The area of the triangle is 3 square units whose vertices are (-3,1), (1,1) and (1,4). We will use distance formulae in this question.
To find the area of a triangle whose vertices are (-3,1), (1,1), and (1,4), we can use the formula for the area of a triangle:
Area = 1/2 * base * height
where the base and height are perpendicular and are formed by any two sides of the triangle.
To apply this formula, we can choose the line segment between (1,1) and (1,4) as the base of the triangle, since it is a vertical line and therefore has a length equal to the height of the triangle. The length of this line segment is 4 - 1 = 3 units.
Next, we need to find the length of the perpendicular segment from the point (-3,1) to the line containing the base. To do this, we can use the formula for the distance between a point and a line:
distance = [tex]|ax + by + c| / \sqrt{(a^2 + b^2)[/tex]
where a, b, and c are the coefficients of the equation of the line and x, y are the coordinates of the point.
In this case, the equation of the line containing the base is x = 1, so a = 1, b = 0, and c = -1. Plugging in the coordinates of (-3,1), we get:
distance = [tex]|1*(-3) + 0*(1) - 1| / \sqrt{(1^2 + 0^2)} = 2[/tex]
Therefore, the height of the triangle is 2 units.
Finally, we can plug these values into the formula for the area of a triangle to get:
Area = 1/2 * base * height = 1/2 * 3 * 2 = 3
So the area of the triangle is 3 square units.
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Ezra works for a company that is headquartered in Canada.
One morning, he receives two checks from the company. The first
is his paycheck for 720 Canadian dollars and the second is a bonus
check for 225 Canadian dollars. He receives 600 U.S. dollars for sup
the first check. What amount, in U.S. dollars, will Ezra receive for his bounus check?
Amount, in U.S. dollars, will Ezra receive for his bounus check Ezra will receive 180 U.S. dollars for his bonus check.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It is used to make sense of numerical data by summarizing it and drawing conclusions from it. Statistics is used in a wide range of fields, from social sciences to medicine, engineering, and business.
To convert Canadian dollars to U.S. dollars, we need to know the exchange rate. Let's assume that the exchange rate is 1 Canadian dollar = 0.80 U.S. dollars.
First, we need to convert Ezra's paycheck from Canadian dollars to U.S. dollars:
720 Canadian dollars * 0.80 U.S. dollars/Canadian dollar = 576 U.S. dollars
So Ezra receives 576 U.S. dollars for his paycheck.
To find out how much he will receive for his bonus check, we need to convert it from Canadian dollars to U.S. dollars:
225 Canadian dollars * 0.80 U.S. dollars/Canadian dollar = 180 U.S. dollars
Therefore, Ezra will receive 180 U.S. dollars for his bonus check.
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look at pic i need answer
Hours, h Total Cost
1 14
2 18
3 22
4 26
What is an equation?Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could divide 12 into two parts, evaluate the information provided by y + 7, and generate y + 7.
Here,
To find the total cost of renting the golf clubs for h hours, we can use the expression:
Total Cost = 10 + 4h
We can use this expression to complete the table as follows:
Hours, h Total Cost
1 10 + 4(1) = 14
2 10 + 4(2) = 18
3 10 + 4(3) = 22
4 10 + 4(4) = 26
Therefore, the completed table is:
Hours, h Total Cost
1 14
2 18
3 22
4 26
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I really need help please help
Answer:
M = 1/8t - 223.05
Step-by-step explanation:
find thelength of side ab
Answer:8.85cm
Step-by-step explanation:
we need to use sinuses theorem:
[tex]\frac{13.5}{sin90} =\frac{x}{sin41} \\sin90=1\\13.5 =\frac{x}{sin41} \\\\13.5*sin41=x\\sin41=0.65\\x=8.85[/tex]
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 155 grams of a radioactive isotope, how much will be left after 5 half-lives?
Answer: After each half-life, the amount of radioactive isotope will be reduced to half its previous amount. Therefore, after 5 half-lives, the amount remaining will be:
155 grams / 2^5 = 4.84 grams (rounded to two decimal places)
So, after 5 half-lives, approximately 4.84 grams of the radioactive isotope will be left.
Step-by-step explanation:
Quadrilateral ABCD is a parallelogram. Find m∠C if m∠C = 6x + 15 and m∠A = 13x − 41. An image of a parallelogram. Question 24 options: 153° 117° 63° 27°
After answering the provided question, we can state that Therefore, the parallelograms measure of angle C is 63°.
What is parallelograms?In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of parallel sides. A parallelogram is a type of quadrilateral in which both sets of opposite sides are parallel and equal. Parallelograms are classified into four types, three of which are unique. The four different shapes are parallelograms, squares, rectangles, and rhombuses. A quadrilateral is a parallelogram when it has two sets of parallel sides. The opposing sides and angles of a parallelogram are both the same length. The interior angles on the same side of the horizontal line are also angles. 360 degrees is the total number of interior angles.
Since ABCD is a parallelogram, opposite angles are congruent. Therefore,
m∠A = m∠C
13x - 41 = 6x + 15
7x = 56
x = 8
m∠C = 6(8) + 15 = 63
Therefore, the measure of angle C is 63°.
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You are driving your car through a roundabout that has a radius of 10 m . Your physics textbook is lying on the seat next to you.What is the fastest speed at which you can go around the curve without the book sliding? The coefficient of static friction between the book and the seat is 0.20..
The fastest speed at which you can go around the curve without the book sliding is equal to 4.43 m/s.
How to determine the fastest speed around the curve without the book sliding?According to Newton's Second law of motion, the centrifugal force which acts on a physical object that is moving around a curve in the x-direction (x-coordinate) and y-direction (y-coordinate) is modeled by the following mathematical equations:
∑Fx = Fc = mv²/r (x-direction)
∑Fy = Fmax = n - W = mg = 0
Fmax = μmg
Where:
m represent the mass.g represent the acceleration due to gravity.v represent the velocity.r represent the radius.Generally speaking, the maximum speed of a physical object would be attained when its static friction is maximum. Therefore, we would have the following:
Fmax = μmg = mV²/r
Making V the subject of formula, we have:
Maximum speed, V = √μgr
Maximum speed, V = √(0.2 × 9.8 × 10)
Maximum speed, V = 4.43 m/s.
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Which of the following expressions are equivalent? Why? If an expression has no match, write 2 equivalent expressions to match it.
a. 2(x+4)
b. 8+2x
c. 2x+4
d. 3(x+4)-(4+x)
e. x+4
Answer:
a and b are equivalent.
c, d and e are not equivalent.
So, 2 equivalent expression for c and are,
c.
( i ) 2 ( x + 2 )
( ii ) ( 4x + 8 ) / 2
d.
( i ) 3x + 16
( ii ) ( 6x + 32 ) / 2
Step-by-step explanation:
a.
2 ( x + 4 )
= 2 ( x ) + 2 ( 4 )
= 2x + 8
b.
8 + 2x can also be written as 2x + 8.
d.
3 ( x + 4 ) + ( 4 + x )
= 3 ( x ) + 3 ( 4 ) + 4 + x
= 3x + 12 + 4
= 3x + 16
Answer:
A and B
Step-by-step explanation:
2(x+4)
2 + x = 2x
2 x 4 = 8
8 + 2x or 2x + 8
Select the correct answer. Consider this absolute value function. f(x) = |x - 21 If function f is written as a piecewise function, which piece will it include? O x + 2, x > 2 -x - 2, x ≥ 2 -x + 2, x < 2 x - 2, x ≤ 2
The piecewise function for f(x) is f(x) = x - 2, x ≥ 2; -x + 2, x < 2, So the correct answer is option C.
Describe Function?In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element of another set (called the range). Functions are a fundamental concept in mathematics and are used to describe relationships between variables, as well as to model and solve a wide range of mathematical problems.
A function is typically denoted using a letter such as "f", and is defined by an equation or formula that specifies how the input (or domain) values are transformed into output (or range) values. For example, the function "f(x) = 2x + 1" assigns each input value "x" to an output value equal to twice the input value plus one.
The absolute value function f(x) = |x - 2| can be written as a piecewise function by separating it into two cases:
Case 1: x - 2 ≥ 0 or x ≥ 2
In this case, the expression inside the absolute value bars becomes x - 2, so f(x) = x - 2.
Case 2: x - 2 < 0 or x < 2
In this case, the expression inside the absolute value bars becomes -(x - 2) = -x + 2, so f(x) = -x + 2.
Therefore, the piecewise function for f(x) is:
f(x) =
x - 2, x ≥ 2
-x + 2, x < 2
So the correct answer is option C.
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Answer: Hope this helps ;)
Step-by-step explanation:
using (4.6), find the polynomial p2(x) that interpolates the following data. in each case, simplify (4.6) as much as possible. g
The required Lagrangian form of the polynomial p2(x) is given by
[(x - x1) × (x - x2) / (x0 - x1) × (x0 - x2)] × y0 + [(x - x0) × (x - x2) / (x1 - x0) × (x1 - x2)] × y1 + [(x - x0) × (x - x1) / (x2 - x0) × (x2 - x1)] × y2
The Lagrangian form of the interpolating polynomial p2(x) corresponding to the data in the table is,
p2(x) = L0(x) × y0 + L1(x) ×y1 + L2(x) ×y2
where Li(x) for i = 0,1,2 are the Lagrange basis polynomials defined by,
L0(x) = (x - x1) × (x - x2) / (x0 - x1) × (x0 - x2)
L1(x) = (x - x0) × (x - x2) / (x1 - x0) × (x1 - x2)
L2(x) = (x - x0) × (x - x1) / (x2 - x0) × (x2 - x1)
Substituting the values of xi and yi from the table, we get,
p2(x)
= [(x - x1) × (x - x2) / (x0 - x1) × (x0 - x2)] × y0 + [(x - x0) × (x - x2) / (x1 - x0) × (x1 - x2)] × y1 + [(x - x0) × (x - x1) / (x2 - x0) × (x2 - x1)] × y2
Note that the indices of xi and yi in the Lagrange basis polynomials correspond to the indices of the data points in the table.
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The given question is incomplete, I answer the question in general according to my knowledge:
Write the Lagrangian form of the interpolating polynomial p2 corresponding to the data in the table below
x0 y0
x1 y1
x2 y2
If an item has a sale price of $40 after it has been discounted 30%, what was the original price
Answer:$
28 dollars
Step-by-step explanation:
Answer:
$57.14
Step-by-step explanation:
Please help, urgent!!!
If correct, I will mark brainliest.
Answer:
perimeter =the circumference around the semicircle
22/7×34/2
=53.43cm
area = (22/7×17^2)/2
454.14cm^2
Answer :
Perimeter of circle = 36 cm Area of circle = 77 cm²Step-by-step explanation :
Question :
Find the perimeter and area of the semicircle.
Given : Diameter = 14 cm
Radius = 14/2 = 7 cm
Solution :
Perimeter of semicircle = πr + d
[tex]\longrightarrow \: \: \dfrac{22}{7} \times 7 + 14 \\ \\ \longrightarrow \: \: 22 + 14 \\ \\ \longrightarrow \: \: 36 \: cm \\ [/tex]
Area of semicircle = 1/2 πr²
[tex]\longrightarrow \: \: \dfrac{1}{2} \times \dfrac{22}{7} \times {(7)}^{2} \\ \\ \longrightarrow \: \: \frac{22}{14} \times 7 \times 7 \\ \\ \longrightarrow \: \: \frac{1078}{14} \\ \\ \longrightarrow \: \: 77 \: {cm}^{2} \\ \\ [/tex]
Answer:
Perimeter of circle = 36 cm Area of circle = 77 cm²The point (2,b) lies on the circle with radius 5 and center (-1,-1). What are the possible values of b?
The point (2,3) and (2,-5) both lie on the circle with center (-1,-1) and radius 5.
Define circleIn geometry, a circle is a closed shape consisting of all points in a plane that are a fixed distance (called the radius) from a given point (called the center). The circle is one of the most basic geometric shapes, and it has many important properties.
In this case, we have a circle with center (-1,-1) and radius 5, so its equation is:
(x + 1)² + (y + 1)² = 5²
We also know that the point (2,b) lies on this circle, so we can substitute x = 2 and y = b into the equation to get:
(2 + 1)² + (b + 1)² = 5²
9 + (b + 1)² = 25
Subtracting 9 from both sides, we get:
(b + 1)² = 16
b + 1 = ±4
Solving for b in each case, we get:
b = -1 ± 4
Therefore, the possible values of b are:
b = 3 or b = -5
So the point (2,3) and the point (2,-5) both lie on the circle with center (-1,-1) and radius 5.
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giving brainlist! ⚠
Solve this Second Order Differential Equations, (but don't use Ai) coz I know if it's from there
The solution to the homogenous equation is M = c₁e⁻(ⁿ² + √[n(n+1)n] + c₂e⁻(ⁿ²-√[n(n+1)n
What is the solution to the second order differential equation?To solve the second order differential equation:
d²M/dn² + 2n (dM/dn) = n
We can use the method of undetermined coefficients. First, we assume a particular solution of the form M = An + B, where A and B are constants to be determined. We then find the first and second derivatives of M:
dM/dn = A
d²M/dn² = 0
Substituting these into the differential equation, we get:
0 + 2n(A) = n
Solving for A, we find:
A = 1/2
So the particular solution is:
M = (1/2)n + B
To find B, we can substitute the particular solution into the original differential equation:
d²M/dn² + 2n (dM/dn) = n
0 + 2n(1/2) = n
So the homogeneous solution is:
Mh = C1n + C2
where C1 and C2 are constants to be determined. The general solution is the sum of the homogeneous and particular solutions:
The solution to the homogenous equation is;
M = c₁e⁻(ⁿ² + √[n(n+1)n] + c₂e⁻(ⁿ²-√[n(n+1)n
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does anyone know what p(p-2) x (2/p) is?
Answer:
Yes, I can help you simplify that expression.
Starting with the expression:
p(p-2) x (2/p)
You can simplify it by first multiplying the terms in the first set of parentheses:
p(p-2) = p^2 - 2p
Then you can rewrite the second term as a fraction with a common denominator of p:
2/p = 2p/p^2 = 2/p^2
Now the expression becomes:
(p^2 - 2p) x (2/p^2)
Next, you can factor out a 2 from the first set of parentheses:
2p(p - 1) x (2/p^2)
Finally, you can simplify the expression by canceling out the p in the second fraction:
2(p - 1)
So the simplified expression is 2(p - 1).
Paint is used to create a circle on a square canvas. The diagram shows the dimensions, in feet (ft), of the canvas. The shaded part of the diagram represents the part of the canvas that is painted blue. which value is closest to the area, in square feet, of the part of the canvas that is painted blue?
a) 5.2
b) 7.7
c) 17.2
d) 26.6
Thus, the closest area of the blue painted region (square - circle) on teh canvas is 7.7 sq. ft.
Explain about the circle:A circle is an a double shape made up of a collection of points that are spaced regularly apart from one another (called the radius) on a plane. The fixed point is referred to as the circle's origin or centre, and the defined distance between each point and the origin is referred to as the radius.
Given data:
Radius of the circle r = 6/2 = 3 ft.canvas is painted with blue colour leaving the circular part.Area of painted region = Area of square - Area of circle
Area of painted region = side² - π*r²
Area of painted region = 6² - 3.14*3²
Area of painted region = 36 - 28.26
Area of painted region = 7.74
Thus, the closest area of the blue painted region (square - circle) on teh canvas is 7.7 sq. ft.
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PLEASE HELP IM SO CONFUSED LATE ASSIGNMENT
Answer:
34%
Step-by-step explanation:
80+10 = 90 (The number of people who do not like meat on their pizzas
Add all the numbers (150+25+80+10) = 265
You do # of people who don't like meat on their pizzas / # of total people
90/265 = 0.339622642
When rounded (Since they're asking for per cent which is 100 because 100 cents make 1 dollar) it will be 0.34 because 0.34 is in it's hundredth place
0.34 x 100(because it is per-cent)
Gives you 34%
progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Which of the following radical expressions has an absolute value symbol in its simplified form?
√81x
O √64x³
O 16x
O V-125x³
Answer:
[tex] \sqrt[4]{16x {}^{4} } [/tex]
Suzanna says that 2/3 and 60% are equal. Is
she correct? Justify your thinking.
Answer:
2/3 is not equal to 60%
Step-by-step explanation:
2/3 of is equal to 66.6%
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Question reads..}[/tex]
[tex]\rm{Suzanna \ says \ that \ \dfrac{2}{3} \ and\ 60\% \ are \ equal.\ Is\ she \ correct?}\\\\\rm{Justify \ your \ thinking.}[/tex]
[tex]\huge\textsf{Let us make the problem easier to solve}[/tex]
[tex]\mathtt{\dfrac{2}{3} = 2\div 3 = 0.666667}\\\\\mathtt{ 0.666667\times100 = 66.67\%}\\\\\mathtt{\dfrac{2}{3} \approx 66.67\%}\\\\\\\\\mathtt{\dfrac{2}{3}\neq 60\%}[/tex]
[tex]\huge\text{Is she correct? Justify your thinking.}[/tex]
[tex]\huge\boxed{\mathtt{No, \she\ is \ incorrect\ because\ \dfrac{2}{3}\ is}}\\\\\huge\boxed{\mathtt{equivalent\ to\ approximately \ 66.67\%}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A class of 33 children were asked to name their favourite colour. All the results are shown in a bar chart below. put the correct numbers on the vertical axis of the bar chart.
This question cannot be answered
Please post the diagram/chart.
Answer: there should be a diagram but where is it
Step-by-step explanation:
Evaluate the given numerical expressions
(12-5)^2 + (-18) x 4 = ?
Evaluate the given numerical expressions
4^3 + (15-3) ÷ 2 = ?
(i need it now pls)
Step-by-step explanation:
The answers to the given numerical expressions are:
(12-5)^2 + (-18) x 4 = 49 + (-72) = -23
4^3 + (15-3) ÷ 2 = 64 + 6 = 70
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Match the equation with the graph
Answer choices are:
Y=3x -5
Y= x
Y= -5x + 3
Y= -x + 2
Y= x - 1
Y= 2x + 2
Y= (x + 3)^2 -2
Y= 1/2x + 2
Y= x
I’ve been having trouble solving #54 can anyone help me?
The summation of the values in the table is -0.65
How to get the value of the summation?Just take the sum between the products of the values in the correspondent rows, the first row gives:
-1*0.999 = -0.999
The second row gives:
349*0.001 = 0.349
Then the sum between these two gives:
-0.999 + 0.349 = -0.65
That is the summation.
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VAT is one of the main source of revenue for the government. Transport industry is exempted from VAT (zero rated). 2.1 Conduct a survey by talking to one taxi driver or owner (the name not to be mentioned) operating between two places (example Mdantsane and East London) by using a neat questionnaire in the form of a table. The questionnaire should contain the following information. The maximum number of people that can be seated in the e taxi, the number of trips in a day, taxi fare, operating time, operating cost, driver's salary and petrol, (ignore wear and tear) total income and total expenses in one day. (15)
Most times, questionnaire, which involves list of questions or items. are used to gather data from respondents about their attitudes, experiences, or opinions. It helps to collect quantitative and/or qualitative information.
Questionnaire for Taxi Driver/Owner Operating between Mdantsane and East London:What is the maximum number of passengers that can be seated in your taxi?How many trips do you typically make in a day between Mdantsane and East London?What is your current taxi fare for a one-way trip between Mdantsane and East London?What are your operating hours on a typical day?What are your daily operating costs, including expenses for petrol, driver's salary, and any other expenses?What is your estimated daily income from operating your taxi between Mdantsane and East London?What are your estimated total expenses for operating your taxi between Mdantsane and East London in one day?Please provide accurate information to the best of your knowledge. Your personal information will not be disclosed.
Thank you for your participation.
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Unit 6, Lesson 9
Cool-down
9.4 Solve Two More Equations
Solve each equation. Show your work, or explain your reasoning.
(1.)-3x - 5 = 16
2. -4(y-2) = 12
Step by step
the solution to the equation -4(y - 2) = 12 is y = -1.
How to solve?
(1.) -3x - 5 = 16
To solve for x, we need to isolate the variable on one side of the equation. We can start by adding 5 to both sides:
-3x - 5 + 5 = 16 + 5
-3x = 21
Next, we can divide both sides by -3 to get the value of x:
x = -7
Therefore, the solution to the equation -3x - 5 = 16 is x = -7.
(2.) -4(y - 2) = 12
To solve for y, we can start by simplifying the left side of the equation by distributing the -4:
-4y + 8 = 12
Next, we can isolate y by subtracting 8 from both sides:
-4y + 8 - 8 = 12 - 8
-4y = 4
Finally, we can solve for y by dividing both sides by -4:
y = -1
Therefore, the solution to the equation -4(y - 2) = 12 is y = -1.
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Complete question:
Solve the following equations and show your work or explain your reasoning:
(1.) -3x - 5 = 16
(2.) -4(y - 2) = 12
A random sample of 36 exam scores is taken from the normally distributed population with unknown mean and a populations standard deviation know and equal to 3. The sample mean score is 68. Find a 90% confidence interval estimate for the population mean of exam scores.
Please round to the nearest hundredths and write your answer in the form ( , ); for example (31,34) or (25,46). Do not type in any extra spaces.
Hope this answer helps.
During their softball season, Jessica had double the amount of hits Sam had. If Jessica and Sam together had 63 hits, write and solve an equation to find the amount of hits each girl had. (IM IN A HURRY WILL GIVE BRAINLIEST IF ANSWERED)
Sam had 21 hits, and Jessica had 42 hits
What is Linear Equatiοn?A linear equatiοn is a mathematical equatiοn that can be written in the fοrm οf "ax + b = c", where "a", "b", and "c" are cοnstants and "x" is the variable being sοlved fοr. Linear equatiοns describe a straight line relatiοnship between variables.
Let's use variables tο represent the number οf hits that Jessica and Sam had.
Let's say that Sam had x hits.
Accοrding tο the prοblem, Jessica had dοuble the amοunt οf hits Sam had, sο Jessica had 2x hits.
Tοgether, they had 63 hits, sο we can write an equatiοn:
x + 2x = 63
Simplifying the equatiοn:
3x = 63
Dividing bοth sides by 3:
x = 21
Sο Sam had 21 hits, and Jessica had dοuble that amοunt, οr 42 hits.
Therefοre, Sam had 21 hits, and Jessica had 42 hits
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1 2 3 4 5 6 7 8 9 10
TIME REMAINING
57:04
Triangle X Y Z is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W Y is 4, the length of Y X is a, the length of Z Y is 3, the length of Z W is c, and the length of W X is b.
What is the value of a?
5 units
5 and one-third units
6 and two-thirds units
7 units
Option B. 5 and one-third units. The value of a in triangle XYZ is 5 and two-thirds units. This is found using the Pythagorean theorem twice and solving for a.
To find the value of a, we can use the Pythagorean theorem in triangles WZY and WYX as follows:
In triangle WZY:
[tex]c^2 = 3^2 + (a + 4)^2[/tex]
In triangle WYX:
[tex]b^2 = 4^2 + a^2[/tex]
Since angle ZWX is a right angle, we can use the Pythagorean theorem in triangle ZWX as follows:
[tex]ZWX^2 = ZW^2 + WX^2[/tex]
We know that ZW = c and WX = b, so we have:
[tex]a^2 + b^2 = c^2[/tex]
Substituting[tex]c^2[/tex] in terms of a and simplifying, we get:
[tex]a^2 + b^2 = 25 + (a + 4)^2[/tex]
Expanding and simplifying, we get:
[tex]a^2 + b^2 = a^2 + 8a + 41[/tex]
Subtracting [tex]a^2[/tex] from both sides, we get:
[tex]b^2 = 8a + 41[/tex]
Substituting [tex]b^2[/tex] in terms of a in the equation [tex]a^2 + b^2 = c^2[/tex], we get:
[tex]a^2 + 8a + 41 = c^2[/tex]
Substituting[tex]c^2[/tex] in terms of a from the equation for triangle WZY, we get:
[tex]a^2 + 8a + 41 = 9 + (a + 4)^2/16[/tex]
Expanding and simplifying, we get:
[tex]16a^2 + 128a + 656 = 9a^2 + 50a + 97[/tex]
Simplifying further, we get:
[tex]7a^2 + 78a - 559 = 0[/tex]
Using the quadratic formula, we get:
[tex]a = (-78 ± sqrt(78^2 + 4(7)(559))) / 14[/tex]
a = (-78 ± sqrt(49379)) / 14
Since a represents a length in a triangle, it must be positive. Therefore, we have:
a = (sqrt(49379) - 78) / 14 ≈ 6.67
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Triangle X Y Z is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W Y is 4, the length of Y X is a, the length of Z Y is 3, the length of Z W is c, and the length of W X is b.
What is the value of a?
A. 5 units
B. 5 and one-third units
C. 6 and two-thirds units
D. 7 units
I need help with this problem. Please answer if you know how to do this.
It should be noted that 768 hand-held color televisions can be sold at $320 per television.
How to solve the word problemA word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
It should be noted that to find the number of hand-held color televisions sold at $320 per television, we need to substitute p = 320 into the supply model or demand model and solve for N.
Using the supply model:
N = 2.4p = 2.4(320) = 768
Therefore, at a price of $320 per television, the supplier is willing to produce 768 hand-held color televisions per week.
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b. In a new scale drawing of the same room, the length of the room measures 4 inches. What is the scale of the new drawing? Explain. Question content area bottom Part 1 a. The scale of the drawing is 1 in. 3 ft. (Type an integer or a decimal.) Part 2 b. The scale is 1 in. = what ft. In the new scale drawing, a length of 4 inches represents an actual length of what feet. So, a length of 1 inch represents an actual length of what feet. (Type integers or decimals.)
a) The scale of the drawing is 1 in. 3 ft.
b) the scale of the new drawing is 1 inch = 4 feet.
What is proportion?
The size, number, or amount of one thing or group as compared to the size, number, or amount of another. the proportion of boys to girls in our class is three to one.
Part 1: The scale of the drawing is 1 in. 3 ft.
Part 2: To find the scale of the new drawing, we can set up a proportion using the scale of the original drawing:
1 inch : 3 feet = x inches : 1 foot
Simplifying this proportion, we get:
1/3 = x/12
Multiplying both sides by 12, we get:
x = 4
So the scale of the new drawing is 1 inch = 4 feet.
In the new scale drawing, a length of 4 inches represents an actual length of 16 feet (since 1 inch represents 4 feet).
Hence, a) The scale of the drawing is 1 in. 3 ft.
b) the scale of the new drawing is 1 inch = 4 feet.
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