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

The cost given shows that the amount left is £12.

From the information given, it was stated that the person saved £60 and spent £42 on coat and £6 on scarf

The amount that the person has left will be:

= £60 - £42 - £6

= £12

In conclusion, the person has £12 left.

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The height of the cylinder is 3.82 m

2. The surface area is 316.5 ft²

The volume is 406.5 ft³

The volume of a cylinder is given by the formula,

V = πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

V = 300 m³

r = 5 m

h = ?

Putting the parameters into the formula, we get

300 = π × 5² × h

300 = π × 25× h

∴ h = 300/25π

h = 3.82 m

Hence, the height of the cylinder is 3.82 m

2.

Diameter = 6 feet 6 inches = 6.5 feet

∴ Radius = 3.25 feet

Height = 12 feet 3 inches = 12.25 feet

Surface area of a cylinder is given by

Surface area = 2πr(r + h)

Where r is the radius

and h is the height

Surface area = 2π×3.25(3.25 + 12.25)

Surface area = 316.5 ft²

For the volume

V = πr²h

V = π × 3.25² × 12.25

V = 406.5 ft³

Hence, the volume is 406.5 ft³

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The x-coordinates of the vertices of the hyperbola are 11 and -11

The hyperbola is given as:

[tex]\frac{x^2}{121} - \frac{y^2}{49} = 1[/tex]

A hyperbola is represented as:

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

Where the coordinate of the vertex is:

Vertex = (±a, 0)

By comparing the above equations, we have:

[tex]a^2= 121[/tex]

Take the square of both sides

a = 11

Substitute 11 for a in Vertex = (±a, 0)

Vertex = (±11, 0)

Hence, the x-coordinates of the vertices of the hyperbola are 11 and -11

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Answer:

16y1yg1gyyq717177171716161yggqg1g2y2gqgq62g2gtqy2g

1jwjqhwhwjmnbhokmbhiknb

13) 120 + 1.5 + 0.25 = 121.75 pounds

14) 4 - 1.5 = 2.5 pints

15) (2.25)(32)= $72

13. Mrs. Smith's current weight is 121.75 pounds.

14. The students should consume an additional 2.5 pints of water.

15. The nurse's overtime earnings amount to $72.00.

Given are words problems based on mixed numbers:

13. To find Mrs. Smith's current weight, we need to add the weight gained over the last two months to her weight last month.

Weight gained in the first month: 1 1/2 pounds

Weight gained in the second month: 1/4 pounds

Total weight gained over the last two months: 1 1/2 + 1/4 = 1 3/4 pounds

Now, to find Mrs. Smith's current weight, we add the total weight gained to her weight last month:

Current weight = Weight last month + Total weight gained

Current weight = 120 pounds + 1 3/4 pounds

Hence, Mrs. Smith's current weight is 121.75 pounds.

14. To calculate the additional water the students should consume to meet the school nurse's recommendation of at least 4 pints daily, we need to find the difference between the recommended amount and the average amount the students currently drink.

The recommended amount is 4 pints, and the average amount the students currently drink is 1 1/2 pints, which can be written as 1.5 pints.

Additional water needed = Recommended amount - Current average amount

Additional water needed = 4 pints - 1.5 pints

Additional water needed = 2.5 pints

Therefore, the students should consume an additional 2.5 pints of water daily to meet the school nurse's recommendation.

15. To calculate the nurse's overtime earnings, you can use the formula:

Overtime Earnings = Overtime Hours × Overtime Pay Rate

First, let's convert the mixed number of overtime hours into an improper fraction:

2 1/4 hours = 2 + 1/4 = 9/4 hours

Now, we can calculate her overtime earnings:

Overtime Hours = 9/4 hours

Overtime Pay Rate = $32.00/hour

Overtime Earnings = (9/4) hours × $32.00/hour

To simplify the calculation, you can convert the fraction to a decimal:

Overtime Earnings = (9/4) hours × $32.00/hour

Overtime Earnings = 2.25 hours × $32.00/hour

Overtime Earnings = $72.00

So, the nurse's overtime earnings amount to $72.00.

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Answer:switch mikes Luke’s and Alex in between each other and let winter keep her own

Step-by-step explanation:

❄ Hi there,

let us start by considering this: What should we do to get x all by itself?

Since it's

we should

So, let's start.

[tex]\sf{\dfrac{-x}{4}\times4 < 2\times4}}[/tex]

[tex]\sf{-x < -8}[/tex]

[tex]\sf{x > 8}[/tex]

When we divide both sides of an inequality by a negative number, we do "the inequality flip" and flip the inequality sign.

❄

Based on the various meals offered by the catering service, the ways that the order can be done is 6,930 ways..

This can be found as:

= (11! / (9!2!)) x (7! / (5!2!)) x (4! / (2!2!)

= 55 x 21 x 6

= 6,930 ways

In conclusion, the order can be made in 6,930 ways.

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Answer:

The answer is $210.

Step-by-step explanation:

60/2 = 30. 30*5= 150. 150+60=210.

well, we know Aaron received $60, and we also know that Aaron and Betty are sharing the total on a 2:5 ratio, thus

[tex]\cfrac{Aaron}{Betty}~~ = ~~\cfrac{2}{5}\implies \cfrac{60}{Betty}~~ = ~~\cfrac{2}{5}\implies (60)(5)=(Betty)(2) \\\\\\ \cfrac{(60)(5)}{2}=Betty\implies 150=Betty~\hfill \underset{\textit{total money shared}}{\stackrel{60~~ + ~~150}{210}}[/tex]

Based on the information given about the equation, y will be 0.5x + 2.

From the information given, it should be noted that the equation of the line it represents was given and the y intercept is = (0, 2).

The function to represent y will be:

y = mx + b

y = (1/2)x + 2

y = 0.5x + 2

In conclusion, y = 0.5x + 2.

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Answer:

Step-by-step explanation:

It would be point B. Since y-intercept is when the x is at 0, the answer would be point B.

Answer:

x is equal to 5

Step-by-step explanation:

Step-by-step explanation:

try this option, answer is marked with red colour.

Answer: 23,5%

Step-by-step explanation:

[tex]23\frac{1}{2} %[/tex]% = [tex]\frac{47}{200}[/tex] = 0,235 = 23,5%

The area of the desktop is 12. 5 feet square

The formula for area of a rectangle;

Area = length × width

Length = 2. 5 feet

Width = 5 feet

Area = 2. 5 × 5

Area = 12. 5 feet square

Thus, the area of the desktop is 12. 5 feet square

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It will take 21 days before there is another day on which he does both.

The lowest common multiple (LCM) of two or more numbers is the lowest possible number which is completely divisible by all the given numbers.

Given,

John goes for a jog every third day and every Saturday he goes to the gym.

That means he goes to the gym on every seventh day, and goes for a jog every third day.

Therefore, he goes for both on the days which are LCM of 3 and 7.

But, LCM of 3 and 7 is 21.

Hence, he goes for both in every 21 days.

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A range of 2 reveals that the smallest and largest data values are 2 units away from each other.

Range is the difference between the highest and lowest values of a set of observations. Range is a measure of variation.

Range = highest value - lowest value

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681×239 = 162,759

..... ......

162,759 is answer

happy to help

336π square millimeter answer

Step-by-step explanation:

Answer:

336pi square millimeters

Step-by-step explanation:

E2020 Geometry B :3 !!

Similar: yes

Similarity statement: [tex]ADCB \sim SVUT[/tex]

Scale factor: 1/3

Answer:

x = ±√10i (i outside the radical), or approximately ±3.62i, or no solution depending on your class.

Step-by-step explanation:

x^2 + 10 = 0

x^2 = -10

x = ±√-10

x = ±√10i (i outside the radical), or approximately ±3.62i.

The solution is not real.

If you meant x^2 - 10 = 0 then x = ±√10 or approximately ±3.62. This solution is real.

Answer:

x² + 1 = 0

a = 1

b = 0

c = 1

[tex]x1.2 = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

[tex]x1.2 = \frac{ - 0 ±\sqrt{ {0}^{2} - (4.1.1) } }{2.1} [/tex]

[tex]x1.2 = \frac{0± \sqrt{0 - 4} }{2} [/tex]

[tex]x1.2 = \frac{± \sqrt{ - 4} }{2} [/tex]

There is no real solution because the discriminant is negative

Note.

Formula diskriminan

√b² - 4ac.

if the diskrimanan is negatif, so the quadratic equatoin dont have solution

Based on the angles of a + b and b + c, the value of b can be calculated to be 40°.

As this is a triangle, all the internal angles must add up to 180°.

This means that:

a + b + c = 180°

As we have the value of b + c, this becomes:

a + 100 = 180

a = 80°

b is therefore:

a + b = 120

80 + b = 120

b = 120 - 80

= 40 °

Full question is:

If in triangle abc, angle a + angle b= 120° and angle b + angle c = 100°, then find angle b.

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The solution to the given system of equation is (3, 3, 3)

Given the following system of equation expressed as:

2x-y+5z=16

X-6у +2z=-9

3x+4y- z=32

Multiply equation 2 by 2 to have:

2x-y+5z=16

2X-12у +4z=-18

Subtract

10y+z = 34 .........4

Similarly

3X-18у +6z=-27

3x+4y- z=32

Subtract

-22y+7z = -59 ........... 5

Equate 4 and 5

10y+z = 34 .........4 * 7

-22y+7z = -59 ........... 5 * 1

_______________________

70y+7z = 238

-22y+7z = -59

Subtract

92y = 297

y = 3

Recall that

10y+z = 34

10(3) + z = 34

z = 3

Since x - 6y +2z = -9

x-6(3)+2(3) = -9
x - 18 + 6 = -9
x = 3

Hence the solution to the given system of equation is (3, 3, 3)

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Answer: (1,3)

Step-by-step explanation:

Let's solve this system of equations by elimination. We will multiply one or both equations such that when we combine the equations, one of the variables will completely cancel out.

Let's multiply the whole first equation by -2 to achieve this:

[tex]-2(x+2y=7)[/tex] now becomes [tex]-2x-4y=-14[/tex]

Now let's add both equations

[tex]-2x-4y=-14[/tex]

[tex]2x-y=-1[/tex]

[tex]-5y= -15[/tex]

Since we got y into a form we can solve it for, lets divide both sides by -5 to isolate it.

[tex]\frac{-5y}{-5} = \frac{-15}{-5}[/tex]

[tex]y=3[/tex]

Now that we have the value of y, we can substitute it into any equation to solve for x. Only if we have both x and y can we make an ordered pair. Let's use the second equation and substitute 3 for y.

[tex]2x-3=-1[/tex]

We can now solve for x.

[tex]2x=2[/tex] [Adding 3 to both sides]

[tex]x=1[/tex] [Dividing by 2 on both sides]

We now have both x and y, so we can put it in an ordered pair to answer the question.

[tex](1,3)[/tex]

The value of the expression is 972

The expression is given as:

27(36)

Express 36 as 18 + 18

27(18+ 18)

Expand

486+ 486

Evaluate the sum

972

Hence, the value of the expression is 972

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Answer: Option C   [tex]\boldsymbol{7^6}[/tex]

Work Shown:

[tex]\frac{7^{13}}{7^{7}}\\\\\\7^{13-7}\\\\\\\boldsymbol{7^6}[/tex]

Subtract the exponents to get the answer. The rule is [tex]\frac{a^{b}}{a^{c}} = a^{b-c}[/tex]. This rule only works when the bases are the same.

The net that represents a cube is (b) net b

A cube has 6 faces

This means that the net must have 6 faces

For a net to represent a cube, there must be four adjacent faces

And 2 two adjacent faces

Where

The net that represents the above scenario is net (b)

Hence, the net that represents a cube is (b) net b

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1. The z-scores corresponding to Kathy's starting salary is -1.5

2. The z-scores corresponding to Linda's starting salary is -2

z = (x - μ) / σ

Where

z = (x - μ) / σ

z = (31500 - 42000) / 7000

z-score for Kathy's starting salary = -1.5

z = (x - μ) / σ

z = (33000 - 45000) / 6000

z-score for Linda's starting salary = -2

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