Convert the line equation to 'y = mx + c' form. We calculate the orthogonal distance from the point to a generic point on the line using the formula 'd = |Ax1 + By1 + C| / sqrt(A^2 + B^2)'. Solve the line equation for 'y' using the computed 'd'. This yields the point closest to (-3,1) on the line.
Explanation:The subject of the question involves the algebra of straight lines, specifically finding points on lines. The given line in the question is '6x + y = 9'. We want to find the point along this line that is closest to a given point (-3,1).
First, rewrite the equation in slope-intercept form: y = -6x + 9. Now recall the formula for the shortest distance from a point to a line, d = |Ax1 + By1 + C| / sqrt(A^2 + B^2), where 'A', 'B' and 'C' are the coefficients in the equation of the line, and '(x1, y1)' is the point.
In this case, A = -6, B = 1, C = -9, and the point is (-3,1). If we plug these into the formula, we can solve for 'd'. Then we solve the given equation for 'y' using the resulting 'd' value and we get the point which is closest to (-3,1) on the line '6x + y = 9'.
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What's the answer ?????
A school crossing sign has the dimensions shown. The sign can be thought of as a composite figure of a rectangle and a triangle, or two identical trapezoids. The area of the sign is ____ in2. (Enter only the number.) ...?
Danielle runs an afterschool program for children. the local baseball team donated 220 game tickets to the program. if danielle divides the tickets evenly among the 4 units in the program, how many tickets will each unit get?
Answer: 55 tickets
Step-by-step explanation:
Given : The local baseball team donated 220 game tickets to the program.
Also, Danielle divides the tickets evenly among the 4 units in the program.
Then, the number of tickets will each unit get =[tex]220\div 4[/tex]
i.e. the number of tickets will each unit get =55
Hence, Each units will get 55 tickets.
How much money will Rachel have in her account in ten years
In circle P, diameter QS measures 20 centimeters.
What is the approximate length of arc QR? Round to the nearest tenth of a centimeter.
9.9 centimeters
19.9 centimeters
21.5 centimeters
43.0 centimeters
Answer:
the answer is 19.9 cm
which percent represents the fraction 4/5
The cost, c(x), for a taxi ride is given by c(x) = 2x + 4.00, where x is the number of minutes. What does the slope mean for this situation
A. The taxi ride costs a total of $4.00
B. The taxi ride costs $2.00 per trip.
C. The rate of change of the cost of the taxi ride is $2.00 per minute.
D. The rate of change of the cost of the taxi ride is $4.00 per minute.
The interpretation is (c) the rate of change of the cost of the taxi ride is $2.00 per minute.
How to interpret the slope?The function is given as:
c(x) = 2x + 4.00
A linear equation is represented as:
c(x) = Slope * x + y-intercept
By comparison, we have:
Slope = 2
This means that the slope of c(x) = 2x + 4.00 is 2
Hence, the interpretation is (c) the rate of change of the cost of the taxi ride is $2.00 per minute.
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The equation h = -16t^2 + 32t + 9 gives the height of a ball, h, in feet above the ground, at t seconds after the ball is thrown upward. How many seconds after the ball is thrown will it reach its maximum height? What is its maximum height?
3/4 1 1/2 simplest form
Whats 913 divide by 29 show your work
The division of 913 by 29 yields a quotient of 31 with a remainder of 14, which can be written as 31 R14 or as a decimal, 31.4827586207.
Calculating 913 Divided by 29:
To calculate 913 divided by 29, you perform long division. Firstly, you determine how many times 29 can fit into the initial digits of 913. Seeing that 29 goes into 91 three times (since 29 x 3 = 87), you write down the 3 above the last digit of 91, subtract 87 from 91, and bring down the next digit of 913, which is 3, next to the 4 remaining from the subtraction, forming 43. Now, you determine how many times 29 can fit into 43 without exceeding it. The answer is once. So you write 1 above the 3 in 913, multiply 29 by 1 to get 29, and subtract this from 43 to get 14. Since there are no more digits in 913 to bring down, you have finished the division process.
The result of the division is 31 with a remainder of 14, which can also be written as 31 R14 or as 31.4827586207 when expressed as a decimal.
A good way to check your math is to multiply the quotient by the divisor and add the remainder. If the result equals the original dividend, your division is correct. In this case, 31 x 29 + 14 equals 913, confirming the division is accurate.
The ratio of the number of cars to the number of motorcycles in a parking lot is 10:3. The ratio of the number of motorcycles to the number of vans is 2:5. There are 30 cans in the parking lot. How many more cars than vans are there?
List the multiples of 3 that are also multiples of 5.
A social service agency finds that, on the average, 2.86 of every 100 families need help from the agency. About how many families can they expect to help in a town of 976 families?
Write a conditional statement from the sentence. "parallel lines do not intersect."
A lady wants to make an open-top box for packing baked goods by cutting equal squares from each corner of an 11in. by 16 in. piece of cardboard as shown in the diagram. she figures that versatility the area of the bottom must be 80in^2. What size of square Should be cut from each corner? (round three decimal places)
Final answer:
The size of the square to be cut from each corner of the cardboard to create a box with a desired area of 80in^2 is approximately 1.553 inches.
Explanation:
The size of the square should be cut from each corner of an 11in. by 16 in. piece of cardboard to create a box with a desired area of 80in2 is approximately 1.553 inches.
To calculate this, we start by finding the area of the original cardboard piece, which is 11*16=176in2. Then, we subtract the area of the four squares cut out, 4x2, from the original area to get the area of the box's base, which is 176 - 4x2=80. Solving for x gives us the size of the square to be cut out.
The given amount converted to units?
120 s; minutes
a. 3.25min b. 1.75min c. 2min d. 1.3min
Please respond with a explanation thank you.
What to the second power equals 9/16?
The number that, when squared, equals 9/16 is 3/4 as the square root of a fraction is the square root of the numerator divided by the square root of the denominator.
Explanation:The question is asking what number raised to the second power (or squared) equals 9/16. In mathematical terms, it's asking for a number n whereby n² = 9/16. Since squaring a number means multiplying it by itself, we can say that n = √(9/16).
The square root of 9/16 can be found by taking the square root of 9 and the square root of 16 separately. This is possible because the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator (√a/b = √a / √b).
So, the square root of 9 is 3 and the square root of 16 is 4. Therefore, √(9/16) = 3/4. Hence, the number that when squared gives 9/16 is 3/4.
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If g(x) = 2 − 1, what is g(−2.3)?
Final answer:
Assuming the function g(x) is 2x - 1, to find g(-2.3) we substitute -2.3 for x, calculate the expression, and obtain
g(-2.3) = -5.6.
Explanation:
The student has provided an incomplete function g(x), as it shows g(x) = 2 - 1 without any variable after the subtraction sign. Assuming this is a typographical error and the student meant g(x) = 2x - 1, we can proceed to evaluate the function for x = -2.3.
To evaluate g(-2.3), we substitute -2.3 into the function:
g(x) = 2x - 1g(-2.3) = 2(-2.3) - 1g(-2.3) = -4.6 - 1g(-2.3) = -5.6Therefore, the value of g(-2.3) is -5.6.
Solve 5x2 = −30x − 65
To solve 5[tex]x^2[/tex] = -30x - 65, we can use the quadratic formula. However, the equation has no real solutions.
Explanation:To solve 5[tex]x^2[/tex] = -30x - 65, we can start by rearranging the equation to form a quadratic equation in standard form. The equation becomes 5[tex]x^2[/tex]+ 30x + 65 = 0. We can then solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
In this case, the quadratic equation does not factor easily, so we can use the quadratic formula. The quadratic formula is x = (-b ± sqrt([tex]b^2[/tex] - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. Plugging in the values, we get x = (-30 ± sqrt([tex](-30)^2[/tex] - 4(5)(65))) / (2(5)). After simplifying, we get x = (-30 ± sqrt(900 - 1300)) / 10.
Since the expression inside the square root is negative, there are no real solutions to the equation. Therefore, the equation 5[tex]x^2[/tex] = -30x - 65 has no solution.
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Write two million three hundred and twenty thousand five hundred and two as a number.
Step-by-step explanation:
i was trying to figure out if I can always handle your math exams would it be possible
Wriye the mixed number as a fraction 4 1/3
Is 35 prime or a composite
Answer: Composite
Step-by-step explanation: To see if 35 is a prime number or a composite number, let's first start by finding the factors of 35.
To find the factors of 35, begin by dividing 35 by 1 which gives us 35. This means that 1 and 35 are factors.
Next, since 35 is not divisible by 2, 3, or 4, we divided 35 by 5 which gives us 7. This means that 5 and 7 are factors.
Next, since 35 is not divisible by 6, we divide 35 by 7 which gives us 5. Notice that 7 and 5 are repeat factors and once we hit repeat factors, this means that all other factors we try will repeat.
Therefore, the factors of 35 are 1, 5, 7, and 35.
Since 35 has more than two factors, it's called a composite number.
Which statement defines the term capacity?
The correct answer is:
Credit grantors' measurement of a person's ability to repay loans.
Explanation:
When lending money, financial institutions look at a variety of factors. One of the most important is the ability of the person taking out the loan to repay it. Financial institutions refer to this as "capacity."
what is the solution for the equation for X -10 equals 2X? X equals blank
a survey of reading habits of 100 students showed that 30 read both comics and novels. 10 read neither comics nor novels and twice as many students read comics as read novels. 1. illustrate the information on a Venn diagram. 2. how many students read only novels. 3. how many students read comics. 4. how many students read only one type of book.
Find the midpoint of each side of the trapezoid. Connect the midpoints. What is the most precise classification of the quadrilateral formed by connecting the midpoints of the sides of the trapezoid?
(photo)
What is the distance between these two points on a number line?
–93 and 114
A.–207
B.–21
C.21
D.207
Quadrilateral ABCD has 2 pairs of parallel sides, and perpendicular diagonals. What is the MOST SPECIFIC name for the quadrilateral?
A)
parallelogram
B)
rectangle
C)
rhombus
D)
square ...?
Answer:
C - Rhombus
Step-by-step explanation:
A rhombus ALWAYS has perpendicular diagonals. A rhombus is just a parallelogram with four equal sides, so two of them have to be parallel, at least.
Answer:
it's a parallelogram
The name of the compound kf is.....
a. sodium chloride
b. potassium fluoride
A student attempts to solve for c in the equation below.
Which statement best applies to the work shown below?
A.
The student followed all rules correctly and solved for c.
B.
In step 2 of the student’s work they made a mathematical error.
C.
The student’s answer is negative but it should be positive.
D.
The student combined like terms incorrectly in step 1.
Answer:
A. The student followed all rules correctly and solved for c
Step-by-step explanation:
Given the equation [tex]3c + 6 - 4c = 12 c + 7[/tex], the student followed all rules correctly because:
step 1: He combined like terms correctly for c in the left side from the equation[tex]3c - 4c = - c[/tex]
step 2: he subtracted 6 from both sides[tex]-c +6 + (-6) = 12c +7+(-6)[/tex]
step 3: To isolate “c”, he substracted 12c from both sides[tex]-c +(-12c) = 12c +(-12c) +1[/tex]
Step 4: finally he divided both sides by [tex]-13[/tex][tex]-\frac{13c}{13}= -\frac{1}{13}[/tex]
And he got it:
[tex]c = -\frac{1}{13}[/tex]
Now we´ll check this work with the original equation:
[tex]3c + 6 - 4c = 12 c + 7[/tex]
[tex]3(-\frac{1}{13}) + 6 - 4(-\frac{1}{13}) = 12(-\frac{1}{13}) + 7[/tex]
[tex]-\frac{3}{13} + 6 +\frac{4}{13} = -\frac{12}{13} +7[/tex]
[tex]6 + \frac{1}{13} = \frac{79}{13}[/tex]
[tex]\frac{79}{13} = \frac{79}{13}[/tex]
Very good √