Write an equation of the line containing the point (3,1) and perpendicular to the line 4x−3y=5.
Final answer:
To find the equation of the line perpendicular to 4x-3y=5 that passes through (3,1), we determine the negative reciprocal of the original line's slope, which is -3/4, and use the point-slope form to establish the new line's equation:
y = (-3/4)x + 13/4.
Explanation:
To write an equation of the line containing the point (3,1) and perpendicular to the line 4x−3y=5, first, we need to find the slope of the given line by rearranging the equation into slope-intercept form (y=mx+b), where m is the slope.
The line 4x - 3y = 5 can be rewritten as 3y = 4x - 5, or y = (4/3)x - 5/3. This gives us a slope of 4/3. The slope of a line perpendicular to this will be the negative reciprocal, hence the perpendicular slope is -3/4.
Next, given the point (3,1), we can use the point-slope form of a line's equation, which is y - y₁ = m(x - x₁), where (x₁,y₁) is the point the line passes through, and m is the slope. Substituting the values, we get y - 1 = (-3/4)(x - 3).
Finally, to express the equation in slope-intercept form (y=mx+b), we expand and simplify: y - 1 = (-3/4)x + 9/4, which gives us y = (-3/4)x + 13/4 as the equation of the line.
11x+7y=49 in y=mx+b format
Tickets for the baseball games were $2.50 for general admission and 50 cents for kids. If there were six times as many general admissions sold as there were kids tickets, and the total receipts were $7750, how many of each type of ticket were sold?
The number of tickets sold of each type is required.
Number of general tickets sold is 3000 and kids tickets is 500.
The cost of general tickets is $2.5
Cost of kids tickets is $0.5
Number of general tickets sold = x
Number of kids tickets sold = y
Total value of tickets sold = $7750
Now,
[tex]x=6y[/tex]
[tex]2.5x+0.5y=7750\\\Rightarrow 2.5(6y)+0.5y=7750\\\Rightarrow 15.5y=7750\\\Rightarrow y=\dfrac{7750}{15.5}\\\Rightarrow y=500[/tex]
[tex]x=6\times 500=3000[/tex]
Number of general tickets sold is 3000 and kids tickets is 500.
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For the following inequality, indicate whether the boundary line should be dashed or solid. 3x ≥ y + 1 dashed solid
Answer:
The boundary line should be solid because it have a 'great/less than or equal to' sign
Step-by-step explanation:
what strategies can be used to divide whole numbers?
HELP PLEASE!!!!!!!!!
XY=11d\ YZ=9d-2\ \ xz=5a+22
A=6 YZ= 38
Which correlation coefficient represents the strongest relationship between two variables?
Scott bought 6 pounds of flour for $4 . how many dollars did he pay per pound of flour?
Final answer:
Scott paid approximately $0.67 per pound of flour, calculated by dividing the total cost of $4 by the total weight of 6 pounds.
Explanation:
The student asked: Scott bought 6 pounds of flour for $4. How many dollars did he pay per pound of flour?
To figure out the cost per pound of flour, you need to divide the total cost by the number of pounds.
Step-by-Step Calculation:
Write down the total cost of the flour, which is $4.
Write down the total weight of the flour, which is 6 pounds.
Divide the total cost by the total weight to find the cost per pound: $4 ÷ 6 pounds
The result is approximately $0.67 per pound.
Scott paid approximately $0.67 for each pound of flour.
Consider the following equation, bh+hr=25 when solving for r
Answer:
[tex]r=\frac{25-bh}{h}[/tex]
Step-by-step explanation:
Given : Consider the following equation, [tex]bh+hr=25[/tex]
To find : Solving for r ?
Solution :
The equation is [tex]bh+hr=25[/tex] solve for r,
Subtract 'bh' both side,
[tex]bh+hr-bh=25-bh[/tex]
[tex]hr=25-bh[/tex]
Divide both side by 'h',
[tex]\frac{hr}{h}=\frac{25-bh}{h}[/tex]
[tex]r=\frac{25-bh}{h}[/tex]
Therefore, [tex]r=\frac{25-bh}{h}[/tex]
Rewrite 1/x^-3/6 in simplest radical form. show each step of your process
The length of the base of an isosceles triangle is 15. what is the range of possible lengths l for each leg?
The range of possible lengths for each leg of the triangle will be greater than 7.5.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The two triangular legs and their opposing angles are congruent in an isosceles triangle.
For a triangle, the sum of the two sides should be greater than the longest side of the triangle.
The length of the foundation of an isosceles triangle is 15.
Let the isosceles sides of the triangle be 'x'. Then the inequality is given as,
x + x > 15
2x > 15
x > 7.5
The range of possible lengths for each leg of the triangle will be greater than 7.5.
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What is the difference between a plane (in geometry) and a piece of paper?
1.75 feet, 1 7/12 feet, and 1 2/3 feet which is the length of the longest bar and what was the length for the shortest bar?
WILL MARK BRAINLYIST!
Which postulate or theorem proves that △RMN and △QPN are congruent?
A. AAS Congruence Theorem
B. SSS Congruence Postulate
C. ASA Congruence Postulate
D. SAS Congruence Postulate
Answer: C. ASA Congruence Postulate proves that △RMN and △QPN are congruent.
Given: △RMN and △QPN where RN=NQ and ∠R=∠Q
To prove: △RMN ≅△QPN
Proof:- In △RMN and △QPN
∠R=∠Q............[given]
RN=NQ............[given]
∠RNM=∠PNQ............[vertically opposite angles]
∴△RMN ≅△QPN [by ASA Congruence Postulate ]
Therefore,C. is the right answer. ASA Congruence Postulate proves that △RMN and △QPN are congruent.
ASA Congruence Postulate states that is two angles and the included side is equal to the two angles and the included side of the other triangle, then the triangles are said to be congruent.
does anyone know this?
Which state of matter has neutral particles that bounce off one another as they collide?
Gas
Liquid
Plasma
Solid
The answer is gas because gas particles move so fast they bounce off one another when they collide. Plasma has Negatively AND Positively charged particles within it.
Gases are the state of matter where neutral particles bounce off one another as they collide. This is due to their constant, random motion and the elastic nature of their collisions.
Explanation:The state of matter that has neutral particles that bounce off one another as they collide is a Gas. This is due to the fact that gases are composed of a large number of particles that are in constant, random motion. These particles collide with each other and with the walls of their container. Importantly, these collisions are perfectly elastic, meaning they conserve both momentum and kinetic energy.
In Liquids and Solids, the particles are held together with stronger intermolecular forces which restrict their motion. In Plasma, the particles are ionized and hence, are not neutral.
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If AB= BC and BC= CD, then AB= CD
Louis spent 12 hours last week practicing guitar. If 1/4 of the time was spent practicing chords, how much time did Louis spend practicing chords?
Final answer:
Louis spent a total of 3 hours practicing chords last week, which is 1/4 of the total 12 hours he dedicated to practicing guitar.
Explanation:
Louis spent 12 hours last week practicing guitar. To calculate the amount of time he spent practicing chords, we need to find 1/4 of 12 hours since 1/4 of the time was dedicated to chords.
Here is the calculation:
Divide the total time by 4 to find 1/4 of 12 hours: 12 hours ÷ 4 = 3 hours.
So, Louis spent 3 hours practicing chords last week.
If the discriminant is 16 in a quadratic equation what is true about its solutions
If the discriminant in a quadratic equation is 16, a positive number, then the quadratic equation will have two distinct real solutions.
Explanation:In mathematics, particularly in quadratic equations, the discriminant plays a vital role in determining the nature of the solutions. The discriminant in a quadratic equation is the part under the square root in the quadratic formula, and it is usually represented by the symbol Δ (Delta). The quadratic formula is given by x = [-b ± sqrt(Δ)] / 2a. Now, if the discriminant is 16 (a positive number), then the quadratic equation will have two distinct real solutions. This is because the square root of a positive number yields two real numbers (one positive and one negative) which provide the two solutions when substituted back into the quadratic formula.
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11.) suppose the correlation between two variables r=0.23. What will the new correlation be if 0.14 is added to all values of the x-variable, every value of the y-variable is double, and the two variables are interchanged?
The correlation coefficient r=0.23 will remain unchanged at 0.23 even after adding a constant to all x-variable values, doubling the y-variable values, and swapping the x and y variables, because the correlation coefficient is unaffected by such transformations.
The correlation between two variables is denoted by the symbol, r, and it measures the strength and direction of a linear relationship between two quantitative variables. When we add a constant to all values of the x-variable or multiply all values of the y-variable by a constant, the correlation coefficient does not change. However, interchanging the x and y variables also does not change the value of r since correlation is symmetrical. Therefore, if r=0.23 initially, after adding 0.14 to all values of x, doubling the y-variable values, and interchanging the two variables, the new correlation will still be 0.23.
Which of the following are steps in practical problem solving? Assign an identifying variable to the quantity to be found. Make a guess at the value of the variable. Write a sentence stating conditions placed on the quantity. Check if the value is correct. Solve the sentence for the variable.
Answer:
1. Assign an identifying variable to the quantity to be found.
2. Write a sentence stating conditions placed on the quantity.
3. Solve the sentence for the variable.
Identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of each parabola.
1.) Y=x^2+4x+1
Write each function in vertex form.
1.) Y=x^2+2x+5
A model for a company's revenue from selling a software package is R= -2.5p^2+500p, where p is the price in dollars of the software. What price will maximize revenue? Find the maximum revenue.
Describe the steps in solving the linear equation 3(3x-8)=4x+6
The value of x is 6.
Given,
3(3x-8)=4x+6
We need to solve for x and show steps by steps.
What are the properties used in solving a linear equation?Distributive property of multiplication over addition.
: a ( b + c ) = a x b + a x c
Distributive property of multiplication over subtraction.
: a ( b - c ) = a x b - a x c
Combining like terms.
: cx + ax + b = x (c + a) + b
: cx - ax - b = x (c - a) + b
We have,
3(3x-8)=4x+6
Removing the brackets.
3x(3x) - 3x8 = 4x + 6
9x - 24 = 4x + 6
Subtracting 4x on both sides.
9x - 24 - 4x = 4x + 6 - 4x
5x - 24 = 6
Adding 24 on both sides.
5x - 24 + 24 = 6 + 24
5x = 30
Dividing 5 into both sides.
5x/5 = 30/5
x = 6
Thus the value of x is 6.
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A student is reading his book at a rate of 15 pages per day.
a. Write the rate in pages per week.
b. Write the rate in pages per hour.
Giving Brainliest! Use graphs and numerical summaries to help you describe how the following three datasets are similar and how they are different (think mean, median, range, and sample standard deviation).
A: 5, 7, 9, 11, 13, 15, 17
B: 5, 6, 7, 11, 15, 16, 17
C: 5, 5, 5, 11, 17, 17, 17
Anyone knows the answer
Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below.
Answer:
581.25
Step-by-step explanation:
Use the formula for when the last term is unknown. It is [tex]s_{n} = \frac{a_{1} - a_{1} (r)^{n} }{1-r}[/tex].
For this equation [tex]s_{n}[/tex] (sum of the numbers)= [tex]s_{5}[/tex], [tex]a_{1}[/tex] (amount of first term) = 300, r (ratio)= .5, and n (number of terms) = 5. Knowing this, we plug them into the equation. It would look like: [tex]s_{10} = \frac{300 - (300)(0.5)^{5} }{1-0.5}[/tex].
First, we solve the exponents. 0.5 to the fifth power = .03125. Now multiply it by the nearest number in parentheses, which is 300. You should get 9.375.
Now, subtract that from 300. 300 - 9.375 = 290.625. Your numerator is 290.625.
Simplify your denominator. 1 - 0.5 = 0.5.
Divide.
[tex]\frac{290.625}{0.5} = 581.25[/tex]
581.25
I tried to make sure there were no typos! Please let me know if I missed something :)
Hank is painting his grandfather's fence. He painted 40 linear feet in 85 minutes. He still has 360 linear feet to paint. His cousins, Sam and Alex, come to help. Sam paints twice as fast as Hank, and Alex paints half as fast as Hank. Find the constant of proportionality for the fence painting rate of Hank, Sam, and Alex combined.
Factor. 2xy+5x−12y−30
Answer: The required factored form of the given expression is [tex](x-6)(2y+5).[/tex]
Step-by-step explanation: We are given to factorize the following expression :
[tex]E=2xy+5x-12y-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following property :
[tex]a(b+c)+d(b+c)=(a+d)(b+c).[/tex]
From expression (i), we have
[tex]E\\\\=2xy+5x-12y-30\\\\=x(2y+5)-6(2y+5)\\\\=(x-6)(2y+5).[/tex]
Thus, the required factored form of the given expression is [tex](x-6)(2y+5).[/tex]