The hypotenuse of a right triangle measures 6 cm and one of its legs measures 3 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Pythagoras' theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The measure of the other leg of the triangle is 5.1961 units.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Let the length of the other leg can be represented by x.
Given the hypotenuse of a right triangle measures 6 cm and one of its legs measures 3 cm. Therefore, the measure of the other legs can be written as,
Hypotenuse² = 3² + x²
6² = 3² + x²
36 = 9 + x²
x² = 27
x = √27
x = 5.1961
Hence, the measure of the other leg of the triangle is 5.1961 units.
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Which equation is equivalent to 4x+3 = 64?
O 2x+6=24
O 22x+6=26
O 42x+6 - 42
O 4X+3 - 46
Answer:
Answer is 2^2x+6=2^6 since it is equivalent to 4^x+3=64
The equivalent equation of [tex]4^x^+^3=64[/tex] is [tex]2^6^x^+^6=2^6[/tex], option B is correct.
The given equation is [tex]4^x^+^3=64[/tex]
Four to the power of x plus three equal to sixty four
x is the variable in the equation
We have to find the equivalent equation
We know that 2×2×2× 2×2×2 , 2⁶=64
[tex]4^x^+^3=2^6[/tex]
Now [tex](2^2)^x^+^3=2^6[/tex]
[tex]2^6^x^+^6=2^6[/tex]
Hence, the equivalent equation of [tex]4^x^+^3=64[/tex] is [tex]2^6^x^+^6=2^6[/tex], option B is correct.
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The price of a box of colored pencils increased from $8.00 to $8.48. What was the percent increase in the price?
Step-by-step explanation:
100% = $8.00
1% = 100%/100 = 8/100 = $0.08
the price went up by $8.48 - $8.00 = $0.48.
how many % is this ?
as many % as 1% fits into this difference :
0.48 / 0.08 = 6%
the price increase was 6%.
PLease Help its a math problem see image attached i am struggling with this
Answer:
f(x) = (x+5)^2-1
Step-by-step explanation:
which figures appear to be congruent
A) 1,4
B) 1,4 and 5
C) 1 and 5
D) 4 and 5
Answer:
Explain your answer C) 1 and 5
On a coordinate plane, rhombus w x y z has points (negative 3, 1), (1, 4), (5, 1), and (1, negative 2). rhombus wxyz is graphed on a coordinate plane. what is the area of the rhombus? 24 square units 28 square units 32 square units 48 square units
The area of the rhombus is 24 square units.
What is a Rhombus?This has to do with the quadrilateral that each side are of the same length.
Calculations and Parameters:Given the data:
Length WY is 3 - (-5) = 8 units.
Length XZ is 4 - (-2) = 6 units.
Hence, the area of the rhombus WXYZ is 1/2 of the diagonal length:
1/2 * 8 * 6
= 24 square units.
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Answer:
A
Step-by-step explanation:
Shara collected two different data sets and labeled them data set S and data set T. Data set S has a correlation coefficient of −0.91, and data set T has a correlation coefficient of 0.89.
Part A: Which data set has a stronger linear relationship?
Part B: How do you know this?
Select two answers, one for Part A and one for Part B.
Data set T has strong linear relationship as it is a perfect positive correlation
What is Correlation Coefficient ?
A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.
In other words, it reflects how similar the measurements of two or more variables are across a dataset.
When one variable changes, the other variables change in the same direction or opposite direction.
Perfect positive correlation :When one variable changes, the other variables change in the same direction.
Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.
Part A &B : Data set T has strong linear relationship as it is a perfect positive correlation
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A graph shows the horizontal axis numbered 1 to 5 and the vertical axis numbered 1 to 5. points and a line show a downward trend. which is most likely the correlation coefficient for the set of data shown? –0.83 –0.21 0.21 0.83
The most likely correlation coefficient for the set of data shown is: -0.21.
Correlation coefficientWe would be using CORREL in excel to determine the correlation coefficient by inputting the set data below
X Y
A (1,4)
B (2, 1.5)
C (3,3)
D (4,4)
E (5,2)
Hence:
Correlation coefficient=-0.20801
Correlation coefficient=-0.21 (Approximately)
Therefore the most likely correlation coefficient for the set of data shown is: -0.21.
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Answer:
B) -0.21.
Step-by-step explanation:
Help me with this extremely hard differentiation question , [Scroll] >>
[tex]\huge\frac{d}{dx}[\sum_{n=0}^{∞}[(\frac{(-1) ^ {n}}{(2n+1)!})(\frac{1}{1+e^{x}})^{2n+1}] ][/tex]
Answer:
[tex]f'(x)=\displaystyle -\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]
Step-by-step explanation:
Recall the power series [tex]\sin(x)=\displaystyle \sum\limits^\infty_{n=0}(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex].
In this case, [tex]x[/tex] is replaced with [tex]\displaystyle \frac{1}{1+e^x}[/tex], so our power series actually works out to be [tex]\displaystyle \sin\biggr(\frac{1}{1+e^x}\biggr) =\sum\limits^\infty_{n=0}(-1)^n\frac{\bigr(\frac{1}{1+e^x}\bigr)^{2n+1}}{(2n+1)!}[/tex]! Amazing, huh?
Now, we find the derivative of the function by using the chain rule:
[tex]\displaystyle \frac{d}{dx}\sin\biggr(\frac{1}{1+e^x}\biggr)=\frac{d}{dx}\biggr(\frac{1}{1+e^x}\biggr)*\cos\biggr(\frac{1}{1+e^x}\biggr)=-\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]
You didn't specify if you just wanted the derivative of the series to be a function or a series, so I'm going to assume you want the function. Let me know if there's more to your problem.
What is the area of this quadrilateral?
41
3 ft
10 ft
10 ft
3D
4 ft
O A. 30 square feet
O B. 36 square feet
O c. 42 square feet
O D. 12 square feet
Answer:
42 square feet
Step-by-step explanation:
10 ×3= 30
4×3=12 divided by two =6 ×2= 12
(multiply because there are two triangular ends)
12+30=42
check the attachment please. I also need to know the value of y
Answer:
Angle MBR = 31°
y = 14
Step-by-step explanation:
There is a tiny red square in angle MBH that means it is a right angle. Right angles are 90°. So the 59° angle and the angle marked (y+17)° together make a 90° angle. That helps us write an equation.
59 + y + 17 = 90
add.
76 + y = 90
subtract 76.
y = 14
Then you can find Angle MBR:
y + 17
= 14 + 17
= 31
Alternatively, you could find MBR first and then find y. It comes out the same either way.
1) Find the volume of the rectangular pyramid below.
21 cm
1 cm
29 cm
Answer:
3349.5 [tex]cm^{3}[/tex]
Step-by-step explanation:
see image
what is the value of x
Answer:
x= 96
Step-by-step explanation:
I know this is might not be the best reasoning, but if 56+40=96, then the other consecutive angle should be 96 degrees by the Consecutive Interior Angles theorem.
a function is graphed on coordinate plane. what is the value of the function when x = -4
Answer:
no graph un asnwerable
Step-by-step explanation:
what is the answer to this question?
Answer:
y = 96
Step-by-step explanation:
given that y is directly proportional to x² then the equation relating them is
y = kx² ← k is the constant of proportion
to find k use the condition when y = 24 , x = 2 , then
24 = k × 2² = 4k ( divide both sides by 4 )
6 = k
y = 6x² ← equation of proportion
when x = 4 , then
y = 6 × 4² = 6 × 16 = 96
Select all the correct figures.
Which figures show starting steps in the construction of an equilateral triangle?
Question 4 (1 point)
(01.01)
Evaluate 48 + 24 = 8-22. (1 point)
O a
ob
51
c
Od
the answer is A 47
Step-by-step explanation:
48+24÷8-2²
48+3-2²
48+3-4
=47
hope it helps!
Help asap. Show your work please :)
Use the function f(x) = 5x2 + 2x − 3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
A) factor f(x) are 3/5 and -1.
B) x-intercepts of the graph of f(x) are (3/5, 0) and (-1, 0).
C) The end behavior is explained by vertex of the graph which is (-0.2, -3.2)
D) The graph is symmetrical about x = -0.2. shown below
What is factorization?Factorizing is a way of writing an expression as a product of its factors using brackets.
Given function is : 5x² + 2x − 3
A)5x² + 2x − 3
= 5x² + 5x-3x − 3
= 5x(x+1)-3(x+1)
=(5x-3)(x+1)
So, factors will be 3/5 and -1.
B) f(x)= 5x² + 2x − 3
The x-intercepts are when f(x) = 0.
So, x-intercepts are (3/5, 0) and (-1, 0).
C) The x-coordinate of the vertex is the midpoint of the zeros.
midpoint= (3/5-1)/2
=-0.2
To find the y-coordinate of the vertex, substitute the found value of x into the given equation:
f(-0.2)= 5(-0.2)² + 2(-0.2) − 3
=-3.2
So, the end behavior is explained by vertex of the graph which is (-0.2, -3.2)
D) By plotting the zeroes and the vertex of the f(x).
The axis of symmetry is the x value of the vertex.
Thus, the graph is symmetrical about x = -0.2.
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In a class of 30 students, 13 of them are boys. What percentage of the class are girls? Give your answer to 1 decimal place.
Answer: 56.7%
Step-by-step explanation:
1) First we need to find the number of girls out of the class of 30:
30-13 = 17 -> 17 girls in the class
2) Then we can set up a part-whole equation like this (I don't know if this is how you learned it, I recommend searching up "part whole percent" if you're confused):
[tex]\frac{17}{30} \frac{x}{100}[/tex] it follows this template: [tex]\frac{part}{whole} \frac{percent}{100}[/tex]
Since we're trying to find the percent and the problem gives us the rest of the info (by the way, that 100 will always stay there, it will never change)
3) Then we cross multiply
17 x 100 = 1700
1700/30 = 56.6666666
4) And since the answer has to be in the 1 decimal place, it would be 56.7
So that means approximately 56.7% of the class are girls
In the diagram below, perpendicular lines e and g are intersected by line f. Based on the angle measures in the diagram, what is the value of x?
Answer:
x = 43
Step-by-step explanation:
the angle in the triangle is vertically opposite 47° and is congruent
the sum of the 3 angles in the triangle = 180° , then
90 + 47 + x = 180
137 + x = 180 ( subtract 137 from both sides )
x = 43
awnser pls quickly :)))
Answer:
P': (5,3)
Q': (10,3)
R': (3,10)
Step-by-step explanation:
What number when added to 1 1/3 is 2
Answer:
2/3 or .66 repeated
Step-by-step explanation:
1 1/3= 1.33
1.33 + .66..7 is 2
Answer:
[tex]\huge\boxed{\sf x = \frac{2}{3}}[/tex]
Step-by-step explanation:
Let the number be x
Given condition:
[tex]\displaystyle 1 \frac{1}{3} +x=2\\\\Subtract\ 1\frac{1}{3} \ to \ both \ sides\\\\x = 2-1\frac{1}{3} \\\\x = \frac{2 \times 3}{1 \times 3} - \frac{4}{3} \\\\x = \frac{6}{3} - \frac{4}{3} \\\\x=\frac{6-4}{3} \\\\\boxed{x = \frac{2}{3}} \\\\\rule[225]{225}{2}[/tex]
You are investing $1500 at 6.2% compounded annually. How much money will you have in 12 years?
Answer:
$3087.35
Step-by-step explanation:
Compound interest formula
[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = principalr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $1500r = 6.2% = 0.062n = 1t = 12 yearsSubstituting given values into the equation and solving for A:
[tex]\begin{aligned}\sf A & =\sf P \left(1+\frac{r}{n}\right)^{nt}\\\\\implies \sf A & = \sf 1500\left(1+\frac{0.062}{1}\right)^{1 \times 12}\\\\& = \sf 1500(1.062)^{12}\\\\& = \sf \$ 3087.35 \: (nearest\:cent)\end{aligned}[/tex]
Help please this needs to be turned in tommorrow soo im trying to rush and when i rush i cant focus
Answer: Hello! Hope this helps.
Step-by-step explanation: 6 - 7x/2
So its the first answer.
A square with diagonals is shown. the distance from one point to the middle point is x. the length from the center point to another point is x. the length of a side is 8. the figure is a square. its diagonals meet to form four right angles. what is the approximate value of x? 2.8 units 3.3 units 4.0 units 5.7 units
The approximate value of x in the square that the diagonals meets to form four right angles is 5.7 units
Properties of a square.All the sides are equal.Opposite sides are parallel to each other.The diagonal intersects at right angle.Using Pythagoras theorem the value of x can be found as follows:
c² = a² + b²
where
c = hypotenuse a and b are other legsTherefore,
8² = x² + x²
64 = 2x²
x² = 64 / 2
x = √32
x = 5.65685424949
x = 5.7 units
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Answer: 5.7 units
Step-by-step explanation:
f(x) = 4(4 + x) whats the answer? and would that be the constant rate?
Answer:
f(x)=16+ 4x
the constant rate would be 4
Step-by-step explanation:
Answer: y=4x+16
Step-by-step explanation:
A child grew 3 1/4 inches one year and 4 3/4 inches the next year. How many inches did the child grow over the two years?
Answer:
8 inches.
Step-by-step explanation:
3 1/4 + 4 3/4
= 3 + 4 + 1/4 + 3/4
= 7 + 4/4
= 7 + 1
= 8 inches.
Answer:
The child grew 8 inches
Step-by-step explanation:
Step 1: Convert to improper fractions
[tex]3\frac{1}{4}[/tex]
[tex]\frac{1+(3*4)}{4}[/tex]
[tex]\frac{1+12}{4}[/tex]
[tex]\frac{13}{4}[/tex]
[tex]4\frac{3}{4}[/tex]
[tex]\frac{3+(4*4)}{4}[/tex]
[tex]\frac{3+16}{4}[/tex]
[tex]\frac{19}{4}[/tex]
Step 2: Combine the fractions
[tex]\frac{13}{4}+\frac{19}{4}[/tex]
[tex]\frac{13+19}{4}[/tex]
[tex]\frac{32}{4}[/tex]
[tex]8[/tex]
Answer: The child grew 8 inches
A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation 23 + 6,2 - 27x= 140 can be used to find x. Height: (x+9) in. Width: (2 - 3) in Length: xin. What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer. O The length is 7 inches, the width is 4 inches, and the height is 16 inches. O The length is 5 inches, the width is 2 inches, and the height is 14 inches. O The length is 4 inches, the width is 1 inch, and the height is 13 inches. O The length is 3 inches, the width is O inches, and the height is 12 inches.
For this case we have the following equation for the volume:
[tex]x^3+6x^2-27x=140 < br/ >[/tex]
Rewriting the equation we have:
[tex]x^3+6x^2-27x=140=0 < br/ >[/tex]
We factor the equation to find the roots of the polynomial.
We have then:
[tex](x-5)(x+4)(x+7)=0 < br/ >[/tex]
Then, we discard the negative roots, because the dimensions of the figure must be positive.
We have then that the length is:
[tex]x=5 < br/ >[/tex]
The height is:
[tex]x+9=5+9=14 < br/ >[/tex]
The width is:
[tex]x-3=5-3=2 < br/ >[/tex]
Thus, the dimensions are:
[tex]5*14*2 < br/ >[/tex]
Answer:
The length is 5 inches, the width is 2 inches, and the height is 14 inches.
function f is shown below
f(-3)
f(4)
find x when f(x) = 5
find x when f(x)= -3
Answer:
See below ~
Step-by-step explanation:
Based on the graph,
f(-3)f(-3) = 02. f(4)
f(4) = -33. x when f(x) = 5
f(x) = 5x = 04. x when f(x) = -3
f(x) = -3x = ±4What is the equation of the circle with center (-3.2, -2.1) and radius 4.3?
The equation of the circle is : [tex]x^{2}[/tex] + [tex]y^{2}[/tex] + 6.4[tex]x[/tex] + 4.2[tex]y[/tex] = 3.84
Meaning of a CircleA circle is a loci or a continuous line that equidistant from the center to any point on the line. it drawn starting from a point and ending on that same point.
The equation of a circle is an equation used to find points on a circle so the circle can be drawn with accurate measurement. it can also be used to find the missing points.
In conclusion, The equation of the circle is : [tex]x^{2}[/tex] + [tex]y^{2}[/tex] + 6.4[tex]x[/tex] + 4.2[tex]y[/tex] = 3.84
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