Find the points of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y = - x + 4, y = 4x - 2

Answer:

[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]

Step-by-step explanation:

We need to evaluate the following integral by interpreting it in terms of areas :

[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx[/tex]

The first step is to separate the integral into two easier integrals

[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=\int\limits^0_{-3} 1 \, dx+\int\limits^0_{-3}\sqrt{9-x^{2}}\, dx[/tex]    (Integral of the sum)

Now we can calculate each integral by studying the area below each function.

For the first integral the function is [tex]f(x)=1[/tex]

(I will attach a file with the functions)

The area below this function is the area of a rectangle with sides 1 and 3 ⇒

[tex]\int\limits^0_{-3}1 \, dx=3[/tex]

For the second integral the function is

[tex]f(x)=y=\sqrt{9-x^{2}}[/tex]

If we study this function :

[tex]y=\sqrt{9-x^{2}}[/tex]

[tex]y^{2}=9-x^{2}[/tex] (I)

[tex]x^{2}+y^{2}=9[/tex]

Which is the equation of a circle centered at (0,0) with radius equal to 3

From the equation (I)

[tex]y^{2}=9-x^{2}[/tex]

[tex]|y|=\sqrt{9-x^{2} }[/tex]

The two possible solutions are :

[tex]y=\sqrt{9-x^{2}}[/tex] (II) and [tex]y=-\sqrt{9-x^{2}}[/tex]

We will use (II) to solve the integral (which is the upper part of the circle)

The area of a circle with radius equal to 3 is

[tex]\pi.3^{2}[/tex]

In the integral we only need a quarter of circle ⇒ We divide the total area by 4 ⇒ [tex]\frac{\pi.3^{2}}{4}[/tex] ⇒ [tex]\frac{9\pi }{4}[/tex]

Finally the integral is equal to

[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]

Answer:

y = 2/7x + 7

Step-by-step explanation:

We start off by putting the original equation into slope-intercept form. Subtract 7x from both sides, then divide both sides by -2. Your new equation should be y = -7/2x - 8. It's important to know that when two lines are perpendicular, their slopes (m) are opposite reciprocals of each other.  So -7/2 becomes 2/7. The first part of your final equation is y = 2/7x + b.

Next, we need to find the y intercept (b). You need to plug the x and y values from the given coordinate point (-7,5) into your final equation. You should end up with: 5 = 2/7(-7) + b. Then, solve for b.

5 = -14/7 + b

5 = -2 + b

7 = b

Finally, plug the b value into your final equation and you will have your answer.

Answer:

y + 8 = 2x + 2

Step-by-step explanation:

Use the points given to find the slope.  Divide the difference in y-values by the difference in x-values.

(-1) - (-7) = 6

5 - (-8) = 3

6/3 = 2

The slope is 2.

Now, pick one of the points to put in point-slope form.  It doesn't matter which.  You will get the right answer either way.  I will use (-1, -8).

y - y₁ = m(x - x₁)

y - (-8) = 2(x - (-1))

y + 8 = 2(x + 1)

y + 8 = 2x + 2

Answer:

24

Step-by-step explanation:

[tex]a^{2}[/tex]= 49 because any number squared is positive.

Since b=2,

2(-4)= -8.

Then this is 49-8-17, which equals 24.

Answer:

24

Step-by-step explanation:

Answer: 3x + 4y - 3z - 3 = 0

Step-by-step explanation:

with the given point (3, 0, 2), the plane is orthogonal to this line so it

has directional ratios (3, 4, -3)

therefore the given equation can be written as;

(x+2)/3 = (y-2)/4 = (z+1)/-3

so equation of the plane passing through point x1, y1 and z1 in the one point form is given as;

a(x-x1) + b(y - y1) + c(z -z1) = 0

abc represent the direction ratio

so we substitute

3(x-3) + 4(y-0) + (-3(z-2)) = 0

3x - 9 + 4y - 0 - 3z + 6 = 0

3x + 4y - 3z - 3 = 0

therefore the equation of the plane through the point is  3x + 4y - 3z - 3 = 0

Answer:

1. 8t

2. 510 + 6t

3. 510 - 2t

Step-by-step explanation:

1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t

2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t

3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.

d' = 510 + 6t - 8t

= 510 - 2t  

Answer:

Option (A)

Step-by-step explanation:

There are 2 main branches of statistics. They are:

1. Descriptive Statistics

2. Inferential Statistics

Descriptive statistics describes the characteristics of observed subjects or items while Inferential statistics makes inferences, based on given or derived data.

Inferential Statistics allow you to decide whether a difference between the experimental group and control group is due to manipulation or chance.

The Experimental group is the group that an effect is tested on while the Control group is the group that is left untested or uninfluenced. Inferential statistics allow you to decide whether a difference between these 2 groups is due to

- manipulation or interference by any force (which may be the experimenter/researcher)

or

- probability which is chance.

Option a. manipulation; chance

Inferential statistics is a statistical method for estimating the characteristics of a larger population from a small but representative sample. In other words, it enables the researcher to make generalizations about a larger group based on a smaller subset of that group.

Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to a. manipulation; chance

For more information:

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Answer:

AA postulate

Step-by-step explanation:

Because both the angle are identical?

Answer:

1). Cinnamon costs $7 per one pound

2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].

Step-by-step explanation:

x-values on the graph define the weight of cinnamon and y-values define the price.

Slope of the line drawn from the origin (0, 0) and (0.75, 5.25) will determine the per lb price of the cinnamon.

Slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

If the points on the given line re (0,0) and (0.75, 5.25),

Slope = [tex]\frac{5.25-0}{0.75-0}[/tex]

          = 7

Therefore, two options are the correct options.

1). Cinnamon costs $7 per one pound

2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].

Answer:

5z-8

Step-by-step explanation:

(8z-8)+3z=

5z-8

Answer:

z-8

Step-by-step explanation:

4(z -2)+3z

4z -8 +3z

-3       -3

z -8

Answer:

6Y

Step-by-step explanation:

We need to solve the statement ' Thrice the product of two and "Y" '.

Thrice means 3 times and product means multiply. It means we have to multiply 3,2 and Y.

Let the result is R. It can be calculated as follows :

[tex]R=3\times 2\times Y[/tex]

We know that, 3×2 = 6

So,

[tex]R=6Y[/tex]

Hence, Thrice the product of two and "Y" is 6Y.

Answer:

25.45 per lesson

Step-by-step explanation:

divide $305.40 by 12

Answer

B

Step-by-step explanation:

Took quiz

Answer:

b = 12

Step-by-step explanation:

15 - 2b = -9

Minus 15 to both sides

-2b = -24

Divide both sides by -2

b = 12

Answer: equation of the plane is 5x - y - z - 7 = 0  

same as ( 5x - y - z = 7 )

Step-by-step explanation:

Given data;

5x - y - z = 6

therefore vector of plane is n° = ( 5, -1, -1)

so equation will be

n°(x-x₀, y-y₀, z-z₀) = 0

( 5, -1, -1) (x-x₀, y-y₀, z-z₀) = 0

5(x- (1)) -1(y - (-1)) -1(z - (-1)) = 0

5x - 5 - y - 1 - z - 1 = 0

5x - y - z - 7 = 0

Therefore equation of the plane is 5x - y - z - 7 = 0  

same as ( 5x - y - z = 7 )

Answer:

9

Step-by-step explanation:

-4.5 x (-2) is equal to 9

Answer:

-4d

Step-by-step explanation:

Answer:

Step-by-step explanation:

12.3 + 9.6 = 21.9

The expression 12.3 - (-9.6) is equivalent to 21.9.

Given is an expression 12.3 -(-9.6) = 12.3 + 9.6, we need to simplify it,

To simplify the expression 12.3 - (-9.6), we can rewrite it as 12.3 + 9.6.

When subtracting a negative number, it is equivalent to adding the positive value of that number.

So, -(-9.6) becomes +9.6.

Therefore, 12.3 - (-9.6) simplifies to 12.3 + 9.6.

Adding 12.3 and 9.6 gives us 21.9.

So, 12.3 - (-9.6) = 21.9.

Learn more about expression click;

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Answer:

Negative infinity

Step-by-step explanation:

The line points down infinitely in the graph.

Answer:

45 words per minute!

Step-by-step explanation:

Divide 900 by 20!

Answer:

Her typing speed is 45 word per minute

Step-by-step explanation:

20x = 900

divided 20 on both sides

x = 45

Answer:

152 (Answer A)

Step-by-step explanation:

The experimental probability of obtaining a head is 19/100, or 0.19.

If the coin is flipped 800 times, the expected number of heads will thus be:

0.19(800 flips) = 152  (Answer A)

Answer:

9 drinks

Step-by-step explanation:

3+3+3=9

Or 3*3=9

Answer:

9

Step-by-step explanation:

Answer:

A) sin 70 = x/10

Step-by-step explanation:

From the angle 70 degrees, 10 is the hypotenuse and x is the opposite and if we go by SOH-CAH-TOA I have an O and a H so its sin.

so we know it's sin so we need to figure out the equation. since we have a hypotenuse as a factor it is on top. and the other number is on the bottom.

so,

A) sin 70 = x/10

Answer:

5 buses

Step-by-step explanation:

You add all the students up to get 168, because that's the total number of students, and divide it by 36. The buses can only carry 36 people, so you will need 4.666 buses, but you can't have 0.666 of a bus, so you will need 5 buses to fit everyone.

Answer:

Step-by-step explanation:

Check boxes.

Sorting (on columns)

Icons that communicate alerts.

Pagination.

Headers Row.

Answer: C. The bakery should conduct an observational study

Step-by-step explanation:

From the question, we are informed that a bakery wants to determine the best placement for day-old goods. The type of data collection source that the bakery should use is an observational study.

An observational study is a form of study whereby the individuals who are to be observed are being studied by the researcher and certain conclusions are derived about them. When the bakery conductd an observational study, the behavior of the customers regarding goods placement can be observed.

Answer:

Step-by-step explanation:

The easiest way to do any of these is to put the fraction into your  calculator and see what comes up.

So for 32/9 you get 3.5555555555 which is the same as 3.5 with a bar over it.

7/30 is the same as .23333333333 which is the same as 0.23 with a bar over the three.

5/3 = 1.6666666 which is 1.6 with a bar over the 6

4/9 is 0.4444444 which is the same as 0.4 with a bar over the 4.

Answer:

Complex numbers

Step-by-step explanation:

Given

[tex](5 + i)[/tex] and [tex](5 - i)[/tex]

Required

Determine what both factors are called

From the list of given options. option "complex numbers" answer the question correctly

This is because when numbers are written in form [tex]a + bi[/tex] where [tex]b \neq 0[/tex] and [tex]i = \sqrt{-1}[/tex];  such a number are referred to as complex number

Some other examples are:

[tex]-7 + 3i[/tex]

[tex]2 - 7i[/tex]

[tex]4 + i[/tex]

And lots more

Answer:

for the first question at the top, x=10

Step-by-step explanation:

x+3+9x=8x+23

(subtract 8x from both sides)

x+3+x=23

(combine the x terms)

2x+3=23

(subtract 3 from both sides)

2x=20

(divide by 2 from each side)

x=10