what is the common difference of the following sequence?
3,5,7,9,11___

16,19,22,25___​

The answer is attached. I hope this helps answer your question!

Answer:

The equation of the parabola is y = x²/4

Step-by-step explanation:

The given focus of the parabola = (0, 1)

The directrix of the parabola is y = -1

A form of the equation of a parabola is presented as follows;

(x - h)² = 4·p·(y - k)

We note that the equation of the directrix is y = k - p

The focus = (h, k + p)

Therefore, by comparison, we have;

k + p = 1...(1)

k - p = -1...(2)

h = 0...(3)

Adding equation (1) to equation (2) gives;

On the left hand side of the addition, we have;

k + p + (k - p) = k + k + p - p = 2·k

On the right hand side of the addition, we have;

1 + -1 = 0

Equating both sides, gives;

2·k = 0

∴ k = 0/2 = 0

From equation (1)

k + p = 0 + 1 = 1

∴ p = 1

Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;

(x - 0)² = 4 × 1 × (y - 0)

∴ x² = 4·y

The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;

y = x²/4.

Answer:

1. 35 degrees

2. 44 degrees

Step-by-step explanation:

1). 35 degree

180-59=121

121+24+ m<1= 180

m<1= 35 degree

2) m<CED= 45 degree

As CED is a right angled triangle, one angle is of 90 degree while other 2 angles are of 45 degree which makes a sum of 180.

Answer:

We know that the height equation is given by:

H(t) = -16*t^2 + 108*t + 28

in ft.

First, we want to find the maximum height of the ball.

The first thing we can see is that the leading coefficient of the quadratic equation is negative, this means that the arms of the graph will open downwards, so the vertex of the quadratic equation is the maximum.

We also know that the ball will reach its maximum height when its velocity is zero (this means that the object stops going upwards at this point).

To get the velocity equation we need to derivate the above equation, we will get:

V(t) = 2*(-16)*t + 1*108

V(t) = -32*t + 108

We need to find the value of t such that this is zero, we will get:

V(t) = 0 =  -32*t + 108

        32*t = 108

             t = 108/32 = 3.375

So the ball reaches its maximum height after 3.375 seconds.

Then the maximum height is given by the height equation evaluated in that time, we will get:

H(3.375) =  -16*(3.375)^2 + 108*3.375 + 28 = 210.25

Then the maximum height of the ball is 210.25 ft

The ball will hit the ground when:

H(t) = 0

Then we just need to solve:

0 =  -16*t^2 + 108*t + 28

Using the Bhaskara's equation we can find that the two solutions for t are:

[tex]t = \frac{-108 \pm \sqrt{(108)^2 - 4*(-16)*28} }{2*(-16)} = \frac{-108 \pm 116}{-32}[/tex]

So the two solutions are:

t = (-108 + 116)/-32 = -0.25

t = (-108 - 116)/-32 = 7

Because t represents time, we should take only the positive value of time (as t = 0 is the time when the ball is thrown).

Then we can conclude that the ball hits the ground after 7 seconds.

Answer:

20

Step-by-step explanation:

Vertical angles are always equal to each other. So the answer is

3x + 4 = 73 - 9                 Are you sure this is what the question is?

3x + 4 = 64                      Subtract 4 from both sides

     -4      -4

3x = 60                           Divide by 3

3x/3 = 60/3

x = 20

Answer:

B and C

Step-by-step explanation:

Using the Pythagorean theorem a²+b²=c², those are the correct answers

Answer:

There are four motorcycles and six cars.

Step-by-step explanation:

Let m represent the number of motorcycles and c represent the number of cars.

Since there are ten vehicles in total, the sum of the number of motorcycles and the number of cars must total ten. Hence:

[tex]m+c=10[/tex]

And since each motorcycle has two wheels and each car has four wheels and there are 32 wheels in total:

[tex]2m+4c=32[/tex]

Solve the system of equations. First, we can divide the second equation by two:

[tex]m+2c=16[/tex]

From the first equation, we can subtract c from both sides:

[tex]m=10-c[/tex]

Substitute:

[tex](10-c)+2c=16[/tex]

Simplify:

[tex]10+c=16[/tex]

Therefore:

[tex]c=6[/tex]

There are six cars.

Using the modified equation:

[tex]m=10-c[/tex]

Solve for m:

[tex]m=10-(6)=4[/tex]

So, there are four motorcycles and six cars.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

x = -4

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x':}}\\\\2(x-7)=10x+18\\------------\\\rightarrow 2x-14 = 10x + 18\\\\\rightarrow 2x - 14 + 14 = 10x + 18 + 14\\\\\rightarrow 2x = 10x + 32\\\\\rightarrow 2x-10x=10x-10x+32\\\\\rightarrow-8x=32\\\\\rightarrow\frac{-8x=32}{-8}\\\\\rightarrow \boxed{x=-4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

The correct answer is - 332 pages.

Step-by-step explanation:

Given:

number of articles submissions - 75

number of pages in the yearbook on current plan = 156

pages required for two articles = 13 pages.

The number of pages to add = ?

Solution:

1 article takes pages in the yearbook = 13/2

= 6.5

the number of pages required for 75 articles = 75*6.5

= 487.5

The number of pages to add in the yearbook = 487.5 - 156

= 331.5 or 332.

Thus, the correct answer is - 332 pages.

Answer:

84 sq meters

Step-by-step explanation:

First, divide the shape in 2 or more parts so that you can find it step by step

Divide this shape in three parts:

One part (blue): 2 m and 3 m rectangle

Second part (orange): 5 m and 12 m rectangle

Third part (red): 6 m and 3 m rectangle

(you can also see this below: in the pic there are three parts so you figure out that which is the correct value for the sides)

Now, find area of each shape by multiplying its values:

1st shape: 3 x 2 = 6

2nd shape: 5 x 12 = 60

3rd shape: 6 x 3 = 18

As you have the area of all the different shapes,

add all of them:

6 + 60 + 18 = 84 sq meters

I hope this helps :)

Answer:

a. 20-degree

b. 110-degree

c.70-degree

d.50-degree

Answer:

b

Step-by-step explanation:

ive done it before

Answer:

0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.

Step-by-step explanation:

For each test, there are only two possible outcomes. Either it is positive, or it is negative. The probability of a test being positive or negative is independent of any other test, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability of an individual blood sample testing positive for the virus is 0.06.

This means that [tex]p = 0.06[/tex]

If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture.

It will be positive if at least one of the tests is positive, that is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.06)^{0}.(0.94)^{3} = 0.8306[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8306 = 0.1694[/tex]

0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.

Answer:

763.41 ft

Step-by-step explanation:

Answer:

The slope of -1.2 means that for each cup of antioxidant a person consumes per day, it's BMI decreases by 1.2.

The intercept of 26 means that a person that does not consume any cup of antioxidant food a day should have an BMI around 26.

Step-by-step explanation:

Line of best fit:

[tex]y = -1.2x + 26[/tex]

Slope:

The slope is the number that multiplies x, that is, -1.2. The slope of -1.2 means that for each cup of antioxidant food a person consumes per day, it's BMI decreases by 1.2.

Intercept:

Value of y when x = 0, that is, 26. The intercept of 26 means that a person that does not consume any cup of antioxidant food a day should have an BMI around 26.

Answer:

the slope is -1.2 and the intercept is 26.

Step-by-step explanation:

our line's equation is y= -1.2x + 26

In the equation y = mx + b, m is the slope and b is the y-intercept. So in this equation, look for where the numbers are placed and that it what you get.

Answer:

The correct answer is 319.

Step-by-step explanation:

it is in the given picture.

( don't mind my writing!!)

Answer:

its would be a and d

Step-by-step explanation:

6 times 5

Answer:

13

Step-by-step explanation:

The two factors  16 and -3.

Percent of free throws = (number of free throws made / total attempts) x 100

Percent = (80/100) x 100 = 80%

The answer is 80%

Answer:

80%

Step-by-step explanation:

[tex]30.87[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \frac{926}{30} \\ = 30 \frac{26}{30} \\ ( \: or \: ) \\ = 30.8666 \\ = 30.87 [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

Ŷ = 76.4064+5.4254X

0.786

Strong positive relationship

Score = 98

Step-by-step explanation:

Using technology, the linear model obtained by fitting the data is :

Ŷ = 76.4064+5.4254X

Where, slope = 5.4254

y = test score ; x = study time

The Correlation Coefficient obtained is 0.786 ; which depicts that there exist a strong positive relationship between the two variables.

Using the model; test score, if x = 4

Ŷ = 76.4064+5.4254(4)

Y = 98.108

Test score = 98

Answer:

32 units

Step-by-step explanation:

the perimeter =

(1 -(-3)) +(0-(-6)) + (1 -(-11) + (√(12-4)²+6²)

= (1+3) +(0+6) +(1+11) +(√(64+36))

= 4+6+12 + 10

=32 units

Answer:

15,140,170,220,310,370,475,520,580,720

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

jjjj

Answer:

[tex]C = 29.53x[/tex]

Step-by-step explanation:

Given

[tex]Unit\ cost = \$29.53[/tex]

Required

The cost of fencing (C)

The cost is calculated as:

[tex]C = Unit\ Cost * Perimeter\ of fencing[/tex]

Let:

[tex]x \to Perimeter\ of fencing[/tex]

So, we have:

[tex]C = Unit\ Cost * x[/tex]

[tex]C = 29.53 * x[/tex]

[tex]C = 29.53x[/tex]

The question cannot be solved further since the dimension of the fence is not given

If you know the dimension, calculate the fence perimeter and substitute the value for x

Answer:

It is an Integer, but it can also be a rational number.

Step-by-step explanation:

My math teacher told meh

===========================================================

Explanation:

For any two vectors defined as follows

u = <a,b>

v = <c,d>

the dot product is computed by

u dot v = a*c + b*d

If the dot product of the vectors is 0, then the vectors are orthogonal. Meaning they are perpendicular to one another.

-------------------

Let's find the dot product of these two given vectors

u = < 2, -4 >

v = < 6, 3 >

u dot v = 2*6 + (-4)*3

u dot v = 12 - 12

u dot v = 0

Therefore, these two vectors form a right angle and are orthogonal

-------------------

Extra info:

If we can show that u = <a, b> and v = <ka, kb> for some real number k, then we have shown that vectors u and v are parallel.

Answer:

[tex]\frac{80}{45} =k[/tex]

Step-by-step explanation:

image/actual=  8/4.5

8(10)/4.5(10)= 80/45

9514 1404 393

Answer:

Step-by-step explanation:

A Hamiltonian circuit visits each node once and returns to its start. There is no simple way to determine if such a circuit exists.

__

For graph 2, if there were a circuit, paths ACB, ADB, and AEB would all have to be on it. Inclusion of all of those requires visiting nodes A and B more than once, so the circuit cannot exist.

__

For graph 3, the circuit must include paths BAD and DFE. That only leaves node C, which can be reached from both nodes B and E, so path ECB completes the circuit.

Answer:

A. 42½ units

Step-by-step explanation:

the volume = 5×2×4¼ = 10×4¼ = 42½

Using the Pythagorean theorem,

[tex]6^{2}+y^{2}=(3+9)^{2}\\\\36+y^2=144\\\\y^2=108\\\\y=\boxed{6\sqrt{3}}[/tex]