premier bank is planning to have a new building constructed

Answers

Answer 1

When you start writing equations, you find the problem statement has a number of holes. We'll do it this way.

Let L, W, N represent the length in feet, width in feet, and number of floors (count). Then it seems we can write
.. L = W +40 . . . . . length is 40 ft more than width
.. 10LW +35000N = 1180000 . . . . . cost is based on foundation area and number of floors. (Here, we assume the 1st floor is sandwiched between the foundation at ground level and whatever it is that is 12 ft high and costs 35,000.)
.. 2(L +W) = 3*(12N) . . . . the height is 12 ft times the number of floors, and the perimeter is 3 times that.

These give rise to a quadratic equation.
.. 10L(L -40) +35000(L +(L -40))/18 = 1180000
Eliminating fractions and dividing by 10, we get
.. 9L^2 +3140L -1132000 = 0
The positive solution is
.. L = (10/9)*(-157 +√126529) ≈ 220.788

There is one solution and it is viable.

_____
The building is approximately 220.8 ft by 180.8 ft and 22.3 floors high.

Answer 2

Answer:

220.8 ft by 180.8 ft and 22.3 floors high.

Step-by-step explanation:

Related Questions

During each minute of a comedy show, Carlin laughs 555 times. Carlin watches 333 comedy shows every day, and each show is 404040 minutes long. How many times does Carlin laugh every day due to the comedy shows?

Answers

74,672,652,600. Take the time of the show and multiply it by the number of times she laughs in a minute. Then multiply that by the number of shows she watches in a day. That number seems pretty large though so you may want to make sure you have the right numbers and that it's not just 5 times, 3 shows, and 40 minutes.

Answer: 600

Step-by-step explanation:

Given : The number of times Carlin laughs in each minute = 5

The number of comedy show Carlin watched = 3

The length of each comedy show = 40 minutes

Total minute she watched Comedy show will be :-

[tex]40\times3=120\text{ minutes}[/tex]

Then , the total number of times Carlin will be :-

[tex]120\times5=600[/tex]

Hence,Carlin laughs 600 times every day due to the comedy shows.

An arrangement of marbles has 12 marbles in the first row and 10 rows in all. In each successive row one marble is added.

What is the explicit rule for this situation, and how many marbles will be in the 10th row?

Drag and drop the answers into the boxes to match the situation.

Explicit rule

Number of marbles in the 10th row

An = 11 + 11n, An = 12 + n, An = 11 + n, An = 12 + 10n, 19, 20, 21,

Answers

Explicit rule: An = 12 + n

Number of marbles in the 10th row: 22

The explicit rule for this situation is An = 12 + n, where "n" represents the row number.

To find the number of marbles in the 10th row, you can plug in n = 10 into the explicit rule:

A10 = 12 + 10

A10 = 22

So, there will be 22 marbles in the 10th row.

Matching the answers:

Explicit rule: An = 12 + n

Number of marbles in the 10th row: 22

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Sean divides 8 cups of granola into 1/4-cup servings. How many servings of granola does he have?

Answers

Think of this, 8 is a whole number right? You can put a 1 under that 8 and it will still be a whole number, You basically flip 1/4 as a fraction, Which will make it 4/1. You can multiply the 8 and 4 which will equal 32, You can add that 1 under the 32 if that helps you but the answer, in general, is 32

1 cup makes 4 servings
8 cups make x

x = 8*4
x = 32 servings

Andy has 9 math books and 6 reading books if you wants to distribute them evenly among some bookshelves so that each has the same combination of books with none left over what is the greatest number of bookshelves Andy can use

Answers

3 is the greatest number of book shelves Andy can use. I solved this by finding the greatest comment factor of 9 and 6, which turned out to be 3.
6/3=2(reading books per shelf)
9/3=3(math books per shelf)
Every shelf there are two reading books and 3 math books

9 math books
6 reading books
First we need to find the greatest common factor.
in this case it would be 3.
9 ÷ 3 = 3
6 ÷ 3 = 2
Here we have our answer
since 3 is not an even number it cannot be split evenly which means each bookcase will have at least 3 math books on it - and 2 reading books as well

*bookcase 1:
3 (math)
2(reading
*bookcase 2:
3 (math)
2 (reading)
*bookcase 3:
3 (math)
2 (reading

Which number completes the inequality? -5.13< ?< -4.8

Answers

-5.14? Not sure if it's correct, but it's my best guess.

Anything from -5.12 to -4.7 would work

GIVEN circle P with arc AE = 53 , arc BA =68 and arc CB =72

match the following angles with their corresponding measurements

Answers

the theory that is mainly used to find out the angles of the above diagram is that;
the sum of the internal angles of a triangle is 180°.
when the angles of arcs have been given(e.g: BA) that means from the centre of the circle to point B has been rotated by 53° to point A.
Next from point A to point E, the angle rotated is 68°

the addition of these 2 angles give the angle rotated from point B to point E,
that is angle no.7

m∠7 = 53° + 68° = 121°
consider ΔPBE,
PB and PE are radii therefore isosceles triangles
In isosceles triangles the angles opposite equal sides are equal
if the angle is x°, then there are 2 angles with values x each
x° +x° + 121° = 180°
2x° = 59°
x = 29.5°
therefore m∠3 = 29.5°

next connect PC and consider ΔPCB,
according to given information, C∠PB = 72°
as PC and PB are radii ΔPCB is an isosceles triangle, then the angles (y°) opposite radii are equal
2y° + 72° = 180°
y° = 54°
then consider ΔPCD, again an isosceles triangle
as a straight line has an angle of 180°
B∠PC + C∠PD = 180°
72° + C∠PD = 180°
C∠PD = 108°
as ΔPCD is an isosceles triangle, P∠CD and P∠DC are equal (take this angle as z°)
2z° + 108° = 180°
z° = 36°
B∠CD is a sum of y and z angles
therefore m∠8 = y + z
m∠8 = 54° + 36° = 90°
there is also a tangent line that cuts point D of the circle. this tangent cuts D and is perpendicular to the PD radius
this indicates that lines PD and HD are perpendicular to each other
hence, forms a right angle where it cuts each other.
therefore H∠DP / m∠4 = 90°
C∠DH /m∠5 is the difference between P∠DH and P∠DC
m∠5 = 90° - 36° = 54°

m∠1 and m∠6 together make a straight line therefore the sum of these 2 angles is 180°
by looking at the options of answers given the 2 angle values given that add up to 180° are 116.5° and 63.5°.
m∠1 is the acute angle therefore m∠1 = 63.5°
m∠6 is the obtuse angle therefore m∠6 = 116.5°

consider ΔDFB
D∠FB is 180° - m∠1 = 180° - °63.5 = 116.5°
D∠FB + F∠DB(w°) + D∠BF (m∠3)= 180°
116.5 + w° + 29.5° = 180°
w° = 34°
m∠2 = m∠4 + w°
= 90° + 34°
= 124°

finally all the answers are
m∠1= 63.5°
m∠2 = 124°
m∠3 = 29.5°
m∠4 = 90°
m∠5 = 54°
m∠6 = 116.5°
m∠7 = 121°
m∠8 = 90°

All the answers are

m∠1= 63.5°

m∠2 = 124°

m∠3 = 29.5°

m∠4 = 90°

m∠5 = 54°

m∠6 = 116.5°

m∠7 = 121°

m∠8 = 90°

The theory that is mainly used to find out the angles of the above diagram is that;

the sum of the internal angles of a triangle is 180°.

when the angles of arcs have been given(e.g: BA) that means from the centre of the circle to point B has been rotated by 53° to point A.

Next from point A to point E, the angle rotated is 68°

the addition of these 2 angles give the angle rotated from point B to point E,

that is angle no.7

m∠7 = 53° + 68° = 121°

consider ΔPBE,

PB and PE are radii therefore isosceles triangles

In isosceles triangles the angles opposite equal sides are equal

if the angle is x°, then there are 2 angles with values x each

x° +x° + 121° = 180°

2x° = 59°

x = 29.5°

therefore m∠3 = 29.5°

next connect PC and consider ΔPCB,

according to given information, C∠PB = 72°

as PC and PB are radii ΔPCB is an isosceles triangle, then the angles (y°) opposite radii are equal

2y° + 72° = 180°

y° = 54°

then consider ΔPCD, again an isosceles triangle

as a straight line has an angle of 180°

B∠PC + C∠PD = 180°

72° + C∠PD = 180°

C∠PD = 108°

as ΔPCD is an isosceles triangle, P∠CD and P∠DC are equal (take this angle as z°)

2z° + 108° = 180°

z° = 36°

B∠CD is a sum of y and z angles

therefore m∠8 = y + z

m∠8 = 54° + 36° = 90°

there is also a tangent line that cuts point D of the circle. this tangent cuts D and is perpendicular to the PD radius

this indicates that lines PD and HD are perpendicular to each other

hence, forms a right angle where it cuts each other.

therefore H∠DP / m∠4 = 90°

C∠DH /m∠5 is the difference between P∠DH and P∠DC

m∠5 = 90° - 36° = 54°

m∠1 and m∠6 together make a straight line therefore the sum of these 2 angles is 180°

by looking at the options of answers given the 2 angle values given that add up to 180° are 116.5° and 63.5°.

m∠1 is the acute angle therefore m∠1 = 63.5°

m∠6 is the obtuse angle therefore m∠6 = 116.5°

consider ΔDFB

D∠FB is 180° - m∠1 = 180° - °63.5 = 116.5°

D∠FB + F∠DB(w°) + D∠BF (m∠3)= 180°

116.5 + w° + 29.5° = 180°

w° = 34°

m∠2 = m∠4 + w°

= 90° + 34°

= 124°

finally all the answers are

m∠1= 63.5°

m∠2 = 124°

m∠3 = 29.5°

m∠4 = 90°

m∠5 = 54°

m∠6 = 116.5°

m∠7 = 121°

m∠8 = 90°

Find the area of the circle with the given radius or diameter. Use pi = 3.14. r = 2

Answers

A of circle = pi• r^2= 3.14•4= 12.56

The product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39.
Find the number

Answers

Let the number be X. Then we find
7X + 3 = 39 - 2X

Now we collect the terms and find
9X = 36

Finally we divide by 9
X = 4

So our answer is 4

If the asymptotes of a hyperbola are the x- and y-axes, it is known as a rectangular hyperbola?

Answers

Yes, This is true. If the asymptotes of a hyperbola are the x- and y- axes, it IS known as a rectangular hyperbola.

Final answer:

A rectangular hyperbola is defined by the angle between its asymptotes being 90°, with its Equation represented as x'y' = a².

Explanation:

Rectangular Hyperbola: When the angle between the asymptotes of a hyperbola is 90°, it is called a rectangular hyperbola. In this case, b = a and the eccentricity is √2. The Equation to a rectangular hyperbola is x'y' = a².

Sierra sawed 10 1/2 inches off the end of a board. the remaining board was 37 1/2 inches long. how long was the boared that sierra started with? please explain answer

Answers

37 1/2 +10 1/2 = 48 inches
48 inches is your answer ;)

find the product of 80x^4/y^3 ×xy/5x^2

Answers

[tex]\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------\\\\ \cfrac{80x^4}{y^3}\times \cfrac{xy}{5x^2}\implies \cfrac{80x^4xy}{y^35x^2}\implies \cfrac{80x^4xx^{-2}}{5y^3y^{-1}}\implies \cfrac{80x^4x^1x^{-2}}{5y^3y^{-1}} \\\\\\ \cfrac{16x^{4+1-2}}{y^{3-1}}\implies \cfrac{16x^3}{y^2}[/tex]

what is the average of -10.25 and 125.75

Answers

add them together and divide it by 2 since there are two numbers
125.75+(-10.25)=115.5
115.5/2= 57.75

the mean is 57.75

Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k. y = 3(x2 + 4x) + 7 y = 3(x2 + 4x +4) + 7 -

Answers

Answer:

A. 12

B. 3

C. -2

D. -5

Step-by-step explanation:

Verified on edge, just finished it

The Vertex form is y= 3(x+ 2)² -5 and a= 3, h= -2, k= -12.

What is Vertex Form?

The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants.

Vertex form, one of the usual forms for quadratic functions, emphasises the coordinates of the vertex of the function's graph.

Given:

y = 3x² + 12x + 7

Now writing the equation in vertex form

y = 3x² + 12x + 7

y = 3x(x + 4) + 7

Adding and subtracting 12 on both side

y= 3(x²+ 4x) + 7 -12 + 12

y= 3(x² + 4x + 4) + 7- 12

y= 3(x+ 2)² -5

Now, Comparing it with y = a(x - h)² + k we get

a= 3

h= -2

and, k= -12

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56. exercise. for natural numbers a and b, give a suitable definition for "least common multiple of a and b", denoted lcm(a, b). construct and compute some examples.

Answers

LCM(a, b) ≡ a×b/GCD(a, b)

LCM(6, 9) = 6*9/3 = 18 . . . . . . . (2 [ 3 ) 3] = 18 . . . ( ) product = 6; [ ] product = 9

LCM(2,5) = 2*5/1 = 10 . . . . . . . . (2 [ 1 ) 5 ] = 10

LCM(27, 45) = 27*45/9 = 135 . . (3 [ 9 ) 5] = 135

_____
In the above LCM products, the number in [ ) brackets is the GCD.

Harper's house is 30 feet wide and 45 feet long. On a scale drawing, the house is 4 inches wide and 6 inches long, and Harper's bedroom is 1.2 inches wide and 1.6 inches long. What are the actual measurements of Harper's bedroom? Enter your answers in the boxes. Harper's bedroom is feet wide and feet long.

Answers

Original dimensions of house:
30 feet wide and 45 feet long.
Dimensions on drawing:
4 inches width and 6 inches long.
Scale is: 1 inch on drawing= 30/4 = 7. 5 ft in original.
Width of bedroom= 1.2 inches
So, actual length= 1.2 x 7.5 = 9 ft
Length of bedroom= 1.6 inches
So, actual length= 1.6 x 7.5 = 12 ft

Actual measurement of Harper's bedroom is 9 ft wide and 12 ft long.

the answer is 9 feet wide 12 feet long i had this on a test

what do you call an object with one fixed endpoint that extends to infinity

Answers

A ray has one fixed endpoint that extends to infinity

This line is called a A ray.

10x - 4 = 2 ( ? ) is it a) 5x - 4 b) 5x - 2 c) 10x - 4 d ) 10x - 8

Answers

we have that

10x - 4 = 2 ( ? )
I proceed to replace the missing value with the given expression

case a-------------> 5x - 4
then
10x - 4 = 2 (5x-4 )--------> 10x - 4 = 10x-8--------> is not solution

case b-------------> 5x - 2
then
10x - 4 = 2 (5x-2 )--------> 10x - 4 = 10x-4--------> is solution

case c-------------> 10x - 4
then
10x - 4 = 2 (10x - 4 )--------> 10x - 4 = 20x-8--------> is not solution

case d-------------> 10x - 8
then
10x - 4 = 2 (10x - 8 )--------> 10x - 4 = 20x-16--------> is not solution

the answer is the option b) 5x - 2

In the standard (x,y) coordinate plane below, the points ( 0,2), (8,2), (3,6), and (11,6) are the vertices of a parallelogram. What is the area, in square units, of the parallelogram

Answers

Your area would be 32, 8 by 4 is what the formula is

The area of the parallelogram is 32 square units.

What is a parallelogram?

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

First, we can plot the points on the coordinate plane to get a better visual understanding of the parallelogram:

| (3,6) (11,6)

| *-----------*

| / /

| *-----------*

| (0,2) (8,2)

Now,

We can see that the base of the parallelogram is the line segment connecting (0,2) and (8,2), which has a length of 8 units.

To find the height of the parallelogram, we can observe that the line segment connecting (0,2) and (3,6) is perpendicular to the base, and has a length of 4 units.

Therefore,

The height of the parallelogram is 4 units.

Now,

The area of a parallelogram is given by the formula:

Area = base x height

Plugging in the values we found, we get:

Area = 8 x 4

Area = 32

Therefore,

The area of the parallelogram is 32 square units.

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a rectangular park is 4 miles long and 2 miles wide. how long is pedestrian route that runs diagonally across the park

Answers

you can use the Pythagorean theorem to solve this
[tex]{x}^{2} = {4}^{2} + {2}^{2} [/tex]
Now solve for x
[tex] {x}^{2} = 16 + 4 \\ {x}^{2} = 20 \\ x = \sqrt{20} [/tex]
Now you can simplify this to
[tex]x = \sqrt{5 \times 4} \\ x = \sqrt{5} \sqrt{4} \\ x = \sqrt{5 } \times 2 \\ x = 2 \sqrt{5} [/tex]
And that's your answer

Write the time another way 23 minutes after 4

Answers

23 minutes after 4 o'clock is the same as 4:23.

4:23

Would be the answer

If the total labor cost is $865,000 and 12 percent is for concession staff, how much of the labor cost is for concession staff?

Answers

12% of $865,000 is $103,800

Choose the correct simplification of the expression (−2x + 4y)(3x − 7y). −6x2 − 2xy − 28y2 6x2 + 26xy − 28y2 −6x2 + 26xy + 28y2 −6x2 + 26xy − 28y2

Answers

Answer:

[tex] - 6 {x}^{2} + 26xy - 28 {y}^{2} [/tex]

Step-by-step explanation:

The given expresion is:

(−2x + 4y)(3x − 7y)

We expand using the distributive property: (a+b)(c+d)=a(c+d)+b(c+d)

We apply this property to get:

[tex]( - 2x + 4y)(3x - 7y) = - 2x \times(3x - 7y) + 4y(3x - 7y)[/tex]

We expand further to obtain:

[tex] - 6 {x}^{2} + 14xy + 12xy - 28 {y}^{2} [/tex]

[tex] - 6 {x}^{2} + 26xy - 28{y}^{2} [/tex]

Answer:

[tex](-2x+ 4y)(3x - 7y)=-6x^2+26xy-28y^2[/tex]

Step-by-step explanation:

We multiply each term in the parentheses, by those of the other parenthesis:

[tex](-2x+ 4y)(3x - 7y)=(-2x)(3x)+(-2x)(-7y)+(4y)(3x)+(4y)(-7y)\\=-6x^2+14xy+12xy-28y^2[/tex]

Now, we simplify.

We have two terms that contain xy:

[tex]=-6x^2+26xy-28y^2[/tex]

Wich will be the correct simplification of the expressionn [tex](-2x+ 4y)(3x - 7y)[/tex]

PLEASE HELP!!!!!

Give the piecewise function shown below select all of the statements that are true

A. f(4)=7

B. f(1)=0

C. f(-1)=2

D. f(-2)=0

Answers

Try this option:
A. f(4)=7 - false; explanation: x=4, it means that x>0 and x²-1=4²-1=15 ⇒ f(4)=15.
B. f(1)=0 - true; explanation: x=1, it means that x>0 and x²-1=1-1=0.
C. f(-1)=2 - true; explanation: x=-1, it means that x<0 and -x+1=1+1=2.
D. f(-2)=0 - false; explanation: x=-2, it means that x<0 and -x+1=2+1=3 ⇒ f(-2)=3.

half of the sum of six and three then divided by seven

Answers

The expression is 1/2 × (6+3) ÷7
1/2 × (6+3) ÷7
1/2 × 9 ÷7
4.5 ÷7
0.64285714
*Last 6 digits are repeating decimals
Hope this was helpful :D

Final answer:

In order to find the answer, put six and three together to obtain nine, then divide nine in half to get 4.5, and then divide 4.5 by seven to get roughly 0.64.

Explanation:

When translated into a mathematical operation, the phrase "half of the sum of six and three then divided by seven" looks like this: Find the value of the sum of 6 + 3 to get 9 first. Then divide by half, or 4.5, to get the answer. Divide this by seven, and you'll arrive at a result that is roughly 0.64 (rounded to two decimal places).

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Simplify: (–5) • (7) – (6) • (–2)

Answers

-5 x 7= -35 - 6= -41 x -2= 82
hope this helped PLEASE ADD ME BRAINIEST :-)

The correct answer is -23.

To simplify the given expression, we need to perform the indicated operations and follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

Given expression: (–5) • (7) – (6) • (–2)

Step 1: Perform the multiplications inside the parentheses.

(–5) • (7) = –35

(6) • (–2) = –12

Step 2: Perform the subtraction operation.

–35 – (–12) = –35 + 12 = –23

Therefore, the simplified expression is:

[tex](-5) \cdot (7) - (6) \cdot (-2) = -35 + (-12) = -23[/tex]

convert 39/5 to a mixed number written in lowest terms

Answers

Hello!

39 ÷ 5 = 7.8

A N S W E R:

7.8 = 7 4/5 (This is in lowest terms)

In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1,000? Really need this I'm giving you maximum points

Answers

The shipmentof 1000 is 1000/400 = 2.5 times as large as the shipment of 400, so 2.5 * 14 = 35 defective parts can be expected.

Two runners are to race one lap on a circular track, the radius to the inside circle is 50m.the radius on the outside lane is 51m. How much of a head start should the runner on the outside get?

Answers

Tmuch of a head start should the runner on the outside get would be = 2πm.

How to calculate the length of head start for the runner outside?

To calculate the length of head start for the runner outside against the inside runner, the following steps should be taken as follows:

The formula for circumferential of circle = 2πr

Circumference of inner circle;

= 2× π×50

= 100π

Circumference of outer circle;

= 2×π×51

= 102π

The length of head start for the runner outside = 102π-100π = 2πm

A rectangular prism has a length of 212 meters, a width of 4 meters, and a height of 214 meters.

What is the volume of the prism?

Enter your answer in the box as a simplified mixed number or a decimal.

m³

Answers

181,472m^3. I don't know why it would be a mixed number or decimal, its multiplication with whole numbers

The volume of the rectangular prism is 22 1/2 m³

What is the volume of the rectangular prism?

A rectangular prism is a three-dimensional object. It is made up of six faces, twelve sides and six vertices.

Volume = length x width x height

2 1/2 x 4 x 2 1/4

5/2 x 4 x 9/4 = 720 / 32 = 22 1/2 m³

Here is the complete question: A rectangular prism has a length of 21/2 meters, a width of 4 meters, and a height of 21/4 meters.

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Jessica grows two types of tomato plants in her garden. For each type, she records the heights, in inches, of five plants.

What can she infer about the heights of the plants?

Type 1: {42, 56, 44, 60, 48}

Type 2: {62, 59, 68, 55, 66}

Type 1 plants and Type 2 plants do not have similar height distributions.
Type 1 and Type 2 plants have similar height distributions.
Type 1 plants and Type 2 plants have identical height distributions.
Type 1 and Type 2 plants have somewhat similar height distributions.

Answers

The answer is D
Type 1 Type 2 plants have somewhat similar height distributions

The inference that can be made is that D. Type 1 and Type 2 plants have somewhat similar height distributions.

What is Inference?

This refers to a statement or assertion that is made about something, which may or may not be true.

Hence, we can see that based on the height of the plants, there is a similarity in the heights of Type 1 and Type 2 plants, hence it can be inferred that Type 1 and Type 2 plants have somewhat similar height distributions.