Answers
Answer:
Perpendicular
Step-by-step explanation:
Let's start by finding the slopes of both lines.
Line A's slope is 3 (this is given).
We can determine line B's slope with the two points given. The slope formula is [tex]m=\frac{y1-y2}{x1-x2}[/tex]. Substitute in the values:
[tex]m=\frac{1-(-1)}{-3-3}[/tex]
and simplify:
[tex]m=\frac{2}{-6}[/tex]
So the slope of line A is -1/3.
-1/3 and 3 multiply to -1, so this indicates that the two lines are perpendicular.
Answer:
Perpendicular
Step-by-step explanation:
If Line A passes through the origin with a slop of 3, then Line A would be
y = 3x
For Line B, using the slope/points method, the line would be
y = -1/3x
When graphing these two lines, they intersect as opposite slopes, so therefore this pair of equations would be Perpendicular
Related Questions
Someone please help me
Answers
Step-by-step explanation:
distance QR :
Pythagoras, as the distance between 2 points is the Hypotenuse (baseline) of a right-angled triangle of the differences of the x and y coordinates.
QR² = (12 - 2)² + (-2 - -7)² = 10² + 5² = 125
QR = sqrt(125) = sqrt(25×5) = 5×sqrt(5)
PQ = 2×QR = 10×sqrt(5) = sqrt(100×5) = sqrt(500)
PQ² = (h - 12)² + (18 - -2)² = h² - 24h + 144 + 20²
500 = h² - 24h + 144 + 400
0 = h² - 24h + 44
since a quadratic equation :
h = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -24
c = 44
h = (24 ± sqrt(576 - 176))/2 = (24 ± sqrt(400))/2 =
= (24 ± 20)/2 = 12 ± 10
h1 = 22
h2 = 2
since the trapezium opens up to the right at the angle Q, it must be the value further to the right : h = 22.
the line QR has the slope (ratio y difference / x difference) :
x changes by +10 (from 2 to 12).
y changes by +5 (from -7 to -2).
the slope is 5/10 = 1/2
SP has the same slope (parallel line).
SR is perpendicular to these 2 lines. its slope is x and y differences upside-down in the ratio, and the sign is flipped.
the SR slope is therefore -2/1 = -2
the general line equation is
y = ax + b
a is the slope, b is the y- intercept (y value when x = 0).
we get b by using the known point coordinates in the half finished equation with the slope.
the SP equation is
y = (1/2)x + b
we know P (22, 18). so,
18 = (1/2)×22 + b = 11 + b
7 = b
the full SP line equation is
y = (1/2)x + 7
the RS equation :
y = -2x + b
we know R (2, -7). so,
-7 = -2×2 + b = -4 + b
-3 = b
the full RS equation is
y = -2x - 3
the coordinates of S we get by crossing RS and SP :
(1/2)x + 7 = -2x - 3
x + 14 = -4x - 6
5x = -20
x = -4
now using that in any of the 2 line equations
y = -2×-4 - 3 = 8 - 3 = 5
so, S = (-4, 5)
the distance SP is
SP² = (22 - -4)² + (18 - 5)² = 26² + 13² = 676 + 169 =
= 845
SP = sqrt(845) = sqrt(169×5) = 13×sqrt(5)
the distance RS is
RS² = (-4 - 2)² + (5 - -7)² = (-6)² + 12² = 36 + 144 = 180
RS = sqrt(180) = sqrt(36×5) = 6×sqrt(5)
the area of the trapezium is the sum of the rectangle of SRQ (and the 4th point being around the middle of SP) and the triangle of PQ and this 4th rectangle point.
the area of the rectangle is
6×sqrt(5)×5×sqrt(5) = 30×5 = 150
the area of the triangle is
base×height/2
height is the same as RS = 6×sqrt(5).
base is the part of SP from the 4th rectangle point to P, and that is the same as
SP - QR = 13×sqrt(5) - 5×sqrt(5) = 8×sqrt(5)
so, we have for the area of the triangle
6×sqrt(5)×8×sqrt(5)/2 = 3×sqrt(5)×8×sqrt(5) = 24×5 = 120
the total area of the trapezium is
150 = 120 = 270
If two numbers are 10 apart, is it likely that their square roots are also 10 apart?
b) How far apart are the square roots of numbers that are 10 apart likely to be?
pls no links!<3 thanks:)
Answers
Answer:
yea that's about right. like the square root of 100 would be 10 and the square root of 90 would be about 9.5 dose that make since?
Yes, it is likely that their square roots are also 10 apart because the square root of 100 is 10.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
If two numbers are 10 apart.
As we know,
The square root of 100 is 10
√100 = 10
Let us assume the number 90 which is near the 100
The square root of the number 90 is 9.48 which is near or after rounding:
√90 = 9.5
Thus, yes it is likely that their square roots are also 10 apart because the square root of 100 is 10.
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1/2 divided by 1 3/7
Answers
Answer:
7/20
Step-by-step explanation:
1/2 divided by 1 3/7
Keep Change Flip
1 3/7=10/7
1/2 x 7/10 = 7/20
The domain for f(x) is all real numbers ___ than or equal to 2
Answers
Step-by-step explanation:
f(x) = 2x² + 5√(x - 2)
Domain
√(x - 2) ≥ 0
x - 2 ≥ 0
x ≥ 2
x is greater than or equal to 2
Answer: Greater than
Step-by-step explanation:
Caleb has 3 apples and he loses 1 apple how many apples does Caleb have?
Answers
Answer:
2 apples
Step-by-step explanation:
he should be more careful next time :)
2. A house costs $30,000. A buyer is given a 1/10 discount. How much money does the buyer save?
Answers
Answer:
3000
Step-by-step explanation:
find the slope of the line that passes through the points
Answers
eleven less than twice a number is 17 more than four times the number
Answers
Let's take the missing number as 'x'.
11 less than twice a number = 11 - 2x
17 more than 4 times the number = 17 + 4x
=》 11 - 2x = 17 + 4x
=》 11 - 17 = 4x + 2x
=》 -6 = 6x
=》 -6/6 = x
=》 -1 = x
______
RainbowSalt2222 ☔
I’m wondering if this is a polygon
Answers
Answer:
They don't need to have parallel lines or right angles. If you think about that, it means that a triangle is a polygon. So are squares, rectangles and, yes, quadrilaterals, parallelograms and trapezoids. They all are closed shapes with many sides, so they're all polygons!
Have a great day!
Brainliest please :)
Please help me with these problems!
Answers
Answer:
143880000 people have dogs and b.
Step-by-step explanation:
327,000,000 * .44(44 percent) = 143880000
the sample of 437 is much smaller than the entire state of texas, so it is incorrect to assume that the small amount of people is representative of the entire state.
Answer:
Step-by-step explanation:
3)
327 Million → 100%
x → 44%
100x = 44×327
100x = 14388
x = 14388/100
x = 143.88 Million people
4) D
I hope I've helped you.
Can someone help me with this, please?
Answers
Answer:
-2x = 4
Step-by-step explanation:
You have 2 negative x tiles on the left side, which is -2x.
You have 4 one tiles on the right side, which is 4.
Hope this helps!
Jessica and her family bought 5 tickets to a
music concert. Tickets for adults cost $5.10 and
tickets for children cost $3.60. Jessica and her
family spent a total of $21. How many tickets
for adults (a) and how many tickets for children
(c) did they buy?
a + c = 5
5.1a + 3.6C = 21
[?] adults [ ] children
Answers
Step-by-step explanation:
work is shown and pictured
Find the value of x that makes p and q
Answers
Answer:
14)
[tex]{ \rm{(5x - 9) \degree + (2x) \degree = 180 \degree}} \\ { \tt{ \{straight \: line \: angles \}}} \\ { \rm{7x - 9 = 180}} \\ { \rm{7x = 189}} \\ { \boxed{ \mathfrak{answer :{ \rm{ \: \: x = 27}} }}}[/tex]
15)
[tex]{ \rm{63 \degree + (9x + 36) \degree = 180 \degree}} \\ { \rm{9x + 99 = 180}} \\ { \rm{9x = 81}} \\ { \boxed{ \mathfrak{answer : \: \: { \rm{x = 9}}}}}[/tex]
[tex]{ \underline{ \mathfrak{ \green{Good \: grace}} \: \:⚜ \: \: { \blue{ \mathfrak{Good \: God}}}}}[/tex]
The other question is in the picture
Activity 2: of Directions: Write T before each item if the statement is TRUE, otherwise write F.
For items 1-2: Use the problem below to answer the following questions.
Your mother invested PhP 10,000.00 in an investment institution at 5% compounded semi-annually for x years.
___1. y = 10 000(1.025)2x is the function that represents mother's total investment
Answers
Using compound interest, it is found that the correct options are:
1. True.
2. True.
Compound interest:
[tex]A(x) = P\left(1 + \frac{r}{n}\right)^{nx}[/tex]
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. x is the time in years for which the money is invested or borrowed.Item 1:
Invested 10000, hence [tex]P = 10000[/tex].Semi-annually, hence [tex]n = 2[/tex].Interest rate of 5%, hence [tex]r = 0.05[/tex]Then:
[tex]A(x) = P\left(1 + \frac{r}{n}\right)^{nx}[/tex]
[tex]A(x) = 10000\left(1 + \frac{0.05}{2}\right)^{2x}[/tex]
[tex]A(x) = 10000(1.025)^{2x}[/tex]
Hence option 1 is True.
Item 2:
Quarterly, hence [tex]n = 4[/tex].Then:
[tex]A(x) = P\left(1 + \frac{r}{n}\right)^{nx}[/tex]
[tex]A(x) = 10000\left(1 + \frac{0.05}{4}\right)^{4x}[/tex]
[tex]A(x) = 10000(1.0125)^{4x}[/tex]
Hence option 2 is also True.
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Alberto has $2.25 in dimes and nickels in his pocket. He has nine more nickels than dimes. How many of each type of coin does he have?
I really need help!
Answers
Alberto has 12 Dimes and 21 Nickels in his pocket.
How many of each type of coin does he have?Dimes value = 0.10$
Nickels value = 0.05$
Let d = number of dimes = 0.10d
Let d+9 = number of nickels = 0.05(d + 9)
Value of the Dimes + Value of the Nickels = total value of the coins
Write the equation:
0.10d + 0.05(d + 9) = 2.25
Distribute:
0.10d + 0.05d + 0.45 = 2.25
0.15d + 0.45 = 2.25
Subtract 0.45 from each side:
0.15d = 1.80
Divide to find the number of dimes.
d = 12
The number of nickels is d +9 = 12 + 9 = 21
Alberto has $2.25 in dimes and nickels in his pocket. He has 12 Dimes and 21 Nickels in his pocket.
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What is - 1+12 Give your answer as a fraction in its simplest form.
Answers
Step-by-step explanation:
as u can use the rules of numbers u can realize -1+12=12-1=11
Answer:
-
Step-by-step explanation:
-1+12
=12-1
=11
:)
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(6x+20)
(7X-10)
105
Answers
Answer:
x = 5
Step-by-step explanation:
Angles in a triangle = 180°
(6x + 20) + (7x - 10) + 105 = 180°
13x + 10 +105 = 180
13x + 115 = 180
-115 = -115
13x = 65
x = 65/13
x = 5
Solve
9
-
)
12
OA)
0010
100
8
OB)
OC)
5
12
OD)
olu
5
12
Answers
(4, 7); y = 3x + 6 plz help me
Answers
y=3x+6.
y=3x-5
I did it with a parallel line
Here is a linear equation: y = 1/4x + 2 What is the x-intercept of the graph of the equation?
Answers
Answer:
(−8,0)
Step-by-step explanation:
The x- intercept is (-8, 0)
What is Intercept?A line's slope and intercept give information on its steepness and the point at which it crosses an axis, respectively. The linear relationship between two variables is defined by the slope and intercept, which can be used to calculate the average rate of change.
Given:
Equation: y= -1/4 x + 2
Now, for x- intercept take y= 0
So, 0 = 1/4x + 2
1/4x = -2
x= -8
Hence, the x- intecrcept is (-8, 0)
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y=-4(x+2)(x-8) rewritten in standard form
Answers
Answer:
y = x + 40
Step-by-step explanation:
I'm assuming to simplify this.
Use the distribution property first.
y = -4x - 8 · 4x + 32
Combine like terms.
y = x · 8 + 32
Solve.
y = x + 40
Hope this this helps!
What is the slope of the line on the graph?
Enter your answer in the box.
Answers
Answer:
I think this is the answer you are looking for. (See below)
Step-by-step explanation:
From the given graph it is noticed that the line is passing through many points.
The coordinates of three given points are (1,5), (-1,-1), (-1,-7)
If a line passing through two points (x1 ,y1) and (x2, y2) , the slope of the lie is defined by, m= y2 - y1/x2 - x1
The line passing through two points (-1,1) and (1,5). So the slope of the line is, m= 5 - 1 / 1 minus -1
m=4/2
Therefore, the slope of the line is 2.
Pls if this is wrong, let me know in the comments. I'm not really good at this topic in math but I hope it helps you. Sorry if it is wrong. Have a good day. :)
Find the ratio as simply as possible in the form a : b.
[tex]3 \frac{1}{2} : 1 \frac{1}{7} [/tex]
Answers
_________
[tex] \: [/tex]
[tex]3 \frac{1}{2} : 1 \frac{1}{7} [/tex]
[tex] = \frac{3 \frac{1}{2} }{1 \frac{1}{7} } [/tex]
[tex] = \frac{ \frac{7}{2} }{ \frac{8}{7} } [/tex]
[tex] = \frac{7}{2} \times \frac{7}{8} [/tex]
[tex] = \frac{49}{16} [/tex]
[tex] = 49 : 16[/tex]
Triangle EFG is dilated by a scale factor of \frac{2}{3}
3
2
to form triangle E'F'G'. What is the measure of side FG?
Answers
Answer:
B. 36°
Step-by-step explanation:
Dilation does not change the angle measures or the direction of the lines. Angle F is the same as corresponding angle F'.
Select the correct answer. Graph the following system of inequalities.
y <2x+1
y<-x-1
A. X
B. Z
C. W
D. Y
Answers
This is because it makes both of the inequalities true
The graph of the inequalities y <2x+1 and y<-x-1 will be shown by graph x. The correct option is A.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to, > ‘greater than, or < ‘less than. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
The inequality functions are y <2x+1 and y<-x-1. When we plot the graph of the functions we can see that the two lines intersect at the point ( -1, 0 ) and overlap below the function.
The graph of the functions is y <2x+1 and y<-x-1 is attached with the answer below.
Therefore, the graph of the inequalities y <2x+1 and y<-x-1 will be shown by graph x. The correct option is A.
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Please help me asap
The line passing through which two points is perpendicular to the line 10x + 2y = 2?
A.) (-2, -7) and (1, 8)
B.) (-5, 5) and (0, 4)
C.) (0,-9) and (5, -8)
D.) (-4, 12) and (-2,2)
E.) (-2, 11) and (1, -4)
Answers
Considering the definition of perpendicular line, the correct option is option C): the line passing through (0,-9) and (5, -8) is perpendicular to the line 10x + 2y = 2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.
m is the slope.
b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷(x₂ - x₁)
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Perpendicular line in this caseIn this case, the line is 10x + 2y=2. Expressed in the form y = mx + b, you get:
2y=2 - 10x
y= (-10x +2)÷ 2
y= -10/2x +2/2
y= -5x +1
The line has a slope of -5. If you multiply the slopes of two perpendicular lines, you get –1, you get:
-5× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-5)
slope perpendicular line= 1/5
The line through two points must have a slope equal to 1/5. So you calculate the slope of each line that passes through two points as follows:
(x₁, y₁)= (-2, -7) and (x₂, y₂)= (1, 8): m= (8 - (-7))÷(1 - (-2)) → m= (8+7)÷ (1+3) → m= 15÷4= 15/4(x₁, y₁)= (-5, 5) and (x₂, y₂)= (0, 4): m= (4- 5)÷(0 - (-5)) → m= (-1)÷ (0 + 5) → m= -1÷5= -1/5(x₁, y₁)= (0, -9) and (x₂, y₂)= (5, -8): m= (-8 - (-9))÷(5 - 0) → m= (-8+9)÷ (5) → m= 1÷5= 1/5(x₁, y₁)= (-4, 12) and (x₂, y₂)= (-2, 2): m= (2 - 12)÷(-2 - (-4)) → m= (-10)÷ (-2+4) → m= -10÷2= -5(x₁, y₁)= (-2, 11) and (x₂, y₂)= (1, -4): m= (-4 -11)÷(1 - (-2)) → m= (-15)÷ (1+2) → m= -15÷3= -5Since the perpendicular line must have a slope equal to 1/5, the line passing through (0,-9) and (5, -8) is the correct line.
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U+t=7
Ut=12
Solve simultaneously using formula method
Answers
Answer:
U= 10 or 11 T=-4 or-3
Step-by-step explanation:
solved using substitution not sure what the formula method is
U+T=7
UT=12
U=12/t
12/t+t=7
12/t=7-t
12=7t-t^2
t^2+7t+12=0
(t+4)(t+3)
t=-4, -3
u-4=7
u=11
u-3=7
u=10
10x + 44
8x - 23
It’s solving for X in triangles
Answers
Answer:
x=33.5
Step-by-step explanation:
help please i don’t understand
Answers
Answer:
567
Step-by-step explanation:
you gotta keep dreaming multiply the 6 then the 5
Answer this question for me ASAP
Answers
Answer:
Option A: (It's just that the y-intercept and slope are in different spots.)
Line in (y=mx+b) form is y = 2x + 4
Slooe is 2
y-intercept is 4
Step-by-step explanation:
Slope-intercept form is written as y=mx+b, where m is slope and b is y-intercept.
By looking at the graph, we can already tell that the y-intercept is positive 4, since the line crosses the y-axis at that point.
Now use rise/run to find slope. (Remember that rise is movement up or down, and run is movement left or right.) With this in mind, the slope is 4/2, and if we simplify it, it's 2/1 (or basically just 2). Because we go upwards 4 units and to the right 2 units.
Hope this helps :)
