Help me with this question please

Answer:

6x+12

Step-by-step explanation:

2x*3= 6x

4*3= 12

6x+12

hope this helps

The radical forms of exponential expressions and the exponential form of the radical expressions can be presented as follows;

19) \((3\cdot r)^{\frac{4}{3} }\) = ∛(3·r)⁴

20) \((2\cdot n)^{\frac{3}{5} }\) = \(\sqrt[5]{(2\cdot n)^3}\)

21) \((7\cdot n)^{\frac{1}{3} }\) = ∛(7·n)

22) \((10\cdot x)^{\frac{3}{2} }\) = √(10·x)³

23) \(x^{\frac{3}{5} }\) = \(\sqrt[5]{x^3}\)
24) \((2\cdot n)^{\frac{1}{6} }\) = \(\sqrt[6]{2\cdot n}\)

25) \((5\cdot r)^{\frac{5}{2} }\) = √(5·r)⁵

26) \(m^{\frac{1}{2} }\) = √m

27) \((6\cdot x)^{\frac{3}{2} }\) = √(6·x)³

28) \((5\cdot a)^{\frac{3}{2} }\) = √(5·a)³

29) ∛(7·x) = \((7\cdot x)^{\frac{1}{3} }\)

30) \(\sqrt[4]{2\cdot n}\) = \((2\cdot n)^{\frac{1}{4} }\)

31) √(7·k) = \((7\cdot k)^{\frac{1}{2} }\)

32) ∛(7·k)⁴ = \((7\cdot k)^{\frac{4}{3} }\)

33) √(10·x)³ = \((10\cdot x)^{\frac{3}{2} }\)

34) ∛(6·m)² = \((6\cdot m)^{\frac{2}{3} }\)

35) √(7·n)³ = \((7\cdot n)^{\frac{3}{2} }\)

36) \(\sqrt[4]{x^5}\) = \(x^{\frac{5}{4} }\)

37) √(6·p)³ = \((6\cdot p)^{\frac{3}{2} }\)

38) (√x)³ = \(x^{\frac{3}{2} }\)

The exponential form of the radical expression \(\sqrt[N]{y^a}\) is; \(y^{\frac{a}{N} }\)

19) \((3\cdot r)^{\frac{4}{3} }\)

The above expression consists of (3·r) raised to power 4/3, which is the cube root of (3·r) raised to the power 4

Therefore, we get;

\((3\cdot r)^{\frac{4}{3} }\) = ∛(3·r)⁵

20) \((2\cdot n)^{\frac{3}{5} }\)

The above expression consists of (2·n) raised to power 3/5, which is the fifth root of (2·n) raised to the power 3

Therefore, we get; \((2\cdot n)^{\frac{3}{5} }\) = \(\sqrt[5]{(2\cdot n)^3}\)

21) \((7\cdot n)^{\frac{1}{3} }\)

The above expression is the cube root of (7·n), therefore, we get;

\((7\cdot n)^{\frac{1}{3} }\) = ∛(7·n)

22) \((10\cdot x)^{\frac{3}{2} }\)

The above expression is the square root of (10·x)³, therefore, we get;

\((10\cdot x)^{\frac{3}{2} }\) = ∛(10·x)³

23) \(x^{\frac{3}{5} }\)

The above expression is the 5th root of x³, therefore, we get;

\(x^{\frac{3}{5} }\) = \(\sqrt[5]{x^3}\)

24) \((2\cdot n)^{\frac{1}{6} }\)

The above expression is the 6th root of (2·n), therefore, we get;

\((2\cdot n)^{\frac{1}{6} }\) = \(\sqrt[6]{(2\cdot n)}\)

25) \((5\cdot r)^{\frac{5}{2} }\)

The above expression is the square root of (5·r)⁵, therefore, we get;

\((5\cdot r)^{\frac{5}{2} }\)= √((5·r)⁵)

26) \(m^\frac{1}{2}\)

The above expression is the square root of m, therefore, we get;

\(m^\frac{1}{2}\) = √m

27) \((6\cdot x)^{\frac{3}{2} }\)

The above expression is the square root of (6·x)³, therefore, we get;

\((6\cdot x)^{\frac{3}{2} }\) = √((6·x)³)

28) \((5\cdot a)^{\frac{3}{2} }\)

The above expression is the square root of (5·a)³, therefore, we get;

\((5\cdot a)^{\frac{3}{2} }\) = √((5·a)³)

29) ∛(7·x)

The above radical expression which is the cube root of (7·x) in exponential form is as follows;

∛(7·x) = \((7\cdot x)^{\frac{1}{3} }\)

30) \(\sqrt[4]{2\cdot n}\)

The above expression which is the quad root of (2·n) in exponential form is as follows;

\(\sqrt[4]{2\cdot n}\) = \((2\cdot n)^{\frac{1}{4} }\)

31) √(7·k)

The above expression which is the square root of (7·k) in exponential form is as follows;

√(7·k) = \((7\cdot k)^{\frac{1}{2} }\)

32) ∛((7·x)⁴)

The above expression which is the cube root of (7·x)⁴ in exponential form is as follows;

∛((7·x)⁴) = \((7\cdot x)^{\frac{4}{3} }\)

33) √(10·x)³

The above expression which is the square root of (10·x)³ in exponential form is as follows;

√(10·x)³ = \((10\cdot x)^{\frac{3}{2} }\)

34) ∛(6·m)²

The above expression which is the cube root of (6·m)² in exponential form is as follows;

∛(6·m)² = \((6\cdot m)^{\frac{2}{3} }\)

35) (√(7·n))³

The above expression which is the square root of (7·n)³ in exponential form is as follows;

√(7·n)³ = \((7\cdot n)^{\frac{3}{2} }\)

36) \((\sqrt[4]{x} )^5\)

The above expression which is the quad root of (x⁵) in exponential form is as follows;

\((\sqrt[4]{x} )^5\) = \((x)^{\frac{5}{4} }\)

37) √(6·p)³

The above expression, which is the square root of (6·p)³ in exponential form, is as follows;

√(6·p)³ = \((6\cdot p)^{\frac{3}{2} }\)

38) √(x³)

The above expression which is the square root of (x³) in exponential form is as follows;

√(x³) = \(x^{\frac{3}{2} }\)

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The equation that describes the graphed function is Option C: g(x) = -f(x) + 2.

The given function is f(x) = √x, which represents the square root function. To determine which equation describes the graphed function, we need to analyze the transformations applied to the original function.

Option A, g(x) = f(-x) + 2:

This equation represents reflecting the graph of f(x) across the y-axis (due to the negative sign in front of x) and then shifting it vertically upward by 2 units. However, this transformation does not match the graph of f(x) = √x.

Option B, g(x) = -f(x + 2):

This equation represents taking the negative of the original function f(x) and shifting it horizontally left by 2 units. This transformation does not match the graph of f(x) = √x.

Option C, g(x) = -f(x) + 2:

This equation represents taking the negative of the original function f(x) and shifting it vertically upward by 2 units. This transformation matches the graph of f(x) = √x.

Option D, g(x) = f(-x + 2)

This equation represents reflecting the graph of f(x) across the y-axis (due to the negative sign in front of x) and shifting it horizontally right by 2 units. This transformation does not match the graph of f(x) = √x.

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Answer:

Because vehicles of different sizes may respond differently to the additive, it may be difficult to conclude whether the additive improves gas mileage for all vehicles.

Step-by-step explanation:

Edge 2021

Whether the addition increases gas mileage for all vehicles may be difficult to determine.

The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive

Because vehicles of different sizes may respond differently to the additive, it may be difficult to conclude whether the additive improves gas mileage for all vehicles.

The type of vehicle is a confounding variable because it is related to both the independent variable (use of the fuel additive) and the dependent variable (gas mileage), and it could potentially influence the results of the study if not controlled for.

This is because the size of the vehicle, a complicating variable, may alter gas economy independently of the addition, making it challenging to assess the additive's actual impact. As a result, the study's findings might be erroneous or misleading.

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Answer:

3x^2+3x4

Step-by-step explanation:

the coefficient comes before the variable

The answer is 12 hope this help

Answer:

Step-by-step explanation:

Answer: 2 6/15 < 2 4/9 < 2 3/5 < 2 2/3

Step-by-step explanation:

The solution to find the five number summary shown below.

When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

To find a five number summary we have follow:

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Answer:

968 ft , I run.

Step-by-step explanation:

Box plot is the use of a rectangle to represent data where the vertical sides of the rectangle represents the lower and upper quartile.

From the box plot,

The minimum is 153 cm

The first quartile is 168.4 cm

The second quartile is 174.2 cm

The third quartile is 183.9

The maximum is 195 cm

See attachment for the missing box plot.

There are 5 vertical lines in a box plot

The first represents the minimum value

The second represents the first quartile

The third represents the second quartile i.e. the median

The fourth represents the third quartile

The last represents the maximum quartile

From the attached box plot.

The first vertical line is 153 cm

The second vertical line is 168.4 cm

The third vertical line is 174.2 cm

The fourth vertical line is 183.9 cm

The firth vertical line is 195 cm

Hence:

The minimum is 153 cm

The first quartile is 168.4 cm

The second quartile is 174.2 cm

The third quartile is 183.9

The maximum is 195 cm

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The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively. This can be solved by using trigonometric functions.

Trigonometric functions are used to describe relationships involving angles and sides of triangles. They are used to calculate the sizes of angles and distances between points. These include sine, cosine, tangent, secant, cosecant and cotangent.

This can be solved by using trigonometric functions.

First we need to find the length of FA to solve the question further.

FA = 1.5+ FD

AG = FA cos 30

AG = 1.5 √3

AG = 1.5 FD √3/2 = 1.5√3  (as cos 30 = √3/2)

DF = 1.5

Thus, FA = AB+BD+FD

FA = 1 + 0.5 + 1.5

So, the length of FA is 3.

Now, for the triangle, ΔABC

as ∠BAC= 30

BC = AB/2

= 0.5

This is because the angle of the right triangle is 30°and we know that when the angle of a right triangle is 30° the length of opposite side is exactly equal to half of the length of the hypotenuse.

For ΔADE,

as ∠DAE= 30, and AD= 1.5

DE= AD/2

= 0.75

For ΔGAF,

as ∠GAF= 30, and FA= 3

FG = FA/2

= 1.5

The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively.

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35 is a reasonable prediction of the number of times he will select 2 yellow socks?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.

In the given question,

The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:

P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25

So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.

To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:

E(X) = n * p

where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.

In this case, n = 175 and p = 1/25. So,

E(X) = 175 * (1/25) = 7

Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.

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Step-by-step explanation:

on the coordinate grid you can imagine a right-angled triangle.

the direct distance between the 2 points is the Hypotenuse (the baseline opposite of the 90° angle).

and the x-coordinate difference and the y- coordinate difference of the 2 points are the 2 legs.

we can then use Pythagoras

c² = a² + b²

with c being the Hypotenuse, a and b being the legs.

so,

distance² = (8-0)² + (2-0)² = 64 + 4 = 68

distance (= length ab) = sqrt(68) = sqrt(4×17) = 2×sqrt(17) =

= 8.246211251...

Answer:

\(8.5x+4y=99.5,\ x+y=17\)

Step-by-step explanation:

\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)

Angle 4 is an exterior angle which is equal to the sum of the two opposite inside angles.

The two opposite inside angles are given as 51 and 51

Angle 3 = 51 + 51 = 102 degrees.

Answer:

\( \displaystyle \angle4 = {108}^{ \circ} \)

Step-by-step explanation:

the sum of the interior angles of a triangle is 180°

thus our equation is

\( \displaystyle {51}^{ \circ} + {51}^{ \circ} + \angle2 = {180}^{ \circ} \)

simplify addition:

\( \displaystyle {102}^{ \circ} + \angle2 = {180}^{ \circ} \)

cancel 102° from both sides:

\( \displaystyle \angle2 = {72}^{ \circ} \cdots \text{I}\)

By straight line theorem we acquire:

\( \displaystyle \angle4 + \angle2 = {180}^{ \circ} \)

substitute:

\( \displaystyle \angle4 + {72}^{ \circ} = {180}^{ \circ} \)

cancel 72° from both sides:

\( \displaystyle \angle4 = {108}^{ \circ} \)

hence, the measure of \(\angle 4\) is 108°

The length of the side of the square is given as follows:

20 cm.

In the figure, there are two expressions used to give the side length to each square, as follows:

In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:

6x - 1 = 4x + 6

2x = 7

x = 3.5 cm.

Then the side length of the square is obtained as follows:

6(3.5) - 1 = 20 cm.

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By using the fact that the sum of the interior angles must be 180°, we wil see that:

x = 110°.

First, remember that the sum of the interior angles of a triangle is alway equal to 180°.

We also can see that the interior angle that is adjacent to x can be written as:

a = 180° - x

Then the sum of the interior angles will give:

30° + 80° + (180° - x) = 180°

30° + 80° - x = 0

110° - x = 0

110° = x

That is the value of x.

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Answer:

<

Step-by-step explanation:

\(24 \: tenths = \frac{24}{10} = 2.4 \\ \\ 2.4 \: \: \red{\bold{ < }} \: \: 2.5\)

The resulting graph is a circle with center at (-3,-1) and radius 3.

The graph of the equation (x+3)²+(y+1)²=9

is a circle with center at (-3,-1) and radius 3. The equation of a circle with center (a,b) and radius r is given by the equation (x-a)² + (y-b)² = r². By comparing the given equation with the standard equation of a circle, we can easily see that the center of the circle is (-3,-1) and the radius is 3. To graph a circle, we need to first plot the center of the circle, which is (-3,-1) in this case. Next, we need to mark the radius of the circle, which is 3 units. We can do this by measuring 3 units from the center in any direction and marking the point. Since the radius of the circle is the same in all directions, we can repeat this process for other directions to get points on the circumference of the circle. We can use a compass to make this process easier. After plotting a sufficient number of points, we can draw a smooth curve passing through all the points to obtain the graph of the circle.

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Answer:

√3(√6+√15)

= 3**1/2(6**1/2 + 15**1/2)

= 3**1/2 · 6**1/2 + 3**1/2 · 15**1/2

= 18**1/2 + 45**1/2

= (2×9)**1/2 + (5×9)**1/2

= 2**1/2 · 9**1/2 + 5**1/2 · 9**1/2

= 2**1/2 · 3 + 5**1/2 · 3

= 3(√2 + √5)

Step-by-step explanation:

Answer: 3 per week.

Step-by-step explanation: 3 x 4 = 12.

Answer:

13 cm

Step-by-step explanation:

To find the perimeter of a triangle you have to add all the sides together

5+5+3=13 cm

This triangle has two sides with the same length, therefore, it is isosceles.

Since, P(male)*P(fail)= 0.33 and P(male and fail) = 0.33 , the two results are equal and independent.

What is Probability?

The possibility of outcome of any event is found by probability. as for an example whenever we toss a coin in the air, then what is the possibility that we get a head? Only based on possible outcomes we can answer this question. It is that part of events which deals with the results of random events. We can basically call it as prediction of any event that is based on study of previous record or the type and no of possible outcome.

Probability of happening of an event= Total no of favorable outcomes/                          Total no of outcomes

Here in this question;

P(male/fail)= P(male and fail)/P(fail)

                 = \(\frac{8/123}{(8+16)/123}\)

                 =\(\frac{8}{24} = \frac{1}{3} = 0.33\)

P(male) = \(\frac{33+8}{123} = \frac{41}{123} =\frac{1}{3} = 0.33\)

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Total length of the two sides of the triangle is 2x² + 4x + 4 and  length of the third side of the triangle is 5x³ - 5x² + 3x - 12.

The total length of the two sides of the triangle is the sum of Side 1 and Side 2:

(3x² - 4x - 1) + (4x - x² + 5)

2x² + 4x + 4

The total length of the two sides of the triangle is 2x² + 4x + 4.

The length of the third side of the triangle can be found by subtracting the sum of Side 1 and Side 2 from the perimeter of the triangle:

Perimeter - (Side 1 + Side 2)

(5x³ - 2x² + 3x - 8) - (3x² - 4x - 1 + 4x - x² + 5)

Combining like terms

5x³ - 5x² + 3x - 12

The length of the third side of the triangle is 5x³ - 5x² + 3x - 12.

The polynomials are closed under addition and subtraction by part A and part B because when we added Side 1 and Side 2, and when we subtracted their sum from the perimeter of the triangle, the resulting expressions were still polynomials with real coefficients.

Therefore, the sum and difference of polynomials with real coefficients are also polynomials with real coefficients.

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Answer:

\(0.0005\) \(= 5 * 10^{-4\)

\(7.1034 * 10^3 = 7103.4\)

Step-by-step explanation:

Solving (a):

\(0.0005\)

Standard form is represented as:

\(a * 10^n\) where \(1 \le a \le 10\)

Move the decimal point to 5 and count the number of times the decimal point is moved forward (forward represents negative).

So:

\(a = 5\)

\(n = -4\)

Hence:

\(0.0005\) \(= 5 * 10^{-4\)

Solving (b):

\(7.1034 * 10^3\)

Express \(10^3\) as \(1000\)

This gives:

\(7.1034 * 10^3 = 7.1034 * 1000\)

\(7.1034 * 10^3 = 7103.4\)

Answer: A. No, Only one Unique Triangle can Be Formed under These Conditions.

Step-by-step explanation: It is not possible for a triangle to have more than one vertex with internal angle greater than or equal to 90°, or it would no longer be a triangle.

The interior angles of a triangle always add up to 180° while the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it. Another way to calculate the exterior angle of a triangle is to subtract the angle of the vertex of interest from 180°.

The sum of the lengths of any two sides of a triangle is always larger than the length of the third side

Pythagorean theorem: The Pythagorean theorem is a theorem specific to right triangles. For any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. It follows that any triangle in which the sides satisfy this condition is a right triangle. There are also special cases of right triangles, such as the 30° 60° 90, 45° 45° 90°, and 3 4 5 right triangles that facilitate calculations. Where a and b are two sides of a triangle, and c is the hypotenuse

Answer:

a.35

Step-by-step explanation:

10 + 20/2 equals 20

20/2+5 equals 15

20+15 equals 35