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3 years ago

Please tell me the vertex, axis is symmetry, and the x and y intercepts. ANSWER FAST PLEASE!!

Mathematics

1 answer:

QveST [7]3 years ago

8 0

The y intercept is -2. There is two x- intercepts because it is a parabola so,

x=-1

x=2

The axis of symmetry is where it splits evenly so, we can conclude it is less than 1 and bigger than 0. I hope this makes sense.

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2. Consider the circle x² + y2 = 1, given in figure. Let OP makes an angle 30° with the x axis.

PolarNik [594]

The equation of the tangent line to the circle passing through the point P is; y = (1/√3)x ± 2/√3

<h3>How to find the equation of the tangent?</h3>

I) We are given the equation of the circle as;

x² + y² = 1

Since angle of inclination is 30°, then slope is;

m = tan 30 = 1/√3

Then equation of the tangent will be;

y = (1/√3)x + c

Put (√3)x + c into the given circle equation to get;

x² + ((1/√3)x + c)² = 1

x² + ¹/₃x² + (2/√3)cx + c² = 1

⁴/₃x² + (2/√3)x + (c² - 1) = 0

Since we need to find value of c for equation to become tangent, then the above quadratic equation must have real and equal roots.

Thus;

((2/√3)c)² - 4(⁴/₃)(c² - 1) = 0

⁴/₃c² - ¹⁶/₃(c² - 1) = 0

⁴/₃c² - ¹⁶/₃c² + ¹⁶/₃ = 0

4c² = ¹⁶/₃

c² = ⁴/₃

c = √⁴/₃

c = ±²/√3

Thus, equation of tangent is;

y = (1/√3)x ± 2/√3

II) Radius from the given equation is 1. Thus, we will use trigonometric ratio to find the x and y intercept;

x-intercept is at y = 0;

0 = (1/√3)x ± 2/√3

-(1/√3)x = ±2/√3

Intercept is positive. Thus;

x = (2/√3)/(1/√3)

x = 1

y - intercept is positive at x = 0;

y = (1/√3)0 ± 2/√3

y = 2/√3

Read more about Equation of tangent at; brainly.com/question/17040970

#SPJ1

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2 years ago

Suppose Jessica opens a savings account with $5000 that compounds interest daily. The APR at the time Jessica opens the account

IrinaK [193]

Hi there

1+0.035=(1+r/360)^360
Solve for r
R=(((1.035)^(1÷360)−1)×360)×100
R=3.44%

6 0

3 years ago

Will mark you brainliest

kumpel [21]

Answer: 37%

Step-by-step explanation:

4 0

3 years ago

What is the area of the composite figure

kati45 [8]

To solve this we will divide the given composite figure into three figures. The three figures will be 2 squares and 1 rectangle. Let's find their areas and add them!

$\boxed{ \sf \: area \: of \: square =side ^{2} }$

Side 3 metre

$\rm \implies \: area = 3 ^{2}$

$\rm \implies9$

<em>Thus, The area of 1st square is 9m²...</em>

The area of second square will be also 9m², because the sides of both squares are equal.

<h3>Now area of the reactangle⤵️</h3>

Length = 6m
Breadth = 7+3=10m

$\sf \: area \: of \: rectangle = length \times breadtg$

$\tt \dashrightarrow \: area = 10 \times 3$

$\tt \dashrightarrow \: area = 30m ^{2}$

<em>Thus, The area of rectangle is 30m²....</em>

Now, Add area of all the figures to get the total area.

$\bf \:total \: area = 9 + 9 + 30 \\ \bf= 48m {}^{2}$

<h3><em>Therefore, The total area of the composite figure is 48m²...~</em></h3>

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2 years ago

Use the triangles below to find the<br> trigonometric ratios.

anzhelika [568]

Hi I did my working on paper. You can see it in the photo.

6 0

2 years ago