Draw a rhombus with the diagonals.
4 right triangles are formed.
The intersection of the diagonals of a rhombus form 90 degree (right) angles (property of a rhombus).
The diagonals of a rhombus bisect each other. This means that they cut each other in half.
So, each of the right triangles have one side = 1, one side = 2.5 and the hypotenuse = unknown (sides of the
rhombus).
Triangle 1. ABC
side a = 2.5, side b = 1
tan A = a/b = 2.5/1 = 2.5
tan A = 2.5
tan 68.2 deg = 2.5
Since, angle C = 90 and angle A = 68.2
angle B = 21.8 deg. (180 - (90 + 68.2))
Since the diagonals bisect angles in each corner of a rhombus (property of a rhombus), therefore, one corner angle is 68.2 + 68.2 = 136.4 deg. and the same side other corner angle is 21.8 + 21.8 = 43.6 deg.
Adjacent sides (ones next to each other) of a rhombus are supplementary. This means that their measures add up to 180 degrees.
Therefore, the opposite corners are
180 - 136.4 = 43.6 and
180 - 43.6 = 136.4.
So, the four angles are,
136.4, 43.6, 136.4, and 43.6----------------------------------------------------------------------------------------------------------"The beautiful thing about learning is that no one can take it away from you"
B.B.King
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You are working for the company Trinity Mathematical Concepts are
asked for create the following logo for the company. If each vertices of the triangle are the centers of the circles, what is the area of the shaded region?
Your answer will be in terms of "x", where "x" is the radius of the circles.
Answer:
[tex](2\pi -3\sqrt{3})x^2/4[/tex]Step-by-step explanation:
The sides of the triangle in the middle are equal to x so tis is equilateral triangle.
Its interior angle is 60°.
Each shaded part is the area of 60° segment of circle with the radius x.
The area of each segment is the difference between 60° sector and the area of triangle.
[tex]A_{segment}=A_{sector}-A_{triangle}[/tex]Area of sector
[tex]A_{sector} = (60/360)*\pi r^2=(1/6)\pi x^2[/tex]Area of triangle
[tex]A_{triangle}=(\sqrt{3}/4)a^2= (\sqrt{3}/4)x^2[/tex]The shaded area is
[tex]A = 3((1/6)\pi x^2 - (\sqrt{3} /4)x^2)=((1/2)\pi -3\sqrt{3} /4)x^2=(2\pi -3\sqrt{3})x^2/4[/tex]PLEASE HELP!! WILL MARK BRAINLIEST.
Answer:
(x-8)^2+(y+8)^2=7
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
Substitute h, k, and r for 8, -8, and √7, respectively.
(x-(8))^2+(y-(-8))^2=(√7)^2
The two negatives in y - (-8) causes it to be a +8. Squaring √7 will make it 7.
Use the diagram below to answer the
following questions.
2x - 1
x + 7
B
X-4
What is the value of x?
X =
=
What is the perimeter of triangle ABC?
The perimeter is
units.
Answer:
34
Step-by-step explanation:
Since this an isosceles triangle we can say the length of AB = AC
2x - 1 = x + 7
2x - x = 7 + 1
x = 8
The perimeter is calculated by adding all side lengths
2x - 1 + x + 7 + x - 4 = Area add like terms
4x + 2 = Area replace x with the value we found
4*8+2 = 34 units square
Find the volume of the figure below.
Answer: it’s a
Step-by-step explanation:
The reason why i said it’s a is because I did this before.
#36
You look up at a drone at an angle of elevation of 23º. Your eyes are 5 feet above the ground, and the distance to
the drone is 210 feet. What is the altitude of the drone? Round your answer to the nnearest tenth.
Altitude: about ___
feet
Using the slope concept, it is found that the height of the drone is of about 94 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The vertical change is of h - 5, in which h is the altitude of the drone.The horizontal change is of 210 ft.The angle is of 23º.Hence:
[tex]\tan{23^\circ} = \frac{h - 5}{210}[/tex]
[tex]h - 5 = 89[/tex]
[tex]h = 94[/tex]
The height of the drone is of about 94 feet.
More can be learned about the slope concept at https://brainly.com/question/18090623
1/17의 십진법 확장에서 반복되는 자릿수 블록의 최대 자릿수는 얼마입니까? 나눗셈을 하여 답을 확인하세요.
what can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? perform the division to check your answer.
Find the lateral surface area of the cylinder. use 3.14 for π, and round your answer to the nearest hundredth. refer to your staar 8th grade math reference sheet for the appropriate formula. question 10 options: 376.99 cm2 362.16 cm2 367.59 cm2 354.18 cm2
The lateral surface area of the given cylinder of radius 10cm and height of 5cm is 314cm sq.
What is the lateral surface area of the cylinder?For a right circular cylinder of radius r and height h, the lateral surface area is the product of diameter to the height and pie.
The lateral surface area of the cylinder = 2πrh
Let assume Radius, r = 10
Height, h = 5.
The lateral surface area of the cylinder = 2πrh
= 2 × 3.14 × 10 × 5
= 314cm sq.
Read more about cylinders;
brainly.com/question/9554871
Which of the following equations would describe the graph shown below?
Answer:
2
Step-by-step explanation:
How many roots does the equation -2x^3 = 0 have?
3
2
1
0
Answer:
3
Step-by-step explanation:
Mrs. Reyes had some apples. If she gave each student 3 apples, she would have 2 apples left have. If she gave each students 4 apples each she would be 2 short. How many apples did she have.
Answer:
14 applesStep-by-step explanation:
Let
Number of apples = aNumber of students = sAccording to question we have equations
a = 3s + 2a = 4s - 2Find the number of students by substitution
3s + 2 = 4s - 24s - 3s = 2 + 2s = 4Find the number of apples
a = 3*4 + 2 = 12 + 2 = 14Answer:
14 apples
Step-by-step explanation:
Let x = number of students
Let y = total number of apples
Create a system of equations with the given information.
Equation 1
If she gave each student 3 apples, she would have 2 apples left:
⇒ y - 3x = 2
Equation 2
If she gave each students 4 apples each she would be 2 short:
⇒ y - 4x = -2
Rewrite Equation 1 to make y the subject:
⇒ y = 2 + 3x
Substitute this into Equation 2 and solve for x:
⇒ (2 + 3x) - 4x = -2
⇒ 2 + 3x - 4x = -2
⇒ 2 - x = -2
⇒ -x = -4
⇒ x = 4
Substitute the found value of x into the rewritten Equation 1 and solve for y:
⇒ y = 2 + 3(4)
⇒ y = 2 + 12
⇒ y = 14
Therefore, Mrs Reyes had 14 apples.
HELP ASAP
Linear equations
Ayudaa no le entiendoo.
[tex]3 {x}^{5} + 2 {x}^{3} + x + {x}^{2} - 2x + 5 = [/tex]
[tex]3 {x}^{5} + 2 {x}^{3} + {x}^{2} - x + 5[/tex]
Answer:
3x⁵ + 2x³ + x² -x + 5
Step-by-step explanation:
(3x⁵ + 2x³ + x) - (-x² + 2x - 5) <== multiply to remove the parenthesis
1(3x⁵ + 2x³ + x) - 1(-x² + 2x - 5)
1(3x⁵) + 1(2x³) + 1(x) + -1(-x²) + -1(2x) + -1(-5) <== remember multiplying 2 negatives, makes a positive
3x⁵ + 2x³ + x + x² - 2x + 5 <== combine any like terms
3x⁵ + 2x³ + x² -x + 5 <== make sure that your answer is in Standard form (in decreasing degrees)
Hope this helps!
which is correct and explain
Answer:
c
Step-by-step explanation:
A square pyramid is shown. What is the surface area of the pyramid? Enter your answer in the box. 100 points
Answer:
33 cm²
Step-by-step explanation:
Formula
Surface Area = 4 x Area (triangle) + Area (square)S.A. = 4 x 1/2 x bh + b²Solving
Given that h = 4 cm and b = 3 cmS.A. = 2 x 4 x 3 + 3²S.A. = 24 + 9 = 33 cm²Answer:
33 cm²
Step-by-step explanation:
Since the pyramid has a square base, the area of each of the triangular sides will be the same.
Therefore, to calculate the total surface area, find the area of one triangle, multiply it by 4, then add it to the area of the square base.
Formulae
Area of a square = x³ (where x is the side length)
Area of a triangle = 1/2 × base × height
Calculation
area of the square base = 3² = 3 × 3 = 9 cm²
area of one triangle = 1/2 × 3 × 4 = 6 cm²
Solution
Total area = area of the square base + 4 × area of one triangle
= 9 + (4 × 6)
= 9 + 24
= 33 cm²
Translate this phrase into an algebraic expression.
7 increased by twice Gail's height
Use the variable g to represent Gail's height.
Answer:
7+2g
Step-by-step explanation:
7 increased by means 7 +
twice Gali's height =2g
everything now becomes 7+2g
30 POINTS! Explanation too, please!
Point A' prime is the image of point A under a rotation about point P. Determine the angles of rotation. Choose all answers that apply: (Choice A) 90 degrees clockwise (Choice B) 90 degrees counterclockwise (Choice C) 180 degrees (Choice D) 270 degrees clockwise (Choice E) 270 degrees counterclockwise
Calculate the zeros of the function f(x) = x2 – 12x + 35 by completing the square.
Answer:
x = 5, x = 7
Step-by-step explanation:
to find the zeros let f(x) = 0 , that is
x² - 12x + 35 = 0 ( subtract 35 from both sides )
x² - 12x = - 35
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 6)x + 36 = - 35 + 36
(x - 6)² = 1 ( take the square root of both sides )
x - 6 = ± [tex]\sqrt{1}[/tex] = ± 1 ( add 6 to both sides )
x = 6 ± 1
then
x = 6 - 1 = 5
x = 6 + 1 = 7
If the volume of a sphere is 83.5cm3 (cubed) what is the radius??
Answer:
2.71
Step-by-step explanation:
Using this formula: Volume= 4 over 3 * π * r cubed.
then do R=(3V4π)⅓=(3·83.54·π)⅓≈2.71144
2.71144 rounded to the nearest 10 is 2.71
if 15% of a class of 20 students were boys, how many boys and girls?
Answer:
15 percent of 20 is 3. so there are 3 boys and 17 girls in the class.
Step-by-step explanation:
The perimeter of a triangle is 29cm. The length of side 2 is double the length of side 1 the length of side 3 is 5 more than side 1. Find the side length of the triangle
Answer: 6 cm, 11 cm, 12 cm
Step-by-step explanation:
B. Study the figure on the right.
1. Name the points on it
2 Name any three segments from the figure,
3. Which segments have B as one endpoint?
4. Which points are endpoints of only two segments?
5. Which points are endpoints of three segments?
6. Which point is the endpoint of six segments?
7. Name the lines with A as one of the points on them.
8. Name any three rays from the figure, 9. How many segments are there in the figure?
10. How many rays can be named from the figure?
Answer:
can you clear more I don't understand
Express the function graphed on the axes below as a piecewise function.
Answer:
f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}
Step-by-step explanation:
To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.
__
Left PieceThe domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.
The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.
The first piece can be written ...
f(x) = x-3 for x ≤ -1
__
Right PieceThe domain is shown as 5 to ∞, with 5 not included.
The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...
y -(-1) = -3(x -5)
y = -3x +15 -1 = -3x +14
The second piece can be written ...
f(x) = -3x +14 for x > 5
__
Whole functionPutting these pieces together, we have ...
[tex]\boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}[/tex]
_____
Additional comment
Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, x > 5.
Write the equation of the circle with the given information: Center: (3,-3) Radius: 2sqrt{6}
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{2\sqrt{6}}{ r} \\\\[-0.35em] ~\dotfill\\\\\ [x-3]^2~~ + ~~[y-(-3)]^2~~ = ~~(2\sqrt{6})^2\implies (x-3)^2+(y+3)^2=24[/tex]
Find measure of the angle UTW
Step-by-step explanation:
Since radii of a circle are congruent, UT is congruent to WT.
Since angles opposite congruent sides in a triangle are congruent, angles UWT and WUT are congruent.
This means the measure of UTV is 180-57-57=66 degrees
Find the value of x.
See picture for full problem. Please and thank you so very much!!
Answer:
x=12
Step-by-step explanation:
The photo might help.
If anything is not understandable I'm here to help :)
Please help what is the product?
Answer: It's A bro
Step-by-step explanation: if you get the brainly app on your phone you can take pics and use that to solve it that's what I did
"Twice the reciprocal of a number plus six equals two thirds." Create an equation and find the number.
Answer:
1/x + 6 = 2/3
x is the number, so there it has to be switched if a reciprocal happens. :) hope this helps
find the surface area of each rectangular prism
How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.
There are 40,320 ways, in which 8 books can be arranged on a shelf.
Solution:Here, we are to find the number of ways in which 8 books can be arranged on a shelf. The total number of books is 8 and the way of arranging books is also 8.
If one book is placed in the first place, then 7 books will be placed in front of it. If 2 books are placed in the 2nd place, then only 6 books can be placed after that book. This sequence will continue till 1 .Permutations :
A permutation is an arrangement of objects in a definite order.➲ P ( n, r )= n ! / ( n - r ) !
n = total number of objectsr = number of objects selectedThe number of ways to arrange 8 books on a shelf will be :
➝ P ( n, r ) = n ! / ( n - r ) !
➝ P ( n, r ) = 8 ! / ( 8 - 8 ) !
➝ P ( n, r ) = 8 ! / 0 !
➝ P ( n, r ) = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 1
➝ P ( n, r ) = 40, 320
ㅤㅤㅤㅤㅤㅤ~ Hence, there are 40,320 ways in which 8 books can be arranged on a shelf !
If the 3 books can't be together (but any 2 of the 3 can be) then it's 36,000 ways. If any one of the 3 books can't touch either of the other 2, it's 15,840 ways.
Explanation:I'm not sure if the question is saying that all three books can't be together in a group (and so biology and history can be together, but biology, history and programming can't), or if the books in that group can't sit next to other books in the group (and so biology and history can't be together). Let's do it both ways - case 1 will be all three together and case 2 will be any 2 together.
Before we work this, let's first see the number of ways we can have all 8 books arranged. Order matters and so we can approach this using a permutation equation. Moreover, since we're using all the books, we'll end up with the total number being:
8 ! = 40 , 320 .
What is the answer to this???
Answer:
Search it up on the internet
Step-by-step explanation:
hope this helps