A Nickel is 5 cents = 5/100 = $0.05
A dime is 10 cents = 10/100 = $0.1
A quarter is 25 cents = 25/100 = $0.25
Let N represent the number of nickels
Let D represent the number of dimes
Let Q represent the number of quarters
Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. It means that
N + D + Q = 81
The total value of the coins was $7.90. It means that
0.05N + 0.1D + 0.25Q = 7.9
The number of Dimes was 7 less than triple the number of Quarters. It means that
D = 3Q - 7
The system of equations is
N + D + Q = 81
0.05N + 0.1D + 0.25Q = 7.9
D = 3Q - 7
Find the point that partitions segment AB in a 1:3 ratio (_,_)Find the point that partitions segment AD in 1.1 ratio (_,_)
AB in 1:3 ratio, Find a pointwhere on one side there is 1/4 of AB and in the other side 3/4 of AB:
Find the domain of the rational function.f(x)=x−1/x+4
Given:
[tex]f(x)=\frac{x-1}{x+4}[/tex][tex]\begin{gathered} \text{Let, x+4=0} \\ x=-4 \end{gathered}[/tex]Domain:
[tex]-\infty<-4<\infty[/tex][tex](-\infty,-4)\cup(-4,\infty)[/tex]h(x)= -1/2 (x+4)^2 +10Writing quadratics in standard form
`Answer:
h(x) = -x^2/2 - 4x + 32
Explanation:
The standard form of a quadratic equation is expresssed as
ax^2 + bx+c
Writing the given equation h(x)= -1/2 (x+4)^2 +10 in stabdard form will give;
h(x)= -1/2 (x+4)^2 +10
h(x)= -1/2 (x^2+8x+16)+40
h(x)= -x^2/2 - 4x - 8 + 40
h(x) = -x^2/2 - 4x + 32
Hence the equation in standard form is expressed as h(x) = -x^2/2 - 4x + 32
find the inverse function of g(x)= x-1÷x+5
1. replace g(x) with y:
[tex]y=\frac{x-1}{x+5}[/tex]2.Replace every x with a y and replace every y with an x
[tex]x=\frac{y-1}{y+5}[/tex]3. Solve for y:
[tex]\begin{gathered} (y+5)x=y-1 \\ yx+5x=y-1 \\ yx-y=-1-5x \\ y(x-1)=-1-5x \\ y=\frac{-1-5x}{x-1} \end{gathered}[/tex]4. Replace y with g−1(x) g− 1 ( x ):
[tex]g(x)^{-1}=\frac{-5x-1}{x-1}[/tex]an athlete eats 45 g of protein per day while training. how much protein will she eat during 23 days of training?
SOLUTION
From the question, the athlete eats 45 g of protein in a day. This means that in 23 days the athlete will eat
[tex]\begin{gathered} 23\times45\text{ g of protein } \\ =23\times45 \\ =1,035g \end{gathered}[/tex]Hence the answer is 1 035 g of protein, or 1.035 kg of protein.
Note that: To change grams to kilograms, we divide by 100.
sin(theta) = .754
What is theta
Answer: I believe it is representing the angular position of a vector
In short, it is a symbol to represent a measured angle.
Which fraction is less than 3/5 is it 5/7, 9/15, 4/6, 7/12
Answer: 7/12
Step-by-step explanation:
3/5=0.6
5/7=0.71428571428
9/15=0.6
4/6=0.66666
7/12=0.583333
Answer: 7/12
Step-by-step explanation:
I have attached my work.
Yesterday, Diane had c baseball cards. Today, she gave 6 away. Using c, write and expression for the number of cards Diane has left.
Answer:
The expression is c-6. She gave away 6 cards so subtract 6 from the original number which is c.
Find the (x , y) coordinate(s) of any hole(s) in h( x ). If there is none, write “n/a”.Round to two decimals.
The hole appears in the rational function when the numerator and the denominator have the same zeroes
Since the rational function is
[tex]h(x)=\frac{x+7}{x^2-49}[/tex]Factorize the denominator
[tex]x^2-49=(x+7)(x-7)[/tex]The rational function h(x) is
[tex]h(x)=\frac{x+7}{(x+7)(x-7)}[/tex]Since (x + 7) is in both numerator and denominator
Then there is a hole at x + 7 = 0
Let us find the value of x
[tex]\begin{gathered} x+7=0 \\ x+7-7=0-7 \\ x=-7 \end{gathered}[/tex]The whole is at x = -7
Then simplify the fraction to find the value of y at x = -7
[tex]h(x)=\frac{(x+7)}{(x+7)(x-7)}[/tex]Cancel the bracket (x+7) up by the same bracket down
[tex]h(x)=\frac{1}{x-7}[/tex]Substitute x by -7
[tex]\begin{gathered} h(-7)=\frac{1}{-7-7} \\ h(-7)=\frac{1}{-14} \\ y=-\frac{1}{14} \end{gathered}[/tex]The hole is at (-7, -1/14)
10. The graph shows the scores of an exam. About what percent of students scored above 86%?Distribution of Exam Scores20Percent1078808286889084Score11%18%6.5%
Answer
Option B is correct.
Percent of students that scored above 86% = 18%
Explanation
To find the percentage of students that scored above 86%, we will need to add the percent of the bars for all the scores greater than 86%.
For 87%, the bar is 8%
For 88%, the bar is 5.8%
For 89%, the bar is 2.2%
For 90%, the bar is 2%
So,
Percent of students that scored above 86% = 8 + 5.8 + 2.2 + 2 = 18%
Hope this Helps!!!
You pick a card at random.
1 2 3 4
What is P(factor of 24)?
Write your answer as a percentage rounded to the nearest tenth
Answer:
100%
Step-by-step explanation:
All of the numbers are factors of 24. So, picking a factor of 24 is guaranteed, so the probability is 1.
This is equal to 100%.
find the sum of the first 44 terms of the following series. to the nearest integer 10,14,18,...
The first term is a=10.
The number of terms is n=44.
The common difference is d=4.
The formula for the sum of n terms is,
[tex]S=\frac{n}{2}\lbrack2a+(n-1)d\rbrack[/tex]Determine the sum of first 44 terms of the series.
[tex]\begin{gathered} S=\frac{44}{2}\lbrack2\cdot10+(44-1)4\rbrack \\ =22\cdot\lbrack20+172\rbrack \\ =22\cdot192 \\ =4224 \end{gathered}[/tex]So answer is 4224.
I need help This is from my trig prep guide
From the question given, we have the following data;
Height of the tree = 80 feet
Angle of elevation to the top of the tree = 68 degrees
Distance from Corey to the tree = unknown
We shall now call the unknown variable x.
With that we shall have the following diagram;
We now have a diagram detailing the triangle and the dimensions showing Corey, the tree and the eagle at the tree top.
To get a better look, Corey moves several steps away from the tree and now determines his new angle of elevation to be 41 degrees.
This can now be illustrated as follows;
From triangle EDC, we shall calculate the distance from point C to point D using trigonometric ratios. The reference angle is at point C, which means the opposite side is side ED. The adjacent side is side CD (labeled x). Using trig ratios we have;
[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 68=\frac{80}{x} \end{gathered}[/tex]We cross multiply and we now have;
[tex]\begin{gathered} x=\frac{80}{\tan 68} \\ U\sin g\text{ a calculator, we have tan 68 as 2.475086}\ldots \\ x=\frac{80}{2.475086} \\ x=32.322109\ldots \\ \text{Rounded to the nearest hundredth of a foot;} \\ x=32.32ft \end{gathered}[/tex]Looking at triangle EDB;
The reference angle is 41 which makes the opposite side ED and the adjacent side BD. To calculate the distance BD, we'll have;
[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 41=\frac{80}{BD} \\ We\text{ cross multiply and we now have;} \\ BD=\frac{80}{\tan 41} \\ BD=\frac{80}{0.869286} \\ BD=92.02955\ldots \\ \text{Rounded to the nearest hundredth;} \\ BD=92.03 \end{gathered}[/tex]Take note that the distance Corey moved before he had a new angle of elevation is line segment CD which is indicated as y. Note also that
[tex]\begin{gathered} BC+CD=BD \\ CD=x=32.32ft \\ BC+32.32=92.03 \\ \text{Subtract 32.32 from both sides;} \\ BC=59.71 \end{gathered}[/tex]The distance Corey stepped back is indicated as y (line segment BC).
ANSWER:
Corey stepped back 59.71 feet
Which x-value is in the domain of the function? Thank you!
Solution:
Given the function;
[tex]f(x)=4\cot(2x)+3[/tex]The graph of the function is;
ANSWER:
[tex]\frac{\pi}{3}[/tex]Which function rule would help you find the values in the table?J K2 -124 -246 -368 -48A k=-12jB k=-6jC k=j - 12D k=j - 6
Solution
As seen from the table
For each values of the table
We define the variation from K to J
[tex]\begin{gathered} K\propto J \\ K=cJ\text{ (where c is constant of proportionality)} \end{gathered}[/tex]When J = 2, K = -12
[tex]\begin{gathered} K=cJ \\ -12=c(2) \\ 2c=-12 \\ c=-\frac{12}{2} \\ c=-6 \end{gathered}[/tex]Therefore, the formula connecting them will be
[tex]k=-6j[/tex]Option B
Identify the measurement that cannot be taken directly if you were constructing a two-
dimensional visual representation of the fish tank.
The measurement that cannot be taken directly in 2-D is depth
What do you mean by measurement?
Measurement is the quantification of an object's or event's properties for comparison with other objects or occurrences. Measurement, in other terms, is the act of establishing how large or little a physical amount is in comparison to a fundamental reference quantity of the same sort. The scope and use of measurement are context and discipline dependent. Measurements do not apply to nominal qualities of things or events in natural sciences and engineering, which is compatible with the recommendations of the International Bureau of Weights and Measures' International lexicon of metrology. However, measures in other domains, such as statistics and the social and behavioral sciences, can have numerous levels.
The measurement that cannot be taken directly in 2-D is depth
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Jo started a business selling fishing supplies. He spent $5200 to obtain his initial supplies, and it costs him $350 per week for general expenses. He earns $750 per week in sales.
Create the linear function, in slope-intercept form, that represents the scenario.
The linear function is given by 5200+350x = 750x
What is linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
Amount spent to obtain merchandise = $5,200
Cost of general expenses = $350
Earnings from sales per week = $750
Now,
Let 'x' be the number of weeks taken to make profit
thus,
Total cost involved = $5,200 + ( $350 × x )
Total profit from sales = $750 × x
Now, the number of weeks after that the cost and earning will be equal, will be given by
5200+350x = 750x
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Question is attached in photo Function : f(x)=x+2 sin x
Answer:
The function is given below as
[tex]f(x)=x+2\sin x[/tex]Using the interval below
[tex]0\leq x\leq2\pi[/tex]A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph).
Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).
Using a graphing tool, we will have the relative maximum and relative minimum to be
Hence,
The relative maximum is at
[tex](\frac{2\pi}{3},3.826)[/tex]The relative minimum is at
[tex](\frac{4\pi}{3},2.457)[/tex]Solve for x. Round to the nearest hundredth. Show all work.
The equation is given as,
[tex]3e^{5x}=1977[/tex]Transpose the term,
[tex]\begin{gathered} e^{5x}=\frac{1977}{3} \\ e^{5x}=659 \end{gathered}[/tex]Taking logarithm on both sides,
[tex]\ln (e^{5x})=\ln (659)[/tex]Consider the formula,
[tex]\ln (e^m)=e^{\ln (m)}=m[/tex]Applying the formula,
[tex]\begin{gathered} 5x=\ln (659) \\ x=\frac{1}{5}\cdot\ln (659) \\ x\approx1.30 \end{gathered}[/tex]Thus, the solution of the given exponential equation is approximately equal to,
[tex]1.30[/tex]A worker uses a forklift to move boxes that weigh either 40 pounds or 65 pounds each. Let x be the number of 40-pound boxes and y be the number of 65-pound boxes. The forklift can carry up to either 45 boxes or a weight of 2,400 pounds. Which of the following systems of inequalities represents this relationship? 40x + 657 $ 2.400 rty < 45 C) | 40r + 657 $ 45 | x + y < 2.400 B) [xu y < 2.100 40x + 657 $ 2.400 xl y < 1
Let:
x = number of 40-pound boxes
y = number of 65-pound boxes
The forklift can carry up to either 45 boxes
This means:
[tex]x+y\leq45[/tex]The forklift can carry up a weight of 2,400 pounds:
This means:
[tex]40x+65y\leq2400[/tex]Suppose that an item regularly costs $100.00 and is discounted 22%. If it is then marked up 22%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
Suppose that an item regularly costs $100.00 and is discounted 22%. If it is then marked up 22%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
1)
we have
100%-22%=78%=78/100=0.78
so
If is discounted 22%
the new price is 100,000*0.78=$78,000
2) If it is then marked up 22%
the new price is
100%+22%=122%=122/100=1.22
78,000*1.22=$95,160
therefore
The new price is not $100,000
the new price is $95,160
please show me how to solve this triangle, thank you!
Statement Problem: Solve for the missing sides of the triangle;
Solution:
The sum of angles in a triangle is 180degrees. Thus,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle B=180^o-\angle A-\angle C \\ \angle B=180^o-42^o-96^o \\ \angle B=42^o \end{gathered}[/tex]Since measure angle A and measure angle B are equal. Thus, the triangle is isosceles and the two sides are equal.
[tex]a=b[/tex]We would apply sine rule to find the missing side a.
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin A}{a}=\frac{\sin C}{c} \end{gathered}[/tex][tex]\begin{gathered} \frac{\sin42^o}{a}=\frac{\sin96^o}{12} \\ a=\frac{12\sin42^o}{\sin96^o} \\ a=8.07 \\ a\approx8.1 \end{gathered}[/tex]Thus,
[tex]a=b=8.1[/tex]CORRECT ANSWERS:
[tex]\begin{gathered} a=8.1 \\ b=8.1 \\ m\angle B=42^o \end{gathered}[/tex]There are 11 oranges, 7 apples, 9 bananas and 13 peaches in the fruit bowl. If you pick a fruit at random, what is the probability you will pick an apple or banana? (give answer as a percentage rounded to the nearest tenth) Plapple or banana)=[answer]
we get that:
[tex]\frac{7+9}{11+7+9+13}=\frac{16}{40}=\frac{2}{5}=0.4\rightarrow40\text{ \%}[/tex]Quadrilateral ABCD with vertices A(0,7) B(1,3), C(-1,-4), and D(-5,1): <7,-3>
We will have the following:
2)
A(0, 7) : <7, -3>
[tex]A^{\prime}(7,4)[/tex]B(1, 3) : <7, -3>
[tex]B^{\prime}(8,0)[/tex]C(-1, -4) : <7, -3>
[tex]C^{\prime}(6,-7)[/tex]D(-5, 1) : <7, -3>
[tex]D^{\prime}(2,-2)[/tex]3)
From the graph we will have the following:
a.
[tex](x,y)\to(x+7,y+5)[/tex]b.
[tex]\langle7,5\rangle[/tex]***Explanation***
For point 2, we will simply apply the vector to the corresponding coordinates, that is:
We have the coordinates:
[tex]A(a,b)[/tex]and the vector:
[tex]\langle c,d\rangle[/tex]So, in order to determine the final image we will have to follow the transformation rule:
[tex]A^{\prime}(a+c,b+d)[/tex]*For point 3, we will simply count the number of units the image has moved to the left or rigth and that will be our transformation rule for the x-axis, and the number of units the image has moved up or down and that will be our transformation rule for the y-axis.
In the case of the problem, the images moved 7 units to the rigth (+7) and then moved 5 units up (+5), so the transformation rule in coordinate notation is given by:
[tex](x,y)\to(x+7,y+5)[/tex]And in order to write it in vector notation, we simply write the units the images move:
[tex]\langle7,5\rangle[/tex]help meeeee pleaseeeee!!!
thank you
The values of the given polynomial are:-
f(0) = 12
f(2) = 28
f(-2) = 52
Given polynomial:-
[tex]f(x)=-x^3+7x^2-2x+12[/tex]
We have to find the values of f(0), f(2) and f(-2).
Putting x = 0 in f(x), we get,
[tex]f(0)=-(0)^3+7(0)^2-2(0)+12[/tex]
f(0) = 0 +0 - 0 + 12 = 12
Hence, the value of f(0) is 12.
Putting x = 2 in f(x), we get,
[tex]f(2)=-(2)^3+7(2)^2-2(2)+12[/tex]
f(2) = -8 + 28 - 4 + 12 = 28
Hence, the value of f(2) is 28.
Putting x = -2 in f(x), we get,
[tex]f(-2)=-(-2)^3+7(-2)^2-2(-2)+12[/tex]
f(-2) = 8 +28 + 4 +12 = 52
Hence, the value of f(-2) is 52.
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2. a) How many sets of opposite faces does this rectangular prism have? ____b) Why is the figure called a rectangular prism?
Answer:
a) 3 sets of opposite faces
b) The given figure is called a rectangular prism because its bases( the bottom face and the top face) are both rectangles.
Explanation:
a) Looking at the given rectangular prism and counting the faces, we can see that there are 6 faces in all. Out of the 6 faces of the rectangular prism, we can see that there are 3 pairs of opposite faces.
b) A prism is any 3-dimensional shape that has two identical shapes called bases facing each other.
If the two identical shapes facing each other are rectangles, then the prism is termed a rectangular prism.
Therefore, we can say that the given figure is called a rectangular prism because its bases ( the bottom face and the top face) are both rectangles.
Benjamin & Associates, a real estate developer, recently built 194 condominiums in McCall, Idaho. The condos were either two-bedroom units or three-bedroom units. If the total number of rooms in the entire complex is 494, how many two-bedroom units are there? How many three-bedroom units are there
x = number of 2 bedrooms units
y= number of 3 bedroom units
194 condominiums
x+y = 194 (a)
the total number of rooms in the entire complex is 494
2x + 3y = 494 (b)
We have the system of equations:
x+y = 194 (a)
2x + 3y = 494 (b)
Solve (a) for x
x = 194-y
Replace x on (b) and solve for y
2 (194-y ) + 3 y = 494
388 - 2y +3 y = 494
-2y+3y = 494-388
y= 106
Replace y on (a) and solve for x
x + 106 = 194
x = 194-106
x= 88
2-bedroom units = 88
3- bedrooms units = 106
Which of the following actions will best help her find out whether the two equations in the system are in fact parallel
Check to see whether the slope of both lines are the same (option A)
Explanation:[tex]\begin{gathered} \text{Given} \\ y\text{ - x = }21 \\ 2y\text{ = 2x + 16} \end{gathered}[/tex]When two system of equations do not intersect, the lines are said to be parallel lines.
This means there is no solution.
To determine if the lines are trully parallel, the slope of each equation need to be determined.
For parallel lines, the slope will be the same
The best action to help her find out whether the two equations are inded parallel, Check to see whether the slope of both lines are the same (option A)
What is the value of the x variable in the solution to the following system ofequations? (5 points)4x - 3y = 35x - 4y = 3O x can be any number as there are infinitely many solutions to this systemThere is no x value as there is no solution to this systemO-303
Step 1:
Write the two systems of equations
4x - 3y = 3
5x - 4y = 3
Step 2:
Use the elimination method to eliminate y.
[tex]\begin{gathered} 4x\text{ - 3y = 3} \\ 5x\text{ - 4y = 3} \\ \text{Use the elimination method to eliminate y} \\ 4x\text{ - 3y = 3 }\times\text{ 4} \\ 5x\text{ - 4y = 3 }\times\text{ 3} \\ 16x\text{ - 12y = 12} \\ 15x\text{ - 12y = 9} \\ 16x\text{ - 15x = 12 - 3} \\ \text{ x = 3} \end{gathered}[/tex]Final answer
x = 3
give the quadratic function a graph for the function f (x)= -(x-3)^2-2
Answer
The graph of the function f(x) = -(x - 3)² - 2, is presented below
Explanation
We are told to graph a given function
f(x) = -(x - 3)² - 2
The first step into making this easy is to open the bracket.
f(x) = - (x² - 6x + 9) - 2
f(x) = -x² + 6x - 9 - 2
f(x) = -x² + 6x - 11
The next step is then to insert different values of x into the function and obtain the corresponding value of the function. This set of ordered pairs arethen plotted to form the graph.
The graph is then plotted and presented under 'Answers' above.
Hope this Helps!!!