Solve the quadratic equation below by Completing the Square STEP-BY-STEP:
x^2+6x=0

Solution:

We know that:

[tex]\frac{\tex\text{Diamonds}}{\text{Emeralds}} = \frac{3}{4}[/tex]

[tex]\text{Emeralds} = 16[/tex]

Substitute the amount of emeralds in the ratio to find the amount of diamonds.

[tex]\dfrac{\tex\text{Diamonds}}{16} = \dfrac{3}{4}[/tex]

[tex]\tex\text{Diamonds} = \dfrac{3 \times 16}{4}[/tex]

[tex]\tex\text{Diamonds} = \dfrac{48}{4} = 12[/tex]

Thus, there were 12 diamonds.

(a)

girls to boys → 2 : 1

2 → 24

1 → 12

There are total 12 boys.

(b)

diamonds to emeralds → 3 : 4

4 → 16

1 → 4

3 → 12

There are 12 diamonds.

Answer:

Graph D

Step-by-step explanation:

Graph A is incorrect because that is a graph of a negative exponential function.

Graph B is incorrect because that is a graph of a square root function.

Graph C is incorrect because that is a graph of a positive exponential function.

Graph D is correct because linear functions are always straight lines. Linear functions have the base equation of y = mx + b . Because there is only one "x" value to the first power, the function increases by the same amount between each "x" value.

Answer:

1764

.

.

.................

....

Answer:

12(5 - 3w)

Step-by-step explanation:

60 - 36w

The GCF of 60 and 36w is 12.

60 - 36w = 12(5 - 3w)

Step-by-step explanation:

Substitute the given values into the expression;

[tex]\frac{5(6)}{3(-4)} +6[/tex]

Multiply;

[tex]\frac{30}{-12} +6[/tex]

Divide;

30 and -12 aren't common factors. To get to 30 with -12, you need to multiply -12 by -2.5.

[tex]-2\frac{1}{2} +6[/tex]

Add;

[tex]3\frac{1}{2} \; or \; 3.5[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &3 \end{cases} \\\\\\ A=2000\left(1+\frac{0.04}{4}\right)^{4\cdot 3}\implies A=2000(1.01)^{12}\implies A\approx 2253.65[/tex]

Answer:

b(a-c-3d)

Hope this helps

Answer:

b(a-c-3d)

Step-by-step explanation:

Answer: 48n + 120

Step-by-step explanation:

12(4n+10)

12(4n) + 12(10)

48n + 120

My bad VectorFundament20, sheesh

Answer:

y=10x

Step-by-step explanation:

So y is basically 10 times x because each y value, 10, 20, 30 is coming from multiplying the x value by 10. For example, 0 = 10* 0, 10 = 10*1, 20 = 10*2, 30 = 10*3.

Answer:

B. The total amount of tweets...

E. NCAA basketball tournament

F. Butterfly population doubles each month

An exponential function is a function that grows exponentially.

Exponential functions have a multiplicative rate of change. This means each term can be multiplied by a specific number to get to the next.

Example of an exponential function:

1, 2, 4, 8, 16, 32, 64, 128, 256...

Knowing this, let's look at each example.

A.

The rocket grows at a rate of 45 m/s, but then goes back down. This is not an exponential function. This is most likely a quadratic function.

B.

Each term is being multiplied by 4. This is correct.

C.

This is too vague. We cannot determine what this is.

D.

This is a linear function. It has an additive rate of change; not a multiplicative one. This is wrong.

E.

Each term is 50% of the previous one. This is correct.

F.

The population is multiplied by 2 each month. This is correct.

Answer:

2, 5, 6

(tweets, basketball, butterfly)

Step-by-step explanation:

Rocket:  Quadratic function

Tweets: Exponential function  (quadruples each time)

Water Park:  Quadratic function (or absolute function)

Savings: Linear function (if simple interest)

**compound interest is exponential, but as it stops earning interest after the first year, it is not continually exponential**

Basketball:  Exponential function  (halves each round)

Butterfly:  Exponential function  (doubles each month)

Answer:

x = 60

Step-by-step explanation:

The sum of exterior angles in a rectangle is equal to 360

so to find the value of x we need to use all given values and write an equation:

x + 2x + x + 2x = 360 add like terms

6x = 360 divide both sides by 6

x = 60

Answer:

Yes because I can see people very sleep-deprived and even if 7 hours is not enough, it's better than 6. For the people who sleep 9 and a half hours, they have 1 more hour to get ready. The median is 8 which most likely means, most of the students will be able to sleep the recommended amount with the extra hour.

Step-by-step explanation:

Answer:

1/144

Step-by-step explanation:

1/(2⁴ * 3²)

1/(16*9)

1/144

Answer:

The expression is half the value of (10 + 12)

Step-by-step explanation:

We see the top part is 10 + 12

The whole thing is a fraction and 2 is in the denominator

You divide your term by your denominator, and diving by 2 is the same as 1/2 if a term.

Answer: $32 is the discount

Step-by-step explanation: i got it right

Answer:

128. It will take away 32$ from 160

Step-by-step explanation:

20% of 160 is 32. 160 - 32 = 128 which will be the cost of the pair of skates.

Answer:

1/7 = 7/1

6= 1/6

1 1/8= 9/8= 8/9

3 1/3 = 10/3 = 3/10

2 1/4 = 9/4 = 4/9

2/5 = 5/2

Step-by-step explanation:

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number.

The reciprocal of a number is the number you would have to multiply it by to get the answer 1.

Answer:

28) 7/1

29) 1/6

30) 8/9

31) 3/10

32) 4/9

33) 5/2

Step-by-step explanation:

Answer:

174.19 cm3 i am not sure though.

Step-by-step explanation:

Answer:

It would be 8 years ago.

Step-by-step explanation:

-First, subtract $14.35 from $16.35, which gives you 2.

-Next, remember that $0.25 is a quarter, so how many quarters make $2?

-0.25x4 gives you a dollar, so 0.25x8 gives you 2 dollars.

Hope it helps!

Answer:

49.6 ft.

Step-by-step explanation:

The formula for circumference is 2πr, so just plug the radius into the formula.

2*π*7.9=49.637 ft

Round that to the nearest tenth to get 49.6 ft.

The correct statement are statements B and C

Given the following equation for the distance of Bicyclist A expressed as:

d = 11.5h + 5

After 1 hour for A

d(1) = 11.5 + 5
d(1) = 16.5

For bicycle B, the distance traveled after 1 hour is 12.5 miles from the graph. Hence B is not traveling 1 mile per hour faster than A.

After 2 hours for A;

d(2) = 11.5(2) + 5

d(2) = 23 + 5 = 28 miles

Hence after 2 hours, A will have traveled a total of 28 miles.

From the graph, we can see that B started from the town (origin), and from the equation, A started from 5 miles from town (y-intercept is 5)

Hence the correct statement are statements B and C

Learn more on the distance-time graph here: https://brainly.com/question/13877898

You didn't include the actual question lol

Answer:

D- 38,430

Step-by-step explanation:

To find 18% of 213.5k, we need to convert 18% back into its decimal form (0.18), then multiply it by 213.5k and boom! there is your answer.

Answer:

False

Step-by-step explanation:

It's only 2 Pi r

Answer:

False

Step-by-step explanation:

Total Surface Area of Cylinder = 2πr(r+h)

Further if you solve it you will get

→ TSA of Cylinder = 2πr² + 2πrh

So, correct answer is False .

Some Additional Points

where,

π is 22/7 or 3.14

h is height of cylinder

r is radius of cylinder

The lines L1 & L2 and the equations y = mx + n & y = px + q are illustrations of linear equations

This is a vertical line that passes through the x = 2

So, the equation of line L1 is x = 2

This is a horizontal line that passes through the y = 2

So, the equation of line L2 is y = 2

The line y = mx + n passes through points (6,3) and (0,0)

This means that n = 0 i.e. the y-intercept.

The value of m is calculated as follows:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

This gives

[tex]m = \frac{0- 3}{0 - 6}[/tex]

[tex]m = 0.5[/tex]

So, the values of m and n in y = mx + n are 0.5 and 0, respectively.

The line y = px + q passes through points (6,3) and (0,12)

This means that q = 12 i.e. the y-intercept.

The value of p is calculated as follows:

[tex]p = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

This gives

[tex]p = \frac{12- 3}{0 - 6}[/tex]

[tex]p = -1.5[/tex]

So, the values of p and q in y = px + q are -1.5 and 12, respectively.

The above region represent the upper region between y=mx +n, y=px+q and line L1

The letter in this region is letter H

The above region represent the lower region between y=mx +n, y=px+q and line L2

The letters in this region are letters A and E

Read more about linear equations at:

https://brainly.com/question/14323743

Answer:

512cm3

Step-by-step explanation:

A lateral surface area of a cube is 256 m2. Find its volume.

A cube is a three-dimensional shape that is made up of 6 congruent square faces.

Answer: If the lateral surface area of a cube is 256 m2, then its volume is 512 cubic meters.

The lateral area of a cube is the sum of areas of all side faces of the cube

Explanation:

The lateral surface area (LSA) of the cube = sum of areas of all 4 side faces.

Let the edge length of the cube be x.

LSA = x2 + x2 + x2 + x2 = 4x2

Given that, LSA of the cube is 256 m2

4x2 = 256

x2 = 256/4

x2 = 64

x = 8

Length of edge of the given cube is 8 m.

The volume of a cube is x3.

The volume of cube = x3 = 83 = 512 m3

Thus, the volume of the given cube is 512 m3.

The volume of the given cube is 512 m³.

The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object.

Given that, the lateral surface area of a cube is 256 m cube.

We know that, the formula to find lateral surface area of a cube is 4a², where a is edge of a cube

Now, 4a²=256

a²=64

a=8 m

The formula to find the volume of a cube is a³, where a is edge of a cube.

Thus, volume of a cube =8³ =512 m³

Therefore, the volume of a cube is 512 m³.

Learn more about the volume of a cube here:

https://brainly.com/question/11168779.

#SPJ2

Answer:

[tex]x = 34[/tex]

......

......

...

Answer:

  x = -3 or 7

Step-by-step explanation:

The zero product property tells you a product will be zero if and only if a factor is zero. This property is used to find the zeros of polynomial functions by factoring them, then considering the variable values that make the factors zero. The zero of a monic linear binomial factor will be the opposite of the constant in that binomial.

__

The factored form of the given polynomial is ...

  y = (x -7)(x +3)

The values of x that make these factors zero are ...

  x -7 = 0   ⇒   x = 7

  x +3 = 0   ⇒   x = -3

The zeros of the polynomial function are x = -3, and x = 7.