What are the vertex and range of y = |2x 6| 2? (0, 2); 2 < y < [infinity] (0, 2); −[infinity] ≤ y < [infinity] (−3, 2); 2 < y < [infinity] (−3, 2); −[infinity] ≤ y < [infinity]

Hello!

Solution:

-4h≤-14

Notice right off the bat that the variable's negative.

Divide both sides by -4:

h≥3.5

If we divide both sides by a negative number, we flop the inequality sign.

Final Answer:

h≥3.5

Every value of h that is greater than or equal to 3.5 will make the inequality true.

I hope it helps!

Good luck & enjoy your day!

-SnowFlake

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Triangle STU is a right triangle.

Thus,

We find :

sides s,t and u

the relationship between them is :

As it is a right triangle

So,

According to the pythagoras theorem,

=>u²= t²+s²

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

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The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

The midpoint formular used in finding the midpoint of a segment is expressed as;

( [x₁+x₂]/2 , [y₁+y₂]/2 )

Given the data in the question;

Point V(-2,5)

Point Z(3,-17)

Plug these values into the equation above.

( [x₁+x₂]/2 , [y₁+y₂]/2 )

( [(-2) + 3]/2 , [5 + (-17)]/2 )

( 1/2 , -12/2 )

( 1/2, -6 )

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

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Answer:

A

Step-by-step explanation:

you do a/18=4/a, cross multiply

a^2=72

a=6 square root of 2

Answer:

Step-by-step explanation:

y= -3/8(x+5)(x-3)

Answer:  I posted the picture, just to help you out in future, you can use the app named desmos to graph, and it’s actually a calculator (even more better than the normal calculator)

Step-by-step explanation:

i)The amount of petrol sold by the petrol station on a particular day is 21,600 L

II) Number of customers who would expect to buy 44 L of petrol is 2.28

i)The amount of petrol sold by the petrol station on a particular day can be estimated using the following equation:

Total petrol sold = Mean amount of petrol per customer x Number of customers

= 36 L x 600 customers

= 21,600 L

ii) To find the number of customers who would expect to buy 44 L of petrol, we need to find the probability of a customer buying that amount. We can use the standard normal table and the z-score formula (z = (x - mean) / std dev) to calculate the probability of a customer buying 44 liters of petrol.

z = (44 - 36) / 7 = 2.57

Using the standard normal table, we can find that the probability of a customer buying 44 liters of petrol is about 0.0038 or 0.38%.

Therefore, we can estimate that about 2.28 customers would expect to buy 44 liters of petrol on that day by multiplying the probability of buying 44 liters of petrol by the total number of customers.

Number of customers who would expect to buy 44 L of petrol = 0.38% * 600 = 2.28

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The complete question is:

The amount of petrol bought by a customer at a petrol station is normally distributed with mean 36 L and standard deviation 7 L.                                                                                                              on a particular day, the petrol station has 600 customers. i) how much petrol would you expect the petrol station to sell on this day? ii) how many customers would you expect to buy 44 l of petrol?          

If x < 3, then the square root of  (x^2 - 6x + 9) can be simplified to (3-x).

First we factorise the quadratic expression:

x^2 - 6x + 9 = (x - 3)^2 ..(i)

(Since the expression is a perfect square trinomial, it can be factored as the square of a binomial.)

Then we will simplify the square root:

√(x^2 - 6x + 9) = √((x - 3)^2).

Now, since x - 3 is squared, taking the square root will eliminate the square, resulting in the absolute value of x - 3.

Final simplified form: √((x - 3)^2) = |x - 3|.

Therefore, the simplified square root expression is |x - 3| when x < 3 which equals to 3-x.

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The measure of the unknown angle in the full circle is calculated as: 310 degrees.

We have,

The angle measure of a full circle equals 360 degrees.

The full circle given is divided into two angles, of which 50 degrees is a measure of one of the angles.

we know that,

A circle is 360 degrees

50 +x = 360

x = 360-50

x = 310

The unknown angle = 360 - 50 = 310 degrees.

Hence, c.) 310° is the measure of the unknown angle.

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Answer:

45 ways

Step-by-step explanation:

Combination method is appropriate for this question since it deals with arrangement.

i.e \(^{n}C_{r}\) = \(\frac{n!}{(n - r)!r!}\)

Since 8 records are to be selected from 10 available records. Then, the number of ways for the arrangement of the records can be determined as;

Let n = 10 and r = 8

\(^{10}C_{8} }\) = \(\frac{10!}{(10 - 8)!8!}\)

       = \(\frac{10!}{2!8!}\)

       = \(\frac{10*9*8*7*6*5*4*3*2!}{2!8*7*6*5*4*3*2!}\)

       = \(\frac{10*9}{2}\)

       = 45

Therefore, the number of ways by which the records can be arranged is 45.

The coordinates are simple. Hope you understand this and you can draw it out.

Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

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Answer:

i think the answer is B.4

The polynomial function f(x)=x²(x+2) in terms of end behavior approaches positive infinity as x approaches positive and negative infinity, the x-intercepts are at x = 0 and x = -2, the y-intercept is at the origin, the zeros are x = 0 (with multiplicity 2) and x = -2, there can be a maximum of 2 turning points.

a) The end behavior of the graph of the function is y approaches positive infinity as x approaches positive infinity and y approaches positive infinity as x approaches negative infinity.

b) The x-intercepts of the graph occur when f(x) = 0, which are x = 0 and x = -2. The y-intercept occurs when x = 0, which is y = 0.

c) The zeros of the function are x = 0 (with multiplicity 2) and x = -2. The lesser zero of multiplicity 2 means the graph touches the x-axis at x = 0. The greater zero of multiplicity 1 means the graph crosses the x-axis at x = -2.

d) The maximum number of turning points on the graph of the function is 2 (a whole number).

e) Graphing the function would require plotting points and connecting them to form the graph, taking into account the x-intercepts, y-intercept, end behavior, and turning points.

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2/45 is the probability that the ball will be both red.

Probability is the measure of the possibility of an event to occur.

It basically ranges from 0 t0 1

10% of the candies are green

10% of the candies are red

20% of the candies are yellow

20% of the candies are blue

20% of the candies are orange.

Hence,

P ( brown ) = .1

P ( red ) = .1

P ( blue ) = .2

P ( yellow ) = .2

P ( orange ) = .2

P ( green ) = .2

The rest is brown. The percentage of brown candies is not important to this problem.

If you pick a candy at random, what is the probability that it is either red or yellow?

Probability of red = 0.1

Probability = (¹⁰C₁ × 0.1 +  ¹⁰C₁ ×0.1) / ¹⁰C₂

                  = 2 / 45

2/45 probability that it is both red.

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Step-by-step explanation:

for that simple request there is nothing to solve, just to follow.

follow the functional definitions given.

we know d(1) and f(1). and you need the first 5 items ?

just calculate d(2) and f(2). from there then d(3) and f(3). and so on.

d(1) = 1

d(2) = d(1)² + 1 = 1 + 1 = 2

d(3) = d(2)² + 1 = 4 + 1 = 5

d(4) = d(3)² + 1 = 25 + 1 = 26

d(5) = d(4)² + 1 = 676 + 1 = 677

f(1) = 1

f(2) = f(1) + 2×2 - 2 = 1 + 4 - 2 = 3

f(3) = f(2) + 2×3 - 2 = 3 + 6 - 2 = 7

f(4) = f(3) + 2×4 - 2 = 7 + 8 - 2 = 13

f(5) = f(4) + 2×5 - 2 = 13 + 10 - 2 = 21

Answer:

5 bags

Step-by-step explanation:

because there are 12 inches

Answer:

I think the answer is 4

Step-by-step explanation:

I think you need to find the area of the rectangle first which is 120 (12 x 10) then you divide 120 by 30 to get 4.

I might have gotten it wrong but  I think the answer is 4.

The third-period class has a higher mean score than the first-period class.

The larger standard deviation of the third-period class compared to the first-period class indicates that the scores in the third-period class were more spread out.

We have,

We can make some general observations.

The third-period class has a higher mean score than the first-period class, indicating that, on average, the students in the third-period class scored higher on the midterm than the students in the first-period class.

The larger standard deviation of the third-period class compared to the first-period class indicates that the scores in the third-period class were more spread out, or more variable, than the scores in the first-period class.

This could be due to a variety of factors, such as differences in the difficulty of the test or differences in the academic abilities of the students.

Thus,

While we cannot draw any definitive conclusions without more information, we can use the mean and standard deviation to gain some insight into the performance of the two classes on the midterm.

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Point (5,19/3), which divides segment AB in a 2:1 ratio, is the point. The act of dividing anything enormous into two or more separate portions is what causes it to be divided into these sections.

When point C internally divides the line segment in the ratio m: n and is located between the line segment's coordinates, we can utilize this formula. Internal Division is another name for it.

calculation

Let's say that point divides segment AB in a ratio of 2:1. (x,y)

\(x = \frac{m1x1 + m2x2}{m1 + m2}\)

\(y = \frac{m1y1 + m2y2}{m1 + m2}\)

the line segment's ends are (x1,y1) and (x2,y2), respectively.

Points A's coordinates (1,3)

Points B's coordinates (7,8)

\(x = \frac{2*7 + 1 *1}{1 + 2}\) = x = 5

Similarly, y = 19/3

So (x, y)≡(5,19/3)

Point (5,19/3), which divides segment AB in a 2:1 ratio, is the point. The act of dividing anything enormous into two or more separate portions is what causes it to be divided into these sections.

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Answer: 113.097

Step-by-step explanation:

The circumference of this circle= d*π = 36*π = 113.097

The equation of the circle C is x² + y² = 80 when it passes through the tangent points (-20, 0) and (0, 10).

Equation of circle:

Equation of the circle refer the position of a circle on a cartesian plane.

Given,

C is a circle with center the origin.

A tangent to C passes through the points (-20, 0) and (0, 10)

Here we need to find the equation of the circle C.

In order to find the equation of our line:

We have to identify the y-intercept which is (0,10).

Now, we need to find the gradient of our line which is:

Than can be calculated by,

=> (10 - 0) / (0- (-20))

=>  10/20 = 0.5

Now, the equation of our line is written as,

y = 0.5x + 10

But, here we know the center of our circle is the origin:

Which is in the following form:

=> x² + y² = r²

where r refers the radius

So, here we need the line to meet our circle at one point, we can substitute the equation for our straight line in for y.

Then the equation of the circle is written as,

=> x² + (0.5x + 10)² = r²

When we simplify it, then we get,

=> x² + (0.5x + 10)(0.5x + 10) = r²

Now, we can expand and simplify the brackets to leave us with:

=> 1.25x² + 10x + 100 = r²

=> 1.25x² + 10x + 100 - r² = 0

Here we know that this is a tangent and so it only meets the circle at one point.

So, this equation should only have one solution.

Then it can be written as,

=> b² - 4ac = 0

=> 10² - 4(1.25)(100 - r²) = 0

When we simplify this one then we get the value of

=> r² = 90

Therefore the equation of the circle is x^2 + y^2 = 80.

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Answer:

A

Step-by-step explanation:

∠ A = ∠ P

∠ C = ∠ R

AC = PR

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

The included side is the side between the vertices of the 2 angles.

Then the triangles are congruent by the ASA postulate

Answer:

2/12 is equivalent fraction for 2/3 divided by 4

Step-by-step explanation:

2

3

&

4

2

3

÷

4= ?

step 2 Multiply 2/3 with reciprocal of 4

=2

3

x1

4

=2

12

The Quotient is 1/3.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Given:

2/3 divided by 4

As, division is not possible in fraction so we will perform the multiplication

= 2/3  ÷ 4

= 2/3 x 1/4

= 2/6

= 1/3

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Random sampling is the correct answer. Which is option (A).

Sampling refers to a method to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is referred to as Random sampling.

What is sampling?

In statistics, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. Sampling is frequently employed in social science research. The method employed to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is known as random sampling.

Content-loaded sampling refers to a form of sampling that is more sophisticated than simple random sampling.

In order to form a sample, it involves first determining which variables (or characteristics) are essential to the study, and then choosing people based on those variables, hence the name "content-loaded."On the other hand, in Stratified sampling, the population is divided into subgroups (strata) based on one or more characteristics that are expected to impact the study's outcomes. The proportion of people chosen from each group should reflect the group's percentage of the overall population.

Snowball sampling is a method for selecting a sample of individuals by locating others who share the characteristics being studied and asking them to suggest additional individuals who might participate in the study. Among the given options, (A) random sampling is the correct answer.

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Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

divide 7/100 which is 0.07

multiply that by 13.75, and you get 0.96

13.75+0.96= $13.20

(this is including sales tax)

Answer:

$12.78

Step-by-step explanation:

I THINK you are supposed to multiply the original price (13.75) by the sales tax as a decimal (0.07) and then subtract that answer from, the original, amount.