Which graph represents the solutions to the inequality 2x-6<4?

It's not a rectangle. Look at the picture.

It is a parallelogram.

The area of the red rectangle:

[tex]A_{\boxed{ \ }}=(4+8)(6+3)=(12)(9)=108[/tex]

The areas of the right triangles:

[tex]A_1=\dfrac{1}{2}(3)(4)=6\\\\A_2=\dfrac{1}{2}(6)(8)=24[/tex]

The area of a parallelogram:

[tex]A=A_{\boxed{ \ }}-(2A_1+2A_2)\\\\A=108-(2\cdot6+2\cdot24)=108-(12+48)=108-60=48[/tex]

Answer:

hell have 120,000

Step-by-step explanation:

Answer:

The domain is all real numbers. The range is {y|y ≤ 16}.

Step-by-step explanation:

The vertex of a parabola is given by

[tex](\frac{-b}{2a}, \frac{4ac-b^2}{4a})[/tex].

As a = -1, b = -2, c= 15 here, then the vertex is at (1,16).

As a is negative, it opens downward, so the range is  {y|y ≤ 16}.

Meanwhile, all parabolic functions have a domain of [tex]\mathbb{R}[/tex].

Answer:

SEgment AC is congruent to segment AB

Step-by-step explanation:

given is a triangle ABC with a segment joining A to D on side BC.

To prove that ABD is congruent to ACD

Let us compare these two triangles.

AD = AD (reflexive) Thus one side is equal.

IF AB = AC, then by isosceles triangles property we have angle B = angle C

Thus we get two sides equal.  But this is a necessary condition not sufficient.

Because to prove congruence we need one more condition either CD = BD or Angle CAD = angle DAB

Thus if either AD is angle bisector, or D is mid point besides AC = AB we get

the two triangles are congruent.

Answer: x = 4

Step-by-step explanation:

[tex]\dfrac{3}{5}(10 + 5x) - \dfrac{1}{3}(6x + 3)=9[/tex]

[tex]\dfrac{3}{5}(10 + 5x)(15) - \dfrac{1}{3}(6x + 3)(15)=9(15)[/tex] multiplied by common denominator

3(10 + 5x)(3) - 1(6x + 3)(5) = 9(15)   reduced all fractions

90 + 45x - 30x - 15 = 135      distributed

15x + 75 = 135      simplified (added like terms)

15x = 60         subtracted 75 from both sides

  x = 4          divided 15 from both sides

Answer:

1.61904761905

Step-by-step explanation:

-5 2/3 is equal to -17/3. We then multiply the two fractions: -2/7 *-17/3, the answer is 1.61904761905 as a decimal or 34/21( or 1 13/21).

Hope this helps! <3

Answer: The price per pound is $18

Answer:

2.3 degrees.      

Step-by-step explanation:

Please find the attachment.

We are told that an airplane must clear a 60-foot pole at the end of a runway 500 yards long.

Let us convert 500 yards to feet.

1 yard= 3 feet.

500 yards= 3*500 feet= 1500 feet.

We can see from our attachment pole and runway are in form of a right triangle. The pole is opposite to angle of elevation of plane and length of runway is adjacent.

Since tangent represents the relation between opposite and adjacent of right triangle, So we will use tangent to find angle of elevation that plane must ascend to clear the pole.  

[tex]tan(\theta)=\frac{60}{1500}[/tex]    

[tex]\theta=\tan^{-1}(\frac{60}{1500} )[/tex]

[tex]\theta=\tan^{-1}(0.04)[/tex]

[tex]\theta=2.290610042639[/tex]

Therefore, the airplane must ascend 2.3 degrees to clear the pole.

Answer:

The answer would be 998.4

Step-by-step explanation:

251,589 divided by 252 = 998.36

round it to 998.4

The distributive property: a(b + c) = ab + ac.

Answer:

d 15+40=5(3+8)

Step-by-step explanation:

Answer:

an = -6+n

or

an = 1 + 7(n-1)

Step-by-step explanation:

a(1)=1 and a(n+1)=a(n)+7

The explicit formula is

an = a1+ d (n-1)

we know a1 =1

Looking at a(n+1)=a(n)+7

We are adding 7 each time so the common difference is +7

an = 1 + 7(n-1)

We can simplify this

an = 1 + 7n -7

an = -6+n

You can use either formula

Answer:

Each pound of chocolate costs $7.30

Step-by-step explanation:

if 5 pounds of chocolate costs $36.50 then you could simply divide the $36.50 by 5 to calculate the cost of 1 pound of chocolate.

So, 36.50 ÷ 5 = 7.30

Each pound of chocolate costs $7.30

To find the cost of each pound of chocolate, you divide the total cost by the total number of pounds. Given a total cost of $36.50 for 5 pounds of chocolate, the resulting calculation is $36.50 ÷ 5 = $7.30. Thus, each pound costs $7.30.

If you have 5 pounds of chocolate that cost $36.50 in total, and you need to find the cost of each pound of chocolate, you can determine this by dividing the total cost by the number of pounds. This is similar to how in our reference material, to compute the cost of each piece of fruit, you divided the total expense by the quantity of fruit.

In this case, you need to divide the total cost, which is $36.50, by the quantity, which is 5 pounds. So the calculation is $36.50 ÷ 5 = $7.30. Therefore, each pound of chocolate costs $7.30.

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Answer:

DAB must equal 52 because same side interior angles are supplementary. Supplementary describes 2 angles whose measures add up to 180

Answer: May or may not be

Step-by-step explanation:

check the picture and trust me

By using the simple addition operation, the total number of cups of coffee sold in the coffee shop, counting espressos, cappuccinos, and lattes, is 8,594 cups.

To find the total number of cups of coffee sold, we should add up the number of espressos, cappuccinos, and lattes. This principle is known as simple summation or addition operation in mathematics. As per the numbers given:

When we add these together, we get the total cups of coffee sold as:

1627 (Espressos) + 2741 (Cappuccinos) + 4226 (Lattes) = 8594 cups of coffee in total

So, the coffee shop has sold a total of 8594 cups of coffee.

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Answer:

20%

Step-by-step explanation:

Percent increase is difference/original

360-300) / 300

60/300 / 60/60 = 1/5 * 20/20 = 20/100

Percent is out of 100

[ Answer ]

Y = -9

[ Explanation ]

Subtract 15 from both sides:

2/3y + 15 - 15 = 9 - 15

Simplify:

2/3y = -6

Multiply each side by 3:

3 * 2/3y = 3 (-6)

Simplify:

2y = -18

Divide both sides by 2:

2y / 2 = -18/2

y = -9

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Using the simplification, it is proven that the y = -9 from the equation 2/3y + 15 = 9.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given that 2/3y + 15 = 9

Subtract 15 from both sides;

2/3y + 15 - 15 = 9 - 15

Now Simplify,

2/3y = -6

Multiply each side by 3,

3  (2/3y) = 3 (-6)

2y = -18

y = -9

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Answer:

Step-by-step explanation:

3x + 5 = 19 - 4x     subtract 5 from both sides

3x = 14 - 4x      add 4x to both sides

7x = 14    divide both sides by 7

x = 2

Answer:

x=2

Step-by-step explanation:

3x + 5 = 19 - 4x

Add 4x to each side

3x + 5 +4x= 19 - 4x+4x

7x+5 = 19

Subtract 5 from each side

7x+5-5 =19-5

7x =14

Divide each side by 7

7x/7 = 14/7

x = 2

Expand to get 35x^3+49x^2-20x-28

Answer:

3x(3x + 2)

Step-by-step explanation:

Answer:

The number of questions in sixth assignment must be less than or equal to 28.

Step-by-step explanation:

The number of questions in first five assignments are 11,10,13,14 and 14.

It is given that Mrs hawk assigns her students an average of no more than 15 questions on each assignment. Therefore the average of six assignments is less than or equal to 15 questions.

Let the number of questions in sixth assignment be x

[tex]\text{Average}=\frac{\text{Sum of observations}}{\text{Number of observations}}[/tex]

Average of six assignments are

[tex]A=\frac{11+10+13+14+14+x}{6}[/tex]

[tex]A=\frac{62+x}{6}[/tex]

Since the average of questions is no more than 15, therefore

[tex]A\leq 15[/tex]

[tex]\frac{62+x}{6}\leq 15[/tex]

[tex]62+x\leq 90[/tex]

[tex]x\leq 28[/tex]

Therefore the number of questions in sixth assignment must be less than or equal to 28.

Put the values of x to the equation y = 2ˣ:

[tex]x=-1\to y=2^{-1}=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right)\\\\x=0\to y=2^0=1\to(0,\ 1)\\\\x=1\to y=2^1=2\to(1,\ 2)\\\\x=2\to y=2^2=4\to(2,\ 4)\\\\x=3\to y=2^3=8\to(3,\ 8)\\\\x=4\to y=2^4=16\to (4,\ 16)[/tex]

Answer:

[tex]\left\{\left(-1,\ \dfrac{1}{2}\right);\ (0,\ 1);\ (1,\ 2);\ (2,\ 4);\ (3,\ 8);\ (4,\ 16)\right\}[/tex]

The average acceleration of the car is 4 m/s²

The given parameters:

initial velocity of the car, u = 2 m/s

final velocity of the car, v = 16 m/s

time of motion of the car, t = 3.5 s

To find:

The average acceleration of the car is calculated as the change in velocity per change in time.

The formula for average acceleration is given below;

[tex]a = \frac{\Delta v}{\Delta t} = \frac{v- u}{t} = \frac{16 - 2}{3.5} = 4 \ m/s^2[/tex]

Thus, the average acceleration of the car is 4 m/s²

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Answer:

The proportional

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

given the geometric sequence then the n th term rule is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] . [tex]r^{n-1}[/tex]

where r is the common ratio and [tex]a_{1}[/tex] the first term

here r = [tex]\frac{192}{48}[/tex] = [tex]\frac{48}{12}[/tex] = 4 and [tex]a_{1}[/tex] = 3, hence

[tex]a_{n}[/tex] = 3 . [tex]4^{n-1}[/tex] ← third option

In the number game that Valerie and Robbie are playing, based on Valerie's clues, the number she is thinking of can be determined using a mathematical equation: x/4 + 5 - 6 = 6. Solving this equation step-by-step, the number Valerie is thinking of is 28.

In the given scenario, Valerie and Robbie are playing a number game. Valerie tells Robbie that she's thinking of a number which, when divided by 4, then added to 5, and subtracted by 6, equals to 6. This can be translated into a mathematical equation:

x/4 + 5 - 6 = 6

We can simplify this step-by-step. First, we can combine the constants:

x/4 -1 = 6

Next, add 1 to both sides to isolate x/4 on the left:

x/4 = 7

Finally, to find x, multiply both sides by 4:

x = 28

So, the number that Valerie is thinking of is 28.

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PL= sqrt(4^2+12^2)=4sqrt(1+9)=4sqrt(10)

Using similarity gives that AM=4/3.

ML=40/3

[PLMU]=40/3 * 4 = 160/3 (53.33)

Or

PM= sqrt(4^2+16/9)=sqrt(160/9)=4sqrt(10)/3

4sqrt(10)*4sqrt(10)/3=160/3 or approximately 53.33

The earnings for selling the same number of each type of sandwich, considering both Turkey and Ham with Pretzel Roll and Bagel options, amount to $48. This is derived from a simplified expression of $29.10x, factored by 11, indicating a total revenue of $4.30 per sandwich.

Earnings for Selling Sandwiches

1: Identify the Given Information

We have two types of sandwiches: Turkey and Ham.

Each type comes in two types of bread: Pretzel Roll and Bagel.

Prices are provided for each combination:

Turkey Pretzel: $2.25

Turkey Bagel: $2.00

Ham Pretzel: $1.55

Ham Bagel: $1.30

2: Represent the Number of Sandwiches with a Variable

Let x represent the number of each type of sandwich sold (both Turkey and Ham, regardless of bread).

3: Calculate Earnings for Each Type of Sandwich

Turkey Sandwich: $11 (given price) * x (number sold) = $11x

Ham Sandwich: $11 (given price) * x (number sold) = $11x

Step 4: Calculate Earnings for Each Bread Type (excluding overlapping information)

Pretzel Roll: (Earnings from Turkey Pretzel + Earnings from Ham Pretzel) = ($2.25 * x) + ($1.55 * x) = $3.80x

Bagel: (Earnings from Turkey Bagel + Earnings from Ham Bagel) = ($2.00 * x) + ($1.30 * x) = $3.30x

5: Combine Earnings for Total Revenue

Total Earnings = Earnings from Turkey Sandwiches + Earnings from Ham Sandwiches + Earnings from Pretzel Rolls + Earnings from Bagels

Total Earnings = $11x + $11x + $3.80x + $3.30x = $29.10x

6: Simplify the Expression

Total Earnings = $29.10x

Since we are selling the same number of each type of sandwich, 11 is a common factor in all four terms.

We can factor out 11 to obtain:

Total Earnings = 11 * ($2.65 + $1 + $0.35 + $0.30) = 11 * $4.30 = $48

Therefore, the earnings for selling the same number of each type of sandwich are $48.

[tex]\begin{array}{c|c}18&2\\9&3\\3&3\\1\end{array}\\\\18=\boxed2\cdot\boxed3\cdot\boxed3\\\\\begin{array}{c|c}72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\72=2\cdot2\cdot\boxed2\cdot\boxed3\cdot\boxed3\\\\GCF(18,\ 72)=\boxed2\cdot\boxed3\cdot\boxed3=\boxed{\boxed{18}}[/tex]

The greatest common factor of 18 and 72 can be found through prime factorization, by identifying the prime factors of each number, finding the common factors, and multiplying them together. In this case, the greatest common factor is 18.

To find the greatest common factor (GCF) of 18 and 72 through prime factorization, follow these steps:

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Answer:

y = 8

Step-by-step explanation:

If y varies directly as x we can write y = kx where k is some constant.

Y = 8 when x = 2 so  8 = k*2

k = 8/2 = 4

so y = 4x

This is the equation of variation.

When x = 6, y = 4*6 = 24  (answer).

Answer:

y =24

Step-by-step explanation:

The equation for direct variation is

y =kx

If we know x and y we can solve for k

y=kx

8 =k*2

Divide each side by 2

8/2 = k2/2

4 =k

y =4x

We want to find y when x=6

y =4*6

y =24

Final answer:

Since ΔACD is an isosceles right triangle, the two legs AC and CD are equal. Given CD = 6 √ 3, AC is also 6 √ 3 units.

Explanation:

In triangle ΔABC, we are given that m∠ACB = 90°, meaning that ΔACB is a right-angled triangle. We are also given that CD is perpendicular to AB and that m∠ACD = 45°. Since CD is perpendicular to AB at D, triangle ΔACD is also a right-angled triangle with a 45° angle, which makes it an isosceles right triangle. In an isosceles right triangle, the lengths of the legs are equal. Therefore, AC will be equal to CD which is given as 6 √ 3.

The length of AC in triangle ΔACB can be found using Pythagoras' theorem, AC = √(AB² + BC²). But here we need only the length of AC in the right-angled ΔACD where AC equals CD.

Hence, AC = 6 √ 3 units.