write (-6, 3) and (4, 3) in slope form

Answer:

5

Step-by-step explanation:

Answer:

[tex]\displaystyle x_1=\frac{5+\sqrt{13}}{2}\approx4.3\text{ and } x_2=\frac{5+\sqrt{13}}{2}\approx0.7[/tex]

Step-by-step explanation:

We are given:

[tex]x^2-5x+3=0[/tex]

And we want to solve this via completing the square.

First, we will subtract 3 from both sides. This yields:

[tex]x^2-5x=-3[/tex]

Next, we will factor out the leading coefficient from the left.

In this case, the leading coefficient is simply 1 so we can leave it as is.

Next, we want to add a constant that is half of the b coefficient squared.

In this case, b = -5.

Half of that is -5/2.

Squaring yields 25/4.

So, we will add 25/4 to both sides. Since our leading coefficient is 1, we don't need to multiply by anything when we add it on the right. Hence:

[tex]\displaystyle x^2-5x+\frac{25}{4}=-3+\frac{25}{4}[/tex]

The left side constitutes a perfect square trinomial as shown:

[tex]\displaystyle (x)^2-2\Big(\frac{5}{2} \Big)(x)+\Big(\frac{5}{2}\Big)^2=-\frac{12}{4}+\frac{25}{4}[/tex]

Factor and subtract:

[tex]\displaystyle \Big(x-\frac{5}{2}\Big)^2=\frac{13}{4}[/tex]

Taking the square root of both sides gives:

[tex]\displaystyle x-\frac{5}{2}=\pm\frac{\sqrt{13}}{2}[/tex]

Hence:

[tex]\displaystyle x=\frac{5}{2}\pm\frac{\sqrt{13}}{2}}=\frac{5\pm\sqrt{13}}{2}[/tex]

Approximate:

[tex]\displaystyle x_1=\frac{5+\sqrt{13}}{2}\approx4.3\text{ and } x_2=\frac{5-\sqrt{13}}{2}\approx0.7[/tex]

Answer:

(-9/2,3/2)

Step-by-step explanation:

x coordinate of mid point=(x1+x2)/2

y coordinate of mid point=(y1+y2)/2

Answer:

You will need to buy 12 feet of border.

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

2000/4=500

500*4=2000

Answer:

500 miles per hour

Step-by-step explanation:

4 multiplied by 500 is 2000

Answer:

8km / 9 hours

Step-by-step explanation:

see the point is on

x axis = 9 = 9 hours

y axis = 8 = 8 kilometers

so the average speed of bus is 8 km in 9 hours

Answer:

mark as brainlest

Step-by-step explanation:

average speed = 9/10

=0.9kms-¹

Answer:

Its B !!!

Step-by-step explanation:

Have a great day

Answer:

x = q +3

Step-by-step explanation:

+ 3 on both sides

hope this helps

Answer: C

Step-by-step explanation:

Answer:

Car 1 : 40 miles per gallon

Car 2: 25 miles per gallon

Step-by-step explanation:

family has two cars. During one particular week, the first car consumed 15 gallons of gas. The second car consumed 25 gallons of gas. The two cars Drove a combined total of 1475 miles and the sum of their fuel efficiency was 65 miles per gallon. What were the fuel efficiency of each of the cars that week

Given that :

Fuel efficiency , car 1 = x

Fuel efficiency , car 2 = y

x + y = 65 - - (1)

15x + 35y = 1475 - - - (2)

x = 65 - y

15(65-y) + 35y

975 - 15y + 35y = 1475

20y = 14875 - 975

20y = 500

y = 25

Put y = 25 in (1)

x + y = 65

x + 25 = 65

x = 65 - 25

x = 40

Answer:

She left a $4.80 tip.

Answer:

Tip $4.80

Total $28.80

Step-by-step explanation:

20% = 0.2

24 x 0.2 = 4.8

24 + 4.8 = 28.8

Answer:

              Food in space

On earth we have a variety of foods, but we can not  enjoy every  food in space. Do you know why?In space astronauts eat non-delicious food but some people think the other way around. preparing food in space is complicated for many reasons, some are microgravity, some foods are not perfected for space  and some foods do not meet the requirements of space food.

preparing food in space can be very different from earth because of microgravity which makes the food float. According to the text “ no pizza in space” the author states  Soft drinks don't work because of microgravity. soda in space is a bit complicated, Because in microgravity the light gas bubbles won’t rush to the top of the liquid to escape.The bubbles of carbon dioxide in carbonated beverages aren't  floatable in a weightless environment, so they remain randomly distributed throughout the fluid, even after drinking. astronauts can't sprinkle salt and pepper on their food in space,They just float away because of microgravity. Scientists have made space food better than before and they will make space food better in the future for astronauts.

Some foods are not perfected to go to space because of many reasons. Milk is one of the foods that is not perfected and  It is also banned for going into space because milk is dehydrated. According to the text “ No Pizza in Space “ Pizzas have not been perfected yet to go to space.Bread is another food that is not perfected and also banned because the bread crumbs float around, and can fly into an astronaut’s eyes and interfere with important equipment.Ice cream is not perfect to go to space because in space shuttle there is no refrigerator and also scientists  have not made an Ice-cream that can go without a refrigerator.  Scientists are predicting more  food for astronauts as they live longer in space.

Some foods do not meet the requirements of space food because they don't have enough nutrition to provide to astronauts. According to the text “ No Pizza in Space?” the author states that they use caloric requirements based on a World Health Organization equation. The most important thing  in developing space foods is making sure that they are tasty, have good nutrient content, and can be easily prepared. Calorie requirements differ for astronauts.  An astronaut can choose from many types of foods such as fruits, nuts, peanut butter, chicken, beef, seafood, candy, brownies, etc.Scientists ensure the food that astronauts eat provides them with a balanced supply of vitamins and minerals. In the past space food did not have enough nutrients to provide to astronauts and now it has triple the nutrients to give to astronauts.

In conclusion,  preparing food in space is complicated for many reasons, some are microgravity, some foods are not perfected and some foods do not meet the requirements of space food. astronauts need to eat a  Nutritionists diet to remain healthy in space as the discover the secrets of the unknown world  

hope it helped

Step-by-step explanation:

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

[tex]\sf\qquad\qquad\qquad{\underline{ Food ~in~ space }}[/tex]

Explorers and travelers throughout history have had to develop methods for preserving food and carrying enough food for their journeys. This problem was especially difficult during the time when people made long sea voyages on sailing ships. Great explorers like Columbus, Magellan and Cook carried dried foods and foods preserved in salt and brine.

More recently, refrigeration and canning have provided solutions to the problem of food preservation. However, space travel required that new methods be devised for keeping foods edible. Foods taken into space must be light-weight, compact, tasty and nutritious. They must also keep for long periods without refrigeration. A variety of menus consisting of foods similar to those displayed here provided each astronaut with 2500 or more calories per day.

Answer:

The height would be 18.99

Answer:

y = -6 + 1.2*x is the answer I would use, but see the note below.

Step-by-step explanation:

Let x = the number of minutes.

Let y = the temperature at any given time.

y = -6 + 1.2*x

This is the equation that you would use if you were calculating y with a calculator. If you are in a chemistry class it should be written as

y = - 6°C + 1.2°x/ min

Answer:

10

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The solution we're looking at here is a set of all the points between two parallel lines. Let's see what we can find out about those lines from the inequality, and use that the pick the correct option.

We can start by splitting the inequality at the top into two seperate inequalities:

[tex]7\leq y-3x<11\\y-3x\geq7\\y-3x<11[/tex]

From here, we can put each inequality into slope-intercept form:

[tex]y\geq3x+7\\y<3x+11[/tex]

Our slope for both lines is positive, so we can immediately eliminate B and D. A and C both display lines with slopes of 3 and y-intercepts of 7 and 11; the only difference is in which line is dashed and which line is solid.

As a reminder, a dashed line means that the line itself is not included in the solution, a solid line means that it is. Dotted lines always pop up when you see the symbols < and >, while solid lines pop up when you see ≤ and ≥.

[tex]y\geq3x+7[/tex] (Solid)

[tex]y<3x+11[/tex] (Dashed)

This matches up very nicely with the graph in A, our solution.

Answer:

1.x

=

105

−

2

y

3

2.x

=

225

−

2

y

Step-by-step explanation:

ad them all up

Answer:

60km

Step-by-step explanation:

we multiply 30 with 2 and we get the answer as 60km in two hours.

Answer:

36π

Step-by-step explanation:

2π9² × 80/360 = area of sector

2π9² × 2/9 = 162π × 2/9 = 18π × 2 = 36π

36π is the area

Answer: [tex]A= 32(\pi-2)\ cm^2, \ \ \ P=8\pi\ cm[/tex]

Step-by-step explanation:

When we consider Area under arc AC is is representing a quarter as ADBC is a square, [tex]\angle D=90^{\circ}[/tex].

Area of quadrant = [tex]\dfrac{\pi r^2}{4}[/tex]

here r= 8 cm

Area under Arc AC= [tex]\dfrac{\pi (8)^2}{4}=16\pi\ cm^2[/tex]

Area of white region ABC = Area of square ADBC - Area under Arc AC

[tex]=8^2-16\pi\ \ [\text{Area of square} = sides^2]\\\\= 64-16\pi\ \ =16(4-\pi)\ cm^2[/tex]

Similarly , Area of white region ADC =  [tex]16(4-\pi)\ cm^2[/tex]

Area of shaded region = Area of square - Area of white region ABC - Area of white region ADC

[tex]=64-(64-16\pi)-(64-16\pi)\\\\= 32\pi-64\ cm^2 \\\\= 32(\pi-2)\ cm^2[/tex]

Area of shaded region =[tex]= 32(\pi-2)\ cm^2[/tex]

Length of arc AC = [tex]\dfrac{Circumference}{4}=\dfrac{2\pi r}{4}[/tex]

[tex]\dfrac{\pi (8)}{2}=4\pi cm[/tex]

Perimeter of shaded region = 2(AC) = [tex]8\pi\ cm[/tex]

Answer: (5 - √1) and (4 + √7)

Step-by-step explanation:

Here we have 4 roots, then this is a polynomial of 4th degree.

We can write it as

a*x⁴ + b*x³ + c*x² + d*x + e = 0

We could rewrite this as the product of two quadratic equations:

(a₁*x² + b₁*x + c₁)*(a₂*x² + b₂*x + c₂) = 0

This will be equal to zero when (a₁*x² + b₁*x + c₁) is equal to zero, and when

(a₂*x² + b₂*x + c₂) is equal to zero.

Then we need to find the roots of these two quadratic equations.

And we know that the roots of a quadratic equation like:

a₁*x² + b₁*x + c₁ are given by:

[tex]x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a} = \frac{-b}{2a} +-\frac{\sqrt{b^2 - 4ac}}{2a}[/tex]

Then the general form of the roots is something like:

[tex]A +-\sqrt{B}[/tex]

This means that if one of the roots is:

5 + √1, we must have another root equal to 5 - √1

And if we have one root equal to 4 - √7, then we must have another root equal to 4 + √7

Then the correct options are:

(5 - √1) and (4 + √7)

Answer:

11x - 3y

Step-by-step explanation:

6x + 5x + 2y - 5y

11x - 3y

Hope this helps

Answer:

400 yards

Step-by-step explanation:

300+x>600

x>300, to be a multiple of 100,  the third side must be 400 yards

Answer:

A

Step-by-step explanation:

Remember that the x-value of the vertex when an equation is given in standard form can be found with the equation [tex]\frac{-b}{2a}[/tex]. So, we can take the coefficients from the equation and plug them in.

[tex]\frac{-b}{2a} \\\frac{-(-16)}{2(1)}\\\\\frac{16}{2}\\\\8[/tex]

Now we know that the x-value of the vertex is 8. Next, the equation for the y-value is [tex]c-ah^2[/tex], where h is the x-value of the vertex (8).

[tex](63)-(1)(8)^2\\63-64\\-1[/tex]

So the vertex is (8,-1).

Finally, the axis of symmetry is the x-value of the vertex, also called h.

Final answer, vertex: (8,-1) and axis of symmetry: x=8

Hope this helps!

Answer:

x>-2

Step-by-step explanation:

-2x+6<10

-2x<10-6

-2x<4

x<4/-2

x>-2 because negative answer

Answer:

5

Step-by-step explanation:

xf