The selling price of the item is $55.
The money charged by the auction company is;
[tex]\begin{gathered} 5.25\text{ \% of \$55} \\ \frac{5.25}{100}\times55 \\ =\text{ \$2.89} \end{gathered}[/tex]The fee paid to the auction company is $2.89
encuentra la medida de dos angulos complementarios. A=7×+4 y B=4×+9
Complementary angles mean that they add up to 90.
Thus, we can write:
[tex]\begin{gathered} A+B=90 \\ 7x+4+4x+9=90 \end{gathered}[/tex]We can use algebra to find x:
[tex]\begin{gathered} 7x+4+4x+9=90 \\ 11x+13=90 \\ 11x=90-13 \\ 11x=77 \\ x=\frac{77}{11} \\ x=7 \end{gathered}[/tex]To find measure of the individual angles, A and B, we simple plug in 7 into x of the expressions of A and B.
Angle A:
7(7) + 4 = 53 degrees
Angle B:
4(7) + 9 = 37 degrees
Use the Square Root Property to solve the quadratic equation 36c2−144c+144=−35. If there are multiple answers, list them separated by a comma, e.g. 1,2. If there is no solution, enter ∅.
The square root property to solve the quadratic equation;
[tex]\begin{gathered} 36c^2-144c+144=-35 \\ 36c^2-144c+144+35=0 \\ 36c^2-144c+179=0 \end{gathered}[/tex]is given as;
[tex]\begin{gathered} c=\frac{-b\pm\sqrt[]{b^2-4ad}}{2a} \\ \\ \text{Where} \\ a=36 \\ b=-144 \\ d=179 \end{gathered}[/tex][tex]\begin{gathered} c=\frac{-(-144)\pm\sqrt[]{(144)^2-4(36)(179)}}{2(36)} \\ c=\frac{144\pm\sqrt[]{-5040}}{72} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Since,} \\ \sqrt[]{b^2-4ad}<0 \\ \text{Then, th}ere\text{ is no real solution for c} \\ c=\phi \end{gathered}[/tex]Estimate 52% of 42 right in a whole number
52% of 42 is 21.84 rounded to the nearest whole number is 22.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
We know 52% of 42 can be numerically expressed as,
(52/100)×42.
= 21.84.
Now, 21.84 rounded to the nearest whole number is 22.
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Which Problems can be solved by performing this multiplication 1/5 x 30
Answer:
c
Step-by-step explanation:
The ratio of the number of adults to the number of students at a field trip has to be 3:8. During a current field trip, there are 190 more students on the trip than there are adults. How many students are attending the field trip? How many adults?
Please put this answer in a easy way (no algebra) use ratios and basic opreations.
The number of students attending the field trip is 304 and the number of adults is 114.
Calculating number of students and adults attending a field tripFrom the question, we are to determine the number of students and adults attending the field trip.
From the given information,
"The ratio of the number of adults to the number of students at a field trip has to be 3:8"
Let the number of students be x and the number of adults be y
Thus,
y/x = 3/8
8y = 3x ------------- (1)
Also,
There are 190 more students on the trip than there are adults
That is,
x - y = 190
Therefore,
x = 190 + y -------------- (2)
Substitute into equation
8y = 3x
8y = 3(190 + y)
8y = 570 + 3y
8y - 3y = 570
5y = 570
y = 570/5
y = 114
Thus, the number of adults is 114
Substitute the value of y into equation (2)
x = 190 + y
x = 190 + 114
x = 304
Hence, the number of students is 304
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Line l passes through the points, (6,-14) and (2,-4) . If line m is parallel to line l, the slope of the line m is equal to
Determine the slope of line l passes through points (6,-14) and (2,-4).
[tex]\begin{gathered} m=\frac{-4-(-14)}{2-6} \\ =\frac{-4+14}{-4} \\ =-\frac{10}{4} \\ =-\frac{5}{2} \end{gathered}[/tex]The line m is parallel to line l and parallel line have equal slope. So slope of line m is equal to -5/2.
Option 3 is correct.
the denominator of a fraction is 3 more than the numerator. if both the numerator and denominator are increased by 4, the new fraction is equal to 3/4. what is the original fraction
Explanations:
Let the numerator of the fraction be x and let the denominator be y.
Hence, the original fraction is:
[tex]\frac{x}{y}[/tex]It is given that the denominator is 3 more than the numerator. It follows that:
[tex]y=x+3[/tex]It is also given that when both the numerator and denominator are increased by 4, the new fraction is equal to 3/4. This implies mathematically to the equation:
[tex]\frac{x+4}{y+4}=\frac{3}{4}[/tex]Simplify this equation:
[tex]\begin{gathered} 4(x+4)=3(y+4) \\ \Rightarrow4x+16=3y+12 \end{gathered}[/tex]Substitute y=x+3 into this equation:
[tex]4x+16=3(x+3)+12[/tex]Solve the equation for x:
[tex]\begin{gathered} \Rightarrow4x+16=3x+9+12 \\ Collect\text{ like terms:} \\ \Rightarrow4x-3x=9+12-16 \\ \Rightarrow x=5 \end{gathered}[/tex]Substitute x=5 into the equation y=x+3:
[tex]y=5+3=8[/tex]Hence, x=5, and y=8.
It follows that the original fraction is 5/8.
Answer:
The original fraction is 5/8.
The ordered pair (8,5) represents a point on the graph of a proportional relationship. Which ordered pair also represents a point on the same graph? A. (5/8, 1) B. (1, 5/8) C. (5,8) D. (1, 8/5)
Given the ordered pair:
(8, 5)
Let's find the ordered pair that represents a point on the same graph assuming this is a graph of a proportional relationship.
Here, we have:
(x, y) ==> (8, 5)
Since this is a graph of a proportional relationship, let's find the constant of proportionality.
We have:
[tex]K=\frac{y}{x}=\frac{5}{8}[/tex]This means when x is 1, y is 5/8.
Thus, the ordered pair that also represents a point on the same graph is:
[tex](1,\frac{5}{8})[/tex]ANSWER:
[tex]\text{ B. (1, }\frac{5}{8})[/tex]when solving the system below algebraically using the substitution method, which of the following could be an equation you could. create to solve for x?A) x = 3y - 3B) -2x + 6(2x + 11) = 6C) -2x - 6 = - 2x - 11D) -2 (3y - 3) + y = 11
We have that the solutions of the system are
[tex]x\text{ = -6 and y = -1}[/tex]So we are going to check which of the answers give that answer, we are going to try with A fisrt
[tex]x\text{ = }3(-1)\text{ }-3\text{ = -6}[/tex]So with A, the solutions are the same, so we have that the answer is A.
Write the quadratic function with the indicated characteristics. The graph passes through the origin and the points (-3, 0) and (-1, 3).
substituteGiven:-
[tex](0,0),(-3,0)(-1,3)[/tex]To find the quadratic equation.
So now we use the formula,
[tex]y=ax^2+bx+c[/tex]So now we subtitute the points and find the value of a,b,c. So we get,
[tex]\begin{gathered} 0=a(0)+b(0)+c \\ c=0 \end{gathered}[/tex]Also,
[tex]\begin{gathered} 0=a(-3)^2+b(-3)+c \\ 0=9a-3b \end{gathered}[/tex]Also,
[tex]\begin{gathered} 3=a(-1)^2+b(-1)+0 \\ 3=a-b \end{gathered}[/tex]So now we simplify both equation. so we get,
[tex]\begin{gathered} 9a-3b=0 \\ 3a-3b=9 \end{gathered}[/tex]Now we add both the equations. we get,
[tex]\begin{gathered} 6a=-9 \\ a=-\frac{3}{2} \end{gathered}[/tex]Now we find the value of b, so we get,
[tex]\begin{gathered} a-b=3 \\ -\frac{3}{2}-b=3 \\ -b=3+\frac{3}{2} \\ -b=\frac{9}{2} \\ b=-\frac{9}{2} \end{gathered}[/tex]So the required values are,
[tex]y=-\frac{3}{2}x^2-\frac{9}{2}x+0[/tex]A chemistry teacher needs to mix a 20% salt solution with a 80% salt solution to make 15 qt of a 40% salt solution. How many quarts of each solution should the teacher mix to get the desired result?20% salt solution qt80% salt solution qt
Given that the chemistry teacher needs to mix a 20% salt solution with an 80% salt solution to make 15 quarts of a 40% salt solution.
Let be "x" the number of quarts of 20% salt solution the teacher should mix to get the desired result, and "y" the number of quarts of 80% salt solution the teacher should mix to get the desired result.
You can write the following System of Equations using the information provided in the exercise:
[tex]\begin{cases}0.2x+0.8y={(0.4)(15)} \\ x+y=15\end{cases}[/tex][tex]\begin{cases}0.2x+0.8y={6} \\ x+y=15\end{cases}[/tex]In order to solve the exercise, you can use the Substitution Method:
1. Solve the second equation for "y":
[tex]y=15-x[/tex]2. Substitute the new equation into the first equation and solve for "x":
[tex]0.2x+0.8(15-x)=6[/tex][tex]0.2x+12-0.8x=6[/tex][tex]\begin{gathered} x=\frac{-6}{-0.6} \\ \\ x=10 \end{gathered}[/tex]3. Substitute the value into the second original equation and solve for "y":
[tex]\begin{gathered} 10+y=15 \\ y=15-10 \\ y=5 \end{gathered}[/tex]Hence, the answer is:
• 20% salt solution:
[tex]10\text{ }qt[/tex]• 80% salt solution:
[tex]5\text{ }qt[/tex]
Nina and Nathan are creating a budget so they can afford paying all their billsand save to move to a nicer apartment. They decide that the ratio of spendingto saving needs to be 7:3. Last month their bills totaled $3975.20. Theymanaged to save $1,248.00. What was their actual spending ratio? At thisrate, will they meet their goal?
The ratio of spending to savings needs to be 7:3.
The actual spending ratio is 3,975.20 : 1,248.00.
In order to reach the goal, the actual spending ratio must the lower than the decided spending ratio.
3,975.20 : 1,248.00 < 7:3.
Dividing the ratios:
3.18 < 2.33
Since 2.33 is not greater than 3.18, they will not reach their goal at this rate.
On March 8, 2017, one U.S. dollar was worth 19.61 Mexican pesos.(a) On that date, how many dollars was 149.23 pesos worth?Round your answer to the nearest hundredth of a dollar.dollars(b) On that date, how many pesos was 63.64 dollars worth?Round your answer to the nearest hundredth of a peso.OPpesosI need help with these two math problems.
ANSWERS
(a) 7.61 USD
(b) 1247.98 MXN
EXPLANATION
We know that on March 8, 2017, 1 USD was worth 19.61 MXN.
(a) To find how many dollars was 149.23 MXN worth on that date, we have to divide this amount by 19.61,
[tex]149.23\text{ }MXN\cdot\frac{1\text{ }USD}{19.61\text{ }MXN}\approx7.61[/tex]Hence, 149.23 Mexican pesos were worth 7.61 US dollars.
(b) Now, to find how many Mexican pesos were 63.64 USD worth on that date, we have to multiply it by 19.61 instead,
[tex]63.64\text{ }USD\cdot\frac{19.61\text{ }MXN}{1\text{ }USD}\approx1247.98\text{ }MXN[/tex]Hence, 63.64 US dollars were worth 1247.98 Mexican pesos.
f the area of the rhombus below is 232 m 2, and diagonal AC = 16 m, find the length of diagonal BD.
The formula for calculating the area of a rhombus is expressed as
Area = 1/2d1d2
where
d1 and d2 are the lengths of the diagonals
From the information given,
Area = 232
d1 = AC = 16
d2 = BD
Thus,
232 = 1/2 x 16 x BD
232 = 8BD
BD = 232/8
BD = 29
Solve the equation. Round the result to two decimal places when appropriate. [tex] {x}^{6} + 36 = 100[/tex]
Sample proportions of size ten were taken from a group of students. Students were asked if they wore glasses while watching TV. The proportion that wore glasses while watching TV was recorded. The standard deviation of the data is 0.19 The margin of error can be given by the formula Margin ferror = 2 * s/(sqrt(n)) where s is the standard deviation and n is the sample size . What is the margin of error for the data collected ?
Margin of error:
[tex]ME=2\times\frac{s}{\sqrt{n}}[/tex]For the given data collected
[tex]\begin{gathered} s=0.19 \\ n=10 \\ \\ ME=2\times\frac{0.19}{\sqrt{10}}=\frac{0.38}{\sqrt{10}}=0.12 \end{gathered}[/tex]Then, the margin of error is 0.1212) Triangle ABC and A'B'C' are shown on the coordinate plane. Which algebraic representation showshow to find the coordinates of triangle A'B'C'?
x,y) ---------> (2/3x, 2/3y)
1) For that dilation, we always start from the pre-image. In this case, the ABC is the bigger one
So taking one point of that triangle as an example.
C(9,3)
And one of that image
C'( 6,2)
Dilating from C to C' all other points follow that same rule.
2) This leads us to conclude
Pre image Image
(x,y) ---------> (2/3x, 2/3y)
Select from the drop-down menus to correctly complete the statement. The expressions 3.22 1 and 10 – 0.33 . 2 should be joined by
we have the expressions
3.2^2-1=10.24-1=9.24
10-0.33*2=10-0.66=9.34
therefore
should be joined by a not equal sign to form an inequality
so
9.24 < 9.34
9.24 is less than 9.34
I’ve completed the question.
Would you like me to elaborate on any point?
Rajesh invested $30,000 into an account that compounds interest monthly at a rate of 2.16%. He has made arrangements to withdraw $300 automatically every month to pay off his 10-year student loan. Will Rajesh have enough money in the account to cover all of the required loan payments? (Round to the nearest tenth of a year.)
By Evaluating the Compound Interest, we come to know that Rajesh will have enough money in the account to cover all of the required loan payments.
The Principal Amount(P) = $30,000
Rate of Interest (r) = 2.16 %
Time(t) = 10 years
Number of Times it is Compounded in a year(n) = 12
Now, we have
[tex]A =P(1+\frac{r}{100n}) ^{nt}[/tex]
Putting all the values, we evaluate the amount,
[tex]A =30,000(1+\frac{2.16}{100*12}) ^{12*10}\\\\A = 30,000 * 1.240\\A = 37,225.84[/tex]
Hence, the Amount after Compound Interest = $37,225.87
Now, The loan amount that he pays = 300 *12*10 = $ 36,000
Yes, he will have enough money in the account to cover all of the required loan payments.
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Round 2.8962 to the nearest hundredth. Do not write extra zeros.
To round the number
2.8962 to the nearest hundredth
First check the digit whose place value is hundredth
The digit is 9
You will either round it up or down depending on the next digit immediately after it which is called the decider
If the decider is from 0-4 then we round the number down
If the decider is from 5 -9 then we round the number up
The decider is 6 so we are rounding the number up
2.8962 ≈ 2.90 to the nearest hundredth
When the 9 increases to ten, we can't write 10 down so we write 0 and add 1 to 8 which makes it 9
Answer:
9
Step-by-step explanation:
help pls for geometry
Answer:
ohhh that one is hard but i think is ur mom
Step-by-step explanation:
i wanted to wast y0our time but hopefully you get the answet
Determine the direction angle (in degrees) for each vector:• Make sure you're using degrees instead of radians.• If you use a decimal approximation, you must be accurate to at least 3 decimal places.a. (5, 3) has direction angle: 0 =b. (-4,5) has direction angle: 0 =c. (8,-8) has direction angle: 0=d. (-12, -3) has direction angle: 0=
Explanation
a vectors makes a rigth angle to the x-positve axis , so
so, the x coordinate is adjacent side and the y-coordinate becomes into the opposite side, then we can use a trigonometric function that relates those values,it is
[tex]\begin{gathered} tan\theta=\frac{opposi\text{te side}}{adjacent\text{ side}} \\ tan\theta=\frac{y\text{ coordinate}}{x\text{ coordinate}} \end{gathered}[/tex]hence
Step 1
a)
let
[tex]\begin{gathered} \langle5,3\rangle, \\ x=5 \\ y=3 \end{gathered}[/tex]replace and solve for the angle
[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{3}{5} \\ \theta=\tan^{-1}(\frac{3}{5}) \\ \theta=30.964° \end{gathered}[/tex]so,
a)Blank1: 30.964
Step 2
b)
let
[tex]\begin{gathered} \langle-4,5\rangle, \\ x=-4 \\ y=5 \end{gathered}[/tex]replace and solve for the angle
[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{5}{-4} \\ \theta=\tan^{-1}(\frac{5}{-4}) \\ \theta=-51.340\~+180(Iquadrant) \\ \theta=128.660 \\ . \end{gathered}[/tex]so,
b)Blank2:128.660
Step 3
c)
[tex]\begin{gathered} \langle8,-8\rangle, \\ x=8 \\ y=-8 \end{gathered}[/tex]replace and solve for the angle
[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{-8}{8} \\ \theta=\tan^{-1}(-1) \\ \theta=-45 \end{gathered}[/tex]so,
c)Blank3:-45 °
Step 4
d)
[tex]\begin{gathered} \langle-12,-3\rangle, \\ x=-12 \\ y=-3 \end{gathered}[/tex]replace and solve for the angle
[tex]\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=\frac{-3}{-12} \\ \theta=\tan^{-1}(\frac{1}{4}) \\ \theta=14.036 \end{gathered}[/tex]so,
direction
[tex]\begin{gathered} direcgtion\text{ =}\theta+180=14.036 \\ angle=194.036 \end{gathered}[/tex]graph
d)Blank4: 194.036
I hope this helps you
I just need the answer to check my work no explanation needed
To solve for z, we proceed as follows:
[tex](\frac{1}{4})^{3z-1}=16^{z+2}\times64^{z-2}[/tex]Now, we simplify the expression on the right-hand side of the equation as follows:
[tex](\frac{1}{4})^{3z-1}=(4^2)^{z+2}\times(4^3)^{z-2}[/tex][tex](\frac{1}{4})^{3z-1}=4^2^{(z+2)}\times4^3^{(z-2)}[/tex][tex](\frac{1}{4})^{3z-1}=4^{2z+4}\times4^{3z-6}[/tex][tex](\frac{1}{4})^{3z-1}=4^{2z+4+3z-6}[/tex][tex](\frac{1}{4})^{3z-1}=4^{5z-2}[/tex]Now, we simplify the expression on the left-hand side of the equation as follows:
[tex](4^{-1})^{3z-1}=4^{5z-2}[/tex][tex]4^{-1(3z-1)}=4^{5z-2}[/tex][tex]4^{-3z+1}=4^{5z-2}[/tex]Now, since we have both expressions on the left and right hand sides to have a base of 4, we can simply equate their indices, as follow:
[tex]\begin{gathered} 4^{-3z+1}=4^{5z-2} \\ \Rightarrow-3z+1=5z-2 \\ \end{gathered}[/tex]Now, we collect like terms:
[tex]-3z-5z=-2-1[/tex][tex]\begin{gathered} -8z=-3 \\ \Rightarrow z=\frac{-3}{-8} \\ \Rightarrow z=\frac{3}{8} \end{gathered}[/tex]Jenny knit a total of 12 centimeters of scarf over 2 nights. How many nights will Jenny have
to spend knitting in order to knit a total of 18 centimeters of scarf? Assume the relationship is
directly proportional.
As we can assume the relationship is directly proportional, we have to build the proportion and do the cross product. So:
[tex]\begin{gathered} \frac{12cm}{\text{2 nights}}=\frac{18cm}{x\text{ nights}} \\ 12x=2\cdot18 \\ 12x=36 \\ x=\frac{36}{12} \\ x=3 \end{gathered}[/tex]She needs 3 nights
Staples sells folders in packs of 12 for 4.80. Office max sells ffolders in packs of 17 for 7.50. Which has the better deal
The first step is to find the unit price of each seller. We were told that Staples sells folders in packs of 12 for 4.80. It means that the price per folder is
4.80/12 = 0.4 per folder
Also, Office max sells folders in packs of 17 for 7.50. It means that the price per pack is
7.50/17 = 0.44
Since the unit rate of Staples is low, then Staples has the better deal
Find the area of the composite figure below. Round your answer to the tenths.
Answer:
54 square units
Explanation:
First, divide the composite figure into common plane shapes as shown below:
Thus, we have two plane shapes:
• A triangle with a base of 10 units and a height of 6 units.
,• A rectangle with a length of 6 units and a height of 4 units.
Therefore:
[tex]\begin{gathered} \text{ Area of the composite figure}=\text{ Area of the triangle+Area of the rectangle} \\ =\frac{1}{2}bh+lh \\ =(\frac{1}{2}\times10\times6)+(6\times4) \\ =30+24 \\ =54\text{ square units} \end{gathered}[/tex]The area of the composite figure is 54 square units.
Write A formula that tells the amount of bacteria in the bottle.A if we are given the number of minutes ,t that have passed
A formula that tells the amount of bacteria in the bottle is Generation time (G) is defined as the time (t) per generation (n is number of generations).
What is the formula for bacteria?The generation time, which is also the bacterial population's doubling time, is used to express the exponential growth rate of a bacterial culture. The time (t) spent on each generation (n = number of generations) is known as the generation time (G).Therefore, generation time calculations (below) arise from the equation G=t/n.The number of germs after t hours is thus given by the function P(t) = 500e1. 3863t.The beginning rate is equal to the slope of the reactant concentration versus time curve at time zero, which is negative.Model of Exponential Growth P(t)=P0(1+r)t. The initial population is P0.To learn more about Exponential Growth refer to:
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What is the difference in elevation between the highest and lowest bodiesof water listed in the table below? Write an equation to show how youfound your answer."Height Above Sea LevelBody ofElevation(in feet)WaterCaspian Sea92Lake Maracaibo0Lake Superior600Lake Victoria3,720
The highest value is the highest positive integer, which is 3720.
The lowest value is the negative value, -92.
To obtain the difference between the two, subtract -92 from 3720. thus we have the following:
[tex]3720-(-92)[/tex]Add the additive inverse of -92 to 3720.
[tex]3720-(-92)=3720+92=3812[/tex]Rhombus ABCD with vertices A(1,0), B(6,-2), C(8,-7), and D(3,-5); 90° counterclockwise rotation about the origin
Given data:
The given coordinates of Rhombus are A(1,0), B(6,-2), C(8,-7), and D(3,-5).
The coordinate of a point after 90 degrees counterclockwise rotation is,
[tex](x,\text{ y)}\rightarrow(-y,x)[/tex]The final coordinate of Rhombus are,
[tex]\begin{gathered} A(1,0)=A^{\prime}(0,\text{ 1)} \\ B(6,\text{ -2)=B'(2, 6)} \\ C(8,\text{ -7)=C'(7},\text{ 8)} \\ D(3,\text{ -5)=D'(5, 3)} \end{gathered}[/tex]Thus, the final coordinate of Rhombus are A'(0,1), B'(2, 6), C'(7, 8) and D'(5, 3).
I need help if because I’m not sure if I was right or not
A trapezium has only 4 sides. This rules out option A
A trapezium has only one pair of parallel sides.
For option c, it is a parallelogram because it has 2 pairs of parallel sides.
For option d, it has no pair of parallel sides.
Thus, the correct option is B