72 ergs
Explanation
Step 1
Kinetic energy varies jointly as the mass and the square of the velocity,then
[tex]E_k=\lambda\cdot m\cdot v^2[/tex]where
m is the mass, v is the velocity and
[tex]\lambda\text{ is a constant}[/tex]A mass of 8 grams and velocity of 3 centimeters per second has a kinetic energy of 36 ergs
[tex]\begin{gathered} E_k=\lambda m\cdot v^2 \\ 36\text{ erg=}\lambda\cdot8\cdot3^2 \\ 36=\lambda\cdot8\cdot9 \\ 36=\lambda\cdot72 \\ \text{divide both sides by 72} \\ \frac{36}{72}=\lambda \\ \lambda=\frac{1}{2} \end{gathered}[/tex]so, the equation is
[tex]\begin{gathered} E_k=\lambda\cdot m\cdot v^2 \\ E_k=\frac{1}{2}\cdot m\cdot v^2 \end{gathered}[/tex]Step 2
now , we know the equation to find the kinetic energy of a object if we know its mass and its velocity
Let
mass= 4 grams
velocity = 6 cms per sec
then
[tex]\begin{gathered} E_k=\frac{1}{2}\cdot m\cdot v^2 \\ E_k=\frac{1}{2}\cdot4gr\cdot(6\frac{\operatorname{cm}}{\sec})^2 \\ E_k=\frac{1}{2}\cdot4gr\cdot36\frac{\operatorname{cm}}{\sec ^2} \\ E_k=72\text{ erg} \end{gathered}[/tex]I hope this helps you
I have a practice problem that I need explained an answered, thank you
From the question, we are given the matrices
We are to find which operation is defined and whic one is not
For the operation
[tex]M-N[/tex]For subtraction operation to be definded
The order of the matrices must be the same
Since the order of M is 4 x 2
And the order of N is 4 x 2
Therefore, the operation M - N is defined
For the operation
[tex]L-N[/tex]Similarly, for the operation to be definded
The order of the matrices must be the same
The oder of matrix L is 2 x 2 while the order of matrix N is 4 x 2
Since the oder of the matrices are not the same then
The operation L - N is not defined
For the operation
[tex]M+P[/tex]For addition operation to be defined, the Order of the matrices must be the same
The order of matrix M is 4 x 2 while the order of matrix P is 2 x 2
Since the order of the matrices are not the same then the operation is not defined
For the operation
[tex]Q+P[/tex]For addition operation to be defined, the Order of the matrices must be the same
The order of matrix Q is 2 x 1 while the order of matrix P is 2 x 2
Since the order of the matrices are not the same then the operation is not defined
The sum of two numbers is 60. The greater number is 6 more than the smaller number which equation can be used to solve for the smaller number
x ----> is the smaller number
x+6 ----> is the greater number
the equation is
[tex]x+(x+6)=60[/tex]Write an equation for the line parallel to the given line that contains B. B(3, 8) ; y = - 4x + 7
You have to write an equation parallel to the line: y=-4x+7 that crosses the point (3,8)
One characteristic that two parallel lines share is that they have the same slope.
The slope for the known line corresponds to the coefficient multiplying the x-term and is m=-4
The line you have to find must have the same slope.
Using the point-slope form you can determine said line. The general structure is:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope
x₁, y₁ are the coordinates of a point crossed by the line.
Using (3, 8) and m=-4
[tex]y-8=-4(x-3)[/tex]Now you have to solve it and write it in slope-intercept form. First step is to solve the term in parentheses by applying the distributive propperties of multiplication:
[tex]\begin{gathered} y-8=-4x-3\cdot(-4) \\ y-8=-4x+12 \end{gathered}[/tex]Next pass "-8" to the other side of the equal sign:
[tex]\begin{gathered} y-8+8=-4x+12+8 \\ y=-4x+20 \end{gathered}[/tex]The equation for the line parallel to y=-4+7 is y=-4x+20
Connie is studying two number patterns. Pattern 1 starts at 0 and has the rule "add 4.Pattern 2 starts at 0 and has the rule "add 2."Drag a number into each box to complete Connie's patternsDrag a phrase into the last box to complete the comparison of the corresponding terms in each pattinPattern 1:0,
Let's start with Pattern 1.
SInce the rule is to add 4, we shall add 4 on the first number that is zero.
The pattern 1 shall be:
[tex]0,4,8,12[/tex]On the other hand, for Pattern 2, the rule is to add 2. So, let's add 2 on the first number that is 0. Pattern 2 shall be:
[tex]0,2,4,6[/tex]Based on these two patterns, we can see that the terms in Pattern 1 are two times the corresponding terms in Pattern 2.
Felipe is a software salesman. His base salary is $2100, and he makes an additional $70 for every copy of math is fun he sells. Let P represent his total pay in dollars, and let N represent the number of copies of math is fun he sells. Write an equation relating P to N then use this equation to find his total pay if he sells 27 copies of math is fun.
Based on the given information, we can determine the constant and the variable payment.
• He gets $2100 as based salary (never changes, constant).
,• The additional $70 depends on ,N ,(variable).
This information can help us build the equation:
[tex]P=70N+2100[/tex]Therefore, if he sells 27 copies, then the total payment is:
[tex]P=70\cdot27+2100[/tex][tex]P=1890+2100[/tex][tex]P=3990[/tex]Answer:
[tex]P=70N+2100[/tex]P( 27 ) = $3990
Which is the measure of an interior angle of a regular decagon?30°36°144°150°
SOLUTION:
We are to find the measure of an interior angle of a regular decagon.
A decagon is a plane figure with ten straight sides and angles.
To find the sum of interior angles in a decagon;
(n - 2) x 180 (where n = 10)
(10 - 2) x 180
= 8 x 180
= 1440 degrees
The measure of an interior angle of a regular decagon is;
1440 / 10
144 degrees
find the measures of the angles labeled in the figure below. measure of angle EFD=measure of angle EHF=measure of angle HFG=measure of angle G=
EXPLANATION:
We must bear in mind that the internal angles of a triangle must add up to 180 degrees.
We will first find values of unknown angles and finally add to find the corresponding measures.
[tex]\begin{gathered} To\text{ find F:} \\ corresponds\text{ }to\text{ the same angle }measure\text{ }54(F) \\ To\text{ find G:} \\ We\text{ add }the\text{ two internal }angles\text{ 54 }and\text{ s}ubtract\text{ }180\colon \\ 54+54=180 \\ 180-54-54 \\ 180-108 \\ 72\text{ ( }angle\text{ G)} \\ To\text{ find E;} \\ We\text{ must }the\text{ measures }H\text{ and G} \\ H=54\text{ ; G= 72 E=X} \\ 54+72=180 \\ 180-54-72 \\ 54(\text{Angle E)} \\ To\text{ find D} \\ We\text{ must the measures: 33 +54 and }substract\text{ 180} \\ 33+54=180 \\ 180-33-54 \\ 93\text{ (angle D)} \end{gathered}[/tex]Now to find the measurements given in the exercise; We must take the values found according to what each exercise asks for and add them.
[tex]\begin{gathered} \text{Measure of angle EFD:} \\ E(54)+\text{ F(54})+D(93)=201 \\ \text{Measure of angle EHF:} \\ E(54)+H(54)+F(54)=162 \\ \text{Measure of angle HFG:} \\ H(54)+F(54)+G(72)=180 \\ \text{Measure of angle G:} \\ G=\text{ 72 degr}ees \end{gathered}[/tex]the table shows the probability distrubution of a random variable Z.Z- -17, -16,-15,-14,-13 P(Z)- 0.02 , 0.73, 0.02, 0.08, 0.15what is the mean of the probability distrubution
In order to find the mean, we have to multiply each value with its probability and then add al the results:
Step 1- multiplying each value by its probabilityStep 2 - adding all the resultsNow, we add all the results we found on the previous step:
Mean = -0.34 - 11.68 - 0.30 - 1.12 - 1.95
Mean = -15.39
Answer: mean = -15.39
751 body temperature measurements were taken. The sample data resulted in a sample mean of 98.1 F and a sample standard deviation of 0.7 F. Use the traditional method and a 0.05 significance level to test the claim that the mean body temperature is less than 98.6 F.
The mean value of the sample is 98.1 F and its standard deviation is 0.7 F.
The margin of error of the mean value is given by 0.7/sqrt(751) = 0.7/27.4 = 0.026 (rounded to the nearest thousandth)
Using the Z test, we got: Z = (98.6 - 98.1)/(0.026) = 0.5/0.026 = 196
Therefore, the mean value of the sample is incompatible with 98.6 and we can claim that the mean body temperature is less than it.
12. Write a paragraph proof.Given: AB = CD, BC = DAProve: AABC = ACDA
Answer:
Triangles ABC and CDA share the side AC, therefore they have three congruent sides. Since AB is congruent to CD and BC is congruent to DA then by the SSS criteria we get that triangles ABC and CDA are congruent.
Need help confirming my answer, do I just put x=1 or x=1,-3/2
Applying quadratic formula to the given quadratic equation, we get the solutions as [tex]x=1,-\frac{3}{2}[/tex].
It is given to us that the quadratic equation is -
[tex]-2x^{2} -1x+3=0[/tex] ---- (1)
We have to solve by this by quadratic formula.
From equation (1), we have
[tex]-2x^{2} -1x+3=0\\= > -2x^{2} -x+3=0\\= > -(2x^{2} +x-3)=0\\= > 2x^{2} +x-3=0[/tex]----- (2)
The above equation (2) is in the form of a quadratic equation
[tex]ax^{2} +bx+c=0[/tex]
where, a = 2
b = 1
and, c = -3
Now, using the quadratic formula, we know
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] and, [tex]x=\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]
Substituting the values of a, b, and c in the above formulas to find the value of x, we get
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} and x=\frac{-b-\sqrt{b^{2} -4ac} }{2a}\\= > x=\frac{-1+\sqrt{(-1)^{2} -4*2*(-3)} }{2*2} and x=\frac{-1-\sqrt{(-1)^{2} -4*2*3} }{2*2}\\= > x=\frac{-1+\sqrt{25} }{4} and x=\frac{-1-\sqrt{25} }{4}\\= > x= \frac{-1+5}{4} and x=\frac{-1-5}{4} \\= > x=\frac{4}{4} and x=\frac{-6}{4} \\= > x=1 and x= -\frac{3}{2}[/tex]
Thus, solving the given quadratic equation through quadratic formula, we get the solutions as [tex]x=1,-\frac{3}{2}[/tex].
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How to graph inequalities y + 6 < 10 or 2y - 3 > 9
We need to graph on the number line the solution to the compounded inequality
[tex]\begin{gathered} y+6<10 \\ \text{or } \\ 2y-3>9 \end{gathered}[/tex]In order to do so, let's work with each inequality separately. The final solution will be the union of the two solutions since it can be one "or" the other.
Step 1
Subtract 6 from both sides of the first inequality:
[tex]\begin{gathered} y+6<10 \\ \\ y+6-6<10-6 \\ \\ y<4 \end{gathered}[/tex]So, the solution to the first inequality is all real numbers less than 4 (not included). Therefore, we graph this solution using an empty circle:
Step 2
Add 3 to both sides of the second inequality, and then divide both sides by 2:
[tex]\begin{gathered} 2y-3+3>9+3 \\ \\ 2y>12 \\ \\ \frac{2y}{2}>\frac{12}{2} \\ \\ y>6 \end{gathered}[/tex]Thus, the solution to this inequality is all the real numbers greater than 6 (not included: empty circle):
Answer
Therefore, the solution to the compounded inequalities is the union of both solutions:
The fox population in a certain region has a continuous growth rate of 9 percent per year.
SOLUTION
The function can be derived from the model
[tex]\begin{gathered} P=P_oe^{(\ln r)t^{}} \\ \\ r\text{ here represents 1 + 9 percent growth rate } \end{gathered}[/tex]So the function becomes
[tex]P(t)=2000_{}e^{(\ln 1.09)t}[/tex]So the fox population in 2008
2008 - 2000 = 8
So our t becomes 8
The population becomes
[tex]\begin{gathered} P=2000_{}e^{(\ln 1.09)t} \\ P=2000_{}e^{(\ln 1.09)\times8} \\ P=\text{ }2000_{}e^{0.086177\times8} \\ =2000_{}e^{0.6894} \\ =\text{ 3985.04} \end{gathered}[/tex]So the Population = 3985
A litter of kittens consists of one gray female, two gray males, two black females and one black male. You randomly pick one kitten, what is the probability it is black?
Total number of kittens = 6
Gray kittens= 1 female+2 males = 3
Black kittens= 2 female+ 1 male =3
Probability of picking one black kitten = black kittens/ total kittens = 3/6 =1/2
Question 1-6
Miriam is buying popsicles for her soccer team. She wants to spend the same amount of money at two different businesses. Food Hub sells popsicles for $1.75 each with a delivery fee of
$5.00 and Foodie Eats sells popsicles for $1.80 each with a delivery fee of $4.39. She wrote an equation to determine the number of popsicles, p, she can buy. Her work is shown below.
1.75p+5 = 1.80p + 4.39
-1.75p
-1.75p
5 = 0.05p + 4.39
- 4.39
-4.39
0.61 0.05
0.05 0.05
12.2 = p
Is the solution to this equation viable in this context?
The solution
viable because she
From the given data , the required equation to find the number of popsicles 'p' which Miriam can buy is given by 1.75p +5 = 1.80p + 4.39 is equal to p =12 .
Solution is viable as we can take the nearest round off value to find the number of popsicles.
As given in the question,
Two different companies where Miriam want to spend same amount of her money.
Equation of Food Hub sells is:
1.75p + $5.00
Equation of Foodie eat sells:
1.80p + $4.39
Where p is the number of popsicles
Required relation to get the value of p we have,
1.75p + 5.00 = 1.80p + 4.39
Take like terms on same side we get,
1.80p - 1.75p = 5.00 -4.39
⇒ 0.05p = 0.61
⇒ p = 12.2
⇒ p = 12 (round off number)
Number of popsicles cannot be in decimals.
Solution is viable as we can take the nearest round off value to find the number of popsicles.
Therefore, from the required equation to find the number of popsicles 'p' which Miriam can buy is given by 1.75p +5 = 1.80p + 4.39 is equal to p =12
Solution is viable as we can take the nearest round off value to find the number of popsicles.
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Which equation is correct? (6 points)Group of answer choicessec x° = opposite ÷ adjacentcot x° = opposite ÷ adjacentcosec x° = opposite ÷ adjacentsec x° = hypotenuse ÷ adjacent
Answer:
Concept:
To figure this question out, we will use the trigonometric ratios below
SOH CAH TOA
[tex]\begin{gathered} SOH \\ sin\theta=\frac{opposite}{hypotenus}=S=\frac{O}{H} \\ \cos\theta=\frac{adjacent}{hypotenus}=C=\frac{A}{H} \\ \tan\theta=\frac{opposite}{adjacent}=T=\frac{O}{A} \end{gathered}[/tex]Using the inverse trigonometric identity,
[tex]\begin{gathered} cosecx^0=\frac{1}{sinx^0} \\ secx^0=\frac{1}{cosx^0} \\ cotx^0=\frac{1}{tanx^0} \end{gathered}[/tex]By simplifying further, we will have that
[tex]\begin{gathered} cosecx^0=\frac{1}{s\imaginaryI nx^{0}} \\ cosecx^0=\frac{1}{\frac{opposite}{hypotenu}}=1\times\frac{hypotenus}{opposite} \\ cosecx^0=\frac{hypotenus}{opposite} \end{gathered}[/tex][tex]\begin{gathered} secx^{0}=\frac{1}{cosx^{0}} \\ secx^0=\frac{1}{\frac{adjacent}{hypotenus}}=1\times\frac{hypotenus}{adjacent} \\ secx^0=\frac{hypotenus}{adjacent} \end{gathered}[/tex][tex]\begin{gathered} cotx^{0}=\frac{1}{tanx^{0}} \\ cotx^0=\frac{1}{\frac{opposite}{adjacent}}=1\times\frac{adjacent}{opposite} \\ cotx^0=\frac{adjacent}{oppos\imaginaryI te} \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow secx^0=\frac{hypotenus}{adjacent}[/tex]Using the diagram below, select all angles that are congruent.DLEoThere are three answers.O ZDOCО / ВОСO ZAOCZAOBZDOBEODDEOCO
We don't know the actual measures of the angles in the diagram but three of them have the same mark. This indicates that the angles are equal.
So the angles ∠EOD, ∠BOC and ∠AOB can be considered congruent.
how many weeks does it take to empty the lake?
The rate of emptying the lake is -1/8.
The rate of filling the lake is 1/15
Let t be the time in weeks to empty the lake,
Now, add the given rate to get the total rate of emptying of -1/t.
[tex]\begin{gathered} \frac{-1}{8}+\frac{1}{15}=-\frac{1}{t} \\ \frac{-15+8}{120}=-\frac{1}{t} \\ -7\times t=-120 \\ t=\frac{120}{7} \end{gathered}[/tex]Thus,
[tex]t=17\frac{1}{7}[/tex]Therefore, it will take 17 weeks and 1 day to empty the lake.
Make the following conversion in the metric system by multiplying by the appropriate conversion factor. Write your answer as a whole number or decimal.20 m to millimeters ?mm
Each meter has 100 centimeters, each centimeters has 10 milimeters, so 20 meters has 20.000 milimeters.
Find the length of each side of an equilateral triangle with perimeter 36 inches.Provide your answer below:inches4
1) Given that an equilateral triangle has three congruent sides, so we can tell that each side has the following measurement:
[tex]\begin{gathered} P_{\Delta}=l+l+l\Rightarrow P_{\Delta}=3l \\ 3l=36 \\ \frac{3l}{3}=\frac{36}{3} \\ l=12" \end{gathered}[/tex]Note that since they are congruent then we can tell that.
is 13/4 and 21/4 equivalent an equivalent fraction?
To determine if they are equivalent we equal them and if when simplified they do not show the same values, they are not. That is:
[tex]\frac{13}{4}=\frac{21}{4}\Rightarrow3.25\ne5.25[/tex]From that, we can see that they are not equivalent fractions.
I need help with getting to the answer to number 6
We have the following pair of functions:
[tex]\begin{gathered} f(x)=x^3+6x \\ g(x)=\sqrt{8x} \end{gathered}[/tex]And we need to find (fog)(2). In order to do this we can start by calculating the composite function (fog)(x)=f(g(x)). Its expression is given by taking the equation of f(x) and replacing x with the expression of g(x). Then we get:
[tex]\begin{gathered} (f\circ g)(x)=f(g(x))=g(x)^3+6g(x)=(\sqrt{8x})^3+6\sqrt{8x} \\ (f\circ g)(x)=(\sqrt{8x})^3+6\sqrt{8x} \end{gathered}[/tex]We need to find (fog)(2) so we just need to take x=2 in the equation above:
[tex]\begin{gathered} (f\circ g)(2)=(\sqrt{8\cdot2})^3+6\sqrt{8\cdot2} \\ (f\circ g)(2)=(\sqrt{16})^3+6\cdot\sqrt{16} \\ (f\circ g)(2)=4^3+6\cdot4 \\ (f\circ g)(2)=64+24 \\ (f\circ g)(2)=88 \end{gathered}[/tex]AnswerThen the answer is 88.
Find the measure of each labeled angle as well as the values of x, y, and z.
Notice that the angle labelled as 3y and the angle with a measure of 72° are supplementary angles. Then:
[tex]3y+72=180[/tex]Substract 72 from both sides of the equation:
[tex]\begin{gathered} 3y+72-72=180-72 \\ \Rightarrow3y=108 \end{gathered}[/tex]The angle labelled as x and the angle labelled as 3y are corresponding angles. Then, they have the same measure:
[tex]x=3y[/tex]Since 3y=108, then:
[tex]x=108[/tex]On the equation 3y=108, divide both sides by 3 to find the value of y:
[tex]\begin{gathered} \frac{3y}{3}=\frac{108}{3} \\ \Rightarrow y=36 \end{gathered}[/tex]Finally, notice that the angle labelled as 3z+18 and the angle labelled as x are corresponding angles. Then, they have the same measure:
[tex]3z+18=x[/tex]Substitute x=108 and isolate z to find its value:
[tex]\begin{gathered} \Rightarrow3z+18=108 \\ \Rightarrow3z=108-18 \\ \Rightarrow3z=90 \\ \Rightarrow z=\frac{90}{3} \\ \Rightarrow z=30 \end{gathered}[/tex]Therefore, the measure of the angles labelled as 3z+18, x and 3y is 108°. The values of x, y and z are:
[tex]\begin{gathered} x=108 \\ y=36 \\ z=30 \end{gathered}[/tex]Solve VABC if a = 34 feet, b = 20 feet, and c = 18 feet. .
Cosine theorem:
[tex]\begin{gathered} a^2=b^2+c^2-2bccosA \\ b^2=a^2+c^2-2ac\cos B \\ c^2=a^2+b^2-2ab\cos C \end{gathered}[/tex]a= 34ft
b = 20ft
c = 18ft
[tex]\begin{gathered} a^2-b^2-c^2=-2bc\cos A \\ \frac{a^2-b^2-c^2}{-2bc}=\cos A \\ \\ A=\cos ^{-1}(\frac{a^2-b^2-c^2}{-2bc}) \end{gathered}[/tex][tex]B=\cos ^{-1}(\frac{b^2-a^2-c^2}{-2ac})[/tex][tex]C=\cos ^{-1}(\frac{c^2-a^2-b^2}{-2ab})[/tex][tex]\begin{gathered} A=\cos ^{-1}(\frac{34^2-20^2-18^2}{-2(20)(18)}) \\ \\ A=\cos ^{-1}(\frac{432}{-720})=126.86 \end{gathered}[/tex][tex]\begin{gathered} B=\cos ^{-1}(\frac{20^2-34^2-18^2}{-2(34)(18)}) \\ \\ B=\cos ^{-1}(\frac{-1080}{-1224})=28.07 \end{gathered}[/tex][tex]\begin{gathered} C=\cos ^{-1}(\frac{18^2-34^2-20^2}{-2(34)(20)}) \\ \\ C=\cos ^{-1}(\frac{-1235}{-1360})=24.75 \end{gathered}[/tex]VABC:
A=126.86º
B=27.07º
C=24.75º
a=34ft
b=20ft
c=18ft
Find the mean with and without the outlier: 66, 55, 65, 44, 54, 10
Answer:
To calculate the mean of the set of values with the outlier, we will use the formula below
Concept:
An outlier is an observation that lies an abnormal distance from other values in a random sample of a population.
The mean with the outlier will be
[tex]mean=\frac{total\text{ addition of numbers}}{number\text{ of data}}[/tex]By substituting the value, we will have
[tex]\begin{gathered} mean=\frac{66+55+65+44+54+10}{6} \\ mean=\frac{294}{6} \\ mean=49 \end{gathered}[/tex]Hence,
The mean of the data with the outlier is = 49
Larry Mitchell invested part of his $22,000 advance at 2% annual simple interest and the rest at 6% annual simple interest if his total yearly interest from both accounts was $760 find the amount invested at each rate The amount invested at 2%The amount invested at 6%( please don’t need an detailed explanation just the answer)
Larry Mitchell invested part of his $22,000 advance at 2% annual simple interest and the rest at 6% annual simple interest if his total yearly interest from both accounts was $760 find the amount invested at each rate
The amount invested at 2%
The amount invested at 6%
Let
x -----> amount invested at 2%
(22,000-x) -----> amount invested at 6%
we have that
x(0.02)+(22,000-x)(0.06)=760
solve for x
0.02x+1,320-0.06x=760
0.06x-0.02x=1,320-760
0.04x=560
x=14,000
(22,000-14,000)=8,000
therefore
amount invested at 2% -----> $14,000amount invested at 6% -----> $8,000Is this a function or non-function {(3,4),(4,-6),(5,-7),(3,2),(-2,5)}
Recall that a set of ordered pairs A represents a function if:
[tex](x,y),(x,z)\in A\text{ if and only if y=z.}[/tex]Now, notice that (3,4) and (3,2) are in the given set of ordered pairs, since
[tex]4\ne2[/tex]we get that the given set does not correspond to a function.
Answer: Non-function.
8. Which of the following ordered pairs is a solution to f(x) = 1/2x -8?(4, - 4)(2, - 7)(10, 3)(-6, 11)
ANSWER
(2, -7)
EXPLANATION
We want to find which of the ordered pairs is a solution for:
[tex]f(x)\text{ = }\frac{1}{2}x\text{ - 8}[/tex]Ordered pairs are usually given in the form (x, f(x)). That is the value of x and the value of the function of x.
We have to put each of the first values in the ordered pairs in the given function and see if it results in the second value.
=> (4, -4)
[tex]\begin{gathered} f(4)\text{ = }\frac{1}{2}(4)\text{ - 8} \\ f(4)\text{ = 2 }-8 \\ f(4)\text{ = -}6 \end{gathered}[/tex]Not a solution
=> (2, -7)
[tex]\begin{gathered} f(2)\text{ = }\frac{1}{2}(2)\text{ - 8} \\ f(2)\text{ = }1\text{ - 8} \\ f(2)\text{ = -}7 \end{gathered}[/tex]This is a solution.
=> (10, 3)
[tex]\begin{gathered} f(10)\text{ = }\frac{1}{2}(10)\text{ - 8} \\ f(10)\text{ = }5\text{ - 8} \\ f(10)\text{ = }-3 \end{gathered}[/tex]Not a solution.
=> (-6, 11)
[tex]\begin{gathered} f(-6)\text{ = }\frac{1}{2}(-6)\text{ - 8} \\ f(-6)\text{ = -3 - 8} \\ f(-6)\text{ = -11} \end{gathered}[/tex]Not a solution.
The only solution there is (2, -7)
Albert has 16 oz of cheddar cheese and 8 oz of mozzarella cheese. He used 5 1/2 oz of the cheddar and 3 1/3 oz of the mozzarella cheese in a recipe. What is the total amount of cheese that Albert has left?
PROBLEM
Total
16 cheddar cheese
8 mozzarella cheese
Solution
He uses
[tex]\begin{gathered} 5\frac{1}{2}\text{ of cheddar out of 16} \\ 3\frac{1}{3}\text{ of mozzarella out of 8} \end{gathered}[/tex][tex]\begin{gathered} \\ \text{Cheddar left = 16 - 5}\frac{1}{2}\text{ = 10}\frac{1}{2} \end{gathered}[/tex][tex]\text{Mozzarella left = 8 - 3}\frac{1}{3}\text{ = 4}\frac{2}{3}[/tex][tex]\begin{gathered} \\ \text{Total ch}eese\text{ left } \\ = \end{gathered}[/tex][tex]\begin{gathered} \\ =\text{ 10}\frac{1}{2}\text{ - 4}\frac{2}{3} \end{gathered}[/tex][tex]=\text{ 5}\frac{5}{6}[/tex]NEED HELP DUE BY WEDNESDAY OR TOMMOROW. Solve each of the equations and select the numbers that represent solutions to more than one of the six equations. Select all that apply. 4x-3=17 8(x + 1) = 24 5(x - 2) = 20 34 - 7x = 20 31 - x = 29 3x +6=21. A. x=1. B. x=2. C. x=3. D. x=4.E. x=5. F. X = 6.
Given
The equations,
4x-3=17, 8(x + 1) = 24, 5(x - 2) = 20, 34 - 7x = 20, 31 - x = 29, 3x +6=21.
To find the solution to each equations.
Explanation:
It is given that,
The equations,
4x-3=17, 8(x + 1) = 24, 5(x - 2) = 20, 34 - 7x = 20, 31 - x = 29, 3x +6=21.
That implies,
1)
[tex]\begin{gathered} 4x-3=17 \\ 4x=17+3 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Hence, the solution is x=5.
2)
[tex]\begin{gathered} 8(x+1)=24 \\ x+1=\frac{24}{8} \\ x+1=3 \\ x=3-1 \\ x=2 \end{gathered}[/tex]Hence, the solution is x=2.
3)
[tex]\begin{gathered} 5(x-2)=20 \\ x-2=\frac{20}{5} \\ x-2=4 \\ x=4+2 \\ x=6 \end{gathered}[/tex]Hence, the solution is x=6.
4)
[tex]\begin{gathered} 34-7x=20 \\ 34-20=7x \\ 7x=14 \\ x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]Hence, the solution is x=2.
5)
[tex]\begin{gathered} 31-x=29 \\ 31-29=x \\ x=2 \end{gathered}[/tex]Hence, the solution is x=2.
6)
[tex]\begin{gathered} 3x+6=21 \\ 3x=21-6 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5 \end{gathered}[/tex]Hence, the solution is x=5.