Answer:
This other side of the triangle is equal to about 11.7 cm
Step-by-step explanation:
In order to find out the third side of the triangle we will just use the Pythagoras Theorem.
[tex]c^{2} =a^{2} + b^{2}[/tex]
Since we know the hypotenuse and we know one of the legs, in order to find the second leg we just substitute the values and solve the equation and so we get...
[tex]c^{2} =a^{2} + b^{2}\\19^{2} = 15^{2} + b^{2}\\361 = 225 + b^{2} \\[/tex]
[tex]b^{2} = 361 - 225\\b^{2} = 136\\b = \sqrt{136} \\[/tex]
And so b ≈ 11.66190
Write the repeating decimal $0.\overline{51}$ as a fully simplified fraction.
Answer:
17/33
Step-by-step explanation:
The repeating decimal [tex]$0.\overline{51}$[/tex] is equal to [tex]$\boxed{\frac{17}{33}}$[/tex].
What is a fraction?A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided. In a simple fraction, both are integers. In a complex fraction, a fraction can be found in either the numerator or the denominator. A suitable fraction has a numerator that is smaller than its denominator.
Let [tex]$x = 0.\overline{51}$[/tex]. Multiplying both sides of this equation by 100 gives,
[tex]$100x = 51.\overline{51}\\[/tex]. Subtracting the first equation from the second equation eliminates the repeating decimal,
giving:
[tex]\begin1100x - x &= 51.\overline{51} - 0.\overline{51}\\ \99x &= 51 \\\ \\end[/tex]
x = 51/99
Therefore, the repeating decimal [tex]$0.\overline{51}$[/tex] is equal to [tex]$\boxed{\frac{17}{33}}$[/tex].
Learn more about fractions here:
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Complete the following statement.
p(x)=x^(2)+7x+3
If is divided by x+4, the remainder is
Answer:
x + 3 with the remainder of -9
Step-by-step explanation:
___x__+__3_____
x + 4 | X^2 + 7x + 3
- (x^2 + 4x)
3x + 3
-(3x + 12)
-9
So the answer is x + 3 with the remainder of -9
plz i need help
In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. What is the value of sinF?
Answer:
Sin F = 0.6
Step-by-step explanation:
From triangle ABC, applying Pythagoras theorem to determine the length AB;
[tex]/hyp/^{2}[/tex] = [tex]/adj1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]
[tex]/AC/^{2}[/tex] = [tex]/BC/^{2}[/tex] + [tex]/AB/^{2}[/tex]
[tex]/20/^{2}[/tex] = [tex]/16/^{2}[/tex] + [tex]/AB/^{2}[/tex]
400 = 256 + [tex]/AB/^{2}[/tex]
[tex]/AB/^{2}[/tex] = 400 - 256
= 144
AB = [tex]\sqrt{144}[/tex]
= 12
AB = 12, AC = 20, BC = 16
Therefore since ΔABC ≅ ΔDEF, and each side of triangle DEF is [tex]\frac{1}{3}[/tex] the length of the corresponding side of triangle ABC.
Then,
DE = [tex]\frac{1}{3}[/tex]AB = [tex]\frac{1}{3}[/tex] x 12
= 4
EF = [tex]\frac{1}{3}[/tex]BC = [tex]\frac{1}{3}[/tex] x 16
= [tex]\frac{16}{3}[/tex]
DF = [tex]\frac{1}{3}[/tex]AC = [tex]\frac{1}{3}[/tex] x 20
= [tex]\frac{20}{3}[/tex]
Then, applying trigonometric function to ΔDEF, we have;
Sin F = [tex]\frac{opposite}{hypotenuse}[/tex]
= [tex]\frac{DE}{DF}[/tex]
= 4 ÷ [tex]\frac{20}{3}[/tex]
= 4 x [tex]\frac{3}{20}[/tex]
= [tex]\frac{3}{5}[/tex]
Sin F = 0.6
I NEED HELP ASAP
How do you write
A number is at least -3
Answer:
negative three
Step-by-step explanation:
i don't get what your asking for.
hiii please help asap ill give brainliest if you give a correct answer tyyyyy
Answer:
25?
Step-by-step explanation:
sorry if im wrong
Simplify 4.2(2x − 0.5y) − 2(4.1x − 0.3y)
The simplified form of the given expression is 0.2x-1.5y.
The given expression is 4.2(2x-0.5y)-2(4.1x-0.3y).
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression can be solved as follows
4.2(2x-0.5y)-2(4.1x-0.3y)
= 8.4x-2.1y-8.2x+0.6y
= 8.4x- 8.2x-2.1y+0.6y
= 0.2x-1.5y
Therefore, the simplified form of the given expression is 0.2x-1.5y.
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Which table shows a constant rate of change 3.25
Answer:
the third one
Step-by-step explanation:
Chase caught 2/3 of the balls hit to left field. Ryan caught 3/5 of the balls hit to right field. Which pair of equivalent fractions will help them find the total amount of the balls they both caught?
Answer:
1 4/15 balls
Step-by-step explanation:
From the question, we are told that:
Chase caught 2/3 of the balls hit to left field.
Ryan caught 3/5 of the balls hit to right field.
The Lowest common denominator for both fraction is given as 15
Hence, the equivalent fractions for each boy is calculated such that the denominators of both fraction is 15
For Chase:
We Multiply both numerator and Denominator by 5
2 × 5 /3 × 5 = 10/15
2/5 = 10/15
For Ryan
We Multiply both numerator and Denominator by 3
3 × 3 /5 × 3 = 9/15
3/5 = 9/15
The total amount of the balls they both caught is:
10/15 + 9/15
= 19/15 = 1 4/15
if the daimeter of a solid cylinder with lenght 140cm is 8cm , find its curved surface area ,
Answer : The curved surface area of solid cylinder is [tex]3520cm^2[/tex]
Step-by-step explanation :
As we are given that:
Diameter of solid cylinder = 8 cm
Length or Height o solid cylinder = 140 cm
Formula used to calculate the curved surface area of cylinder is:
Curved surface area of cylinder = [tex]2\pi r\times h[/tex]
where,
r = radius of cylinder
h = height or length of cylinder
Radius of cylinder = [tex]\frac{Diameter}{2}=\frac{8cm}{2}=4cm[/tex]
Now putting all the given values in above formula, we get:
Curved surface area of cylinder = [tex]2\times \frac{22}{7}\times 4cm\times 140cm[/tex]
Curved surface area of cylinder = [tex]3520cm^2[/tex]
Therefore, the curved surface area of solid cylinder is [tex]3520cm^2[/tex]
Given:
Diameter of a solid cylinder = 8cm
Length (height) of cylinder = 140 cm
To find:
The curved surface area of the cylinder.
Solution:
We have,
Diameter = 8cm
Radius = [tex]\dfrac{8}{2}=4\text{ cm}[/tex]
Height = 140 cm
Curved surface area of a cylinder is
[tex]CSA=2\pi rh[/tex]
where, r is radius and h is height.
Putting r=4 and h=140 in the above formula, we get
[tex]CSA=2\times \dfrac{22}{7}\times 4\times 140[/tex]
[tex]CSA=2\times 22\times 4\times 20[/tex]
[tex]CSA=3520[/tex]
Therefore, the curved surface area of the cylinder is 3520 square cm.
if a tables f(x) is being divided by 3, what is the common ratio
For one of my math assignments I have to find out which solution is,
One solution
Infinite solution
and No solution
what i've got for it is
y=x+6 and 3x-3y=-18 (Infantaly amount of solutions)
y=-4x+11 and -6+y=11 (One solution)
y=-2x+5 and 2x+y=-7(no solution)
Is this correct?
Answer:
yeah i think they are all right :)
Step-by-step explanation:
What is y=-2/9x+3 written in standard form using integers?
Answer:
2x-9y=-27
Step-by-step explanation:
hope this helps. :)
78=6 f please help solve ion have much time
Answer:
hii
Step-by-step explanation:
At the neighborhood grocery, 4.5 pounds of chicken breast cost $53.28. Benjamin
spent $59.20 on chicken breast. How many pounds of chicken breast did he buy, to
the nearest hundredth of a pound?
find the slope of the line
Answer:
slope: -2
Step-by-step explanation:
trying not to pull another 1am night help would be nice
will give brainliest :)
Answer:
1) AB
2) BC
3) AC
ABC
4) PA and OH
5) SO and CP
6) CA and SH
hope you can get to bed soon!
8/10 lies _____ on number line.
8/10 = 0.8
Therefore, 0.8 (8/10) is put on the number line shown below.
what is 10 x 10 -9x 6 + 7 first to answer will get brainlyest
Help? Show work!
Triangle PQR ≅ Triangle XYZ
PQ = 3a + 4 and XY = 5a – 12. Find a and PQ.
Given:
[tex]\Delta PQR\cong \Delta XYZ[/tex]
[tex]PQ=3a+4[/tex]
[tex]XY=5a-12[/tex]
To find:
The value of a and PQ.
Solution:
We have,
[tex]\Delta PQR\cong \Delta XYZ[/tex]
[tex]PQ\cong XY[/tex] (CPCTC)
So,
[tex]PQ=XY[/tex]
[tex]3a+4=5a-12[/tex]
Isolating variable terms, we get
[tex]3a-5a=-4-12[/tex]
[tex]-2a=-16[/tex]
Divide both sides by -2.
[tex]a=\dfrac{-16}{-2}[/tex]
[tex]a=8[/tex]
Now,
[tex]PQ=3a+4[/tex]
[tex]PQ=3(8)+4[/tex]
[tex]PQ=24+4[/tex]
[tex]PQ=28[/tex]
Therefore, the value of a is 8 and the value of PQ is 28.
Figure #2
2. What is x?
А 58
C 122
990
B
48
D
218
42
For the past ten years, Michelle has been tracking the average annual rainfall in Boynton Beach, Florida by recording her data in the given table. She has concluded that the relationship can be modeled by a linear function. Year 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Average Rainfall(in inches) 62.33 61.8 61.27 60.74 60.21 59.68 59.15 58.62 58.09 57.56Use the values provided in the table to create a linear graph of the data. On the graph, let represent the year 2004. Be sure to include all proper labels on the graph.
Answer:
The answer is below
Step-by-step explanation:
A linear function is a function in the form y = mx + b, where y and x are variables, b is the y intercept (value of y at x = 0) and m is the slope (rate of change).
Let x represent the year and y represent the amount of rainfall in inches. The linear function can be gotten by selecting any two pair of points from the table in the form (x, y).
Let us use the points (2004, 62.33) and (2007, 60.74). The equation is gotten using:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-62.33=\frac{60.74-62.33}{2007-2004}(x-2004) \\\\y-62.33=-0.53(x-2004)\\\\y-62.33=-0.53x+1062.12\\\\y=-0.53x+1124.45[/tex]
The graph is plotted using geogebra.
The average rainfall from 2004 to 2013 is 59.945
Given data of rainfall:
2004 62.33
2005 61.8
2006 61.27
2007 60.74
2008 60.21
2009 59.68
2010 59.15
2011 58.62
2012 58.09
2013 57.56
what is the average value?it is the sum of all the observations divided by the total number of observations.
average rainfall A
(62.33+61.8+61.27+60.74+60.21+59.68+59.15+58.62+58.09+57.56)/10
A= 59.945
thus, the average rainfall from 2004 to 2013 is 59.945
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Which expression is equivalent to 12(4m−2n+4)?
1.2m−n+2
2.2m−2n+4
3.8m−4n+4
4.8m−4n+8
Answer:
1. 2m - n + 2
Step-by-step explanation:
12×4m - 12×2n + 12×4. ( because 12 is multipled by whole bracket)
48m - 24n + 48.
2m - n + 2. (by finding common factor 24)
Hi I need help
I’m new on this app
Answer:
.60 I think
I hope you get it right
Need help ASAP!!!!!!!
If you were planning a meal for 24 people,
how many dozens
of eggs would you need to buy if each person were to have 2 eggs each?
Answer:
4 dozen.
Step-by-step explanation:
Total number of eggs required =2*24 = 48
One dozen = 12 so the answer is 4 dozen eggs.
For Items 16-28, determine whether each function is
even, odd, or neither.
f(x) = -x + 2x + 5
f(x) = x + 8x
f(x) = -7x² + 5
f(x) = 5x + 3x? – 7x + 1
Answer:
f(x) = -x + 2x + 5
is odd since f(x) = -5
f(x) = x + 8x
is neither because f(x) = 0
f(x) = -7x² + 5
is odd since f(x) = √5/7
f(x) = 5x + 3x? – 7x + 1
is odd
please help me out in optional maths
Help plssssss!!!!!!!!!?????
Answer:
the first box is 7, the second would be -10, but since it already has ‘x -‘, just put 10
Step-by-step explanation:
I need help does someone know this?!
I need to use the Pythagorean Theorem to find X. I don’t know how to do that!!
Answer:
17) x=8
18) [tex]x=\sqrt{189}[/tex] or [tex]x= 3\sqrt{21}[/tex]
Step-by-step explanation:
So the rule is [tex]a^{2} +b^{2} =c^{2}[/tex], "c" being the hypothenuse, or the long line that is opposite to the right angle.
17) We know that both values of x are equal to each other, which makes everything 10x easier!
[tex]x^{2} +x^{2} =(8\sqrt{2}) ^{2}[/tex]
(by the way we know the x values are our a and b values because they are legs! the way I like to remember the legs is that they are connected to the right angle box, and therefore support the hypothenuse)
simplify (╥︣﹏╥)
[tex]2x^2=8^2(\sqrt{2} )^{2}[/tex]
[tex]2x^2=64(2)[/tex]
[tex]2x^2=128[/tex]
[tex]x^{2}= 128/2[/tex]
[tex]x^{2} =64[/tex]
x=8
18) Just pretend that the flipped triangle doesn't exist. It's parallel to the other triangle with values on it, and basically servers no purpose other than being parallel to the sister triangle :)
Anyways, since we know the hypothenuse (15) but we don't know one of our leg values (x), we're going to change our equation a bit!
[tex]c^{2} - b^{2} = a^{2}[/tex]
It doesn't matter if you put the one leg value in a or b, just as long as you stick to that same equation you started with the entire time!
[tex]15^{2} -6^{2} =x^{2}[/tex]
[tex]225-36=x^{2}[/tex]
[tex]x^{2} =189[/tex]
[tex]x=\sqrt{189}=3\sqrt{21}[/tex]
The more you do these, the easier they'll get, so don't worry!