A 6-foot- tall electric pole casts a shadow that is 24 feet long. What is the ratio
of the pole's height to its shadow?

In terms of the calculation, the answer is 39/4 in improper fraction.

An improper fraction has a denominator that is greater than or equal to the numerator. Based on the numerator and denominator values, proper fractions and improper fractions are the two main types of fractions in mathematics.

A mixed fraction is a fraction formed by combining a natural number and a proper fraction. It is a shortened version of an improper fraction.

The given equation is [tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] .

Taking 4 as LCM from the above equation.

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13/4) + (13/2)

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13+26)/4

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = 39/4

Now, since the solution must be proffered in an improper fraction.

Therefore, the obtained improper fraction is 39/4.

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259 pieces of candy can be distributed in 80 bags to give 3 candy per bag and there will be 19 candies remaining

The concept for distributing the required candies is achieved by the mathematical operation called division.

Division is an inverse of multiplication. With division we can share and determine number of candy per bag

The question is solved by

= 259 ÷ 80

= 259 / 80

= 3 19/80

This means that there will be 3 candies per bag and after sharing among the nags there will be 19 candies remaining.

Putting this in decimal gives

= 3.2375 ≅ 3.24

In a situation where we are to count the candies if they are 3.25 pieces per bag the we multiply as follows

= 3.25 * 80

= 260

in this case the total number of candies should be 260

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The perimeter of the regular polygon is 108 units.

A regular polygon is a polygon that has all its sides equal to each other.

Therefore,

5(x + 2) = 7x + 4

5x + 10 = 7x + 4

5x - 7x = 4 - 10

-3x  = -6

x = -6 / -3

x = 2

The perimeter of a regular polygon is the sum of the whole sides of the polygon.

Therefore,

each side of the regular polygon = 7(2) + 4

each side of the regular polygon = 14 + 4

each side of the regular polygon = 18

Hence the regular polygon has 6 sides

perimeter of the regular polygon = 18  × 6

perimeter of the regular polygon = 108 units

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Answer:

1. 39, 46

2. 180

Step-by-step explanation:

1. count up by 7

2. not sure..

The Sumerians were different from other people of their time as they wee more advanced.

The Sumerians were a southern Mesopotamian people whose civilisation flourished between approximately 4100 and 1750 BCE. Sumer was an ancient civilization that flourished in the Fertile Crescent region of Mesopotamia, between the Tigris and Euphrates rivers. Sumerians are regarded as the creators of civilisation as we know it today, according to their advancements in language, governance, building, and other fields.

They were able to take technologies produced elsewhere and use them on a far larger scale. This allowed them to mass-produce commodities such as textiles and pottery, which they could subsequently trade with others.

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Using the properties of equality, the value for m in the equation is: m = pV.

For any given equation, to solve for a variable in the equation, we have to isolate the variable to one side of the equation in order to determine its value. To do this, several properties of equality need to be applied to isolate the variable to one side of the given equation.

Given the equation, p = m/V, we need to isolate the variable m to one side of the equation in order to solve for m.

p = m/V

Multiply both sides of the equation by V

p × V = m/V × V [multiplication property of equality]

Simplify the equation:

pV = m

m = pV

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Answer:

769 and 858

Step-by-step explanation:

Every hour, the distance between the two planes increases by 2x + 89

2 hours = 4x + 178

3254 = 4x + 178

4x = 3076

x = 769

The average speed of this particle over the interval 2 ≤ t ≤ 10 is 25 , the correct option is (b)25  .

In the question ,

it is given that

the position of the particle that travels along the x-axis at time t is given by the function

x(t)=2t²+t

the average speed of the particle can be calculated by using the formula

average speed = (change is distance)/(change in time)

particle position at t=2

x(2) = 2(2)²+2 = 2*4+2 = 10

particle position at t=10

x(10) = 2(10)²+(10)

= 2*100+10

= 200+10

= 210

So, change in distance = 210-10= 200

change in time = 10-2 = 8

Putting the values in the average speed formula we get

average speed = 200/8

= 100/4

=25

Therefore , the average speed of this particle over the interval 2 ≤ t ≤ 10 is 25 , the correct option is (b)25  .

The given question is incomplete , the complete question is

A particle travels along the x-axis such that its position at time t is given by the function x(t)=2t²+t . What is the average speed of this particle over the interval 2 ≤ t ≤ 10?

(a) 4

(b) 25

(c) 32

(d) 200

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A set of parallel lines and a set of perpendicular lines are: BF║CG, AD⊥BF.

Parallel lines are straight lines that are of equal distance at every point away from each other, and therefore, do not intersect each other at any point. The sign "║" is used to indicate that two lines are parallel lines.

Lines that are said to be perpendicular lines are lines that intersect each other at right angle or 90 degrees. That is, at the point of their intersection, a right angle is formed which is 90 degrees. The sign "⊥" is used to indicate that two lines are perpendicular lines.

In the image given, lines BF and CG do not intersect at any point and they are of equal distance away from each other at every point, therefore, CG and BF are perpendicular lines.

Also, we can see that a right angle is formed at the point of intersection of lines AD and BF, therefore AD and BF are perpendicular lines.

Thus, we can state that: BF║CG, AD⊥BF.

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SINCE A OF A RECTANGLE IS =L×B

[tex] = (12x - 6)(14 \frac{1}{6} ) \\ = (12x - 6)( \frac{25}{6} ) \\ = \frac{25}{6} (12x) + \frac{25}{6} ( - 6) \\ = 50x - 25[/tex]

THE SIMPLIFIED AREA IS =50x-25

Answer:

brand A. The bag weights for brand A have less variability than the bag weights for brand B

Answer:

y = (1/4)x - 5

Step-by-step explanation:

We'll look for an equation having the form y=mx+b, where m is the slope and b is the y-intercept, the value of y when x=0.

We are told the slope, m, is (1/4):

  y = (1/4)x+ b

We need to find a value of b such that it forces the line to go through point (8,-3).  Enter that point in the equation:

  y = (1/4)x + b

  -3 = (1/4)(8) + b    for (8,-3)

   -3 = 2 + b

b = -5

The equation is y = (1/4)x - 5

See attached graph.

The resulting coordinate of △ D'E'F' is translated by the vector is

(-1, -2),  (3,-4), and (1, -7)

Given the vertices of ∆DEF are D(2,5), E(6,3), and F(4,0).

we are asked to graph ∆DEF and its image when you translate ∆DEF using the vector (-3,-7)​.

If the coordinate of the vertices is translated by the vector (-3, -7), the resulting coordinates of △ D'E'F' will be expressed as:

D'= (2-3, 5 - 7) = (-1,-2)

E' = (6 - 3, 3 - 7) = (3, -4)

F' = (4 -3 , 0 - 7) = (1, -7)

Hence we get the required coordinates of the translated image.

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Answer:

1.95 hours or 1 hour and 57 minutes.

Step-by-step explanation:

You can read the problem as 13% of the battery. "Of" is a keyword that means to multiply.

The battery lasts 15 hours, so multiply by 13%. You need to change 13% to a decimal first by dividing it by 100, or moving the decimal left two places.

13% = 0.13

Now solve.

0.13 × 15 = 1.95

If you need to convert the 0.95 to minutes, multiply it by 60 since there are 60 minutes in an hour.

0.95 x 60 = 57 minutes.

Answer: 1. Complementary

2. Supplementary

3. 116

4. 17

5. A- 28 B-152 C-118

Answer:

a. Yes

Step-by-step explanation:

If you plug the numbers in, 1 is x and -1 is y. The equation would look something like this:

4-5=-1

Now, do 4-5

4-5=-1

-1=-1

The answer would be a, yes.

Hope this helps! :D

Answer:

A) y = 23°

B) ∠A = 67°, ∠C = 113°, ∠D = 113°

Step-by-step explanation:

Hello!

Angle A and B are vertical angles, meaning they are equal in measure. We can solve for y by setting the two equations equal to each other.

Vertical angles are the opposite angles formed by the intersection of 2 lines.

Supplementary angles are angles that add up to 180°.

The value of y is 23°.

Measure of Angle A is 67°, as Angle A and B are vertical and equal in measure

Measure of Angle C is 113°, because the sum of angles on a line are equal to 180°, and are supplementary.

Measure of Angle D is also 113°, because it is vertical to Angle C.

The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²

Missing data from the problem:

radius of the barrel = 0.4 meters

height of the barrel = 1.2 meters

The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:

A = 2. πr² + 2. πr.h

Where:

r = radius

h = height

Plug the parameters into the formula:

A = 2. π(0.4)² + 2. π(0.4).(1.2)

A = 13 m²

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The length of x in the isosceles right triangle is 15.6 units.

An isosceles triangle is a triangle that has two sides equal to each other and two angles congruent to each other.

The triangle above is an isosceles triangle. The triangle is also a right angle triangle. A right angle triangle is a triangle that has one of it's angles as 90 degrees.

Using Pythagoras's theorem, let's find the side x

c² = a² + b²

where

Therefore,

11² + 11² = x²

121 + 121 = x²

x = √242

x = 15.5563491861

Therefore,

x = 15.6 units

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Each child will receive the 1.1 cup of milk.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that a container of milk contains 8 cups of milk. if paul sets aside [tex]1\dfrac{2}{5}[/tex] cups of milk for use in a recipe , then we get the leftover;

8  -  [tex]1\frac{2}{5}[/tex] = 8 -  7/5

= 40- 7/5

= 33/5

= 6.6

The the rest cups of milk = 6.6

Then the rest evenly among his three children 6.6/3 = 1.1

Hence, Each child will receive the 1.1 cup of milk.

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The possible values of the expression 1/a = 1/2 is 2

The expression is the simple fraction form = 1/a

The expression is the defined as the a sentence with a minimum of two  variables and at least one math operation.

The simple fraction is fraction that contains the numerator and denominator as whole number. The term one the top of the simple fraction called as the numerator and bottom term is called as the denominator.

Here it is given that

1/a = 1/2

Therefore the value of a = 2

Hence, the possible values of the expression 1/a = 1/2 is 2

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Answer:

2a + b = 180
 a + b = 118

a = 64, b = 56

Step-by-step explanation:

If you look at the triangle on the top right of the diagonal, there are 3 angles a, a and b. Since the 3 angles of a triangle add up to 180°

      a + a + b = 180

=>   2a + b = 180.......(1)

We are given that the largest angle is 118°

The largest angle of the parallelogram is a + b. Remember that opposite angles of a parallelogram are equal and the sum of the angles add up to 360

Therefore a + b = 118 ....(2)

Given equations (1) and (2), subtract (1) from (2):

Eq (1) - Eq(2) :

2a + b - (a + b) = 180 - 118

a = 62

Substitute for a in equation (2) to get

a + b = 118

62 + b = 118

b = 118 - 62 = 56

So the two angles are a = 64° and b = 56°

Answer:

a = 62, b = 56

Step-by-step explanation:

given the largest angle is 118° , then

a + b = 118 ( subtract b from both sides )

a = 118 - b → (1)

the sum of the interior angles of a quadrilateral = 360°

the angle adjacent to a is b ( alternate angles ) , then

a + b + a + a + b + a = 360

4a + 2b = 360 → (2)

substitute a = 118 - b into (2)

4(118 - b) + 2b = 360

472 - 4b + 2b = 360

472 - 2b = 360 ( subtract 472 from both sides )

- 2b = - 112 ( divide both sides by - 2 )

b = 56

substitute b = 56 into (1)

a = 118 - 56 = 62

a = 62 and b = 56

The cost of endless chicken wings at Restaurant X is $5. So cost equation for n chicken wings at Restaurant X is,

The cost of chicken wings at Restaurant Z is 20 cents and $1.40 for sauce. So cost equation for Restaurant Z is,

So answer is,

Restaurant X: c = 5

Restaurant Z: 0.20n + 1.40

(b)

Plot the system of equation on the graph.

(c)

The lines of two restaurant X and restaurant Z intersect each other at point (18,5). This means that restaurant X and restaurant Z has same cost 5 at n = 18. So both restanurant has same cost for 18 chicken wings.

Answer: 18

The resulting value for the quotient of 21 and a equals 30 is 7/10.

The result of dividing two numbers is known as the quotient. Six divided by two results in the number three.

Latin's "how many times" is the meaning of the word "quotient." That is really logical. For instance, the quotient of a and b is a/b

Given the statement "the quotient of 21 and a equals 30", this can be written mathematically as;

21/a = 30

Cross multiply

30a = 21

Divide both sides by 30

30a/30 = 21/30

a = 21/30

a = 7/10

Hence the value of a from the equivalent expression is 7/10.

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The proof explained below shows that the triangles are congruent by the AAS congruence theorem.

The AAS congruence theorem states that two triangles can be proven to be congruent to each other if the two angles and a non-included side in one triangle is equal or congruent to two corresponding angles and a corresponding non-included sides in the other triangle.

This implies that, once the criteria needed prove that two triangles are congruent by the AAS congruence theorem are two pairs of congruent angles and a pair of non-included congruent sides.

Using the AAS congruence theorem, the two-column proof that shows each statement and the reason are explained below.

Statement                                   Reason                                        

1. CA bisects angle BAD          1. Given

angle B ≅ angle D                                  

2. Angle CAB ≅ angle CAD     2. Congruent angles formed from bisection

3. Side AC ≅ side CA               3. Reflexive property

4. Triangle ABC ≅ triangle ADC    4. AAS congruence theorem

Thus, the above reasons and statements shows that the two triangles, triangle ABC and triangle ADC, are congruent by the AAS congruence theorem.

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Answer:

2ln5 + ln4 + ln5

Step-by-step explanation:

Think about how we can write 500 in terms of 4 and 5.

[tex]500 = 5^2*(4*5)[/tex]

So ln(500) can be written as ln(5^2*4*5)

Using log rules [tex]log_b(x*y)=log_b(x)+log_b(y)\\logb(x^a)=a*log(x)[/tex]

we can rewrite ln(500) to 2ln5 + ln4 + ln5

Answer:

x = –1/3 and y = 11/3

or can be written as (–1/3, 11/3)

Solve the system of equations:

1x + 2y = 7

y = –2x + 3

Substitute y = –2x + 3 for y in the first equation:

1x + 2y = 7

1x + 2(–2x + 3) = 7

Substract 6 from both sides:

–3x + 6 = 7

–3x + 6 – 6 = 7 – 6

–3x = 1

Divide:

–3x/–3 = 1/–3

x = –1/3

Substitute –1/3 for x in the second equation:

y = –2x + 3

y = –2(–1/3) + 3

y = 11/3

Solution:

x = –1/3 and y = 11/3

or can be written as (–1/3, 11/3)

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The value of x from the given linear equation is equivalent to 1.1

Linear equations are equation that has a leading degree of 1. An example of a linear equation is y = mx + b

Given the equation

19+2 In x=25

2lnx = 25 - 19

Simplify to have:

2lnx = 6

lnx = 6/2

lnx = 3

Take the exponent of both sides

e^lnx = ln3

x = ln3

Hence the approximate solution to the given linear equation is 1.1.

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Answer: f(7) = 52

Step-by-step explanation:

x = 7, so you would substitute x for 7

f(7) = 6(7) + 10

f(7) = 42 + 10

f(7) = 52

Hope this helps!

The probability that one or more of them tests negative is 0.85.

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

If Marv and Patricia will each take a Covid test, then the events that will occur are : both will test positive, both will test negative, or one of them will test negative.

Based on the given information, the probability that both will test positive is 0.15. Subtract it from 1 to and get the probability that one or more of them tests negative.

probability = 1 - 0.15

probability = 0.85

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