find the y coordinate of a point on the line y=2x + 3 that is closest to the point 0,7

Answers

Answer 1

To find the y coordinate of a point on the line y = 2x + 3 that is closest to the point (0, 7), we need to follow the steps below:

Step 1: We have the equation of the line y = 2x + 3, which can also be written in slope-intercept form as y = mx + b, where m is the slope of the line and b is the y-intercept of the line.

Step 2: Find the slope of the line by comparing its equation with y = mx + b. From the equation, we can see that m = 2.

Step 3: Since we have the slope of the line, we can find the equation of a line perpendicular to it that passes through the point (0, 7). A line perpendicular to a line with slope m has a slope of -1/m.

Therefore, the slope of the perpendicular line is -1/2.

The equation of the perpendicular line passing through (0, 7) is y - 7 = (-1/2)(x - 0).

Simplifying, we get y = -x/2 + 7.

Step 4: The point of intersection of the line y = 2x + 3 and the line y = -x/2 + 7 is the point on the line y = 2x + 3 that is closest to the point (0, 7). Solving the system of equations y = 2x + 3 and y = -x/2 + 7, we get x = 1 and y = 5.

Step 5: Therefore, the y coordinate of the point on the line y = 2x + 3 that is closest to the point (0, 7) is 5.

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Related Questions

Find the variance and standard deviation of the data. Round your answers to the
nearest hundredth.
78, 83, 85, 89, 92, 95

Answers

83, 85, 89, 92, 95 it should be this

1. Five more than the product of 4 and m a. 4+m+5 b. 4m+5 c.5m+4N​

Answers

Answer:

b. 4m+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

(b − 7)(b + 3). SOLUTION: 4. (4n + 3)(n + 9). SOLUTION: 5. (8h − 1)(2h − 3) ... (m. 2. − 5m + 4)(m. 2. + 7m − 3). SOLUTION: 28. (x. 2. + 5x − 1)(5x. 2. − 6x + 1) ... The value of x must be greater than 4. If x = 4 ... c. SYMBOLIC For a sum of the form a + b, write an expression for the square of the sum. ... Then, for five days,.

Each lap around the track is 400 meters. How many meters does someone run if they run 5 laps?

Answers

Answer:

2000 meters

Step-by-step explanation:

400×5=2000

pls pls pls, I beg you to how to put a link I want you to answer this correctly without a link please answer this correctly I beg you

Answers

Answer:

1. −51,−41,−38,13,41,50

2. $140 each pair of shoes costs $20 (80 divided by 4). 20 times 7 is 140

3. 5x +6y+1

4. 5+15(n) or using instead of using n for hours use h so, 5+15(h)

5. cylinder

Answer/Step-by-step explanation:

-51, -41, -38, 13, 41, 50

140

5x + 6y + 1

5 + 15h

Cube.

If function g is a quadratic function that contains the points (-3,5) and (0,14), which statement is true over the interval [-3,0]?

Answers

Your answer for this question is B

The average rate of change of f(x) is less than average rate of change of g(x). Then the correct option is C.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function f(x) is given in the table, then the rate of change of the function f(x) will be

Rate of change of f(x) = (-2 + 4.5) / (-2 + 3)

Rate of change of f(x) = 2.5

If function g is a quadratic function that contains the points (-3,5) and (0,14).

Then the rate of change of the function g(x) will be

Rate of change of g(x) = (14 - 5) / (0 + 3)

Rate of change of g(x) = 9/3

Rate of change of g(x) = 3

Thus, the average rate of change of f(x) is less than average rate of change of g(x).

Then the correct option is C.

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Show step-by-step solution. Compute manually.

2. A salary loan of 70,000 pesos is to be repaid by equal monthly payments for 18 months. The annual interest rate is 10% compounded monthly. How much is the monthly payment?

Answers

The monthly payment for a salary loan of 70,000 pesos at a 10% annual interest rate compounded monthly for 18 months is approximately 4,530.79 pesos.

To calculate the monthly payment for the salary loan, we can use the formula for the equal payment amount in an amortizing loan:

Payment = (Principal * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-n))

Where:

Principal = 70,000 pesos (loan amount)

Monthly Interest Rate = Annual Interest Rate / 12 = 10% / 12 = 0.0083333

n = number of payments (18 months)

Let's calculate the payment amount:

Payment = (70,000 * 0.0083333) / (1 - (1 + 0.0083333)^(-18))

Payment = 4,530.79 pesos

Therefore, the monthly payment for the salary loan is approximately 4,530.79 pesos.

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What is the volume of a sphere with a radius of 60.5 ft, rounded to the nearest tenth
of a cubic foot?

Answers

Answer:

If rounded to the nearest tenth of a cubic foot, would be: 927587.2

Step-by-step explanation:

The equation of finding the equation of the volume of a sphere is "4π[tex]\frac{radius^{3} }{3}[/tex]"

If values are inserted in for radius as 60.5, the answer will be 927587.2 when rounded to the nearest tenths.

Hope this helps!

WILL GIVE BRAINLIEST PLEASE HELP ASAP, BEST ANSWER GETES BRAINLIEST. NOT A SCAM AND ITS NOT CAP WHAT SO EVER

Answers

Answer:

A. 60 + x = 90

Step-by-step explanation:

Complementary angles add up to 90 degrees so

60 + x = 90

Answer:

The answer is A: 60 + x = 90

Step-by-step explanation:

Complimentary angles are two angles that add up to 90, so the equation 60 + x = 90 is what you need to use to find the complimentary angle. I hope this helps :)

Find the Median of the following set of data. (Round to the
nearest tenths place.)
1,1,3,0, 7, 2,0, 3, 1, 6, 8, 1
PLEASE HELP ASAP

Answers

Answer:

12

Step-by-step explanation:

put the numbers in least to greatest. so that would be 0,0,1,1,1,1,2,3,3,6,7,8, then find the one or two. in this case it is two. the medians in the one in the middle

Which of the following would be the FIRST step to take when solving the given equation? -11n - 1 = 87

A) Divide both sides of the equation by 11
B) Subtract 11 from both sides of the equation
C) Subtract 1 both sides of the equation
D) Add 1 to both sides of the equation

Answers

Answer:

D) Add 1 to both sides of the equation

Step-by-step explanation:

-11n - 1 = 87

-11n = 87 + 1

Why does the moon goes through phases?

A.
The moon rotates around its axis.

B.
The moon revolves around Earth.

C.
Earth rotates around its axis.

D.
Earth revolves around the sun.

Answers

Ccccccc don’t click the link they are hackers

It is because the moon revolves around Earth.

Hope it helps you...

(1/2)x x 3/43=


Pls im so close for finishing 20 POINTS

Answers

3/86 I believe because; 1/2 x 3/43 = 1x3 and 2x43 as denominator = 3/86 MULTIPLY both numerators and denominators.

Answer:

It's 3[tex]x^{2}[/tex]/86

hope this helps:)

Define the following matrix norm for an n x n real matrix B: || B||M. = sup {||Bx|lo : X ER", ||$||20 = 1}. Show that || B||M. = max = max {Bijl {3B41 } 1

Answers

The matrix norm for an n x n real matrix B is  ||B||M = max{|Bij|}

First, we will prove that ||B||M ≤ max{|Bij|}. Let's assume k is the index that achieves the maximum value, i.e., max{|Bij|} = |Bkj|. Consider the vector x = (0, 0, ..., 0, 1, 0, ..., 0)T, where the 1 is in the k-th position. Then, ||x||2 = 1. Now, let's calculate ||Bx||M:

||Bx||M = sup{||Bx||2 : ||x||2 = 1}

= sup{√((Bx)T(Bx)) : ||x||2 = 1}

= sup{√(xTBTBx) : ||x||2 = 1}

= sup{√(xTBTBx) : ||x||2 = 1, xk = 1}

≤ √((BTB)kk) (using the fact that xTBTBx is a scalar and sup{scalar} = scalar)

= √(|Bkj|²)

= |Bkj|

= max{|Bij|}

Therefore, we have shown that ||B||M ≤ max{|Bij|}.

Now, let's prove the reverse inequality: max{|Bij|} ≤ ||B||M. Consider the vector x = (x1, x2, ..., xn)T, where xi = 1 for the index i that achieves the maximum absolute value of Bij, and xi = 0 for all other indices. Then, ||x||2 = 1. Now, let's calculate ||Bx||M:

||Bx||M = sup{||Bx||2 : ||x||2 = 1}

= sup{√((Bx)T(Bx)) : ||x||2 = 1}

= sup{√(xTBTBx) : ||x||2 = 1}

= sup{√(xTBTBx) : ||x||2 = 1, xi = 1 for some i}

≥ √((BTB)ii) (using the fact that xTBTBx is a scalar and sup{scalar} = scalar)

= sqrt(|Bij|²)

= |Bij|

= max{|Bij|}

Therefore, we have shown that max{|Bij|} ≤ ||B||M.

Combining both inequalities, we conclude that ||B||M = max{|Bij|}.

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Kyle is building a model out of cardboard, as shown below. He needs to construct the top and sides of each section of the model but not the bottom. How many surfaces will Kyle need to find the area of in order to determine how much cardboard he will need? A. 17 B. 14 C. 8 D. 3

Answers

Answer:

The answer is B

Step-by-step explanation:

Answer: its B i did the quiz lol

Step-by-step explanation:

Does anyone know the answer so this question

Answers

Step-by-step explanation:

f(3)= -2*3^2 +3 -5

= -2*9 +3 -5

= 16

Which point is found on the line represented by the equation y+6=x ?
A (−5,1)
B (2,−4)
C (3,9)
D (6,6)

Answers

The point that satisfies the equation  y+6=x is :

A (−5,1)

The line represented by the equation y+6 = x can be rewritten as x - y = -6. The equation is in the standard form:

Ax + By = C.

The x-intercept and y-intercept can be found using the standard form. Then, plot these points on the graph and draw a straight line between them to complete the graph of the equation.

Using the equation x - y = -6 to find the x-intercept, set y = 0 and solve for x.

Thus, x - 0 = -6x = -6

The x-intercept of the line is (-6, 0).

Using the equation x - y = -6 to find the y-intercept, set x = 0 and solve for y.

Thus, 0 - y = -6y = 6

The y-intercept of the line is (0, 6).

Plot the x-intercept (-6,0) and the y-intercept (0,6) on the coordinate plane. Then, draw the line through these points.

Now, we need to find which point is found on the line represented by the equation y+6 = x.

We can now plug in the values of the points to the equation:

y + 6 = x

x - y = -6(-5) - 1 = -6

The point A (-5,1) satisfies the equation since x - y = -6.

So, the answer is A (−5,1).

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Frank owns a $141,000 home, for which he has a 30-year mortgage in the
amount of $700 a month. Once he has paid off the mortgage, how much will
he have paid in interest?
A. $111,000
B. $120,000
C. $141,000
D. $109,000

Answers

Answer: the answer is A !!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

After paying off the mortgage, Frank will have accrued interest costs of $111,000 in total. $111,000 is the correct response.

What is compound interest?

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. [tex]A = P(1 + r/n)^{nt[/tex], where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

The total amount paid by Frank over 30 years will be the product of the monthly payment and the number of months in 30 years:

The total amount paid = Monthly payment × Number of months

Total amount paid = $700/month × 12 months/year × 30 years

Total amount paid = $252,000

However, this total amount includes both the principal (the original loan amount of $141,000) and the interest. To find the amount of interest paid, we need to subtract the principal from the total amount:

Interest paid = Total amount paid - Principal

Interest paid = $252,000 - $141,000

Interest paid = $111,000

Therefore, Frank will have paid $111,000 in interest once he has paid off the mortgage. The answer is A. $111,000.

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okay last one . help

Answers

The answer should be option C!
Answer : The answer is Letter C

Step by step explanation is look closely

What is the measure of the third angle?

Answers

Answer:

90

Step-by-step explanation:

Answer:

90 degrees

Step-by-step explanation:

Step One: In order to solve this problem, you need to know that all angles in a triangle add up to 180 degrees.

Step Two: Now that we know that information, we need to add the angles we do know together: 34+56= 90 degrees.

Step Three: We subtract 90 from 180 to figure out the missing angles: 180-90= 90 degrees.

You can practice on this problem. 1. A sample of men agreed to participate in a study to determine the relationship between several variables including height, weight, waste size, and percent body fat. A scatterplot with percent body fat on the y-axis and waist size (in inches) on the horizontal axis revealed a positive linear association between these variables. Computer output for the regression analysis is given below: Dependent variable is: WBE R-squared - 67.8% S - 4.713 with 250-2 - 248 degrees of freedom Variable Constant Waist Coefficient -42.734 1.70 se of coeff 2.717 0.0743 t-ratio -15.7 22.9 prob <.0001 <.0001 (a) Write the equation of the regression line (be sure to use correct notation and define your variables): (b) Explain/interpret the information provided by R-squared in the context of this problem. Be specific, (c) Calculate and interpret the correlation coefficient (r). (d) One of the men who participated in the study had waist size 35 inches and 10% body fat. Calculate the residual associated with the point for this individual.

Answers

(a)  The equation of the regression line Percent Body Fat = -42.734 + 1.70 * Waist Size

(b) The higher the R-squared value, the better the regression line fits the data and the stronger the relationship between the variables.

(c) It means that as waist size increases, the percentage of body fat also tends to increase, and vice versa.

(d) The residual associated with this point is approximately -6.766

(a) The equation of the regression line can be written as:

Percent Body Fat = -42.734 + 1.70 * Waist Size

In this equation, Percent Body Fat represents the dependent variable, Waist Size represents the independent variable, -42.734 is the intercept (constant), and 1.70 is the coefficient for the Waist Size variable.

(b) R-squared is a measure of how well the regression line fits the data. In this context, R-squared of 67.8% indicates that 67.8% of the variation in the percent body fat can be explained by the linear relationship with waist size. The higher the R-squared value, the better the regression line fits the data and the stronger the relationship between the variables.

(c) To calculate the correlation coefficient (r), we can take the square root of the R-squared value. In this case, the correlation coefficient would be approximately √(0.678) ≈ 0.823.

Interpretation: The correlation coefficient (r) of 0.823 indicates a strong positive linear relationship between waist size and percent body fat. It means that as waist size increases, the percentage of body fat also tends to increase, and vice versa.

(d) To calculate the residual associated with the point for an individual with a waist size of 35 inches and 10% body fat, we need to substitute the waist size value into the regression equation and calculate the difference between the actual percent body fat and the predicted percent body fat.

Using the regression equation: Percent Body Fat = -42.734 + 1.70 * Waist Size

Substituting Waist Size = 35:

Percent Body Fat = -42.734 + 1.70 * 35 = -42.734 + 59.5 ≈ 16.766

The actual percent body fat for this individual is 10%. Therefore, the residual can be calculated as:

Residual = Actual Percent Body Fat - Predicted Percent Body Fat

Residual = 10 - 16.766 ≈ -6.766

The residual associated with this point is approximately -6.766. This indicates that the actual percent body fat is about 6.766 units lower than the predicted value based on the regression equation.

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HURRY HELP ASAPPP Question 23 of 25
If WXYZ is a square, which statements must be true? Check all that apply.
A. WXYZ is a trapezoid.
B. Wis a right angle.
C. WXYZ is a rhombus.
D. WXXY
E. WXYZ is a rectangle.
OF. WXYZ

Answers

I believe the answers would be b. and c.

WX is perpendicular to XY, W is congruent to X, W is supplementary to X, WXYZ is a rhombus, and WX is parallel to YZ and this can be determined by using the properties of a square.

What is quadrilateral?

A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.

Given that, WXYZ is square.

The properties of a square are given below:

All sides are equal in length.

The two consecutive sides are perpendicular.

Opposite sides are parallel to each other.

All the interior angles are 90 degrees.

The diagonals bisect one another.

The area of the square whose sides are 'a' is .

The perimeter of the square whose sides are 'a' is 4a.

Diagonal are equal.

Therefore, the correct statements about the square WXYZ are A), B), C), D), and F).

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The population standard deviation for the heights of dogs, in inches, in a city is 3.4 inches. If we want to be 90% confident that the sample mean is within 1 inch of the true population mean, what is the minimum sample size that can be taken?

Answers

Answer:

The minimize size that can be taken is - 31.28 or 31 .

Step-by-step explanation:

Lets calculate -

    Population standard deviation, [tex]\sigma=3.4 inches[/tex]

    Margin of error, E = 1

    Critical value , [tex]z_0_._0_5 =1.645[/tex]

Now , the size of the sample , [tex]n=(\frac{z\times \sigma}{E} )^2[/tex]

   Putting the given values ,

                    [tex]=(\frac{1.645\times 3.4}{1})^2[/tex]

                  = 31.28 or 31 .

The given table of the question has been attached here .

Hence , the answer is 31.

You purchase a new flat screen TV for $878.99. You are charged sales tax at a rate of 6%. What is your total balance due when you go to pay for the TV?

Answers

Answer:

Sales tax: $52.74

■ Cost/Price before ST: $878.99

■ Total Cost/Price including ST: $931.73

Step-by-step explanation:

X^2-2(x+5)
Help me PLSSS

Answers

Answer:

hope this helpss

Step-by-step explanation:

Answer:

Step-by-step explanation:

if you have to simplify it then distribute -2

x²-2(x+5)=x²-2x-10

if problem is as mentioned by other answerer,then

[tex]\frac{d}{dx} (x^2-2(x+5))=-2\\x^2-2x-10= \int (-2dx)+c\\x^2-2x-10=-2x+c\\x^2=c+10\\x=\pm \sqrt{c+10}[/tex]

Find the volume of the composite shape to the right to the nearest while number

Answers

U just need to add all the numbers together

I need help please help me asp

Answers

New Mexico is the correct option with coordinates (-2.5,-1).

To find the midpoint between two points in the Cartesian plane, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2).

Here's a step-by-step process to find the midpoint:

1. Identify the coordinates of the two points you want to find the midpoint between. Let's say the coordinates are (x₁, y₁) and (x₂, y₂).

2. Add the x-coordinates of the two points together: x = x₁ + x₂.

3. Divide the sum by 2 to find the x-coordinate of the midpoint: x = x / 2.

4. Add the y-coordinates of the two points together: y = y₁ + y₂.

5. Divide the sum by 2 to find the y-coordinate of the midpoint: y = y / 2.

6. The coordinates (x, y) obtained from steps 3 and 5 represent the midpoint between the two given points.

In the given questions, we need to find the mid-point of Fairfield(-10,1) & Montgomery, Alabama(5,-3).

Let the point be N, N = ((-10 + 5) / 2, (1 + (-3)) / 2).

N = (-2.5,-1)

Therefore, From the given options ,the point where we stop is New Mexico marked at (-2.5,-1).

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Preventive medicine services are based on which of the following criteria?
A) Documentation of history, physical examination, and
medical decision making.
B) Age of the patient
C) Amount of time spent with the patient
D) The final diagnosis for the visit

Answers

Preventive medicine services are primarily based on documentation of history, physical examination, and medical decision making.

The correct answer is A) Documentation of history, physical examination, and medical decision making. Preventive medicine services focus on preventing or identifying potential health issues before they become more serious. To determine the appropriate preventive measures, healthcare professionals assess various factors. Among these, documentation of the patient's medical history is crucial to understand their individual health risks and needs.

Physical examination allows for a comprehensive assessment of the patient's current health status, identifying any existing conditions or potential areas of concern. Medical decision making refers to the process by which healthcare providers use the gathered information to determine appropriate preventive measures and interventions. Factors like the patient's age, time spent with the patient, and the final diagnosis may be relevant to specific aspects of healthcare but are not the primary criteria for preventive medicine services.

The focus lies on comprehensive documentation and medical decision making to promote and maintain optimal health.

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A sandwich shop sells sandwiches for $3.50 each, including tax. The shop received a total of $80.50 from the sales of sandwiches one afternoon. Which equation can be used to determine the number of sandwiches, x, sold by the sandwich shop that afternoon? A. 3.50 + x = 80.50 C. 3.50x = 80.50 B. 3.50 + 80.50 = x D. 3.50 ÷ x = 80.50

Answers

A= 3.50+x=80.50 is the answer

Identify the measure of the angle indicated.
76
х
The value of 2 that makes lines a and b parallel is

Answers

Answer:

x = 76°

Step-by-step explanation:

76° and x are alternative interior angles, so they are congruent when lines a and b are parallel

SIGNS. *
If 2(3.8x – 10) - 2 = -1.2x(3 - 6) + 3x, what does
equal?
A5.5
B-5.5
C22
D-22

Answers

im not smart enough lol

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