How do I plot a decimal on a coordinate plane?

Answer:

Part a) The vertex is the point (-2,-8)

Part b) The equation of the axis of symmetry is x=-2

Part c) The y-intercept is the point (0,-4)

Part d) The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2} +k[/tex]

where

(h,k) is the vertex of the parabola

if a> 0 then the parabola open upward (vertex is a minimum)

if a<0 then the parabola open downward (vertex is a maximum)

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

x=h ----> equation of the axis of symmetry

In this problem we have

[tex]y=x^{2}+4x-4[/tex]

This is the equation of a vertical parabola open upward

The vertex is a minimum

Part a)

what is the vertex of this function?

Convert the function into vertex form

[tex]y=x^{2}+4x-4[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y+4=x^{2}+4x[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]y+4+4=(x^{2}+4x+4)[/tex]

[tex]y+8=(x^{2}+4x+4)[/tex]

Rewrite as perfect squares

[tex]y+8=(x+2)^{2}[/tex]

[tex]y=(x+2)^{2}-8[/tex] ----> equation in vertex form

The vertex is the point (-2,-8)

Part b) what is the equation of the axis of symmetry?

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

x=h ----> equation of the axis of symmetry

The vertex is the point  (-2,-8)

The x-coordinate of the vertex is -2

therefore

The equation of the axis of symmetry is x=-2

Part c) What is the y- intercept?

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]y=(0)^{2}+4(0)-4[/tex]  

[tex]y=-4[/tex]

The y-intercept is the point (0,-4)

Part d) Graph the line of symmetry. Plot the vertex and the point containing the y-intercept. Then plot another point on the graph and use the plotted points and the axis of symmetry to plot two more points. Draw the graph of the function through the points

To plot the function find the x-intercepts

we know that

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0=(x+2)^{2}-8[/tex]

[tex](x+2)^{2}=8[/tex]

square root both sides

[tex]x+2=(+/-)2\sqrt{2}[/tex]

[tex]x=-2(+/-)2\sqrt{2}[/tex]

[tex]x1=-2(+)2\sqrt{2}=0.828[/tex]

[tex]x2=-2(-)2\sqrt{2}=-4.828[/tex]

the graph in the attached figure

the x value of point a is 5

The x value of point A is; 5

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line.

We have been given a graph representing the point A.

therefore, we need to find the coordinate of the given point.

So, we can see that the coorddinate of the point A is (5, 5)

The value x in the point A would be 5.

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your answer to this question would be (3x+4) (2x-7)

ANSWER

[tex](2x-7)(3x+4)[/tex]

EXPLANATION

The given expression is:

[tex] 6{x}^{2} - 13x - 28[/tex]

We find ac=6×-28=-168

Two factors of -168 that, if added will give us -13 are 8 and -21

We split the middle term to obtain,

[tex]6{x}^{2} + 8x - 21x- 28[/tex]

We now factor by grouping to obtain:

[tex]2x(3x + 4) - 7(3x + 4)[/tex]

Factor further to obtain;

[tex](2x-7)(3x+4)[/tex]

Step 1: 3x in the first equation and -3x in the second equation cancel each other out, since summing them together give you zero (look at image below)

Step 2: Now you have the equations:  -2y = 12 and 8y = -6. You can combine the two equations by adding -2y and 8y together and also 12 plus -6 (look at image below)

Step 3: Current formula is 6y = 6. To isolate y divide 6 to both sides and you will get y = 1

Step 4: Choose either equation and input 1 for y and solve for x

3x - 2(1) = 12

3x - 2 = 12

3x = 14

x = 14/3

(14/3, 1)

Below you can see the graph I checked it on, and the two lines indeed intersect at (14/3, 1) (aka - (4.667, 1)

Hope this helped!

Answer:

[tex]\large\boxed{x=\dfrac{14}{3},\ y=1}[/tex]

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}3x-2y=12\\-3x+8y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad6y=6\qquad\text{divide both sides by 6}\\.\qquad\qquad\boxed{y=1}\\\\\text{Put the value of y to the first equation:}\\3x-2(1)=12\\3x-2=12\qquad\text{add 2 to both sides}\\3x=14\qquad\text{divide both sides by 3}\\\boxed{x=\dfrac{14}{3}}[/tex]

y = 6/x - 6

To a function be linear we need

y = ax + b

Not y = a/x + b

So it's non linear.

Answer:

It is non linear

Step-by-step explanation:

It is a different type of function which looks like the picture I put down below

Answer:

-2324522934

Step-by-step explanation:

These are the terms of a geometric sequence with n th term

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{-6}{-2}[/tex] = 3 and a = - 2, hence

[tex]a_{20}[/tex] = - 2 × [tex]3^{19}[/tex] = - 2324522934

Final answer:

The 20th term of the geometric sequence provided is calculated using the formula for the nth term of a geometric series. The term is found to be -2 multiplied by 3 to the power of 19, which equals -2,324,522,934.

Explanation:

The sequence provided is a geometric sequence where each term is multiplied by 3 to get the next term (-2, -6, -18, -54, -162...). To find the 20th term of a geometric sequence, we use the formula: an = a1  imes r(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number. In this case, a1 is -2, r is 3, and n is 20. Therefore, the 20th term is calculated as follows:

a20 = (-2) times 3(20-1) = -2 times 319

Using a calculator, we can find that 319 equals 1,162,261,467. Therefore, the 20th term of the sequence is -2  imes 1,162,261,467 = -2,324,522,934

Mary is 10 yrs old now.

Explanation:

10+20=30

30÷3=10

So, Mary has to be 10yrs old now.

Mary is currently 10 years old.

Given that in coming 20 years Mary's age will be 3 times her present age, we need to calculate her present age,

Let's assume Mary's current age is represented by "x". According to the given information, in 20 years, Mary will be three times as old as she is now. Therefore, her age in 20 years will be 3 times her current age, which can be expressed as 3x.

So, we can set up the equation:

x + 20 = 3x

To solve this equation, we can subtract x from both sides:

20 = 2x

Then, we can divide both sides by 2:

x = 10

Therefore, Mary is currently 10 years old.

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____________________________________________________

Answer:

Your answer would be 36 kg m²/s²

____________________________________________________

Step-by-step explanation:

To find the canoe's kinetic energy, we would need to use the kinetic energy formula in order to get the actual kinetic energy of the moving canoe.

The equation for this problem would be:

[tex]KE = 1/2mv^2[/tex]

With what we know from the questions, our mass would be 18, and our speed would be 2. We would plug those numbers in our equation. Your equation should look like this:

[tex]KE = 1/2(18)(2)^2[/tex]

Now, we solve:

[tex]KE = 1/2(18)(2)^2\\\\KE=1/2(18)(4)\\\\KE=(9)(4)\\\\KE=36[/tex]

Once you're done solving, you should get the answer of 36.

Therefore, the canoe's kinetic energy would be 36 kg m²/s².

36 kg m²/s² should be your FINAL answer.

____________________________________________________

Answer:

C

Step-by-step explanation:

The shape consists of a cylinder and a hemisphere.

The volume of a cylinder is:

V = πr²h

where r is the radius (half the diameter) and h is the height.

The volume of a hemisphere is:

V = ⅔ πr³

where r is the radius (half the diameter).

The cylinder and hemisphere both have a diameter of 8 cm, or a radius of 4 cm.  The cylinder has a height of 17 cm.

So the total volume is:

V = π(4 cm)²(17 cm) + ⅔ π(4 cm)³

V = π (272 + 128/3) cm³

V ≈ 988.6 cm³

115 degrees is the measure because angle 4 and angle 115 are transversal angles so yeah

Answer:

[tex]\large\boxed{x=-1\ \vee\ x=1}[/tex]

Step-by-step explanation:

[tex]8x^2+4=12\qquad\text{subtract 4 from both sides}\\\\8x^2+4-4=12-4\\\\8x^2=8\qquad\text{divide both sides by 8}\\\\\dfrac{8x^2}{8}=\dfrac{8}{8}\\\\x^2=1\to x=\pm\sqrt1\\\\x=-1\ \vee\ x=1[/tex]

Battery is down currently = 2/5

Battery drains at the rate of 1/9 every hour.

Remaining battery life of Vera = 1 -2/5 = 3/5

Let y we the number of hours battery will last.

So, 1/9 y = 3/5

y = 27/5

y = 5 + 2/5 hours

y = 5 hrs and 24 mins

So battery will last another 5 hrs and 24 mins.

hope this helps:)

Answer: I believe the answer is the second choice.  

81y^4 - 16x^2, the difference of squares.

Step-by-step explanation:

Answer:

y = 2x + 1

Step-by-step explanation:

When given a point and a slope, use point-slope form of a line.

y - y₁ = m (x - x₁)

Here, (x₁, y₁) is (1, 3), and m = 2.

y - 3 = 2 (x - 1)

We can convert to slope-intercept form by solving for y:

y - 3 = 2x - 2

y = 2x + 1

Use the FOIL method.

3a * 2a + 3a * 4b + b * 2a + b * 4b

Combine like terms.

6a + 12ab + 2ab + 4b^2

6a^2 + 14ab + 4b^2

Answer

[tex]6a^2 + 14ab + 4b^2[/tex]

Answer:

3y² + 7y + 4 = (3x + 4)(x + 1)

Step-by-step explanation:

* To factor a trinomial in the form ax² ± bx ± c:

- Look at the c term

# If the c term is positive

∵ c = r × s ⇒ r and s are the factors of c

∴ r and s will have the same sign (sign of b)

∵ a = h × k ⇒ h , k are the factors of a

∴ rk + hs = b

∴ (hx + r)(kx + s) ⇒ if b +ve  OR  (hx - r)(kx - s) ⇒ if b -ve

# If the c term is negative

∵ c = r × s ⇒ r and s are the factors of c

∴ r and s will not have the same sign

∵ a = h × k ⇒ h and k are the factors of a

∴ rk - hs = b OR hs - rk = b

(hx + r)(kx - s) OR (hx - r)(kx + s)

* Now lets solve the problem

∵ 3y² + 7y + 4

∵ ax² + bx + c

∴ a = 3 , b = 7 , c = 4

∵ a = h × k

∵ 3 = 3 × 1

∴ h = 3  , k = 1

∵ c = r × s

∵ 4 = 4 × 1

∴ r = 4 , s = 1

∵ c is positive

∴ hs + rk = b

∴ 3(1) + 4(1) = 7 ⇒ same value of b

∴ 3y² + 7y + 4 = (3x + 4)(x + 1)

Answer:

The factors of 3y^2 + 7y + 4 are

(y +1) and (3y + 4)

Step-by-step explanation:

It is given a quadratic equation in variable y

3y^2 + 7y + 4

To find the factors using splitting method

3y^2 + 7y + 4 can be written as,

3y^2 + 7y + 4 = 3y^2 + 3y + 4y + 4

 = 3y(y + 1) + 4(y + 1)

 = (y + 1)(3y + 4)

Therefore the factors of 3y^2 + 7y + 4 are

(y +1) and (3y + 4)

Answer:

16, 26, 36

Step-by-step explanation:

In order to solve this problem, you MUST find the number that is making the pattern flow. The first method you should try is to subtract the first number from the second. That means -24 - (-14), which equals 10. If you continue to do this is every number, 10 will be the answer. Now that we have the number add 10 to the number and the next number, to find the answers.

Ex.

[tex]6 + 10 = 16\\16 + 10 = 26\\26 + 10 = 36[/tex]

This is how you solve this problem.

Answer:

[tex]\large\boxed{r=\dfrac{1}{4}}[/tex]

Step-by-step explanation:

[tex]y=rx\to r=\dfrac{y}{x}\\\\\text{From the table:}\\\\x=8,\ y=2\to r=\dfrac{2}{8}=\dfrac{1}{4}\\\\x=16,\ y=4\to r=\dfrac{4}{16}=\dfrac{1}{4}\\\\x=32,\ y=8\to r=\dfrac{8}{32}=\dfrac{1}{4}[/tex]

Answer:

• positive answer: 9

• negative answer: -6

Step-by-step explanation:

Since you know your multiplication tables, you are familiar with the fact 6·9 = 54. One of these factors is 3 larger than the other, so is the answer you seek.

The number is 9.

___

These multiplication problems often have negative solutions as well. Usually, the negative solution is the other factor of the pair, but with a minus sign. Here, that is -6:

(-6)(-9) = 54 . . . . . where -9 is 3 less than -6.

Answer:

9

Step-by-step explanation:

Let's break it down

" A number is multiplied "

Okay so we know that a number is being multiplied

" by the number 3 less than itself"

So whatever number it is, (lets use x) is being multiplied by a number (lets use y) 3 less then itself. So x - 3 = y and x·y = 54

So I started dividing all the numbers 1 - 9

54 ÷ 9 = 6

54 ÷ 8 = 6.75

54 ÷ 7 = 7.71~

54 ÷ 6 = 9

Then I stopped

Read the question again

"A number is multiplied by the number 3 less than itself. The result is 54."

A number - 9

Multiplied by the number 3 LESS then itself - 6

The result is 54 - 9 × 6 = 54

Hope that helps ^^

Answer:x + 10

Step-by-step explanation:

Answer:

J=x+10

Step-by-step explanation:

We know the equation is about Jenna's money. We can use J to represent Jenna and X to represent Alyssa's Dollars.

We know that J has 10 more than A. We can say J=X+10

It’s hard to see the graph but from what I can see 15°

1 = C      2 = I     3 = B  have a good day

Answer:

-(√5)/3

Step-by-step explanation:

The tangent being negative means the sine and cosine have opposite signs. Using the identity ...

cos(o) = ±√(1 -sin(o)^2)

we find ...

cos(o) = -√(1 -(2/3)^2) = -√(5/9)

cos(o) = -(√5)/3

Answer:

Hello :))

Step-by-step explanation:

You should set this up as a proportion equation. 8.1kg /1hr =x/7hr You would cross multiply here and end up getting the equation... 1x=8.1*7 (x=56.7 kg)

Hope this helps! :))

Answer:

It has no solution

Step-by-step explanation:

I just did the test and got this right (as a matter of fact, I got 100% ^^)

It has no solution because no matter how much you multiply the two fractions to the left, it will always equal to 1/2, and 2/4, no matter how many times you multiply it, will always equal to 1/2 as well. Therefore, since those two cancel out, and the leftover numbers in the equation aren't the same, there is no possible solution for this equation.  

Hope this helps you mate

What the test is looking for is obviously x<=5 (the second one), but I'd actually say 0 is equal or less than x that is equal or less than 5, where x is a natural number.

You cannot have a negative quantity of books, nor can you have 4.3627272828 ones.

Answer:  The correct option is (B) [tex]x\leq 5.[/tex]

Step-by-step explanation:  We are given to write an inequality for the following situation :

"No more than 5 books are in your backpack".

Let the number of books in the backpack  be x.

The given situation implies that there will be either less than or equal to 5 books in the backpack.

Therefore, the required situation can be written as

[tex]x\leq 5.[/tex]

Thus, (B) is the correct option.

Answer:

x = 75

Marta's jump rope is 75 inches long

Step-by-step explanation:

Hello!! This is how you solve it:

x + ( x - 10 x 3 ) = 120

2x - 10 x 3 = 120

2x - 30 = 120

+ 30. + 30

2x = 150

--- ------

2. 2

x = 75

Final answer:

Marta's jump rope is 87.5 inches long. This was determined by setting up an equation based on the information that Marta's rope is 10 inches shorter than three times Dilbert's rope length, and together they measure 120 inches.

Explanation:

The question involves finding the length of Marta's jump rope when it is known to be 10 inches shorter than three times the length of Dilbert's rope, and when both ropes laid end-to-end measure 120 inches long. Let's denote the length of Dilbert's jump rope as D inches. Therefore, the length of Marta's jump rope can be expressed as 3D - 10 inches. Since the combined length of both ropes is 120 inches, we can write the equation: D + (3D - 10) = 120.

Combining like terms, we get 4D - 10 = 120. Adding 10 to both sides gives 4D = 130, and dividing both sides by 4 yields D = 32.5 inches. Thus, Dilbert's rope is 32.5 inches long, and Marta's rope, being 3(32.5) - 10, calculates to 87.5 inches long.

Answer:

The least and the greatest weights are 315 grams and 325 grams

Step-by-step explanation:

* Lets explain what is the upper and lower bounds

- The lower bound is the smallest value that would round up to the

  estimated value.

- The upper bound is the smallest value that would round up to the next

 estimated value.

- Ex: a mass of 70 kg, rounded to the nearest 10 kg, has a lower

 bound of 65 kg, because 65 kg is the smallest mass that rounds to

 70 kg. The upper bound is 75 kg, because 75 kg is the smallest mass

 that  would round up to 80 kg, then 65 ≤ weight < 75

- So to understand how to find them divide the nearest value by 2

 and then subtract it and add it to the approximated value

* Lets solve the problem

- A packet of crisps weighs 32 grams to the nearest gram

- The nearest value is 1 gram

∴ 1 ÷ 2 = 0.5

- To find the lower bound subtract 0.5 from the approximated value

∵ The approximated value is 32

∴ The lower bound = 32 - 0.5 = 31.5 grams

- To find the upper bound add 0.5 from the approximated value

∵ The approximated value is 32

∴ The upper bound = 32 + 0.5 = 32.5 grams

∴ 31.5 ≤ weight of one packet < 32.5

∵ A multipack of crisps contain 10 packets

- To find the least and greatest weights of the multipack multiply the

  the lower bound and the upper bound by 10

∵ The least value of one packet is 31.5

∴ The least weight of the mulipack = 31.5 × 10 = 315 grams

∵ The greatest value of one packet is 32.5

∴ The greatest weight of the mulipack = 32.5 × 10 = 325 grams

∴ 315 ≤ weight of multipack < 325

* The least and the greatest weights are 315 grams and 325 grams

Least weight of the multipack: 315 grams. Greatest weight of the multipack: 325 grams. Each packet ranges from 31.5 grams to 32.5 grams.

let's work through this step by step.

1. **Weight of a single packet of crisps**: Given that a packet of crisps weighs 32 grams to the nearest gram, this means the actual weight could be anywhere from 31.5 grams to 32.5 grams. Since we're considering the least and greatest weights, we'll use these bounds.

  - Least weight: 32 grams - 0.5 grams = 31.5 grams

  - Greatest weight: 32 grams + 0.5 grams = 32.5 grams

2. **Weight of the multipack**: Since the multipack contains 10 packets, we'll multiply the least and greatest weights of a single packet by 10 to find the least and greatest weights of the multipack.

  - Least weight of the multipack: 31.5 grams/packet x 10 packets = 315 grams

  - Greatest weight of the multipack: 32.5 grams/packet x 10 packets = 325 grams

So, the least weight of the multipack is 315 grams, and the greatest weight is 325 grams.

Answer:

Isn't this just 1?

Step-by-step explanation:

5/7 + 2/7 = 7/7 = 1

Hello There!

We are going to be finding the sum of 5/7 and 2/7

STEP 1 We already have common denominators so now, it's just about adding what we already have.

STEP 2 Add 5 and 2 together and you will get a sum of 7 and your denominator will be left alone.

STEP 3 We will get a answer of 7/7 which is the same thing as 1.

Your Answer Is 1