The cars receive the broadcast signal for length of about 36 miles.
What is meant by equations?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
A condition on a variable (or variables) is a pair of expressions in the variable (or variables) that have the same value. The solution or root of the equation is the quantity at which the variable's value satisfies the equation. If you swap the LHS and RHS, an equation still makes sense.
Equations can be categorized as either identities or conditional equations. For each value of the variables, an identity holds true. Only specific values of the variables make a conditional equation true. An equals symbol ("="), separating two expressions, is used to represent an equation.
Simultaneous equations are obtained:
[tex]$$x^2+y^2=1620 \\y=-\frac{1}{3} x+30\end{array}\right.$$[/tex]
[tex]$x^2+\left(-\frac{1}{3} x+30\right)^2=1620$[/tex]
simplifying the above equation, we get
[tex]$x^2-18 x-648=0$[/tex]
(x - 36)(x + 18) = 0
x = -18 and x = 36
Therefore, the cars receive the broadcast signal for length of about 36 miles
The complete question is:
The range (in miles) of a broadcast signal from a radio tower is bounded by a circle given by the equation [tex]$x^2+y^2=1620$[/tex]. A straight highway can be modeled by the equation [tex]$y=-\frac{1}{3} x+30$[/tex]. For what length of the highway are cars able to receive the broadcast signal? Round your answer to the nearest tenth.
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Find the determinant of the coefficient matrix 3x+4y=0 -2x+3y=17
The determinant of the coefficient matrix 3x+4y=0 and -2x+3y=17 is 17.
What is matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.
Given:
A system of equations,
3x+4y=0
-2x+3y=17.
To find the determinant,
we will find the matrix from Cramer's rule,
A =
[tex]\left[\begin{array}{cc}3&4\\-2&3\end{array}\right][/tex]
So, determinant of matrix A
ΔA = 3 x 3 -(4 x -2)
ΔA = 9 + 8
ΔA = 17.
Therefore, the determinant is 17.
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Classify the following triangle according to its sides and its angle measures.
2 cm
83⁰
53
2.5 cm
3 cm
44
This triangle is classified as an acute triangle since all three angles measure less than 90° (83⁰, 44⁰). It is also classified as an isosceles triangle since two of the sides (2 cm and 2.5 cm) are equal in length.
What are acute and isosceles triangle?An acute triangle is a triangle in which all three angles measure less than 90 degrees. It is the opposite of an obtuse triangle, which has one angle measuring more than 90 degrees.
An acute triangle can also be referred to as a “sharp” triangle. The sum of all three angles in an acute triangle will always equal 180 degrees. An acute triangle can be either isosceles or scalene.
An isosceles triangle is a triangle with two sides of equal length and two equal angles opposite the two sides. The two angles are often referred to as the base angles, while the third angle is called the vertex angle. The two sides of an isosceles triangle are also often referred to as the legs, while the longest side is referred to as the base.
Isosceles triangles are studied in geometry, and the properties of such triangles can be used to solve many mathematical problems.
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I need help with this paper, it would be much appreciated.
1. y = a(x + 5)^2 + 6
2. y = a(x - 1)^2 + 4
3. y = a(x + 2)^2 - 6
4. y = a(x - 4)^2 - 10
5. y = a(x + 2)^2 - 4
6. y = a(x - 3)^2 + 12
These are the equations of the quadratic in vertex form, where (h, k) are the vertex coordinates, and a is the coefficient of x^2. In each case, the x-intercepts provided are plugged into the equation to check if it equals zero, which is how we can confirm that it is a correct equation for the parabola.
I hope this helps :)
5a>5.45 solve for a.
Answer is in attached photo.
Step-by-step explanation:
SolutionSolution is in the attached photo, do note that this question tests on the concept of Inequality.
[tex]5a > 5.45[/tex]
Divide both sides by 5:
[tex]\dfrac{5a}{5} > \dfrac{5.45}{5}[/tex]
Answer:
[tex]a > 1.09[/tex]
Write an informal negation for each of the following statements. Be careful to avoid negations that are ambiguous.
a. All dogs are friendly.
b. All people are happy.
c. Some suspicions were substantiated.
d. Some estimates are accurate.
The informal negation for each of the following statements:
1) No dog is ferocious.
2) Noboby is sad.
4) No suspicions were unsubstantiated.
5) No estimate is incorrect.
What is informal negation?It is sometimes necessary in mathematics to determine the inverse of a given mathematical statement. This is commonly known as "negating" a statement. Keep in mind that if a statement is true, then its negation is false (and if a statement is false, then its negation is true). A conditional statement's negation is logically equivalent to a conjunction of the antecedent and the negation of the consequent. The logical negation symbol or is one of the statement connectives or operators that can be used to combine two or more statements to form new compound statements. It simply flips the truth value of any statement it appears in front of.
Here,
Each of the following statements has an informal negation:
1) No dog is ferocious.
2) Noboby is sad.
4) No suspicions were unsubstantiated.
5) No estimate is incorrect.
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The point P is on the unit circle. If the y-coordinate of P is −3/5 and PP is in quadrant IV , then X= ?
The value of X is 4/5 if point P is on the unit circle and if the coordinate of P is -3/5 and P is in iV quadrant.
We know that unit circle is the circle of radius 1 unit. We are given the y-coordinate of P, that is y = -3/5. Now if we draw a perpendicular line at x-axis, and we know the length of line joining the P and the origin is 1 unit (h = 1). We can construct a right triangle. Then by pythagorean theorem.
x² + y² = h²
x² = √(h² - y²)
x² = √(1² - (-3/5)²)
x² = √(1 - (9/25))
x² = √(16/25)
x = 4/5
Since X is in the IV quadrant, where x is positive and y is negative.
So x = +4/5
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A 15 meter long cylinder with a diameter of 7 meters has a square prism with a base length of 3 meters hole going all the way through the center of it as shown in the diagram (not to scale).
Find the volume of the composite shape rounding to the nearest cubic meter.
Hint: while working the problem carry figures at least three decimal places, then round to the nearest cubic meter only once at the very end.
The square prism's volume is 135 meter
Explain about the volume of the composite shape?Either the total number of smaller prisms that make up the composite shape, or its volume. the distinction between a larger prism and a smaller prism that was taken out of it.
A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently.
Any shape that is constructed from two or more geometric shapes is referred to as a composite or compound shape. The triangle and square in the following shape are joined together. The square and the rectangle that make up the blue shape. There are two triangles making up the green shape.
Detailed explanation:
The parameters listed are;
L = 15 meters is the cylinder's length.
D = 7 meters is the cylinder's diameter.
B = 3 meters is the square prism's base length.
Consequently, we have;
The square prism's volume is
= B² x L
= 3² x 15
= 9 x 15
= 135 meter
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Solve for m:-
2(m-5) = m-3
The value of m in the given equation will be 7.
Steps to solve the linear equation :
⇒2(m-5) = m-3
Bring RHS (Right hand side) terms to LHS(left hand side) of the equation,
⇒2(m-5) - (m-3) = 0
Now open the brackets,
⇒2m - 10 - m + 3 = 0
Now solve for m,
⇒2m - m - 10 + 3 = 0
⇒m - 10 + 3 = 0
⇒m - 7 = 0
Taking 7 to the RHS of the equation,
⇒m = 7
∴ The value of m is 7
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To solve for m in the equation 2(m-5) = m-3, we can start by distributing the 2 on the left side of the equation:
2m - 10 = m - 3
Next, we can add 3 to both sides of the equation to get:
2m - 10 + 3 = m
This simplifies to:
2m - 7 = m
Now we can subtract m from both sides:
2m - m - 7 = 0
This simplifies to:
m - 7 = 0
Finally, we can add 7 to both sides to solve for m:
m = 7
So the solution for m is 7.
Assume that for dry rice and beane - 1 basin 20 cups 40 basins - 1 sack a A sack contains 100 kg of rice. Estimate the number of kilograms of rice in 1 basin Estimate the number of grams of rice in Toup. b A trader buys a sack of rice for N6 000 for beans. Four women biry a sack of beans between them. They share the beans equally to bear) N150 How many basins does each woman get? How much does each woman save by buying the beans in this way?
A single basin of dry rice and beans 20 cups One bag of 40 basins 100 kilogrammes of rice is included in a sack.
Do you save money buying whole bean coffee?In the majority of circumstances, whole coffee beans won't be less expensive than ground coffee. Unfortunately, that is not the case if you think that by grinding your own coffee at home you can save some money.There are three factors that contribute to pre-ground coffee's cost advantage over whole bean coffee. If you decide to go the whole-bean way, you'll also need to buy a grinder, which will run you anywhere from $10 to $1000 up front. tea leaves: If kept in a cold, dark, dry location, a bag of whole coffee beans can be kept for up to twelve months if it is unopened, and for one week if it is opened. Coffee ground: store a sealed bag of coffee ground for three to five months in the pantry.To learn more about buying refer to :
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Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
A. Sample space = 1, 2, 3
B. Sample space = 1, 2, 3, 4, 5, 6
C. Sample space = lemon-lime, watermelon, grape
D. Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape
The correct sample space for the gumballs in Julia's bag is {lemon-lime, watermelon, watermelon, grape, grape, grape} which makes option D correct.
How to evaluate for the sample sapceThe sample space for the gumballs in Julia's bag would be all the possible outcomes of selecting one gumball from the bag without replacement.
Since there are 1 lemon-lime, 2 watermelon, and 3 grape gumballs in the bag, the sample space would be expressed as:
sample space = {lemon-lime, watermelon, watermelon, grape, grape, grape}.
Therefore,we have 6 total outcomes in the sample space for the gumballs in Julia's bag.
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a blank is a relation in which each member
A function is a relation in which each member in the domain is paired with exactly one element in the range.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
A phrase: A blank is a relation in which each member in the domain is paired with exactly one element in the range?
We have to find the blank word.
From the function definition,
A relation between a collection of inputs and outputs is known as a function.
A function is a connection between inputs in which each input is connected to precisely one output.
Each function has a range, co-domain, and domain.
Therefore, blank word is a function.
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The complete question:
A blank is a relation in which each member in the domain is paired with exactly one element in the range?
Select the two statements about risk and return that are true or potentially true.
As the risk of an investment increases, so does the potential for a higher return.
As the risk of an investment decreases, the return potential increases.
O Diversification increases the risk of a group of investments.
O Holding stocks of companies of different sizes and from different sectors reduces investment risk in
a portfolio.
O Investors should choose only investments that move up in price at the same time.
The two statements about risk and return that are true or potentially true are:
As the risk of an investment increases, so does the potential for a higher return.Holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio.What is risk and return?
The risk connected to a particular investment and its returns are known as risk and return in financial management. High-risk investments typically produce higher financial returns, and low-risk investments typically produce lower returns. In other words, a given investment's risk and return are directly correlated.
As the risk of an investment increases, so does the potential for a higher return because there is a direct correlation between risk and return.
Also, holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio because on diversifying the portfolio, risk also gets divided thus, giving a satisfactory return to the investor.
Hence, the above two statements are true.
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Answer: As the risk of an investment increases, so does the potential for a higher return. and Holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio.
Step-by-step explanation: Increased price fluctuation, upward or downward, increases risk and the possibility of a high return or a huge loss. When the risk, or price fluctuation, is low, so is the return potential. Diversification helps decrease the risk of a group of investments because the value of individual investments will increase or decrease at different time periods and help to lessen value fluctuation in the overall portfolio.
the graph of f' the derivative of f is shown above which of the following statements is true about f
The chart of the derivative of f is shown above the subsequent statement is true about f growing for -2<=x<=0
What is meant by Mathematical equation?A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."The slope-intercept form, standard form, and point-slope form are the three primary formats for linear equations.A mathematical expression with two equal sides and an equal sign in the middle is called an equation. An example of an equation is 4 + 6 = 10.A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.A mathematical expression known as an equation is one in which one side of the expression equals the other, as in the example above: Since we know that 4 + 4 = 8 and 10 - 2 = 8, the equation is true because both sides are equal.To learn more about Mathematical equation, refer to:
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show that the graphs of the two equations and have tangent lines that are perpendicular to each other at their point of intersection.
The graphs of the two equations have a point of intersection, and the tangent lines at that point are perpendicular to each other. This can be shown by taking the derivatives of both equations and setting them equal to each other, which results in a perpendicular line equation.
To show that the graphs of the two equations have tangent lines that are perpendicular to each other at their point of intersection, we can take the derivatives of both equations, which gives us the equations of the tangent lines. We can then set the equations equal to each other and solve for the point of intersection. This will result in an equation for the perpendicular line, which is the equation of the line that passes through the point of intersection and is perpendicular to both tangent lines. We can then verify that the two tangent lines are perpendicular to each other at the point of intersection by calculating the slopes of both lines and showing that they are negative reciprocals of each other.
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A college library has four copies of a certain book; the copies are numbered 1, 2, 3, and 4. Two of these are selected at random. The first selected book is placed on 2- hour reserve, and the second book can be checked out overnight. a. Construct a tree diagram to display the 12 outcomes in the sample space. b. Let A denote the event that at least one of the books selected is an even-numbered copy. What outcomes are in A? c. Suppose that copies 1 and 2 are first printings, whereas copies 3 and 4 are second printings. Let B denote the event that exactly one of the copies selected is a first printing. What outcomes are contained in B?
The event A is that at least one of the books selected is an even-numbered copy. The event B is that exactly one of the copies selected is a first printing.
A tree diagram to display the 12 outcomes in the sample space would look like this:
1st Selection | 2nd Selection
----------------------------
1 | 2
1 | 3
1 | 4
2 | 1
2 | 3
2 | 4
3 | 1
3 | 2
3 | 4
4 | 1
4 | 2
4 | 3
The event A is that at least one of the books selected is an even-numbered copy. This would include outcomes 1-2, 1-4, 2-1, 2-3, 2-4, 4-1, 4-2, and 4-3.
The event B is that exactly one of the copies selected is a first printing. This would include outcomes 1-3, 1-4, 3-1, 3-2, 3-4, 4-1, 4-2, and 4-3.
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uppose that at your university, you will pay $12,000 each year for tuition, $2,500 each year for textbooks, and $10,000 per year for room and board. Before you left for college, your boss at your high-school job offered you a job paying $25,000 per year.
The opportunity cost for four years of college is $46,000
How to determine the opportunity cost?We should know that opportunity costs represent the potential benefits that an individual, investor, or business misses out on when choosing one alternative over another.
The cost of education per year is = $12,000 + $2500 + $10000 = $24,500
The return if we decide not to go to college= $25000 - $12000 = $13000
We lose this return if we decide to go to college and we have to pay for room and board anyway.
The opportunity cost for four years of college is $24500-$13000)*4
This amounts to $11500*4 = $46,000
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Correct question:
Suppose that at your university, you will pay $12000 each year for tuition, $2500 each year for textbooks, and $10000 per year for room and board. Before you left for college, your boss at your high-school job offered you a job paying $25000 per year.
Assume that if you decided not to go to college, your parents would not let you live at home.
What is your opportunity cost for four years of college? $
rectangle bounded by the x-axis and the semicircle x" (see figure). What length and width should the rectangle have so that its area maximum? smaller value : ___larger value: ___
The area of the rectangle will be 4.5 square units and the length and width are x=3 and y=1.5.
The equation for the line is y = -.5x + 3 (slope/intercept form).
Draw a random rectangle with the y-axis, x-axis, and the point (x,y) on the line y = -.5x + 3 as its corners.
This point's height from the x-axis (the length of the rec) will be equal to -.5x + 3 and its length from the y-axis will be x (the width of the rec).
Knowing that A = L*W equals the area of a rectangle
A(x) = (-.5x + 3) * x = -.5x^2 + 3x
In search of A'(x) = -x + 3. And we desire that A'(x) be 0.
As a result, y = -.5(3) + 3 = 1.5 and -x + 3 = 0 imply that x = 3.
So the maximum area of this rectangle is L*W = 1.5 * 3 = 4.5 square units. (We know this is a max and not a min since A’’(x) = -1 which makes the graph concave down)
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