Given f(x)=x^2, after Performing the following transformation: shift upward 86 units and shift 27 units to the right the new function g(x)=

Answer:

  \(\dfrac{-5x^2+34x-32}{x^2-10x+24}\)

Step-by-step explanation:

Write each fraction using a common denominator, then combine numerators and collect terms. "Simplify" usually means "eliminate parentheses."

  \(\dfrac{8}{x-4}-\dfrac{4}{x-6}-\dfrac{5x}{x-4}=\dfrac{8(x-6)}{(x-4)(x-6)}-\dfrac{4(x-4)}{(x-4)(x-6)}-\dfrac{5x(x-6)}{(x-4)(x-6}\\\\=\dfrac{8(x-6)-4(x-4)-5x(x-6)}{(x-4)(x-6)}=\dfrac{8x-48-4x+16-5x^2+30x}{(x-4)(x-6)}\\\\=\boxed{\dfrac{-5x^2+34x-32}{x^2-10x+24}}\)

Answer:

\(\sec \theta = \frac{\sqrt{22}}{4}\)

Step-by-step explanation:

Given

\(\tan^2 \theta = \frac{3}{8}\)

Required

\(\sec\ \theta\)

We have:

\(\sec^2\theta = 1 + \tan^2 \theta\)

This gives:

\(\sec^2\theta = 1 + \frac{3}{8}\)

Take lcm and solve

\(\sec^2\theta = \frac{9+3}{8}\)

\(\sec^2\theta = \frac{11}{8}\)

Take square roots

\(\sec \theta = \frac{\sqrt{11}}{\sqrt 8}\)

\(\sec \theta = \frac{\sqrt{11}}{2\sqrt 2}\)

Rationalize

\(\sec \theta = \frac{\sqrt{11}}{2\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}\)

\(\sec \theta = \frac{\sqrt{22}}{4}\)

Answer:

answer is B

Step-by-step explanation:

i got it right on edg

The midpoint of a line segment is the point that is halfway between the two ends of the line segment. A midway separates a line segment into two equal parts.

This is further explained below.

Generally, In the field of geometry, a line segment is defined as the portion of a line that is enclosed by two unique points on the line.

Alternatively, we may say that a line segment is the portion of a line that is between two points. A line does not have any endpoints and may stretch endlessly in any direction, however, a line segment has two endpoints that are fixed or definite in some way.

In conclusion, The term "midpoint" refers to the point along a line segment that is situated exactly midway between the beginning and ending points. A midway separates a line segment into two equal parts.

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Answer:

\(-4\)

Step-by-step explanation:

So we have the two functions:

\(h(x)=4x+5\text{ and } g(x)=3x+5\)

And we want to find:

\((h+g)(-2)\)

This is the same as:

\(h(-2)+g(-2)\)

Let's substitute them for their functions:

\(=(4(-2)+5)+(3(-2)+5)\)

Multiply:

\(=(-8+5)+(-6+5)\)

Add:

\(=-3-1\)

Subtract:

\(=-4\)

And we're done!

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

Answer: x=14 and y=8

*Note: x and y are used as variables to solve the problem. Just know that the sides for one square is 14 and the other, 8.

Step-by-step explanation:

For this problem, we can use system of equations to solve. Let's use x for one side of a square and y for the other.

Equation 1:

x²+y²=260

We get this equation from the sum of the areas. The x² and y² are from the area. Since all sides of a square are equal lengths, we can directly square them.

Equation 2:

4x-4y=24

This equation comes from the difference of the perimeters. 4x and 4y are perimeters because perimeter is adding all sides of the square together. There are 4 sides to a square, therefore we get 4x and 4y.

We can use substitution method to solve.

4x-4y=24                                   [add both sides by 4y]

4x=24+4y                                  [divide both sides by 4]

x=6+y

Now that we have x, we can plug it into any equation and solve.

(6+y)²+y²=260                            [expand]

y²+12y+36+y²=260                    [combine like terms]

2y²+12y+36=260                       [subtract both sides by 36]

2y²+12y=224                              [factor out 2]

2(y²+6y)=224                             [divide both sides by 2]

y²+6y=112                                   [subtract both sides by 112]

y²+6y-112=0                                [factor equation]

(y-8)(y+14)=0                              [set each factor equal to 0 to solve]

y=8 and y=-14

We know that y=8 because (y+14)=0 gives you y=-14, but a length or area can NEVER be negative, only positive.

Now that we have y, we can plug it into any equation to find x.

4x-4(8)=24                                 [combine like terms]

4x-32=24                                   [add both sides by 32]

4x=56                                         [divide both sides by 4]

x=14

Now, we have x and y. x=14 and y=8.

The missing variables are b, x, x and y are 3.73m, 7.88 units, 41.06 units and 8.94 units respectively

We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent or tan = sin/cos

The opposite is the side the angle of consideration is facing

The hypotenuse is the side the right angle  is facing

The adjacent is the side left after determining the opposite and hypotenuse

1st triangle

tan 25° = b/8   (tan = opp/adj)

b = 8 tan 25° = 3.73m

2nd triangle

sin 21° = x/22    (sin = opp/hyp)

x = 22 sin 21° = 7.88 units

3rd triangle

cos 47° = 28/x    (cos = adj/hyp)

x =  28/cos 47° = 41.06 units

4th triangle

Use Pythagoras' theorem:

12² = 8² + y²

y² = 12² - 8²

y² = 144 - 64

y² = 80

y = √80 = 8.94 units

Therefore, the missing variables are b = 3.73m, x = 7.88 units, x = 41.06 units and y = 8.94 units

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Answer:

Henri invested $ 4,500 in bonds and $ 19,500 in stocks.

Step-by-step explanation:

Given that Henri has $ 24000 invested in stocks and bonds, and the amount in stocks is $ 6000 more than three times the amount in bonds, to determine the amount that Henri invested in stocks (S) and the amount he invested in bonds (B), the following calculations must be performed:

6000 + 3B + B = 24000

3B + B = 24000 - 6000

4B = 18000

B = 18000/4

B = 4500

S = 6000 + 3x4500

S = 6000 + 13500

S = 19500

Thus, Henri invested $ 4,500 in bonds and $ 19,500 in stocks.

The requried ball reached a maximum height of approximately 62 feet

Let the ball is thrown vertically upward, we can use the following formula to find the maximum height it reaches:

\(h(t) = -16t^2 + vt + h_0\)

here, h(t) is the height of the ball at time t, v is the initial velocity of the ball (in feet per second), and h0 is the initial height of the ball (in feet). We can also use the fact that the ball remains in the air for 3.8 seconds, which means that the time it takes to reach the maximum height is half of that or 1.9 seconds.

At the highest point, the ball's velocity is zero, so we can find the initial velocity by setting v = 0 in the above formula and solving for h₀:

h₀ = h(t) + 16t²

   = 4 + 16(1.9)²

   ≈ 4 + 57.76

   ≈ 61.76

Therefore, the ball reached a maximum height of approximately 62 feet

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In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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At least 20 people can attend the party

Answer:

3

Step-by-step explanation:

Use KCF method

Keep the first number, Change division to multiplication and flip the second number.

4 ÷ \(\frac{4}{3} = 4 * \frac{3}{4} = 1 * 3 = 3\)

Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

Answer:

17

Step-by-step explanation:

_____________ Hair color

Eye color ___ Brown ___ Black ___ total

Green _____ 22 ________ 15 ____ 37

Blue _______ 18 ________ 19 ____ 37

Total _______40 ________34 ____ 74

Calculate the expected frequency of Blue Eyes and Black Hair?

The expected frequency Count ;

(row total * column total) / total number of observations

Expected frequency ;

Blue eye n black hair = (37 * 34) / 74

Expected frequency count = 1258 / 74 = 17

Expected count = 17

Answer:

The row total of blue eyes is 18 + 19 = 37.

The column total of black hair is 15 + 19 = 34.

The total of the whole table is 22 + 15 + 18 +19 = 74.

Step-by-step explanation:

E=(37)(34)/74=1258/74=17

Answer:

(x + 8) × 4 = 21 × 4

Explanation:

x + 8 = 21

21 - 8 = 13

(13 + 8) × 4 = 21 × 4

21 × 4 = 21 × 4

84 = 21 × 4

84 = 84

Answer:

h(8) = 76.8 ft  h(9) = 91.8 ft  h(10)= 80 ft h(11) = 19.8 ft

Step-by-step explanation:

Recall that to be able to add or subtract two matrices, they have to be the same size.

Therefore:

1) A 3x2 matrix and a 2x4 matrix have not the same size, therefore you cannot add them.

2) A 1x2 matrix and a 1x2 matrix have the same size, therefore you can subtract them.

3) A 2x4 matrix and a 4x2 matrix have not the same size, therefore you cannot subtract them.

Answer:

1) False.

2) True.

3) False.

Answer:

(whats 1girl + 1 girl=) uhh ima go with 2girl ;)

Step-by-step explanation:

whats 1girl + 1 girl=?

well 1+1=2 so 1girl + 1 girl= 2girl

A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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Answer: 7.635 square meters

Step-by-step explanation:

Both triangles have the diameter as one of their sides and they both have a vertex on the circumference of the circle. Thus, the two triangles are right triangles, and the hypotenuse of the triangles is the diameter.

Use the Pythagorean Theorem: \(a^2+b^2=c^2\)

Square root both sides to isolate c (hypotenuse/diameter): \(c=\sqrt{a^2+b^2}\)

Plug in the values of a and b to calculate c: \(c=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\)

The diameter of the circle is 5 meters, so the radius of the circle is 2.5 meters.

Plug in the radius into the equation for the area of a circle: Area = \(\pi r^2=\pi *2.5^2=6.25\pi\) square meters.

The equation for the area of a triangle is \(\frac{1}{2}bh\), where b is the base of the triangle and h is the height of the triangle.

Since we have two congruent triangles, the total area of the two triangles combined is simply b*h.

Plug in the values of b and h to get b*h = 3*4 = 12 square meters.

Subtract the total area of the two triangles combined from the area of the circle to get the area of the shaded region: \(6.25\pi - 12=7.635\) square meters.

\(x=-\frac{1}{2}\)

You could solve this problem by either: Factoring or by using the Quadratic Formula.

SOLVING BY FACTORING STEPS

STEP 1: Move (2x−1)(x+1) to the left side of the equation by subtracting it from both sides.

\(2x^2+3x-(2x-1)(x+1)=0\)

STEP 2: Simplify 2x^2+3x−(2x−1)(x+1).

\(2x+1=0\)

STEP 3: Simplify each term.

\(2x^2+3x-2x^2-x+1=0\)

STEP 4: Simplify by adding terms.

\(2x+1=0\)

STEP 5: Subtract 1 from both sides of the equation.

\(2x=-1\)

STEP 6: Divide each term by 2 and simplify.

\(x=-\frac{1}{2}\)

SOLVE BY USING THE QUADRATIC FORMULA STEPS

STEP 1: Move all terms to the left side of the equation and simplify.

\(2x+1=0\)

STEP 2: Subtract 1 from both sides of the equation.

\(2x=-1\)

STEP 3: Divide each term by 2 and simplify.

\(x=-\frac{1}{2}\)

Answer:

(x-2)²=9

sqrt both sides

don't forget positive and negative roots

x-2=+/-3

well, she is partially correct

x-2=3 is one answer

she didn't remember the other one the x-2=-3

Step-by-step explanation:

(x-2)²=9

sqrt both sides

don't forget positive and negative roots

x-2=+/-3

well, she is partially correct

x-2=3 is one answer

she didn't remember the other one the x-2=-3

Given:

HML = 180°

KMG = 180°           (since both are lines)

∠KML = 83°

To find:

Measurement of ∠KMH

Steps:

Since we know HML is a line and equals to 180°, then

∠LMK + ∠KMH = ∠HML

    83° + ∠KMH = 180°

             ∠KMH = 180° - 83°

             ∠KMH = 97°

Therefore the measurement of ∠KMH is 97°

Happy to help :)

If you need any help in any other question, feel free to ask

Also x = 20.75 (if you need steps pls ask)

Answer:

14 cm²

Step-by-step explanation:

           l = length of rectangular prism = 3 cm

           w = width of rectangular prism = 2 cm

           \(\sf \text{\sf h =height of the rectangular prism = $\sf 1\dfrac{1}{2} =\dfrac{3}{2} \ cm$}\)

         \(\boxed{\text{\bf Volume of rectangular prism = l *w *h}}\)

                                                                \(\sf = 3 * 2 * \dfrac{3}{2}\\\\\\=3*3\\\\= 9 \ cm^2\)

             \(\text{\sf base = $2\dfrac{1}{4} = \dfrac{9}{4} \ cm$}\)

         altitude = 3 cm

         \(\text{Area of triangle = $\dfrac{1}{2}*base*altitude$}\)

                                    \(\sf =\dfrac{1}{2}* 3*\dfrac{9}{4}\\\\\\=\dfrac{27}{8}\\\\= 3.375 \ cm^2\)

     \(\text{\sf height of the triangular prism = H = $1\dfrac{1}{2}=\dfrac{3}{2} \ cm$}\)

           \(\boxed{\text{\bf Volume of triangular prism = area of triangle * H}}\)

                                                                \(\sf = 3.375 * \dfrac{3}{2}\\\\\\= 5.0625 \\\\= 5 \ cm^2\)

Volume of the complex figure:

 To find the volume of complex figure, add the volume of rectangular prism and volume of the triangular prism.

    Volume of the complex figure = 9 +5

                                                       = 14 cm²

Answer:

\(x < -3\text{ or }x > 3\)

Step-by-step explanation:

\(|1-2x|-4 > 1\\|1-2x| > 5\\\\1-2x > 5\\-2x > 6\\x < -3\\\\1-2x < -5\\-2x < -6\\x > 3\)

Based on the information given, we know that the two triangles have two pairs of congruent angles. This is sufficient to prove that the two triangles are congruent using the AAS (Angle-Angle-Side) postulate. Therefore, the method I would use to prove the two triangles congruent is **AAS**.

Answer:

A) E(x) = n ( 1 - p ) = u ( 1 - 1 ) =0

B) \(_{n} C_{x} .P(1-p)_{n-x}\)

Step-by-step explanation:

In other to make money ( M ) you have to flip more head than tail

where : 0 < N < M

N = dollars in your pocket

M = money made from flipping the coin

A) Show that with the probability one that the money in your pocket ends in a 0 or M  as the game ends

This is a binomial distribution problem hence to show that the money in your pocket ends in a 0 or M can be shown as

E(x) = np = u * 1

p = p( head )

1 - p = P ( tail ( failure ))

Hence

E(x) = n ( 1 - p ) = u ( 1 - 1 ) =0

b) probability that the game ends with M dollars in your pocket

To end up with M dollars you have to flip a head more often than a tail

P( head ) = p

P( tail ) = 1 - p

Hence the probability that the game ends with M dollars in your pocket

= \(_{n} C_{x} .P(1-p)_{n-x}\)

n = number of successions

p = probability of flipping a head

p-1 = probability of flipping a tail

In this exercise we have to use the knowledge of probability and binomials to calculate what is asked in this way we find that:

A) \(E(x) = n ( 1 - p ) = u ( 1 - 1 ) =0\)

B) \(nC_xP(1-p)_{n-x}\)

In other to make money ( M ) you have to flip more head than tail where : \(0 < N < M\)

A) Show that with the probability one that the money in your pocket ends in a 0 or M  as the game ends. This is a binomial distribution problem hence to show that the money in your pocket ends in a 0 or M can be shown as:

\(E(x) = np = u * 1\\p = p( head )\\1 - p = P ( tail ( failure ))\\E(x) = n ( 1 - p ) = u ( 1 - 1 ) =0\)

b) probability that the game ends with M dollars in your pocket. Hence the probability that the game ends with M dollars in your pocket:

To end up with M dollars you have to flip a head more often than a tail:  

\(P( head ) = p\\P( tail ) = 1 - p\\nC_xP(1-p)_{n-x}\)

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