Complete or justify each step. 2(2h + 2)2(3h + 5) - 12 Distributive Property 4h + 4 < 6h-2 Simplify (combine like terms). 4h+ 4- 6h 6h-2-6h - 2h + 4<-2 simplify-2h<-6 simplify h>3​

area of trapezoid: 153 units²

Here given information:

trapezium area = [tex]\sf \frac{1}{2}[/tex] * ( side 1 + side 2 ) * height

[tex]\hookrightarrow \sf \dfrac{1}{2} * ( 10 + 24) * 9[/tex]

[tex]\hookrightarrow \sf 153 \ units^2[/tex]

Check the picture below.

well, let's assume a year has 365 days, so 75 days is simply 75/365 of a year.  We also know that your loan was $650 and you paid back $680 or namely 30 bucks extra, so the interest on those $650 is really 30 bucks.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill &\$30\\ P=\textit{original amount deposited}\dotfill & \$650\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{75}{365}\dotfill &\frac{15}{73} \end{cases} \\\\\\ 30 = (650)(\frac{r}{100})(\frac{15}{73})\implies 30=\cfrac{9750r}{7300}\implies 30=\cfrac{195r}{146}\implies 4380=195r \\\\\\ \cfrac{4380}{195}=r\implies \stackrel{\%}{22.46}\approx r[/tex]

She needs to consume 3 full bags of coffee before saving money.

Since Georgia is a coffee enthusiast and drinks three coffee drinks a day from a local coffee shop costing $1.25 each, and being concerned with the expense of her coffee habit Georgia looks into making her own manual brewed coffee, and a bag of premium coffee beans costs $70.00, a coffee grinder costs $120.00, and the manual coffee brewer costs $40.00, to determine, if a bag of coffee makes enough for 100 cups, how many full bags of coffee does she need to consume before saving money, the following calculation must be performed:

Therefore, she needs to consume 3 full bags of coffee before saving money.

Learn more about amount calculation in https://brainly.com/question/27271814

The effective current when an AC peak voltage of 18V is applied to a lamp with 4 ohm resistance is 3.18 A.

Current is the flow of electrons through a conductor when voltage is applied across the conductor.

Given the peak voltage of 18 V, hence:

[tex]V_{rms}=\frac{Peak\ value}{\sqrt{2} } =\frac{18}{\sqrt{2} } =12.73 V\\\\I_{rms}=\frac{V_{rms}}{resistance } =\frac{12.73}{4 } =3.18 A\\[/tex]

The effective current when an AC peak voltage of 18V is applied to a lamp with 4 ohm resistance is 3.18 A.

Find out more on current at: https://brainly.com/question/24858512

Answer:

W = 5

L = 15

Step-by-step explanation:

Formula for Area of Rectangle is L × W

Since stated triple;

L = 3W

Area = L×W = 3W² = 75

It'll be:

3W² = 75

Divide both sides with 3:

3W² = 75

3 3

W² = 25

Then square root both sides:

w = 5

Again stated that length is triple the width:

L = 5 × 3

L = 15

Therefore;

W = 5

L = 15

Answer:

Step-by-step explanation:

he paid a 3 dollar fee so we can remove that 23.79-3 = 20,79

now we devide 20,79 by 11 or 189 minutes.

Step-by-step explanation:

the ratio of the pool lengths is 3/5.

that means for every 3 meters of length on Shantel's pool, there are 5 meters of length on Juan's pool.

it the other way around : to get to the size of Shantel's pool, every 5 meters of length on Juan's pool are converted to 3 meters.

x = length of Juan's pool

x × 3/5 = 30

3x = 150

x = 50 meters

you see the relationship ?

3/5 = 30/50 = 300/500 = ...

but it is true for any factor

3/5 = 15/25 = 24/40 = 6/10 = ...

once you see the factor for one part of the ratio, you know there is the same factor for the other part (or parts) of the ratio. otherwise the ratio would not stay the same and keep the relationship.

Answer:

y=-41

Step-by-step explanation:

[tex]\frac{y+31}{2} =-5\\y+31=-5 \times 2\\y+31=-10\\y=-10-31\\y=-41[/tex]

Answer: 1250 square feet!

Step-by-step explanation:

A (25)=25•(100-2•25)=25•50=1250 Sq Ft

If you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall.

Any rectangle's length and width differences must be as small as possible for the area to be maximized.

The largest area you can enclose

A =25×(100-2•25)

A=25•50

A=1250 Sq Ft

Thus, if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ5

Answer:

Step-by-step explanation:

assume that [tex]y=\sqrt{x}[/tex] is [tex]f(x)=\sqrt{x}[/tex] and [tex]y=\sqrt{-2x+6}+3[/tex] is

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

The transformation from the first equation to the second equation can be found by finding a,h and k for each equation.

[tex]y=a\sqrt{x-h}+k[/tex]

factor a 1 out of the absolute value to make the coefficient of x equal to 1

[tex]y=\sqrt{x}[/tex]

factor a 2 out of the absolute value to make the coefficient of x equal to 1

[tex]y=\sqrt{2}\sqrt{x-3}+3[/tex]

find a, h and k for [tex]y=\sqrt{2}\sqrt{x-3}+3[/tex]

[tex]a=1.41421356\\ h=3\\k=3[/tex]

the horizontal shift depends on the value of h when [tex]h > 0[/tex], the horizontal shift is described as:

[tex]g(x)=f(x+h)[/tex] - the graph is shifted to the left h units

[tex]g(x)=f(x-h)\\[/tex] - the graph is shifted to the right h units

the vertical shift depends on the value of k

Answer:

  [tex]\left[\begin{array}{ccc}0&3&-5\\0&-1&-2\end{array}\right][/tex]

Step-by-step explanation:

Rotation 180° (in either direction) about the origin causes each coordinate to have its sign changed. Effectively, the coordinate matrix is multiplied by -1.

__

Additional comment

This is equivalent to reflection across the origin.

The value of x in the special right triangle is 39.60 ft.

Right angle triangle has one of its angles as 90 degrees. The side and angles can be found using trigonometric ratios.

Therefore, let's find the base of the triangle with 30 degrees.

sin 30° = opposite / hypotenuse

1 / 2 = 7 / b

b = 14 ft

Let's use the value(14 ft) to find the height of the biggest triangle.

sin 30 = opposite / hypotenuse

sin 30 = 14 / h

0.5h = 14

h = 14 / 0.5

h = 28 ft

Therefore, let's find the value of x .

sin 45° = 28 / x

x = 28 / 0.70710678118

x = 39.5979797464

x = 39.60 ft

learn more on right triangle here: https://brainly.com/question/10412877

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Consider the number as x

let's solve ~

[tex]\qquad \sf  \dashrightarrow \:6(x + 20) = 26[/tex]

[tex]\qquad \sf  \dashrightarrow \:6x + 120 = 26[/tex]

[tex]\qquad \sf  \dashrightarrow \:6x = - 120 + 26[/tex]

[tex]\qquad \sf  \dashrightarrow \:6x = -94[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = - 94 \div 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{ - 47}{3} [/tex]

・ ．━━━━━━━†━━━━━━━━━．・

Answer:

[tex](x + 20) 6 = 26[/tex]

[tex]6x + 120 = 26[/tex]

[tex]6x = 26 - 120[/tex]

[tex]6x = - 94[/tex]

[tex] \displaystyle \: x = \frac{ - 94}{6} [/tex]

[tex] \displaystyle{x = \frac{ - 47}{3} }[/tex]

[tex]\red {\rule{35pt}{2pt}} \green{ \rule{35pt}{2pt}}\orange{ \rule{35pt}{2pt}}\pink{ \rule{35pt}{2pt}}\blue{ \rule{35pt}{2pt}}\purple{ \rule{35pt}{2pt}}\red{ \rule{35pt}{2pt}}[/tex]

[tex] \bold{ \displaystyle{x = - \frac{47}{3} }}[/tex]

The random number simulator of Molly's throws is an illustration of probability.

The probability of making both free throws is 30%

From the complete question, we understand that:

The simulator is based on numbers 0 to 9

Given that she makes 70% of her free throws, then it means that 7 of the 10 numbers would represent a successful throw, while the other three would represent a missed throw

So, we have:

From the random numbers, she has two successful free throws in:

21 50 64 66 42 03 --- 6 numbers of 20

The probability of making two free throws is then calculated as:

P = 6/20

Evaluate

P = 30%

Hence, the probability of making both free throws is 30%

Read more about probability at:

https://brainly.com/question/251701

Answer: Its 28.

Step-by-step explanation:

The missing number in the card s 28

Represent the missing number with x.

So, we have:

x, 19, 22 and 31

The mean of a dataset is:

Mean = Sum/Count

So, we have:

25 = (x + 19 + 22 + 31)/4

Multiply both sides by 4

100 = x + 19 + 22 + 31

Evaluate the sum

100 = x + 72

Subtract 72 from both sides

x = 28

Hence, the missing number is 28

Read more about mean at:

https://brainly.com/question/14532771

Using proportions to relate the amount of cups needed, it is found that she should use:

a) 0.25 cups of cereal.

b) 0.75 cups of water.

A proportion is a fraction of a total amount.

In this problem, for 4 servings, 3 cups of water and 1 cup of cereal is needed. One serving is one-fourth of the amount, hence:

Item a:

1/4 x 1 = 0.25 cups of cereal.

Item b:

1/4 x 3 = 3/4 = 0.75 cups of water.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

As Per Provided Information

Area of given square slice of cheese is 25 square inches .

We have been asked to determine the perimeter of the slice of cheese .

First we will find the side of square slice of cheese .

Let us assume the side of square slice of cheese be s .

Now Let's Solve

[tex] \boxed{\bf \:Area_{(Square)} = {Side}^{2}}[/tex]

Substituting the value and we obtain

[tex] \sf \longrightarrow \: 25 = {s}^{2} \\ \\ \\ \sf \longrightarrow \: \sqrt{25} = s \\ \\ \\ \sf \longrightarrow \: s \: = 5 \: inch[/tex]

So, the side of square slice cheese is 5 inch

Now let's calculate the Perimeter of cheese

[tex] \boxed{\bf \: Perimeter_{(Square)} = 4 \times side}[/tex]

Substituting the value we obtain

[tex] \longrightarrow \sf \: Perimeter_{(Square)} = 4 \times 5 \\ \\ \\ \longrightarrow \sf \: Perimeter_{(Square)} =20 \: inches[/tex]

Therefore,

Answer:

divide the anser in the pasage

Step-by-step explanation:

divide the two numbers

The units use for Tamara's cats is an illustration of metric units

Tamara's unit of feeding her cats is cups

From the complete question, the amount of feed Tamara gives her cat to be:

Amount = 1/8 cups

This means that the unit of feed Tamara used is cups

Hence, Tamara's unit of feeding her cats is cups

Read more about metric units at:

https://brainly.com/question/2555957

Step-by-step explanation:

Step 1: Take the First Derivative This means only differentiate once.

Disclaimer: Since absolute value only take positve outputs and quadratics only take positve outputs, we can get rid of the absolute value signs so we now have

[tex]e {}^{ {x}^{2} - 1 } [/tex]

We have the function x^2-1 composed into the function e^x.

So we use chain rule

Which states the derivative of a function composed is the

derivative of the main function times the derivative of the inside function.

So the derivative of the main function is

[tex] \frac{d}{dx} (e {}^{x} ) = e {}^{x} [/tex]

Then we replace x with x^2-1

[tex]e {}^{ {x}^{2} - 1} [/tex]

Then we take the derivative of the second function which is 2x so qe multiply them

[tex]e { }^{ {x}^{2} - 1 } 2x[/tex]

Step 2: Set the equation equal to zero.

[tex]e {}^{x {}^{2} - 1} 2x = 0[/tex]

Since e doesn't reach zero. We can just set 2x=0.

[tex]2x = 0 = x = 0[/tex]

So the critical point is 0.

Since e^x will never reach zero

Since 0 is the only critical point, this where the max or min will occur at.

Next we pick any numbergreater than zero, and plug them in the derivative function which gives us a positve number.

Any pick less than zero will give us a negative number.

Since the function is decreasing then increasing, we have a minimum.

Since 0 is the only critical point, we have a absolute minimum at 0.

To find the y coordinate, plug 0 in the orginal function.

Which gives us

[tex]e {}^{ {0}^{2} - 1 } = e {}^{ - 1} = \frac{1}{e} [/tex]

So the minimum occurs at

(0,1/e).

Answer:2 squared +3 squared and the square root of that number

Step-by-step explanation:

Answer:

m∠2 = 95°

m∠3 = 85°

m∠4 = 95°

Step-by-step explanation:

Vertical Angle Theorem:

When two straight lines intersect, the opposite vertical angles formed are always equal (congruent) to each other.

Therefore,

m∠3 = 85°

m∠2 = m∠4

Linear pair:

Two adjacent angles which, when combined, form a line, so the sum of a linear pair is 180°.

Therefore,

85° + m∠2 = 180°

m∠3 + m∠4 = 180°

If  85° + m∠2 = 180°

⇒ m∠2 = 180° - 85°

⇒ m∠2 = 95°

As  m∠2 = m∠4  then  m∠4 = 95°

Answer:

624

Step-by-step explanation:

Answer:

C = [tex]\frac{963}{92}[/tex]

Step-by-step explanation:

given A varies directly as B and inversely as C then the equation relating them is

A = [tex]\frac{kB}{C}[/tex] ← k is the constant of variation

to find k use the condition A = 6 , B = 10 , C = 15 , then

6 = [tex]\frac{x10k}{15}[/tex] ( multiply both sides by 15 )

90 = 10k ( divide both sides by 10 )

9 = k

A = [tex]\frac{9B}{C}[/tex] ← equation of variation

when A = 92 and B = 107 , then

92 = [tex]\frac{9(107)}{C}[/tex] ( multiply both sides by C )

92C = 963 ( divide both sides by 92 )

C = [tex]\frac{963}{92}[/tex]

Answer:

C = 963/92

Step-by-step explanation:

Given :

Finding the constant of variation, k

Finding C

Answer:

y=x-5

Step-by-step explanation:

try that my good sir