find the solution to the systems of equations y=-7x+3 and y=-x-3

Answer:

Option 3

Step-by-step explanation:

we know that

The solution show in the graph represent the interval [4,∞)

All real numbers greater than or equal to 4

In a number line the solution is the shaded area at right of x=4 (closed circle)

The number 4 is included in the solution set

therefore

Option 3

Answer:

  110

Step-by-step explanation:

You want the remainder from the division ...

  [tex]\dfrac{4x^3+2x^2-18x+38}{x-3}[/tex]

The remainder theorem tells you the remainder of ...

  f(x)/(x -a)

is f(a).

We can compute f(a) directly, or we can do it using synthetic division. The attachment shows the synthetic division approach.

If we want to evaluate f(x), it is convenient to write it in Horner Form:

  f(x) = 4x³ +2x² -18x +38 = ((4x +2)x -18)x +38

Then, for x = 3, this is ...

  ((4·3 +2)·3 -18)·3 +38 = (14·3 -18)·3 +38 = 24·3 +38 = 110

The remainder from the division is 110.

The residual is 1.5

Step-by-step explanation:

Given the regression line equation as : y=1.2x +3.5

The formula for residual = Observed y-value - Predicted y-value

This gives the vertical distance from the actual plotted point to the point on the regression line. You should find how far the data fall from the regression line.

In this case, at y=5, from the graph, to get the vertical distance, perform subtraction as;

5.0 - 3.5 = 1.5

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Keywords : residual, regression line, modeled, data

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Answer: OPTION D.

Step-by-step explanation:

For this exercise it is important to remember that:

1.  Direct proportion equations have the following form:

[tex]y=kx[/tex]

Where "k" is the constant of proportionality.

2. The graph of Direct proportions is an straight line that passes through the origin.

Observe the picture attached.

If you join the points G, C and A, you get a straight line that passes through the origin,

If you join the points F, G and H, you also get a straight line that passes through the origin,

Therefore, the sets of points show "x" in Direct proportion to "y", are:

[tex]\{F, G, H\}[/tex] and   [tex]\{{G, C, A}\}[/tex]

Answer:D){F, G, H} and {G, C, A} only

Step-by-step explanation:

Answer:

6 chaperones on 80 students.

Step-by-step explanation:

Here is the complete question: School guideline required that there must be 2 chaperones for every 25 students on a school trip. how many chaperones must there be for 80 students?

Given: There must be 2 chaperones on every 25 students.

Now, we will use unitary method to solve.

We know 2 chaperones = 25 students

∴ one student required [tex]\frac{2}{25}\ chaperones[/tex]

Next for 80 students, we require= [tex]\frac{2}{25} \times 80 = \frac{160}{25}[/tex]

∴ For 80 students, we require [tex]6.4 \ chaperones[/tex], however, we cannot use decimal for number of person, so we can round off the number to 6 chaperones on every 80 students.

The factored form of given expression is:

[tex]16x^2(x-3)(x+3)[/tex]

Step-by-step explanation:

The identity that can be used to factorize the given expression is:

[tex]a^2-b^2 = (a+b)(a-b)[/tex]

Given

[tex]16x^4-144x^2[/tex]

As 16 is a factor of both terms

[tex]=16x^2(x^2-9)[/tex]

Using the identity

[tex]=16x^2[(x)^2-(3)^2]\\=16x^2[(x-3)(x+3)][/tex]

Hence,

The factored form of given expression is:

[tex]16x^2(x-3)(x+3)[/tex]

Keywords: Factorization, polynomials

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1. non-random and biased.

2. random and unbiased.

The domain of the function f(x) = (2/5) * sqrt(x) is all real numbers x ≥ 0, or in interval notation, [0, ∞). This is because square roots are only defined for non-negative real numbers.

The domain of a function refers to all possible values that can be input into the function, usually represented by 'x'. For the given function f(x) =  \frac{2}{5} \sqrt{x}, we need to determine the set of x-values for which the function is defined. Since we cannot take the square root of a negative number in the set of real numbers, the smallest value for 'x' must be 0. Thus, the domain of the function f(x) = \frac{2}{5} \sqrt{x} includes all real numbers greater than or equal to 0.

This is written mathematically as “x ≥ 0” or in interval notation as [0, ∞). It's important to note that, for real numbers, square roots are only defined for non-negative values, which is why the domain starts at 0 and continues to positive infinity.

Answer: x = 21

Step-by-step explanation:

look at the picture

Answer:

d=5

Step-by-step explanation:

-5d+10=2d-25

-5d-2d=-25-10

-7d=-35

7d=35

d=35/7

d=5

(24 + 2y) + (7y)

(24 +  8) + 28

32 + 28

60

Answer:

60

Step-by-step explanation:

(24 + 2y) + (7y)

(24 + 2 x 4) + (7 x 4)

(24 + 8) + (28)

32 + 28 = 60

Answer:

[tex]ec = \frac{6 \times 5}{4} = 7.5 [/tex]

Answer:

1 point

Step-by-step explanation:

The number of games in the tournament is:

₄C₂ = 6

Another way to look at it: Team 1 plays 3 games against Team 2, 3, and 4.  Then, Team 2 plays 2 games against Team 3 and 4 (Team 2 already played Team 1).  Finally, Team 3 plays a game against Team 4.  So the total is 3 + 2 + 1 = 6.

If there's a total of 6 games, then there's a total of 6 points.  So if x is the number of points Team 4 has:

x + 1 + 3 + 1 = 6

x + 5 = 6

x = 1

Team 4 has 1 point.

Check the picture below.

Answer:

Option B [tex]\frac{Kg*m^2}{s^2}[/tex]

Step-by-step explanation:

we know that

The formula to calculate the work is equal to

[tex]W=Fd[/tex]

where

W represents work

F represents force

d represents distance

The units are

[tex]F=(\frac{Kg*m}{s^2})[/tex] ---> Newtons

[tex]d=m[/tex] ---> meters

substitute the units in the formula

Remember that when multiply exponents with the same base, adds the exponents and maintain the same base

[tex](m)(m)=m^{1+1}=m^2[/tex]

so

[tex]W=(\frac{Kg*m}{s^2})(m)=(\frac{Kg*m^2}{s^2})[/tex]

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) Given figure is a parallelogram

Area = 144 cm²

base  * altitude = 144

16 * x = 144

x =144/16

x = 9 cm

2)2) Trapezium

Area = [tex]\frac{a+b}{2}*h[/tex]      ; {a and b are parallel sides of trapezium}

( 37 +27 /2) * x  = 480 cm²

64/2 * h = 480

32 *  h = 480

h = 480/32

h = 15 cm

Answer:

[tex]p =\{\text{all even numbers that are less than or equal to 20}\}\\\\p=\{n|n=2k\ \wedge\ n\leq20\ \wedge\ k\in\mathbb{N}\}=\{0,\ 2,\ 4,\ 6,\ 8,\ 10,\ 12,\ 14,\ 16,\ 18,\ 20\}[/tex]

Answer:

[tex]c=11.8\ units[/tex]

Step-by-step explanation:

we know that

The formula of law of cosines is equal to

[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]

where

a, b and c are sides. C is the angle opposite side c

In this problem we have

[tex]a=3\ units\\b=10\ units[/tex]

[tex]C=120^o[/tex]

substitute the given values

[tex]c^2=3^2+10^2-2(3)(10)cos(120^o)[/tex]

[tex]c^2=109-(60)cos(120^o)[/tex]

[tex]c^2=109-(60)(-0.5))[/tex]

[tex]c^2=109+30[/tex]

[tex]c^2=139[/tex]

[tex]c=11.8\ units[/tex]

Using the cross product property on this proportion gives us the following equation:

6 (3x + 3) = 7 (x + 16)

Use the distributive property

18x + 18 = 7x + 112

Subtract both sides by 7x

11x + 18 = 112

Subtract both sides by 18

11x = 94

Divide both sides by 11

x = 94/11

This fraction is already fully simplified and cannot be simplified further. This should be your answer.

Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

6(3x+3) = 7(x+16)

18x+18=7x+112

-7 on both sides

11x+18=112

-18 on both sides

11x/11 = 94/11

x=8.5

Answer:C

Step-by-step explanation: fixed cost = 10.47+4.25

Variable cost =1.35m

Total cost= 10.47+4.25+1.35m<=30

Answer:

Option C 10.47 +4.25 + 1.35m 2 30

Step-by-step explanation:

Data:

DoorDash charges a fee of =  $4.25

Fee per mile = $ 1.35

Cost of a meal = $ 10.47

The maximum number of miles is given by:

10.47 + 4.25  + 4.25 < 30

Therefore, option C is correct.

Answer:

The number of years in which saving gets double is 8 years .

Step-by-step explanation:

Given as :

The principal amount saved into the account = p = $8,000

The rate of interest applied = r = 9%

The Amount gets double in n years = $A  

Or, $A = 2 × p = $8,000 × 2 = $16,000

Let the number of years in which saving gets double = n years

Now, From Compound Interest method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, 2 × p = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or, $16,000 = $8,000 × [tex](1+\dfrac{\textrm 9}{100})^{\textrm n}[/tex]

Or, [tex]\dfrac{16,000}{8,000}[/tex] = [tex](1.09)^{n}[/tex]

Or, 2 = [tex](1.09)^{n}[/tex]

Now, Taking Log both side

[tex]Log_{10}[/tex]2 = [tex]Log_{10}[/tex] [tex](1.09)^{n}[/tex]

Or, 0.3010 = n × [tex]Log_{10}[/tex]1.09

Or, 0.3010 = n × 0.0374

∴ n = [tex]\dfrac{0.3010}{0.0374}[/tex]

I.e n = 8.04 ≈ 8

So, The number of years = n = 8

Hence, The number of years in which saving gets double is 8 years . Answer

Answer:

We know that

P(X) = Dividor × Quotient

So dividor = x-1

Quotient = x2 + 7 + 5/x-1

So,

P(x) = x3 - x2 + 7x -2

Step-by-step explanation:

Taking LCM of quotient we will get

(x3 - x2 + 7x - 2)/(x-1)

Now by multiplying the above equation with x-1,

Only thing remaining will be

x3 - x2 + 7x - 2

This is P(x).

The polynomial p(x) in standard form, when given the quotient formed from dividing p(x) by (x - 1), is x^3 - x^2 + 7x - 2.

The function p(x) can be expressed in standard form by multiplying divisor (x - 1) by the quotient, (x^2 + 7 + 5/(x - 1)) according to polynomial division rules. To get p(x), you multiply the quotient by the divisor and add the remainder. However, since there is no remainder mentioned, we assume it's zero and ignore it.

Therefore, p(x) is (x - 1)(x^2 + 7 + 5/(x - 1)). To simplify further, distribute (x - 1) across each term in the parenthesis:

So, the polynomial p(x) is x^3 - x^2 + 7x - 7 + 5 or, simplified further, x^3 - x^2 + 7x - 2.

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In the beginning, 362 meters below sea level, or -362 meters (if we consider sea level as 0).

Because the Dead Sea is 71 meters below where she was, the equation to solve this would be

-362 - 71 = -433

The answer is -433.

Hope this helps!

Since Zoey is 362 meters below sea level while visiting a part of Israel and she descends 71 meters to visit the Dead Sea, the integer that represents the elevation, in meters, of the Dead Sea is a) -433.

We can use the mathematical operation of subtraction to determine the elevation of the Dead Sea as follows:

The present elevation of Zoey = -362 meters

The descent that she makes to visit the Dead Sea = -71 meters

The elevation of the Dead Sea = -433 (-362 - 71).

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Complete Question:

Zoey is 362 meters below sea level while visiting a part of Israel. She descends 71 meters to visit the Dead Sea. Which integer represents the elevation, in meters, of the Dead Sea?

a) -433

b) -391

c) -311

d) -291

Answer:

The value of x is 4, 3rd point.

Step-by-step explanation:

Move all the variables to one side & move unknown value to the other side :

4x - 3 = 2x + 5

4x - 2x = 5 + 3

2x = 8

Then solve it :

2x = 8

x = 8/2

x= 4

Answer:

C. x = 4

Step-by-step explanation:

4x - 3 = 2x + 5

4x - 2x - 3 = 2x - 2x + 5

2x - 3 = 5

2x - 3 + 3 = 5 + 3

2x = 8

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

x = 4

The perimeter of a square is calculated by multiplying the length of one side by 4.

The perimeter of a square is the sum of all four sides. Since a square has equal sides, you can find the perimeter by multiplying the length of one side by 4. The formula for the perimeter of a square is P=4s, where P is the perimeter and s is the length of one side.

For example, if the length of one side is 5 units, the perimeter would be 4 * 5 = 20 units. If the length of one side is 8 centimeters, the perimeter would be 4 * 8 = 32 centimeters.

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Answer:

Millileters

Step-by-step explanation:

If it held 400 liters, it would be a pretty gigantic cup

Answer:

400 millieters

Step-by-step explanation:

because a cup is measured in milliters

Answer:

20 cans of tuna.

Step-by-step explanation:

4 x 15 = 60

3 x ? = 60

3 x 20 = 60

The equation of the line is y = 2x+ 5.

1. Identify the slope:

Lines are considered parallel if they have the same slope.

To find the slope of the given line, we can rearrange the equation 4x-2y=8 to slope-intercept form (y = mx + b) by isolating y: y = 2x - 4.

Therefore, the slope of both the given line and the parallel line we want to find is 2.

2. Use the point-slope form:

We can use the point-slope form of the equation to create the equation of the new line: y - y₁ = m(x - x₁)

Substituting the known point (-2, 1) and the slope (2): y - 1 = 2(x - (-2))

Simplifying the equation: y - 1 = 2x - 4

Combining like terms: y = 2x + 5

Therefore, the equation of the line that passes through (-2, 1) and is parallel to the line 4x-2y=8 is y = 2x + 5.

To find a parallel line to 4x-2y=8 that passes through (-2, 1), we determine the slope of the given line (which is 2) and use point-slope form to write the equation of the new line, resulting in y = 2x + 5.

The student is asking for the equation of a line that passes through a specified point and is parallel to a given line. The equation of the existing line is 4x-2y=8. To find a parallel line, we must have the same slope. First, let's find the slope of the given line by rewriting its equation in slope-intercept form (y=mx+b), where m is the slope and b is the y-intercept. The original equation is 4x - 2y = 8, which can be rewritten as y=2x-4. Thus, the slope is 2.

Since the new line must be parallel, it will also have a slope of 2. Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1,y1) is the point the line passes through, we substitute the point (-2,1) and the slope of 2 to get the equation y - 1 = 2(x + 2). Simplifying this, we get y = 2x + 5 as the equation for the line that is parallel to 4x-2y=8 and passes through the point (-2, 1).

Answer:

5040

Step-by-step explanation:

When a number is in the Parenthesis that means you multiply. First you do 42*3 The answer would be 126. Since there is another Multiplication sign you just plug in your quotient (answer) into the problem. Now the equation is 126*40. 126*40=5040

Answer:

4^6

Step-by-step explanation: