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The x-axis is equivalent to x = 4, x + y = 0, x = y, and y = 4, and the value of the x-axis is y = 0.

Expressions that are equivalent do the same thing even when they have distinct appearances.. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s)

((This presupposes that we're referring to the Cartesian plane, i.e. we are limiting ourselves to two dimensions.)

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Answer: infinite

Step-by-step explanation: since they have the same slope and y interscept it is a coincident line and has infinite solutions

y= 4-x

y= 4-x

Answer:

infinitely many

Step-by-step explanation:

when you simplify, you get the following two equations:

y=-x+4

y=-x+4

those two equations are the same, therefore it is many

Given:

LCM(a,b) = 90 and GCD(a,b) = 3.

b is three more than a.

To find:

The values of a and b.

Solution:

We have,

LCM(a,b) = 90

GCD(a,b) = HCF(a,b) = 3

According to the question,

[tex]b=a+3[/tex]

If a and b are two positive integers, then

[tex]a\times b=HCF(a,b)\times LCM(a,b)[/tex]

[tex]a\times (a+3)=3\times 90[/tex]

[tex]a^2+3a=270[/tex]

[tex]a^2+3a-270=0[/tex]

Splitting the middle terms, we get

[tex]a^2+18a-15a-270=0[/tex]

[tex]a(a+18)-15(a+18)=0[/tex]

[tex](a+18)(a-15)=0[/tex]

Using zero product property, we get

[tex]a+18=0[/tex] and [tex]a-15=0[/tex]

[tex]a=-18[/tex] and [tex]a=15[/tex]

a is a positive integer so it cannot be negative. So, a=15.

Now,

[tex]b=a+3[/tex]

[tex]b=15+3[/tex]

[tex]b=18[/tex]

Therefore, the value of a is 15 and the value of b is 18.

Step-by-step explanation:

if they are parallel they must be equal

Heres the answer welcome btw

(A) just trust

ITs too good

Answer:

Y= 30

X= 0.75

Step-by-step explanation:

If the first Y was 1,200 and X was 30, then that means every time your divide Y by 40, you will get your X. It's the exact opposite if you want to find Y.

So you want to divide your Y, which is 30, by 40. Once who find your answer, you should have gotten 0.75 for X.

Why divide by 40? Good question. You divide by 40 because if you multiply your X example Y= 1,200, X= 30, you will get 30x40 which is 1,200. Do it the other way around divide 1,200 by 40, you get 30.

All in all your answer should be X= 0.75. If not tell me.

Thank You For Your Time

Answer:

24:?

Step-by-step explanation:

it depends on the ratio of cups of water to sugar.

For example: if there is one cup of sugar for every 12 cups of water. the ratio would be 24:2

Answer:

x= 12

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

-2(x+6)=-36

distribute the -2

-2x-12=-36

add 12 to both sides

-2x=-24

divide both sides by -2

x=12

Answer:

17.5 hours

Step-by-step explanation:

divide 15 by 3 to get 5,

multiply 5 by the amount of hours it takes to draw 3 illustrations so 5 x 3.5, the answer is 17.5

Answer:

[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]

Step-by-Step explanation:

We have the function:

[tex]\displaystyle y=\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt[/tex]

And we want to find the interval for which y is concave upwards.

Therefore, we will need to find the second derivative of y, find its inflection points (where y''=0), and test for values.

So, let's take the derivative of both sides with respect to x. So:

[tex]\displaystyle y^\prime=\frac{d}{dx}\Bigg[\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt\Bigg][/tex]

By the Fundamental Theorem of Calculus:

[tex]\displaystyle y^\prime=\frac{1}{3+x+3x^2}[/tex]

So, we will take the derivative again. Hence:

[tex]\displaystyle y^\prime^\prime=\frac{d}{dx}\Big[\frac{1}{3+x+3x^2}\Big]=\frac{d}{dx}\Big[(3+x+3x^2)^{-1}\Big][/tex]

We will use the chain rule. Let:

[tex]\displaystyle u=x^{-1}\text{ and } v=3+x+3x^2[/tex]

Differentiate:

[tex]\displaystyle y^\prime^\prime=-(3+x+3x^2)^{-2}(1+6x)[/tex]

Rewrite:

[tex]\displaystyle y^\prime^\prime=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]

So, points of inflection, where the concavity changes, is whenever the second derivative is 0 or undefined.

We can see that the second derivative will never be undefined since the denominator can never equal 0.

So, our only possible inflection points are when it's equal to 0. Hence:

[tex]\displaystyle 0=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]

Multiplying both sides by the denominator gives:

[tex]0=-(6x+1)[/tex]

Then it follows that:

[tex]\displaystyle x=-\frac{1}{6}[/tex]

So, our only possible point of inflection is at x=-1/6.

We will test for values less than and greater than this inflection point.

Testing for x=-1, we see that:

[tex]\displaystyle y^\prime^\prime=-\frac{6(-1)+1}{3+(-1)+3(-1)^2}=1>0[/tex]

Since the result is positive, y is concave up for all values less than -1/6.

And testing for x=0, we see that:

[tex]\displaystyle y^\prime^\prime=-\frac{6(0)+1}{3+(0)+3(0)^2}=-\frac{1}{3}[/tex]

Since the result is negative, y is concave down for all values greater than -1/6.

Therefore, the interval for which y is concave up is:

[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]

Note that we use parentheses instead of brackets since at exactly x=-1/6, our graph is neither concave up nor concave down.

Answer:

3/4

Step-by-step explanation:

21/16 ÷ 7/4

21/16 × 4/7

3/4

The value of x is 32 degrees.

Rhombus

A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. The rhombus is also called a diamond or rhombus diamond.

It is given in the question that there is a rhombus ABCD with ∠ DAC = 58 degrees.

We have to find the angle x or  ∠ ADB.

We know the property that the diagonals of the rhombus perpendicularly bisect each other.

Hence, the rhombus is divided into 4 right triangles.

Hence,

∠DAC +  ∠ADB = 180 - 90  = 90 degrees

58 + x = 90 degrees

x = 90 - 58

x = 32 degrees.

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[tex]12a+18a^2-1[/tex]

Answer: 12a+6a^2 -1

Step-by-step explanation:

4(3a)+2(3a)^2-1

Answer:

Where's the drawing at because I don't see anything man

Answer:

0.443 hours

Step-by-step explanation:

time = total distance / mph

time = 50 / 112.9094

time ≈ 0.443 hours

Answer:

0.443 hours

Explanation:

Given following:

Formula:

[tex]\sf time \ taken = \dfrac{distance}{speed}[/tex]

Substitute values to find time taken:

[tex]\sf \rightarrow time = \dfrac{50}{112.9094 }[/tex]

evaluate

[tex]\sf \rightarrow time = 0.4428329262[/tex]

rounded to nearest thousandth

[tex]\sf \rightarrow time = 0.443[/tex]

Answer: after eliminating B due to Hare Method, A will have a total of 67 VOTES

Step-by-step explanation:

Given that;

The results are

ABC : 41

BAC : 26

CAB : 42

NOW

A>B>C = 41 ⇒ A has 41 votes

B>A>C = 26 ⇒ B has 26 votes

C>A>B = 42 ⇒ C has 42 votes

According to Hare method, least votes gainers will be eliminated and once eliminated, his/her/its votes will be transferred to the next choice of person/thing.

based on the question; B will be eliminated

so we have;

A>B>C = 41 ⇒ A has 41 votes

B>A>C = 26 ⇒ B has 26 votes

we eliminate B, the votes are transferred to the next (A)

A>C = 26 ⇒ A has 26 votes

C>A>B = 42 ⇒ C has 42 votes

SO in total

A votes = 41 + 26 = 67 VOTES

Therefore after eliminating B due to Hare Method, A will have a total of 67 VOTES

After eliminating B due to Hare Method, A will have a total of 67 votes

We have given that,the results are

ABC : 41

BAC : 26

CAB : 42

A>B>C = 41 ⇒ A has 41 votes

B>A>C = 26 ⇒ B has 26 votes

C>A>B = 42 ⇒ C has 42 votes

The Hare method is least votes gainers will be eliminated and once eliminated,The  votes will be transferred to the next choice of person/thing.

From the given question we have B will be eliminated

Therefore  we have

A>B>C = 41 ⇒ A has 41 votes

B>A>C = 26 ⇒ B has 26 votes

We eliminate B, the votes are transferred to the next (A)

A>C = 26 ⇒ A has 26 votes

C>A>B = 42 ⇒ C has 42 votes

Therefore the total votes are

A votes = 41 + 26 = 67 votes

Therefore after eliminating B due to Hare Method, A will have a total of 67 votes.

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Answer:

In Step 2.

Step-by-step explanation:

They should have distributed the 2 to the x and 1 instead of subtracting it.

Answer:

288

Step-by-step explanation:

please review the attachment for step by step soluation

Answer:

2 2/3

Step-by-step explanation:

Answer:

x = 55

y = 55

z = 70

Step-by-step explanation:

x + 125 is a straight line, 180⁰ x+125=180 x=55⁰

since this is an isosceles triangle, x = z

and the sum of all angles in any triangle is 180⁰

55+55+y=180⁰

y = 70⁰

Answer:

x=55º, y=70º, z=55º

Step-by-step explanation:

We have that xº = 180º - 125º = 55º

As it is an isosceles triangle, we have xº = zº = 55º

Therefore, yº = 180º - (xº + zº) = 180º - (55º + 55º) = 180º - 110º = 70º

The area of the given doormat is 0.4 meter square.

Here, we are given that Sammy has a rectangular doormat. The dimensions of the doormat are given as follows-

The length of the doormat is = 4/5 meters

and the breadth of the doormat is = 1/2 meters

The area of a rectangular figure is given by the formula as follows-

Area of a rectangle = length × breadth

Let the area of the rectangular doormat be A

Thus, in this case, we have-

A = 4/5 × 1/2

A = 4/ 10

A = 2/5

Now, converting the area obtained into a decimal number we get-

A = 0.4

Thus, the area of the given doormat is 0.4 meter square.

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Answer:

240 Pints

Step-by-step explanation:

To convert 30 gallons into pints you need to multiply 30 by the conversion factor in order to get the volume amount from gallons to pints.

Answer: 240 pints

Step-by-step explanation:

One pint is equal to 0.125 gallons.

[tex]\frac{x}{2}-\frac{2}{x+1}=1[/tex]

We have 2 denominators that we need to get rid of. Whenever there are the denominators, all we have to do is multiply all whole equation with the denominators.

Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)

[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)][/tex]

Then shorten the fractions.

[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)[/tex]

Distribute in all.

[tex]x^2+x-4=2x+2[/tex]

We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.

[tex]x^2+x-4-2x-2=0\\x^2-x-6=0\\[/tex]

We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)

[tex](x-3)(x+2)=0\\x=3,-2[/tex]

Thus, the answer is x = 3, -2

Answer:

for the 1st one x=9 y=4

Step-by-step explanation:

the second triangle is twice the size of the first one

The tax rate is 4.50% if Julius earns $47,800 a year working for delivery service. He is single and pays $2,152.60 in state income tax each year.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Julius earns $47,800 a year working for delivery service. He is single and pays $2,152.60 in state income tax each year.

To find the tax rate:

tax rate = (2152.60/47800)×100

tax rate = (0.045)×100

tax rate = 4.50%

Thus, the tax rate is 4.50% if Julius earns $47,800 a year working for delivery service. He is single and pays $2,152.60 in state income tax each year.

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Answer:

1: 2 and $3.072

Step-by-step explanation:

According to the question, the data provided is as follows

10 half gallons

For this she paid $15.36

Based on the above information,

The ratio in fractional form is

= 1 ÷ 2

= 1 : 2

And, the cost of gasoline per gallon is

Since  half of 10 gallons is 5

And, the amount paid is $15.36

So, the cost of gasoline per gallon is

= $15.36 ÷ 5

= $3.072

Step-by-step explanation:

Answer:

Top one

Step-by-step explanation:

It is more appropriate to measure the speck of dust using millimeters because that is most similar to the scale of the speck's size.