Input the equation of the given line in slope intercept form. The line through 1,0 and parallel to x-y=7

Answers

Answer 1

Answer: x - y = 7
y = x - 7....the slope here is 1. A parallel line will have the same slope.

y = mx + b
slope(m) = 1
(1,0)...x = 1 and y = 0
now we sub and solve for b, the y int
0 = 1(1) + b
0 = 1 + b
-1 = b

so ur parallel line is : y = x - 1

Answer 2

Answer:

We know that a parallel line has the same slope. And the slope-intercept form in y=mx+b.

1. simplify x-y=7 to isolate y.

subtract x: -y=-x+7

then divide by -1: y=x-7

so the slope is 1 (m=1)

2. plug in m=1 and (1,0) *******alternate solution below

0=1(1)+b

0=1+b subtract 1

-1=b (b=-1)

3. y=mx+b plug in numbers. ( in bold)

y=1x-1

your answer is y=x-1

*****alternate answer solution from step 2 (using step 1)

2. use the formula y-y1=m(x-x1) (y1 and x1 is with the 1 below the letters BTW)

plug in (1,0)

y-0=1(x-1)

y=1x-1

y=x-1 is your answer.

So it comes out as the same answer. Just 2 different ways to doing it! :)

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Helllllllllllllllllllllllllllllllllllp

Answers

x/4-9=5
x/4=14
x=14/4
x=7/2
x=3.5

Micah found the vertex for the function y= -9.5x? 47.5x+ 63 as shown. Find and correct Micah's error. Explain the error?

Answers

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as Micah's workings is not attached. So, there's no way to determine where Micah's error is.

However, I'll solve for the vertex of the given function.

Given

$y = -9.5x^2 + 47.5x + 63$

Vertex, V is of the form:

$V= (h,k)$

Where

$h = -(b)/(2a)$

and

$k = f(h)$

Solving for h:

$y = -9.5x^2 + 47.5x + 63$

$y = ax^2 + bx + c$

So:

$a = -9.5$

$b = 47.5$

$c = 63$

$h = -(b)/(2a)$

$h = -(47.5)/(2 * -9.5)$

$h = -(47.5)/(-19)$

$h = (47.5)/(19)$

$h = 2.5$

Solving for k

$k = f(h)$

$k = f(2.5)$

Substitute 2.5 for x in $y = -9.5x^2 + 47.5x + 63$

$k = -9.5 * 2.5^2 + 47.5* 2.5 + 63$

$k = -59.375+ 118.75 + 63$

$k = 122.375$

Hence:

The vertex is

$V = (2.5,122.375)$

The correct vertex for the function $y = -9.5x^2 + 47.5x + 63$ is (2.5, 122.375).

The given function is $y = -9.5x^2 + 47.5x + 63$ .

To find the vertex of a quadratic function in the form $y = ax^2 + bx + c$ , we can use the formula x = -b / (2a) to find the x-coordinate of the vertex.

In this case, the coefficient of $x^2$ is -9.5, the coefficient of x is 47.5, and there is no constant term.

Using the formula, we can find the x-coordinate of the vertex:

$x = (-b )/( 2a)\nx = (-47.5 )/( (2 * -9.5))\nx = 2.5$

Now, substitute this x-coordinate back into the original function to find the y-coordinate:

$y = -9.5(2.5)^2 + 47.5(2.5) + 63\ny = -9.5(6.25) + 118.75 + 63\ny = -59.375 + 118.75 + 63\ny = 122.375$

Therefore, the correct vertex for the function $y = -9.5x^2 + 47.5x + 63$ is (2.5, 122.375).

Micah's error might be related to incorrectly calculating the x-coordinate of the vertex or substituting the wrong value back into the function.

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1. Find the surface area of the sphere 40 feet

Answers

Answer:

r≈1.78

Step-by-step explanation:

Please help me with this! I would appreciate it :)

Answers

1. b. Commutative Property of Addition
Reason: There is no multiplication used

2. a. 60
Reason: 36 + 24 = 60

3. b. 3d + 9
Reason: Simplification and combining like terms :)

4. b. 4,-1
Reason: Coefficients are the numbers in front of variables

5. b. 36m + 9
Reason: Just use distributive property (multiply 9 into both terms inside parenthesis)

6. b. 95.488
Reason: b = 165.288 - 39.7 - 30.1

7. The question is cut off, unanswerable

8. c. 5a, -3a
Reason: Like terms are things you can combine. So technically the answers could be b. and c. but just go with c. because they have variables.

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Best of luck to you!

Which of the following is NOT a solution to the system of inequalities? (2, 3)

(1, 3)

(0, 3)

(0, 4)

Answers

The point that is not the solution to the system of inequalities is (2, 3), the correct option is A.

What is a System of Inequality?

A system of Inequality is a set of inequalities in one or more variables.

The inequalities in the graph have a common solution shown by the shaded area.

The points (1,3), (0,3) and (0,4) lie in the shaded region.

Point (2,3) is out of the shaded area.

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For a point to be a solution, it has to be on the green shaded area including the solid red line to the left above the intersection of the lines but not the dashed red line to the right.

(2, 3) is outside the shaded area, so it is not a solution.

(1, 3) is inside the green shaded area, so it is a solution.

(0, 3) is on the red line above the intersection, so it is a solution.

(0, 4) is inside the green shaded area, so it is a solution.

Answer: A. (2, 3)

For the following data distribution, find the value that best defines the central tendency of the distribution and characterize the distribution.{23, 29, 12, 14, 27, 23, 23, 18, 23, 1, 7, 18, 43, 24, 28, 17, 32, 33, 38}

Answers

To characterize the distribution, the data have to be put into a frequency distribution graph.

After graphing the data, the distribution is a bit skewed to the right although it could be considered symmetrical.
Here are the values that define the central tendency:
mean = 22.79
median = 23
mode = 23

The three are almost equal. So, the distribution can be classified as symmetrical.

Answer:

Step-by-step explanation:

The given data set is:

23, 29, 12, 14, 27, 23, 23, 18, 23, 1, 7, 18, 43, 24, 28, 17, 32, 33, 38

firstly arrange the given data set in ascending order, we have

1, 7, 12, 14, 17, 18, 18, 23, 23, 23, 23, 24, 27, 28, 29, 32, 33, 38, 43

Now, Mode is the observation point which occurs frequently in the given data set, thus

Mode=23

Mean is given as:

$Mean=(sum of observations)/(total no. of observations)$

$Mean=(433)/(19)=22.7$

$Mean$ ≈ $23$

Median of the given data set is the middle value of the given set, thus

Median=23

Hence, the value that would best describe the central tendency is 23. Since, the values to the left of 23 are more scattered than those to its right, the distribution exhibits negative.

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