tex]|w-20|\leq 0.4[/tex]

Step-by-step explanation:

The manufacturer requires that the weight differs from 20 oz in at most 0.4 oz, therefore we can write this difference (which can be either above or below 20 oz, to be smaller than or equal to 0.4 oz.

The weight can be:

1) smaller than or equal to 20 oz + 0.4 oz:  [tex]w\leq 20+0.4[/tex]  then [tex]w-20\leq 0.4[/tex]

2) larger than or equal to 20 oz - 0.4 oz:  [tex]20-0.4\leq w[/tex]  then  [tex]-0.4\leq w-20[/tex]

and which combined, can be written as a double inequality;

[tex]-0.4 \leq w-20\leq 0.4[/tex]

This double condition can also be written using the absolute value symbol as:   [tex]|w-20|\leq 0.4[/tex]

==================================================

Explanation:

We'll use the hinge theorem here. This says (more or less) that the larger an angle is, the side opposite of that will be longer.

Imagine that the segments with the single tickmarks represent a door swinging open/shut. The more open a door is, the further the distance it is from the handle to the frame. In terms of these triangles, the segment 25 is larger than 5x-10 because the angle 90 (opposite the 25) is larger than the angle 85 degrees (opposite the 5x-10)

In symbols we say

5x - 10 < 25

We also say 5x - 10 > 0 or 0 < 5x - 10 to ensure that the segment of length 5x-10 is not 0 or negative.

Put the two inequalities together and we get 0 < 5x - 10 < 25

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

Solve for x

0 < 5x - 10 < 25

0+10 < 5x - 10 < 25 + 10 .... adding 10 to all sides

10 < 5x < 35

10/5 < 5x/5 < 35/5 ... dividing all sides by 5

2 < x < 7

We have x between 2 and 7, and not equal to either endpoint.

Answer:

8.4 ft

Step-by-step explanation:

Perimeter = side x 4

(Re-arrange)

Side = Perimeter / 4

34/4 = 8.4 ft

Answer:

8.5 feet

Step-by-step explanation:

Divide 34 by 4. A square has 4 sides which are all the same.

Answer:

( x+2)^2 + (y+5)^2 = 1

Step-by-step explanation:

The equation of a circle can be written in the form

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

where ( h,k) is the center and r is the radius

( x- -2)^2 + (y- -5)^2 = 1^2

( x+2)^2 + (y+5)^2 = 1

Answer:

[tex](x + 2)^{2} + (y + 5)^{2} = 1[/tex]

Step-by-step explanation:

The guy above is correct! I just finished the quiz and checked the answer key.

from the above picture

2,3 = 1 quadrant

5,-6 = 4 quadrant

2,0 = on x axis

-5,2 = 2 quadrant

-2,-4 =3 quadrant

0,-2 = on y axis

Answer:

the second one........the shape of the conic section os circle