Max is asked to find 15 solutions of a liner equation. How could Max use a graph to help him find these solutions?

An equation for the line that passes through (-14, 14) and whose slope is undefined is x = -14.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-14, 14) and an undefined slope, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 14 = undefined(x - (-14))

y - 14 = undefined(x + 14)

x = -14

In conclusion, the equation of a line that has an undefined slope represents a vertical line that crosses the x-axis only i.e x = -14.

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Step-by-step explanation:

In construction, we use trigs. For figuring areas of triangular shapes ( gabled roofs and exterior wall cladding). Similar to many concepts and phenomena in Maths, it can be found in many aspects of life if we observe and examine carefully.

The solution set of given inequalities are represented by Part A.

The given inequalities are

⇒ y ≥ x + 1 and y + x > -1

Hence, The related equations of both inequalities are

y = x + 1

Put x=0, to find the y-intercept and put y=0, to find x intercept.

y = 0 + 1

y = 1

And, 0 = x + 1

x = - 1

Therefore, x-intercept of the equation is (-1,0) and y-intercept is (0,1).

Similarly, for the second related equation

y + x = - 1

y + 0 = - 1

y = - 1

0 + x = - 1

x = - 1

Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,-1).

Now, join the x and y-intercepts of both lines to draw the line.

Now check the given inequalities by (0,0).

0 ≥ 0 + 1

0 ≥ 1

It is a false statement, therefore the shaded region is in the opposite side of origin.

0 + 0 ≥ - 1

0 ≥ - 1

It is a true statement, therefore the shaded region is about the origin.

Hence, From the below figure we can say that the solution set of given inequalities are represented by Part A.

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Answer:

Hello There!

According to the question,

Base=6

And

Height =4

Let's know the formula

\( \frac{1}{2} \times base \times height \\ so \\ \frac{1}{2} \times 6 \times 4 \\ \)

simplify 2 with 6 then it will look like this

\( \frac{1}{1} \times3 \times 4 \\ \\ \)

1 has no value so

\(3 \times 4 = 12 {ft}^{2} \\ \)

So third option

\(a = 12 {ft}^{2} \)

is correct.

\(\Large\textsf{Hope \: It \: Helped}\)

Answer:

Area = 12 sq ft

Step-by-step explanation:

The formula to find the area of a triangle is

1/2 bh so we will replace the letters with their number value

1/2 (6x4)

1/2 x 24 = 12

So, 12 is your answer!

Answer:

True

Step-by-step explanation:

To compare the two speeds, we can calculate the speed of each in miles per hour (mph) and then compare them.

22 miles in 20 minutes = (22/20) miles per minute = 1.1 miles per minute

To convert to mph, we can multiply by 60 to get:

1.1 x 60 = 66 mph

38 miles in 30 minutes = (38/30) miles per minute = 1.27 miles per minute

To convert to mph, we can multiply by 60 to get:

1.27 x 60 = 76.2 mph

Therefore, 38 miles in 30 minutes is faster than 22 miles in 20 minutes, as 76.2 mph is greater than 66 mph.

In other words, the statement "22 miles in 20 minutes is less than 38 miles in 30 minutes" is true.

we know that

The recipe calls for 2 3/4 cups of flour

Robert added 1 1/4 cups of flour

so

To find out how much more flour needs

subctract

2 3/4 - 1 1/4

but first

convert mixed numbers to an improper fractions

2 3/4=2+3/4=11/4

1 1/4=1+1/4=5/4

substitute

11/4-5/4=6/4

simplify

6/4=3/2=1.5 cups

convert to mixed number

1.5=1+0.5=1+1/2=1 1/2 cups

therefore

the answer is 1 1/2 cups of flour

Answer:

\(\sqrt[4]{256}\)

Step-by-step explanation:

1. simplify the expression

4^4 = 256

2.  calculate the fourth root of 256 because we used the power of 4

\(\sqrt[4]{256}\) = 4

The number makes the expression equivalent is m = 0.2584.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 12(- 1.4m + 0.4) = m + 0.2.

- 16.8m + 4.8 = m + 0.2.

- 16.8m - m = 0.2 - 4.8

- 17.8m = - 4.6.

m = (-4.6/-17.8).

m = 0.2584.

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Using the length formula we know that the length of the given arc is 30.144 miles.

In mathematics, an arc is a portion of the boundary of a circle or curve. It is sometimes referred to as an open curve.

The measurement around a circle that determines its edge is called the circumference, often known as the perimeter.

So, the formula to find the length of the arc is:

Length of an Arc = θ × r

Now, insert values and calculate as follows:

Length of an Arc = θ × r

Length of an Arc = 4π/5 × 12

Length of an Arc = 4π/5 × 12

Length of an Arc = 12.56/5 * 12

Length of an Arc = 2.512 * 12

Length of an Arc =  30.144

Therefore, using the length formula we know that the length of the given arc is 30.144 miles.

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The length of the hypotenuse is 7m.

Let the side opposite to 30° be the shortest leg.

The side opposite to 60° is the longest leg.

So, the side opposite to 90° is hypotenuse.

Length of the shortest side is x.

Length of longest side is \(\sqrt{3}x\)

Length of the hypotenuse is 2x.

We know x = 7

So, \(\sqrt{3}(x)=\sqrt{3}(7)\)

Thus, the length of the longer leg is \(\sqrt{3}(7)\) m

Length of hypotenuse = 2x = 2(7) = 14m

\(x^{2} +(\sqrt{3} x)^2 =(2x)^2\\\\(7)^2+(\sqrt{3} (7))^2=(2x)^2\\\\49 + (3(49)) = (2x)^2\\\\49 + 147= (2x)^2\\\\(2x)^2=196\)

Taking square root on both sides:

\(2x = \sqrt{196}\)

2x = 14

x = 7

Therefore, the length of the hypotenuse is 7m.

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Answer:

He can order 4 toppings

Step-by-step explanation:

600-325=275

$2.75 left

275/065=4.2

Answer:

s=9

Step-by-step explanation:

8s=72

Divide 72 and 8

s=9

Step-by-step explanation:

=9feet

On solving the question, we can say that second function has vertical asymptote at x=2

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.

The function that represents the graph is f(x) = 1/x-2 .

The graph of the function

From the given graph , the vertical asymptote is at x=2

Lets find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator =0

f(x) = 1/2x

2x = 0

x = 0

f(x) = 1/x-2

x-2 = 0

x = 2

The second function has vertical asymptote at x=2

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Answer:

3.75 ounces  or 3 3/4

Step-by-step explanation:

The ratio 81:108 can be simplified to 9:13. To find the simplest form of the ratio, you can divide both numbers by the greatest common factor. The greatest common factor of 81 and 108 is 9, so you can divide both numbers by 9 to get the simplified ratio of 9:13.

The uncertainty of the total distance is 0.2 cm.

As per the given data, the distance between the diffraction slit and the screen on which the pattern forms,

\(x_{1}\) = (15.8 ± 0.2) cm

\(x_{2}\) = (6.7 ± 0.1) cm

\(x_{3}\) = (11.3 ± 0.1) cm

Let, the uncertainty in the measurements,

\(x_{1}\), \(x_{2}\) and \(x_{3}\)  is \(e_{1}\), \(e_{2}\) and \(e_{3}\) respectively.

So,

\(e_{1}\) = 0.2 cm

\(e_{2}\) = 0.1 cm

\(e_{3}\) = 0.1 cm

Again, let the uncertainty in the total distance

\(\mathrm{x} =\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3\) is e(error propagation).

The impact of a variable's uncertainty on the uncertainty of a function depending on it is known as propagation of uncertainty. When the variables are experimental measurement values, measurement limits cause uncertainties that are propagated via the function's combination of variables.

Then the error propagation is given as,

e = \(\sqrt{\mathrm{e}_1^2+\mathrm{e}_2^2+\mathrm{e}_3^2} \\\)

So, e = \(\sqrt{(0.2)^2+(0.1)^2+(0.1)^2} \\\)

Therefore e = \(\sqrt{0.06} \\\)

e = 0.245 cm

e ≅ 0.2 cm

Therefore uncertainty of the total distance 0.2 cm

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The rule of reflection over the line y = x is:

The coordinates of A' = (1,-2) , B' = ( 3 , -4 )

So, the coordinates of A'' and B'' will be :

We need to find the rule of transformation from A to A''

The coordinates of A = (1,2) and B = ( 3 , 4 )

So,

The last rule is the rule of rotation 90 counter - clockwise

Or the rule of the rotation 270 clockwise

Answer: 125

Step-by-step explanation:

The sum of all 3 interior angles of a triangle is 180.

18 + (12y + 5) + (4y - 3) = 180

20 + 16y = 180

Subtract 20 from both sides

16y = 160

Divide both sides by 16

y = 10

Now plug y back into equation for angle A

12y + 5

12(10) + 5

120 + 5 = 125

The statement "there exists x ∈ S ∖ m" means that there exists an element x that belongs to the set S but does not belong to the set m. In other words, x is an element that is present in S but is not present in m.

The phrase "m ⊊ m ∪ {x} ∈ X" states that the set m is a proper subset of the set m ∪ {x}, and this union belongs to the set X. This implies that the set m ∪ {x} contains all the elements of m along with the additional element x.

The phrase "a contradiction" indicates that the statement or assumption being made leads to a logical inconsistency or contradiction. In this context, the contradiction arises from the fact that the assumption that x is not in m contradicts the statement that m ∪ {x} is a proper superset of m.

Overall, the given statement implies that the existence of an element x in S, which is not in m, leads to a contradiction when considering the relationship between m and m ∪ {x}.

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Answer:

No entiendo ingles perdon

The slope of the line passing through points A and B is 1/3.

The formula for the slope of a line to find the slope passing through points A and B. The formula is:

slope = (change in y) / (change in x)

Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).

Then, substitute the values and calculate the slope:

slope = (y₂ - y₁) / (x₂ - x₁)

slope = (3 - 2) / (3 - 0)

slope = 1 / 3

Therefore, the slope of the line passing through points A and B is 1/3.

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No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

y-intercept:  (0, 75) ⇒ y = 75

x-intercepts:  (3, 0) and (5, 0) ⇒ x = 3 and x = 5

vertex: (4, -5)

Step-by-step explanation:

Let the x-axis be the ground (when y = 0).  Therefore underground when y < 0 and overground when y > 0

The function is a quadratic:  f(x) = ax² + bx + c

If the coaster enters the tunnel three seconds after the first descent starts and stays in the tunnel for a total of 2 seconds, then y = 0 when x = 3 and x = 5

Also, when x = 1, y = 40

Solve 2 equations simultaneously:

⇒ a = 5  b = -40  c = 75

⇒ f(x) = 5x² - 40x + 75

y-intercept

when x = 0

⇒ f(0) = 5(0²) - 40(0) + 75 = 75

⇒ y-intercept = (0, 75)

x-intercepts

x = 3 and x = 5

Vertex

If the x-intercepts are when x = 3 and x = 5, then vertex is when x = 4

⇒ f(4) = 5(4²) - 40(4) + 75 = -5

⇒ vertex = (4, -5)

Answer:

non fic, fiction, children, school

Step-by-step explanation:

fiction: 1/4= 0.25

non fic: 1/2=0.50

school: 1/10= 0.10

children: 3/20= 0.15

Given: A table showing total shipment, successful, and missed

To Determine: The error in the table

Solution

Let us add the successful shipment to the missed shipment and compare with the total

Day 1

Day 2

Day 3

Day 4

From the above calculations, we can see that an error occurred in Day 2.

Hence, A math error was made when computing total shipments for Day 2, OPTION C

Answer:

Start of the year: 77 End of the year: 87

Step-by-step explanation:

1 dot equals the number represented below, so I multiplied up to the answers for both! (Hope you pass ur test :D)

Answer:

x² + 2x - 3

Step-by-step explanation:

Step 1: Write expression

(4x² - 3x + 1) - (3x² - 5x + 4)

Step 2: Distribute negative

4x² - 3x + 1 - 3x² + 5x - 4

Step 3: Combine like terms (x²)

x² - 3x + 1 + 5x - 4

Step 4: Combine like terms (x)

x² + 2x + 1 - 4

Step 5: Combine like terms (constants)

x² + 2x - 3

Answer:

228-12 = 6w +12 -12

216 = 6w

divide both sides by 6

216/6 =6w/6

36 = w

so width = 36 feet

then the length is ..

l = 2w + 6

= 2*36 +6

= 72 +6=78

so the length = 78 feet

Answer:

The answer is in the attached picture below.