In this diagram, lines AC and DE are parallel and line DC is perpendicular to each of them. What is a reasonable estimate for the length of side DE

Answer:

Step-by-step explanation:

3.6

Answer:

x = 8

Step-by-step explanation:

1. Group all x terms on the left side of the equation

1/3· x+4=-2/3·x+12

Add  2/3x to both sides:

1/3x+4+2/3·x=-2/3x+12+2/3·x

Group like terms:

1/3·x+2/3·x+4=-2/3·x+12+2/3·x

Combine the fractions:

1+2/3·x+4=-2/3·x+12+2/3·x

Combine the numerators:

3/3·x+4=-2/3·x+12+2/3·x

Find the greatest common factor of the numerator and denominator:

1·3/1·3·x+4=-2/3·x+12+2/3·x

Factor out and cancel the greatest common factor:

1x+4=-2/3·x+12+2/3·x

Simplify the left side:

x+4=-2/3·x+12+2/3·x

Group like terms:

x+4=-2/3·x+2/3·x+12

Combine the fractions:

x+4=-2+2/3·x+12

Combine the numerators:

x+4=0/3·x+12

Reduce the zero numerator:

x+4=0x+12

Simplify the arithmetic:

x+4=12

2. Group all constants on the right side of the equation

Subtract 4 from both sides:

x+4-4=12-4

Simplify the arithmetic:

x=12-4

Simplify the arithmetic:

x=8

Answer:

x=8

Step-by-step explanation:

1/3x +4= -2/3 +12

Subtract 4 from both sides: 1/3x + 4-4 = -2/3x + 12 -4

Simplify: 1/3x = 2/3x + 8

Add 2/3x to both sides: 1/3x + 2/3x = -2/3x + 8 + 2/3x

Simplify: x=8

Answer:

$7.01

Step-by-step explanation:

Answer:

$7.01

Step-by-step explanation:

You have seven whole dollars, which goes before the decimal point, then your cents go behind the decimal point.

[tex](14)\\\\x^2 + 14x +45\\\\=x^2 +5x +9x +45\\\\=x(x+5) +9(x+5)\\\\=(x+9)(x+5)\\\\(15)\\\\x^2 +18x +45\\\\=x^2 +15x +3x +45\\\\= x(x+15) +3(x+15)\\\\=(x+3)(x+15)\\\\\\(16)\\\\x^2+46x+45\\\\=x^2 +45x +x +45\\\\=x(x+45) +(x+45)\\\\=(x+45)(x+1)[/tex]

Answer:

y = 16/9x - 7 2/9

Step-by-step explanation:

lmk if you want an explanation

Answer:

1 and 3

Step-by-step explanation:

Answer:

B) N is the midpoint of line segment JL.

D) MN = 1/2 KJ

Step-by-step explanation:

edgeeee

Answer:

Yes, your simultaneous equations are correct;

Solve them like so:

170 + 1.6449σ = 180 - 0.8416

2.4865σ = 10

σ = 4.0217...

μ = 170 + 1.6449(4.0217...)

μ = 176.615...

MS is correct, you must've made an error in solving or rearranging

The area of a sector is 339.336 cm²

The area of a sector is defined to be as the region of space bounded by a boundary from the center of the circle.

It can be determined by using the formula:

[tex]\mathbf{A = \dfrac{\theta }{360}\times \pi r^2 }[/tex]

Given that;

Then. the area of the sector can be calculated as:

[tex]\mathbf{A = \dfrac{120}{360}\times \pi (18)^2 }[/tex]

[tex]\mathbf{A = \dfrac{1}{3}\times 3.142 \times 324 }[/tex]

A = 339.336 cm²

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The expression that is equivalent to the expression, 3 + 2x − 9 − 4x + 11 + 5x − x, is: 2x + 5.

Expressions that have the same value are said to be equivalent expressions.

Evaluate 3+2x−9−4x+11+5x−x:

3 + 2x − 9 − 4x + 11 + 5x − x

Add like terms together

2x - 4x + 5x - x + 3 - 9 + 11

2x  + 5

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Answer:

Step-by-step explanation:

The expression that is equivalent to the expression, 3 + 2x − 9 − 4x + 11 + 5x − x, is: 2x + 5.

Hello there! :)

We are given that the line passes through the point (4,5) and that it's perpendicular to the line y=2x-3.

Perpendicular lines have slopes that are opposite reciprocals.

This means we take a number, make it negative, and flop it over:

2

-2

-1/2

So the slope of the line perpendicular to y=2x-3 is -1/2.

Now, we have the slope and a point that the line passes through, so we can write the equation in point-slope form, which looks like so:

y-y1=m(x-x1)

Where

y1 is the y-coordinate of the point

m is the slope

x1 is the x-coordinate of the point

Now, let's plug our values into the equation:

y-y1=m(x-x1)

y-5=-1/2(x-4)

y-5=-1/2x+2

y=-1/2x+2+5

y=-1/2x+7

Hence, that is the equation of the line.

Hope it helps.

~A lonely teen who helps others with a smile

-Grace :-)

Good luck.

Answer:3,312.50

Step-by-step explanation:1. We assume, that the number 2500 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 2500 is 100%, so we can write it down as 2500=100%.

4. We know, that x is 3.25% of the output value, so we can write it down as x=3.25%.

5. Now we have two simple equations:

1) 2500=100%

2) x=3.25%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

2500/x=100%/3.25%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

Answer:

The domain of "Per Night Stay" would amount to $125 surcharge by day amounting to $3000 total cost function

Step-by-step explanation:

Answer:

x = - 5, x = 1

Step-by-step explanation:

let f(x) = 0 , that is

(x + 5)(x - 1) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 1 = 0 ⇒ x = 1

Plot the points - 5 and 1 on the number line

Answer:

45 bumblebee, 30 star.

Step-by-step explanation:

2:3 = 5

75/5 = 15

15 X 2= 30

15 X 3= 45

Answer:

4√2 cm

Step-by-step explanation:

ABCD is a square.

Each side measures 8 cm.

So,

AB = BC = CD = AD = 8 cm

P, Q, R, and S are mid - points of ABCD.

P is the mid - point of AB.

So,

AP = PB

AP + PB = AB

AP + AP = AB

2AP = 8

AP = 8 / 2

AP = 4 cm

S id the mid - point of AD.

So,

DS = SA

DS + SA = AD

SA + SA = AD

2SA = 8

SA = 8 / 2

SA = 4 cm

Property of a square : The angle between two sides is 90°.

So,

The angle between side SA and AP is 90°.

So,

SA, AP and SP forms a right angled triangles.

By Pythagoras theorem,

( SP)² = ( SA )² + ( AP )²

( SP )² = 4² + 4²

= 16 + 16

( SP )² = 32

SP = √32

SP = 4√2 cm

Since PQRS is also a square.

In square, all sides are equal.

So,

PQ = QR = RS = SP

Since SP = 4√2 cm

Hence,

PQ = 4√2 cm

Therefore,

the length of PQ is 4√2 cm.

Answer: 5.7

Step-by-step explanation:

Midpoint means the middle of line. So to find the middle of the line I just need to divide the line by 2.

So the midpoint of AB is:

8/2=4 = BP

Since Q is also a midpoint so BQ is equal to 4.

We know BP=BQ=4. Looking at the diagram we can tell PBQ is a triangle.

The hypotenuse of the triangle is PQ.

Pythagoras's theorem helps us to find the hypotenuse. So we just plug in the values to find PQ.

P's Theorem : a²+b²=c²

basically in the case of this question it means:

(BP)²+(BQ)²=(PQ)²

now we just subsiture the values and solve for PQ:

4²+4²=(PQ)²

16+16=(PQ)²

32=(PQ)²

PQ=5.65...

= 5.7(rounded to one decimal place)

Answer:

A

Step-by-step explanation:

The solutions to the given quadratic equation are x=-8 and x=3. Therefore, option A is the correct answer.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given quadratic equation is 2x²+10x-48=0.

Here, x²+5x-24=0

x²+8x-3x-24=0

x(x+8)-3(x+8)=0

(x+8)(x-3)=0

(x+8)=0 and (x-3)=0

x=-8 and x=3

Therefore, option A is the correct answer.

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Answer:

x > 12/7

x > 1  5/7

Step-by-step explanation:

7x + 8 > 20

Subtract 8 from each side

7x+8-8 > 20-8

7x > 12

Divide each side by 7

7x/7 > 12/7

x > 12/7

Changing to a mixed number

x > 1 5/7

Answer:

x < 57

Step-by-step explanation:

Answer:

19,250 I think.

Step-by-step explanation:

2,750 x 7 19,250

Answer:

C

Step-by-step explanation:

∠ ABC = 90° ( angle in a semicircle )

Using the cosine ratio in right triangle ABC and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{10}{AC}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

AC × [tex]\sqrt{3}[/tex] = 20 ( divide both sides by [tex]\sqrt{3}[/tex] )

AC = [tex]\frac{20}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ( rationalising denominator )

AC = [tex]\frac{20\sqrt{3} }{3}[/tex]

radius AO = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × [tex]\frac{20\sqrt{3} }{3}[/tex] = [tex]\frac{10\sqrt{3} }{3}[/tex] → C

Answer:

Step-by-step explanation:

Find the miles per gallon rate of each car

Blue car:

Red car:

According the rates, the blue car could travel the greater distance

Step-by-step explanation:

2x = 18

Divide both sides by 2

x = 9

Answer:

29 - 3t = 54 - 8t

-29 -29

-3t = 25 - 8t

+8t +8t

5t = 25

/5 /5

t = 5

The snowmen will have an equal height after 5 hours.

Answer:

f(-9) = 135

Step-by-step explanation:

Replace x with -9, and evaluate the expression.

f(x) = 2x² + 3x

f(-9) = 2(-9)² + 3(-9)

f(-9) = 2(81) - 27

f(-9) = 162 - 27

f(-9) = 135

Answer:

5/4

Step-by-step explanation:

The original line is

7 - 3 / 4 - 9

4/-5, so the slope is -4/5

Perpendicular means the opposite sign and reciprocal.

5/4

Answer:

Step-by-step explanation:

The value of b Lois gave to Clark to satisfy the given equation is -7.

The given parameters;

2x + 7 - x = 4x + 2b – 3x - 3b

To obtain the value of b, simplify the equation as follows;

2x + 7 - x = 4x + 2b – 3x - 3b

collect similar terms together

(2x - x) + 7 = (4x - 3x) + (2b - 3b)

x + 7 = x - b

(x - x) + 7 = -b

0 + 7 = -b

7 = -b

-7 = b

b = -7

Thus, the value of b Lois gave to Clark to satisfy the given equation is -7.

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Answer:

so that's how you plot their intersection