[tex]\bold{\text{Answer:}\quad f(x)=\bigg\{\begin{array}{ll} -x-2&;x<0\\ -\frac{1}{2}x&;x\geq0 \end{array}}[/tex]
Step-by-step explanation:
Find the equation of each line in Slope-Intercept form: y = mx + b
Line 1 passes through (-5, 3) and (0, -2) --> m = -1, b = -2
--> y = -x - 2
Line 2 passes through (0, 0) and (4, -2) --> m = -1/2, b = 0
--> y = -(1/2)x + 0
Now that you have the equations, evaluate which x-values are included.
Line 1: open dot at x = 0 and line goes to the left --> x < 0
Line 2: closed dot at x = 0 and line goes to the right --> x ≥ 0
Now you have all the information you need to write the piecewise function:
[tex]\large\boxed{f(x)=\bigg\{\begin{array}{ll} -x-2&;x<0\\ -\frac{1}{2}x&;x\geq0 \end{array}}[/tex]
The piece wise function can be written as
[tex]f(x) = -x-2 \; for\; x < 0[/tex]
[tex]f(x) = \dfrac{-1}{2}x \; for\; x \geq 0[/tex]
The Equation of line passing through [tex](x_1,y_1)\; and \; (x_2,y_2)[/tex] can be given by equation (1)
[tex]y -y_1 = \dfrac{y_2 -y_1 }{x_2 - x_1} (x-x_1) ........(1)[/tex]
The equation of line passing through (0,-2) and (-5,3) =
[tex]y-(-2) = \dfrac{3-(-2)}{-5-0}\times (x-0)[/tex]
[tex]y +2 = -x\\y = -x -2 ......(2)[/tex]
Similarly the line passing through (0,0) and (4,-2) =
[tex]y- 0 = \dfrac{-2 -0}{4-0} (x-0)\\y = \frac{-1}{2} x......(3)\\2y =-x \\x +2y =0[/tex]
The first line has an open circle at (0, -2) and continues up through (-5, 3) with an arrow instead of an endpoint.
The second line has a closed circle at (0, 0) and continues down with a negative slope through (4, -2) with an arrow instead of an endpoint. [tex]f(x) = \dfrac{-1}{2}x \; for\; x < 0[/tex]
Hence the piece wise function can be defined by equations (2) and (3)
[tex]f(x) = -x-2 \; for\; x < 0[/tex]
[tex]f(x) = \dfrac{-1}{2}x \; for\; x \geq 0[/tex]
For more Information please refer to the link below
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Let's start by solving this equation:
4(x + 4) = 7x - 5
Please answer quick
Answer: x=7
Step-by-step explanation: 4(7+4)=44. 7(7)-5=44.
Answer:
x=7
Step-by-step explanation:
4(x + 4) = 7x - 5
Distribute
4x+16 = 7x-5
Subtract 4x from each side
4x+16 -4x = 7x-5-4x
16 = 3x -5
Add 5 to each side
16+5 = 3x-5+5
21 = 3x
Divide by 3
21/3 = 3x/3
7 =x
Ms. Gantt has a $15 gift card to Starbucks. She buys 2 muffins for $2.65 each, 2 hot chocolates for $1.79 each, and a juice for $3.05. How much remains on her gift card? Help please I will mark you brainiest.
Answer:
Remains on her gift card:
$3.07
Step-by-step explanation:
15 - ((2*2.65) + (2*1.79) + (1*3.05))
= 15 - (5.3 + 3.58 + 3.05)
= 15 - 11.93
= 3.07
Remains on her gift card:
$3.07
Rewrite in simplest terms: - 10(5t + 5) – 10(10t + 6)
Answer:
Hey there!
10(5t+5)-10(10t+6)
50t+50-100t-60
-50t-10
Let me know if this helps :)
3-3+x^3+6x^3-3y-3-4x^3
Answer:
3x³ - 3y - 3 or 3(x³ - y - 1)
Step-by-step explanation:
3 - 3 + x³ + 6x³ - 3y - 3 - 4x³
group like terms
= x³ + 6x³ - 4x³ - 3y + 3 - 3 - 3
add similar terms
= 3x³ - 3y - 3 or 3(x³ - y - 1)
London is driving to a concert and needs to pay for parking. There is an automatic fee of $10 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. How much total money would London have to pay for parking if she left her car in the lot for 5 hours? How much would London have to pay if she left her car in the lot for tt t hours?
Answer:
1.) 20 dollars
2.) (2t + 10) dollars
Step-by-step explanation:
Given that There is an automatic fee of $10 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot.
1.) How much total money would London have to pay for parking if she left her car in the lot for 5 hours?
5 × 2 = 10 dollars
Then add the automatic price which is $10
Therefore, London will pay a total of
10 + 10 = 20 dollars
2.) How much would London have to pay if she left her car in the lot for tt t hours?
(2 × t) + 10
2t + 10
Five less than tvice a number is equal to one half the difference of three times the number and 13. Find the number.
I think it's -3
[tex]2x - 5 = \frac{1}{2} (3x - 13)[/tex]
[tex]4x - 10 = 3x - 13[/tex]
[tex]x = - 3[/tex]
A certain game is played on a board that shows a portion of the xy-coordinate plane. During one move in the game, a marker at a point (a,b) is first moved to the point (b,a) and then moved 3 units to the left. During such a move, a marker that is at (4,3) will be moved to
Answer: (0,4)
Step-by-step explanation:
Given: During one move in the game, a marker at a point (a,b) is first moved to the point (b,a) . (i)
And then moved 3 units to the left. (ii)
Translation rule to move a point (x,y) c units left : (x,y)→(x-c,y)
Now, (4,3) first will become (3,4) [using (i)]
Then, (3,4)→(3-3,4)=(0,4) [using (ii) and translation rule]
Hence, During such a move, a marker that is at (4,3) will be moved to (0,4).
george is loading freight into an elevator. He notices that the weight limit for the elevator is 1000 lbs. He knows that he weighs 210 lbs. He has loaded 15 boxes into the elevator. Each box weighs 50 lbs. identify the rate of change for this situation. Plz help
Answer:
Step-by-step explanation:
The rate of change in this case is 50 pounds per box. The fixed amount that the elevator must carry is 210 pounds, which is how much he weighs. The amount that varies with additional boxes is 50 pounds per box, making it the rate of change. If this situation was graphed, George's weight would be the y-intercept and the rate of change would be the slope.
what is the length of CC’
Answer:
5.385 Units
Step-by-step explanation:
5²+2²=c²
25+4=c²
29=c²
c=√29
c=5.385
Answer:8
Step-by-step explanation:
Explain how you would find the product of 20 to the power of 12 and 20 to the power of 8. Include either the exponent rule or the expanded method in your explanation. Give your answer in exponential form.
Answer:
See explanation below
Step-by-step explanation:
Using the exponent rule for products:
[tex]x^a\,*\,x^b = x^{(a+b)}[/tex]
we can write:
[tex]20^{12}\,*\,20^8=20^{(12+8)}=20^{20}[/tex]
Jake wants to find out which can of pineapple is the best buy. He has a choice of four different-size cans. Which can has the lowest unit price per ounce
Answer:
Step-by-step explanation:
Find the distance between the two points rounding to the nearest tenth (if necessary).
(4,2) and (8,8)
Answer:
≈ 7.2
Step-by-step explanation:
Use distance formula:
d = √(8-4)² + (8-2)²
You work at a flower shop designing bouquets. You need to create bouquets of roses and calla lilies for a wedding. Calla lilies cost you $2.40 each and roses cost $1.90 each. If you need 64 of each type of flower, how much money do you need to spend to make the bouquets?
The total money needed $ 275.2
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Calla lilies cost you $2.40.
roses cost $1.90.
If we need 65 lilies then it will cost
=64 * 2.40
= $153.60
and, If we need 65 roses then it will cost
=64 * 1.90
= $121.60
So, the total money needed
=153.6 + 121.6
=$ 275.2
Learn more about unitary method here:
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How do I write the following expression on my computer?
Answer:
YOU HAVE TO WRITE YOUR QUESTION ON COMPUTER AS ,
Step-by-step explanation:
4/(2*x-3)
I hope it will work
A cylinder has a height of 7 in. and a diameter of 6 in. What is the volume of the cylinder to the nearest cubic inch? V = 66 in^3 V = 132 in^3 V = 198 in^3 V = 792 in^3
Answer:
The answer is
V = 198 in³Step-by-step explanation:
Volume of a cylinder = πr²h
where
h is the height
r is the radius
From the question
h = 7 in
To calculate the radius from the diameter we use the formula
radius = diameter/2
From the question
diameter = 6
radius = 6/2 = 3 in
Volume of the cylinder is
(3)²(7)π
= 9(7)π
= 63π
= 197.9203
We have the final answer as
V = 198 in³ to the nearest cubic inchHope this helps you
Question 1
Translate the following information into the
language of algebra. You answer should include an
algebraic expression, and clear definitions of any
variables.
Sophia is in a room filled with people. She is
counting all the shoes in the room.
She thought that the number of shoes would just be
double the number of people in the room. However,
there is also a cupboard in the room containing 4
extra shoes,
Answer:
let people=x
and shoes=y
now,as per the question
2x-4=y
Solve for a: a - 17 = -10
Answer:
a = 7
Step-by-step explanation:
a - 17 = -10
Add 17 to each side
a - 17+17 = -10+17
a = 7
Answer:
a = 7
Step-by-step explanation:
Add 17 to each side, so it cancels out the -17. It should now looks like this: a = 7I hope this helps!
NEED HELP ASAP ALGEBRA 2
Answer:
[tex]2\sqrt{71}[/tex]
Step-by-step explanation:
[tex]a^{2} + b^{2}=c^{2}[/tex]
[tex]59+225=284[/tex]
[tex]\sqrt{284}= 2\sqrt{71}[/tex]
Answer:
c=[tex]2\sqrt{71}[/tex]
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2} \\15^{2} +(\sqrt{59} )^{2}=c^{2}\\225+59=c^{2}\\284=c^{2} \\2\sqrt{71} =c[/tex]
If Log 4 (x) = 12, then log 2 (x / 4) is equal to A. 11 B. 48 C. -12 D. 22
Answer:
[tex]\huge \boxed{\mathrm{D. \ 22}}[/tex]
Step-by-step explanation:
[tex]\mathrm{log_4 (x)=12}[/tex]
Make the base 4 from both sides.
[tex]\mathrm{4^{log_4 (x)}=4^{12}}[/tex]
Simplify the equation.
[tex]\mathrm{x=16777216}[/tex]
[tex]\mathrm{log_2 (\frac{x}{4} )}[/tex]
Let x = 16777216
[tex]\mathrm{log_2 (\frac{16777216}{4} )}[/tex]
[tex]\mathrm{log_2 (4194304)}[/tex]
Evaluate.
[tex]22[/tex]
Answer:
[tex]log_2(\frac{x}{4} )=22[/tex]
which is your answer "D"
Step-by-step explanation:
If [tex]log_4(x)=12[/tex] this means that : [tex]x=4^{12}[/tex] based in the definition of logarithm.
And this exponential expression can also be written using that [tex]4=2^2[/tex]:
[tex]x=4^{12}=(2^2)^{12}=2^{24}[/tex]
so now we know what x is with base 2 (which is needed for the second expression:
[tex]log_2(\frac{x}{4} )=?[/tex]
And this also can be written in exponent form (using the unknown "?" we need to find) as:
[tex]2^?=\frac{x}{4} \\x=4\,*\,2^?\\x=2^2\,*\,2^?\\x=2^{2+?}[/tex]
Since we know the value of x in base 2 (from our first analysis), then:
[tex]x=2^{2+?}=2^{24}\\then\\2+?=24\\?=22[/tex]
Therefore,
[tex]log_2(\frac{x}{4} )=22[/tex]
Andrea makes Mother's Day bouquets each year for extra income. This year her goal is to make $300. If she sells each bouquet for $12.50, how many bouquets must she sell to reach her goal?
Answer:
24 bouquet
Step-by-step explanation:
300 divide by 12.50
The football team need to buy Gatorade for Saturdays big game . They have two option. The first option us they can buy it pre-made in a 48 ounce for $3.84 for each bottle. Or they can buy packet and mix it with water. Each packet make 64 ounces and it will cost $4.80. Find the ounce per cost
The question is incomplete. Here is the complete question.
The football team needed to buy Gatorade for Saturday's big game. They have two options. The first option is they can buy it pre-made in 48 ounces bottles for $3.84 for each bottle. Or they can buy packets and mix with water. Each packet makes 64 ounces and will cost $4.80.
a) Find the cost per ounce of each.
b) Which size costs less?
c) The team will need to buy 192 ounces of Gatorade. How much do you save using the choice from answer b?
Answer: a) Pre-made: $0.08 cost per ounce; Packet: $0.075 cost per ounce
b) Packets
c) Save $0.96.
Step-by-step explanation:
a) Cost per ounce:
Pre-made:
[tex]\frac{3.84}{48}[/tex] = 0.08
Packet:
[tex]\frac{4.8}{64}[/tex] = 0.075
b) Comparing costs per ounce, packets costs less than pre-made.
c) Buying packets, the cost will be:
0.075*192 = $14.4
Buying pre-made:
0.08*192 = $15.36
Comparing costs, pre-made is 0.96 more than packets, so they will save 96 cents.
John has gross biweekly earnings of $743.61. By claiming 1 more withholding allowance, John would have $19 more in his take home pay. How many withholding allowances does John currently claim?
Answer:
Total withholding allowances are 39.
Step-by-step explanation:
Given the gross earning of John = $743.61
It is given that 1 withholding allowance = $19
Now we have to find the total number of withholding allowances. Here, the number of withholding allowances can be determined by dividing the total earnings with $19.
Number of withholding allowances = 743.61 / 19 = 39.14 or 39 (round off).
Complete the description of The transformation f(x)=|x| g(x)=|x+9|-5
Answer:
f(x) down 5 units
and shifted to the left 9 units
Step-by-step explanation:
Transforming f(x) = |x| into g(x) = |x+9| - 5
involves:
1) shifting the graph horizontally 9 units to the left (with the subtraction of -9 from the variable "x", getting x+9 inside the absolute value symbols, and
2) shifting its graph 5 units down by subtracting 5 from the full expression
3. Which of the following quadratic equations has no solution? A) 0 = −2(x − 5)2 + 3 B) 0 = −2(x − 5)(x + 3) C) 0 = 2(x − 5)2 + 3 D) 0 = 2(x + 5)(x + 3)
Answer:
D) 0 = 2(x + 5)(x + 3)
Step-by-step explanation:
Which of the following quadratic equations has no solution?
We have to solve the Quadratic equation for all the options in other to get a positive value as a solution for x.
A) 0 = −2(x − 5)2 + 3
0 = -2(x - 5) × 5
0 = (-2x + 10) × 5
0 = -10x + 50
10x = 50
x = 50/10
x = 5
Option A has a solution of 5
B) 0 = −2(x − 5)(x + 3)
Take each of the factors and equate them to zero
-2 = 0
= 0
x - 5 = 0
x = 5
x + 3 = 0
x = -3
Option B has a solution by one of its factors as a positive value of 5
C) 0 = 2(x − 5)2 + 3
0 = 2(x - 5) × 5
0 = (2x -10) × 5
0 = 10x -50
-10x = -50
x = -50/-10
x = 5
Option C has a solution of 5
D) 0 = 2(x + 5)(x + 3)
Take each of the factors and equate to zero
0 = 2
= 0
x + 5 = 0
x = -5
x + 3 = 0
x = -3
For option D, all the values of x are 0, or negative values of -5 and -3.
Therefore the Quadratic Equation for option D has no solution.
What is 4(x-7)=2(x+3)?
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
4(x−7)=2(x+3)
Simplify both sides of the equation.
4(x−7)=2(x+3)
4x+−28=2x+6
4x−28=2x+6
Subtract 2x from both sides.
4x−28−2x=2x+6−2x
x−28=6
Add 28 to both sides.
2x−28+28=6+28
2x=34
Divide both sides by 2.
2x/2 = 34/2
x = 17
Answer:
x = 17
Step-by-step explanation:
[tex]4(x-7)=2(x+3)\\\\4x-28=2x+6\\\\4x-28+28=2x+6+28\\\\4x=2x+34\\\\4x-2x=2x-2x+34\\\\2x=34\\\\\frac{2x=34}{2}\\\\ \boxed{x=17}[/tex]
Hope this helps.
why isn’t the square root of 10 an integer, answer asap please
Answer:
because the square root of 10 is an irrational number, and only rational numbers are integers. integers are whole numbers and have no fractions or decimels... hope it helps
Juan went to the store to buy some apples. The price per pound of the apples is $4 per pound and he has a coupon for $1.25 off the final amount. With the coupon, how much would Juan have to pay to buy 4 pounds of apples? Also, write an expression for the cost to buy p pounds of apples, assuming at least one pound is purchased.
Answer:
I don’t know this one sorry
Step-by-step explanation:
which is a subset of {1, 2, 4, 5, 6}?
{0, 1, 2}
{3, 4}
{5, 6, 7}
{2, 6}
(believe its the last one but just want to make sure)
Answer:
{2, 6}
Step-by-step explanation:
Subset: A subset is a set of which all the element are contained or can be find in the universal set.
From the question above,
μ = {1,2,4,5,6}
* The first option {0,1,2} is wrong because 0 is not contained in the universal set.
* The second option {3,4} is wrong because, 3 is not contained in the universal set.
* The third option {5,6,7} is wrong because 7 is not contained in the universal set.
* The last option {2,6} is correct because all of the element of the set are contained in the universal set, and as such makes it a subset.
Hence the subset of {1,2,4,5,6} is {2, 6}
Suppose you are a scientist who wants to grow cells. Sample 1 is a cell that divides every twenty minutes. Sample 2 is a cell that divides every thirty minutes. Will there be more cells of Sample 1 or 2 after three hours? How many more?
Answer:
a. Assuming we are starting out with the same mass or number of both cells, definitely there would be more cells of sample 2 after three hours
b. If there are equal number of both cells initially, there would be 8 times more of cell 2 than cell 1
Step-by-step explanation:
a.The first part of the question asks if there would be more cells of sample 1 or 2 after three hours.
Now, the first assumption we shall be making is that we have equal numbers or let’s say mass of both cells initially.
Okay, let’s say we have x g of both cells initially.
Now sample 1 cell divides every 20 minutes.
How many times will have divided in 3 hours? The correct way to tackle this is by knowing the number of two minutes in 3 hours.
In an hour, we have 3 20 minutes. So in 3 hours, we will have 9 20 minutes
Let’s take a look at the sample 2 cell.
it divides every 30 minutes.
Now, in an hour, we have 2 30 minutes. In 3 hours, we will be having 6 30 minutes
Since cell 2 underwent 6 divisions while cell 1 underwent 9 divisions within the same 3 hours and they both have the same mass initially, then we will have more of cell 2 after three hours.
b. We want to know by how many more.
Now, for cell 1 since the division is 9 times, and it is definitely an exponential division, the mass or amount of the original left after 9 half divisions would be;
(1/2)^9 = 1/512
So 1/512 of x would be left and that would be x/512 left
For cell 2, we have the same approach. There are six divisions.
The amount left after the 6th division would be;
(1/2)^6 = 1/64
So the amount left after the sixth division would be x * 1/64 = x/64
Now, we want to know by which amount is the division of cell 2 greater.
That would be x/64 divided by x/512 = x/64 * 512/x = 8
how to put these in a simply form?
(-2)* (-2)* 10 *10 *10 *10.
21*21*21+(-1)(-1)(-1)(-1).
Answer:
370,4440,001
Step-by-step explanation:
(-2) • (-2) • (10) • (10) • (10) • (10) = 40,000
21 • 21 • 21 = 9261
(-1) • (-1) • (-1) • (-1) = 1
(40,000) (9261) + 1
(370,440,000) + 1 = 370,4440,001
--
exponents
(-2)² + 10⁴ + 21³ + (-1)⁴