Answer:
[tex]\frac{1}{16} x^2-\frac{1}{2} x-10[/tex]
Step-by-step explanation:
When (x,y) is a point on the parabola, the distance from the focus is equal to its distance from the directrix.
Given point as (4,-7) and directrix as y=-15 then;
distance to focus=distance to directrix
Apply formula for distance
[tex]\sqrt{(x-4)^2+(y+7)^2} =(y+15)[/tex]
square both sides
[tex](x-4)^2+(y+7)^2=(y+15)^2\\\\\\x^2-8x+16+y^2+14y+49=y^2+30y+225\\\\\\\\x^2-8x+y^2-y^2+14y-30y+16+49-225=0\\\\\\16y=x^2-8x-160\\\\y=\frac{1}{16} x^2-\frac{1}{2} x-10[/tex]
Final answer:
The equation of the parabola with a focus at (4, -7) and a directrix of y = -15 is [tex]y = (1/16)x^2 - (1/2)x - 2.[/tex] However, none of the provided options match this equation, suggesting an error in the options or the interpretation of the question.
Explanation:
To derive the equation of a parabola with a focus at (4, -7) and a directrix of y = -15, we start by noting that the vertex lies midway between the focus and the directrix. The distance from the focus to the directrix is 8 units (|-7 - (-15)| = 8), thus the vertex is 4 units above the focus (at y = -3) and since the focus has an x-coordinate of 4, this is also the x-coordinate of the vertex. Therefore, the vertex is at (4, -3).
Next, we use the standard form of a vertical parabola (x-h)^2 = 4p(y-k), where (h,k) is the vertex and 4p is the distance from the vertex to the focus and the directrix. Because our parabola opens upwards (the focus is below the vertex), and the value of p is half the distance from the vertex to the focus or directrix, p = 4. Substituting h = 4, k = -3, and p = 4 into the equation yields [tex](x-4)^2 = 16(y+3[/tex]). We simplify the equation to:
x^2 - 8x + 16 = 16y + 48
By moving the term 16y to the left and then dividing all terms by 16, we get:
[tex]x^2/16 - x/2 + 1 = y + 3[/tex]
To obtain the standard form y = ax^2 + bx + c, we subtract 3 from both sides:
[tex]y = (x^2/16) - (x/2) + 1 - 3[/tex]
[tex]y = (1/16)x^2 - (1/2)x - 2[/tex]
The closest options provided in the question lack proper coefficients to match the derived equation, indicating a potential error in the provided options or in the interpretation of the question.
The graph represents the piecewise function
let's take a peek in the graph on the area from -3 to 0, namely -3 ⩽ x < 0, tis a line, so hmmm let's use two points off of it to get the equation hmmm (-3, -6) and (0,0)
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-(-6)}{0-(-3)}\implies \cfrac{0+6}{0+3}\implies \cfrac{6}{3}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-6)=2[x-(-3)] \\\\\\ y+6=2(x+3)\implies y+6=2x+6\implies y=2x[/tex]
now the smaller line from 1/2 to 3/2 well, heck is just a flat-line, namely y = 3
[tex]\bf f(x)= \begin{cases} 2x&,-3\leqslant x < 0\\ 3&,\frac{1}{2}<x<\frac{3}{2} \end{cases}[/tex]
Which of the following statements is correct about the data set 2,4,6,8,10,12,14,16?
A. The data set has a median that is not in the data set
B. The data set has a mode that is not in the data set
C. The data set has an interquartile range of 9
D. The data set has the same median and mode
Answer:
A. The data set has a median that is not in the data set
Step-by-step explanation:
The given data is:
2,4,6,8,10,12,14,16
The median for the data set is:
(8+10)/2 = 9
The data set has no mode as no number is repeated in the data set.
The IQR is:
= [(12+14)/2-(4+6)/2)]
=[26/2 - 10/2]
=13-5
=8
By looking at the options, we can see that the correct answer is:
A. The data set has a median that is not in the data set
as 9 is not a member of the data set ..
If a line or a segment is perpendicular to another segment at its midpoint, it is called the perpendicular bisector.
True or False
Answer:
True
Step-by-step explanation:
Bisector means to cut into two equal halves. The midpoint is the middle point so it halves the line too.
If a segment is perpendicular to while cutting it in half, then it is called a perpendicular bisector.
Help?????????????????????
Answer:
B. Graph B
Step-by-step explanation:
A graph with no solutions is one where the lines never intersect.
In Graph A, you have a solution at about (-2, 2).
In Graph C, all real numbers are solutions.
What does the number 2 represent in this function
Your answer is C) The ant is crawling at 2 feet per minute.
This is because in the function y = 2t + 5, the 2 represents the slope of the line, which means that for every 1 unit that you go across, you need to go 2 units up. Therefore, for every 1 minute, the ant gains 2 feet so it is crawling at 2 feet per minute.
I hope this helps! Let me know if you have any questions :)
Determine the solution for x2 + 36 > 12x
Final answer:
To solve the inequality x^2 + 36 > 12x, rearrange the terms to have all variables on one side and the constant on the other side. Subtracting 12x from both sides, we get x^2 - 12x + 36 > 0. This is now a quadratic inequality. The solution is x > 6 or x < 6.
Explanation:
To solve the inequality x^2 + 36 > 12x, we need to rearrange the terms to have all variables on one side and the constant on the other side. Subtracting 12x from both sides, we get x^2 - 12x + 36 > 0. This is now a quadratic inequality. To solve it, we can factor the expression into (x-6)(x-6) > 0. From this, we see that the inequality is satisfied when x > 6 or x < 6, since the parabola opens upwards and the expression is equal to zero at x = 6.
what is the vertex form of y=2x^2-8x+1
Answer:
[tex]2(x-2)^2-7[/tex]
Step-by-step explanation:
[tex]y=2x^2-8x+1[/tex]
When comparing to standard form of a parabola: [tex]ax^2+bx+c[/tex]
[tex]a=2[/tex][tex]b=-8[/tex][tex]c=1[/tex]Vertex form of a parabola is: [tex]a(x-h)^2+k[/tex], which is what we are trying to convert this quadratic equation into.
To do so, we can start by finding "h" in the original vertex form of a parabola. This can be found by using: [tex]\frac{-b}{2a}[/tex].
Substitute in -8 for b and 2 for a.
[tex]\frac{-(-8)}{2(2)}[/tex]
Simplify this fraction.
[tex]\frac{8}{4} \rightarrow2[/tex]
[tex]\boxed{h=2}[/tex]
The "h" value is 2. Now we can find the "k" value by substituting in 2 for x into the given quadratic equation.
[tex]y=2(2)^2-8(2)+1[/tex]
Simplify.
[tex]y=-7[/tex]
[tex]\boxed{k=-7}[/tex]
We have the values of h and k for the original vertex form, so now we can plug these into the original vertex form. We already know a from the beginning (it is 2).
[tex]a(x-h)^2+k\\ \\ 2(x-2)^2-7[/tex]
To find the vertex form of a quadratic equation \( y = ax^2 + bx + c \), we can complete the square to transform it into the vertex form, which is written as \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
The quadratic equation given is \( y = 2x^2 - 8x + 1 \).
Here, \( a = 2 \), \( b = -8 \), and \( c = 1 \).
First, find \( h \) using the formula \( h = -\frac{b}{2a} \):
\[
h = -\frac{-8}{2 \cdot 2} = \frac{8}{4} = 2
\]
Next, we will use the value of \( h \) to find \( k \). The value of \( k \) is the y-value of the vertex, which we find by plugging \( h \) into the original equation:
\[
k = 2h^2 - 8h + 1
\]
Now substituting \( h = 2 \) into this formula, we get:
\[
k = 2(2)^2 - 8(2) + 1 = 2 \cdot 4 - 16 + 1 = 8 - 16 + 1 = -7
\]
Therefore, the vertex \( (h, k) \) is \( (2, -7) \).
Now, we rewrite the original quadratic equation in vertex form using the values of \( h \) and \( k \):
\[
y = a(x - h)^2 + k
\]
Substitute \( a = 2 \), \( h = 2 \), and \( k = -7 \) into this equation:
\[
y = 2(x - 2)^2 - 7
\]
So, the vertex form of the equation \( y = 2x^2 - 8x + 1 \) is \( y = 2(x - 2)^2 - 7 \).
Which method will NOT get you to the point (5,2.5)?
(5,2.5)
R
CHECK
Starting at the origin, go 5 spaces to the right and then 2.5
spaces up
Starting at the origin, go 2.5 spaces up and then 5 spaces
to the right
Starting at the origin, go 2.5 spaces to the right and then
5 spaces up
Put one finger on 5 on the x-axis, and put another finger
halfway between 2 and 3 on the y-axis. Move the first
finger up and the second finger to the right until they meet.
Answer:
Starting at the origin, go 2.5 spaces to the right and then 5 spaces up.
Step-by-step explanation:
This is the RIGHT answer. It only goes 2.5 spaces on the X axis and the X axis is at 5
Answer:
Startingat the origin, go 2.5 spaces to the right and then go 5 spaces up.
Step-by-step explanation:
I got it right on IM
Remember it was asking for the wrong answer in the problem! This is the way that you SHOULDN'T answer the problem!
Help what polynomials are there??
Answer:
All of them are polynomials except c.
Step-by-step explanation:
Polynomials are in the form:
[tex]a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+\cdots +a_nx^n[/tex]
You can see here there are no extra symbols like square root, cube root, absolute value, and so on on the variable x...
We also don't have division by a variable. All the exponents are whole numbers.
a) While it has a square root, it is not on a variable so a is a polynomial. The exponents on the variables are whole numbers.
b) b is a polynomial also because all the exponents are whole numbers.
c) This is not a polynomial because there is a square root on a variable.
d) This is a polynomial. All the exponents are whole numbers.
The volume of a rectangular prism is given by the function V = lwh. Which statement is true?
A The volume of the prism depends on the product of only the length and the width.
B The volume of the prism depends on the product of only the length and the height.
CThe volume of the prism depends on the product of the length, the width, and the height.
D The volume of the prism depends on the product of only the width and the height.
Answer:
CThe volume of the prism depends on the product of the length, the width, and the height.
Step-by-step explanation:
V = lwh
Volume is the product of l, which is length, w which is width and h which is height
Answer:
C.The volume of the prism depends on the product of the length, the width, and the height.
Step-by-step explanation:
If the volume of a rectangular prism is given by the function V = lwh, the volume of the prism depends on the product of the length, the width, and the height.
If a cylinder has a diameter of 10 units what is the radius
Answer:
the radius is 5
Step-by-step explanation:
First, divide the diameter by 2 and plug the values for volume, pi, and radius into the formula for volume of a cylinder.
How can I put -2-3=5/4(-2*(2)) into slope intercept form
Answer:
Slope intercept form is: -5=5/4(-4)
Step-by-step explanation:
The general form of slope intercept form is
y = mx+b
where m is the slope and b is y intercept
We are given the equation:
-2-3=5/4(-2*(2))
-5=5/4(-4)
so, y =-5, m= 5/4, x =-4, and b=0
so, Slope intercept form is: -5=5/4(-4)
What is the measure of angle A in the triangle below?
a small candle costs $2.25 an a large candle costs $4.75. jerome cannot spent more than $80. write an inequality that models the amount spent on small and large candles. then given that jerome needs to buy at least 15 candles for his school play write an inequality that models the number of small and large candles he can buy.
Answer:
(1) 2.25s + 4.75l ≤ 80
(2) s + l ≥ 15
Step-by-step explanation:
2.25s = cost of a small candle
4.75l = cost of a large candle
2.25s + 4.75l = total cost of candles
You have two conditions:
A. Amount spent on small and large candles
(1) 2.25s + 4.75l ≤ 80
B. Number of small and large candles
(2) s + l ≥ 15
Answer:
2.25x+4.75y < 80
An elevator started on the 14th floor. It went down 7 floors, up 4 floors, up 9 floors, and down 3 floors. On what floor did the elevator finally stop?
Answer:
17
Step-by-step explanation:
14 - 7 = 7
7 + 4 +9 =20
20 - 3 = 17
Which of the following are solutions to the equation below x^2+8x+16=2
Answer:
[tex]x_{1} =-4+\sqrt{2} \\x_{2} =-4-\sqrt{2} \\[/tex]
Step-by-step explanation:
Using quadratic formula:
[tex]\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]
We will have 2 solutions.
x^2+8x+16=2
x^2+8x+14=0
a= 1 b=8 c= 14
[tex]x_{1}= \frac{-8+\sqrt{8^{2}-4*1*14} }{2*1} \\\\x_{2}= \frac{-8-\sqrt{8^{2}-4*1*14} }{2*1} \\[/tex]
We can write:
[tex]x_{1}= \frac{-8+\sqrt{{64}-56} }{2} \\\\x_{2}= \frac{-8-\sqrt{{64}-56} }{2} \\[/tex]
[tex]x_{1}= -4+\frac{\sqrt{{64}-56} }{2} \\\\x_{2}= -4-\frac{\sqrt{{64}-56} }{2} \\[/tex]
so, we have:
[tex]x_{1}= -4+\frac{\sqrt{{}8} }{2} \\\\x_{2}=-4-\frac{\sqrt{{}8} }{2} \\[/tex]
simplifying we have:
[tex]x_{1}= -4+\frac{\sqrt{{}2*4} }{2} \\\\x_{2}= -4-\frac{\sqrt{{}2*4} }{2} \\[/tex]
Finally:
[tex]x_{1}= -4+\sqrt{2} \\\\x_{2}= -4-\sqrt{2} \\[/tex]
What is the equation of the following line? (-3, 1) and (0,0)
Answer:
[tex]y = -\frac{1}{3} x[/tex]
Step-by-step explanation:
We are given the following two points and we are to find the equation of the line which passes through them:
(-3, 1) and (0,0)
Slope = [tex]\frac{0-1}{0-(-3)} =-\frac{1}{3}[/tex]
Substituting the given values and the slope in the standard form of the equation of a line to find the y intercept:
[tex]y=mx+c[/tex]
[tex]0=-\frac{1}{3} (0)+c[/tex]
[tex]c=0[/tex]
So the equation of the line is [tex]y = -\frac{1}{3} x[/tex]
Answer:
[tex]y = -\frac{1}{3}x[/tex]
Step-by-step explanation:
The equation of a line in the pending intersection is:
[tex]y = mx + b[/tex]
Where m is the slope of the line and b is the intercept with the y axis.
If we know two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] then we can find the equation of the line that passes through those points.
[tex]m =\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]b=y_1-mx_1[/tex]
In this case the points are (-3, 1) and (0,0)
Therefore
[tex]m =\frac{0-1}{0-(-3)}[/tex]
[tex]m =\frac{-1}{3}[/tex]
[tex]b=1-(\frac{-1}{3})(-3)[/tex]
[tex]b=0[/tex]
Finally the equation is:
[tex]y = -\frac{1}{3}x[/tex]
The length of segment XY is 9cm which statements regarding XYX are correct check all that apply
Answer:
The 1st, 3rd, and 5th statements are correct.
Step-by-step explanation:
YZ has the same angle as XY, so the length is the same.
A^2+B^2=C^2 shows that XZ equals 9 sqrt 2 cm.
The hypotenuse is always the longest segment in the triangle.
You need 320 mL of a 65% alcohol solution. On hand, you have a 60% alcohol mixture. How much of the 60% alcohol mixture and pure alcohol will you need to obtain the desired solution?
You will need
____ mL of the 60% solution
and
_____ mL of pure alcohol.
Answer:
You will need
280 mL of the 60% solution
and 40 mL of pure alcohol.
Step-by-step explanation:
Let 'x' be the amount of 60% alcohol solution and y the amount of pure alcohol.
Therefore:
(0.6x + y)/320 = 0.65 ⇒ 0.6x + y = 208
x + y = 320
Solving the sistem of equations:
x = 280 and y = 40
Therefore, You will need
280 mL of the 60% solution
and 40 mL of pure alcohol.
if f(x)=3 x and g(x)= 1/x , what is the domain of (g o f)(x)?
Answer:
The domain is (-∞ , 0)∪(0 , ∞) OR The domain is {x : x ≠ 0}
Step-by-step explanation:
* Lets revise the composite function
- A composite function is a function that depends on another function.
- A composite function is created when one function is substituted into
another function.
- Ex: f(g(x)) is the composite function that is formed when g(x) is
substituted for x in f(x).
- In the composition (f ο g)(x), the domain of f becomes g(x).
* Lets solve the problem
∵ f(x) = 3x and g(x) = 1/x
- In (g o f)(x) we will substitute x in g by f
∴ (g o f)(x) = 1/3x
- The domain of the function is all real values of x which make the
function defined
- In the rational function r(x) = p(x)/q(x) the domain is all real numbers
except the values of x which make q(x) =0
∵ (g o f)(x) = 1/3x
∵ 3x = 0 ⇒ divide both side by 3
∴ x = 0
∴ The domain of (g o f)(x) is all real numbers except x = 0
∴ The domain is (-∞ , 0)∪(0 , ∞) OR The domain is {x : x ≠ 0}
In the diagram, the only figure that could be parallel to line
c is
line a.
line b.
line d.
plane Q.
Answer:
The correct option is line d.
Step-by-step explanation:
The correct option is line d.
Two parallel lines are always on the same plane and never touch each other. They are always same distance apart....
Answer:
the answer is line d . just took the test.
Step-by-step explanation:
Simplify the expression
(2b/3)^4
A. 16b^4/81
B. 16b^4/3
C. 8b^4/12
D. 6b^4
Answer:
A.16b^4/81
step-by-step explanation:
(2b/3)^4
= (2b)^4/3^4
= (2^4×b^4)/3^4
=16b^4/81
(as 16 and 81 cant simplify each other)
Answer:
A. 16b^4/81
Step-by-step explanation:
(2b/3)^4
We know (a/b)^c = a^c / b^c
(2b)^4 / 3^4
We also know (ab)^c = a^c * b^c
2^4 * b^4 / 3^4
16 b^4/ 81
(2x^2+x+3)/(x-2)with remainder
Answer:
2x+5 r. 13
Step-by-step explanation:
So using long division, you can solve for the quotient and the remainder.
Please look at the attached for the solution.
Step 1: need to make sure that you right the terms in descending order. (If there are missing terms in between, you need to fill them out with a zero so you won't have a problem with spacing)
Step 2: Divide the highest term in the dividend, by the highest term in the divisor.
Step 3: Multiply your result with the divisor and and write it below the dividend, aligning it with its matched term.
Step 4: Subtract and bring down the next term.
Repeat the steps until you cannot divide any further. If you have left-overs that is your remained.
Which graph shows the solution to the system of linear inequalities below?
ys-3x+2
y> 2x-3
Answer:
I think your answer should be 5x and -5x
The solution of the inequality on the graph is the very dark region.
InequalityInequality is an expression that shows the non equal comparison of two or more numbers and variables.
Given the inequalities y ≤ –(1/3)x + 2 and y > 2x – 3, plotting the two inequalities using the geogebra online graphing tool.
The solution of the inequality on the graph is the very dark region.
Find out more on Inequality at: https://brainly.com/question/24372553
Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
The equation of the line that passes through (-2, 4) with a slope of 2/5 is y = (2/5)x + 24/5. This is found using the point-slope form of a line and then simplifying it into the slope-intercept form.
Explanation:To find an equation of a line that passes through a given point with a specific slope, you can use the point-slope form of the equation of a line, which, after simplifying, can be converted to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Given the point (-2, 4) and the slope 2/5, we first use the point-slope form:
y - y1 = m(x - x1)
Substituting the given point and slope, we have:
y - 4 = (2/5)(x + 2)
Expanding and simplifying gives us the equation:
y = (2/5)x + (2/5)(2) + 4
y = (2/5)x + 4/5 + 20/5
y = (2/5)x + 24/5
So, the slope-intercept form of the line that passes through (-2, 4) with a slope of 2/5 is y = (2/5)x + 24/5.
A circle has its center at (1, 4) and a radius of 2 units. What is the equation of the circle? (1 point) (x + 2)2 + (y + 4)2 = 2 (x − 1)2 + (y − 4)2 = 4 (x + 1)2 + (y − 4)2 = 4 (x − 1)2 + (y − 4)2 = 2
Answer:
3rd one. The general form of a circle is set equal to the radius squared. So right side is 4 then plug in values until true.
Answer:
The answer is the second option
[tex](x-1)^{2}+(y-4)^{2}= 4[/tex]
Step-by-step explanation:
The general equation of a circle is:
[tex](x-h)^{2}+(y-k)^{2}= r^{2}[/tex]
in this equation (h,k) is the center of the circle and r is the radius, so if the center is in (1,4) and the radius is 2, the values of the constants are:
h = 1
k = 4
r = 2
And the formula for this circle is:
[tex](x-1)^{2}+(y-4)^{2}= 2^{2}[/tex]
[tex](x-1)^{2}+(y-4)^{2}= 4[/tex]
4. Cindy bought a car for $21.330. A few years later, she sold the car for $19,700. Find the percent of change in the value
(SHOW WORK)
Answer:
-7.64%
Step-by-step explanation:
1. Find out how much the car went down in value.
21,330 - 19,700 = 1,630
2. Calculate how much 1% of the original value ($21,330) was. One percent is 1/100, which is .01 when divided.
21,330 × .01 = 213.3
3. Since we now know 1% is equal to $213.30 we can divide $1,630 by $213.30. Doing this will show us how many 1%s are in 1,630.
1,630/213.30 = 7.64181903
4. There are 7.64181903 1%s in 1,630. Because the car's value went down by 1,630, this also means it went down by 7.64181903% We will round this to the nearest hundredth for simplicity's sake.
7.64181903 → 7.641 one is less than 6 so we will round down → 7.64
5. The car decreased by 7.64% in value. This will be written as -7.64% because a decrease is negative.
Answer:
-7.64%
Step-by-step explanation:
Which ordered pairs could be points on a line parallel to the line that contains (3, 4) and (–2, 2)? Check all that apply.
Answer:
Step-by-step explanation:
As we go from (–2, 2) to (3, 4), x increases by 5 and y increases by 4. Thus, the slope of the line through (–2, 2) and (3, 4) is
m = rise / run = 4/5.
Use the slope-intercept form of the equation of a straight line:
y = mx + b becomes 4 = (4/5)(3) + b. Multiplying all three terms by 5, we eliminate the fraction: 20 = 12 + b. Thus, b = 8, and the equation of the line through (–2, 2) and (3, 4) is y = (4/5)x + 8.
A line parallel to this one would have the form y = (4/5)x + b; note that the slopes of these two lines are the same, but the y-intercept, b, would be different if the two lines do not coincide.
Unfortunately, you have not shared the ordered pairs given in this problem statement.
You could arbitrarily let b = 0. Then the parallel line has equation
y = (4/5)x; if x = 3, then y = (4/5)(3) = 12/5, and so (3, 12/5) lies on the parallel line.
he possible ordered pairs are b) (–1, 1) and (–6, –1) , d) (1, 0) and (6, 2) and e) (3, 0) and (8, 2).
To find points on a line parallel to the line containing the points (3, 4) and (-2, 2), we need to find a line with the same slope. The slope of the line containing the points (3, 4) and (-2, 2) can be calculated using the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]\[ m = \frac{2 - 4}{-2 - 3} \]\[ m = \frac{-2}{-5} \]\[ m = \frac{2}{5} \][/tex]
So, the slope of the given line is 2/5.
Now, let's check the slopes of the other lines to see if they match 2/5:
a) Slope of the line passing through (−2, −5) and (−7, −3):
[tex]\[ m = \frac{-3 - (-5)}{-7 - (-2)} = \frac{2}{-5} \][/tex]
The slope matches, so point a) is a possible point on a line parallel to the given line.
b) Slope of the line passing through (−1, 1) and (−6, −1):
[tex]\[ m = \frac{-1 - 1}{-6 - (-1)} = \frac{-2}{-5} = \frac{2}{5} \][/tex]
The slope matches, so point b) is a possible point on a line parallel to the given line.
c) Slope of the line passing through (0, 0) and (2, 5):
[tex]\[ m = \frac{5 - 0}{2 - 0} = \frac{5}{2} \][/tex]
The slope does not match, so point c) is not a possible point on a line parallel to the given line.
d) Slope of the line passing through (1, 0) and (6, 2):
[tex]\[ m = \frac{2 - 0}{6 - 1} = \frac{2}{5} \][/tex]
The slope matches, so point d) is a possible point on a line parallel to the given line.
e) Slope of the line passing through (3, 0) and (8, 2):
[tex]\[ m = \frac{2 - 0}{8 - 3} = \frac{2}{5} \][/tex]
The slope matches, so point e) is a possible point on a line parallel to the given line.
Complete question: Which ordered pairs could be points on a line parallel to the line that contains (3, 4) and (–2, 2)? Check all that apply.
a-(–2, –5) and (–7, –3)
b-(–1, 1) and (–6, –1)
c-(0, 0) and (2, 5)
d-(1, 0) and (6, 2)
e-(3, 0) and (8, 2)
One day Mr. Pritz drove for 6 1/3 hours. The next day he drove 9 1/2 hours. For how many hours did he drive during the two days?
Answer:
Step-by-step explanation:
First convert them into improper fractions: [tex]6\frac{1}{3} =\frac{19}{3}[/tex] and [tex]9\frac{1}{2} =\frac{19}{2}[/tex]. Now we add: [tex]\frac{19}{2}+\frac{19}{3}=\frac{95}{6}[/tex] or [tex]15\frac{5}{6}[/tex].
Divide and express 3.7/2 to the nearest tenth.
3.7 divided by 2 is 1.85, rounded to the nearest tenth is 1.9.
To divide 3.7 by 2 to the nearest tenth, you first perform the division:
[tex]\[ \frac{3.7}{2} = 1.85 \][/tex]
Now, to express this result to the nearest tenth, you look at the first decimal place after the decimal point. Here, it's 8, which is closer to 9 than to 0. So, you round up the digit in the tenths place.
Thus, 3.7 divided by 2, rounded to the nearest tenth, is [tex]\(1.9\).[/tex]