A straight line is given as 2 x+4 -2 y-5=-3 z-6 (a) Determine the vector equation of the straight line. (b) Find the intersection point between the straight line with the plane yz​

The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

We have,

To factor x² + 12 using the difference of squares formula, we need to express it as the difference between two squares:

x² + 12 = x² + (2√3)²

Now we can use the difference of squares formula, which states that:

a² - b² = (a + b)(a - b)

In this case, we have a = x and b = 2√3. So we can write:

= x² + 12

= x² + (2√3)²

= (x + 2√3)(x - 2√3)

Therefore,

The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The missing probability is P(A|B) is 12/25 if P(B) is 1/4P and (A and B) is 3/25P.

P(B) = 1/4

P(A and B) = 3/25

The conditional probability is used to find the P(A|B):

P(A|B) = P(A and B) / P(B)

Conditional probability is defined as the number of possible outcomes from a given event based on the previous outcomes of the events.

By substituting the given values in the given probability, we get:

P(A|B) = (3/25) / (1/4)

Divide the fraction and multiply it with its reciprocal:

P(A|B) = (3/25) * (4/1)

P(A|B) = 12/25

Therefore, we can conclude that the missing probability is P(A|B) is 12/25.

To learn more about Probability

https://brainly.com/question/30034780

#SPJ1

The complete question is:

Find the missing probability.

P(B)=1/4P

(AandB)=3/25P

P(A|B)=?

The area of the given figure is 133 m²

Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,

The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height

Therefore,

The area of the given figure = 9.5 x 14 = 133

Hence, the area of the given figure is 133 m²

Learn more about parallelograms click;

https://brainly.com/question/29147156

#SPJ1

Answer:

B. More streetlights are installed on one street and people are then asked if they like the change.

Step-by-step explanation:

An experiment is a type of research method that involves manipulating one or more variables and measuring their effects on other variables. In this case, the experiment is to change the color of the product packaging and see how many people like the change. This is because the outcome of the experiment (the number of people who like the change) depends on chance and can be measured using numerical data. The other options are not experiments, but surveys or observations. Surveys involve asking people questions and collecting their opinions or preferences. Observations involve watching and recording people's behavior or reactions without interfering with them.

Answer:

34

Step-by-step explanation:

1. Plug in the week's salary into the formula

S=400+35v

1590=400+35v

2. Solve for v.

1590=400+35v

Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.

1190=35v

Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.

34=v

The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.

The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.

This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.

Find out more on temperature at https://brainly.com/question/30554883

#SPJ1

The graph will look like a circle centered at (2, 1) with radius 3.

To graph the equation [tex]x^2 - 4x + y^2 - 2y - 4 = 0[/tex]  by completing the square, we need to rearrange the terms as follows:

[tex](x^2 - 4x + 4) + (y^2 - 2y + 1) = 9[/tex]

This can be simplified to:

[tex](x - 2)^2 + (y - 1)^2 = 3^2[/tex]

So the equation represents a circle with a center at (2, 1) and a radius 3. To graph the circle, we can plot the center point (2, 1) and then draw a circle with radius 3 around that point.

Learn more about graphs here:

https://brainly.com/question/17267403

#SPJ1

Okay, let's break this down step-by-step:

* The telephone pole is 54 feet tall

* The guy wire runs 83 feet from point A (top of pole) to point B (ground)

* So the hypotenuse (AB) of the right triangle is 83 feet

* The opposite side (AC) is 54 feet (height of pole)

To find the adjacent side (BC), we use the Pythagorean theorem:

a^2 + b^2 = c^2

54^2 + BC^2 = 83^2

Solving for BC gives:

BC = sqrt(83^2 - 54^2) = sqrt(1296 - 2916) = sqrt(1620) = 40 feet

So the guy wire is secured 40 feet from the base of the telephone pole.

Rounded to the nearest tenth is 40.0 feet.

Therefore, the final answer is:

40.0

Let me know if you have any other questions!

Okay, here are the steps to solve this problem:

1) The height (h) of the rocket t seconds after launch is given as: h = - 3t2 + 0t + 48

2) We want to find the time (t) when the rocket hits the ground (h = 0)

3) Set the formula equal to 0: - 3t2 + 0t + 48 = 0

4) Factor the left side: - 3(t2 - 0t) + 48 = 0

5) Solve for t2 - 0t: t2 - 0t = 16

6) Add 0t to both sides: t2 = 16 + 0t

7) Take the square root of both sides: t = 4

Therefore, the time for the rocket to hit the ground is 4 seconds.

So in this case, t = 4

Let me know if you have any other questions!

Answer:

4 seconds.

Step-by-step explanation:

When the rocket hits the ground, its height will be 0. Therefore, since we are given an expression for the height of the rocket dependent on the time, we can simply set it equal to 0 and solve for the time and find how long the rocket will take to hit the ground. I'm assuming the equation is[tex]h = -3t^{2} + 48[/tex]

Now set this equal to 0

[tex]0 = -3t^2+48[/tex]. Solve for t by isolating it.

[tex]-48 = -3t^2[/tex]

[tex]16 = t^2[/tex]

From here, by taking the square root, we see that t is either equal to 4 or -4 in seconds. Since we can't have negative time, we can clearly see that the answer is 4 seconds.

Hope this helps

The correct matrix representation is;  [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,

Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)

Given here the points are P₁(1, 3) and P₂(5, 2)

Thus, by the coordinates of the two vectors, we can represent the matrix  ;

[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Hence, Option A) is the correct answer.

Learn more about vector matrix  here:

brainly.com/question/29990847

#SPJ1

Answer:

20

Step-by-step explanation:

She biked an equal amount each day for 8 days to a total of 32 miles. We can write that as 8x = 32. 32/8 = 4 so x = 4. To find how much shell bike in 5 days, we multiply it by x(4). 5*4 = 20.

Answer:

Center: (-3, 2)

Radius: 4

Step-by-step explanation:

x2 + 6x + y2 - 4y = 3​

x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4

(x + 3)² + (y - 2)² = 16

(x + 3)² + (y - 2)² = 4²

Center: (-3, 2)

Radius: 4

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

To learn more about equations click on,

https://brainly.com/question/29266004

#SPJ1

Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

According to the information, there are thousands of different lunch options in this restaurant.

To calculate the number of different lunches in the restaurant we must carry out the following mathematical procedure. We must multiply the different options as shown below:

4 green options x 5 protein options x 8 vegetable options x 4 extra options x 6 topping options = 4 x 5 x 8 x 4 x 6 = 4,800 different lunch options.

Based on the above, we can infer that 4,800 different lunch options can be created with the available ingredients.

Learn more about combination at: https://brainly.com/question/20211959

#SPJ1

The coordinates in the solution to the systems of inequalities is (12, 1)

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

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

Read more about inequalities at

brainly.com/question/30977554

#SPJ1

The amount of poster board left over will be 1275 square inches, the equation used is  A = (b₁ + b₂)h/2.

To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,

we need to find the area of the trapezoid window and subtract it from the area of the poster board.

The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.

Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.

Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.

To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.

Finally, we subtract the area of the window from the area of the poster board using the equation:

1500 - 225 = 1275 square inches.

Therefore, the amount of poster board left over will be 1275 square inches.

To know more about Area here

https://brainly.com/question/14994710

#SPJ1

The complete question is

Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?

[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]

is the equation of the given system.

Equation of the line using the coordinates (-3, 0) and (0, 3), we get:

slope = (3 - 0) / (0 - (-3)) = 1

Now we have the slope of the line. Next, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Using the point (-3, 0) and the slope we just found (which is also the slope of the line passing through the point (0, 3)), we get:

y - 0 = 1(x - (-3))

Simplifying, we get:

y = x + 3

Therefore, the equation of the line passing through (-3, 0) and (0, 3) is y=x+3.

Similarly, the equation of the line passing through (1, -1) and (0, -4) is y = -3x + 2.

Thus, from the graph the equation of the system is,

[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]

Learn more about graphs here:

https://brainly.com/question/17267403

#SPJ1

Using ratios and proportions, the number of 20 mg tabs that should be given in place of 40 mg po qd for 60 days is 120 tabs.

Using ratios and proportions, the number of tabs of 20 mg that should be given in place of 40 mg qd for 60 days is determined as follows:

Order: Zocor 40 mg po qd for 60 days

= 60 tabs since it is once per day (qd)

Total mg = 2,400 mg (40 mg x 60 tabs)

On hand: 20 mg tabs

Proportionately, 20 mg = 120 tabs (2 x 60) since 40 mg is for 60 tabs

Total mg = 2,400 mg (20 mg x 120 tabs)

Learn more about ratios and proportions at https://brainly.com/question/29774220.

#SPJ1

The percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.

To solve this problem, we can use the properties of the normal distribution and the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of buyers who paid between 150,000 and 153,300.

According to the empirical rule, given a normal distribution:

approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the  three standard deviations of the mean, the data are contained.

In this case, we want to find the percentage of buyers who paid between 150,000 and 153,300, which is one interval of length 3300 above the mean. To use the empirical rule, we need to standardize this interval by subtracting the mean and dividing by the standard deviation:

z1 = (150,000 - 150,000) / 1100 = 0

z2 = (153,300 - 150,000) / 1100 = 3

Here, z1 represents the number of standard deviations between 150,000 and the mean, and z2 represents the number of standard deviations between 153,300 and the mean.

Since the interval we are interested in is within three standard deviations of the mean (z2 <= 3), we can use the empirical rule to estimate the percentage of buyers who paid between 150,000 and 153,300:

Approximately 68% of the buyers paid within one standard deviation of the mean, which is between 149,000 and 151,000 (using z-scores of -1 and 1).

Approximately 95% of the buyers paid within two standard deviations of the mean, which is between 148,000 and 152,000 (using z-scores of -2 and 2).

Therefore, the remaining percentage of buyers who paid between 152,000 and 153,300 is approximately (100% - 95%) / 2 = 2.5%.

So, the percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.

For such more questions on percentage

https://brainly.com/question/27210997

#SPJ11

Answer:

3



Step-by-step explanation:

Area = 7pi/5

56/360 × pi r² = 7pi/5

Pi is canceled on both sides.

r² = 7/5 ÷ 56/360 = 9

r = root 9 = 3

The volume of the rectangular pyramid is 144.48 cubic feet.

A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.

The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.

The volume of a rectangular pyramid is given as:

[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]

[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]

[tex]\sf V = \dfrac{433.44 }{3}[/tex]

[tex]\sf V = 144.48 \ cubic \ feet[/tex].

Hence, the volume of the rectangular pyramid is 144.48 cubic feet.

Learn more about volume here:

brainly.com/question/1578538

The condition that will prove the two triangles similar is

side JL = 8 * side ZX

angle L = angle Z

Similar triangles are  triangles which have the  similar shape however not necessarily the equal size. More officially, two triangles are comparable if their corresponding angles are congruent and their corresponding aspects are in proportion.

This means that if we had been to scale one triangle up or down uniformly, the ensuing triangle could be much like the original triangle.

In the figure, the scale is 8

Learn more about similar triangles

https://brainly.com/question/14285697

#SPJ1

The slope field for the differential equation would be D . Graph D .

A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .

The length of line segments represents the magnitude, while the direction indicates the sign of the slope.

The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.

Find out more on slope fields at https://brainly.com/question/30194885

#SPJ1

The measurement of DE is 10 inches.

If we know that E is the point where the diagonals of the rectangle intersect, then we know that DE is equal to half the length of the diagonal BD.

Using the Pythagorean theorem, we can relate the length of the diagonal BD to the sides of the rectangle.

Let's assume that the length of the rectangle is L and the width of the rectangle is W. Then, the length of the diagonal BD is given by:

BD = √(L^2 + W^2)

Since we know that the diagonals of a rectangle are equal, we have:

AC = BD

BD = 20

Therefore, DE = 1/2 BD = 1/2 (20) = 10 inches.

Learn more about rectangles here:

https://brainly.com/question/29147156

#SPJ1

Step-by-step explanation:

The 'solution ' is the point where the two lines intersect :    ( 0,-1)

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

The sample proportion who said they pray is approximately 0.84, or 84%.

The sample proportion of college students who said they pray can be calculated by dividing the number of students who said they pray (105) by the total number of students in the sample (125).

Sample proportion = Number of students who said they pray / Total number of students in the sample

Sample proportion = 105 / 125

Sample proportion = 0.84

Therefore, the sample proportion who said they pray is approximately 0.84, or 84%.

Read more on sample proportion here:https://brainly.com/question/24232216

#SPJ1

Answer:

Hold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully load

Step-by-step explanation:

Hold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully load