Answers
Step 1
Find the value of s
we know that
In a Rhombus all sides are congruent
so
[tex]AB=BC=CD=DA[/tex]
[tex]AB=9s+29\\CD=10s-16[/tex]
equate AB and CD
[tex]9s+29=10s-16\\[/tex]
Combine like term
[tex]10s-9s=29+16\\[/tex]
[tex]s=45\ units[/tex]
The answer Part a) is
the value of s is [tex]45\ units[/tex]
Step 2
Find the value of side AB
[tex]AB=9s+29[/tex]
substitute the value of s
[tex]AB=9*45+29=434\ units[/tex]
Remember that the sides are congruent
[tex]AB=BC=CD=DA[/tex]
therefore
the answer Part b) is
The length of the side BC is [tex]434\ units[/tex]
The value of s is 45 and the length of side BC is; 434.
What is a Rhombus?A rhombus is a plane shape of the form given I'm the attached image with all its sides equal.
Hence,
AB = BC = CD = DATo determine the value of s;
10s - 16 = 9s + 2910s-9s = 29+16s = 45.The length of side BC = CD = 10(45) - 16 = 450 - 16
The length of side BC = 450 -16 = 434
Read more on Rhombus;
https://brainly.com/question/20627264
Related Questions
Please I'm stuck in this problem
Answers
Which expression is equivalent to (7^3)−2
A- 1 over 7 times 7 times 7 times 7 times 7 times 7
B- 7
C- 1 over 7
D-negative 1 over 7 times 7 times 7 times 7 times 7 times 7
Answers
Department w had 2,400 units, one-third completed at the beginning of the period; 16,000 units were transferred to department x from department w during the period; and 1,800 units were one-half completed at the end of the period. assume the completion ratios apply to direct materials and conversion costs. what is the equivalent units of production used to compute unit conversion cost on the cost of production report for department w? assume the company uses fifo.
Answers
The equivalent units of production for calculating conversion costs in Department W using FIFO are 16,900 units. This consists of 16,000 units transferred out and 900 equivalent units for the 1,800 units at half completion stage.
Explanation:To calculate the equivalent units of production for unit conversion cost in Department W, using the FIFO method, we need to account only for the work done in the current period. Department W had 2,400 units at the beginning that were one-third completed, which means 800 units (2,400 units * 1/3) were already processed in the previous period. Therefore, these do not count for the current period. During the period, 16,000 units were transferred out. We also need to consider the 1,800 units at the end at one-half completion, which contributes 900 equivalent units (1,800 units * 1/2) for the current period.
To determine the number of equivalent units for conversion costs, we perform the following calculation:
Equivalent units for units transferred to Department X: 16,000 units (these are complete with respect to Department W's work).Equivalent units for ending work-in-process: 1,800 units * 1/2 = 900 units.Total equivalent units of production for conversion costs: 16,000 units + 900 units = 16,900 units.
How do you find a vector that is orthogonal to 5i + 12j ?
Answers
[tex]\bf \boxed{5i+12j}\implies \begin{array}{rllll} \ \textless \ 5&,&12\ \textgreater \ \\ x&&y \end{array}\quad slope=\cfrac{y}{x}\implies \cfrac{12}{5} \\\\\\ slope=\cfrac{12}{{{ 5}}}\qquad negative\implies -\cfrac{12}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{12} \\\\\\ \ \textless \ 12, -5\ \textgreater \ \ or\ \ \textless \ -12,5\ \textgreater \ \implies \boxed{12i-5j\ or\ -12i+5j}[/tex]
if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.
so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.
so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.
or using a unit vector for those above, then
[tex]\bf \textit{unit vector}\qquad \cfrac{\ \textless \ a,b\ \textgreater \ }{||\ \textless \ a,b\ \textgreater \ ||}\implies \cfrac{\ \textless \ a,b\ \textgreater \ }{\sqrt{a^2+b^2}}\implies \cfrac{a}{\sqrt{a^2+b^2}},\cfrac{b}{\sqrt{a^2+b^2}} \\\\\\ \cfrac{12,-5}{\sqrt{12^2+5^2}}\implies \cfrac{12,-5}{13}\implies \boxed{\cfrac{12}{13}\ ,\ \cfrac{-5}{13}} \\\\\\ \cfrac{-12,5}{\sqrt{12^2+5^2}}\implies \cfrac{-12,5}{13}\implies \boxed{\cfrac{-12}{13}\ ,\ \cfrac{5}{13}}[/tex]
To find a vector orthogonal to 5i + 12j, we can use the property that orthogonal vectors have a dot product of 0. By setting up equations and solving them accordingly, you can find a vector that is perpendicular to 5i + 12j.
Orthogonal vectors: To find a vector orthogonal to 5i + 12j, we need to find a vector with a dot product of 0 with 5i + 12j. Since the dot product of orthogonal vectors is zero, we can set up equations and solve them to find a vector that is perpendicular to 5i + 12j.
hey can you just please help me solve these two problems
1- according to the bipartisan policy center (BPC), 57.5% of all eligible voted in the 20112 presidential elections. while there are over 350 million Americans, the BPC estimates that only 219 million are eligible to vote. how many eligible voters in 2012 election?
2-sarah's sandwich shop sells a specialty sandwich for $4.95 that contains a quarter of a pound of turkey. if sarah buys 12 pounds of turkey meat but eats a tenth of a pound on the way to her sandwich shop, what is the maximum number of sandwiches she can make?
Answers
well, she needs 1/4lb to make a sandwich, well, she bought 12lbs and then she couldn't resist, because she got some ketchup also I gather, she couldn't resist giving it a nibble and ate 1/10lb
so.. is 12 - 1/10, and how many times 1/4 goes into that difference
[tex]\bf 12-\cfrac{1}{10}\implies \cfrac{120-1}{10}\implies \cfrac{119}{10} \\\\\\ \textit{how many times }\frac{1}{4}\textit{ goes in to }\frac{119}{10}? \\\\\\ \cfrac{\frac{119}{10}}{\frac{1}{4}}\implies \cfrac{119}{10}\cdot \cfrac{4}{1}\implies \cfrac{238}{5}\implies \boxed{47\frac{3}{5}} \\\\\\ \cfrac{47\cdot 5+3}{5}\implies \cfrac{238}{5}[/tex]
well, noone is going to buy a half-eaten sandwich or 3/5 of a sandwich, so, she can only make 47 whole sandwiches, hmmmm I'm thinking she can just give the 3/5 to the dogs.
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −1 1 s2 − 720 s7
Answers
The inverse Laplace transform of [tex]\( \frac{1}{s^2 - 720s^7} \) is \( (1 - \frac{1}{720})t + e^{720t} \).[/tex]
To find the inverse Laplace transform of [tex]\( \frac{1}{s^2 - 720s^7} \),[/tex] we can use the method of partial fraction decomposition. First, factor the denominator:
[tex]\[ s^2 - 720s^7 = s^2(1 - 720s^5) \][/tex]
Now, we can write the partial fraction decomposition as:
[tex]\[ \frac{1}{s^2(1 - 720s^5)} = \frac{A}{s} + \frac{B}{s^2} + \frac{Cs^5 + D}{1 - 720s^5} \][/tex]
Multiplying both sides by [tex]\( s^2(1 - 720s^5) \)[/tex], we get:
[tex]\[ 1 = As(1 - 720s^5) + Bs(1 - 720s^5) + (Cs^5 + D)s^2 \]\[ 1 = As - 720As^6 + Bs - 720Bs^6 + Cs^7 + Ds^2 \][/tex]
Equating coefficients:
For [tex]\( s^6 \):[/tex]
-720A - 720B = 0
A + B = 0
A = -B
For [tex]\( s^7 \):[/tex]
C = 0
For [tex]\( s^2 \):[/tex]
D = 1
Substituting back:
A = -B
D = 1
C = 0
So, the partial fraction decomposition is:
[tex]\[ \frac{1}{s^2(1 - 720s^5)} = \frac{-B}{s} + \frac{1}{s^2} + \frac{D}{1 - 720s^5} \][/tex]
Now, we can find the values of [tex]\( A \), \( B \), and \( D \):[/tex]
A = -B
D = 1
Now, we can use Theorem 7.2.1 to find the inverse Laplace transform:
[tex]\[ \mathcal{L}^{-1}\left( \frac{1}{s^2(1 - 720s^5)} \right) = -B \mathcal{L}^{-1}\left( \frac{1}{s} \right) + \mathcal{L}^{-1}\left( \frac{1}{s^2} \right) + D \mathcal{L}^{-1}\left( \frac{1}{1 - 720s^5} \right) \][/tex]
[tex]\[ = -B + t + D \mathcal{L}^{-1}\left( e^{720t} \right) \][/tex]
[tex]\[ = -B + t + De^{720t} \][/tex]
Since [tex]\( B = \frac{1}{720} \), \( D = 1 \)[/tex], the inverse Laplace transform is:
[tex]\[ \mathcal{L}^{-1}\left( \frac{1}{s^2(1 - 720s^5)} \right) = -\frac{1}{720}t + t + e^{720t} \][/tex]
[tex]\[ = \left( 1 - \frac{1}{720} \right)t + e^{720t} \][/tex]
Complete Question:
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of [tex]\( \frac{1}{s^2 - 720s^7} \).[/tex]
simplify the expression I-30I
Answers
0.2(x + 1) + 0.5x = –0.3(x – 4)
Answers
Andrei has a job in the circus walking on stilts. Andrei is 11/10 meters tall. The foot supports of his stilts are 23/10 meters high.
How high is the top of Andrei's head when he is walking on his stilts?
Answers
The top of his head will be 3.4m high.
There was 2/3 of a pan of a lasagna in the refrigerator. Bill and his friends ate half of what was left. Write a number sentence and draw a model to represent the problem. How much of the pan did they eat?
Answers
The principal $3000 is accumulated with 3% interest, compounded semiannually for 6 years.
Answers
A=p (1+r/k)^kt
A accumulated amount?
P principle 3000
R interest rate 0.03
K compounded semiannually 2
T time 6 years
A=3,000×(1+0.03÷2)^(2×6)
A=3,586.85
Can someone please help me solve this triangle problem, picture is shown.
Answers
3(4t) (multiplication form)
these are two forms you can use to get your answer
answer: 12t
hope this helps
and
perimeter = 4t * 3
A bag of fruit contains 3 apples and 2 oranges and 1 banana and 4 pears.Gerald will randomly selected two pieces of fruit one at a time from the bag and not put is back. What is the probability that the first piece of fruit Gerald selects will be a banana and the second piece of fruit will be a pear??
Answers
Final answer:
The probability that Gerald will first select a banana and then a pear from the bag without replacement is 2/45.
Explanation:
To determine the probability that Gerald selects a banana first and then a pear without replacement, we have to consider the total number of possible outcomes for each draw and the favorable outcomes for the event.
For the first draw, the total number of fruits is 10 (3 apples + 2 oranges + 1 banana + 4 pears). The favorable outcome of drawing a banana is 1 since there's only one banana.
The probability of drawing a banana on the first draw is therefore 1/10. After drawing the banana, there are 9 fruits left in the bag with 4 pears among them.
The probability of then drawing a pear is 4/9. To find the total probability of both events happening in sequence (a banana first and then a pear), multiply the two probabilities:
P(banana first and pear second) = P(banana first) × P(pear second)
= (1/10) × (4/9)
= 4/90
= 2/45.
The simplification process shows that the probability Gerald will first select a banana and then a pear is 2/45.
please factor this problem x^2+7x-8
Answers
Check:
8-1=7
8*-1=-8
Convert 64.32° into degrees, minutes, and seconds.
Answers
The conversion factors necessary to answer this item are,
1° = 60'
1' = 60''
number of minutes = (0.32°)(60' / 1°) = 19.2'
We already have 19' and 0.2'.
number of seconds = 0.2' x (60'' / 1') = 12''
Thus, the answer is 64°19'12''.
A ship traveled for 4 hours heading east and for 3 hours heading north. If the total distance traveled was 149 miles, and the ship traveled 3 miles per hour faster heading north, at what speed was the ship traveling east?
Answers
if the ship travelled a total of 149 miles, then let's say it travelled East "d" miles and thus it travelled North the slack of 149 and "d", thus " 149 - d".
now, if the rate travelling East is say "r", then the faster rate going North is " r + 3".
[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ East&d&r&4\\ North&149-d&r+3&3 \end{array} \\\\\\ \begin{cases} \boxed{d}=4r\\ 149-d=(r+3)3\\ ----------\\ 149-\boxed{4r}=3(r+3) \end{cases}[/tex]
solve for "r".
Write the equation of the line that is parallel to the line 7−4x=7y 7 − 4x = 7 y through the point (2,0).
Answers
To find the equation of a line parallel to the given line, we can use the slope of the given line and the point-slope form of a line. The equation of the line parallel to 7−4x=7y and passing through the point (2,0) is y = (7/4)x - (7/2).
Explanation:To find the equation of a line parallel to the given line, we need to find the slope of the given line first. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Rearranging the given equation, we have y = (7/4)x - 1. Dividing the coefficient of x by the coefficient of y, we find that the slope of the given line is 7/4. Since the line we're looking for is parallel to this line, it will also have a slope of 7/4. Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point on the line. Substituting in the values (2, 0) and slope (7/4), we can solve for y to find the equation of the line.
Using the point-slope form, we have y - 0 = (7/4)(x - 2). Simplifying, we get y = (7/4)x - (7/2), which is the equation of the line parallel to the given line and passing through the point (2, 0).
Final answer:
The equation of the line parallel to 7 - 4x = 7y through the point (2, 0) is y = (-4/7)x + 8/7.
Explanation:
To find the equation of a line parallel to the line 7 - 4x = 7y, we need to find the slope of the given line. First, rearrange the equation in the form y = mx + b, where m is the slope. So, 7y = 7 - 4x becomes y = (-4/7)x + 1. The slope of this line is -4/7. Since the line we want is parallel, it will have the same slope.
Next, we have the point (2, 0) through which the line passes. To find the equation, we'll use the point-slope form: y - y1 = m(x - x1). Substituting the given values, we have y - 0 = (-4/7)(x - 2). Simplifying, we get y = (-4/7)x + 8/7.
Therefore, the equation of the line parallel to 7 - 4x = 7y through the point (2, 0) is y = (-4/7)x + 8/7.
Find the value of x in 4000(1.5x) = 25,000. show all work
Answers
25000/4000 = 1.5x
6.25 = 1.5x
25/6 = x
1.5x=6.25 divide both sides by 1.5
x=25/6
x=4 1/6
But that is pretty simplistic, I suspect that you actually meant this was an exponential function of the form:
4000(1.5^x)=25000 divide both sides by 4000
1.5^x=6.25 take the natural log of both sides
xln(1.5)=ln(6.25) divide both sides by ln(1.5)
x=ln(6.25)/ln(1.5)
x≈4.52 (to nearest hundredth)
Sidney made $26 more than seven times Casey's weekly salary. If x represents Casey's weekly salary, write an expression for sidney's weekly salary
Answers
What is the value of k in the equation below? 5k - 2k = 12? 1 1/5, 1 5/7, 3, 4
Answers
5k - 2k = 12
Solve for K
3k = 12
Divide both sides by 3
3k/3 = 12/3
k = 4
The correct answer is : 4
I hope that helps!
Brainliest answer :)
Answer:4
Step-by-step explanation:
Without solving, decide what method you would use to solve each system: graphing, substitution, or elimination. Explain. 4s-3t=8 ; t=-2s-1
Answers
4s-3(-2s-1)=8
Triple my number add six and subtract twice my number my number plus three
Answers
N + 6 = N + 3
N cancels out.
Therefore it is a false statement.
How many inches are in a foot?
Answers
An earthquake with a rating of 3.2 is not usually felt. What is the value of x when the Richter scale rating is 3.2? Round your answer to the nearest hundredth.
Answers
Find the rectangular coordinates of the point with the polar coordinates. ordered pair negative 5 comma 5 pi divided by 3
Answers
write the smallest numeral possible using the digits 9, 3 and 6
Answers
The smallest numeral that can be created from the digits 9, 3, and 6 is 369. This is achieved by arranging the digits in ascending order.
Explanation:The smallest numeral that can be formed using the digits 9, 3, and 6 is 369. In mathematics, when we are to create the smallest possible numeral from a given set of digits, we arrange the digits in increasing order from left to right, that means the smallest digit will be on the left-most side and the largest digit will be on the right-most side.
So, with the digits 9, 3, and 6, we place 3 first as it's the smallest, then 6 as it's the next smallest, and finally 9, resulting in the smallest numeral 369.
Learn more about Creating smallest numeral here:https://brainly.com/question/32283211
#SPJ2
The smallest numeral possible using the digits 9, 3, and 6 is 369, arranged in ascending order.
To write the smallest numeral possible using the digits 9, 3, and 6, we arrange the digits in ascending order. The smallest digit is placed at the beginning, followed by the larger ones. Therefore, the smallest numeral we can create is 369.
The sun’s rays are striking the ground at a 55° angle, and the length of the shadow of a tree is 56 feet. How tall is the tree?
select one:
a. 80.0 feet
b. 45.9 feet ( Incorrect)
c. 34.2 feet (incorrect)
d. 32.1 feet
Answers
h = 56 tan 55
= 79.98 feet
Its a
There is a line through the origin that divides the region bounded by the parabola
y=4x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?
Answers
or
x(4-3x)=0
=>
x=0, x=4/3
The area enclosed by the parabola over the x-axis is therefore
A=integral f(x)dx from 0 to 4/3=[2x^2-x^3] from 0 to 4/3 = 32/27
Let the line intersect the parabola at a point (a,f(a)) such that the area bounded by the line, the parabola and the x-axis is half of A, or A/2, then the area consists of a triangle and a section below the parabola, the area is therefore
a*f(a)/2 + integral f(x)dx from a to 4/3 = A/2 = 16/27
=>
2a^2-3a^3/2+a^3-2a^2+32/27=16/27
=>
(1/2)a^3=16/27
a=(32/27)^(1/3)
=(2/3)(4^(1/3))
=1.058267368...
Slope of line is therefore
m=y/x=f(a)/a=4-2(4^(1/3))
=0.825197896... (approx.)
Quadrilateral ABCD is similar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet, 40 feet, and 30 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long, how long is the 4th side on quadrilateral ABCD?
Answers
Final answer:
The length of the fourth side on quadrilateral ABCD is 120 feet.
Explanation:
Given that quadrilateral ABCD is similar to quadrilateral EFGH, we can use the property of similar figures to find the length of the fourth side on quadrilateral ABCD.
If the two shortest sides of quadrilateral EFGH are 6 feet and 12 feet long, we can set up a proportion using the corresponding sides of the two quadrilaterals.
Let x be the length of the fourth side on quadrilateral ABCD.
Using the property of similar figures, we have:
(60/6) = (x/12)
Cross multiplying, we get:
6x = 720
Dividing both sides by 6, we find:
x = 120
Therefore, the length of the fourth side on quadrilateral ABCD is 120 feet.
What is the distance between (–6, 2) and (8, 10) on a coordinate grid?
Answers
(-6 , 2) and (8 , 10)
x₁ y₁ x₂ y₂
d = √(8 - (-6))² + (10 - 2)²
d = √(8+6)² + (10 - 2)²
d = √(14)² + (8)²
d = √(196) + (64)
d = √ 260
d = 2√65
I think this is right, but I am not sure.
Answer:
D. √260
Step-by-step explanation:
Use the distance formula then input the points (–6, 2) and (8, 10) into it to get √(-6 −2)^2 + (2 −10)^2. Finaly simplify/solve and you get √260.