Rhombus $ABCD$ has perimeter $148$, and one of its diagonals has length $24$. What is the area of $ABCD$?
Answers
Answer:
Area of the rhombus=840
Step-by-step explanation:
Perimeter of a rhombus=4a
148=4a
a=148/4
=37
a=37
The diagonal divides the rhombus into two congruent triangle,
Each congruent triangle= 37 x 37 x 24.
To get the area of the rhombus, we will find the area of one of the congruent triangle, then multiply by 2.
Using Hero's formula to find the area of a triangle, we will use the three sides
Area = √[ s(s-a)(s-b)(s-c) ]
where a, b, and c are the lengths of the three sides: a = 37, b = 37, and c = 24.
s=semiperimeter
s = (a + b + c) / 2
= (37 + 37 + 24)/2
= 98/2
= 49.
s=49
Substitute all the values into the formula
Area = √[ s(s-a)(s-b)(s-c) ]
= √[ 49(49-37)(49-37)(49-24) ]
=√[ 49(12)(12)(25) ]
=√[49(3600)]
=√(176,400)
= 420
Area of one triangle=420
Area of a rhombus=Area of one triangle×2
=420×2
=840
Answer:
840
Step-by-step explanation:
The four sides of a rhombus all have equal length, so if the perimeter is 148, then each side has length 148/4 = 37. Also, the diagonals of a rhombus bisect each other at right angles, so the diagonal of length 24 is cut into two pieces of length 12. We can show this information in a diagram (shown below.)
Applying the Pythagorean Theorem to any of the four right triangles in our diagram, we have
12² + x² = 37².
Solving this equation for positive x, we get x = √37² - 12² = √1369 - 144 = √1225 = 35. The length of the long diagonal is x + x = 70.
The area of a rhombus is half the product of its diagonals. In this case, that is 24 ∙ 70/2 = 12 ∙ 70 = 840.
Related Questions
What is the value of x to the nearest tenth? The figure is not drawn to scale.
5.4
6.3
11.2
x
Answers:
A. x=2.1
B. x=3.4
C. x=9.6
D. x=13.1
Answers
Answer:
we need picture
Step-by-step explanation:
probaby d tho
Given: F(x) = 2x - 4; GX) = 3x + 2; Hpx)=x2
Find FG H(2)
0 121
27
071
Answers
24
Explanation
The format of the question is convoluted, I will assume you mean:
F(x) = 2x - 4
G(x) = 3x + 2
H(x) = x^2
And you want to find FGH(2) ?
1) To evaluate H(2), substitute
x = 2 into the function H(x) = x^2
H(2) = 2^2 = 4
2) To evaluate G(H(2)) substitute
x = 4 (since this is value obtained from H(2)) into the function
G(x) = 3x + 2
G(4) = 12 + 2 = 14
3) To evaluate F(G(4)) substitute x = 14 into the function F(x) = 2x - 4
F(14) = 28 - 4 = 24
Answer:
FG H(2) = F*G*H(2) = 0
Step-by-step explanation:
Your F(x) = 2x - 4; GX) = 3x + 2; Hpx)=x2 requires a bit of guesswork for the reader to understand it. I believe you meant:
F(x) = 2x - 4; G(X) = 3x + 2; H(x)=x2 Find FG H(2)
First find F(2): f(2) = 2(2) - 4 = 0
Because this multiplicand is zero, further multiplication will result in zero also. Thus, the final answer is zero (0).
Jackson is attending a lacrosse game that is halfway through the first quarter.
4) What fractional part of the game is left?
5) If 7 minutes of playing time have past, how many total minutes of playin
time are there in the game?
6) How many minutes of playing time are left in the game?
(I'll also need help on the shading for the fraction picture)
Answers
Answer:
4) 1/8
5) 56
6) 49
First shaded boxes = 4/7
Second shaded boxes = 1 out of 8 boxes are shaded = 1/8
Step-by-step explanation:
1/2x1/4=1/8
7X8=56
59-7=49
First shaded boxes = 4 out of 7 are shaded = 4/7
Second shaded boxes = 1 out of 8 boxes are shaded = 1/8
The fractional part of the game is left [tex]\frac{7}{8}[/tex] , total minutes of playing time 56 mins and playing time are left in the game is 49 mins .
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.
According to the question
Jackson is attending a lacrosse game that is halfway through the first quarter
i.e, Game played = [tex]\frac{1}{2} *\frac{1}{4}[/tex]
Game played = [tex]\frac{1}{8}[/tex]
a) fractional part of the game is left
Game left = 1 - [tex]\frac{1}{8}[/tex] (treated complete game as 1 )
= [tex]\frac{7}{8}[/tex]
b) If 7 minutes of playing time have past,
i.e [tex]\frac{1}{8}[/tex] part of game is completed in 7 mins
therefore,
1 whole will complete in 7*8 = 56 mins
c) Minutes of playing time are left in the game
As,
total time to complete the game - game played time
= 56 - 7
= 49 mins
as in the fraction of shading question
a) [tex]\frac{4}{7 } is shaded[/tex]
b) [tex]\frac{1}{8}[/tex] is shaded
Hence , the fractional part of the game is left [tex]\frac{7}{8}[/tex] , total minutes of playing time 56 mins and playing time are left in the game is 49 mins .
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The position of an object at time t is given by s(t) = -9 - 3t. Find the instantaneous velocity at t = 8 by finding the derivative. 20 POINTS
Answers
Work Shown:
s(t) = -9 - 3t
s ' (t) = -3 ... apply the derivative
The position function is linear, so the derivative is constant. The slope of any straight line is the same regardless of where you are on it, so that's why the velocity is a single fixed number. Put another way, the slope of the line is exactly the velocity (since slope = rise/run = change in distance over change in time). It doesn't matter what the value of t is, the velocity will be -3
Answer:
Step-by-step explanation:
i am doing the SAME THING
Giving Brainly Please Help I Am In A Rush: A 2-column table with 5 rows titled Games Played. Column 1 has entries a percent, a percent, a percent, a percent, b percent. Column 2 has entries c, c, c, c, d. So far this season, a team has won 51 out of 68 games. Identify the values of a, b, c, and d that complete the bar diagram for this situation. a = 10, 25,51,100 b = 25,51,68,100 c = 12.75,14,17,51 d = 30,51,68,100
Answers
Answer:
the answer is below
Step-by-step explanation:
a = 25
b = 100
c = 17
d = 68
Answer:
The correct answer is
a= 25
b = 100
c = 17
d = 68
Step-by-step explanation:
What properties must a quadrilateral possess in order for the quadrilateral to be classified as a.. trapezoid isosceles trapezoid
Answers
Answer:
Step-by-step explanation:
The typical isosceles trapezoid will have a uniform width, measured vertically, but two ends that are not square (not perpendicular to the x-axis. The two sloping ends are congruent (their slopes have exactly the same slope.
The same could be said of an isosceles trapezoid that is vertical; the sloping ends have the same slope.
Answer:
2 parallel sides
2 non-parallel, congruent sides
Step-by-step explanation:
As any other quadrilateral, an isosceles trapezoid has 4 sides. 2 sides must be parallel. The other two sides cannot be parallel but must be congruent.
Please help me with this geometry question:((
Answers
Answer:
7.06
Step-by-step explanation:
Write a proportion using similar triangles.
DF / DG = DE / GE
x / 8 = 15 / 17
x = 7.06
X = 7.06
Why Taraaaaaaa >:C Can somebody please help me?
Answers
Answer:
4 hours
Step-by-step explanation:
3/5 of 8 hours
3/5 * 8 = 4.8 hours
Then she lost 1/6 of the 4.8 hours
4.8 * 1/6
.8
4.8 - .8 = 4
She got 4 hours of sleep
On a trip, a car traveled 80 miles in an hour and a half, then was stopped in traffic for 30 minutes, then traveled 100 miles during the next 2 hours. What was the car's average speed in miles per hour for the 4-hour trip?
Answers
Answer:
45 mph
Step-by-step explanation:
Help plz help I need help
Answers
Answer:
Step-by-step explanation:
There is a 1/20 chance of getting a 1.
This is a 5% chance.
I would say it's highly unlikely.
If this helped, please mark brainliest :D
Answer:
highly unlikely
Step-by-step explanation:
It's certainly not impossible because there is a 1 on the board. However, the probability of landing on the 1 is 1/20 and since that number is really small, it is highly unlikely.
Plz help me 3y+x=7 4x-2y=0
Answers
Answer: 3
Step-by-step explanation:
Help me ASAP for this question Sean buys a binder for $12. If tax is 8%, what is the total cost of the binder?
$12.96 $13 $12.80 $12.08
Answers
Answer:
The cost of the binder is 12.96
Step-by-step explanation:
A number squared added to 16
Answers
Answer:
Sry i dont understand what ur trying to say but if ur asking what number squared will give u 16 its 4
Step-by-step explanation:
Answer:
im pretty sure the answer is 4 but i don't rlly understand the question
Step-by-step explanation:
Jerry solved the system of equations. x minus 3 y = 1. 7 x + 2 y = 7. As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement? The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution. The variable x in the second equation has a coefficient of 7 so it will be easy to divide 7 by 7. The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2. The variable x in the second equation has the largest coefficient. When dividing by 7, the solution will be a smaller number.
Answers
Answer:
A. The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Step-by-step explanation:
Given
[tex]Equation\ 1: x - 3y = 1[/tex]
[tex]Equation\ 2: 7x + 2y = 7[/tex]
Required
Efficient way of solving the equations
The efficient way of solving this problem is by solving for x in the first equation because it has a coefficient of 1;
The evidence is shown as follows;
Make x the subject of formula in equation 1
[tex]x = 1 + 3y[/tex]
Substitute 1 + 3y for x in equation 2
[tex]7x + 2y = 7[/tex]
[tex]7(1 + 3y) + 2y = 7[/tex]
Open bracket
[tex]7 + 21y + 2y = 7[/tex]
[tex]7 + 23y =7[/tex]
Make y the subject of formula
[tex]23y = 7 - 7[/tex]
[tex]23y = 0[/tex]
Divide both sides by 23
[tex]\frac{23y}{23} = \frac{0}{23}[/tex]
[tex]y = 0[/tex]
Recall that x = 1 + 3y
Substitute 0 for y in the above expression
[tex]x = 1 + 3(0)[/tex]
[tex]x = 1 + 0[/tex]
[tex]x = 1[/tex]
Solving for y in the second equation will take more steps
Answer:
A: The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Step-by-step explanation:
Can someone please help with this question below!! i’ll put question 18 in another post right now
Answers
Answer: B
Step-by-step explanation:
In an equilateral triangle, altitudes are also medians. Thus, the bisect their vertex angles.
Hope it helps <3
Akira receives a prize at a science fair for having the most informative project. Her trophy is in the shape of a
square pyramid and is covered in shiny gold foil.
3 in
How much gold foil did it take to cover the trophy, including the bottom?
inches
Answers
Answer:
45 square inches
Step-by-step explanation:
Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the trophy including the bottom
Total surface = surface area of the base square + area of 4 triangles
Calculate the surface area of the base square
surface area of the square = s^2
where s= side length
s=3 in
The surface area of the base =s^2
=3^2
= 9 square inches
The surface area of the side triangles
The area of the triangle = (1/2)* side length* slant height
Side length=3 in
Slant height=6 in
substituting the values,
The area of the triangle =1/2*3*6
= 18/2
= 9 square inches
There are 4 triangles
The area of 4 triangles = 4 x 9
= 36 square inches
Therefore,
Total surface = surface area of the base square + area of 4 triangles
= 9 + 36
= 45 square inches
Answer:
IT'S 216 TRUST ME!
Step-by-step explanation:
1) x2 + 5x + 6
2) x2 + 9x + 20
3) x2 - x+6
4) x2 + 3x - 2
5) x2 – 36
6) 9x? - 25
7) x + x - 42
8) x2 + 7x-12
Please help, I’m struggling
Answers
Answer:
Step-by-step explanation:
x2+12w
2) (x+4) (x+5)
3 & 4 it’s not factorable
5) (x+6) (x-6)
6) (3x+5) (3x-5)
7) 2 (x-21)
8) not factorable
2/9 converted into decimal rounded to the nearest hundreth
Answers
Answer:
0.22
Step-by-step explanation:
2/9 as a decimal is 0.22222222
This number rounded off to its nearest hundredth is 0.22
Hope it helped
Answer:
[tex]\boxed{\sf 0.22}[/tex]
Step-by-step explanation:
[tex]\sf \frac{2}{9} =0.2222222222222222...[/tex]
[tex]\sf Round \ to \ nearest \ hundredth.[/tex]
[tex]\sf \frac{2}{9} \approx 0.22[/tex]
A Magic Carpet is 12 feet long and 10 feet wide. However, only the purple part of the Magic Carpet has magic power. If the magic part is 2 feet wide, find the area of the magic part of the Magic Carpet.
Answers
Answer:
24 ft.
Step-by-step explanation:
2x12=24
The temperature at noon is -4 degrees Celsius. The temperature at 6:00pm is -12 degrees Celsius. What is the difference between the noon and the 6:00pm temperatures?
Answers
Answer: -8 degrees
Step-by-step explanation: 12-4 is 8 so the difference is -8
Harrison ordered 6 cases of pickles for his restaurants. Each case contained p jars of pickles. Harrison delivered an equal number of jars to each of his 7 restaurants. Which expression represents the number of jars of pickles that each restaurant received? A. 6p-7 B. [tex]\frac{6p}{7}[/tex] C. 6p+7 D. 7(6+p) E. [tex]\frac{6}{7p}[/tex]
Answers
Answer:
B. 6p/7
Step-by-step explanation:
6p = the total amount of pickles
The problem says that he distributes them evenly to 7 restaurants, so that's dividing.
So your answer is 6p/7
Answer: b 6p/7
Step-by-step explanation: 6p = the total amount of pickles. The problem says that he distributes them evenly to 7 restaurants, so that's dividing. So your answer is 6p/7.
Type the correct answer in each box. In 2013, the population of the state of New York was approximately 19.65 million, and the population of New York City was 8,406,000. In 2013, how many people in New York state did not live in New York City? The answer in standard notation is______. The answer in scientific notation is p × 10q, where p is_____and q is ____.
Answers
Answer:
The answer in standard notation is 11'244,000. The answer in scientific notation is p * 10∧7, where p is 1.1244 and q is 7.
Step-by-step explanation:
Let's answer the question correctly this way:
Population of New York State = 19'650,000
Population of New York City = 8'406,000
Population that do not live in New York City = 19'650,000 - 8'406,000
Population that do not live in New York City = 11'244,000
Population that do not live in New York City in scientific notation = 1.1244 * 10⁷
The answer in standard notation is 11'244,000. The answer in scientific notation is p * 10∧7, where p is 1.1244 and q is 7.
What is the value of log,(5)1252
3
5
15
25
Answers
Pls, help my sister I will mark the brainliest! Very easy!
Write equivalent fractions of
2/3 5/6 1/4
Answers
Answer:
4/6
10/12
3/2
Step-by-step explanation:
2/3=2/3*2/2=4/6
5/6=5/6*2/2=10/12
1/4=1/4*3/3=3/12
You can multiply the fraction with any whole number to get the equivalent fraction of any fraction.
Hope this helps ;) ❤❤❤
4/6
10/12
3/2
Step-by-step explanation:
2/3=2/3*2/2=4/6
5/6=5/6*2/2=10/12
1/4=1/4*3/3=3/12
Mr. Avogadro started with 5.14x10^22 atoms of Pa-234. Ten days later Mr. Avogadro calculated the original sample had only 6.43 X 10^21 atoms of Pa-234. What's the half life of Pa-234? PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
is 1
step by step explanation:
Compare 6 ⋅ 108 to 3 ⋅ 106.
Answers
Answer:
6*108>3*106
Step-by-step explanation:
If you multiply 6, and 108, you would get 648.
And if you were to multiply 3 and 106 you would get 318. And 648>318.
Therefore, 6*108>3*106
3*106=318
COMPARE:
648(6*108) is greater than 318(3*106)
hope this helps <3 if you have any questions comment them ;)
Which number is the largest 1.2 x 104, 4.5 x 10–3, 3.8 x 103, 7.5 x 103
Answers
The correct answer is the last one, 7.5 x 104. (the sum is 772.5)
Step-by-step explanation:if you multiply it the sum is 772.5, and all the other ones sum is less than 772.5
I hope this helped (:
What is the measure of ACE in the diagram below?
A. 46
B. 104
C. 29
D. 58
Answers
Answer:
C
Step-by-step explanation:
The secant- secant angle ACE is half the difference of the measures of the intercepted arcs, that is
∠ ACE = [tex]\frac{1}{2}[/tex] (AE - BD ) = [tex]\frac{1}{2}[/tex] (104 - 46)° = [tex]\frac{1}{2}[/tex] × 58° = 29° → C
***HOPE THIS HELP YOU***
At a concession stand,three hot dog(s) and two hamburger(s) cost $8.25;two hot dog(s) and three hamburger(s) cost $8.00. Find the cost of one hot dog and the cost of one hamburger. What is the cost of one hot dog? $_____
Answers
Answer:
The cost of one hot dog and the cost of one hamburger is $3.25
The cost of one hot dog is $1.75
Step-by-step explanation:
Let the number of hot dogs be represented by d and hamburgers be h
3d + 2h = 8.25 ----- eqn(I)
2d + 3h = 8.00 ----- eqn(II)
From eqn(I): d = (8.25 - 2h)/3
substitute the expression for d into eqn(II)
2d + 3h = 8
2(8.25 - 2h)/3 + 3h = 8
(16.50 - 4h) + 3h(3) = 8(3)
16.50 - 4h + 9h = 24
5h = 24 - 16.50
5h = 7.50
h = 7.50/5 = 1.50
One hamburger costs $1.50
d = (8.25 - 2h)/3 = (8.25 - 2×1.50)/3 = (8.25 - 3.00)/3 = 5.25/3 = 1.75
One hot dog costs $1.75
Cost of one hot dog and cost of one hamburger = $1.75 + $1.50 = $3.25
Graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin.
Answers
==================================================
Explanation:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2 means we multiply each coordinate of each point by the value 2
A = (0,0) becomes A' = (0,0). No change happens. This point is fixed
B = (2,-4) becomes B' = (4,-8). This point does move
C = (-4,-4) becomes C' = (-8,-8). This moves as well
So all you need to do from here is draw triangle A'B'C'.
-----------------
Side note: the lengths of triangle A'B'C' are twice as long as their counterparts on triangle ABC. Consequently, this means the perimeter of A'B'C' is twice as long as the perimeter of ABC. Also, triangle A'B'C's area is four times larger than the area of triangle ABC.
Triangle with the three corner points at
A' = (0,0). B' = (4,-8). C' = (-8,-8). what is Dilation?Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the objects. The result of this transformation is an image with the same shape as the original.
Given:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2
A = (0,0) --> A' = (0,0).
B = (2,-4) --> B' = (4,-8).
C = (-4,-4) --> C' = (-8,-8).
Learn more about Dilation here:
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