Characterize the slope of the line in the graph.​

#1

False

#2

False

#3

False

None of the above

Answer:

None of these

Step-by-step explanation:

To convert the parametric curve into Cartesian form,
rewrite the equation for [tex]x[/tex] to make [tex]\sin t[/tex] the subject:

[tex]x=2\sin t[/tex]

[tex]\implies \sin t=\dfrac{x}{2}[/tex]

Substitute this into the given equation for [tex]y[/tex]:

[tex]\begin{aligned}y & =3 \sin t\\\implies y & = 3 \left(\dfrac{x}{2}\right)\\y& = \dfrac{3}{2}x\end{aligned}[/tex]

Therefore, the Cartesian form of the parametric curve is:

[tex]y=\dfrac{3}{2}x[/tex]

Further Information

[tex]\dfrac{x^2}{2}+\dfrac{y^2}{3}=1 \quad \textsf{is the equation of a vertical ellipse}[/tex]

[tex]\textsf{with center (0, 0), co-vertex }\sf \sqrt{2}, \textsf{ and vertex }\sqrt{3}[/tex]

[tex]x^2+y^2=6 \quad \textsf{is the equation of a circle}[/tex]

[tex]\textsf{with center (0, 0) and radius }\sf \sqrt{6}[/tex]

[tex]3x^2+2y^2=1 \quad \textsf{is the equation of a vertical ellipse}[/tex]

[tex]\textsf{with center (0, 0), co-vertex }\sf \dfrac{\sqrt{3}}{3}, \textsf{ and vertex }\dfrac{\sqrt{2}}{2}[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Concept : As we know, Angle made by an arc on the centre of the circle is double the angle made by the same arc on the part of circle.

Therefore, we can infer that :

[tex]\qquad \sf  \dashrightarrow \:\angle O= 2 × \angle R[/tex]

[tex]\qquad \sf  \dashrightarrow \:\measuredangle O= 2 × 28 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \:\measuredangle O= 56 \degree[/tex]

I hope that helps ~

Answer:

C. y = -9x - 8

Step-by-step explanation:

Setting up the equation:

eight LESS (so minus sign before the 8) THAN (so 8 is being subtracted from the -9x) negative (-) nine TIMES (multiplication) a number, (variable) x.

We want to get the variable y alone, so this can be written as y = -9x - 8

The circumference of the circle is about 339 cm.

The area of the circle is about  9, 156 cm∧ 2

NOTE :

The circumference of a circle is known to be the perimeter of the circle.

It is determined using ;

Circumference, C = 2 π r

The area of a circle is known to be the axis occupied by the circle in a two-dimensional plane.

It is determined using ;

Area, A = π r ∧2

How to determine the area and circumference of a circle

Parameters:

π = 3.14

radius, r =54 cm

Circumference, C = 2 π r = 2 × 3.14 × 54 = 339. 12 cm

Circumference , C in the nearest hundredth = 339 cm

Area, A = π r∧ 2 = 3. 14 × 54 × 54 =  9,156.24 cm∧ 2

Area, A in the nearest hundredth = 9,156 cm∧2

Thus, the circumference of the circle in the nearest hundredth is 339cm and the area of the circle in the nearest hundredth is 9, 156 cm∧2

Answer:

Relative frequency for each discount :

10% - 0.4925, 20% - 0.3325, 40% - 0.175

Since only 33.25% of customers got 20% discount, it is not an appropriate method.

Step-by-step explanation:

relative frequency = number of frequency/total number of frequency

you can find out relative frequency for each number and add them up to get relative frequencies of discounts.

Answer:

1) 9y^10

2) 560u^16 v^15

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Because your total is 182 desserts and you want to arrange them into 13 rows you will divide the two numbers. So, 182/13 is 14. so 14 is your answer.

Hope that helped

Answer:

14 Tropical cupcakes per row

Hope this helped :)

Step-by-step explanation:

182 ÷ 13 = 14

Check:

14 × 13 = 182 ✓

Answer:

19 %

Step-by-step explanation:

589 is what percetage of 3100?

589 / 3100  * 100 % = 19%

Answer:

19%

Step-by-step explanation:

589 = x% of 3100?

589 / 3100  * x/100= 19%

Hopefully this helped you, and have a good day!

Answer:

A is the answer

Step-by-step explanation:

3×5+6=15+6=21

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

      Find the slope of the line that passes through (10, 7) and (3, 15).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

We can find the slope using the following formula:-

[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]

Replace the letters with numbers:-

[tex]\boxed{\frac{15-7}{3-10}}[/tex]

[tex]\bigstar[/tex] On simplification,

[tex]\boxed{\frac{8}{-7}}[/tex]

[tex]\bigstar[/tex] The slope is

[tex]\boxed{-\frac{8}{7}}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

s = 132 square cm

Step-by-step explanation:

s = area of base + area of lateral faces

Area of base (triangle)

A = 1/2bh

A = 1/2(3)(4)

A = 1/2(12)

A = 6

There are two bases (triangles), so multiply the answer by 2.

6 x 2 = 12

Area of lateral faces (3 rectangles)

First rectangle:

A = lw

A = 5(10)

A = 50

Second rectangle:

A = lw

A = 4(10)

A = 40

Third rectangle:

A = lw

A = 3(10)

A = 30

Add all the areas together.

s = 12 + 30 + 40 + 50

s = 132 square cm

Answer:

The answer is Vertex

Step-by-step explanation:

Answer: height of a building

Step-by-step explanation:

a^2 + b^2 = c^2

used for finding missing side angle of a triangle

Step-by-step explanation:

Represent D and E as x because you don't know them

Now the sum of all these angles is 180

so,D+E+90(THE SIGN AT THE TOP)=180

D which is x the E which is also x

x+x+90=180

2x+90=180

2x=180-90

2x=90

[tex] \frac{2x}{2} = \frac{90}{2} [/tex]

cancel and you will get x as 45

therefore x is 45 degrees

Answer: Either angle QPO or  angle OPQ

Explanation:

When naming an angle, we always have the vertex as the middle letter. That vertex is P. It's where the two rays are joined.

So we could have the name "angle QPO" or "angle OPQ" since the order of the other letters doesn't matter. All that we care about is P is in the middle.

Answer:

Mean-average

Median-middle

Mode-Most Often Digit Entered (Most Common Digit)

Range-Least To Greatest

Step-by-step explanation:

Based on the Gauss-Jordan Elimination method, and the matrix given, the next step would be to b. divide R2 by 2 and R3 by 3.

The first row has already gone as low as it can so rows two and three need to be worked on.

The best way to do this is to divide Row 2 by 2 and Row 3 by 3. This then leads to the augmented matrix becoming:

[1    0     0   I  5]

[0    1     0   I  4]

[0    0    1    I  3]

In conclusion, option B is correct.

Find out more on the Gauss-Jordan Elimination method at https://brainly.com/question/12090959.

#SPJ4

The quadratic expression cannot be factorized, because the discriminant is less than 0

The expression is given as:

x²+12x+180

Calculate the discriminant of the expresison using:

D = B² - 4AC

So, we have:

D = 12² - 4* 1 * 180

Evaluate

D = -576

Because the discriminant is less than 0, then the expression cannot be factorized

Read more about quadratic expressions at:

https://brainly.com/question/8649555

#SPJ1

Answer:

Step-by-step explanation:

The task is to draw the parabola of the equation [tex]x^{2} -4x+4[/tex] on the given graph.

The first step we can take to doing this is to use the table on the left hand side to work out our x and corresponding y-values to use as plotting coordinates. To do this you want to substitute the given value for x which will give you a corresponding y-value.

E.g:

x | [tex]x^{2} -4x+4[/tex]      | y

0 | [tex](0)^{2} -4(0)-4[/tex] | -4

Here we have gotten the coordinates (0, -4) so this will be a point on the graph.

Repeat with all other values on the table and you should get a bunch of dots which lead upwards in a curved line from a point. Extend the lines to form a parabola shape (A u-shape).

Once you have drawn the graph, label the parts.

Roots: The places where the line crosses the x-axis

Vertex: The lowest point of the parabola

Line of symmetry: The vertical line in which the parabola reflects/ is the same either side (Has equation x=_).

y-intercept: The point where the line crosses the y-axis.

Hope this helped!

Answer:

see the attachment.

Answer:

C, -1.5

Step-by-step explanation:

edge

Answer:

Exterior angle = sum of opposite interior angles

Step-by-step explanation:

Answer:

1st option y-5 = 3(x-1)

Step-by-step explanation:

graph shows y intercept of 2

1st option has a y intercept of 2

Answer:

Option 1

Step-by-step explanation:

Clearly, the slope of the line is 3. (As it cannot be negative in this case and it's more vertical so it's not 1/3)

The point slope form is written as :

y - y₁ = m(x - x₁)

Substituting m = 3 :

y - y₁ = 3(x - x₁)

Option 1 is the only option with the value of m as 3.

Answer:

540

Step-by-step explanation:

If you divide 540 by 100 (100%) you get 5.4 then multiply it by 10 (10%) to get 54 again. THIS WAS TO CHECK TO GET: 10% or 100% is 10 so multiply 54•10=540

Hope this helps! ;-)

Answer:

Step-by-step explanation:

To get the final answer, isolate the variable y on one side of the equation.

First, multiply by 4 from both sides.

[tex]\Longrightarrow: \sf{4*\dfrac{1}{4}y\geq 8*4 }[/tex]

Solve.

8*4=32

[tex]\boxed{\sf{y\geq 32}}[/tex]

I hope this helps, let me know if you have any questions.

Answer:

  (c)  2205 cm³

Step-by-step explanation:

The volume of the original prism is the product of its dimensions. The volume of one of two identical pieces will be half that.

__

  V = LWH

  V = (21 cm)(21 cm)(10 cm) = 4410 cm³

Each piece will have a volume that is half that:

  V = 4410 cm³ ÷ 2 = 2205 cm³ . . . volume of each part

Answer:

[tex]A = 66\ yd^2[/tex]

Step-by-step explanation:

You can either add up all the areas of the faces of the rectangular prism, or you can use the following formula:

[tex]A = 2(wl+hl+hw)\\A = 2(3 \times 3 + 4 \times 3 + 4 \times 3)\\A = 2(9+12+12)\\A = 2(33)\\A = 66[/tex]

Answer:

The surface area of the rectangular prism is [tex]66\ yd^2[/tex]

Step-by-step explanation:

Step 1:  Find the area of the front and back

[tex]A = l * w[/tex]

[tex]A = 3\ yd * 4\ yd[/tex]

[tex]A = 12\ yd^2 * 2[/tex]

[tex]A = 24\ yd^2[/tex]

Step 2:  Find the area of the top and bottom

[tex]A = l * w[/tex]

[tex]A = 3\ yd * 3\ yd[/tex]

[tex]A = 9\ yd^2 * 2[/tex]

[tex]A = 18\ yd^2[/tex]

Step 3:  Find the area of the left and right sides

[tex]A = l * w[/tex]

[tex]A = 3\ yd * 4\ yd[/tex]

[tex]A = 12\ yd^2 * 2[/tex]

[tex]A = 24\ yd^2[/tex]

Step 4:  Total area

[tex]A_{total} = 24\ yd^2 + 18\ yd^2 + 24\ yd^2[/tex]

[tex]A_{total}= 66\ yd^2[/tex]

Answer:  The surface area of the rectangular prism is [tex]66\ yd^2[/tex]