what are the common factors of 42 and 28

A.1,2,4,7,14

B. 1,2,6,7,14

C. 1,2,4,6,7,14

D. 1,2,7,14



Need help ASP

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

168

Step-by-step explanation:

No of cans of soda Dixie has = 185 - 17 = 168

Another way:

Let Dixie has x cans of soda

Therefore,

Viola has = (x + 17) cans

According to the given information:

x + 17 = 185

x = 185 - 17

x = 168

Answer:

x= 3/4 or 0.75

Step-by-step explanation:

multiply by 7

-7x+3= 14x-25

3=21x-25

28=21x

x=3/4

Answer:

x=4/3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−x+3/7=2x+−25/7

Step 2: Subtract 2x from both sides.

−x+3/7−2x=2x+−25/7−2x

−3x+3/7=−25/7

Step 3: Subtract 3/7 from both sides.

−3x+3/7−3/7=−25/7−3/7

−3x=−4

Step 4: Divide both sides by -3.

−3x/−3=−4/−3

x=4/3

Given: A function y,

Required: To find the zeroes of the given function.

Explanation: For finding the zeroes of the function put y=0 i.e.,

which gives the value of x as

Final Answer: Option C is correct.

Answer:

x = 4

Step-by-step explanation:

6x + 3x = 9x

31 + 5 = 36

9x / 36 = 4

Have a good day :)

Answer:

y=3x-10

Step-by-step explanation:

Slope: (y2-y1)/(x2-x1)

(2-8)/(4-6)

slope= -6/-2 = 3

Point: (6,8)

Slope-intercept: y-y1=m(x-x1)

y-8=3(x-6)

y-8=3x-18

y=3x-10

Answer:

x = -2/3; -20/9 so A

Step-by-step explanation:

im 100% percent sure:)

The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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Answer:

hi your answer is 0.8 or .8 inches thinner look below for explanation!

Step-by-step explanation:

ok so look below for steps!

step 1: write it out 7/8-3/5

step 2: subtract 7/8-3/5=0.8

step 3: write the answer =0.8

HOPE THIS HELPS HAVE A GREAT DAY!

BRAINLIEST?

0.8 as a fraction is 4/5!

I had this for one of my imagine math questions. I don´t know, it doesn't match what the other person said but it was for me 11/40.

Work; 7/8 - 3/5 = 11/40

Answer:

Triangle CED

Step-by-step explanation:

C and M need to both be at the same places in their respective equations.

Zookeepers have expanded one’s definition of care, including concern for the animal’s mental state as well as for its physical well-being.

The present perfect is a verb tense that is used to indicate that an action has already occurred, either once or several times. There are other, less typical uses for the present perfect besides talking about events or changes that have occurred. Continue reading for in-depth explanations, illustrations, and present-perfect tasks.

Forms in the present tense

Has/have + past participle creates the present perfect. The subject has/have been inverted to express a question. Negatives are created by omitting.

You've seen that movie numerous times.

Have you viewed the movie numerous times?

Negative: You've never watched that movie a lot.

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Answer:

Step-by-step explanation:

6 2/5

Number 5 is denominator, keep it for denominator.

Numerator will be 6x5+2 =32

so, a fraction of 6 2/5 greater than 1 is 32/5

Answer: 1/30 is the probability.

The length of the reflected line segment is approximately 11.66 units.

The endpoints of the line segment mentioned in the question are (0,5) and (6,5). After the line segment is reflected across the x-axis, the endpoints of the reflected line segment are (0, -5) and (6, -5).To find the length of the reflected line segment, we will use the distance formula.

Using the distance formula:d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (5 - 5)²]d = √[36 + 0]d = √36d = 6 units. So the length of the original line segment is 6 units.Now, let's find the length of the reflected line segment.Using the distance formula :d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (-5 - 5)²]d = √[36 + 100]d = √136d = 11.66 (approx) units. So the length of the reflected line segment is approximately 11.66 units.

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The locus of points equidistant from the sides of a triangle is called the Incenter. In other words, the Incenter is the point that is equidistant from each side of the triangle.

To construct the Incenter of a triangle, one can draw the angle bisectors of each angle of the triangle. The three angle bisectors intersect at a single point, which is the Incenter. The Incenter is also the center of the circle that is inscribed in the triangle, which is called the Incircle.

The Incenter has some interesting properties. For example, it is the center of the largest circle that can be inscribed in the triangle. This circle is called the Incircle, and it is tangent to each side of the triangle at a single point. Additionally, the distance from the Incenter to any side of the triangle is equal to the radius of the Incircle.

The Incenter also plays an important role in geometry and trigonometry. It is used in various formulas to find the area, perimeter, and angles of a triangle. For instance, the formula for the area of a triangle in terms of its Inradius (the radius of the Incenter) is A = rs, where A is the area, r is the Inradius, and s is the semi perimeter (half of the perimeter).

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Answer:

m<DCB=34

Step-by-step explanation:

90-56=34

The m<DCA would be 56, not the m<DCB

Answer:

Step-by-step explanation:

The area of a regular polygon is

\(A=\frac{1}{2}ap\) where a is the apothem and p is the perimeter. Perimeter is simple: just count the number of sides the polygon has and multiply it by 3 (the length of one side).

p = 3(9) is 27 inches for the perimeter.

We have what we need now to find the area:

\(A=\frac{1}{2}(4.1)(27)\) and

\(A=\frac{1}{2}( 110.7)\) so

A = 55.35 square inches

In order for f(x) to be a linear function, determine the value of k in the data set.

x = {-7, -2, 2, 5}

f(x) = {-15, k, 3, 9}

The value of k is {-5}.

Given that to find the value of k in the data set such that the data set represents a linear function.

Linear Function is a straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.

Here, f(x) or y is the dependent variable, m is a slope of the line, x is the independent variable and b is the y-intercept.

Here,(x,f(x)) are {(-7,-15),(-2,k),(2,3),(5,9)}

The slope of the function,

(x, f(x)) = (2,3) and (5,9)

Slope formula is m=\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\).

Slope m= \(\frac{9-3 }{5-2}\)

Slope m=\(\frac{6}{3}\)

Slope m=2.

Using the point slope form, determine the linear function's equation.

\(y-y_{1} =m(x-x_{1})\)

Here, \((x_{1},y_{1})=(-7,-15)\) and m=2

We get

y + 15 = 2 (x + 7)

y = 2x - 1

Now at x = -2 and f(x) = k

k = 2(-2) - 1

k = -4-1

k=-5

Therefore, the value of k is -5.

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The area of the triangle is 24.5a square units. Thus, the solution to the given problem is that the area of the triangle enclosed by the lines y = 0, x = 7, and the tangent line to the curve y = -atx is 24.5a square units.

Given the curve y = -atx, where a is a positive real number and x is a variable, we can find the equation of the tangent line and calculate the area of the triangle enclosed by the lines y = 0, x = 7, and the tangent line.

The derivative of y with respect to x is dy/dx = -at. The slope of a tangent line is equal to the derivative at the point of tangency, so the tangent line to the curve y = -atx at a point (x, y) has a slope of -at. The equation of the tangent line can be written as: y - y1 = -at(x - x1) ...(1)

Let (x1, 0) be the point where the tangent line intersects the x-axis. Solving equation (1) when y = 0, we get: 0 - y1 = -at(x - x1)

This simplifies to: x - x1 = y1/at

Therefore, x = x1 + y1/at.

Let (7, y2) be the point where the tangent line intersects the line x = 7. The equation of the tangent line can also be written as: y - y2 = -at(x - 7) ...(2)

Solving equations (1) and (2) to find (x1, y1) and y2, we get: x1 = 49/7, y1 = -49a/7, and y2 = -7a.

The vertices of the triangle enclosed by the lines y = 0, x = 7, and the tangent line are: A(0, 0), B(7, 0), and C(49/7, -49a/7). The base of the triangle is AB, which has a length of 7 units. The height of the triangle is the distance between the line AB and point C. The equation of the line AB is y = 0, and the equation of the perpendicular line from point C to AB is x = 49/7. The distance between line AB and point C is given by the absolute value of (-49a/7 - 0), which is 49a/7.

Therefore, the area of the triangle enclosed by the lines y = 0, x = 7, and the tangent line is given by:

(1/2) × base × height

= (1/2) × 7 × (49a/7)

= 24.5a.

Hence, the area of the triangle is 24.5a square units. Thus, the solution to the given problem is that the area of the triangle enclosed by the lines y = 0, x = 7, and the tangent line to the curve y = -atx is 24.5a square units.

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Answer:

the answer is 4/12

Step-by-step explanation:

Answer:

4/15

Step-by-step explanation:

Probability = 6/10 x 4/9 = 4/15

Topic: Probability

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The probability of drawing a white marble on the first draw, followed by a black marble on the second is 4/15.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of drawing a white marble on the first draw, followed by a black marble on the second  = (number of white marbles / total number of marbles) x (number of black marbles / total number of marbles - 1)

6/10 x 4/9 = 24/90 = 4/15

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The octagon's remaining equal angles are each 121.5 degrees.

The sum of the interior angles of any polygon is given by the formula:

Sum of interior angles = (n - 2) * 180 °

where n is the number of sides of the polygon.

In the case of an octagon, which has 8 sides, the sum of the interior angles is:

Sum of interior angles = (8 - 2) * 180°

= 6 * 180°

= 1080°

Now, we subtract the known angles from the sum:

1080 ° - (120 ° + 110° + 130 ° + 144° + 90°) = 486°

We are left with 486 °, which is the sum of the equal angles in the octagon. Since there are four equal angles remaining, we divide 486 ° by 4:

486° / 4 = 121.5°

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The size of each of the equal angles is 162 degrees. All the remaining three angles are equal to each other and have a value of 162 degrees.

We know that the sum of all interior angles in a polygon = (n-2)180

where n is the number of sides of that polygon.

In this case, we have an octagon,

The sum of all interior angles in an octagon = (8-2) 180

n = 8 ( an octagon has 8 sides)

The sum of all interior angles in an octagon, A = 1080 degrees.

Sum of given angles = 120 + 110 +130 +144 + 90 = 594

We have 3 more angles in the octagon which are all equal, let's say x

A + x + x + x = 1080

594 + 3x = 1080

3x = 486x

x = 162 degrees

Hence, the remaining equal angles are 162 degrees.

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The projectile will stay in the air for 4 seconds.

The given function is:

\(f(x) =-10x(x-4)\), which is a quadratic function.

A function f(x) in the form of \(ax^{2} +bx+c\) a quadratic function.

As we know the equation of projectile motion is a quadratic equation whose non-zero root provides us the time when motion lasts or we can say it provides the time when an object will hit the ground from the time it was launched in the air.

The roots of the given function are 0 and 4.

So, non-zero root i.e. 4 will be the total time for which projectile stays in the air

Therefore, The projectile will stay in the air for 4 seconds.

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Answer:

D) 4 seconds

Step-by-step explanation:

Got it right on edge! Good Luck <3

Answer:

0.53333333333333

Step-by-step explanation:

Plan B is expected to be worth the most in 100 years due to its exponential growth nature.

Based on the given information, Plan B will be worth the most in 100 years. This is because Plan B grows according to an exponential function, while Plan A grows according to a linear function.

Exponential growth means that the value of an investment increases at an increasing rate over time. In the context of a long-term investment like the one mentioned, exponential growth can lead to significant gains over time.

On the other hand, linear growth implies a constant rate of increase. While Plan A may still yield positive returns, it is likely to be outperformed by the exponential growth of Plan B over a 100-year period.

Therefore, Plan B is expected to be worth the most in 100 years due to its exponential growth nature.

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Based on the given simple statements, "The scroll is open" and "The writings are visible," we can determine which compound statements would also be true.

The scroll is not open or the writings are visible.

This compound statement would be true. Since the first simple statement states that the scroll is open, the negation of this statement would be that the scroll is not open. The second simple statement states that the writings are visible, which aligns with this compound statement. Therefore, this compound statement is true.

The scroll is open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, the second part of this compound statement contradicts the given information.

The scroll is open or the writings are visible.

This compound statement would be true. It directly matches the given simple statements, where both the scroll being open and the writings being visible are mentioned. Therefore, this compound statement is true.

The scroll is not open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, neither part of this compound statement aligns with the given information.

The compound statements that would be true are:

The scroll is not open or the writings are visible.

The scroll is open or the writings are visible.

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Explanation:

Multiply the side length by itself to get the area

area = side*side = (1/4)*(1/4) = 1/16 square inches

Answer:

DirectoryResearch Maniacs

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Square Root of 72 in Simplest Radical Form

Simplest Radical Form

Here we answer "What is the square root of 72 (√72) in simplest radical form?" The square root of 72 in its simplest form means to get the number 72 inside the radical √ as low as possible.

Here is how to do that! First we write the square root of 72 like this:

√72

The largest perfect square of the factors of 72 is 36. We can therefore convert √72 like this:

√36 × 2

Next, we separate the numbers inside the √ as such:

√36 × √2

√36 is a perfect square that equals 6. We can therefore put 6 outside the radical and get the final answer to square root of 72 in simplest radical form as follows:

6√2