(2 square root 7+3 square root 6)(5 square root 2+4 square root 3)

Final answer:

The surface area of a pyramid with a base side of 2.5 inches and a slant height of 3 inches is calculated by finding the area of the base and the four triangular faces separately and then adding them together, resulting in a total surface area of 21.25 square inches.

Explanation:

To find the surface area of a pyramid with a square base of 2.5 inches and a slant height of 3 inches, we need to calculate the area of the base and the area of the four triangular faces.

For the base, which is a square:

Area of base = side × side = 2.5 inches × 2.5 inches = 6.25 square inches

For each triangular face:

Area of one triangle = (base × slant height) / 2 = (2.5 inches × 3 inches) / 2 = 3.75 square inches

Since there are four such triangles, we multiply the area of one triangle by 4:

Total area of four triangles = 3.75 square inches × 4 = 15 square inches

Finally, add the area of the base and the total area of the triangular sides to get the total surface area:

Total surface area = area of base + total area of triangles = 6.25 square inches + 15 square inches = 21.25 square inches

The surface area of the pyramid is therefore 21.25 square inches.

Answer:

A. Length of PQ = Length of P′Q′

Step-by-step explanation:

We are given,

Figure PQRS is rotated by 180° counter-clockwise about the origin to obtain P'Q'R'S'.

Since, we know that, 'Rotation' is a transformation that turns the figure around a fixed point to a certain degree.

We get that, rotation does not affect the length of the figure.

So, the length of PQ = length of P'Q' and length of RS = length of R'S'

Thus, according to the options, we get that option A i.e. Length of PQ = Length of P′Q′ is correct.

The annual interest rate is 4.5%.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$5000, simple interest=$2250 and time period= 10 years.

Here, 2250= (5000×R×10)/100

225000=50000R

R=225000/50000

R=4.5%

Therefore, the annual interest rate is 4.5%.

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The geometric mean of given numbers 9 and 11, using the formula is 9.95.

If a and b are two numbers

Their geometric mean = [tex]\sqrt{a*b}[/tex]

Given numbers are 9 and 11

So, the geometric mean of 9 and 11 will be:

[tex]\sqrt{9*11} \\\\\sqrt{99} \\\\9.95[/tex]

Therefore, the geometric mean of given numbers 9 and 11 is 9.95

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The point was reflected over the y -axis and translated up 4 units.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have,

A point located at (5, -2) undergoes two transformations.

Its image is located at (-5, 2).

The point was reflected over the y-axis and translated up 4 units, as shown by the coordinates becoming (-5, -2), respectively, when the point was reflected over the y-axis and (-5,2).

So, The point was reflected over the y -axis and translated up 4 units.

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The area of the parallelogram is approximately [tex]\( 1216.35 \)[/tex] square centimeters, with a longer side of 45 cm and height 27.03 cm.

To find the area of the parallelogram given the dimensions and conditions described, we can follow these steps:

1. Identify Key Dimensions:

  - The shorter side [tex]\( a = 29 \)[/tex] cm.

  - The longer side is divided into two segments: 33 cm and 12 cm. Therefore, the longer side [tex]\( b = 33 + 12 = 45 \)[/tex] cm.

2. Determine the Height Corresponding to the Longer Side:

  - We need to find the height [tex]\( h \)[/tex] of the parallelogram with respect to the longer side [tex]\( b = 45 \)[/tex] cm.

3. Utilize the Perpendicular Segment Information:

  - The perpendicular from the point of intersection of the diagonals to the longer side divides it into two segments: 33 cm and 12 cm.

  - This perpendicular segment represents the height [tex]\( h \)[/tex] from the base to the opposite side.

4. Use Geometric Properties of the Parallelogram:

  - In a parallelogram, the point of intersection of the diagonals divides each diagonal into two equal segments.

  - Since the perpendicular divides the longer side into two segments, we can use these to find the height [tex]\( h \)[/tex].

Given that the point of intersection of the diagonals and the perpendicular segment splits the longer side into two segments (33 cm and 12 cm), we note that this splitting essentially occurs at the mid-point of the segments because the diagonals bisect each other.

5. Calculate the Area:

  - The area [tex]\( A \)[/tex] of a parallelogram is given by the formula:

    [tex]\[ A = \text{base} \times \text{height} \][/tex]

  - Here, the base is the longer side [tex]\( b = 45 \)[/tex] cm, and the height [tex]\( h \)[/tex] needs to be calculated using the right triangle formed by the height and the segments.

6. Determine Height Using Right Triangle:

  - We use the properties of the right triangle formed by the height and the segments:

    [tex]\[ h^2 + \left(\frac{33 - 12}{2}\right)^2 = 29^2 \][/tex]

  - This simplifies to:

    [tex]\[ h^2 + 10.5^2 = 29^2 \][/tex]

    [tex]\[ h^2 + 110.25 = 841 \][/tex]

    [tex]\[ h^2 = 841 - 110.25 \][/tex]

    [tex]\[ h^2 = 730.75 \][/tex]

    [tex]\[ h = \sqrt{730.75} \][/tex]

    [tex]\[ h \approx 27.03 \text{ cm} \][/tex]

7. Calculate the Area:

  - Now that we have [tex]\( h \approx 27.03 \)[/tex] cm, the area [tex]\( A \)[/tex] of the parallelogram is:

    [tex]\[ A = b \times h = 45 \times 27.03 \approx 1216.35 \text{ cm}^2 \][/tex]

Therefore, the area of the parallelogram is approximately [tex]\( 1216.35 \text{ cm}^2 \)[/tex].

Answer:

$800

Step-by-step explanation:

Kevin earns a base pay = $325 /week

He also make some extra earning in the form of commission. Let this extra earning be “$X”

Thus, Base pay + Extra earning through commission = $1125 -------------Equation (A)

Substituting the values in equation A, we get –  

$325 + $X = $1125

$X = $1125 - $325

= $ 800

Answer:C

$35 + (−$7) + (−$5)

hope this helps :}

Answer: Hello there!

Let's define x = age of parent 1, and y = age of parent 2, and suppose that y is the oldest one.

we know that:

x + y = 92

x*y = 2107

now we have a system of equations that we need to solve:

the first step is isolate one of the variables in one of the equation, let's isolate x in the first equation:

x = 92 - y

now we can replace it in the second equation and find the value of y.

x*y = 2107

y*(92 - y) = 2107

92y - y^2 = 2107

now we need to solve a cuadratic equation!

-y^2 + 92y - 2107 = 0

using the Bhaskara formula, we get:

[tex]y = \frac{-92 +/- \sqrt{92^{2} -4 *(-1)*(-2107) } }{-2} = \frac{-92 +/- \sqrt{36} }{-2} = \frac{-92 +/- 6}{-2}[/tex]

so we have two solutions:

y = (-92 + 6)/(-3) = 43

y = (-92 - 6)/(-2) = 49

because y is the oldest one, we need to take the biggest solution, this is y = 49.

so the oldest parent has 49 years.

if you want to find the age of the other parent, replace this in the first equation:

y + x = 92

49 + x = 92

x = 92 - 49 = 43