What is the nature of the solution set to the following system of equations?

4x + 3y = 2

3x − 2y = 10

Answer:

A) Equation of the line of best fit: y = -5x + 62

B) y = -3

Explanation:

Given points: {(5, 38), (6, 34), (7, 27), (8, 21), (9, 17), (10, 14)}

Plot these points on the graph and draw a straight line between them.

A)

The points (7, 27), (9, 17)

Find slope:

[tex]\sf slope: \dfrac{17-27}{9-7} = -5[/tex]

Equation:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 27= -5(x - 7)[/tex]

[tex]\sf y = -5x + 35 + 27[/tex]

[tex]\sf y = -5x + 62[/tex]

B) If x = 13, then approximate value of y is

insert x = 13 in equation

y = -5x + 62

y = -5(13) + 62

y = -3

The answers are :

A) y = -5x + 64

B) -1

Part (A) :

Finding the slope : Take the points (6, 34) and (10, 14)

m = Δy/Δx

m = 14 - 34 / 10 - 6

m = -20/4

* m = -5 *

Using point slope formula to find equation :

y - y₁ = m (x - x₁)

y - 34 = -5 (x - 6)

y - 34 = -5x + 30

y = -5x + 64

Part (B) :

Substitute x = 13 in the line of best fit equation

y = -5(13) + 64

y = -65 + 64

y = -1

Answer: A

Step-by-step explanation:

[tex]P(x) Q(x)=R(x)\\\\(x+1)Q(x)=2x^3 + 2x^2 - 3x-3\\\\Q(x)=\frac{2x^3 + 2x^2 - 3x-3}{x+1}\\\\Q(x)=\frac{2x^2 (x+1)-3(x+1)}{x+1}\\\\Q(x)=2x^2 - 3[/tex]

For the following pair of functions, the vertex of g(x) 2 units to the right of f(x),

f(x) = x² and g(x) = (x - 2)²

What are functions?

Defining a relationship between an independent variable and a dependent variable using mathematical expressions, rules, or laws is known as a function. Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.

Determining the Correct Pair of Functions

For a given function f(x), its horizontal translation would be f(x + a). Here, a is the distance translated, owing to which f(x + a) is generated.

If a > 0, then it indicates a right translation of a units.

If a < 0, then it indicates a left translation of a units.

The required functions are to be such that the vertex of g(x) is 2 units to the right of the vertex of f(x).

Thus, if f(x) = x², then g(x) = (x - 2)²

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The value of x in the trapezoid is 11.

Therefore, the angle 9x and 7x + 4 are supplementary.

Hence,

9x + 7x + 4 = 180

16x + 4 = 180

16x  = 180  - 4

16x = 176

x = 176 / 16

x = 11

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Answer:11

Step-by-step explanation:Easy

Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

According to the statement

we have given that the Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal.

and we have to find that the expected value of the difference between the number of days.

So, the total number of days in a year is 365 days.

Chance to get a prime number on a die = 3/6

Chance to get a prime number on a die = 1/2.

and chances to get a composite number = 2/6

chances to get a composite number = 1/3

and chances to get a 1 on a die = 1/6.

Then the expected value =

so, expected value = 365(1/6) + 365(1/3) + 365(1/2)

then after calculating

Expected value = 1+2+1

then the value become is 4

and by this way he eat 171 days sweet cereal and other days he eat unsweetened.

So, Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

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Answer:

$13.20

Step-by-step explanation:

A dozen consists of 12 items. If you have 3 you must multiply the current amount by 4 to get 12. Therefore you must also multiply the price by 4.

3.30*4=13.20

Answer:

screenshot attached of graph

Step-by-step explanation:

in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3

Standard form is simply a value with an exponential powerl

Given the values;

It is important to note that any number to the power of O is equivalent to 1

So, we have

10^ 0 = 1

4( 10^-3) = 37

5(10^3) = 5000

Now, let's substitute the values

(10°) + 4 (10-3) + 5 (10³)

It is equivalent to

⇒1 + 4 × 10^-3 + 5 × 10^3

⇒1 + 37 + 5000

Add the values

= 5038

Let's convert it to standard form, we have

= 5. 04 × 10 ^3

Thus, in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3

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The graph that shows the minimum amount due for a credit amount of x given that the credit limit is $2,000 is graph B.

Let x represent the credit amount  and y represent the minimum amount due.

For a bill of less than $100, the entire amount is due. That is for 0 ≤ x < $100, y = x

For a bill of at least $100 but less than $500, the minimum due is $100. That is for $100 ≤ x < $500, y = 100

For a bill of at least $500 but less than $1,000, the minimum due is $300. That is for $500 ≤ x < $1000, y = $300

For a bill of $1,000 or more, the minimum due is $500. But the credit limit is $2000. That is For $1000 ≤ x < $2000, y = $500

The graph that shows the minimum amount due for a credit amount of x  is graph B.

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The logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

The equation is given as

13^2=169

Take the logarithm of both sides

log(13^2) = log(169)

This gives

2log(13) = log(169)

Divide both sides by log(13)

[tex]\log_{13}(169) = 2[/tex]

Hence, the logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

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Fencer X attacks. Fencer Y makes a parry, and scores a riposte to the valid target of Fencer X. During the parry, Fencer Y strikes Fencer Xs mask with the bell guard. annual the touch fencer Y recieves  a RED CARD.

what are the fencing rules ?

Penalty cards or flags are also used in modern fencing. Each card has a unique meaning. A fencer who receives a yellow card is warned, but no further action is taken. A fencer who receives a red card is warned, and their opponent receives a touch. A fencer who receives a black card is disqualified from the competition and may be disqualified from the tournament, expelled from the venue, or suspended from future tournaments if the offence is serious. However, black cards are rarely given to fencers. It should be noted that spectators can (and occasionally are) carded or expelled.

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Answer:

A. y= cos x - 1

Step-by-step explanation:

short answer: this is basically the parent graph cos(x), just vertically shifted down 1 unit.

longer answer:

standard form is y = a cos(bx-c) +d

a = amplitude

b = 2pi/period

c = horizontal shift

d = vertical shift (also equal to midline)

for this graph

a=1

period is 2pi, so b=1

there is no horizontal shift so c=0

d= -1 because it is shifted down one unit from axis (midline is at -1)

Answer:

Option B: 3

Step-by-step explanation:

#1: Substitute in 6 for [tex]y[/tex] and 3 for [tex]x[/tex]: [tex]13=(3)(6)-5[/tex]

#2: Multiply 3 and 6: [tex]13=18-5[/tex]

#3: Evaluate the equation: [tex]13=18-5[/tex] → [tex]13=13[/tex]

#4: Check if the solution is equal: [tex]13=13[/tex] ✓

[tex]x[/tex] is equal to 3 (Option B).

The volume of the shape will be 50cm3.

It should be noted that the volume van be found by multiplying the area by the height. The volume will be:

= 10 × 5

= 50cm³

The standard deviation volume will be:

= 0.1 × 50

= 5cm

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Answer:

? = 4

Step-by-step explanation:

4/5 = 4/1 x 1/5

4/5 = 4/5

Answer:

5 hours 20 minutes.

Step-by-step explanation:

8 * 2/3

= 16/3

= 5 1/3

= 5 hours 20 minutes.

Answer:

5x - y = 9

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = 5x - 9 ( subtract 5x from both sides )

- 5x + y = - 9 ( multiply through by - 1 )

5x - y = 9 ← in standard form

Answer: plot points (0,-2) (1.-5) (2.-8) (-1.1) (-2.1) makes a upside down V

-3|0+2|+4=-2

-3|1 +2|+4= -5

-3|2+2|+4= -8

-3|-1+2|+4=1

+3|-2+2|+4=1

Step-by-step explanation:

The mass of the same nickel which is 5 grams in milligrams is 5,000 milligram.

Weight of a nickel = 5 gram

Weight of same nickel in milligram = 5 grams × 1000

= 5,000 milligram

Therefore, the mass of the same nickel is 5,000 milligram

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The relationship of the data can be classified as a fairly strong positive correlation.

Correlation is a statistical measure used to measure the relationship that exists between two variables.

Positive correlation is when two variables move in the same direction. If one variable increases, the other variable also increases. When there is a positive correlation, the graph of the variables is upward sloping

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The solution to the given inequality is y < 5

Inequality are equations  not separated by an equal sign. Given the following parameters

15 > y + 10

Subtract 10 from both sides

15 - 10 > y + 10 - 10

5 > y

Swap

y < 5

Hence the solution to the given inequality is y < 5

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Answer:

See below

Step-by-step explanation:

The larger is  

7-6 = 1 unit bigger than the smaller....and this unit = 24 gallons

   each unit is 24 gallons

larger barrel holds   24 * 7 = 168 gal

smaller barrel holds  24 * 6 = 144 gal

Answer:

Small barrel=144 large barrel=168

Step-by-step explanation:

The ratio is 6 to 7 so lets assign x as a factor.

6x=Small barrel (S)

7x=Large barrel (L)

7x-6x=x

x is the difference so x is 24

x=24

6*24=144=S

7*24=168=L

The surface area of the composite figure is 444m²

Given a composite figure which is shown in the question.

The  area of ​​a shape (in square units) is the number of unit squares required to cover the entire area without gaps or overlaps. If a hologram has planes, those faces are called faces. Area is the sum of the areas of the faces.

Firstly, we will find the area of front and end triangles by using the formula

Area=(1/2)×b×h and we will multiply this area by 2 because we are finding the area of two same triangles.

Here, h=6 and b=16 and substitute these values in the formula, we get

A₁=2×(1/2)×16×6

A₁=2×8×6

A₁=96m²

Now, we will find the area of the left and right side rectangles which joined both the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=10 and b=5 and substitute these values in the formula, we get

A₂=2×10×5

A₂=100m²

Further, we will find the area of the front and end side rectangles that joined both by the base of the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=16 and b=4 and substitute these values in the formula, we get

A₃=2×16×4

A₃=128m²

Furthermore,  we will find the area of the left and right side rectangles which joined by the front and end rectangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=4 and b=5 and substitute these values in the formula, we get

A₄=2×4×5

A₄=40m²

Now, we will find the area of the base of the composite figure which is rectangle.

We will find the area by using the formula Area=l×b.

here, l=16 and b=5 and substitute these values in the formula, we get

A₅=16×5

A₅=80m²

So, the surface area of the given composite figure will be

Surface area=A₁+A₂+A₃+A₄+A₅

Surface area=96m²+100m²+128m²+40m²+80m²

Surface area=444m²

Hence, the surface area of the given composite figure is 444m².

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The derivative and domain of the function f(x) = x²-2x³  is :[tex](-\infty, \infty)[/tex].

The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.

Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.

Calculation for the derivative:

Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).

[tex]\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}[/tex]

       [tex]\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}[/tex]

       [tex]=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}[/tex]

Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.

      [tex]\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}[/tex]

f and f' are polynomials, so their domains are all real numbers.

Therefore,  for f(x) = x²-2x³      domain of f and f' :[tex](-\infty, \infty)[/tex].

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The complete question is -

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.

The value of f⁻¹(f(58)) is 58 and the value of the function f(f(5)) is 11

As a general rule, we have:

f⁻¹(f(x)) = x

Substitute 58 for x

So, we have:

f⁻¹(f(58)) = 58

Hence, the value of f⁻¹(f(58)) is 58

Also, we have:

f(f(5))

From the table, we have:

f(5) = 9

So, we have:

f(f(5)) = f(9)

From the table, we have:

f(9) = 11

So, we have:

f(f(5)) = 11

Hence, the value of the function f(f(5)) is 11

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Answer: 8r + 9.8s + 8.1

Step-by-step explanation:

   Given:

-(-8r-9.8s)+8.1

   Distribute:

   ↳ A - times a - becomes a +, a -times a + stays a -

8r + 9.8s + 8.1

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Answer:

A varicocele measures more than 2 mm in diameter.

Step-by-step explanation:

pampiniform plexus veins measuring more than. 2 mm in diameter at rest and which increased in diameter by 1 mm, and subjective color Doppler.

The additional information which would be sufficient to conclude that LMNO is a parallelogram is; ML ∥ NO, LO ≅ MN, and ML ≅ LO.

The condition for a quadrilateral to be a parallelogram is that; the opposite pairs must be parallel and consequently opposite pairs are congruent as they have equal length measures.

On this note, it can be concluded that the additional information which would be sufficient are; ML ∥ NO, LO ≅ MN, and ML ≅ LO.

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(A.) ML ∥ NO,

(C.) LO ≅ MN.

Have a great day and hydrate!! <3