Mr. Logan runs 3.7 miles each day. If he runs the same distance each day, about how many miles will Mr. Logan run in 7 days?

The image of the triangle is missing, so i have attached it.

Also, the options are;

A) The apothem can be found using the Pythagorean theorem.

B) The apothem can be found using the tangent ratio.

C) The perimeter of the equilateral triangle is 15 cm.

D) The length of the apothem is approximately 2.5 cm.

E) The area of the equilateral triangle is approximately 65 cm².

Answer:

Options A, B & D are true

Step-by-step explanation:

A) We are told that the triangle is an equilateral triangle.

Thus, the 3 sides equal 8.7 cm.

Now from the image, b is half of one of the sides.

Thus, b = 8.7/2 = 4.35 cm

Now, we want to find the apothem "a".

Using Pythagoras theorem, we have;

a² + 4.35² = 5²

a² = 25 - 18.9225

a² = 6.0775

a = √6.0775

a ≈ 2.5 cm.

Thus, option A is true as pythagoras theorem was able to calculate the apothem "a"

B) since the main triangle is equilateral, it means each angle is 60°.

Now,the radius line from one corner point to the centre will divide the 60° angle into 2 equal parts.

Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°

Now,from tangent ratios, we know that;

Opposite/Adjacent = tan θ

In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm

Thus;

a/4.35 = tan 30

a = 4.35 tan 30

a ≈ 2.5 cm.

Thus, option B is correct as Tangent ratio can be used to find the apothem

C) The perimeter of equilateral triangle = 3x

Where x is length of one side.

One side is 8.7 cm

Thus, perimeter = 3 × 8.7 = 26.1 cm

Thus option C is not correct.

D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.

Thus, option D is true.

E) Area of triangle is;

A = ½ × base × height

Base = 8.7 cm

To get height, we will use trigonometric ratio. Thus;

h/8.7 = sin 60°

h = 8.7 sin 60°

Thus;

A = ½ × 8.7 × 8.7 sin 60°

A = 32.77 cm²

Thus is not equal to 65 cm². Thus, option E is not correct.

Answer:

A, B, D

Step-by-step explanation:

Answer:

6 kids ate pizza

Step-by-step explanation:

3/4 divided 1/8

Answer:

6 kids

Step-by-step explanation:

if each kid ate a 1/8 piece of the whole pizza => have [tex]\frac{3}{4}:\frac{1}{8}=6[/tex] (kids)

Answer:  the slope of y=−4x+10 is: −4.

Step-by-step explanation:

Answer:

102.6

Step-by-step explanation:

add 99.2 + 3.4

Given :

Each pitcher of power smoothie that Ginger makes has 2 scoops of pineapple, 4 scoops of strawberries, 1 scoop of spinach, and 1 scoop of kale.

To Find :

If Ginger makes 6 pitchers of power smoothies, how many scoops will she use in all.

Solution :

Let, Ginger makes x pitchers of power smoothies :

[tex]Total \ scoops = 2x+4x+x+x+6x[/tex]

Now, it is given that Ginger makes 6 pitchers of power smoothies.

Total scoops are :

[tex]T=2(6)+4(6)+6+6+6(6)\\\\T=84\ scoops[/tex]

Therefore, number of scoops Ginger used is 84.

Hence, this is the required solution.

Answer:

x=2

Step-by-step explanation:

Answer:

x = 30°, y = 90°

Step-by-step explanation:

[tex](y + x) + (y - x) = 180 \\ 2y = 180 \\ y = 90 \\ [/tex]

[tex]2x + y + x = 180 \\ 3x + 90 = 180 \\ 3x = 90 \\ x = 30[/tex]

Answer:

A

Step-by-step explanation:

it's so hard to explain but I'm pretty sure A is the answer

Answer:

you get the equation by following the given patterns. y=2×+4

Answer:0.75

Step-by-step explanation:

Answer: (1)/(9)-:(5)/(4)

Step-by-step explanation:

*^*^c(1)/(9)-:(5)/(4)*^*^

*^*^(1)/(9)-:(5)/(4)*^*^

*^*^The result can be shown in multiple forms. *^*^

*^*^Exact Form:4  45 *^*^

*^*^Decimal Form:

*^*^0.0 8

Answer:

2/8 more days

Step-by-step explanation:

5/8-3/8=2/8

Answer:

pft

Step-by-step explanation:

Answer:

Total number of puppies in the litter = 11

Step-by-step explanation:

Let the number of yellow puppies in the litter = y

And the number of black puppies in the litter = b

If there was one less black puppy, ratio of yellow to black puppies = [tex]\frac{2}{3}[/tex]

[tex]\frac{y}{b-1}=\frac{2}{3}[/tex]

2(b - 1) = 3y

3y - 2b = -2 -----(1)

If there was one more black puppy, ratio of yellow puppies to black puppies = [tex]\frac{1}{2}[/tex]

[tex]\frac{y}{b+1}=\frac{1}{2}[/tex]

2y = b + 1

2y - b = 1 -------(2)

Equation (1) - 2× equation (2)

(3y - 2b) - 2(2y - b) = -2 - 2

3y - 4y - 2b + 2b = -4

y = 4

From equation (1),

3×4 - 2b = -2

12 - 2b = -2

-2b = -14

b = 7

Total number of puppies in the litter = 7 + 4 = 11

Answer: slope intercept is y=mx+b

standard form is Ax+By=C.

point slope form is y-y₁=m(x-x₁)

so y=2/3x+2 is slope intercept

Answer:

+Slope-intercept is... y=mx+b

+The standard form is... Ax+By=C.

+A point-slope form is... y-y₁=m(x-x₁)

+So... y= x+2 is... slope-intercept

 ❤ I hope this helps you, ma'am/sir/whatever your pronouns are! ❤

Answer:y=9

Step-by-step explanation:

Answer:

Im pretty sure its 2/7

Step-by-step explanation:

you multiply across the top and the bottom so now you have 6/21. then you simplify it to be 2/7.

Answer:

2/7 or 0.285714 (repeating decimal)

Answer:

D. reflection then rotation

Step-by-step explanation:

ABC then A'B'C' then A''B''C''

Following this order, you can see that ABC is reflected across the x-axis to create A'B'C'.

A'B'C' is then rotated anticlockwise to create A''B''C''. How do we know this? The vertexes are pointing in different directions. If it was translated then B' would have been facing downwards instead of facing to the right

Answer:

             [tex]\bold{x_1=1\ ,\quad x_2=-\dfrac83}[/tex]

Step-by-step explanation:

[tex]3x^2+5x-8=0\quad\implies\quad a=3\,,\ b=5\,,\ c=-8\\\\x=\dfrac{-5\pm\sqrt{5^2-4(3)(-8)}}{2\cdot3}=\dfrac{-5\pm\sqrt{25+96}}{6}=\dfrac{-5\pm\sqrt{121}}{6}\\\\ x_1=\dfrac{-5+11}{6}=1\ ,\qquad x_2=\dfrac{-5-11}{6}=\dfrac{-16}6=-\dfrac83[/tex]

Okay I got the answer, so -28 is (LESS) than -3, and 28m below sea level is a (GREATER) depth than 3m below sea level! i took the test and I got it right.

Step-by-step explanation:

Complete statement is as follows -

−28 is less than −3, but 28 m below sea level is greater depth than 3 m below sea level.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given is Becky who went scuba diving. She writes an inequality statement that compares the magnitude of two depths that she reached.

We have the following expression -

|- 28| > |- 3|

The absolute value of the expression, will be -

28 > 3

Now, 28 is greater than 3.

But is we compare -28 and -3, then -28 is less than -3.

Now, if we compare the depth of 28 m and 3 m below the sea level, then 28 m represent more depth as compared to 3 m.

Therefore, we can write the complete statement as -

−28 is less than −3, but 28 m below sea level is greater depth than 3 m below sea level.

To solve more questions on inequalities, visit the link below-

brainly.com/question/26434651

#SPJ5

The independent variable represents the cost of the meal for 70 people.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given when the manager quotes a price for a banquet, she is including the cost of renting the room plus the cost of the meal for each person. A banquet for 70 people costs $1300. For 120 people, the cost is $2200.

The expression will be written as,

Total cost = 70x + cost of rent

Therefore, the independent variable represents the cost of the meal for 70 people.

To know more about an expression follow

https://brainly.com/question/13665601

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Answer:

2.Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

Step-by-step explanation:

The object of "Euclidean geometry" (more commonly called "plane geometry") is, in principle, the study of the shapes and properties of natural bodies. However, geometry is not an experimental science since its object is not to study certain aspects of nature but a necessarily arbitrary reproduction of it.

After the definitions, Euclid then poses his famous postulates (his requests), the fifth of which has remained Euclid's postulate, often called axiom (or postulate) of parallels and which was the subject of much research and controversy as to its necessity:

From the above explanation, we could deduce that the correct option is Option 2.

Answer:

The answer is B, Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

Step-by-step explanation:

Answer:

The real answer is -17, do the math.

Step-by-step explanation:

28 - 45= -17

28 + 17 = 45

45 - 28 = 17

Answer:

40 appointments

Step-by-step explanation:

From the question, we have the following information

Amount of time to trim a customer's hair = 1/4 hour

Amount of time to style a customer's hair = 1/6 hour.

Total time spent on a customer

= (1/4 + 1/6)hour

L.C.M = 12

= (3 + 2/12) = 5/12 hour spent on a customer for trimming and styling

She plans to work for 3 1/3 hours per day for 5 days a week.

The total number of hours in a week that she works is calculated as:

3 1/3 × 5

= 10/3 × 5 = 50/3 hours = 23 1/3 hours

1 customer = 1 appointment = 5/12 hour

Therefore, the number of appointments she can schedule for 5 days a week if the customer must trim and style is calculated as:

5/6 hour = 1 appointment

50/3 hours = x appointments

Cross Multiply

5/6 hour × x = 50/3 hour × 1 appointment

x = 50/3 ÷ 5/12

x = 50/3 × 12/5

= 40 appointments.

The number of appointments she can schedule for 5 days a week if the customer must trim and style is 40 appointments.

Answer;

C ; (3,2)

Explanations;

Mathematically, the equation of the distance between two points can be given as;

D^2 = (y2-y1)^2 + (x2-x1)^2

The distance we are dealing with is 25

Mathematically, the square of 3 and the square of 4 added together gives 25

So the coordinates that will be our answer will be such coordinates that will not give 3 and 4 for either of x or y axes

Looking at it;

Let’s work with the first option;

D^2 = (5-2)^2 + (2-(-2))^2

D^2 =3^2 + 4^2

We can see that this works

Second option;

D^2 = (5-1)^2 + (2-5)^2

D^2 = 4^2 + (-3)^2

Since (-3)^2 is same as 3^2, this option works too

Third option

D^2 = (5-2)^2 + (2-3)^2

D^2 = (3)^2 + (-1)^2

We can see that the sum here won’t give 25 , so this is our answer

Answer:

2d<10 or 10>2d

Step-by-step explanation:

Answer:

2d < 10

Step-by-step explanation:

Answer: -23, -4, -126/42, .4, 5/6, square root of 36, 8, 17

Step-by-step explanation: you simplify all the fractions and square roots then determine the order.