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Which system of inequalities is shown in the graph?
A) 2x + 3y ≤ 5 and -3x + 2y < 6
B) 2x + 3y < 5 and -3x + 2y ≤ 6
C) 2x + 3y ≥ 5 and -3x + 2y > 6
D) 2x + 3y > 5 and -3x + 2y ≥ 6

An interpretation of the relationship between the variables in this graph is that: C. you leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally, you continue at a slower (but constant) speed than before.

A graph can be defined as a type of chart which is used to graphically represent the relationship between the variables in a data set, on both the horizontal and vertical lines of a cartesian coordinate i.e x-axis and y-axis.

By critically observing the graph attached in the image below, we can infer and logically deduce that an interpretation of the relationship between the variables in this graph is that you drove at a constant speed for 2 hours, and then stopped for 1 hour. Finally, you continued at a slower, but constant speed than before.

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You will have $50,000 in your account after 50 years.

We have,

Simple interest formula is given by:

I = Prt

Where:

I = interest earned

P = principal amount (initial investment)

r = interest rate

t = time (in years)

Here,

P = $10,000

r = 8%

t = 50 years

So, the interest earned after 50 years will be:

I = Prt

= 10000 x 0.08 x 50

= $40,000

The total amount in the account after 50 years will be the initial investment plus the interest earned:

Total amount = $10,000 + $40,000 = $50,000

Therefore,

You will have $50,000 in your account after 50 years.

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The equation formed after the transformations is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

The parent function in this problem is defined as follows:

\(f(x) = \sqrt{x}\)

For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x}\)

For the translation left 3 units, we have that x -> x + 3, hence:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

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To find the axis of symmetry (AOS) for the equation x^2+x-6=0, we can start by completing the square. This involves adding and subtracting the same value to the equation to make it have the form (x + a)^2 = b. In this case, we can add and subtract 9/4 to the equation to get:

\(x^2 + x - 6 = (x + 1/2)^2 - 9/4\)

This equation has the form \((x + a)^2 = b\), where a = 1/2 and b = -9/4. The axis of symmetry (AOS) is the vertical line that passes through the point where the parabola defined by the equation opens. In this case, the AOS is the vertical line that passes through the point (-1/2, 0), which is the point where the parabola defined by the equation x^2 + x - 6 = 0 opens. Therefore, the AOS for this equation is the vertical line x = -1/2.

Answer:

\(x=-\dfrac{1}{2}\)

Step-by-step explanation:

The axis of symmetry of a quadratic equation in the form y = ax² + bx + c, is a vertical line that passes through the vertex of the corresponding parabola, dividing it into two symmetrical halves.

The formula for the axis of symmetry is:

\(\large\boxed{x=-\dfrac{b}{2a}}\)

For the given equation, x² + x - 6 = 0:

Substitute the values of a and b into the formula:

\(x=-\dfrac{1}{2(1)}=-\dfrac{1}{2}\)

Therefore, the axis of symmetry of the given quadratic equation is:

\(\large\boxed{x=-\dfrac{1}{2}}\)

The graph of equation is shown in figure.

We have to given that,

The equation is,

⇒ y = - 2x² + 12x - 17

Now, We have the given equation is a quadratic equation.

Hence, We can simplify as,

⇒ y = - 2x² + 12x - 17

⇒ y = - 2 (x² + 6x) - 17

⇒ y = - 2 (x² - 6x + 3² - 3²) - 17

⇒ y = - 2 (x - 3)² + 18 - 17

⇒ y = - 2 (x - 3)² + 1

Hence, This represent the equation of parabola with vertex (3, 1).

Thus, The graph of equation is shown in figure.

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Step-by-step explanation:

I just did in the other posting. how often did you post it ?

this is a trick question. the triangle at the top is not an isoceles triangle.

we use Pythagoras for an the steps.

so, the left part of the baseline (split by the height) is calculated by

12² = 10² + part²

144 = 100 + part²

part = sqrt(44) = 6.633249581... ft

the other part is then

20 - 6.633249581... = 13.36675042... ft

and the second leg of the large triangle is

leg² = 10² + 13.36675042...² = 278.6700168...

leg = 16.69341238... ft

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

please see the answer to the other posting for more details.

Problem

The function c(x) = 0.47x + 20 represents the cost (in dollars) of a one-day truck rental when the truck is driven x miles.What is the truck rental cost when you drive 80 miles?​

Solution

For this case we just need to replace into the function given by:

c(x) = 0.47x + 20

For this case we just need to replace x=80 mi and we got:

c(80)= 0.47*80 +20= 37.6 +20= 57.6

The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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Answer:

x = 24

Step-by-step explanation:

Lets isolate x.

Add 16 on both sides.

x-16 = 8

+16  +16

x should be isolated now.

x = 24

It is isolated.

So... x = 24

Both angles 1 and 2 are supplementary and linear angles.

So, options (1) and (3) are the correct options.

If consider, ∠1 and ∠2 are supplementary. If two angles form a linear pair, the angles are supplementary. A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.  

If consider complementary angles. They are equals if the two intersected lines by the transversal are parallel. In the figure, angles 1 and 2 are corresponding. The 1 is external and the 2 is internal. Angles that are on opposite sides of the transversal of two other lines.

If consider linear pair angles. The sum of angles of a linear pair is always 180 degrees. Consider the image as shown. Here angle 2 and angle 1 are said to be a linear pair because they are formed on the same line with a standard arm S and common vertex point Q. Also, the sum of angles 1 and 2 is equal to 180 degrees.

Two angles are said to be adjacent angles, if, they share a common vertex, a common side and they do not overlap. Observe the following figure to understand what adjacent angles look like. Angle 1 and 2 are adjacent because they have a common side BD and a common vertex B.

A pair of vertically opposite angles are always equal to each other. Also, a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. For example, if two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°.

We can see all images.

So, that

When two lines intersect each other at a point, angles formed on the point are called as linear pair.

Since pair of linear angles is supplementary, sum of linear angles will be 180°.

m∠1 + m∠2 = 180°

Therefore, both angles 1 and 2 are supplementary and linear angles.

Options (1) and (3) are the correct options.

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Answer:

9

Step-by-step explanation:  Y=mc^2

Answer:

y = 20x + 200

Step-by-step explanation:

The 200 is the constant.  It is only added once, but the monthly deposits are added at 20 every month.  

After 1 month:

y = 20x + 200

y = 20(1) + 200

y = 20 + 200

y =220       money deposited.

After 2 months:

y = 20x + 200

y = 20(2) + 200

y = 40 + 200

y =240 money deposited.

After 3 months:

y = 20x + 200

y = 20(3) + 200

y = 60 + 200

y = 260  money deposited

And so on, and so on, and so on...

Answer: To determine which equation gives the line shown on the graph, we need to examine the slope (m) and y-intercept (b) of the line.

Looking at the given options, we can determine the equation by comparing the slope and y-intercept values with the line on the graph.

The line on the graph passes through the point (0, 1) and (6, 13). We can calculate the slope using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Using the points (0, 1) and (6, 13):

m = (13 - 1) / (6 - 0)

m = 12 / 6

m = 2

Now, let's compare the slope and y-intercept values with the given equation options:

   y = 2x - 4

   y = x + 4

   y = 2x + 4

   y = -x - 4

From the calculation above, we determined that the slope of the line on the graph is 2. Comparing this with the slope values in the equation options, we find that options 1 and 3 have a matching slope of 2.

Next, we can compare the y-intercept of the line on the graph, which is (0, 1), with the y-intercept values in the equation options:

   y = 2x - 4 -> y-intercept: -4

   y = x + 4 -> y-intercept: 4

   y = 2x + 4 -> y-intercept: 4

   y = -x - 4 -> y-intercept: -4

From the comparison, we see that option 3, y = 2x + 4, matches both the slope and y-intercept of the line on the graph.

Therefore, the equation that gives the line shown on the graph is y = 2x + 4.

Step-by-step explanation:

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

The proof that shows that ΔLMN ≅ ΔQPN by either SSS or SAS is explained below.

If we can show that two triangles have two pairs of congruent sides and a pair of corresponding congruent included angles, then we can state they are congruent triangles based on the SAS theorem.

On the other hand, if all three corresponding side lengths are congruent to each other, then the triangles are congruent by the SSS theorem.

The proof that can be used to show that the two triangles are congruent by SAS is shown below:

Statement                                 Reasons                                  

1. ∠L ≅ ∠Q, LM ≅ QP,              1. Given

MN ≅PN, NL ≅ NQ

2. ΔLMN ≅ ΔQPN                    2. SSS

Based on the given information we are given, another way of writing this proof can be:

Statement                                 Reasons                                  

1. ∠L ≅ ∠Q, LM ≅ QP,              1. Given

MN ≅PN, NL ≅ NQ

2. ΔLMN ≅ ΔQPN                    2. SAS

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The correct  equation is D. x2 + y2 + 6x − 24y + 148 = 0.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.


This equation is the general form of a circle with center A and radius 5. The equation can be derived from the coordinates of the center A and the radius of the circle. The center of the circle is located at (-3, 12). To get the equation, first calculate the distance between the center A and a point on the circumference of the circle, which is the radius of the circle, 5. Then, use the Pythagorean theorem to calculate the equation of the circle: x2 + y2 + 6x – 24y + 148 = 0.
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Answer:

=12x+42

Step-by-step explanation:

−3(4x+2)+6(4x+8)

Answer: 12x+42

Step-by-step explanation: −3(4x+2)+6(4x+8)

(−3)(4x)+(−3)(2)+(6)(4x)+(6)(8)

−12x+−6+24x+48

(−12x+24x)+(−6+48)

12x+42

Answer:

46

Step-by-step explanation:

Given :

Lowest scoring 20% ; this corresponds to score below (1 - 0.2) = 0.8

Mean, m = 60

Standard deviation, s = 17

Zscore = (x - mean) / standard deviation

Therefore, the Zscore for the bottom 20% equals ; P(x > Z) = 0.8

Using a Z probability calculator ;

The Zscore = -0.842

Therefore to Obtian the score, x

Zscore = (x - mean) / standard deviation

-0.842 = (x - 60) / 17

-0.842 * 17 = (x - 60)

-14.314 = x - 60

-14.314 + 60 = x

x = 45.686

To secure a second interview, candidate must score, 46 (nearest whole number).

The marks (to the nearest whole number) must a candidate achieve in order to secure a second interview is 46 and this can be determined by using the z-score formula.

Given :

Let 'x' be the mark must a candidate achieve in order to secure a second interview.

So, through the z-score formula, the value of 'x' can be determined.

\(\rm z_{score} = \dfrac{x-mean}{Standard\; Deviation}\)

\(\rm -0.842 = \dfrac{x-60}{17}\)

\(17\times -0.842 = x - 60\)

x = 60 - 14.314

x = 45.686

So, the marks (to the nearest whole number) must a candidate achieve in order to secure a second interview is 46.

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The degree of a vertex is defined as the number of edges that touch the vertex. The (i, j)-th entry of the adjacency matrix tells you whether vertex i touches vertex j (1 if yes, 0 if no). Then the degree of vertex i is equal to the sum of the i-th row in the adjacency matrix.

• vertex 1 : degree = 0 + 1 + 0 + 0 + 1 = 2

• vertex 2 : degree = 1 + 0 + 1 + 1 + 1 = 4

• vertex 3 : degree = 0 + 1 + 0 + 1 + 0 = 2

• vertex 4 : degree = 0 + 1 + 1 + 0 + 1 = 3

• vertex 5 : degree = 1 + 1 + 0 + 1 + 0 = 3

So, the correct answer is A. 2.

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Answer:

A straight angle changes the direction you are pointing in. A straight angle looks like a straight line. It has an angle measurement of 180 degrees. Straight angles can be composed of several angles, as long as the angles add up to 180 degrees.

Step-by-step explanation:

Answer: Angles on a straight line add up to 180°.

Step-by-step explanation:

Answer:

the factors of 200 are 1,2,4,5,8,10,20,25,40,50,100, and200

The expression arcctg(tg(x)) simplifies to arcctg(tan(x)).

To simplify the expression arcctg(tg(x)), we can apply trigonometric identities and properties.

The function arcctg(x) is the inverse cotangent function, which is the angle whose cotangent is x. Similarly, tg(x) represents the tangent function.

First, let's simplify the expression inside the arcctg function, which is tg(x):

tg(x) = sin(x) / cos(x)

Now, we can substitute this value into the original expression:

arcctg(tg(x)) = arcctg(sin(x) / cos(x))

Using the property of inverse trigonometric functions, we can rewrite this as:

arcctg(sin(x) / cos(x)) = arcctg(1 / tan(x))

Now, we can simplify further using the identity:

1 / tan(x) = cot(x)

Therefore:

arcctg(1 / tan(x)) = arcctg(cot(x))

Using another identity, we know that the cotangent function is the reciprocal of the tangent function:

cot(x) = 1 / tan(x)

Therefore, we can simplify the expression to:

arcctg(cot(x)) = arcctg(1 / tan(x)) = arcctg(tan(x))

Finally, we arrive at the simplified expression:

arcctg(tg(x)) = arcctg(tan(x))

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Answer:

5

Step-by-step explanation:

\(35/a\), when a = 7

Substitute

\(35/7\) \(=5\)

Answer:

5

Step-by-step explanation:

You substitute 7 for a in the equation.

35/a ——> 35/7

Evaluate it and your answe is 5.

I hope it helps! Have a great day!

Lilac~