You are part of a construction company that is supposed to build houses. An architect has left you plans to build houses on each island. Bridges connect the islands. Island A and Island B have a total of 30 houses. Island A and Island C have a total of 40 houses. Island B and Island C have a total of 36 houses. A total of 53 houses is to be built on the three islands. Determine how many houses are to be built on each island. Show how to represent the problem in each of the following ways and solve them. (This is the verbal description, use sentences to explain) I. Concrete or pictoral representation II. Graph III. Algebraic Formula IV. Table

2x - 1 < 4

First, let's add 1 to both sides.

2x < 5

Divide both sides by 2

x < 5/2 or (-∞, [tex]\frac{5}{2}[/tex])

-5x - 3 > -3

Add 3 to both sides.

-5x > 0

Divide both sides by -5

x < 0 or (-∞, 0)

The solution set of the given set of linear inequations 2x - 1 < 4 and -5x - 3 < -3 is [tex]\left ( -\infty , 0 \right )[/tex].

Algebraic expressions can be related to each other in many ways. When two expressions are equal to each other, they are called equations and are represented with an equal sign between them (=). When two expressions are not equal, they are called inequations and are represented by non-equal signs between them (>, <, ≥, ≤).

In the question, we are asked to solve the given inequations:

2x - 1 < 4 ... (i), and -5x -3 > -3 ... (ii).

First, we will solve (i), in the following ways:

2x - 1 < 4.

or, 2x - 1 + 1 < 4 + 1 (Adding 1 to both sides of the inequation)

or, 2x < 5 (Simplifying)

or, 2x/2 < 5/2 (Dividing both sides of the inequation by 2)

or, x < 5/2 (Simplifying)

or, x ∈ [tex]\left ( -\infty , \frac{5}{2} \right )[/tex] ...(iii)

Now, we will solve (ii), in the following ways:

-5x -3 > -3.

or, -5x - 3 + 3 > -3 + 3 (Adding 3 to both sides of the inequation)

or, -5x > 0 (Simplifying)

or, -5x/(-5) < 0/(-5) (Dividing both sides of the inequation by -5, sign of the inequality reverses as we are dividing by a negative number)

or, x < 0 (Simplifying)

or, x ∈ [tex]\left ( -\infty , 0 \right )[/tex] ...(iv)

For the solution set, we need the intersection of (iii) and (iv)

[tex]\left ( -\infty , \frac{5}{2} \right )[/tex] ∩ [tex]\left ( -\infty , 0 \right )[/tex]

= [tex]\left ( -\infty , 0 \right )[/tex]

∴ The solution set of the given set of linear inequations 2x - 1 < 4 and -5x - 3 < -3 is [tex]\left ( -\infty , 0 \right )[/tex].

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Answer:

52 is correct answer ✔️

Answer:

648 im each bank

Step-by-step explanation:

Answer:

2890

Step-by-step explanation:

g(-4) means that we are solving for y when x = 20

y = 8(20)² - 16(20) + 10

y = 8(400) - 320 + 10

y = 3200 - 320 + 10

y = 2880 + 10

y = 2890

Best of Luck!

Answer:

CE would be half of AD.

Step-by-step explanation:

A, E and D are all points on the circumference of the circle.  

AD is the diameter.  

CE is the radius.  

CE would be half of AD.

Answer: The first angle is 35°, the second angle is 67° and the third angle is 78°.

Step-by-step explanation:

Wee will represent the first angle by f,the second by s, and the third by t.

If gives us the information that the second angle is 3 less than twice the first one, that can be represent by the equation  s= 2f-3  .

The third angle is 8 more than twice the first so it can also be represent by the equation t= 2f + 8 .

Now we know the interior of angles of a triangle adds up to 180 degrees. so see the measures equal 180 to solve for f.

f+ (2f+8) + (2f -3) = 180  Combine like terms on the left side

5f + 5 = 180  

     -5      -5

5f= 175  

f = 35  

So the first angle is 35 degrees.

Second angle.

s=2(35) - 3  

s= 70 -3

s = 67  

The second angle is 67.

Third angle.

t = 2(35) + 8

t= 70 + 8

t= 78

The third angle is 78 degrees.

Now add the angles up to see if they equal 180 degrees.

35 + 67 + 78 = 180  

   180 = 180

The correct answer is C. The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground.

Explanation:

Two key features of living organisms are energy processing and response to stimuli. These two features imply organisms require nutrients, which can be taken from the environment or created through a process such as photosynthesis and they sense their surroundings and respond to it.

Moreover, these two features are exemplified by mushroom (fungi) in the sentence "The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground" because the first section shows the developing mushroom takes nutrients from the soil or its environment and this is essential for growing and survival. Also, the second section of the sentence shows the developing mushroom can sense its environment and respond by developing only in appropriate conditions.

Answer:

C

Step-by-step explanation:

Got it right on edge 2020

Answer:

Yes

Step-by-step explanation:

If y is the total cost, then this would be correct.

Answer:

f(4y) = -8y - 3

Step-by-step explanation:

Step 1: Define variables

f(x) = -2x - 3

f(4y) = x = 4y

Step 2: Plug in x = 4y

f(4y) = -2(4y) - 3

f(4y) = -8y - 3

Answer:

11.2 feet

Step-by-step explanation:

The two furthest corners of the bed are at (8, 6) and (5, 10).  To determine which is the furthest from the origin, use the distance formula.

d = √((x₂ − x₁)² + (y₂ − y₁)²)

d = √((8 − 0)² + (6 − 0)²)

d = 10

d = √((x₂ − x₁)² + (y₂ − y₁)²)

d = √((5 − 0)² + (10 − 0)²)

d = 5√5

d ≈ 11.2

Therefore, the corner at (5, 10) is the furthest from the origin, about 11.2 feet away.

Answer:

Inconsistent System of Equations

Explanation:

There is no solution for the system of equations that graphs as parallel lines.

Parallel lines never cross, therefore there is no intersection. This is an inconsistent system of equations.

Answer:

The answer is (2,7)

Step-by-step explanation:

Answer:

172 kids and 160 adults

Step-by-step explanation:

We can create two equations with the information given.

1.5x + 4y = 898

x + y = 332

We can then bring the x in the second equation over to the other side.

y = 332 - x

We can now plug this equation into the one before.

1.5x + 4(332 - x) = 898

We now do the distributive property on the equation and result with

1.5x + 1328 - 4x = 898

Then we can combine like terms and add 1.5x and -4x together and bring 1328 over by subtracting it from 898.

-2.5x = -430

-430 / 2.5x = 172

x = 172

x is defining how many children when to the park.

Now we just need to figure out y by subtracting it from the total amount of people (aka plugging it into the second equation)

y = 332 - 172

y= 160

We end up with

x = 172

y = 160

172 children and 160 adults

Step-by-step explanation:

1. Add all the different candies together

1/8 + 1/2 + 2/3=

2. Find the lowest common multiple of all the denominators

All the denominators can evenly multiply to 24 so 24 is the Lowest Common Denominator.

3. Multiply to make all the denominators 24

8x3=24 2x12=24 3x8=24

4. Whatever you did to the denominators, do the same thing to the numerators of that specific denominator.

1x3/8x3 1x12/2x12 2x8/3x8

5. Now that the denominators are the same for all the fractions, add all the numerators together.

3/24 + 12/24 + 16/24

3+12+16= 31

ANSWER: Natalie had 31/24 pounds of candy in all

Note: The decimal form is 1.292 pounds

Answer: the product is always positive.

Step-by-step explanation: Rule 1: The product of a negative integer and a positive integer is a negative integer. Rule 2: The product of two positive integers or two negative integers is a positive integer. That means if you multiply two OF the same sign numbers, the product is always positive.

Answer: No because the product of a positive integer and a negative integer is always negative.

2.

The domain of this function is 3≤x≤5 in interval notation that is [3,5]

The range is -3≤y≤3. In interval notation that is [-3,3]

4.

The domain of this function is -5≤x≤-1 in interval notation that is [-5,-1]

The range is 1≤y≤5. In interval notation that is [1,5]

:)

Answer:

13(n-20)=322

Step-by-step explanation:

13 times n-20 equals 322

Answer:

In a room of just 23 people there's a 50-50 chance of at least two people having the same birthday. In a room of 75 there's a 99.9% chance of at least two people matching. Put down the calculator and pitchfork, I don't speak heresy.

Step-by-step explanation:

Answer:

3840

Step-by-step explanation:

Using the fundamental counting principle

The restaurant is offering five kinds of soup, three kinds of salad, four kinds of appetizers, six entrees, five desserts, and four beverages.

There are 5 independent events happening (5 prixe dinners)

(1) soup or salad (not both)

We have five kinds of soup, three kinds of salad

soup or salad (not both), = 5 + 3

= 8

(2) appetizer = 4

(3) entrees = 6

(4) dessert = 5

(5) Beverage = 4

Hence,

8 × 4 × 6 × 5 × 4

= 3840

The number of different prix fixe dinners are possible is 3840

Answer/Step-by-step explanation:

Recall: the ratio of the areas of two similar figures = the square of the ratio of the corresponding sides of the similar figures.

This will give us the scale factor.

The scale factor indicates how many times larger the second triangle is than the area of the first.

Let's find how many times larger is the area of the second triangle is to the first:

1. ∆ G And ∆ F

[tex] \frac{Area_{F}}{Area_{G}} = \frac{side_{F}^2}{side_{G}^2} [/tex]

[tex] \frac{Area_{F}}{Area_{G}} = \frac{6^2}{3^2} [/tex]

[tex] = \frac{36}{9} = 4 [/tex]

∆F is 4 times larger than ∆G

2. ∆ G And ∆ B

[tex] \frac{Area_{B}}{Area_{G}} = \frac{side_{B}^2}{side_{G}^2} [/tex]

[tex] \frac{Area_{B}}{Area_{G}} = \frac{2^2}{4^2} [/tex]

[tex] = \frac{4}{16} = 0.25 [/tex]

∆B is 0.25 times ∆G

3. ∆ B And ∆ F

[tex] \frac{Area_{G}}{Area_{B}} = \frac{side_{F}^2}{side_{B}^2} [/tex]

[tex] \frac{Area_{F}}{Area_{B}} = \frac{8^2}{2^2} [/tex]

[tex] = \frac{64}{4} = 4 [/tex]

∆F is 16 times larger than ∆B

4. ∆ F And ∆ H

[tex] \frac{Area_{H}}{Area_{F}} = \frac{side_{H}^2}{side_{F}^2}} [/tex]

[tex] \frac{Area_{H}}{Area_{F}} = \frac{2^2}{6^2} [/tex]

[tex] = \frac{4}{36} = \frac{1}{9} [/tex]

∆H is ⅑ times ∆F

5. ∆ G And ∆ H

[tex] \frac{Area_{H}}{Area_{G}} = \frac{side_{H}^2}{side_{G}^2} [/tex]

[tex] \frac{Area_{H}}{Area_{G}} = \frac{2^2}{3^2} [/tex]

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

∆G is 4/9 times ∆G

6. ∆ H And ∆ B

[tex] \frac{Area_{B}}{Area_{H}} = \frac{side_{B}^2}{side_{H}^2} [/tex]

[tex] \frac{Area_{B}}{Area_{H}} = \frac{1.5^2}{2^2} [/tex]

[tex] = \frac{2.25}{4} = 0.6 [/tex] (nearest tenth)

∆B is 0.6 times ∆H

Given :

An automobile manufacturer introduces a new model that averages 27 miles per gallon in the city.

Standard deviation , S.D = 3 miles per gallon .

To Find :

The probability that the person will purchase a car that averages less than 20 miles per gallon for in-city driving.

Solution :

We have to find the probability , [tex]P(X\leq 20)[/tex] .

Here , we will use the excel function

So ,

[tex]P(X\leq 20)=NORMADIST( 20, 27 , 3 , 1 )=0.009815[/tex] .

Therefore , probability is 0.009815 .

Answer:

y=-5

Step-by-step explanation:

Answer:

it's -5

Step-by-step explanation:

4y−34y−3−4y−3−3−2−5=====5y+25y+2−4yy+2y+2−2ySubtract 4y from each side.Combine like terms.Subtract 2 from each side.Simplify.

Answer:

Step-by-step explanation:

is it 34 because you haven't moved the bodies. however including you there's 35???

This is a simple algebra problem. The answer is 5.

We know that:

Initially, there are 34 people in the garden.

Then you enter, so now there are 35.

Then we lose 30 of these people, so the final number of people in the garden will be: 35 - 30 = 5

Finally, there are 5 people in the garden.

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Answer: Choice B  [tex]\{x | \ x \le 4.5\}[/tex]

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Explanation:

The endpoint is at 4.5 and this endpoint is a filled in circle. So we'll have "or equal to" as part of the inequality sign. This is because we are including the endpoint as part of the shaded solution region.

The other part of the inequality sign is "less than" because the shading is to the left of the endpoint. Any point in the shaded region is less than 4.5, or it could be equal to 4.5

Put another way: x is either 4.5 or smaller

We write that as [tex]x \le 4.5[/tex] which is read out as "x is less than or equal to 4.5"

Surrounding this in curly braces tells the reader we're dealing with a set of values. The first part "x |" means "x such that"

All together we end up with the answer [tex]\{x| \ x \le 4.5\}[/tex] which translates to "x such that x is less than or equal to 4.5"

Answer:

B

Step-by-step explanation:

Answer:

8b and 80

Step-by-step explanation:

Answer:

The expression that represents the area of this rectangle is 8b

When b = 10, the area of the rectangle is 80 square units.

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

because it is tilted so z+4 +2 so -2+4=2