answer: second choice
why?: if muliply with the signs, you would get a negative product for the second choice. when you do it with the others, they come out with a positive product or 0 as the answer.
hope this helps! ❤ from peachimin
4x - y = 6 and 2x - y/2 =4
I don’t get solving equations with variables on both sides word problems. Can someone please help explain it to me because my teacher doesn’t really explain very good
The object of any equation with a variable (whether it is on one side or both) is to isolate the variable. We do this by moving all of the x's to one side of the equation and everything else to the other side.
For example:
3x - 5 = 2x + 1
-2x -2x
x - 5 = 1
+5 +5
x = 6
Now, there are 3 different types of solutions:
1) x = ____ there is one solution
2) 0 = 0 or some other TRUE statement there are infinite solutions because every value for x is a solution
3) 0 = 1 or some other FALSE statement there are no solutions because no value for x will provide a solution
HOPE THIS HELPED!
does anyone know this one
It's A. if a = b, then a^2 = b^2
simplify by combining like terms 8x^2+7xy+5y^2+8x^2-xy+y^2
By combining the like terms; the simplified answer in the correct way is 16x^2+6xy+6y^2
How to get answer:
- Find how many terms are in the algebraic equation. Counting I got 6 terms.
There are 2 xy's and 2 x's and 2y's
- Next combine all like terms
[tex]8x^{2} + 8x^{2} = 16x^{2}[/tex]
7xy+-xy=6xy
[tex]5y^{2} + y^{2}[/tex]=[tex]6y^{2}[/tex]
- Next Simplify
[tex]16x^{2}+6xy+6y^{2}[/tex]
A jar contains 4 green, 5 blue, 1 red, 5 black marbles. Two marbles are drawn from the jar at random without replacement. What is the probability both marbles drawn are blue
5/15 because there are 5 blue marbles and 15 marbles all together.
A line passes through the points (6, 10) and (4, -2).
(a) Find the slope of the line. Show all your work.
(b) Write the equation of the line in point-slope form. Show all your work
(c) Write the equation of the line in slope-intercept form. Show all your work
For this case we have:
Part A:
Point 1: [tex](x1, y1) = (6,10)\\[/tex]
Point 2:[tex](x2, y2) = (4, -2)\\[/tex]
We know that the slope m is given by:
[tex]m = \frac{(y2-y1)}{(x2-x1)}\\\\m = \frac{(- 2-10)}{(4-6)}\\\\m = \frac{(- 12)}{(- 2)}\\[/tex]
[tex]m = 6\\[/tex]
The slope is [tex]m = 6\\[/tex]
Part b:
The equation of the line in point-slope form is given by:
[tex](y-y1) = m (x-x1)\\[/tex]
Substituting the point 1 [tex](x1, y1) = (6,10)[/tex]we have:
[tex](y-10) = 6 (x-6)\\[/tex]
Thus, the point-slope equation is: [tex](y-10) = 6 (x-6)\\[/tex]
Part c:
The equation of the line in slope-intersection form is given by:
[tex]y = mx + b\\[/tex]
Rewriting the equation of part b we have:
[tex]y = 6 (x-6) +10\\\\y = 6x-36 + 10\\\\y = 6x-26\\[/tex]
Thus, the equation of the line in slope-intersection form is
[tex]y = 6x-26\\[/tex]
Answer:
[tex]m = 6\\\\(y-10) = 6 (x-6)\\\\y = 6x-26[/tex]
The table represents a linear function. What is the slope of the function? The graph and choices are attached.
Answer:
The answer is probably 4.
Step-by-step explanation:
Answer:
Option C.
Step-by-step explanation:
The given table represents a linear function.
If a linear is graphed by a line and the line passes through two points (x, y) and (x', y'), slope of the line is calculated by the formula
Slope = [tex]\frac{y-y'}{x-x'}[/tex]
Since line passes through two points (-2, -2) and (-1, 1)
Therefore, slope = [tex]\frac{1+2}{-1+2}[/tex]
= [tex]\frac{3}{1}[/tex]
= 3
Slope of the line will be 3.
Option C. is the answer.
A soda can has a diameter of 6 cm. What is the circumference of the can? (C = πD) A) 1.19 cm B) 9.14 cm C) 18.84 cm D) 28.26 cm
Solution :
Given a soda can has a diameter of 6 cm.
As we know, the circumference of circle with radius r is , [tex]C=2\pi r[/tex].
And diameter of the circle [tex]D = 2r[/tex]
So, the circumference of the circle with diameter D is , [tex]C=\pi D[/tex]
Put D= 6
[tex]\Rightarrow C=6 \pi\\\\Using\: \pi=3.14\\\Rightarrow C=6\times3.14\\\\\Rightarrow C=18.84[/tex]
Hence, the circumference of the can is 18.84 cm. (option C)
If 3/10 = 30/100 than 4/10 = ?/100
I'm pretty sure 4/10=40/100
Here is the equation:
[tex]\frac{3}{10} = \frac{30}{100} \rightarrow \frac{4}{10} =\frac{x}{100}[/tex]
To find the missing number, you have to cross multiply. Here's the equation:
[tex]\frac{4}{10} = \frac{x}{100} \\ \\ 100 \times 4 = 10x[/tex]
Multiply:
[tex]100 \times 4 = 400 \\ 400 = 10x[/tex]
To leave the variable x alone, you need to divide both sides by 10
[tex]\frac{400}{10} = \frac{10x}{10}[/tex]
Divide:
[tex]400 \div 10 = 40 \\ x = 40[/tex]
Your answer is 40
If you have any questions, feel free to ask in the comments! :)
Mr tan invested 5000 Swiss francs(CHf) bank A at a nominal annual interest rate of r% compounded monthly, for four years. The total interest he received was 1866 CHF.
A) calculate value of r
Mr black invested 5000 CHF in a Bank at a nominal annual interest rate of 3.6% compounded quarterly for four years
B)calculate the total interest he received at the end of the four years give your answer two decimal places.
Given : Invested amount = $5000.
Rate of interet = r% compunded monthly.
Number of years = 4 years.
Total interest received = $1866.
Therefore, total amount after 4 years = 5000+1866 = $6866.
We know, formula for compound interest :
[tex]A=P(1+\frac{r}{n})^{t\times n}[/tex], where P is the invested amount, n is the number of monthly installments in an year.
Number of months in an year are 12.
Plugging n=12, P=5000, t=4 in the formula now, we get
[tex]6866=5000{(1+\frac{r}{12})^{12\times 4}[/tex]
[tex]6866=5000{(1+\frac{r}{12})^{48}[/tex]
Dividing both sides by 5000, we get
[tex]\frac{6866}{5000} =\frac{5000}{5000} {(1+\frac{r}{12})^{48}[/tex]
[tex]\frac{6866}{5000} = {(1+\frac{r}{12})^{48}[/tex]
[tex]1.3732= {(1+\frac{r}{12})^{48}[/tex]
Taking 48th root on both sides, we get
[tex]\sqrt[48]{1.3732} = \sqrt[48]{(1+\frac{r}{12})^{48}}[/tex]
[tex]\sqrt[48]{1.3732}=\left(1+\frac{r}{12}\right)[/tex]
[tex]1.00662903758=1+\frac{r}{12}[/tex]
Subtracting 1 from both sides, we get
0.00662903758 = [tex]\frac{r}{12}[/tex]
Multiplying by 12 on both sides, we get
r=0.07954845101
r≈0.0795
Or 7.95%.
A) The value of r is 7.95% compounded monthly.Now, we need to find the interest after four years if the rate of interest is 3.6% compounded quarterly.
There are 4 quarters in an year.
So, n=4 and r=3.6%= 0.036.
Plugging values in compound interest formula now, we get
[tex]A=5000{(1+\frac{0.036}{4})^{4\times 4}[/tex]
[tex]\mathrm{Divide\:the\:numbers:}\:\frac{0.036}{4}=0.009[/tex]
[tex]A=5000\times \:1.009^{16}[/tex]
[tex]A=5000\times \:1.15414\dots[/tex]
[tex]=5770.70222\dots[/tex]
A≈5770.70
Subtracting 5770.70 -5000.00 = 770.70.
B) Therefore, the total interest he received at the end of the four years upto two decimal places is $770.70.(A)
We are given
Mr tan invested 5000 Swiss francs(CHf) bank
so,
[tex]P=5000[/tex]
nominal annual interest rate of r% compounded monthly
so, n=12
t=4
total interest he received was 1866 CHF
I=1866
we can use formula
[tex]I=P(1+\frac{r}{n} )^{nt}-P[/tex]
now, we can plug values
[tex]1866=5000(1+\frac{r}{12} )^{12*4}-5000[/tex]
now, we can solve for r
[tex]r=0.0795[/tex]
so, interest rate is 7.95%..........Answer
(B)
we are given
P=5000
r=0.036
n=4
t=4
so, we can use interest formula
[tex]I=P(1+\frac{r}{n} )^{nt}-P[/tex]
now, we can plug values
[tex]I=5000(1+\frac{0.036}{4} )^{4*4}-5000[/tex]
now, we can simplify it
and we get
[tex]I=770.702[/tex]
The total interest is 771 CHF...........Answer
An employee was hired at a wage of $8 per hour. After a raise, the employee earned $8.75 per hour. What was the percent increase?
I believe 0.75/ 8=0.09375 so 0.09375 is the answer i hope i helped
The percent increase to earned money will be 9.375%.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
An employee was hired at a wage of $8 per hour.
After a raise, the employee earned $8.75 per hour.
Now, The increase percent will be calculate as;
Increase percent in money = Increase money/Actual money x 100
= (8.75 - 8.00) / 8 x 100
= (0.75/8) x 100
= 75/8
= 9.375
Thus, The percent increase to earned money will be 9.375%.
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A city bus company sold 36 one-way tickets and 20 round-trip tickets from West Elmwood to East Elmwood. One-way tickets cost $14. Round trip tickets cost $29. How much money did the bus company collect?
$504 + $580= $1084 is how much the bus company got in all.
Answer:
$1,084
Step-by-step explanation:
Multiply 36 by $14 and you get 504.
Then multiply 20 by $29 an you will get 580.
In order to figure out how much money they collected in total, you should add your two answers together, which will then be 1,084. The bus company collected $1,084
Can you please tell me the answers to all of these
be smart be funny be kind smell good watch tv do homework
The sum of two consecutive intergers is no more than 209 . Whatbis the large of two integers
104 and 105 are consecutive numbers that add up to 209. Maybe this answers your question? Let me know otherwise.
The graph of a linear function is shown which word describes the slope of the line
A slope is also known as the gradient of a line. The slope of the line is positive and is equal to 0.2.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
Since the line is passing through the origin and (5,1). The slope of the line is,
m = (1-0)/(5-0) = 1/5 = 0.2
Hence, the slope of the line is positive and is equal to 0.2.
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The Jones family traveled 314 miles each day until they reached their destination, which is 1,256 miles away from their starting point. How many days did they drive until they arrived at their destination?
Which expression is equivalent to x8 - 256?
A) (x – 2)(x + 2)(x2 + 8)(x4 + 8)
B) (x – 2)(x – 2)(x2 + 4)(x4 + 16)
C) (x – 2)(x + 2)(x2 + 4)(x4 + 16)
D) (x + 2)(x + 2)(x2 + 4)(x4 + 16)
Answer:
C) (x – 2)(x + 2)(x² + 4)(x⁴ + 16)
Step-by-step explanation:
The difference of squares is factored like this:
... a² - b² = (a - b)(a + b)
The given expression is the difference of squares:
... (x⁴)² - (2⁴)²
so can be factored as ...
... (x⁴ - 2⁴)(x⁴ + 2⁴) . . . . . . . 2⁴=16
Once again, the difference term is the difference of squares, so it can be factored as ...
... x⁴ - 2⁴ = (x² -2²)(x² + 2²) . . . . . . 2²=4
And the difference in the first factor is also the difference of squares and can be factored.
... x² -2² = (x - 2)(x + 2)
Putting each factorization in its place in the whole expression, we get
... x⁸ - 256 = (x - 2)(x + 2)(x² +4)(x⁴ +16)
Ms.Thomas ordered 5 pencil packs, n notebooks, and 5 sets of markers. Write and algebraic expression that represents the cost of ms.Thomas’s order. Pencil pack: $1.50. Notebook: $2.
Markers: $2.50
5(1.50)+5(2.50)+2n
or
7.5+12.5+2n
20+2n= Cost
The algebraic expression for the cost of Ms. Thomas's order is:
$2n + $20
How to solve Algebra word problems?Ms. Thomas ordered 5 pencil packs, n notebooks, and 5 sets of markers. We are asked to write an algebraic expression that represents the cost of Ms. Thomas's order. The cost of each item is given as follows:
Pencil pack: $1.50
Notebook: $2
Markers: $2.50
To write an algebraic expression for the cost of Ms. Thomas's order, we need to multiply the cost of each item by the number of items ordered, and then add the products together.
The cost of 5 pencil packs is 5 x $1.50 = $7.50.
The cost of n notebooks is n x $2 = $2n.
The cost of 5 sets of markers is 5 x $2.50 = $12.50.
Therefore, the algebraic expression for the cost of Ms. Thomas's order is:
$7.50 + $2n + $12.50
Simplifying this expression, we get:
$2n + $20
Therefore, the algebraic expression for the cost of Ms. Thomas's order is $2n + $20
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K=5r-s you are solving for r
K= = 5r -s
subtract s from both sides
K + s = 5r
divide 5 from both sides
r = K + s / 5
Which is a benefit of investing? A. not having to work to earn money B. living comfortably after you retire C. spending lavishly now and living off investments later
I would say the answer would be B. or C.
not sure which but i hope i helped narrow it down..
Answer:
Its B
Step-by-step explanation:
researchers asked 250 families whether or not they were homeowners and how many cars they had. 20 were homeowners with no car or one car. 90 with two or more cars. 50 not homeowner with no car or one car. 90 with two or more cars
can you give more detail
Suppose an average book in the library is 0.02 meter thick . How many meters of shelf space are needed for all 14,650 books ?
The answer is 293 meters because you multiply the 14650 books by how thick they are which is 0.02, and that should reveal your answer. Hope this helps!
During one winter snow storm in Denver Colorado Jesse noted that 16 inches of snow fell in 5 1/3 hours what was the rate of snowfall in one hour
Answer:
3 inches/hour
Step-by-step explanation:
During one winter snow storm in Denver Colorado Jesse noted that 16 inches of snow fell in [tex]5\frac{1}{3}[/tex] hours = [tex]\frac{16}{3}[/tex] hours
the snow fell in [tex]\frac{16}{3}[/tex] hours = 16 inches
snow fell in 1 hour = [tex]\frac{16}{\frac{16}{3}}[/tex]
= [tex]\frac{16\times 3}{16}[/tex]
= [tex]\frac{48}{16}[/tex]
= 3 inches
The rate of snowfall would be 3 inches/hour.
Each team in a soccer league has 43 players on it. There are 24 teams in the league. How many total players are in the league? A) 168 B) 258 C) 812 D) 1,032
The answer to your question is,
D) 1,032
-Mabel <3
Option D. 1,032 , would be correct.
Here we can use key words to help us realize, if we are adding, subtracting, multiplying or dividing.
In this case, we know we will be dividing or multiplying because of the word ¨each¨. It might be division, but in the last sentence it asks ¨how many total¨ so we know it will be multiplication.
Therefore...
24 × 43 = 1,032
There are 1,032 total players in the league.
Please help I’m so confused (picture has question)
Answer:
C.
Step-by-step explanation:
all you do is go look and see which one is in the exact same spot
C
ΔABC and ΔGHI are congruent by SAS
AB = GI , the included angles ∠B = ∠I and BC = HI
the formula to find the volume of a sphere is v=4/3 pie r ^3 where r is the radius of the sphere . what is the formula in terms of r
r = [tex]\sqrt[3]{\frac{3V}{4\pi } }[/tex
given [\frac{4}{3}[/tex]πr³ = V ( multiply both sides by 3 to eliminate fraction )
4πr³ = 3V ( divide both sides by 4π )
r³ = [tex]\frac{3V}{4\pi }[/tex] ( take the cube root of both sides )
r = [tex]\sqrt[3]{\frac{3V}{4\pi } }[/tex]
A total of 812 tickets were sold for the school play. They were either adult tickets or student tickets. There were 62 more student tickets sold than adult tickets. How many adult tickets were sold?
A total of 812 tickets were sold for the school play. 375 adult tickets were sold.
Let's assume the number of adult tickets sold is "A" and the number of student tickets sold is "S."
We are given two pieces of information:
The total number of tickets sold is 812:
A + S = 812
There were 62 more student tickets sold than adult tickets:
S = A + 62
Now, we can set up a system of equations to represent the given information:
A + S = 812
S = A + 62
Now, we can solve the system of equations to find the values of A and S.
Substitute equation (2) into equation (1):
A + (A + 62) = 812
Combine like terms:
2A + 62 = 812
Subtract 62 from both sides:
2A = 812 - 62
2A = 750
Now, divide by 2 to solve for A:
A = 750 / 2
A = 375
So, 375 adult tickets were sold.
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Final answer:
375 adult tickets were sold.
Explanation:
Let's denote the number of adult tickets sold as x. According to the information provided, there were 62 more student tickets sold than adult tickets. So, the number of student tickets sold can be represented as x + 62.
Since a total of 812 tickets were sold, we can write the equation x + (x + 62) = 812. This equation represents the sum of adult tickets and student tickets being equal to the total tickets sold.
Solving this equation, we have 2x + 62 = 812. Subtracting 62 from both sides, we get 2x = 750. Then, dividing both sides by 2, we find that x = 375. Therefore, 375 adult tickets were sold.
use the diagram to answer the question. Fill in the blank for the letter given with the missing reason in the flow
I do not know what diagram that you are talking about, but it might be the one that I am thinking, so if this is the questions on your page, then let me know.
A - Vertex angles
B - 5 is congruent to 4
C - 5 and 4 are alternate interior angles, or Z angles
P and R are parrallel.
Hope I helped.
As per given information: m∠5 = 40° and m∠2 = 140°. It then uses the theorems that supplementary angles are congruent and that if two same-side interior angles are congruent, then the lines are parallel, to conclude that a || b.
The proof begins with the givens: m∠5 = 40° and m∠2 = 140°. From this, we can conclude that ∠5 and ∠2 are supplementary angles (since their measures add up to 180°).
We also know that ∠5 and ∠2 are same-side interior angles (since they are both on the same side of the transversal and inside the two lines).
Now, we can use the following theorems to complete the proof:
Theorem 1: Supplementary angles are congruent.
Theorem 2: If two same-side interior angles are congruent, then the lines are parallel.
Proof:
Given: m∠5 = 40° and m∠2 = 140°
∠5 and ∠2 are supplementary angles. (Theorem 1)
∠5 and ∠2 are same-side interior angles.
If two same-side interior angles are congruent, then the lines are parallel. (Theorem 2)
Therefore, a || b.
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What is the domain range and zeros of the graph ?
The domain is how far the graph stretches horizontally (on the x-axis).
Domain: ( -∞ , ∞ ) or -∞ < x < ∞
The range is how long the graph stretched vertically (on the y-axis).
Range: ( -∞ , 2 ] or -∞ < y ≤ 2
The zeros are where the graph intersects with the x-axis. In other words, the x-values when y=0.
Zeros: x = -1 and x = 3
Consider parallel lines cut by a transversal. Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.
Answer:
Corresponding angle theorem, vertical angle theorem, and the transitive property of congruence.
Step-by-step explanation:
Considering a set of parallel lines cut by a transversal. (Refer the attached image).
Now that lines J and K are parallel, then by "corresponding angle theorem"
[tex]\angle 1=\angle 5[/tex]
By "vertical angle theorem"
[tex]\angle 5 = \angle 7[/tex]
Using, "transitive property of congruence"
[tex]\angle 1 = \angle 7[/tex]
And that is our required proof. In this whole proof we have used "corresponding angle theorem", "vertical angle theorem", and the "transitive property of congruence".
Angles between a transversal line and parallel lines are congruent based on vertical angle theorem, corresponding angles and transitive property.
I will use the attached figure to explain the congruence of the angles.
Corresponding Angles Theorem
From the attached figure, the following angles are congruent based on corresponding angle theorem
[tex]\angle 2 = \angle 6[/tex]
[tex]\angle 1 = \angle 5[/tex]
[tex]\angle 4 = \angle 8[/tex]
[tex]\angle 3 = \angle 7[/tex]
Vertical Angle Theorem
From the attached figure, the following angles are congruent based on vertical angle theorems
[tex]\angle 2 = \angle 3[/tex]
[tex]\angle 1 = \angle 4[/tex]
[tex]\angle 5 = \angle 8[/tex]
[tex]\angle 6 = \angle 7[/tex]
Transitive Property
From the attached figure, the following angles are congruent based on transitive property
[tex]\angle 1 = \angle 7[/tex]
[tex]\angle 4 = \angle 6[/tex]
[tex]\angle 5 = \angle 3[/tex]
[tex]\angle 2 = \angle 8[/tex]
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