Solve the system of linear equations by graphing.
y = x-7
y = -2x + 5

Answer:

300

Step-by-step explanation:

A=wl=10·30=300

multiply the length of the rectangle by the width of the rectangle.

The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.

Answer:

Area = 378.5 ft²

Step-by-step explanation:

The figure is having two semi circles and one rectangle.

\({ \sf{area = area \: of \: semicircles + area \: of \: rectangle}} \\ \\ { \sf{area = 2( \frac{1}{2} \pi {r}^{2}) + (l \times w) }} \\ \\ { \sf{area = \pi {r}^{2} + (l \times w) }} \\ \\ { \sf{area = 3.14 \times {5}^{2} + (30 \times 10)}} \\ \\ { \sf{area = 378.5 \: {ft}^{2} }}\)

Step-by-step explanation:

is the answer something like x^12=-2

The equation of the line containing the paints A and B is y = -1/3x + 4

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

The graph

Where, we have

(6, 2) and (0, 4)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 4

Using the other points, we have

6m + 4 = 2

So, we have

6m = -2

Evaluate

m = -1/3

So, we have

y = -1/3x + 4

As an equation, we have

y = -1/3x + 4

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Answer: The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

Step-by-step explanation:

Hope this is right!!!!

Answer:

35

Step-by-step explanation:

You can easily graph this in desmos for a visual understanding.

The slope of a line is received by (y2-y1)/(x2-x1). Assuming that Days is X and the cost is Y, we get (160-90)/(4-2), and it makes 70/2, which equates out to 35. Because the prices become more and more expensive, the slope is positive 35.

The equation of the line in slope - intercept form is -

y = - 5x + 77.

The equation of a straight line in slope - intercept form is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation as -

77 - y = 5x

We have the equation in the slope - intercept form as -

77 - y = 5x

y = 77 - 5x

y = - 5x + 77

Therefore, the equation of the line in slope - intercept form is -

y = - 5x + 77.

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(a) 12 cm 40° : Area of shaded segments = 301.44 sq. cm.

(b) 58° 16 cm ​: Area of shaded segments = 777.04 sq. cm.

Two radii that meet at the center to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle calculation and radius measurement are both crucial for solving circle-related difficulties.

Area of sector of circle = Ф/360 * πr²

π = 3.14

r  is the radius

Ф is the angle subtended.

(a) 12 cm 40°

Area of shaded segments = 40/60 * 3.14* 12²

Area of shaded segments = 40/60 * 452.16

Area of shaded segments = 301.44 sq. cm.

(b) 58° 16 cm ​

Area of shaded segments = 58/60 * 3.14* 16²

Area of shaded segments = 58/60 * 803.84

Area of shaded segments = 777.04 sq. cm.

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The diagram for the question is attached.

Answer:

642000000000000000000000 kg

Step-by-step explanation:

The approximate mass of Mars is 6.42x10^23 kilograms. It is given in scientic notation.

We need to write the mass in standard notation. It is the normal way of writing any number. To write it in standard form, we move the decimal to the right side.

The standard form will be :

6.42x10^23 kg = 642000000000000000000000 kg

Hence, this is the required solution.

Answer:

\(y-2=3(x-4)\)

Step-by-step explanation:

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Substitute 3 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=3(x-x_1)\)

Now, substitute 4 as \(x_1\) and 2 as \(y_1\).

\(y-2=3(x-4)\)

Topic: parallel and perpendicular lines

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Answer: it’s 25

Step-by-step explanation:

15 +10

Let's solve

\(\\ \rm\rightarrowtail x+2<-3\)

\(\\ \rm\rightarrowtail x<-3-2\)

\(\\ \rm\rightarrowtail x<-5\)

So

Option B

Answer:

B

Step-by-step explanation:

it is the opposite of A, which is true, as |-8| = 8

The trigonometric identities are verified that they are true.

What are trigonometric expressions?

Trigonometric identities are, by definition, reciprocal. These formulas show the connections between the sine/cosine functions and tangents.

1. LHS = sec x [ sec x - cos x]+(sin x+ cos x)/sin x- cot x

       = sec²x - sec x cos x +(sin x+ cos x)/sin x - cos x/sin x

       = sec²x - cos x/cos x +(sin x+ cos x- cos x)/sin x

       = sec²x - 1 + sin x /sin x

       = sec²x - 1 +1

      = sec²x

      = RHS

2. LHS = cos (π-Θ)+ sin (π/2 + Θ)

           = - cos Θ + cos Θ

           = 0

          = RHS

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Answer:

C = 50P

750 dollars

Step-by-step explanation:

$50 per person and P represents each person, and C is the total cost basically, so:

C = 50P, is the equation

To find 15 people, just plug it in

C = 50P

C = 50(15)

C = 750

Answer:

2

Step-by-step explanation:

We take the equation

\(x(y+3)/(3+y)z\)

and substitute the values for each individual variable in the problem. It looks like this:

\(12(1+3)/(3+1)6\)

Now we can solve the equation.

When solved, it equals 2.

Answer:

b

Step-by-step explanation:

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

\(\cfrac{x}{7}=\cfrac{28}{x}\implies x^2=196\implies x=\sqrt{196}\implies x=14\)

Answer: Yes

Step-by-step explanation: We're going to have to substitute

in the coordinates of that ordered pair into the equation.

I am going to substitute in the x and substitute in the y.

So it's really 5(2) + 3(-3) = 1.

From here it should be pretty straightforward,

all we are doing is evaluating the statement.

Simplifying on the left we have 10 + -9 = 1 or 1 = 1.

Now we know that the ordered pair (2, -3) satisfies this equation.

Answer:

x=29 angle a=63 Ang b=46 and c=71

Step-by-step explanation:

2x+5+x+17+3x-16=180 (sum of angles in triangles)

value of x is 29 substitute it in angle a b c

a=2*29+5

=63

b=29+17 = 46

c=3*29-16 = 71

9514 1404 393

Answer:

  cos(210°) = -(√3)/2

Step-by-step explanation:

The terminal ray of a 210° angle is in the third quadrant. The angle it makes with the -x axis is (210° -110°) = 30°. This is the "reference angle". In the 3rd quadrant, the x-coordinate of the terminal ray's intersection with the unit circle has a negative sign. This will be the sign of the cosine of the angle.

__

The reference angle of 30° tells you that the trig functions of the angle can be found from the side ratios of the "special right triangle" with angles of 30°, 60°, and 90°. The side ratios, shortest to longest, in that triangle are 1 : √3 : 2.

The cosine of the angle is the ratio ...

  Cos = Adjacent/Hypotenuse

In the above special triangle, the side adjacent to the 30° angle is the one that is √3 ratio unis. The hypotenuse is 2 ratio units. So, the cosine of 30° is ...

  cos(30°) = (√3)/2

As we said above, the sign of the adjacent side of the reference angle for 210° has a negative value. (The hypotenuse is always considered to be positive.) Then the desired cosine is ...

  cos(210°) = -cos(30°)

  cos(210°) = -(√3)/2

Answer:

y = 2

Step-by-step explanation:

0 = 2 - y

-2 = -y

y = 2

Answer:

it'll always be the number it is if it's going by 0

Answer:

C

Step-by-step explanation:

The compound inequality on the number line is shown below.

We have been given a compound inequality. We are asked to graph the given inequality on number line.    

x>8 and x≤3

The solution for the inequality is all values of x less than or equal to 3 and greater than or equal to 8.

We will have solid dots at  x>-8 and x≤-3 .

One arrow of the number line would be from 3 to left of the number line (towards negative infinity). The other arrow will be from 8 to right side of number line towards positive infinity.

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Answer:

Option (4)

Step-by-step explanation:

Party planner has used an arc of balloons for the parade.

This arc starts from x = 0 along the ground and f(x) defines the height of the arch.

From the table attached, it is clear that at x = 4 maximum height of the arch is 9.6 feet.

Therefore, clearance space below the arc is 9.6 feet which is greater than 9 feet, minimum height required for the clearance of the parade.

Option (4) will be the answer.

Answer:

D. yes, because the maximum height of the arch is 9.6 feet

Step-by-step explanation:

EDGE 2020 :)

Missing Part of the question:

a) Assume you wish to determine the maximum and minimum temperatures you would experience. the domain to study for the function H(x) would be?

b)The is one critical number for the function on the domain in part a and it is?

c) The maximum temperature you would experience is ?

d) The minimum temperature you would experience is ?

Answer:

a. Domain : \(4 \leq x \leq 41\)

b. Critical point: \(x = 12.33\)

c. The maximum is 115.09

d. The minimum is 100.62

Step-by-step explanation:

Given

\(H(x) = 100 + \frac{60}{x^2} + \frac{240}{(45 - x)^2}\)

Solving (a): The domain of H(x)

From the question, we understand that the distance between the two stores is 45ft

Let the first stove be at point A (0 ft) and

the second stove be at point B (45ft)

Since you move back and forth within 4ft from either stoves, then

Your maximum distance at A is (0 + 4) ft = 4ft

Your minimum distance at B is (45 - 4) ft = 41ft

Hence, the domain is: \(4 \leq x \leq 41\)

Solving (b): Critical Value

First, we have to differentiate H(x) w.r.t x

\(H(x) = 100 + \frac{60}{x^2} + \frac{240}{(45 - x)^2}\)

Differentiate

\(H'(x) = 0 -\frac{120}{x^3} + \frac{480}{(45- x)^3}\)

\(H'(x) = -\frac{120}{x^3} + \frac{480}{(45- x)^3}\)

Equate H'(x) to 0

\(0 = -\frac{120}{x^3} + \frac{480}{(45- x)^3}\)

Rewrite as:

\(\frac{120}{x^3} = \frac{480}{(45- x)^3}\)

Cross Multiply

\(480 * x^3 = 120 * (45 -x)^3\)

\(480 * x^3 = 120 * (45 -x)*(45 -x) * (45 -x)\)

\(480 * x^3 = 120 * (2025 -90x +x^2) * (45 -x)\)

\(480 * x^3 = 120 * (91125 -4050x +45x^2 -2025x - 90x^2 - x^3)\)

\(480 * x^3 = 120 * (91125 -4050x -2025x+45x^2 - 90x^2 - x^3)\)

\(480 * x^3 = 120 * (91125 -6075x-45x^2 - x^3)\)

Divide both sides by 120

\(4x^3 =91125 -6075x-45x^2 - x^3\)

\(4x^3 +x^3-91125 +6075x+45x^2= 0\)

\(5x^3-91125 +6075x+45x^2= 0\)

\(5x^3+45x^2 +6075x-91125= 0\)

Divide through by 5

\(x^3+9x^2 +1215x-18225= 0\)

Solving for x, we have that

\(x\approx \:12.33067\)

\(x = 12.33\)

Hence, the critical point is 12.33

Solving (x): Maximum temperature

Here, we simply substitute the endpoints of the domain in \(H(x) = 100 + \frac{60}{x^2} + \frac{240}{(45 - x)^2}\)

Let x = 4

\(H(4) = 100 + \frac{60}{4^2} + \frac{240}{(45 - 4)^2}\)

\(H(4) = 100 + \frac{60}{16} + \frac{240}{(41)^2}\)

\(H(4) = 100 + \frac{60}{16} + \frac{240}{1681}\)

\(H(4) = 100 + 3.75+ 0.14277215942\)

\(H(4) = 103.892772159\)

\(H(4) = 103.89\) --- approximated

Let x = 41

\(H(41) = 100 + \frac{60}{41^2} + \frac{240}{(45 - 41)^2}\)

\(H(41) = 100 + \frac{60}{41^2} + \frac{240}{4^2}\)

\(H(41) = 100 + \frac{60}{1681} + \frac{240}{16}\)

\(H(41) = 100 + 0.03569303985 + 15\)

\(H(41) = 115.03569304\)

\(H(41) = 115.04\) ---- approximated

Compare both values: The maximum is 115.09

Solving (d): The minimum temperature

In (b), we have that:

\(x = 12.33\) --- critical point

The minimum occurs at this point

Substitute 12.33 for x in \(H(x) = 100 + \frac{60}{x^2} + \frac{240}{(45 - x)^2}\)

\(H(12.33) = 100 + \frac{60}{12.33^2} + \frac{240}{(45 - 12.33)^2}\)

\(H(12.33) = 100 + \frac{60}{12.33^2} + \frac{240}{32.67^2}\)

\(H(12.33) = 100 + \frac{60}{152.0289} + \frac{240}{1067.3289}\)

\(H(12.33) = 100 + 0.39466180443 + 0.22486039682\)

\(H(12.33) = 100.619522201\)

\(H(12.33) = 100.62\) --- approximated

Hence, the minimum is 100.62