Given that ABCD is a rhombus, find the value of x (x-10)
Answers
To start, a rhombus will have perpendicular bisectors.
With that, we know that the section where these bisectors cross will create 90 degree angles.
So now we have angles: x, (x-10), and 90.
A triangle will total 180 degrees in total. So if we add up all of these angles, it will total to exactly 180.
In other words: 90+x+(x-10)=180.
So, in this situation, we want to isolate the variables, and find the value of x.
This is the easy part:
Here's that equation again
90+x+(x-10)=180
Subtract 90 from both sides
90-90+x+(x-10)=180-90
x+(x-10)=90
Add 10 to both sides
x+x-10+10=90+10
x+x=100
2x=100
Divide by 2 on both sides
2x/2=100/2
x=50
There's your x value.
Related Questions
Maria is playing a game where she is trying to draw a spade from a standard deck of cards. if she doesn't get a spade, she replaces the card, shuffles the deck, and tries again. if she draws a card 3 times and doesn't get a spade, she loses. what is the probability that maria loses the game?
A.17.8%
B.23.7%
C.42.2%
D.31.6%
Answers
Answer:
The correct answer is C. 42.2%
Step-by-step explanation:
Total number of cards in the deck of playing cards = 52
Number of spades in the deck of playing cards = 13
Number of cards other than spade = 52 - 13
= 39
If she draws a card 3 times and doesn't get a spade, she loses.
So, She loses only if he gets all the three cards other than spade
[tex]\text{Probability that she does not get a spade in first draw = }\frac{39}{52}[/tex]
Now, The card is replaced if she does not get a spade.
[tex]\text{So, Probability that she does not get a spade in second draw = }\frac{39}{52}[/tex]
[tex]\text{Similarly, Probability that she does not get a spade in third draw = }\frac{39}{52}[/tex]
[tex]\text{Thus, Probability that she will lose the game = }\frac{39^3}{52^3}=0.422[/tex]
[tex]\text{Also, The percentage of Probability that she will lose the game = }0.422\times 100=42.2\%[/tex]
Hence, The correct answer is C. 42.2%
need help for question one in polynomials
Answers
Answer:
a) monomial
b) constant
c) binomial
d) trinomial
e) binomial
f) constant
g) monomial
Step-by-step explanation:
Let's start by defining the terms in the question:
A monomial is an expression with a single term, regardless of how many variables are in the term.
A binomial is an expression with two different terms, which cannot be combined into a single term due to their variables not matching.
A trinomial is an expression with three different terms, which cannot be combined into a binomial or monomial because their variables do not match.
A constant is an integer that lacks a variable attached to it. An integer with a variable attached to it would be a monomial, and the integer itself would be called a coefficient.
Now, we can get into the parts of the question:
a) 8a²b is two variables however it is still a single term so this is a monomial.
b) -39 is an integer with no variables attached. Therefore, it is a constant.
c) x + y is two variables and two different terms that cannot be combined into one single term. It is a binomial.
d) -12xy + 5y - x² showcases three different variables and three different terms that cannot be consolidated. Thus, it is a trinomial.
e) 2x² + 2y² demonstrates two different variables and two different terms that are not alike. As such, we have a binomial.
f) 3/4 is an integer with no variables in sight. We have here a constant.
g) -32m²n² has two variables but is only a single term on its own. This is a monomial.
I would appreciate it if someone could take a look at my work on this calculus question and let me know if my work is correct!
Answers
_____
The second blue line in part A should identify the point on the curve as (-1, 1).
You can stop at any point in the development of the equation for a line, as the problem only asks for "an equation", not one in any specific form.
In the diagram below what is the approximate length of the minor arc XY
Answers
The formula for arc length is s = r(theta) Theta must be in radians, so convert 40 degrees to radians, which is 2pi/9. Multiply 2pi/9 by the radius, 9, and then you'll get the answer. Hopes this helps!
Answer:
B. 6.3 cm
Step by step explanation:
We have been given measure of central angle which intercepts to our minor arc XY.
Since we know that the formula to find measure of arc length is:
[tex]\text{Arc length}=\frac{\theta}{360}\times \text{circumference of circle}[/tex]
[tex]\text{Arc length}=\frac{\theta}{360}\times {2\pi r}[/tex]
Now let us substitute our given values in above formula.
[tex]\theta=40^{o}[/tex] and [tex]radius=9 cm[/tex]
[tex]\text{Arc length}=\frac{40}{360}\times {2\pi \cdot 9}[/tex]
[tex]\text{Arc length}=\frac{1}{9}\times {2\pi \cdot 9}[/tex]
[tex]\text{Arc length}=2 \pi [/tex]
[tex]\text{Arc length}=6.2831853071795865\approx 6.3[/tex]
Therefore, length of minor arc XY is 6.3 cm and option B is the correct choice.
you deposit $400 in a saving account with an annual rate of 4%. At this rate how much money will you have after 10 years?
Answers
A = original amount
r = rate of interest
t = time
Plug in the numbers: y = 400(1.04)^10
y = $592.10
Help Please thank you!
Answers
Subtract 6 from both sides of the equation and then divide by 3. the solution is x = 5
Two angels re supplementary. The larger angle is 48 degrees more than the 10 times the smaller angle. Find the measure of each angle.
Answers
STEP 1:
find the value of x
x= smaller angle
10x + 48= larger angle
Add the two angles above to equal 180.
x + (10x + 48)= 180
combine like terms
11x + 48= 180
subtract 48 from both sides
11x= 132
divide both sides by 11
x= 12° smaller angle
STEP 2:
find the value of the second angle
=10x + 48
=10(12) + 48
=120 + 48
=168° larger angle
CHECK:
12° + 168°= 180°
180°= 180°
ANSWER: The smaller angle is 12° and the larger angle is 168°.
Hope this helps! :)
Need help ASAP ! Please !!
Answers
Hope this helps.
a bag contains 30 lottery balls numbered 1-30 a ball is selected replaced then another is drawn find each probability
p ( and even,then odd )
p ( 7, then a number greater than 16)
p ( a multiple of 5, then a prime number )
p ( two even number )
Answers
Answer:
Given : A bag contains 30 lottery balls numbered 1-30 a ball is selected replaced then another is drawn.
To find : Each probability
1) p ( and even,then odd )
2) p ( 7, then a number greater than 16)
3) p ( a multiple of 5, then a prime number )
4) p ( two even number )
Solution :
[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}[/tex]
1) There are 15 even numbers and 15 odd numbers.
Probability of getting even first then odd is
[tex]\text{P(even,then odd)}=\frac{15}{30}\times\frac{15}{30}[/tex]
[tex]\text{P(even,then odd)}=\frac{225}{900}=\frac{1}{4}[/tex]
2) Number greater than 16 out of 30 are 14.
Probability of getting 7 first then a number greater than 16 is
[tex]\text{P(7, then a number greater than 16)}=\frac{1}{30}\times\frac{14}{30}[/tex]
[tex]\text{P(7, then a number greater than 16)}=\frac{14}{900}=\frac{7}{450}[/tex]
3) Multiple of 5 - 5,10,15,20,25,30=6
Prime numbers - 2,3,7,9,11,13,17,19,23,29=10
Probability of getting a multiple of 5, then a prime number is
[tex]\text{P(a multiple of 5, then a prime number )}=\frac{6}{30}\times\frac{10}{30}[/tex]
[tex]\text{P(a multiple of 5, then a prime number )}=\frac{60}{900}=\frac{1}{15}[/tex]
4) There are 15 even numbers.
Probability of getting two even number is
[tex]\text{P( two even number)}=\frac{15}{30}\times\frac{15}{30}[/tex]
[tex]\text{P( two even number)}=\frac{225}{900}=\frac{1}{4}[/tex]
Mark runs 3/4 of a mile each day for 5 days. What is the total distance that Mark has run after 5 days? A.3 3/4 B.4 1/4 C.5 3/4 D.6 2/3
Answers
Your answer is A.
Final answer:
To find the total distance Mark has run after 5 days, multiply his daily distance of 3/4 mile by 5 days, resulting in A.3 3/4 miles.
Explanation:
The question asks us to find the total distance that Mark runs over 5 days, given that he runs 3/4 of a mile each day. To find the total distance, we simply multiply the daily distance by the number of days.
Multiply the daily distance (3/4 mile) by the number of days (5 days):
(3/4) × 5 = 15/4
Convert the improper fraction to a mixed number:
15/4 is equivalent to 3 whole miles and 3/4 of a mile, which can be written as 3 3/4 miles.
Therefore, after 5 days, Mark has run a total distance of A.3 3/4 miles.
Please help. Web making by spiders is an example of which of the following
A. Innate behavior
B. Courtship
C.defensive behavior
D.reproducing
Answers
C. It's not defensive. It's meant to trap food. Spiders are carnivores and they eat what they catch. Webs are sticky and their pray can't get away.
A. Webs are constructed out of different types of silk, depending on what the web is for. The only thing you can eliminate is C. The silk itself is attractive to the opposite sex so courtship is a possibility. After the spider reproduces, the egg can be placed in a very dense covering of silk.
A is the all encompassing answer to the 11 things webs their silk are used for by spiders.
A <<<< answer.
Jordan travels 3/4 of a mile longer to school each day than harisson does. combined, they have traveled 5 1/4 miles to school. how far does each trave;?
Answers
let harissom travel Y mile
given
X=Y plus 3/4 of y =1.75Y (3/4=0.75)
X+Y = 5.25(1/4=0.25)
now we can just put thevalue of X and we get
X+Y=5.25
1.75Y + Y= 5.25
Y=1.909
x= 1.75 × 1.909= 3.341
PLS HELP! THIS IS FOR STATE TESTS TOMORROW!! Shannon has a garden that is 18 by 27 feet. Find the perimeter of the garden. Please submit your answer and explain how to find the perimeter.
Answers
Perimeter = 2( 18 + 27) = 2(45) = 90 feet.
Answer: 90 feet
Marge correctly guessed whether a fair coin turned up "heads" or "tails" on sic consecutive flips. What is the probability that she will correctly guess the outcome of the next coin toss?
Answers
P(guessing the 7th flip, after six consecutive flips) = 0.5
Also, we can use the compound probability, which can be found by simply multiplying the probabilities of each event:
P(guessing 7 in a row) = 0.5 × 0.5 × 0.5 × 0.5 × 0.5 × 0.5 × 0.5
= (0.5)⁷
= 0.0078
Hence, the probability that Marge correctly guesses the 7th flip is still 50%, but in general, the probability of guessing 7 consecutive flips is 0.78%.
Answer with explanation:
It is given that ,Marge correctly guessed whether a fair coin turned up "heads" or "tails" on sic consecutive flips.
When we flip a coin , there are two possible Outcomes, one is Head and another one is Tail , that is total of 2.
Probability of an event
[tex]=\frac{\text{Total favorable Outcome}}{\text{Total Possible Outcome}}[/tex]
Probability of getting head
[tex]=\frac{1}{2}[/tex]
Probability of getting tail
[tex]=\frac{1}{2}[/tex]
⇒There can be two guesses , either it will be true and another one will be false.
So, Possible outcome of correct guess={True, False}=2
--Probability of Incorrect(False) guess
[tex]=\frac{1}{2}[/tex]
--Probability of Correct(True) guess in seventh toss
[tex]=\frac{1}{2}\\\\=\frac{1}{2} \times 100\\\\=50 \text{Percent}[/tex]
⇒Probability that she will correctly guess the outcome of the Seventh coin toss, if previous sixth tosses has correct guess
=T×T×T×T×T×T×T, where T=True guess
= 0.5×0.5×0.5×0.5×0.5×0.5×0.5
=0.0078125
=0.0078 (approx)
Volume of pyramids and cones day 1
Answers
and the volume of the pyramid is = V= l w h/3
Hope this helps!
can I get a brainleist
A card is drawn from a well shuffled deck of 52 cards. find the probability of drawing a club or a diamond
Answers
[tex] |\Omega|=52\\
|A|=26\\\\
P(A)=\dfrac{26}{52}=\dfrac{1}{2}=50\% [/tex]
The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s. when the length is 14 cm and the width is 9 cm, how fast is the area of the rectangle increasing?
Answers
Differentiate with respect to time:
dA
----- = L*(dW/dt) + W*(dL/dt)
dt
Here,
dA
----- = (14 cm)*(5 cm/sec) + (9 cm)*(3 cm/sec)
dt
Finish the indicated multiplication and addition to obtain your final answer.
The area of the rectangle at L = 14 cm and B = 9 cm is increasing at 97 cm²/s.
What is the area of rectangle?
The area of a rectangle is given by -
A[R] = L x B
Given is the length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s.
Now, we can write -
dL/dt = 3 cm/s
dB/dt = 5 cm/s
We know, that the area is -
A = LB
differentiating both sides with respect to [t], we get -
dA/dt = L dB/dt + B dL/dt
dA/dt = 5L + 3B
At L = 14 cm and B = 9 cm.
(dA/dt) [14, 9] = 5 x 14 + 3 x 9 = 70 + 27 = 97 cm²/s
Therefore, the area of the rectangle at L = 14 cm and B = 9 cm is increasing at 97 cm²/s.
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A rectangular storage box is 12in. wide,15. long,and 9 in. high.how many square inches of colored paper are needed to cover the surface of the box?
Answers
(I had a question just like this)
I need the answer I need help with this question
Answers
The origin is the midpoint between each vertex and its image.
Negate every coordinate value, for example, J(-5, -3) gets rotated to J'(5, 3).
the frequency of the musical note E3 is about 164.81 Hz.
what is the frequency of the note a perfect fifth above E3.
Answers
Therefore, we can set the proportion:
164.81 : x = 2 : 3
which gives:
x = 164.81 × 3 ÷ 2
= 247.21
Hence, the perfect fifth above E₃ will have a frequency of 247.21Hz which corresponds to a B₃.
Answer: 247.215 Hz
Step-by-step explanation:
We know that in music theory, a perfect fifth is a musical interval having inverse perfect fourth that corresponds a pair of pitches with a frequency ratio of 3:2.
Let the frequency of the note a perfect fifth above [tex]E_3[/tex] be x, then we have the following proportion.
[tex]x:164.81::3:2\\\\\Rightarrow x=\dfrac{3\times164.81}{2}=247.215[/tex]
Hence, the frequency of the note a perfect fifth above [tex]E_3[/tex] is 247.215 Hz.
a two way frequency table allows you to organize what data?
Answers
A two-way frequency table is used to organize bivariate data into a format that helps calculate relative frequencies, empirical probabilities, and analyze marginal and conditional distributions.
Explanation:A two-way frequency table allows you to organize bivariate data. This type of table is particularly useful in displaying data concerning two categorical variables, such as gender and sports preferences. The table sets up data in a way that makes it easier to calculate relative frequency and, as a result, empirical probability. It also assists in organizing the data for marginal and conditional distributions. Joint frequencies are the counts in the body of the table, while the marginal frequencies are located in the table's margins, summarizing the totals for each variable across all categories. Conditional distributions can then be analyzed, focusing on particular subsets within the table to assess probabilities within those subsets.
What is (4a)^2 without exponents?
Answers
The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions of the rectangle.
Answers
2x - 6 = the width as given in the description.
Area of a rectangle is length * width. Now we plug in.
108 = x(2x - 6)
108 = 2x² - 6x
We are going to get all terms on the same side and factor.
2x² - 6x - 108 = 0
Factor out and divide each term by a GCF of 2 to get:
x² - 3x - 54 = 0
x² + 6x - 9x - 54 = 0
x(x + 6) - 9(x + 6) = 0
Your factors are (x + 6)(x - 9) = 0. Now we set each binomial equal to zero. This gives us x = - 6 and x = 9. Distance cannot be measure in negative numbers so we know to use x = 9 to find our measurements.
The length (x) is 9 kilometers. The width (2x - 6) is 12 kilometers when you plug in 9 where the x is.
The dimensions of the rectangle are [tex]\( \boxed{9 \text{ km} \times 12 \text{ km}} \)[/tex].
Let's denote the length of the rectangle as [tex]\( l \)[/tex] kilometers, and its width as [tex]\( w \)[/tex] kilometers.
From the problem statement, we have two pieces of information:
1. The width is 6 kilometers less than twice the length:
[tex]\[ w = 2l - 6 \][/tex]
2. The area of the rectangle is 108 square kilometers:
[tex]\[ lw = 108 \][/tex]
Now we can substitute the expression for \( w \) from the first equation into the second equation:
[tex]\[l(2l - 6) = 108\][/tex]
Expand and simplify the equation:
[tex]\[2l^2 - 6l = 108\][/tex]
Subtract 108 from both sides to set the equation to zero:
[tex]\[2l^2 - 6l - 108 = 0\][/tex]
Divide every term by 2 to simplify:
[tex]\[l^2 - 3l - 54 = 0\][/tex]
Now, we'll solve this quadratic equation using the quadratic formula, [tex]\( l = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex], where [tex]\( a = 1 \)[/tex], [tex]\( b = -3 \)[/tex], and [tex]\( c = -54 \)[/tex]:
[tex]\[l = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-54)}}{2 \cdot 1}\][/tex]
[tex]\[l = \frac{3 \pm \sqrt{9 + 216}}{2}\][/tex]
[tex]\[l = \frac{3 \pm \sqrt{225}}{2}\][/tex]
[tex]\[l = \frac{3 \pm 15}{2}\][/tex]
This gives us two possible solutions for [tex]\( l \)[/tex]:
[tex]\[l = \frac{18}{2} = 9 \quad \text{or} \quad l = \frac{-12}{2} = -6\][/tex]
Since length cannot be negative, we take [tex]\( l = 9 \)[/tex] kilometers.
Now, substitute [tex]\( l = 9 \)[/tex] back into the expression for [tex]\( w \)[/tex]:
[tex]\[w = 2l - 6 = 2 \cdot 9 - 6 = 18 - 6 = 12\][/tex]
Therefore, the dimensions of the rectangle are:
- Length [tex]\( l = 9 \)[/tex] kilometers
- Width [tex]\( w = 12 \)[/tex] kilometers
To verify, calculate the area:
[tex]\[l \times w = 9 \times 12 = 108 \text{ square kilometers}\][/tex]
Since this matches the given area, the dimensions [tex]\( l = 9 \)[/tex] kilometers and [tex]\( w = 12 \)[/tex] kilometers are correct.
Thus, the dimensions of the rectangle are [tex]\( \boxed{9 \text{ kilometers} \times 12 \text{ kilometers}} \)[/tex].
Dylan wants to construct the midpoint M of RS which diagram shows a way Dylan can accurately construct M using only a compass and a straight edge
Answers
because of doing the correct steps:
step1: put the point of your compass on the left endpoint of the segment, A.
Open the compass to be more than half the length of the segment. Then leave a half-circle mark.
step2: do the same thing on the other point B. and find the middle point.
One hose can fill a pool in 12 hours. another hose can fill the same pool in 8 h
Answers
Explanation:
One hose can fill a pool in 12 hours.
The other house can fill the same pool in 8 hours.
If they fill the pool together,
[tex]\text {Time Needed } = \cfrac{12 \times 8}{12 + 8} = 4.8 hours [/tex]
What are the coordinates of the center of a circle whose equation is (x + 7)2 + (y – 5)2 = 16?
Answers
The standard form of the equation of a circle is the following:
[tex](x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} [/tex]
In this equation r represents the radius of the circle and the point (a, b) is its centre.
Therefore, the centre of the circle
[tex](x + 7) {}^{2} + (y - 5) {}^{2} = 16[/tex]
is the point ( - 7, 5).
BRAINLIEST IF RIGHT
The image represents what geometric construction?
A) Copy an angle construction
B) Parallel lines construction
C) Copy a segment construction
D) Perpendicular from a point not on the line
Answers
C) Copy a segment construction
Without the visual reference of an image, the specific geometric construction represented can not be accurately determined. The provided options relate to different types of geometric constructions. These include copying angles, constructing parallel lines, copying segments, and creating perpendiculars from a point not located on a line.
Explanation:The geometric construction represented by the image is not entirely clear without an image. However, if we are to interpret the options, we can make some educated assumptions. Copy an angle construction involves replicating an existing angle in a new location. A parallel lines construction typically involves creating a line parallel to an existing one. To copy a segment construction, you would reproduce a particular line segment. The option of creating a perpendicular from a point not on the line would typically involve making a line perpendicular to an existing line from a specific point not originally on that line. Without the image, we can't definitively answer the question.
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If 5 balls are placed randomly into 3 bins, what is the expected number of balls in each bin?
Answers
Find the measure of an angle with measure between 0° and 360° that is coterminal with an angle measuring –800°. °
Answers
-800+360=-440
-440+360=-80
-80+360=280
So the angle is 280 degrees.
Answer:
280
Step-by-step explanation:
Find an explicit rule for the nth term of the sequence. 9, 36, 144, 576, ...
Answers
The answer is an = 9 • 4n - 1
The explicit rule for the [tex]nth[/tex] term of the given sequence is [tex]a_n=9(4)^{n-1}[/tex].
Given:
The given sequence is [tex]9,36,144,576[/tex].
To find:
The explicit rule for the [tex]nth[/tex] term of the given sequence.
Explanation:
the first term of the sequence is [tex]9[/tex].
The ratios of two consecutive terms are:
[tex]\dfrac{36}{9}=4[/tex]
[tex]\dfrac{144}{36}=4[/tex]
[tex]\dfrac{576}{144}=4[/tex]
The given sequence is a geometric sequence because the sequence has a common ratio [tex]4[/tex].
The explicit formula for the [tex]nth[/tex] term is:
[tex]a_n=ar^{n-1}[/tex]
Where, [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio.
Substituting [tex]a=9,r=4[/tex], we get
[tex]a_n=9(4)^{n-1}[/tex]
Therefore, the explicit rule for the [tex]nth[/tex] term of the given sequence is [tex]a_n=9(4)^{n-1}[/tex].
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