9a^4+3a^2+21 please answer

A triangle PQR is right angled at R, with PQ=80cm and R=60cm. find QR? pythagorus theorem

algol13

Answer:

Solution given:

A triangle PQR is right angled at R, with hypotenuse{h}PQ=80cm

and

base[b]PR=60cm.

perpendicular [P]= QR

by using Pythagoras law

h²=p²+b²

80²=QR²+60²

QR²=80²-60²

QR= $\sqrt{2800}$

QR=20 $\sqrt{7}$ =52.9=53cm

QR=53cm.

5 0

3 years ago

Molly, a purchasing agent for a high-tech firm, is ordering computers for a new branch office. Laptops cost $540 apiece and desk

NISA [10]

Answer:

540x+680y<=20000

Step-by-step explanation:

x will be the number of laptops. Since they are $540 each, 540x is the amount spent on laptops, depending on how many (x) are purchased.

y will be the number if desktops. Since they are $680 each, 680y is the amount spent on desktops, depending on how many (y) are purchased.

Adding all the money spent on laptops and desktops, we get

540x + 680y. This amount must be less than the $20000. It can be exactly $20000 also. But it cannot be more than $20000.

540x+680y<=20000

3 0

2 years ago

Let v1 =(-6,4) and v2=(-3,6) compute the following what i sthe angle between v1 and v2

Agata [3.3K]

$\bf ~~~~~~~~~~~~\textit{angle between two vectors }
\\\\
cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\stackrel{\textit{magnitude product}}{||u||~||v||}} \implies 
\measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right)\\\\
-------------------------------$

$\bf \begin{cases}
v1=\ \textless \ -6,4\ \textgreater \ \\
v2=\ \textless \ -3,6\ \textgreater \ \\
------------\\
v1\cdot v2=(-6\cdot -3)+(4\cdot 6)\\
\qquad \qquad 42\\
||v1||=\sqrt{(-6)^2+4^2}\\
\qquad \sqrt{52}\\
||v2||=\sqrt{(-3)^2+6^2}\\
\qquad \sqrt{45}
\end{cases}\implies \measuredangle \theta =cos^{-1}\left( \cfrac{42}{\sqrt{52}\cdot \sqrt{45}} \right)
\\\\\\
\measuredangle \theta =cos^{-1}\left( \cfrac{42}{\sqrt{2340}} \right)\implies \measuredangle \theta \approx 29.74488129694^o$

8 0

3 years ago

1. You have $10 saved. Each week you receive $5 in allowance. Let x represent the number of weeks you

bazaltina [42]

That looks hard sorry I don’t know answer good luck

7 0

3 years ago

Read 2 more answers

1. Assume O P || NM.

ipn [44]

1. Assuming OP || NM, considering the triangle proportionality theorem possible measurements for the segments are: ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units

2. The possible values are decided by assuming $\frac{ON}{LO} = \frac{PM}{LP} = 3$ using the triangle proportionality theorem.

3. Another method is applying the AA Similarity Theorem to compare corresponding side lengths of the triangles that are proportional to each other.

<h3>What is the Triangle Proportionality Theorem?</h3>

Triangle proportionality theorem states that if a line is parallel to one of the sides of a triangle intersects two of the other two sides, it divides the two sides into proportional corresponding segments.

1. Assuming that OP || NM, we would apply the triangle proportionality theorem to have the following ratio:

$\frac{ON}{LO} = \frac{PM}{LP}$

Using the above ratio, we can choose the following possible lengths for the segments:

ON = 3 units

LO = 1 unit

PM = 6 units

LP = 2 units

2. The values are decided assuming that the ratio, $\frac{ON}{LO} = \frac{PM}{LP} = 3$

This means that the ratio of the proportional segments, irrespective of the their measurement should give you an assumed equal ratio of 3:1.

Therefore, since:

$\frac{3}{1} = 3\\\\\frac{6}{2} = 3$

The measurements, ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units are therefore possible measurements.

3. Using the AA Similarity Theorem to prove that ΔLPO ≅ ΔLMN, the corresponding sides of both triangles will be proportional.

LP/LM = LO/LN = PO/MN

We can use this to choose possible measurements while assuming a ratio between the proportional sides of both triangles.

Let's assume that: LP/LM = LO/LN = PO/MN = 1/4

Let,

LO = 1 unit

LN = 4 units

Therefore, ON = LN - LO = 4 - 1 = 3 units.

Same way the other possible measures can be gotten provided a ratio is assumed.

Learn more about triangle proportionality theorem on:

brainly.com/question/24804474

4 0

2 years ago