Given below are descriptions of two lines.
Line 1: Goes through (1,1) and (-2,7)
Line 2: Goes through (-1,4) and (1,0)
The slope of Line 1 is m =
|
The slope of Line 2 is m =
The slope of Line 1 is m = -2
The slope of Line 2 is m = -2
For Line 1;
(x₁, y₁) = (1, 1);
(x₂, y₂) = (-2, 7);
m₁ = (7-1)/(-2-1) = -2;
For Line 2;
(x₃, y₃) = (-1, 4);
(x₄, y₄) = (1, 0);
m₂ = (4-0)/(-1-1) = -2;
To learn more about this; visit: https://brainly.in/question/49507300
#SPJ9
If EF = 5x, FG = 10, and EG = 10x, what is EF?
geometry
If points E,F,G are collinear, then,
EF+FG = EG
5x+10 = 10x
10 = 10x-5x
10 = 5x
5x = 10
x = 10/5
x = 2
So,
EF = 5x = 5*2 = 10EG = 10x = 10*2 = 20As a check, EF+FG = 10+10 = 20 = EG to help confirm the answer
Final Answer: EF = 10Answer:
EF = 10
Step-by-step explanation:
EF = 5x
FG = 10
EG = 10x
Find a + b, 9a + 3b, |a|, and |a − b|. a = 9i − 4j + 3k, b = 6i − 9k
1) a + b = ?
→ (9i − 4j + 3k) + (6i − 9k)
→ 15i - 4j - 6k
2) 9a + 3b = ?
→ 9(9i − 4j + 3k) + 3(6i − 9k)
→ (81i - 36j + 27k) + (18i - 27k)
→ 99i - 36j
3) |a| = ?
→ |9i − 4j + 3k|
→ 9i + 4j + 3k
4) |a − b| = ?
→ |(9i − 4j + 3k) - (6i − 9k)|
→ |3i - 4j + 12k|
→ 3i + 4j + 12k
Answer:
[tex]a+b=15i-4j-6k[/tex]
[tex]9a+3b=99i-36j[/tex]
[tex]|a| = 9i+4j+3k[/tex]
[tex]|a-b| = 3i+4j+12k[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}a = 9i-4j+3k\\b=6i-9k\end{cases}[/tex]
[tex]\begin{aligned}a+b & = (9i-4j+3k)+(6i-9k)\\& = 9i-4j+3k+6i-9k\\& = 9i+6i-4j+3k-9k\\& = 15i-4j-6k\\\end{aligned}[/tex]
[tex]\begin{aligned}9a+3b & = 9(9i-4j+3k) + 3(6i-9k)\\& = 81i-36j+27k+ 18i-27k\\& = 81i+ 18i-36j+27k-27k\\& = 99i-36j\end{aligned}[/tex]
[tex]\begin{aligned}|a| & = |9i-4j+3k|\\& = 9i+4j+3k\end{aligned}[/tex]
[tex]\begin{aligned}|a-b| & = |(9i-4j+3k)-(6i-9k)|\\& = |9i-4j+3k-6i+9k|\\& = |9i-6i-4j+3k+9k|\\& = |3i-4j+12k|\\& = 3i+4j+12k\end{aligned}[/tex]
How to I round this imperfect square √11
Answer: 3.32
Step-by-step explanation:
√11=
3.3166=
3.3166=3.32 ==>When rounding to the hundredth place, if the thousandth's digit is 5 or greater, increase the hundredth's digit by 1.
Find the slope of the line shown on the graph to the right.
Question content area bottom left
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
The slope would be [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Answer:
-4/-5
Step-by-step explanation:
Remember the formula to slope:
(y2 - y1)/(x2-x1) given two points on the line that are (x1, y1) and (x2, y2).
The two points given on this line are: (2,2) from the top left and (-3,-2) from the bottom left. Let's say (2,2) = (x1, y1) and (-3,-2) = (x2, y2). Plug the points into the formula:
(-2 - 2)/(-3-2) = -4/-5
FINAL ANSWER: -4/-5
Please help simplify
Answer: B. 24
Step-by-step explanation:
|3x| = 11.4 absolute value of X
Step-by-step explanation:
The absolute value of x is g(x)=f(x)+k.
GUY!!! PLEASE HELP it’s due in abit and I just need this final question! I’ll mark you brainliest
(geometry)
what is the perimeter of the rectangle ABCD?
Answer:
37.9 units (nearest tenth)
Step-by-step explanation:
As ABCD is a rectangle, AD = BC and AB = DC.
Find the length of AD and AB using the distance formula.
[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}}[/tex]
From inspection of the given diagram:
A = (-5, -9)B = (7, -5)D = (-7, -3)Therefore:
[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(-7-(-5))^2+(-3-(-9))^2}\\& =\sqrt{(-2)^2+(6)^2}\\& =\sqrt{4+36}\\& =\sqrt{40}\end{aligned}[/tex]
[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(7-(-5))^2+(-5-(-9))^2}\\& =\sqrt{(12)^2+(4)^2}\\& =\sqrt{144+16}\\& =\sqrt{160}\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Perimeter of a rectangle} & = \sf 2(length + width)\\& = 2(AB+AD)\\& = 2(\sqrt{160}+\sqrt{40})\\& = 2(18.97366596...)\\& = 37.94733192...\\& = 37.9\: \sf units\:(nearest\:tenth)\end{aligned}[/tex]
Therefore, the perimeter of the rectangle ABCD is 37.9 units (nearest tenth).
Learn more about the distance formula here:
https://brainly.com/question/28144723
https://brainly.com/question/28247604
A car is traveling at a speed of 45 kilometers per hour. What is the car's speed in meters per second? How many meters will the car travel in 2 seconds?
Answer:
12.50m/s
in 2 seconds: 25
im not really good at math but i tried
In 2008, the number of digital cameras shipped totaled 186 million. There were 24 million shipped in 2013. Find and
interpret the average rate of change in the number of digital cameras shipped per year.
Step-by-step explanation:
the average change rate for a function g(x) is defined for an interval of x values as
(g(interval end) - g(interval begin))/(interval end - interval begin)
in our case that is
(g(2013) - g(2008))/(2013 - 2008) =
= (24 mil. - 186 mil)/5 = -162 mil./5 =
= -162,000,000 / 5 = -32,400,000
that means that as a mean value there were 32,400,000 digital cameras shipped less every year.
in other words, fewer and fewer digital cameras are sold. the demand is strongly declining.
actually, following the mean values and their trend, there should have been no new digital cameras shipped in 2014 anymore (as 24 mil. - 32.4 mil is less than 0).
Find the dimensions of a rectangle given that its perimeter is 80 cm and its length is 1 cm more than twice its width.
Set up your solution using the variables L for the length, W for the width, and P for the perimeter.
Part a: Using the definition of perimeter, write an equation for P in terms of L and W .
Part b: Using the relationship given in the problem statement, write an equation for L in terms of W .
Solve the equations from parts a and b.
Answer:
The length should equal 27.
The width should equal 13.
A: P= 2L+ 2W
B: L=2W+1
Step-by-step explanation:
Perimeter is always equal to all of the sides added up.
You can find out the width and length by subsititution.
80=2(2W+1) +2W
80=4W+2+2W
80=6W+2
78=6W
W=13
L=(13*2)+1
L=27
A square that is 7 yd on a side is placed inside a rectangle that has a width of 9 yd and a length of 14 yd. What is the area of the region inside the rectangle that surrounds the square?
Answer: 77 yd^2
Step-by-step explanation:
S=Area of Square. s=side length of square. w=width of rectangle
l=length of rectangle. R=Area of Rectangle
S=s^2
S=7^2
S=49 yd^2
R=l*w
R=9*14
R=126 yd^2
R-S=
126-49=77 yd^2
Four thousand five hundred eleven ten-thousandths in standard decimal form?
What is the solution of −|t+3| + 3 ≥ −4?
Answer:
[tex]-1t+31 +3 \geq -4[/tex]
[tex]-1t +34 \geq -4[/tex]
[tex]-1t \geq 30[/tex]
[tex]t \geq -30[/tex]
1=|8-2y| what’s the value of y
Answer:
y=-7/2
Step-by-step explanation:
1=|8-2y|
1=8+2y
-7=2y
2y=-7
y=-7/2
Brian is buying gifts bags for all of the students in his class. The graph shows the relationship between the number of bags and the cost of the bags. Write an equation relating the number of bags, x, and the cost, y.
An equation that relates the number of bags, x, to the cost, y is y = 5x.
What is an equation?An equation is a mathematical statement that claims that the two sides are equal.
An equation involves two or more variables that require some mathematical operations to obtain their equivalent value.
Therefore, an equation contains numbers, variables, and operators, which show a value after the mathematical operations.
Data and Calculations:Let the number of bags for the class = x (number of students)
Let the unit cost of a bag = $5
Let y = the total cost
Equation, y = 5x
Thus, an equation that relates the number of bags, x, to the cost, y is y = 5x.
Learn more about equations at https://brainly.com/question/2972832
#SPJ1
How do I figure out x and y
Answer:
x = 7, y = 45
Step-by-step explanation:
[tex]7x+13=6x+20[/tex]
[tex]x=20-13\\x=7[/tex]
Angle
[tex]7(7)+13=49+13=62^{0}[/tex]
supplementary angle
180 - 62 = 118°
[tex]3y-17=118[/tex]
[tex]y=\frac{118+17}{3} =135/3=45[/tex]
Hope this helps
ASAP HELP PLEASE!!!!
Answer:
x^21/5
Step-by-step explanation:
To change this expression to an expression with a rational exponent, we need to change the radical to a rational (fractional) exponent. Just as square root is a one half power and cuberoot is a one-third power, a fifth root is a one-fifth power.
Once the radical is changed to a fraction, we will just use the exponent rule that says when you raise a power to a power, you multiply exponents.
see image.
Please help! thanks!
What numbers are a distance of 34 unit from 18 on a number line?
Select the locations on the number line to plot the points.
Answer:
[tex]\dfrac{7}{8} \textsf{ and } -\dfrac{5}{8}[/tex]
Step-by-step explanation:
To find numbers that are [tex]\dfrac{3}{4}[/tex] units distance from [tex]\displaystyle \dfrac{1}{8}[/tex] , add and subtract [tex]\dfrac{3}{4}[/tex] to and from [tex]\displaystyle \dfrac{1}{8}[/tex]
One of the points is at [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4}[/tex] units away and the other at [tex]\displaystyle \dfrac{1}{8} - \dfrac{3}{4}[/tex] units away
Compute [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4} :[/tex]A rectangular picture has dimensions of length (2x-1) inches and width (x+7) inches. The area of the picture is 108 in^2. What are the length and width of the picture?
The numerical length and width of the rectangular picture are 9in and 12in respectively.
What are the length and width of the picture?Area of a rectangle is expressed as;
A = length × width
Given the data in the question;
Length = 2x -1Width = x + 7Area = 108in²To determine the numerical length and width of the rectangular picture, first plug the given values into the equation and solve for x.
A = length × width
108 = (2x -1)(x+7)
Expand
108 = 2x² + 14x - 1x -7
108 = 2x² + 13x -7
Reorder
2x² + 13x -7 = 108
2x² + 13x - 7 - 108 = 0
2x² + 13x - 115 = 0
Solve by grouping
(x-5)(2x+23) = 0
x-5 = 0, 2x+23 = 0
x = 5, 2x = -23
x = 5, x = -23/2
x = 5, x = -11.5
But the dimension cannot be negative, hence;
x = 5
Next, determine the numerical length and width.
Length = 2x - 1 = 2(5) - 1 = 10 - 1 = 9in
Width = x + 7 = 5 + 7 = 12in
Therefore, the numerical length and width of the rectangular picture are 9in and 12in respectively.
Learn more about area of rectangles here: https://brainly.com/question/27612962
#SPJ1
The probability that a live birth requires a cesarean delivery in a certain American state is 0.248. If 8 live births occur independently in this state, compute the probability that at least one of the births requires a cesarean delivery.
i need help on this question
The probability that at least one of the births requires a cesarean delivery is 0.897.
To calculate prob(x >= 1):
prob(x>=1) = 1 - prob(x = 0)
= 1 - (1-0.248)^8
= 0.897
To learn more about this; visit: https://brainly.com/question/11234923
#SPJ9
Question
Your bank account has a balance of −$12. You deposit $60. What is your new balance?
Your new balance is $
.
Answer: $52 is your new balance
Step-by-step explanation: -12+60=52
Solve the equation P = b + a + c for b.
b= ?
Answer:
b= p-(a+c)
Step-by-step explanation:
版 < The population of a village 10 years ago was 7500. The population is now 5700. What percentage decrease is this? Type here to search O 21 7 I %
two angles are complementary. The measure of the larger angle is 6 degrees less than 3 times the measure of the smaller angle. The measure of the smaller angle is _______ degrees and the measure of the larger angle is______ degrees
Step-by-step explanation:
complementary means together they are 90°.
x = 3y - 6
x + y = 90
(3y - 6) + y = 90
4y - 6 = 90
4y = 96
y (the smaller angle) = 24°
x (the larger angle) = 3y - 6 = 3×24 - 6 = 72 - 6 = 66°
Please HELP ME!!!! This is really confusing. HOW DO I DO THIS?!?!?!
Answer:
Flying Disc should be 72
Step-by-step explanation:
circumference = πd
HD Coin C = 3π
9.42477796077
Flying Disc. C = 23π
72.2566310326
Jar Lid C = 8π
25.1327412287
Flower Pot C = 15π
47.1238898038
Susan Marciano invested part of her $12,000 bonus in a fund that paid 8% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was $300 .
Answer:y=mx+b
Step-by-step explanation:
Answer:
Let x be the amount invested in funds that earned 8%.
Then the amount invested in stock that suffered 3% loss is 18,000 - x.
The profit from investment in funds is 8%x
The loss from investment in stock is 3%(18,000 - x).
The net profit is 8%x - 3%(18,000 - x).
As the net profit given in the problem is $780, we have:
8%x - 3%(18,000 - x) = 780
Step-by-step explanation:
A 5.ft tall man casts a shadow along the ground that is 8 ft. long. At the same time a giraffe casts a shadow that is 12 ft. long. How tall is the Giraffe?
Answer : 7.5 ft
Step-by-step explanation:
when the length of the shadow is 8ft, the actual height of the man = 5ft
8:5
let the giraffe be 'x' ft tall.
if the length of the shadow is 12ft, actual height = x ft
12:x
8:5 x 12:x
[tex]\frac{8}{5}[/tex] × [tex]\frac{12}{x}[/tex]
x= [tex]\frac{15}{2}[/tex]
x=7.5 ft
Therefore, the giraffe is 7.5ft tall.
Answer:
[tex]7.5\; {\rm ft}[/tex].
Step-by-step explanation:
The height of objects nearby under the sun are approximately proportional to the length of their shadows.
In other words, if the man and the giraffe are near each other and under the sun:
[tex]\begin{aligned} \frac{\text{height of man}}{\text{length of shadow of man}} = \frac{\text{height of giraffe}}{\text{length of shadow of giraffe}}\end{aligned}[/tex].
Given that:
[tex](\text{height of man}) = 5\;{\rm ft}[/tex], [tex](\text{length of shadow of man}) = 8\;{\rm ft}[/tex], and [tex](\text{length of shadow of giraffe}) = 12\; {\rm ft}[/tex].Rearrange the equation to find [tex](\text{height of giraffe})[/tex]:
[tex]\begin{aligned} (\text{height of giraffe}) &= (\text{length of shadow of giraffe})\times \frac{\text{height of man}}{\text{length of shadow of man}} \\ &= 12\; {\rm ft} \times \frac{5\; {\rm ft}}{8\; {\rm ft}} \\ &= 7.5\; {\rm ft}\end{aligned}[/tex].
A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total admission revenue, not including sales tax, and had a total of 450 guests.
The system of equations below can be used to model the number of guests that were children, x, and the number of guests that were adults, y.
First, place a point on the graph representing the solution to the system of equations. Notice that one of the equations in the system has already been graphed.
Then, determine the approximate number of guests that were children and the approximate number of guests that were adults for that day.
The approximate number of guests that were children are 172 and adults are 278
How to determine the approximate number of guests that were children and adults for that day?From the complete question, we have the following system of equations
25x + 12y = 9014
x + y = 450
Make y the subject in x + y = 450
y = 450 -x
Substitute y = 450 - x in 25x + 12y = 9014
25x + 12(450 - x) = 9014
Expand the expression
25x + 5400 - 12x = 9014
Evaluate the like terms
13x = 3614
Divide both sides by 12
x = 278
Substitute x = 278 in y = 450 -x
y = 450 - 278
Evaluate
y = 172
Hence, the approximate number of guests that were children are 172 and adults are 278
Read more about system of equations at:
https://brainly.com/question/14323743
#SPJ1
