Find the coordinates of the vertices of the figure formed by each system of inequalities.
y + x ≥ –4
y ≥ x – 6

3y + x ≤ 10

A(1, –5), (–14, 8), (–11, 7)

B(1, 5), (7, 1), (11, 7)

C(1, 7), (–11, 1), (7, –5)

D(1, –5), (7, 1), (–11, 7)

Answer:

A'(-2, -1), B'(0, 1), C'(-2, 0)

Step-by-step explanation:

When dilation is about the origin, the scale factor multiplies each individual coordinate.

  A' = (1/3)A = (-6/3, -3/3) = (-2, -1) . . . . for example

The rest is mental arithmetic, since all given coordinate values are divisible by 3.

Answer:

- 3/8

Step-by-step explanation:

- 3/4  - (-3/8)

= -3/4 + 3/8

= -6/8 + 3/8

= - 3/8

Answer: 740 miles

Step-by-step explanation:

You know that [tex]\frac{3}{8}inches[/tex] on the map is actually 60 miles and the distance between these two cities is [tex]4\ \frac{5}{8}inches[/tex].

You can express this distance as a decimal number:

[tex](4+0.625)inches=4.625inches[/tex]

Therefore, let be "d" the distance in miles between these two cities.

Then, you get:

[tex]d=\frac{(4.625inches)(60miles)}{(\frac{3}{8}inches)}\\\\d=740miles[/tex]

Answer:

[tex]f^{-1} (x)=-\frac{1}{6}x+1[/tex]

Step-by-step explanation:

To find the inverse of a function in equation form, first I recommend changing the f(x) to a y:

y = -6x + 6

Next step is to switch the x and y:

x = -6y + 6

Now solve for the new y:

x - 6 = -6y and

[tex]-\frac{1}{6}x + 1=y[/tex]

You can put the inverse notation back in for y like I did in the answer section above.

Answer: 1,7 and 1,5 on coefficient

Step-by-step explanation:

Equation at the end of step  1  :

 (((5•(x4))+(x3))+3x2)-7

Step  2  :

Equation at the end of step  2  :

 ((5x4 +  x3) +  3x2) -  7

Step  3  :

Checking for a perfect cube :

3.1    5x4+x3+3x2-7  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  5x4+x3+3x2-7  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  3x2-7  

Group 2:  5x4+x3  

Pull out from each group separately :

Group 1:   (3x2-7) • (1)

Group 2:   (5x+1) • (x3)

3.3    Find roots (zeroes) of :       F(x) = 5x4+x3+3x2-7

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  5  and the Trailing Constant is  -7.

The factor(s) are:

of the Leading Coefficient :  1,5

of the Trailing Constant :  1 ,7

The factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].

Given

Expression; [tex]\rm 5x^4+x^3+3x^2-7[/tex]

The leading coefficient of the polynomial of the term has the highest degree of the polynomial.

The factors of the constant term;

[tex]\rm 5x^4+x^3+3x^2-7=0\\\\ 5x^4-4x^3+7x^2-7x+5x^3-4x^2+7x-7=0\\\\(x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex]

Hence, the factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].

To know more about the Leading coefficient click the link given below.

https://brainly.com/question/13577114

Answer:

24

Step-by-step explanation:

If you use Pascal's triangle, which I did, you will look at the 5th row of the triangle which contains the numbers 1, 4, 6, 4, 1

If we expand using a = 2x and b = -1, then the expansion looks like this:

[tex]1(2x)^4(-1)^0+4(2x)^3(-1)^1+6(2x)^2(-1)^2+4(2x)^1(-1)^3+1(2x)^0(-1)^4[/tex]

If you simplify all that down by multiplying, you'll get

[tex]16x^4-32x^3+24x^2-8x+1[/tex]

If you don't know how to use Pascal's triangle, you need to learn.  It's so very cool!

Answer:

-4y = x², or y = - x²/4, or y = -(1/4)x²

Step-by-step explanation:

Because the focus is beneath the directrix, this vertical parabola opens down.  The general formula is 4py = x².  

Because the distance between focus and directrix is 2 units, p = -1 here.  The negative sign shows that the parabola opens down.

4py = x² becomes 4(-1)y = x², or -4y = x², or y = - x²/4

Answer:

[tex]\dfrac{2\sqrt{15\pi}}{\pi}[/tex]

Step-by-step explanation:

[tex]\displaystyle\sqrt{\frac{60}{\pi}}=\sqrt{\frac{4\cdot 15\pi}{\pi^2}}=\frac{2}{\pi}\sqrt{15\pi}[/tex]

She will take 6 weeks.

Answer:

She will take 6 weeks.

hope this helps

A fraction is closer to 1/2 than to 0 or 1 if its numerator is more than half of 0 and less than half of the denominator. For instance, 3/5 is closer to 1/2 than to 0 or 1 because its numerator is more than half of 0 and less than half of 5.

To determine which fraction is closer to 1/2 than to 0 or 1, consider the numerical value of the fractions in relation to 1/2. As a rule of thumb, if a fraction has a numerator that is half the denominator, it equals 1/2. When the numerator is less than half the denominator, the value is less than 1/2; when the numerator is over half the denominator, the value is greater than 1/2.

For example, if we take 1/3, it is clear that this value is less than 1/2 because the numerator, 1, is less than half of the denominator, 3. Comparatively, the fraction 2/3 is closer to 1 than to 1/2 since the numerator, 2, is greater than half of the denominator, 3.

Another example would be comparing 3/5 and 4/5 to 1/2. The fraction 3/5 has a numerator that is more than half of the denominator, making it closer to 1/2 than to 0 or 1, while 4/5 is closer to 1. Therefore, 3/5 is the fraction that is closer to 1/2 than to 0 or 1.

A fraction closer to 1/2 than to 0 or 1 falls in the range (> 1/3 but < 2/3); 5/8 is an example of such a fraction. An intuitive understanding and the use of a common denominator can aid in identifying and comparing these fractions.

Determining which fraction is closer to 1/2 than to 0 or 1 involves understanding the number line and how fractions fall on it.

To identify such a fraction, it should be evident that any fraction greater than 1/2 will naturally be closer to 1, while any fraction less than 1/2 is closer to 0.

Therefore, we look for a fraction in the range (> 1/3 but < 2/3) to ensure it is closer to 1/2.

By using the intuitive sense of fractions, which is like having an understanding of fractions through visualization or practical examples, we can gauge the closeness to 1/2.

For instance, we know that 1/3 is less than 1/2, and similarly, 2/3 is more than 1/2.

Following this line of reasoning, the addition of fractions (1/3 + 1/6 = 1/2) indicates that 1/6 is the gap needed to reach from 1/3 to 1/2.

A fraction such as 5/8 would be a good example of a fraction closer to 1/2.

This fraction is more than 1/2 (4/8) but less than 3/4 (6/8), placing it comfortably closer to 1/2 on the number line.

Employing the common denominator strategy also helps to compare fractions effectively, by aligning them to a unifying reference point.

Answer:

Please see the attached image below, to find more information about the graph

The figures that are obtained by a single reflection are shown in the image inside a red rectangle.

The axis of reflection is shown with a black line.

- The figure from the left shows horizontal reflection

- The figure from the right shows vertical reflection

Answer: A, it is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.  

Answer:

Option A is correct.

Step-by-step explanation:

Kendra surveyed a random sample of 100 members of a local gym. She found that 40% of the gym members surveyed had taken a yoga class.

Kendra performed 100 trials of a simulation. Each trial simulated a sample of 100 gym members under the assumption that 50% of the population had taken a yoga class.

The best conclusion based on the plot is - A. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.

Answer:

square; 60; 225.

Step-by-step explanation:

1) using the vectors rules to calculate the lengths of the sides AB; BC; CD and AD. When AB=BC=CD=AD it means, the shape is a square of rhombus.

2) using the vectors rules to calculate the lengths of the diagonales AC and BD. When AC=BD it means, the shape is a square.

3) The perimeter of the square ABCD is 15*4=60.

4) The area of the square ABCD is 15*15=225.

All the details are in the attached picture; answers are marked with colour.

Answer:

125,970

Step-by-step explanation:

Even if jury are assigned numbers, the order in which they are picked has no importance.  That means that it's a combination, not a permutation.

The formula to calculate possible combinations is:

[tex]C(n,r) = \frac{n!}{(r! (n-r)!)}[/tex]

Where n is the global population, and r is the number of selected items.

In our case, n = 20 and r = 12, so...

[tex]C(20,12) = \frac{20!}{(12! (20-12)!)} = 125970[/tex]

There are 125970 different ways to select 12 jury members out of 20 people.

there are 125970 different 12 person juries that can be chosen from a pool of 20 people.

The question is asking how to determine the number of different ways to choose a 12-person jury from a pool of 20 potential jurors. This type of problem is solved using the concept of combinations in mathematics, specifically the binomial coefficient formula which is given by the following:

C(n, k) = n! / (k!(n - k)!)

where:

n represents the total number of items (in this case, jurors).

k represents the number of items to choose (jurors to be selected for the jury).

n! means factorial of n, which is the product of all positive integers up to n.

In this scenario, n = 20 and k = 12. Therefore, the number of different 12 person juries that can be chosen is calculated as:

C(20, 12) = 20! / (12!(20 - 12)!)

Further calculation yields:

C(20, 12) = 20! / (12!8!) = 125970

Therefore, there are 125970 different 12 person juries that can be chosen from a pool of 20 people.

Answer:

We have to prove

sin⁡(α+β)-sin⁡(α-β)=2 cos⁡ α sin ⁡β

We will take the left hand side to prove it equal to right hand side

So,

=sin⁡(α+β)-sin⁡(α-β)      Eqn 1

We will use the following identities:

sin⁡(α+β)=sin⁡ α cos⁡ β+cos⁡ α sin⁡ β

and

sin⁡(α-β)=sin⁡ α cos ⁡β-cos ⁡α sin ⁡β

Putting the identities in eqn 1

=sin⁡(α+β)-sin⁡(α-β)

=[ sin⁡ α cos ⁡β+cos⁡ α sin⁡ β ]-[sin⁡ α cos ⁡β-cos ⁡α sin ⁡β ]

=sin⁡ α cos⁡ β+cos⁡ α sin ⁡β- sin⁡α cos⁡ β+cos ⁡α sin ⁡β

sin⁡α cos⁡β will be cancelled.

=cos⁡ α sin ⁡β+ cos ⁡α sin ⁡β

=2 cos⁡ α sin ⁡β  

Hence,

sin⁡(α+β)-sin⁡(α-β)=2 cos ⁡α sin ⁡β

Answer:

D

12²

Step-by-step explanation:

Given in the question, an integer = 144

To find the exponential form 144 we will do factorisation

The prime factorisation of 144 is

2 × 2 × 2 × 2 × 3 × 3

So the exponential form is 2[tex]^{4}[/tex] × 3²

The other way is

√144 = 12

which means

12² = 144

Answer: 12^2=144

Step-by-step explanation:

Which means (12)(12)=144

Answer:

106

Step-by-step explanation:

VPL=1/2VkP

VKP=148

VPL=74

JPV+VPL=180

JPV=106

The measurement of angle JPV from the considered situation is found as m∠JPV = 106°

The radius which touches the point where the tangent touches too on a specified circle, is perpendicular to the tangent (90 degrees angle with the tangent).

Referring to the image attached below, we're provided that:

m arcVKP = central angle arc VKP subtends = m∠VOP = 148°

The perpendicular from center O on the line VP (VP is a chord) bisects it, and therefore, the triangle ODP and ODV are congruent by SAS congruency [ side OD is common, the angle (the 90 degree) on either side of OD is of same measure, and VD and DP are of same measure due to OD bisecting VP).

Thus, we get:

[tex]m\angle POD = m\angle VOD[/tex]

But since we have:

m∠POD + m∠VOD  = m∠VOP = 148°

thus, m∠POD + m∠POD = 148°

or  m∠POD = 148°/2 = 74° = m∠VOD

Now, as sum of angles in a triangle is 180°, therefore, for triangle OPD, we get:

[tex]m\angle OPD + m\angle ODP + m\angle POD = 180^\circ\\x^\circ + 90^\circ + 74^\circ = 180^\circ\\x = 16[/tex]

Thus, we get the measurement of angle JPV as:

[tex]m\angle JPV = m\angle JPO + m\angle OPD\\ m\angle JPV = 90^\circ + x^\circ = (90 + 16)^\circ = 106^\circ[/tex]

Thus, the measurement of angle JPV from the considered situation is found as m∠JPV = 106°

Learn more about tangent here:

https://brainly.com/question/7942024

Answer:

A = (16π -32) in²

P = (4π +8√2) in

Step-by-step explanation:

The area is that of a quarter-circle of radius 8 inches less half the area of a square with side length 8 inches. Two formulas are useful:

area of a circle = πr² . . . . .r = radius

area of a square = s² . . . . s = side length

Then your area is ...

A = (1/4)π(8 in)² - (1/2)(8 in)² = (64 in²)(π/4 -1/2)

A = (16π -32) in²

____

The applicable formulas for the side lengths of your figure are ...

arc BD = (1/4)(2πr) = π(r/2) = π(8 in)/2 = 4π in

segment BD = (8 in)√2

The perimeter is the sum of these lengths, so is ...

P = (4π +8√2) in

_____

Of course, you are very familiar with the fact that an isosceles right triangle with side lengths 1 has a hypotenuse of length √(1²+1²) = √2. Scaling the triangle by a factor of 8 inches means the segment AB will be 8√2 inches long.

Answer:

x > -2

Step-by-step explanation:

12x > 6 (x - 2)

12x > 6x - 12

6x > - 12

x > - 2

Answer:

Step-by-step explanation:

2 meter is like 6.4 yards

so i would say B is the answer

Final answer:

The work done by the crane in lifting 50 Newtons over a distance of 2 meters is 100 Nm.

Explanation:

The work done by a crane can be calculated by multiplying the force applied by the distance over which the force is applied. In this case, the crane is lifting 50 Newtons over a distance of 2 meters. Therefore, the work done is:

Work = Force x Distance

Work = 50 N x 2 m = 100 Nm

So, the correct answer is 100 Nm.

3) For Zach, if his heart beats 15 times in 10 seconds, his heart beats 1.5 times in 1 second. Multiply this by 25 to get the number of times his heart will beat in 25 seconds → 1.5 * 25 = 27.5 times per 25 seconds. 1.5 * 60 = 90 times per minute. 1.5 * 120 = 180 times per two minutes. Do the same for your heart beats. 14 beats per 10 seconds is 1.4 beats per second. 1.4 * 25 = 35 times per 25 seconds. 1.4 * 60 = 84 times a minute. 1.4 * 120 = 168 times per two minutes.

4) Zach's equation would be H = 1.5n and yours would be H = 1.4n

5) Your heat beats just a little bit slower than Zachs. Everyone is different and there are many different things that can affect heart rate. Maybe he walked a little more than you did or maybe he was stressing about something which made his heart beat a little faster.

I hope this helps you!

Answer:

9

Step-by-step explanation:

The solution to ...

n +6 ≥ 15

is found by subtracting 6:

n ≥ 9

__

The solution to ...

n +5 < 15

is found by subtracting 5:

n < 10

__

The only integer that is at least 9 and less than 10 is 9.

The value of the unknown integer, n, is 9.

Answer:

see below

Step-by-step explanation:

[tex]\sqrt[4]{162b^8}=\sqrt[4]{2\cdot 3^4b^8}=\sqrt[4]{2(3b^2)^4}\\\\=3b^2\sqrt[4]{2}[/tex]

Answer:

I think C

Step-by-step explanation:

Answer:

The lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.

Step-by-step explanation:

Without graphing, this is the equation of a circle with center at the origin,

(0, 0) and with a radius of 3 units. The general equation of a circle with center (a, b) and with radius r units is given as;

[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]  

The graph of the function is as shown in the attachment below;

A line of symmetry cuts the graph of a function into two equal parts such that these parts become mirror images of each other.

For the case of a circle, the line that divides the circle into two equal portions is the diameter. Any given circle has infinite number of diameters.

Therefore, the lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.

Answer:

A. x² -3x -30

Step-by-step explanation:

Using the distributive property to eliminate parentheses, we get ...

3x² +5x -12 -2x² -8x -18

Then, collecting terms gives ...

= (3-2)x² +(5-8)x +(-12-18)

= x² -3x -30 . . . . . . . . . . . . . matches selection A

Answer:

  550 mm^2

Step-by-step explanation:

A net can be drawn as shown in the first figure attached. Each square represents 5 mm by 5 mm, so is 25 mm^2. Altogether, there are 22 of them, so the total area is ...

  (25 mm^2)·22 = 550 mm^2

The second attachment shows that net folded up to make the given figure.

_____

In the first attachment, the green shades represent the left- and right-side faces. (Darker green is left side.) The red and blue shades represent the front- and back-side faces. The white rectangles represent the top and bottom faces. The dark black lines are the cut lines. If you want to fold the figure up, the lighter lines are the fold lines.

The second attachment is just verification that all faces are accounted for and the net actually corresponds to the given figure.

Answer:

Answer me please??!!

Step-by-step explanation:

Check the picture below.

so is filled with those cubes, recall that a cube has all equal sides, in this case 1/3, so the volume of each cube is simply the product of length*width*height.

[tex]\bf \stackrel{\textit{volume of one cube}}{\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\implies \cfrac{1}{27}}\qquad \qquad \stackrel{\textit{if there are \underline{x} cubes inside then their total volume is}}{\cfrac{1}{27}x~~~~=~~~~\stackrel{\textit{volume of prism}}{4}} \\\\\\ x=27\cdot 4\implies x=108[/tex]