Find the distance between the 2 planes to the nearest tenth.

Answer:

(x + 5)(3x - 2)

Step-by-step explanation:

Assuming you require the expression factorised.

3x² + 13x - 10

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = + 13

The factors are + 15 and - 2

Use these factors to split the x- term

3x² + 15x - 2x - 10 ( factor the first/second and third/fourth terms )

= 3x(x + 5) - 2(x + 5) ← factor out (x + 5) from each term

= (x + 5)(3x - 2) ← in factored form

The original price of the item was $70 if Joyce paid $31.50 for an item at the store that was 55 percent off the original price.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let x be the original price of the item. Then, we can write the equation:

x - 0.55x = 31.50

from the given expression we need to solve the value of x to get the original price if Joyce paid $31.50 for an item at the store that was 55 percent off the original price

Simplifying the given equation, we get:

0.45x = 31.50

Dividing both sides by 0.45, we get:

x = 70

Therefore, the original price of the item was $70.

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Answer:

(2,-11) is the vertex

Answer:

Step-by-step explanation:

[tex]f(x)=3x^2-12x+1\\\\f(x)=3(x^2-4x)+1\\\\f(x)=3(x^2-2\cdot x\cdot2+2^2-2^2)+1\\\\f(x)=3(\underline{x^2-4x+4}-4)+1\\\\f(x)=3[(x-2)^2-4]+1\\\\f(x)=3(x-2)^2-12+1\\\\f(x)=3(x-2)^2-11[/tex]

the vertex form of parabola's equation is: f(x) = a(x - h)² + k with vertex (h,k)

x-h = x-2  ⇒  h = 2

+k = -11    ⇒   k = 11

Step-by-step explanation:

Equation of straight line is y=mx+c

choose any two points on straight line

for me I choose:(-3,11) and (3,-1)

use these two points to find gradient,m.

m= (-1-11)/(3-(-3))

m= -2

now, y=-2x+c

choose any point on the straight line

I choose point (3,-1)

sub the point into the equation to find c

-1=-2(3)+c

c=5

equation: y=-2x+5

Answer:

0

Step-by-step explanation:

5(x+3) replace x with -3

5(-3+3)

5(0)

0

Answer:

Hope it help you

Stayhomestaysafe

Plz mark my answer brainliest✍️✍️

Step-by-step explanation:

Answer is -4

REAL NAME - SHRESTH DUBEY

-4 is the Answer.

-32/8 would be -4

Answer:

a)1 , 5 , 9 , 13 , 17, 21 , 25

Answer:

Do 180-110=70 Then have it where 70/2=35. 35+4=39, 35-4=31, so the three angles are 39, 110, and 31.

Step-by-step explanation:

Answer:

83 points.

Step-by-step explanation:

Answer:

2/3

24/36

32/48

are all equivalent to 8/12

Answer:

32/48

Step-by-step explanation:

32 divided by 4 is 8

48 divided by 4 is 12

Answer:

4.53%

Step-by-step explanation:

We are told that:

From the question, we have a 6.5 % coupon

Hence = 6.5 × $10

= $65

Price of the bond one year later = $1,037.19

$1,054.47 - $1,037.19

= $17.28

Rate of Return

= ($65.00 - $17.28)/$1,054.47

47.72 ÷ 1054.47 = 0.045254962

0.045254962 × 100 =

4.5254962 %

Approximately = 4.53%

1. meters/second

2. $/pound

3. $/ tire

4. people/class

5. miles/gallons

6. calories/serving

Answer:

[tex]8x^{3}+3-\frac{4}{x-8}[/tex]

Step-by-step explanation:

Set up the synthetic division using the coefficients of the numerator and the root in the denominator. Divide using the rules for synthetic division.

Answer:

The correction is  D

Step-by-step explanation:

From the question we are told that

    The maximum height is  [tex]h_m = 18 ft[/tex]

    The minimum height is [tex]h_i = 4 ft[/tex]

     The function that models the height of the blade is [tex]h(x) =- 14 sin(x) + 18[/tex] here x is time in seconds

 Now at maximum height

       [tex]18 = - 14 sin(x) + 18[/tex]

=>     [tex]-14 sin(x) =0[/tex]

=>     [tex]sin(x) =0[/tex]        

=>     [tex]x =sin^{-1}[0][/tex]

=>     [tex]x =0 \ s[/tex]    

 Now at minimum  height

        [tex]4 = -14 sin(x) + 18[/tex]

=>      [tex]-14 = -14 sin(x)[/tex]

=>     [tex]sin (x) = 1[/tex]

=>     [tex](x) = sin^{-1}[1][/tex]

=>     [tex]x = 1.6 \ s[/tex]

Now this values is the time taken to move from the higher position of the blade to the lower position of the blade

Now it will take this same amount of time to complete the circle

So the total time take is

    [tex]x_t = 2 * |x|[/tex]

=>   [tex]x_t = 2 * 1.6[/tex]

=>   [tex]x_t = 3.2 \ s[/tex]

Answer:

y = (-1/2)x + 4

Step-by-step explanation:

Slope (m): (-1/2)

down one, right two

y-intercept (b): 4

y = mx + b

The slope-intercept equation if the line is [tex]y=-\frac{1}{2}x+4[/tex]

To find the slope, you must put the 2 points into the slope equation.

[tex]\frac{3-4}{2-0}=\frac{-1}{2}[/tex]

And to find the y-intercept, you must find where the line crosses the y-axis.

(0,4)

Answer:

Some points are: (1, 4), (0, 9), and (3, -6), just to name a few.

Step-by-step explanation:

We can find out an ordered pair for this equation by plotting the line 5x + y = 9 on a graph. If you graph 5x + y = 9, then we see that the point (1, 4) is a point that the line intersects. Let's substitute that values:

5(1) + 4 = 9

Order of operations, multiply first...

5(1) = 5

Then it becomes...

5 + 4 = 9

We can see that 5 plus 4 actually does equal 9, so the point (1, 4) works. Let's try a different point. We can see the point (0, 9) is another point that the line intersects. Same process for this point too.

5(0) + 9 = 9

Then...

5(0) = 0

0 + 9 = 9

We see that 0 plus 9 ALSO works, but let's try one more time. Another point that works is the point (3, -6) Again, same process.

5(3) + -6 = 9

That is equal to:

5(3) - 6 = 9

Simplify...

5(3) = 15

15 - 6 = 9

15 minus 6 works as well! Any point that the line intersects will be a solution for the equation. I hope this helps!

Answer:

ll

Step-by-step explanation:

Answer:

Similarity is it is beautiful like your mom

Step-by-step explanation:

All 3 angles of the triangle added up will be equal to 180 degrees.

Hope this helps, brainliest pls!

Answer:

$5.58

Step-by-step explanation:

Because divide 12 by 67:

67 ÷ 12 = 5.58

5.58 is the answer

Hope this helped! Pls Brainliest!

Answer:

$5.58

Step-by-step explanation:

$67.00÷12=$5.58

Hope this helps!

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

its D i took test 2020 edge

Answer:

x=8

Step-by-step explanation:

set the equations equal to themselves and solve

3x-9=2x-1

+9 and -2x

x=8

Check:

3(8)-9=2(8)-1

24-9=16-1

15=15

Answer:

Total cost of membership will be the same for both gyms after 5 months.

Step-by-step explanation:

Given: Suzy's Sculpting gym charges a $10 application fee and $12 per month for membership.

Tami's Toning does not charge an application fee, but charges $14 per month for membership.

To find: After how many months will the total cost of membership be the same for both gyms

Solution:

Let [tex]t[/tex] denotes number of months after which total cost of membership will be the same for both gyms

For Suzy's Sculpting gym,

Total charges [tex]= 10+12t[/tex]

For Tami's Toning,

Total charges [tex]=14t[/tex]

Now solve [tex]10+12t=14t[/tex]

[tex]10+12t=14t\\10=14t-12t\\10=2t\\t=\frac{10}{2}\\ t=5[/tex]

So, total cost of membership will be the same for both gyms after 5 months.

Answer: A rotation of 180° around the origin.

Step-by-step explanation:

When we have a point (x, y) and we want to reflect it over a given line, the distance between the point and the line remains invariant under the transformation.

This is equivalent as a rotation around a point, the "radius" of the circle that we are creating when we do a rotation is constant.

Now, let's analyze our case:

First a reflection over x-axis, and then a reflection over the y-axis.

This means that if our point starts in quadrant 1 then:

-The reflection over the x-axis will leave our point in quadrant 4.

-The reflection over the y-axis will leave our point in quadrant 3.

Now, if our point stated on quadrant 2.

-The reflection over the x-axis will leave our point in quadrant 3.

-The reflection over the y-axis will leave our point in quadrant 4.

So essentially, these transformations "move" our point to the opposite quadrant, such that the rules of the reflection are applied.

This means that:

The distance between our point and the x-axis does not change.

The distance between our point and the y-axis does not change.

But if the distances to both axes do not change, then the distance between our point and the origin also does not change.

This means that we can find a rotation that is equivalent to this transformation.

So we must look at a rotation that moves our point 2 quadrants.

a rotation that moves our point 2 quadrants will be:

A rotation of 180° around the origin.

Answer:

I'm guessing 28

Step-by-step explanation:

because 3/4 of 21 is 28

Answer:

Mercury 1.3, Venus 3.3, Jupiter 39.2, Saturn 33.1, Uranus 14, Neptune 13.6

Step-by-step explanation:

The scaled diameter of each planet is:

Mercury - 1.3 cm

Venus - 3.3 cm

Jupiter - 39.2 cm

Saturn - 33.1 cm

Uranus - 14 cm

Neptune - 13.6 cm

Given,

The ratio between the earth's actual diameter and its scaled diameter can be used to find the scaled diameter of the other planets.

Earth's diameter of 12,756 kilometers is scaled to 3.5 centimeters as shown in the table.

Using the calculations shown, Mars's diameter of 6,792 would be scaled to 1.9 centimeters.

Use this same process to complete the table with the scaled diameters of the other planets.

Round each answer to the tenths place.

If two given ratios are equal we say that the ratios are in proportion.

Example:

1/2 and 4/8 are in proportion.

- 1/2

- 4/8 = 1/2

We have,

Earths diameter = 12,756 km

It is scaled to 3.5 cm

The ratio is:

= 12,756 km /3.5 cm

Since each planet is in proportion with each planet.

We have,

Let the scaled diameter be d.

- Mercury d

12,756 / 3.5 = 4879 / d

d =  (4879 x 3.5) / 12756

d = 1.3 cm

- Venus d

12,756 / 3.5 = 12104 / d

d = (12104 x 3.5) / 12756

d = 3.3 cm

- Jupiter d

12,756 / 3.5 = 142984 / d

d = (142984 x 3.5) / 12756

d = 39.2 cm

- Saturn d

12,756 / 3.5 = 120,536 / d

d = (120536. x3.5) / 12756

d = 33.1 cm

- Uranus d

12,756 / 3.5 = 51118 / d

d = (51118 x 3.5) / 12756

d = 14 cm

- Neptune d

12,756 / 3.5 = 49, 528 / d

d = (49528 x 3.5) / 12756

d = 13.6 cm

Thus the scaled diameter of each planet is:

Mercury - 1.3 cm

Venus - 3.3 cm

Jupiter - 39.2 cm

Saturn - 33.1 cm

Uranus - 14 cm

Neptune - 13.6 cm

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