Explain why there must be at least two lines on any given
plane

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer:

i think its obr (capitalized sry, this thing keeps on saying there's smth innaporpriate ;-;)

Answer:c= a +b

Step-by-step explanation:

The number of items is discrete and the total time is a continuous variable recorded by the pet store.

The two things recorded by the pet store;

first is the number of items purchased and another is the time between the given interval of 8 am to 11 am.

we know that

the number of items was counted so it will be discrete and the total time was measured so it will be a continuous variable.

Therefore, the types of variables recorded by the pet store are the number of items as a discrete variable and the total time as a continuous variable.

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Answer:

x = 300 feet

Step-by-step explanation:

In the given right triangle,

Length of the string of the kite = 324 feet

Angle between the string and the ground = 68°

By applying law of Sines in the given right triangle,

\(\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}\)

Now we substitute the values of angles and sides in the formula,

\(\frac{\text{Sin68}}{x}=\frac{\text{Sin90}}{324}\)

\(\frac{\text{Sin68}}{x}=\frac{1}{324}\)

x = 324 × Sin(68)°

x = 300.41 feet

x ≈ 300 feet

Therefore, measure of side x = 300 feet will be the answer.

Answer:

The answer would be  There are three cups of water to 2 cups of rice.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Im pretty sure u know this... but i'll do it anyway to get points.

6. 4 chores = 30 minutes of television time

He needs 120 minutes of television time

So he will need to multiply both sides by 4 to get the amount of chores he needs to do to watch the movie.

Therefore, he does 16 chores( 4 x 4 ) to earn enough television time.

7. Make the amount of minutes the same to see how the speed they walk at.

If we convert Isabelle's robot' s speed to feet in 4 minutes, we can just compare both robots normally.

20/2= 10 feet in 4 minutes(Isabelle's robot) < 12 feet in 4 minutes(Brian's robot)

Therefore, Brians robot walks faster.

Answer:

The solution to the equation x + 9 = 18 + -2x is x = 3.

Step-by-step explanation:

To solve this equation for x, you can first simplify both sides of the equation by combining like terms.

x + 9 = 18 + -2x

Add 2x to both sides:

x + 2x + 9 = 18

Combine like terms:

3x + 9 = 18

Subtract 9 from both sides:

3x = 9

Finally, divide both sides by 3 to solve for x:

x = 3

Therefore, the solution to the equation x + 9 = 18 + -2x is x = 3.

HOPE THIS HELPED:)))

Answer:

3

Step-by-step explanation:

replace the + with - signs

x+9=18−2x

add the 2x to both equations and x becomes a 1 since we dont know its value.

3x+9=18

then you got to subtract 9 by 18 and that equals to 9 then

3x=9 3 divided by 9 is 3 and when simplified

and the answer is 3

The missing values are:

angle DGE = 45 degrees

angle EDG = 85 degrees

FD = 10

GD = 10√2

EG = (20 + 13√3) / 2

The missing sides in the figure is solved as follows

angle DGE = angle BAG = 45 degrees (alternate angles are equal)

angle EDG = angle ADC (vertical angles are equal)

angle ADC + 45 + 50 = 180 (sum of angles in a triangle)

angle ADC = 180 - 50 - 45

angle ADC = 85 degrees

Since DGE = 45 degrees and FG = 10

tan 45 = FD / FG

tan 45 = FD / 10

FD = 10

solving for GD

GD² = FD² + FG² = 10² + 10² = 200

GD = 10√2

solving for EG

EG = EF + FG

cos 50 = EF / 13

EF = 13 cos 50 = 13√3 / 2

EG = EF + FG = 13√3 / 2  + 10 = (20 + 13√3) / 2

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The total value of the furniture sold by Joyce last week is A = $ 6,733.33

Given data ,

Let's call the value of the furniture Joyce sold "x".

She receives 10% commission on the first $1,200 of sales, which is $120:

Commission on first $1,200 = 0.1 * 1200 = 120

The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:

Remaining sales = x - 1200

She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:

Commission on remaining sales = 0.15 * (x - 1200)

Her total earnings from commission last week was $950. So we can write an equation:

Commission on first $1,200 + Commission on remaining sales = $950

Substituting the expressions we found for the two commissions, we get:

120 + 0.15(x - 1200) = 950

120 + 0.15x - 180 = 950

On simplifying the equation , we get

0.15x - 60 = 950

0.15x = 1010

x = 6,733.33

Hence , the value of the furniture Joyce sold last week was $6,733.33

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The limits of the function for this problem are given as follows:

In this problem, we are given the graph of the function, hence the limit is given by the value of the function as the function approaches x = a, not the actual numeric value of the function at x = a.

At x = -2, we have that:

As the lateral limits are equal, lim x -> -2 f(x) = 3.

At x = 1, we have that:

As the lateral limits are different, the lim x -> 1 f(x) does not exist.

At x = 4, we have that:

As the lateral limits are equal, lim x -> 4 f(x) = -3.

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Answer:

k/10

Step-by-step explanation:

Quotient of k and 10 simplified to k/10

the answer is C 61 because 10x is 40 plus 21 is 61

Answer:

Option C

The answer is 61

Step-by-step explanation:

10x + 21 when x = 4

10(4) + 21

40 + 21 = 61

Thus, The answer is 61

-TheUnknownScientist 72

Answer:

SSS.

Step-by-step explanation:

The text above described the Side-Side-Side Theorem, which states that two triangles are congruent if three sides of one are equal or proportional respectively to three sides of the other (SSS=SSS).

Step-by-step explanation:

sum=addition

3/10 +1/3

find the LCM of 10 and 3 Which is 30

9+10/30=19/30

I hope it helps ☺️

Answer:

$7,126.12

Step-by-step explanation:

Final investment value

$7,126.12

Total interest earned

$1,126.12

Initial balance

$6,000.00

Total monthly deposits

$0.00

Effective Annual Rate (APY)

3.5%

compounded annually

The number of seats is an illustration of inequalities

The inequality expression is: \(400 + 20x < 1000\)

The given parameters are:

Fewer than means less than (<)

So, the inequality expression is:

\(400 + 20x < 1000\)

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Answer:

Solution given:

<ABC+<QRS=180° (supplementary)

m<QRS=180°-41°=139° is your answer

Answer:

\(m_{perpendicular}\) = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x + 6y = - 24 ( subtract x from both sides )

6y = - x - 24 ( divide through by 6 )

y = - \(\frac{1}{6}\) x - 4 ← in slope- intercept form

with slope m = - \(\frac{1}{6}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{6} }\) = 6

Answer:

pleasse elaborate more

Step-by-step explanation:

Based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid.

The teacher surveyed his homeroom class about their post-graduation plans. He found out that most of his students plan to become soldiers.

An inference is a conclusion that can be drawn from a given set of data. In this case, the inference that can be made is that a significant number of students in the homeroom class plan to become soldiers.Therefore, the inference is valid based on the data provided.

However, it is essential to keep in mind that the sample size in the homeroom class is relatively small and may not be representative of the entire population. If the teacher had surveyed a more extensive and diverse population, the results might have been different.

In conclusion, based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid. However, this may not apply to the entire population, and it is crucial to consider the sample size when drawing inferences.

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Answer:

Step-by-step explanation:

The modulus is the magnitude of the complex number; the argument is its angle (usually in radians).

__

The complex number can be cleared from the denominator by multiplying numerator and denominator by its conjugate:

  \(\dfrac{-9+3i}{1-2i}=\dfrac{(-9+3i)(1+2i)}{(1-2i)(1+2i)}=\dfrac{-9+3i-18i-6}{1+4}=-3-3i\)

The magnitude of this number is the root of the sum of the squares of the real and imaginary parts:

  modulus = √((-3)² +(-3)²) = 3√2

The argument is the arctangent of the ratio of the imaginary part to the real part, taking quadrant into consideration.

  arg = arctan(-3/-3) = -3π/4  or  5π/4 . . . . radians

__

  modulus∠argument = (3√2)∠(-3π/4)

The linear and exponential equations for the amount of money in the banks indicates;

TCF Bank Equation

y = 100·x + 1000

Well Fargo Bank Equation

y = (1.06)ˣ

The number of years it will take for both accounts to have the same amount of money is about 17 years

An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.

The equation for calculating the amount in each bank, based on the details are;

TCF Bank;

Amount invested = $1,000

Amount added each year = 100·x

Well Fargo Bank Equation

The percentage of the amount earned as interest each year = 6% = 0.06

The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ

Therefore; y = 1000·(1.06)ˣ

When the amount in the two accounts have the same amount of money, we get;

1000·(1.06)ˣ = 100·x + 1000

Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1

(1.06)ˣ = 0.1·x + 1

Solving the above equation using the substitution method and graphing indicates that we get;

x = 0, and x ≈ 17.125732

Therefore, it takes about 17 years for the two accounts to have the same amount of money

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Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

5.0 gm/cm³

Step-by-step explanation:

Density is defined as mass per unit volume or mass/volume

So simply divide he mass 30.6 by the volume 6.1 and you get

30.6/6.1 = 5.016 = 5.0 gm/cm³ rounded to the tenths place

For the forecasting process to be effective, internal data should be highly disaggregated

Predicting the future based on historical and current facts is the forecasting process. The most popular method for doing this is trend analysis. It is typically ideal to use internal data that is significantly disaggregated for forecasting to be successful. This means that rather than aggregating or summarizing the data at a high level, it should be broken down into as much detail as feasible.

Since highly disaggregated data presents a more complete and precise picture of the variables that may impact future events, forecasting can be done more accurately and dependably. This can include information about previous sales, manufacturing rates, inventory levels, costs, and other elements that can be important for forecasting. Whereas, using highly aggregated data can lead to less accurate and reliable forecasts, as it may not capture the full range of factors that may influence future outcomes.

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Answer:

There is 4/6 as a fration or 4.6

Step-by-step explanation:

Answer:

2:3 is equivalent to 4:6

Step-by-step explanation:

I know that these ratios are equivalent because each side of the ratio 4:6, are divided by the same number, 2, 4 divided by 2 is 2 and 6 divided by 2 is 3 which gives us a equivalent ratio of 2:3

Answer:

-560 is the answer

Step-by-step explanation:

658 - (-560 )= 98

Answer:

Hello!!! erz here ^^

Step-by-step explanation:

658 - 560 = 98

Hope this helps!! :D

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

200

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Google told me that 20% of 1000 is 200