Find the missing side of this righttriangle.X712X = V[?Enter the number that belongs in the green box.
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SOLUTION
We will apply the Pythagoras theorem in solving this.
The Pythagoras theorem states that the square of the hypotenuse, which is the longest side is equal to the sum of the squares of the other two sides.
Here the hypotenuse is x, therefore
[tex]\begin{gathered} x^2=7^2+12^2 \\ x^2=\text{ 49+144} \\ x^2=193 \\ x\text{ = }\sqrt[]{193} \\ x\text{ =13.8924} \end{gathered}[/tex]Therefore, the answer is 13.89 to the nearest hundredth.
Related Questions
Please help me !!!
Suppose that a and b are real numbers with a+5b=10 find the greatest possible value of the expression a*b enter the exact value.
The greatest possible value is ? Which occurs when a= ? And b=?
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The maximum value of (a x b) would be 1.472 at a = 0.8 and b = 1.84.
What is maxima and minima?In mathematical analysis, the maxima and minima of a function, known collectively as extrema, are the largest and smallest value of the function, either within a given range, or on the entire domain.
Given is a + 5b = 10.
It is given to find the maximum value of the product of [a] and [b].
We can write -
a + 5b = 10
b = 2 - a/5
So, we can write -
a x b as a(2 - a/5)
So, we can write that -
y = f(a) = a(2 - a/5)
Differentiate with respect to [a], we get -
dy/da = a d/da (2 - a/5) + (2 - a/5) d/da (a)
dy/da = a(0 - 1/5) + (2 - a/5)
dy/da = - a/5 + 2 - a/5
dy/da = 2 - 0.4a
For maximum value -
dy/da = 0
2 - 0.4a = 0
2 = 0.4 a
a = 2 x 0.4
a = 0.8
Therefore -
5b = 10 - 0.8
5b = 9.2
b = 1.84
The maximum value of a x b will be -
0.8 x 1.84
1.472
Therefore, the maximum value of (a x b) would be 1.472 at a = 0.8 and b = 1.84.
To solve more questions on maxima and minima, visit the link below-
https://brainly.com/question/12870695
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(7.8x10^7) + (9.9x10^7) write in scientific notation And (3.1x10^6)x(2.7x10^-2)
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Explanation:
The question is given below as
[tex]7.8\times10^7+9.9\times10^7[/tex]Step 1:
Factorise the expression above, we will have
[tex]\begin{gathered} 7.8\times10^7+9.9\times10^7 \\ (7.8+9.9)\times10^7 \\ 17.7\times10^7 \\ 1.77\times10^1\times10^7 \\ 1.77\times10^{1+7} \\ 1.77\times10^8 \end{gathered}[/tex]Hence,
The final answer in scientific notation is
[tex]1.77\times10^8[/tex]The second part of the question is given below as
[tex]\begin{gathered} 3.1\times10^6\times2.7\times10^{-2} \\ 3.1\times2.7\times10^6\times10^{-2} \\ 8.37\times10^{6+(-2)} \\ 8.37\times10^{6-2} \\ 8.37\times10^4 \end{gathered}[/tex]Hence,
The final answer is scientific notation is
[tex]8.37\times10^4[/tex]Exercise 3: Show that each of the following values for the given variable is a solution to thegiven equation. Show the calculations that lead to your answer.(a) 5x + 2 = 12for x = 2(b) = 6for x = 15(C) x2 – 2x = 8for x = 4
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the points (-4,0) and (s,-1) fall on a line with a slope of -1/8.what is the value of s?
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We will use the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]m=-1/8 x₁= -4 y₁=0 x₂=s y₂=-1
[tex]-\frac{1}{8}=\frac{-1-0}{s+4}[/tex][tex]-\frac{1}{8}=\frac{-1}{s+4}[/tex]-1(s+4) = -8
multiply both-side of the equation by -1
s+4 = 8
subtract 4 from both-side of the equation
s + 4 - 4 = 8 -4
s = 4
Toby eats tacos every 5 days. Toby also drinks horchata every 6 days. If Toby has horchata and tacos today how many days will he have too wait to enjoy his favorite treats on the same day again?
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We are given the following information
Toby eats tacos every 5 days.
Toby also drinks horchata every 6 days.
If Toby has horchata and tacos today how many days will he have to wait to enjoy his favorite treats on the same day again?
We need to find the least common multiple (LCM) of 5 and 6 days.
Multiples of 5 = 5, 10, 15, 20, 25, 30
Multiples of 6 = 6, 12, 18, 24, 30
As you can see, the least common multiple (LCM) of 5 and 6 is 30
Therefore, Toby has to wait for 30 days to enjoy his favorite treats on the same day again.
Use graphs and tables to find the limit and identify any vertical asymptotes of the function. See the picture below.
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The Solution:
Given:
Required:
Evaluate the given limit.
The limit is undefined.
Below is the graph:
So,
The limit is undefined.
The vertical asymptote is: x = 1
The Horizontal asymptote is: y = 0
The area of a circle is 50.24 square millimeters. What is the circle's radius?A = 50.24 mm2Use 3.14 for u.
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The area of a circle is 50.24 square millimeters. What is the circle's radius?
A = 50.24 mm2
Use 3.14 for u.
Remember that
the area is equal to
A=pi*(r^2)
we have
A=50.24 mm2
pi=3.14
substitute given values
50.24=3.14*(r^2)
solve for r
r^2=50.24/3.14
r^2=16
square root
r=4 mmPart 2we have
C=31.4 in
Remmeber that the circumference is equal to
C=2pir
we have
C=31.4
pi=3.14
substitute
31.4=2(3.14)r
solve for r
r=31.4/(2*3.14)
r=5 inWhich is the product of (-1 2/5) (-2 3/4)
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The product of :
[tex]-1\frac{2}{5}\text{ and -2}\frac{3}{4}[/tex]We convert the mixed fractions to improper fractions and then multiply the two.
Thus, we have:
[tex]\begin{gathered} \frac{-7}{5}\text{ }\times\text{ }\frac{-11}{4} \\ \frac{77}{20}=\text{ 3}\frac{17}{20} \end{gathered}[/tex]
If the square root of C is equal to 8 , what is C equal to ?
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The first thing we have to do is turn the statement into an equation:
[tex]\sqrt[2]{C}=8[/tex]To solve for C we can raise the expression on both sides to the square and thus eliminate the root
[tex]\begin{gathered} (\sqrt[2]{C})^2=(8)^2 \\ C=64 \end{gathered}[/tex]Solving we can see that C is equal to 64A) what is the maximum height of the ball ? B) how many seconds does it take until the ball hits the ground ?
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Given:
[tex]h(t)=-16t^2+104t+56[/tex]Models the balls height height about the ground.
Required:
To find the maximum height of the ball.
Explanation:
Consider
[tex]\begin{gathered} h(t)=-16t^2+104t+56 \\ a=-16 \\ b=104 \\ c=56 \end{gathered}[/tex][tex]\begin{gathered} t=-\frac{b}{2a} \\ \\ t=-\frac{104}{2(-16)} \\ \\ t=\frac{204}{32} \\ \\ t=3.25 \end{gathered}[/tex]At t = 3.25 the maximum height is
[tex]\begin{gathered} h(3.25)=-16(3.25)^2+104(t)+56 \\ =225 \end{gathered}[/tex]Final Answer:
The maximum height of the ball is 225 feet.
Dion's rectangle measures 2 1/4 unjts by 3 1/2 units what is the are?
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so the area is
[tex]\frac{9}{4}\cdot\frac{7}{2}=\frac{63}{8}=7\frac{7}{8}[/tex]The area of a rectangle is 50m^2, and the length of the rectangle is 5 m less than three times the width. Find the dimensions of the rectangle.(Length= m)(Width= m)
Answers
Given:
Area of the rectangle is 50 sq. m.
The length of the rectangle is 5 m less than three times the width.
That is,
l=3w-5
To find the dimensions:
The formula for the area of the rectangle is , A=lw
Therefore,
[tex]\begin{gathered} A=(3w-5)() \\ 50=3w^2-5w \\ 3w^2-5w-50=0 \\ (3w-15)(3w+10)=0 \\ 3w=15,3w=-10 \\ w=5,w=-\frac{10}{3} \end{gathered}[/tex]Since, width can not be negative.
So, -10/3 can be neglected.
Hence, w=5
So, the length is,
[tex]\begin{gathered} l=3(5)-5_{} \\ =15-5 \\ =10 \end{gathered}[/tex]Hence, the dimensions are, l=10 m and w=5 m.
find the perimeter of the rectangle picture above
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Okay, here we have this:
As the perimeter is the sum of all the sides, so:
Perimeter=29+29+17+17=92.
Finally we obtain that the perimeter of the rectangle is 92 units.
COULD YOU PLEASE JUST HELP WITH NUMBER 9 I DONT UNDERSTAND
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ANSWER
• Mean = 24.5
,• Median = 27.5
,• Mode = 28
EXPLANATION
When we add or subtract a constant from each data in a data set, the mean, median and mode change in the same amount.
So if before we had that the mean = 21.5, median = 24.5 and mode = 25 and we add $3 to each data, then all three values change by adding 3:
• new mean, = previous mean + 3 = 21.5 + 3 =, 24.5
,• new median, = previous median + 3 = 24.5 + 3 =, 27.5
,• new mode, = previous mode + 3 = 25 + 3 = ,28
Here is a graph for one of the equations in a system of two equations Select all the equations thar could be the other equation in a system A: y=-3xB: y=-3/2x+6C: y=-1/6x+3D: y=2/3x-1E: y=1/2x-1F: y=4x-2
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To be able to determine which equations could be the other equation in a system
Can You Describe A Scale Copy?
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A scale copy is basically to copy the same geometrically figure but at different sizes of the original figure. The copy will be bigger or smaller than the original one. It will depend on the factor to scale the figure.
For example, if we want to duplicate the size of the original figure, we need to multiply by 2 each size of the figure. In this case, the figure is bigger than the original one by a factor of 2.
Conversely, if we need to have a smaller representation of the original one, we can multiply each side of the original figure by a fraction. It could be 1/2, 1/10, 1/75, and even 1/100, and so forth. The factor will depend on the needs about how to represent the original figure on an appropriate scale. In this way, if we have a size of b, we need to multiply it by the factor above mentioned, for instance:
[tex]\frac{1}{2},\frac{1}{10},\frac{1}{75}\frac{1}{100},\frac{1}{500}[/tex]Scale copy is fundamental in Design, and whenever is necessary to represent the original object on a different scale.
how to solve this one i need help with number 5 and 8
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5.
Apply the power to each number and simplify
8.anythig raised to the zero power is equal to one
6.multiply
7.substract
Last year, Henry had $30,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 5% simple interest per year. After one year, he received a total of $1760 in interest. How much did he invest in each account? First account: Second account:
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Solution
Step 1
Total amount invested = $30,000
Step 2:
First account
Money invested = m
interest rate = 7%
Time = 1 year
Interest = ?
Second account
Money invested = 30000 - m
interest rate = 5%
Time = 1 year
Interest = ?
Step 3:
Interest received from the first investment
[tex]\begin{gathered} Interest\text{ = }\frac{PRT}{100}\text{ = }\frac{m\times7\times1}{100}\text{ = 0.07m} \\ \end{gathered}[/tex]Interest received from the second investment
[tex]Interest\text{ = }\frac{PRT}{100}\text{ = }\frac{\lparen30000-m\rparen\times5\times1}{100}\text{ = 0.05\lparen30000 - m\rparen}[/tex]Step 4:
Total interest = $1760
[tex]\begin{gathered} \text{0.07m + 0.05\lparen30000 - m\rparen = 1760} \\ 0.07m\text{ + 1500 - 0.05m = 1760} \\ 0.02m\text{ = 1760 + 1500} \\ 0.02m\text{ = 260} \\ \text{m = }\frac{260}{0.02} \\ \text{m = \$13000} \end{gathered}[/tex]Final answer
How much did he invest in each account?
First account: $13000
Second account: $17000
How do I use synthetic division to find the other zeros
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Given the function below
[tex]f(x)=x^4-11x^3+40x^2-48x^{}[/tex]Where
[tex]x=3\text{ is a zero of the function.}[/tex]To find the other zeros,
[tex]\begin{gathered} x=3x \\ x-3=0\text{ is a factor} \end{gathered}[/tex]And x is common, factor out x, i.e
[tex]\begin{gathered} f(x)=x^4-11x^3+40x^2-48x^{} \\ f(x)=x(x^3-11x^2+40x-48) \end{gathered}[/tex]Divde the function by the factor x - 3
The quotient of the function after dividing by x - 3 is
[tex]f(x)=(x-3)(x^3-8x^2+16x)[/tex]Factor out x
[tex]\begin{gathered} f(x)=(x-3)(x^3-8x^2+16x) \\ f(x)=x(x-3)(x^2-8x+16) \end{gathered}[/tex]Factorize the remaining equation
[tex]\begin{gathered} f(x)=x(x-3)(x^2-8x+16) \\ f(x)=x(x-3)(x^2-4x-4x+16) \\ f(x)=x(x-3)\mleft\lbrace x(x-4\mright)-4(x-4)\} \\ f(x)=x(x-3)\mleft\lbrace(x-4\mright)(x-4)\} \\ f(x)=x(x-3)(x-4)^2 \end{gathered}[/tex]To find the zeros of the above factored function, using the zero factor principle
[tex]\begin{gathered} xy=0 \\ x=0\text{ and y}=0 \end{gathered}[/tex][tex]\begin{gathered} x(x-3)(x-4)^2=0 \\ x=0 \\ x-3=0 \\ x=3 \\ x-4=0 \\ x-4=0 \\ x=4 \\ x=0,3,4(\text{twice)} \end{gathered}[/tex]Hence, the othe two zeros of the function f(x) are
[tex]x=0,x=4[/tex]Simplify (-64)3/2 ? Hint: Not a real number.
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We want to simplify
[tex](-64)^{\frac{3}{2}}[/tex]When we exponentiate a number by a fraction, we exponentiate the number by the numerator, and the denominator is the radical of the root. Since our denominator is 2, we have a square root.
[tex](-64)^{\frac{3}{2}}=\sqrt[]{(-64)^3}[/tex]Expanding this expression, we have
[tex]\begin{gathered} \sqrt[]{(-64)^3}=\sqrt[]{(-1)^3(64)^3} \\ =\sqrt[]{(-1)^{}(64)^2(64)} \\ =64\sqrt[]{(-1)(64)} \\ =64\sqrt[]{(-1)(8)^2} \\ =64\cdot8\sqrt[]{(-1)^{}} \\ =512\sqrt[]{-1^{}} \end{gathered}[/tex]The square root of minus one is also know as the imaginary number.
[tex]512\sqrt[]{-1^{}}=512i[/tex]"When finding all the unknown values in similar right triangles you have choices: you can useproportional relationships or the Pythagorean Theorem. Which would you use for each of theseexamples, and why?"
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We know that triangles ABC and DEF are similar. So, in order to find all the unknown values we can use proportional relationships because we have all values of the small triangle and at least, one value of the big triangle.
For instance, if we want to know the lenght of segment FD, the following ratio must be preserved:
[tex]\frac{BC}{AC}=\frac{FE}{FD}[/tex]since BC=5 , AC=4 and EF=10, we have
[tex]\frac{5}{4}=\frac{10}{FD}[/tex]so ED is equal to
[tex]\begin{gathered} FD=\frac{4\cdot10}{5} \\ FD=\frac{40}{5} \\ FD=8 \end{gathered}[/tex]Similarly, we can obtain ED as
[tex]\frac{ED}{10}=\frac{3}{5}[/tex]so, ED is
[tex]\begin{gathered} ED=\frac{10\cdot3}{5} \\ ED=\frac{30}{5} \\ ED=6 \end{gathered}[/tex]A movie club surveyed 250 high school students. The students were asked how often they go to the movies and whether they prefer action movies or dramas. their responses are summarized in the following table.
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a) From the given table, there are 83+17 = 100 students who prefer action movies. Since the total of people surveyed is 250, the percentage is given by
[tex]\frac{100}{205}\times100\text{ \% = 40 \%}[/tex]b) On the other hande, there are 17+48 = 65 students who go to the movies three times a month or more, then the percentage is given as
[tex]\frac{65}{250}\times100\text{ \%=26 \%}[/tex]Therefore, the answers are:
[tex]\begin{gathered} a)\text{ 40 \%} \\ b)\text{ 26 \%} \end{gathered}[/tex]Can we conclude that x - 5 is a factor of the polynomialHow do you know?
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Answer:
Recall that:
x-a is a factor of a polynomial p(x) if and only if p(a)=0.
Evaluating the given polynomial at x=5 we get:
[tex]5^3-5^2-17\cdot5-15=125-25-85-15=0.[/tex]Therefore x-5 is a factor of the polynomial x³-x²-17x-15.
The perimeter of a semicircle is 24.672 inches. What is the semicircle's diameter? Use 3.14 for n.
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Given:
The perimeter of a semicircle is 24.672 inches.
Explanation:
To find the semicircle's diameter:
Using the formula of the perimeter of a semicircle,
[tex]\begin{gathered} P=(\pi+2)r \\ 24.672=(3.14+2)r \\ 24.672=(5.14)r \\ r=\frac{24.672}{5.14} \\ r=4.8\text{ inches} \end{gathered}[/tex]Then, the diameter is,
[tex]\begin{gathered} d=2r \\ d=2(4.8) \\ d=9.6\text{ inches} \end{gathered}[/tex]Thus, the diameter of the semicircle is d = 9.6 inches.
Evaluate [(12 - 5) - 12) = 6 Enter your answer in the box
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For this problem we have the following expression given:
[tex]\left\lbrack (12-5)-12\right\rbrack =6[/tex]We assume that the question is verify if the equation is correct so first we solve the numbers in the parenthesis:
[tex]\left\lbrack 7-12\rbrack=-5\right?[/tex]And then the final answer for this case would be -5 and not 6 so then the statement for this case is False.
What is the factor for the medicine remaining in a person with each passing hour?How much medicine will remain in a person after 4 hour?
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Assuming Medicine remaining (in miligrams) in a person is representd by r and time is represented by t, the relationship between r and t can be determined by using two point form as,
[tex]\begin{gathered} \frac{r-50}{t-0}=\frac{50-40}{0-1} \\ r-50=t(-10) \\ r=-10t+50 \end{gathered}[/tex]Find the dimension of the matrix. Determine if it's a square, column, or row matrix. (can be more than one type of matrix).
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The size of a matrix is equal to a number of rows multiplicated by a number of columns:
[tex]\begin{gathered} \text{Size}=\text{rows}\cdot\text{columns} \\ \text{Size}=4\cdot4 \end{gathered}[/tex]If the matrix has the same number of rows and columns, is a square matrix.
Given the parametric equations x = t 2 + 2 and y = t 3 − 4t, where −3 ≤ t ≤ 3, which of the following graphs represents the curve and its orientation?
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Hello there. To solve this question, we'll have to remember some properties about orientation of parametric curves and how to determine their graphs.
First, given the parametric equations:
[tex]\begin{gathered} x=t^2+2 \\ y=t^3-4t \end{gathered}[/tex]We can solve the first equation for t, such that:
[tex]\begin{gathered} t^2+2=x \\ t^2=x-2 \\ t=\pm\sqrt[]{x-2} \end{gathered}[/tex]Since t is between - 3 and 3, we have to analyze which values of x are possible using the end points:
(-3)² + 2 = 3² + 2 = 9 + 2 = 11
So as you can see, the values of x are
[tex]2\le x\le11[/tex]Plugging the first solution into the equation for y, we have
[tex]\begin{gathered} _{}y=(\sqrt[]{x-2})^3-4\sqrt[]{x-2}_{} \\ y=(x-6)\sqrt[]{x-2} \end{gathered}[/tex]And as x is between 2 and 11, we get that y is between
[tex]-15\le y\le15[/tex]Sketching this curve, we have
With the other solution, we get
[tex]\begin{gathered} _{}y=(-\sqrt[]{x-2})^3-4\cdot(-\sqrt[]{x-2}) \\ y=-(x-2)\sqrt[]{x-2}+4\sqrt[]{x-2} \\ y=(6-x)\sqrt[]{x-2} \end{gathered}[/tex]The two curves together looks like
Finally, we have to determine the orientation
For this, let's take a point in the first solution, say we take t = 1 then t = 2
Plugging it into the equations, we get
[tex]\begin{gathered} x=1^2+2=1+2=3 \\ y=1^3-4\cdot1=-3 \end{gathered}[/tex]Now with t = 2
[tex]\begin{gathered} x=2^2+2=4+2=6 \\ y=2^3-4\cdot2=0 \end{gathered}[/tex]So as t increses, we go from:
So this is the orientation of the curve and it is the answer contained in the fourth option.
please help me solve.I have na for blank 1 and 4/3 for blank 2. but it's incorrect
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Blank 1 is
[tex]\frac{4}{3}[/tex]Blank 2 is
3
How to Divide 96 by 0.032