The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal BD if you know that the perimeter of △ABD is 8 cm.
Answers
Let
P1-------------> Perimeter of parallelogram ABCD
P2-------------> Perimeter of △ABD
we know that
P1=10 cm
P1=2*(AD)+2*(AB)=10------------> AB+AD=5-----------> equation 1
and
P2=AD+AB+DB
P2=8 cm------------>AD+AB+DB=8-------- AB+AD=8-DB-----> equation 2
I substitute 1 in 2
(5)=8-DB----------> DB=8-5-----------> DB=3 cm
the answer is DB=3 cm
The length of the diagonal BD is 3 centimeters.
Procedure - Length determination in a parallelogram sideA parallelogram is a quadrilateral where each pair of parallel sides have the same length and can be form by two congruent triangles which share the same side (diagonal).
Expressions for the parallelogramPerimeter equations for the parallelogram are the following:
[tex]AB + BD + AD = 8\,cm[/tex] (1)
[tex]2\cdot AB + 2\cdot AD = 10\,cm[/tex] (2)
Where:
[tex]AB[/tex], [tex]AD[/tex] - Side lengths of the parallelogram, in centimeters. [tex]BD[/tex] - Diagonal length of the parallelogram, in centimeters.Resolution of the systemBy (2) we have the following conclusion:
[tex]AB + AD = 5\,cm[/tex]
And we find the length of the diagonal BD by (1):
[tex]5\,cm + BD = 8\,cm[/tex]
[tex]BD = 3\,cm[/tex]
The length of the diagonal BD is 3 centimeters. [tex]\blacksquare[/tex]
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Related Questions
Which expression is equivalent to to the equivalent -1/2(-3/2x+6x+1)-3x
Answers
Answer:
Step-by-step explanation:
Bonjour
Which expression is equivalent to the equivalent -1/2(-3/2x+6x+1)-3x
= 3/4 x - 3x - 1/2 - 3x
= 3/4 x - 24/4 x - 1/2
= -21/4 x - 1/2
Chen can jump rope 60 times a minute at that rate how many jumps can he make in 9 minutes
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So
9min=60÷1×9
=540 jumps
A letter grade of a B+ average in a regular class counts for how many points?
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Answer:
3.33
Step-by-step explanation:
if (-4,-2) and (2,6) are opposite points on a circle, what is the equation of the circle?
Answers
The equation of the circle is
.. (x +1)^2 +(y -2)^2 = 25
You work two jobs. You earn $11.90 per hour as a salesperson and $10.50 per hour stocking shelves. Your combined earnings this month are $178.50. Let x represent the number of hours worked stocking shelves and let y represent the number of hours worked in sales. Graph the equation that models this situation
Answers
x = represent the number of hours worked stocking shelves
y = represent the number of hours worked in sales
We write the equation:
11.90y + 10.50x = 178.50
Observe that the equation represents a line of negative slope.
Answer:
See graphic in attached image.
Answer:
The required equation model the situation is [tex]10.50x+11.90y= 178.50[/tex]
Step-by-step explanation:
Let 'x' represent the number of hours worked stocking shelves
Let 'y' represent the number of hours worked in sales.
You earn $11.90 per hour as a salesperson i.e. 11.90y.
You earn $10.50 per hour stocking shelves i.e. 10.50x.
Your combined earnings this month are $178.50.
i.e. [tex]10.50x+11.90y= 178.50[/tex]
The required equation model the situation is [tex]10.50x+11.90y= 178.50[/tex]
To plot the graph we find x and y intercept,
For x-intercept put y=0,
[tex]10.50x+11.90(0)= 178.50[/tex]
[tex]x=\frac{178.50}{10.50}[/tex]
[tex]x=17[/tex]
Point is (17,0).
For y-intercept put x=0,
[tex]10.50(0)+11.90y= 178.50[/tex]
[tex]y=\frac{178.50}{11.90}[/tex]
[tex]y=15[/tex]
Point is (0,15).
Refer the graph attached below.
Which of the following describes the polynomial function?
Answers
Explanation:
1) The leading coefficient is the coefficient of the leading term. The leading term is the the term with the highest degree.
The leading term is dominant when x grows. So, for x → infinity the value of a polynomial trends toward infinity if the leading coefficient is positive and toward negative infinity if the leading coefficient is negative.
The graph shows that the function goes to infinity as x grows, so the leading coefficient is positive, which discards the first choice (that the function has a negative leading coefficient).
2) It is right that the polynomial has an odd degree.
The degree of a polynomial is the highest degree of its individual terms.
Odd-degree polynomials have ends that head off in opposite directions, while the ends of even-degree polynomilas come in and leave out the same quadrant.
It is easy to remember is you think that even-degree polynomials behave, on their ends, like quadratics, and all odd-degree polynomials behave, on their ends, like cubics.
3) The other statements are easy to discard: there are two turns on the graph and the function has 3 x-intercepts.
Answer:
The function has an odd degree
Step-by-step explanation:
Edge 2020
On Monday 21 dvd's were checked out at the library. This is 3 less than half the amount of books check out that day. How many books were checked out?
Answers
21 = 1/2b - 3
b = (21 + 3) divide by 1/2
=24 × 2
The answer is 48 books.
HELP ME RN PLZ HURRY PLZ PLZ PLZ WILL GIVE BRAINLIEST COME ANSWER ME QUESTION!!!!!|
Find the missing measures for the rectangle.
l = _?_
w = 2 cm
A = _?_
P = 25 cm
12.5 cm; 21 cm2
10.5 cm; 21 cm2
12.5 cm; 25 cm2
10.5 cm; 25 cm2
Answers
[area of rectangle]=l*w
[perimeter of rectangle]=2*[l+w]
w=2 cm
P=25 cm
so
[perimeter of rectangle]=2*[l+w]--------> 25=2*[l+2]----> l=(25/2)-2---> l=10.5 cm
[area of rectangle]=l*w--------> 10.5*2--------> 21 cm²
the answer is
l=10.5 cm
A=21 cm²
A rectangular prism has a length of 20 in a width of 2 in and a height of 3 1/4 in the prism is filled with cubes that have edge lengths of 1/4 in how many cubes are needed ro fill the rectangular prism
Answers
Edge lengths are
.. 80 cubes by 8 cutes by 13 cubes
so total volume is
.. (80 * 8 * 13) = 8320 cubes
In cubic inches, the volume is
.. (20 in)*(2 in)*(3 1/4 in) = 130 in^3.
The volume of a 1/4-in cube is (1/4 in)^3 = 1/64 in^3.
Then the number of cubes that will fit in the prism is
.. (130 in^3)/(1/64 in^3) = 8320 . . . . cubes
8320 cubes are needed to fill the rectangular prism.
A box of fruit has three times as many nectarines as grapefruit. Together there are 36 pieces of
fruit. How many pieces of each type of fruit are there?
write an equation to repsent this problem
Answers
The total amount of fruit is g+n which is also g+3g=4g. But there are 36, so 4g=36. That means g=9. That also means that n=27.
There are 9 grapefruits and 27 nectarines.
Final answer:
The problem involves forming and solving a linear equation to determine the number of nectarines and grapefruits in a box, where the total count is 36 and the nectarines are three times as many as the grapefruits. By setting up the relationship as 'n = 3g' and 'n + g = 36', we can solve for 'g' and 'n' to find that there are 9 grapefruits and 27 nectarines.
Explanation:
The student's question involves solving a linear equation to find the number of nectarines and grapefruits in a box when given a specific ratio and total. Let's denote the number of grapefruits as 'g' and the number of nectarines as 'n'. According to the problem, there are three times as many nectarines as grapefruit, so we can write this relationship as 'n = 3g'. Also, we know that the total number of fruit is 36, which gives us another equation: 'n + g = 36'.
Now we have a system of two equations:
n = 3gn + g = 36To find the values of 'g' and 'n', we can substitute the first equation into the second one, resulting in '3g + g = 36', which simplifies to '4g = 36'. Dividing both sides by 4 gives us 'g = 9'. Having found the number of grapefruits, we can now determine the number of nectarines by multiplying the number of grapefruits by 3, thus 'n = 3 times 9 = 27'.
So, there are 9 grapefruits and 27 nectarines in the box.
In Mark's class, there are 15 students with brown hair, 3 students with blonde hair, and 5 students with black hair. What is the ratio of students with brown hair to students with black hair?
Answers
Answer: 3 : 1
Step-by-step explanation:
We know that the ratio of A to B is given by :-
[tex]\dfrac{A}{B}[/tex] or A : B .
Given : Number of students having brown hair = 15
Number of students having black hair = 5
Then , the ratio of students with brown hair to students with black hair will be :-
[tex]=\dfrac{\text{No. of students with brown hair}}{\text{No. of students with black hair}}\\\\=\dfrac{15}{5}=\dfrac{3}{1}[/tex]
Hence, the ratio of students with brown hair to students with black hair = 3 : 1.
Answer:
3 to 1
Step-by-step explanation:
I did the quiz
There are 30 dogs at the park. 5/6 of the dogs are large. Which method is a way to find the number of large dogs at the park?
Answers
Answer:
Divide 30 by 6 and then multiply the quotient by 5.
HELLLPPP PLLZZZZ IIII BEEEEGGGG UUU
HELPPP PLLLZZZ III BEEEG
For what value of x is the square of the binomial x+1 twenty greater than the square of the binomial x–3?
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Draw a number line and mark all described points.
x2=4
Question solved! please dont answer
Answers
x ^ 2 = 4
We clear x to find the points described by the expression:
x = + / - root (4)
x = + / - 2
Therefore, the points sought are:
x1 = 2
x2 = -2
Answer:
x1 = 2
x2 = -2
Note: see attached image
please help me find the simple interest.
Answers
I = $925*0.0775*(30/360)
I = $5.97
The simple interest is $5.97.
Maria wrote the equation log(x/2)+log(20/x^2)=log8. What is the solution to Maria's equation?
a. x=3/10
b. x=4/5
c. x=5/4
d. x10/3
Answers
We use the properties of logs to rewrite the equation:
[tex]\log[(\frac{x}{2})(\frac{20}{x^2})]=\log8 \\ \\\log(\frac{20x}{2x^2})=\log8 \\ \\\log(\frac{10}{x})=\log8[/tex]
Get all of the logs on the same side of the equation y subtracting log 8:
[tex]\log(\frac{10}{x})-\log8=\log8 - \log8 \\ \\\log(\frac{10}{x})-\log8=0[/tex]
Use the properties of logs to rewrite:
[tex]\log(\frac{10}{x}\div8)=0 \\ \\\log(\frac{10}{x}\div\frac{8}{1})=0 \\ \\\log(\frac{10}{x}\times\frac{1}{8})=0 \\ \\\log(\frac{10}{8x})=0[/tex]
Exponentiate:
[tex]10^0=\frac{10}{8x} \\ \\1=\frac{10}{8x}[/tex]
Multiply both sides by 8x:
1*8x = (10/8x)*8x
8x=10
Divide both sides by 8:
8x/8 = 10/8
x = 10/8 = 5/4
Answer:
C. x=5/4
Step-by-step explanation:
Correct answer on edge 2022
What is 48% of $430.00?
(calculate the percent or value)
I need answers!
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Jason and Donny painted a room and received $300. To complete the painting job Jason spent 4 hours and 25 minutes and Donny spent 2 hours and 15 minutes. If they split the $300 in proportion to the time each spent painting, how much did Donny receive?
Answers
Donny spent 2.25 hours painting, while Jason spent 4.4167 hours. The total time spent was 6.6667 hours, and Donny's percentage of this time was approximately 33.75%. Therefore, Donny received $101.25 of the $300 payment.
To determine how much Donny received from the $300 for the painting job, we first need to calculate the total amount of time Jason and Donny spent painting, then divide the total earnings based on the proportion of time spent. Jason spent 4 hours and 25 minutes, which is equivalent to 4.4167 hours (4 hours and 25 minutes / 60 minutes). Donny spent 2 hours and 15 minutes, which is equivalent to 2.25 hours (2 hours and 15 minutes / 60 minutes).
The total time spent on the painting job is the sum of Jason's time and Donny's time, which is 4.4167 + 2.25 = 6.6667 hours. The proportion of time Donny spent is 2.25 hours / 6.6667 total hours, which equals approximately 0.3375 (or 33.75%).
Therefore, Donny's share of the $300 is 0.3375 * $300, which equals $101.25. As a result, Donny received $101.25 for his part of the painting job.
if cos28 = x/4, find x(3sf)
Answers
The value of x when cos(28°) = x/4 is found by solving the equation, leading to x = 3.53 to three significant figures. This involves basic trigonometry and arithmetic operations.
Explanation:If cos(28°) = x/4, we are asked to find the value of x to three significant figures. This type of problem involves trigonometry, a branch of mathematics that deals with the relationships between the sides and angles of triangles. To solve for x, we use the equation given and manipulate it to isolate x.
Given that cos(28°) = x/4, we can find x by multiplying both sides of the equation by 4:
x = 4 * cos(28°)Using a calculator, cos(28°) approximately equals 0.8829. Therefore, x is equal to 4 * 0.8829, which simplifies to:
x = 3.5316To three significant figures, x = 3.53.
∠1 and ∠2 are a linear pair. m∠1 = x - 29, and m∠2 = x + 61. Find the measure of each angle.
Answers
The Answer is letter B
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. refer to exhibit 6-5. what is the probability that a randomly selected item will weigh more than 10 ounces?
Answers
_____
My probability app says the probability is 0.15866.
A rock is dropped into a water well and it travels approximately 16t2 in t seconds. If the splash is heard 3.5 seconds later and the speed of sound is 1087 feet/second, what is the height of the well?
Answers
Which expression is equivalent to −1/4x + 1/2 ?
−1/4 (−x + 1/2)
1/4 (−x + 1/2)
−1/4 (x + 2)
1/4 (−x +2)
Answers
= (1/4)(-x) + (1/4)(2) . . . . . . factor 1/4 from each term. (1/2 = 2/4)
= 1/4 (-x +2)
Melinda needs 6 gallons of punch for her party. the grocery only sells quarts of punch. how many quarts will she need?
Answers
4 x 6 = 24. She will need 24 quarts to equal 6 gallons.
Brainliest please?
Sketch the region bounded by the curves y=3x3, x+y=4, and y=0. Find the coordinates of the centroid.
Answers
To sketch the region, find the intersection points and use them to form a triangle. The centroid is found by taking the average of the x and y values of the vertices.
Explanation:To sketch the region bounded by the curves y=3x^3, x+y=4, and y=0, we first need to find the x-coordinates of the points where the curves intersect. Setting the equations equal to each other, we get 3x^3 + x = 4. Solving for x, we find x = 1. The region bounded by the curves is a triangle with the vertices (0,0), (1,0), and (1,3).
To find the coordinates of the centroid, we first find the x-coordinate by taking the average of the x-values of the vertices: (0 + 1 + 1)/3 = 2/3. Next, we find the y-coordinate by taking the average of the y-values of the vertices: (0 + 0 + 3)/3 = 1. So, the coordinates of the centroid are (2/3, 1).
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Find two consecutive whole numbers that the square root of 17 lies between.
Answers
The square root of 17 is between the integers 4 and 5
In order to know which two whole numbers the square root of 31 fall ib between, we need to get a perfect square that is less than 31 and also greater than 31
The two perfect numbers are 16 and 325
Taking the square root of these numbers;
√16 = √4 *4 = 4
√25 = √5 * 5 = 5
This shows that the square root of 17 is between the integers 5 and 6
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A parallelogram has an area of 108 square centimeters. If the base measures 18 centimeters, what is the height?
Answers
The height of the parallelogram is 6cm.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
We have,
Area of parallelogram = 108 square cm
Base = 18 cm
So, Area of parallelogram
108 = base x height
108 = 18 x height
Height= 108/ 18
Height = 6 cm
Thus, the height is 6 cm.
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if a circle has a radius of 12 inches what is the arc length inside the interior angle 90 degrees
Answers
2(3.14)(12)(90/360)
2(3.14)(12)(0.25)
18.84
Hope that helps :)
Find the zeros of f(x) = 4x 2 + 5x - 21.
Answers
For f(x)=4x^2 + 5x -21
The zeros of the function are: x=-3, x=7/4
Hope this helps!
The required zeros of the given polynomial equation are x = 7/4 and x = -3.
Zeros of an equation is defined as the value of the independent variable where the equation or function gives zero.
here,
Given expression,
f(x) = 4x² + 5x - 21.
Putting the above expression equal to zero,
4x² + 5x - 21 = 0
Factorizing the above equaiton gives,
(x - 7/4)(x + 3) = 0
Now,
x = 7/4 and x = -3
Thus, the required zeros of the given polynomial equation is x = 7/4 and x = -3.
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A prism with a volume of 360yd^3 is scaled down to a volume of 45yd^3. What is the scale factor? Enter your answer, as a decimal or a fraction in simplest form, in the box.
Answers
in volume
[the scale factor]=∛{[reduced volume]/[initial volume]}
[the scale factor]=∛{45/360}------> ∛0.125
[the scale factor]=(1/2)
the answer is (1/2)