Use f(x) = 1
2
x and f -1(x) = 2x to solve the problems.

f(2) =
1

f−1(1) =
⇒ 2

f−1(f(2)) =
⇒ 2

f−1(−2) =
1
⇒ -4

f(−4) =
2
⇒ -2

f(f−1(−2)) =
2
⇒ -2

In general, f−1(f(x)) = f(f−1(x)) =

No, there are three different values for x when each expression is set equal to 10.

To calculate the total surface area of a triangular prism, we need to find the area of each face and add them up.

The triangular faces have base 5cm and height 12cm, so each one has an area of:

(1/2) x 5cm x 12cm = 30cm²

There are two of these faces, so their combined area is:

2 x 30cm² = 60cm²

The rectangular faces have dimensions 5cm x 10cm and 5cm x 13cm, so their areas are:

5cm x 10cm = 50cm²

5cm x 13cm = 65cm²

Again, there are two of these faces, so their combined area is:

2 x (50cm² + 65cm²) = 230cm²

Finally, we add up the areas of all the faces to get the total surface area:

60cm² + 230cm² = 290cm²

Therefore, the total surface area of this triangular prism is 290cm².

The equation of the tangent line at (0, 2) to the circle is 2x + 3y = 6.

We have,

To find the equation of the tangent at the point (0, 2) to the circle with equation (x + 2)² + (y + 1)² = 13,

We can use the following steps:

- Find the slope of the tangent line:

The slope of the tangent line at a point on the circle is equal to the negative reciprocal of the slope of the radius passing through that point. Since the center of the circle is at (-2, -1) and the point of tangency is

(0, 2), the slope of the radius passing through the point of tangency can be calculated as:

The slope of radius = [tex](y_2 - y_1) / (x_2 - x_1)[/tex] = (2 - (-1)) / (0 - (-2)) = 3/2.

Using the point-slope form:

[tex]y - y_1 = m(x - x_1),[/tex] where [tex](x_1, y_1)[/tex] is the point of tangency and m is the slope, we can substitute the values of [tex](x_1, y_1)[/tex] = (0, 2) and m = -2/3 into the equation:

y - 2 = (-2/3)(x - 0)

Simplifying the equation:

y - 2 = -2/3x

Multiplying both sides by 3 to eliminate the fraction:

3y - 6 = -2x

Rearranging the equation to the standard form:

2x + 3y = 6.

Therefore,

The equation of the tangent line at (0, 2) to the circle is 2x + 3y = 6.

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Answer:

C

Step-by-step explanation:

First it is a reflection of the original then a fractional dilation that makes the reflection SMALLER...it is no longer CONGRUENT, but it is SIMILAR

The value of measure of arc JK is,

⇒  (arc KJ) = 28 degree

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Measure of arc KL = 152°

Now, We know that;

⇒ m (arc LK) + m (arc KJ) = 180°

Substitute given values, we get;

⇒ 152° + m (arc KJ) = 180

⇒ m (arc KJ) = 180 - 152

⇒  (arc KJ) = 28 degree

Thus, The value of measure of arc JK is,

⇒  (arc KJ) = 28 degree

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Ab=3.14xRadious to the power of 2

then to the area of the rectange you do B x H = YOUR ANSWER

Answer: The answer is D, reflection, then rotation results in an image that is congruent to the original.

Step-by-step explanation:

It is upsetting to get a question wrong and the teacher doesn't really explain the right answer. You were so close but you just needed to flip the answers rotation and reflection around.

In the first image, the two triangles ACB and EDF are symmetrically are across from each other, which is called reflection.

ACB-reflection-BCA

Then in the second image, triangle GHI is rotated 90 degrees counterclockwise, which would obviously be called rotation.

A                  

C -rotation- BCA

B

Therefore, the first step is reflection, and the second step is rotation, making the answer to this question d. Hope this helps with the clarified explanation!

-From a Fifth Grade Honors Student!

Answer: x = 112°, z = 31°

Step-by-step explanation:

We can find the measurement of angle x since ∠x and 68° are same-side interior angles and they are supplementary.

            180° - 68° = x

            112° = x

            x = 112°

Next, we can find the measurement of angle x because of the corresponding angles and vertical angles.

            x = (4z - 12)

            112° = (4z - 12°)

            124° = 4z

            z = 31°

Answer:

£26.77

Step-by-step explanation:

450(100% + 2%)^6

= 450 (1.02)^6

= 506.77.

506.77 - 480 - 26.77.

Riley had £26.77 left.

Gabe uses a total of 10 feet of string for all his puppets in art class.

In art class, Gabe is creating marionettes by attaching strings to puppets. He ties 6 inches of string to the head of each puppet and 9 inches of string to each of the 2 arms. Since Gabe has a total of 5 puppets, let's calculate the total amount of string he uses.

For each puppet, Gabe uses 6 inches of string for the head. Since he has 5 puppets, the total string used for the heads is 5 puppets × 6 inches/puppet = 30 inches.

Similarly, Gabe uses 9 inches of string for each arm of each puppet. Since each puppet has 2 arms, he uses a total of 2 arms × 9 inches/arm = 18 inches of string per puppet. For 5 puppets, the total string used for the arms is 5 puppets × 18 inches/puppet = 90 inches.

To find the total string used, we add the string used for the heads and arms: 30 inches + 90 inches = 120 inches.

Since there are 12 inches in a foot, the total string used by Gabe is 120 inches / 12 inches/foot = 10 feet.

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An equation of the circle that has center (3,5) and a diameter with length of 6 units is (x - 3)² + (y - 5)² = 3².

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided, we have the following parameters for the equation of this circle:

Center (h, k) = (3, 5)

Radius (r) = diameter/2 = 6/2 = 3 units.

By substituting the given parameters, we have:

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 5)² = 3²

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The coordinates of the point X on the line segment is (-2/7, 48/7).

Given that, a point X on a segment with endpoints W(-2, 9) and Y(2, 4) partitions the segment in a 3:4 ratio.

Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:

P(x, y) = P(x, y) = [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)]

Here, P(x, y) = [(3×2+4×(-2))/(3+4), (3×4+4×9)/(3+4)]

= (-2/7, 48/7)

Therefore, the coordinates of the point X on the line segment is (-2/7, 48/7).

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Answer:

Just some background:

Congruent means that a triangle has the same angle measures and side lengths of another triangle.

SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.

Let's look at A first.

The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.

Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.

Therefore both triangles are the same by Side-Angle-Side or SAS.

Now look at B.

It's a right triangle. We are missing 1 side of each triangle.

Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).

so 2^2 + b^2 = 4^2

4 + b^2 = 16

b^2 = 16-4

b^2 = 12

That missing side is the [tex]\sqrt{12}[/tex].

This does NOT match the triangle on the left.

Theses two triangles are NOT congruent.

The experimental probability of the computer generating a 3 or a 4 will be 28%.

Experimental probability can be found in the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event;

[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]

We are given that a computer generates 75 integers from 1 to 8 at random. The results are recorded in this table.

Outcome;

1 2 3 4 5 6 7 8

Number of times outcome occurred;

12 16 9 12 4 7 5 10

Therefore,

P_e(E) = 9 + 12 /2

P_e(E) =28%

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Answer:28%

Step-by-step explanation:
i took the quiz<33

Answer:

1st question, see attachment (-32 is answer). 2nd question, answer is (x+3).

Step-by-step explanation:

please see attachment for 1st question.

2nd question:

-3 means x + 3

for any number A

(-A) is x + A

(A) is x - A

f(0) just means put 0 wherever x is in equation

Answer:  To estimate the value of csc 120° using the graph of y = csc x, we can locate the point on the graph that corresponds to 120° and read the y-coordinate (csc value) from there.

On the graph of y = csc x, we observe that the csc value is undefined at x = 0° and x = 180° due to vertical asymptotes. Additionally, csc x has maximum and minimum points at multiples of 90°.

To estimate csc 120°, we can look for the nearest maximum or minimum point on the graph. The closest maximum point to 120° is at 90°, and the closest minimum point is at 180°.

Since the maximum value of csc x is 1, we can estimate csc 120° to be approximately 1.

Therefore, the estimated value of csc 120° is 1 (rounded to the nearest tenth).

Step-by-step explanation:

Based on law of sine, the value of angle C is equal to 94.5 degree.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

we have, by law of sines,

We will use the law of sines to find c as;

sin c                sin 97.5

--------------- = -------------

14.5                      13.7

(13.7)sin c= 14.5 sin 97.5

sin c =  14.5 sin 97.5 / (13.7)

sin c = - 0.1168

Angle c = 94.5

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To determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle, we can compare the given information with the formulas for each law.

The Law of Sines states:

a / sin(A) = b / sin(B) = c / sin(C)

The Law of Cosines states:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we are given the lengths of all three sides of the triangle (a = 6.0, b = 7.7, c = 13.6). Therefore, we have enough information to use the Law of Cosines to solve the triangle.

Using the Law of Cosines, we can find the measures of the angles:

c^2 = a^2 + b^2 - 2ab * cos(C)

(13.6)^2 = (6.0)^2 + (7.7)^2 - 2 * 6.0 * 7.7 * cos(C)

184.96 = 36 + 59.29 - 92.4 * cos(C)

184.96 = 95.29 - 92.4 * cos(C)

92.67 = -92.4 * cos(C)

cos(C) ≈ -1

Since the cosine of an angle cannot be greater than 1 or less than -1, it is not possible for the given triangle to have an angle with a cosine of -1. Therefore, the triangle is not solvable with the given side lengths.

In this case, the Law of Cosines is needed, but the triangle cannot be solved with the given information.

The z-score corresponding to a student who scored 85% in Clarice's class is 1.

To calculate the z-score for a student with a score of 85% in Clarice's class, we need to use the formula:

z = (x - μ) / σ

where:

z is the z-score

x is the individual student's score

μ is the mean score

σ is the standard deviation

Given:

x = 85% (the student's score)

μ = 75% (mean score)

σ = 10% (standard deviation)

Plugging in these values into the formula, we get:

z = (85% - 75%) / 10%

Simplifying the equation:

z = 10% / 10%

z = 1

Therefore, the z-score corresponding to a student who scored 85% in Clarice's class is 1.

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Answer:

x = 3; y = 4

Step-by-step explanation:

adilenechapa22 wrote the correct answer first so they deserve the Brainiest for the question.  However, I can help you understand how we get to the answer.

Step 1:  Isolate y in 4x + y = 16 by subtracting 4x from both sides to prepare for the substitution:

(4x + y = 16) - 4x

y = -4x + 16

Step 2:  Substitute this equation for y in the first equation to first solve for x:

6x + 5(-4x + 16) = 38

6x - 20x +80 = 38

-14x + 80 = 38

-14x = -42

x = 3

Step 3:  Plug in 3 for x in 4x + y = 16 to solve for y:

4(3) + y = 16

12 + y = 16

y = 4

Optional Step 4:  We can check that we've found the correct solutions by plugging in 3 for x and 4 for y in both equations in the system and seeing that we get 38 and 16:

Checking solutions in first equation:

6(3) + 5(4) = 38

18 + 20 = 38

38 = 38

Checking solutions in second equation:

4(3) + 4 = 16

12 + 4 = 16

16 = 16

The statement is proved: PX = 12√6/5 and PY = 12√6/7.

To prove that PX = 12√6/5 and PY = 12√6/7, we will use the properties of similar triangles and the Pythagorean theorem.

First, let's denote the intersection point of the diagonals as O.  

We know that triangle ABP is similar to triangle CDP, as they share the same angles due to being vertical angles.

Therefore, we can write the following proportion:

AB/CD = BP/PD

Substituting the given values, we have:

6/12 = BP/PD

Simplifying, we find:

BP = PD/2

Since CP/PD = 1, we can conclude that CP = PD.

Now, let's consider triangle ABP and triangle CBO.

These triangles are similar because they share the same angles (due to being vertical angles) and have proportional sides.

We can write the following proportion:

AB/BC = BP/CO

Substituting the given values, we have:

6/7 = BP/CO

Rearranging the equation, we find:

CO = (7/6)BP

Now, let's focus on triangle ODP.

Using the Pythagorean theorem, we can write the following equation:

[tex]OD^2 = OP^2 + PD^2[/tex]

Since we want to find PX and PY, which are the altitudes from P to AD and BC respectively, we need to express OP in terms of PX and PD, and OD in terms of PY and PD.

Looking at triangle ODP, we can see that OP = PX + OX and OD = PY + OY.

Substituting these expressions into the Pythagorean theorem equation, we have:

[tex](PX + OX)^2 = OP^2 = (PY + OY)^2 + PD^2[/tex]

Expanding and simplifying the equation, we get:

[tex]PX^2 + 2PXOX + OX^2 = PY^2 + 2PYOY + OY^2 + PD^2[/tex]

Since OX = OY = 0 (the altitudes are perpendicular to the bases), the equation simplifies to:

[tex]PX^2 = PY^2 + PD^2[/tex]

Now, let's substitute the given values into this equation:

[tex](PX)^2 = (12\sqrt{6/7} )^2 + (PD)^2[/tex]

Simplifying further, we get:

[tex](PX)^2 = 72/7 + (PD)^2[/tex]

We know that PD = CP = CD - CP = 12 - PD, so we substitute this expression into the equation:

[tex](PX)^2 = 72/7 + (12 - PD)^2[/tex]

Now, we can solve for [tex](PX)^2:[/tex]

[tex](PX)^2 = 72/7 + 144 - 24PD + (PD)^2[/tex]

Simplifying, we find:

[tex](PX)^2 = 216/7 - 24PD + (PD)^2[/tex]

Since CP/PD = 1, we can write PD = 12 - PD, which gives us PD = 6.

Substituting this value into the equation, we have:

[tex](PX)^2 = 216/7 - 24(6) + (6)^2[/tex]

Simplifying further, we get:

[tex](PX)^2 = 72/7[/tex]

Taking the square root of both sides, we find:

PX = √(72/7) = 12√6/5

Similarly, we can prove that PY = 12√6/7.

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Answer:

Step-by-step explanation:

[tex]P(6,6)=\frac{1}{5} \times \frac{1}{5} =\frac{1}{25}[/tex]

Step-by-step explanation:

They are chords that cover the same arc length, so the chords are =

2s = s + 11     subtract 's' from both sides of the equation

s = 11

The value of length of segment t in the intersecting chords is determined as 6.93.

The value of length of segment t is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that the product of two segments of a chord is equal to the product of the two segments of the second intersecting chord in the circle.

From the diagram, the length of t is calculated by setting up the following equation;

4 x ( 4 + 8)  = t x t

4 (12) = t²

48 = t²

t = √ (48)

t = 6.93

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Step-by-step explanation:

Using prime factorization:

3 = 3 x 1

5 = 5 x1

6 = 2 x 3

9 = 3 x 3       take the bold numbers and multiply them 3 x 5 x 2 x 3 = 90

Answer:

15-18

Step-by-step explanation:

The IQR is the middle 50% of a set of numbers

There are 8 numbers, so its the middle 4

The middle 4 consists of 15,15,16,18

The range is 15-18

Answer: 12^2

Step-by-step explanation:

The formula for the Pythagorean Theorem is a^2+b^2=c^2

We are given a & c.

9^2 + b^2 = 12^2

12^2 = 255

9^2 = 81

225 - 81 = 144

[tex]\sqrt{144}[/tex] = 12

Therefore 12^2 is your correct answer.

Answer:

3700kg

Step-by-step explanation:

Use this idea.

"percent" means "per hundred"

Over 100% is more than what you started with.

To do math with percents, change them to a decimal.

145% is 1.45

1.45x = 5365

divide both sides by 1.45

x = 3700

The original value is calculated by dividing 5365 kg by 1.45, which gives approximately 3700 kg as the result.

To find the original value, you need to understand that 145% is equivalent to 145/100 or 1.45. This means that what we have (5365 kg) is 1.45 times the original value. So, to find the original value, we need to divide 5365 kg by 1.45.

Step 1: Convert 145% to a decimal by dividing 145 by 100 to get 1.45.

Step 2: Divide 5365 kg by 1.45.

The calculation looks like this: 5365 kg / 1.45 = 3700 kg (approximately)

So, the original value is about 3700 kg.

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Hello !

Answer:

[tex]\boxed{ \sf a =3 }[/tex]

Step-by-step explanation:

We want to find the value of a that satisfies the following equation :

[tex]\sf 24 = 6(3a - 5)[/tex]

First, let's expand the right side :

[tex] \sf 24 = 6 \times 3a + 6 \times ( - 5) \\\sf 24 = 18a - 30[/tex]

Now let's add 30 to both sides of the equation :

[tex] \sf 24 + 30 = 18a - 30 + 30 \\ \sf54 = 18a[/tex]

Finally, let's divide both sides by 18 :

[tex] \sf\frac{54}{18} = \frac{18a}{18} \\ \boxed{ \sf a =3 }[/tex]

Have a nice day ;)