referring to question 1, what is the predicted strength of a weld with a diameter of 51? a. -812.72 b. -503.16 c. -81.82 d. we should not use the least squares regression line to calculate this value

The slope of the line of image 1 is 2

The slope of the line of image 2 is 5/2

The slope of the line of image 3 is 2/5.

The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.

The slope of the line of image 1 is:

The line is passing through the points (6, 10 and (2, 2)

So,

Slope=(y₂-y₁)/(x₂-x₁)

m=(2-10)/(2-6)

m=8/4

m=2

Therefore, the slope of the line for image 1 is 2.

Hence, option A is correct.

The slope of the line for image 2 is:

The line is passing through the points (3, 4) and (7, 14)

Slope=(y₂-y₁)/(x₂-x₁)

m=(14-4)/(7-3)

m=10/4

Therefore, the slope of the line for the image 2 is 5/2.

Hence, option F is correct.

The slope of the line for image 3 is:

The line is passing through the points (2, 1) and (7, 3)

Slope=(y₂-y₁)/(x₂-x₁)

m=(3-1)/(7-2)

m=2/5

Therefore, the slope of the line for the image 3 is 2/5

Therefore, option D is correct.

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The length of the sides of the special triangles, found using the relationship between the sides of the triangles are as follows;

(1) Length of the legs is 20 each

Length of the hypotenuse = 20·√2

(2) Length of the leg = 5

Length of the hypotenuse = 5·√2

5-50 a. Length of the leg is 10·√3

Length of the hypotenuse is 20

b. Length of the leg = 4

Length of the hypotenuse = 4·√2

c. Length of each leg = 8

d. Length of the leg = 9·√3

Length of the hypotenuse = 18

e. Length of the shorter leg = 4.5

Length of the longer leg = 4.5·√3

f. Length of the legs = 3·√2 each

5-51

What are triangles?

A triangle is a three sided polygon, that has a sum of interior angles of 180°

The lengths of the missing sides in the triangles found using the 30°–60°–90°, and 45°–45°–90°, triangle patterns are as follows;

In a 30°, 60°, 90° triangle, if the length of the shortest leg is x, the length of the hypotenuse is 2·x, and the length of the other leg is x·√3

In a 45°, 45°, 90° triangle, the length of the legs are the same, and the length of the hypotenuse is √2 multiplied by the length of one leg.

(1) The length of the legs are the same and equivalent to 20

The length of the hypotenuse side is 20·√2

(2) The length of the legs are the same and equivalent to 5

The length of the hypotenuse 5·√2

5-50 a. In the 30°, 60°, 90° triangle, the length of the adjacent, longer leg is 10·√3

The length of the hypotenuse side is 2·x

b. The triangle is a 45°, 45°, 90°, triangle

The length of the legs are 4 unit each

The length of the hypotenuse is 4·√2

c. The length of the hypotenuse in the 45°, 45°, 90° is 8·√2, therefore, the length of the legs are;

8 units each

d. The length of the shortest leg in the 30°, 60°, 90°, right triangle is 9, therefore, the length of the hypotenuse side is 2 × 9 = 18

The length of the longest leg is 9·√3

e. The length of the hypotenuse in the 30°, 60°, 90°, right triangle is 9 units, therefore, the length of the shortest leg is 4.5 units

The length of the longest leg is 4.5·√3

f. The length of the hypotenuse side of the 45°, 45°, 90°, right triangle is 6, therefore;

The length of the legs are 6/√2 = 3·√2

5-51

The dimensions of the side length of the special right triangles are;

In a 30°-60°-90° triangle, if the length of the shortest leg is x, then;

The length of the hypotenuse is 2·x

The length of the longer leg is x·√3

In a 45°-45°-90° right triangle, the length of the legs are the same, and the length of the hypotenuse is √2 multiplied by the length of one leg.

Please attached diagrams of the 45°, 45°, 90°, and the 30°, 60°, 90° triangles created with MS Word

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Applying the formula of the surface area of a box, the total amount of plastic wrapping needed to cover the box is: 697 cm².

The total surface area of a box is the sum of all the areas of the six faces of the box.

The area of each face can be found by multiplying the length by the width of that face.

The area of each face is given as:

Area = length * width.

To find the amount of plastic wrapping needed to cover the entire box, you first need to find the surface area of the box.

The surface area of the box is given by:

Surface area = 2(19 cm * 14 cm) + 2(19 cm * 1.5 cm) + 2(14 cm * 1.5 cm)

= 2(266 cm²) + 2(28.5 cm²) + 2(21 cm²)

= 532 cm² + 57 cm² + 42 cm²

= 631 cm²

To find the total amount of plastic wrapping needed to cover the box, you need to add the extra 66 cm² needed to allow for the overlapping at the edges.

This gives a total of 631 cm² + 66 cm² = 697 cm² of plastic wrapping needed to cover the box.

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Answer:

x=1,13

Step-by-step explanation:

(x – 7)^2 = 36

To solve for x take the square root of each side

sqrt((x – 7)^2) = sqrt(36)

x-7 = ±6

Splitting into two equations

x-7 = 6    x-7 = -6

Add 7 to all sides

x-7+7 = 6+7    x-7+7 = -6+7

x=13                          x=1

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(x - 7)^2 = 36}[/tex]

[tex]\mathsf{(x - 7)(x - 7) = 36}[/tex]

[tex]\mathsf{x^2 - 14x + 49 = 36}[/tex]

[tex]\text{SUBTRACT 36 to BOTH SIDES}[/tex]

[tex]\mathsf{x^2 - 14x + 49 + 49 = 36 + 49}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x^2 - 14x + 13 = 36 + 49}[/tex]

[tex]\mathsf{x^2 - 14x + 13 = 0}[/tex]

[tex]\text{FACTOR the LEFT SIDE of your equation}[/tex]

[tex]\mathsf{(x - 1)(x - 13) = 0}[/tex]

[tex]\text{SET the FACTORS to EQUAL to 0}[/tex]

[tex]\mathsf{Equation\ \#1.)\ \rightarrow x - 1 = 0}[/tex]

[tex]\mathsf{Equation\ \#2.)\ \rightarrow x - 13 = 0}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x = 1 \ or\ x = 13}[/tex]

[tex]\huge\text{Thus, your answer should be: } \boxed{\mathsf{x = 1 \ or\ x = 13}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The value of x for the given expressions is 3.

Triangles are classified into three different types based on their sides. An isosceles triangle, a scalene triangle, and an equilateral triangle. Equilateral triangles are different from isosceles and scalene triangles.

An equilateral triangle is a triangle with all three equal sides and equal angles. An equilateral triangle is also called an equilateral triangle because each angle has a value of 60 degrees. Equilateral triangles are considered regular polygons or equilateral triangles because they have equal angles and equal sides.

In ∆ ABC

∠A= ∠B=∠C

Triangle is equilateral triangle.

All the triangle side will be equal

6x-3=3x+6=5x

=6x-3 =3x+6

=3x=g

X=3

Thus, X = 3

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The probability that out of 52 card the selected 3 cards are not a face card is 0.183.

There are 12 face cards in a deck of 52 cards.

The probability of selecting 3 cards which should not be a face card is ,

=30c3 / 52c3

= 4060 / 22,100

= 0.183

Combination is a means to choose items from a collection without worrying about their order. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

It is easy to count the number of combinations in smaller cases, but the likelihood of a set of combinations is also higher in cases with many groups of components or sets. As a result, a formula has been developed to determine the number of items that could be chosen, i.e., nCr .

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Answer: 6.40

Step-by-step explanation:

1.20 times 3 = 3.60

10 - 3.60 = 6.40

The required elementary matrix E such that EA = B is

[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].

Any matrix obtained by performing a single elementary row operation on the identity matrix is called an elementary matrix.

The elementary operations are as follows:

1. Interchange the two rows of a matrix

2. Multiply a row of a matrix by the non-zero scalar k.

3. Add k-times of a row into another row of the matrix.

Each type of elementary operation may be performed by matrix multiplication, using square matrices called elementary operators.To perform an elementary row operation on A, an n×m matrix, take the following steps:

1. To find E, the elementary row operator, apply the operation to an n×n identity matrix.

2. To carry out the elementary row operation, premultiply A by E.

We want to interchange the first and second rows of A, a 3×3 matrix to  get B. To create the elementary row operator E, we interchange the first and second rows of the identity matrix I3:

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex] is changed to  [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].

So, [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex][tex]\left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right][/tex]

Thus, the required elementary matrix E such that EA = B is

[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]

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The indicated angles in the parallel lines cut by the transversal are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, linear angles, vertically opposite angles, alternate exterior angles etc.

Therefore, according to the diagram the two parallel lines are cut by a transversal. Let's use the angle relationships to find the m ∠1 and m∠3.

m ∠6 = 78 degrees.

m ∠1 = m ∠ 7 (alternate exterior angles)

Alternate exterior angles are congruent.

Hence,

m ∠7 = 180 - 78 = 102 degrees

m ∠ 1 = 102 degrees

m ∠ 1 = m ∠ 3 (vertically opposite angles)

vertically opposite angles are congruent.

m ∠ 3 = 102 degrees.

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Answer:

88 feet

Step-by-step explanation:

Use this formula

Circumference= 2*22/7*Radius

22/7 * 14=

2*44 =

88 feet

y = 5 - x. is the linear equation in point-slope form.

Points  (1,4) and (6,-1).

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).

where , m = slope of the line. x₁ = the x-coordinate of the first point.

m = (-1 - 4) / (6 - 1 ).

m= -1

Substitute the values into the point-slope form,

y − y 1 = m ( x − x 1 ) .

y − 4 = -1 ( x − 1) .

y − 4 =  1 - x.

y = 5 - x.

complete question : Write the linear equation in point-slope form that passes through the given points. (1, 4) and (6, -1).

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Answer:

volume = 960π m³ ; surface area = 368π m²

Step-by-step explanation:

base area = 8²π = 64π m²

base perimeter = 8 x 2 x π = 16π m

lateral area = 16π x 15 = 240π m²

surface area = 2 x 64π + 240π = 128π + 240π = 368π m²

Volume = 64π x 15 = 960π m³

The value after simplifying the number 10^3(10)^4 is 10⁷.

The simplification of given number can be done through the rule of exponent -

[tex] {a}^{m} [/tex] × [tex] {a}^{n} [/tex] = [tex] {a}^{m+n} [/tex], where m and n are the powers of a.

Now, keeping the values in formula -

Value = [tex] {10}^{3} [/tex] × [tex] {10}^{4} [/tex]

Based on the rule, the simplified for these powers will be

Value = [tex] {10}^{3+4} [/tex]

Performing addition of powers on Right Hand Side of the equation

Value = [tex] {10}^{7} [/tex]

Alternatively, the numbers can be expanded and multiplied. Further write the result in scientific notation as above. However, it will a long method which is not practical for very large numbers.

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Answer:

3. 44 root= between 6 and 7 (more on the 7 side)

The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:

C. m∠5 + m∠6 =180°.

D. m∠2 + m∠3 = m∠6.

E. m∠2 + m∠3 + m∠5 = 180°.

In Geometry, the Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two (2) adjacent angles would be equal to 180º when two (2) parallel lines are cut through by a transversal:

m∠5 + m∠6 =180°.

In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:

m∠2 + m∠3 = m∠6.

Additionally, the sum of all the angles that are formed by a triangle is equal to 180º and this is given by:

m∠2 + m∠3 + m∠5 = 180°,

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The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)

A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.

Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)

x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)

Factoring x^2 – x – 20,

x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)

Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:

(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)

Note: The question is incomplete.  The complete question probably is:  What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)

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Answer:

-3.7%, 0.3%,7%,17%,70%

Step-by-step explanation:

Answer:

£5.174

Step-by-step explanation:

Because you do 25.87 divided by 5

The number of apples that Jayden bought is 4 and the number of bananas he wants to buy is 8.

The number of ways we can have twice as many bananas as apples is:

8 bananas 4 apples

10 bananas 5 apples

12 bananas 6 apples

The first step is to form of system of equations that represent the question:

x + 0.50y = 8  equation 1

y  = 2x equation 2

The substitution method would be used to determine the required values.

x + (0.50 x 2x) = 8

x + x = 8

2x = 8

x = 8 / 2

x = 4

Substitute for x in equation 2:

y  = (2 x 4)

y = 8

The total number of fruits bought is 12 (4 + 8):

The number of ways we can have twice as many bananas as apples :

8 bananas 4 apples

10 bananas 5 apples

12 bananas 6 apples

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The correct statements regarding Marc's account balance are given as follows:

Mark's account balance is the amount of money that he has on his account.

Hence the balance is obtained as follows:

The statements are given by the image shown at the end of the answer.

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The equation part of the given word problem is x+y=52 and y=x+16.

a) Let x = number of green eyed dolls

And let y = number of blue-eyed dolls

Now we are told the following:

x+y=52 → eq1

and

y=x+16 → eq2

b) substitute y = x+16 from eq2 into eq1:

x+x+16 = 52 subtract 16 from each side

x+x+16-16 = 52-16 collect like terms

2x = 36 divide each side by 2

x = 18 → number of green-eyed dolls

substitute x = 18 into equation2

y = 18+16 =34 → number of blue-eyed dolls

18+34=52

52=52

and

18+16=34

34=34

THIS PROBLEM CAN ALSO BE SOLVED USING ONE EQUATION AND ONE UNKNOWN:

Let x = Number of green-eyed dolls

Then 52-x = Number of blue-eyed dolls

Now we are told that:

x+16 = 52-x add x to and subtract 16 from each side

x+x+16-16 = 52-16-x+x collect like terms

2x=36 → same as before

x = 18.

Hence, the equation part of the given word problem is x+y=52 and

y=x+16.

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The derivative of function y =eu is dy/dx = dy/du × du/dx

                                        Derivative refers to the rate of change of a variable with respect to any independent variables.

The function that has such a differentiable element which is also a function of other variable is termed as composite function. The method of differentiating composite function is called chain rule for differentiation.

In the above question, y is a composite function as y is a function of u and at the same time u is a function of x.

given, y =eu, where u is differentiable function of x, let u = g(x)

now, y =eu is differentiated using chain rule and we get dy/dx = dy/du×du/dx

hence, the derivative is dy/dx = dy/du×du/dx

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Answer: 68 kilometers per hour

Step-by-step explanation:

Take 238 divided by 3.5 hours = 68 km per hour

Answer:10

Rewriting input as fractions if necessary:

3/5, 1/2

For the denominators (5, 2) the least common multiple (LCM) is 10.

LCM(5, 2)

Therefore, the least common denominator (LCD) is 10.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

3/5 = 3/5 × 2/2 = 6/10

1/2 = 1/2 × 5/5 = 5/10

Answer:

Step-by-step explanation:

1/2 + 3/5 = 5/10 + 6/10 = (5+6)/10 = 11/10 or 1 1/10 Your pair of fractions is 5/10 and 6/10

Answer:

x∈(−∞,−22)∪(12,+∞)

Step-by-step explanation:

Evaluate

−∣x+5∣<−17

Calculate

∣x+5∣>17

Separate the inequality into 2 possible cases

​x+5>17x+5<−17​

Solve the inequality for x

​x>12x+5<−17​

Solve the inequality for x

​x>12x<−22​

Solution

x∈(−∞,−22)∪(12,+∞)

The numbers that are greater than -9 are 2.895, -8.92, 0.504, -2.9

What is a positive number?

A number can be zero, negative, or positive. Zero has no positive or bad aspects. The most frequent positive numbers in daily life include 34, 9.22, and other examples such as these. They are typically depicted on a number line to the right of zero, growing larger as you move to the right.

Given number is -9 which is a negative number.

All positive numbers are always greater a negative number

In the given number, the positive numbers are 2.895, 0.504.

Thus 2.895 and 0.504 are greater than -9.

The negative numbers whose absolute less than 9, they are also greater than -9.

The absolute value of -10.56, -8.92, -15.782, -2.9, -18.376 are

|-10.56| = 10.56 >9

|-8.92| = 8.92 <9

|-15.782| = 15.782 > 9

|-2.9| = 2.9 < 9

|-18.376| = 18.376 >9

Therefore -8.92 and -2.9 are also greater than -9.

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The solution to the inequality 4x + 10 < 6 is x < -1.

Given the inequality;

4x + 10 < 6

Solve for x.

Move all terms not containing x to the right side of the inequality by subtracting 10 from both sides of the inequality.

4x + 10 < 6

4x + 10 - 10 < 6 - 10

4x < 6 - 10

Subtract 10 from 6

4x < -4

Divide each term by 4 and simplify

4x < -4

4x/4 < -4/4

Simplify the left-hand side

x < -4/4

Simplify the right-hand side

x < -1

The result in inequality form is x < -1.

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Answer:

Add and subtract the second term to the expression and factor by grouping.

     (2 x -1) ( x^2 + 4)

Hope this helps!