we have that
parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.
therefore
the answer is
The two lines have the same distance between them.I need help with this problem, please help
Answer:
d.
Step-by-step explanation:
the slope is the factor of x.
a perpendicular slope turns the original slope upside-down and flips the sign.
the original slope is -3/7.
the perpendicular slope is then 7/3.
the only answer option with the correct slope is d.
so, d. must be correct.
let's check that (-2, 2) is on this line :
2 = 7/3 × -2 + 20/3 = -14/3 + 20/3 = 6/3 = 2
2 = 2
correct.
so yes, the point (-2, 2) is on this line, and d. is indeed correct.
3. A student solved an order of operations problem asshown.(2 - 4)2 – 5(6 - 3) + 13(-2)2 - 30 - 3 + 134 - 33 + 13-16What error did this student make? Explain in completesentences. What should the correct answer be?
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
Parentheses first
[tex]\begin{gathered} (2-4)=-2 \\ (6-3)=3 \\ \end{gathered}[/tex]substitute
[tex]\begin{gathered} (-2)2-5(3)+13 \\ -4-15+13 \\ -4-2 \\ -6 \\ \end{gathered}[/tex]The student error was misapplication of the comutative property
f(x) = x ^ 3 + 3x ^ 2 + 4x + 5 and g(x) = 5 , then g(f(x)) =
we have the functions
[tex]\begin{gathered} f\mleft(x\mright)=x^3+3x^2+4x+5 \\ g(x)=5 \end{gathered}[/tex]so
g(f(x))=5Solve for x using trigonometry. Round to the nearest tenth. (hint: One decimal place) 17 x 19
By definition,
sin(angle) = opposite/hypotenuse
From the picture,
sin(x) = 17/19
x = arcsin(17/19)
x = 63.5°
Irene is 54 ⅚ inches tall. Theresa is 1 ⅓ inches taller than Irene and Jane is 1 ¼ inches taller than Theresa How tall is Jane
Let be "n" Irene's height (in inches), "t" Theresa's height (in inches) and "j" Jane's height (in inches).
You know Irene's height:
[tex]n=54\frac{5}{6}[/tex]You can write the Mixed number as an Improper fraction as following:
- Multiply the Whole number by the denominator.
- Add the product to the numerator.
- Use the same denominator.
Then:
[tex]\begin{gathered} n=\frac{(54)(6)+5}{6}=\frac{324+5}{6}=\frac{329}{6} \\ \end{gathered}[/tex]Now convert the other Mixed numbers to Improper fractions:
[tex]\begin{gathered} 1\frac{1}{3}=\frac{(1)(3)+1}{3}=\frac{4}{3} \\ \\ 1\frac{1}{4}=\frac{(1)(4)+1}{4}=\frac{5}{4} \end{gathered}[/tex]Based on the information given in the exercise, you can set up the following equation that represents Theresa's height:
[tex]t=\frac{329}{6}+\frac{4}{3}[/tex]Adding the fractions, you get:
[tex]t=\frac{337}{6}[/tex]Now you can set up this equation for Jane's height:
[tex]undefined[/tex]Express 1.27times 10^3 in decimal notation
1.27 x 10^3
10^3 is 1000
1.27 x 10^3 = 1.27 x 1000 = 1270
[tex]1.27x10^3\text{ = 1.27}x1000\text{ = 1270}[/tex]Answer:
1270
Surface are of the wood cube precision =0.00The weight of the woo cube precision =0.00 The volume was 42.87 in3
Given:
The volume of the cube is 42.87 cubic inches.
The volume of a cube is given as,
[tex]\begin{gathered} V=s^3 \\ 42.87=s^3 \\ \Rightarrow s=3.5 \end{gathered}[/tex]The surface area of a cube is,
[tex]\begin{gathered} SA=6s^2 \\ SA=6\cdot(3.5)^2 \\ SA=73.5 \end{gathered}[/tex]Answer: the surface area is 73.5 square inches ( approximately)
I am trying to create a study guide and I need step by step explanation on this question please
Answer:
[tex]-5a^3[/tex]Explanation:
We are given the expression:
[tex]\begin{gathered} \frac{10a^6}{-2a^3} \\ We\text{ can simplify the expression further to become:} \\ =\frac{10}{-2}\times\frac{a^6}{a^3} \\ =-5\times a^3 \\ =-5a^3 \\ \\ \therefore\frac{10a^6}{-2a^3}\Rightarrow-5a^3 \end{gathered}[/tex]Having simplified the expression, the answer obtained is: -5a^3
find the width of a newer 48-in TV whose screen has an aspect ratio of 16:9what is the width?
The width of the TV is 41.84-in
Explanations:The diagonal size of the TV, d= 48 in
The aspect ratio= 16 : 9
The aspect ratio is usually given in form of width : Height
Let the width = w
Let the height = h
The diagram looks like:
[tex]\begin{gathered} \frac{w}{h}=\text{ }\frac{16}{9} \\ h\text{ = }\frac{9w}{16} \end{gathered}[/tex]Using the Pythagoras theorem:
[tex]\begin{gathered} d^2=h^2+w^2 \\ 48^2\text{ = (}\frac{9w}{16})^2+w^2 \\ 2304\text{ = }\frac{81w^2}{256}+w^2 \\ \text{Multiply through by 256} \\ 589824=81w^2+256w^2 \\ 589824\text{ = }337w^2 \\ w^2\text{ = }\frac{589824}{337} \\ w^2\text{ = 1750.22} \\ w\text{ = }\sqrt[]{1750.22} \\ w\text{ = 41.84 } \end{gathered}[/tex]The width of the TV is 41.84-in
O GRAPHS AND FUNCTIONSDomain and range from the graph of a piecewise function
ANSWER:
[tex]Domain:(-5,-4]\cup[-1,2][/tex][tex]Range:[-3,0)\cup[1,4][/tex]EXPLANATION:
Given:
To find:
The domain and the range
Recall that the domain of a function is the set of possible input values for which the function is defined.
To determine the domain of a function from a graph, we consider the possible x-values from left to right.
So the domain of the given function can be written as;
[tex]Domain:(-5,-4]\cup[-1,2][/tex]The range of a function is the set of possible output values.
To determine the range of a function from a graph, we consider the possible y-values from the bottom to the top.
So the range of the given function can be written as;
[tex]Range:[-3,0)\cup[1,4][/tex]Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
316.21 is the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We need to find the savings plan balance after 8 months with an APR of 8% and monthly payments of $300.00.
Let 8% is changed to decimal value by dividing with hundred.
8/100=0.08.
Now we are required to find the growth factor.
growth factor = (1 + (0.08 / 12)) per month = 1.00667
After 9 months, the balance is
($300.00)*(1.00667)8
316.21 is the balance after 6 months.
Hence 316.21 is the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
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what does this mean i dont get it pls help :)
Answer:
Left circle: 6x + 2y
Bottom middle circle: 5x
Bottom right rectangle: 3x + y
Step-by-step explanation:
According to the question, the expression in each circle is the result of the sum of the two rectangles connected to it.
The expression in the left circle is the sum of the expressions in the rectangles above and below it:
⇒ (4x + 3y) + (2x - y)
⇒ 4x + 3y + 2x - y
⇒ 4x + 2x + 3y - y
⇒ 6x + 2y
Therefore, the expression in the left circle is 6x + 2y.
The expression in the right circle is the sum of the expressions in the rectangles above and below it, however the expression in the rectangle below this circle is missing.
To find the missing expression, subtract the expression in the rectangle above the circle from the expression in the circle:
⇒ (4x + 5y) - (x + 4y)
⇒ 4x + 5y - x - 4y
⇒ 4x - x + 5y - 4y
⇒ 3x + y
Therefore, the expression in the lower right rectangle is 3x + y.
The expression in the bottom middle circle is is the sum of the expressions in the rectangles to its left and right:
⇒ (2x - y) + (3x + y)
⇒ 2x - y + 3x + y
⇒ 2x + 3x - y + y
⇒ 5x
Therefore, the expression in the bottom middle circle is 5x.
8% of the students at Jemerson Middle School are absent because of illness. If there are 150 students in the school, how many are absent? 12015128
12 students
Explanation
when you have 8% , it means 8 of every 100 students are absent
find the decimal form
[tex]8\text{ \% = }\frac{8}{100}=0.08[/tex]then, to find the 8% of any number, just multiply the number by 0.08
Step 1
If there are 150 students in the school, how many are absent?
[tex]\begin{gathered} \text{absent}=\text{total}\cdot0.08 \\ \text{absent}=150\cdot0.08 \\ \text{absent}=12 \end{gathered}[/tex]so, 12 students are absent
the sum of two numbers is 24 . one number is 3 times the other number . find the two numbers
We are given that the sum of two numbers is 24. If "x" and "y" are the two numbers then we have that:
[tex]x+y=24[/tex]We are also given that one number is three times the other, this is expressed as:
[tex]x=3y[/tex]Now, we substitute the value of "x" from the second equation in the first equation:
[tex]3y+y=24[/tex]Now, we add like terms:
[tex]4y=24[/tex]Now, we divide both sides by 4:
[tex]y=\frac{24}{4}=6[/tex]Therefore, the first number is 6. Now, we substitute the value of "y" in the second equation:
[tex]\begin{gathered} x=3(6) \\ x=18 \end{gathered}[/tex]Therefore, the other number is 18.
Find the area of the compound shapes on the coordinate plane below.
Answer
Part A: 100 square units
Part B: 39 square units
Part C: 48 square units
Explanation
Part A
Scale: 1cm represent 2 units on x-axis and 1cm represents 5 units on y-axis.
Firstly, we convert the figure into two composite plane shapes, that is, a rectangle and a triangle.
Area of composite shapes = area of rectangle + area of triangle
= Length x Width + 1/2(base x height)
= 10 x 8 + 1/2(10 x 4)
= 80 + 20
= 100 square units
Part B
Scale: 1cm represent 3 units on x-axis and 1cm represents 1 unit on y-axis.
Convert the figure into two composite plane shapes, that is, a rectangle and a trapezium.
Area of composite shapes = area of rectangle + area of trapezium
= Length x Width + 1/2(sum of parallel sides)(perpendicular height)
= 3 x 9 + 1/2(3 + 9)(2)
= 27 + 1/2(24)
= 27 + 12
= 39 square units
Part C
Scale: 1cm represent 2 units on x-axis and 1cm represents 2 units on y-axis.
Convert the figure into two composite plane shapes, that is, a trapezium and a triangle.
Area of composite shapes = area of trapezium + area of triangle
= 1/2(sum of parallel sides)(perpendicular height) + 1/2(base x height)
= 1/2(4 + 8)(6) + 1/2(4 x 6)
=1/2(12 x 6) + 1/2(24)
= 36 + 12
= 48 square units
For the parabola given by 4y – 9 = x2 – 6x, find the vertex and focus.
Solution
Gievn the equation below
[tex]4y-9=x^2-6x[/tex]To find the vertex and focus of the given equation, we apply the parabola standard equation which is
[tex]4p(y-k)=(x-h)^2[/tex]Where p is the focal length and the vertex is (h,k)
Rewriting the equation in standard form gives
[tex]\begin{gathered} 4y-9=x^2-6x \\ 4y=x^2-6x+9 \\ 4y=x^2-3x-3x+9 \\ 4y=x(x-3)-3(x-3) \\ 4y=(x-3)^2 \\ 4(1)(y-0)=(x-3)^2 \end{gathered}[/tex]Relating the parabola standard equation with the given equation, the vertex of the parabola is
[tex]\begin{gathered} x-3=0 \\ x=3 \\ y-0=0 \\ y=0 \\ (h,k)\Rightarrow(3,0) \\ p=1 \end{gathered}[/tex]Hence, the vertex is (3,0)
The focus of the parabola formula is
[tex](h,k+p)[/tex]Where
[tex]\begin{gathered} h=3 \\ k=0 \\ p=1 \end{gathered}[/tex]Substitute the values of h, k and p into the focus formula
[tex](h,k+p)\Rightarrow(3,0+1)\Rightarrow(3,1)[/tex]Hence, the focus is (3, 1)
I need help with this answer can you explain it
The solution.
The correct answer is y-intercept at (0,1) and decreasing over the interval
[tex]\lbrack-\infty,\infty\rbrack[/tex]Hence, the correct answer is the last option (option D)
Hello am just trying to see if I did this right
Answer
Variable
c = Cost of one bag of chips
Equation
2.50 + 3c = 5.05
Solution
c = Cost of one bag of chips = 0.85 dollars
Explanation
Cost of one juice pouch = 1.25 dollars
Cost of 2 juice pouches = 2(1.25) = 2.50 dollars
Cost of a bag of chips = c dollars
Cost of 3 bags of chips = (3)(c) = (3c) dollars
(Cost of two juice pouches) + (Cost of three bags of chips) = Total Cost
2(1.25) + 3c = 5.05
2.50 + 3c = 5.05
Subtract 2.50 from both sides
2.50 + 3c - 2.50 = 5.05 - 2.50
3c = 2.55
Divide both sides by 3
(3c/3) = (2.55/3)
c = 0.85 dollars
Hope this Helps!!!
Find the length of the rectangle pictured above, if the perimeter is 82 units.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
From the information given,
width = 16
Perimeter = 82
Thus, we have
82 = 2(length + 16)
By dividing both sides of the equation by 2, we have
82/2 = 2(length + 16)/2
2 cancels out on the right side of the equation. We have
41 = length + 16
length = 41 - 16
length = 25
3. If you ordered a pizza to share with others, which of the following sets ofnumbers would best describe the part of the pizza you ate.a. Integerb. WholeC. Naturald. Rational
rational, because you've split the pizza
So for example if you cut the pizza into 12 pieces to one of your friends you gave 1/12
A gift box is 12 inches long 8 inches wide and 2 inches high how much wrapping paper is needed to wrap the gift box
Given that a box is 12 inches long 8 inches wide and 2 inches high, the area of wrapping paper needed to wrap the gift box is equal to the total surface area of the box.
[tex]\begin{gathered} \text{length l =12 inches} \\ \text{width w = 8 inches} \\ \text{ height h = 2 inches} \end{gathered}[/tex]The total surface area of the box can be calculated using the formula;
[tex]undefined[/tex]Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
Answer: [tex]\frac{5}{2\sqrt{5x+3\\} }[/tex]
Step-by-step explanation:
First, use the chain rule to quickly find the answer so that you can check after you go through the ridiculous process that is the bane of every calculus 1 student's existence.
f(x) = (5x + 3)^(1/2)
(d/dx) (5x + 3)^(1/2) =
(1/2)(5x + 3)^(-1/2) * (5) =
5/[2(5x+3)^(1/2)]
Now, we enter the first gate of hell:
f'(x) = the limit as h approaches 0 of [(f(x+h) - f(x))/h]
lim as h -> 0 of [(5(x+h)+3)^(1/2) - (5x+3)^(1/2)/h]
lim as h -> 0 of [(5x+5h+3)^(1/2) - (5x+3)^(1/2) / h]
Multiply numerator and denominator by the conjugate of the numerator, which is (5x+5h+3)^(1/2) + (5x+3)^(1/2).
lim as h -> 0 of
[√(5x+5h+3) - √(5x+3) ] [√(5x+5h+3) + √(5x+3) ]
______________________________________
h[√(5x+5h+3) - √(5x+3) ]
Simplify the numerator via FOIL:
5x+5h+3 + √(5x+5h+3)√(5x+3) - √(5x+3)√(5x+5h+3) - (5x+3)
The remaining radicals in the numerator cancel each-other, giving us:
5x + 5h + 3 - 5x - 3
Simplify Further:
5h
Now that we have simplified our numerator, let's continue:
lim as h -> 0 of (5)(h)/[(h)((5x+5h+3)^(1/2) + (5x+3)^(1/2))]
The h in the numerator cancels the h in the denominator.
lim as h -> 0 of 5/[(5x+5h+3)^(1/2) + (5x+3)^(1/2)]
Now, we directly substitute h with 0 in the equation.
5/[ (5x+3)^1/2 + (5x+3)^(1/2) ]
In the denominator, both sides of the addition sign are the same, so we can simplify it further to:
5/[ 2(5x+3)^(1/2) ]
This is the same answer we received using the chain rule, so it is correct!
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 149 millimeters, and a standard deviation of 8 millimeters.
If a random sample of 50 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 3.3 millimeters? Round your answer to four decimal places.
The probability that the sample mean will differ from the population mean by more than 1.8 mm = 0.9949
Given,
In the question:
According to the given problem the mean diameter μ= 149 mm (population mean) and the standard deviation is σ = 8mm
random sample size, n= 50 steel bolts is selected
Let the random variable that represents the diameter of steel bolts be denoted by x and from the problem we have x = 3.3mm
Let z = (x-μ) / (σ/√n ) ....(1)
using formula (1) and when the sample mean differs from the population mean by more than 1.8mm
z = (3.3 - 149) /(8/√50 )
⇒z = -2.575
The probability that the sample mean will differ from the population mean by more than 1.8 mm
P( z > -2575) = 1 - P(z< -2.575) = 1 - 0.0051 = 0.9949
Hence, The probability that the sample mean will differ from the population mean by more than 1.8 mm = 0.9949.
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Hi, I am testing the service for Brainly. Can you help me find the median for this set of numbers: 3, 4, 15, 27, 53, 54, 68, 77?
To find the median of a set of numbers, the first step is:
1 - Put the numbers in crescent order
This set of numbers is already in crescent order, so we can skip this step
2 - Count how many numbers there are in the set.
In our set we have 8 numbers, so in this case, the median of the set will be the average value between the two central numbers (that is, the fourth and fifth numbers)
The fourth number is 27, and the fifth number is 53, so the median is the average of these two numbers:
[tex]\text{median = }\frac{(27\text{ + 53)}}{2}=\frac{80}{2}=40[/tex]So the median of this set of numbers is 40.
Do they have the same value? Is +3 equal to -3 and -10 equal to +10? Why?
+3 and -3 do not have the same value
+10 and -10 do not have the same value
Explanation:+3 is a positive number while -3 is a negative number
+3 ≠ -3 (Since one is positive and the other is negative)
The difference between +3 and -3 = 3 - (-3) = 6
Therefore, +3 and -3 do not have the same value
+10 is a positive number while -10 is a negative number
+10 ≠ -10 (Since one is positive and the other is negative)
The difference between +10 and -10 = 10 - (-10) = 20
Therefore, +10 and -10 do not have the same value
"People who are generous help those in need however they can."
To which theory of ethics is the person who made this statement likely appealing?
Conventionalism
Virtue-based ethics
Kantian deontology
Egoism
Answer: Conventionalism
Step-by-step explanation:
The person who made the statement, "People who are generous help those in need however they can," is appealing to virtue-based ethics.
What is Virtue ethicsVirtue ethics is a way of thinking about what is right and wrong. It focuses on becoming a good person and practicing good qualities.
This focuses on helping people develop good qualities such as being generous, caring, and kind. In this situation, the statement means that being kind and helping people who need it is seen as doing the right thing.
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Determine the slope by using the slope formula and add two points on the line check your answer by drawing a right triangle and labeling the rise and run right numbers in simplest form select undefined if Applicable
Answer:
The slope is -2
Explanation:
The slope can be calculated as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.
Replacing (x1, y1) by ( 0, -1) and (x2, y2) by (1, -3), we get:
[tex]m=\frac{-3-(-1)}{1-0}=\frac{-3+1}{1}=\frac{-2}{1}=-2[/tex]Now, we can check the answer using the following drawing
Since rise over run is also equal to 2/(-1) = -2. We can say that the slope is -2.
The bases of the prism below are rectangles. If the prism's height measures 3 units and its volume is 198 units^3. solve for x
The volume of a rectangular prism is given by
V=L*W*H
where
V=198 units3
L=6 units
W=x units
H=3 units
substitute given values
198=(6)*(x)*(3)
solve for x
198=18x
x=198/18
x=11 unitswrite the slope-interference form of the equation of each line
The slope interference form of straight line is given by
[tex]y=mx+c[/tex]Here is the slope of the line and c is the y-intercept
Now, from the graph, it is seen that the line passes through the points (0,4) and (3,5)
So,
[tex]\begin{gathered} \frac{y-4}{5-4}=\frac{x-0}{3-0} \\ \frac{y-4}{1}=\frac{x}{3} \\ 3(y-4)=x \\ 3y=x+12 \\ y=\frac{x}{3}+4 \end{gathered}[/tex]So, the required equation is
[tex]y=\frac{x}{3}+4[/tex]
2) Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.
Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.
we know that
Applying the Pythagorean Theorem
DE^2=DEx^2+DEy^2
DEx -----> is the distance in the x-coordinate
DEy -----> is the distance in the y-coordinate
DEx=(-5-4)=-9 ------> subtract the x-coordinates
DEy=(-7+3)=-4 -----> subtract the y-coordinates
substitute in the formula
DE^2=(-9)^2+(-4)^2
DE^2=97
[tex]DE=\sqrt[]{97}\text{ units}[/tex]c^2=a^2+b^2
c -----> is the distance DE
a ----> horizontal leg
b ----> vertical leg
we have
a=(-5-4)=-9 ------> subtract the x-coordinates
b=(-7+3)=-4 -----> subtract the y-coordinates
substitute
c^2=(-9)^2+(-4)^2
c^2=97
[tex]c=\sqrt[]{97}\text{ units}[/tex]