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2 years ago

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Point T is located at (6, –2) and point S is located at (1, 13). What are the coordinates of the point that is `\frac{4}{5}` of

the way from T to S?

1 answer:

vlabodo [156]2 years ago

7 0

The coordinates of the point that is 4/5 of the way from T to S is (2,10)

<h3>How to determine the coordinates of the point?</h3>

The given parameters are:

T = (6,-2)

S = (1,13)

Location = 4/5

The location 4/5 means

Ratio, m : n = 4 : 1

The coordinate is then calculated as:

$(x,y) = \frac{1}{m +n} * (mx_2 + nx_1,my_2 + ny_1)$

This gives

$(x,y) = \frac{1}{4 +1} * (4 * 1 + 1 * 6 , 4 * 13 + 1 * -2)$

Evaluate

$(x,y) = \frac{1}{5} * (10 , 50)$

This gives

(x,y) = (2,10)

Hence, the coordinates of the point that is 4/5 of the way from T to S is (2,10)

Read more about line segment ratio at:

brainly.com/question/12959377

#SPJ1

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To help with her retirement savings, Donna has decided to invest. Assuming an interest rate of 3.59% compounded quarterly, how m

cricket20 [7]

Answer:

We get the value of Principal amount i.e initial investment = $61640

Step-by-step explanation:

Interest rate r = 3.59% or 0.0359

Compounded quarterly n = 4

Future Amount A = 117,300

Time t = 18 years

We need to find initial investment i,e Principal Amount P

The formula used is: $A=P(1+\frac{r}{n})^{nt}$

Putting values and finding P

$A=P(1+\frac{r}{n})^{nt}\\117300=P(1+\frac{0.0359}{4})^{4*18} \\117300=P(1+0.008975)^{72}\\117300=P(1.008975)^{72}\\117300=P(1.903)\\P=\frac{117300}{1.903}\\P=61640$

So, We get the value of Principal amount i.e initial investment = $61640

7 0

3 years ago

The sum of a number and 17 is no less than 26

Tema [17]

We put this into an algebraic equation, where <span>x = the number .
x + 17 > 26
x > 9

This </span>> is the greater than sign, we use this because it's no less than 26.
Ideally we would use this sign:
<span>http://etc.usf.edu/clipart/41700/41712/fc_greateq_41712_md.gif
because it could be equal to 26.

</span><span>The number is <u>greater or equal to 9</u>

</span>

6 0

4 years ago

Read 2 more answers

Let |u| = 10 at an angle of 45° and |v| = 13 at an angle of 150°, and w = u + v. What is the magnitude and direction angle of w?

mixer [17]

Given:

$|u|=10$ at an angle of 45°.

$|v|=13$ at an angle of 150°.

$w=u+v$

To find:

Magnitude and direction angle of w.

Solution:

We have,

$w=u+v$

$\theta = 45^\circ, \phi = 150^\circ$

Now,

$u_x=|u|\cos \theta=10\cos 45^\circ=7.071$

$u_y=|u|\sin \theta=u_y=10\sin 45^\circ=7.071$

$v_x=|v|\cos \phi=13\cos 150^\circ=-11.25833$

$v_y=|v|\sin \phi=u_y=13\sin 150^\circ=6.5$

Using these information, we get

$R_x=u_x+v_x=7.071-11.25833=-4.18733$

$R_y=u_y+v_y=7.071+6.5=13.571$

$\text{Direction angle}=\tan^{-1}(\dfrac{R_y}{R_x})$

$\text{Direction angle}=\tan^{-1}(\dfrac{13.571}{-4.18733})$

$\text{Direction angle}=-72.8239$

$\text{Direction angle}=107.1476$

$\text{Direction angle}\approx 107.1$

Now,

$|w|=\sqrt{(|u|\cos \theta +|v|\cos \phi)^2+(|u|\sin \theta +|v|\sin \phi)^2}$

$|w|=\sqrt{(10\cos(45)+13\cos 150)^2+(10\sin(45)+13\sin 150)^2}$

$|w|=\sqrt{(10(\dfrac{1}{\sqrt{2}})+13(-\dfrac{\sqrt{3}}{2}))^2+(10(\dfrac{1}{\sqrt{2}})+13(\dfrac{1}{2}))^2}$

$|w|=14.20236$

$|w|\approx 14.20236$

Therefore, the correct option is D.

4 0

3 years ago

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What is the value of tan (B) in the diagram?

hodyreva [135]

Answer:

The correct answer is third option

1/√3

Step-by-step explanation:

From the figure we can see a right angled triangle ABC.

Right angled at C.

AB = 10

AC = 5

BC = 5√3

<u>Points to remember</u>

Tan θ = Opposite side/Adjacent side

<u>To find the value of tan(B)</u>

Tan B = Opposite side/Adjacent side

= AC/BC

= 5/5√3

= 1/√3

Therefore the value of tan(B) = 1/√3

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4 years ago

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A telemarketing company had a loss of $2113.15 in July, a loss of $597.11 in August, and a profit of

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Yes , -2113.15 + (-597.11) + 4121.55 = 1411.29 so the total profit was 1411.29

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3 years ago