What are the integer solutions to the inequality below?

3<3x−3≤2x+2

Answer:

D

Step-by-step explanation:

The gradient of the line y = -3x+2 is -3 so the gradient of the perp line will be ⅓

Now y=mx+c

8 = (⅓×6) + c

C = 6

Y = ⅓x + 6

Answer:x=(1-sqrt(33))/4=-1.186

x=(1+sqrt(33))/4=1.686

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 (22x2 -  2x) -  8  = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  4x2 - 2x - 8  =   2 • (2x2 - x - 4)

Trying to factor by splitting the middle term

3.2     Factoring  2x2 - x - 4

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -4

Step-1 : Multiply the coefficient of the first term by the constant   2 • -4 = -8

Step-2 : Find two factors of  -8  whose sum equals the coefficient of the middle term, which is   -1 .

     -8    +    1    =    -7

     -4    +    2    =    -2

     -2    +    4    =    2

     -1    +    8    =    7

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

3

:

 2 • (2x2 - x - 4)  = 0

STEP

4

:

Equations which are never true:

4.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Parabola, Finding the Vertex:

4.2      Find the Vertex of   y = 2x2-x-4

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 2 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   0.2500  

Plugging into the parabola formula   0.2500  for  x  we can calculate the  y -coordinate :

 y = 2.0 * 0.25 * 0.25 - 1.0 * 0.25 - 4.0

or   y = -4.125

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 2x2-x-4

Axis of Symmetry (dashed)  {x}={ 0.25}

Vertex at  {x,y} = { 0.25,-4.12}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-1.19, 0.00}

Root 2 at  {x,y} = { 1.69, 0.00}

Solve Quadratic Equation by Completing The Square

4.3     Solving   2x2-x-4 = 0 by Completing The Square .

Divide both sides of the equation by  2  to have 1 as the coefficient of the first term :

  x2-(1/2)x-2 = 0

Add  2  to both side of the equation :

  x2-(1/2)x = 2

Now the clever bit: Take the coefficient of  x , which is  1/2 , divide by two, giving  1/4 , and finally square it giving  1/16

Add  1/16  to both sides of the equation :

 On the right hand side we have :

  2  +  1/16    or,  (2/1)+(1/16)

 The common denominator of the two fractions is  16   Adding  (32/16)+(1/16)  gives  33/16

 So adding to both sides we finally get :

  x2-(1/2)x+(1/16) = 33/16

Adding  1/16  has completed the left hand side into a perfect square :

  x2-(1/2)x+(1/16)  =

  (x-(1/4)) • (x-(1/4))  =

 (x-(1/4))2

Things which are equal to the same thing are also equal to one another. Since

  x2-(1/2)x+(1/16) = 33/16 and

  x2-(1/2)x+(1/16) = (x-(1/4))2

then, according to the law of transitivity,

  (x-(1/4))2 = 33/16

We'll refer to this Equation as  Eq. #4.3.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(1/4))2   is

  (x-(1/4))2/2 =

 (x-(1/4))1 =

  x-(1/4)

Now, applying the Square Root Principle to  Eq. #4.3.1  we get:

  x-(1/4) = √ 33/16

Add  1/4  to both sides to obtain:

  x = 1/4 + √ 33/16

Since a square root has two values, one positive and the other negative

  x2 - (1/2)x - 2 = 0

  has two solutions:

 x = 1/4 + √ 33/16

  or

 x = 1/4 - √ 33/16

Note that  √ 33/16 can be written as

 √ 33  / √ 16   which is √ 33  / 4

Solve Quadratic Equation using the Quadratic Formula

4.4     Solving    2x2-x-4 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     2

                     B   =    -1

                     C   =   -4

Accordingly,  B2  -  4AC   =

                    1 - (-32) =

                    33

Applying the quadratic formula :

              1 ± √ 33

  x  =    —————

                   4

 √ 33   , rounded to 4 decimal digits, is   5.7446

So now we are looking at:

          x  =  ( 1 ±  5.745 ) / 4

Two real solutions:

x =(1+√33)/4= 1.686

or:

x =(1-√33)/4=-1.186

Two solutions were found :

x =(1-√33)/4=-1.186

x =(1+√33)/4= 1.686

Answer:

x = 1

Step-by-step explanation:

[tex] {4}^{x} + 2 \times {2}^{x} - 8 = 0 [/tex]

[tex] {2}^{2x} + 2 \times {2}^{x} - {2}^{3} = 0[/tex]

[tex]substitute \: {2}^{x} = a[/tex]

[tex]a > 0[/tex]

[tex] {a}^{2} + 2 \times a - 8 = 0[/tex]

According to the Wiet theorem:

[tex]a1 = 2[/tex]

[tex]a2 = - 4[/tex]

[tex]when \: a = 2 \: \: \: \: {2}^{x} = {2}^{1} [/tex]

[tex]x = 1[/tex]

[tex]when \: a = - 4 \: \: \: \: {2}^{x} = - 4 \: \: \\ \: \: \: \: \: \: - 4 < 0[/tex]

[tex]x∈∅[/tex]

A)  120 is 30% percent of 400.

Percent Proportion - 120 : 400 = 3 : 10

Percent Equation - 120 = 30% of 400

Percentage means a number οr a ratiο represented in the fοrm οf fractiοns οf 100. It is represented using the percentage sign ‘%’. The abbreviatiοns used tο represent the percentage are ‘pct’ οr ‘pc’. In οther wοrds, the percentage is defined as hοw much οf οne quantity is made by anοther quantity and it is evaluated in terms οf 100.

A) Let x be the unknown percentage.

We can write:

120 = x % of 400

To solve for x, we can divide both sides by 400:

120/400 = x/100

Simplifying the left side:

0.3 = x/100

To solve for x, we can cross-multiply:

100x = 30

x = 30/100

x = 0.3

Converting to a percentage:

x = 0.3 * 100

x = 30%

Percent Proportion - 120 : 400 = 3 : 10

Percent Equation - 120 = 30% of 400

B) x = 4% of 975

x = 4/100 × 975

x = 39

Percent Proportion - 39 : 975 = 1 : 25

Percent Equation - 39 = 4% of 975

C) x = 12.5% of $100

x = 12.5/100 × 100

x = $12.5

Percent Proportion - 12.5 : 100= 1 : 8

Percent Equation - $12.5 = 12.5% of $100

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When a rectangular prism is sliced diagonally, the cross-section will have five sides. The answer is 8.

A rectangular prism has six faces, and when it is cut diagonally, three of the faces will be cut in two.

When the prism is cut diagonally, the two rectangles are cut in half, and the triangle is divided into three parts.

This results in eight sides to the cross-section.

The equation to calculate the number of sides to a cross-section of a rectangular prism is as follows:

N = F + (1/2 * T), where N is the number of sides, F is the number of faces, and T is the number of triangles.

In this, N = 6 + (1/2 * 4)

= 6 + 2

= 8.

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The calculated surface area of the figure is 337 square meters

from the question, we have the following parameters that can be used in our computation:

SA = hp + 2B

From the figure, we have

B = 1/2 * 7 * 9 = 31.5

p = 7 + 9 + √(7² + 9²) = 27.40

h = 10

So, we have

SA = 10 * 27.40 + 2 * 31.5

Evaluate

SA = 337

Hence, teh surface area is 337 square meters

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Answer:

1/6

Step-by-step explanation:

theres only 1, 3 and 6 possibilities

Answer:

Possible Outcomes and Sums Just as one die has six outcomes and two dice have 6 2 = 36 outcomes, the probability experiment of rolling three dice has 6 3 = 216 outcomes. This idea generalizes further for more dice.

Answer:

3.25%

Step-by-step explanation:

To find the percentage commission Juliana earned, we need to divide her commission by the selling price of the house and then multiply by 100 to convert the decimal to a percentage.

Commission rate = (Commission / Selling price) x 100%

Commission rate = ($10,725 / $330,000) x 100%

Commission rate = 0.0325 x 100%

Commission rate = 3.25%

Answer:its 4

Step-by-step explanation:

none

The equation to find out how many bottles of water Dawud's brother drank can be expressed as:

x = 1.5(3) = 4.5

Where x represents the number of bottles of water Dawud's brother drank, and 1.5(3) is the expression for one and a half times the amount Dawud drank. Since Dawud drank three bottles of water, his brother drank 1.5 times that amount, which is 4.5 bottles. Therefore, Dawud's brother drank 4.5 bottles of water.

It's worth noting that after running, it's essential to replenish the fluids lost through sweat to avoid dehydration. The amount of water needed may vary depending on factors such as individual physiology, weather, and the intensity of the exercise. Still, a general guideline is to drink enough fluids to replace the amount lost during the workout.

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To check our answer, we can verify that the number of quarters is 1.7 times the number of dimes, which would be 102. And the total value of her dimes and quarters would be:  $31.50

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's start by using algebra to solve the problem.

Let x be the number of dimes that Carol has saved.

According to the problem, there are 70% more quarters than dimes. We can express the number of quarters in terms of x as 1.7x, since 1.7 times the number of dimes is equal to the number of quarters.

We also know that the combined value of her quarters and dimes is $31.50. We can express this as an equation:

0.10x + 0.25(1.7x) = 31.50

Simplifying and solving for x, we get:

0.10x + 0.425x = 31.50

0.525x = 31.50

x = 60

Therefore, Carol has 60 dimes.

Therefore, To check our answer, we can verify that the number of quarters is 1.7 times the number of dimes, which would be 102. And the total value of her dimes and quarters would be:

60 * $0.10 (dimes) + 102 * $0.25 (quarters) = $31.50

which matches the information given in the problem.

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Answer:

Remark

Secants going through a circle form a ratio that's the same for all secants going through the circle and beginning at 1 point. See the diagram below for the ratio. Follow the Line designations carefully. This comes up many times.

General Ratio is (segment from the external point to the the first intersect point of the circumference divided by the distance from the external point to the second intercept point on the circumference).

General Ratio

Put in terms of the diagram the general ratio is (OA / OB)

Equation

OA/OB = OC/OD

Substitute and Solve

9/(9 + 11) = 10/(10 + x)

9/20 = 10/(10 + x)  Notice that you can't combine the right side. Cross Multiply

9*(10 + x) = 10 * 20  Remove the brackets on the left. Combine the right factors.

90 + 9x = 200          Subtract 90 from both sides.

9x = 200 - 90      

9x = 110                  Divide by 9

110 / 9 = 12.22

Answer:

see below

Step-by-step explanation:

[tex]\text{Average = total points / total students}[/tex]

[tex]95 = (19\times97 + \text{x}) \div 20[/tex]

[tex]1900 = 1843 + \text{x}[/tex]

[tex]\text{x} = 57[/tex]

[tex]\text{The lowest the last test score can be for the whole class to average a 95 is} \0 \ \bold{57.}[/tex]

The co-ordinates of the x and y intercept of the line equation is 2y+ 3x = 1, are (1/2,0) and (0, 1/3) respectively. Gradient of above line is equals to the -3/2.

The X and Y intercepts and the Slope are collectively called the line properties. Gradient is used to measure the steepness of a slope. The formula to determine the gradient of a line is written as, m = Δy/Δx, where m represents the gradient of the line. We have an equation

2y + 3x = 1 --(1)

First, we determine the co-ordinates of x and y intercept of the line (1). For x intercept, substitute y = 0, then

=> 2(0) + 3x = 1

=> 3x = 1

=> x = 1/3

Similarly, for y intercept substitute x = 0 in line (1)

=> 2y + 3(0) = 1

=> 2y = 1

=> y = 1/2

Thus, x and y intercept are 1/3 and 1/2 respectively. Rewrite the equation of line (1) that is in slope-intercept form, 2y + 3x = 1

=> 2y = -3x + 1

dividing by 2

=> y = (-3/2)x + 1/2 --(2)

comparing this equation (2) with y = mx + c, where m is slope of line, so m = -3/2. Therefore, the gradient of line is (-3/2).

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Answer:384

Step-by-step explanation:

Answer:

Step-by-step explanation:

let x be the price of chair and y be the price of table

x = 3+ y/2

3x+y=54

putting the value of x in 2nd equation we get

9+3y/2 +y =54

5y/2=45

y/2=9

y=18

x=12

i hope you find it helpful

Answer: 63 degrees

Step-by-step explanation: On a triangle, all 3 of the angles add up to 180 degrees. I added the 2 angles we know, 92 degrees and 25 degrees. This gave me an answer of 117. Then I took 180-117, and got the answer of 63. That is why angle 3 is 63 degrees.

Answer:

83% or 0.83

Step-by-step explanation:

The probability that a randomly selected customer likes hot or iced coffee can be found using the formula:

P(H or I) = P(H) + P(I) - P(H and I)

where P(H) is the probability that the customer likes hot coffee, P(I) is the probability that the customer likes iced coffee, and P(H and I) is the probability that the customer likes both hot and iced coffee.

We are given that P(H) = 0.75, P(I) = 0.30, and P(H and I) = 0.22. Therefore:

P(H or I) = 0.75 + 0.30 - 0.22 = 0.83

So the probability that a randomly selected customer likes hot or iced coffee is 0.83, or 83%. This makes sense because some customers may like both hot and iced coffee, and so we cannot simply add the probabilities of liking each type of coffee. By subtracting the probability of liking both, we account for these customers and obtain the correct probability.

Answer:(3x-2)2

Step-by-step explanation: hope this helps

Answer: (3x-2)^2

Step-by-step explanation:

Answer:

1. -3

2. 3

Step-by-step explanation:

Given, a = 1 and b = 2

1. ( 1 + 2 )( 1 - 2 )

= (3) × (-1)

= - 3

2. ( 1 + 2 )( 2 - 1 )

= (3) × (1)

= 3

pls like and mark as brainliest if it helps!

Using trigonometric functions, we can find the value of hypotenuse to be 5.88m.

The six basic trigonometric operations take the angle of the right triangle as their domain input value and produce a range of numbers as their output.

The range of the trigonometric function, commonly referred to as the "trig function," of f(x) = sinθ is [-1, 1], and its domain is the angle, expressed in degrees or radians. The other functions have a similar domain and scope. Algebra, geometry, and calculus all make extensive use of trigonometric functions.

Here in the figure,

The angle given is 31°.

Now the opposite angle inside the triangle will be 31° due to the congruent angle theorem.

Now Sin 31° = 3/Hypotenuse

⇒ Hypotenuse = 3/Sin31°

⇒ H = 3/0.51

⇒ H = 5.88

Therefore, length of the hypotenuse = 5.88m

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There are 15 different 2-member committees that can be formed from the 6 members of the high school student council as per combination.

In mathematics, a combination is a way of selecting objects from a larger group without considering the order in which they are chosen. A combination is also known as a binomial coefficient or a choose function, and is denoted by the symbol "n choose k", where n is the total number of objects and k is the number of objects to be selected.

In mathematics, a permutation is an arrangement of objects in a specific order. The number of possible permutations of a set of n distinct objects is given by n!, which is the product of all positive integers up to n.

The number of different 2-member committees that can be formed from a group of 6 members is given by the combination formula:

C(6, 2) = 6! / (2! * (6 - 2)!) = 15

where C(n, r) represents the number of combinations of r items that can be selected from a group of n items.

Therefore, there are 15 different 2-member committees that can be formed from the 6 members of the high school student council to attend the rally in Washington D.C.

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Answer:

Because the vertices are horizontal, we know that the standard form is..

Since no specific figure or measurements were provided in the student question, it's important to follow these steps for any given 3-dimensional shape.

To find the volume and surface area of a figure, follow these steps:
Identify the type of figure
Determine the shape of the figure, whether it's a sphere, cube, cylinder, or another 3-dimensional shape.
Determine the necessary measurements
Depending on the figure, gather measurements like the length, width, height, or radius.
Calculate the volume
Use the appropriate formula for the figure's volume:
- Cube: [tex]V = L^3[/tex](L = length)
- Rectangular prism: V = L * W * H (L = length, W = width, H = height)
- Sphere: V = (4/3) * π * [tex]r^3[/tex](r = radius)
- Cylinder: V = π *[tex]r^2[/tex] * h (r = radius, h = height)
Calculate the surface area
Use the appropriate formula for the figure's surface area:
- Cube: SA = 6 *[tex]L^2[/tex] (L = length)
- Rectangular prism: SA = 2 * (L * W + L * H + W * H) (L = length, W = width, H = height)
- Sphere: SA = 4 * π * [tex]r^2[/tex] (r = radius)
- Cylinder: SA = 2 * π * r * (r + h) (r = radius, h = height)
Round your answers to the nearest hundredth, if necessary
Use standard rounding rules to round the calculated volume and surface area to the nearest hundredth.

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Answer:

107 hamburgers

Step-by-step explanation:

Let's call hamburgers A and cheese burgers B.

We know that A + B = 321

And that the number of cheeseburgers sold was two times the number of hamburgers sold which means ->  B = 2A

So A + 2A = 321

3A = 321

Now you need to divide both sides of the equation by 3 and you get:

A= 107

It is assumed that the vending machine contains cans of grapefruit juice that cost 75 cents each, but the machine isn't functioning properly. The likelihood that the machine accepts a coin is 10 percent.Angela has a quarter and five dimes. We are expected to determine the probability that she would have to attempt the

coins at least 50 times before receiving a can of grapefruit juice.

Let p = 0.1 be the likelihood that the machine accepts a coin, and q = 0.9 be the likelihood that it doesn't.Let's consider X = number of trials required to acquire a can of grapefruit juice. We are looking for P(X ≥ 50).This is a geometric probability issue, and we may utilize the formula:

[tex]P(X ≥ k) = qk-1p[/tex], where k is the number of trials required.

The probability that it will take at least 50 attempts before obtaining a can of grapefruit juice is:

[tex]P(X ≥ 50) = (0.9)49(0.1)≈0.003 or 0.3[/tex] percent (rounded to one decimal place).

Therefore, the likelihood that Angela would have to attempt the coins at least 50 times before acquiring a can of grapefruit juice is 0.3 percent.

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To prove ΔABC ≅ ΔMQR using the SAS criterion, the two options that provide the required information are AB = QR = 31 cm and m∠A = m∠M or CB ≅ RQ and m∠C = m∠Q.

To prove that ΔABC ≅ ΔMQR using the SAS (Side-Angle-Side) criterion, we need to show that two sides and the included angle of one triangle are congruent to the corresponding sides and angle of the other triangle. Therefore, we need to choose two options that provide us with the required information.

The two options that provide the required information are:

AB = QR = 31 cm and m∠A = m∠M: This option provides us with the congruent sides AB and QR and the included angle ∠A = ∠M, as both have a measure of 64°. This satisfies the SAS criterion.

CB ≅ RQ and m∠C = m∠Q: This option provides us with the congruent sides CB and RQ and the included angle ∠C = ∠Q, as both have a measure of 56°. This satisfies the SAS criterion.

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The given question is incomplete, the complete question is:

What additional information could be used to prove ΔABC ≅ ΔMQR using SAS? Select two options. m∠A = 64° and AB = MQ = 31 cm CB = MQ = 29 cm m∠Q = 56° and CB ≅ RQ m∠R = 60° and AB ≅ MQ AB = QR = 31 cm?