If the triangle above is reflected over the y-axis, what is the correct coordinate for A'?
A'(0,5)
A'(2,5)
A'(5,2)
A'(-5, -2)

Answer:

x²+y²=58

Step-by-step explanation:

(x-x₁)²+(y-y₁)²=r²

(0,0)=(x₁,y₁) [centre of the circle)

x²+y²=r²

The point (3,7) belongs to the circle.

3²+7²=r²

r²=9+49

r²=58

x²+y²=58

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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1. 4

2.2

3.0,5

IT IS SAYING TO WORK OUT WHAT THAT LINE REPRESENTS

Answer: help me pleaz

Step-by-step explanation:

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:

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.

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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Answer:384

Step-by-step explanation:

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]

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:

She spent 7 minutes on her math homework.

Step-by-step explanation:

Answer:(3x-2)2

Step-by-step explanation: hope this helps

Answer: (3x-2)^2

Step-by-step explanation:

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:

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

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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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:

2x is equals to 100

x is equals to 100 / 2

x is equals to 50

therefore x=50

A. The length of its edge is 512 cubic units, B. The volume of the sphere is 268.08 cubic units and C. The fraction of the cube is 67 / 128 and the percentage is 52.34%.

A. We are given that the volume of the cube is 512 cubic units.

We are required to find the length of its edge. So, Let the length of an edge of a cube be a units.

Then, the volume of the cube = (length of edge)3

We have the volume of the cube = 512 cubic units.

So, (length of edge)3 = 512 cubic units

Now, we can find the length of the edge by finding the cube root of 512.

So,Length of edge = Cube root of 512 cubic units = 8 units

Now, we need to find the volume of the sphere which fits snugly inside the cube. When a sphere is inscribed in a cube, its diameter is equal to the edge of the cube.

Thus, the diameter of the sphere = 8 units.

Hence, the radius of the sphere = 8 / 2 = 4 units

B. volume of the sphere = (4 / 3)πr3

= (4 / 3) × π × 43

= 4/3 × 3.14 × 64= 268.08 cubic units

C. The fraction of the cube that is taken up by the,

sphere = volume of sphere/volume of cube

= 268.08 / 512= 67 / 128

So, the percentage of the cube taken up by the sphere is,

percentage of cube taken up by sphere = (67 / 128) × 100= 52.34% (approx)

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Answer:

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

The percentage of students who have grade point averages between 1.28 and 3.92 is therefore 99.7%.

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.6 and a standard deviation of 0.44.

Using the empirical rule, the percentage of the students who have grade point averages between 1.28 and 3.92 is 99.7%.

The empirical rule, which is often known as the three-sigma rule, states that in any normal distribution of data, the following percentage of data will be within one, two, or three standard deviations of the mean:-

68.27% of the data will lie within one standard deviation of the mean.- 95.45% of the data will lie within two standard deviations of the mean.- 99.73% of the data will lie within three standard deviations of the mean.

For this question, we want to know what percentage of students have grade point averages between 1.28 and 3.92, which is two standard deviations below and above the mean.

Using the empirical rule, we know that approximately 95% of the data will fall within two standard deviations of the mean, so 95% of the students will have grade point averages between (2.6 - 0.88) = 1.72 and (2.6 + 0.88) = 3.48. However, we want to know what percentage of students fall within the range of 1.28 to 3.92, which is slightly beyond two standard deviations from the mean. Since the empirical rule only provides estimates, we can assume that the additional percentage of students who fall beyond two standard deviations from the mean is roughly 2.5% on each side.

Therefore, the percentage of students who have grade point averages between 1.28 and 3.92 is approximately 95% + 2.5% + 2.5% = 99%.

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Answer: The transformation r y=x reflects the point (x, y) across the line y = x, and the transformation T -3,3 translates the point (x, y) three units to the left and three units up. To find the image point of (-8, 2) after these transformations, we can follow these steps:

Apply the reflection r y=x to the point (-8, 2):

(-8, 2) reflects to (2, -8).

Apply the translation T -3,3 to the reflected point (2, -8):

(2, -8) translates to (-1, -5).

Therefore, the image point of (-8, 2) after the transformation r y=x T -3,3 is (-1, -5).

Step-by-step explanation:

There are 60 possible outcomes for this experiment.

The problem asks to determine the total number of outcomes for an experiment consisting of three steps with different numbers of possible outcomes at each step.

To solve this problem, we need to apply the multiplication principle, which states that the total number of outcomes for a sequence of events is equal to the product of the number of outcomes at each event.

In this case, there are two possible outcomes for the first step, six possible outcomes for the second step, and five possible outcomes for the third step.

Therefore, the total number of outcomes possible is:

2 * 6 * 5 = 60

Therefore, there are 60 possible sequences of events that can occur in this experiment.

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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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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 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?