Solve the system of equations. Remember: systems with one solution will have an answer in the form of an ordered triplet.

Example: (3, -4, 10)



For systems with infinite solutions or no solutions, write the words ‘infinite solutions’ or ‘no solutions’.



x + 2y -z = 2

2x - 7y + 5z = 3

-4x + y + 2z = 4

Using scientific notation, The value of  8x10⁹ is 8000000000

In scientific notation, the correct format is an x 10 b, where an is an integer or decimal number whose absolute value is more than or equal to one and less than ten, or 1 |a| 10. In order for the scientific notation to be mathematically identical to the original number, b must be a power of 10.

The given problem is written in scientific notation,

The multiplication of the given number will be-

8x10⁹ = 8000000000

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Answer:

$4,872.00

Step-by-step explanation:

Convert 8% into a decimal and multiply

$60,900.00 x 0.08 = $4,872.00

Answer:

Step-by-step explanation:

The total worth of shares that he has is 24000$

To calculate earnings per share, take a company's net income and deduct preferred dividends from it. Divide the total by the average number of outstanding common shares.

Given Sergio purchased 2000 shares at four dollars each

the cost price of shares is 4$ each

Therefore total shares worth he has  = 2000 * 4

                                                             = 8000 $

He now expects the stock to triple in value by the end of next year.

total amount of shares he owns = 8000 * 3

                                                      = 24000$

Therefore, the total amount of shares he owns is 24000$

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The angle of elevation of the sun from the ground to the top of a tree is 36°.

We are given that:

The sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long.

Now by using the trigonometric identity .

tan θ = P / B

As figure is  given below .

AB =  Perpendicular = 10 yards

BC =  Base = 14 yards

Putting all the values in the trigonometric identity .

tan θ = 10 / 14

θ = 36°

Therefore, the angle of elevation of the sun from the ground to the top of a tree is 36°.

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Answer:

40

Step-by-step explanation:

For this equation, all we do is simply plug in the values.

-4 (c) (a)

-4 (-5) (2)

-4*-5*2

Now, multiply, and you get your answer.

-4 * -5 = 20

20 * 2 = 40

40 is your answer

Answer:

(7-8) / (-7/16) = -2 -(.8) + (1/4) = -.55 -2+ -.55= -2.55

Step-by-step explanation:

Answer:

1×32

2×16

4×8

8×4

16×2

32×1

Step-by-step explanation:

This question about arranging pictures is just trying to get you to explore the factors of 32, maybe for practicing the math ideas of factoring, or area, or max/min, or matrices.

Think of what numbers go into 32:

1, 2, 4, 8, 16, 32

Pair them up!

1×32 and 32×1 will look differently if they are pictures on a wall. So we'll list them separately. Then there's also 2×16 and 16×2, and 4×8 and 8×4.

The ratio of red cars to blue cars in a parking lot was 5:3, total blue cars are 24.

A ratio in mathematics shows how many times one number is included in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

Given, the ratio is 5:3.

Total red cars = 40

⇒ 5x = 40

⇒ x  = 8

Blue cars  = 8 × 3

= 24

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The velocity at t = 0 will be 4 meters per second.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given function is s(t) = √ ( t + 16 ).

The value of the function is calculated as below:-

s ( t ) = √ ( t + 16 ).

s( 0 ) = √ ( 0 + 16 ).

s( 0 ) = √ ( 16 ).

s( 0 ) = 4

Therefore, the velocity at t = 0 will be 4 meters per second.

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6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.

Given,

The expression : 6x³ + 2x² + 3x - 4

We have to divide the given expression by x² + 3x - 4.

Let's take 6x³ + 2x² + 3x - 4 as p(x) and x² + 3x - 4 as g(x).

If p(x) is divisible by the factors of g(x), then p(x) is divisible by g(x).

So, let's factorize  x² + 3x - 4

x² + 3x - 4 = (x - 1) (x + 4)

Now,

p(x) = 6x³ + 2x² + 3x - 4

By using remainder theorem,

If p(1) = 0 and p(4) = 0, then p(x) is divisible by g(x).

So,

p(1) = 6 × 1³ + 2 x 1² + 3 x 1 -4

p(1) = 6 + 2 + 3 - 4

p(1) = 11 - 4

p(1) = 7

Next,

p(4) = 6 x 4³ + 2 x 4² + 3 x 4 - 4

p(4) = 6 x 64 + 2 x 16 + 12 - 4

p(4) = 384 + 32 + 12 - 4

p(4) = 424

Here, p(1) and p(4) is not 0.

So, p(x) is not divisible by g(x).

That is, 6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.

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(a) the domain of f would be an interval (−3,6]

(b) the range of f would be an interval (−6,3]

(c) the zero(s) of f are x = −0.5 and x=6.

(d) the value of f(-3.5) would be 2

(e) the intervals at (−3,3) which f is increasing

(f) the intervals at (3,6] which f is decreasing

(g) the values are (−3,−0.5] for which f(x) ≤0

(h) x = 3 which is a relative maximum point

(i) the value of x is 3 for which f(x) = 3

(j) the function would be positive if f(0)

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The domain of the function shown in the graph is given by the set of values x that has a point on the graph.

In other words, by launching the graph onto the x-axis we will cover the interval (−3,6]

The range of the function shown in the picture is given by the set of values y that has a point on the graph.

In other words, by launching the graph onto the y-axis we will cover the interval (−6,3]

The zeros of the function are the x-intercepts of the function, so the zeros are x = −0.5 and x=6.

The value of f(-3.5) is given by the y- coordinate of the point of intersection of the graph with the vertical line x=-3.5 So, f(-3.5)≈2.

The function is increasing whenever the y- coordinate increases if we trace the graph in the direction of positive x values.

So, the graph is increasing on (−3,3), where x=3 corresponds to the x- coordinate of the turning point on the graph.

The function is decreasing whenever the y- coordinate decreases if we trace the graph in the direction of positive x values.

So, the graph is decreasing on (3,6].

The values of x where f(x) ≤0, correspond to the points where the graph is below the x-axis, so the values of x for which f(x) ≤0 are (−3,−0.5].

The relative maxima or minima are the x-coordinate points where the continuous function has a turning point, like x=3 which is a relative maximum point

.

There are no relative minimum points for the given function.

The value of x for f(x)=3 is the x- coordinate of the point of intersection of the graph with the horizontal line y=3

So, x≈3.

we will determine the  y = coordinate of the point of intersection of the graph with the vertical line

x=0, which is above 2, so f(0) is positive.

Therefore, the domain of the function is interval (−3,6], and the range of the function is interval (−6,3].

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Answer:

Step-by-step explanation: I think the answer would be B or D they seem the most logical

The required answer for 25:4 and 45:10 as a complex fraction is 1/(4/25) and 1/(2/9).

Fractions represent the parts of a whole or collection of objects.

A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.

Now given ratio are,

25:4 and 45:10

Now converting the given ratio into fraction,

25:4 = 25/4

and,

45:10 = 45/10

Now for 25/4 we have,

Numerator = 25

Denominator = 4

Now dividing numerator and denominator by 25 we get,

Numerator = 25/25 = 1

Denominator = 4/25

Thus, the complex fraction of 25/4 we get is,

25/4 = 1/(4/25)

Similarly for 45/10

Numerator = 45

Denominator = 10

Now dividing numerator and denominator by 45 we get,

Numerator = 45/45 = 1

Denominator = 10/45 = 2/9

Thus, the complex fraction of 25/4 we get is,

45/10 = 1/(2/9)

Thus, the required answer for 25:4 and 45:10 as a complex fraction is 1/(4/25) and 1/(2/9)

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The parameter of the shaded shape is 50 meters

The parameter of any shape is sum of all sides

Measurements of some of the sides are given and some needs to be find out so the calculations are -

first side = 7m

second side = 14m

third side is equal to first side so= 7m,

fourth side = 1m

fifth side is equal to seventh side =4m

sixth side is second side- fourth side- eighth side = 14- 1-4= 9m

seventh side=4m

eighth side =4m

parameter of the shape = sum of all side = 7+ 14+ 7+ 1+4+9+4+4

                                     =50 m

So, the parameter of the shaded shape is 50 meters

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The tenth of a gram closest to it is 151.79 grams.

The flour's mass is 141.6 grams.

10.19 grams are added.

The amount of flour in the bag =141.6+ 10.19

= 151.79.

A physical quantity is mass. The weight of a body serves as the unit of mass measurement. It can be measured in normal mass quantities such grams, kilograms, and pounds. Although grams are used to measure smaller objects, the kilogram is the SI unit of mass.

In the metric measurement system, a gram is a unit of weight that is one thousandth of a kilogram. When something is extremely light, its weight is measured in grams.

Therefore, 151.79 grams of flour, to the nearest tenth of a gram, are in the bag.

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Answer:

the second option

[–3, 6) ∪ (6, ∞)

Step-by-step explanation:

f(x) = 1/(x - 3)

the domain is every value of x that does not turn the denominator to 0. so, x <> 3.

g(x) = sqrt(x + 3)

the domain is every value of x that does not turn (x+3) into a negative value. so, x >= -3.

f(g(x)) = 1/(sqrt(x + 3) - 3)

the domain is all values of x that are valid for g(x) AND that do not generate range values of g(x) that violate the domain of f(x).

so, it is (x >= -3) AND (sqrt(x + 3) <> 3).

and sqrt(x + 3) = 3, if (x + 3) = 9.

that means x = 6.

so, 6 is forbidden, every other value of x is allowed here.

therefore, the domain of f(g(x)) is

(x >= -3) AND (x <> 6)

and that is equivalent to

[-3, 6) u (6, infinity)

everything larger or equal to -3 and different from 6.

Answer:

y = -4x - 1

Step-by-step explanation:

Let's first find the equation of the line segment AB. The equation of a line in slope-intercept form is y = mx + b where m represents the slope and b represents the y-intercept. Start by finding the slope.

The equation for slope is:  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. These variables represent any pair of coordinates on the line. In this case since the two points chosen are A and B, thus:

[tex]x_2=-2\\x_1=3\\y_2=15\\y_1=-5[/tex]

If we plug these values into the equation, we get:

[tex]\frac{15-(-5)}{-2-3}=\frac{20}{-5}=-4[/tex]

Now we need to find the equation of a line that passes through the point (-1, 3) and is parallel to AB. If two lines are parallel they share the same slope. The equation of the line parallel to AB is y = -4x + b. We can plug in the coordinate (-1, 3) into the equation to solve for b.

[tex]y = mx+b\\3 = -4(-1) +b\\3=4+b\\\text{Subtract 4 from both sides}\\b=-1[/tex]

Therefore the equation of the line that passes through the point (-1, 3) and is parallel to AB is y = -4x - 1.

The domain of f(x) is all real numbers & satisfies function f(x+1)=2f(x).

For  x∈(0,1], the function f(x)=x(x-1). For value x∈(-[tex]\infty[/tex],m], f(x)≥[tex]\frac{-8}{9}[/tex]. What is the value of m?​

the smallest value m=[tex]\frac{7}{3}[/tex].

Given that, for x∈(0,1], f(x)=x(x-1)

Let's plot this function

We'll go from 0 to 1 and let's graph what this function is look like

f(x)=x(x-1) will be a parabola and it's going to go between the points (0,0) and (1,0).

Will graph it in figure1 we can see.

The minimum value of this parabola is right in the middle and it is

f(0.5)=-0.25

Now, let try and graph the function in the other intervals

We know f(x+1)=2f(x)

Now we can evaluate couple of points

f(0+1)=2f(x)

f(0.5+1)=2f(0.5)

f(1+1)=2f(1)

And we quickly deduce that the graph in(1,2] is twice the height of the graph in (0,1].

We will graph a parabola in figure 2 we can see.

This parabola is going to have a graph of 2 between its twice as tall and this can be multiplied by the quantity of (x-1) multiplied by the quantity of (x-2).

It is 2(x-1)(x-2).

We graph next interval twice the height of the graph in the interval from 2 to 3. We can see the graph in figure3.

This parabola will have an equation 4 times the quantity of (x-2) and (x-3).

We can also shift this graph to the left and it going to be half the height.

Looking at this graph we want f(x)≥[tex]\frac{-8}{9}[/tex].

In the 3 interval from 2 to 3 its going to intersect .

we want to look for the points where f(x)≥[tex]\frac{-8}{9}[/tex].

We are looking for m which f(x)≥[tex]\frac{-8}{9}[/tex].

parabolas equation =[tex]\frac{-8}{9}[/tex].

4(x-2)(x-3)=[tex]\frac{-8}{9}[/tex]

[tex]x^{2} -5x+6=\frac{-2}{9} \\(x-\frac{7}{3})(x-\frac{8}{3})=0\\ x= \frac{7}{3},\frac{8}{3}\\\\[/tex]

Therefore, We will take the smallest value m=[tex]\frac{7}{3}[/tex].

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Answer:

31/18 which is changed to 1³¹/¹⁸

Step-by-step explanation:

9/18+7/18+15/18 I found the lcm or the lowest common multiple of all the three and multiplied it by each fraction first then u can add all of them and put it over 18 or add each

a) The graph will have a "V" shape, which opens upwards.

b) The horizontal shift of 1 unit to the left.

c) The vertical shift is of 5 units downwards.

Here we have the absolute value function:

f(x) = |x + 1| - 5

First we want to describe the graph shape, we know that it is an absolute value function, so it will have a "V" shape.

The arms will make an angle of 45° with the vertical and horizontal (because the slope is 1)

And it will open upwards, because the slope is positive.

Now, remember that if the parent function is:

f(x).

A translation is written as:

g(x) = f(x + a) + b

Where a is the horizontal translation and b is the vertical translation, such that:

In this case we have:

f(x) = |x + 1| - 5

So this is a translation of 1 unit to the left and 5 units down of the parent absolute value function.

b) The horizontal shift of 1 unit to the left.

c) The vertical shift is of 5 units downwards.

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Answer:4.98

Step-by-step explanation:

trust me

The greatest number of flowers in each group is 20.

In order to determine the greatest number number of flowers in each group, the highest common factor of 100 roses and 60 daises have to be determined.

The factor of a number is a number that divides a number perfectly into whole numbers. The highest common factor is the highest factor that is common to two or more numbers

Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50 and 100.

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Common factors of 100 and 60 - 1, 2, 5, 10, 20

Highest common factor = 20

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Mediante el uso de porcentajes, concluimos que la clase tiene una población total de 30 estudiantes.

En este problema tenemos a 12 estudiantes procedentes de una clase que participan en un evento cultural de su escuela y también se conoce que equivalen al 40 por ciento de su clase. El total de estudiantes de la clase se obtiene al dividir el número de estudiantes por el porcentaje:

x = 12 / 40 %

x = (12 · 100) / 40

x = 30

La clase tiene una población total de 30 estudiantes.

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Answer:

Step-by-step explanation:

1.true

2.true

3.true

Answer:

1)  True

2)  False

3)  True

Step-by-step explanation:

Set Notation

[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]

Question 1

The union of two sets is denoted by the symbol ∪.

The union of two sets is the set that comprises all elements in A or B or both.

Question 2

Given sets:

[tex]\begin{aligned} \implies \sf A \cup B & =\sf \{ 2, 3, 4\} \cup \{3, 4, 5, 6 \}\\& =\sf \{ 2, 3, 4, 5, 6\}\end{aligned}[/tex]

Question 3

Given sets:

[tex]\begin{aligned}\implies \sf M \cap N & =\sf \{ a, e, i, o, u\} \cap \{l, o, v, e \}\\& =\sf \{ o, e\}\end{aligned}[/tex]

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It can be written as 13/35.

how do we rewrite a fraction.

Divide the numerator by the denominator

Write down the whole number result

Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.

A number that will divide evenly into both the numerator and denominator so it can be reduced, or

The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number

4/5-3/7

⇒4×7-3×5/ 35     ( 5 and 7 have no common divisor).

⇒ 28- 15/35

⇒13/35

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Answer: 236 square inches

Step-by-step explanation:

Three 6" x 6" and two 8" x 8" electrical boxes are installed in a wall between two studs

The answer is 236

The range of the function, f(x)=4x+2 for the domain {–2, –1, 1, 4} includes (-6, -2, 6, 18).

The range of the function,  f(x)=4x+2, includes all the possible output values of the function.

The domain of a function,  f(x)=4x+2, is the set of all possible input values (domain {–2, –1, 1, 4}) of the function.

Remember that a function is a mathematical expression that equates an independent variable with a dependent variable.

f(x)=4x+2

Domain =  {–2, –1, 1, 4}

The range for -2:

f(x)=4x+2 = 4(–2) + 2 = -6

Range for -1:

f(x)=4x+2 = 4(–1) + 2 = -2

Range for 1:

f(x)=4x+2 = 4(1) + 2 = 6

The range for 4:

f(x)=4x+2 = 4(4) + 2 = 18

Thus, the range of the function, f(x)=4x+2 for the domain {–2, –1, 1, 4} includes (-6, -2, 6, 18).

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