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The value of x is 20 units and the measure of DE is 35 units.

A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.

Given that, DE=x+15, DF=55, and EF=10.

Here, DF=DE+EF

55=x+15+10

55=x+25

x=20

So, DE=x+15=35

Therefore, the value of x is 20 units and the measure of DE is 35 units.

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Answer: 10.6cm

Step-by-step explanation:

refer to the image for steps

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 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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Answer:

B.The car had been driven 65,000 miles when Franklin purchased it.

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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Two parallel lines called the x axis and the y axis are employed for graph or plot points. The x axis is on the horizontal number line, while the y axis is on the vertical line. The positive and negative axes of the x axis are arranged to the right and left of the origin, respectively.

The following format is employed to plot a point's coordinates: (x, y). As is evident, the x-coordinate is frequently placed first. For example, we have determined the x and y coordinates for the respective points B and D in the diagram we have been using. Point B's x-coordinate is 100.

Any position on the plane may have its x- and y-coordinates established using its horizontal and vertical distances from the origin. In essence, what we do when we sketch a point is the complete antithesis of what we do here.

Labelling:

Our x-coordinate is as follows:

Positive if it's in the appropriate area of our plane.

If it is on the left side of our plot, it is not ideal.

If it is on the x-axis, then it is 0.

Our y-coordinate is as follows:

If it is in the top part of our plot, it is a good indicator.

If it is in the bottom part of our plot, it is not good.

If it is on the y-axis, it will be 0.

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Answer: 9.49 or (484/51)

Step-by-step explanation:

121/12.75 = 9.49 as a decimal or 484/51 as a fraction

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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The average rate of change in the number of inches of snowfall from January 8 to January 11 include the following: A. 2/3 in.

In Mathematics, the rate of change is sometimes referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of snowfall (y) with respect to the date (x), which represents a line that is passing through the data points (8, 10) and (11, 12):

Rate of change, m = (12 - 10)/(11 - 8)

Rate of change, m = 2/3.

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Complete Question:

Find the average rate of change in the number of inches of snowfall from January 8 to January 11.

Choose: 2/3 in. 2 in. 3 in. 6 in.

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:

x<13

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

x+25/5=8

x+25=40

x=40-25

x=15

The factors of equation, x²- 9x + 18 = 0 are (x- 3)(x- 6), where x is variable.

Factorization is a mathematical process that is applied to split a number, an expression, matrix etc. into the product of factors such that when we multiplied these factors again we get the original one. We have, an equation is x² - 9x + 18 = 0 --(*) and we have to factorize it. Steps to factorize the quadratic equation, ax² + bx + c = 0, are :

Now, comparing the equation (*) with standard equation we get, a = 1 , b = -9 , c = 18.

So, Split the number 9, into 6 and 3

=> x² - 9x + 18

=> x² - 6x - 3x + 18

=> (x² - 6x) - (3x - 18) [ grouping]

=> x( x - 6) - 3( x-6) [ factors of group ]

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

so, x² - 9x + 18 = (x- 3)(x- 6) = 0 helps to get the solution of it (x- 3)(x- 6) = 0 => x = 6,3

Hence, the required factors are (x- 3)(x- 6).

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Complete question:

What is the factor of x² - 9x + 18 = 0?.

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 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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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:

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.

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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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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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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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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Since the line is constantly at 6, it crosses the y-axis at that point. The slope is 0 because the line is horizontal.

The slope is 0 0 when expressed in the slope-intercept form. All parallel lines to y=6 have a slope of 0, which is the same.

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

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Answer:

So, the area of the rectangle is

13

×

3

=

39

square centimeters.

The figure was divided such that none of the shapes overlapped.

However, the shapes combinedly form the entire figure.

So, the area of the entire figure is

36

+

39

=

7

The percentage of 100 square quadrilateral grid shaded is 96%.

since there are 4 unshaded grids and rest 96 are shaded then the percentage will be

shaded percentage = 96 × 100/100 = 96%

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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

Mr. Sahid has 215 pages left to read.

To determine how many pages Mr. Sahid has left to read, you simply need to subtract the number of pages he has already read (177) from the total number of pages in the book (392).

392 pages (total number of pages in the book)

177 pages (number of pages already read)

= 215 pages (number of pages left to read)

So, Mr. Sahid has 215 pages left to read.

It's important to note that this calculation assumes that Mr. Sahid has not skipped any pages and has read every page from start to finish.

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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