what is the length of the side of a square if the apothem is 7

Answers

Answer 1

Even though this is a square, it is still technically a polygon. That square has a center. From that center we can draw 4 radii to each of the pointy parts of the square, creating 4 interior angles. Each one of those interior angles measures 90 degrees, cuz 360 degrees is all the way around the interior angles, ending up where you started off. So that means that one of those representative triangles has a top vertex of 90. When we drop the apothem from that vertex, which is also the altitude of the triangle, we can cut that representative triangle into 2 right angles. The altitude cuts not only the angle of 90 degrees in half (45 degrees), it cuts the side it goes through directly in half, too. That's what we are solving for. Actually, when we solve that it will only give us half the length of the base of the whole representative trianlge, but we can just multiply whatever length we find by 2 to find the whole base of the trianlge, which of course is the side length we are looking for. When we pull out one of those right triangles, we have a top angle of 45, another angle of 90, so the third angle has to be a 45 as well (45-45-90) with a height of 7. We can then use one of our right triangle trig identities to solve for the missing side of the right triangle. If we use the base angle of 45 and the height of 7 (which is opposite the angle) and we are solving for the base (which is adjacent to the angle) we know that tangent has us covered:
[tex]tan45= \frac{7}{x} [/tex]
[tex]x*tan45=7[/tex]
[tex]x= \frac{7}{tan45} [/tex]
and x=7. Now remember that that is only half the base of the whole triangle so the base is 7*2 which is 14. 14 is the length of one side of the square. Well, actually 14 is the length of every side of the square right?

Related Questions

What is 3y+5x=-15 written in slope-intercept form

Answers

Slope-intercept form is y=mx+b, so we simply have to solve for y...

3y+5x=-15 subtract 5x from both sides

3y=-5x-15 divide both sides by 3

y=-5x/3-5 or more neatly in my opinion...

y=(-5x-15)/3

hey broskey your answer is option B :)

Maureen is taking an antibiotic. The table below shows the amount of antibiotic f(t), in mg, that was present in her body after time t:

t (hours) 1 2 3 4 5
f(t) (mg) 150 90 54 32.4 19.4

Ken was administered 200 mg of the same antibiotic. The amount of antibiotic f(t) in his body after time t is shown by the equation below:

f(t) = 200(0.976)t

Which statement best describes the rate at which Maureen's and Ken's bodies eliminated the antibiotic?
Maureen's body eliminated the antibiotic faster than Ken's body.
Maureen's body eliminated the antibiotic at the same rate as Ken's body.
Maureen's body eliminated the antibiotic at half of the rate at which Ken's body eliminated the antibiotic.
Maureen's body eliminated the antibiotic at one-fourth of the rate at which Ken's body eliminated the antibiotic.

Answers

One way to test this is by using the equation for Ken on Maureen. Let's say in the first hour,

f(t) = 200(0.976)^1 = 195.2 mg

In the second hour,

f(t) = 200(0.976)^2 = 190.52 mg

In the third hour,

f(t) = 200(0.976)^3 = 186 mg

If you compare this with Maureen's data which is 150, 90 and 54 for the first, second and third hour, respectively, you will see that Maureen's rate is much faster. However, you cannot tell by what factor because the function is exponential, not a multiple. There is no constant difference between their rates. Therefore, we only know that Maureen's rate is much faster.

The answer is Maureen's body eliminated the antibiotic faster than Ken's body.

Answer:

(A)Maureen's body eliminated the antibiotic faster than Kens body

Step-by-step explanation:

We already have the table for Maureen, so lets figure out the table for Ken. We've been given the formula 200(0.976)^t.

we already know our starting point is 0, 200

first we substitute 1 into t, which would look like this 200(0.976)^1

So we would solve the power of 0.976 to the power of 1, which is just 0.976. so now we do 200 x 0.976 which results in 195.2. on the chart, the point would be (1, 195.2). now lets solve for the rest doing the same steps.

(2, 1905.5)

(3, 181.4)

(4, 135.5)

(5, 01.9)

What is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? y − 5 = −3(x + 2) y − 5 = 3(x + 2) y − 11 = −3(x − 2) y − 11 = −3(x + 2)

Answers

hello :

Hello : let A(0,5) B(-2,11)
the slope is : (YB - YA)/(XB -XA)
(11-5)/(-2-0) = 6/(-2)
the slope is : -3

the equation in point-slope form of the line is : y-11 = -3(x+2)

Answer: [tex]y-11=-3(x+2)[/tex]

Step-by-step explanation:

Given points : (0, 5) and (−2, 11)

Slope of the line passing through given points .

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-5}{-2-0}=\frac{6}{-2}=-3[/tex]

Thus, slope of line passing through given points m=-3

We know that the equation of a line passing through points [tex](x_0,y_0)[/tex] with slope 'm' is [tex](y-y_0)=m(x-x_0)[/tex]

Thus, equation of a line passing through (−2, 11) with slope m=-3 will be

[tex](y-11)=(-3)(x-(-2))\\\Rightarrow\ y-11=-3(x+2)[/tex]

Hence, the equation of line is [tex]y-11=-3(x+2)[/tex]

which of the following represents the zeros of the function f(x) = 4x3 -13x2 -37x +10

Answers

(5,0) (1/4,0) (-2,0)

What value of x makes the denominator of the function equal zero? y= 4/3x-33

Answers

3x - 33 = 0
3x = 33
x = 11

answer is 11

Answer: 11 is your answer

Step-by-step explanation:

What is the length of x-component of v?

Answers

length of x-component of v = 2

answer is B. 2

help please

Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)

Answers

Given the vertices of a triangle as A(2, 5), B(4, 6) and C(3, 1).

a.) A transformation, R_x-axis means that the vertices of the rectangle were reflected across the x-axis.
When a point on the coordinate axis is refrected across the x-axis, the sign of the y-coordinate of the point changes.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule R_x-axis are A'(2, -5), B'(4, -6), C'(3, -1)

b.) A transformation, R_y = 3 means that the vertices of the rectangle were reflected across the line y = 3.
When a point on the coordinate axis is refrected across the a horizontal line, the distance of the point from the line is equal to the distance of the image of the point from the line.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule are A'(2, 1), B'(4, 0), C'(3, 5)

c.) A transformation, T<-2, 5> means that the vertices of the rectangle were shifted 2 units to the left and 5 units up.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<-2, 5> are A'(0, 10), B'(2, 11), C'(1, 6).

d.) A transformation, T<3, -6> means that the vertices of the rectangle were shifted 3 units to the right and 6 units down.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<3, -6> are A'(5, -1), B'(7, 0), C'(6, -5).

e.) A transformation, r(90°, o) means that the vertices of the rectangle were rotated 90° to the right about the origin.
When a point on the coordinate axis is rotated about the origin b 90°, the quadrant of the point changes to the right with the x-value and the y-value of the point interchanging.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule r(90°, o) are A'(5, -2), B'(6, -4), C'(1, -3)

Answer with explanation:

Vertices of ∆ABC are A (2,5), B (4,6) and C (3,1).

Plotting the points on coordinate plane

a.→ [tex]R_{x}[/tex]

We have to find vertices of image , that is ΔA'B'C' when ∆ABC is reflected across x axis.

The Distance from each of the vertices of ∆ABC from X axis will be same as Perpendicular distance from each of vertices of ∆A'B'C' from X axis.

Result is shown in the image 1.

b.→[tex]R_{y}=3[/tex]

We have to find the image of vertices of triangle through line, y=3.

The Distance from each of the vertices of ∆ABC from line,y=3 will be same as Perpendicular distance from each of vertices of ∆A'B'C' from line, y=3.

Result is shown in the image 2.

c. →T(-2,5)

Translation of vertices of triangle ABC by 2 units left and 5 units up.

[tex]A(2,5)_{-2,5} \rightarrow (2-2,5+5)\rightarrow (0,10)\\\\B(4,6)_{-2,5} \rightarrow (4-2,6+5)\rightarrow (2,11),\\\\C(3,1)_{-2,5} \rightarrow (3-2,1+5)\rightarrow (1,6)[/tex]

d.→T(3,-6)

Translation of vertices of triangle ABC by 3 units right and 6 units left.

[tex]A(2,5)_{3,-6} \rightarrow (2+3,5-6)\rightarrow (5,-1)\\\\B(4,6)_{3,-6} \rightarrow (4+3,6-6)\rightarrow (7,0),\\\\C(3,1)_{3,-6} \rightarrow (3+3,1-6)\rightarrow (6,-5)[/tex]

e.→Rotation by 90° with respect to Origin

When rotated in clockwise direction ,vertices of ΔABC changes by the rule ,that is (x,y)→(y,-x) and in anticlockwise direction ,(x,y)→(-y,x).

In clockwise direction

A(2,5)→A"(5,-2)

B(4,6)→B"(6,-4)

C(3,1)→C"(1,-3)

In Anti clockwise direction

A(2,5)→A'(-5,2)

B(4,6)→B'(-6,4)

C(3,1)→C'(-1,3)

Image is depicted below.

(14 + 13) + 2 = 29 Choose an equivalent addition sentence that shows the associative property of addition. 29 = (14 + 13) + 2 (14 + 13) + 2 = 29 14 + (13 + 2) = 29 14 + 13 + 2 = 29

Answers

Final answer:

An equivalent addition sentence showing the associative property of addition in the given example is 14 + (13 + 2) = 29, where the grouping changes but the sum remains the same, rooted in the commutative property of addition.

Explanation:

The question is about the associative property of addition which essentially states that when you add three or more numbers, the way in which you group them doesn't affect the sum. To illustrate with the given example $(14 + 13) + 2 = 29$, an equivalent sentence that demonstrates the associative property would be 14 + (13 + 2) = 29. Here, the grouping has changed, but the resulting sum remains the same. The reason this works is due to the commutative property of addition which tells us that changing the order of the numbers we're adding doesn't change the sum, expressed as A + B = B + A. This universality is showcased by the idea that regardless of 'real-world context' or 'complexity of calculation', the same rules apply.

In △ABC , m∠A=53°,m∠B=17°, and a=27. Find the perimeter of the triangle.

Answers

Using the Law of Sines (sinA/a=sinB/b=sinC/c) and the fact that all triangles have a sum of 180° for their angles.

The third angle is C is 180-53-17=110°

27/sin53=b/sin17=c/sin110

b=27sin17/sin53, c=27sin110/sin53

And the perimeter is a+b+c so

p=27+27sin17/sin53+27sin110/sin53 units

p≈68.65 units (to nearest hundredth of a unit)

Answer:

Step-by-step explanation:

I got it correct on founders edtell

Three bags of of potatoes and four cases of corn cost $40. Five bags of potatoes and two cases Of corn cost $34. Find the cost of one bag of potatoes and the cost of one case of corn. Show your work

Answers

P = potato C = corn

3P + 4C = $40
5P + 2C = $34

Multiply -2 to the 2nd equation to get
-10P - 4C = -68

Add it to the 1st equation

3P + 4C = 40
-10P - 4C = -68
-----------------------
-7P = -28

Solve for P
P = $4

Substitute 4 into P(potato) to find what C(corn) is

Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon.

50 in2
59 in2
85 in2
90 in2

Answers

Answer: choice B) 59 square inches

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

Work Shown:

A1 = Area of rectangle = length*width = 7*4 = 28 square inches
A2 = Area of triangle on top = 0.5*base*height = 0.5*7*6 = 21 square inches
A3 = Area of triangle on right side = 0.5*base*height = 0.5*4*5 = 10 square inches

Total Area = A1 + A2 + A3
Total Area = 28 + 21 + 10
Total Area = 59 square inches

An athlete eats 45g of protein per day while training. How much protein will she eat during 25 days of training?

Answers

1125g of protein an athlete will be eating

Write a recursive formula for 16, 9, 7, 2, 5

Answers

Notice that:

7=16-9
2=9-7
5=7-2

the next term would be: 2-5=-3

so each term of the sequence is equal to its previous term, subtracted from the second previous term:

Also, in order to describe the formula, we need to express the 2 first terms, 1 is not enough.

The recursive formula is:

[tex]a_1=16[/tex]
[tex]a_2=9[/tex]
[tex]a_n_2=a_n_1-a_n[/tex]

The width of a rectangular poster is its length.the area of the poster is 128 square feet what is the width of the poster

Answers

since the length and width are the same, it is actually a square

area of a square is S^2

sqrt(128) = 11.3137

round off as needed

A yogurt with 1 topping is sold for $3.65. Additional toppings can be added for $0.45 cents each. If y represents the total cost and x represents the total number of toppings added, which function rule describes this pattern? A. y=0.45x+3.65 B. y=3.65+0.45(x-1) C.y=3.65+0.45(x+1) D.3.65(x-1)+0.45

Answers

since the 3.65 price includes 1 topping when you calculate the cost of the additional toppings it would be x-1

so the equation would be y=3.65 +0.45(x-1)

What are the possible values of x in x2 + 3x + 3 = 0?

Answers

I'm assuming that that is a quadratic equation:
[tex] x^{2} +3x+3=0[/tex]
The only way to solve this is to use the quadratic formula. When you do that you get a negative number under the square root sign which we all know is illegal, UNLESS you factor out the imaginary "i". So your roots would be this:
[tex]x= \frac{-3+ \sqrt{3}i }{2} ,x= \frac{-3- \sqrt{3}i }{2} [/tex]

William can run 5 laps in 9 2/3 minutes. If one lap is 2/5 of mile how fast is William running in miles per minute?

Answers

I better get some kind of special treatment for solving this one. First of all is William related to Barry Allen in any way? My mans william is running 2 miles in 9 2/3 minutes and he's running 1 mile in 4 5/6! William is running .21 miles per minute. This wasn't worth it for 5 points...

Final Answer ( 0.21 miles per minute)

The legs of a right triangle have lengths of 3 and 4. What is the length, to the nearest tenth, of the altitude to the hypotenuse?

Answers

a² + b² = c²
9 + 16 = c²
25 = c²
5 = c
The lenght of the hypotenuse is 5

(20 points)In 2008, there were 6.7 × 10^9 people living on earth. What is that number in standard notation?

A. 6,700,000
B. 67,000,000
C. 6,700,000,000
D. 67,000,000,000

Answers

Answer is: 6700000000

C. 6,700,000,000

6.7*10^9;
6.7*1,000,000,000
6,700,000,000
So, the answer is
C)6,700,000,000

The sum of two numbers is 47 and the difference is 25 . what are the numbers?

Answers

The numbers are: 36 and 11 .
______________________________________________
Explanation:
______________________________________________
Let us represent the TWO (2) numbers with the variables;
         "x" and "y" .
__________________________________________
     x + y = 47 .

     y − x = 25.
__________________________________________
Since: " y − x = 25 " ;

Solve for "y" in terms of "x" ;

y − x = 25 ;

Add "x" to each side of the equation:
_____________________________________________
   y − x + x = 25 + x ;

to get:

   y = 25 + x .

Now, since:

x + y = 47 ;

Plug in "(25 + x)" as a substitution for "y"; to solve for "x" :

x + (25 + x) = 47 ;

x + 25 + x + 47 ;

2x + 25 = 47 ;

Subtract "25" from each side of the equation:

2x + 25 − 25 = 47 − 25 ;

2x = 22 ;

Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; and to solve for "x" ;

2x / 2 = 22 / 2 ;

    x = 11 ;
______________________________________________
x + y = 47 ;

Plug in "11" for "x" into the equation ; to solve for "y" ;

11 + y = 47 ;

Subtract "11" from EACH SIDE of the equation;
to isolate "y" on one side of the equation; and to solve for "y" ;

11 + y − 11 = 47 − 11 ;

            y = 36 .
___________________________________________
So: x = 11 , y = 36 ;
___________________________________________
Let us check our work:

y − x = 25 ;

36 − 11 =? 25 ? Yes!

x + y = 47 ;

36 + 11 =? 47 ? Yes!
______________________________________________
The numbers are: 36 and 11 .
______________________________________________

In the above figure, AE = 2, CE = 3, and DE = 4. What is the length of BE?

Answers

BE= 6. I had this question not too long ago. Hope this helps. :)

Answer:

its 6 i think

Explanation:

if you have the choices 6, 8, 12, 5.. then 6 is ur answer. why?

well u do CE x DE = AE x BE

(3)(4)= (2)(BE)

12=2x

12÷2= 6

If the ratio of the sides of two similar prisms is 3:5 and the volume of the first prism is 54, what is the volume of the second prism?

Answers

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{s^3}{s^3}=\cfrac{\textit{volume of smaller}}{\textit{volume of larger}}\implies \cfrac{3^3}{5^3}=\cfrac{54}{v} \\\\\\ v=\cfrac{5^3\cdot 54}{3^3}[/tex]

The square root of 32, expressed in terms of a simple radical is

Answers

see attached picture for answer:

The following system of equations can be used to find the roots of the equation x3 + 72 = 5x2 + 18x. y = x3 + 72 y = 5x2 + 18x Graph this system of equations on the graphing calculator. How many intersection points can you see in the default viewing window?

Answers

Answer:

he following system of equations can be used to find the roots of the equation

x3 + 72 = 5x2 + 18x.

y = x3 + 72

y = 5x2 + 18x

Graph this system of equations on the graphing calculator.

How many intersection points can you see in the default viewing window?

✔ 1

Adjust the window so you can find all of the points of intersection for the system of equations.

What are the roots of the original polynomial equation? Check all that apply.

–6

✔ 6

✔ –4

✔ 3

Step-by-step explanation:

Which of the following sets represents the range of the function shown?

{(−3, 4), (5, 11), (9, −1), (10, 13)} (5 points)

{−3, 5, 9, 10}
{−1, 4, 11, 13}
{(4, −3), (11, 5), (−1, 9), (13, 10)}
{−3, −1, 4, 5, 9, 10, 11, 13}

Answers

{−1, 4, 11, 13}
................................

Answer:

it's B guys

Step-by-step explanation:

To the nearest degree what is the measure of each exterior angle of a regular octagon

Answers

Each exterior angle = each central angle = 360 / #of sides.
Each exterior angle = 360 / 8
Each exterior angle = 45 degrees

Answer:

The measure of exterior angle of regular octagon is 45°

Step-by-step explanation:

Given the regular octagon we have to find the measure of exterior angle of regular octagon.

The formula to find the measure of exterior angle of regular octagon is

[tex]\frac{360}{n}[/tex]

where n is number of sides.

Number of sides in octagon=8 sides

Hence, the measure of exterior angle is

[tex]\frac{360}{8}=45^\circ}[/tex]

What would be the point of discontinuity in the following function f(x)=x^2+5x+6/x+3

Answers

The point of discontinuity can be easily detected when you see the face of the graph. If it contains any breaks, there are points of discontinuity. You can determine this analytically if when you substitute x to the equation, the answer would be undefined. Undefined numbers are ∞-∞, 0/0, 0×∞, 0^0, 1^∞ or any number divided by zero.

For the expression f(x)=x^2+5x+6/x+3, you see that there is a term 6/x. Therefore, the expression can be continuous when x=0 because 6/0 or any number divided by zero is undefined. To verify this, let's see the graph by assigning values of x and plotting them against their values of y. As you can see, the curves only approach zero but never touches zero. These are called asymptotes.

how to make d the subject of V=ldh

Answers

d is being multiplied by l and h to isolate easily we can divide by lh on either side resulting in the answer equation: (V/lh)=d

V=ldh
d = V / lh

hope that helps

What is the area of the sector bound by the center of the circle and arc CD in the circle below? Radius is 6 ft and central angle is 30 degrees.

Answers

The answer is 9.42 for the ones wondernig what it was! I calculated it and took the exam and it was correct.

*WILL GIVE BRAINLIEST* (08.03)Consider the following set of equations:

Equation C: y = 2x + 8
Equation D: y = 2x + 2

Which of the following best describes the solution to the given set of equations?
No solution
One solution
Two solutions
Infinite solutions

Answers

Answer:

No solution

Step-by-step explanation:

This is because either way you do it it still doesnt make any sense and doesent line up correctly. THis is high school workand im doing it in 8th grade

Answer:

no solution

Step-by-step explanation:

because it just is

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