If the side length of a square increases from 3 inches to 7 inches the square’s perimeter:

To find the product of all integer divisors of 105 that also divide 14, we need to first find all the divisors of 105 and then find which of those divisors also divide 14.

The divisors of 105 can be found by listing all the positive integers that divide 105 exactly. To do this, we can use a divisibility test for each number up to the square root of 105:

Does 1 divide 105 exactly? Yes, so 1 is a divisor of 105.

Does 3 divide 105 exactly? Yes, so 3 is a divisor of 105.

Does 5 divide 105 exactly? Yes, so 5 is a divisor of 105.

Does 7 divide 105 exactly? Yes, so 7 is a divisor of 105.

Does 11 divide 105 exactly? No.

Does 15 divide 105 exactly? Yes, so 15 is a divisor of 105.

Does 21 divide 105 exactly? Yes, so 21 is a divisor of 105.

Does 35 divide 105 exactly? Yes, so 35 is a divisor of 105.

Since 105 is a composite number, the divisors of 105 can also be found by multiplying pairs of the divisors found above. This gives us the following divisors of 105:

1, 3, 5, 7, 15, 21, 35, 105

Next, we need to find which of these divisors also divide 14. To do this, we can perform a similar divisibility test for each divisor:

Does 1 divide 14 exactly? Yes, so 1 is a divisor of 14.

Does 3 divide 14 exactly? No.

Does 5 divide 14 exactly? No.

Does 7 divide 14 exactly? Yes, so 7 is a divisor of 14.

Does 15 divide 14 exactly? No.

Does 21 divide 14 exactly? No.

Does 35 divide 14 exactly? No.

So, the divisors of 105 that also divide 14 are 1 and 7. To find the product of these divisors, we simply multiply them:

1 * 7 = 7

Thus, the product of all integer divisors of 105 that also divide 14 is 7.

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Answer:

8 / 47 = 0.17021276595 btw u can just use a calculator

The system of equations is x + y = 16 & 6x + 4y = 76, then  the amount x is 6 yards of regular quilting fabric and the amount y is 10yards of sateen fabric she purchased.

She bought 6 Sateen fabrics and 10 quilting fabrics.

She uses quilt to make two types of fabrics.

Let the amount of each sateen fabric = x

Let the amount of each quilting fabric = y

The Sateen fabrics cost $6 per yard.

Therefore, for x amount it will be as follows:

6x

The quilting fabrics cost $4 per yard.

Therefore, for y amount it will be as follows:

4y

A system of equations is a collection of two or more equations with a same set of unknowns.

According to the condition the amount of quilting is 'x' and the amount of sateen is 'y', then the price of the quilting fabric is 6x and the price of then sateen fabric is 4y;

The 76$ she spends can be written as 4x+6y=76;

Total of 16 yards can be written as x+y=16;

So the required system of Equations is:

⇒4x+6y=76

⇒x + y=16

Therefore,

⇒x + y = 16

⇒6x + 4y = 76

⇒6x + 6y = 96

⇒6x + 4y = 76

⇒2y = 20

⇒y = 20 / 2

⇒y = 10

⇒x + y = 16

⇒x + 10 = 16

⇒x = 16 - 10

⇒x = 6

Therefore, the system of equations is x + y = 16 & 6x + 4y = 76, then  the amount x is 6 yards of regular quilting fabric and the amount y is 10yards of sateen fabric she purchased.

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Answer:

Step-by-step explanation:

Let's call the number of rows "x". The number of plants in each row would be 2x - 10. We know that the total number of plants is 600, so we can set up an equation:

x * (2x - 10) = 600

Expanding the left side:

x^2 + 10x - 600 = 0

We can solve for x using the quadratic formula:

x = (-10 ± √(10^2 - 4 * 1 * -600)) / 2 * 1

x = (-10 ± √(100 + 2400)) / 2

x = (-10 ± 50) / 2

x = 20 or -5 (but x cannot be negative, as the number of rows must be a positive integer)

So, there are 20 rows with 10 plants in each row. The number of plants in each row is 2x - 10 = 2 * 20 - 10 = 30.

The number of mice in the category is 38

From the question, we have the following parameters that can be used in our computation:

The histogram

The total number of mice with birth weights below 12 g is the sum of the frequency of bars less than 12 g

Using the above as a guide, we have the following:

Total = 4 * 4 + 4 + 4 + 7 + 7

Evaluate

Total = 38

Hence, the number of mice is 38

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The minimum payment of the credit card will be $40.37.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Daniel's credit card has a minimum monthly payment of 2.78% of the card's balance. If Darryl currently owes $1,452.28.

The minimum payment will be calculated as;-

Minimum payment = ( 1452.28 )  x ( 2.78 / 100 )

Minimum payment = $40.37

Therefore, the minimum amount for the credit card bill is $40.37.

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60<5x+40

60-40<5x

20<5x

x>4

Answer:

y = -3(x + 0.5)² - 45.25

Step-by-step explanation:

a = -3

b = -3

c = -47

h = -b/2a = -(-3)/2(-3) = -1/2

k = c - b²/(4(-3)) = -46 - (-3)²/(-12) = -45.25

f(x) = -3(x - (-1/2))² - 45.25

y = -3(x + 0.5)² - 45.25

The infinite series ax/a+x can be written in the form of a summation notation as [tex]Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex], which can be used to calculate the sum of the series for any value of x and a.

The infinite series representing ax/a+x can be written as:

[tex]∑n=0∞(−1)nx^n+1a^n+1[/tex]

The first 5 terms of this series can be calculated as follows:

[tex]Term 1 = (x/(a+x))Term 2 = -(x^2/a^2+2ax+x^2) 4Term 3 = (x^3/a^3+3a^2x+3ax^2+x^3) Term 4 = -(x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4)Term 5 = (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5)[/tex]

The general formula for the infinite series can be written as:

[tex]∑n=0∞(−1)nx^n+1a^n+1 = (x/(a+x)) - (x^2/a^2+2ax+x^2) + (x^3/a^3+3a^2x+3ax^2+x^3) - (x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4) + (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5) + ...[/tex]

The summation notation for this series can be written as:

[tex]∑n=0∞(−1)nx^n+1a^n+1 = Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex]

This formula can be used to calculate the sum of the infinite series for any value of x and a.

The infinite series ax/a+x can be written in the form of a summation notation as [tex]Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex], which can be used to calculate the sum of the series for any value of x and a.

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Answer:

x = 3

Step-by-step explanation:

[tex]2x - 9 = -3[/tex]

[tex]2x = 6[/tex]

[tex]x = 3[/tex]

Answer:

7.8 cm

Step-by-step explanation:

One tenth of a centimeter = [tex]\frac{1}{10} (1 cm)[/tex] = 0.1 cm . This means the answer has to be rounded to 1 decimal place.

Length of BE = Length of ED = [tex]\frac{6}{2}[/tex] = 3 cm

Focus on the triangles AED and CED. These two are right-angled triangles.

In both triangles, sides AE and CE are perpendicular sides, whose lengths will be calculated using Pythagorean Theorem:

Triangle AED:

[tex]AD^{2} = AE^{2} + ED^{2}[/tex]

[tex]AD^{2} - ED^{2} = AE^{2}[/tex]

[tex]AE^{2} = 6^{2} - 3^{2}[/tex]

Taking square root on both sides of the equation to get rid of the square:

[tex]AE = \sqrt{6^{2} -3^{2} }[/tex]

[tex]AE = \sqrt{36 - 9}[/tex]

[tex]AE = \sqrt{27}[/tex] cm

Triangle CED:

[tex]CD^{2} = CE^{2} + ED^{2}[/tex]

[tex]CE^{2} = CD^{2} - ED^{2}[/tex]

[tex]CE^{2} = 4^{2} - 3^{2}[/tex]

Taking square root on both sides of the equation to get rid of the square:

[tex]CE = \sqrt{4^{2} -3^{2} }[/tex]

[tex]CE = \sqrt{16 - 9}[/tex]

[tex]CE = \sqrt{7}[/tex] cm

Length of AC = Length of AE + Length of EC

∴ Length of AC = [tex](\sqrt{27} + \sqrt{7})[/tex] cm

                          = 7.841 cm

  Length of AC = 7.8 cm (Rounded to the nearest tenth of a centimeter)

The value of t is 8 and the value of r is 8√2. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of triangle sides, angles, and relationships is the focus of the mathematical field of trigonometry.

We are given a right angled triangle with an angle 45° and the perpendicular measuring 8.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan 45° = 8/t

⇒1 = 8/t (tan 45° = 1)

⇒t = 8

Similarly,

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos 45° = 8/r

⇒1/√2 = 8/r (cos 45° = 1/√2)

⇒r = 8√2

Hence, the value of t is 8 and the value of r is 8√2.

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Since, there are multiple questions so, the question answered above is attached below.

Answer:

Let x be the number of red M&Ms.

Then the number of blue M&Ms is x + 5, the number of yellow M&Ms is x - 9, and the number of brown M&Ms is (1/2)x + 13.

The total number of M&Ms is 135, so we can write an equation:

x + (x + 5) + (x - 9) + (1/2)x + 13 = 135

Simplifying this equation, we get:

3.5x + 9 = 135

Subtracting 9 from both sides, we get:

3.5x = 126

Dividing both sides by 3.5, we get:

x = 36

So there are 36 red M&Ms, 41 blue M&Ms (36 + 5), 27 yellow M&Ms (36 - 9), and 31 brown M&Ms (1/2 * 36 + 13).

Answer:

Step-by-step explanation:

r: the number of red M&Ms

b: the number of blue M&Ms

y: the number of yellow M&Ms

br: the number of brown M&Ms

We can translate the given information into equations:

r + b + y + br = 135 (the total number of M&Ms is 135)

b = r + 5 (there are five more blue M&Ms than red ones)

y = r - 9 (there are nine less yellow M&Ms than red ones)

br = 13 + (1/2)r (there are thirteen more brown M&Ms than half the number of red ones)

We can use equations 2, 3, and 4 to substitute for b, y, and br in equation 1:

r + (r + 5) + (r - 9) + (13 + (1/2)r) = 135

Simplifying this equation, we get:

3.5r + 9 = 135

Subtracting 9 from both sides, we get:

3.5r = 126

Dividing both sides by 3.5, we get:

r = 36

Now that we know the value of r, we can use equations 2, 3, and 4 to find the values of b, y, and br:

b = r + 5 = 36 + 5 = 41

y = r - 9 = 36 - 9 = 27

br = 13 + (1/2)r = 13 + (1/2)(36) = 31

Therefore, the number of red, blue, yellow, and brown M&Ms in the mixture are 36, 41, 27, and 31, respectively.

The BEST estimate for the x-coordinate of the solution to this system is -4

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we can see that the lines intersect at

Approximately (-4, 3)

This means that the x-cooridnate of the solution is

x = -4

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Answer:

Step-by-step explanation:

Answer:

[tex]slope = - \frac{8}{5} [/tex]

Step-by-step explanation:

So it looks like on the line, we have two dots.

Let's find those points, starting from the left one.

The left point is: (-1, 4) --- (x1, y1)

The right point is: (4, -4) --- (x2, y2)

**These are in (X, Y) form**

Now to find the slope, you use this equation

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Now let's plug our numbers into this equation

[tex]m = \frac{ - 4 - 4}{4 - ( - 1)} = \frac{ - 8}{5} = - \frac{8}{5} [/tex]

Two negatives make a positive, so 4-(-1) is the same as 4+1.

Answer:

$ 56.34

Step-by-step explanation:

    height = h = 2. 1m

    diameter = 0.7m

            radius = diameter ÷2

                    r  = 0.7 ÷ 2 = 0.35 m

Substitute the values of r and h in the below mentioned formula and find the surface area of the tank.

[tex]\boxed{Area \ of \ cylindrical \ tank = 2\pi r((r + h)}[/tex]

                                            = 2 * 3.14 * 0.35 (0.35 + 2.1)

                                            = 2 * 3.14 * 0.35 * 2.45

                                            = 5.39 square meter

To find the cost of painting the surface area of tank, multiply the cost of painting per square meter by the total surface area of tank.

Cost of painting = 5.93 * 9.50

                           = $ 56.34

The surface area and volume of the figure is 108 cm² and 96 cm³ respectively

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The surface area of the figure = 2(1/2 * 4 cm * 3 cm) + (8 cm * 3 cm) + (8 cm * 4 cm) + (8 cm * 5 cm) = 108 cm²

The volume of figure = area of base * height = (1/2 * 4 cm * 3 cm) * 8 cm = 96 cm³

The surface area and volume of the figure is 108 cm² and 96 cm³ respectively

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The area of the brick walkway in the front yard is 122 square feet.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

We know, The area of a trapezoid is,

(1/2)×(sum of the two parallel sides)×height, And The area of a rectangle is (length×width).

From the given, Diagram the total area would be the sum of the area of a rectangle and a trapezoid which is,

= [(15×6) + (1/2)(10 + 6)×4] square feet.

= [90 + 32] square feet.

= 122 square feet.

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A triangle has three bisectors, each of which is a line that divides one of the angles of the triangle into two equal parts.The incenter is equidistant from the three sides of the triangle and is the center of the inscribed circle, which is the circle that is tangent to all three sides of the triangle.

A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is one of the simplest and most fundamental shapes in geometry, and it is widely studied in mathematics, science, and engineering. Triangles can have different types of angles and sides, which give rise to various classifications and properties. For example, a triangle can be classified as equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), or scalene (all sides and angles are different).

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Answer:

Step-by-step explanation:

A = bh.

To solve, find factors of seven the fit the description such as 7 and 1.

The length is 7, the width is 6 units less.

So, the width is 1un and the length is 7un.

Answer:

[tex] \frac{ - 17}{2} [/tex]

Step-by-step explanation:

[tex]3(x - 4) = 5(x + 1)[/tex]

[tex]3x - 12 = 5x + 5[/tex]

[tex]3 - 12 - 5x = 5x + 5 - 5x [/tex]

[tex]3x - 12 - 5x = 5[/tex]

[tex]3x - 12 - 5x + 12 = 5 + 12[/tex]

[tex]3x - 5x = 5 + 12[/tex]

[tex]3x - 5x = - 2x[/tex]

[tex]5 + 12 = 17[/tex]

[tex] - 2x = 17[/tex]

[tex] \frac{ - 2x}{2} = \frac{17}{ - 2} [/tex]

[tex]x = \frac{17}{ - 2} [/tex]

[tex]x = \frac{ - 17}{2} [/tex]

The coordinate for the image of point H( -1, -5) under a 90° clockwise rotation about the origin is, (- 5, 1)

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The coordinate of the point H( -1, -5)

Now, The rule for the 90° clockwise rotation about the origin is,

(x, y) = (y, - x)

Hence, The coordinate for the image of point H( -1, -5) under a 90° clockwise rotation about the origin is,

(- 1, - 5) = (- 5, 1)

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The values of x in the triangles are x = 17 and x = 52

Triangle 1

From the question, we have the following parameters that can be used in our computation:

The triangle

Using the law of cosines to solve for x, we have

x^2 = 7^2 + (8√2)^2 - 2 * 7 * (8√2) * cos(135 degrees)

Evaluate the like terms and multiply

x^2 = 289

Take the square roots

x = 17

Triangle 2

Here, we have"

Using the law of cosines to solve for x, we have

x^2 = 28^2 + 32^2 - 2 * 28 * 32 * cos(120 degrees)

Evaluate the like terms and multiply

x^2 = 2704

Take the square roots

x = 52

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Then you have 6 different combination to choose from.

"Information available from the question"

For dessert you can choose

Apple, cherry, blueberry, or peach pie to eat, and milk or juice to drink.

To find the how many different combinations of one pie and one beverage are possible?

Now, According to the question:

To eat: Apple pie, Cherry pie, or peach pie = 3 desserts

To drink: milk or juice = 2

Then you can choose one from each:

Then your choices are:

(apple, milk) (apple, juice) (cherry, milk)(cherry, juice) (peach, milk) and (peach, juice)= 6

Then you have 6 different combination to choose from.

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The values of the expressions when evaluated are 10000 and 1000

From the question, we have the following parameters that can be used in our computation:

This means that

Species = 10^4 = 10000

Threatened = 10^3 = 1000

Hence, the values are 10000 and 1000

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Answer:

2×(a+b)

Step-by-step explanation:

to find the perimeter of a rectangle, we should use this formula

This is my answer so if I am wrong then correct me

Erik’s average speed was 113.957 miles per hour.

Average speed refers to the overall speed of an object over a certain time period. To find average speed, we need to divide the total distance traveled by the time it took to travel that distance.

In this case, Erik rode his motorbike 2623 miles in 23 hours, so we need to divide 2623 by 23 to find his average speed in miles per hour.

Mathematically, average speed can be represented as follows:

Average speed = Total distance ÷ Total time

So in this case,

Average speed = 2623 miles ÷ 23 hours

Calculating the answer, we get

Average speed = 113.957 mph

Complete Question:

Erik rides his motorbike 2623 miles in 23 hours. What is Erik’s average speed in miles per hour? Enter the number in the box.

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The standard form of the given exponent is 0.00000094359.

What are Exponents?

A number's exponent demonstrates how many times we are multiplying a given number by itself. 3⁴, for instance, indicates that we are multiplying 3 by four. 3 × 3 × 3 × 3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.

[tex]9.4359 \times 10^{-7}[/tex]

Use  [tex]10^{-7} = 1/10^7[/tex]  Because a⁻ᵇ = 1/aᵇ

= 9.4359  ×1/10⁷

= ( 9.4359)/10⁷

= ( 9.4359)/10000000

= 0.00000094359

The standard form of the given exponent is 0.00000094359

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The length of the steering device will be 4.5 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The steering device extends to point T, and the diameter of the steering wheel is 15 inches long. Then the length of the steering device is given as,

7.5² = h² + 6²

56.25 = h² + 36

h² = 56.25 - 36

h² = 20.25

h = 4.5 inches

The length of the steering device will be 4.5 inches.

The diagram is given below.

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