-10x+5y=0 -4x-6y=54 find the solution of this system of equations

Answer:

Part 1) [tex]-3x^4+3x^3+8x^2-2x-5[/tex]

Part 2) The graph in the attached  figure

Part 3) [tex]16y^8-24y^7+40y^5[/tex]

Part 4) [tex]x1=\frac{-1+\sqrt{139}i} {14}[/tex]  and [tex]x2=\frac{-1-\sqrt{139}i} {14}[/tex]

Part 5) Harold reads more than [tex]90[/tex] pages, but less than [tex]180[/tex] page

Part 6)  [tex](30,68)[/tex], [tex](40,60)[/tex]

Part 7) [tex]\$576[/tex]

Part 8) [tex]23 + 2i[/tex]

Step-by-step explanation:

The complete answers in the attached figure because is too long  

Part 1) Subtract (enter answer is standard form)

we have

[tex](-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)[/tex]

Eliminate parenthesis

[tex]-2x^4-2x^3+8x^2+2-x^4+5x^3-2x-7[/tex]

Combine like terms

[tex](-2x^4-x^4)+(-2x^3+5x^3)+8x^2-2x+(2-7)[/tex]

[tex]-3x^4+3x^3+8x^2-2x-5[/tex] ------> standard form

Part 2) Which graph represents the inequality?

we have

[tex]2x-3y\leq 6[/tex]

Rewrite the inequality ------> [tex]3y\geq2x-6[/tex]

the solution is the shaded area above the solid line

the equation of the line is equal to [tex]3y=2x-6[/tex]

the slope of the line is positive

the y-intercept of the line is the point [tex](0,-2)[/tex] ---> value of y when the value of x is equal to zero

the x-intercept of the line is the point [tex](3,0)[/tex] ---> value of x when the value of y is equal to zero

The solution in the attached figure

Part 3) Multiply

we have

[tex]8y^4(2y^4-3y^3+5y)\\=( 8y^4*2y^4)-(8y^4*3y^3)+(8y^4*5y)\\=16y^8-24y^7+40y^5[/tex]

Part 4) Solve for x

we have

[tex]0=7x^2+x+5[/tex]

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]7x^2+x+5=0[/tex]

so

[tex]a=7\\b=1\\c=5[/tex]

substitute in the formula

[tex]x=\frac{-1(+/-)\sqrt{1^{2}-4(7)(5)}} {2(7)}[/tex]  

[tex]x=\frac{-1(+/-)\sqrt{-139}} {14}[/tex]

remember that

[tex]i=\sqrt{-1}[/tex]

so

[tex]x=\frac{-1(+/-)\sqrt{139}i} {14}[/tex]

[tex]x1=\frac{-1+\sqrt{139}i} {14}[/tex]

[tex]x2=\frac{-1-\sqrt{139}i} {14}[/tex]

Part 5) Harold and Helen both spend [tex]3[/tex] hours reading a novel. Helen reads [tex]30[/tex] more pages than Harold. Helen reads at least [tex]40[/tex] pages in [tex]1[/tex] hour, but no more than [tex]70[/tex]pages in  [tex]1[/tex] hour.  

Which statement correctly describes the range of pages Harold reads?

Let

x------> the number of pages that Harold read

y------> the number of pages that Helen read

we know that

[tex]y=30+x[/tex] -----> equation A

[tex]y\geq 40\ pages[/tex] ------> in one hour

so

in three hours -------> [tex]y\geq 120\ pages[/tex] ------> inequality B

[tex]y\leq 70\ pages[/tex] ------> in one hour

so

in three hours ------->[tex]y\leq 210\ pages[/tex] ------> inequality C

Substitute equation A in the inequality B

[tex]x+30\geq 120\ pages[/tex] ------>  [tex]x\geq 90\ pages[/tex]

Substitute equation A in the inequality C

[tex]x+30\leq 210\ pages[/tex] ------> [tex]x\leq 180\ pages[/tex]

therefore  

Harold reads more than [tex]90[/tex] pages, but less than [tex]180[/tex] page

Part 6) Let

x------>  the number of Standard Specials sold last Monday  

y------>  the number of Deluxe specials sold last Monday

we know that

[tex]2x+4y\geq 200[/tex] -----> inequality A

[tex]0.50x+1.25y\leq100[/tex] -----> inequality B

[tex]x\geq30[/tex] -----> inequality C

Remember that

If a ordered pair representing a combination  of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

then

the ordered pair must satisfy all restrictions

Verify

A) [tex](30,68)[/tex]  

Substitute the value of x and y in each inequality

Inequality A

[tex]2(30)+4(68)\geq 200[/tex]

[tex]332\geq 200[/tex] ------> is true

Inequality B

[tex]0.50(30)+1.25(68)\leq100[/tex]

[tex]100\leq100[/tex] -----> is true

Inequality C

[tex]30\geq30[/tex] -----> is true

The ordered pair [tex](30,68)[/tex]  represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

B) [tex](80,40.5)[/tex]  

The value of [tex]y=40.5[/tex] not make sense in the context of the situation, because is not a whole number

C) [tex](60,70)[/tex]  

Substitute the value of x and y in each inequality

Inequality A

[tex]2(60)+4(70)\geq 200[/tex]

[tex]400  \geq 200[/tex] ------> is true

Inequality B

[tex]0.50(60)+1.25(70)\leq100[/tex]

[tex]117.5\leq100[/tex] -----> is not true

therefore

the ordered pair [tex](60,70)[/tex] is not a solution

D) [tex](40,60)[/tex]  

Substitute the value of x and y in each inequality

Inequality A

[tex]2(40)+4(60)\geq 200[/tex]

[tex]320\geq 200[/tex] ------> is true

Inequality B

[tex]0.50(40)+1.25(60)\leq100[/tex]

[tex]95\leq100[/tex] -----> is true

Inequality C

[tex]40\geq30[/tex] -----> is true

The ordered pair[tex](40,60)[/tex]   represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

E) [tex](50.5,40)[/tex]  

The value of [tex]x=50.5[/tex] not make sense in the context of the situation, because is not a whole number

To find the probability, calculate the probabilities of selecting a jelly treat and a mint stick. Then multiply these probabilities together to find the overall probability.

To find the probability that Mick's first two pieces will be a jelly treat and a mint stick, we need to calculate the probability of selecting a jelly treat and a mint stick from the bag.

First, we need to find the total number of pieces in the bag: 2 mint sticks + 11 jelly treats + 7 fruit tart chews = 20 pieces.

The probability of selecting a jelly treat as the first piece is: 11 jelly treats / 20 total pieces = 0.55 or 55%.

After Mick has eaten one piece, there are now 19 pieces left in the bag.

The probability of selecting a mint stick as the second piece is: 2 mint sticks / 19 remaining pieces = 0.105 or 10.5%.

Therefore, the probability that Mick's first two pieces will be a jelly treat and a mint stick is 55% * 10.5% = 0.055 or 5.5%.

Harry is required to pay an additional $100 as interest for one year on the $2000 sofa, bringing the total payment to $2100 at the end of the year.

Harry buys a sofa set at a cost of $2000 with an installment plan that includes an interest rate of 5% per annum. To calculate the total amount Harry needs to pay at the end of one year, you need to calculate the interest and then add it to the principal amount.

The interest for one year is calculated as follows:

Interest = Principal imes Rate imes Time.

Interest = $2000 imes 5% imes 1 year.

Interest = $2000 imes 0.05  imes 1.

Interest = $100.

Now, we add the interest to the principal amount to find the total amount Harry has to pay by the end of the year:

Total Amount = Principal + Interest.

Total Amount = $2000 + $100.

Total Amount = $2100.

Therefore, Harry will have to pay a total of $2100 at the end of one year.

Answer:

54

Step-by-step explanation:

Let

x--------> the number

we know that

1) the phrase, "the sum of 12 and a number"

represent the expression --------> [tex](12+x)[/tex]

and

2) the complete phrase, "one third the sum of 12 and a number"

represent the expression --------> [tex]\frac{1}{3}(12+x)[/tex]

therefore

the answer is

[tex]\frac{1}{3}(12+x)[/tex]

Her gross pay was the amount of $450 for last week.

The commission is determined by the product of the commission rate and the total sales.

Commission = Commission rate x Total sales

As per the question, we have data :

Commission rate = 12 %

Total sales = $3,000

The base salary = $90

We know that,

Commission = Commission rate x Total sales

= 12% x $3,000

= 0.12 x $3,000

= $360

The total pay is then the base salary increased by the commission:

Total pay = base salary + Commission

Total pay = $90+ $360

Total pay = $450

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The functions f(x)=x² and g(s)=s² are essentially the same function with different variable notations. The f(x)=2x graph is linear, and the red graph g(x) with the same shape would also be linear, involving a transformation that retains the proportional relationship between x and y.

Based on the provided information, the equation of f(x) is given as f(x) = x². If the blue graph represents this function, and we are looking for the red graph equation g(x), which has the same shape, we need to understand the transformation involved.

Regarding the equations provided in the examples, functions f and g are both defined as taking an input, squaring it, and outputting the result. Although they use different variable names (x for f and s for g), they are effectively the same function. When you have a transformation such as f(x-2), the graph of the function shifts to the right without changing its shape. Similarly, if the red graph were g(x) = 2x, the transformation applied would be to double the output, stretching the graph vertically relative to f(x).

Since the blue graph equation is given as f(x) = 2x and the red graph has the same shape, it means the red graph, g(x), also has a linear relation with a proportional transformation applied. Common linear transformations include multiplying by a scalar to scale the graph or adding/subtracting a number to shift the graph along the x-axis or y-axis.

Answer:

A

Step-by-step explanation:

78 ft

This is basically a GCF problem. To find the GCF, we list the factors of each number.
24 = 1×24, 2×12, 4×6, 8×3 ...

16 = 1×16, 2×8, 4×4, ... 

The greatest common factor is 8 because it is the greatest factor we can find.
So 8 arrangements

Answer:

1 g/cm 3

Step-by-step explanation:

The Mississippi River is closer to sea level.

It is the measure of distance between the two points called length.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The elevation of Death Valley is 282 feet.

The Mississippi River in Illinois has an elevation of 279 feet.

If the length of the elevation of Death Valley 282 is greater than the length of the Mississippi River 279.

The Mississippi River is closer to sea level.

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When functions are defined by more than one equation, they are called Piecewise defined functions.

What is Piecewise- defined function?

A Piecewise defined function is one which is defined not by a single equation, but by two or more.

Hence,

When functions are defined by more than one equation, they are called Piecewise defined functions.

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x +5x =18

6x =180

x = 180/6 = 30

1 number is 30

2nd number is 5*30 = 150

Final answer:

To evaluate the function for x = m/4, substitute m/4 for x in the function[tex]f(x) = 8x^2 - 4x[/tex]and simplify to get the result [tex]m^2/2 - m.[/tex]

Explanation:

To evaluate the function [tex]f(x) = 8x^2 - 4x[/tex] for x = m/4, we substitute m/4 for x in the function and simplify.

Substitute x with m/4:

[tex]f(m/4) = 8(m/4)^2 - 4(m/4)[/tex]

Simplify the equation:

[tex]f(m/4) = 8(m^2/16) - m[/tex]

[tex]f(m/4) = (8/16)m^2 - m[/tex]

[tex]f(m/4) = m^2/2 - m[/tex]

Therefore, the correct answer is D.  [tex]m^2/2 - m.[/tex]

Answer:

c) x - 4

Step-by-step explanation:

To do a factorization of this kind of trinomial there is a technique very easy to do it.

First, you need to see the numbers that are along with the x and the independent number.

In this case -3 and -4 (I will call them b and c)

Next, you need to think in two numbers that can acomplish the following:

x * y = c

x + y = b

So, first, think, which are two numbers that you can multiply between them to give as a result -4?.

In this case it would be -4 and 1 (-4*1 = -4)

These numbers if you do a sum you'll get -3:

-4 + 1 = -3

So the factorization becomes this:

(x - 4) (x - 1)

So, one of the factors is x - 4. Option c