What is the solution to the system of equations?
y= 1/3x-10
2x + y = 4

When you know the area and one side of a rectangle, divide the area by the known side to find the length of the other side.

Length = 63/6

Length = 10.5 inches

Answer: 120 yds

Step-by-step explanation:

48+30+24+18+120 yds

The coordinates of point G are G(1.5, -4) .

The Reflection of point G across x-axis and y-axis lies in quadrant 4 , and the coordinates of that point are G"(-1.5, 4)

From the given graph, we can see the point located at the right bottom quadrant and the coordinates are: G(1.5, -4)

Now, the transformation rule for a Reflection of point G across x-axis is:

(x, y)→(x, -y)

The rule for a reflection over the y -axis is (x,y)→(−x,y)

Thus, the coordinates of G after both reflections is:

G"(-1.5, 4)

Now, the coordinate will lie in the top left quadrant of the graph.

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Answer:

D.

Step-by-step explanation:

x  =  ±√36

x  =  ±6

hopes this helps :)

Answer:

D

Step-by-step explanation:

The square root of 36 is +6 and -6

Answer:

18/5 which also equals 3 3/5 would be the answer

An equation for f', the inverse function is: f¹(x) = (x - 3)/7, for x ≥ 4.

The equation is correct as it has been shown that f(f'(x)) = x and f'(f(x)) = x.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of function f. This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

f(x) = y = 7x + 3

x = 7y + 3

7y = x - 3

y' = f¹(x) = (x - 3)/7, for x ≥ 4.

Proof:

f(f'(x)) = f[(x - 3)/7] = 7[(x - 3)/7] + 3

f(f'(x)) = f[(x - 3)/7] = x - 3 + 3

f(f'(x)) = f[(x - 3)/7] = x.

f'(f(x)) = x

f'(f(x)) = f¹[(7x + 3)]

f'(f(x)) = (7x - 3 + 3)/7

f'(f(x)) = 7x/7

f'(f(x)) = x

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The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

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The ratios are;

Sin θ =  5/6

Cos θ = √11/6

Tan θ =  5√11/11

Sec  θ =  6√11/11

Cosec  θ = 6/5

Cot θ =  √11/5

These trigonometric ratios are used to relate the angles of a right triangle to the lengths of its sides

We can see that the hypotenuse is obtained from;

x =√\((10)^2 + (2\sqrt{} 11)^2\)

x = √100 + 44

x = 12

Then;

Sin θ = 10/12 = 5/6

Cos θ =  2√11/12

= √11/6

Tan θ = 10/2√11

= 20√11/44

= 5√11/11

Sec  θ =  1/Cos  θ

=  6/√11

= 6√11/11

Cosec  θ = 1/Sin

 θ = 6/5

Cot θ = 1/tan θ

= 11/ 5√11

= 55√11/275

= √11/5

Sinβ = 2√11/12

= √11/6

Cos β = 10/12

= 5/6

Tan β = 2√11/10

= √11/5

Sec β = 6/5

Cosec β = 6√11/11

Cot β = 5√11/11

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Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

The highest temperature on Day 7 is equal to 60 degrees.

The day in which the highest temperature was 60 degrees is day 3.

Yes, the high temperature is a function of the day because it is dependent variable.

No, the day is not a function of the high temperature because it is an independent variable.

In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter, scientist, or a researcher.

This ultimately implies that, an independent variable is always considered as the cause in an experiment and it is represented by the x-axis value on a graph.

In this context, we can reasonably infer and logically deduce that time measured in days represent the independent variable while the highest temperature measured in degree Fahrenheit represent the dependent variable.

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Answer:

108 is your answer

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

The average number of likes will be 16.5. the correct option is D.

Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is calculated by adding all the data points and dividing it by the total number of the data.

Given that Bethany has a photo website where she places photos that she has taken so others can see them. Below is how many likes each of her current photos was given: 10, 13, 15, 15, 17, 29.

The average will be calculated as:-

Mean = ( 10 + 13 + 15 + 15 + 17 + 29 ) / 6

Mean = 99 / 6

Mean = 16.5

Therefore, the average number of likes will be 16.5. the correct option is D.

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The expanded form of the expression is 10 + 9 + 0.3 + 0.00 + 0.005

He runs the 100 meters dash in 19.305 seconds.

Therefore, the seconds he runs the race can be represented in expanded form as follows:

Expanded form is a way to write a number by adding the value of its digits.

We can use a place value chart to think of the value of a number's digits.

Therefore,

19.305 in expanded form is as follows:

19.305 = 10 + 9 + 0.3 + 0.00 + 0.005

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Answer:

  (-∞, -3] or [-3, ∞)

Step-by-step explanation:

You want the largest domain interval(s) on which the function shown in the graph could be one-to-one.

A one-to-one function must pass the horizontal line test. That is, no horizontal line can intersect its graph in more than one place.

For that to be true of the given function, the interval on which it is defined cannot include values on both sides of x=-3, where the graph has a minimum. That is, the domain must be either x ≤ -3, or x ≥ -3, (or some subset of either of these).

The largest intervals on which the function has an inverse are ...

  (-∞, -3]  or  [-3, ∞)

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To make the given function one-to-one and have an inverse, we can restrict its domain to (-∞, a) or (a, ∞), where 'a' is the x-coordinate of the highest or lowest point on the graph.

To make the given function one-to-one and have an inverse, we need to restrict its domain. The largest domains, in interval notation, that can be used are: (-∞, a) or (a, ∞) where 'a' is the x-coordinate of the highest or the lowest point on the graph, depending on the function type.

If the graph has a highest point, the domain is restricted to (a, ∞), where 'a' is the x-coordinate of the highest point. If the graph has a lowest point, the domain is restricted to (-∞, a), where 'a' is the x-coordinate of the lowest point.

For example, if the graph has a highest point at (3, 5), the domain would be restricted to (3, ∞) to make the function one-to-one and have an inverse.

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Answer:

4x+8=24

4x=24-8

4x=16

4x=16

x=16÷4

x=4

840 different numbers can be created selecting 4 of the digits from the number

From the question, we have the following parameters that can be used in our computation:

Number =  8712395

Digits = 4

The count of digits in the number is 7

Using the above as a guide, we have the following:

So, we have

Numbers = 7 * 6 * 5 * 4

Evaluate

Numbers = 840

Hence, 840 numbers can be formed

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Based on their given probabilities, e would expect the color blue or green to be spun approximately 75 times in this experiment.

To find the expected number of times the color blue or green will be spun, we first need to add their probabilities:

0.25 + 0.125 = 0.375

This means that, on average, we would expect to see blue or green spun 0.375 times for every spin. To find the expected number of times this will happen over 200 spins, we can multiply the probability by the number of spins:

0.375 x 200 = 75

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Answer:

-152

Step-by-step explanation:

-152 < 12

-152 is negative, which means it is less than 1.

12 is positive, which means it is greater than 1.

Therefore, -152 is the lesser of the two given numbers.

Have a great rest of your day! :)

Hi!

-152 is less than 12, because:

\(\mathbb{NUMBER \ LINE}\)

\(_ < \!\!\!\rule{300}{1}\!\!\!_ >\)

     \(-152\)                                                                         \(12\)

Cheers!

Have a nice day!

I hope this helps!

Based upon this information, (2) I and III only statements can be proven.

From the given information, we can prove that statement II is true, i.e., BD bisects ABC.

Proof:

Since BD is the perpendicular bisector of ADC, we have AD = CD and ∠ADB = ∠CDB = 90°. Thus, triangles ABD and CBD are congruent (by the hypotenuse-leg congruence criterion), which implies AB = BC and ∠ABD = ∠CBD. Therefore, BD bisects ∠ABC.

However, we cannot prove that statements I or III are true based solely on the given information.

Statement I (BD is a median) would be true if we had additional information that AD = DB = DC, but this is not necessarily true based on the given information.

Statement III (△ABC is isosceles) would be true if we had additional information that AB = BC, but this is not necessarily true based on the given information. In fact, it is only guaranteed that AB = BC if AD = BD = DC, which is not necessarily the case.

Therefore, the correct answer is (2) I and III, only.

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Answer:

\(a(1) = 144\)

\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)

\(a(n) = - \frac{1}{6} a(n - 1)\)

Answer:

It's option C. only 3

Step-by-step explanation:

A line of symmetry is a line which will cut any shape in exactly half. In your given picture, only line 3 is symmetrical because if you were to fold the shape after you cut it in half, both halves would match and be equal.

For measuring the vegetable garden, Matsu should use the unit of feet.

Finding a number that represents the amount of anything is what measurement is all about.

For the given question;

The dimensions of the garden are the length. This could be calculated by using the two values in the option; That is inches and feet.

But as inches is a used for measuring the small length ad feet is the larger unit.

Thus, dimensions of the vegetable garden of Matsu are calculated by using feet.

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Answer:

For measuring the vegetable garden, Matsu should use the unit of feet.

What is defined as the measurement units?

Finding a number that represents the amount of anything is what measurement is all about.

A measurement unit is a unit of measurement that is used to represent a physical quantity.

For example, the unit of measurement is the defined magnitude of quantity that is being used as the norm for measuring the same type of quantity, as adopted and specified by law or convention.

The imperial unit, also known as the British imperial system, is the standard or default weights and measures system.

Metric System: The metric system is by far the most recent and widely used international system of measurement.

Natural System: Natural units are physical units of measurement that are entirely based on common physical constants.

For the given question;

The dimensions of the garden are the length. This could be calculated by using the two values in the option; That is inches and feet.

But as inches is a used for measuring the small length ad feet is the larger unit.

Thus, dimensions of the vegetable garden of Matsu are calculated by using feet.

Step-by-step explanation:

Answer:

y = -1/4x + 1/4

Step-by-step explanation:

y = -1/4x + b

-1 = -1/4(5) + b

-1 = -5/4 + b

b = 1/4

Answer:

128 degrees

Step-by-step explanation:

Opposite interior angles

If a function, f(x) is translated d units downwards, the new function would be

f(x) - d

The original function that we were given is

y = 3^x

It can also be written as

f(x) = 3^x

the function after the shift is

y = 3^x - 2

It can also be written as

f(x)' = 3^x - 2

By comparing with the function stated earlier, - d = - 2

Thus, the function was translated 2 units downwards

D) Down

Answer:

  x = 17

Step-by-step explanation:

In order to make any sense of this problem, we must assume the lines that look parallel are parallel. With that assumption, the two marked angles are supplementary:

  61° +7x° = 180°

  7x = 119 . . . . . . . subtract 61°, divide by °

  x = 17 . . . . . . . . divide by 7

Answer:

0.42

Step-by-step explanation:

they are both multiples of 0.06

think of it like 6 x 6= 36 and 6 x 8 = 48

6 x 7 = 42 would be halfway

Answer:

0.42

Step-by-step explanation:

To find the half, add da numbers and divide by 2. So 0.36 and 0.48 added together is 0.84. That divided by 2 is 0.42.

Answer:

x = 80

Step-by-step explanation:

The sum of the angles of a triangle is 180

30+70+x = 180

100 +x = 180

x = 180-100

x = 80