If the value of a is negative the line is what?

Answer:

1). AC=8.25cm

2). DB=7cm & EC=14cm

3). See Explanation

Step-by-step explanation:

According To the Question,

Given That, In ∆ABC, D and E are points on the sides AB and AC respectively such that DE is parallel to BC.

1). If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC.

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD / BD = AE / EC

⇒ 2.5 / 3 = 3.75 / EC

On Solving we get,  

⇒ EC * 2.5 = 3.75 * 3  

⇒ EC * 2.5 = 11.25  

⇒ EC = 11.25 / 2.5  

⇒ EC = 4.5 cm

Thus,  

AC = AE + EC

⇒ AC = 3.75 + 4.50

⇒ AC = 8.25 cm  

Hence the measure of AC is 8.5 cm.

2). If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD / BD = AE / EC

⇒ 4 / (x-4) = 8 / (3x-19)

on solving we get,

⇒ 3x-19 = 2(x-4)

⇒ 3x-19 = 2x-8

⇒x=11

Thus, DB =x–4 ⇒ 11-4 ⇒ DB=7cm

And, EC =3x-19 ⇒ 3×11-19 ⇒ EC=14cm

3). If AD=2cm , BD= 4cm , show that BC = 3 DE

Thus, AB = AD + DB = 2+4 = 6cm

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD/AB = DE / BC

⇒ 2 / 6 = DE / BC

on solving we get

⇒ BC = 3 DE Hence, Proved

Answer:

1441.08 in^3

Step-by-step explanation:

Volume of rectangular prism = 15 * 9 * 9 = 1215 in^3

radius = 3 in

Volume of the cylinder = 3^2 * 3,14 * 8 = 226.08 in^3

Total volume = 1215 + 226.08 = 1441.08 in^3

Answer:

HJHJGHJHG

Step-by-step explanation:

JGHU45565677689789

Answer:

prime numbers only have two factors...

7 is the only prime in the list

Step-by-step explanation:

Answer:

yes , k = 9

Step-by-step explanation:

The equation of a proportional relationship is

y = kx ← k is the constant of proportion

To find k divide both sides by x

[tex]\frac{y}{x}[/tex] = k

Check each ordered pair in the table

k = [tex]\frac{18}{2}[/tex] = 9

k = [tex]\frac{45}{5}[/tex] = 9

k = [tex]\frac{63}{7}[/tex] = 9

Thus the relationship is proportional with k = 9

Answer:

[tex]10\sqrt{3}[/tex]

Step-by-step explanation:

One is given the following expression:

[tex]\sqrt{30}*\sqrt{10}[/tex]

One property of multiplying square roots is that one can multiply the numbers under the radical by each other, and then put the radical on top of the result. The following is an example of this general format of this property:

[tex]\sqrt{a}*\sqrt{b}=\sqrt{ab}[/tex]

Apply this to the real problem:

[tex]\sqrt{30}*\sqrt{10}=\sqrt{30*10}[/tex]

Simplify,

[tex]\sqrt{30*10}=\sqrt{300}[/tex]

Rewrite as (300) as the product of two numbers, such that one number is a perfect square:

[tex]\sqrt{300}=\sqrt{3*10^2}[/tex]

Simplify, take a term out of the radical:

[tex]\sqrt{3*10^2}=10\sqrt{3}[/tex]

Answer: hello there here is your answer:

7%

Step-by-step explanation:

if you divide the difference between the two numbers it will give you a decimal ....you need to convert that decimal into a percent which is 7%

hope this help have a good day bye

Answer:

the other person is correct

Step-by-step explanation:

Answer:   [tex]\huge\boxed{x=3\frac{1}{3} \quad ;\quad y=-3}[/tex]

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol+\ \left \{ {{6x+4y=8} \atop {-4y=12}} \right. \Longrightarrow\\\\\\ 6x+ 4y\!\!\!\!\!\diagup-4y\!\!\!\!\!\diagup=12+8 \\\\6x=20 \\\\x=\frac{20}{6} =\frac{10}{3} =3\frac{1}{3} \quad ; \quad y=-3[/tex]

Answer:

???

Step-by-step explanation:

Answer:

He drove there at 60 mph, and he drove back at 36 mph.

Step-by-step explanation:

one way distance = d = 270 miles

average speed on way back = s

average speed on the way there = s + 24

time driving there = t

time driving back = 12 - t

average speed = distance/time

distance = speed * time

going there:

270 = (s + 24)t

270 = st + 24t

going back

270 = s(12 - t)

270 = 12s - st

We have a system of equations:

270 = st + 24t

270 = 12s - st

Solve the first equation for t.

t(s + 24) = 270

t = 270/(s + 24)

Substitute in the second equation.

270 = 12s - s[270/(s + 24)]

270 = 12s - 270s/(s + 24)

Multiply both sides by s + 24.

270s + 6480 = 12s^2 + 288s - 270s

12s^2 - 252s - 6480 = 0

Divide both sides by 12.

s^2 - 21s - 540 = 0

(s - 36)(s + 15) = 0

s = 36 or s = -15

The average speed cannot be negative, so we discard the solution s = -15.

s = 36

s + 24 = 60

Answer: He drove there at 60 mph, and he drove back at 36 mph.

Answer:

+2633 ft

Step-by-step explanation:

The city is above sea level meaning it is a positive number.

Answer:

[tex]2187[/tex]

Step-by-step explanation:

[tex] {3}^{7} \\ = (3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3) \\ = 2187[/tex]

Answer:

2187

Step-by-step explanation:

3*3=9

9*3=27

27*3=81

81*3=243

243*3=729

729*3=2189

Answer:

$110

Step-by-step explanation:

We are looking for the decrease in money per desk purchased. Because the x-axis is the number of desks purchased, what we have to find is the (opposite) of the slope. The formula to represent slope can be written as:

[tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]

We can substitute the points given, (2, 480) and (5, 150) and simplify:

[tex]\frac{150-480}{5-2} =\frac{-330}{3} = -110[/tex]

We would multiply by -1 because we are asking for the decrease, and negative increase is decrease. -1 * -110, gives us $110

Answer:

Both ate 12 sunscreens all together

5 + 7 = 12

Srsly tho, like who in their right mind eats sunscreen

Answer:

216 different cakes are possible.

Step-by-step explanation:

Given that a bakery offers 4 different flavors of cake, 3 types of icing, 6 toppings, and 3 different sizes, if one option is chosen from each list, to determine how many different cakes are possible the following calculation must be performed:

4 x 3 x 6 x 3 = X

12 x 18 = X

216 = X

Therefore, 216 different cakes are possible.

Answer: meh

Meh

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

y = -6x - 5

The equation is put in slope intercept form

( y = mx + b )

Where m = slope and b = y intercept

-6 is in the spot of "m"

Meaning that the slope would be -6

Answer:

slope is -6

Step-by-step explanation:

y = mx+b

m is slope :)

b is the point, where the line intersects the y axis

Answer:

t = 14 seconds

Step-by-step explanation:

Given that,

A package is accidentally dropped from a helicopter from a height of 3,136ft.

The equation for height as a function of time is :

[tex]h(t) = -16t^2 + \text{initial height}[/tex]

So,

[tex]h(t) = -16t^2 +3,136[/tex]

When it hits the ground, h(t) = 0

So,

[tex]-16t^2 +3,136=0\\\\-16t^2=-3136\\\\t^2=\dfrac{3136}{16}\\\\t^2=196\\\\t=14\ s[/tex]

So, it will take 14 seconds for the package to hit the ground.

Answer:

x = 24

Step-by-step explanation:

Mathematically, in a cyclic quadrilateral; two opposite angles are supplementary

what this mean is that the opposite angles add up to equal 180 degrees

mathematically, we have this as;

(4x + 9) + (3x + 3) = 180

4x + 3x + 3 + 9 = 180

7x + 12 = 180

7x = 180-12

7x = 168

x = 168/7

x = 24

Answer:

11.2

Step-by-step explanation:

[tex]p =\frac{160.16}{14.3}=\frac{160.16*10}{14.3*10}\\\\p = \frac{1601.6}{143}\\\\[/tex]

p = 11.2

Answer:

The person above me is correct I just did the work and I got the same answer as them :)

Step-by-step explanation:

Answer:

B. 35°

Step-by-step explanation:

m<4 = x + 20

m<8 = 2x + 5

✔️First, find the value of x:

m<4 = m<8 (corresponding angles are equal)

Substitute

x + 20 = 2x + 5

Collect like terms

x - 2x = -20 + 5

-x = -15

Divide both sides by -1

x = 15

✔️Find m<8:

m<8 = 2x + 5

Plug in the value of x

m<8 = 2(15) + 5

m<8 = 30 + 5

m<8 = 35°

Answer:

First one.

-3 is added to the previous term.

Answer:

A. ^3√5 is the answer.

Step-by-step explanation:

5^( 1 / 3 ) = ^3√5

Answer:

- [tex]\frac{2\sqrt{3} }{3}[/tex]

Step-by-step explanation:

Using the identity and the exact value

csc x = [tex]\frac{1}{sinx}[/tex]  and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

- 120° is in the third quadrant where sin < 0 , then

csc - 120° = - sin60° , then

csc - 120°

= [tex]\frac{1}{-sin60}[/tex]

= - [tex]\frac{1}{\frac{\sqrt{3} }{2} }[/tex]

= - [tex]\frac{2}{\sqrt{3} }[/tex] ( rationalise the denominator )

= - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= - [tex]\frac{2\sqrt{3} }{3}[/tex]

The equivalent value of the trigonometric relation cosec ( -120 )° = 2√3/3

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

We know that the cosecant function is defined as the reciprocal of the sine function:

cosec (θ) = 1 / sin(θ)

Therefore, to evaluate cosec(-120°), we first need to find sin(-120°).

We know that sine is an odd function, which means that sin(-θ) = -sin(θ). Therefore,

sin(-120°) = -sin(120°)

We can now use the fact that the sine function has a period of 360 degrees, which means that sin(120°) is the same as sin(120° - 360°) = sin(-240°).

Using the same logic as before, we get:

sin(-240°) = -sin(240°)

Now , from the trigonometric relations , we get

Now, we can use the fact that sin(240°) = sin(240° - 360°) = sin(-120°), which means that:

sin(-240°) = -sin(-120°)

Therefore, we have:

sin(-120°) = -sin(120°) = -sin(-240°) = sin(240°)

Now, we can use the unit circle or trigonometric identities to find sin(240°). One way to do this is to draw a 30-60-90 degree triangle in the third quadrant of the unit circle, with the angle of 240° as the reference angle:

In this triangle, the opposite side (O) has a length of √3, the adjacent side (A) has a length of -1, and the hypotenuse (H) has a length of 2.

Therefore, sin(240°) = O/H = (√3)/2.

Finally, we can use the definition of the cosecant function to find cosec(-120°):

cosec(-120°) = 1/sin(-120°) = 1/sin(240°) = 1/((√3)/2) = 2/√3 = (2√3)/3.

Hence , cosec(-120°) is equal to (2√3)/3.

To learn more about trigonometric relations click :

https://brainly.com/question/14746686

#SPJ2

Answer:

True

Step-by-step explanation:

Yes! The diagonal of a rectangle is longer than any of its sides.

Consider PQRS as a rectangle. It is known to us that each interior angle of a rectangle measures 90°. Now, after making the diagonal of the rectangle PQRS, the rectangle has been split into 2 right-angled triangles i.e, ∆PRS and ∆RPQ. In the right angled triangle, hypotenuse is always the longest side. Here, in ∆PRS and ∆RPQ, the bases are RS and QP ; perpendiculars are PS and QR and both triangles' hypotenuse is PR. As, hypotenuse is always the longest side, so PR will be longer than RS,QP,PS and QR. Clearly, the diagonal of a rectangle is longer than any of its sides.

Answer:

x = 3

Step-by-step explanation:

f(x) means function of x, and could be replaced by y to just give a y = mx + b equation. So if f(x) = y = 11, you're pretty much solving for x with the equation

11 = 3x + 2

From there, isolate x, and you have your answer.

11 = 3x + 2

9 = 3x

x = 3

Answer:

45 and 135

Step-by-step explanation:

Same Side Interior Angles = 180

x + 3x = 180

4x = 180

x = 45

3x = 135

Answer:

Angle 1 = 45 degrees

Angle 2 = 135 degrees

Step-by-step explanation:

All same side exterior angles are supplementary so if one is three times the other which means a ratio of 3:1.

180/4 = 45

First angle = 45 degrees

Second angle = 135 degrees

Answer:

176mm

Step-by-step explanation:

Given

Diameter of the pencil = 7mm

First, we need to find the length of one roll of paper

Circumference of one roll = πd

Circumference of one roll = 22/7  *7

Circumference of one roll = 22mm

Since a student winds a strip of paper eight times around a cylindrical pencil, then the length of the paper = 8 * 22  = 176mm

Answer:

$20

Step-by-step explanation:

5 copies cost $1.

25 copies cost $5.

So you have to do 100/5=$20 for 100 copies.

Answer:The answer is 20

Step-by-step explanation:

Answer:

76°,60°

Step-by-step explanation:

sum of angles of a triangle=180

x+64+x+80+44=180

2x+188=180

2x=180-188=-8

x=-8/2=-4

so angles are -4+60=60°

and -4+80=76°

Answer:

a^2 -25

Step-by-step explanation:

5a-25 + a^2 - 5a

a^2 - 25