We are to solve the equations
[tex]\begin{gathered} y=-2x+1 \\ 0.5x-y=4 \end{gathered}[/tex]The equation can be rewritten as
[tex]\begin{gathered} y+2x=1------------\text{equation 1} \\ -y+0.5x=4-----------\text{equation 2} \end{gathered}[/tex]Using substitution method
From equation 1
[tex]y=1-2x--------\text{equation 3}[/tex]Substitute 1 - 2x for y into equation 2
This gives
[tex]\begin{gathered} -(1-2x)+0.5x=4 \\ -1+2x+0.5x=4 \\ -1+2.5x=4 \\ 2.5x=4+1 \\ 2.5x=5 \\ x=\frac{5}{2.5} \\ x=2 \end{gathered}[/tex]Therefore, x = 2
Substitute 2 for x into equation 3
This gives
[tex]\begin{gathered} y=1-2(2) \\ y=1-4 \\ y=-3 \end{gathered}[/tex]Therefore the solution to the equations is
x = 2, y = -3
What can be concluded from the statement ∠1+∠2m∠1+m∠2 = 90°?
When two angles add to 90º they are called complementary angles.
Then, if in the given statement the sum of angles 1 and 2 is equal to 90º, angles 1 angle 2 are complementary.
Answer: <1 and <2 and <1and <2 are complementaryWhich statement is true of the graphed function? (PICTURE OF GRAPH BELOW)a) More information is needed to determine whether the graphed function is even, odd, or neither.b)The function is neither an even nor an odd function.c) The function is an even function.d) the function is an odd function
To determine if a function is even or odd, we start from its definition.
While for an EVEN FUNCTION we have: F(x) = F(-X), for an ODD FUNCTION we have F(-X) = -F(X)
Now, from this, we can check that all the values the function achiever for any X value, the -X has same height. The function presents a symmetry over the Y-axis, and this implies in a function to be an EVEN FUNCTION.
And from the solution developed above, the only statement that is true is the
C) The function is an even function.
Solve the inequality.16-x^=0
Inequalities
Solve:
[tex]16-x^2\le0[/tex]For a better understanding, we first multiply the inequality by -1. Recall by doing so, the sign must be flipped:
[tex]x^2-16\ge0[/tex]Factor the binomial:
[tex](x-4)(x+4)\ge0[/tex]We have a product of two variable expressions and it must be positive or zero. That can only be possible if:
* Both factors are positive or zero
* Both factors are negative or zero
The answer can come from any of the conditions stated above, so the solution is the OR combination of the individual solutions.
The first condition states:
x - 4 ≥ 0 AND x + 4 ≥ 0
This leads to the solution:
x ≥ 4 AND x ≥ -4
If x must be greater or equal to 4 and greater or equal to -4, then the AND combination gives the solution: x ≥ 4
The second condition states:
x - 4 ≤ 0 AND x + 4 ≤ 0
This leads to:
x ≤ 4 AND x ≤ -4
The AND combination gives the second solution x ≤ -4
The final solution is the first solution OR the second solution, that is:
x ≤ -4 or x ≥ 4
Representing the solution in the number line, we get the graph below:
Expressed in interval form: (-∞ , -4] U [4, +∞)
Jim, Eduardo, Larry, Simone, Ian, Dawn, Tyrone, and Kim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Jim arrive first and Kim Last?
c. Find the probability that Jim will arrive first and Kim last.
Part a: The people can arrive in 5040 ways
Part b: In 120 ways, Jim can arrive first and Kim last
Part c: The probability that Jim will arrive first and Kim last is 1/42
People invited to the party: Jim, Eduardo, Larry, Simone, Ian, Dawn, Tyrone, and Kim
Part a:
Since there are 7 people, the number of ways they can arrive is 7*6*5*4*3*2*1 =.5040 ways
Part b:
For Jim to arrive first and Kim last:
The remaining 5 people can arrive in any order so, the number of ways in which they can arrive is 5*4*3*2*1 = 120 ways
Part c:
The probability that Jim will arrive first and Kim last is given by:
Number of ways Jim can arrive first and Kim last/ Total number of ways in which all the people can arrive at the party
= 120/5040 = 1/42
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You are catering at a ceremony and have a budget of R1 200 to spend on meat. You
want to serve chicken and steak. Chicken costs R30 per kilogram and steak costs R120
per kilogram.
3.1.1 In the problem description in 3.1 above, state what changes and what remains
the same. In other words, mention the variables for the problem.
Answer:
Step-by-step explanation:
Question:
Find all critical points of the function g(x)=sin^2(11x). Express your answer in terms of pi.
(Use symbolic notation and fractions where needed. Use n for all integer values.)
Critical points are the points where the slope of the function is zero thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of function g(θ) = sin²(11θ).
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
As per the given function,g(θ) = sin²(11θ).
The critical points are the points where the slope of the tangent of the function is zero.
The slope of the tangent of a function is the first derivative thus,
g'(θ) = 0 ⇒ 2× 11 sin(11θ)cos(11θ) = 0
Sin(11θ) = 0 ⇒ θ = 0
Cos(11θ) = 0 ⇒ 11θ = π/2
θ = π/22
Since, sinusoidal functions are repeating thus,
Next critical point = π/22 + π/22 = π/11 and so on.
Hence "Critical points are the points where the slope of the function is zero thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of function g(θ) = sin²(11θ)".
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A baker has a bag with 20 cups of flour. The baker plans to use the flour to make 4 loaves of bread. Each loaf of
bread uses 3 cups of flour.
How many cups of flour will remain in the bag when the baker has finished making the bread?
Enter your answer in the space provided.
b.This interval includes one endpoint but not the other; do you see why?We can express this range of values in inequality notation and in interval notation:• Inequality notation: -4 << 4 (alternatively: z>-4 AND 2 ≤4)• Interval notation: (-4,4)Rewrite each of the following inequalities in interval notation:a.-8 -7-6-8 -7-6 -5 -4-8 -7 -6 -5 -4 -3-8 -7 -6-5 -4-B -7 -6-5C.d.0.-5 -4 -3 -2 -10123as an inequality: -7<< -5in interval notation:-1 0 12 3as an inequality: -6 ≤ ≤6in interval notation:-2 -1 0 1 2 3as an inequality: -7 < x < -1in interval notation:-2 -1 0 12 3as an inequality: 5 ≤ ≤7in interval notation:-3-2 -1 0 1 2 3as an inequality: -2 << -1.in interiell-4-34444455555
Given
To find the interval.
Explanation:
It is given that,
That implies,
a) The interval notation is, (-7,-5).
b) The interval notation is, [-6,6].
c) The interval notation is, (-7,-1).
d) The interval notation is, [5,7].
e) The interval notation is, [-2,-1).
Diego's current ago is five times Martina's age ten years ago. If Martina is currently m years old, what is Diego's current age in terms of m?
Given that Diego's current age is five times Martina's age ten years ago.
Martin is currently m years old.
Ten years ago, Martin's age was (m-10) yers.
Since, Diego's current age is five times Martina's age ten years ago., therefore, Diego's current age is
5(m-10).
So, Diego's current age is 5(m-10).
How many solutions does -14 + 6b + 7 - 2b = 1 + 5b have
The number of solutions that -14 + 6b + 7 - 2b = 1 + 5b has is 1 solution.
How to illustrate the information?It should be noted a equation is important to illustrate the relationship between the variables. In this case, the equation given is illustrated as:
-14 + 6b + 7 - 2b = 1 + 5b
Collect like terms
-8 + 6b - 2b = 5b
b = -8
Therefore, it has only one solution.
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The surface area S of a cylinder is
S
=
2
π
r
2
+
2
π
r
h
where r is the base radius and h is the height. What is h, in inches, when S is 175 square inches and r is 6 inches?
The value of height (h) will be 1.35 inches.
What is Surface area?
The space occupied by a plat surface is called Surface area.
Given that;
Surface area (S) = 2πr² + 2πrh
Where, r is the base radius and h is the height.
Now, When Surface area = 175 square inches
Radius (r) = 6 inches.
Then, We can calculate height as;
Since,
Surface area (S) = 2πr² + 2πrh
175 = 2 × 3.14 × (6)² + 2 × 3.14 × 6 h
175 = 226.08 + 37.68h
175 - 226.08 = 37.68 h
- 51.08 = 37.68 h
h = - 51.08 / 37.68
h = - 1.35
Thus, The value of height (h) will be 1.35 inches.
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Evaluate using order of operations: (8 + 7) + (3.5)
Answer:
Step-by-step explanation:
18.5
Answer:
18.5
Step-by-step explanation:
PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)
(8+7)+(3.5)
(15)+(3.5)
18.5
K increased by the product of 5 and 3 what is the expression
K (5 * 3)
K * 15
15K
The answer is 15K based on the information available. I asked the student twice if he has more details about this exercise but he become unresponsive.
Hope that this is the answer to the actual exercise.
Closing the session.
There were 18,652 geese on a lake. What is this number rounded to the tenthousands place?A20,000B19.600C19.000D18.600car mechanic rounds a car's weight to the nearest thousand. He says theweight is 4,000 pounds. What is the least and the greatest amounts the carcould actually weigh? Explain.
Step 1
There are 18,652 geese on a lake
Required: To round this off to the ten thousand place
Step 2
Hence, we will approximate the thousands and add its value to the ten thousand.
[tex]=\text{ 20,000}[/tex]Step 3
The mechanic rounds the weight of the car to the nearest thousand and gets 4000 lb.
Using the rule below;
[tex]\begin{gathered} (4000\text{ - 500)lb - least} \\ or \\ (4000\text{ + 49}9)lb-\text{ greatest} \\ \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{If we subtract 500 from 4000 we get 3500lb} \\ 3500lb\text{ is the least weight of the car} \\ \text{Notice that 3500 rounded off to the nearest thousand = 4000} \\ \text{Any number less than that say 3499 rounded off to the nearest thousand}=3000 \end{gathered}[/tex][tex]\begin{gathered} \text{If we add 499 to 4000, we get 4499 pounds} \\ 4499\text{ pounds is the greatest weight of the car} \\ \text{Notice if you round off 4499 to the nearest thousand = 4000} \\ \text{Any number more than this say 4500 rounded to the nearest thousand=5}000lb \\ \text{Hence the greatest weight of the car= 4499} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Least weight of the car = 3500}lb \\ \text{Greatest weight of the car = }4499lb \end{gathered}[/tex]Help with this problem
I₃ indifference curve represents the highest utility
What is an indifference curve?
An indifference curve is a graph that illustrates numerous pairings of two goods or commodities that leave the customer equally well off or satisfied—hence indifferent—when it comes to owning any pairing of the two items that is represented along the curve.
A consumer must give up more of one good in order to buy more of another, hence an indifference curve will always have a negative slope.
The given indifference map is a fast food meals per week vs movie tickets per week graph .
In which I₃ yields more than I₂ .
And I₂ yields more than I₁.
Thus, I₃ curve represents the highest utility.
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The measures of the angles of a triangle are shown in the figure below. Solve
for x.
62⁰
82⁰
(x+12)
Answer: 24
Step-by-step explanation:
The angles of a triangle add to 180 degrees, so:
[tex]62+82+x+12=180\\\\156+x=180\\\\x=24[/tex]
Identify the zeros of the funtion using a graphing calculator.
2
f(x)=x(squared) - 9
enter your answer in {brackets} from least to greatest
The zeros of the function are x = 3 and x = -3
How to determine the zeros of the function?The equation of the function is given as
f(x) = x(squared) - 9
Rewrite the equation properly
So, we have the following equation
f(x) = x^2 - 9
Express the equation as a difference of two squares
So, we have the following equation
f(x) = (x - 3)(x + 3)
Set the equation to 0
(x - 3)(x + 3) = 0
Split
x - 3 = 0 and x + 3 = 0
Solve for x
x = 3 and x = -3
Hence, the solutions are -3 and 3
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write an equivalent expression for (925x to the 3rd times y to the negative 4th times z to the second) 0
Answer:
1
Step-by-step explanation:
Anything to the power of 0 is 1.
Ex:
[tex]x^{0} =1\\3643737737^{0} =1\\[/tex]
Geometry help for A and B. Answer B approximate volume?
The volume of the silo with given height and diameter is 4374π ft or 13734.36 ft. (approximately).
What is volume?
Volume is a measurement of 3-D space that is occupied. Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up.
Given in the question,
The diameter of the cylindrical silo is 18 ft,
and its height is 54 ft.
Volume of a cylinder can be calculated using the formula:
[tex]V = \pi r^2 h[/tex]
Here, V = volume, r = radius, h = height,
We know that, radius is half of diameter. So, radius = 18/2 = 9 ft
Putting the given value in the formula:
[tex]V = \pi 9^2 \times 54[/tex]
[tex]V = \pi \times 81 \times 54[/tex]
V = 4374π ft.
Putting the value of π as 3.14 (approximately)
So, volume of the silo becomes 13734.36 ft.
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Determine whether the point (4,2) is in the solution set of the system of inequalities below. 4x + y < 2, y > -2
The point (4,2) is not in the solution set as it do not satisfy the first inequality 4x+y<2.
To be in the solution set of the system of inequalities the point (4.2) must satisfy both the given linear inequalities.
So, 4x + y < 2
when x = 4, y = 2
4(4) + 2 = 18 which is not less than 2
So, point do not satisfies this linear inequality
Now, for y>-2,
y = 2 which satisfies the inequality
Therefore, we say that the point (4,2) is not in the solution set of the system of inequalities.
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Mei and Dennis compare the numbers graphed on the number line below. Mei writes theinequality -9 <-3. Dennis writes the inequality -3 <-9. Which statement is true?FILE-10 -9 -8 -7 -6 -5 -4 -3 -2 -10A)Mei is correct because -9 is greater than 3.B)Mei is correct because -9 is to the left of -3 onthe number line.C)Dennis is correct because 3 is less than 9.D)Dennis is correct because -3 is to the right of--9 on the number line.
The correct answer is:
Mei statement that the inequality is -9 < -3 is True.
Mei is correct because -9 is to the left of -3 on the number line. ( first option in the picture).
There are 500 fish in a pond, to 1sf. What is the least possible number of fish that could be taken from
the pond so that there are 400 fish in the pond to 1sf
Answer:
one
Step-by-step explanation:
The least number of fish COULD be 450 ....this would be 500 to 1 S.F.
if you take ONE fish away there are then 449 which would be 400 to 1 S.F
Albert is taking a 60 item multiple choice test. He knows the correct answers to all,except 1/5 of the items.If he guesses correctly on 3/4 of these questions,how many items correctly?
57 items are correct.
What is an item?
Items are a fundamental component of an OracleAS Portal page. Item types are used to categorize items. Item types determine the contents of an item as well as the information kept about it. Users with the necessary permissions can add an item or create an item type. The properties of an object type define the information stored about it. The item types that you can add to a page differ depending on whatever item types the page group administrator has included in the page group. If the built-in item types are insufficiently flexible, users with proper access can develop new custom item kinds to fulfill their needs.
1/5 of 60 items = 60/5 = 12 items
3/4 of 12 items = 12x3/4 = 9 items
Total no. of correct items = 60 - 12 + 9 = 57 items
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Choose all the correct answers using the diagram below.
What is the length of the diagonal?
2
√2
1
√3
No answer text provided.
We want to find the diagonal length of the square given in the question.
[tex]x=?[/tex]Since this shape is a square, all four sides are of equal length. Therefore, each side of the square must be [tex]1[/tex] unit.
Next, we will use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle. This value is also equal to the length of our diagonal. We can find the length of the diagonal using the formula below;
[tex]a^2+b^2=c^2[/tex]Therefore, the correct answer to our question is the following equality;
[tex]x^2=1^2+1^2[/tex][tex]x^2=2[/tex][tex]\sqrt{x^2} =\sqrt{2}[/tex][tex]x=\sqrt{2}[/tex]Second option should be the answer.
Let f(x)=(x−7)(x+6)(x−5). Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0.
2. Find the x-intercept(s). List your answers as points in the form (a,b).
Answer:
ez
Step-by-step explanation:
ezz
The circumference of a circle is 12.56 miles. What is the circle's diameter?
Answer:
d= 4 miles
Step-by-step explanation:
C=2πr
d=2r
d=C
π=12.56
π≈3.99797mi
Mary sold 192 worth of greeting cards if she received 25% Commission on all sales how much commission did she receive
25% of 192 = 192 * 25/100 = 192 * 0.25 = 48
Answer:
Mary received $48
Solve quickly!3(x+10)=4(x-2)
ANSWER
x = 38
EXPLANATION
To solve this equation, first, we have to apply the distributive property of multiplication over addition to eliminate the parenthesis,
[tex]\begin{gathered} 3\cdot x+3\cdot10=4\cdot x-4\cdot2 \\ \\ 3x+30=4x-8 \end{gathered}[/tex]Subtract 3x from both sides of the equation,
[tex]\begin{gathered} 3x-3x+30=4x-3x-8 \\ \\ 30=x-8 \end{gathered}[/tex]And add 8 to both sides,
[tex]\begin{gathered} 30+8=x-8+8 \\ \\ 38=x \end{gathered}[/tex]Hence, the solution is x = 38.
The population of a certain city has been increasing exponentially accordingto the functionP (t) = 800, 000e0.051where t is the time in years (with t = 0 corresponding to 2014).a.) What was the population in the year 2014?b.) In what year will the population reach 1,200,000?c. what was the rate of change of the population in the year 2019?
(b) To determine the year the population will reach 1,200,000, substitute p(t) = 1,200,000 into p(t) above and calculate the value of t
[tex]\begin{gathered} \text{ p(t) = 1,200,000} \\ 1,200,000=800,000e^{0.05t} \\ \text{divide both sides by 800,000} \\ \frac{1200000}{800000}\text{ =}\frac{\text{ 800000}e^{0.05t}}{800000} \\ \\ 1.5=e^{0.05t} \\ \text{take }\ln \text{ of both sides} \\ \ln 1.5\text{ = }\ln e^{0.05t} \\ \ln 1.5=0.05t\ln e \\ \ln 1.5=0.05t(1) \\ \ln 1.5\text{ = 0.05t} \\ \text{divide both sides by 0.05} \\ \frac{\ln 1.5}{0.05}\text{ = t} \\ t=8 \end{gathered}[/tex]The year when t= 8, given that t=0 in 2014 is the year 2022
(c) the rate of change of the population in the year 2019
Firstly, differentiate p(t) with respect to t
[tex]\begin{gathered} p(t)\text{ = }800,000e^{0.05t} \\ \frac{\text{ dp}}{\text{ dt}}\text{ = 0.05(800,000)}e^{0.05t} \\ \frac{dp}{\mathrm{d}t}\text{ = 40,000}e^{0.05t} \\ \text{ This means that the rate of change of the function at any time t is 40,000}e^{0.05t} \\ \end{gathered}[/tex]In the year 2019, t = 5
Substitute t=5 into the rate of change above
[tex]\begin{gathered} \text{ at t= 5, } \\ \text{rate of change = 40,000}e^{0.05(5)} \\ =\text{ 40,000}e^{0.25} \\ =40,000(1.284025) \\ =51361 \end{gathered}[/tex]whats 1 plus 1 in mathmaticals
Answer:
2
Step-by-step explanation:
If you have 1 cookie and someone gives you another cookie you now have 2.