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3 years ago

7

Find the length of x

1 answer:

IRISSAK [1]3 years ago

3 0

To solve you insert into proportions, then cross-multiply and simplify.
But first, add 5 and 6 to get the full side length of the bigger triangle

$\frac{x}{5} x \frac{5.5}{11}$

11x = 27.5
x = 2.5

Hope this helps!

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marusya05 [52]

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2 years ago

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Write the equation in vertex form and then find the vertex, focus, and directrix of a parabola with equation x=y^2+18y-2

kakasveta [241]

Answer:

Part 1) The vertex is the point (-83,-9)

Part 2) The focus is the point (-82.75,-9)

Part 3) The directrix is $x=-83.25$

Step-by-step explanation:

step 1

Find the vertex

we know that

The equation of a horizontal parabola in the standard form is equal to

$(y - k)^{2}=4p(x - h)$

where

p≠ 0.

(h,k) is the vertex

(h + p, k) is the focus

x=h-p is the directrix

In this problem we have

$x=y^{2} +18y-2$

Convert to standard form

$x+2=y^{2} +18y$

$x+2+81=y^{2} +18y+81$

$x+83=(y+9)^{2}$

so

This is a horizontal parabola open to the right

(h,k) is the point (-83,-9)

so

The vertex is the point (-83,-9)

step 2

we have

$x+83=(y+9)^{2}$

<em>Find the value of p</em>

$4p=1$

$p=1/4$

<em>Find the focus</em>

(h + p, k) is the focus

substitute

(-83+1/4,-9)

The focus is the point (-82.75,-9)

step 3

Find the directrix

The directrix of a horizontal parabola is

$x=h-p$

substitute

$x=-83-1/4$

$x=-83.25$

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3 years ago

Marat540 [252]

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2 years ago

In kite PQRS , TQ=3 cm and TP=4 cm. What is SP ? Enter your answer in the box.

yawa3891 [41]

Answer:

Kite is a quadrilateral in which two disjoint pairs of consecutive sides are congruent

Given: In kite PQRS

where PR and SQ are the diagonals of Kite respectively as shown in the figure given below.

Given: TQ = 3 cm and TP = 4 cm

Let PR is the main diagonal and SQ is the cross diagonal of kite PQRS as shown in figure, also let T is the intersection point of PQRS.

By Property of Kite, diagonal SQ bisects PR at perpendicular angle i.e, 90 degree.

i,e

Then, in right angle ΔQTP

$PQ = \sqrt{TQ^2+TP^2}$ [Using Pythagoras theorem]

Substitute the given values of TQ and TP we have;

$PQ = \sqrt{3^2+4^2} =\sqrt{9+16} =\sqrt{25} = 5 cm$

Also, PQ = SP [by definition of kite]

therefore, the side SP = 5 cm.

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2 years ago

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