Answers
6a+10 = 3a+ 55
6(15) + 10 = 3(15) + 55
6x 15 = 90 + 10 = 100
3 x 15 = 45 + 55 = 100
hope this helps
Related Questions
The table below shows four systems of equations: System 1 System 2 System 3 System 4 4x − 5y = 2 3x − y = 8 4x − 5y = 2 10x − 7y = 18 4x − 5y = 2 3x − 8y = 4 4x − 5y = 2 10x + 3y = 15 Which pair of systems will have the same solution?
Answers
Answer:
System 1 and System 2 are equivalent.Step-by-step explanation:
The first and second system have the same solutions, the are equivalent systems of equations. Let's calculate solutions to demonstrate it:
System 1.[tex]\left \{ {{4x - 5y = 2} \atop { 3x - y = 8}} \right.[/tex]
If we multiply the second equations by -5, we can eliminate one variable and find the first solution:
[tex]\left \{ {{4x - 5y = 2} \atop { -15x +5y = -40}} \right.\\-11x=-38\\x=\frac{38}{11}[/tex]
Now, we use this value to find the other solution:
[tex]3x - y = 8\\3(\frac{38}{11})-y=8\\\frac{114}{11}-8=y\\ y=\frac{114-88}{11}=\frac{26}{11}[/tex]
The solution of the first system is [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]
System 2.[tex]\left \{ {{4x - 5y = 2} \atop { 10x - 7y = 18}} \right.[/tex]
We do the same process than we did before, but this time we have to multiply by [tex]-\frac{5}{7}[/tex]:
[tex]\left \{ {{4x - 5y = 2} \atop { -\frac{50}{7}x + 5y = \frac{90}{7} }} \right.\\\frac{28x-50x}{7}=\frac{-90+14}{7}\\-22x=-76\\x=\frac{38}{11}[/tex]
Then,
[tex]4x - 5y = 2\\4(\frac{38}{11})-5y=2\\\frac{152}{11}-2=5y\\ 5y=\frac{152-22}{11}\\y=\frac{130}{5(11)}=\frac{26}{11}[/tex]
The solution of the second system is [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]
Therefore, system 1 and system 2 are equivalent.
if a mixture of a 6% acid solution with an 11% acid solution is to be made, how much of each solution is needed to make 10 liters of an 8% acid solution
Answers
y - 11%
We need 10 liters of 8%.
A) x + y = 10
B) .06x + .11y = (10 * .08)
Multiplying equation A by -.06
A) -.06x + -.06y = -.6 Then adding this to B)
B) .06x + .11y = (10 * .08)
.05y = .2
y = 4 liters of 6%
x = 6 liters of 11%
the following table:
| Amount Part Total
-------------------|-------------------------------------------------------------------
1st Item | x 6% 0.06x
-------------------|--------------------------------------------------------------------
2nd Item | y 11% 0.11y
-------------------|-------------------------------------------------------------------
TOTAL | (x + y) =10 8% 0.08(10 =0.8)
(a) (b)
a) x + y =10
b) 0.06x +0.11y = 0.8
Solving this equation gives x = 6 and y = 4, in other terms:
x = 6 at 6% and y = 4 at 11%
Complete the multiplication: AB.
A.
B.
C.
D.
Answers
x+3y=5
2x+y=1
x+y=10
In matrix form that would be
[tex] \left[\begin{array}{ccc}1&3&5\\2&1&1\\1&1&10\end{array}\right] [/tex]
where the first column are the coefficients of x, the second column the coefficients of y and the third column is the constants, When you multiple matrices, just multiply the same number on the same column number and the same row number. For this problem, the solution is
[tex] \left[\begin{array}{ccc}3*2&0*8\\2*0.6&-1*3\end{array}\right] = \left[\begin{array}{ccc}6&0\\1.2&-3\end{array}\right] [/tex]
Please solve. best answer gets rewarded! show step by step.
Answers
Let's write the problem.
[tex]2x-4-5x=2[/tex]
Add like terms...
[tex]-3x-4=2[/tex]
Add [tex]4[/tex] to both sides.
[tex]-3x-4+4=2+4[/tex]
[tex]-3x=6[/tex]
Divide both sides by [tex]-3[/tex].
[tex]\frac{-3x}{-3}=\frac{6}{-3}[/tex]
Our final answer would be,
[tex]x=-2[/tex]
Thanks!
-TetraFish
2x -5x= -3x
-4-3x= 2
+4 +4
------------
-3x = 6
------------------
-3 -3
x = -2
f={(x,y)| y=x+3} find f(3.6) & f(-0.2)
Answers
f(3.6)=3.6+3=6.6
f(-0.2)=-0.2+3=2.8
A jet flies at a rate of 1.3 x 10^ 6 feet per hour. Written in scientific notation, which is the best estimate of how many feet the jet will travel in 2.8 x 10^ 3 hours?
Answers
(1.3*2.8)(10^6*10^3)
Rule (a^b)(a^c)=a^(b+c)
(3.64)(10^(6+3))
3.64(10^9)
3.64X10^9 ft
Technically we only had two significant figures and the answer should be:
3.6X10^9 if we were to express our answer to the correct number of significant figures....
3.64 * 10^9 <==
What is the distance between -14 and 5
Answers
|-14 - 5| = |-19| = 19
So, the distance between -14 and 5 is 19 units.
What is the area of the triangle given below?
Answers
Answer:
26 sq. units
Step-by-step explanation:
a-p-e-x
The area of the triangle is 26 sq.unit, the correct option is B.
What is a Triangle?A triangle is a polygon with three sides, angles and vertices.
The triangle is classified into various types on the basis of the angle and on the basis of the equality of the length of the sides, as obtuse , acute and right angled triangle and scalene, isosceles and equilateral triangle.
The triangle is shown in the figure has side 13 and height 4 units.
The area of the triangle whose base and height is given is calculated by using the formula:
Area = (1/2) * base * height
Substituting the value in the formula.
Area = (1/2) * 13 *4
Area = 13 * 2
Area = 26 sq.unit
To know more about Triangle
https://brainly.com/question/2773823
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A gutter at the edge of a roof drops 2 inches for every 30 feet of length. The measure of the angle to the nearest tenth of a degree that the gutter makes with the roof is ____ degrees. (Enter only the number.)
Answers
so 1 in=1/12 ft,
this means 2 in=2/12=0.1667 ft.
check the picture,
let the black line segment represent 30 ft of the roof, the blue line segment represent the gutter.
let α be the angle formed by the roof and the gutter.
tan α =(opposite side)/(adjacent side)= 0,1667/30=0.00556
then, α=arctan(0.00556)=0.39 (degrees)
the last result is found using a scientific calculator or other software.
Answer: 0.39 (degrees)
Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit.
Select all that apply.
1 (0,0)
2 (9.2, 1.5)
3 (9.6, 3.5)
4 (5.3, 9.8)
5 (3.5, 9.6)
Answers
Inputing these equation to the last two columns yield the values shown in the picture.The 'NUM' means that the equation at that value of x is undefined. From the values, the correct solution would be
(0,0), (9.2,1.5) and (9.6,3.5) to the f(x) equation
(9.6,3.5) to the g(x) equation
Final answer:
To approximate solutions for the system of equations, enter them into graphing technology, look for intersection points, and match them to the provided coordinates, rounding to the nearest tenth.
Explanation:
To approximate the solution(s) to the system of equations using technology, such as a graphing calculator or graphing software, you typically enter the equations into the device or program and view their intersection points. These intersection points represent the solutions to the system of equations. To get an accurate approximation to the nearest tenth of a unit, you may zoom in on the graph to clearly see where the lines intersect or use the device's built-in features to find the intersection.
You would then compare the given coordinates to the intersection points you found graphically and select the ones that match:
(0,0)
(9.2, 1.5)
(9.6, 3.5)
(5.3, 9.8)
(3.5, 9.6)
Remember to round your values to the nearest tenth as required and to quickly check if these values make sense in the context of the original problem.
John intends to roll a six-sided number cube 100 times. What probability model can he use to predict whether or not each roll will give a result that is a prime number?
Each roll has a 0.117 probability of being prime.
Each roll has a 0.333 probability of being prime.
Each roll has a 0.5 probability of being prime.
Each roll has a 0.667 probability of being prime.
Answers
2 , 3 and 5 are the prime numbers on a cube
so 3/6 = 0.5 probability
Answer:
0.5 sorry for same answer just want points T-T
Step-by-step explanation:
the answer to the triangle the hexagon and the Diamond
Answers
Diamond=3
Hex=7
Proofs:
1+3+3=7
1+1+1=3
1+3+7=11
7-3=4*1
how to calculate the volume of a equilateral triangular prism
Answers
Answer:
I believe the answer would be "Multiply the area of the triangular base by the prism’s height." i'm not sure tho
Step-by-step explanation:
you can correct me if im wrong
Three subtracted from x is less than or equal to -17
Answers
1/4 is to 1 1/4 as 2 is to b
what is b equal to?
Answers
1 1/4 is 5 times larger than 1 /4
so b is 5 times larger than 2
5*2 =10
so 1/4 is to 1 1/4 as 2 is to 10
b=10
At a grocery store, an uncooked beef roast is on sale for $4.99/lb. At the same store, prepared roast beef is at the deli for $2.99/100g. How many times more expensive is the deli roast compared to the uncooked roast?
Answers
cost of 100g=0.221lb is $2.99
cost of 1 lb will therefore be:
1/0.221*2.99
=$13.53/lb
therefore the number of times more expensive the deli roast is compared to uncooked roast is:
[price of 1lb roasted meat]/[price of 1 lb uncooked meat]
=13.53/4.99
=2.7 times
what is the value of y?
Answers
2y + 60 = 180
2y = 120
y = 60
answer.
D. 60
Answer:
The correct option is D) 60°
Step-by-step explanation:
Consider the provided triangle.
From the provided figure it is given that one angle is 60° and we need to find the value of y.
As we know the sum of all interior angle in a triangle is 180°.
y°+y°+60°=180°
Now solve the above equation to find the value of y.
2y°+60°=180°
2y°=180°-60°
2y°=120°
y°=120°÷2
y°=60°
Hence, the value of y is 60°.
Thus, the correct option is D) 60°
What is the solution to the system of linear equations?
Answers
The point of intersection of lines represents the common solution of the system of linear equations. The solution of linear equations given in the graph is (0,2).
Linear equation represents a line on the graph. The system of linear equations represents couple/s of linear equations or lines.
The solution of system of linear equations means the common point satisfying the different linear equations.
Graphically, the point of intersection of two lines represents the common solution of these two lines or simply the solution of the system of linear equations.
So, the point of intersection from the given graph is (0,2).
Therefore, the solution of linear equations given in the graph is (0,2).
For more details, refer to the link:
https://brainly.com/question/16515610
What is the solution to this system of linear equations?
x − 3y = −2
x + 3y = 16
Answers
B) x + 3y = 16
Adding the equations we get
2x = 14
x = 7
y = 3
Answer:
the correct answer is A 7,3
Step-by-step explanation:
hope this helps
When combining functions, what operation requires that you restrict the domain of one or both functions?
Answers
simplify (2 (radical 5) - 4) (3 (radical 5) +2)
Answers
Pick the geometric term that matches the real-word object: a lip-gloss tube.
Answers
Answer: Cylinder.
Step-by-step explanation: Lip-gloss tubes may have different shapes, but the usual form of a lip-gloss tube is, as the name says, a tube.
This means that it has a circular base and a circular top, and a given height that connects the base and the top, the geometrical shape that has this shape is called a cylinder.
The cost of a service call to fix a washing machine can be expressed by the linear function y = 45x + 35, where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent?
the cost for each hour it takes to repair the machine
the cost for coming to look at the machine
the total cost for fixing the washing machine
the amount of time that it takes to arrive at the home to make the repairs
Answers
Answer:
A
Step-by-step explanation:
What is the value of theta , if tan theta = -1/squareroot3
Answers
make sure your calculator is in Degree mode, if you need the angle in degrees, or Radian mode if you need the radian.
Solve the triangle. B=36 a=41 c=20
Answers
In the triangle with B = 36°, a = 41, c = 20, b ≈ 45.3, C ≈ 29.5, A ≈ 114.5.
To solve the triangle, we can use the Law of Sines and the fact that the sum of angles in a triangle is 180 degrees.
Given:
[tex]- Angle \( B = 36° \)[/tex]
[tex]- Side \( a = 41 \)[/tex]
[tex]- Side \( c = 20 \)[/tex]
First, we need to find angle [tex]\( A \)[/tex]. We can use the fact that the sum of angles in a triangle is 180 degrees:
[tex]\[ A = 180 - B - C \][/tex]
We can find angle [tex]\( C \)[/tex] using the Law of Sines:
[tex]\[ \frac{\sin C}{c} = \frac{\sin B}{b} \][/tex]
Solving for [tex]\( C \):[/tex]
[tex]\[ \sin C = \frac{c \times \sin B}{b} \][/tex]
[tex]\[ \sin C = \frac{20 \times \sin 36°}{b} \][/tex]
[tex]\[ \sin C = \frac{20 \times 0.5878}{b} \][/tex]
[tex]\[ \sin C = \frac{11.756}{b} \][/tex]
Now we can find angle [tex]\( C \)[/tex] using the inverse sine function:
[tex]\[ C = \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
Now, we can substitute [tex]\( C \) i[/tex]nto the equation for [tex]\( A \)[/tex] and solve for [tex]\( b \):[/tex]
[tex]\[ A = 180 - B - C \][/tex]
[tex]\[ A = 180 - 36 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
[tex]\[ A = 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
Since we know all three angles of the triangle, we can find [tex]\( b \)[/tex] using the Law of Sines again:
[tex]\[ \frac{\sin A}{a} = \frac{\sin B}{b} \][/tex]
[tex]\[ \sin A = \frac{a \times \sin B}{b} \][/tex]
[tex]\[ \sin A = \frac{41 \times \sin 36}{b} \][/tex]
[tex]\[ \sin A = \frac{41 \times 0.5878}{b} \][/tex]
[tex]\[ \sin A = \frac{24.0678}{b} \][/tex]
Now, we can find [tex]\( b \)[/tex] using the inverse sine function:
[tex]\[ b = \frac{24.0678}{\sin A} \][/tex]
Finally, we'll use the given values and calculate the closest option:
[tex]\[ A \approx 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
[tex]\[ b \approx \frac{24.0678}{\sin A} \][/tex]
[tex]\[ c \approx 20 \][/tex]
B = 36°
[tex]\[ a = 41 \][/tex]
After the calculation, the closest option is:
[tex]\[ b \approx 45.3, \ C \approx 29.5, \ A \approx 114.5 \][/tex]
Complete Question:
Solve the triangle.
B = 36°, a = 41, c = 20
choices:
b ≈ 27.5, C ≈ 115.5, A ≈ 28.5
b ≈ 45.3, C ≈ 25.5, A ≈ 118.5
b ≈ 45.3, C ≈ 29.5, A ≈ 114.5
b ≈ 27.5, C ≈ 25.5, A ≈ 118.5
mary and jolene are both growing tomatoes in thier backyards to sell.jolene had 3 times as many as mary.but birds had eaten 6 before she picked them all.for the season they have a total of 54 tomotoes.how many did mary grow?
Answers
Mary grew 15 tomatoes. A simple algebraic equation was formulated and solved to determine the quantity: m + 3m - 6 = 54, where m represents the number of tomatoes grown by Mary.
Given that Jolene had 3 times as many tomatoes as Mary and birds ate 6 of Jolene's tomatoes, and together they have 54 tomatoes, we need to set up an equation to solve for the number of tomatoes Mary grew.
Let's denote the number of tomatoes Mary grew as m. Therefore, Jolene grew 3m tomatoes. Since birds ate 6 of Jolene's tomatoes, we have 3m - 6 for the number of tomatoes left with Jolene. The equation representing the total number of tomatoes then becomes m (Mary's tomatoes) + (3m - 6) (Jolene's remaining tomatoes) = 54. Simplifying this equation:
m + 3m - 6 = 54
4m - 6 = 54
4m = 60
m = 15
Therefore, Mary grew 15 tomatoes.
What is the approximate measure of acute ∠A when cosA=0.1045cosA=0.1045? Make sure your calculator is in degree mode. Round to the nearest degree.
Answers
To find the acute angle A when cosA=0.1045, use a calculator in degree mode to perform the inverse cosine operation and round the result to the nearest degree, which is approximately 84 degrees.
Explanation:To find the measure of acute ">∠A when cosA=0.1045, we use the inverse cosine function (also known as arccos or cos-1). Make sure your calculator is in degree mode. The approximate measure of acute ∠A can be calculated as follows:
Enter the value 0.1045 into the calculator.Press the inverse cosine button (often labeled as cos-1, acos, or similar) to find the angle whose cosine is 0.1045.Round the result to the nearest degree.Using a calculator set to degree mode, the result for cos-1(0.1045) should be approximately 84 degrees, when rounded to the nearest whole degree.
Find the missing term. If y = 1 + i, then y3 − 3y2 + (-3y) (-3y + 1) (3y) (3i ) − 1 = -i .
Answers
-3-4i = -3(1+i) - i
So we have to add 3(1+i) to get to -i.
3(1+i) = 3y, so 3y is the answer.
Answer:3y is the answer
Step-by-step explanation:
The cost of a long-distance phone call is $0.46 for the first minute and $0.37 for each additional minute. if the total charge for a long-distance call is $6.75, how many minutes was the call?
Answers
1st minute = 0.46
additional minutes = 0.37
6.75 -0.46 = 6.29
6.29/0.37 =17
17 +1 = 18 total minutes
Which coordinates will best represent point B'?