Given:
The change all in nickels and pennies.
Let the number of nickels = x
Let the number of pennies = y
Total coins = 31
so, x + y = 31
1 nickel = 5 cents
1 penny = 1 cent
The change = $0.87 = 87 cents
so, 5x + y = 87
so, we have the following system of equations:
[tex]\begin{gathered} x+y=31\rightarrow(1)\times-1 \\ 5x+y=87\rightarrow(2) \\ ------------- \\ (5x-x)+(y-y)=87-31 \\ \\ 4x=56 \\ \\ x=\frac{56}{4}=14 \\ \\ y=31-14=17 \end{gathered}[/tex]So, the number of nickels = x = 14
And the number of pennies = y = 17
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros..g(x)=(x+2)(x-1)(x-2).g(x)=(x+3)(x+2)(x-3).g(x)=(x+2)(x-2)(x-3).g(x)=(x+5)(x+2)(x-5).g(x)=(x+7)(x+1)(x-1).
Let's say the function is :
[tex]g(x)=(x+2)(x-1)(x-2)[/tex]To determine the end behavior, substitute a very large number to x, one for a negative value and one for positive.
So if we substitute a positive large number to x, the sign of the function will be :
[tex]\begin{gathered} g(x)=(+)(+)(+) \\ g(x)=+ \end{gathered}[/tex]The sign of g(x) will be positive.
And if we substitute a negative large number to x, the sign of the function will be :
[tex]\begin{gathered} g(x)=(-)(-)(-) \\ g(x)=- \end{gathered}[/tex]The sign of g(x) will be negative.
So we can conclude that as x goes to + infinity, g(x) goes to + infinity
and as x goes to - infinity, g(x) goes to - infinity
The y-intercept is the value of g(x) when x = 0
Substitute x = 0, then solve for g(x)
[tex]\begin{gathered} g(x)=(0+2)(0-1)(0-2)_{} \\ g(x)=2(-1)(-2) \\ g(x)=-4 \end{gathered}[/tex]Therefore, the y-intercept is at (0, 4)
For the zeros, the zeros are values of x when g(x) = 0
Set g(x) = 0, then solve for x :
[tex]\begin{gathered} g(x)=(x+2)(x-1)(x-2) \\ 0=(x+2)(x-1)(x-2) \end{gathered}[/tex]x + 2 = 0 => x = -2
x - 1 = 0 => x = 1
x - 2 = 0 => x = 2
The zeroes are :
(-2, 0), (1, 0) and (2, 0)
all of the following expressions are equivalent except (5 - 5) x-5(x - 1)-5 x + 55 - 5 x
we solve each expression
1.
[tex]\begin{gathered} (5-5)x \\ 0x \\ =0 \end{gathered}[/tex]2.
[tex]\begin{gathered} -5(x-1) \\ (-5\times x)+(-5\times-1) \\ -5x+5 \end{gathered}[/tex]3.
[tex]-5x+5[/tex]4.
[tex]\begin{gathered} 5-5x \\ -5x+5 \end{gathered}[/tex]the the wrong expression is first
Answer:
It is the first one
Step-by-step explanation:
it was a simple question to answer!
Have a awesome day
How many pennies, how many dimes,how many nickels, and how many quarters
Let n represents the number of nickel
Let p represents the number of pennies
Let d represents the number of dimes
Let q represents the number of quarters
Recall that
1 nickel = $0.05
1 penny = $0.01
1 dime = $0.1
1 quarter = $0.25
From the information given,
n + p + d + q = 12-------------------------------------------------(1)
0.05n + 0.01p + 0.1d + 0.25q = 1.67-------------------------(2)
p = n --------------------------------------------------------------------(3)
n + d = q ----------------------------------------------------------------(4)
Solving the four equations simultaneously, we have
Substitute equations (3) and (4) into equations (1) and (2)
n + n + d + n + d = 12
0.05n + 0.01n + 0.1d + 0.25(n + d) = 1.67
3n + 2d = 12-----------------------------------------(5)
0.31n + 0.35d = 1.67--------------------------------(6)
multiply equation (6) by 200 and equation (5) by 35, we have
105n + 70d=420------------------(7)
62n + 70d =334--------------------(8)
subtract equation (8) from (7)
43n = 86
n=86/43
n=2
put n=2 into equation (8)
62(2) + 70d = 334
124 + 70d = 334
70d = 334 - 124
70d = 210
d = 210/70
d=3
but p = n = 2
p = 2
n + d = q
q = 2 + 3 = 5
Hence, max have
2 nickels, 2 pennies, 3 dimes, 5 quarters
which rational number also belongs to the set of natural numbers. 9, 1/4, -9 or 0.933........
Note that natural numbers are integer values that are greater than 0. They can also be called positive integers or counting numbers
Out of all the rational numbers given, only 9 is a positive integer, hence it
Find P (X > 80) if X follows a normal distribution with a mean of 75 and a standard deviation of 5.
Given that X follows a normal distribution with a mean of 75 and a standard deviation of 5;
Using the Z-value formula;
[tex]Z=\frac{X-\mu}{\sigma}[/tex]Given;
[tex]undefined[/tex]Write2796asaRomanNumeral.
the roman numeral of 2796 is MMDCCXCVI.
use the points 50,25 and 200,100 to calculate the slope
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, the points are (50,25) and (200,100), then the slope is:
[tex]m=\frac{100-25}{200-50}=\frac{75}{150}=\frac{1}{2}[/tex]It is 1.9 miles from a house to a restaurant and 1.2miles to a pier, as shown at the right. The anglebetween the two lines of sight is 87°. How far is it fromthe pier across the water to the restaurant.
Since two side sides of the triangle and an angle is known, we apply the Cosine rule
Formula for Cosine rule is given below,
Where a is distance between the house and pier,
b is the distance between the house and restaurant,
c is the distance between the pier and the restaurant,
C is the angle opposite c
[tex]c^2=a^2+b^2-2ab\cos C[/tex][tex]\begin{gathered} \text{Where,} \\ a=1.2\text{ miles} \\ b=1.9\text{ miles and } \\ c=unknown^{} \\ C=87^0 \end{gathered}[/tex]Substituting the variables into the given formula above,
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ c^2=(1.2)^2+(1.9)^2-2(1.2)(1.9)\cos 87^0 \\ c^2=1.44+3.61-4.56(0.05234) \\ c^2=5.05-0.2387 \\ c^2=4.8113 \\ \sqrt[]{c^2}=\sqrt[]{4.8113} \\ c=2.1935\text{ miles} \\ c\approx2.19\text{ miles} \end{gathered}[/tex]Hence, the distance from the pier to the restaurant is 2.19 miles.
The two options are x > 1, x < 1which one is it?
In a inequality you have next sings:
< (less than) and ≤ (less than or equal to)
> (greather than) and ≥ (greather tan or equal to)
To graph the first pair of sings you draw a line to the left of the given number
To grpah the second pair of sings you draw a line to the right of the given number
In this case you have a line to the left of 1 (as the point in 1 is not a filled point it menas that the answer doesn't include the 1).
Then, the given graph is for the inequality: x<1Circle A has a diameter of 9 inches, a circumference of 28.26 inches, and an area of 63.585 square inches. The diameter of circle B is 5 inches, The circumference is 15.70 inches and the area is 19.625Part A: using the formula for circumference, solve for the value of pi for each circlePart B: use the formula for area to solve for the value of pi for each circle
Given:
The parameters for circle A:
diameter = 9 inches
circumference = 28.26 inches
area = 63.585 square inches
The parameters for circle B:
diameter = 5 inches
circumference = 15.70 inches
area = 19.625 square inches
The formulas for the area and circumference of a circle:
[tex]\begin{gathered} \text{Circumference of a circle = 2}\pi r \\ \text{Area of a circle = }\pi r^2 \end{gathered}[/tex]Part A
Using the formulas, we can solve for pi for each cicle:
Circle A:
[tex]\begin{gathered} 2\pi r\text{ = 28.26} \\ \pi d\text{ = 28.26} \\ \pi\text{ }\times\text{ 9 = 28.26} \\ \text{Divide both sides by 9} \\ \pi\text{ = 3.14} \end{gathered}[/tex]Circle B:
[tex]\begin{gathered} 2\pi r\text{ = }15.70 \\ \pi d\text{ = 15.70} \\ \pi\text{ }\times\text{ 5 = 15.70} \\ \text{Divide both sides by 5} \\ \pi\text{ = 3.14} \end{gathered}[/tex]Part B:
Circle A:
[tex]\begin{gathered} \pi r^2\text{ = 63.585} \\ \pi\text{ }\times(\frac{d}{2})^2\text{ = 63.585} \\ \pi\text{ }\times20.25\text{ = 63.585} \\ \pi\text{ = 3.14} \end{gathered}[/tex]Circle B:
[tex]\begin{gathered} \pi r^2\text{ = }19.625 \\ \pi\text{ }\times(\frac{d}{2})^2\text{ = 19.625} \\ \pi\text{ = }\frac{19.625}{6.25} \\ =\text{ 3.14} \end{gathered}[/tex]write the explicit formula for the following sequence then find the 7th term 500, 100, 20, 4
The first term of sequence is a = 500.
Determine the common ratio for the sequence.
[tex]\begin{gathered} r=\frac{500}{100} \\ =5 \end{gathered}[/tex]The general explicit formula is,
[tex]a_n=a(r)^{n-1}_{}[/tex]Here n is position of term in sequence.
Substitute the value of a and r in the sequence to obtain explicy formula of sequence.
[tex]undefined[/tex]What is the explicit formula for the following sequence 4,8,16,32,64?
In a geometric sequence, the ratio between two consecutive terms remains the same. In this case, this common ratio (r) is:
[tex]r=\frac{8}{4}=\frac{16}{8}=\frac{32}{16}=\frac{64}{32}=2[/tex]Therefore, the sequence is geometric.
Geometric sequence explicit formula
[tex]a_n=a_1(r)^{n-1}[/tex]where aₙ is the nth term, a₁ is the first term, and r is the common ratio.
In this case, the first term is a₁ = 4, and the common ratio is r = 2. Substituting these values into the formula, we get:
[tex]a_n=4(2)^{n-1}[/tex]What is the slope of a line perpendicular to the line whose equation is 4.x - y = 9.Fully simplify
-1/4
Explanation:Given equation:
[tex]4x\text{ - y = 9}[/tex]Rewriting the equation in the form y = mx + b:
[tex]\begin{gathered} 4x\text{ = y + 9} \\ 4x\text{ - 9 = y} \\ y\text{ = 4x - 9} \end{gathered}[/tex]For a line to be perpendicular to another line, the slope of one line will be the negative reciprocal of the second line.
From the equation above:
y = 4x - 9
m = slopeof the 1st line = 4
b = y - intercept = -9
reciprocal of the slope = 1/4
negative reciprocal = -1/4
slope of 2nd line = -1/4
The slope of the line perpendicular to the equation 4x - y = 9 is -1/4
y = 2x - 1y=9x + 6Does this system have a solution? If so, what is the solution? Explain. helppp
The given system is,
[tex]\begin{gathered} y=2x-1 \\ y=9x+6 \end{gathered}[/tex]From the first equation, we have,
[tex]\begin{gathered} 2x=y+1 \\ x=\frac{y+1}{2} \end{gathered}[/tex]Substituting this value in the second equation, we have,
[tex]\begin{gathered} y\text{ =9(}\frac{y+1}{2})+6 \\ 2y=9y+9+12 \\ -7y=21 \\ y=-3 \end{gathered}[/tex]Therefore,
[tex]x=\frac{-3+1}{2}=-\frac{2}{2}=-1[/tex]Thus, y = -3 and x = -1
Thus, the system has solution.
Answer:
x = - 1, y = - 3
Step-by-step explanation:
y = 2x - 1 → (1)
y = 9x + 6 → (2)
substitute y = 9x + 6 into (1)
9x + 6 = 2x - 1 ( subtract 2x from both sides )
7x + 6 = - 1 ( subtract 6 from both sides )
7x = - 7 ( divide both sides by 7 )
x = - 1
substitute x = - 1 into either of the 2 equations and solve for y
substituting into (1)
y = 2(- 1) - 1 = - 2 - 1 = - 3
solution is (- 1, - 3 )
Researchers collect data on a certain bird in their region. They want to know if there is a relationship between the number of chirps the bird does and the temperature outside. What trend, if any, do the researchers notice based on the data below
The image above is that of an exponential function. Considering the shape of the graph which is a curve and looking at the graph in question we can conclude there is a relationship between the number of chirps the bird does and the temperature outside. Also, it follows an exponential trend.
Find the permeter of the figure 2x 3x - 1 5x + 4
We are given a figure and asked to find the perimeter.
Recall that the perimeter of a figure is the sum of all of its lengths.
Since we are given the lenghts of the sides of the figure, let us add them together to find the perimeter.
[tex]P=(2x)+(3x-1)+(5x+4)_{}[/tex]Simplify the equation
[tex]\begin{gathered} P=2x+3x-1+5x+4 \\ P=2x+3x+5x-1+4 \\ P=10x-1+4 \\ P=10x+3 \end{gathered}[/tex]Therefore, the perimeter of the given figure is
[tex]P=10x+3[/tex]Option C is the correct answer.
2. (-4, 8), (-1, 2), (2, -4), (5, -10) is it a function and why??
Answer:
Its an function
Step-by-step explanation:
Since there is one value of y for every value of x
x
I need help with the attached question. Another tutor was working with me and we lost connectivity. We determined perimeter is calculated adding all sides together but I missed a few of his points just before the final solution
In order to determine the perimeter of the figure, first simplify the radicals, as follow:
2√20 = 2√(5*2^2) = 4√5
4√12 = 4√(3*2^2) = 8√3
2√48 = 2√(3*2^4) = 8√3
√80 = √(5*2^4) = 4√5
Now, add the previous results:
P = 4√5 + 8√3 + 8√3 + 4√5 = 8√5 + 16√3
Hence, the perimeter of the figure is 8√5 + 16√3 inches
square pyramid volume 225 cubic inches , base Edge 5 in
Square pyramid volume 225 cubic inches , base Edge 5 in
hi
what is your question
__________________________
Square pyramid volume = a^2 * h/3
225= 5^2 * h / 3
h* 5^2 = 225*3
h* 25 = 225*3
h= 225*3/25
h=27 in
_______________________________________
The height of the square pyramid is 27 in
Do you have any questions regarding the solution?
you like to watch at the local cinema. you have to payment options A is to hit a discount which will cost 160 a d then 20 per movie options b pays 40 per movie what will the total cost of the two options
Let x be the number of movies you watch.
Option A will cost you:
[tex]20x+160[/tex]Option B will cost you:
[tex]40x[/tex]The two options will cost the same when:
[tex]\begin{gathered} 20x+160=40x \\ 160=40x-20x \\ 20x=160 \\ x=\frac{160}{20} \\ x=8 \end{gathered}[/tex]Therefore, after 8 movies the two options will cost the same.
Hello,can you please help me with question 25 in the photo?Thank you
Given:
The arithmetic sequence:
[tex]7,3,-1,-5,...[/tex]Required:
We need to find the nth term equation and value of 20 th term.
Explanation:
The first term of the given arithmetic sequence is a =7.
[tex]d=3-7=-4[/tex]The common difference is d =-4.
Consider the nth term formula for the arithmetic sequence.
[tex]a_n=a+(n-1)d[/tex]Substitute a =7 and d =-4 in the formula.
[tex]a_n=7+(n-1)(-4)[/tex][tex]a_n=7+n(-4)-1(-4)[/tex][tex]a_n=7-4n+4[/tex][tex]a_n=11-4n[/tex]The equation for the nth term of the given sequence is
[tex]a_n=11-4n.[/tex]Substitute n=20 in the equation to find the value of 20 th term.
[tex]a_{20}=11-4(20)[/tex][tex]a_{20}=11-80[/tex][tex]a_{20}=-69[/tex]Final answer:
[tex]a_n=11-4n[/tex][tex]a_{20}=-69[/tex]Find the fourth term of the binomial expansion(2x + y)^7
In order to find the appropriate coefficients for the binomila expansion in the case of such high exponent, it is convenient to use Pascal's triangle .
I am pasting an image of a Pascal triangle up to the power 7 below:
Notice that the coefficients are lasted from left to right as the first one with power 7 for the 2x term, and no inclusion of the term y, and then decreasing the power of the 2x term, as the term in y increases power.
That is, the terms ordered from highest in 2x to lower go like:
(2x)^7 + 7 (2x)^6 (y) + 21 (2x)^5 (y)^2 + 35 (2x)^4 (y)^3 + ...
We stop here since we are asked specifically for the fourth term, which is:
35 (2x)^4 (y)^3 = 35 * 16 x^4 y^3 = 560 x^4 y^3
If wallpaper costs $1.25 per squared foot, how much will it cost to put new wallpaper in a room with area dimensions of 17 ft long by 16 ft wide?
Calculate the area of the wall using the formula for the area of a rectangle:
[tex]A=b\times h[/tex]Then:
[tex]\begin{gathered} A=(17ft)(16ft) \\ =272ft^2 \end{gathered}[/tex]Since each square foot of wallpaper costs $1.25, multiply 272 times 1.25 to find the total cost of covering the rectangular wall:
[tex]272\times\text{1}.25=340[/tex]Therefore, the total cost would be $340 for one wall.
What are the new coordinates of these pre-image points after a 90° CCW rotation? A (-3,2), B (4, -7), C (-9,-8)
The 90 degree counter clockwise Rotation can be represented by the rule;
[tex](x,y)\rightarrow(-y,x)[/tex]Given the points A, B and C, applying the rule to each we have;
[tex]undefined[/tex]Find the measures of the labeled angles. (x +116)° =..... ° (Type a whole number.) 5x = ....°(Type a whole number.)
We know that the two angles with measures (x+116) and (5x) have the same measure, as they are vertical angles.
Then, we can write:
[tex]\begin{gathered} x+116=5x \\ x-5x=-116 \\ -4x=-116 \\ x=\frac{-116}{-4} \\ x=29 \end{gathered}[/tex]With the value of x, we can find the measure of both angles, as they have the same measure:
[tex]5x=5\cdot29=145[/tex]Answer:
(x +116)° = 145°
5x = 145°
Determine the lateral and total surfacearea of the pyramid.
ANSWER
• Lateral surface area: ,73 cm²
,• Total surface area: ,93 cm²
EXPLANATION
The lateral surface area is the sum of the areas of the triangles. There are two triangles with dimensions: base = 4cm, height = 8cm and two triangles with dimensions: base = 5cm, height = 8.2cm.
The lateral surface area LSA is:
[tex]\begin{gathered} \text{LSA}=2\cdot(\frac{4\cdot8}{2})+2\cdot(\frac{5\cdot8.2}{2}) \\ \text{LSA}=4\cdot8+5\cdot8.2 \\ \text{LSA}=73\operatorname{cm}^2 \end{gathered}[/tex]The total surface area SA is the LSA plus the area of the base of the pyramid, which is a rectangle with dimensions: 4cm x 5cm:
[tex]\begin{gathered} SA=\text{LSA}+4\cdot5 \\ SA=73\operatorname{cm}+20\operatorname{cm}^2 \\ SA=93\operatorname{cm}^2 \end{gathered}[/tex]May I please get help with this math. I need help figuring out the lengths and whether they can be a sides of a triangle
we know that there are three type of traingles based on the length of sides
Equilateral, isosceles and scalene .
we used pythagorean theorem to find the lengths of the traigle
longest length in a traingle known as hypotenious .
there are two other lengths base and perpendicular
The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 eachand adult tickets cost $4 each. If the total receipts were $1740, how many students attendedthe talent show?
In total 530 tickets
Students tickets cost $3
Adult tickets cost $4
in total receipts were $1740
x= students
y=adults
we can have the next two equations
x+y=530
3x+4y=1740
we can rewrite the first equation
x=530-y
we substitute the equation above in the second equation
[tex]\begin{gathered} 3(530-y)+4y=1740 \\ 1590-3y+4y=1740 \\ y=1740-1590 \\ y=150 \end{gathered}[/tex]then we substitute the value of y in x=530-y
[tex]\begin{gathered} x=530-150 \\ x=380 \end{gathered}[/tex]In total 380 students attended the talent show
Answer:
380
Step-by-step explanation:
Determine if the order pairs is part of the solution
The given equation is expressed as
x + 3y = 6
To determine wether the ordered pairs are solutions of the equation, we would substitute the values of x and y in the ordered pairs into the equation. If both sides of the equation are equal, then the ordered pair is a solution. We have
a) For a = 3 and y = 1, we have
3 + 3(1) = 6
3 + 3 = 6
6 = 6
It is a solution
b) For x = 6 and y = 0
6 + 3(0) = 6
6 + 0 = 6
6 = 6
It is a solution
c) - 2 + 3(2/3) = 6
- 2 + 2 = 6
0 is not equal to 6
It is not a solution
The correct answers are options a and b
For the water balloon fight, your mom filled up one hundred balloons with 5 gallons of water. How many ounces of water did she use?*There are 128 oz in a gallon*
we have the next equivalence
1 gallon - 128 oz
5 gallon - x
(5 gallon times 128 onz )/ 1 gallon = 640 onz