Complete the series. 9 = 4, 21 = 9, 22 = 9, 24 = 10, 8 = 5, 7 = 5, 99 = 10, 100 = 7, 16 = ?, 17 =?

A) Proportional

y is 1/2 times x

B) Not proportional

y is 3/2 times x

C) Proportional

y is 1/2 times x

Graph a and Graph b are not proportional and Graph c is proportional and for graph c y is 1/2 times of x

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.

(a) Not proportional

(0,0),(2,1)(4,4)

The relationship between these is not same.

The graph a is not proportional.

(b) Not proportional

(2,0)(4,3)(6,6)

The relationship between these is not same.

The graph b is not proportional.

(c)Proportional

(0,0)(2,1)(4,2)

y is 1/2 times of x

The graph c is proportional.

Hence Graph a and Graph b are not proportional and Graph c is proportional and for graph c y is 1/2 times of x

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Answer:

Step-by-step explanation:

Let the current display rate be f (in frames per second).  If the new computer is 40% faster, then the new display rate will be 1.40f (frames per second).

" The exact number of additional frames per second that can be displayed on the faster computer cannot be determined without specific information about the software's performance on the current computer. However, if the software's performance scales linearly with the computer's speed, the faster computer could potentially display 40% more frames per second than the slower one.

To solve this problem, we need to understand the relationship between the speed of a computer and the number of frames per second (FPS) it can display. The term ""faster"" in the context of computers generally refers to the processing speed, which can be influenced by factors such as the central processing unit (CPU) clock speed, efficiency of the software code, and the performance of other hardware components.

If we assume that the software's performance is directly proportional to the computer's speed (which is a simplification and may not hold true in all cases due to various bottlenecks and limitations in real-world scenarios), then a computer that is 40% faster should be able to perform 40% more operations in the same amount of time.

Let's denote the number of frames per second that the current computer can display as \( F \). If the new computer is 40% faster, it should be able to display \( F \) frames in[tex]\( 1 - 0.40 = 0.60 \)[/tex] of the time it takes the current computer. To find out how many frames the new computer can display in the original time frame (1 second), we would divide 1 second by 0.60 seconds and then multiply by \( F \):

[tex]\[ \text{New FPS} = \frac{1}{0.60} \times F = \frac{5}{3} \times F \][/tex]

To find the additional frames per second, we subtract the original FPS from the new FPS:

[tex]\[ \text{Additional FPS} = \text{New FPS} - F = \left( \frac{5}{3} \times F \right) - F \][/tex]

[tex]\[ \text{Additional FPS} = \frac{5F}{3} - \frac{3F}{3} \][/tex]

[tex]\[ \text{Additional FPS} = \frac{5F - 3F}{3} \][/tex]

[tex]\[ \text{Additional FPS} = \frac{2F}{3} \][/tex]

This represents a 40% increase in the number of frames per second. However, without knowing the exact value of \( F \) (the FPS on the current computer), we cannot provide a specific number for the additional frames per second.

 In summary, if the software's performance scales perfectly with the computer's speed, a 40% faster computer should be able to display [tex]\( \frac{2F}{3} \)[/tex]additional frames per second. However, in practice, the actual increase in FPS may be less due to various factors such as software limitations, hardware bottlenecks, and the complexity of the tasks being performed."

Answer:

Step-by-step explanation:

c. The point (10,100) reprensents that after 10 business hours, it costs $100 for electricity

d. c=10h

sqrt(4x) / 2x + 1 = 3

Set domain :

2x + 1 cannot equal 3

2x cannot equal 2 | :2

x cannot equal 1

sqrt(4x) = 3(2x + 1)

sqrt(4x) = 6x + 3

4x = 36x^2 + 9

36x^2 - 4x + 9 / f(x) = ax^2 + bx + c

16-4*36*9

16-1296 = - 1280

There's no solutions in Real Number set.

See the image for solution

2)

P(4,-4) -->(-4, 7)

4 - 8 = -4           -------->left 8

-4 + 11 = 7         -------->up 11

Answer: left 8;  up 11

3)

C(3,-1) , left 4 up 1

3 - 4 = -1    -------->left 4

-1 + 1 = 0   -------->up 1

a)

(x , y) -->(x - 4 , y +1)

C(3, -1) -->C'(-1 , 0)

b)

(x , y) --> (x - 4, y + 1); (-1 , 0)

Check the picture below.

namely, is the volume of the rectangular prism Paraffin, equals or less than the volume of the cone made from it?

[tex]\bf  \textit{volume of a rectangular prism}\\\\ V=Lwh~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=8\\ w=6\\ h=4 \end{cases}\implies V=8\cdot 6\cdot 4\implies \boxed{V=192} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=25 \end{cases}\implies V=\cfrac{\pi (5)^2(25)}{3}\implies \boxed{V\approx 654.5}[/tex]

well, clearly the cone has enough room to take the 192 cm³.

Answer: A,B,C

Step-by-step explanation: I did it on Imagine Math :)

Answer:

I  -3/20

Step-by-step explanation:

-3       2

---- * -----

8       5

Multiply the numerators

-3*2 = -6

Multiply the denominators

8*5= 40

The fraction is

-6/40

Both the top and the bottom can be divided by 2

-6/2 = -3

40/2 =20

The fraction becomes

-3/20

[tex] {x}^{2} - 2x - 24 \\ = {x}^{2} - 6x + 4x - 24 \\ = x(x - 6) + 4(x - 6) \\ = (x - 6)(x + 4)[/tex]

Answer:

20%

Step-by-step explanation:

What we are looking for is 125*x = 25, where x is the percentile (represented as a decimal)

By dividing both sides by 125, we get that x = 0.2, which means that 25 is 20% of 125, as in percentile, 1 = 100%.

To find out '25 is what percent of 125', you divide 25 by 125, and then multiply by 100. The result is 20. Thus, 25 is 20% of 125.

To find out 25 is what percent of 125, you need to understand the concept of percentage. The term percentage means 'per 100', or 'out of 100'. In your case, you're trying to find out how much 25 is out of 125 in terms of per 100. The formula to find a percentage is:

(Part / Whole) * 100

In your case, the part is 25 and the whole is 125. So, you substitute these values into the formula:

(25 / 125) * 100

That calculation results in 20. Therefore, 25 is 20 percent of 125.

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ANSWER

[tex]h = - 4,k = - 6[/tex]

Minimum value: y=-6

Occurs at: x=-4

EXPLANATION

Given

[tex]f(x) = {x}^{2} + 8x + 10[/tex]

We need to write the equivalent of this function in vertex form:

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

where (h,k) is the vertex.

We must complete the square to get the function to this form.

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 8x +( \frac{8}{2}) ^{2} - ( \frac{8}{2}) ^{2} + 10[/tex]

This gives us;

[tex]f(x) = {x}^{2} + 8x +16- 16 + 10[/tex]

The first three terms form a perfect square quadratic trinomial.

[tex]f(x) =( x + 4) ^{2} - 6[/tex]

or

[tex]f(x) =( x - - 4) ^{2} - 6[/tex]

Therefore we compare to

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

h=-4 and k=-6

The minimum value of the function is

[tex]y = - 6[/tex]

and this occurs at;

[tex]x = - 4[/tex]

Answer:

g(x) is the image of f(x) after stretched horizontally

by scale factor = 5

Step-by-step explanation:

∵ f(x) = x² ⇒ quadratic function

∵ g(x) = (1/5 x)² ⇒ The image of f(x) after one transformation

* Stretches or compresses horizontally:

  It means stretches away from the y-axis

  or compresses toward the y-axis

* If f(x) = (ax)²  :

∵ |a| > 1 is a compression by factor of 1/a

∵ 0 < |a| < 1 is a stretch by factor of 1/a

∵ x-coordinate of f(x) multiplied by 1/5

∵ 0 < 1/5 < 1

∴ The transformation is ⇒ stretched horizontally

∴ g(x) is the image of f(x) after stretched horizontally

  by scale factor = 1 ÷ 1/5 = 5

Answer: the first one, second, third, and fourth.

I advise you to get a scientific calculator to do these.

Answer:

d. 64

Step-by-step explanation:

x^1/2 = 8

Square each side

(x^1/2 )^2=( 8)^2

x = 64

Answer:

(d) 64

Step-by-step explanation:

Please write either x^(1/2) or x^0.5 or √x, to reduce the chances of misinterpreting your input.

√x = 8 becomes x = 64 when both sides are squared.

This corresponds to answer (d).

The equation would look like this: -3(x + 6) = 4. Then solve to find x.

-3x -18 = 4 → -3x = 22 → x = -7.3

You can substitute this number into the equation to check.

-3(-7.3 + 6) = 4 → 3.9 = 4. As you can see the number isn't exact becuase -7.3 is a repeating decimal.

Answer:

-7 1/3

Step-by-step explanation:

Answer:

Range:

{−7,−2,1,2}

Step-by-step explanation:

Answer:

Expand the polynomial using the FOIL method.

a ^2 + a − 6

Hope This Helps!     Have A Nice Day!!

Answer: The answer will be .... a^2 + a - 6

Use the foil method.

F. irst

O. utside

I. nside

L. ast

Answer:

[tex]\boxed{\bold{\left(3x-2\right)^2}}[/tex]

Step By Step Explanation:

[tex]\bold{\left(3x\right)^2-2\cdot \:3x\cdot \:2+2^2}[/tex]

[tex]\bold{\left(3x\right)^2-2\cdot \:3x\cdot \:2+2^2}[/tex]

[tex]\bold{\left(3x-2\right)^2}[/tex]

ANSWER

[tex]9 {x}^{2} - 12x + 4 = (3x - 2) ^{2} [/tex]

EXPLANATION

The given expression is

[tex]9 {x}^{2} - 12x + 4[/tex]

This is in the form

[tex]a {x}^{2} + bx + c[/tex]

[tex]a=9,b=-12 ,c=4[/tex]

[tex]ac=9 \times 4 = 36[/tex]

Split with -6x-6x

[tex]9 {x}^{2} - 6x - 6x + 4[/tex]

[tex] = 3x( 3x - 2) - 2(3x - 2)[/tex]

Factor further to obtain,

[tex] = (3x - 2)(3x - 2)[/tex]

[tex] = (3x - 2) ^{2} [/tex]

Answer:

(x+1) meters

Step-by-step explanation:

Area is length times width so x^2-x-2 = L * (x-2)

factor and divide x-2 to get x+1

The amount to which $500 will grow to is $881.17.

From the question, we have the following parameters that can be used in our computation:

Principal = 500

Rate = 12%

Time = 5 years

The future value is calclated as

FV = P * (1 + r)ⁿ

substitute the known values in the above equation, so, we have the following representation

FV = $500 * (1 + 0.12)⁵

Evaluate

FV = $881.17

Hence, the amount is $881.17

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Answer:

x and see others below

Step-by-step explanation:

To find the equivalent expression, multiply the terms using exponent rules.

Exponent rules state to add the exponent of same bases being multiplied.

[tex]x^{\frac{1}{2}} *x^{\frac{1}{2}} =x^{\frac{1+1}{2}} =x^{\frac{2}{2}} = x^1 = x[/tex]

Each of the parts of the expression are equivalent. The simplified equivalent expression is x.

Answer:

3/24 or 1/8

Step-by-step explanation:

1. convert 1/4 and 2/3 into fractions with common denominators of 24 (since there are 24 pieces.

2. find the multiples of 4 and 3

    4, 8, 12, 16, 20, 24  = 5

    3, 6, 9, 12, 15, 18, 21, 24 = 8

3. convert the fractions

    1/4 * 5/5 = 5/24

    2/3*8/8 = 16/24

4. add the fractions.

    5/24 + 16/24 = 21/24

5. subtract 21/24 from 24/24 = 3/24

6. reduce by dividing both terms by 3 = 1/8

Will and Tommie ate a total of 22 pieces from the 24-piece candy bar. Therefore, 2 pieces remain.

Will and Tommie bought a giant candy bar composed of 24 pieces. Will ate 1/4 of the bar, which equals 6 pieces (since 1/4 of 24 is 6). Tommie ate 2/3 of the bar, which is 16 pieces (since 2/3 of 24 is 16). To find out how many pieces are left, we subtract the amount eaten by both from the total number of pieces:

Total candy bar pieces = 24

Pieces eaten by Will = 1/4 of 24 = 6

Pieces eaten by Tommie = 2/3 of 24 = 16

Pieces remaining = Total - (Pieces eaten by Will + Pieces eaten by Tommie)

Pieces remaining = 24 - (6 + 16) = 2 pieces.

Therefore, there are 2 pieces of the giant candy bar left.

The answer 5 (1/4) because if you add 1 and a quarter to it then that would make it 6 and a half

Answer:

B, C,and E

Step-by-step explanation:

edge 2020

Answer:

y = -4

Step-by-step explanation:

Assuming the problem is [tex]8^{2y+4}=16^{y+1}[/tex], it would be nice if we could convert both sides of this equation to the same base; that way, we could compare the exponents directly in an equation of their own. Fortunately, 8 and 16 are both powers of 2 -- [tex]2^3[/tex] and [tex]2^4[/tex], we can rewrite the original equation by substituting those in:

[tex](2^3)^{2y+4}=(2^4)^{y+1}[/tex]

When you have an exponent raised to another exponent, you multiply those exponents together, so we can simplify our equation by distributing a 3 in the left exponent and a 4 in the right:

[tex]2^{3\cdot(2y+4)}=2^{4\cdot(y+1)}\\2^{3\cdot2y+3\cdot4}=2^{4\cdot y+4\cdot1}\\2^{6y+12}=2^{4y+4}[/tex]

With both of our bases the same, we can now simply compare their exponents directly to solve for y:

[tex]6y+12=4y+4\\2y=-8\\y=-4[/tex]

Division and subtraction.

Associative property does not work for Subtraction and Division.

The associative property states that after grouping the expressions in different ways the outcome will not change.

(a + b) + c = a +(b + c)

So associative property is applicable for addition.

( a X b) X c = a X ( b X c) = abc

So associative property is applicable for multiplication

(a ÷ b) ÷ c ≠ a ÷ (b ÷ c)

So, the associative property is not applicable for  Division

(a-b) - c ≠ a - (b -c)

So,  the associative property is not applicable for Subtraction

So, we can say associative property does not work for Subtraction and division.

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Let x represent the unknown number.

7x - x = -48

Group like terms together.

6x = -48

Divide both sides by 6.

x = -8

Hence, the number is negative eight.

Answer:x=-8

Step-by-step explanation:

What I did was set up my equation and my equation was 7x-x=-48. My second step was to combine like terms and then I had 6x=-48 lastly I divided both sides by 6x then my final answer was x=-8.

Let x= the distance that Jana lives from school. Then, x < 2/3

Answer:

Use the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods.

First, converting R percent to r a decimal

r = R/100 = 5.5%/100 = 0.055 per year.

Solving our equation:

A = 30000(1 + (0.055 × 7)) = 41550  

A = $41,550.00

The total amount accrued, principal plus interest, from simple interest on a principal of $30,000.00 at a rate of 5.5% per year for 7 years is $41,550.00.

Step-by-step explanation:

Answer:

11550

Step-by-step explanation:

Formula for calculating simple interest is : Simple Interest=P x R x T/100

Step 1: Identify P,R,T

P: Principal amount-basic amount of the loan (30,000)

R: The interest rate of the loan (5.5%)

T: Time of payment of loan-in years (7 years)

Step 2: Substitute the values

Simple Interest= P x R x T/100

Simple Interest= 30,000 x 5.5 x7

                                     100

Simple Interest= 1155000

                                100

Simple Interest= 11550

Let's answer the first part of the question: "How much does he owe?"

Step 1: We have calculated simple interest which is 11550.

Step 2: The principal amount has to be paid with the simple interest.

Step 3: Formula- Total money owed= Principal amount + Simple Interest

Total money owed= 30,000 + 11550=41550

Now let's answer the second part of the question: "What is the monthly payment if he chooses the 7-year loan payment plan?"

Step 1: Calculate how many months are there in 7 years. Each year has 12 months therefore 7 years have (7 x 12) 84 months.

Step 2: Divide the total amount that has to be paid by the number of months it has to be paid in.

Monthly payment = Total money owed/ total number of months

Monthly payment = 41550/ 84

Monthly payment = 494.64

Answer:

[tex]y=-222[/tex]

Step-by-step explanation:

When "y varies directly with x" this means that:

[tex]y=k\times x[/tex]

where k is a number we need to find out (called the constant of proportionality if you care about that).

We can figure out what k is because they tell us when y= -252, x=84. Substituting those values into our equation we get:

[tex]-252 = k \times 84[/tex]

and therefore:

[tex]k=-3[/tex].

So our equation or formula between y and x is:

[tex]y= -3x[/tex].

So when x = 74, then:

[tex]y=-3 \times 74 = -222[/tex]