Answer:
x + y = 3 (1)
55x + 40y = 135 (2)
Step-by-step explanation:
Since x to represent the number of hours driving on a highway and y to represent the number of hours driving on other roads and the total time for driving is 3 hours,
x + y = 3 (1)
Also, You drive 55 miles per hour on highways and 40 miles per hour on the rest of the roads, the distance moved on highways is 55x and the distance moved on the rest of the roads is 40y (since distance = speed × time).
Since the total distance moved is 135 miles, we have
55x + 40y = 135 (2)
So, the system of linear equations that represent the situation is
x + y = 3 (1)
55x + 40y = 135 (2)
A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophia places a 11-foot tall pole to support the guy wire. After placing the pole, sophia measures the distance from the stake to the pole to be 4 ft. She then measures the distance from the pole to the tower to be 32 ft. Find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot, is 201 ft.
Refer to the diagram attached below for the given information
We have two similar right triangles, ΔABE and ΔCDE.
CD = 11 ft
DE = 4 ft
BD = 32 ft
Length of the guy wire (AE)
Since ΔABE ~ ΔCDE, therefore,
AB/CD = BE/DE (proportional sides)
Plug in the values:
AB/11 = (32 + 4)/2
AB/11 = 36/2
Cross multiply:
AB = (36 × 11)/2
AB = 198 ft
Apply Pythagorean Theorem to find AE:
AE = √(AB² + BE²)
AE = √(198² + 36²)
AE = 201 ft (nearest foot)
Therefore, the length of the guy wire, to the nearest foot is 201 ft.
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We have two similar right triangles, ΔABE and ΔCDE.
CD = 11 ft
DE = 4 ft
BD = 32 ft
Length of the guy wire (AE)
Since ΔABE ~ ΔCDE, therefore,
AB/CD = BE/DE (proportional sides)
AB/11 = (32 + 4)/2
AB/11 = 36/2
AB = (36 × 11)/2
AB = 198 ft
AE = √(AB² + BE²)
AE = √(198² + 36²)
AE = 201 ft (nearest foot)
Does asymptote mean undefined?
What is the solution to the system of equations y =- 5 3 y 1?
The solution to the system of equations y = -5x + 3 and y = 1 is x = 0.4 and y = 1.
Therefore, the answer is (0.4, 1).
To solve the system of equations :
y = -5x + 3 (1)
y = 1 (2)
In the given equation, coefficient of y is same in both equations. So subtracting equation (2) from equation (1) we get
y - y = -5x + 3 - 1
0 = -5x + 2
Adding 5x on both sides
0 + 5x = -5x + 2 + 5x
5x = 2
Dividing both sides by 5
x = 2/ 5
x = 0.4
--The question is incomplete, answering to the question below--
"What is the solution to the system of equations?
y = -5x + 3 and y = 1"
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What is the nature of roots of 2x² 4x 3 0?
The given quadratic equation 2x²-4x+3=0 has no real roots.
The roots of the quadratic equation are real and equal if the discriminant equals zero, a, b, and c are real values and a≠0.
The roots of the quadratic equation are real and unequal if the discriminant is greater than zero, a, b, and c are real values, and a≠0.
The quadratic equation's roots are imaginary and unequal if the discriminant is less than zero, a, b, and c are real integers and a≠0.
2x²-4x+3=0
Comparing the equation with ax²+bx+c=0
We know that,
D = b²-4ac
= (-4)²-4(2)(3)
= 16- 24
= -8
Since D < 0
Hence, the given equation 2x²-4x+3=0 has no real roots.
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Hodor combines 3 quarts of a 5% sugar solution and 2 quarts of an 8% sugar solution. How many additional quarts of a 12% sugar solution must be added to make a 10% sugar solution?
Katie needs 9.5 quartz of the 12% sugar solution to make the 10% sugar solution.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The volume of the 12% sugar solution required, 'X' for a given volume of the 8% sugar solution, 'Y' is;
X = (2·Y + 15)/2
When the volume of the 8% sugar solution, Y = 2 quartz, the volume of the 12% sugar solution required, X = 9.5 gallons
The data of the sugar solutions are;
The volume of 5% sugar solution Kate has = 3 quarts
The volume of the 12% sugar solution = X
Let 'Y' represent the volume of the 8% sugar solution, we have;
The volume of the resultant solution, Z = X + Y + 3
The concentration of the resultant solution = 10%
0.05 × 3 + 0.08·Y + 0.12·X = 0.1·(X + Y + 3)
Solving gives the relationship between the volume of the 12% sugar solution, 'X', and the 8% sugar solution, 'Y' in quartz, as follows;
X = (2·Y + 15)/2
When the volume of the 8% sugar solution, Y = 2 quartz, we have;
X = (2 × 2 + 15)/2 = 9.5 Quartz
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Pls help and explain
Answer:
$48/4 pizzas
Step-by-step explanation:
⭐ A ratio is a fraction that relates one variable to another.
⭐ A proportion is when you make two ratios equal to each other to solve for one of the variables.
We want to find what it costs for Mike to buy 4 pizzas. To achieve this, we must make a proportion.
The first ratio we are given is $12/1 pizza, which means that it costs $12 for 1 pizza.The ratio for Mike buying 4 pizzas is x/4 pizzas, where x is the cost of buying 4 pizzas.Set these two ratios equal to each other and solve for x. *remember: keep the numerators and denominators the same units.[tex]\frac{12}{1 pizza} = \frac{x}{4 pizzas}[/tex]Multiply both sides of the equal sign by 4 to isolate the variable x.[tex]\frac{12}{1 pizza} (4) = \frac{x}{4 pizzas} (4)[/tex][tex]48 = x[/tex]∴ It costs Mike $48 for 4 pizzas.Now we need to write the ratio of cost to pizzas for buying 4 pizzas.$48/4 pizzasNeed help with this question. Please !!!!!
The required coordinates of point B are (2, 3) which is the correct answer would be option (C).
To find the coordinates of point B, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by the formula (x₁ + x₂)/2, (y₁ + y₂)/2.
As per the question, we are given the coordinates of points A and O, which are (4, 5) and (3, 4), respectively.
We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AO.
Let the coordinates of B would be (x, y)
Substituting the coordinates of points A and O into the midpoint formula gives us :
3 = (x+4)/2 ; 4 = (y+5)/2
6 = x +4; 8 = y + 5
x = 2; y = 3
Therefore, the required coordinates of point B are (2, 3).
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For the polynomial function f(x) = x5-x4-9x3 + 9x2, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.
A.) x = -3, cross; x = 0, cross; x = 1, cross; x = 3, cross
B.) x = -3, cross; x = 0, cross; x = 1, cross; x = 3, touch
C.) x = -3, cross; x = 0, touch; x = 1, cross; x = 3, cross
D.) x = -3, cross; x = 0, cross; x = 1, touch; x = 3, touch
Answer:
C.) x = -3, cross; x = 0, touch; x = 1, cross; x = 3, cross
Step-by-step explanation:
You want the zeros and their multiplicity of f(x) = x^5 -x^4 -9x^3 +9x^2, along with a description of whether the graph crosses or touches the x-axis at each zero.
FactorsThe equation can be factored as ...
f(x) = x^2(x^3 -x^2 -9x +9)
The cubic can be factored as ...
x^3 -x^2 -9x +9 = x^2(x -1) -9(x -1) = (x^2 -9)(x -1)
and the quadratic factor can be factored as the difference of square. The complete factorization is then ...
f(x) = x^2(x -1)(x -3)(x +3)
ZerosThe zeros are the values of x that make the factors zero:
x = 0, multiplicity 2x = -3, multiplicity 1x = 1, multiplicity 1x = 3, multiplicity 1Touch/CrossWhen the multiplicity of a zero is even, the graph touches the x-axis. Here, that means the graph will touch at x=0, where the multiplicity of the zero is 2.
When multiplicity is odd, the graph will cross the x-axis. The graph crosses at the zeros -3, -1, +3.
__
Additional comment
As soon as you recognize that the x^2 factor means the multiplicity of x=0 is even, you can identify the correct answer choice: the only one that says "touch" for x=0.
Can two equilateral triangles always be congruent Is it true or false?
The eccentricity of the conic section below is
A. Closer to 0 than 1
B. Closer to 1 then 0
The eccentricity of the conic section below is: A. closer to 0 than 1.
What is a conic section?In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.
In Mathematics, there are four (4) types of conic section and these include the following with their eccentricity:
Hyperbola: its eccentricity is greater than one (1).Parabola: its eccentricity is equal to one (1).Ellipse: its eccentricity is 0 < e < 1.Circle: its eccentricity is equal to zero (0).In this context, we can reasonably infer and logically deduce that the eccentricity of the conic section is closer to zero (0) than one (1) because it represents a circle.
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Circle A has center of (2, 3), and a radius of 5 and circle B has a center of (1, 4), and a radius of 10. What steps will help show that circle A is similar to circle B? (6 points) Group of answer choices
Dilate circle A by a scale factor of 2.
Translate circle A using the rule (x + 1, y − 1).
Rotate circle A 180° about the center.
Reflect circle A over the y-axis.
One of the solutions to the quadratic equation x - 12x – 45 = 0 is x = -3 Which statement is true? Select all that apply. (Check Screenshot)
Answer:
1st and 3rd 4th
graph of f(x) = x² - 12x-45 has an x-intercept at x = -3
-3 is a zero of the function f(x) = x²-12x- 45
x + 3 is a factor of x² - 12x-45
Steps:
other solution is (x - 15) or x = 15
x² - 12x-45
2 numbers that when multiplied give -45 & when added give -12 are -15 & 3
(x-15) (x+3)
"zero" is a fancy way for asking for the answer or root
imaginary number is i which is √-1 so
if you have √-9 = √9 * √-1 = 3i
if you have √-20 = √4 * √-1 * √5 = 2i√5
.
The table describes the quadratic function p(x).
x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2
The equation of the quadratic function is (c) f(x) = 3(x - 1)² - 2
How to determine the equation of the quadratic function?From the question, we have the table of values that can be used in our computation:
A quadratic equation is represented as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
From the graph, we have the vertex to be
(h, k) = (1, -2)
Substitute (h, k) = (1, -2) in f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 1)² - 2
Also, from the graph, we have the point (0, 1)
This means that
a(0 - 1)² - 2 = 1
So, we have
a(1) = 3
Divide both sides by 1
a = 3
Substitute a = 3 in f(x) = a(x - 1)² - 2
f(x) = 3(x - 1)² - 2
Hence, the equation is f(x) = 3(x - 1)² - 2
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What is the mean of the following data set 4 8 11 12 13?
Answer:
9.6
Step-by-step explanation:
What is the mean of the following data set 4 8 11 12 13?
Mean: is the average of values so:
(4 + 8 + 11 + 12 + 13) / 5 = 9.6
How many angles are formed when 2 parallel line are split by a transversal?
When two parallel lines are cut by a transversal, eight angles are formed. Interior angles are supplementary to corresponding exterior angles and the sum of an interior and its corresponding exterior angle is 180 degrees.
Two parallel lines are cut by a transversal, eight angles are formed. Four of these angles are interior angles, which are the angles formed between the two lines and the transversal that lie within the region bounded by the parallel lines. The other four angles are exterior angles, which are the angles formed between the two lines and the transversal that lie outside the region bounded by the parallel lines. Interior angles are equal in measure and are supplementary to the corresponding exterior angles. In other words, the sum of an interior angle and its corresponding exterior angle is equal to 180 degrees. Understanding the properties of interior and exterior angles is important in geometry, as they can be used to prove the parallelism of lines.
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Which would cost more: 15 trips to Boston or 11 trips to New York? Explain
Answer:
I think 11 trips to New York because it's a popular tourist attraction.
How do the base and height of the rectangle compare to the base and height of the parallelogram?
In Parallelogram: Area = base x height(perpendicular distance).
In rectangle: Area = base x height.
Explain some properties of the parallelogram?Parallelogram:
A parallelogram is a particular sort of polygon. It's a quadrilateral in which the opposite side pairs are parallel to one another.
Congruent sides are those when AB = DC.Congruent opposite angels are D = B.(A + D = 180°) Consecutive angles are supplementary.All angles are correct if just one of them is.A parallelogram's diagonals cut each other in half.A parallelogram can be divided into two congruent pieces along each diagonal.Area = base x height(perpendicular distance)
Rectangle:
A quadrilateral having four equal internal angles is a rectangle.A rectangle's opposing sides are equal as well as parallel to one another.Each vertex of a rectangle has a 90° internal angle.The total of a rectangle's internal angles is 360°.The diagonals cut each other in half.The diagonals are all the same length.Area = base(length) x height(width).
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Write the equation of the line that passes through the points (-9,-9) and (−8,1).
Answer: slope= change in y-intercept and x-intercept
Step-by-step explanation:
1-9=-8
-8- -9=1
-8/1=-8
Suppose y varies directly proportional with "x" y=6 when x=8 Find y when x=10
Step-by-step explanation:
directly proportional means
y = kx
to find k we use the first given pair (8, 6) :
6 = k×8
k = 6/8 = 3/4
so, for x = 10
y = 3/4 × 10 = 30/4 = 7.5
What are the factors of 3x² 4x 4?
The factors of the quadratic equation 3x² -4x -4 are (3x + 2)(x - 2) .
The process of factoring the quadratic equation means expressing the given equation as the product of two linear factors.
The quadratic expression is given as 3x² -4x -4 ;
it can be written as ⇒ 3x² -6x +2x -4 ,...by using split the middle term method .
⇒ 3x(x - 2) + 2(x - 2) ..taking 3x common from first two terms and 2 common from the last two terms .
⇒ (3x + 2)(x - 2)
Therefore , the factors are (3x + 2)(x - 2) .
The given question is incomplete , the complete question is
What are the factors of the quadratic equation 3x² -4x -4 ?
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What are the 5 ways to prove triangles similar?
Five different ways to prove the given triangles are similar is given by :
SAS, SSS, ASA, AA, and RHS.
Five different ways to prove triangles are similar is given by:
1. SAS (Side-Angle-Side) : If the corresponding sides of one triangle are in proportion to the other triangle and included angle is of equal measure.
2. SSS(Side-Side-Side): If the corresponding sides of one triangle are in proportion to the other triangle
3. ASA(Angle - Side- Angle) : If the two angles of one triangle are equal to the angles of other triangle and included side is in proportion.
4. AA( Angle-Angle) : If two adjacent angle of one triangle is equal to the measure of other triangle.
5. RHS(Right angle- Hypotenuse - side). If the hypotenuse and one of one right triangle are in proportion to another.
Therefore, five different ways to prove the given triangles are similar is given by : SAS, SSS, ASA, AA, and RHS.
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a cylinder whose height is 7cm and total surface area is 1936/7 . find radius
The radius of the cylinder 37cm.
How to find radius?The radius of a circle is the distance a circle's center from any point along its circumference. Usually, "R" or "r" is used to indicate it.Cylinder y's Curved Surface Area (CSA) Its other name is lateral surface area (LSA). The formula for the curved surface area (CSA) of a cylinder with base radius "r" and height "h" is: CSA of cylinder = 2rh sq. units.cylinder's entire surface area is equal to 2r(h+r).
total surface area = 1936 square cm
height=7 cm
radius is
therefore,
2πr(h+r)=1936
2πr(r+7)=1936
44(r+7)=1936
r+7 = 1936/44
r+7=44
r= 44-7 =37
r=37cm.
The radius of the cylinder 37cm.
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what is the weekly average proportion of opposed feeling? group of answer choices 0.225 0.025 none of the above 0.125 0.200
The weekly average proportion of opposed feeling is 0.0375. (Option D)
A sample proportion is the proportion of individuals in a sample who have a particular characteristic of interest. It refers to the number of successes (success means that an individual possesses the characteristic of interest) of the sample divided by the sample size. According to the provided data, the number of successes in the sample size is 30 and the sample size is 100. Hence, the sample proportion is:
Sample proportion = 30/100 = 0.3
As the survey is conducted weekly for eight weeks, the average proportion of the samples is determined by sample proportion divided by number of weeks. Hence,
Average proportion = 0.3/8 = 0.0375
Note: The question is incomplete. The complete question probably is: A Glassboro township is concerned about adverse public reaction to a trash recycling project that is currently in progress. Because of this, the commissioner of public works has authorized a weekly survey to be constructed of township residents. Each week, a sample of 100 residents are questioned on their feeling toward the project. The results to date are shown below. What is the weekly average proportion of opposed feeling? (3 pts.) a. 0.0250 b. 0.1250 c. 0.3000 d. 0.0375 e. None
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17. एउटा वस्तुको अङ्कित मूल्यमा 20% छुट दिएपछि 13% भ्याट जोडेर रु. 18080 मा बिक्री गरियो भने उक्त वस्तुको अङ्कित मूल्य पत्ता लगाउनुहोस् । (Allowing 20% discount on the marked price of an article, the value of the article will be Rs. 18080 when a VAT of 13% is added, find its marked Ans: Rs. 20,000 price.)
Answer:
11111111111111111111
Describe what is happening in the graph below.
A. The function is steady, and then it increases
B. The function decreases sharply, and then it stays the same
C. The function increases a little, and then it decreases sharply
D. The function stays constant, and then it decreases sharply
(Picture of graph included)
D.
The line never increases, so we can cancel out A and C.
The line starts off straight, so it's not B.
So, the answer is D. since it starts off constant and then decreases sharply.
You are planning on installing a security system at your home. For Safety First Security, you can get monitoring for $2 a day with a one-time set-up fee of $150. For Home Safety Security, you can get
monitoring for $1.50 a day with a one-time set-up fee of $200. Using substitution, find the number of days for which both companies would cost the same.
Step-by-step explanation:
a one-time set-up fee of $200. so that's one day a one-time set-up fee of $150. and that's day 2Rewrite the equation using completing the square.
Answer: 8*8=64
6*6*=216
64-216+21=0
Step-by-step explanation:
Which way is negative infinity?
Negative infinity is a concept that has no direction and function. It is the lowest possible number and is represented by the symbol "-∞".
Negative infinity is the lowest possible number, meaning there is no lower number than negative infinity. It is a concept that has no direction, meaning it is not a specific point on a number line. It is represented by the symbol "-∞", which can be thought of as a point before the beginning of the number line. Negative infinity is an abstract concept, but it is still used in mathematical operations. For example, if you have a set of numbers that contains negative infinity, then the sum of all the numbers in the set will be negative infinity. This is because negative infinity is the lowest possible number, so no matter how large the other numbers in the set are, the sum will always be lower than all of them.Negative infinity can also be used to represent undefined limits. For example, if you are looking at a graph of a function, and the y-axis goes to negative infinity, then the limit of the function at that point is undefined. This is because there is no lower number than negative infinity, so the limit cannot be determined.Negative infinity is a concept that can be confusing, but it is an important part of mathematics. It is used to represent the lowest possible number, as well as undefined limits. It is represented by the symbol "-∞" and has no direction.
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The last step mentioned in building equations to solve real-world problems is to check your answer by substituting it into the original equation. Another way to check your answer is to use estimation and to make sure the answer is reasonable for the situation. In the problem above, are all of the solutions reasonable for the given situation? Why or why not?
Graphing, substitution, and elimination are the three techniques used to solve systems of equations.
What is meant by linear equation ?There is only one way to know the unknown variable X. As a result, d has a value of 1. To find an equation, we must know the variable(s) that are missing as well as any associated known variable(s).
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The first-degree equations are linear equations. This is the formula for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.Anything connected to a line is said to be linear.
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A diver leaps from the edge of a diving platform into a pool below. The figure shows the initial position of the diver and her position at a later time. At time t seconds after she leaps, the horizontal distance from the front edge of the platform to the diver's shoulders is given by xXt and the vertical distance from the water surface to her shoulders is given by t), where x(t) and yt) are measured in meters. Suppose that the diver's shoulders are 11.4 meters above the water when she makes her leap and that d0.8 and dar 3.6 9.8t for Os ts A, where A is the time that the diver's shoulders enter the water. image y0) Note: Figure not drawn to scale Question 1 (3 points) Find the maximum vertical distance from the water surface to the diver's shoulders. Question 2 (2 points) Find A, the time that the diver's shoulders enter the water Question 3 (2 points) Find the total distance traveled by the diver's shoulders from the time she leaps from the platform until the time her shoulders enter the water. Question 4 (2 points) Find the angle e. 0くθ 〈 π , between the path of the diver and the water at the instant the diver's shoulders enter the water.
A- The maximum vertical distance from the water surface to the diver’s
shoulders are 12.061 meters.
B- The time that the diver’s shoulders enter the water is 1.936 seconds.
C- The total distance traveled by the diver’s shoulders from the time
she leaps from the platform until the time her shoulders enter the water is 12.946 meters.
D- The angle, θ between the path of the diver and the water at the instant the diver’s shoulders enter the water is 1.519.
A-
[tex]\frac{dy}{dx} =0[/tex] only when [tex]t=0.36735[/tex]. Let [tex]b=0.36735[/tex]
The maximum vertical distance from the water surface to the diver’s
shoulders is y(b)=11.4 + [tex]\int\limits^b_0 \frac{dy}{dT} dt = 12.061[/tex] meters.
B-
[tex]y(A)=11.4+\int\limits^A_0 \frac{dy}{dt} dt = 11.4+3.6A- 4.9A^{2} =0[/tex]
when A= 1.936 seconds.
C-
[tex]\int\limits^A_0 {\sqrt{(\frac{dx}{dt} )^{2} + (\frac{dy}{dt} )^{2} } } \, dt = 12.946 m[/tex]
At time A, dy/dx = [tex]\frac{dy/dt}{dx/dt} | _{t=A} = -19.21913[/tex]
D- The angle between the path of the diver and the water is [tex]tan^{-1} (19.21913) = 1.518 or 1.519[/tex]
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