Answers
Given:
There are given the two systems of the equation:
[tex]\begin{gathered} \frac{3}{5}x+\frac{2}{3}y=1...(1) \\ 18x+20y=30...(2) \end{gathered}[/tex]Explanation:
According to the question:
We need to solve the equation by using the elimination method.
So,
To solve the above equation, we need to perform the elimination method.
So,
[tex]\begin{gathered} 18(\frac{3}{5}x+\frac{2}{3}y=1)=(\frac{54}{5}x+12y=18)...(3) \\ \frac{3}{5}(18x+20y=30)=(\frac{54}{5}x+12y=18)...(4) \end{gathered}[/tex]Then,
We need to subtract equation (3) from equation(4):
Then,
[tex]\begin{gathered} (\frac{54}{5}x+12y=18)-(\frac{54}{5}x+12y=18) \\ 0 \end{gathered}[/tex]Final answer:
Hence, the solution is 0.
Related Questions
I need help with this question please. The ending of the question says: give the leading coefficient.
Answers
Given the polynomial:
[tex]-x^3+10x-4x^5+3x^2+7x^4+14[/tex]You need to remember the following definitions:
- The degree of a polynomial is the highest exponent.
- The Leading Coefficient is the number that multiplies the variable with the highest exponent.
- The Standard Form of a polynomial shows the terms in descending numerical order.
In this case, you can identify that:
1. The highest exponent of the polynomial is 5. Therefore:
[tex]Degree\colon5[/tex]2. The Constant Term is:
[tex]14[/tex]Therefore, you can rewrite it in descending numerical order:
[tex]\begin{gathered} \\ =-4x^5+7x^4-x^3+3x^2+10x+14 \end{gathered}[/tex]Now you can identify that the Leading Coefficient is:
[tex]-4[/tex]Hence, the answer is: Last option.
. When you carry a credit card, it is very easy to buy on impulse.
True
False
Answers
True. It is very easy to buy on impulse when we carry a credit card.
An impulse purchase is a case when we buy goods without any prior plan to do so instantly according to our own whims. This is more often than not done by the use of a credit card.
A credit card is an instrument that allows us to purchase goods/ services by borrowing within a certain limit from the bank.
Since when we use a credit card we do not have to pay instantly, we reason our purchase by a near raise in a job or some profit in business. Also, usually, we need to pay in installments for the items we used the credit for, the amount seems very small.
Therefore, we quickly decide to buy the item that might be unnecessary for us or might be too expensive.
To know more about impulse buying visit
https://brainly.com/question/19351797?referrer=searchResults
There are 5 blue marbles, 2 red marbles, and 3 green marbles in a bag. What is theprobability of selecting NOT a green marble? Your answer can be a fraction, decimalor percent.
Answers
Given
Total marbles 5+2+3 =10
[tex]\begin{gathered} \text{probability of selecting blue=}\frac{5}{10}=\frac{1}{2} \\ \\ \text{porbability of selceting red =}\frac{2}{10}=\frac{1}{5} \\ \text{Probalility of selecting gr}een\text{=}\frac{3}{10} \\ \end{gathered}[/tex]Now probability of NOT selecting green Marble
[tex]\begin{gathered} \text{Probability of selecting NOT gr}een\text{ marbles=1-}\frac{3}{10} \\ \\ \text{Probability of selecting NOT gr}een\text{ marbles=}\frac{1}{1}\text{-}\frac{3}{10} \\ \text{Probability of selecting NOT gr}een\text{ marbles=}\frac{10-3}{10}=\frac{7}{10} \end{gathered}[/tex]Alternatively (second method )
Probability of selecting NOT a green marble means you will be selecting either blue marbles or red marbles
[tex]\text{Probability of selecting NOT a green =}\frac{5}{10}+\frac{2}{10}=\frac{7}{10}[/tex]The final answer
[tex]\begin{gathered} \text{Fraction }\frac{7}{10} \\ \text{Decimal 0.7} \\ \text{Percetages 70\%} \end{gathered}[/tex]
A large bucket of 200 golf balls is divided into 4 smaller buckets. hiw many golf balls are in each small bucke?
Answers
Given:
Number of golf balls in larger bucket, N=200
The larger bucket is divided into 4 smaller buckets
The objective is to find the number of golf balls (x) in the smaller buckets.
The formula to find the smaller bucket is,
What is the reference angle of -139 degrees
Answers
41º
1) Since we want to find the reference angle for a -139º angle, we need to resort to the following formula
[tex]Reference\:Angle\:\:Quadrant\:III=180^{\circ}-139^{\circ}=41^{\circ}[/tex]2) Note that a -139 angle is in quadrant III, since negative angles are clockwise oriented
3) Thus the Reference Angle is 41º
Answer:
41°
Step-by-step explanation:
Find the acute angle in the first quadrant used as a reference for
−139°.
41°
Find the area of the triangle with a = 19, b = 14, c = 19. Round to the nearest tenth.
Answers
In order to find the area of a triangle with 3 sides, we use the Heron's formula which says if a, b, and c are the three sides of a triangle, then its area is,
[tex]\begin{gathered} Area=A=\sqrt[]{S(S-a)(S-b)(S-c)} \\ S=\text{Semiperimeter}=\frac{a+b+c}{2} \end{gathered}[/tex]Given a triangle with a = 19, b = 14, c = 19, the area is as shown below:
[tex]\begin{gathered} S=\frac{19+14+19}{2} \\ S=\frac{52}{2} \\ S=26 \end{gathered}[/tex][tex]\begin{gathered} A=\sqrt[]{S(S-a)(S-b)(S-c)} \\ A=\sqrt[]{26(26-19)(26-14)(26-19)} \\ A=\sqrt[]{26(7)(12)(7)} \\ A=\sqrt[]{15288} \\ A=123.6447 \\ A=123.6(\text{nearest tenth)} \end{gathered}[/tex]Hence, the area of the triangle is 123.6 square unit correct to the nearest tenth
1. Find the roots of x^2 + 5 = -5x
Answers
To find the roots of the equation:
[tex]x^2+5=-5x[/tex]we can use the general formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]First we need to write the equation in the form:
[tex]ax^2+bx+c=0[/tex]Then the equation given takes the form:
[tex]x^2+5x+5=0[/tex]now we identify that a=1, b=5 and c=5. Plugging this values into the general formual we have:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4(1)(5)}}{2(1)} \\ =\frac{-5\pm\sqrt[]{25-20}}{2} \\ =\frac{-5\pm\sqrt[]{5}}{2} \end{gathered}[/tex]Hence the roots are:
[tex]\begin{gathered} x=\frac{-5+\sqrt[]{5}}{2} \\ \text{and} \\ x=\frac{-5-\sqrt[]{5}}{2} \end{gathered}[/tex]what is the value of r?
Answers
Angles TMB and DMG are congruent because they are both vertical angles. Therefore, you would set them equal to each other.
r - 86 = 82
Add 86 on both sides
r = 168
What is the range of the function y=x+5 ?O y2-5O y20O y 15Oy25
Answers
Since the value inside a square root needs to be positive or zero, the minimum value y can assume is 0, wheorn x = -5.
Then, for values of x greater than -5, the values of y increases, towards positive infinity.
The range of a function is all y-values the function can assume.
If the minimum value of the function is y = 0, the range is:
[tex]y\ge0[/tex]Therefore the correct option is the second one.
Vhat type of move takes Figure Ato Figure B? Explainyour reasoning
Answers
Figures A and B appear to be congruent, i.e. they are from equal size.
This is a reflection over the e line.
The image looks like it's a 180º rotation.
Question 11 or 12 whichever u can answer see photo
Answers
Explanation
(11)
[tex]f(t)=\frac{t^2}{t^3+4}[/tex]
the average value of a function is given by:
[tex]average=\frac{F(b)-f(a)}{b-a}[/tex]Step 1
evaluate the function in the given limits
a)t=3
[tex]\begin{gathered} f(t)=\frac{t^2}{t^3+4} \\ f(3)=\frac{3^2}{3^3+4} \\ f(3)=\frac{9}{27+4}=\frac{9}{31} \\ f(3)=\frac{9}{31} \\ so \\ a=3,\text{ f\lparen a\rparen=}\frac{9}{31} \end{gathered}[/tex]b) t= 6
[tex]\begin{gathered} f(t)=\frac{t^2}{t^3+4} \\ f(6)=\frac{6^2}{6^3+4} \\ f(6)=\frac{36}{216+4}=\frac{36}{220}=\frac{18}{110}=\frac{9}{55} \\ f(6)=\frac{9}{55} \\ b=6\text{ and F\lparen b\rparen=}\frac{9}{55} \end{gathered}[/tex]Step 2
now, replace in the formula
[tex]\begin{gathered} average=\frac{F(b)-f(a)}{b-a} \\ average=\frac{\frac{9}{55}-\frac{9}{31}}{6-3} \\ average=\frac{\frac{9}{55}-\frac{9}{31}}{3}=\frac{-\frac{216}{1705}}{\frac{3}{1}}=-\frac{216}{5115} \end{gathered}[/tex].so the answer is
[tex]-\frac{216}{5115}[/tex]I hope this helps you
What are the values of a and b in the exponential function given two points on thegraph?(2, 6400) and (4, 4096)
Answers
Ok, so:
I suppose that the exponential function you mean is this one: y = ae^(bx).
To find a and b, we replace:
6400 = ae^(2b) (1 equation)
4096 = ae^(4b). (2 equation)
We can solve this system as this:
If we find a in the first equation:
a = (6400) / (e^(2b).
Now we replace this fact in equation 2:
4096 = (6400)/e^(2b)) * (e^(4b)).
Simplifying:
4096 = 6400 * e^(2b)
0.64 = e^(2b)
Now, we apply the natural logarithm to both sides:
ln (0.64) = ln(e^(2b)).
This is
ln (0.64) = 2b.
Then, b= ln(0.64)/2. which is approximately -0.22.
Now, we find a if we replace b in any equation:
6400 = ae^(2b)
6400 = ae^(2(-0.22))
6400 = ae^(-0.44))
a = 6400 / e^(-0.44) which is approximately 9937.3
Move numbers to the blanks to rewrite each square root. 2i -2 4i V51 -15 ivs
Answers
To rewrite each square root, factor each number and use one of the properties of roots, this way:
[tex]\sqrt[]{-4}=\sqrt[]{4\cdot-1}=\sqrt[]{4}\cdot\sqrt[]{-1}=2i[/tex][tex]\sqrt[]{-5}=\sqrt[]{5\cdot-1}=\sqrt[]{5}\cdot\sqrt[]{-1}=i\sqrt[]{5}[/tex]The blanks must be filled in with 2i and i sqrt(5) respectively.
reflect the point (2, -4) I very rhe y-axis
Answers
To reflect a point over the y-axis, you have to reverse the sign of the x-coordinate, the y-coordinate remains the same.
For example for a point P with coordinates (x,y) the reflection is
Original point → y-axis reflection
P(x,y) → P'(-x,y)
For the point (2,-4) the reflection over the y-axis is:
(2,-4) → (-2,-4)
Question 3(Multiple Choice Worth 1 points)(08.02 LC)Complete the square to transform the expression x2 – 2x – 2 into the form a(x – h)2 + k.(x - 1)2 + 3(x - 1)2 - 3(x - 2)2 - 3(x - 2)2 + 3
Answers
We need to add and subtract the same number in the expression so we can write it as a square and a constant, as in the following expression:
[tex]a\left(x-h\right)^2+k[/tex]The given expression is:
[tex]x^2-2x-2[/tex]In order to find the number that must be added and subtracted, let's expand the general expression:
[tex]\begin{gathered} a(x-h)^{2}+k \\ \\ a(x^2-2hx+h^2)+k \\ \\ ax^2-2ahx+ah^2+k \end{gathered}[/tex]Comparing the coefficients of the general and the given expression, we have:
[tex]\begin{gathered} x^{2}-2x-2 \\ \\ ax^{2}-2ahx+ah^{2}+k \\ \\ x^2=ax^2\Rightarrow a=1 \\ \\ -2x=-2ahx=2hx\Rightarrow h=1 \\ \\ -2=ah^2+k=1+k\Rightarrow k=-3 \end{gathered}[/tex]So, using a = 1, h = 1, and k = -3, we can write:
[tex]x^2-2x-2=1(x-1)^2-3=(x-1)^2-3[/tex]Notice that we obtain the same result by adding 3-3 to the original expression:
[tex]x^2-2x-2=x^2-2x-2+3-3=(x^2-2x+1)-3=(x-1)^2-3[/tex]Therefore, the answer is:
[tex]\begin{equation*} (x-1)^2-3 \end{equation*}[/tex]quadrilateral ABCD is inscribed in circle O as shown below. which of the following would be used to find the measure of angle 3
Answers
Answer:
180° -m∠1
Explanation:
• Quadrilateral ABCD is a cyclic quadrilateral.
,• The opposite angles of a cyclic quadrilateral add up to 180 degrees.
Therefore:
[tex]\begin{gathered} m\angle3+m\angle1=180\degree \\ \implies m\angle3=180\degree-m\angle1 \end{gathered}[/tex]Therefore, the second option would be used to find the measure of angle 3.
A food company distributes its tomato soup in two cans of different sizes. For the larger can, the diameter has been increased by 10%, and the height remains the same. By what percentage does the volume increase from the small can to the larger can? Round your answer to the nearest percent.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
df ====> do + 10%
height f = height o
% v = ?
Step 02
df = do + 10%
= do(1 + 0.1)
= do (1.1)
V = h π r² = h π ( d /2)²
%V = (Vf - Vo / Vo) * 100
Vf - Vo = h π ( df /2)² - h π ( do /2)²
= ( 1.1 do /2)² - ( do /2)²
= 1.21/ 4 do² - 1/4 do ²
= 0.0525 do ²
% V = (0.0525 do² / do ²) * 100
% V = 5.25 %
The answer is:
Volume increased by 5%.
which expression will be easier to simplify if you use the associative property to change the groupingA.[-12+(-5)]+36B.[21+(-14)]+(-53)C.67+[3/2+(-1/2)]D.(70+30)+72
Answers
The expression:
[21+(-14)]+(-53)
will be easier to simplify using associative property as follows:
21 + [(-14) + (-53)]
So that, the two negative numbers are combined first.
i need help with this question what does y represent?
Answers
In the given graph, we can observe the amount of allowed weight remaining in a given shipment depending on the number of boxes of screws already included.
Then, we can say in the x-axis we have the number of boxes already included and in the y-axis, we have the allowed weight remaining.
So, when x=0, there is any box in the shipment, y=70, so the total allowed weight in the given shipment is 70.
Answer: y reprensents the allowed weight remaining in the shipment.
Find the solution set of this inequality. Select the correct graph
Answers
Given
The inequality,
[tex]|5x-15|<-5[/tex]To find the solution set for this inequality.
Explanation:
It is given that,
The inequality is,
[tex]|5x-15|<-5[/tex]Also, it is known that,
Absolute value cannot be less than 0.
Then, the inequality
[tex]|5x-15|<-5[/tex]has no solution.
Hence, the answer is option A).
can you help me please? im doing practice questions for when school opens next month and this is the answer i got. is this correct?
Answers
Given:
Amount = $3000
Interest rate = 18% per year
A = 3000(1.18)^t
To find:
[tex]\frac{A(12)-A(6)}{12-6}[/tex]Step-by-step solution:
We will now the value in the given expression:
[tex]\begin{gathered} =\frac{A(12)-A(6)}{12-6} \\ \\ =\frac{3000[(1.18)^{12}-(1.18)^6]}{6} \\ \\ =500[7.28-2.69] \\ \\ =500\times4.59 \\ \\ =2294.02 \end{gathered}[/tex]From the above calculation, we can say that the average total amount between t = 6 years to t = 12 years is 2294.02
Thus we can say that Option A is the correct answer.
find the absolute change and the percentage change for the given situation. 128 is increased to 704
Answers
SOLUTION
The absolute change is the difference between the final value and the initial value
[tex]\begin{gathered} \text{Absolute change =final value-initial value } \\ \text{ final value=704} \\ \text{ initial value=128} \end{gathered}[/tex]
I need help with this practice It is trig from my ACT prep guideI will send an additional picture later of my attempted answer of this
Answers
ANSWER
EXPLANATION
Angle α lies in quadrant II, which means that its sine is positive and its cosine is negative.
Angle β lies in quadrant IV, which means that its cosine is positive and its sine is negative,
The cosine of a difference of two angles is,
[tex]undefined[/tex]Use the graph of f(x) below, and the fact that x2 + 3x + 3 is a factor of f(x), to find the equation of the third degreepolynomial f(x), with leading coefficient one.
Answers
Answer:
Explanation:
From the given graph, we see that its x-intercept is 3
This means x - 3 is a factor.
The third degree polynomial is now:
[tex](x^2+3x+3)(x-3)[/tex]This is also written as:
[tex]undefined[/tex]if m is the midpoint of a line XY, find the coordinates of x if m(-3, -1) and Y(-8, 6)
Answers
ANSWER:
X(2, -8)
Given:
m(-3, -1), Y(-8, 6)
To find the coordinates of X, use the midpoint formula below:
[tex](x_{m.}y_m)\text{ = (}\frac{x1+x2}{2},\text{ }\frac{y1+y2}{2})[/tex]Where,
(xm, ym) = (-3, -1)
(x2, y2) = (-8, 6)
Let the coordinates of x be (x1, y1)
Therefore, we have:
[tex]\begin{gathered} x_m\text{ = }\frac{x1+x2}{2} \\ \text{Substitute values to solve for x}1 \\ -3\text{ =}\frac{x1+(-8)}{2} \\ -6\text{ = x1 - 8} \\ x1\text{ = -6 + 8} \\ x1\text{ = 2} \end{gathered}[/tex][tex]\begin{gathered} \text{For y1:} \\ y_m\text{ = }\frac{y1+y2}{2} \\ Substitute\text{ values in the equation to find y1:} \\ -1\text{ = }\frac{y1+6}{2} \\ 2(-1)\text{ = y1 + 6} \\ -2\text{ = y1 + 6} \\ y1\text{ = -6 - 2} \\ y1\text{ = -8} \end{gathered}[/tex]The coordinates of X(x1, y1) = X(2, -8)
Simplify the expression. Answer should be written with positive exponent
Answers
The given expression is
(x^5)^3 * x^5/x^4
We would apply the following rules of exponents
(a^b)^c = a^bc
a^b * a^c = a^(b + c)
a^b / a^c = a^(b - c)
By applying the first rule,
(x^5)^3 becomes x^(5 * 3) = x^15
By applying the third rule,
x^5/x^4 becomes x^(5 - 4) = x^1 = x
The expression becomes
x^15 * x
Finally, we would apply the second rule. The final expression would be
x^(15 + 1)
= x^16
Find the surface area of the pyramid . The surface area of the pyramid is _m2(Do not round until final answer .Then round to the nearest whole number as needed .)
Answers
surface area of the pyramid is
[tex]\begin{gathered} Atotal=Abase+\frac{Pbase\cdot Apothem}{2} \\ \end{gathered}[/tex]then
[tex]\begin{gathered} \text{Abase}=\frac{P\cdot\text{Apothembase}}{2} \\ \text{Abase}=\frac{18\cdot6\cdot9\sqrt[]{3}}{2}=841.77 \end{gathered}[/tex]and the total area is:
[tex]\text{Atotal}=841.77+\frac{6\cdot18\cdot18}{2}=841.77+\frac{1944}{2}=841.77+972=1814[/tex]answer: 1814 m^2
If an employee makes $20.50 an hour and works 80 hours every 2 weeks, what is that employees annual income?
Answers
There are 52 weeks in a year.
The employee works 80 hours every 2 weeks. This means that his weekly hours worked wll be:
[tex]\frac{80}{2}=40\text{ hours per week}[/tex]If he earns $20.50 per hour, his weekly wages will be:
[tex]\Rightarrow20.50\times40=\$820[/tex]For 52 weeks in the year, he will earn:
[tex]52\times820=\$42640[/tex]The employee's annual income is $42,640.
question will be in picture
Answers
The simple interest formula is given by
[tex]A=P\times r\times t[/tex]where A is the future value, P is the initial value (Principal), r is the rate and t is the time. In our case P=1200, r=0.08 and t= 2 years. By substituting these values into our formula, we get
[tex]\begin{gathered} A=1200\times0.08\times2 \\ A=192 \end{gathered}[/tex]then, the answer is option a: $192
Depending on the context of the problem P( A and B) can mean different things, so basically can A and B be different in a probability problem
Answers
Solution
Depending on the context of the Problem P(A and B) can mean different thing
TRUE
When We have a Mutually Exclusive Event
[tex]p(A\cap B)=0[/tex]When we have an Indepedent Event
[tex]p(A\cap B)=p(A)\times p(B)[/tex]Hence, the P(A and B) depend on the context of the problem
This is TRUE