on a piece of paper, graph the system of equations. Find the solution to the system. y=2x-1 y=x+5

Answer:

use a calculator or try math app

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: 8i[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 2 {x}^{2} = - 128[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - \frac{ 128}{2} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - 64[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 64} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{( - 1) \sdot(64)} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ 64} \sdot \sqrt{ - 1} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = 8 \sdot i[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = 8i[/tex]

[ i = iota, and i² = -1 ; (complex number) ]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]x=8i[/tex]

Step-by-step explanation:

Given equation:

[tex]2x^2=-128[/tex]

Divide both sides of the equation by 2:

[tex]\implies \dfrac{2x^2}{2}=\dfrac{-128}{2}[/tex]

[tex]\implies x^2=-64[/tex]

Square root both sides:

[tex]\implies \sqrt{x^2}=\sqrt{-64}[/tex]

[tex]\implies x^2=\sqrt{-64}[/tex]

Rewrite -64 as 8² · -1:

[tex]\implies x=\sqrt{8^2 \cdot-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies x=\sqrt{8^2}\sqrt{-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies x=8\sqrt{-1}[/tex]

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

[tex]\implies x=8i[/tex]

Imaginary numbers

Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter i.

An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].

C that's because the angles are vertically opposite

The number of quarters, Richard have is 3 out of 198 coins he have.

For the given question,

The total number of coins Richard have is 18.

The fraction of dimes is 1/3.

1/3 of 18 = (1/3)×18 = 6

The number of dimes is 6.

The fraction of nickles is 1/2.

1/2 of 18 = (1/2)×18 = 9

Let the number of quarters be 'x'.

Total coin = dimes + nickles + quarters.

18 = 6 + 9 + x

x = 18 - 15

x = 3

Thus, the number of quarters, Richard have is 3.

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If Amy, Ravi, and Bob have a total of $127 in their wallets. Bob has 4 times what Ravi has. Ravi has $7 less than Amy. The amount they have  have in their wallets is : Army has $22.33, Ravi $89.33, Henry $15.33.

Let Army represent x dollars

Let Ravi represent   4x

Let Bob represent  x - 7

Hence,

x + x - 7 + 4x = 127

Simplify by combining like terms

6x - 7 = 127

Add 7 to both sides of the equation leaving 6x

6x = 127+7

6x = 134

x =134/6

x = 22.33

x = Army has $22.33

Ravi

4x  where x = 22.33

4(22.33) = 89.33

Bob

x - 7 where x = 22.33

22.33 -7 = 15.33

Prove :

Ravi + Bob + Henry = 127

= 22.33 +89.33 + 15.33 = 126.99 ≅127 (Approximately)

Therefore the have $22.23, $89.33 and 15.33 respectively.

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7.031 is greater than 7.03.

The given value is having a 2-digit decimal place.

The options which are provided are:

1)7.031

2)7.030

3)7.003

4)7.0

Comparing the first decimal placeholder of each option with the question, all options have the same digit which is zero.

Comparing the second decimal placeholder of each option with the question, only option 1)7.031 and option 2)7.030 is having .03 the rest of the options, option 3)7.0003 and 4)7.0 have .00 has their second digit hence both option 7.0003 and 7.0 are smaller than 7.03.

Out of the remaining options, when options 1)7.03 and 2)7.031 are compared it can be seen that 7.031 is greater because the third decimal placeholder of 7.031 is 1 and 7.03 is 0 hence 7.031 is greater than 7.03.

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Given the word exprssion:

Seventy less than 9 times a number is 375

Where h represents the number.

We have:

Seventy less than 9 times a number: 9h - 70

Seventy less than 9 times a number is 375: 9h - 70 = 375

Therefore, the equation that is a correct translation of Seventy less than 9 times a number is 375 is: 9h - 70 = 375

ANSWER:

9h - 70 = 375

Answer:

3(h + 6)

Step-by-step explanation:

Since we are starting with

h•3 + 6•3, try to see that there are two terms here h•3 and 6•3. In both of these terms is the factor 3. We can factor out the 3. This leaves behind (h + 6).

h•3 + 6•3

= 3(h + 6)

Its like "un-distributive" property. (this is not a technical term)

The solution to the expression | a − 5 | − 1 is 2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

| a − 5 | − 1

Also, we have the values to be

a = 2 , b = − 3 , c = − 4 , h = 6 , y = 4 , and z = − 1

Substitute these values in the given equation

So, we have the following equation

| a − 5 | − 1 = | 2 − 5 | − 1

Evaluate the difference

So, we have the following equation

| a − 5 | − 1 = | −3 | − 1

This gives

| a − 5 | − 1 = 3 − 1

Evaluate the difference

| a − 5 | − 1 = 2

Hence, the value is 2

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f(x) is maximum at x=3 and the maximum value of f(x) = 5.

The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to collectively as the function's extrema. The plural forms of the maximum and minimum functions are maxima and minima, respectively.

The given quadratic function is [tex]f(x) = -2 (x-3)^{2} +5[/tex]

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

Here, a= -2, h =3 and k = 5.

Since a is negative, so parabola is open downward.

Therefore, the quadratic function has a maximum value.

Here, the vertex is (h,k) =(3,5)

Therefore, f(x) is maximum at x=3 and the maximum value of f(x) = 5.

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Answer:

m∠QPT = 32°

Step-by-step explanation:

∠QPT and ∠SPR are vertical angles, meaning that the measure of their angles are congruent (the same).

Vertical angles are formed when two lines intersect, creating opposite angles. Those opposites are congruent (equal).

Step 1: Set the measure of the angles to equal each other.

[tex]\implies m \angle QPT = m \angle SPR[/tex]

[tex]\implies (2x+12) = (4x - 8)[/tex]

Step 2: Subtract 4x from both sides.

[tex]\implies 2x-4x+12 = 4x - 4x - 8[/tex]

[tex]\implies -2x+12 = - 8[/tex]

Step 3: Subtract 12 from both sides.

[tex]\implies -2x+12-12 = - 8-12[/tex]

[tex]\implies -2x = -20[/tex]

Step 4: Divide both sides by -2.

[tex]\implies \dfrac{-2x}{-2} = \dfrac{-20}{-2}[/tex]

[tex]\implies x = 10[/tex]

Step 5: Find the measure of ∠QPT by substituting 10 for x.

[tex]\implies [2(10)+12]^{\circ}[/tex]

[tex]\implies 32^{\circ}[/tex]

Therefore, the measure of ∠QPT is 32°.

commutative property is an example of the blank property.

What in mathematics is a commutative property?

What is a commutative property example?

2(x+3) = 2x+6

Commutative Property used in this function.

4x-3

put x=2

4(2)-3 =  Commutative Property used in this function.

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Answer:

y<4

Steps:

18 + 6y < 42

6y < 42 - 18

y < 24/6

y < 4

Answer:

y<4

Step-by-step explanation:

18+6y<42

Subtract 18 from both sides.

6y<42−18

Subtract 18 from 42 to get 24.

6y<24

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

[tex]y < \frac{24}{6} [/tex]

Divide 24 by 6 to get 4.

y<4

According to the given problem,

(i) It is given that,

The cost price of 1000 packets of peanuts = Rs. 50

We need to find the cost price of 1 packet of peanut = [tex]\frac{50}{1000}[/tex] = Rs. 0.05

(ii) Selling price at which Sipho continues to sell 1 packet = Rs. 1

Then Selling price of 1000 packets = 1000 x 1 = Rs. 1000

Then Profit made by sipho = Selling Price - Cost Price

= 1000 - 50

= Rs.950

Profit percentage gained by Sipho = [tex]\frac{Profit}{Cost Price}[/tex] x 1000

= [tex]\frac{950}{50}[/tex] x 1000

= 1900 %

(iii) The profit earned by sipho remains same, we nee to find the cost price at which Sipho should sell 100gm of her peanuts is Rs. 1

(iv) I would advice Sipho to sell peanuts at a selling price more than the cost price in order to gain profit

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Answer:

y=-1/3x+5

Step-by-step explanation:

Use rise/run

Answer:

Step-by-step explanation:

Jan 15, 2020 — this line also pass through 0,8 and 2,2. slope is -3. the equation is y-2= -3(x-2). heart outlined. Thanks 10.

2 answers

·

10 votes:

Answer:this line also pass through 0,8 and 2,2. slope is -3. the equation is y-2= -3(x-2)

Missing: OY ‎| Must include: OY

Answer:

i cant really see the words

Step-by-step explanation:

Answer:[tex]75m^{2}[/tex]

Step-by-step explanation: Just have to square root 5625m2 to get each side length

Step 1. The expression we have for the graph is:

To find the inequality that represents the graph, we need to solve for y first.

Step 2. Solve for y in the equation:

We can also represent this as follows:

Move 5x to the right side as a -5x:

Move the two that is multiplying on the left side, to divide on the right side:

Simplify:

This is the equation of the line.

Step 3. Find the inequality.

Since the shaded part is below the line, and it has a dotted line, the inequality that represents this is:

Which are the values below the dotted line.

Answer:

The painting is a square, which means all its sides are equal.

If x is the length of one side, then, all the remaining 3 sides also have the same length: x.

The area of a square is the square if its side, then, for a square with sides x:

We know that the area of the painting will be 400 square inches, then:

a. The equation that can be set up to find the length of a side is:

b. We can solve the equation by finding a number that multiplied by itself gives 400. For this case, we have two solutions. 20 and -20, since:

And:

-20 is also a solution because as a negative number, when multiplied by itself, gives a positive one. (A product between negative numbers gives always a positive number).

c. We have two solutions, however, only one of them makes sense: the 20. A negative length makes no sense, so we can discard the second solution (-20).

d. The length of the wood trim needed to go around the painting is then 20 inches. (we should not forget the units.)

The lengths of the axes in the elipse are given as follows:

The equation of an elipse of center (x*, y*) is given according to the following rule:

(x - x*)²/a² + (y - y*)²/b² = 1.

The lengths of the axes are given as follows:

In this problem, the equation of the elipse is given as follows:

(x - 3)²/212 + (y + 4)²/224 = 1.

Hence the measures of a and b are calculated as follows:

Hence the lengths of the axes have numeric values given by:

The difference in the measures is because I suppose there was a typo in the equation of the ellipse, but the procedure is as presented in this problem.

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Answer:

23

Step-by-step explanation:

3-(-20)

The constant of proportionality (K ) we will write

Perimeter = 3 ( side)  where K = 3

Perimeter of any polygon is defined as the sum of all sides of  polygon.

Given polygon is a triangle. A triangle is any polygon which has three sides.

And as the sides of a polygon increases the perimeter also increases.

One can say that perimeter and side of a polygon has a direct relationship.

That is when we write it mathematically we write it like:

Perimeter ( P ) ∝ Sides of polygon

However given is an equilateral triangle

this means that all sides of the triangle are equal

so let us consider the side of the triangle as "s"

Thus we get that perimeter will be 3 times s

which when mathematically written will be:

Perimeter ∝ ( side)

to remove the constant of proportionality (K ) we will write

Perimeter = 3 ( side)  where K = 3

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The value of x is 4

The value of m ∠VUR = 126°

From the image shown, we have that;

Note that all the sides of a equilateral triangle are equal.

Then, we have;

Now, equate the side lengths of the inscribed triangle, we have;

3x + 8 = 6x - 4

collect like terms

3x - 6x = -4 - 8

subtract the like terms

-3x = -12

Make 'x' the subject of formula

x = -12/-3

Find the quotient

x = 4

Note that m ∠VRS and m ∠VUR are on a straight line, we have;

m ∠VRS +  m ∠VUR = 180

substitute the values

54° +  m ∠VUR = 180

m ∠VUR = 180 - 54

m ∠VUR = 126°

Hence, the values are 4 and 126°

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The missing lengths of the sides of the congruent triangles described are:

AC = 25 units.

PQ = 3 units.

The corresponding side lengths of any two or more triangles that are congruent to each other are always equal in measure. That is, the three sides of one triangle have lengths that are equal to the corresponding three sides of the other triangle, if both triangles are congruent triangles.

We are told that triangles ABC and LMN are congruent to each other, therefore:

AB = LM = 41 units [corresponding sides]

AC = LN = 25 units [corresponding sides]

BC = MN = 38 units [corresponding sides].

Therefore, the length of AC is 25 units.

Also, it is assumed that triangles FGH and PQR are congruent triangles, therefore:

FG = PQ = 3 units [corresponding sides]

GH = QR = 4.5 units [corresponding sides]

Therefore, the length of PQ is 3 units.

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