Answers
Answer:
Explanation:
In problem 5, we can see that there is a right triangle with legs x and 16 and a hypotenuse equal to (x + 8).
So, by Pythagorean theorem, we can write the following equation
[tex](x+8)^2=x^2+16^2[/tex]Now, we can expand the left side
[tex]\begin{gathered} x^2+2(8)(x)+8^2=x^2+16^2 \\ x^2+16x+64=x^2+256 \end{gathered}[/tex]Then, subtract x² from both sides
[tex]\begin{gathered} x^2+16x+64-x^2=x^2+256-x^2 \\ 16x+64=256 \end{gathered}[/tex]Subtract 64 from both sides
[tex]\begin{gathered} 16x+64-64=256-64 \\ 16x=192 \end{gathered}[/tex]Finally, divide by 16
[tex]\begin{gathered} \frac{16x}{16}=\frac{192}{16} \\ \\ x=12 \end{gathered}[/tex]Therefore, the value of x is 12
Related Questions
Given A = {(1, 3X-1, 5}(6, 4)), B = {(2, 0X4, EX-4, 5x0, 0)) and C = {(1, 1x0, 2x0, 3)(0, 4X-3, 5)), answer the following multiple
choice question:
From the list of sets A, B, and C above, choose the set of relations that correctly represents a function.
O Set A only
O Sets A and C only
O Sets A and B only
Answers
The functions is Set A and Set B.
What is meant by function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A relation in a set is said to be a function, if every first element of an ordered pair in a set is related with a unique element of a second element.
No, two distinct second elements of an ordered pair, has the same first element.
For, example, {(1,2), (1,3), (4,5)}, is not a function, but it is a relation.
In Ordered pair, (x, y)
x=First Element
y= Second Element
→In Set A
First Element Second Element
1 3
-1 5
6 4
Every First element of set A has a unique second element. So, it is a function.
→In Set B
First Element Second Element
2 0
4 6
-4 5
0 0
Every First element of set B has unique second element and no two distinct Second element of set B, has same first element. So, it is a function.
→In Set C
First Element Second Element
1 1
0 2
0 3
-3 5
As, two same first elements of set C has distinct second element. So, it is not a function.
Therefore, Set A and Set B, are functions .
To learn more about function refer to:
https://brainly.com/question/25638609
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find the volume round to the nearest tenth use 3.14 for pi 5km
Answers
Step 1
List all parameters
[tex]\begin{gathered} \pi\text{ = 3.14} \\ r\text{ = 5km} \\ \end{gathered}[/tex]Step 2
Write the volume of a sphere
[tex]undefined[/tex]A 51-inch TV suggests that the main diagonal of the TV is 51 inches. Determine the dimensions of the screen of a 51 -inch TV with a 16:9 aspect ratio.Please see attached photo
Answers
The aspect ratio 16:9 indicates the next relation between x and y:
[tex]\frac{y}{x}=\frac{16}{9}[/tex]Applying the Pythagorean theorem to the right triangle formed:
[tex]51^2=x^2+y^2[/tex]Isolating y from the first equation:
[tex]y=\frac{16}{9}x[/tex]Substituting in the second equation:
[tex]\begin{gathered} 51^2=x^2+(\frac{16}{9}x)^2 \\ 2601=x^2+(\frac{16}{9})^2x^2 \\ 2601=x^2+\frac{16^2}{9^2}^{}x^2 \\ 2601=x^2+\frac{256}{81}^{}x^2 \\ 2601=\frac{337}{81}^{}x^2 \\ 2601\cdot\frac{81}{337}=x^2 \\ 625.166172=x^2 \\ \sqrt[]{625.17}\approx x \\ 25\approx x \end{gathered}[/tex]Replacing in the equation of y:
[tex]\begin{gathered} y=\frac{16}{9}\cdot25 \\ y\approx44.44 \end{gathered}[/tex]The approximate dimensions are:
length = 25 in
height = 44.44 in
A rectangular prism is shown below.A formula for the volume of a rectangular prism V = Bh. The volume, V, of this prism is 600 cm³. Which expression can be used to find x, the width of the prism in centimeters? A: 600/15B: 600/8C: 600/(8)(15)D: (8)(8)(15)(15)/600
Answers
Volume of a rectangular prism = base length x width x heigth
Where;
Volume = 600 cm3
base length = 15
width = x
height = 8
Replacing:
600 = (15) (x) (8)
Isolate x
600/ (15)(8) = x
x = 600/ (8)(15)
option C
Annie's backyard deck cost $61.75 per square meter to build. The deck is 7 meters wide and14 meters long. How much did it cost to build the deck?
Answers
ANSWER
the cost to build the deck is $6051.5
EXPLANATION
Given that;
The length of the deck is 14 m
The width of the deck is 7m
1 m^2 is equivalent to $61.75
Follow the steps below to find the cost to build the deck
Step 1; Find the area of the deck
[tex]\begin{gathered} \text{ Recall, that the deck is a rectangular shape} \\ \text{ Area of a rectangle = length }\times\text{ width} \\ \text{ Area of a reactangle = 14 }\times\text{ 7} \\ \text{ Area of a rectangle = 98m}^2 \end{gathered}[/tex]Step 2; Find the total cost of the deck
Let x represents the total cost to build the deck
[tex]\begin{gathered} \text{ 1m}^2\text{ }\rightarrow\text{ \$61.75} \\ \text{ 98m}^2\text{ }\rightarrow\text{ \$x} \\ \text{ cross multiply} \\ \text{ 1m}^2\text{ }\times\text{ \$x = \$61.75 }\times\text{ 98m}^2 \\ \text{ Isolate \$x }\frac{}{} \\ \text{ \$x = }\frac{\text{ \$61.75}\times98\cancel{m^2}}{1\cancel{m^2}} \\ \text{ \$x = \$61.75 }\times\text{ 98} \\ \text{ \$x = \$6051.5} \end{gathered}[/tex]Therefore, the cost to build the deck is $6051.5
what is 12/8 × 18/16
Answers
First of all, simplify the given fractions
on a map, the scale is 5 cm = 2km what is the missing distance?town A distance to 5.6km is the actual distance
Answers
The distance on the map is 14 cm
Explanation:Parameters:
Map scale: 5 cm = 2 km
Given actual distance = 5.6km
Let x be the distance on map, then
x = 5.6 km
2x = 5 * 5.6
2x = 28
x = 28/2
= 14 cm
Given the vectors u =-7j and w=-9i+4j, find 8u and u+w.Write your answers in the form ai+bj.
Answers
Recall that:
[tex]\begin{gathered} \text{For all a, b, c, d, e real numbers:} \\ (ai+bj)+(ci+dj)=(a+c)i+(b+d)j, \\ e(ai+bj)=(ea)i+(eb)j\text{.} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 8u=8(-7j)=8(0i-7j)=(8\cdot0)i+(8\cdot(-7))j=0i-56j=-56j\text{.} \\ u+w=(-7j)+(-9i+4j)=(0i-7j)+(-9i+4j)=(0-9)i+(-7+4)j \\ =-9i-3j\text{.} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} 8u=-56j\text{.} \\ u+w=-9i-3j\text{.} \end{gathered}[/tex]Find the cardinal number of the setWhere N denotes the set of all natural numbers
Answers
And x is divisible by 6 . The natural number of x will be
[tex]x=\mleft\lbrace36,42,48,54\mright\rbrace[/tex]The 7th grade took a field trip to the zoo. 50 students rode in cars and the rest of the students were split equally onto 4 buses. There are 142 total 7th graders. How many students were on each bus?
Answers
traveledGiven:
The total number of students is N = 142.
The number of students riding in a car is n(C) = 50.
The total number of buses is b = 4.
The objective is to find the number of students traveling on each bus.
Explanation:
Consider the number of students travelled in each bus as s.
Then, the total number of students traveling in 4 buses will be 4s.
The algebraic expression for the total number of students N can be represented as,
[tex]N=n(C)+b(s)\text{ . . . . .(1)}[/tex]On plugging the given values in equation (1),
[tex]142=50+4s[/tex]On further solving the above equation,
[tex]\begin{gathered} 142-50=4s \\ 4s=92 \\ s=\frac{92}{4} \\ s=23 \end{gathered}[/tex]Hence, the number of students traveling on each bus is 23.
Which is the graph of the solution set of -2x + 5y > 15?10 1310 138896421OT810x2468 10622-4Ox681010 138642X246810
Answers
To graph the solution set, first, we know that the border of the shaded area will be delimited by the dashed line:
[tex]-2x+5y=15.[/tex]Now, to know if the shaded area will be on top or below the line, we evaluate the point (0,0):
[tex]-2(0)+5(0)=0<15,[/tex]therefore, the origin is not a point of the solution set.
Answer:The table shows the weights of bananas at a grocery store. Complete the table so that there is a proportional relationship between the number of bananas and their weight.Number Of Bananas. Weight In Kilograms. 2 ? 0.72 15 ?
Answers
Let u make the first box x and the second box y.
If there is a proportional relationship between the number of bananas and their weights, it means that:
[tex]\frac{2}{x}=\frac{6}{0.72}=\frac{15}{y}[/tex]We can take the first pair and solve for x as follows:
[tex]\begin{gathered} \frac{2}{x}=\frac{6}{0.72} \\ 6x=2\times0.72=1.44 \\ x=\frac{1.44}{6} \\ x=0.24 \end{gathered}[/tex]We can solve for y in the same manner:
[tex]\begin{gathered} \frac{6}{0.72}=\frac{15}{y} \\ 6y=15\times0.72=10.8 \\ y=\frac{10.8}{6} \\ y=1.8 \end{gathered}[/tex]Therefore, the boxes are filled as shown below:
3. By elimination 2x - 3y =- 55x + 2y =16
Answers
By elimination, it means that we should apply algebraic operations so we find the value of one variable. So first, lets multiply the first equation by 5. We get
[tex]5\cdot(2x-3y)=5\cdot-5\text{ = 10x-15y = -25}[/tex]Now, lets multiply by 2 the second equation
[tex]2\cdot(5x+2y)\text{ = 16}\cdot2\text{ = 10x+4y=32}[/tex]With this two equations, lets subtract the second equation from the first equation
[tex]10x+4y-(10x-15y)\text{ = 32-(-25)}[/tex]We get
[tex]19y\text{ = 57}[/tex]If we divide y by 19 we get
[tex]y=\frac{57}{19}=3[/tex]Now, using this value in the second equation we get
[tex]5x+2\cdot3\text{ = 16 }=5x+6[/tex]If we subtract 6 on both sides, we get
[tex]16-6\text{ = 5x = 10}[/tex]Finally, we divide by 5 on both sides and we get
[tex]x=\frac{10}{5}=2[/tex]Question 1 of 14, Step 1 of 10/19CorrectDetermine if the following expression is a polynomial.4 – 8x + x²AnswerKeyboaO Yes O No
Answers
Solution
Given
[tex]4-8x+x^2[/tex]We want to determine if it's a Polynomial
A polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Hence 4 - 8x + x^2 is a Polynomial
the relationship between the minutes a candle is burned and the size of the candle in millimeters is shown on the graph.
Answers
The function is a decreasin line so the more time goes the side will decrease so the correct answer is:
The candle started at 9mm and shrinks 5mm every 4 minutes
Answer this question
Answers
Okay, in this case the statement talks about the sum, according with this we need to find the sum of the number blue bikes (b) and 9 red bikes.
So, in this case the correct option is A. b+9 because it says sum
Simplify.4n + 12 + 7n4 n + 1923 n16 n +711 n+ 12
Answers
11 n+ 12
In this expression, to simplify means to reduce it to the simpler expression. Hence:
1) Grouping similar terms
4n + 12 + 7n =
2) Adding them up:
4n+7n+12=
11n +12
What is the solution to the equation below? Round your answer to two decimal places.ln x = 0.2A.x = 1.58B.x = -0.70C.x = -1.61D.x = 1.22
Answers
Given the equation:
[tex]\ln \left(x\right)=0.2[/tex]Apply the properties of logarithms:
[tex]e^{ln(x)}=e^{0.2}[/tex]Simplify:
[tex]x=e^{0.2}=1.22[/tex]Answer: D. x = 1.22
prove that 1+3+5+......2n-1=n²
Answers
As given by the question
There are given that the series
[tex]1+3+5+\cdots+(2n-1)=n^2[/tex]Now,
For step 1:
Put n=1
Then LHS =1
And
[tex]\begin{gathered} R\mathrm{}H\mathrm{}S=(n)^2 \\ =(1)^2 \\ =1 \end{gathered}[/tex]So,
[tex]\therefore L.H.S=R.H.S[/tex]P(n) is true for n=1.
Now,
Step 2:
Assume that P(n) istrue for n=k
Then,
[tex]1+3+5+\cdots+(2n-1)=k^2[/tex]Adding 2k+1 on both sides
So, we get:
[tex]1+3+5\ldots+(2k-1)+(2k+1)=k^2+(2k+1)=(k+1)^2[/tex]P(n) is true for n=k+1
By the principle of mathematical induction P(n) is true for all natural numbers n.
Hence,
[tex]1+3+5+\cdots+(2n-1)=n^2[/tex]For all n.
Hence proved.
Given quadrilateral MNPQ which of the following set of conditons would not be enough to know that MNPQ is a parrelogram?
Answers
For a shape to be considered a parallelogram it has to meet the following conditions:
0. The opposite sides must be equal
,1. The opposite sides are equal
,2. Adjacent sides are supplementary
,3. The diagonals bisect each other
,4. The opposite sides are parallel
For the quadrilateral to be considered a parallelogram then, the conditions that should be met are:
MN=QP and MQ=NP
MN || QP and MQ || NP
The diagonals MP and NQ bisect each other.
∠M=∠P and ∠N=∠Q
From the given options, the second one and the third one are not enough to determine MNPQ as a parallelogram
slove equations with variables on both sides-4k - 10 = -5k
Answers
We will investigate how to solve an equation consisting of one variable
We have the following equation at hand:
[tex]-4k\text{ -10 = -5k}[/tex]The basic rule applied in solving equation like above is mathematical operations. We apply basic operations like:
[tex]\text{adding, subtracting, multiplying, division}[/tex]on both sides of the equation accompained by a variable or a number in an attempt to isolate the variable ( k ).
To isolate the variable ( k ) we need all the terms involving the variable ( k ) on one side of the equation.
We will add ( 4k ) on both sides of the equation as follows:
[tex]\begin{gathered} -4k\text{ -10 + 4k= -5k + 4k} \\ (\text{ 4k - 4k ) - 10 = -k} \\ -10\text{ = -k} \end{gathered}[/tex]Now to remove the negative sign accompained by ( k ) on the right hand side of the equation. We wil multiply both sides with ( -1 ) as follows:
[tex]\begin{gathered} -1\cdot(-10)\text{ = -1}\cdot(-k) \\ 10\text{ = k} \end{gathered}[/tex]Hence, the value of ( k ) is:
[tex]10[/tex]
Using the hottest and coolest months data, find the equation for line of best fit for this data showing all steps by hand.
Answers
Let
x -----> average temperature
y ----> Electricity Bill
we take the points
(99,150) and (69,80)
step 1
Find out the slope
m=(80-150)/(69-99)
m=-70/-30
m=7/3
step 2
Find out the equation of the line in slope-intercept form
y=mx+b
we have
m=7/3
point (69,80)
substitute and solve for b
80=(7/3)(69)+b
b=80-161
b=-81
the equation is
y=(7/3)x-81
using a graphing tool
Remember that the value of y cannot be a negative number
The current student population of Kansas City is 2700. If the population increases at a rate of 5.2% each year. What will the student population be in 4 years?Write an exponential growth model for the future population P(x) where x is in years:p(x)=What will the population be in 4 years? (Round to nearest student)
Answers
ANSWER
P(x) = 2700(1.052)^t
P(4) = 3307. (Rounded to nearest student)
EXPLANATION
Given:
1. The current student population to be 2700
2. The growth rate = 5.2% = 0.052
Desired Outcome
1. The exponential growth model
2. Population of the students in 4 years
The Exponential Growth Model
[tex]\begin{gathered} P(x)\text{ = 2700\lparen1 + 0.052\rparen}^t \\ P(x)\text{ = 2700\lparen1.052\rparen}^t \end{gathered}[/tex]Population in 4 years
[tex]\begin{gathered} P(4)\text{ = 2700\lparen1.052\rparen}^4 \\ P(4)\text{ = 2700}\times1.2248 \\ P(4)\text{ = 3306.96} \end{gathered}[/tex]Hence, the Exponential Growth Model P(x) = 2700(1.052)^t and the Population of the students in 4 years P(4) = 3307. (Rounded to nearest student)
The entire graph of the function h is shown in the figure below.Write the domain and range of h using interval notion.(a) domain=(b) range=
Answers
The graph of the function is defined for x greater than or equal to -2 and less than 3. So domain of the function is,
[tex]\lbrack-2,3)[/tex]The value of the function lies between -2 and 3. The function value is greater than or equal to -2 and less than 3. So range of function is,
[tex](-2,3\rbrack[/tex]Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 2 ≤ x ≤ 6.
Answers
To find the average rate of change over an interval we need to calculate how much the function has changed over that interval by subtracting the final value by the initial one and dividing by the lenght of the interval. With this in mind we have:
[tex]\begin{gathered} \text{rate}=\frac{19-13}{6-2} \\ \text{rate}=\frac{6}{4} \\ \text{rate}=1.5 \end{gathered}[/tex]The average rate of change for this interval is 1.5
the line contains the point (-3,5) and is perpendicular to the line y=3x-4
Answers
two lines are perpendicular when the multiplication of their slopes is equal to -1. The slope of y = 3x - 4 is 3. Then the slope of a perpendicular line is:
[tex]\begin{gathered} m\cdot3=-1 \\ m=-\frac{1}{3} \end{gathered}[/tex]Slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. Replacing with point (-3, 5) and m = -1/3, we get:
5 = -1/3(-3) + b
5 = 1+ b
5 - 1 = b
4 = b
Then, the equation is:
y = -1/3x + 4
find the value of f (4)
Answers
we know that
f(4) is the value of the function f(x) when the value of x is equal to 4
so
For x=4
Look at the graph
The value of the function f(x) is equal to 3
therefore
f(4)=3(4.7 x 10-3) x 351Simplify the expressionusing scientific notation and express your answer(2.5 x 10') < (3.3 X 100)in scientific notation. Round your answer to the nearest thousandth.AnswerKeypadKeyboard Shortcutsx10
Answers
Given:
[tex]\frac{(4.7\times10^{-3})\times351}{(2.5\times10^5)\times(3.3\times10^6)}[/tex]Remove the brackets and multiply common terms
[tex]\begin{gathered} \frac{(4.7\times10^{-3})\times351}{(2.5\times10^5)\times(3.3\times10^6)} \\ =\frac{4.7\times10^{-3}\times351}{2.5\times10^5\times3.3\times10^6} \\ =\frac{4.7\times351\times10^{-3}}{2.5\times3.3\times10^5\times10^6} \\ =\frac{1649.7\times10^{-3}}{8.25\times10^{11}} \end{gathered}[/tex]Simplify further to get
[tex]\begin{gathered} \frac{1649.7\times10^{-3}}{8.25\times10^{11}} \\ =\frac{16497\times10^{-1}_{}\times10^{-3}}{825\times10^{-2}\times10^{11}} \\ =\frac{16497\times10^{-4}}{825\times10^9} \end{gathered}[/tex]This further gives
[tex]\begin{gathered} \frac{16497\times10^{-4}}{825\times10^9} \\ =\frac{16497}{825}\times\frac{10^{-4}}{10^9} \\ =19.996\times10^{-4-9} \\ =19.996\times10^{-14} \end{gathered}[/tex]Therefore, the answer is
[tex]19.996\times10^{-14}[/tex]Please help me!A bag holds 5 pounds of pet food. If Paul uses the 5 pounds of food to fill 6 plastic containers equally, how much pet food will each container hold?0.830.80.8030.83
Answers
We must divide the 5 pound bag in 6 different containers, therefore:
[tex]\frac{5}{6}=0.83[/tex]Each container will hold 0.83 pet food
Write each fraction in terms of the LCD.x2x + 12x - 1x + 13x22x – 111X + 1X + 13Need Help?Watch ItAdditional Materials
Answers
The given fractions are,
[tex]\frac{x^2}{2x-1},\text{ }\frac{x+1}{x+13}[/tex]The LCD of fractions is the least common multiple of the denominators.
So, the LCD of the above fractions is,
[tex](2x-1)(x+13)[/tex]Multiplying the numerator and the denominator of the fraction by a common term does not change the fraction.
So, the first fraction can be expressed in terms of the LCD as,
[tex]\frac{x^2}{2x-1}=\frac{x^2(x+13)}{(2x-1)(x+13)}[/tex]The second fraction can be expressed in terms of the LCD as,
[tex]\frac{x+1_{}^{}}{x+13}=\frac{(x+1)(2x-1)}{(2x-1)(x+13)}[/tex]