Answer:
Step-by-step explanation:
12x −3y=36 ⇔ 3y = 12x - 36
y = 4x - 12
y = 0 ⇔ 4x - 12 = 0 ⇔ 4x = 12 ⇔ x = 12/4 = 3
So (0 ; - 12) and (3 ; 0)
Answer:
x-intercept=3, y-intercept=-12
Step-by-step explanation:
at x-intercept y=0 such that:
12x-3(0)=36
12x=36
[tex]x=\frac{36}{12} =3[/tex]
additionally, at y-intercept x=0 such that
12(0)-3y=36
-3y=36
[tex]y= \frac{36}{-3}=-12[/tex]
You deposit Php1000 in a savings account that earns 6% interest per year Compound interest
Answer:
that is all I could do. hope you have gotten your answer.good day.
Which expression below can be obtained from 4sin4t by using a power reducing formula?
Select the correct answer below:
1+2cos(4t)
32−2cos(2t)+12cos(4t)
32+2cos(2t)+12cos(4t)
3−2cos(2t)+2cos(4t)
Step-by-step explanation:
4×sin(4t) = 4×sin(2t + 2t) =
= 4×(sin(2t)cos(2t) + cos(2t)sin(2t)) =
= 4×2×sin(2t)cos(2t) = 8×sin(2t)cos(2t)
but that did not lead anywhere near to any of the answer options.
so, i guess, you made typos in the description and in the answer options.
did you mean maybe
4×sin⁴(t) ?
sin⁴(t) = (3 - 4×cos(2t) + cos(4t))/8
4×sin⁴(t) = 4×(3 - 4×cos(2t) + cos(4t))/8 =
= (3 - 4×cos(2t) + cos(4t))/2 =
= 3/2 - 2×cos(2t) + 1/2 × cos(4t)
is that the real answer option 2 ?
then that is the correct answer.
What is the equation of the parabola? coordinate plane with a parabola facing up with vertex at 0 comma 2, the point 0 comma 5 and a horizontal line going through 0 comma negative 1 y = −one twelfthx2 − 2 y = one twelfthx2 − 2 y = −one twelfthx2 2 y = one twelfthx2 2
The equation of the parabola is y = 2/25x^2 + 2
How to determine the parabola equation?The complete question is in the image
The given parameters are:
Vertex, (h, k) = (0,2)
Point (x,y) = (-5, 4)
The parabola is represented as;
y = a(x - h)^2 + k
Substitute (h, k) = (0,2)
y = a(x - 0)^2 + 2
This gives
y = ax^2 + 2
Substitute (x, y) = (-5,4)
4 = a(-5)^2 + 2
This gives
4 = 25a + 2
Subtract 2 from both sides
25a = 2
Divide by 25
a = 2/25
Substitute a = 2/25 in y = ax^2 + 2
y = 2/25x^2 + 2
Hence, the equation of the parabola is y = 2/25x^2 + 2
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Select the properties of a rectangle Select the properties of a rectangle
Answer:
[tex]\large \boxed{\checkmark}} \quad \textsf{has four right angles}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{opposite sides are congruent}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{diagonals bisect each other}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{opposite sides are parallel}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{opposite angles are congruent}[/tex]
[tex]\large \boxed{\checkmark}} \quad \textsf{diagonals are congruent to each other}[/tex]
Step-by-step explanation:
Properties of a rectangle:
Two-dimensional quadrilateral (4-sided figure)Opposite sides are equal in lengthOpposite sides are parallel to each otherFour equal interior angles (each angle is 90°)Diagonals bisect each other (divide into 2 equal parts)Length of diagonals are equalTherefore, the correct answer options are:
has four right anglesopposite sides are congruentdiagonals bisect each otheropposite sides are parallelopposite angles are congruentdiagonals are congruent to each otherJoyce has as much money as George; then they bet 5 cents each and George lost. If, after the bet, George has x cents, how much does Joyce have ?
Answer:
x+10
Step-by-step explanation:
So they did a bet, and placed 5 cents each. George lost the bet that gives Joyce 5 points plus 5 more that make 10.
After the bet George has: x cents
Before the bet George had: x + 5 cents
Before the bet Joyce had also x + 5 cents
Since Joyce won 5 cents, after the bet she has x + 5 + 5 = x + 10 cents.
please help me in this :")
The numbers of runners that are 50 and above are 3000.
How to find the runners that are 50 and above in the pie chart?Using the pie chart,
If there are 1500 runners that are under 20, therefore,
1500 = 10 / 100 × x
where
x = total number of runners
10x = 150000
x = 15000
Therefore,
the number of runners that are 50 and above = 20 / 100 × 15000 = 3000
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Find all real zeros of the function y= -9x - 1
A. -9
B. - 1/9
C. 1/9
D. -9, -1
Answer: -1/9 which is choice B
Explanation:
The term "zeros" refers to the x intercepts.
Plug in y = 0 and solve for x.
y = -9x-1
0 = -9x - 1
9x = -1
x = -1/9
Add: - 14 + (-12) + 4
Answer:
-22
Step-by-step explanation:
-14+(-12）+4
=-14-12+4
=-26+4
=-22
Line segment PQ is a directed line segment beginning at P(6,-5) and ending at QX-2,4).
Find point R on the line segment PQ that partitions it into the segments PR and RQ in the ratio 3:2.
O A. (8,3)
OB. (¹,-)
oc. (-1,3)
C.
O.D. (1,3)
The coordinates of R is (1.2, 0.4)
How to determine the partition?The points are given as:
P= (6, -5)
Q = (-2, 4)
The ratio is given as:
m : n = 3 : 2
The location of R is calculated as:
[tex]R = \frac{1}{m + n}* (mx_2 + nx_1, my_2 + ny_1)[/tex]
So, we have:
[tex]R = \frac{1}{3 + 2}* (3 * -2 + 2 * 6, 3 * 4 + 2 * -5)[/tex]
Evaluate the products
[tex]R = \frac{1}{5}* (6, 2)[/tex]
This gives
R = (1.2, 0.4)
Hence, the coordinates of R is (1.2, 0.4)
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You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
The company's first task is to cast the lead female roles of Fantine, adult Cosette, and Éponine, and the lead male roles of Jean Valjean, Inspector Javert, and Marius. You have received headshots and resumes from 28 women and 22 men who are interested in auditioning for these parts.
A: If no one has been cast yet, how many different ways are there to cast Fantine from the 28 women?
B: If Fantine has already been cast, how many different ways are there to cast adult Cosette from the remaining women?
C: If Fantine and adult Cosette have already been cast, how many different ways are there to cast Éponine from the remaining women?
Select one answer choice for part A, one answer choice for part B, and one answer choice for part C.
B: 27P2
C: 26
C: 26!
A: 28P3
B: 27
C: 26P1
A: 28
B: 27!
A: 28!
Question 2:
A: Which of the following expressions will calculate the number of ways the three lead female roles could be cast?
B: Evaluate the permutation from part A.
Select one answer choice for part A, and one answer choice for part B.
B: ≈3.05×10^29
A: 28P3
B: 19656
A: 3P28
B: ≈5.08×10^28
A: 28P25
The permutation shows that when one has been cast yet, the different ways that are there to cast Fantine from the 28 women is 28.
How to calculate the value?The different ways that are there to cast Fantine from the 28 women will be:
= 28!/(28 - 1)!
= 28!/27!
= 28
When Fantine has already been cast, the number of ways that are there to cast adult Cosette from the remaining women will be:
= 27!(27 - 1)!
= 27!/26!
= 26
When Fantine and adult Cosette have already been cast, the different ways that are there to cast Éponine from the remaining women is:
= (28 - 2)!/(28 - 2 - 1)!
= 26!/25!
= 25
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The midpoint of the line segment from P₁ to P₂ is (-4,1). If P₁ = (-9,5), what is P2?
[tex] - 4 = \frac{ - 9 + x}{2} \\ - 8 = - 9 + x \\ x = 1[/tex]
[tex]1 = \frac{5 + y}{2} \\ 2 = 5 + y \\ y = - 3[/tex]
P² ( 1 , -3 )Help me with this please :V
Answer:
refer to the above attachment
Given that
f
(
x
)
=
x
2
+
7
x
and
g
(
x
)
=
x
+
7
, calculate
(a)
(
f
∘
g
)
(
−
5
)
Answer:
18
Step-by-step explanation:
We want to find the composite function at a specific value (-5).
Thus, we can write and think of the function like this:
f[g(-5)]
So we substitue the -5 for every x in the g(x) function:
g(x) = -5 + 7 = 2
Then we substitute this 2 for every x in the f(x) function:
f(x) = 2^2+7(2) = 4 + 14 = 18
A fair die is rolled 1200 times. Find the approximate probability that the sum falls between
5000 and 6300. Clearly indicate any theorems that you are using / where any rounding has been done.
Your final answer should be accurate to two decimal places.
Answer:
abcdefghijklmnopqrstuvwxyz
Step-by-step explanation:
these are the alphabets
The term "freshman 15" refers to the claim that college students typically gain 15lbs during freshman year at college. Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of 2.9 lb and a standard deviation of 10.4 lb. Find the probability that a randomly selected male college student gains 15 lb or more during their freshman year. What does the result suggest about the claim of the "freshman 15"?
The probability that a randomly selected male college student gains 15 lb or more during their freshman year is 11.6%
What is Probability ?Probability is defined as the likeliness of an event to happen.
Let X be a random variable that shows the term "freshman 15" that claims that students typically gain 15lb during their freshman year at college.
It is given that
X follows is a normal distribution with a mean of 2.1 lb (μ) and a standard deviation (σ) of 10.8 lb.
Population Mean (μ) = 2.1
Population Standard Deviation (σ) = 10.8
We need to compute Pr(X≥15). The corresponding z-value needed to be computed is:
[tex]\rm Z_{lower} = \dfrac{ X_1 -\mu }{\sigma}\\\\Z_{lower} = \dfrac{ 15-2.1 }{10.8}\\\\\\Z_{lower} = 1.19[/tex]
Then the probability is given as
[tex]\rm Pr(X \geq 16 ) = Pr (\dfrac{X -21}{10.8} \geq \dfrac{15-21}{10.8})\\\\= Pr (Z \geq \dfrac{15-2.1}{10.8}\\\\= Pr (Z\geq 1.19)\\\\ = 0.1162[/tex]
Pr(X≥15)=0.1162. (11.6%)
The probability that a randomly selected male college student gains 15 lb or more during their freshman year is 11.6%
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A washer and a dryer cost $572 combined. The washer cost $78 less than the dryer. What is the cost of the dryer?
Answer:
$325
Step-by-step explanation:
Let the dryer price be x, then the washer price would be x-78
x+x-78 = 572
2x = 650
x = 325
Find (f-g)(x) where f(x) = -x^2, g(x) = -(x+4)²
Answer:
8x + 16
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
g(x) = -(x+4)(x+4)
= -(x² + 4x + 4x + 16)
= -(x² + 8x + 16)
= -x² - 8x - 16
1) Subtract the two functions.
= (-x²) - (-x² - 8x - 16)
= -x² + x² + 8x + 16
= 8x + 16
Use a half angle formula to find the exact value of the expression tan 22.5 degree
Answer:
Step-by-step explanation:
The distance, y, in miles, traveled by a car for a certain amount of time, x, in hours, is shown in the graph below: A graph titled Motion of a Car is shown with Time in hours labeled on x-axis and Distance from Starting Point in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, and the scale on the y-axis shows the numbers 0, 12, 24, 36, 48, 60, 72. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 1, 12. The second straight line joins 1,12 and 2,12 and the third straight line joins ordered pair 2,12 with the ordered pair 5,36. Which of the following best describes the motion of the car shown? It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours. It travels for 2 hours, then stops for 1 hour, and finally travels again for 2 hours. It travels for 1 hour, then stops for 2 hours, and finally travels again for 5 hours. It travels for 2 hours, then stops for 3 hours, and finally travels again for 5 hour
The best description of the car's motion as shown in the graph is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.
How to Analyze a Distance-Time Graph?In a distance-time graph, an horizontal line implies no distance was covered within that time frame, meaning there was a stop.
Thus, in the graph given, the stop occurred 1 and 2, which is equivalent to an hour. From 2 to 5 on the x-axis means there was movement for up to 3 hours.
Therefore, the best description is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.
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Rewrite 4/10 : 1/25 as a unit rate
Answer:
0.4 : 0.04
Step-by-step explanation:
4 ÷ 10 = 0.4
1 ÷ 25 = 0.04
(1 point) A tank contains 50 kg of salt and 1000 L of
water. A solution of a concentration 0.025 kg of salt
per liter enters a tank at the rate 5 L/min. The solution
is mixed and drains from the tank at the same rate.
(a) What is the concentration of our solution in the
tank initially?
concentration = .05 (kg/L)
(b) Find the amount of salt in the tank after 1 hours.
O (kg)
amount =
(c) Find the concentration of salt in the solution in the
tank as time approaches infinity.
concentration = .025 (kg/L)
Your answers for (a) and (c) are correct.
(b) Salt flows into the tank at a rate of
[tex]\left(0.025 \dfrac{\rm kg}{\rm L}\right) \left(5 \dfrac{\rm L}{\rm min}\right) = 0.125 \dfrac{\rm kg}{\rm min} = \dfrac18 \dfrac{\rm kg}{\rm min}[/tex]
If [tex]A(t)[/tex] is the amount of salt (in kg) in the tank at time [tex]t[/tex] (in min), then the salt flows out of the tank at a rate of
[tex]\left(\dfrac{A(t)}{1000+(5-5)t} \dfrac{\rm kg}{\rm L}\right) \left(5 \dfrac{\rm L}{\rm min}\right) = \dfrac{A(t)}{200} \dfrac{\rm kg}{\rm min}[/tex]
The net rate of change in the amount of salt in the tank at any time is then governed by the linear differential equation
[tex]\dfrac{dA}{dt} = \dfrac18 - \dfrac{A(t)}{200}[/tex]
[tex]\dfrac{dA}{dt} + \dfrac{A(t)}{200} = \dfrac18[/tex]
I'll solve this with the integrating factor method. The I.F. is
[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{200}\right) = e^{t/200}[/tex]
Distributing [tex]\mu[/tex] on both sides of the ODE gives
[tex]e^{t/200} \dfrac{dA}{dt} + \dfrac1{200} e^{t/200} A(t) = \dfrac18 e^{t/200}[/tex]
[tex]\dfrac d{dt} \left(e^{t/200} A(t)\right) = \dfrac18 e^{t/200}[/tex]
Integrate both sides.
[tex]\displaystyle \int \frac d{dt} \left(e^{t/200} A(t)\right) \, dt = \frac18 \int e^{t/200} \, dt[/tex]
[tex]e^{t/200} A(t) = \dfrac{200}8 e^{t/200} + C[/tex]
[tex]A(t) = 25 + Ce^{-t/200}[/tex]
Given that [tex]A(0)=50\,\rm kg[/tex], we find
[tex]50 = 25 + Ce^0 \implies C = 25[/tex]
so that
[tex]A(t) = 25 + 25e^{-t/200}[/tex]
Then the amount of salt in the tank after 1 hr = 60 min is
[tex]A(60) = 25 + 25e^{-60/200} = \boxed{25 \left(1 + e^{-3/10}\right)}[/tex]
Find so that the distance between (−2,3) and (,1) is √13
The distance between (-2, 3) and (-5, 1) is √13.
or, the distance between (-2, 3) and (1, 1) is √13.
We know that the length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two points. Therefore, by measuring the length of the line segment that connects the two points, the distance between them can be determined. If (a, b) and (c, d) be two points, then the distance between them is [tex]\sqrt[]{(b - a)^{2} +(d- c)^{2} }[/tex].
Here, one point is (-2, 3).
Let the other point be (x, 1).
Given that the distance is √13.
Now, [tex]\sqrt[]{(x - (-2))^{2} +(1 - 3)^{2} } = \sqrt{13}[/tex]
i.e. [tex]\sqrt[]{(x + 2)^{2} +( - 2)^{2} } =\sqrt{13}[/tex]
i.e. [tex]\sqrt[]{x^{2}+4x +4 +4 }=\sqrt{13}[/tex]
i.e. [tex]x^{2}+4x +8 =13[/tex]
i.e. [tex]x^{2}+4x + 8- 13=0[/tex]
i.e.[tex]x^{2}+4x -5=0[/tex]
i.e. [tex]x^{2} +5x - x -5=0[/tex]
i.e. [tex]x(x+5)-1(x+5)=0[/tex]
i.e. [tex](x+5)(x-1)=0[/tex]
i.e. [tex]x=-5,1[/tex]
So, the point is either (-5, 1) or (1, 1).
Therefore, the required point is either (-5, 1) or (1, 1).
i.e. the distance between (-2, 3) and (-5, 1) is √13.
or, the distance between (-2, 3) and (1, 1) is √13.
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Please solve this for me, thank you!
The answer to this question is y = 847728300000/1366991599
Given 4y/1.025⁴ ₊ y ₋ 2y × 1.05² = 1500
1. covert decimal to fraction
= 4y/(1025/1000)⁴ ₊ y ₋ 2y × (105/100)² = 1500
2. Calculate the power
4y/2825761/2560000 ₊ y ₋ 2y × 441/400 = 1500
3. Divide the fraction by multiplying its reciprocal
4y × 2560000/2825761 ₊ y ₋ 2y × 441/400 = 1500
4. Multiply the monomials
10240000/2825761 y ₊ y ₋ 2y × 441/400 =1500
5. Combine like terms
10240000/2825761 y ₊ y ₋ 441/200 y = 1500
1366991599/565152200 y = 1500
6. Divide both sides of the equation by the coefficient of variable.
y = 1366991599/565152200 × 1500
y = 847728300000/1366991599
Hence we get the final value as y = 847728300000/1366991599
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Brian wants to buy the latest iPhone for $1000. He has
$100 and earns $15 for 1 hour (h) of tutoring.
Enter the minimum number of hours Brian must tutor to
be able to buy the iPhone.
0000
15h+1001000, h-60
15h 100 1000, h>=60
15h 1001000, h>60
15h 100 1000, h-60
Answer:
Step-by-step explanation:
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.
The probability that exactly 8 individuals do not cover their mouth is
The probability that exactly 8 individuals do not cover their mouth is 0.0037.
How to calculate the probability?It should be noted that the probability will be solved by using the binomial distribution.
From the information, the probability that a randomly selected individual will not cover his or her mouth when sneezing is 0.267.
Therefore, the probability that thee person will not cover their mouth will be:
= 1 - 0.267
= 0.733
This will be:
= 12C8 × (0.267)^8 × (1 - 0.267)⁴
= 12C8 × (0.267)^8 × 0.733⁴
= 495 × 0.00002582 × 0.28867
= 0.0037
In conclusion, the probability is 0.0037.
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Manny plans to save 1/14 of his salary each week. If his weekly salary is $378, find the amount he will save each week.
Answer:
27
Step-by-step explanation:
Could someone help me out?
The equation of the line is y = -11x + 232
How to determine the equation?The given parameters are:
Slope (m)= -11
Point (x1, y1) = (31, -109)
The linear equation is then calculated as:
y = m(x - x1) + y1
This gives
y = -11(x - 31) - 109
Evaluate the product
y = -11x + 341 - 109
Evaluate the like terms
y = -11x + 232
Hence, the equation of the line is y = -11x + 232
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Theorems Involving Similarity
The theorem of similarity implies that the line segment divided the triangle into the proportional segment.
How to illustrate the theorem?It should be noted that the theorem of similarity states that the line segment splits two sides of a triangle into proportional segments.
This occurs when the side is parallel to the third side of the triangle.
These three theorems, known as Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side are foolproof methods for determining similarity in triangles.
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what is the functions domain ?
what is the functions range ?
find the values of the function f(-5)= and f(-1)=
Answer:
domain: -∞ < x < ∞range: -∞ < y ≤ -1f(-5) = -2f(-1) = -4Step-by-step explanation:
Function values and the extent of the graph can be determined by reading the graph.
DomainThe domain of the function is the set of values for which the function is defined. It is the horizontal extent of the graph. The graph shows the function is defined for all real numbers.
The domain is -∞ < x < ∞.
RangeThe range of the function is the set of output values the function may have. It is the vertical extent of the graph. The graph shows the function can have any value no greater than -1.
The range is -∞ < y ≤ -1.
Function valuesFunction values can be read from the graph by locating the x-value on the x-axis, and following the vertical line to its intersection with the function graph. The y-value of that point is the function value.
f(-5) = -2
f(-1) = -4
Or, we can write the function definition based on the graph, and use that definition to find the values at specific points. The graph is of the absolute value function reflected over x and translated <-4, -1>.
f(x) = -|x+4| -1
f(-5) = -|-5 +4| -1 = -1 -1 = -2
f(-1) = -|-1 +4| -1 = -3 -1 = -4
x + 8 = -3 solution for x