2(4x-6) = 4(3x-7) what is x​

Answer:500 cm

Step-by-step explanation:

Given

height of ethan = 180 cm

length of shadow =144 cm

Distance of ethan from lamp =256 cm

from diagram, we can write

[tex]\Rightarrow tan \theta =\frac{FC}{EC}\quad \ldots(i)[/tex]

[tex]\Rightarrow \tan \theta =\frac{AB}{BE}\quad \ldots (ii)[/tex]

From (i)  and (ii)  we get

[tex]\tan \theta =\frac{FC}{EC}=\frac{AB}{BE}[/tex]

[tex]\Rightarrow \frac{180}{144}=\frac{h}{144+256}[/tex]

[tex]\Rightarrow h=\frac{180}{144}\times 400[/tex]

[tex]\Rightarrow h=500\ cm[/tex]

So, height of lamp post AB is [tex]500\ cm[/tex]

Answer:

There are 7,725 square feet of grass on the trapezoidal field

Step-by-step explanation:

Here in this question, we are interested in calculating the square feet of grass present on the trapezoidal field.

What this question is actually asking us is to calculate the area of the trapezoid-shaped grass field.

To calculate this area, what we need to do

simply is to use the formula for the area of a trapezoid.

Mathematically, the area of a trapezoid can be calculated using the formula;

Area of trapezoid = 1/2 * (a + b) * h

where a and b refers to the length of the parallel lengths of the trapezoid and h refers to the height of the trapezoid.

From the question;

a, b = 81ft and 125 ft

h = 75 ft

Substituting these values, we have :

Area = 1/2 * (81 + 125) * 75

Area = 1/2 * 206 * 75 = 83 * 75 = 7,725 ft^2

Answer:

Nancy had 7 correct answers.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.  Let's assign the variable c to represent the number of correct answers Nancy had and the variable i represent the number of incorrect answers she had.

We know that the total number of answers is 10 because it is given that she answered all 10 problems.  This lets us set up the first equation as follows:

c + i = 10

Then, we can set up a second equation using the number of points (29 total).  We know that +5 points were added for each correct response (c) and -2 points were added for each incorrect response (i).  Our next equation will look like this:

5c - 2i = 29

There are many different strategies one can use to solve systems of equations.  In this case, I am going to use combination.  This means I am going to add the two equations together.  However, first I should multiply our first equation by 2 so that the "I" variable terms cancel out.  This is modeled below:

2c + 2i = 20

Now we can add the two equations:

5c + 2c +2i - 2i = 20 +29

Now we can simplify the equation by combining the like terms to get:

7c = 49

Finally, we should divide both sides of the equation by 7 in order to get the variable c by itself on the left side of the equation.

c = 7

Therefore, the correct number of responses Nancy gave was 7.

Hope this helps!

Answer: 107.5

Step-by-step explanation:

120 x 14= 1680

90 x 10= 900

Now you add 1680+900= 2580

Then you divide the distance (2580) between the speed (14+10)

2580/24= 107.5

Step-by-step explanation:

As we can see, the line on the bottom is a perfectly straight 180º line, so the two angles, a and 50º are supplementary angles. Remember: Supplementary angles = 180º, and complementary angles = 90º.

Since this is a 180º line, all we have to do is to subtract 50 from 180 to get our angle a.

180-50 = 130º

Our answer: a = 130º

Answer:

y=30

Step-by-step explanation:

f(-2)=18+3(-2)^2

f(-2)=18+3*4

f(-2)=18+12

f(-2)=30

Answer:

y= 6

Step-by-step explanation:

substitute x= -2 in the equation y=18+3x^2

from there you'll get your final answer

Answer:

-19

-2/5

0

4/7

2.89

Step-by-step explanation:

a rational number is any number that can be converted to a fraction, I know this because I took a test a while back and it helped me understand it.  I hope this helps!!! :)

Answer:

-217

Step-by-step explanation:

Add them both together because it is asking for the "sum".

-354+137= -217

Answer:

16, 56, ...

Step-by-step explanation:

It looks like you have to put in each cell the multiplication of the row and the column, so the columns are 2, 7, 4 etc., and the row is always 8.

First cell: 2x8 = 16

Second cell: 7x8 = 56

and so on

It teaches you to apply the multiplication in a random sequence; you should be able to do this in your head.

Q1

[tex]n > \frac{81}{2} [/tex]

Q2 D

sry I don't hv time to ans more

Answer:

10

Step-by-step explanation:

We can show this as:

Since

Then

The closest number in the list is 10 as all the rest are greater than 10

Second choice is the correct one

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              Hi my lil bunny!

  ❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\sqrt{90}[/tex]

[tex]= \sqrt{10}[/tex] (Decimal: 9.486833)

( I don't know it might be wrong )

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

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       Have a great day/night!

                  ❀*May*❀

Answer:

Step-by-step explanation:

y = -1/2 x – 7

when x is 0

y = -1/2(0) - 7

y = - 7

(0,-7)

when y is 0

0 = -1/2 x - 7

1/2 x = -7

x = -7(2)

x = -14

(-14,0)

The graph of equation y = -1/2x – 7 is shown in figure.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line is,

⇒ y = - 1/2x - 7

Hence, We get;

The graph of equation y = -1/2x – 7 is shown in figure with slope - 1/2 and y - intercept is - 7.

Thus, The graph of equation y = -1/2x – 7 is shown in figure.

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Answer:

He has memorized 18 words

Step-by-step explanation:

(3/4)*24 = 18

Answer:

c) 135°

b) 72°

d) 90°

a) 115°

Step-by-step explanation:

A supplementary pair are two angles whose measures added is equal to 180°. Set an equation with the given values plus a number (the other angle) equal to 180:

c) [tex]x+45=180[/tex]

Solve. Subtract 45 from both sides:

[tex]x+45-45=180-45\\\\x=135[/tex]

The supplement is 135°

b) [tex]108+x=180[/tex]

Solve. Subtract 108 from both sides:

[tex]108-108+x=180-108\\\\x=72[/tex]

The supplement is 72°

d) [tex]x+90=180[/tex]

Solve. Subtract 90 from both sides:

[tex]x+90-90=180-90\\\\x=90[/tex]

The supplement is 90°

a) [tex]x+65=180[/tex]

Solve. Subtract 65 from both sides:

[tex]x+65-65=180-65\\\\x=115[/tex]

The supplement is 115°

:Done

Answer:

5.2x + 24.4

Step-by-step explanation:

1.2(x-3) + 4 (x+7)

=1.2x - 3.6 + 4x + 28

=5.2x + 24.4

Hope this helps..

Answer:

no triangles

Step-by-step explanation:

why?

the triangle inequality theorem

this theorem states that the sum of any two sides must be bigger than or equal to the third side. however, the sum of 2.1 and 2.6 is less than 4.8

Answer:

A and D

Step-by-step explanation:

3 - 5x > 2

= -5x > 2-3

= -5x > -1

= x < 1/5

Answer:

The correct answer is A. x = 1 or D. x = 7.

Step-by-step explanation

For this problem, we can substitute each of the values and see which ones make the inequality true.

Using x = 1

3 - 5(1) > 2

3 - 5 > 2

-2 > 2

This is not true, so this is not our solution. However, I will show the rest of the solutions anyways.

Using x = 0

3 - 5(0) > 2

3 - 0 > 2

3 > 2

This is true, so x = 0 is a solution to the inequality.

Using x = -1

3 - 5(-1) > 2

3 + 5 > 2

8 > 2

This is true, so x = -1 is a solution to the inequality.

Using x = 7

3 - 5(7) > 2

3 - 35 > 2

-32 > 2

This is not true, so x = 7 is not a solution to the inequality.

Answer:

Hey there!

-3(2x-1)

-6x+3

Let me know if this helps :)

Answer:

[tex]- 6x + 3[/tex]

Step-by-step explanation:

[tex] - 3(2x - 1) \\ = - 6x + 3[/tex]

Answer:

10 sqrt(10)

Step-by-step explanation:

sqrt(1000)

sqrt(100*10)

we know that sqrt(a*b) = sqrt(a) sqrt(b)

sqrt(100) * sqrt(10)

10 sqrt(10)

=> R.H.S

[tex] \frac{ \sin(4x) }{ \cos(2x) } = \frac{ \sin(2x + 2x) }{ \cos(2x) } [/tex]

[tex] = \frac{ 2 \sin(2x) \cos(2x) }{ \cos(2x) } [/tex]

[tex] = 2 \sin(2x) [/tex]

[tex] = 2(2 \sin(x) \cos(x) )[/tex]

[tex] = 4 \sin(x) \cos(x) [/tex]

R.H.S = L.H.S

PROVED!

Answer:

Below

Step-by-step explanation:

● 4 sin(x) cos(x) = sin(4x)/cos(2x)

Let's prove that:

● 4 sin(x) cos(x) cos(2x) = sin(4x)

It's easier to prove it than the first one

■■■■■■■■■■■■■■■■■■■■■■■■■■

● 4 sin(x) cos(x) cos (2x)

● [2 sin(x) cos(x)] 2 cos(2x)

We khow that [2 sin(x) cos(x)]= sin(2x)

So:

● sin(2x) 2 cos(2x)

Based on the same relation

● sin(4x)

It's proved

Given that :-

→ N represent the number of bikes .

→ Weight of container including bikes is 250+23(n-1) pounds.

To Find :-

→ Weight of container when we have 20 bikes.

Solution :-

→ Weight = 250+23(n-1) pounds

Putting the value of n here .

→ Weight = 250+23(20-1)

→ Weight = 250 +23(19)

→ Weight = 250 + 437

An expression is defined as a set of numbers, variables, and mathematical operations. The container weight with 20 bikes in it will be 687.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given that the weight of the container in pounds, including the bikes, can be modeled using the expression 250 + 23 (n-1). Therefore, the container weighs 20 bikes in it will be,

Weight of container = 250 + 23(n - 1)

                                 = 250 + 23(20 - 1)

                                 = 250 + 23(19)

                                 = 250 + 437

                                 = 687

Hence, the container weight with 20 bikes in it will be 687.

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Answer:

B

Step-by-step explanation:

Step 1: Find √11

√11 is between perfect squares √9 and √16

√9 < √11 < √16

3 < √11 < 4

So it is between 3 and 4

Step 2: Evaluate

√11 = 3.31662

Closest dot is B.

Answer:

The data we have is:

the probability that a civil servant own a car is 1/6

Two civil servants are selected at random.

a) The probability that each own a car.

Ok, here we have two events:

Person 1 haves a car.

Person 2 haves a car.

The probability of each of those events is the same, 1/6.

P1 = 1/6

P2 = 1/6

Now, the probability of both events happening at the same time is equal to the product of the individual probabilities.

P = P1*P2 = (1/6)*(1/6) = 1/36.

b) Only one has a car.

Suppose that Person 1 has the car and Person 2 has not a car.

The probability for person 1 is 1/6.

And for person 2, is the negation of having a car:

So if we have prob of having a car = 1/6

Then the probability of not having a car is = 1 - 1/6 = 5/6.

Then we have:

P1 = 1/6

P2 = 5/6.

The joint probability is:

P = P1*P2 = (1/6)*(5/6) = 5/36.

But we also have the case where person 1 does not have a car, and person 2 does have one, then we have a permutation, and the actual probability is two times the obtained above.

P = 2*(5/36) = 10/36

Answer:

33000

Step-by-step explanation:

Substituting 250 for x and -120 for y, we get:

(250)^2 + 2(250) - (250)(120)  =  62500 + 500 - 30000, or

32500 + 500, or 33000

Answer:B&D

Step-by-step explanation:

Answer:

72ft.

Step-by-step explanation:

18(18)=324

18(4)=72

Answer:

Length = 82.5 feet

Width = 17.5 feet

Step-by-step explanation:

The formula for the Perimeter of a rectangle = 2(Length + Width)

= 2L + 2W

We are told in the question that: Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard

Hence, The perimeter of the rectangular front yard = 200 feet

200 = 2( L + W).........Equation 1

Also, the length is 5 feet less than 5 times the width

L = 5W - 5

Hence,

200= 2(5W - 5 + W)

200 = 2(5W + W - 5)

200 = 2(6W - 5)

200 = 12W - 10

Collect the like terms

200 + 10 = 12W

210 = 12W

W = 210/12

W = 17.5 feet

Substitute 17.5 for W in Equation 1

200 = 2( L + W).........Equation 1

200 = 2( L + 17.5)

200 = 2L + 35

200 - 35 = 2L

2L = 165

L = 165/2

L = 82.5 feet

Therefore, the Length of the rectangular fence = 82.5 feet while the Width of the rectangular fence is 17.5 feet.

Answer:

B = 4

Step-by-step explanation:

Given that B is directly proportional to A then the equation relating them is

B = kA ← k is the constant of proportionality

To find k use the condition B = 3 when A = 18 , then

3 = 18k ( divide both sides by 18 )

k = [tex]\frac{3}{18}[/tex] = [tex]\frac{1}{6}[/tex]

B = [tex]\frac{1}{6}[/tex] A ← equation of proportion

When A = 24, then

B = [tex]\frac{1}{6}[/tex] × 24 = 4

Answer:

Solution : First Option

Step-by-step explanation:

This equation is quadratic as there is a " x^2 " term present. If you were to expand the equation,

x(x - 6) = - 5,

x^2 - 6x = - 5,

x^2 - 6x + 5 = 0

As you can see this resembles a quadratic equation. Your solution will be the first option, 1. The equation is a quadratic equation because there is an x^2 term

Answer:

The equation is an quadratic equation because there is an x^2-term 2

Step-by-step explanation: