Answers
Answer:
a = 6 units
[tex]c= 6\sqrt{2}\ units[/tex]
Step-by-step explanation:
Given:
Let Labelled the diagram first
Δ ABC right angle at ∠ C = 90°
∠ B = 45 °
AB = c
BC = a
AC = 6
To Find:
a =?
c =?
Solution:
In Δ ABC
∠ A + ∠ B + ∠ C = 180°.....{Angle Sum Property of a Triangle}
∴ ∠ A + 45 + 90 = 180°
∴ ∠ A = 180 - 135
∴ ∠ A = 45°
Now ∠ A = ∠ B = 45° in Δ ABC
∴ Δ ABC is an Isosceles Triangle.
∴ Two sides are equal of an Isosceles Triangle.
∴ AC = BC = a = 6 units
Now for c we use Pythagoras theorem
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
Substituting the given values we get
c² = a² + 6²
c² = 6² + 6²
c² = 36 + 36
c² = 72
∴ c = ±√72
as c cannot be negative
∴ [tex]c = 6\sqrt{2}\ units\\[/tex]
a = 6 units
[tex]c= 6\sqrt{2}\ units[/tex]
Related Questions
If the water moves -7/16 in 3 years how much does the water move in 1 year?
Answers
Answer:
-7/48 in
Step-by-step explanation:
Assuming that the movement varies linearly with time,
3 years ------> -7/16 in
1 year -------> -7/16 ÷ 3 = -7/48 in
Combine like terms to create an equivalent expression.
-5.8c+4.2-3.1+1.4c−5.8c+4.2−3.1+1.4c
Answers
Answer:
The simplified expression is -4.4c+1.1−4.4c+1.1
how many pounds of candy worth $12 per pound should be mixed with candy costing $19 per pound to produce a 70 pound mixture that sells for $15 per pound?
Answers
Answer:
40 pounds
Step-by-step explanation:
Given: Cost of a candy [tex](c_1)[/tex]= [tex]\$ 12[/tex] per pound
Cost of candy [tex](c_2) = \$ 19\ per\ pound[/tex]
Total amount of mixture of be produced = [tex]70\ pound[/tex]
Selling price of mixture = [tex]\$ 15 \ per\ pound[/tex]
Let´s x be the amount of [tex]c_1 [/tex] to be mixed in the mixture.
∴ Cost of [tex]c_1[/tex] in the mixture = 12x
Next, Cost of [tex]c_2[/tex] in the mixture = [tex](70 - x)\times 19[/tex]
And we know the cost of final mixture = [tex]70 \times 15 = 1050[/tex]
Now, putting all the value in the equation
⇒ [tex]12x + 19 \times (70 - x) = 1050[/tex]
⇒ [tex]1330 - 7x = 1050[/tex]
⇒ [tex]-7x = -280[/tex]
∴ [tex]x = 40\ pound[/tex]
∴ 40 pounds of candy worth $12 per pound to be mixed in the mixture.
13) Mary sold half of her comic books and
then bought seventeen more. She now has
30. With how many did she begin?
Answers
Answer: 26
Step-by-step explanation:
30-17=13
13+13=26
Answer:
26 boi
Step-by-step explanation:
Triangle A B C is shown. Side A B has a length of 12. Side B C has a length of x. Side A C has a length of 15. The value of x must be greater than ________. 0 1 3 7
Answers
Answer:
3
Step-by-step explanation:
According to the Triangle Inequality Theorem, the sum of any 2 sides of any triangle must be greater than the length of the third side. That is:
AB + BC > AC and AB + AC > BC and AC + BC > AB
So in this case:
if AC + AB > BC
x + 12 > 15
After substracting 12 from each side of the equation, we get that:
x > 3
Hence, the value of x must be greater than 3.
Answer:
Here we have to use the Triangle Inequality Theorem, because the problem it's asking about the restriction of one side, with two sides given. This theorem, in words, states that the sum of the minor sides is more than the length of the major sides of all three. So, if we translate this to equation, we have:
[tex]AB + BC > AC[/tex]
Where [tex]AB=12[/tex]; [tex]BC=x[/tex] and [tex]AC=15[/tex]
Assuming that [tex]AC[/tex] is the longest side we applied the theorem to this problem. Now, replacing all values we have:
[tex]12+x>15\\x>15-12\\x>3[/tex]
Therefore, the unknown side must be greater than 3 to not violate the Triangle Inequality Theorem, which is always true about every triangle.
Students were packed shoulder to shoulder in a gym for a pep rally. The students were in a rectangular shaped area of 7,500
ft. If each student on average took up a circular space with a diameter of 2.5 ft what is the best estimate for the number of
students at the pep rally?
A)600
B)900
C)1,200
D)1,800
Answers
Answer:
c)1200
Step-by-step explanation:
Given: Students were packed shoulder to shoulder in a gym for a pep rally. The students were in a rectangular shaped area of [tex]7500[/tex] ft.
To Find: If each student on average took up a circular space with a diameter of [tex]2.5[/tex] ft what is the best estimate for the number of students at the pep rally.
Solution:
Consider the figures attached
A student took up a circular space, if they were packed in rows each student acquired a circular space of [tex]2.5[/tex] ft and left some unused area as given in figures
Now,
Area acquired by a student is a square of side [tex]2.5[/tex] ft as given in figure
Area acquired by single student[tex]=(\text{length of square})^2[/tex]
[tex]=2.5\times2.5[/tex]
[tex]6.25\text{sq.ft}[/tex]
Total number of students [tex]=\frac{\text{total area of rectangular gym}}{\text{area acquired by single student}}[/tex]
[tex]\frac{7500}{6.25}[/tex]
[tex]1200[/tex]
there are approximately [tex]1200[/tex] students in gym hence option b is correct.
What are the coordinates of the vertex of the graph of f(x) = -3 |x-1|? I need help in how to solve it.
Answers
Answer: f(x) = -3| x - 1 | is really just f(x) = -3| x - 1 | + 0.
now, what value of "x" makes the absolute value expression to 0?
well, let's just set it to 0 and check,
x - 1 = 0
x = 1
so if "x" ever becomes 1, the | x - 1| will turn to 0, therefore, the vertex is at
f(x) = -3| (1) - 1 | + 0 --------------> ( 1, 0 )
find the solutions to the following equation:
[tex] \frac{x + 1}{3} - \frac{2x - 1}{x} = - 1[/tex]
Answers
Answer:
x=1+/-4i
Step-by-step explanation:
(x+1)/3-(2x-1)/x=-1
find the common denominator,
in this case, it's going to be 3x.
(x^2+x)/3x-(6x-3)/3x=-1
(x^2+x-6x+3)/3x=-1
x^2-5x+3=-3x
x^2-5x-(-3x)+3=0
x^2-5x+3x+3=0
x^2-2x+3=0
apply the quadratic formula in order to find the roots for x.
Since ax^2+bx+c=0, in this case,
a=1, b=-2, c=3
--------------------------
x=(-b+/-sqrt(b^2-4ac))/2a
x=(2+/-sqrt(4-12))/2
x=(2+/-8i)/2
x=1+/-4i
Help ASAP!!! How did it take Escher time 18 liters of water were drained is it A) 1/4 min B) 1/2 min c) 1min or D) 1/3min?
Answers
Answer:
A) 1/4 min
Step-by-step explanation:
Find the equation for the graph:
y = mx + b
Find the slope using two random points (0, 360) and (5, 0)
m = (y2 - y1) / (x2 - x1)
m = (0-360) / (5-0)
m = -360/5
m = -72
b is 360, the y-intercept.
Substitute m= -72 and b=360 into slope-intercept form.
y = -72x + 360
x represents time and y represents the total amount of water at the time.
We are looking for when only 18 liters were drained.
360 - 18 = 342 <= Total amount of water when 18 liters are drained
Substitute 342 for y in the equation and isolate x.
342 = -72x + 360
-18 = -72x
x = 18/72
x = 1/4
Therefore, it will take 1/4 of a minute to drain 18 liters.
Answer: 1/4
Step-by-step explanation:
I got it right on khan academy.
Hope this helps
The population density of New York is 24,403 people per square mile. If 12,383,007 people live in New York City. What is the city’s area?
Answers
Answer:
City's Area = 507.44 sq. mi.
Step-by-step explanation:
We will use population density formula to solve this problem easily.
We have:
Population Density = Total Population/ Land Area
Given,
Population Density = 24,403
Total Population = 12,383,007
We want land area, so we simply plug in the numbers into the formula and solve for City's Area. Shown below:
[tex]Population \ Density = \frac{Total \ Population}{Land \ Area}\\24,403=\frac{12,383,007}{Land \ Area}\\Land \ Area = \frac{12,383,007}{24,403}\\Land \ Area = 507.44[/tex]
THe units is Square Miles, so we can say:
City's Area = 507.44 sq. mi.
a school netball team won ten matches , lost four and drew 1/8 of the total played . how many matches were drawn and what fraction did the team win ?
Answers
The school net ball team drew 2 matches. The team won [tex]\frac{5}{8}[/tex] of total matches played
Solution:Given, A school netball team won ten matches, lost four and drew [tex]\frac{1}{8}[/tex] of the total played
Let the total number of matches played be "n"
Number of matches drawn = [tex]\frac{1}{8}[/tex] of n
Total matches played = number of won matches + number of lost matches + number of drawn matches
[tex]\begin{array}{l}{n=10+4+\frac{1}{8} n} \\\\ {n-\frac{1}{8} n=10+4}\end{array}[/tex]
Taking "n" as common from left hand side,
[tex]\begin{array}{l}{\mathrm{n}\left(1-\frac{1}{8}\right)=14} \\\\ {\mathrm{n} \times \frac{8-1}{8} \quad 14} \\\\ {\mathrm{n} \times \frac{7}{8}=14} \\\\ {\mathrm{n}=16}\end{array}[/tex]
So, they played 16 matches in total
Number of matches drawn = [tex]\frac{1}{8}[/tex] of n = [tex]\frac{1}{8} \times 16 = 2[/tex][tex]\text { Fraction of won matches }=\frac{\text { number of matches won }}{\text { number of matches played }}=\frac{10}{16}=\frac{5}{8}[/tex]
[tex]\text { Hence, the team drew } 2 \text { matches and won } \frac{5}{8} \text { of total played matches. }[/tex]
A man is standing on a bridge 30 feet above sea level. A turtle is swimming directly belo him 7 feet below sea level. What is the distance between the man and the turtle
Answers
You add the feet you need to get to sea level 30 to the distance the turtle is from sea level 7 and you get 37 feet between them
A car uses 7 litres of petrol for every 100 km travelled. Which is the best estimate for the amount of petrol (in litres) needed to travel 590 km?
Answers
Answer:
41.2876137159
Step-by-step explanation:
100 divided by 7 is 14.2857142857 km per litres. Then 590 divded by 14.2857142857 is 41.2876137159 or 41.29 rounded
The number y of hits a new website receives each month can be modeled by
y = 4090ekt,
where t represents the number of months the website has been operating. In the website's third month, there were 10,000 hits. Find the value of k. (Round your answer to four decimal places.)
Answers
Answer:
k = 0.2980
Step-by-step explanation:
Given:
number of months t =3
number of hits y = 10000
The equation is modeled as
[tex]y= 4090e^{kt}[/tex]
We need to find value of k.
Now Substituting the values in above equation we get.
[tex]10000= 4090e^3k\\e^{3k}=\frac{10000}{4090}\\\\[/tex]
Now taking Anti log on both side to remove e we get,
[tex]3k = \ ln \frac{10000}{4090}\\\\3k = 0.8940\\k = \frac{0.8940}{3}= 0.2980[/tex]
Hence the value of k = 0.2980.
The value of k is 0.2981.
We are given that in the website's third month (t = 3), there were 10,000 hits. We need to find the value of k.
1. First, substitute y = 10000 and t = 3 into the given equation:
10000 = 4090e3k
2. Next, solve for the exponential term:
10000 / 4090 = e3k
This simplifies to:
10 / 4.09 = e3k
2.444 = e3k
3. Take the natural logarithm (ln) of both sides to solve for k:
ln(2.444) = 3k
Calculating ln(2.444) yields approximately 0.8944.
0.8944 = 3k
4. Finally, solve for k:
k = 0.8944 / 3
k ≈ 0.2981
Therefore, the value of k, rounded to four decimal places, is approximately 0.2981.
a magazine is offering a special subscription rate of $30 per year for 12 issues the regular price for the magazine is $4 per issue if you subscribe at the special rate how much money will you save for the year
Answers
Answer:
Step-by-step explanation:
c
Answer:
$18
Step-by-step explanation:
12*4=48
48-30=18
Megan has 12 star sticker. 1/2 of her stickers are yellow, 1/3 are green, and the rest are blue. What fraction of Megan’s star sticker are blue?
Answers
Answer:
1/6
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
1/2 of 12 is 6 so she has 6 yellow stickers
1/3 of 12 is 4 so she has 4 green stickers
that means she only has 2 stickers left because 6+4=10
2/12 of her stickers are blue but you can simplify it to 1/6 by dividing the numerator and denominator by 2
Wendy picks a marble at random, puts it back, and then picks another marble at random.
Are these two events dependent or independent?
dependent
independent
Answers
Independent. Two events are dependent if knowing the result of the first one influences what you'd expect from the second.
Consider this example: if I have a sack with 3 black marble and 1 white marble, I have probability 75% of picking a blakc marble, and 25% of picking the white one.
If I pick the white one, and don't replace, the second pick will be dependent on the first one, because now I'm sure that I'll pick one of the black marbles, since they are the only ones left in the sack.
In your example, though, Wendy replaces the marble she picks first. This means that the second pick will take place in the exact same conditions of the first one, and knowing which marble she picked at first doesn't affect in any way the result of the second pick.
As another example, consider rolling two dice. Suppose that the first die lands showing 4. Does this affect in any way what you'd expect from the second die? Well, no: the numbers 1-6 are still equally probable to show up.
Which quadrilaterals always have diagonals that are perpendicular?
Answers
Answer:
Rhombi is the answer...
That is option C
Answer:
C
Step-by-step explanation:
Rhombi has quadrilateral with diagonal and are perpendicular.
4x+3(2x-1)-4x
I need an equivalent expression please.
Answers
Answer:
6x - 3
Step-by-step explanation:
Distribute first.
4x + 6x - 3 - 4x = 10x - 4x - 3 = 6x - 3
The equivalent expression for 4x + 3(2x - 1) - 4x is 6x - 3, achieved by distributing the multiplier in the parenthese and then combining like terms.
Explanation:The expression 4x + 3(2x - 1) - 4x can be simplified by first distributing the 3 in the term 3(2x - 1), then combining like terms.
1. Distribute the 3 to get : 4x + 6x - 3 - 4x
2. Combine like terms: 6x - 3
So, the equivalent expression of 4x + 3(2x - 1) - 4x is 6x - 3
Learn more about Algebra here:https://brainly.com/question/32436021
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Dan buys candy that costs$5 per pound. He will spend at least $35 on candy. What are the possible numbers of pounds he will buy?
Answers
Answer:
7 and up
Step-by-step explanation:
35 / 5 = 7
Dan buys at least 7 bags
need help
with these
Answers
1. 4(2+3c) = 56
c = 4
3. -29 = 5(2a-1)+2a
a = -2
5 . 7p-(3p+4) = -2(2p-1)+10
p=2
7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)
x=4
Step-by-step explanation:
1. 4(2+3c) = 56
[tex]4(2+3c) = 56\\8+12c = 56[/tex]
Subtracting 8 from both sides
[tex]8-8+12c = 56-8\\12c = 48[/tex]
Dividing both sides by 12
[tex]\frac{12c}{12} = \frac{48}{12}\\c = 4[/tex]
Checking:
[tex]4[2+3(4)] = 56\\4(2+12) = 56\\4(14) = 56\\56 = 56[/tex]
3. -29 = 5(2a-1)+2a
Simplifying
[tex]-29 = 10a-5+2a\\-29 = 12a-5[/tex]
Adding 5 on both sides
[tex]-29+5 = 12a - 5+5\\-24 = 12a[/tex]
Dividing both sides by 12
[tex]\frac{12a}{12} = \frac{-24}{12}\\a = -2[/tex]
Checking:
[tex]-29 = 5(2a-1)+2a\\-29 = 5[2(-2)-1]+2(-2)\\-29 = 5(-4-1) -4\\-29 = 5(-5) -4\\-29 = -25-4\\-29 = -29[/tex]
5 . 7p-(3p+4) = -2(2p-1)+10
Simplifying
[tex]7p-3p-4 = -4p+2+10\\4p-4 = -4p+12[/tex]
Adding 4 on both sides
[tex]4p-4+4 = -4p+12+4\\4p = -4p+16[/tex]
Adding 4p on both sides
[tex]4p+4p = -4p+4p+16\\8p = 16[/tex]
Dividing both sides by 8
[tex]\frac{8p}{8} = \frac{16}{8}\\p = 2[/tex]
Checking:
[tex]7p-(3p+4) = -2(2p-1)+10\\7(2)-[3(2)+4] = -2[2(2)-1] +10\\14 - (6+4) = -2 (4-1) +10\\14 - 10 = -2(3) +10\\4 = -6+10\\4=4[/tex]
7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)
Simplifying
[tex]\frac{1}{2} (-4+6x) = \frac{1}{3}x+\frac{2}{3}(x+9)\\\frac{-4}{2}+\frac{6x}{2} = \frac{x}{3} +\frac{2x}{3} + \frac{18}{3}\\-2+3x = \frac{x+2x+18}{3}\\-2+3x = \frac{3x+18}{3}\\3(-2+3x) = 3x+18\\-6+9x = 3x+18[/tex]
Adding 6 on both sides
[tex]-6+6+9x = 3x+18+6\\9x = 3x+24[/tex]
Subtracting 3x from both sides
[tex]9x-3x = 3x-3x+24\\6x = 24[/tex]
Dividing both sides by 6
[tex]\frac{6x}{6} = \frac{24}{6}\\x = 4[/tex]
Checking:
[tex]\frac{1}{2} [-4+6(4)] = \frac{1}{3}(4)+\frac{2}{3}(4+9)\\\frac{1}{2}(-4+24) = \frac{4}{3}+\frac{2}{3}(13)\\\frac{1}{2}(20) = \frac{4}{3} +\frac{26}{3}\\15 = \frac{4+26}{3}\\15 = \frac{30}{3}\\15=15[/tex]
Keywords: Linear equations
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$5 off a $50 item is a better deal than 25% off the same item
True
or
False
Answers
Answer:
false.
Step-by-step explanation:
$5 off is well $5 off so, we would be paying $45 for the item. If we took 25%, thats $12.50 therefore you would only pay $37.50. So the 25% saves you $7.50 so it si false. $5 is a worse deal.
how to discover the domain of the function?
Answers
Answer:
set the bottom equal to zero and exclude the x value you find when you solve the equation.
Step-by-step explanation:
Answer:
Remember that domain = x. You can discover the domain by looking at where the smallest and largest points of a graph are according to the x-axis. For example, look at the graph below. The domain would be - ∞ to + ∞ because the parabola widens forever.
The simple interest on a sum of money for 2 years at 12% p.a is rupees 1380. Find the sum of
money.
Answers
Answer:
Simple interest = PRT/100
1380 = P x 12 x 2/100
138000 = 24P
Therefore P = 5750 Rs.
Hope this helps!
To find the principal amount given the simple interest, rate, and time, use the formula P = SI / (R × T). Substituting the values, the principal amount is 5750 rupees.
To find the sum of money (principal) using the given simple interest, we can use the simple interest formula:
Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)
Here, we know that:
SI = 1380 rupeesR = 12% per annum or 0.12T = 2 yearsRearranging the formula to solve for the principal (P):
[tex]P = \frac{SI }{(R * T)}[/tex]
Substitute the known values:
P = 1380 / (0.12 × 2)
Solving the equation:
P = 1380 / 0.24
P = 5750 rupees
Therefore, the sum of money is 5750 rupees.
Evaluate 10.2x+9.4y when x=2 and y=3
Answers
Steps to solve:
10.2x + 9.4y when x = 2 and y = 3
= 10.2(2) + 9.4(3)
= 20.4 + 28.2
= 48.6
______
Best Regards,
Wolfyy :)
Answer:
48.6 is the answer
Step-by-step explanation:
Okay, first you plug in the variables x and y .
So now the new equation is 10.2x2 this is ,because everytime a number get put next to another number you multiply. So .....
(10.2x2) + (9.4x3)=
20.4+28.2=
48.6
If AD=6x+10 and CD=2x+12, find the length of AC
Answers
Answer:
The correct answer is that AC = 4x - 2 or 2(2x - 1)
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
AD = 6x + 10
CD = 2x + 12
2. Let's find the length of AC
AC = AD - CD
Replacing with the real values:
AC = (6x + 10) - (2x + 12)
AC = 6x + 10 - 2x - 12
AC = 6x - 2x + 10 - 12
AC = 4x -2 or 2(2x - 1)
Which of the following statements about the data set 56, 21, 48, 17, 18 is correct?
The median is 21.?
The median is 32.?
The mean is 21.?
The mean is 39.?
Answers
Final answer:
The median of the data set 56, 21, 48, 17, 18 is 21, and the mean is 32 after arranging the data in ascending order and performing the necessary calculations.
Explanation:
To determine which statement about the data set 56, 21, 48, 17, 18 is correct, we need to calculate both the median and the mean.
To calculate the median:
First, we must order the data from least to greatest: 17, 18, 21, 48, 56.Since there are five numbers in the set, the median will be the third number, which is 21.To calculate the mean:
Add all the numbers together: 17 + 18 + 21 + 48 + 56 = 160.Divide the sum by the number of data points, which is 5: 160 / 5 = 32.The correct statements about the data set are: The median is 21 and the mean is 32.
Henry is building bookshelves to sell at a furniture store. First, he built 10 small bookshelves and 1 large bookshelf, using a total of 412 nails. Later, he built 10 small bookshelves and 8 large bookshelves, using a total of 776 nails. How many nails does Henry use to build the shelves?
Answers
Answer:
Henry uses 36 nails in large bookshelves and 52 nails in small bookshelves.
Step-by-step explanation:
Let in each large bookshelves Henry uses x nails and in each small bookshelves, Henry uses y nails.
Now, he built 10 small bookshelves and 1 large bookshelf, using a total of 412 nails.
So, 10x + y = 412 ......... (1)
Again, he built 10 small bookshelves and 8 large bookshelves, using a total of 776 nails.
So, 10x + 8y = 776 ........... (2)
Now, subtracting equation (1) from equation (2) we get, 7y = 364
⇒ y = 52
Again, from equation (1) we get, 10x = 412 - 52 = 360
⇒ x = 36
Therefore, Henry uses 36 nails in large bookshelves and 52 nails in small bookshelves. (Answer)
Final answer:
Henry uses 36 nails for a small bookshelf and 52 nails for a large bookshelf, according to the system of equations derived from the information given.
Explanation:
Calculating the Number of Nails Used by Henry
To solve this problem, we will use a system of equations.
Let's define x as the number of nails used for a small bookshelf and y as the number of nails used for a large bookshelf. From the question, we have the following equations based on the information given:
10x + 1y = 412 nails (first scenario with 10 small and 1 large bookshelf)
10x + 8y = 776 nails (later scenario with 10 small and 8 large bookshelves)
We can use these two equations to find out the values of x and y. Let's subtract the first equation from the second to eliminate x from our calculations:
10x + 8y − (10x + 1y) = 776 − 412
7y = 364
y = 52
Now we know that Henry uses 52 nails for a large bookshelf. Next, we will find the number of nails for a small bookshelf by substituting the value of y into the first equation:
10x + 1(52) = 412
10x = 412 − 52
10x = 360
x = 36
Hence, Henry uses 36 nails for a small bookshelf.
-4r - 2r + 5 = ? combining like terms with negative coefficients
Answers
Answer:
-6r + 5
Step-by-step explanation:
-4r - 2r + 5
= (-4 -2)r + 5
= -6r + 5
Ten times the sum of a number and 9
Answers
Answer:
10(x+9)
Step-by-step explanation:
Answer: 14
Step-by-step explanation: