What is the solution to the system of equations shown below?

2x + 5y + 3z = 10
3x ­ - y + 4z = 8
5x - ­ 2y + 7z = 12

a(7, 1, ­-3)
b(7, ­-1, ­-3)
c(7, 1, 3)
d(­-7, 1, -­3)

Explanation:

1.  Sine and Cosine are never greater than 1 because they are the ratio of the leg of a right triangle to the hypotenuse. The hypotenuse is never shorter than one of the legs of a right triangle, so the ratio is at most 1.

__

2. Secant and cosecant are the reciprocals of the cosine and sine (respectively), so are the reciprocals of numbers that are at most 1. Therefore, they can never be less than 1 (in magnitude).

__

3. Tangent and cotangent (and secant and cosecant) are sometimes undefined because they are the ratios of triangle side lengths. The side length used in the denominator may be zero, causing the ratio to be undefined.

Answer:

ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])

Step-by-step explanation:

* Lets explain the reflection and the translation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Now lets solve the problem

∵ The vertices of ABCD are:

   A = (-5 , 2) , B = (-3 , 4) , C = (-2 , 4) , D = (-1 , 2)

- If ABCD reflected over the y-axis we will change the sign of the

 x-coordinate of all the points

∴ The image of A = (5 , 2)

∴ The image of B = (3 , 4)

∴ The image of C = (2 , 4)

∴ The image of D = (1 , 2)

∴ The image of ABCD after reflection over the y-axis will be at

   the first quadrant  

- The figure EHGF is left and down the image of ABCD after

 the reflection over the y-axis

∴ The image is translate to the left and down

∵ E = (1 , -2) and E is the image of A after reflection and translation

∵ The image of a after reflection is (5 , 2)

- That means 5 became 1 and 2 became -2

∵ 1 - 5 = -4

∴ The image of A after reflection translate 4 units to the left

∵ -2 - 2 = -4

∴ The image of A after reflection translate 4 units down

∴ ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])

* You can check the rest of points

# B with H

∵ B = (-3 , 4) after reflection over y-axis is (3 , 4) after translation is

   (3 + [-4] , 4 + [-4]) = (-1 , 0) the same with point H = (-1 , 0)

# C with G

∵ C = (-2 , 4) after reflection over y-axis is (2 , 4) after translation is

   (2 + [-4] , 4 + [-4]) = (-2 , 0) the same with point G = (-2 , 0)

# D with F

∵ D = (-1 , 2) after reflection over y-axis is (1 , 2) after translation is

   (1 + [-4] , 2 + [-4]) = (-3 , -2) the same with point F = (-3 , -2)

Certainly! In order to assist you effectively with your math question involving transformation, please provide me with the specific details or instructions regarding the transformation problem you're facing.
Are you looking to translate, rotate, reflect, or dilate a geometric figure? Please provide the specifics such as the type of transformation, the figure involved, and any parameters (like the direction and distance of a translation, the angle and direction of a rotation, the line of reflection, or the scale factor and center of dilation for a dilation).
Once you provide these details, I'll be able to guide you through the mathematical process to solve your transformation problem step by step.

Answer:

  A.  24  hm

Step-by-step explanation:

The formula for the circumference of a circle is ...

  C = 2πr

Fill in the given values and solve.

  150.7968 hm = 2×3.1416×r

  (150.7968 hm)/6.2832 = r = 24 hm . . . . . divide by 2π

The radius of the circle is 24 hm.

Answer:

so width of border is 10 inches

Step-by-step explanation:

Given data

board size = 12 * 16 inches

border area = 380 square inches

to find out

width of border

solution

let us assume width of border is x

first we find area of board i.e. 12 × 16 = 192 sq inches

and border area is given = 380 square inches

so total area of border and board is 192 + 380 = 572 sq inches

so we can say ( x+ 12 ) (x +16 ) = 572

solve this equation we get

x² +16x + 12x + 192 = 572

x² + 28x + 192 = 572

x² + 28x - 380 = 0

solve this equation and we get two value of x i.e.

x = 10 and x = -38

we will consider positive value here

so width of border is 10 inches

Answer:

The width of the border is 5 inches.

Step-by-step explanation:

Let x be the width of the border,

Given,

The rectangular board has the dimension 12 inches by 16 inches,

Thus, the dimension of the figure by joining the border with the board is,

(12+2x) inches by (16+2x) inches,

= (12+2x)(16+2x)

Hence, the area of the border = area of the figure by joining the border with the board - area of the board

= (12+2x)(16+2x) - 12 × 16

According to the question,

The area of the border = 380 square​ inches,

[tex](12+2x)(16+2x) - 12\times 16=380[/tex]

[tex]192+24x+32x+4x^2-192=380[/tex]

[tex]4x^2+56x-380=0[/tex]

[tex]4x^2+76x-20x-380=0[/tex]

[tex]4x(x+19)-20(x+19)=0[/tex]

[tex](4x-20)(x+19)=0[/tex]

By zero product property,

[tex]x=5\text{ or }x=-19[/tex]

Since, width can not be negative,

Hence, the width of the border is 5 inches.

Answer:

 intercept is 3 

X intercept is -3/7

For this case we have the following equation:

[tex]y = 7x + 3[/tex]

To find the y-intersection values we do [tex]x = 0[/tex]:

[tex]y = 7 (0) +3\\y = 0 + 3\\y = 3[/tex]

To find the x-intersection values we do[tex]y = 0[/tex]

[tex]0 = 7x + 3[/tex]

Subtracting 3 on both sides:

[tex]-3 = 7x[/tex]

Dividing between 7 on both sides:

[tex]x = - \frac {3} {7}[/tex]

So, we have:

x-intersection: [tex](- \frac {3} {7}, 0)[/tex]

y-intersection: [tex](0,3)[/tex]

Answer:

Option B

Answer:

20

4x will be 80

5x will be 100

Step-by-step explanation:

So those two how pink arrows means those opposite sides are parallel.

The side at the bottom is acting as a transversal through the parallel lines.

The angle that has measurement 5x and the one that has 4x are actually same-side interior angles; some people like to call it consecutive angles.

These angles add up to be 180 degrees when dealing with parallel lines.

So we have 5x+4x=180

which means 9x=180

Divide both sides by 9 giving us x=180/9

x=180/9=20.

The angle labeled 4x will then be 4(20) which is 80.

The angle labeled 5x will then by 5(20) which is 100.

To solve for x in vector problems, identify the axes, decompose each vector into its components using trigonometric functions, combine the components to find the resultant vector, and ensure that the solution is reasonable. Be sure to use radians for angles in calculations.

To find the value of x, we need to follow specific steps when dealing with vectors and their components. The given information suggests we have vectors A and B with specific magnitudes and angles relative to the x-axis. Here's how to proceed:

For example, given A = 53.0 m, θA = 20.0°, B = 34.0 m, and θB = 63.0°, we can find the x-components as Ax = A cos θA. It is important to use radians when calculations involve angles.

https://brainly.com/question/24550128

#SPJ2

Answer: 0.2140

Step-by-step explanation:

Given : A company produces steel rods. The lengths of the steel rods are normally distributed with

[tex]\mu=92.6 \text{ cm}[/tex]

[tex]\sigma=2\text{ cm}[/tex]

Sample size : [tex]n=12[/tex]

Let x be the length of randomly selected item.

z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x=92 cm

[tex]z=\dfrac{92-92.6}{\dfrac{2}{\sqrt{12}}}\approx-1.04[/tex]

For x=92.4 cm

[tex]z=\dfrac{92.4-92.6}{\dfrac{2}{\sqrt{12}}}\approx-0.35[/tex]

The probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm by using the standard normal distribution table

= [tex]P(92<x<92.4)=P(-1.04<z<-0.35)=P(z<-0.35)-P(z<-1.04)[/tex]

[tex]= 0.3631693-0.14917=0.2139993\approx0.2140[/tex]

Hence, the probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm is 0.2140.

Answer:

3

Step-by-step explanation:

I don't see the graph.

So I'm going to do algebra and should be x-coordinate of the intersection you see in front of you.

If y=-x+5 and y=x-1, then -x+5=x-1.

-x+5=x-1

Add x on both sides:

   5=2x-1

Add 1 on both sides:

   6=2x

Divide 2 on both sides:

  6/2=x

Simplify

   3=x

You should see them cross when x is 3.

The y there should by 3-1=2.

They should cross at the ordered pair (3,2).

Answer:

3

Step-by-step explanation:

If a graph shows a system of equations: y = -x + 5 and y = x - 1, the x-coordinate of the solution to the system of equations is 3.

y=-x+5

y=x-1

-x+5=x-1

Answer:

She used 49 of type B

Step-by-step explanation:

Step-by-step explanation:

Same steps, different problem.

x - pounds of type A coffee for current month

y - pounds of type B coffee for current month

x+y=145

4.2x+5.3y=659.9

x+y=145 -> multiply both sides by 4.2

4.2x+5.3y=659.9

4.2x+4.2y=609

1.1y=50.9

Answer:

The area of the circle is A = 12.56 m²

Step-by-step explanation:

* Lets explain how to solve the problem

- The area of any circle is A = π r² , where r is the radius of the circle

- In any circle the length of the radius is half the length of its diameter

* Lets solve the problem

- The diameter of the circle is 4 meters

∵ The radius of the circle = 1/2 diameter

∵ The diameter = 4 meters

∴ The radius = 1/2 × 4 = 2 meters

- The area of the circle is A = π r²

∵ The value of π = 3.14

∵ The length of r = 2 meters

- Substitute the value of r in the rule of the area

∵ A = π r²

∴ A = 3.14 × (2)²

∴ A = 3.14 × 4 = 12.56 meters²

* The area of the circle is A = 12.56 m²

Answer:

1/root 3

Step-by-step explanation:

pi =180degrees

11×180/6

11×30

330

tan 330=tan (360-30)

=-tan30

=1/root3

i have answered ur question

Answer: binomial probability

Step-by-step explanation:

A binomial probability indicates to the probability of having exactly x successes on n repeated trials in an particular binomial experiment which has only two possible outcomes.

If the probability of success on an single trial is b (which does not change) , then , the probability of failure will be (1-b)  .

The binomial probability for success in x trials out of n trials is given by :-

[tex]^nC_x\ b\ (1-b)^{n-x}[/tex]

Final answer:

The distribution called for a fixed number of independent trials with a constant success probability is the binomial probability distribution, defined by the equation P(X = x).

Explanation:

The probability distribution that shows the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a binomial probability distribution. The key characteristics of a binomial distribution include a fixed number of independent trials with two possible outcomes (success or failure) and a constant probability of success in each trial.

Mathematically, the binomial distribution is defined using the equation P(X = x) = (n choose x) * px * qn-x, where p is the probability of success, q = 1 - p is the probability of failure, and (n choose x) is the combination of n taken x at a time.

Answer:

72.5°

Step-by-step explanation:

This is a right triangle problem.  The ladder is the hypotenuse, and we have a length for that of 50 feet.  We also have the distance along the ground that the ladder's base is from the wall against which it is leaning.  This is the side adjacent to the angle for which we are seeking, so it the side adjacent to the angle, and it measures 15 feet.

We need a trig ratio that relates the side adjacent to the hypotenuse.  That will be the cosine.  Setting up:

[tex]cos\theta =\frac{adjacent}{hypotenuse}[/tex] and then filling in:

[tex]cos\theta=\frac{15}{50}[/tex]

Use the 2nd button on your calculator, and then press cos and you will get a display on your screen that looks like this:

[tex]cos^{-1}([/tex]

After that open parenthesis enter the fraction 15/50 and hit enter and you'll get the angle of 72.5 degrees, rounded.

just an addition to that superb reply above by @Luv2Teach

to the risk of sounding redundant.

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

y = 1/2x +6

Step-by-step explanation:

We have a point and a slope.  Therefore we can use the point slope form to create a line

y-y1 = m(x-x1)

y-5 = 1/2(x--2)

y-5 = 1/2(x+2)

Distribute the 1/2

y-5 = 1/2x +1

Add 5 to each side

y-5+5 = 1/2x +1+5

y = 1/2x +6

This is in slope intercept form

Answer:  (a)  (602.95,705.37)

(b) 33

Step-by-step explanation:

(a) Given : Sample size : [tex]n=40[/tex]

Sample mean : [tex]\overline{x}=654.16[/tex]

Standard deviation : [tex]\sigma= 165.23[/tex]

Significance level :[tex]\alpha=1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}=1.96[/tex]

The confidence interval for population mean is given by :-

[tex]\mu\ \pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]=654.16\pm(1.96)\dfrac{165.23}{\sqrt{40}}\\\\\approx654.16\pm51.21\\\\=(654.16-51.21,\ 654.16+51.21)=(602.95,705.37)[/tex]

Hence, the 95% (two-sided) confidence interval for true average [tex]CO_2[/tex] level in the population of all homes from which the sample was selected.

(b) Given : Standard deviation : [tex]s= 167\text{ ppm}[/tex]

Margin of error : [tex]E=\pm57\text{ ppm}[/tex]

Significance level :[tex]\alpha=1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}=1.96[/tex]

The formula to calculate the sample size is given by :-

[tex]n=(\dfrac{z_{\alpha/2}s}{E})^2\\\\\Rightarrow\ n=(\dfrac{(1.96)(167)}{57})^2=32.9758025239\approx33[/tex]

Hence, the minimum required sample size would be 33.

Answer:

Part 1) The polygon is a square

Part 2) The perimeter is equal to [tex]20\ units[/tex]

Part 3) The area is equal to [tex]25\ units^{2}[/tex]

Step-by-step explanation:

we have

[tex]A(5,0), B(2,4), C(-2,1),D(1,-3)[/tex]

Plot the points

see the attached figure

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

[tex]A(5,0),B(2,4)[/tex]

substitute in the formula

[tex]d=\sqrt{(4-0)^{2}+(2-5)^{2}}[/tex]

[tex]d=\sqrt{(4)^{2}+(-3)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]AB=5\ units[/tex]

Find the distance BC

[tex]B(2,4), C(-2,1)[/tex]

substitute in the formula

[tex]d=\sqrt{(1-4)^{2}+(-2-2)^{2}}[/tex]

[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]BC=5\ units[/tex]

Find the distance CD

[tex]C(-2,1),D(1,-3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3-1)^{2}+(1+2)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(3)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]CD=5\ units[/tex]

Find the distance AD

[tex]A(5,0),D(1,-3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3-0)^{2}+(1-5)^{2}}[/tex]

[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]        

[tex]AD=5\ units[/tex]

we have that

AB=BC=CD=AD

Find the distance BD (diagonal)

[tex]B(2,4),D(1,-3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3-4)^{2}+(1-2)^{2}}[/tex]

[tex]d=\sqrt{(-7)^{2}+(-1)^{2}}[/tex]

[tex]BD=\sqrt{50}\ units[/tex]        

Verify if the polygon is a square

If the triangle BDA is a right triangle, then the polygon is a square

Applying the Pythagoras theorem

[tex]BD^{2}=AD^{2}+AB^{2}[/tex]

substitute

[tex](\sqrt{50})^{2}=5^{2}+5^{2}[/tex]

[tex]50=50[/tex] -----> is true

so

The triangle BDA is a right triangle

therefore

The polygon is a square

Find the Area of the polygon

The area of a square is equal to

[tex]A=b^{2}[/tex]

we have

[tex]b=5\ units[/tex]

[tex]A=5^{2}=25\ units^{2}[/tex]

Find the perimeter of the polygon

The perimeter of a square is equal to

[tex]P=4b[/tex]

we have

[tex]b=5\ units[/tex]

[tex]P=4(5)=20\ units[/tex]

Answer:

Answer choice C is the correct answer.

Step-by-step explanation:

Answer choice A, 4/9, is equal to roughly .44.

Answer choice B, 2/5, is equal to exactly .4.

Answer choice C, 3/6, is equal to exactly .5.

Answer choice D, 5/12, is equal to roughly .42.

A proportion implies that the fractions will equal each other in value. The fraction 7/14 is equal to 1/2 or .5. Answer choice C, when simplified, is equal to 1/2 or .5, making it the correct answer.

Answer:

The correct option is B.

Step-by-step explanation:

It is given that Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip.

[tex]Time=\frac{Distance}{Speed}[/tex]

Time taken by Susan in first 30 miles is

[tex]T_1=\frac{30}{30}=1[/tex]

Time taken by Susan in remaining 30 miles is

[tex]T_2=\frac{30}{60}=0.5[/tex]

Total distance covered by Susan is

[tex]D=30+30=60[/tex]

Total time taken by susan to complete 60 miles trip is

[tex]T=T_1+T_2[/tex]

[tex]T=1+0.5=1.5[/tex]

Susan's avg speed in miles/hr for the entire trip is

[tex]S=\frac{60}{1.5}=40[/tex]

The average speed of susan for entire trip is 40. Therefore the correct option is B.

Final answer:

In propositional logic, the statement translates to ‘m → (e ∨ p)’, which denotes that seeing the movie 'm' can happen if the person is over 18 'e' or has parental permission 'p'.

Explanation:

The student is asking to translate a given statement into propositional logic. The statement in question is "You can see the movie only if you are over 18 years old or you have the permission of a parent." Using the propositions provided, where m represents "You can see the movie," e represents "You are over 18 years old," and p represents "You have the permission of a parent," we can express the logical relation in the following way:

In terms of logic, the statement can be written as a conditional: if you can see the movie (m), then you are over 18 years old (e) or you have the permission of a parent (p). This can be expressed as:

m → (e ∨ p)

This states that seeing the movie is the consequence of the condition of being over 18 years old or having parental permission. The conditional statement here establishes a necessary and sufficient relationship, while the use of or indicates that at least one of the conditions (being over 18 or having permission) must be met for the consequence (seeing the movie) to be true.

Answer:

The most appropriate answer option is D) The girls are generally taller than the boys.

Step-by-step explanation:

A) The shortest boy is taller than the shortest girl:

The shortest guy is not taller than the girl so its false.

B) The range for the girls is greater than the range for the boys:

Range for girls = 56 - 44 = 12

Range for boys = 54 - 41 = 13

C) There is an outlier in the data for the boys, but not for the girls:

It is present in both.

D) The girls are generally taller than the boys:

Average height of boys = [tex]\frac{(41)+(44\times3)+(46\times3)+(48\times2)+(50\times3)+(52\times)+(54\times4)}{20}[/tex] = 49.05

Average height of girls = [tex]\frac{(44\times2)+(46\times2)+(48)+(50\times3)+(52\times4)+(54\times3)+(56\times4)}{20}[/tex] = 50.9

Therefore, the correct answer option is D) The girls are generally taller than the boys.

Answer:

D) The girls are generally taller than the boys.

Step-by-step explanation:

The heights of a group of boys and girls at a local middle school are shown on the dot plots. When comparing the shapes of the two sets of data, the girls are generally taller than the boys.

Answer:

  x = 5

Step-by-step explanation:

Ordinarily, one would not need the distributive property to solve this equation. It is quickly and easily solved by making use of the multiplication property of equality: multiply both sides of the equation by 1/3.

  3x(1/3) = 15(1/3)

  x = 5

___

To use the distributive property, we need the sum of two terms that have a common factor. We can get that form by subtracting 15 from both sides of the equation (subtraction property of equality):

  3x - 15 = 15 - 15 . . . . subtract 15

  3x -15 = 0 . . . . . . . . .simplify

Now, we can apply the distributive property to remove a factor of 3:

  3(x -5) = 0

And we can use the multiplication property of equality to multiply by 1/3:

  3(1/3)(x -5) = 0(1/3)

  x -5 = 0 . . . . . . . . . . simplify

Finally, we can add 5 to both sides of the equation (addition property of equality):

  x -5 +5 = 0 +5

  x + 0 = 5 . . . . . . simplify

  x = 5 . . . . . . . . . .simplify more

Answer:

X=5

Step-by-step explanation:

i believe this is the correct answer!

No, it is not a proportional relationship because the graph does not go through the origin. A proportional relationship is supposed to be a straight line, starting from the origin. It starts on the number 4.

The true statement is (b) No, it is not a proportional relationship because the graph does not go through the origin

Proportional relationships are represented with linear equations that begin from the origin.

From the attached figure, we can see that: the graph begins from (0,4)

For the graph to be proportional it must begin from (0,0) as the origin

This means that, the graph does not represent a proportional relationship.

Hence, the true statement is (b)

Read more about proportional relationships at:

https://brainly.com/question/24312388

Answer:

It’s A, D, and E

The magnetic field lines flow from Earth’s geographic South Pole to Earth’s

geographic North Pole.

The magnetic field is generated in Earth’s core.

The magnetic field is similar to the magnetic field of a bar magnet.

thank youhave a good day

Answer:

It’s A, D, and E.

Step-by-step explanation: Try and find out :)

Jk Jk it's right.

Answer:

0

Step-by-step explanation:

If you think in degrees easier than in radians, then make this conversion.

pi = 180 degrees

(3/2)*pi = (3/2) * 180 = 180 * 3/2 = 270

Sin(270) = -1

cos(270) = 0

==========

sin(270) * cos(270) = -1 * 0 = 0

Answer:

Step-by-step explanation:

The area of the base is given by the formula ...

  A = πr²

so the radius is ...

  r = √(A/π) = √(1386/(22/7)) = √441 = 21 . . . units

__

The volume is given by ...

  V = (1/3)Bh

where B is the area of the base, and h is the height (equal to the radius). Filling in the numbers, we have ...

  V = (1/3)(1386)(21) = 9702 . . . . cubic units

Answer: the lower the price the more people want to come to the baseball game.

Step-by-step explanation:

Answer:

  a)  p = -x/3000 + 19 2/3

  b)  $9.83

Step-by-step explanation:

a) The 2-point form of the equation for a line can be used with the two given points. The attendance is said to be the independent variable.

  y = (y2 -y1)/(x2 -x1)(x -x1) + y1

Here "y" is the price (p), and "x" is the attendance, so we have ...

  p = (10 -12)/(29000 -23000)(x -23000) +12

  p = -1/3000(x -23000) +12

  p = -x/3000 + 19 2/3 . . . . price as a function of attendance

__

b) Revenue is the product of attendance and price. We can find the attendance associated with maximum revenue, then find the corresponding price.

  R(x) = x·p = x(-x/3000 +19 2/3)

This has zeros at x=0 and x=3000(19 2/3) = 59,000. The maximum revenue corresponds to attendance halfway between these values, at x = 29,500. The demand function tells us the ticket price should be ...

  p = -29500/3000 +19 2/3 = 9.83 . . . . dollars

_____

Comment on the problem working

I might have written the "demand function" to use price as the independent variable. Then the price is what you know when you find the maximum revenue; you don't have to do an extra step to find it.

  x = 3000(19 2/3 -p)

  xp = 3000p(19 2/3 -p) is maximized at p = (19 2/3)/2 = 9 5/6 ≈ 9.83

Answer:

Option 2 is the correct answer.

Step-by-step explanation:

We know that

[tex]Speed=\frac{Distance}{time}[/tex]

We have 1 mile = 5280 feet thus 6 miles = 31680 feet

Similarly 1 hour = 3600 seconds

Applying values in the equation above we get

[tex]Speed=\frac{31680feet}{3600sec}\\\\Speed=8.8feet/sec[/tex]

Thus his average speed is less than 18feet/sec

Answer:

The correct option is 1.

Step-by-step explanation:

Rhombus is a special case of parallelogram.

The properties of a parallelogram and rhombus:

1. Opposite sides parallel and equal.

2. Diagonals bisect each other.

3. Opposite angles are congruent.

The consecutive sides of a parallelogram may or may not be equal. But a rhombus has four congruent sides.

If a parallelogram has four congruent sides, then that parallelogram is known as rhombus.

The required statement that describe a parallelogram must be a rhombus is  "parallelogram with four congruent sides ".

Therefore the correct option is 1.

Answer:

This is what i got

The system of equations provided consists of a circle and a line:

1. [tex]\( x^2 + y^2 = 49 \)[/tex] (This represents a circle with a radius of 7, centered at the origin.)

2. [tex]\( y = -x - 7 \)[/tex] (This is a linear equation.)

The first equation has already been graphed, showing a circle with a radius of 7. To find the intersection points of the circle and the line, which are the solutions of the system, we can substitute the expression for y from the second equation into the first one:

[tex]\[ x^2 + (-x - 7)^2 = 49 \][/tex]

[tex]\[ x^2 + x^2 + 14x + 49 = 49 \][/tex]

[tex]\[ 2x^2 + 14x + 49 - 49 = 0 \][/tex]

[tex]\[ 2x^2 + 14x = 0 \][/tex]

[tex]\[ x(2x + 14) = 0 \][/tex]

This gives us two solutions for x:

[tex]\[ x = 0 \quad \text{or} \quad 2x + 14 = 0 \][/tex]

[tex]\[ x = 0 \quad \text{or} \quad x = -7 \][/tex]

Now we can substitute these x-values into the second equation to find the corresponding y-values:

For [tex]\( x = 0 \)[/tex]:

[tex]\[ y = -0 - 7 \][/tex]

[tex]\[ y = -7 \][/tex]

For [tex]\( x = -7 \)[/tex]:

[tex]\[ y = -(-7) - 7 \][/tex]

[tex]\[ y = 7 - 7 \][/tex]

[tex]\[ y = 0 \][/tex]

Therefore, the system of equations has two solutions where the line intersects the circle:

[tex]\[ (0, -7) \quad \text{and} \quad (-7, 0) \][/tex]

These calculations provide us with the step-by-step solution to the system of equations. The graphical solution would show the line [tex]\( y = -x - 7 \)[/tex] intersecting the circle [tex]\( x^2 + y^2 = 49 \)[/tex] at these two points.

Here is the graph showing the system of equations:

- The circle represented by [tex]\( x^2 + y^2 = 49 \)[/tex].

- The line represented by [tex]\( y = -x - 7 \).[/tex]

The red points indicate where the line intersects the circle, which are the solutions to the system of equations. These points are at (0, -7) and (-7, 0).

Answer:

1-a

2-b

3-e

4-c

5-g

6-d

7-f

Step-by-step explanation:

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