A cell phone tower that is 80 meters tall is built on level ground and casts a shadow 170 meters long at a particular moment Find the angle of elevation of the sun relative to an observer standing at the tip of the shadow .

the answer is D : 4

According to the problem statement, one side of the rectangle is of length 5 cm. The other side can have any length greater than 4 cm (since the area of the rectangle should be greater than 4 cm^2).

Let's call this other side "x".

We know that the area of a rectangle is given by the formula A = l*w, where l is the length and w is the width.

Therefore, we can write the equation: 5*x = A, where A is the area of the rectangle.

We can also say that the area of the square and the rectangle is equal to 4 cm^2.

If we call the side of the square "y", then we can write the equation: y^2 = 4 cm^2.

Solving for y, we get: y = 2 cm.

Therefore, the length of the rectangle that can be cut into a square and a rectangle of area 4 cm^2 is 5 cm - y = 5 cm - 2 cm = 3 cm.

So, there are 4 possible rectangles that can be cut into a square and a rectangle of area 4 cm^2: (5,3), (3,5), (6,4), and (4,6).

So the answer is D : 4

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The Equations  is b/4 + 2= 8 and b = 24.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.

Mathematical statements called expressions must contain at least two phrases including numbers, variables, or both, and they must be joined by an operator.

Given Two more than the quotient of a number and 4 is 8,

Let number be b

b/4 + 2= 8

b/4 = 8 -2

b/4 = 6

b = 24

Hence, two more than the quotient of a number is 24.

Hence the equation for phrase is b/4 + 2= 8 and b = 24.

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When solving a system of two equations there are three possible outcomes for the solution of a system of three variables and two solutions for two variables.we can say that system of equation have infinite solutions.

There are three methods used to solve systems of equations graphing, substitution, and elimination. To solve a system by graphing you simply graph the given equations and find the point(s) where they all intersect.Solve the linear equation for the remaining variable.

To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.

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a. The sum of 1/3+1/5= 8/15

b. The sum of 1/8+2/6 = 3/8

c. the sum of 8/9+11/12= 1 87/108

d. the sum of 1/7+5/8= 1 7/36

e. the sum of 1/4+2/4= 3/4

f. the sum of 1/2+3/9= 5/6

g. the sum of 1/10+1/4= 7/20

h. the sum of 3/11+11/12 = 1 25/132

Sum of fractions is the addition of fractions. This is obtained by by using the L.C.M of the denominator method.

a. 1/3 + 1/5 = (5+3)/15 = 8/15

b. 1/8+2/6 = (3+6)/24 = 9/24 = 3/8

c. 8/9 + 11/12 = (96+99)/108 = 195/108 = 1 87/108

d. 1/7+ 5/8 = (8+35)/56 = 43/36 = 1 7/36

e. 1/4+ 2/4 = (2+1)/4 = 3/4

f. 1/2 + 3/9 = (9+6)/18 = 15/18 = 5/6

g. 1/10+1/4 = (2+5)/20 = 7/20

h. 3/11+ 11/12 = (36+121)/132 = 157/132 = 1 25/132

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The mean is 2, the missing data point must be 2 - 6 = -4. Therefore, the missing number of chicken nuggets is -4.

To find the mean of the data set, we need to add up all of the data points and divide by the number of data points. In this case, the sum of the data points is 1 + 3 + 0 + 6 = 10. Since there are 5 data points in total, the mean is 10 / 5 = 2.

Since the mean is 2, the missing data point must be 2 - 6 = -4. Therefore, the missing number of chicken nuggets is -4.

Mean is a type of average, which is a measure of central tendency. It is calculated by adding up a group of numbers and then dividing the sum by the number of numbers in the group. Mean is often referred to as the "arithmetic average".

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As per the given mean, the missing number of chicken nuggets is 5

The term mean in math is defined as the process of adding all numbers in the data set and then dividing by the number of values in the set.

Here we have given that the question assumes there are 5 people at the table.

And the number of nuggets are written as,

=> 1,3,0,6,and x.

Here x refers the missing number of chicken nuggets.

Then the equation is written as

=> 1 + 3 + 0 + 6 + x = 10 + x

Here we can multiply both sides by 5 to clear the denominator:

Then we have to isolate the x by subtracting 10 from both sides.

=> 10 + x - 10 = 15 - 10

Then the value of x is written as

=> x = 5

Therefore, the missing number of nuggets is 5.

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The value of x = ±5.

What is Quadratic Equation?

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x).

Method 1 :

⇒ 16x² - 400 = 0

⇒ 16x² = 400

⇒ x² = 400/16

⇒ x² = 25

⇒ x = ±5

Method 2 :

⇒ 16x² - 400 = 0

⇒ 16(x² - 25) = 0

⇒ x² - 25 = 0

⇒ x² = 25

⇒ x = ±5

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Check the picture below.

The number of quarts of soil in each pot will be 3.25 quarts.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

13 quarts of soil are used to completely fill 4 flower pots. If each pot holds the same amount of soil.

Then the number of quarts of soil in each pot will be given as,

⇒ 13 ÷ 4

⇒ 13 / 4

⇒ 3.25

The number of quarts of soil in each pot will be 3.25 quarts.

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If each term in the sum a1+a2+a3...+an is  7 and the sum equals 350, C: 40 would be equal to n.

In equation form, it is:  

                  7s +  77t = 350

In this equation,

          s represents the number of 7's

          t represents the number of 77's

          thus, the number of terms i.e n = s + t =?

now solving the equation,

        7 (s + 11t) = 350

        7 (s + 11t) = 350

            s + 11t = 50

            s + 11t = 50

now, if  

       s=39     &      t =1  

then

         s + 11t = 50 -> 39 + 11 (1)  = 50

Since the number of terms n = s + t

        n = s + t

        n = 39 + 1

        n = 40

Hence, the if each term in the given sum is 7 which gives a total sum as 350, then number of terms in the given series is 40.

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The equation of a circle with a center at (4,−9) and a radius of 5 is

(x−4)^2+(y+9)^2=25. The correct Option C.

A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.

The equation of a circle with center (h, k) and radius r units is

(x−h)^2+(y−k)^2=r^2 .

where h = 4

k = -9

r = 5

The equation of the circle

(x−4)^2+(y−(-9))^2 = 5^2

The equation of the circle

(x−4)^2+(y+9)^2 = 25

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We have prepared the table and drawn the graph.

What is a graph of a function?

A graph of a function is a visual representation of the relationship between the inputs (x-coordinates) and the outputs (y-coordinates) of a function. The inputs are typically represented on the x-axis and the outputs are represented on the y-axis.

Table:

x (days) y (number of cells)

0        1000

1        2000

2       4000

Graph:

The graph would be a line graph with x-axis showing the day passed and y-axis showing the number of bacteria cells,

The point (0,1000) would be plotted on the graph, representing the initial number of bacteria cells on the first day.

The point (1,2000) would be plotted on the graph, representing the second day and the number of bacteria cells.

The point (2,4000) would be plotted on the graph, representing the third day and the number of bacteria cells.

The graph would be a upward sloping line, representing the growth of bacteria cells.

Hence we have prepared the table and drawn the graph.

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

Work Shown:

C = 2pi*r

9pi = 2pi*r

r = (9pi)/(2pi)

r = 4.5

A = pi*r^2

A = pi*(4.5)^2

A = 20.25pi  square cm

------------------

Explanation:

The first portion involves using the circumference C = 9pi to determine the radius r. The circumference is the perimeter around the circle.

Once we know that r = 4.5 cm, we then plug that into the area of a circle formula A = pi*r^2

Side notes:

Answer:

Step-by-step explanation:

pass it then

The only expression that can be solved using product rule of exponents is; (11²a⁻⁵)(11a⁹b⁷) / 5²

The Product Rule for Exponents states that to find the product of two numbers with the same base, add the exponents.

For example : a² * a³ = a²⁺³

1) We are given the exponential expression as; (4⁵ a⁰)(7²b⁻⁶)

From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.

2) We are given the exponential expression as; (8⁵a⁻⁴)(b⁷c⁻⁵)

From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.

3) We are given the exponential expression as; a⁻⁷b¹⁰ / c⁷ d¹⁴ . 15

From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.

4) We are given the exponential expression as; (11²a⁻⁵)(11a⁹b⁷) / 5²

Using product rule of exponents, we have;

(111/25) * (a⁻⁵⁺⁹) * b⁷

= (111/25)a⁴b⁷

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the solutions to the system of inequalities are (1,1) and (-2,3).

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

2х + 3у > 2

3x + 5y > 1

for (1,1):

2+3 > 2 (true)

3+5 > 1 (true)

for (-2,-1)

-4-3 > 2 (false)

for (-2,3):

-4+9 >2 (true)

-6+15>1 (true)

for (7,-4):

14-12>2(false)

Hence, the solutions to the system of inequalities are (1,1) and (-2,3).

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The measure of the value of x in the expression for the angle (2·x + 1)°, obtained using vertical angles theorem is; x = 33°

Vertical angles are angles formed when two lines intersect. Vertical angles are the angles vertically opposite each other, formed by the intersection of the two lines.

Vertical angles theorem states that the vertical angles formed by the intersection of two straight lines are congruent.

The angles (2·x + 1)° and 67° are vertical angles. therefore;

(2·x + 1)° ≅ 67° (Vertical angles theorem)

(2·x + 1)° = 67°, by the definition of congruency

(2·x)° = 67° - 1° = 66°

x = 66° ÷ 2 = 33°

Therefore, plugging in the value of x = 33°, in the expression; (2·x + 1)° + 67°, we get;

(2·x + 1)° + 67° = (2 ×33 + 1)° + 67°

(2 ×33 + 1)° + 67° = 67° + 67° = 134°

The measure of the sum of the angles, (2 ×33 + 1)° and 67° is 134°

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The indicated operation 1/3 x 6/7 can be performed as 2/7.

The concept that will be used in this operation is the multiplication operation.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream. By multiplying their outputs, you can multiply one function by another.

Given operation is  1/3 x 6/7

1/3 x 6/7

=[ (1 x 6)/(3 x 7) ]

= (6/21)

= 2/7

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check the correct question:

Perform the indicated operation. 1/3 x 6/7

Answer:

13. x=4

14. x=8

Step-by-step explanation:

We know that these are both isosceles triangle because the two base angles are the same on #13, and the two sides are the congruent on #14. So all we need to do is make equations of equivalence. So #13 9x-8=28 and #14 11x-18=70. Look at the work shown in the image and follow those steps.

-Hope this helped & Happy New Year!

Answer:

C (2)

Step-by-step explanation:

• √32 = 4√2 ( bc √32 = √16×2 = √16×√2 = 4×√2 )

• √8 = 2√2 ( bc √8 = √4×2 = √4×√2 = 2×√2 )

So √32 ÷ √8 is equal to 4√2 ÷ 2√2

And there √2 cancels for both

So what you're left with is 4 ÷ 2

And 4÷2 = 2

In the replacement set, 9 is the solution to this equation 3 (n+7) = 48.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 3 (n + 7) = 48

And, Replacement set: {8, 9, 10}

Now, We can solve the expression as;

⇒ 3 (n + 7) = 48

Divide by 3,

⇒ n + 7 = 48/3

⇒ n + 7 = 16

Subtract 7, we get;

⇒ n = 16 - 7

⇒ n = 9

Thus, The solution of the equation is, 9.

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Answer:

3rd option: 32/24

Step-by-step explanation:

8/6 = 4/3

1st option: Now let's change the denominator to 24:

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

2nd option: Now let's change the numerator to 24:

4/3 ==> 24/?

4/3 =

4*6 / 3*6 = 24/18, not 24/32

24/32 = 3/4, not 4/3 ==> don't get confused by this

3rd option: 32/24 is correct [Look at the explanation for 1st option]

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

Hence, the 3rd option is correct.

When Henry ran 1 5/8 miles in the morning and 9/10 miles in the afternoon, In all he a total of 2 21/40 miles

The number of miles Henry ran is calculated by addition operation

The sum of the miles Henry ran in the morning plus the number of miles he ran in the afternoon gives the what Henry ran in all

The procedure involves addition of tractions and done as follows

= 1 5/8 + 9/10

= 13/8 + 9/10

adding both fractions will result to

= 101/40 miles

= 2 21/40 miles (as a mixed number)

Henry ran a sum of 2 21/40 miles

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Answer:

A

Step-by-step explanation:

For an ideal gas : PV=RT

And the internal energy of an ideal gas:

E

in

​

=

2

3

​

RT

E

in

​

=

2

3

​

PV

V

E

in

​

​

=

2

3

​

P

Energy density (E)=

2

3

​

P

P=2/3E

The solution to the equation 9(6^3x) - 13(6^3x) + 4(6^3x) = 0 is x = 0.

Generally, To solve the equation we try to get the values to be coherent by writing as

9(6^3x)-13*(6^3x)+4*(6^3x)=0

Therefore we solve the coefficients of the solution

To solve this equation, we can first distribute the constants in front of the parentheses:

9(6^3x) - 13(6^3x) + 4(6^3x) = 0

This simplifies to:

(9 - 13 + 4)(6^3x) = 0

Then, we can simplify the expression in the parentheses:

(0)(6^3x) = 0

This means that either (0) = 0 or (6^3x) = 0.

The second case is not possible, because the base of an exponent can't be zero. So, the only solution to this equation is x = 0.

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A child's ticket would cost $10 while and adult's ticket would cost $18.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

5 is an example of a constant.

The expressions are;

3a + 4c = 94 ---- 1

2a + 3c = 66 ---- 2

Multiplying equation 1 by 2 and equation 2 by 3

6a + 8c = 188 ---- 3

6a + 9c = 198 ---- 4

--------------------------

     - c = - 10

therefore;

c = 10

Substituting c in equation 3

6a + 8(10) = 188

6a + 80 = 188

6a = 188 - 80

6a = 108

a = 18

Therefore, child's ticket costs $10 while and adult's ticket cost $18.

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(4x + 7)(3x-5) are the factors of trinomial 12x²-x-35

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given trinomial is 12x²-x-35

Break the expression into groups

(12x²+20x)+(-21x-35)

12x²+20x-21x-35=0

Now take the gcf of first two terms

4x(3x+5)-7(3x+5)=0

(4x-7)(3x+5)=0

Hence, (4x + 7)(3x-5) are the factors of trinomial 12x²-x-35

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Completing the table with the appropriate percentage and decimals will be:

Fraction Decimal Percentage

1/4. 0.25. 25% of 1

1/10. 0.1. 10% of 1

3/4. 0.75. 75% of 1

1/5. 0.2. 20% of 1

3/2. 1.5. 150% of 1

7/5. 1.4. 140% of 1

It should be noted that based on the information, 0.1 will be 1/10. The percentage will be:

= 1/10 × 100

= 10%

0.1 to fraction will be:

= 1/10

The percentage for 1/5 will be:

= 1/5 × 100

= 20%

1/5 to decimal will be:

= 1/5

= 0.2

The decimal 1.5 will give 150%

The fraction for 1.5 will be:

= 1.5 / 1

= 15 / 10

= 3/2

Also 3/4 as percentage will be:

= 3/4 × 100

= 75%

75% to decimal will be:

= 75 / 100

= 0.75

140% to fraction will be:

= 140 / 100

= 7 / 5.

The decimal for 140% will be:

= 140 / 100

= 1.4

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Answer:

105

Step-by-step explanation:

y=kx where k is a constant

When y=15 and x=3

15=k3

k=15/3

k=5

Therefore y=5x

So, when x=21

y=21x5

=105

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