Answer:
Option C
Step-by-step explanation:
x - 3 = 0
Add 3 to both sides;
x = 3
x + 2 = 0
Subtract 2 from both sides;
x = -2
x - 2 = 0
Add 2 to both sides;
x = 2
which of the following equations is equivalent to y=lnx?
a. y=e^x
b. x=e^y
c. x=y^e
d. y=x^e
Answer:
B. x=e^y
Step-by-step explanation:
Took the quiz.
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is B.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given the expression y=ln(x). Therefore, if we simplify the expression then we can write,
y = ln (x)
Taking anti-log,
x = e^y
Hence, the correct option is B.
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PLEASEE HELP ILL GIVE BRAINLIEST!!
Answer:
V
Step-by-step explanation:
a= 1/2bh
b= 12in
a= 54^2in
Answer:
h=9
Step-by-step explanation:
54=1/2(12)h
54=6h
9=h
Tyler and Han are trying to solve this system by substitution: x+3y=-5 9x+3y=3 Tyler's first step is to isolate x in the first equation to get x=-5-3y. Han's first step is to isolate 3y in the first equation to get 3y=-5-x. Show that both first steps can be used to solve the system and will yield the same solution.
Answer:
Yes, they can both be solved and get the same answer.
Step-by-step explanation:
Tyler's way:
Since Tyler solved first by isolating x, resulting in x=-5-3y, he can then go and look at the second equation and solve for y there. In the second equation you're going to want to subtract 9x from the right side and left side to then get 3y=3-9x. Now you're going to divide by 3 on both sides to isolate y. You'll get y=1-3x. Now we know what y equals. Plug that back into the first equation and you'll get x=-5-3(1-3x). Use the distributive property to simplify that and you'll get x=-5-3+9x. That simplified is x=-8+9x. Add 8 on both sides and you'll get 8+x=9x. Subtract x from the both sides and you'll get 8=8x. Divide by 8 on both sides and you'll get the final answer: 1=x, or x=1.
Han's way:
Since Han solved first by isolating 3y, resulting in 3y=-5-x, he can then go and look at the second equation and solve for y there. In the second equation you're going to want to subtract 9x from the right side and left side to then get 3y=3-9x. Now you're going to divide by 3 on both sides to isolate y. You'll get y=1-3x. Now we know what y equals. Plug that back into the first equation and you'll get 3(1-3x)=-5-x. Use the distributive property to simplify that and you'll get 3-9x=-5-x. Add 9x to both sides and you'll get 3=-5+8x. Add 5 to both sides to isolate 8x and you'll get 8=8x. Divide by 8 on both sides and you'll get the final answer: 1=x, or x=1.
Determine if both first steps can be used to solve the system and will yield the same solution
Both Tyler and Han's first step can be used to solve the system and will yield the same solution
Given:
x + 3y = -5
x + 3y = -5 9x + 3y = 3
Tyler
isolate x in the first equation to get
x = -5 - 3y
substitute into second equation
9x + 3y = 3
9( -5 - 3y) + 3y = 3
-45 - 27y + 3y = 3
- 24y = 3 + 45
-24y = 48
y = 48/-24
y = -2
Recall,
x = -5 - 3y
= -5 - 3(-2)
= -5 + 6
x = 1
Han:
isolate 3y in the first equation to get
3y = - 5 - x
substitute into second equation
9x + 3y = 3
9x + (-5 - x) = 3
9x -5 - x = 3
8x = 3 + 5
8x = 8
x = 1
Recall,
3y = - 5 - x
3y = -5 - (1)
3y = -5 - 1
3y = - 6
y = -2
Therefore, both first steps can be used to solve the system and will yield the same solution.
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Determine if both first steps can be used to solve the system and will yield the same solution
Both Tyler and Han's first step can be used to solve the system and will yield the same solution
Given:
x + 3y = -5
x + 3y = -5 9x + 3y = 3
Tyler
isolate x in the first equation to get
x = -5 - 3y
substitute into second equation
9x + 3y = 3
9( -5 - 3y) + 3y = 3
-45 - 27y + 3y = 3
- 24y = 3 + 45
-24y = 48
y = 48/-24
y = -2
Recall,
x = -5 - 3y
= -5 - 3(-2)
= -5 + 6
x = 1
Han:
isolate 3y in the first equation to get
3y = - 5 - x
substitute into second equation
9x + 3y = 3
9x + (-5 - x) = 3
9x -5 - x = 3
8x = 3 + 5
8x = 8
x = 1
Recall,
3y = - 5 - x
3y = -5 - (1)
3y = -5 - 1
3y = - 6
y = -2
Therefore, both first steps can be used to solve the system and will yield the same solution.
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What is the unit rate of 92 dollars for 2 video games
Answer:
It is $46 per video game because 92 divided by 2 is 46.
Step-by-step explanation:
Marlene expects her gross income to be $54,000 this year, and she expects her required deductions to amount to $15,000. Her employer covers 90% of the cost of a $4800-per-year health insurance plan and 80% of the cost of a $900-per-year life insurance plan, with the remainder of the cost coming out of Marlene's pay, and Marlene also expects to contribute 8% of her gross income this year to her 401(k) plan. She wants to calculate how much she will receive for each of her bimonthly paychecks.
Answer:
Marlene will receive $1,417.50 for each of her bimonthly paychecks.
Step-by-step explanation:
This can be calculated using the following 3 steps:
Step 1: Calculation of annual deductions to bear by Marlene
Required deductions = $15,000
Contribution to cost of health insurance plan per-year = $4800 * 10% = $480
Contribution to cost of life insurance plan per-year = $900 * 20% = $180
Contribution to this year's 401(k) plan = $54,000 * 8% = $4,320
Step 2: Calculation of annual paychecks
Annual paychecks = Gross income - Required deductions - Contribution to cost of health insurance plan per-year - Contribution to cost of life insurance plan per-year - Contribution to this year's 401(k) plan = $54,000 - $15,000 - $480 - $180 - $4,320 = $34,020
Step 3: Calculation of bimonthly paychecks
Bimonthly paychecks = Annual paychecks / 24 = $34,020 / 24 = $1,417.50
Therefore, Marlene will receive $1,417.50 for each of her bimonthly paychecks.
F. The relationship between x and y is not a straight line.
Does anyone know the answer??
Answer:
[tex]y=\frac{1}{3}x-1[/tex]
As the line equation represents a straight line, so the relationship between x and y is a straight line.
Therefore, option E is true.
Step-by-step explanation:
Taking two points from the given line
(3, 0)(-3, -2)Finding the slope between two points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(3,\:0\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-2\right)[/tex]
[tex]m=\frac{-2-0}{-3-3}[/tex]
[tex]m=\frac{1}{3}[/tex]
From the graph, the y-intercept can be calculated by setting the x=0 and then check the corresponding value of y.
at x = 0, y=-1
Thus, the y-intercept = -1
We know that the slope-intercept form is
[tex]y=mx+b[/tex]
where m is the slope, and b is the y-intercept
substituting the values of m=1/3 and the y-intercept b = -1
[tex]y=mx+b[/tex]
[tex]y=\frac{1}{3}x+\left(-1\right)[/tex]
[tex]y=\frac{1}{3}x-1[/tex]
As the line equation represents a straight line, so the relationship between x and y is a straight line.
Therefore, option E is true.
Determine whether KM and ST are parallel, perpendicular, or neither.
K (-3, -7), M(3, -3), S(0, 4), T(6, -5)
Answer:
So, KM and ST are perpendicular lines
Step-by-step explanation:
Find the slope of KM and ST.
K (-3, -7), M(3, -3)
Slope of KM = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{-3-[-7]}{3-[-3]}\\\\= \frac{-3+7}{3+3}\\\\ = \frac{4}{6}\\\\= \frac{2}{3}[/tex]
S(0 , 4) & T(6 , -5)
Slope of ST = [tex]\frac{-5-4}{6-0}[/tex]
[tex]=\frac{-9}{6}\\\\=\frac{-3}{2}[/tex]
Slope of KM * slope of ST = [tex]\frac{2}{3} * \frac{-3}{2}[/tex]
= -1
So, KM and ST are perpendicular lines
Answer:
perpendicular
Step-by-step explanation:
1. The measures of the angles in a triangle are x, 2x, and 2x - 20. What is the measure of the largest angle?
Answer:
Sum of the three angles of a triangle = 180 degrees
x+x+20+2 x=180
4 x=160
x=40
The angles are 40,(40+20).(2*40)
Answer 40,60,80
3n + 1 + 8n2 – 8n – 7 A) 16n? – 11n - 2 B) 16n2 – 5n - 2 C) 16n² – 5n - 6 D) 8n? – 5n - 6
Answer:
The answer is D.
Step-by-step explanation:
There is only one 8n^2, and that means that it cannot combine with anything.
PLEASE FOR THE LIVE OF GOD HELP ME
Given the interval notation, choose the correct graph.
Answer:
A.
or
4.
Step-by-step explanation:
ok,,,, I have to admit to not listening in class. What does sin, cos, and tan meannn
Albert needs $133 to buy a new hard drive. He earns $4.75 for each car he washes. If he spends $19 in supplies, write and solve an equation to find the number of cars he needs to wash to reach his goal.
Answer:
Albert needs 32 cars to wash to reach his goal.
Step-by-step explanation:
We know that the slope-intercept form of a linear function is
[tex]y = mx+b[/tex]
where m is the slope or rate of change and b is the y-intercept
It is stated that Albert needs $133 to buy a new hard drive.
Let 'y' be the amount Albert needs.As earns $4.75 for each car he washes. Thus, $4.75 the rate of change or slope will be.
As he spends $19 on supplies. Since it is an expense, so -19 is basically the y-intercept 'b'.
Let 'x' be the number of cars he needs to wash to reach his goal.
Thus, substituting the value m = 4.75, y = 133, and b=-19 in the slope-intercept form of a linear function
y = mx+b
133 = 4.75x - 19
133+19 = 4.75x
152 = 4.75x
x = 152 / 4.75
x = 32
Therefore, Albert needs 32 cars to wash to reach his goal.
The solution to a system of equations is (5,-19) choose two equations that might make up the system
A. y=-3x-6
B. y=2x-23
C. y=-7x+16
D. y=x-17
E. y=-2x-9
Answer:
E
Step-by-step explanation:
By definition,
Linear equationLinear or first degree equations are of the type ax + b = y, with a≠0, or any other equation in which when operating, transposing terms and simplifying they adopt that expression.
A solution to an equation is a number that can be entered into the variable to make a true number statement.
This caseIn this case, you know that the solution to a system of equations is (5,-19). This is, x=5 and y=-19.
Replacing the value of x in linear expressions, I can calculate the value of y and I must get that y=-19.
A. y=-3×5 -6 → y= -15 -6 → y= -21
B. y=2×5 -23 → y= 10-23 → y= -13
C. y=-7×5+16 → y= -35 +16 → y= -19
D. y=5-17 → y= -12
E. y=-2×5-9 → y= -10 -9 → y= -19
Observing the solutions obtained, the equations that satisfy the solution and make uo the system are option C. and E.
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I need help with that plzzzzzz
Answer:
.25 or 25%
Step-by-step explanation:
I simplied it to 30 and 7 so then I expiremended with different percents and got that 25 percent equals 7.5 so I checked it and is 25 %
HELP!
Ella swims four times a week at her club’s pool. She swims the same number of laps on Monday, Wednesday, and Friday, and 15 laps on Saturday. She swims a total of 51 laps each week. Write an equation for the problem.
Answer: 3x + 15 = 51
x is the number of laps that she swims on Monday, Wednesday, and Friday. Since she swims the same amount, we can multiply x by three. Since Saturday gives us an explicit answer, we can just add that to the equation.
Hope this helps :)
4(1 – x) + 2 x = -3( x + 1)
Answer:
Step 1: Simplify both sides of the equation.
4(1−x)+2x=−3(x+1)
(4)(1)+(4)(−x)+2x=(−3)(x)+(−3)(1)(Distribute)
4+−4x+2x=−3x+−3
(−4x+2x)+(4)=−3x−3(Combine Like Terms)
−2x+4=−3x−3
−2x+4=−3x−3
Step 2: Add 3x to both sides.
−2x+4+3x=−3x−3+3x
x+4=−3
Step 3: Subtract 4 from both sides.
x+4−4=−3−4
x=−7
Step-by-step explanation:
Wanna chat add me as a friend OR COME TO Snap (ADAMBELAL839)
What is the value of s?
units
Answer:
[tex]s = 17[/tex]
hope this helps
Please give me the brainliest
Have a nice day
I need help with number 39 and 40 ASAP
(please)
Answer:
40.) $7,959.18
Step-by-step explanation:
If 1.5% of 7,841.56 is 117.62, add them both together to get her total income for the week. In this case, that's $7,959.18.
the cylindrical part of an architectural column has a height of 305 cm and a diameter of 30 cm find the volume of the cylindrical part of the column.use 3.14 for pi and round youre answer to the nearest cubic centimete if needed.
Answer:
215482.5
ep-by-step explanation:
i need help! what is the y-intercept of the line 2x + 3y = 6?
Answer:
The y-intercept of this line is 2.
Step-by-step explanation:
To find where this line reaches the y axis, you simply need to assign the value 0 to x, and solve for y:
[tex]2x + 3y = 6\\2(0) + 3y = 6\\3y = 6\\y = 6/3\\y = 2[/tex]
So the y intercept of that line is 2
the lines whose equations are 2x + 3y = 4 and y = mx + 6 will be perpendicular when
Answer:
These lines will be perpendicular when m = ³⁄₂
Step-by-step explanation:
Two lines are perpendicular when the product of their gradients equal to -1. So:
m₁ * m₂ = -1
Let's get the first equation in gradient-intercept form (same as equation two).
2x + 3y = 4
3y = -2x + 4
y = -⅔x + ⁴⁄₃
We know the first gradient, and now we can find the gradient of the second line (which when multiplied will result in -1 as these lines are perpendicular). So:
-⅔ * m₂ = -1
m₂ = ³⁄₂
Which of the following describes the graph of {x | 2 < x < 2}? an open circle on 2 and arrows pointing out no solution just a closed circle on 2 the entire number line
PLZ HURRY
Answer:
open circle one and 2
Step-by-step explanation:
there will be open circle because there is no equal sign in the problem....there will be a line segment in between...because basically, u would put an open circle on 1, and open circle on 2 and shading in between
Answer:
The answer is no solution.
Hi! (-: This is due really soon, so any help would be appreciated!
Write an expression to represent the expenses of the fundraiser in the following paragraph.
The varsity basketball team is selling t-shirts as a fundraiser. It costs them $100 to have the shirts professionally designed, and they have to pay $5 for each shirt. They plan on selling the shirts for $10 each.
Answer:
5x-10x+100 or a simplified version: -5x+100 where x is the number of shirts
Step-by-step explanation:
5x is for every shirt they have to pay for and it adds to the cost
-10x is for every shirt they sell which decreases the total cost
100 is for the upfront cost of having the shirts professionally designed
hope this helped and if i misunderstood something lmk so i can change it :))
Carla can roll 18 pretzels in 12 minutes. How many can she roll in 40 minutes?
Answer: 60
Step-by-step explanation:
To find how much she rolls in 1 minute, you divide 18 by 12. This gets you 1.5. Multiply 1.5 by 40 and you get 60.
I need help with 13 and 14
Answer:
13) x = 62
14) x = 2.5
y = 5.88888889
Step-by-step explanation:
x = 62 because x is the alternate interior angle of 62.
37x - 19 = 29x + 1 (subtract 29x on both sides)
8x - 19 = 1 (add 19 on both sides)
8x = 20 (divide by 8)
x = 2.5
Plug 2.5 into 29x + 1 to find 9y + 25
29(2.5) + 1 = 73.5
9y + 25 = 73.5 (subtract 25 on both sides)
9y = 48.5 (divide by 9 on both sides)
y = 5.388888889
It all checks out!
HOPE THIS HELPS!
He national debt of a country is $298,800,000,000,000 and the population is 53,980,000. What is the debt per person? Write the answer without exponents.
Answer:
5535383.47 units
Step-by-step explanation:
Given that,
The national dept of a country = 298,800,000,000,000
Population of the country = 53,980,000
We need to find the debt per person. It can be calculated by dividing national dept of a country to its total population. Let it is d.
[tex]d=\dfrac{298800000000000}{53980000}\\\\=5535383.47\ \text{units}[/tex]
Hence, the debt per person is 5535383.47 units.
What is the quotient when (x + 2) is divided into the polynomial 2x^2- 2x - 12?
A. X+ 3 with a remainder of -2
B. 2x-6 with no remainder
C. 2x-5 with no remainder
D. 2x-3 with a remainder of 5
Two lines that have the same y intercept and different slopes intersect at exactly one point.
True
False
Answer:
False. They will be parallel to each other
Answer:
false they would be parallel lines
You put a barrier around the garden and cover it with a layer of mulch. The barrier costs $1.50 per foot. One bag of mulch covers 8 square feet and costs $6. How much do you spend
Answer:
I spent $14.5 on the garden
Step-by-step explanation:
This problem can be solved by simply adding the individual costs of the items put in the garden
Cost of the barrier:
We can get the cost of the barrier by first of all determining the perimeter of land the barrier covers. We have a hint in the question given: "One bag of mulch covers 8 square feet "
We can assume the shape of the garden to be a square and the area to be 8 square feet.
The length of the garden will be = [tex]\sqrt{area}[/tex] because the garden is a square.
Length = [tex]\sqrt{8} =2\sqrt{2}[/tex]
perimeter = [tex]4 \times 2\sqrt{2}=4\sqrt{2} feet[/tex]
The barrier costs $1.50 per foot. for [tex]4\sqrt{2}[/tex] feet, =$8.5
Cost of barrier = $8.50
Cost of Mulch
The cost of mulch = $ 6
Total sum of money spent = 8.5 +6 = $14.5
Therefore, I spent $14.5 on the garden
Answer:
149.02
Step-by-step explanation:
51.72 plus 97.33 is 149.02