Which graph shows the solution to the system of linear inequalities?

x – 4y < 4

y < x + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.

On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.

Answer:

Using the simple mathematical relations and formulas we get the following correct answers.

1. Option A

2. Option C
3. Option D

4. Option C

5. Option D

Step-by-step explanation:

1. The approximate room temperature is 20°C. Option A is correct.

2. 1 day has 24 hrs. 5 days will have 5×24 = 120 hrs. Option C is correct.

3. The discharge is 56m³/sec. 1m³ has 1000L. So the discharge is 56000L/sec. Option D is correct.

4. The speed is 25cm/min or (25×0.01×60)m/hrs. = 15m/hrs. For 75m the snail would take 75/15 = 5hrs. Option C is correct.

5. The relation between °C and °F is (F-32)/1.8. The equivalent temperature is (105-32)/1.8 = 40.56°C. Option D is correct.

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Answer:

B

Step-by-step explanation:

Similar to the one you asked earlier.

Given from the table

1 Gallon of gas = $2.15

15 gallons of gas = $2.15 x 15

= $32.25 (B)

Answer:

The value of x is 117°  by using Alternative interior angle theorem

Step-by-step explanation:

Alternative interior angle theorem: It states that the angles made by transverse between two parallel lines are congruent.

as in figure

Angle A = 42°

Angle B = 108°

Angle C = x

Angle D = 51°

draw two parallel lines passing through B and C .

According to Alternative interior angle theorem angle B is written as 42° + 66°

and angle C is written as x1 + x2 .

Now x1 = 51° as x1 and D are alternative angles

And similarly x2 = 66°

As x = x1 + x2

Therefore x = 51° + 66° = 117°

The value of x is 117°

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Step-by-step explanation:

To multiply the fractions, like

[tex] \frac{1}{4} \times \frac{1}{9} [/tex]

Multiply the top,

then multiply the bottom.

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

Try to use a calculator if you aren't arithmetic heavy, but I suggest you to try to remember them because they are going to be helpful for courses like Algebra, Calculus, Statistics, etc.

To divide fractions, like

[tex] \frac{ \frac{1}{5} }{ \frac{1}{8} } [/tex]

You take the top number,

[tex] \frac{1}{5} [/tex]

Then you flip the bottom number,

[tex] \frac{8}{1} [/tex]

Then multiply the two

[tex] \frac{1}{5} \times \frac{8}{1} = \frac{8}{5} [/tex]

And that is your answer. Comment if you need more clarification

Answer:

On a coordinate plane, an absolute value graph has a vertex at (0, 0.5).

Step-by-step explanation:

properties of the given function

Answer: it's the second option

Step-by-step explanation:

Answer:

[tex]x=\frac{15}{4}=3\frac{3}{4}[/tex]

Equation:

[tex]\frac{2}{3}x+\frac{5}{6} =\frac{10}{3}[/tex]

_____________________________________

1. Group all constants on the right side of the equation

[tex]\frac{2}{3}\cdot x+\frac{5}{6}=\frac{10}{3}[/tex]

Subtract [tex]5/6[/tex] from both sides:

[tex]\frac{2}{3}x+\frac{5}{6}-\frac{5}{6}=\frac{10}{3}-\frac{5}{6}[/tex]

Combine the fractions:

[tex]\frac{2}{3}\cdot x+\frac{5-5}{6}=\frac{10}{3}-\frac{5}{6}[/tex]

Combine the numerators:

[tex]\frac{2}{3}\cdot x+\frac{0}{6}=\frac{10}{3}-\frac{5}{6}[/tex]

Reduce the zero numerator:

[tex]\frac{2}{3}\cdot x+0=\frac{10}{3}-\frac{5}{6}[/tex]

Simplify the arithmetic:

[tex]\frac{2}{3}\cdot x=\frac{10}{3}-\frac{5}{6}[/tex]

Find the lowest common denominator:

[tex]\frac{2}{3}\cdot x=\frac{10\cdot 2}{3\cdot 2}+\frac{-5}{6}[/tex]

Multiply the denominators:

[tex]\frac{2}{3}\cdot x=\frac{10\cdot 2}{6}+\frac{-5}{6}[/tex]

Multiply the numerators:

[tex]\frac{2}{3}\cdot x=\frac{20}{6}+\frac{-5}{6}[/tex]

Combine the fractions:

[tex]\frac{2}{3}\cdot x=\frac{20-5}{6}[/tex]

Combine the numerators:

[tex]\frac{2}{3}\cdot x=\frac{15}{6}[/tex]

Find the greatest common factor of the numerator and denominator:

[tex]\frac{2}{3}\cdot x=\frac{5\cdot 3}{2\cdot 3}[/tex]

Factor out and cancel the greatest common factor:

[tex]\frac{2}{3}\cdot x=\frac{5}{2}[/tex]

2. Isolate the x

[tex]\frac{2}{3}\cdot x=\frac{5}{2}[/tex]

Multiply both sides by inverse fraction 3/2:

[tex]\frac{2}{3}x\cdot \frac{3}{2}=\frac{5}{2}\cdot \frac{3}{2}[/tex]

Group like terms:

[tex]\frac{2}{3}\cdot \frac{3}{2}x=\frac{5}{2}\cdot \frac{3}{2}[/tex]

Simplify the fraction:

[tex]x=\frac{5}{2}\cdot \frac{3}{2}[/tex]

Multiply the fractions:

[tex]x=\frac{5\cdot 3}{2\cdot 2}[/tex]

Simplify the arithmetic:

[tex]x=\frac{15}{2\cdot 2}[/tex]

Simplify the arithmetic:

[tex]x=\frac{15}{4}[/tex]

______________________

Why learn this

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

__________________________

Terms and topics

Answer:  3 3/4

Step-by-step explanation: i took the test (sorrry i cant tell why, im bad at explaining)  

The answer choice which represents a polynomial which is factored completely is; (y³ - 4y² +5)

The polynomials as given in the task content are;

4(4x⁴ -1) + 2x

(y³ - 4y² +5)

3x (9x² -1)

5x² -17x +14

Hence it follows that the polynomial which cannot be further factorised is; (y³ - 4y² +5).

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Answer:3 x (9 x squared + 1)

it is c because i did the test and put b but got it wrong

Step-by-step explanation:

The time when the object will be 6 inches above the rest position is C. 4.62 seconds.

From the information, the object is attached to a spring and is stretched and released.

The given model is given as:

d = -8 cos (π/6t)

In this case, it's important to plot the graph based on the model given. Therefore, the time when the object will be 6 inches above the rest position is 4.62 seconds.

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Answer:

2.4

Step-by-step explanation:

We must do the inverse of every operation:

15 + 12 = 27

27/5 = 5.4

5.4 - 3 = 2.4

Answer:

894.035793467 or roughly 894

Step-by-step explanation:

I square rooted it by using a calculator, and by working it out on paper.

[tex]2 {x}^{5} {y}^{8} [/tex]

Step-by-step explanation:

yes

Step-by-step explanation:

I am not sure I can see the room limitations.

what I see is that the kitchen is one large rectangle from

(-8, 8) to (0, 0).

the rec room is Amado one large rectangle from

(5, 6) to (8, -7).

I am basing the rest in this.

for the area calculations, please consider that the area of a rectangle is length × width, and the area of a triangle is half of the rectangle it splits in half with its baseline (as diagonal).

A)

area 1 =

rectangle (-8, 8) to (-5, 3)

plus

half of the rectangle (-5, 8) to (-3, 3)

3×5 + 1/2 × 2×5 = 3×5 + 1×5 = 15 + 5 = 20 yd²

area 2 =

half of the rectangle (-5, 8) to (-3, 3)

plus

rectangle (-3, 8) to (0, 3)

1/2 × 2×5 + 3×5 = 20 yd²

area 3 = area 4 =

half of the rectangle (-8, 3) to (0, 0)

1/2 × 8×3 = 4×3 = 12 yd²

B)

the total area of the kitchen is the sum of all 4 areas

20 + 20 + 12 + 12 = 64 yd²

we can also calculate this in general, seeing that the general dimensions of the kitchen are 8×8 : from (-8, 8) to (0, 0).

8×8 = 64 yd²

Negative

The complete question is

"The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. Which statement is correct?

a. The domain of this function represents the total cost for a job

b. H is a function of C

c. The painter charges a $35 service fee in addition to an hourly rate

d. The painters hourly rate is $35.00"

The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. So, the correct option is D. The painters hourly rate is $35.00

Function is a type of relation, or rule, that maps one input to specific single output.

The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours.

The fixed fee, or service fee, is $60.

$35 is the hourly fee since in the function, it is 35 that is multiplied by the number of hours.

So, the correct option is D. The painters hourly rate is $35.00

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The probability that the spinner will land on white for all three spins is 1/216

The probability is given as:

P(White) = 1/6

The event that the spinner lands on white all three times is:

White White White

The probability is then represented as:

P  = P(White)^3

So, we have:

P = (1/6)^3

Evaluate

P =1/216

Hence, the probability that the spinner will land on white for all three spins is 1/216

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The square for the  equation:  [tex]y=2x^{2} + 12x +1[/tex] is [tex]y=2(x+3)x^{2} -17[/tex]

The square for the  equation:  [tex]y=4x^{2} +48x-10[/tex] is [tex]y=4(x+6)x^{2} -154[/tex]

a)

[tex]y=2x^{2} +12x +1[/tex]

[tex]y = 2[(x^{2} + 6x)] + 1[/tex] ( taking common)

[tex]y = 2[(x+3)^{2} - 9] + 1[/tex] ( adding and subtracting 9 to make a square term

[tex]y = 2(x+3)^{2} - 18 + 1[/tex] ( multiplying by 2)

[tex]y=2(x+3)x^{2} -17[/tex]

b)

[tex]y=4x^{2} +48x-10[/tex]

[tex]y = 4[(x^{2} + 12x)] - 10[/tex]  (taking 4 common)

[tex]y = 4[(x+6)^{2} - 36)] - 10[/tex] (adding and subtracting 36)

[tex]y = 4(x+6)^{2} - 144 - 10[/tex](multiplying by 4)

[tex]y=4(x+6)x^{2} -154[/tex]

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Answer:

30

Step-by-step explanation:

P=2(b+h)=2·(10+5)=30

2p-4p ≤ -2

-2p ≤ 2

[tex]\frac{-2p}{-2} \leq \frac{-2}{-2}[/tex]  (Sign flips as both sides it is getting divided by NEGATIVE 2)

p≥1

Interval notation: [1, infinity)

Hope it helps!

Answer: x = 12

Step-by-step explanation: The given triangle is an equilateral triangle. Equilateral triangles have all angles and all sides equal. Thus, let's solve for x knowing all 3 equations are equal. For this, only 2 equations are necessary.

5x - 22 = 4x - 10

Adding 22 to both sides, we get:

5x = 4x + 12

Subtracting 4x to 5x, we get:

x = 12.

Thus 5*12 - 22 = 38, and 4*12 - 10 = 38, and so is 3*12 + 2 = 38. Thus, we know this is correct.

Answer:

x = 12

Step-by-step explanation:

Hello!

All three angles are congruent, indicating that this is an equilateral triangle.

The rules of this triangle say that all sides are congruent.

We can solve for x by setting any 2 sides equal to each other. I'm picking AB and BC.

The value of x is 12.

Answer:

80 m is distance traveled

Step-by-step explanation:

if object moves at 20m/s, then in 4 seconds the expression 20 x 4 is used to get 80. 80 m traveled

Answer:

6n-5

Step-by-step explanation:

Some different types of sequences

To find sequence patterns, often the sequences are arithmetic (adding by a constant amount) or geometric (multiplying by a constant amount).  

To test if something is a geometric sequence, find the quotient of (divide) adjacent terms.

To test if something is an arithmetic sequence, find the difference of (subtract) adjacent terms.

Finding the type of our sequence

Note the following:

19-13=6

13-7=6

7-1=6

So, to get each next term, add 6.  However, what is the nth term?

Finding an expression for our sequence

You'll be adding up "n" sixes to get there (expressed with multiplication, because multiplication is shorthand for repeated addition), but we need a starting point so that when n=1, the expression equals 1, and when n=2, the expression equals 7... and so on.  This starting point shifts the "6n" piece of our expression so that it lines up on the sequence.  I'm going to call this starting point "b" for the base that is supporting this sequence.

So the expression will look something like [tex]6n+b[/tex]

Knowing that the expression needs to equal 1 when n=1, we can set up an equation and solve for "b".

[tex]6n+b=n^{\text{th}} \text{ term}\\6(1)+b=(1)\\6+b=1\\(6+b)-6=(1)-6\\b=-5[/tex]

So, the expression for the nth term of the sequence is [tex]6n-5[/tex]

Verifying

To verify that the expression we found is right, we can test our expression for each of the terms we do know:

The first term (n=1) is 1

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(1)-5 \overset{?}{=} (1)[/tex]

[tex]6-5 \overset{?}{=} 1[/tex]

[tex]1 \overset{\checkmark}{=} 1[/tex]

The second term (n=2) is 7

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(2)-5 \overset{?}{=} (7)[/tex]

[tex]12-5 \overset{?}{=} 7[/tex]

[tex]7 \overset{\checkmark}{=} 7[/tex]

The third term (n=3) is 13

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(3)-5 \overset{?}{=} (13)[/tex]

[tex]18-5 \overset{?}{=} 13[/tex]

[tex]13 \overset{\checkmark}{=} 13[/tex]

The fourth term (n=4) is 19

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(4)-5 \overset{?}{=} (19)[/tex]

[tex]24-5 \overset{?}{=} 19[/tex]

[tex]19 \overset{\checkmark}{=} 19[/tex]

Step-by-step explanation:

Most standard rain gauges have a wide funnel leading into the cylinder and are calibrated so that one-tenth of an inch of rain measures one inch when it collects inside.

Answer:

c

Step-by-step explanation:

week 4 = 11

start = 3

11 - 3 = 8

answer is c

The correct Answer is: C. 8 inches

Step-by-step explanation:

If the plant started out at 3 inches and finished after 4 weeks at 11 inches, we can do 11-3 to find how much growth the pepper plant had.

11 - 3 = 8, therefore our answer is

C. 8 inches

Answer:

dSutlrysl07tris5eiruwf3rtst47er747y3utgxgudjdudufnlgjfngvi

Answer:

Step-by-step explanation:

If AC is a supplementary line, then

x + 90° + x = 180°

solution:

2x + 90° = 180°   |subtract 90° from both sides

2x = 90°    |divide both sides by 2

x = 45°

Answer:

[tex] \sf \: b) \: {45}^{o} [/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ x + x + 90° = 180°

Then the value of x will be,

→ x + x + 90° = 180°

→ 2x = 180° - 90°

→ 2x = 90°

→ x = 90° ÷ 2

→ [ x = 45° ]

Hence, the value of x is 45°.

Answer:

[tex]-2x^2-x[/tex]. Your answer was wrong because "x-squared" terms didn't cancel.

Step-by-step explanation:

To solve this problem, set up an equation.  We know something is supposed to be added to the expression [tex]2x^2+2x[/tex], and the result should be x. So:

[tex]2x^2+2x+(\text{ ? })=x[/tex]

We want to solve for the question mark... the unknown thing that we're adding to the original expression, in order to get x.

It is uncommon to put question marks in equations to represent quantities. Usually we use a letter. Since x is already being used in the equation, we should pick something else ... we could use "y".

[tex]2x^2+2x+(\text{ } y \text{ })=x[/tex]

...or just...

[tex]2x^2+2x+y=x[/tex]

Algebra allows us to solve the equation and find out what "y" is equivalent to.

To solve, we want to get the "y" by itself. To do so, we try to eliminate the other "terms" from the left side of the equation.

Understanding "terms" & "like terms"

Terms

"Terms" in an equation are either a number multiplied to other things, or just a single number that isn't multiplied to anything else.

For example, the various terms in our equation above are

[tex]2x^2[/tex], [tex]2x[/tex], [tex]y[/tex], [tex]x[/tex]

You might ask why the last things, which don't have a number, are considered terms.

Remember that multiplying by 1 doesn't change anything, so we could imagine each of the last two terms as being 1 times the letter.

So, we can rewrite our equation:

 [tex]2x^2+2x+1y=1x[/tex]

Like terms

"Like terms" are terms where the "other stuff the numbers are multiplied to" is the same, so for instance, the [tex]2x[/tex] and the [tex]1x[/tex] are like terms. They are like terms because, the "other stuff" that the numbers are multiplied to are "x" for both terms. Note that [tex]2x[/tex] and [tex]2x^2[/tex] are not "like terms" because the "stuff" is different:

[tex]x[/tex] is different than [tex]x^2[/tex]

"Like terms" are important because only like terms can be "combined" into a single simplified term.

Solving equations

To solve an equation, we isolate what we're solving for, y, by disconnecting the other terms from it, and simplify.

Starting with subtracting 2x from both sides of the equation:

[tex]2x^2+2x+1y=1x\\(2x^2+2x+1y)-2x=(1x)-2x[/tex]

Subtraction is the same as "adding a negative":

[tex]2x^2+2x+1y+(-2x)=1x+(-2x)[/tex]

Since all terms are now connected by addition, we can add in any order we want (because of the Commutative Property of Addition), and we can combine like terms.

Thinking just about the number parts, since [tex]1+(-2)=-1[/tex],  then [tex]1x+(-2x)=-1x[/tex].

Returning to our main equation, the right side simplifies:

[tex]2x^2+2x+1y+(-2x)=1x+(-2x)\\2x^2+2x+1y+(-2x)=-1x[/tex]

On the left side: [tex]2x[/tex] and [tex]-2x[/tex] are like terms.

Fact: [tex]2+(-2)=0[/tex]

So, [tex]2x+(-2x)=0x[/tex]

Since anything times zero is just zero, [tex]0x=0[/tex]. Furthermore, adding zero to anything doesn't change it.  So when the [tex]2x[/tex] and [tex]-2x[/tex] terms on the left side of our main equation are combined, they "disappear" (While we talked through are a lot of rules/steps to justify why that works, it is common to omit those justifications, and to just combine those like terms and make them disappear.)

So, [tex]2x^2+2x+1y+(-2x)=-1x[/tex] simplifies to:

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

Similarly for the [tex]2x^2[/tex] term, we subtract from both sides:

[tex]2x^2+1y=-1x\\(2x^2+1y)-2x^2=(-1x)-2x^2\\2x^2+1y+(-2x^2)=-1x+(-2x^2)[/tex]

Combining like terms on the left, they disappear.

[tex]1y=-1x+(-2x^2)[/tex]

There are no like terms on the right.

Since the two terms on the right are added together, we can use the commutative property of addition to rearrange:

[tex]1y=-2x^2+(-1x)[/tex]

Addition of a negative can turn back into subtraction, and simplify multiplication by 1.

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

Remembering we chose "y" as the unknown thing we wanted to know, that's why the "correct answer" is what it is.

Verifying an answer

Verifying can double check an answer, and helps explain why the answer you chose doesn't work.

To verify an answer, the original statement said add something to the expression and get a result of "x". So, let's see if the "correct answer" does:

[tex]2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-2x^2-x)\\2x^2+2x+(-2x^2-1x)\\2x^2+2x+(-2x^2)+(-1x)[/tex]

Combining the "x-squared" terms, completely cancels...

[tex]2x+(-1x)[/tex]

Combining the "x" terms, and simplifying...

[tex]1x\\x[/tex]

So it works.

Why isn't the answer what you chose:

[tex]2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-x^2-x)\\2x^2+2x+(-1x^2-1x)\\2x^2+2x+(-1x^2)+(-1x)[/tex]

Combining the x-squared terms, things don't completely cancel...

[tex]1x^2+2x+(-1x)[/tex]

Combining the x terms...

[tex]1x^2+1x\\x^2+x[/tex]

So adding the answer that you chose to the expression would not give a result of "x", which is why it is "wrong"

An equation is formed of two equal expressions. The value of r in the given equation is 6.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution for the value of r in the given equation will be,

5r - r - 9 = 15

5r - r - 9 + 9 = 15 + 9

4r = 24

r = 6

A.) The first step is to Use the addition property of equality. Thus, the correct option is B.

B.) The value of r in the given equation is 6.

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