given the side length of 35m and a height of 22m, calculate the length of the slant edge ( E ) the base angle the distance between the center of the base and the corner of the pyramid and the area of the side of the pyramid


Work shown please!

Answer:

a² +3ab - 5ab - 15b² = (a+3b) (a-5b)

Step-by-step explanation:

We need to factorize a² +3ab - 5ab - 15b². Firstly we need to rearrange the expression such that,

[tex]a^2-5ab+3ab-15b^2=(a^2-5ab)+(3ab-15b^2)[/tex]

Now taking a common from the first two terms and 3b from last two terms, then :

[tex](a^2-5ab)+(3ab-15b^2)=a(a-5b)+3b(a-5b)[/tex]

In the above expression, a factor (a-5b) is in both the terms. It would mean that,

[tex]a(a-5b)+3b(a-5b)=(a+3b)(a-5b)[/tex]

So, the factors of a² +3ab - 5ab - 15b² are (a+3b) (a-5b).

Answer:

x=8

Step-by-step explanation:

Area is equal to

A = l * w

50 = ( x+2) ( x-3)

FOIL

50 = x^2 -3x+2x -6

Combine like terms

50 = x^2 -x -6

Subtract 50 from each side

0 = x^2 -x -56

Factor

What two numbers multiply to -56 and add to -1

-8*7 = -56

-8+7 = -1

0 = ( x-8) ( x+7)

Using the zero product property

x-8 =0   x+7 =0

x = 8   x=-7

Since the length cannot be negative x cannot be negative

x=8

Answer:

8

Step-by-step explanation:

put the 50 under area and continue with like that

Answer:

B.

Step-by-step explanation:

First, let's start from the parent function. The parent function is:

[tex]f(x)=\sqrt{x}[/tex]

The possible transformations are so:

[tex]f(x)=a\sqrt{bx-c} +d[/tex],

where a is the vertical stretch, b is the horizontal stretch, c is the horizontal shift and d is the vertical shift.

From the given equation, we can see that a=1 (so no change), b=3, c=-3 (negative 3), and d=3.

Thus, this is a horizontal stretch by a factor of 3, a shift of 3 to the left (because it's negative), and a vertical shift of 3 upwards (because it's positive).

Answer:

[tex]\boxed{x=R}[/tex], where R stands for all real numbers.

Step-by-step explanation:

Part 1: Solving one equation for its variable

First, we need to solve one of the equations for one of its variables. I will use the second equation.

[tex]2x+y=18[/tex]   Subtract [tex]2x[/tex] from both sides to isolate the [tex]y[/tex].

[tex]\boxed{y = -2x + 18}[/tex]

Part 2: Substituting the solved variable value into the other equation

Now, simply substitute this value in the place of the [tex]y[/tex] in the first equation and solve for [tex]x[/tex].

[tex]6x+3(-2x+18) =54[/tex]    Distribute the coefficient of the equation.

[tex]6x -6x + 54 = 54[/tex]    Simplify the equation.

[tex]0 = 0[/tex]

This answer is perfectly okay to get. This means that your equations have an infinite number of solutions.

Answer:

[tex]m^{10}[/tex]

Step-by-step explanation:

[tex]m^2m^5m^3\\=m^{2+5+3}\\\\=m^{10}[/tex]

===============================================

Explanation:

I'm assuming you meant to write m^2 * m^5 * m^3

If so, you add the exponents to get 2+5+3 = 10 which is the exponent over the original base m. The base does not change.

The rule I used is a^b*a^c = a^(b+c). We see that the base stays the same at 'a' the whole time.

-----------

A longer way to do this is to expand out m^2 into m*m. We have two copies of m multiplied together.

Similarly, m^5 = m*m*m*m*m. We have five copies now.

Saying m^2*m^5 will have seven copies because

m^2*m^5 = (m*m) times (m*m*m*m*m) = m*m*m*m*m*m*m = m^7

Tacking on m^3 will add on three more copies of m to multiply out, giving 10 copies of m total to multiply. This alternative method is not advised since there is a possibility to lose track and make an error somewhere. The formula in the previous section is preferred. Though I recommend you try this second method out to see how/why the formula works.

Answer:

0.2

Step-by-step explanation:

it works out to be 0.2 as a decimal and 20% as a percentage.

Answer:

.2

Step-by-step explanation:

Answer:

Equation of the circle

(x - 0.7)² + (y - 1.3)² = 12.58

Step-by-step explanation:

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle.

a) We are told in the question that the equation of the circle passes through point(2, -2)

Hence,

Substituting 2 for x and -2 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(2 - a)² +(-2 - b)² = r²

Expanding the bracket

(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²

4 - 2a - 2a +a² +4 +2b +2b +b² = r²

4 - 4a + a² + 4 + 4b + b² = r²

a² + b² -4a + 4b + 4 + 4 = r²

a² + b² -4a + 4b + 8 = r²............Equation 1

We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y

Hence,

Substituting 3 for x and 4 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(3 - a)² +(4 - b)² = r²

Expanding the bracket

(3 - a) (3 - a) + (4 - b)(4- b) = r²

9 - 3a - 3a +a² +16 -4b -4b +b² = r²

9 -6a + a² + 16 -8b + b² = r²

a² + b² -6a -8b + 9 + 16 = r²

a² + b² -6a -8b + 25 = r²..........Equation 2

The next step would be to subtract Equation 1 from Equation 2

a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²

a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²

Collecting like terms

a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0

2a + 12b -17 = 0

2a + 12b = 17...........Equation 3

Step 2

We are going to have to find the values of a and b in other to get our equation of the circle.

Since the center of the circle(a, b) lies on x + y = 2

Therefore, we have

a + b = 2

a = 2 - b

2a + 12b = 17 ..........Equation 3

Substituting 2 - b for a in

2(2 - b) + 12b = 17

4 - 2b + 12b = 17

4 + 10b = 17

10b = 17 - 4

10b = 13

b = 13/10

b = 1.3

Substituting 1.3 for b in

a + b = 2

a + 1.3 = 2

a = 2 - 1.3

a = 0.7

hence, a = 0.7, b = 1.3

Step 3

We have to find the value of r using points (2, -2)

(x - a)² + (y - b)² = r²

Where x = 2 and y = -2

(-2 - 0.7)² + (-2 - 1.3)² = r²

(-2.7)² + (-3.3)² = r²

1.69 + 10.89 = r²

r² = 12.58

r = √12.58 = 3.55

Step 4

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle

a = 0.7

b = 1.3

r² = 12.58

Equation of the circle =

(x - 0.7)² + (y - 1.3)² = 12.58

Answer:

The area of the square is 85 units^2

Step-by-step explanation:

Okay, here in this question, we are interested in calculating the area of the unknown square.

Kindly note that, since each of the other shapes are squares too, it means that the length of their sides is simply the square root of their areas.

Thus, the length of the squares are ;

√35 units and √50 units respectively

Now to find the area of the larger square, we employ the use of Pythagoras’ theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides

Let’s call the unknown length X

x^2 = (√35)^2 + (√50)^2

x^2 = 35 + 50

x^2 = 85

x = √85 units

Now as we know that the area of a square is simply the length of the side squared,

The area of the biggest square is simply (√85)^2 = 85 units^2

Answer:

greater than

Step-by-step explanation:

An exponential growth function has a base that is__greater than__one.

If the base is less than one, it will be a decay function.

Note: the above assumes an exponent greater than one as well.

Answer:

Fred's

Step-by-step explanation:

Igloo 1.75(60) + 75 = 180

Tasty 2(60) + 80 = 200

Fred's 1.25(60) + 90 = 151.25

Answer: fred's

Step-by-step explanation:

Answer:

2.5, -1.8

Step-by-step explanation:

½(x¹+x²) ,½(y¹+y²)

½(3.5+1.5) ,½(2.2+(-4.8)

½(5.0), ½(2.2-4.8)

2.5 ,½(-3.6)

2.5, -1.8

Answer: It’s 2.5, -1.3, the other person must’ve misclicked lol

Answer:

3 = x

Step-by-step explanation:

5(x+4) = 35

distribute: 5x + 20 = 35

subtract 20 to both sides

15 = 5x

divide by 5 to make x independent

x=3

Answer:

75.36 yd²

Step-by-step explanation:

To solve, you need to consider the walkway and the pool as one circle and find the are.  The diameter of this circle is 25 yd.  This means that the radius is 12.5 yd.

A = πr²

A = π(12.5)²

A = 156.25π

A = 490.625 yd²

Then, you need to find the area of the pool alone.  Since the diameter of the pool is 23 yd., the radius is 11.5 yd.

A = πr²

A = π(11.5)²

A = 132.25π

A = 415.265 yd²

Subtract the two areas to find the are of the walk.

490.625 - 415.265 = 75.36 yd²

The area is 75.36 yd²

Answer:

Option (1)

Step-by-step explanation:

Given quadratic equation in this question is,

y < -x²+ 4x + 5

Now we will convert this standard quadratic equation into vertex form,

y < -(x² - 4x) + 5

y < -[x² - 2(2)x + 2²] + 5

y < -(x - 2)²+ 5

This equation is in the form of y < a(x - h)² + k

where (h, k) is the vertex of the parabola.

Therefore, y < -(x - 2)²+ 5 will show the parabola with properties as,

1). Parabola having vertex at (2, 5).

2). Coefficient 'a' is negative, so parabola will open downwards.

3). In the inequality notation of less than, (sign < ) will show the solution area inside the parabola.

[If an inequality has a sign of greater than, solution area will be outside the parabola.]

Therefore, Option (1) will be the answer.

Answer:

Step-by-step explanation:

identitiy property

Answer:

A. an = 3(6)^(n-1)

Step-by-step explanation:

1st generation: n = 1:

a1 = 3*6^(1-1) = 3*6^0

= 3

n = 2:

a2 = 3*6^2-1

= 3*6

=18

n = 3

a3 = 3*6^(3-1)

= 3*6^2

= 106.

The solution is Option A.

The geometric progression is given by the equation aₙ = 3 ( 6 )ⁿ⁻¹ , where n is the number of terms

What is Geometric Progression?

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the geometric progression be represented as A

Let the number of terms be represented as n

Now , the first term a₁ = 3 rabbits

The second term a₂ = 3 x 6 = 18 rabbits

The third term a₃ = 18 x 6 = 108 rabbits

So , the common ratio r = second term / first term

Substituting the values in the equation , we get

Common ratio r = 18/6 = 6

Now , the geometric progression A is given by the equation ,

The nth term of a GP is aₙ = arⁿ⁻¹

Substituting the values in the equation , we get

aₙ = 3 ( 6 )ⁿ⁻¹

Therefore , the value of A is aₙ = 3 ( 6 )ⁿ⁻¹

Hence , the equation is aₙ = 3 ( 6 )ⁿ⁻¹

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Answer:

y = 100

Step-by-step explanation:

x = 25

x+y + 55 = 180 since it is a straight line

25+y+ 55 = 180

Combine like terms

80+y = 180

Subtract 80 from each side

y = 180-80

y = 100

The value of x is 3

The above expression in the question is referred to as an Algebraic expression

7+ 2x/3 = 5

7 x 3 + (2x/3) x 3 = 5 x 3

21 + 2x = 5 × 3

21 + 2x = 15

21 - 21 + 2x = 15 - 21

2x = -6

2x/2 = -6/2

x = -3

Therefore, the value of x is  -3

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Answer:

0.0398 dollars

Step-by-step explanation:

We are told in the question that

An apple picker in China earns an average wage of 45 cents per hour.

Mathematically

1 hour= 45 cents............ Equation 1

An apple picker can harvest about 2.0 bushels of apples each hour.

Mathematically

2.0 bushels = 1 hour ..............Equation 2

We are told that each bushel contains about 126 apples

1 bushel = 126 apples

2 bushels =

126 × 2

= 252 apples

Combining Equation 1 and 2 together,

We can say

An apple picker in 1 hour harvests 2 bushels of apples which is 252 apples and is paid 45 cents

1 hour = 2 bushels of apples

1 hour = 252 apples

1 hour = 45 cents

Hence we can say fro harvesting 252 apples, an apples picker is paid 45 cents

Mathematically,

252 apples = 45 cents

One gallon of apple juice requires 40 apples

We are to calculate the labor cost of one gallon of apple juice in dollars

If : 252 apples = 45 cents

40 apples = X cents

Cross Multiply

40 × 25 = 252 × X

X = (40× 25) ÷ 252

X = 3.984063745 cents

Hence the labor cost of 40 apples = 3.984063745 cents

Approximately = 3.98 cents

Converting 3.98 cents to dollars

100 cents = 1 dollar

3.98 cents =

= 3.98/100

= 0.0398 dollars.

Therefore, the labor cost of one gallon of apple juice in dollars is 0.0398 dollars.

Answer:

  52°

Step-by-step explanation:

Angle AOB is the a.pex angle of the isosceles triangle AOB.* Then angles at A and B are congruent and each is the complement of half the angle at O:

  ∠OAB = 90° -(1/2)(76°) = 90° -38°

  ∠OAB = 52°

_____

* You know ΔAOB is isosceles because OA and OB are both radii of the circle, hence the same length.

Answer:

A. Undefined slope (no slope)

B. [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

A slope is rise over run.

The points (6, 2) and (6, -3) are located on the same x coordinate, therefore they have an undefined slope.

However, the points (-4, -7) and (4, 3) do have a slope. The rise is 10 ( | -7+ 3 | ) and the run is 8 ( | -4 + 4 | ). 10/8 is equivalent to 5/4.

Hope this helped!

Answer:

Choice C

Step-by-step explanation:

[tex] -3.55g \le -28.4 [/tex]

Divide both sides by -3.55; remember that by dividing both sides of an inequality by a negative sign, you need to change the direction of the inequality sign.

[tex] \dfrac{-3.55g}{-3.55} \ge \dfrac{-28.4}{-3.55} [/tex]

[tex] g \ge 8 [/tex]

Answer: Choice C

Answer:

Third answer

Step-by-step explanation:

the sign less than or equal to gets flipped when you divide by a negative

solid circle and points to the right because now it is greater than or equal to.

Answer:

g(x)=6 when x=-4

g(x)=-2 when x=3

Answer:

g(x) = 6 when x=-4

g(x)= -2 x=3

Step-by-step explanation:

plz check the graph of g(x) ,

when x= -4, the value of y = 6

when x=3, the value of y =-2

Answer:

( x-7)^2 + ( y+12) ^2 = 81

Step-by-step explanation:

The equation of a circle can be written in the form

( x-h)^2 + ( y-k) ^2 = r^2  where ( h,k) is the center and r is the radius

( x-7)^2 + ( y--12) ^2 = 9^2

( x-7)^2 + ( y+12) ^2 = 81

Answer:

(x - 7)² + (y + 12)² = 81

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

Here (h, k) = (7, - 12) and r = 9, thus

(x - 7)² + (y - (- 12))² = 9², that is

(x - 7)² + (y + 12)²= 81

Answer:

b    y = 9sin(36)

Step-by-step explanation:

sin A = opp/hyp

for the 36-deg angle, opp = y, and hyp = 9.

sin 36 = opp/hyp

sin 36 = y/9

y = 9 * sin 36

Answer: b   y = 9sin(36)

Answer:

D. ​Population, because it is a collection of salaries for all teachers in the school.

Step-by-step explanation:

In research, population refers to a complete set of subjects that share a characteristic and that the researcher is interested in. On the other hand, a sample is a subset of a population and it's usually the one the researcher takes to make a study with.

In this example, we have "The salary of each teacher in a school" since we are taking ALL the teachers of this school, this would be a population. If we were working with the salary of only a portion of the teachers of said school, it would be a sample.

Thus, the right answer is  D. ​Population, because it is a collection of salaries for all teachers in the school.

Answer:

C) 118.8; 28.8

Step-by-step explanation:

for eating, it didn't make sense for it to be 288 degrees, so i eliminated the two off the list. For sleeping, it made more sense for it to be a 118.8 degree angle, so I narrowed it down to C.

The central angle for sleeping is 118.8 degrees and the central angle for eating is 28.8 degrees.

The angle formed by an arc of the circle at the center of the circle is called central angle of a pie chart.

central angle = [tex]\frac{sector}{100}[/tex] × 360

According to the given question

We have a pie chart

In which, time spend by students in different activities is given.

Now,

The measure of central angle for sleeping is given by

Central angle for sleeping = [tex]\frac{sector}{100}[/tex] × 360

⇒ Central angle for sleeping =[tex]\frac{33}{100}[/tex] × 360 = 118.8 degrees.

Similarly,

The measure of central angle for eating is given by

Central angle for eating = [tex]\frac{8}{100}[/tex] × 360 = 28.8 degrees

Hence, first option is correct.

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Answer:

r = -0.83

strong negative correlation

r = -0.08

weak negative correlation

r = 0.96

strong positive correlation

r = 0.06

weak positive correlation

Step-by-step explanation:

In this question, what we are expected to do is to match the values of the correlation given with the type of correlation in which the values are.

When we talk of correlation, we are simply referring to the extent of agreement between the values in the data field.

Correlation has a value between -1 and +1, meaning it could be negative or positive.

Values closer to the extremes i.e (-1 or +1) indicates strong correlation while values farther away, i.e closer to zero indicates a weak relationship.

Let’s answer the questions specifically now:

r = -0.83

This is closer to -1 and it indicates a strong negative correlation

r = -0.08

This indicates a weak negative correlation as it is closer to zero and farther away form -1

r = 0.96

This indicates a strong positive correlation

r = 0.06

This indicates a weak positive correlation

Answer:

18

Step-by-step explanation:

Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.

Sidenote: I hope this answer helps!

The properties of a pentagon and the given right triangle formed by

segments EF and FD give the measure of ∠FDE.

Response:

The given parameters are;

A, E, F are points on the same line.

ABCDE is a regular pentagon

∠EFD = 90°

Required:

The measure of ∠FDE

Solution:

The points A and E are adjacent points in the pentagon, ABCDE

Therefore;

line AEF is an extension of line side AE to F

Which gives;

∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;

The sum of the acute angles of a right triangle = 90°

Therefore;

∠DEF + ∠FDE = 90°

Which gives;

72° + ∠FDE = 90°

∠FDE = 90° - 72° = 18°

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Answer:

5 cm

Step-by-step explanation:

The length of the drawing will be 450 / 90 = 5 cm.