TREC is a rectangle. What is the length of ET?

Answer: 5/8

Step-by-step explanation:

Answer:

k = [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

The standard form of an equation representing proportion is

y = kx ← k is the constant of proportionality

y = [tex]\frac{5}{8}[/tex] x ← is in this form

with k = [tex]\frac{5}{8}[/tex]

Answer:

∠1 = 90°

Step-by-step explanation:

The angle inscribed in a semicircle is always 90°

∠1 = 90°

Answer:

x=5

Step-by-step explanation:

7/5=(2x-3)/x

5(2x-3)=7x

3x=15, x=5

Answer:

The Solution Set

Step-by-step explanation:

Despite missing some context, the output we could get as result of an expression/equation it is what we call a Solution set. A set which makes the initial statement of equation/expression true, therefore valid.

[tex]x^{2} -7x+12=0\\(x-3)(x-4)=0\\S=\{3,4\}[/tex]

Therefore, the elements of the Solution set, 3 and 4 when plugged into the equation make the statement of the quadratic equation true.

[tex](3)^{2}-7(3)+12=0\\-12+12=0\\0=0[/tex]

The output or possible values you could get as a result from an expression or equation is the solution set of the equation

Take for instance, we have the following equation

[tex]x^2 = 4[/tex]

When solved, the equation becomes

[tex]x = \pm 2[/tex]

This can be rewritten as:

[tex]x = \{-2,2\}[/tex]

This means that -2 and are the solution set of the equation [tex]x^2 = 4[/tex]

Hence, the output or possible values are called solution set

Read more about equations at:

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Answer: 60

Step-by-step explanation:

Cost of 1 cup = 80

Actual cost of 6 cups = 80 x 6 = 480

1/2 dozen cups were bought for 420

Discount 480 - 420 = 60

Answer:

C : Measure using the distance formula

Step-by-step explanation:

A Venn diagram is a diagram which shows the relation of all different sets

Just like it is given in the attachment there is a relation between the perimeter and the area.

The distance formula is

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 }[/tex]

where,

[tex](x_1, y_1)[/tex] is the first point coordinates

[tex](x_2, y_2)[/tex]  is the first point coordinates

By using the distance formula as discussed above shows the intersection of the Venn diagram

Hence, the correct option is C.

Answer:

Step-by-step explanation:

We can setup the equation as

x/28 = 1/8

Cross multiplying we get

8x = 28

Dividing by 8 we get

x = 28/8 = 7/2

Answer:

Im pretty sure its the 1st one

Step-by-step explanation:

Answer:

option 3 π

Step-by-step explanation:

Circumference = πd

Circumference : diameter = πd : d

                                            = π : 1 = π

Answer:

D

Step-by-step explanation:

[tex]f(x)=3x+5 \\\\g(x)=x^2 \\\\(f-g)(x)=(3x+5)-(x^2)=-x^2+3x+5[/tex]

Therefore, the correct answer is choice D. Hope this helps!

Answer:

Solve the rational equation by combining expressions and isolating the variable  

Answer:

Step-by-step explanation:

I assume that the equation is

[tex]e^x+\frac{e^{-x}}{e^x} -e^{-x}=t \\[/tex]

[tex]e^x+\frac{1}{e^{2x}}-\frac{1}{e^x} = t[/tex]

[tex]e^{3x}+1-e^x=e^{2x}t[/tex]

[tex]e^{3x}-te^{2x}-e^x=-1[/tex]

Let u = e^x

[tex]u^3-tu^2-u=-1[/tex]

[tex]u(u^2-tu-1) = -1[/tex]

if u=1, then [tex]u^2-tu-1 =-1 \longleftrightarrow u^2-tu=0[/tex]

then u = 0 (reject) or u = t

So far, we have u = 1 and u = t

if u =1, e^x =1 , then x = 0

if u = t, then e^x = t or x = lnt

Answer:

a₆ = 6

Step-by-step explanation:

There is a common ratio r between consecutive terms in the sequence, that is

r = [tex]\frac{216}{-1296}[/tex] = [tex]\frac{-1296}{7776}[/tex] = [tex]\frac{7776}{-46656}[/tex] = - [tex]\frac{1}{6}[/tex]

This indicates the sequence is geometric.

To obtain any term in the sequence, multiply the previous term by r, thus

a₅ = 216 × - [tex]\frac{1}{6}[/tex] = - 36

a₆ = - 36 × - [tex]\frac{1}{6}[/tex] = 6

Answer:

It's 6

Step-by-step explanation:

Got it right!

1 –46,656

2 7,776

3 –1,296

4 216

5 36

6 6

divided by 6 every time

Answer:

no whole number

Step-by-step explanation:

263 is a prime number, so it can be divided only by 1 and 263. So, no whole number will be square root for 263.

Answer:

The width of the rectangle is k+4 inches

Step-by-step explanation:

you have [tex]k^{2}+19k+60[/tex] which can be factorized to (k+4)(k+15)

if the length of the rectangle is k-5 that would mean that we can write [tex]k^{2}+19k+60[/tex] as (k-5)n which we know is false, so the only one that applies is k+4

The true statement is:

"The width of the rectangle is k + 4"

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

So we want to factorize the area equation, which is a quadratic equation, into a product of two terms.

A = k^2 + 19k + 60

The two zeros are given by Bhaskara's formula:

[tex]k = \frac{-19 \pm \sqrt{19^2 - 4*1*60} }{2} \\\\k = \frac{-19 \pm 11 }{2}[/tex]

So we have two zeros, these are:

k = (-19 - 11)/2 = -15

k = (-19 +11)/2 = -4

So we can factorize the area as:

A = (k - (-15))*(k - (-4)) = (k + 15)*(k + 4).

From this, the only statement that can be true is:

"The width of the rectangle is k + 4"

If you want to learn more about quadratic equations, you can read:

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Answer: x= -3 + 2[tex]\sqrt{2\\}[/tex] or -3 -2 [tex]\sqrt{2}[/tex]

Step-by-step explanation:

First you want to get the quadratic formula

in this case a=1 b=6 and c=1

plug it in and solve the equations

(sorry don't know how to put in equations here)

Answer:

Answer: x= -3 + 2\sqrt{2\\} or -3 -2 \sqrt{2}

Step-by-step explanation:

First you want to get the quadratic formula

in this case a=1 b=6 and c=1

plug it in and solve the equations

Answer:

The width is 2x+1

Step-by-step explanation:

10x^2 +5x

Divide this by 5x

10x^2 /5x = 2x

+

5x/5x =1

Add this together

2x+1

The width is 2x+1

Answer:

( 2x + 1 )

Step-by-step explanation:

10x^2 + 5x

it could also be;

5x (2x + 1)

so, the width is( 2x +1)

Answer:

2:3

Step-by-step explanation:

We know that there are 24 red and black cards in the 48 pack because their ratio is 1:1. When 8 red cards are removed we have 16 red and 24 black cards. The ratio of this is 16:24 which simplifies to 2:3.

The ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1

The total amount of cards (red or black) in the pack is = 48

The ratio of the number of red cards to the number of black cards is = 1:1

The number of cards removed from the pack = 8

Therefore the total number of cards( red or black = 48 -8

= 40 cards

But to calculate the number of red card

= 1+1 = 2

40/2 = 20 red cards

The number of black cards

1+1 = 2

40/2 = 20 black cards

The ratio of red is to black cards = 20:20 or 20/20 = 1:1 or 1/1

Therefore the ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1

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tan X = |YZ| / |XZ| = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

The size of angle ∠YXZ is 68.3° given that sides YZ=20cm and XZ=8cm by using trigonometric ratios.

In a right angled triangle, if A is an angle other than right angle then trigonometric ratios are

sin A =[tex]\frac{opposite side}{hypotenuse}[/tex]

cos A=[tex]\frac{adjacent side}{hypotenuse}[/tex]

tan A =[tex]\frac{opposite side}{adjacent side}[/tex]

Given YZ=20cm and XZ=8cm

Since the triangle is right angled, and opposite side and adjacent side are given we can find tan(∠YXZ )

tan (∠YXZ ) =20/8 =2.5

∠YXZ = arctan (2.5) =68.2°

Hence the size of angle ∠YXZ is 68.2° given that sides YZ=20cm and XZ=8cm.

Learn more about trigonometric ratios here :

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Answer:

  a.  75%

Step-by-step explanation:

Let "p" represent the probability that Jeffrey will eat pizza, and "c" represent the probability that he will drink cola.

We are given ...

  P(p) = 0.40

  P(p&c) = 0.30

The conditional probability of interest is ...

  P(c|p) = P(p&c)/P(p) = 0.30/0.40 = 0.75

The probability Jeffrey will drink cola, given that he eats pizza, is about 0.75.

Answer: The equation is 45-10=x the answer is 35

Step-by-step explanation: To make the equation you need to have and = sign so, we can do what he has (45) and subtract what he gives away (10) which would equal what he has left (x)

Answer:

45 (initial amount) - 10 (given to brother) = x (number of cd's left)

Equation:

    45 - 10 = x

Answer:

    35 CDs

Answer:

No ABC is not a triangle

Step-by-step explanation:

Perimeter = 22 cm

AB = 8 cm ; BC = 8 cm

AC = 22 - ( 8 + 8 ) = 6 cm

But all those sides doesn't follow Pythagorean Theorem(AB^2 + BC^2 = AC^2) ....because 8^2 + 8^2 isn't equal to 6^2 ......

Had it followed the theorem , it could have been a right angle triangle...

Answer:

90.80

Step-by-step explanation:

6x+4

= (6)(13)+4

= 78+4

=82

3x

=(3)(13)

= 39

So we know the sides are 39 and 82

Pythagoras theorem in triangles

= a2+b2= c2

Now, we know the value of a and B but not c (the hypotenuse)

Therefore,

c2 = (39)^2 + (82)^2

= 1521+ 6724

= 8245

so, c = √8245

= 90.80 unitd

Answer:

[tex]\fbox{\begin{minipage}{13em}Option D: 2(3x + 4)(3x - 4)\end{minipage}}[/tex]

Step-by-step explanation:

      [tex]A = 18x^{2} - 32\\[/tex]

Find the sharing components:

<=> [tex]A=2*9*x^{2} - 2*16[/tex]

Apply the inverse of associative property:

<=> [tex]A = 2(9x^{2} - 16)[/tex]

Identify two square components inside the parenthesis:

<=> [tex]A = 2((3x)^{2} - 4^{2} )[/tex]

Factorize:

<=> [tex]A = 2(3x + 4)(3x - 4)[/tex]

=> Option D is correct

Hope this helps!

:)

Answer:

A line in form of y = ax + b passes (0, 2)

=> 2 = 0x + b => b = 2

This line also passes (4, 6)

=> 6 = 4x + 2 => x = 1

=> Equation of this line: y = x + 2

=> Option C is correct

Hope this helps!

:)

Answer:

A line in form of y = ax + b passes (0, 2)

=> 2 = 0x + b => b = 2

This line also passes (4, 6)

=> 6 = 4x + 2 => x = 1

=> Equation of this line: y = x + 2

=> Option C is correct

Hope this helps!

:)

Step-by-step explanation:

Answer:

Its 2!

Step-by-step explanation:

Just got it correct on edge 2020

The projectile is on the ground for 2 seconds.

A projectile is an object this is propelled via the application of external pressure and then movements freely underneath have an impact on gravity and air resistance.

Learn more about projectile here https://brainly.com/question/12870645

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Answer:

62 degrees

Step-by-step explanation:

all triangles equal 180 degrees so you would add both angles together then subtract the sum of that by 180

Answer:

[tex]x=62^o[/tex]

Step-by-step explanation:

Since the addition of all internal angles of a triangle should add up to [tex]180^o[/tex], then, the missing angle can be found by subtracting the two known angles from [tex]180^o[/tex]:

[tex]x=180^o-68.5^o-49.5^o=62^o[/tex]

Answer:

x^3   +  3x^2    +   9x    +  27   +   88 / [x - 3]

Step-by-step explanation:

x ^4 + 7 by x - 3 x^3   +  3x^2    +   9x        +  27 x - 3  [  x^4  +   0x^3    +   0x^2    +   0x    +   7   ]. x^3  -    

3x^3 ________________________________ 3x^3   +     0x^2 3x^2  

-     9x^2 ______________ 9x^2      +   0x 9x^2

   -    27x ____________ 27x    +   7 27x  

 -  81 _________ 88 S

Answer:  So the result is :      x^3   +  3x^2    +   9x    +  27   +   88 / [x - 3]

Please mark me brainliest

Hope this helps.

Answer:

Ace Electronics buys 30, Hi-Fi Stereo buys 50, and CD World buys 115

Step-by-step explanation:

Let x represent the number of items Ace Electronics buys

Let y represent the number of items Hi-Fi Stereo buys

Let z represent the number of items CD World buys

Since Ace Electronics, Hi-Fi Stereo, and CD World buy a total of 195 DVD players:

x + y + z = 195   (1)

Since CD World buys 35 more units than the other two stores combined:

z = x + y + 35   (2)

If you substitute z in equation 1 from equation 2:

x + y + (x + y + 35) = 195

2(x + y) = 195- 35

x + y = 80   (3)

Since z = x + y + 35:

z = 80 + 35

z = 115

Since CD World's cost is $160 per unit, Hi-Fi 's cost is $165 per unit and Ace Electronics's cost is $170 per unit and the total payment received is $31,750

170x + 165y + 160z = 31750   (Substitute x from equation 3 and z as 115)

170(80-y) + 165y + 160(115) = 31750

13600 - 170y  + 165y + 18400 = 31750

32000 - 5y = 31750

5y = 250

y = 50

Since x + y = 80:

x + 50 = 80

x = 30

Answer:

number of students who ate soup = 60

number of students who didn't ate soup

= 300-60

= 240

60/240 = 1/4