The net of a square pyramid is shown below: Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 2 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square. What is the surface area of the solid? (5 points) 10 square inches 16 square inches 24 square inches 28 square inches

Answer:

Step-by-step explanation:

18.) 19 - 3x = 14 + 2x

To solve for x, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side:

19 - 3x = 14 + 2x

19 - 14 = 2x + 3x

5 = 5x

x = 1

To check our solution, we can substitute x = 1 back into the original equation and see if it holds true:

19 - 3(1) = 14 + 2(1)

19 - 3 = 14 + 2

16 = 16

Since both sides of the equation are equal when x = 1, we have verified that x = 1 is the correct solution.

19.) 2(7 + 5y) - 3y = -35

We can start by simplifying the left-hand side of the equation by using the distributive property:

2(7 + 5y) - 3y = 14 + 10y - 3y = 14 + 7y

Now, we can solve for y by moving the constant term to the other side:

14 + 7y = -35

7y = -49

y = -7

To check our solution, we can substitute y = -7 back into the original equation and see if it holds true:

2(7 + 5(-7)) - 3(-7) = -35

2(7 - 35) + 21 = -35

-56 + 21 = -35

-35 = -35

Since both sides of the equation are equal when y = -7, we have verified that y = -7 is the correct solution

20.) 14 + 4(x - 5) = 6 - 2x

We can start by simplifying the left-hand side of the equation by using the distributive property:

14 + 4(x - 5) = 14 + 4x - 20 = 4x - 6

Now, we can solve for x by moving the constant term to the other side:

4x - 6 = 6 - 2x

6x = 12

x = 2

To check our solution, we can substitute x = 2 back into the original equation and see if it holds true:

14 + 4(2 - 5) = 6 - 2(2)

14 - 12 = 6 - 4

2 = 2

Since both sides of the equation are equal when x = 2, we have verified that x = 2 is the correct solution.

Answer:

B

HOPE THIS HELPS

Answer: -1/2

Step-by-step explanation: The formula is y=mx+b where m is your slope and b is your y-intercept. Therefore, your b or y-intercept is -1/2

Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

In the equation [tex]y=mx+b[/tex], m is the slope and b is the y intercept. In this equation, we are given the slope is 4 and the y intercept as [tex]-\frac{1}{2}[/tex] because the equation can be simplified to [tex]y=4x+-\frac{1}{2}[/tex]

The linear equation for coordinate points (-2,8) and (5,-6) is option B: y = -2x + 4.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Since there are two points on the graph, use the slope-intercept form of a linear equation to find the equation that matches the graph.

The slope-intercept form is -

y = mx + b

Where m is the slope and b is the y-intercept.

To find the slope, we use the two given points -

m = (y2 - y1) / (x2 - x1)

m = (-6 - 8) / (5 - (-2))

m = -14 / 7 = -2

To find the y-intercept, we can use one of the points and the slope -

y = mx + b

8 = (-2) × (-2) + b

8 = 4 + b

b = 4

So the equation that matches the graph is -

y = -2x + 4

Therefore, the equation is -2x + 4.

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Answer:

the probability is that the teacher will most likely pick between 2-4 boys and the rest would be girlso so the probability of it being all girls unless he choosing all girls on pourpose it would be a slim chance. if you need a percentage it would probably be like a 1.25% chance

Step-by-step explanation:

Answer:

Step-by-step explanation:

x inter for line a = 1

x inter for line B = -4

Line A is greater then Line B

To factorize 6x²2 - 4xy, we can factor out the greatest common factor (GCF), which is 2x:

6x²2 - 4xy = 2x(3x - 2y)

What is factorization?

Factorization is the process of finding two or more expressions that, when multiplied together, produce a given expression. In other words, it is the process of breaking down a mathematical expression into simpler factors.

For example, consider the expression x²2 - 4x - 21. We can factorize it by finding two expressions that, when multiplied together, give us x²2 - 4x - 21. One way to do this is to factor the expression into (x - 7)(x + 3):

x²2 - 4x - 21 = (x - 7)(x + 3)

This is an example of factorization, where the expression on the left-hand side has been broken down into the simpler factors on the right-hand side.

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Answer:

Step-by-step explanation:

radius of a circle is half of the diameter

Diameter :D , Raduis : R

D = 2R

R = 1.4 angstrom

1 angstrom = 0.00000001 cm = 10^-7 cm

R = 1.4 * 10^-7 cm

D = 2.8 * 10^-7 cm

The Diameter is 2.8x10^-7 cm

The analysis shows that the company experienced significant growth in assets from 2017 to 2018, which could be a positive sign for investors and stakeholders.

Horizontal analysis is used to examine a company's financial statements over time. It is typically represented as a percentage increase over the same line item in the base year. Horizontal analysis enables users of financial statements to quickly identify trends and growth patterns.

To perform a horizontal analysis, we need to compare the changes in the values of assets between two years (2017 and 2018) as a percentage of the base year (2017). The analysis is as follows:

Assets                                    2017        2018        Change   % Change

Cash                                     $2,500 $3,900  $1,400  56%

Accounts receivable, net    $35,000 $40,000  $5,000     14%

Inventory                               $85,000 $122,000  $37,000   44%

Other current assets            $3,400      $4,110       $710        21%

Total current assets              $125,900  $170,010   $44,110    35%

PPE, net                                 $180,000  $230,000  $50,000  28%

Other assets                         $15,000    $26,000   $11,000    73%

Total assets                          $320,900   $426,010  $105,110 33%

Interpretation

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Part A: You can decompose Figure ABCDE into two triangles and two rectangles. The two triangles are triangle ABC and triangle AED. The two rectangles are rectangle BCD and rectangle AEB.

Part B: The length of Side AB is 4 units and the length of Side AE is 5 units.

Part C: To find the area of Figure ABCDE, we can simply add the areas of the two triangles and two rectangles. The area of triangle ABC is 3 units2, the area of triangle AED is 6 units2, the area of rectangle BCD is 10 units2, and the area of rectangle AEB is 3 units2. Thus, the area of Figure ABCDE is 3 + 6 + 10 + 3 = 22 units2.

the area of the rectangle will be 1.5w².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

The given length of the rectangle is w

The width will be 1.5w

So the rectangle of the white figure is Area = w*1.5w = 1.5 w²

hence the area of the rectangle will be 1.5w².

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The mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The number of patients experiencing side effects in a sample of 100 patients as a binomial distribution with n = 100 and p = 0.20.

The mean of a binomial distribution is given by:

μ = np

Substituting n = 100 and p = 0.20, we get:

μ = 100 × 0.20 = 20

Therefore, the mean is 20.

The variance of a binomial distribution is given by:

σ²= np(1 - p)

Substituting n = 100 and p = 0.20, we get:

σ² = 100 × 0.20 × (1 - 0.20) = 16

Therefore, the variance of the number of patients experiencing side effects in a sample of 100 patients is 16.

The standard deviation of a binomial distribution is the square root of its variance:

σ =√Variance

=√16

= 4

Hence, the mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

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The standard equation of a hyperbola centered at the origin and a vertical transverse axis values of a=8 and b=9 is  y²/64 - x²/81 = 1.

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The standard equation of a hyperbola centered at the origin and a vertical transverse axis is given by

y²/a² - x²/b² = 1

We are given that;

a = 8

b = 9

Now, putting the values of the variables into the equation;

y²/a² - x²/b² = 1

y²/8² - x²/9² = 1

y²/64 - x²/81 = 1

Therefore, the standard equation will be  y²/64 - x²/81 = 1.

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Answer:

2x + h - 5

Step-by-step explanation:

To find f(x + h) we simply plug (x + h) into the function f(x), anywhere we see an x.

[tex]f(x) = x^{2} -5x+9\\f(x+h) = (x+h)^{2}-5(x+h)+9[/tex]

Now we can plug them into the fraction:

[tex]\frac{((x+h)^{2}-5(x+h)+9)-(x^{2} -5x+9)}{h}[/tex]

Expanding all of the terms, we get:

[tex]\frac{(x^{2} +2hx + h^{2} -5x-5h+9)-(x^{2} -5x+9)}{h}[/tex]

Distributing the negative we get:

[tex]\frac{x^{2} +2hx + h^{2} -5x-5h+9-x^{2} +5x-9}{h}[/tex]

Now we see that [tex]x^{2} -x^{2} ,-5x+5x,[/tex] and [tex]9-9[/tex] all cancel, leaving us with:

[tex]\frac{2hx + h^{2}-5h}{h}[/tex] (Notice the only terms left are those with h in them)

As every term contains an h, we can remove an h from every term, giving us:

2x + h - 5

The loan's future value A, or the total amount due at time t is equal to $3,720.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 3,000 × 6/100 × 5

S.I = 3,000 × 0.06 × 4

S.I = $720.

Next, we would calculate the future value as follows;

Future value, A = S.I + P

Future value, A = $720 + $3,000

Future value, A = $3,720.

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Answer:

The equation is false

Step-by-step explanation:

(x+5)^2 = x^2+25

FOIL the left hand side.

(x+5)(x+5)

x^2 +5x+5x+25

x^2 +10x+25

This does not equal x^2+25.

Answer: 7/13

Step-by-step explanation:

2(x-5)(x-3)/3(x-5)(x-2)

take (x-5) away from both

2x-3/3x-2

2(5)-3/3(5)-2

=7/13

Answer:

Step-by-step explanation:

Let's start by finding the six even numbers. We know that the median is 9, so the middle two numbers in the set must be 9. Since all of the numbers are even, these two numbers must be 8 and 10.

So we have four numbers remaining, and we know that they are even. We also know that the range is 8, which means that the largest number in the set minus the smallest number in the set is 8. Since the largest number is 10, the smallest number must be 2.

So far, we have the following numbers in the set:

2, 8, 9, 9, 10

Now we need to find one more even number to make a set of six. We are given that the mode is 6, which means that one of the numbers in the set must be 6. However, we cannot add 6 to the set because it is odd. Therefore, the other number in the set that is closest to 6 must appear twice in the set, making it the mode. The number closest to 6 is 8, so we can add one more 8 to the set.

The final set of six even numbers that satisfy the given conditions is:

2, 8, 8, 9, 9, 10

Using translation the graph of y = (x - 2)² - 5 is the graph of y = x² shifted 2 units to the right and 5 units down.

What is translation?

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

To translate the graph of y = x² to y = (x - 2)² - 5, apply the following transformations -

Shift the graph to the right by 2 units.

This means that we replace x with x - 2, which moves the graph 2 units to the right.

Shift the graph down by 5 units.

This means that we subtract 5 from the entire function, which moves the graph 5 units down.

So the transformed function is -

y = (x - 2)² - 5

To see how this transformation changes the graph, compare the original function y = x² to the transformed function y = (x - 2)² - 5.

The vertex of the parabola has moved from the origin (0,0) to the point (2,-5).

Therefore, the graph is shifted using translation.

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a.  The probability that they are actually lying is 0.3214. b. The polygraph test must be 98.7% in order that this probability is at least 80%.

It is simpler to construct and see every possible scenario using the tree diagram. Its two main sites are the ends and the branches of the tree. The probability is written on each branch, and the ends hold the final findings. Use tree diagrams to identify when to multiply and when to add.

The probability of lie = 0.5

The probability of truth = 1 - 0.5 = 0.95

The liars that pass polygraph = 0.10

The liars that fail the polygraph is = 0.90

The truth that pass on polygraph = 0.90

The truth that fails on polygraph = 0.10

a. The probability that they are actually lying is:

P (Lying| fair) = P (fair| Lying) P (lying) / P (fair)

= (0.90)(0.05)/ (0.70)(0.05) + (0.10)(0.95)

= 0.3214

b. P (Lying| fair) > 0. 80

= (x)(0.05)/ (x)(0.05) + (1-x)(0.95) > 0.80

x > 0.987

Hence, the polygraph test must be 98.7% in order that this probability is at least 80%.

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The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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Jane, Judy, and John will next play together in 30 years, which is 2009 + 30 = 2039.

What is the least common multiple (LCM)?

The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them

To solve this problem, we need to find the least common multiple (LCM) of the numbers 2, 3, and 5. The LCM is the smallest number that is a multiple of all three numbers.

Prime factorizing the numbers, we have:

2 = 2

3 = 3

5 = 5

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers, and multiply them together. Therefore, the LCM of 2, 3, and 5 is:

LCM = [tex]2^1 * 3^1 * 5^1 = 30[/tex]

Hence, Jane, Judy, and John will next play together in 30 years, which is 2009 + 30 = 2039.

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Answer:

Area = 380 square inch

Volume = 697 cubic inch

Step-by-step explanation:

Diameter = 11

=> radius = 11/2 = 5.5

A = 4πr^2 =4·π·(5.5^2) ≈ 380 square inch

V=4/3πr^3=4/3·π·(5.5^3) ≈ 697 cubic inch

Applying the law of sines, the value of c is calculated as: c ≈ 11.8.

The Law of Sines, also known as the Sine Rule, is a theorem in trigonometry that relates the side lengths of a triangle to the sine of its angles.

Specifically, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle. Mathematically, this can be expressed as:

a / sin A = b / sin B = c / sin C

Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

Applying the law of sines, we have:

c/sin 105 = 7/sin 35

Cross multiply:

c * sin 35 = 7 * sin 105

c = 7*sin 105/sin 35

c ≈ 11.8

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The area of the isosceles trapezoid is 281.25 square cm.

Let's denote the length of the base of the trapezoid as "b".

According to the problem statement, the length of each of the equal sides is one-half the length of the base, which means each equal side has length b/2.

The height of the trapezoid is given as one-fourth the length of the base, so we can write it as h = b/4.

To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

The two parallel sides of length b each contribute b to the perimeter, while the other two sides of length b/2 contribute a total of b to the perimeter.

Therefore, we can write:

Perimeter = 2b + 2(b/2) = 3b

We know that the perimeter of the trapezoid is 45 cm, so we can set up an equation:

3b = 45

Solving for b, we get:

b = 15

Now we can use the formula for the area of a trapezoid to find the area of this isosceles trapezoid. The formula is:

Area = (1/2)h(b1 + b2)

where h is the height, b1 and b2 are the lengths of the two parallel sides. In this case, b1 and b2 are both equal to b (since it's an isosceles trapezoid), and h = b/4.

Substituting these values, we get:

Area = (1/2)(b/4)(b + b) = (1/2)(b/4)(2b) = b^2/8

Substituting b = 15, we get:

Area = 15^2/8 = 281.25 sq cm

Therefore, the area of the isosceles trapezoid is 281.25 square cm.

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In an isosceles trapezoid, the length of the equal sides is one-half the length of the base, while the height is one-fourth the length of the base. If the perimeter of the trapezoid is 45 cm.

Find the areae

The coordinates of the point on the directed line segment is (- 6, 4).

A line segment is a subset of a line that has two endpoints.

We know, When a line segment is divides another line segment in the ratio of m : n at (x, y), The coordinate of the intersecting points is,

x = (nx₁ + mx₂)/(m + n) and y = (ny₁ + my₂)/2.

Therefore, The coordinates of the point directed on the line segment is,

x = (1×2 + 2×- 10)/(1 + 2).

x = (2 - 20)/3.

x = - 18/3.

x = - 6.

And,

y = (- 8×1 + 10×2)/(1 + 2).

y = 12/3.

y = 4.

So, The coordinates are (- 6, 4).

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Answer:

The equation that represents inverse variation for the given values of x=6 and y=1/2 is y = 3/x.

Step-by-step explanation:

Inverse variation is a type of relationship between two variables, in which the product of the variables is constant. The equation that represents inverse variation is:

y = k/x

where y and x are the variables, and k is the constant of proportionality.

To find the equation that represents inverse variation for the given values of x=6 and y=1/2, we can first substitute these values into the equation:

1/2 = k/6

To solve for k, we can multiply both sides by 6:

k = 6 * (1/2)

k = 3

Now that we know the value of k, we can substitute it back into the equation to get the final equation for the inverse variation:

y = 3/x

Therefore, the equation that represents inverse variation for the given values of x=6 and y=1/2 is y = 3/x.

Answer: Length = 7 and Width = 2

Step-by-step explanation:

Perimeter = 2(length + width)  
18 = 2(L+W)
[tex]\frac{18}{2}[/tex] = (L+W)  
9 = L+W  
Make width the subject.
w = 9-L ------Equation 1

  Area = Length × Width
⇒14 = L×(9-L)   | Substitute Eq.1 in place of Width
⇒14 = 9L - L²
⇒L² - 9L + 14 = 0
⇒L² -7L - 2L + 14 = 0
⇒L×(L-7) -2×(L-7) = 0
⇒(L-7)(L-2) = 0
∴ L=7(Answer) or L=2(Not Applicable since length can't be larger than width)

Substitute the value into eq.1
when L=7
W=9-7      
  =2      

Lenth=7
Width=2

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Answer:

Step-by-step explanation:

Let the length of the plank be "l" and the width be "w".

The perimeter of the plank is the sum of the lengths of all four sides, which is:

2(l + w) = 18

Simplifying the equation, we get:

l + w = 9

The area of the plank is given by:

lw = 14

We can solve for one of the variables in terms of the other by rearranging the equation:

l = 14/w

Substituting this expression for "l" into the equation for the perimeter, we get:

(14/w) + w = 9

Multiplying both sides by "w", we get:

14 + w^2 = 9w

Rearranging the terms, we get:

w^2 - 9w + 14 = 0

This is a quadratic equation that can be factored as:

(w - 7)(w - 2) = 0

Therefore, the possible values of "w" are 7 and 2.

If we take "w = 7", then using the equation l = 14/w, we get:

l = 14/7 = 2

Therefore, the length and width of the plank are 2 feet and 7 feet, respectively.

If we take "w = 2", then using the equation l = 14/w, we get:

l = 14/2 = 7

Therefore, the length and width of the plank are 7 feet and 2 feet, respectively.

In summary, the plank could have a length of 2 feet and a width of 7 feet, or a length of 7 feet and a width of 2 feet, given its perimeter of 18 feet and area of 14 square feet.

Answer:

The first thing you want to d is find out how many centimeters are in 1 foot, because if a flat bar cost 2 pesos per centimeter, and they want 1 foot, then you will multiply how many centimeters in 1 foot, by how much each centimeter cost: 2 pesos:

There are exactly 30.48 centimeters in 1 foot, so you will multiply that by 2:

2 * 30.48 = 60.96

It will cost 60.96, or rounded up to 61 pesos for a 1 foot flat bar.

Step-by-step explanation:

Hope it helps! =D