Find an equation for the line with the given properties. Express the equation in slope-intercept form.
Containing the points P = (-3,1) and Q = (-1,0). What is the equation of the line?
y =

Answer:

A

Step-by-step explanation:

To simplify the expression multiply the numerator and denominator by the conjugate of the denominator.

Note that i² = - 1

The conjugate of 6 - 4i is 6 + 4i , then

= [tex]\frac{(4-3i)(6+4i)}{(6-4i)(6+4i)}[/tex] ← expand numerator./ denominator using FOIL

= [tex]\frac{24+16i-18i-12i^2}{36+24i-24i-16i^2}[/tex]

= [tex]\frac{24-2i+12}{36+16}[/tex]

= [tex]\frac{36-2i}{52}[/tex]

= [tex]\frac{2(18-i)}{52}[/tex]

= [tex]\frac{18-i}{26}[/tex] → A

Answer:

SSS

Step-by-step explanation:

We do not know any of the angles, and we also do not know if the triangles are right triangles. Thus, SSS is the only option left. We know that all three sides are congruent anyway.

Answer:

SSS

Step-by-step explanation:

AC = OD

AT = OG

CT = DG

You have three congruent sides making ΔACT & ΔODG congruent by SSS.

Answer:

1/8 of a chance to flip 3 coins and get that exact combination in that order

Explanation:

a coin has 2 sides, heads and tails, with an equal chance to land on each of them. 1/2 chance to get tails on the first flip x  1/2 chance to get heads on the second flip x 1/2 chance to get tails on the third flip. 1/2 x 1/2 x 1/2 = 1/8.

Answer:

Step-by-step explanation:

$13.1

Answer:

210*pi

Step-by-step explanation:

Surface area=2*pi*r*(r+h)

=2*pi*5*(21)=210*pi

Answer:

see explanation

Step-by-step explanation:

The sum to n terms of a geometric series is

[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]

where a₁ is the first term and r the common ratio

Given a₁ = 3 and r = - 2 , then

3 × - 2 = - 6

- 6 × -2 = 12

12 × - 2 = - 24

- 24 × - 2 = 48

48 × - 2 = - 96

- 96 × - 2 = 192

The positive terms are in a geometric progression

3, 12, 48, 192, ....

with a₁ = 3 and r = 12 ÷ 3 = 48 ÷ 12 = 4 , then

S₈ = [tex]\frac{3(4^{8}-1) }{4-1}[/tex] = [tex]\frac{3(65536-1)}{3}[/tex] = 65536 - 1 = 65535

Answer:

It's 13.2

Step-by-step explanation:

From pythogras theorem:

[tex]{ \bf{ {a}^{2} = {b}^{2} + {c}^{2} }}[/tex]

[tex] = \sqrt{ {20}^{2} - {15}^{2} } \\ = \sqrt{175} \\ = 13.2[/tex]

Answer:

62 ft

i know its a late answer but i just did the test

If the length of ST is 62 feet the length of RS or the distance across a body of water will also be 62 feet.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅. When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

It is given that the length of s ST is 62 feet and PS = PQ.

The measurements of the sides and angles of two or more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. If the pairs of corresponding sides and angles of two triangles are equal, they are said to be congruent.

Since the one angle in both triangles is 90° and the two sides are equal the two triangles are equal.

The ratio of the sides is equal if the triangle is congruent. As a result,

PS / PQ = RS / ST

1 = RS / ST

RS =  ST

RS = 62 feet

Thus, if the length of ST is 62 feet the length of RS or the distance across a body of water will also be 62 feet.

Learn more about the congruent triangle here:

brainly.com/question/12413243

#SPJ5

Answer:

13

Step-by-step explanation:

The average rate of change is

f(7) - f(1)

---------------

7-1

f(7) = 7^2 + 5*7 +14 = 49 +35 +14=98

f(1) = 1^2 +5(1)+14 = 1+5+14=20

98-20

--------

7-1

78/6

13

Answer: x  ≈  1.59688927,  −1.60312387,  −4.67045686,  4.69039614,  7.872914,  −7.91513776,  −10.89002194

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Simplify 2*cosx*(2x+30°) + √3=0

    Simplify each term.  

       Apply the distributive property.

Answer:

Step-by-step explanation:

please click thanks and mark brainliest if you like :)

Answer:

RS, RT, ST

Step-by-step explanation:

We require the third angle in the triangle

∠ T = 180° - (92 + 71)° = 180° - 163° = 17°

The shortest side is opposite the smallest angle

∠ T = 17° → opposite side RS

The longest side is opposite the largest angle

∠ R = 92° → opposite side ST

Then sides from shortest to longest is

RS, RT, ST

If you double each side the volume is 8 times

Must click thanks and mark brainliest

Answer: 96

Step-by-step explanation:

This equation helps

X / 100 = is / of

32/100 = X / 300 (cross multiplication)

32 times 300, divided by 100

= 96

Answer:

96

Step-by-step explanation:

every percent is out of hundred so (32 * 300)/100 = 96

Answer:

-80

Step-by-step explanation:

We can write the quadratic as

ax^2 + bx+c

4x^2 +8x+9

a=4  b = 8  c=9

The discriminant is

b^2 -4ac

8^2 - 4(4)(9)

64 - 144

-80

Answer:

-80

Step-by-step explanation:

The discriminant is the value under the radical in the quadratic formula. The part of the quadratic formula that is under the radical is [tex]\sqrt{b^2-4ac}[/tex]. So, plug in the needed values and solve for what is under the radical. The b-value is 8; this squared is 64. Then, plug in a and c, 4 and 9. Then multiply these by 4, 4*4*9=144. Finally subtract, 64-144=-80.

Answer:

Step-by-step explanation:

(A). y = 110 , z = 63

Answer:

BC = 29.4

Step-by-step explanation:

30² = 20² + BC² -2•20•BC•cos(108)

900 = 400 +BC² -12.4•BC

900 -400 = BC² -12.4•BC

BC² -12.4•BC -500 = 0

Solve the equation using Bhaskara and you'll find two possible values for BC, which are:

BC = -17 and BC = 29.4

A negative number doesn't make sense because it is a side of a triangle, so we choose BC = 29.4

Answer:

3.

Step-by-step explanation:

p(x) + q(x)

= -x^3 - 7x^2 - 9x - 4

- whose degree is 3   ( the highest index is 3)

Answer:

It's option D. -3 ± √5x+7/2

See the images below for step by step explanation. I also included a graph for better understanding of the inverse.

Answer:

25 x^2 + 30 x + 12

Parcelas

Plots

Parcelas

Figura geométrica

parabola

Formas alternativas

x (25 x + 30) + 12

(5 x + 3)^2 + 3

5 x (5 x + 6) + 12

Raíces complejas

x = -1/5 i (sqrt(3) + -3 i)

x = 1/5 i (sqrt(3) + 3 i)

Step-by-step explanation:

Answer:

a= 75°

β= 30°

Step-by-step explanation:

α = 75° This is because triangle PQR isosceles. Thus two of its angles are equal and these two are angle α and the one labelled 75.

β = 30° This is because angles in a triangle sum up to 180°. We already know two of these angles. To find β you say 180 - ( 75 × 2)

The answer becomes 30°.

HOPE THIS HELPED

Answer:

d no.

Step-by-step explanation:

because in my my personal opinion the function shown on the graph has a smaller rate of change, but a higher starting point

Answer:

Hello

answer :B and C

Step-by-step explanation:

√25=5 is an integer

b) is not an integer

c) is not an integer=0.75

d) is an integer

================================================

Explanation:

Plug in x = 3 to get

h(x) = x^2 + 10x + 32

h(3) = 3^2 + 10*3 + 32

h(3) = 71

Repeat for x = 11

h(x) = x^2 + 10x + 32

h(11) = 11^2 + 10*11 + 32

h(11) = 263

Now use the average rate of change formula

m = average rate of change

m = ( h(b) - h(a) )/(b - a)

m = ( h(11) - h(3) )/(11 - 3)

m = (263 - 71)/(11 - 3)

m = 192/8

m = 24

Answer:

-9

Step-by-step explanation:

Since the signs are different, subtract the two numbers and take the sign of the larger number

78 - 69

9

Since 78 is the larger number and it was negative

-9

Answer:

-9

Step-by-step explanation:

-78+69

=-9

happy to help

Answer:

18

Step-by-step explanation:

To find this answer you would need to use the formula x(x+2) = 360 where x is an even number.  This is the formula because any number plus 2 equals the next consecutive, even whole number.   If we look at the factors of 360 we see the factors-

360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

If we look through all of the factors 18 and 20 are the only ones with a 2 number difference.

Next, if we plug 18 into the equation:

x(x+2) =360

18(18+2) = 360

324+36 = 360

360 = 360

Since the equation works, x = 18.

9514 1404 393

Answer:

  about 0.31°

Step-by-step explanation:

First of all, solve for sin(2θ):

  3000 = (1/32)(3000^2)sin(2θ)

  32(3000)/3000^2 = sin(2θ)

  4/375 = sin(2θ) . . . . . . . simplify

Now, we find the corresponding angle:

  2θ = arcsin(4/375) ≈ 0.61117°

  θ ≈ 0.30558° ≈ 0.31°

The angle of elevation must be about 0.31°.

Answer:

4/15

Step-by-step explanation:

Add up the unshaded part

1/3 +2/5

Get a common denominator

1/3 *5/5 + 2/5 *3/3

5/15 + 6/15

11/15

Subtract this from 1 for the entire circle

15/15 -11/15

4/15

4/15 is shaded

Answer:

answer is

[tex] \frac{4}{15} [/tex]

Step-by-step explanation:

explanation is in the picture!

Answer:

Two consecutive even terms and LCM = 180

Let’s assume the two terms:

1st term : 2x

2nd term : 2x + 2

There is a rule which states that

If ‘a’ and ‘b’ are two numbers, then their product is equal to the product of their LCM and HCF.

i.e,

a∗b=HCF∗LCM  - (i)

We can logically say that the HCF of any two consecutive even numbers is always equal to ‘2’ provided that the smallest no. is at least ‘2’.

i.e.,

HCF of ‘2x’ and ‘2x + 2’ is ‘2’ - (ii)

Therefore,

from (i) and (ii),

2x∗(2x+2)=  HCF * LCM

2x∗(2x+2)=2∗180  

x∗(2x+2)=180  

2x2+2x−180=0  

Solving the quadratic equation we get,

x=9,−10 (we discard -10 since it is negative)

Therefore, the numbers are

2∗9=18  (1st no.)

2∗9+2=18+2=20  (2nd no.)

Answer :  18,20

Step-by-step explanation:

9514 1404 393

Answer:

  13

Step-by-step explanation:

Let n represent that number.

  (2 +n)/(5 +n) = 5/6 . . . . . . . . n is added to numerator and denominator

  6(2 +n) = 5(5 +n) . . . . . . . . . multiply by 5(5+n)

  12 +6n = 25 +5n . . . . . . . . . eliminate parentheses

  n = 13 . . . . . . . . . . . subtract 5n+12

Adding 13 to each term will give 5/6.

__

Check

  (2 +13)/(5 +13) = 15/18 = (3·5)/(3·6) = 5/6

_____

Alternate solution

The difference of denominator and numerator in 2/5 is 5-2 = 3. The difference of denominator and numerator in 5/6 is 6-5 = 1. In order to make the latter difference 3, we must have (3/3)(5/6) = 15/18. We can get 15/18 from 2/5 by adding 13 to numerator and denominator.

Answer:

cos N = 7/25 =.28

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj side / hypotenuse

cos N = MN/ LN

We need to find the ad

Using the Pythagorean theorem

a^2+b^2 = c^2

MN^2 + 48^2 = 50^2

MN^2 + 2304 =2500

MN^2 = 2500-2304

MN^2 =196

Taking the square root

MN =14

cos N = MN/ LN

cos N = 14/50

cos N = 7/25

Answer: CosN (0.28)

A²+B²=C²

In this case we are trying to find the base so

C²-A² = B²

So 50² subtract 48²= B²

2,500 subtract 2,304 = 196

Square root of 196 = 14

Now we have all 3 sides of the triangle we find

Soh Cah Toa

Cah means Cos=Adjacent / hypotenuse

First we identify the Angle before we can decide which of the sides is labelled opposite anx adjacent

We have Angle N and we know our hypotenuse (The longest side of the triangle)

The opposite of the angle would be our opposite and the one thats niether our opposite or hypotenuse is our adjacent

In this cse the angle we solved for B²= 14

Again back "Cah" Cos= Adjacent/hypotenuse

So, 14/50 = 0.28

Step-by-step explanation: