Which equation represents a line that is parallel to the
line shown on the graph?

Answer:

Line AB is perpendicular to line CD.

Explanation:

For the lines to be parallel they must have the same slope.

For the lines to be perpendicular they must have negative reciprocal slopes.

Else neither of them is true.

Given the coordinates;

The slope can be calculated for each line as;

Using the formula to calculate the slope of each line;

For line AB;

For line CD;

Since the slope of line AB and line CD is not the same, they are not parallel.

The slope of line AB is a negative reciprocal of the slope of line CD

Therefore, Line AB is perpendicular to line CD.

The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

Learn more about the area;

https://brainly.com/question/1658516

#SPJ1

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:

Complemenraty angles are two angles with sum of 90°. In the given triangle ∠A and ∠B are complementary.

Now, the sine and cosine

Find the sine of ∠A and cosine of ∠B

Since right sides are equal, left sides are equal too

Similarly, we can show that

Proved

The main belt is not located between these all planets.

What is orbit?

A route that an object in space follows around another is known as an orbit. A satellite is a thing that orbits the earth. An Earth- or moon-like natural satellite is one possibility. Moons are satellites that orbit many planets. A man-made satellite is also possible, such as the International Space Station.

The belt of asteroids is located between the orbits of Mars and Jupiter. The asteroids in this region, known as the main belt, are made up of small rocky bodies that orbit the sun in a region between about 2.2 and 3.2 astronomical units (AU) from the sun.

The distance from the sun to the Earth is about 1 AU, and the distance from the sun to Venus is about 0.7 AU, so the main belt is located beyond the orbits of both Venus and Earth.

The orbits of Saturn and Uranus are much farther out from the sun, at distances of about 9.5 and 19.2 AU, respectively, so the main belt is not located between these planets.

Hence, The main belt is not located between these all planets.

To know more about orbit visit,

https://brainly.com/question/18496962

#SPJ4

Answer:

33 , 39

Step-by-step explanation:

given

9 , 15 , 21 , 27

there is a common difference between consecutive terms, that is

15 - 9 = 21 - 15 = 27 - 21 = 6

to obtain terms in the sequence add 6 to the preceding term

27 + 6 = 33

33 + 6 = 39

the next two terms are 33 and 39

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

Read more about distance from angle of elevation at: https://brainly.com/question/25748640

#SPJ1

Answer:

45 hour GIVE BRAINLY PLZ

The magnitude of force is  364.65 Kg / ( m/s²)

An influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate.

given:

m = 85 Kg

a= 4.29 m/s²

We know

Force = mass x acceleration

F= 85 x 4.29

Force = 364. 65

Hence, the magnitude of force is 364.65 Kg / ( m/s²)

Learn more about force here:

https://brainly.com/question/21578845

#SPJ1

-4/3

For your question: Suppose cos(x) =1/(sqrt(5)) and sin(x) >0. What is the value of tan(2x)?

The value of tan(2x) is equal to -4/3

The polygon shown in the figure is the Rhombus.

What is a polygon?

A polygon is a closed figure made up of three or more line segments connected end to end.

Regular polygons have all side the same and that apothem bisects the side in two parts, (provable by symmetry).

A square is always a rectangle, parallelogram, rhombus and quadrilateral but its reverse statement may or may not be true.

A rhombus is a parallelogram but all sides of the same length.

An exterior angle is a measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended.

Hence the answer is the polygon shown in the figure is Rhombus.

To learn more about regular polygon click here https://brainly.com/question/1592456

#SPJ4

============================================================

Explanation:

He sold $4950 worth of items. Take 12% of this amount to get

12% of 4950 = 0.12*4950 = 594

So he earns $594 in commission on top of the $350 base salary paid every week. In total, he earns 594+350 = 944 dollars for that week

This isn't the per week pay because he would need to sell exactly $4950 worth of goods each week to keep this same weekly pay.

The area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangle is given as 3 cm and the width is given as 2 cm.

Area of the rectangle = Length * Width

Plugging in the given values:

Area = 3 cm * 2 cm

Multiplying 3 cm by 2 cm gives us:

Area = 6 cm²

Therefore, the area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².

The area of a rectangle represents the amount of space enclosed within its boundaries. In this case, since the rectangle is two-dimensional, the area is measured in square units, which in this case is square centimeters (cm²).

For more questions on rectangle

https://brainly.com/question/25292087

#SPJ8

Answer:

...

Step-by-step explanation:

,,,,,,,,,,,,,

Answer:

\(\huge\boxed{\sf 38}\)

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

The expression which has a negative value according to the number line drawn in the task content where points P and S are as given is; Choice D; P + 1.

It follows from the task content that the expression which has a negative value among the given answer choices is to be identified.

As evident in the number line, the number S is greater than 1, and hence, is a positive number.

Also, the number P is less than -1 and hence, is a negative number.

Since, the task content requires that the expression with negative value be identified, it follows that the required expression is; Choice D.

This follows from the fact that, hypothetically, the value of P is -1.8, hence; P + 1 = -1.8 + 1

= -0.8

Ultimately, The expression which has a negative value according to the number line drawn in the task content where points P and S are as given is; Choice D; P + 1.

Read more on number line;

https://brainly.com/question/28003708

#SPJ1

Answer:45%

Step-by-step explanation:

Answer:

C, 9

Step-by-step explanation:

Start by substituting. \(a-10b/c\) should turn into \(2 - 10(1/2) / -(1/3)\). Then do all the multiplying in the parentheses to get \(2-5/-(1/3)\). Subtract 2-5 to get \(-3/-(1/3)\). 1/3 goes into one three times, so it goes into three nine times. By negating both 1/3 and 3, the nine stays positive, so the answer is 9.

ANSWER:

STEP-BY-STEP EXPLANATION:

In an experimental design we have the following:

Explanatory variable: It is the variable that you manipulate or observe changes

Response variable: It is the result of the change given by the explanatory variable

Treatment: Specific condition applied to the individuals in an experiment

Experimental units are the individuals on which the experiment is done

Knowing the above, we can classify each part just like this:

With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5

Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Know more about triangle similarity here:

https://brainly.com/question/14285697

#SPJ1

Answer:3/4 * 1/5 = 3/20 = 0.15

Step-by-step explanation:Multiple: 3/

4 * 1/5 = 3 · 1/4 · 5 = 3/20

Multiply both numerators and denominators. The result fraction keep to the lowest possible denominator GCD(3, 20) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - three quarters multiplied by one-fifth is three twentieths.

For the system of equations, there are infinitely many solutions exist.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equations are,

⇒ - 2x + 2y = 10  .. (i)

⇒ y = x + 5  .. (ii)

Here, From (i) equation,

⇒ - 2x + 2y = 10

Take 2 as common,

⇒ 2 (- x + y) = 10

⇒ - x + y = 5

⇒ y = x + 5

Which is same as equation (ii).

Hence, There are infinitely many solutions exist.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

5 pages

Step-by-step explanation:

6 times 5 is 30

Answer:

Step-by-step explanation:

5

The general formula for simple interest I is;

Where;

I = the simple interest

P = Principal (in this case the initial deposit)

R = Rate per year

T = Time in years

For the given question, we are given the following;

So, substituting the given into the general formula for simple interest, we have;

Therefore, the interest she would be paid after 6 years is $1,200

Answer: 2x^3y^4 sqrt 2x or C on edge

Step-by-step explanation:

Answer:

I think x = 4.

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3x + x +10 + 5x + 2x + 2 =56

(3x + x + 5x + 2x) + (10 + 2) = 56 (Combine Like Terms)

11x + 12 = 56

11x + 12 = 56

Step 2: Subtract 12 from both sides.

11x + 12 − 12 = 56 − 12

11x = 44

Step 3: Divide both sides by 11.

11x/11 = 44/11

x = 4

The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

Learn more about system of equation on:

https://brainly.com/question/12526075