First of all, we need to know what a function is.
A function is a binary relation between two sets that
How many kernels of corn will be in the bag on the 26 days
Notice that each day the number of kernels doubles, then we can model that behavior with the following equation:
[tex]N=2^{n-1}.[/tex]Where N is the number of kernels on the nth day.
Evaluating the above function at n=26 we get:
[tex]N=2^{26-1}=2^{25}=33554432.[/tex]Answer: 33554432.
Simplify (k^5)^2 k^2 Write your answer with only positive exponents.
To simplify this expression, we will need to use two properties:
[tex]\begin{gathered} b^a\cdot b^c=b^{a+c} \\ (b^a)^c=b^{ac} \end{gathered}[/tex]Applying the second property first, we have:
[tex](k^5)^2k^2=k^{5\cdot2}k^2=k^{10}k^2[/tex]Applying the first property now, we have:
[tex]k^{10}k^2=k^{10+2}=k^{12}[/tex]So, the simpification is:
[tex]k^{12}[/tex]Look at the angles below. Which is not a true statement about the angles?
To solve the exercise, let us analyze the answer options:
Option A.A straight angle is an angle whose sides line in opposite directions from the vertex in the same straight line.
As we can see in the graph, the angle KJL is straight. Therefore, the measure of angle KJL is 180°.
Therefore, the statement is true.
Option B.
The angles KJM and MJL are supplementary, that is, angles add up to 180°.
Then, we can write and solve for x, the following equation:
[tex]\begin{gathered} 112\text{\degree}+(3x+50)\text{\degree}=180\text{\degree} \\ 112\text{\degree}+(3x)\text{\degree}+50\text{\degree}=180\text{\degree} \\ \text{ Add similar terms} \\ 162\text{\degree}+(3x)\text{\degree}=180\text{\degree} \\ \text{ Subtract 162\degree{}from both sides of the equation} \\ 162\text{\degree}+(3x)\text{\degree}-162\text{\degree}=180\text{\degree}-162\text{\degree} \\ (3x)\text{\degree}=18\text{\degree} \\ \text{ Divide by 3\degree from both sides of the equation} \\ \frac{(3x)\text{\degree}}{3\text{\degree}}=\frac{18\text{\degree}}{3\text{\degree}} \\ $$\boldsymbol{x=6}$$ \end{gathered}[/tex]Therefore, the statement is true.
Option C.The angles HJK and MJL are vertical, that is, opposite angles made by intersecting lines. Vertical angles are congruent, that is, they have the same measure.
In this case, we have:
[tex]m\angle HJK=m\angle MJL[/tex]Then, to find the measure of angle HJK, we replace x = 6 in the equation of the angle MJL:
[tex]\begin{gathered} m\angle HJK=m\angle MJL \\ m\angle HJK=(3x+50)\text{\degree} \\ m\angle HJK=(3\cdot6+50)\text{\degree} \\ m\angle HJK=(18+50)\text{\degree} \\ m\angle HJK=68\text{\degree} \end{gathered}[/tex]Therefore, the statement is not true.
Option D.The angles KJM and HJL also are vertical. Then, these angles are also congruent.
[tex]\begin{gathered} m\angle KJM=m\angle HJL \\ 112\text{\degree}=m\angle HJL \end{gathered}[/tex]Thus, this statement is true.
Therefore, the statement that is not true about the angles is the one shown in option C.
Can some one help me solve this sequence? It’s 121,97,73,49,25
We have the sequence:
121, 97, 73, 49, 25.
First, we have to look if there is a common difference between the terms of the sequence:
[tex]\begin{gathered} 97-121=-24 \\ 73-97=-24 \\ 49-73=-24 \\ 25-49=-24 \end{gathered}[/tex]We have a common difference of d=-24, so we can write the sequence in recursive form as:
[tex]a_n=a_{n-1}-24[/tex]help me pls!!!!!!!???
The sum of a number squared and three less than the number is 129.
Mathematical expression: x^2 + ( 2 x - 3 ) = 129
x^2 + 2 x -3 = 129
x ^2 + 2x - 3 - 129 =0
x ^2 + 2x - 132 = 0
For which inequality would x = 4.5 not be a solution?8 x ÷ 5 > 012 - x ≥ 8x + 6 ≥ 109 x - 5 < 80
We need to identify the inequality for which x = 4.5 is not a solution.
We can do so by replacing x on the left side of each equation, evaluating the expression, and checking if the inequality holds.
We have:
[tex]8x\div5=8\cdot4.5\div5=36\div5=7.2>0[/tex][tex]12-x=12-4.5=7.5<8\text{ \lparen not }\geqslant8)[/tex][tex]x+6=4.5+6=10.5\geqslant10[/tex][tex]9x-5=9\cdot4.5-5=40.5-5=35.5<80[/tex]Therefore, the only inequality for which x = 4.5 is not a solution is:
Answer
12 - x ≥ 8
Denmark uses the kroner as its currency. Before a trip to Denmark, Mia wants to exchange $1,700 for kroner. Does Bank A or Bank B have a better exchange rate? Explain
Let x be the dollars and y be the Kroners
A proportional relationship is given by
[tex]y=kx[/tex]Where k is the constant of proportionality.
We need to find out k for both banks A and B.
Exchange rate of Bank A:
As you can see from the table, 408 Kroners for $80
[tex]\begin{gathered} y=kx \\ k=\frac{y}{x}=\frac{408}{80}=5.1 \end{gathered}[/tex]So, the exchange rate of Bank A is 5.1
[tex]y=kx=5.1\cdot1700=8670[/tex]This means that Bank A will give you 8670 Kroners in exchange for $1700.
Exchange rate of Bank B:
From the given graph, locate any one x, y point
Let us select x = 10 and y = 50
[tex]\begin{gathered} y=kx \\ k=\frac{y}{x}=\frac{50}{10}=5 \end{gathered}[/tex]So, the exchange rate of Bank B is 5
[tex]y=kx=5\cdot1700=8500[/tex]This means that Bank B will give you 8500 Kroners in exchange for $1700.
As you can see, Bank A has a better exchange rate and would give Mia more Kroners.
Determine the ratio that represent tan (0) in the picture
Joe walks on a treadmill at constant rate the equation below describes the relationship between t the time he walks in hours and d the distance he walks in milesThe equation for his journey is d=4t.Find the graph that represents the equation?how do i get the answer?
Given:
The equation that represents Joe's journey is :
[tex]\begin{gathered} d\text{ = 4t} \\ Where\text{ t is the time} \\ and\text{ d id the distance travelled} \end{gathered}[/tex]From the equation, we can determine that:
At t = 1 hr
[tex]\begin{gathered} d\text{ = 4 }\times\text{ 1} \\ =\text{ 4 miles} \end{gathered}[/tex]At t = 2hrs:
[tex]\begin{gathered} d\text{ = 4 }\times\text{ 2} \\ =\text{ 8 miles} \end{gathered}[/tex]At t = 3hrs:
[tex]\begin{gathered} d\text{ = 4 }\times\text{ 3} \\ =\text{ 12 miles} \end{gathered}[/tex]We have the points (1, 4), (2, 8), (3, 12)
We can now check the options for the graph that has the points.
Checking through the options, we can see that the graph that has the points we have obtained is the chart A
Answer: Option A
Solve the system of equations using elimination.15q – 4r = 625q + 8r = 86
SOLUTION:Thank
In this question, we are meant to solve the system of equations using the elimination method:
15q – 4r = 62 --------- equ 1
5q + 8r = 86 ----------- equ 2
To eliminate q , we need to multiply equ 2 by 3, 15q + 24 r = 258 ------- equ 3
Then solving equ 1 and equ 3, we have:
15q – 4r = 62 ---------equ 1
15q + 24 r = 258 ------- equ 3
equ 3 - equ 2, we have:
15 q - 15 q + 24 r - ( - 4r ) = 258 - 62
24 r + 4 r = 196
28 r = 196
Dividing both sides by 28, we have:
r = 7.
Next, we put the value of r = 7, in equ 1,
15q – 4r = 62 --------- equ 1
15 q - 4 ( 7 ) = 62
15q - 28 = 62
15q = 62 + 28
15q = 90
Dividing both sides by 15, we have :
q = 6.
CONCLUSION: The value of r = 7 and q = 6.
A 250-mL aqueous solution contains 1.56 x 10^–5 g of methanol and has a density of 1.03 g/mL. What is the concentration in ppm? A 6.1 X 10^-8 ppmB 1.5 X 1-^-5 ppmC 0.061 ppmD 15 ppm
ppm or part er million is used to measure the concentration of solute in a given volume of solution.
We can calculate it by the formula
[tex]ppm=\frac{mass\text{ of solute \lparen in mg\rparen}}{Volume\text{ of solution \lparen in L\rparen}}_[/tex]In our question we have the next data:
*Mass of methanol
[tex]1.56\text{ }\times10^{\frac{-}{}5}g=1.56\times10^{-2}mg[/tex]where we have to convert from g to mg.
* The volume of the solution is:
[tex]250\text{ ml = 0.250 L}[/tex]where we have to convert from ml to L
Putin the values on the right-hand side of the equations above we get:
[tex]ppm=\frac{1.56\times10^{-5}mg}{0.250\text{ L}}=0.0624[/tex]Looking at the option in the question, by similarity we chose the option c, that is , we chose ppm=0.0611
A motorboat maintained a constant speed of 13 miles per hour relative to the water in going 42 miles upstream and then returning. The total time for the trip was 6.5 hours. Use this information to find the speed of the current.
The speed of the current is 1 miles per hour.
Let x represent speed of the current.
We have been given that a motorboat maintained a constant speed of 13 miles per hour relative to the water in going 42 miles upstream and then returning.
The speed of motorboat while going upstream would be 13 - x
The speed of motorboat while going downstream would be 13 + x
Time taken while going upstream would be 42 / (13 - x)
Time taken while going downstream would be 42/(13 + x)
Now we will compare sum of both times with total time 6.5 hours and solve for x as:
42 / (13 - x) + 42 / (13 + x) = 6.5
1092 = 6.5((13 - x)(13 + x))
546 + 42x + 546 - 42x = 6.5((13 - x)(13 + x))
1092 = 1098.5 − 6.5x²
x² = 1
x = ±√1
x = ±1
Therefore, the speed of the current is 1 miles per hour.
Learn more about the speed here:
https://brainly.com/question/2004627
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Graph the compound function in #12 in the picNo equal to (x less than 0)
Given:
The compound function is,
[tex]f(x)=\begin{cases}x^2,x>0 \\ -x,x<0\end{cases}[/tex]Explanation:
Plot the compound function on the graph.
Evaluate the following expression.7 1/4 * 2^2 + (8 1/2 - 2) ÷ 331 1/660 1/648 1/236 5/6
We have to evaluate:
[tex]7\frac{1}{4}\cdot2^2+(8\frac{1}{2}-2)\div3[/tex]We then can write:
[tex]\begin{gathered} 7\frac{1}{4}\cdot2^2+(8\frac{1}{2}-2)\div3 \\ 7\frac{1}{4}\cdot4+(6\frac{1}{2})\div3 \\ (7\cdot4+\frac{1}{4}\cdot4)+(\frac{6}{3}+\frac{1}{2\cdot3}) \\ (28+1)+(2+\frac{1}{6}) \\ (28+1+2)+\frac{1}{6} \\ 31+\frac{1}{6} \\ 31\frac{1}{6} \end{gathered}[/tex]Answer: 31 1/6
You are party planner in charge of selecting the best laster tag party option for a group of 14 players. The following party packges. are available, and packges may not be combined.
Answer:
The deal with the lowest cost for 14 players is Package 3.
"$25.75 per player no limit on the number of players"
[tex]\begin{gathered} \text{Total cost for 14 players is = 14(\$25.75)} \\ =\text{ \$360.50} \end{gathered}[/tex]Therefore, Package 3 has the best deal for 14 players.
Explanation:
Given the table in the attached image.
We want to find the price with the best deal for 14 players.
For deal 1;
$365 for 14 players maximum 14 players
[tex]\text{Total cost for 14 players is = \$365}[/tex]For deal 2;
$250 for 10 players, $30 for each additional player limited to 20 players
[tex]\begin{gathered} \text{Total cost for 14 players is = \$250+4(\$30)} \\ =\text{ \$370} \end{gathered}[/tex]For deal 3;
$25.75 per player no limit on the number of players
[tex]\begin{gathered} \text{Total cost for 14 players is = 14(\$25.75)} \\ =\text{ \$360.50} \end{gathered}[/tex]From the deals, the deal with the lowest cost for 14 players is deal 3.
"$25.75 per player no limit on the number of players"
[tex]\begin{gathered} \text{Total cost for 14 players is = 14(\$25.75)} \\ =\text{ \$360.50} \end{gathered}[/tex]Therefore, Package 3 has the best deal for 14 players.
Find the equation of each line with the following general information. (a) y-intercept b and slope m (b) x-intercept a, y-intercept b
Answers:
(a) y = mx + b
(b) y = (-b/a)x + b
Explanation:
The equation of a line has the form:
y = mx + b
Where x and y are the variables, m is the slope and b is the y-intercept.
So, the equation of a line with slope m and y-intercept b is:
y = mx + b
On the other hand, if we have an equation with the x-intercept equal to a, then when x = a, y is equal to 0.
So, we can write the following equation:
y = mx + b
0 = ma + b
Now, we can solve the equation for m as follows:
0 - b = ma + b - b
-b = ma
-b/a = ma/a
-b/a = m
Therefore, an equation with x-intercept a is an equation with slope -b/a, so the equation of the line with x-intercept a and y-intercept b is:
y = (-b/a)x + b
True or false similar triangles always have equal lengths of corresponding sides
Hello,
The answer to the question is true
whenever we have two triangles that are similar, then thier corresponding angles and sides must be equal. They're refered to as congurent triangles
Congurent triangles are triangles that their corresponding sides are of equal length.
for example if triangle ABC is similar to triangle XYZ
The side lengths of the two triangles above are in proportion
Therefore,
[tex]\frac{XY}{AB}=\text{ }\frac{XZ}{AC}\text{ = }\frac{YZ}{BC}[/tex]What is the decimal equivalent of (22/9) \frac{22}{9}
2.44
Explanation
Step 1
when you have a fraction, just make the division to find the decimal equivalent
[tex]\frac{22}{9}=2.444[/tex]Hence, the decimal equivalent is 2.44
9. The distance a car travels at a rate of 65 mph is a function of the time, t, the car travels inhours. Express this function and evaluate it for f(3.5).AB.f(t)= 65t: 2275 miesf() = 65t: 2275 miles10= 65.1 : 18.57 milesf(t)=65: 0.05 milesfC350-15353C.D.
Given:
Rate at which the car travels = 65 mph
Thus, we have the function:
f(t) = 65t
To find f(3.5) substitute t for 3.5 in the function above.
f(3.5) = 65(3.5) = 227.5 miles
ANSWER:
f(t) = 65t: 227.5 miles
The VOLUME of the pyramid is 700 cm 3. What is thevalue of the HEIGHT?
It is given that the volume of the pyramid is 700 cubic centimeters.
The Formula for the volume of square pyramid is given by:
[tex]V=\frac{1}{3}a^2h[/tex]Where a is the side of base and h is the height
Here V=700 and a=10 so it follows:
[tex]\begin{gathered} 700=\frac{1}{3}\times10^2\times h \\ h=\frac{2100}{100} \\ h=21 \end{gathered}[/tex]Hence the height of the pyramid is 21 centimeters.
In AABC, AB = BC = 6 and ZABC = 120°. What is the area of AABC? A) 23 B) 473 C) 673 D) 9V3
in the given triangle,
AB = BC = 6
As, the two sides are equal so, the given triangle is isosceles.
also, the angle < ABC = 120 degrees,
the area of the isosceles triangle is,
[tex]A=\frac{1}{2}\times a^2\times\sin \theta^{}[/tex]here a = length of two congruent sides,
theta = the angle between congruent sides.
put the values,
A = 1/2 x 6^2 x sin 120
[tex]A=\frac{1}{2}\times6^2\times\sin 120[/tex][tex]\begin{gathered} A=\frac{36}{2}\times\frac{\sqrt[]{3}}{2} \\ A=9\sqrt[]{3} \end{gathered}[/tex]thus, the correct answer is option D
The dimensions of the base of Box 2 are:O width: x; length: 3width: x; length: 4x - 10 width: x; length: x-40 width: x; length: 4x + 1DONE
Answer:
Explanation:
There are 2 boxes:
Box 1:
The length is 3 times the width:
[tex]\begin{gathered} length=3*width \\ l=3w \\ If:w=x \\ \Rightarrow l=3x \\ \\ width=x,length=3x \end{gathered}[/tex]Box 2:
The length is 1 less than 4 times the width:
[tex]\begin{gathered} length=4w-1 \\ If:w=x \\ \Rightarrow length=4x-1 \\ \\ width=x,length=4x-1 \end{gathered}[/tex]Answer: B
Step-by-step explanation: correct wander 100%
How many 2/5 lb burgers can you make with 2 2/3 lbs of ground beef
Data:
• 2/5 lb per burger
,• 2(2/3)lb of ground beef.
Procedure:
0. We have to convert the mixed fraction to an improper fraction to be able to do any calculation. We will do it as follows:
[tex]2\cdot\frac{2}{3}=\frac{8}{3}[/tex]Then, based on that, we can calculate how many burgers we get:
[tex]\frac{1burger}{\frac{2}{5}lb}\cdot\frac{8}{3}lbbeef[/tex][tex]=\frac{\frac{8}{3}}{\frac{2}{5}}=\frac{20}{3}\approx6.67[/tex]Answer: 6 complete burgers
-4(3x - 5) = -16 - 12x
The question here is to solve for the value of x.
We will use the distributive property to make the left-hand side of the equation easier to work with.
Distributive Property:
[tex]a(b\pm c)=ab\pm ac[/tex]LHS becomes:
[tex]-4\left(3x-5\right)=-4(3x)-4(-5)=-12x+20[/tex]Now the equation becomes:
[tex]-12x+20=-16-12x[/tex]We put all the x's to one side and numbers to another (remember to change signs when changing sides):
[tex]\begin{gathered} -12x+20=-16-12x \\ -12x+12x=-16-20 \\ 0x=-36 \\ 0=-36 \end{gathered}[/tex]Now wait!
It doesn't make sense.
So, this equation is faulty. There is no solution.
6. In the isosceles trapezoid shown, GJ =5 and HI =9. Determine the length of the midsegment of the trapezoid.14B.7C.9D. 5
Explanation:
The median of a trapezoid is half the sum of their bases:
[tex]\begin{gathered} m=\frac{1}{2}(GJ+HI) \\ m=\frac{1}{2}(5+9)=\frac{1}{2}\cdot14=7 \end{gathered}[/tex]Answer:
The correct option is B. 7
True or false: The equation for the axis of symmetry for the function, y = 2x^2 - 8x + 3 is x = 2.
ANSWER
True
EXPLANATION
We want to find the equation of the axis of symmetry of the given function:
[tex]y=2x^2-8x+3[/tex]The axis of symmetry of the function is given by:
[tex]x=-\frac{b}{2a}[/tex]where b = coefficient of x
a = coefficient of x²
From the given function:
[tex]\begin{gathered} a=2 \\ \\ b=-8 \end{gathered}[/tex]Therefore, the equation for the axis of symmetry of the function is:
[tex]\begin{gathered} x=-\frac{-8}{2(2)} \\ \\ x=-\frac{-8}{4}=-(-2) \\ \\ x=2 \end{gathered}[/tex]Therefore, it is true.
Question is down below - the same drop down menus in the same for all.
Given that a bag can hold 2 pounds of dog food.
We need a new bag which holds 40 pounds of dog food.
[tex]\frac{40}{2}=20[/tex]The scale factor of the volume of the bags of dog food is 20 which means the scale factor of the dimension of the two bags is 20.
Therefore the scale factor of the surface area of the two bags is 20.
What is the value of y? 6(2+y) = 3(3 - y)
Answer
y = -1/3
Step-by-step explanation:
Given the following equation
6(2 + y) = 3(3 - y)
Step 1: open the parentheses
6 * 2 + 6 * y = 3 * 3 - 3* y
12 + 6y = 9 - 3y
collect the like terms
12 - 9 = -3y - 6y
3 = -9y
Divide both sides by -9
3/-9 = -9y/-9
y = -1/3
Hence, the value of y = -1/3
Simplify.5y(4x - 3z)20 xy - 3 z54 xy - 53 yz4 x - 15 yz20 xy - 15 yz
Explanation
Given:
[tex]5y(4x-3z)[/tex]We need to expand the expression using distribution:
[tex]\begin{gathered} 5y(4x-3z)=5y(4x)-5y(3z) \\ =20xy-15yz \end{gathered}[/tex]Hence, the answer is 20xy - 15yz.
x+6=-12Write which property of equality you used
The given expression is
[tex]x+6=-12[/tex]Then,
[tex]\begin{gathered} x+6-6=-12-6 \\ x=-18 \end{gathered}[/tex]Hence, the property is "the subtraction property of equalities".