The figures are similar. Find x.

Mathematics

1 answer:

kipiarov [429]3 years ago

6 0

6/9=x/21
x=21*6/9
=126/9
x=14

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What point is 2/3 of the distance from point A(3, 1) to point B(3, 19)?

8_murik_8 [283]

Answer: (3, 13)

Step-by-step explanation:

If we let the point be P, then AP:BP=2:1.

$P=\left(\frac{(2)(3)+(1)(3)}{2+1}, \frac{(2)(19)+(1)(1)}{2+1} \right)=(3, 13)$

5 0

2 years ago

Please help solve for PQ.

DerKrebs [107]

This problem cannot be solved unless we are given figure NPQR is a rhombus.
In that case, then all sides are equal, meaning
5x+16=9x-32
Solve for x
9x-5x=16+32
4x=48
x=12

Each side (including PQ) then equals 5x+16=5*12+16=76

8 0

3 years ago

Xy=22 as a proportion please! :)

Elina [12.6K]

I’m sorry if I’m wrong but I do think your answer is X=22y^-1

5 0

1 year ago

Read 2 more answers

A box has a volume of 546cm3 and a surface area of 422cm2. What are the Length, Width and Height?

Klio2033 [76]

We know that the formula for the volume of a box is:

$V =lwh$

Where:
l = length
w = width
h = height

The formula of the surface area of a box is:
$SA=2(lw+lh+wh)$

Based on the given we know the following:
$546cm^{3} =lwh$

and

$422cm^{2}=2(lw+lh+wh)$

If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:

$546=6*7*13$

Let:
l = 6cm
w = 7cm
h = 13cm

Now let's try this on the surface area formula:
$422cm^{2}=2(lw+lh+wh)$
$422cm^{2}=2((6cm*7cm)+(6cm*13cm)+(7cm*13cm))$
$422cm^{2}=2(42cm^{2}+79cm^{2}+91cm^{2})$
$422cm^{2}=2(211cm^{2})$
$422cm^{2}=422cm^{2}$

The answer is then:
l = 6cm
w = 7cm
h = 13cm

Any order would be fine.

4 0

3 years ago

A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between

vagabundo [1.1K]

What we know so far:
Side 1 = 55m
Side 2 = 65m
Angle 1 = 40°
Angle 2 = 30°

What we are looking for:
Toby's Angle = ?
The distance x = ?

We need to look for Toby's angle so that we can solve for the distance x by assuming that the whole figure is a SAS (Side Angle Side) triangle.

Solving for Toby's Angle:
We know for a fact that the sum of all the angles of a triangle is 180°; therefore,
180° - (Side 1 + Side 2) = Toby's Angle
Toby's Angle = 180° - (40° + 30°)
Toby's Angle = 110°

Since we already have Toby's angle, we can now solve for the distance x by using the law of cosines r² = p²+ q²<span>− 2pq cos R where r is x, p is Side1, q is Side2, and R is Toby's Angle.
</span>
x² = Side1² + Side2² - 2[(Side1)(Side2)] cos(Toby's Angle)
x² = 55² + 65² - 2[(55)(65)] cos(110°)
x² = 3025 + 4225 -7150[cos(110°)]
x² = 7250 - 2445.44
x = √4804.56
x = 69.31m

∴The distance, x, between two landmarks is 69.31m

8 0

3 years ago