How many linear solutions are there?.

The variable restrictions on the rational equation 2x/5 = x+6/4 are 0,-6/4

Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

Given;

2x/5 = x+6/4

Now, to find out the restrictions of the variable;

2x/5=0

2x=0

x=0

x+6/4=0

x=-6/4

Therefore, by simplification the restrictions will be 0 and -6/4

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The radian measure of an angle theta is the length of the arc that subtended angle 2Pi

We can measure angles in two forms degrees or Radians.

Radian can be described as a measure of the angle subtended by a circular arc. It can be defined as the ratio of the arc length subtending angle to the radius of the circle.

One radian is the measure of the angle subtended by an arc that is equal to the radius of the circle.

Therefore, the radians measure an angle theta the length of the arc.

Θ =s/r ,

where theta is the angle subtended, s is the arc length and r is the radius of the circle.

We know that the 2π radians = 360 degrees.

That subtends the angle in a circle of radius 2Pi

Therefore, The radian measure of an angle theta is the length of the arc that subtended angle 2 Pi

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C.) right and isosceles, but not equilateral

Answer:

C.) right and isosceles, but not equilateral

Step-by-step explanation:

Answer: 3/11

Step-by-step explanation:

first add all the flowers, 3 roses, 4 daisies, and 4 lilies. 3 + 4 + 4 = 11. if only one flower is pink, and there are 3 roses, then there is a 3/11 chance its a rose.

The equation has to be a true statement.  

Start with a true statement:  8 = 8

Now add 4x to both sides:  4x + 8 = 4x + 8
It's still a true statement.

Factor the right side:  4x + 8 = 4 (x+2)

Subtract 3 from both sides:  4x + 5 = 4(x+2) - 3

There's an example of an equation with infinitely many solutions.  To solve it, work the process we used to create it in reverse.

Answer:

Step-by-step explanation:

Answer: C. 4

Step-by-step explanation:

The number 1.006 x 10⁷ has four significant figures. The power of 10 in scientific notation doesn't influence the number of significant figures.

The number of significant figures in the number 1.006 x 10⁷ is determined by the digits of the number itself, excluding any powers of 10. The power of 10 in scientific notation doesn't influence the number of significant figures. So, here, we only consider 1.006 which has four digits, all of which are significant. Therefore, the number 1.006 x 10⁷ has 4 significant figures.

So, the answer is B) 4.

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A recent college graduate is looking to begin saving for retirement. Option A is a savings account with 3.5% annual simple interest. Option B is a savings account with 3.5% annual interest compounded monthly. If the principal investment is the same for both options, the account which would have a larger balance after 10 years is  Option B because compound interest generates earnings from both principal and interest which is denoted as option C.

This is referred to as the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

Compound interest makes a sum of money grow at a faster rate than simple interest, because in addition to earning returns on the money you invest, you also earn returns on those returns or interest accrued at the end of every compounding period.

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Answer:

Option B will have the larger balance after 10 years because compound interest generates earnings from both principal and interest.

Answer:

A. y = 8 - 10sin(5πt)

B. y = 8 - 10sin(5π(17.2)) = 8 - 10sin(86π) ≈ 8 - 10(-0.99) ≈ 18.9

C. At 40 seconds, the point on the wheel is coming out of the water.

Answer:

Step-by-step explanation:

Given two complementary angles labeled (4x)° and (x-5)°, you want an equation for finding x, and the measures of the two angles.

The equation will reflect the fact that the angles have a sum of 90°:

  4x +(x -5) = 90

The equation simplifies to ...

  5x -5 = 90

  5x = 95

  x = 19

  ∠1 = 4x° = 76° . . . . . . measure of larger angle

  ∠2 = (x -5)° = 14° . . . . . measure of smaller angle

__

Additional comment

The little square at the vertex of the angles means that is a right-angle corner. Its measure is 90°. The two angles 1 and 2 together make up that right angle. That is the relation you use to form the equation.

Rewriting (simplifying) the sum ...

  4x +(x -5) = 5x -5

tells you nothing about the value of x. Any value for x will satisfy this equation. In order to find x, you need to relate this sum to something other than itself. (There is a reason why the angle is marked as a right angle.)

Answer:

117 miles

Step-by-step explanation:

174 miles ⇒ 58 gallons

A miles ⇒ 39 gallons

A = 174 miles * 39 gallons / 58 gallons

A = 117 miles

The sinusiodal function created from 2 given points is y = 3 sin (πx + 90) + 3

From the case, we have:

Minimum point = (-3,0)

Maximum point = (-9,6)

The sinusoidal fuction would be in the form of:

y = A sin (Bx - C) + D

where:

A = amplitudo

B = 2π / Period

C = Phase shift

D = Midline

First, we need to find the amplitudo:

A = (Y max - Y min) / 2

A = (6 - 0) / 2

A = 3

Periode = (X max - X min) x 2

Periode = (-9 - (-3) x 2

Periode = -6

B = 2π / Periode

B = 2π / 6

B = 1/3 π

D = (Y max + Y min) / 2

D = (6 + 0) / 2

D = 3

We can use one point to find the value of C:

0 = 3 sin (π/3 (-3) - C) + 3

0 = 3 sin (π - C) + 3

-3 = 3 sin (π - C)

sin (π - C) = -1

(π - C) = 270

C = -1/2 π

C = - 90

Then the sinusiodal function would be:

y = 3 sin (πx + 90) + 3

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Running a mile in five minutes is similar to moving at 12 mph (19.4 kph) on a treadmill.

the statutory mile, which has a length of 5,280 feet, is one example of a mile (1.609 km). Its original unit of measurement was the 5,000-foot-long Roman mile passus, often known as the "thousand paces."

Discover the distance formula, a Pythagorean theorem application, to determine the separation between two places. To get the separation between any two points, we can rewrite the Pythagorean theorem as d=((x 2-x 1)2+(y 2-y 1)2).

The formula for the distance between the points (a,b) and (c,d) is square root of (a,c)2 + (b,d)2. The distance in three dimensions between points (a, b, c) and (d, e, f) is equal to the square root of (a, d), (b, e), and (c, f)2.

We have,

Car speed = 0.4 miles per minute

We need to find the distance traveled in 30 minutes with a speed of 0.4 miles per minutes.

Speed is given by:

Speed = Distance / Time

Distance = Speed x Time

Distance = 0.4  x  30

Distance = 12 miles

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Answer:

To find the equation of the line passing through the point (3,2) and parallel to line x + 2y = 5, we need to use the point-slope form of a linear equation. The point-slope form of a linear equation is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

We know that two lines are parallel if they have the same slope. Since the given line x + 2y = 5 has a slope of -1/2, the equation of the line passing through (3,2) and parallel to x + 2y = 5 is y - 2 = -1/2 (x - 3), or simplifying y = -1/2x + 7/2

To find the equation of the line passing through the point (2,5) and parallel to the line x + 3y - 8, we need to use the point-slope form of a linear equation. The point-slope form of a linear equation is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

We know that two lines are parallel if they have the same slope. Since the given line x + 3y - 8 has a slope of 1/3, the equation of the line passing through (2,5) and parallel to x + 3y - 8 is y - 5 = 1/3 (x - 2), or simplifying y = 1/3x + 1/3

It's important to note that the lines are parallel because they have the same slope and different y-intercept, which means that they will never intersect.

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

Represent 15 out of 50 in fractions:

15/50

Simplify the fraction if you can and multiply by 100:

15/50 = 3/10

3/10 × 100 = 30%

An average and standard deviation in R is straightforward. The mean() function calculates the average and the sd() function calculates the standard deviation.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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Step-by-step explanation:

-2.4 + 0.4f - 12 - 6 can be simplified as follows:

-2.4 - 12 = -14.4

0.4f - 6 = 0.4f - 6

So, the simplified expression is:

-14.4 + 0.4f

or

-14.4 + 0.4f is the simplified form of -2.4 + 0.4f - 12 - 6

Answer: 10.6cm

Step-by-step explanation:

refer to the image for steps

The area of the shape as a sum is 2x^2 + 5x + 2.

The area of the shape as a product is (x+2) (2x+1).

What is area of a shape?

A figure surrounded by a barrier is referred to as a shape. Numerous things in shapes like square, rectangle, round, etc. are all around us.

The space around by a shape's perimeter or boundary is known as its area. Using particular mathematical methods, we may determine the area of shape for various geometric shapes.

Area as a sum

For this, we will simply add all the values given in the figure

⇒ x^2 + x^2 + x + x + x + x + x + 1 + 1

⇒ 2x^2 + 5x + 2

So, the area of the shape as a sum is 2x^2 + 5x + 2.

Area as a product

The shape given is a rectangle

Area of a rectangle is length * width

Now, the length is x+2 and the width is 2x+1

So, the area is

⇒(x+2) (2x+1)

So, the area of the shape as a product is (x+2) (2x+1).

Hence, the area of the shape as a sum and as a product are obtained.

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The difference in volume between the cereal box and pastry box is 167.991 cubic inches.

What are Dimensions?

Dimensions refer to the measurement of the size or extent of an object or space in a particular direction, such as length, width, and height. In the context of boxes, dimensions are used to describe the length, width, and height of a box, usually given in inches or centimeters.

To find the volume of a rectangular box, we use the formula:

Volume = length x width x height

Let's first find the volume of the cereal box:

Volume of cereal box = 7 inches x 12 inches x 2 inches = 168 cubic inches

Now let's find the volume of the pastry box:

Volume of pastry box = 3% inches x 3% inches x 2% inches = 0.009 cubic inches

Now, to find the difference in volume between the two boxes, we subtract the volume of the pastry box from the volume of the cereal box:

168 cubic inches - 0.009 cubic inches = 167.991 cubic inches

Hence, the difference in volume between the cereal box and pastry box is 167.991 cubic inches.

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According to the model, the systolic blood pressure increases by 1 unit (e.g. mmHg) for each year of age.

What is scatter ?

A scatter plot, also known as a scatter diagram or scatter graph, is a type of graph used to display the relationship between two quantitative variables. It is a useful tool for visualizing and analyzing data.

A scatter plot consists of a set of points, each representing a pair of (x, y) values. The x-axis represents one variable and the y-axis represents the other variable. The points on the plot are placed based on the values of the two variables.

The equation given is Y = x + 95, where Y represents the systolic blood pressure and x represents the age.

The slope of the linear equation represents the rate of change of the dependent variable (systolic blood pressure) with respect to the independent variable (age). In this case, the slope of the equation is 1.

Therefore, according to the model, the systolic blood pressure increases by 1 unit (e.g. mmHg) for each year of age.

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Answer:

blab blah??

Step-by-step explanation:

thats not a good question tbh

1) y intercept in the given equation is 6

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function-t he x-intercept and the y-intercept. A function's intercept is the location on the axis where the function's graph crosses it.

An equation of a straight line is written in the form: y=mx+c

where y is the y-coordinate,

m is the slope of the line,

x is the x-coordinate

and c is the y-intercept

Thus, from the question, y=3/4x+6, we can say

m=3/4 and c=6

Thus, y intercept for this equation is 6

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(h x $6.25) - $20 is a equation to figure how how many hair products she needs to sell to generate a profit of $120.

Profit is just the money left over after costs are paid. A loss is deemed to have occurred if the expenses exceeded the income.

A gain is a positive figure, whereas a loss is a negative one.

To determine whether a contract is lucrative or not, the phrases profit and loss are utilized. These words are frequently used in ordinary conversation. If the selling price exceeds the cost price, the difference between the two amounts is known as the profit.

The equation to determine how many hair products Jackie must sell to make a profit of $120 would be:

$120 (profit) = (h x $6.25) - $20 (cost of online membership)

where h is the number of hair products sold.

To solve for h, we can first add $20 to both sides of the equation:

$120 + $20 = h x $6.25

Next, we can divide both sides of the equation by $6.25 to find the value of h:

h = ( $120 + $20 ) / $6.25

h = 20

So Jackie must sell 20 hair products to make a profit of $120.

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(h x $6.25) - $20 is an equation to figure how many hair products she needs to sell to generate a profit of $120.

Profit is just the money that remains after expenses are covered. A loss is deemed to have occurred if the expenses exceeded the income.

A gain is a positive figure, whereas a loss is a negative one.

The terms profit and loss are used to assess how valuable a transaction is. In everyday discourse, these terms are often employed. The difference between the two sums is referred to as the profit if the selling price is higher than the cost price.

The equation to determine how many hair products Jackie must sell to make a profit of $120 would be:

$120 (profit) = (h x $6.25) - $20 (cost of online membership)

where h is the number of hair products sold.

To solve for h, we can first add $20 to both sides of the equation:

$120 + $20 = h x $6.25

Next, we can divide both sides of the equation by $6.25 to find the value of h:

h = ( $120 + $20 ) / $6.25

h = 20

So Jackie must sell 20 hair products to make a profit of $120.

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To solve for x in an equation, you will need to use algebraic techniques to isolate x on one side of the equation. The specific steps will depend on the equation you are trying to solve.

Here are a few examples of how to solve for x in different types of equations:

Linear equation: An equation of the form ax + b = 0, where a and b are constants. To solve for x, you would subtract b from both sides and then divide both sides by a.

Quadratic equation: An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants. To solve for x, you would factor the equation or use the quadratic formula.

System of equations: A set of equations with multiple variables, such as 2x + 3y = 5 and 4x + 6y = 10. To solve for x, you would use elimination or substitution method.

The equation could be described by "the product of three and the reciprocal of four divided by three"

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

To solve this problem we must perform the corresponding algebraic operations with mixed fraction.

Original equation:

4 / (1 1/3)

A mixed operation is solved as follows:

For the denominator: the same denominator is placed.

For the numerator:

We transform the mixed fraction into improper fraction and we have:

1 1/3 = [(3*1) + 1)] /3  = [3+ 1] /3 = 4/3

Now, describing the equation with the improper fraction we get:

4 / (4/3)

Solving the division with fractions we have:

(4*3) / 4

This means that "the product of three and the reciprocal of four divided by three"

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Answer:

$807.39

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the compound interest formula and solve for A:

[tex]\implies A=500\left(1+\dfrac{0.04}{12}\right)^{12 \cdot 12}[/tex]

[tex]\implies A=500\left(1.00333333...\right)^{144}[/tex]

[tex]\implies A=500\left(1.61478492...\right)[/tex]

[tex]\implies A=807.392461...[/tex]

Therefore, Alyson will have $807.39 (nearest cent) in her account at the end of 12 years.

When we have a right triangle, Cos = a / h, according to the cosine law. In this situation, the letter "a" stands for adjacent.

The hypotenuse, denoted by the letter "h," can be calculated using the Pythagorean Theorem. All you need to get cosine is the hypotenuse and the neighboring side.

The ratio of the length of the side next to the angle divided by the length of the triangle's hypotenuse is known as the cosine of an angle.

The triangle's sides, a, b, and c, are determined using the cosine formula, which is given as

c = [a2 + b2 - 2ab cos C]

According to the Cosine Rule in trigonometry, the square of the length of any side of a given triangle equals the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle that separates them.

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the value x in this equation will be ±√1/3.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally, the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The given equation x² - 1/3 =0

x² = 1/3

taking square root both side

x = ±√1/3

Hence the value x in this equation will be ±√1/3.

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