Given three different prime numbers [tex]p_1 \ \ ; \ \ p_2[/tex] and [tex]p_3[/tex] satisfy equation [tex]p_1+p_2+p_3=202[/tex] . Find the maximum value of

[tex]\pmb {p_1 \times p_2\times p_3=?}[/tex]

Answer:

[tex]a_n=a_{n-1}+8,n\geq 1[/tex]

[tex]a_1=-11[/tex]

Step-by-step explanation:

We are given that a sequence

-11,-3,5,13,...

[tex]a=a_1=-11[/tex]

[tex]a_2=-3[/tex]

[tex]a_3=5[/tex]

[tex]a_2-a_1=-3-(-11)=-3+11=8[/tex]

[tex]a_3-a_2=5-(-3)=5+3[/tex]

[tex]a_3-a_2=8[/tex]

Common difference between two consecutive terms is equal.

Hence, the sequence is Arithmetic.

Common difference, d=8

[tex]a_2=a_1+8=-3[/tex]

[tex]a_3=a_2+8=5[/tex]

[tex]a_4=a_3+8=13[/tex]

:

:

:

[tex]a_n=a_{n-1}+8, n\geq 1[/tex]

[tex]a_1=-11[/tex]

The correct option is B)

Let the fourth vertex D =(x,y)

We know that the diagonals of a parallelogram bisect each other. So, the.

The midpoint of AC is the same as the midpoint of BD.

Midpoint of two points (x 1 ,y 1 ) and (x 2,y 2) is  calculated by the formula ( 2x 1+x 2, 2y 1+y2 )

So, the midpoint of AC= Midpoint of BD

=>( 2−2+8, 23+3)=( 26+x, 27+y

=>( 6, 26)=( 26+x, 27+y)

=>6+x=6;7+y=6

=>x=0;y=−1

Hence, D=(0,−1)

Solve any question of Coordinate Geometry with.

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Answer:

Step-by-step explanation:

If the position function is

[tex]h(t)=-40t^2+200t[/tex] and we are looking for time when the height is 0, we sub in a 0 for h(t) and solve for t:

[tex]0=-40t^2+200t[/tex] and the easiest way to do this is to factor by taking the GCF of -40t:

0 = -40t(t - 5) and by the Zero Product Property,

-40t = 0 or t - 5 = 0. Solving for t, we get

t = 0 (which is before the object is launched) and

t = 5 (which is how long it takes the object to go from the ground, up to its max height, and then back to the ground again).

Your choice is c) 5

Answer:

8 years.

Step-by-step explanation:

Mara is 6.

6+8=14

Alberto is 20.

20+8=28

14*2=28.

In 8 years, Alberto will be twice Mara's age.

Answer:

Ruby is sphere

Shriya's is incorrect

Abhishek's is correct

Step-by-step explanation:

Ruby's definition matches a sphere because it is 3D and Shriya's is wrong.

Answer:

y = 1.4x + 21.4

Step-by-step explanation:

Given :

Total cost and number of units made have a linear relationship

Mathematically,

Total cost, y = b * number of units made, x + c

If cost increases by $1.4 for each additional unit, the slope, b = 1.4

If total cost of 24 units = $55

Total cost = 1.4 * number of units made + c

55 = 1.4*24 + c

55 = 33.6 + c

c = 55 - 33.6

c = 21.4

c = intercept

The linear relationship between total cost and number of units made is :

y = 1.4x + 21.4

Answer:

Check the explanation for the answer please. Thank you!

Step-by-step explanation:

a. Nina is correct, because the formula P = 2l + 2w would be a correct perimeter formula. Alexander, however, is wrong, because the formula P = 2(l + w) would be an incorrect perimeter formula.

b. P = L + L + W + W would be another correct perimeter formula, as it is the same thing to P = 2l + 2w.

c. One reason the paint was empty after their calculations were correct would be because of their argument before determining the perimeter amount of paint that they need. Another reason the paint was empty after their calculations were correct was because of the fact that they probably don't know how to perfectly do the paint within the perimeter. [I might be wrong about this, but it should be an opinion question anyway.] DO NOT WRITE/TYPE THE PARENTHESIS INTO THIS PROBLEM!!!

Hope this helped!

Answer:

(x-3)^2+(y-16)^2=9

Step-by-step explanation:

Answer:

The answer is 9

Step-by-step explanation:

(x-3)^2+(y-16)^2=9

Hope this helps :)

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

Explanation:

Replace every copy of "w" with "x"

So the function we graph is y = (1500-2x)*x/2

I used GeoGebra to make the graph below. Note the scale on the xy axis. In this case, x is incrementing by 100 while y is incrementing by 50,000. The scale is important so you have a good viewing window. You don't have to have this scale exactly, but something close to it should do the trick. Without the proper scale, you probably won't see the curve at all. You may see a straight line instead, or it may appear completely blank.

You can use Desmos to make the graph. Just keep in mind the scale of course.

Once you have the graph set up, use the max feature of your graphing calculator or graphing software to locate the vertex point. In GeoGebra, the function I used is "Max". I typed in Max(f, 0, 800) where f is the function mentioned earlier. With Desmos, you simply need to click on the curve itself to have the max point show up. Click on the vertex point to have the coordinates listed.

The max point is located at A = (375, 140625) as shown in the diagram below. The x coordinate is the value of "w" that we replaced earlier. So a width of w = 375 feet corresponds to the max area of 140625 square feet.

Side note: later on in your math career, you have the option to use calculus to solve a problem like this. Though for now, we can rely on a graphing calculator to get the job done quickly.

Answer:

C.52

Step-by-step explanation:

In a parallelograms opposite sides are congruent

This means that side SP = side RQ as they are opposites

Hence 1/4y = 13

Note that we've just created an equation that we can use to solve for y.

We now solve for y algebraically using the equation we've just created

1/4y = 13

Divide both sides by 1/4

1/4y / 1/4 = y

13 / 1/4 = 52

We're left with y = 52

If PQRS is a parallelogram, the value of y in the parallelogram PQRS is 52. Therefore, option C, 52, is the correct answer.

To find the value of y in the parallelogram PQRS, we can use the properties of parallelograms.

In a parallelogram, opposite sides are equal in length. Therefore, PQ is equal to RS, and QR is equal to SP.

Given that PQ = 11 and RS = 11, we can conclude that QR = SP.

Substituting the given values, we have:

1/4 y = 13

To isolate y, we multiply both sides of the equation by 4:

4 * (1/4 y) = 4 * 13

This simplifies to:

y = 52

Using the property of a parallelogram where opposite sides are equal, we determine that QR is equal to SP. Substituting the given values, we find that 1/4 y is equal to 13. By multiplying both sides of the equation by 4, we isolate y and find that its value is 52.

Therefore, option C, 52, is the correct answer.

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Answer:

This is called "completing the square"

It is a technique to  solve a quadratic equation. It involves "moving all

of the constants to the right" , then doing a "move" on the left hand side. This move "creates a perfect square".. This is done by taking 1/f of the "B" term and squaring it... this will "un-balance" the  sides of the equation... to balance it out you have to "add" some stuff to the right hand side... when done the left side will be "a perfect square" .. last step will be take the square root of both sides.

Step-by-step explanation:

[tex]x^2 + 12x + 15 = 0[/tex]

[tex]x^2 + 12x + 15 -15 = -15[/tex]

[tex]x^2 + 12x = -15[/tex]

[tex]b = 12 ... (1/2 b)^2 = 6^2 = 36[/tex]

[tex]x^2 + 12x + 36 = -15 + 36[/tex]

[tex]x^2 + 12x + 36 = 21[/tex]

[tex](x+ 6)^2 = 21[/tex]

[tex]\sqrt{(x+ 6)^2 } =[/tex] ± [tex]\sqrt{21}[/tex]

[tex]x+ 6[/tex]= ± [tex]\sqrt{21}[/tex]

x = -6 ±[tex]\sqrt{21}[/tex]

Answer:

Step 1: -15

Step 2: b = 12, c = 36

Step 3-4: x² + 12x + 36 = -15 + 36, which simples to (x + 6)² = 21

If there is a step that has you solve for x, it should be -6 + √21 or -6 - √21.

Step-by-step explanation:

Step 1 is pretty simple. All we have to do is subtract 15 from 0 to get the first blank.

x² + 12x = 0 - 15

x² + 12x = -15

Step 2:

b is the coefficient on x, which is 12.

Then, use the formula mentioned:

[tex]c = ( \frac{b}{2})^{2} \\ c = ( \frac{12}{2} )^{2} \\ c ={6}^{2} \\ c = 36[/tex]

As a result of that, c is 36.

Now to substitute and simplify. (Steps 3-4)

x² + 12x + 36 = -15 + 36

To factor an equation, think about it like this: Find two numbers that add to the coefficient of x, and multiply to the constant. So what two numbers add to 12, and multiply to 36? That would be 6 & 6 (6 + 6 = 12; 6 × 6 = 36).

(x + 6)² = -15 + 36

Add 36 to -15 to get 21.

(x + 6)² = 21

That should solve steps 1-4, but I will go on ahead and give the final answer to the entire problem.

(x + 6)² = 21

Yes, you are about see what I just factored be expanded back over again. It's part of the process.

x² + 12x + 36 = 21

Now subtract 21 from both sides.

x² + 12x + 36 - 21 = 21 - 21

x² + 12x + 15 = 0

Now onto the hard part of this: the quadratic formula. a = (the understood) 1, b = 12, and c = 15.

x = (-b ± √b² - 4ac)/2a

x = -12 ± √12² - 4(15)/2

x = -12 ± √144 - 60/2

x = -12 ± ✓84/2

x = -6 + √21 or -6 - √21

Answer:

x = 0

Step-by-step explanation:

a = 10

=> x + a = 10

=> x + 10 = 10

=> x = 10 - 10

=> x = 0

Answer:

D

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 3x - 2 + x² + 1 ← collect like terms

= x² + 3x - 1 → D

The combination function (f+g)(x) is x²+3x-2.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=3x-2 and g(x)=x²+1.

Here, (f+g)(x)=f(x)+g(x)

= (3x-2)+x²+1

= x²+3x-2

Therefore, the combination function (f+g)(x) is x²+3x-2.

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Answer:

When x = 0, the value of f(x) is -3

Each time x increases by 1, f(x) increases by 2

f(x) = 2x - 3

Step-by-step explanation:

✔️From the graph given, values of x is plotted in the horizontal axis while values of f(x) is plotted on the vertical axis.

Thus:

When x = 0, the value of f(x) is -3. => (0, -3)

✔️Each time x increases by 1, f(x) increases by 2. i.e. when x increases from 3 to 4 on the y axis, f(x) increases from 3 to 5 on the why axis.

✔️The equation that models the function can he written in the form of f(x) = ax + b, where:

a = rate of change = rise/run

b = y-intercept = the point on the y-axis that the line intercepts.

Rate of change between the two points on the line (0, -3) and (4, 5):

Rate of change (a) = rise/run = (5 - (-3))/(4 - 0) = 8/4

a = 2

b = y-intercept = -3

✅To write the equation, substitute a = 2 and b = -3 into f(x) = ax + b:

f(x) = 2x + (-3)

f(x) = 2x - 3

Answer:

[tex]\boxed {\boxed {\sf y= 6x+5}}[/tex]

Step-by-step explanation:

We are asked to find the slope-intercept equation of a line. Slope-intercept form is one way to write the equation of a line. It is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

We are given a point (-1, -1) and the line is parallel to the line y= 6x-2. Since the line is parallel to the other line, they have the same slope, which is 6. We have a point and a slope, so we should use the point-slope formula to find the equation of the line.

[tex]y-y_1= m (x-x_1)[/tex]

Here, m is the slope and (x₁, y₁) is the point. We know the slope is 6 and the point is (-1, -1). Therefore:

Substitute the values into the formula.

[tex]y- -1 = 6(x- -1) \\y+1= 6(x+1)[/tex]

Distribute the 6. Multiply each value inside the parentheses by 6.

[tex]y+1 = (6*x)+ (6*1) \\y+1= 6x+6[/tex]

Slope-intercept form requires y to be isolated. 1 is being added to y. The inverse of addition is subtraction. Subtract 1 from both sides.

[tex]y+1-1=6x+6-1 \\y= 6x+5[/tex]

The equation of the line in slope-intercept form is y=6x+5

Answer:

<2 = 40

Step-by-step explanation:

Angles 2 and 3 are alternate interior angles and alternate interior angles are equal when the lines are parallel

<2 =<3 = 40

Answer:

21

Step-by-step explanation:

2.8 for 8 means a ratio of

2.8/8

now we need to transform this ratio to show x/60.

for that we need to multiply the numerator and the denominator with the same factor.

which factor ?

well, the one turning 8 into 60.

so,

8×f = 60

f = 60/8 = 15/2 = 7.5

so,

x = 2.8 × 7.5 = 21

he will need 22 gains for 60 doors.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

m = 3

(7, -2)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

The equation given is in point-slope form.

⸻⸻⸻⸻

[tex]y - y_1 = m(x-x_1)\\\\m-\text{slope}\\\\(x_1,y_1)-\text{point}[/tex]

⸻⸻⸻⸻

The '3' is in the 'm' spot.

The y value is '-2', (y -(-2)) and the 'x' value is 7.

The point of the line is (7, -2) and the slope is 3.

⸻⸻⸻⸻

»»————-　★　————-««  

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

Answer:

[tex]\sf [0,∞)[/tex] is the inequality.

Step-by-step explanation:

This is the inequality represented by this graph. The main reason is this inequality contains zero to infinity.

Answer:

[tex]\sf{[0,\infty) }[/tex]

Step-by-step explanation:

this inequality contains zero to infinity

Answer:

x > 7

Step-by-step explanation:

Let x be the unknown number

x+3 > 10

Subtract 3 from each side

x+3-3 > 10-3

x > 7

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{\underline{The sum of a number and 3 is greater than 10.}}[/tex]

[tex]\large\textsf{Well, the word sum simply means add. The word number}\\\large\textsf{ is unknown so we will label it as x.}[/tex]

[tex]\large\textsf{We will make this your equation: x + 3 } \mathsf{ > } \large\textsf{ 10}[/tex]

[tex]\large\textsf{Now lets solve for your answer.}\downarrow[/tex]

[tex]\large\textsf{x + 3 }\mathsf{>}\large\textsf{ 10}[/tex]

[tex]\large\textsf{SUBTRACT 3 to BOTH SIDES}[/tex]

[tex]\large\textsf{x + 3 - 3 } \mathsf{>} \large\textsf{ 10 - 3}[/tex]

[tex]\large\textsf{CANCEL out: 3 - 3 because that gives you 0}[/tex]

[tex]\large\textsf{KEEP: 10 - 3 because that helps what is being compared to the x-value}[/tex]

[tex]\large\textsf{x } \mathsf{>} \large\textsf{ 10 - 3}[/tex]

[tex]\large\textsf{10 - 3 = \bf 7}[/tex]

[tex]\large\textsf{\bf x } \mathsf{\bf >\ } \large\textsf{ \bf 7}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, your answer is: \bf x}>\textsf{\bf 7}\huge\textsf{ (Option B.)}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Yes

Step-by-step explanation:

From the origin means from the centre or middle but about a vertex is from a named point.

Answer:

-10/3 < x < 2

so the answer is  x<-10/3 or x>2

Step-by-step explanation:

:)

Answer:

y = (x-15)/-8

Step-by-step explanation:

When solving for an inverse function, swap x and y without bringing the x coefficient with it, just simply swap the variables. Then, solve for y, and that's it.

y = -8x + 15

x = -8y + 15

x-15 = -8y

(x-15)/-8 = y

Step-by-step explanation:

Hey there!

Given function is: y = -8x + 15

~ Interchange"X" and "y".

x = -8y + 15

~ Solve it

8y = 15-x

y = (15-x)/8

Therefore, the inverse of function is y = (15-x)/8.

Hope it helps!

Step-by-step explanation:

Given that,

The area of a rectangle, A = 35 cm²

Let x is the length.

Width, Y = 12-x

We know that,

The area of a rectangle is given by :

[tex]A=lb[/tex]

[tex]x(12-x)=35\\\\12x-x^2=35\\\\-x^2+12x-35=0\\\\or\\\\x^2-12x+35=0[/tex]

Hence, [tex]x^2-12x+35=0[/tex].

Answer:

C is the answer 3rd one...

3x ² - 2x + 1 = 2x ² - 3x + 7

x ² + x - 6 = 0

(x + 3) (x - 2) = 0

x + 3 = 0   or   x - 2 = 0

x = -3   or   x = 2

Answer:

Step-by-step explanation:

That was some horse.

20*t + 30*t = 800           Each day he rode the same amount of time (t). On the first day, he rode a distance of 20*t. On the second day, he rode a distance of 30*t

50t = 800

t = 800/50

t = 16

Each day he rode 16 hours

Total time = 32 hours.

Answer:

32 hours

Step-by-step explanation:

Answer:

Step-by-step explanation: