What are the intercepts of the graphed function?
x-intercept = (–1, 0)
y-intercept = (–3, 0)
x-intercept = (0, –1)
y-intercept = (0, –3)
x-intercept = (0, –1)
y-intercept = (–3, 0)
x-intercept = (–1, 0)
y-intercept = (0, –3
Answers
y-intercept: (0,-3)
we know that
The x-intercept is the value of x when the the value of y is equal to zero
and
The y-intercept is the value of y when the the value of x is equal to zero
In the graphed function we have that
the value of x when the the value of y is equal to zero is [tex]-1[/tex]
therefore
the x-intercept is equal to the point [tex](-1,0)[/tex]
the value of y when the the value of x is equal to zero is [tex]-3[/tex]
therefore
the y-intercept is equal to the point [tex](0,-3)[/tex]
the answer is
x-intercept = (–1, 0)
y-intercept = (0, –3)
Related Questions
Write 11760825 in word form
Answers
Determine whether the given differential equation is exact. if it is exact, solve it. (if it is not exact, enter not.) (3x + 6y) dx + (6x − 8y3) dy = 0
Answers
The ODE is exact if [tex]\dfrac{\partial M}{\partial y}=\dfrac{\partial N}{\partial x}[/tex]. We have
[tex]\dfrac{\partial M}{\partial y}=6[/tex]
[tex]\dfrac{\partial N}{\partial x}=6[/tex]
so the equation is indeed exact.
We're looking for a solution of the form
[tex]\Psi(x,y)=C[/tex]
By the chain rule, we have
[tex]\dfrac{\partial\Psi}{\partial x}+\dfrac{\partial\Psi}{\partial y}\dfrac{\mathrm dy}{\mathrm dx}=0[/tex]
[tex]\iff\dfrac{\partial\Psi}{\partial x}\,\mathrm dx+\dfrac{\partial\Psi}{\partial y}\,\mathrm dy=0[/tex]
which means [tex]\dfrac{\partial\Psi}{\partial x}=M[/tex] and [tex]\dfrac{\partial\Psi}{\partial y}=N[/tex].
Now
[tex]\dfrac{\partial\Psi}{\partial x}=M\implies\displaystyle\int\frac{\partial\Psi}{\partial x}\,\mathrm dx=\int M\,\mathrm dx[/tex]
[tex]\implies\Psi(x,y)=\dfrac32x^2+6xy+f(y)[/tex]
Differentiating with respect to [tex]y[/tex] yields
[tex]\dfrac{\partial\Psi}{\partial y}=N\implies 6x+f'(y)=6x-8y^3[/tex]
[tex]\implies f'(y)=-8y^3\implies f(y)=\displaystyle\int(-8y^3)\,\mathrm dy=-2y^4+C[/tex]
and so the general solution is
[tex]\Psi(x,y)=\dfrac32x^2+6xy-2y^4+C=C[/tex]
[tex]\implies\Psi(x,y)=\dfrac32x^2+6xy-2y^4=C[/tex]
The given differential equation (3x + 6y) dx + (6x − 8y3) dy = 0 is exact because its mixed partial derivatives are equal. To solve it, first integrate M with respect to x to get a function involving an unknown function of y, then compare it with N to determine the unknown function.
Explanation:To determine if the given differential equation is exact, we need to check if the partial derivative of M with respect to y is the same as the partial derivative of N with respect to x. In this given differential equation (3x + 6y) dx + (6x − 8y3) dy = 0, M = 3x + 6y and N = 6x - 8y3. First, compute the partial derivative of M with respect to y (∂M/∂y) which is 6, then the partial derivative of N with respect to x (∂N/∂x), which is 6 as well. Since ∂M/∂y=∂N/∂x, the given differential equation is exact.
To solve this exact differential equation, we integrate M dx, i.e., ∫M dx, to get ψ(x,y) =1.5x^2+6xy+h(y), where h(y) is an arbitrary function of y. Next, differentiate ψ(x,y) with respect to y, then compare the result with N: ψy=6x+dh/dy=6x-8y³. Solving for dh/dy gives dh/dy=-8y³, so integrating this gives h(y)=-2y⁴+C, where C is a constant. Therefore, the solution to the differential equation is ψ(x,y)=1.5x²+6xy-2y⁴=C.
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Find a vector parametric equation for the parabola y=x2 from the origin to the point (3,9) using t as a parameter.
Answers
The parametric vector equations for the parabola y=x² from the origin to the point (3,9) is x = t and y = t² for the parameter range 0 <= t <= 3.
Explanation:The required parametric vector equation for the parabola y=x² from the origin to the point (3,9) is given by the equations x = t and y = t². Here, t is the parameter. At t=3, these equations give us the coordinates x=3 and y=9, which corresponds to the point (3,9). Thus, these equations accurately represent the parabola y=x² from the origin to the point (3,9) for the parameter range 0 <= t <= 3.
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In the parametric form, the path of a point on the parabola y=x² from the origin to point (3,9) is represented by a vector (t, t²) with t ranging from 0 to 3.
Explanation:To find a vector parametric equation for the parabola y=x² from the origin to the point (3,9), we first need to understand that the parabola y = x² is not a vector in itself.
But, we can describe its trajectory through a parametric form using t as a parameter. For a given t, the parabola is represented by a vector (x(t), y(t)), where x(t) and y(t) are functions of t. For the specific parabola y = x², we can define the functions as x(t) = t and y(t) = t².
This means the vector at time t is given by (t, t²). From the origin (0,0) to the point (3,9), we now have a parameter t ranging from 0 to 3.
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Samantha threw an apple out of a window. The equation -16t^(2)+120=y can be used to represent the apple's height above the ground, where t = time in seconds after she threw the apple. how long did it take for the apple to hit the ground. Round to nearest hundredth
Answers
[tex]\bf -16t^2+120=0\implies 120=16t^2\implies \cfrac{120}{16}=t^2\implies \cfrac{15}{2}=t^2 \\\\\\ \sqrt{\cfrac{15}{2}}=t[/tex]
bear in mind the square root would give us a +/- roots, however, since this is seconds, a negative unit would be unfeasible, thus we only used the positive root from it.
the sum of three numbers is 123. the second number is 9 less than two times the first number. the third number is 6 more than three times the first number. find the three number
Answers
x + 2x−9 + 3x+6 = 123
Collect like terms:
6x − 3 = 123
Solve:
6x = 126
x = 21
Plug the x-value back in:
(2 x 21) − 9 = 33
(3 x 21) + 6 = 69
The three numbers are 21, 33, and 69.
All of the following expressions are equivalent except _____. -4 - y -4 + y -y - 4 -y + (-4)
Answers
All of the expressions are equivalent except (b) -4 + y.
All the expressions involve adding -4 and - y in various orders, resulting in equivalent expressions due to the commutative property of addition.
However, the expression -4 + y is different because it combines the positive y term with the negative 4, resulting in - 4 + y.
The other expressions either have y added to -4 ( -4 - y) or have -4 added to y (-y - 4, -y + (-4)).
While addition is commutative, changing the order of the terms can affect the overall expression when dealing with negative terms.
So, while mathematically equivalent, the form of -4 + y stands out due to its structure.
Complete Question:
All of the following expressions are equivalent except _____.
(a) -4 - y
(b) -4 + y
(c) -y - 4
(d) -y + (-4 )
-5g-3/h-3 + 7g+9/h-3 find the sum
Answers
= 2g + 6/(h-3) if we want it as one fraction it would be:
2g + 6/(h-3) = [2g(h-3) + 6]/(h-3) = [tex] \frac{2gh - 6gh + 6}{h-3} [/tex]
A store is selling two mixtures of coffee beans in one-pound bags. The first mixture has 12 ounces of Sumatra combined with 44 ounces of Celebes Kalossi, and costs $42. The second mixture has 44 ounces of Sumatra and 12ounces of Celebes Kalossi, and costs $30. How much does one ounce of Sumatra and one ounce of Celebes Kalossi cost?
Answers
12s + 44c = 42
44s + 12c = 30
Take either equation and solve for either s or c.
12s + 44c = 42
12s = 42 - 44c
s = (42 - 44c) / 12
s = (21 - 22c) / 6
Substitute into 2nd equation
44s + 12c = 30
22((21 - 22c) / 3) + 12c = 30
22(21 - 22c) + 36c = 90
-448c +462 = 90
-448c = -372
c = -372/-448
c = 93/112
c = 0.83
Substitute into the 2nd equation
44s + 12c = 30
44s = 30 - 12c
s = (30 - 12 (93/112)) / 44
s = (30 - 279 / 28) / 44)
s = (30 - 9 27/28) / 44
s = 0.46
Prove
12s + 44c = 42
12(0.46) + 44(0.83) = 42
5.52 + 36.52 = 42
42.04 = 42
44s + 12c = 30
44(0.46) + 12(0.83) = 30
20.24 + 9.96 = 30.16
Assuming minor rounding issues this looks accurate.
A domino consists of two congruent squares placed side by side. the perimeter of the domino is 60 units. what is the area of the domino, in square units?
Answers
Answer:
200
Step-by-step explanation:
So say the dominoes' short side is x. Then the long side is 2x, so altogether there is 6x. So 6x=60, so x=10. So the area is 10*(10*2), which is 10*20 which is 200.
you have 5 antiques and want to display 3 on a shelf. how many different 3 antique arrangements are possible
Answers
Darcy kicks a ball that is represented by the function h\left( t \right) = - 16{t^2} + 50t h ( t ) = − 16 t 2 + 50 t where t stands for time and h(t) stands for the height of the ball in feet. How long will it take for the ball to hit the ground?
Answers
[tex]\bf h(t)=-16t^2+50t\implies 0=-16t^2+50t\implies 0=-t(16t-50) \\\\\\ \begin{cases} 0=-t\implies &0=t\\ ------\\ 0=16t-50\\ 50=16t\\ \frac{50}{16}=t\implies &\frac{25}{8}=t \end{cases}[/tex]
it hits it twice, once at the beginning, 0 seconds, and when it hits the ground at the end.
which inequality can be uses to determine
Answers
#2 is the correct answer
5h would be the amount he earned helping his brother
+ 26 is how much he has
so those 2 amounts need to equal or be greater than 48
If fixed costs are $561,000 and the unit contribution margin is $8.00, what is the break-even point in units if variable costs are decreased by $0.50 a unit?
Answers
Answer:
66,000 units
Step-by-step explanation:
Break-Even Sales (units) = Fixed Costs ÷ Unit Contribution Margin = $561,000 ÷ ($8 + $0.50) = 66,000 units
The break-even point in units after the decrease in variable costs is 66,000 units.
Given that the fixed costs are $561,000 and the original unit contribution margin is $8.00, we first calculate the original break-even point:
[tex]\[ \text{Original Break-even point in units} = \frac{561,000}{8} \][/tex]
[tex]\[ \text{Original Break-even point in units} = 70,125 \text{ units} \][/tex]
Now, since variable costs are decreased by $0.50 a unit, the new unit contribution margin becomes:
[tex]\[ \text{New Unit Contribution Margin} = 8 + 0.50 \][/tex]
[tex]\[ \text{New Unit Contribution Margin} = 8.50 \][/tex]
Using the new unit contribution margin, we calculate the new break-even point:
[tex]\[ \text{New Break-even point in units} = \frac{561,000}{8.50} \][/tex]
[tex]\[ \text{New Break-even point in units} = 66,000 \text{ units} \][/tex]
Therefore, the new break-even point in units, after the decrease in variable costs, is 66,000 units.
What's (8 + 3i)(3 + 5i).
Answers
(8 + 3i)(3 + 5i)
We must distribute each number/variable to the others in the opposite parenthesis.
8(3 + 5i) = 24 + 40i
3i(3 + 5i) = 9i + 15[tex] i^{2} [/tex]
Combine like-terms.
40i + 9i = 49i.
Now, put your simplified answer in Standard Form;
15[tex] i^{2} [/tex] + 49i + 24
This is your answer.
I hope this helps!
The tables represent two linear functions in a system.
What is the solution to this system?
Answers
The solution to this system is (x, y) = (8, -22).
The y-values get closer together by 2 units for each 2-unit increase in x. The difference at x=2 is 6, so we expect the difference in y-values to be zero when we increase x by 6 (from 2 to 8).
You can extend each table after the same pattern.
In table 1, x-values increase by 2 and y-values decrease by 8.
In table 2, x-values increase by 2 and y-values decrease by 6.
The attachment shows the tables extended to x=10. We note that the y-values are the same (-22) for x=8 (as we predicted above). That means the solution is ...
... (x, y) = (8, -22)
Answer:
(8,-22)
Step-by-step explanation:
Table 1)
To form equation we will use two point slope form
[tex](x_1,y_1)=(-4,26)\\(x_2,y_2)=(-2,18)[/tex]
Formula :[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substitute the values :
[tex]y-26=\frac{18-26}{-2+4}(x+4)[/tex]
[tex]y-26=-4(x+4)[/tex]
[tex]y-26=-4x-16[/tex]
[tex]y=-4x-16+26[/tex]
[tex]y=-4x+10[/tex] ---1
Table 2)
To form equation we will use two point slope form
[tex](x_1,y_1)=(-4,14)\\(x_2,y_2)=(-2,8)[/tex]
Formula :[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substitute the values :
[tex]y-14=\frac{8-14}{-2+4}(x+4)[/tex]
[tex]y-14=-3(x+4)[/tex]
[tex]y-14=-3x-12[/tex]
[tex]y=-3x+2[/tex] ---2
Now we are supposed to solve 1 and 2
Substitute the value of y from 1 in 2
[tex]-4x+10=-3x+2[/tex]
[tex]8=x[/tex]
Substitute the value of x in 2
[tex]y=-3(8)+2[/tex]
[tex]y=-22[/tex]
Hence the solution to this system is (8,-22)
You have been offered a project paying $300 at the beginning of each year for the next 20 years. what is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment?
Answers
First we figure out how much money you're spending in total, which is $300 each year, for 20 years, so 300 x 20 = 6,000. Now, since the problem is asking for a maximum amount for percentage rate, this means we find the 9% for all 20 years combined and not individually. 9% of 6,000 is of course 540, so if we subtract 540 from 6,000, we get 5,460.
This means your answer is $5,460
Find a polynomial f(x) of degree 3 that has the following zeros. 6,2,-7,0 leave your answer in factored form
Answers
given that the solution is x=6,x=2 and x=-7, it implies that roots are :
(x-6), (x-2) and (x+7)
Therefore the polynomial will be:
y=(x-6)(x-2)(x+7)
y=x^3-x^2-44x+84
How many positive integers not exceeding 1000 are not divisible by either 4 or 6?
Answers
There are 667 positive integers not exceeding 1000 that are not divisible by either 4 or 6.
Explanation:This is a question about number theory and involves the comprehension of divisibility. To identify the positive integers that are not divisible by either 4 or 6 and not exceeding 1000 is an application of the principle of inclusion and exclusion.
First, we need to figure out how many numbers up to 1000 are divisible by 4, which is 1000/4 = 250. Then, we look at how many numbers are divisible by 6, which is 1000/6 = about 166 (we only consider the whole numbers).
However, some numbers are divisible by both 4 and 6, so we have over-counted and need to correct for this. These would be the numbers divisible by the least common multiple (LCM) of 4 and 6, which is 12. There are 1000/12 = about 83 such numbers.
Thus, according to the principle of inclusion and exclusion, the total number of numbers divisible by 4 or 6 would be 250 + 166 - 83 = 333. The last step is to subtract this from the total number of integers from 1 to 1000, so the answer would be 1000 - 333 = 667.
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Choose the best definition for the following term: variable (1 point)
Answers
Answer:
The Meaning of term Variable is that Quantity Represented by small or Capital Alphabets of English whose value is not fixed.It can vary on different Situations.For example , Human diet can be called Variable.
In morning , you ate total of 0.25 Kg, in Afternoon you ate =0.50 Kg in total, and in the evening you ate total of 1 Kg.
So, if x is a variable of my Diet taken from Morning to evening, it has taken three distinct values, which are, x= 0.25, 0.50,1.
Here, x is a Variable, and 0.25,0.50 and 1 are Constant.
EASY 5 POINTS!!! Which point shows the midpoint of segment JKJK?
Answers
total length of the line is:
J = -10
K = 8
for a total of 18 units long
midpoint would be 18/2 =9
-10+9 = -1
so need the point that is located at negative 1, which is point N
so N is the midpoint
How many squares with sides that are 6 inches long are needed to cover a square with a side length of 30 inches without overlapping
Answers
Twenty-five squares with a side length of 6 inches are required to cover a square with a side length of 30 inches.
Explanation:To find out how many squares with sides that are 6 inches long are needed to cover a square with a length of 30 inches, you first need to find the area of each square.
The area of a square is found by multiplying the length of one side by itself.
So, the area of the smaller square is 6 * 6 = 36 square inches, and
the area of the larger square is 30 * 30 = 900 square inches.
Then, you divide the area of the larger square by the area of the smaller square:
900/36 = 25.
Therefore, 25 squares with sides of 6 inches are needed to cover a square with a side length of 30 inches.
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Allana 3/5 used yard of fabric to make a scarf. Can she make 2 of these scarves with 1 7/10 yards of fabric, and why?
Please Help
Answers
Use rounding or compatible numbers to estimate sum 198+727
Answers
727 round to 730
200+ 730 is 930
The answer is 930. Hope this helps!
Please help with this
Answers
The order of letters is very important. Form the given congruence we can write the following ratio:
[tex] \frac{VW}{KL} = \frac{WX}{LJ} = \frac{VX}{KJ} =1[/tex]
(notice that we do not mix the order: the first 2 letters of VWX are compared to the first 2 letters of KLJ and so on)
the ratio is one because the corresponding sides are equal.
[tex]\frac{VW}{KL}=1\\\\ \frac{2z-1}{z+2}=1\\\\2z-1=z+2\\\\2z-z=2+1\\\\z=3 [/tex]
[tex]|VW|=2z-1=2.3-1=6-1=5[/tex]
Answer: 5 units
a jar contains nickels and pennies. there are 56 coins in the jar in all. the total value of the coins is 1.52. how many pennies are in the jar
Answers
one nickel is 5 pennies or 5c
alrite...
p = amount of pennies in the jar
n = amount of nickels in the jar
we know there are 56 coins in the jar, thus whatever "p" and "n" are,
p + n = 56
we also know, the total value of all pennies and nickels is one buck and 52 cents, or 1.52.. that's 152 pennies.
now, we know there are 5 pennies in one nickel, so in "n" nickels, there are 5*n pennies, or 5n, thus
p + 5n = 152
[tex]\bf \begin{cases} p+n=56\implies \boxed{n}=56-p\\ p+5n=152\\ ----------\\ p+5\left( \boxed{56-p} \right)=152 \end{cases}[/tex]
solve for "p", to see how many penny coins are there.
what about the nickels? well, n = 56 - p.
After solving the equations, it is found that there are 32 pennies in the jar.
To solve the problem of determining the number of pennies in the jar, first we establish two variables: let's denote P for the number of pennies and N for the number of nickels.
According to the problem, there are 56 coins in total, which gives us the equation P + N = 56. Also, we know that the total value of the coins is $1.52, and because each penny is worth 1 cent and each nickel is worth 5 cents, we have another equation, which is P + 5N = 152 (since there are 100 cents in a dollar).
Now we have a system of two equations to work with:
P + N = 56
P + 5N = 152
To find P, we can subtract the first equation from the second equation to eliminate P and solve for N:
0P + 4N = 96
N = 96 / 4
N = 24
Now that we know there are 24 nickels, we can find the number of pennies by substituting N back into the first equation:
P + 24 = 56
P = 56 - 24
P = 32
Therefore, there are 32 pennies in the jar.
Eyjafjallajökull is a Volcano in Ice land. During a recent eruption, the volcano, spewed out copious amounts of ash. One small was ejected from the volcano with an initial velocity of 368ft/sec. The height H, in feet, of our ash projectile is given by the equation H= -16t +368t
1. When does the ash projectile reach its maximum height?
2. What is its maximum height?
3. When does the ash projectile return to the ground?
Answers
H` ( t ) = ( -16 t² + 368 t )` = - 32 t + 368
- 35 t + 368 = 0
35 t = 368
t = 368 : 32
t = 11.5 sec.
2. H max = - 16 · 11.5² + 368 · 11.5 = - 2,116 + 4.232
H max = 2,116 ft
3. It returns to the ground after:
t = 2 · 11.5 = 23 seconds.
HELP??? Which expression is NOT equal to the volume of the prism?
Answers
So remember that the volume of a prism can be determined through this formula... l * w * h
Now if we apply that rule with this prism.... the volume will be found as 36 cubic centimeters...
Next let's check all the choices to see if one of the answers does not sum up to or multiply to 36 cubic centimeters...
After evaluation the answer that is NOT the volume of the prism is choice C or 6 + 3 + 2
I hope this helps! ^__^
On Saturday a local shop shop sold a combine TOTAL of 345 hamburgers and cheeseburgers. The number of cheeseburgers sold was 2 times the number of hamburgers. How many hamburgers were sold on Saturday?
Answers
x = hamburgers
2x = cheeseburgers
x +2x = 345
3x = 345
x = 345/3 = 115
115 hamburgers were sold
Cory predicts it will take him 64 minutes to travel to Baltimore from Washington D.C. If the trip actually took 74 minutes, what was Cory's percent error? Round your answer to the nearest tenth of a percent.
Answers
Cory's percent error for his trip time prediction was 13.5% after rounding to the nearest tenth of a percent.
To calculate Cory's percent error for predicting his travel time to Baltimore from Washington D.C., we can use the formula for percent error:
Percent Error =[tex]|(Actual Value - Predicted Value) / Actual Value| \times 100%[/tex]
In this case, Cory's predicted time (Predicted Value) is 64 minutes, and the actual time taken (Actual Value) is 74 minutes. We can plug these values into the formula:
Percent Error = [tex]|(74 - 64) / 74| \times 100%[/tex]
Percent Error = [tex]|10 / 74| \times 100%[/tex]
Percent Error =[tex]0.1351 \times 100%[/tex]
Calculating further:
Percent Error = 13.51%
When rounded to the nearest tenth, Cory's percent error is 13.5%.
The price of a notebook was $3.50 yesterday. Today, the price rose to $4.00 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
0.50 / 3.50...* 100
0.1428 * 100
14.28% ...this rounds to 14.3% <==
The percentage increase of the notebook is 14.3%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the price of a notebook was $3.50 yesterday. Today, the price rose to $4.00
The percent increase will be calculated as,
P = [ (4.00 - 3.50) / 3.50 ] x 100
P = [ 0.50 / 3.50 ] x 100
P = 0.1428 x 100
P = 14.28% or 14.3%
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