[tex]\text{Given that,}\\\\(x_1,y_1) = (0,-1) ~ \text{and}~ (x_2, y_2) = (3,-3)\\\\\text{Slope, m}= \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{-3+1}{3-0} = -\dfrac 23\\\\\\\text{Point slope - form}\\\\y-y_1 = m(x-x_1)\\\\\implies y - (-1) = -\dfrac 23 (x -0)\\\\\implies y +1 = -\dfrac 23 x[/tex]
solve each given equation
Answer:
x = 30
Infinite Solutions
No Solutions
Step-by-step explanation:
First, combine like terms
Then move all variable to one side and isolate them by undoing the action being done to them
Example 1:
6x + 4x - 6 = 24 + 9x
10x - 6 = 24 + 9x
-9x -9x
x - 6 = 24
+6 +6
x = 30
Example 2:
25 - 4x = 15 - 3x + 10 -x
25 - 4x = 25 - 4x
Since they are the same on both sides, this equation has Infinite Solutions
Example 3:
4x + 8 = 2x + 7 + 2x -20
4x + 8 = 4x - 13
-4x -4x
8 = -13
This statement is untrue, therefore this equation has No Solution
PLEASE HELP!!! very confused
Answer:
Step-by-step explanation:
The vertices lie on the x-axis, as is determined by their coordinates. This makes the center of this hyperbola (0, 0) because the center is directly between the vertices. The fact that the foci also lie on the x-axis tells us that this is the main axis. What this also tells us is which way the hyperbola "opens". This one opens to the left and the right as opposed to up and down. The standard form for this hyperbola is:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex] and so far we have that h = 0 and k = 0.
By definition, a is the distance between the center and the vertices. So a = 5, and a-squared is 25. So we're getting there. Now here's the tricky part.
The expressions for the foci are (h-c, k) and (h+c, k). Since we know the foci lie at +/-13, we can use that to solve for c:
If h+c = 13 and h = 0, then
0 + c = 13 and c = 13.
We need that c value to help us find b:
[tex]c^2=a^2+b^2[/tex] and
[tex]13^2=5^2+b^2[/tex] and
[tex]169=25+b^2[/tex] and
[tex]144=b^2[/tex] so
b = 12. Now we're ready to fill in the equation:
[tex]\frac{x^2}{25}-\frac{y^2}{144}=1[/tex] and there you go!
(x+5). (x-4)-(x+2)^2+(2x+3)^2=(2x-1) (4x^2+2x-1)+18x(2x+3)
Answer:
x ≈ -0.73151
Step-by-step explanation:
Amanda rented a bike from Ted's Bikes.
It costs $10 for the helmet plus $4.25 per hour.
If Amanda paid about $33.38, how many hours did she rent the bike?
a) Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answer:
≈ 5.51 hours
Equation: 4.25h + 10
The number of hours Amanda rented the bike is 5.5 hours.
The equation used to solve this problem is 33.38 = 10 + 4.25h.
The rent cost for the helmet is $10.
The rent cost for the bike per hour is $4.25.
We need to find the number of hours Amanda rented the bike as she paid $33.38 in total.
We also have to make an equation that would solve this problem.
Consider h = number of hours Amanda rented the bike.
The cost for renting the helmet = $10.
And rent cost for the bike per hour = $4.25.
Amanda's total cost = Helmet rent cost + bike rent cost
Since we do not know the number of hours the bike was rented we will denote bike rent cost = $4.25 x h
We have,
$33.38 = $10 + $4.25 x h
33.38 = 10 + 4.25 x h
33.38 - 10 = 4.25 x h
23.38 = 4.25 x h
h = 23.38 / 4.25
h = 5.5011
Rounding to the nearest tenths we get,
h = 5.5 hours
The number of hours Amanda rented the bike is 5.5 hours.
The equation used to solve this problem is 33.38 = 10 + 4.25h.
Learn more about solving word problems using equations here:
https://brainly.com/question/16369335
#SPJ2
Help. Needs to find the value of x
Step-by-step explanation:
angle marked on diagram = 180 - 75 = 105° (supplementary angles)
x = 105° (alternate angles are equal)
convert 3.35 hours into hours and minutes
3.35 hours is 3 hours and 21 minutes.
3.35 hours is also equivalent to 201 minutes and 0 seconds or 12060 seconds.
Hope this helps!
Have a wonderful day!
Answer:
3 hours and 21 minutes
Step-by-step explanation:
If n(A)=36, n(B)=10, n(AU B) = 40 and n(A) = 27 find n(U) and n(AB
Answer:
n(A∪B)=n(A)+n(B)−n(A∩B)−−−−−−−(1)
Given n(A)=7
n(B)=9
n(A∪B)=14
Substituting in 1
14=7+9−n(A∩B)
⇒n(A∩B)=16−14=2
Step-by-step explanation:
ok
Answer:
The question is incomplete.
It should be:
If n(A)=36, n(B)=10, n(A∪B)=40, and n(A')=27. Find n(∪) and n(A∩B)Find n(U)
n(A') = n(∪) - n(A)27 = n(∪) - 36n(∪) = 27 + 36n(∪) = 63Find n(A∩B):
n(A∪B) = n(A) + n(B) - n(A∩B)40 = 36 + 10 - n(A∩B)n(A∩B) = 46 - 40n(A∩B) = 6The set of whole numbers and their opposites are known as ?
( a ) 2x + 3y − 5z ( ) 32
( b ) x + y + z ( ) 8
( c ) x
2 + 2xy + z
2
( ) 36
( d ) (x + y)(x + z) ( ) −1
( e ) −(x
2 − y
2
) ( ) −16
Answer:
Step-by-step explaWe are losing Earth's greatest biological treasures just as we are beginning to appreciate their true value. Rainforests once covered 14% of the earth's land surface; now they cover a mere 6% and experts estimate that the last remaining rainforests could be consumed in less than 40 years.
One and one-half acres of rainforest are lost every second with tragic consequences for both developing and industrial countries.
Rainforests are being destroyed because the value of rainforest land is perceived as only the value of its timber by short-sighted governments, multi-national logging companies, and land owners.
Nearly half of the world's species of plants, animals and microorganisms will be destroyed or severely threatened over the next quarter century due to rainforest deforestatioue to rainforest deforestation. That equates to. As the rainforest species of tesrees anddisappear, so do many possible that 1% plants have been tested by sciMost rainforests are cleared by chainsaws, bulldozers and fires for its timber value and then are followed by farming and ranching operations, onian Rainforest five centuries ago. Today there are less than 200,000.
In Brazil alone, European colonists have destroyed more than 90 indigenous tribes since the 1900's. With them have gone centuries of
nation:
Which type of transformation is this?
The type of transformation in this situation is refelction on the x-axis.
It cannot possibly be translated or rotated around the origin.
Hope this helps!
Have a wonderful day!
Find the length of BC⎯⎯⎯⎯⎯⎯⎯⎯
Answer:
≅ 53.679
Step-by-step explanation:
tan(x) = opposite leg / adjacent leg
tan(54) = BC / 39
1.37638... = BC / 39
BC = 1.37638... x 39
= 53.67889...
What is the Compound interest on Rs.1000 at the rate of 20% p.a. semiannually for 1 year and 10 months?
A. Rs. 420.31
B. Rs. 400.29
C. Rs. 419.73
D. Rs. 409.13
Answer:
420.31
Step-by-step explanation:
A
.Rs.420.31
20ejjdj
Answer:
I think A rs 420.31 is right answet
Hey can anyone help with this question?
Answer:
Step-by-step explanation:
When you learn calculus you'll be able to do this by hand (without a calculator) but for now we have to just kind of guess. We know that 8 x 8 = 64 and 9 x 9 = 81, so the number is between 8 and 9. Since 68 is closer to 64 than it is to 81, the number is closer to 8. Like less than 8.5. 8.1 squared is 65.61, (you can do this by hand...without a calculator) and 8.2 squared is 67.24, and 8.3 squared is 68.89. 8.3 squared is too high while 8.1 squared was too low; the estimation to the nearest tenth is 8.2
ABCDEFGHIJ is a regular decagon and the measure of <D is 144º. What is the measure of <A?
A) 90°
B) 100°
C) 144°
D 220°
ABC is an equilateral triangle and the measure of <A is 60°. What is the measure of <C?
A) 45°
B) 60°
C) 90°
D) 180°
Answer:
1. 144⁰
2. 60⁰
Step-by-step explanation:
The formula to find the measure of the interior angles of a regular polygon is:
m< = (n - 2) • 180/n where n = the number of sides
For a decagon, there are 10 sides.
m< = (10-2) • 180/10 = 144°
A regular polygon/equilateral triangle is defined as having equal sides and angles.
Answer:
given ABCDEFGHIJ is a decagon
As we know the sum of all ten interior angles of a decagon = 1440°
so measure of each angle of decagon = (1440/10)° = 144°
so the measure of ∠A would be 144° (C)
given Δ ABC is a equilateral triangle
As we know the sum of all three interior angles of a equialter traingle = 180°
so if one angle of an equilateral triangle is 60°
then the remaining of the angles would have the measure of 60° each
So answer = 60°(B)
Hope it helps
Find the value of y.
Answer:
y = √(1×8) = 2√2
z = √(8×9) = 6√2
Answered by GAUTHMATH
Answer:
[tex]y=2\sqrt{2}[/tex]
[tex]y\approx 2.82843[/tex]
Step-by-step explanation:
The given triangle is a right triangle, this is indicated by the box around one of the angles in the triangle. The Pythagorean theorem is a property that applies to right triangles, this property comes in the form of an equation, which can be simply put as the following:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs of the right triangle, or the sides adjacent to the right angle of the right triangle. The parameter (c) indicates the hypotenuse or the side opposite the legs of the right triangle.
Look at the smallest triangle in the entire image. Using the Pythagorean theorem, one can form an equation and solve for the unknown parameter, (y).
[tex]a^2+b^2=c^2[/tex]
Substitute,
[tex](1)^2+(y)^2=(3)^2[/tex]
Simplify,
[tex](1)^2+(y)^2=(3)^2[/tex]
[tex]1+y^2=9[/tex]
[tex]y^2=8[/tex]
[tex]y=\sqrt{8}[/tex]
[tex]y=2\sqrt{2}[/tex]
[tex]y\approx 2.82843[/tex]
(a) The radius of a circle is 5.6 cm. Find the angle in degrees subtended by an arc of 22 cm at the
centre of the circle.
DO NO A PLEASE
Answer:
225 degrees
Step-by-step explanation:
Given the following data;
Radius, r = 5.6 cmLength of arc = 22 cmTo find the angle in degrees subtended by an arc;
Mathematically, the length of the arc of a circle is given by the formula;
S = rA
Where;
S is the length of the arc.A is the angle measured in radians.Substituting the values into the formula, we have;
22 = 5.6 * A
[tex] A = \frac {22}{5.6} [/tex]
A = 3.9286 radians.
Next, we would convert the value of the angle in radians to degrees;
Conversion:
[tex] 1 \; radian = \frac {180}{\pi} \; degrees [/tex]
[tex] 3.9286 \; radians = X \; degrees [/tex]
Cross-multiplying, we have;
[tex] X = \frac {180}{\frac {22}{7}} * 3.9286 [/tex]
[tex] X = \frac {180 * 7}{22} * 3.9286 [/tex]
[tex] X = \frac {1260}{22} * 3.9286 [/tex]
[tex] X = 57.2727 * 3.9286 [/tex]
X = 225.0015 ≈ 225 degrees
find the missing side. Round it to the nearest tenth.
Answer:
37.3
Step-by-step explanation:
tan63 = opposite/adjacent = x/19
x = 19tan63 = 37.2895 = 37.3
Formula used: [tex]b=\sqrt{c^2-a^2}[/tex]
a = 19
b = x
c = 63
solution
b = [tex]\sqrt{c^2-a^2}[/tex]
b = [tex]\sqrt{63^2-19^2}[/tex]
b = [tex]\sqrt{3,969 -361}[/tex]
b = [tex]\sqrt{3,608}[/tex]
b = [tex]\sqrt{60.0666}[/tex]
rounded off: 60.0 or just 60
x = 60
Jol 26, 12:24:35 PM
Solve for x. Round to the nearest tenth, if necessary.
5.7
71
Answer: 2
Submit Answer
attempt 1 out of 2
PLS HELP i really need to finish this
Answer:
x = 16.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 71 = x /5.7
5.7 tan 71 = x
x=16.55400
Rounding to the nearest tenth
x = 16.6
What is the area of the following circle?
Answer:
[tex]16\pi\:\mathrm{units^2}\text{ or }50.24\:\mathrm{ units^2}[/tex]
Step-by-step explanation:
The area of a circle with radius [tex]r[/tex] is given as [tex]A=r^2\pi[/tex].
In the question, we're given [tex]r=4[/tex] and asked to solve for [tex]A[/tex].
Substituting [tex]r=4[/tex] into [tex]A=r^2\pi[/tex], we get:
[tex]A=4^2\pi,\\A=\boxed{16\pi\:\mathrm{units^2}}[/tex]
If we use [tex]\pi=3.14[/tex] as mentioned in the question, we would have:
[tex]A=16\pi=16\cdot 3.14=\boxed{50.24\:\mathrm{units^2}}[/tex]
A woman making $32,000
a year receives a cost-of-living increase that raises her salary to $32,768
per year. Find the percent of increase in her yearly salary.
Percentage increase= $768÷32000=0.024
=0.024×100=2.4%
WILL GIVE BRAINLISEST Solve for m∠NLM
GOOD LUCKJ!
Answer:
[tex]m<NLM = 30[/tex]
Step-by-step explanation:
1. Approach
The easiest way to solve this problem is to find the degree measure of the parameter (x). Use the fact that line (LN) is a diameter to solve for (x), beacause the angle measure of a circle on either side of the diameter is (180) degrees. One can then find the measure of arc (mNM), and then find the measure of the angle (<NLM) using the inscribed angles theory.
2. Find the measure of (x)
A diameter is the largest chord or segment in a circle. It intersects a circle at two points and runs through the center of a circle. The degree measure of a circle on either side of the diameter is (180) degrees. As per the given image, line (LN) is a diameter. The arcs (mLM) and (mNM) make up half of the circle, or rather one side of the diameter. With this information, one can form an equation and solve for the parameter (x) using this information:
[tex](mLM)+(mNM)=180[/tex]
Substitute,
[tex](mLM)+(mNM)=180[/tex]
[tex](13x-10)+(7x-10)=180[/tex]
Simplify,
[tex](13x-10)+(7x-10)=180[/tex]
[tex]20x-20=180[/tex]
Inverse operations,
[tex]20x-20=180[/tex]
[tex]20x=200[/tex]
[tex]x=10[/tex]
3. Find the measure of angle (<NLM)
The inscribed angles theorem states that an angle with its vertex on the circumference (outer edge) of a circle is equal to half of the surrounding arc. One can form an equation and solve for the measure of angle (<NLM).
[tex]m<NLM=\frac{1}{2}(mNM)[/tex]
Substitute,
[tex]m<NLM=\frac{1}{2}(mNM)[/tex]
[tex]=\frac{1}{2}(7x-10)[/tex]
[tex]=\frac{1}{2}(7(10)-10)\\\\=\frac{1}{2}(70-10)\\\\=\frac{1}{2}(60)\\\\=30[/tex]
PLEASE SOMEONE ANSWER THIS ASAP !!!!!!!!!
Graph the function f(x) = 2*-7 on the set of axes below.
If g(x)= 1.5x-3, determine if f(x) > g(x) when x = 4. Justify your answer.
IMAGE NEEDED!!!!!
Answer:
for the second one,
f(4)= 2⁴-7= 9
g(4)= 1.5x4-3= 3
therefore 9>3
f(4)>g(4)
618 000 in standard form
6.18000 x 10 5
This is the standard form of 618,000
Thanks , Please mark me brainliest
TyrantMC
Are the triangles similar? If so, what postulate or theorem proves
their similarity?
O No, the triangles are not similar
Yes, by AA Similarity Postulate
O Yes, by SSS Similarity Theorem
O Yes, by SAS Similarity Theorem
Answer:
Yes, by SSS Similarity Theorem
Step-by-step explanation:
the triangles are similar because the sides are proportional, the common ratio is 1.5.
if you look at the corresponding sides of the triangle and multiply 1.5 to the smaller triangle measurements, you get the bigger triangle's corresponding measurements:
3 * 1.5 = 4
4 * 1.5 = 6
6 * 1.5 = 9
Yes the triangle are similar by SSS Similarity Theorem.
What is Similarity?Triangles' similarity can be characterized based on their attributes.
If two triangles are similar,
(I) their respective angles are equal, and
(ii) their corresponding sides have the same proportion (or proportion
We have two triangles.
From the triangle we can write
AB / ED = 4/ 6 = 2/3
and, AC / FD = 6 / 9 = 2/3
and, BC / EF = 3 / 4.5 = 30 /45 = 2/3
Thus, AB / ED = AC / FD = BC / EF = 2/3
By SSS Similarity Criteria triangles are similar.
Learn more about Similarity here:
https://brainly.com/question/26451866
#SPJ5
Find the volume of each figure. Round your answers to the nearest tenth, if necessary
Answer:
1.92 m³
hopefully this answer can help you to answer the next question.
2. In a certain company, the senior employees have an average of 16 years of work experience and the junior employees have an average of 4 years of work experience. If the average number of years of experience for all the senior and junior members is 7 years, then what is the ratio of senior members to junior members at the company
Answer:
The ratio of senior members to junior members at the company is 1 : 3
Step-by-step explanation:
The given average number of years of experience of the senior employees, x = 16 years
The given average number of years of experience of the junior employees, y = 7 years
Let a represent the number of senior employees in the company, and let b represent the number of junior workers in the company, we have;
(16·a + 4·b)/(a + b) = 7
∴ (16·a + 4·b) = (a + b) × 7 = 7·a + 7·b
16·a - 7·a = 7·b - 4·b
9·a = 3·b
a/b = 3/9 = 1/3
a/b = 1/3
The above equation, expressed as a ratio is, a : b = 1 : 3
Therefore;
The ratio of senior members to junior members at the company, a : b = 1 : 3.
B. If p +q= 3 and pq - 4. find the value of p³+q³
Answer:
p³ + q³ is -9
Step-by-step explanation:
[tex]{ \tt{ {(p + q)}^{3} = ( {p}^{2} + {q}^{2} + 2pq)(p + q) }} \\ { \tt{ {(p + q)}^{3} = ( {p}^{3} } + 3p {q}^{2} + 3 {p}^{2} q)} \\ { \tt{ {p}^{3} + {q}^{3} = {(p + q)}^{3} - 3pq(p + q)}} \\ { \tt{ {p}^{3} + {q}^{3} = {(3)}^{3} - 3(4)(3) }} \\ = - 9[/tex]
a man sells an article at rupees 600 and makes a profit of 20% of selling price calculate is profit percentage
Answer:
25%
Step-by-step explanation:
profit percentage = (profit/cost price) * 100
selling price = 600
profit = 600 * 20/100 = 120
cost price = 600-120 =480
profit percentage = (120/480) * 100 = 25
Which is the graph of f(x) = 4[½]^x?
Answer:
from left to right the second graph
Step-by-step explanation:
f(x) = 4(1/2)^x
y = 4(1/2)^x
-find the y-intercept
if x=0 then y = 4(1/2)^0 = 4*1 =4, the y-intercept is (0,4)
so is first or second graph
-look at the second graph and check if the function go trough the point (1, 2)
if x=1 then y = 4(1/2)^1 = 4/2 = 2
so the second graph it is
(X+3)= 1
(2x+5)=(3n+2)
Hello!
(x + 3) = 1
x + 3 = 1
x = 1 - 3
x = -2
(2x + 5) = (3n + 2)
[2 × (-2) + 5] = (3n + 2)
(-4 + 5) = (3n + 2)
1 = (3n + 2)
1 = 3n + 2
3n + 2 = 1
3n = 1 - 2
3n = -1
n = -1 : 3
n = -1/3
Good luck! :)
