Perpendicular lines have slope negative reciprocal to each other .
-1/0=ooEquation of line in point slope form
[tex]\\ \rm\Rrightarrow y-y_1=m(x-x_1)[/tex]
[tex]\\ \rm\Rrightarrow y-11=\infty(x+8)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{y-11}{\infty}=x+8[/tex]
[tex]\\ \rm\Rrightarrow x+8=0[/tex]
[tex]\\ \rm\Rrightarrow x=-8[/tex]
Some formats of line
[tex]\boxed{\begin{array}{c|c}\boxed{\bf Form} &\boxed{\bf Equation} \\ \sf Slope\: intercept\:form &\sf y=mx+b \\ \sf Intercept\:form &\sf \dfrac{x}{a}+\dfrac{y}{b}=1\\ \sf Normal\:form &\sf xcos\omega+ysin\omega=p \\ \sf Two\: point\:form &\sf y-y_1=\left(\dfrac{y_2-y_1}{x_2-x_1}\right)(x-x_1)\\ \sf Point\:slope\:form &\sf y-y_1=m(x-x_1) \\ \sf Standard\:form &\sf Ax+By+C=0 \end{array}}[/tex]
Graph the following equation y+2=3/5(x+3)
Answer:
Step-by-step explanation:
It is given
2x−3y=5
we can write it as
3y=2x−5
So we get
y=32x−5
Substituting x=4 in the given equation
y=32(4)−5
So we get
Y=38−5
y=33
By division we get
y=1
Substituting x=−2 in the given equation
y=32(−2)−5
So we get
y=3−4−5
y=3−9
By division we get
y=−3
x 4 -2
y 1 -3
Now draw a graph using the points (4,1) and (−2,3)
Join the point through a line and find the value of y
(i) Based on the graph
consider x=4 on X-axis
Now the line joining the two points and a point on the Y-axis gives the value of y
Therefore,when x=4 the value of y=1
(ii) Based on the graph,
Consider y=3 on Y-axis
Now the line joining the two points and a point on the X-axis the value of x
Therefore, when y=3 the value of x=7
A bag contains 4 black balls and 6 white balls. Sarah picks a ball at random from the bag and replaces it back in the bag. She then picks another ball at random from the bag.
You may draw a tree diagram on paper to answer the following questions.
Calculate the probability that she picks
a) 2 white balls or 2 black balls
Answer:
13/25
Step-by-step explanation:
number of black balls = 4
number of white balls = 6
⇒ total number of balls = 10
As the balls are always replaced after being picked:
probability of picking a black ball = P(B) = 4/10probability of picking a white ball = P(W) = 6/10Therefore,
P(W) and P(W) = 4/10 x 4/10 = 16/100 = 4/25
P(B) and P(B) = 6/10 x 6/10 = 36/100 = 9/25
P(W and W) or P(B and B) = 4/25 + 9/25 = 13/25
Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 90 miles per hour. The eastbound train travels at 80 miles per hour. How long will it take for the two trains to be 374 miles apart?
If you open a bank account with a $200 starting balance and it earns 2.5% interest, compounded annually, how much interest will you earn in 10 years?
Answer:
$56.02
Step-by-step explanation:
The account balance after 10 years is given by the future value formula:
FV = P(1 +r)^t . . . . . principal P invested at rate r compounded annually for t years
FV = $200(1 +0.025)^10 ≈ $256.02
The amount in excess of the original investment is the interest earned:
$256.02 -200.00 = $56.02 . . . . interest earned in 10 years
Answer:
$256.02
Step-by-step explanation:
Here is the formula: 200(1.025)^10.
The .025 is the percentage of the interest, and the 1 is the money you already have (which is 200). The ^10 is the 10 years.
If you take the (1.025)^10, you'll get an incredibly large number, 1.2800....
Take that large number and multiply it by the amount of money you originally have, $200. Then you'll get something like 256.0169... Round to the near hundredth, and you'll have 256.02
please help me with this math problem (:
Answer:
[tex] {x}^{2} + ( \frac{ \sqrt{3} }{2} ) {}^{2} = 1 \\ {x}^{2} = \frac{1}{4} \\ x = \frac{1}{2} \: \: or( \frac{1}{2} ) \\ x > 0 \\ therefore \: \: x = \frac{1}{2} [/tex]
Answer:
[tex]x=-\frac{1}{2}[/tex]
Step-by-step explanation:
equation of a circle: [tex](x - h)^2+(y-k)^2=r^2[/tex]
where (h, k) = center and r = radius
From inspection, we can see that the center of the circle = (0, 0)
and the radius = 1
[tex]\implies (x - 0)^2+(y-0)^2=1^2[/tex]
[tex]\implies x^2+y^2=1[/tex]
Substitute [tex]y=\frac{\sqrt{3}}{2}[/tex] into [tex]x^2+y^2=1[/tex] and solve for [tex]x[/tex]:
[tex]\implies x^2+(\frac{\sqrt{3}}{2})^2=1[/tex]
[tex]\implies x^2+\frac{3}{4}=1[/tex]
[tex]\implies x^2=\frac{1}{4}[/tex]
[tex]\implies x=\pm \sqrt{\frac{1}{4}}[/tex]
[tex]\implies x=\pm\frac{1}{2}[/tex]
As point P is in quadrant 2, [tex]x[/tex] is negative, so [tex]x=-\frac{1}{2}[/tex]
what are the measures of the angles of a triangle (4x-4) 58 (8x-18)
Find the diameter and the radius of the circle 13yd
Answer:
52
Step-by-step explanation:
This is because the formula is dr
The expression (x3)(x-17) is equivalent to x". What is the value of n?
Answer:
Hello how are you
n equals -14
what is 92 to the power of 3? please answer this!
Answer:
778688
Step-by-step explanation:
because you do 92 times 92 times 92!
please mark brainliest i need 2 more
using Nets
Using the net below, find the surface area
of the rectangular prism.
5 in
3 in.
5 in.
5 in.
3 in.
5 in
3 in.
3 in.
Surface Area =
?) in.
Please help
Answer:
behold... the answer is..... 110! :)
Can you help solve problem 11
Answer:
i dont know that try looking it up
Determine whether the triangles are similar by AA, SSS, SAS, or not similar
Answer:
Step-by-step explanation:
If Δ JKL ~ Δ JHG , then
[tex]\frac{LJ}{GJ}[/tex] = [tex]\frac{KJ}{HJ}[/tex]
[tex]\frac{95}{68}[/tex] ≠ [tex]\frac{87}{72}[/tex] ⇒ triangles are not similar
y-6≤=15+8y
pls dont report
Answer:
-4, -10, -2
Step-by-step explanation:
[tex]y-6\leq 15+8y\\-21\leq 7y\\y\geq -3\\[/tex]
so the answer is -4, -10, -2
Answer:
99.9% sure it's -4, -10, -2
Step-by-step explanation:
y−6≤15+8y
−21≤7y
y≥−3
so that be providing that you're gonna get
-4, -10, -2
PLS HELP ME!!!! Use the graph to find the relationship between the two variables. Select all that apply.
Answer:
The graph is not visible!
You could have positive or negative correlation.
Hope this helps!
There are 6 classes going on a field trip. Each class has 26 students.
Each car can hold 5 students. How many cars are needed to get all
he students to the field trip?
Answer:
32 cars
Step-by-step explanation:
If each class has 26 students, we can multiply the number of classes, 6, by the amount of students in each class, to find the total amount of students going on the field trip.
6 * 26 = 156 students
Each vehicle can hold 5 students. To find the amount of vehicles needed to transport all the children, we need to divide the number of students by 5.
156 / 5 = 31.2 vehicles
I don't think they plan on driving 0.2 of a vehicle, so we would have to round. We can't round down because if we did, there would be one student left.
31 * 5 = 155 students
Unless the student plans on biking there, they would have to have 32 cars ready to drive the students to the field trip.
The total cost of an eraser, 2 similar pens and a ruler is $13. The total cost of 2 similar erasers, a pen and a ruler is $11. The cost of 3 erasers is the same as that of 2 rulers. Find the cost of a ruler.
Answer:
$3
Step-by-step explanation:
Let the cost of an eraser, a pen and a ruler be $e, $p, and $r respectively.
Given:
e +2p +r= 13 -----(1)
2e +p +r= 11 -----(2)
3e= 2r -----(3)
(1) ×3:
3e +6p +3r= 39 ----(4)
Substitute (3) into (4):
2r +6p +3r= 39
6p +5r= 39 -----(5)
(2) ×3:
6e +3p +3r= 33 -----(6)
Substitute (3) into (6):
2(2r) +3p +3r= 33
4r +3p +3r= 33
3p +7r= 33 -----(7)
Let's rewrite equations (5) &(7) so it's easier to compare them:
6p +5r= 39 -----(5)
3p +7r= 33 -----(7)
We can eliminate the term p to find the value of r. This can be done by making sure that the coefficient of p is equal in both equations.
(7) ×2:
6p +14r= 66 -----(8)
(8) -(6):
6p +14r -(6p +5r)= 66 -39
Expand:
6p +14r -6p -5r= 27
9r= 27
r= 27 ÷9
r= 3
Thus, the cost of a ruler is $3.
Gerald fi nds that it takes 30 ml of a
standard solution to neutralize 12 ml of
a solution of unknown concentration.
If he starts with 20 ml of the unknown
solution, it takes 50 ml of standard
solution to neutralize it. Assuming a linear
relationship exists between the amount
of unknown solution and the amount of
standard solution required to neutralize
it, how much unknown solution can
be neutralized with 175 ml of standard solution?
Help please.
Which statements apply to the expression 3/5 ³
Answer:
A is true. (3/5)³ has base 3/5
C is true. (3/5)³ has exponent 3.
D is true. (3/5)³ = 3/5 × 3/5 × 3/5.
G is true. (3/5)³ = 3/5 × 3/5 × 3/5 = 27/125
How to solve questions
Solve the following inequality.
-10 < 5 + X <-5
[?] < < <[ ]
Enter
Solution:
Simplify the inequality one by one:
-10 ≤ 5 + x < -5=> -10 - 5 ≤ x => -15 ≤ x => 5 + x < -5=> x < -5 - 5=> x < -10This means that...
-15 ≤ x < -10Hoped this helped!
Required solution :
First solving for -10 < 5 + x
⇒-10 - 5 < x
⇒ -15 < x
Now for 5 + x < -5
⇒ x < -5 - 5
⇒ x < -10
Therefore,
-15 < x < -10giveing free ponits :) but u must tell me answer whats 9798 ÷456464 answer it or report
Answer:
See below.
Step-by-step explanation:
The answer is 0.02146500052, or 0.02.
-hope it helps
(Thanks.)
A circle is shown 10 cm. What is the circumference of the circle, to the nearest tenth of a centimeter
Answer:
31.42cm
Step-by-step explanation:
Answer. We know that C = πd. Since the diameter is 10cm, we know that C = π x 10cm = 31.42cm (to 2 decimal places).
You have $575 to spend on clothes for the school year. You want to by 8 pairs of pants that cost $352.45 including tax and hoodies that will have a 8.7 % sales tax. What is the inequality that represents the amount of money you have to spend?
Answer:
352.45 + 1.087x ≤ 575
Step-by-step explanation:
The most you can spend is $575, so the total you spend must be ≤ 575.
You already have a total for the pants of $352.45.
352.45 + price of hoodies ≤ 575
Let x = total price of the hoodies before tax.
The price of the hoodies with tax is
x + 8.7% of x = x + 0.087x = 1.087x
The inequality is
352.45 + 1.087x ≤ 575
~Giving brainliest!~ (im really desperate right now and very overwhelmed so im asking ANYONE to help me answer this! thank u.
Answer:
15. 420 hours
16. not sure sorry
Step-by-step explanation:
15. there are 168 hours in a week, so 168 * 2 1/2 is 420
16. your gonna have to find the answer from someone else sorry
1 kg = 2.2 lb. Dan weighs 170 lb. How many kilograms does he
weigh?
Round answer to the nearest tenth.
10. Jan purchased 140 shares of stock in the ABC Company at a price of $18.75 per share. During the
next three days, the value declined by $1.00, $1.75 and $1.50. What was the value of a share of ABC
stock at the end of three days?
[tex]\bold{\huge{\orange{\underline{ Solution }}}}[/tex]
[tex]\bold{\underline{ Given :- }}[/tex]
Jan purchased 140 shares of stock in ABC company at a price of $18.75 per share During the next 3 days, the value of share declined by $1.00 , $1.75 and $1.50[tex]\bold{\underline{ To \: Find :- }}[/tex]
We have to find the value of a share of ABC stock at the end of 3 days[tex]\bold{\underline{ Let's \: Begin :- }}[/tex]
According to the question,
Cost of 1 share of ABC company = $18.75
Therefore,
Cost of 140 shares purchased by Jan in the ABC company
[tex]\sf{ = 140 × 18.75 }[/tex]
[tex]\sf{ = 2625\: dollars }[/tex]
Now,
For next 3 days, the value of share declined
[tex]\sf{ = (1 + 1.75 + 1.50)dollars }[/tex]
[tex]\sf{ = 4.25 \: dollars }[/tex]
Therefore,
The value of shares after 3 days will be
[tex]\bold{ = }{\bold{\frac{2625 - 4.25}{ 140}}}[/tex]
[tex]\bold{ = }{\bold{\frac{ 2620.75}{ 140}}}[/tex]
[tex]\bold{\red{ = 18.75\: dollars}}[/tex]
Hence, The value of share after 3 days will be $18.75 .
When an object falls due to gravity on Earth, the acceleration is 9.8 m/s. A student drops a rock
down a mineshaft. It takes 3.00 seconds for the rock to hit the bottom of the shaft. What is the
velocity of the rock as it impacts?
Answer:
29.4 m/s
Step-by-step explanation:
Use v = at with a = 9.8 m/s^2 and t = 3.00 sec
v = 9.8 * 3.00 = 29.4 m/s
Complete the statement below.
The
property can be used to remove the parentheses in the expression 1.7(x + 9).
Answer:
I believe it is the "square root" sign
Answer:
distributive
Step-by-step explanation:
If an exterior angle measure of a regular
polygon is 20°, how many sides does the
polygon have? What is the measure of each interior angle?
Answer:
n=18 sides
Step-by-step explanation:
Given: Exterior angle =20°
Find: sides of a regular polygon
Solution: θ=(360°)/side , θ=20°
Let n= number of sides
θ=360°/n
20=360/n
n=360/20
n=18
find the value of x and give reasoning in the following image
Answer: 80
Step-by-step explanation:
Angle FGB = 80 degrees b/c supplementary angles.
By the sum of interior angles of a quadrilateral, angle FEB = 360 - 75 - 95 - 90 = 100 degrees.
x is supplementary with this angle and is this 180 - 100 = 80.