Answers
[tex]m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{2-(-6)}{3-(-3)} \\ \\ m=\frac{8}{6} \\ \\ m=\frac{4}{3}[/tex]
The y-intercept of the graph is -2
The graph is shaded upwards, so we will be using the greater than symbol, but since the line is dotted we will not be using any of the "equal to" symbols.
Hence, the solution of the graph is [tex]y>m=\frac{4}{3} x-2[/tex]
Option: C is the correct answer.
C. [tex]y>\dfrac{4}{3}x-2[/tex]
Step-by-step explanation:By looking at the graph we observe that the line is dotted this means that the inequality will be strict.
Also, this line passes through the point (-3,-6) and (3,2).
Hence, the equation of line is calculated by using a two point form i.e. a line passing through two points (a,b) and(c,d) is calculated with the help of formula as:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here (a,b)=(-3,-6) and (c,d)=(3,2)
i.e.
[tex]y-(-6)=\dfrac{2-(-6)}{3-(-3)}\times (x-(-3)}\\\\i.e.\\\\y+6=\dfrac{2+6}{3+3}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{8}{6}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{4}{3}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{4}{3}x+4\\\\i.e.\\\\y=\dfrac{4}{3}x-2[/tex]
Also, the shaded region is towards the origin.
Hence, the inequality is:
[tex]y>\dfrac{4}{3}x-2[/tex]
Related Questions
100 Points last one i promise! helpp!
Answers
Answer:
$40.35
Step-by-step explanation:
First, solve for the sales price. Change the percentage into a decimal:
60% = 60/100 = 0.60
Next, multiply 0.60 with the original price, 97:
97 x 0.60 = 58.2
Subtract 58.2 from the original price:
97 - 58.2 = 38.8
Now, change the tax percentage into a decimal.
4% = 4/100 = 0.04
Multiply 0.04 with the sales price:
38.8 x 0.04 = 1.552
Add the sales price (rounded to nearest hundredth) to the sales price:
1.55 + 38.8 = 40.35
$40.35 is your answer.
~
Answer:
40.35
Step-by-step explanation:
First find the discount
97 * 60%
97 *.6 = 58.2
Subtract the discount to find the new price
97-58.20 =38.80
Next find the tax
38.80 * 4%
38.80 * .04
1.55
We add the tax to the sales price
38.8+1.55
40.35
In the diagram, C and D are located such that AB is divided into three equal parts. What are the coordinates of C and D?
Answers
Step-by-step Answer:
Topic: Points of division
There are scary looking formulas that can be used, but it is much easier to calculate by reasoning.
Given : A(-3,6), B(6,-3)
Solution:
The idea is to subdivide the DIFFERENCE in coordinates into thirds, and add onto that of A. We choose A as the starting point, but method works equally well if we chose B.
Difference in coordinates (delta) between A & B is then
delta(Bx-Ax, By-Ay)
=(6-(-3), -3-6)
=delta(9, -9)
One third of difference (for point C)
=delta/3 = (3,-3)
So coordinates of point C
= A(-3,6)+(3,-3)
= C(0,3)
Two thirds of difference (for point D)
= (2/3)delta = (6, -6)
Coordinates for point D
= A(-3,6)+(6,-6)
= D(3,0)
If you prefer to use formulas, it would be
New coordinates = (Xa+(Xb-Xa)*k, Ya+(Yb-Ya)*k)
where
Xa,Xb = x-coordinates of points A & B respectively.
Ya,Yb = y-coordinates of points A & B respectively.
k=ratio (usually less than 1)
Here
k for point C = 1/3
k for point D = 2/3
Coordinate of C is: (0,3)
and Coordinate of D is: (3,0)
Step-by-step explanation:We know that if a point C(x,y) divides the given line segment A(a,b)B(c,d) into ratio of m:n
then the coordinates of points C are:
[tex]x=\dfrac{m\times c+n\times a}{m+n},\ y=\dfrac{m\times d+n\times b}{m+n}[/tex]
Point C cuts the line segment AB in the ratio 1:2.Here A(a,b)=A(-3,6)
and B(c,d)=B(6,-3)
This means that the coordinate of Point C are:
[tex]x=\dfrac{1\times 6+2\times (-3)}{1+2},\ y=\dfrac{1\times (-3)+2\times 6}{1+2}\\\\i.e.\\\\x=\dfrac{6-6}{3},\ y=\dfrac{-3+12}{3}\\\\i.e.\\\\x=0,\ y=\dfrac{9}{3}\\\\i.e.\\\\x=0,\ y=3[/tex]
Hence, the coordinates of Point C are: (0,3)
Similarly Point D cuts the line AB in the ratio 2:1Hence, the coordinates of point D is calculated by:
[tex]x=\dfrac{2\times (6)+1\times (-3)}{1+2},\ y=\dfrac{2\times (-3)+1\times 6}{1+2}\\\\i.e.\\\\x=\dfrac{12-3}{3},\ and\ y=\dfrac{-6+6}{3}\\\\i.e.\\\\x=\dfrac{9}{3},\ y=\dfrac{0}{3}\\\\i.e.\\\\x=3,\ y=0[/tex]
Hence, the coordinate of Point D is: (3,0)
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −5
0 −1
1 3
g(x)
g(x) = 2x − 7
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Answers
Answer:
Part A:The function f(x) has a greater slope than function g(x).Part B:The function f(x) has a greater y-intercept than function g(x).Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\=============================[/tex]
[tex]f(x):\\\\given:\ (-1,\ -5),\ (0,\ -1),\ (1,\ 3)\\\\m=\dfrac{3-(-5)}{1-(-1)}=\dfrac{8}{2}=4\\\\(0,\ -1)\to b=-1\\\\f(x)=4x-1\\\\---------------------------\\\\g(x)=2x-7\to m=2,\ b=-7[/tex]
Answer:
Part A: The slope of F(x) is greater than the slope of g(x)
Part B: The Y-intercept of f(x) is greater than that of g(x)
Step-by-step explanation:
To calculate the slope on f(x) we just have to take two points from the table and use the formula for slope:
[tex]m=\frac{y^{2} -y^{1} }{x^{2}- x^{1} }[/tex]
Now the points to use will be:
P1:(0,-1)
P2:(1,3)
Now we just put this values into the formula:
[tex]m=\frac{y^{2} -y^{1} }{x^{2}- x^{1} }[/tex]
[tex]m=\frac{3-(-1) }{1- (0)} }[/tex]
[tex]m=\frac{4}{1}\\ m=4[/tex]
Now to know the slope of g(x) we just have to remember that in the function form y=mx+c the "m" represents the slope, so if g(x)=2x-7 the slope would be "2".
Now we know that f(x) has a greater slope.
To know the greater Y intercept we just take the point in the table where x is "0" since it´s where the Y intercepts with the Y axis, and in f(x) that point is (0,-1), now in g(x) we just evaluate the function to x=0.
[tex]g(x)=2x-7\\g(x)=2(0)-7\\g(x)=-7[/tex]
The Y intercept in g(x) would be in (0,-7), since -1 is greater than -7, we can say that f(x) has the greatest Y-intercept.
What is the product?
2x(x-4)
a.2x2-4
B.2x2-8
C.2x2-4x
D.3x2-8x
Answers
Answer:
Step-by-step explanation:
By the distributive property of multiplication, 2x(x-4) = 2x^2 - 8x. This could be re-written as 2(x^2 - 8).
Answer:
B. 2x^2-8
Step-by-step explanation:
Got Correct On MyPath.
Identify the similar triangles and find x. Then find the measures of the indicated sides.
Answers
Answer:
The similar triangles are Δ KMJ and Δ NML
The value of x is 3
KM = 6 and NM = 3
Step-by-step explanation:
* Lets revise the cases of similarity
1) AAA similarity : two triangles are similar if all three angles in the first
triangle equal the corresponding angle in the second triangle
- Example : In ΔABC and ΔDEF, m∠A = m∠D, m∠B = m∠E and
m∠C= m∠F then ΔABC ≈ ΔDEF by AAA
2) AA similarity : If two angles of one triangle are equal to the
corresponding angles of the other triangle, then the two triangles
are similar.
- Example : In ΔPQR and ΔDEF, m∠P = m∠D, m∠R = m∠F then
ΔPQR ≈ ΔDEF by AA
3) SSS similarity : If the corresponding sides of two triangles are
proportional, then the two triangles are similar.
- Example : In ΔXYZ and ΔLMN, if
then the two triangles are similar by SSS
4) SAS similarity : In two triangles, if two sets of corresponding sides
are proportional and the included angles are equal then the two
triangles are similar.
- Example : In triangle ABC and DEF, if m∠A = m∠D and
then the two triangles are similar by SAS
* Now lets solve the problem
- ∠KMJ is a aright angle and M is on JL
∴ m∠JML = 180° ⇒ straight angle
∵ m∠JMK + m∠LMN = m∠JML
∴ 90° + m∠NML = 180° ⇒ subtract 90° from both sides
∴ m∠NML = 90°
- In Δ KMJ and ΔNML
∵ m∠KMJ = m∠NML ⇒ proved
∵ m∠KJM = m∠NLM ⇒ given
- By using the second case above (AA similarity)
∴ Δ KMJ ≈ Δ NML
* The similar triangles are Δ KMJ and Δ NML
- From similarity
∴ Their sides are proportion
∴ [tex]\frac{KM}{NM}=\frac{MJ}{ML}=\frac{KJ}{NL}[/tex]
∵ KJ = 10 and NL = 5
∵ KM = 3 + x and NM = x
- Substitute these values in the proportion relation
∵ [tex]\frac{KM}{NM}=\frac{KJ}{NL}[/tex]
∴ [tex]\frac{3+x}{x}=\frac{10}{5}[/tex]
- By using cross multiplication
∴ 5(3 + x) = 10(x) ⇒ simplify
∴ 5(3) + 5(x) = 10x
∴ 15 + 5x = 10x ⇒ subtract 5x from both sides
∴ 15 = 5x ⇒ divide both sides by 5
∴ 3 = x
* The value of x is 3
∵ KM = 3 + x
∵ x = 3
∴ KM = 3 + 3 = 6
∵ NM = x
∴ NM = 3
* KM = 6 and NM = 3
- Check the ratio
∵ KM/NM = 6/3 = 2
∵ KJ/NL = 10/5 = 2
∴ The sides are proportion
Answer:
Triangle JMK is similar to triangle LMN.
[tex]x = 3[/tex].
[tex]\rm \overline{KM}= 6[/tex].
[tex]\rm \overline{NM} = 3[/tex].
Step-by-step explanation:
The angle [tex]\rm N\hat{M}L[/tex] is a right angle for it is complementary with another right angle, [tex]\rm K\hat{M}J[/tex].
The diagram also indicates that angle [tex]\rm \hat{J}[/tex] is equal to angle [tex]\rm \hat{L}[/tex]. As a result, [tex]\rm \triangle JMK \sim \triangle LMN[/tex] for two of their angles are equal.
Consequently,
[tex]\displaystyle \rm \frac{(\overline{MN})}{(\overline{MK})} = \frac{(\overline{LN})}{(\overline{JK})}[/tex].
Let [tex]x[/tex] be the length of segment [tex]\rm MN[/tex].
[tex]\displaystyle \frac{x}{3+x} = \frac{5}{10}[/tex].
Cross multiply. In other words, multiply both sides by [tex]10(3 + x)[/tex].
[tex]10x = 5(3 + x)[/tex].
[tex]x = 3[/tex].
[tex]\rm \overline{KM} = 3 + \mathnormal{x} = 6[/tex].
[tex]\rm \overline{MN} = \mathnormal{x} = 3[/tex].
HELP PLEASE! Thank youuuuu
Answers
Answer:
A
Step-by-step explanation:
note that the exact value of
sin ( [tex]\frac{\pi }{4}[/tex] ) = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ← the value of the x- coordinate
:
Malik received a $300 gift card from his grandparents and is using it only to pay for his karate lessons, which cost $30 per month.
Determine what amount, in dollars, remains on the card after 8 months.
Answers
Answer:
60$ will be left
Step-by-step explanation: 30x8 = 240. subtract 300-240 and you get 60
Answer:
60
Step-by-step explanation:
30*8=240
300-240=60
Help plz. Ignore the orange color around the choices.
Answers
Hello There!
Your answers would be #1 and #3
If Earl jogged 5 yards forward and then jogs 9 yards back, we are subtracting 9 from 5 and we get a difference of -4. This is because he jogged backward from his position after 5 yards.
If Clarissa had $49 in her checking account, we subtract $53 because she bought a pair of shoes so we get a difference of also -4
Answer:
the first one was the answer
What is 270° converted to radians?
A.) pi/6
B.) 3/2
C.) 3pi/2
D.) 3
Answers
Answer:
the answer C) 3pi/2 semoga membantu
17x - 6 + 3x - 5 = x + 11 + 4x
Answers
Answer:
x = 22/15
Step-by-step explanation:
17x - 6 + 3x - 5 = x + 11 + 4x
Combine like terms on each side.
20x - 11 = 5x + 11
Add 11 to both sides. Subtract 5x from both sides.
15x = 22
Divide both sides by 15.
x = 22/15
Answer: 20x-11=5x+11
Step-by-step explanation:
if alpha and beta are the roots of a quadratic polynomial 3x^2-6x-1 find the values of (Alpha-beta)
Answers
Answer:
Either [tex]-4\sqrt{6}[/tex] or [tex]4\sqrt{6}[/tex], depending on whether [tex]\alpha[/tex] is larger than [tex]\beta[/tex].
Step-by-step explanation:
The two roots (might necessarily be distinct or real) of the quadratic equation
[tex]ax^{2} + bx + c = 0[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are constants and [tex]a\ne 0[/tex] are
[tex]\displaystyle x_1 = \frac{-b+\sqrt{\text{b^{2} - 4ac}}}{2a}[/tex], and[tex]\displaystyle x_2 = \frac{-b-\sqrt{\text{b^{2} - 4ac}}}{2a}[/tex].The difference between the two will be either:
[tex]x_1 - x_2 = 2\sqrt{b^{2} - 4ac}[/tex] or
[tex]x_2 - x_1 = -2\sqrt{b^{2} - 4ac}[/tex].
For this question,
[tex]a = 3[/tex], [tex]b = -6[/tex], and[tex]c = -1[/tex].[tex]x_1 - x_2 = 2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = 4\sqrt{6}[/tex], or
[tex]x_1 - x_2 = -2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = -4\sqrt{6}[/tex].
Plzzz helppp me!!! And thank
Answers
1. Slope is 4
2. Y-intercept is 8
3. 4x + 8
Hope this helpsn
Answer:
A. The slope is 4.
B. The y-intercept is 8.
C. The equation is y = 4x + 8
Step-by-step explanation:
We know that there is a flat $8 cost in addition to $4 per ride. We can express this by using:
y = 8 + 4x.
y is the total cost
x is the number of rides
The question wants the equation in slope-intercept form.
Slope-intercept form of a line: y = mx + b
m = slope
b = y-intercept
y = 8 + 4x ➵ y = 4x + 8
Now that we have the slope-intercept form of the line, we can answer the problems.
A. The slope is 4.
B. The y-intercept is 8.
C. The equation is y = 4x + 8
What is the answer to this question
Answers
Answer: about 34.6
Step-by-step explanation: 11 is the radius, but you need the diameter which is 22. multiply 22 by pi and divide that number by 2 since it is half a circle.
What is the value of x and the length of segment DE?
10x + 15 = 9(9)
x =
Length of =
units
Answers
Answer:
Part 1) [tex]x=6.6\ units[/tex]
Part 2) [tex]DE=16.2\ units[/tex]
Step-by-step explanation:
Part 1) Find the value of x
we know that
Triangles CDF and FDE are similar
therefore
The ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
[tex]CD/FD=FD/DE[/tex]
[tex]\frac{5}{9}=\frac{9}{2x+3} \\ \\5*(2x+3)=9*9\\ \\10x+15=81\\ \\10x= 81-15\\ \\10x=66\\ \\ x=6.6\ units[/tex]
Part 2) Find the length of DE
[tex]DE=2x+3[/tex]
substitute the value of x
[tex]DE=2(6.6)+3=16.2\ units[/tex]
Answer:
x = 6.6
Length of = 16.2 units
Which of the following are solutions to the equation 3x2 + 7x + 4 = 0
Select all that apply
O x=-1
O x=-4/3
x=3/4
x=1
Answers
For this case we have the following quadratic equation:
[tex]3x ^ 2 + 7x + 4 = 0[/tex]
Where:
[tex]a = 3\\b = 7\\c = 4[/tex]
According to the quadratic formula we have:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Substituting:
[tex]x = \frac {-7 \pm \sqrt {7 ^ 2-4 (3) (4)}} {2 (3)}\\x = \frac {-7 \pm \sqrt {49-48}} {6}\\x = \frac {-7 \pm \sqrt {1}} {6}\\x = \frac {-7 \pm1} {6}[/tex]
We have two roots:
[tex]x_ {1} = \frac {-7 + 1} {6} = \frac {-6} {6} = - 1\\x_ {2} = \frac {-7-1} {6} = \frac {-8} {6} = - \frac {4} {3}[/tex]
Answer:
[tex]x_ {1} = - 1\\x_ {2} = - \frac {4} {3}[/tex]
Answer:
x = -4/3 x=-1
Step-by-step explanation:
3x^2 + 7x + 4 = 0
Factor the equation
(3x+4) (x+1) = 0
Using the zero product property
3x+4 =0 x+1 =0
3x+4-4=0-4 x+1-1=0-1
3x=-4 x=-1
3x/3 = -4/3
x = -4/3 x=-1
Jonah and his brother want to earn at least $400 this month, so they rented a lawn mower to mow lawns. They plan to charge $25 per lawn. The monthly rental fee for the lawn mower is $85. At this rate, what is the fewest number of lawns Jonah and his brother would have to cut to make their goal? Let m represent the number of lawns mowed. In the box, enter the inequality that models the situation.
Answers
Answer: 400<=25m-85
Step-by-step explanation: 400 is how much he wants to AT LEAST make so it’ll be more than or equal to four hundred. Then he gets payed 25 dollars per law. Number of laws are unknown so its m making 25m. Lastly he has to pay 85 dollars for the law mower so that subtracts his from his pay making it 25m-85.
What is the result of 2 divided by 4/10
Answers
Answer:
5
Step-by-step explanation:
When you are dividing fractions you must flip the second digit and the sign should be changed to multiplication sign.
So in this equation it will be
2 / 4/10 =
2 * 10/4=
20/4=
5
Hope you found this answer helpful
You flip the second digit and change the sign to multiplication
Hi my sister needs help with this
Answers
Answer:
Step-by-step explanation:
Book A: Mass is 1000 g + 700g + 10 g, or 1720 g.
Book B: Mass is 1500 g + 100 + 80, or 1680 g.
Book A has the greater mass: 1720 g versus 1680 g.
The difference in mass is 1720 g - 1680 g, or 40 g
Answer:
Book A has the greater mass: 1720 g versus 1680 g.
The difference in mass is 1720 g - 1680 g, or 40 g
Step-by-step explanation:
Book A: Mass is 1000 g + 700g + 10 g, or 1720 g.
Book B: Mass is 1500 g + 100 + 80, or 1680 g.
Help me now..
Which cell organelle is primarily responsible for ATP synthesis
Answers
Answer:
Mitochondria
Step-by-step explanation:
Mitochondria is the cell organelle responsible for ATP synthesis.
Hope this helps!
Feel free to ask if you have anymore questions!
Answer: the mitochondria
Step-by-step explanation: it’s the power source of the cell. Hope this helps! :)
What is the base of expression 9^12
Answers
Answer:
the answer is 9
Step-by-step explanation:
For the following geometric sequence, find the explicit formula.
{1, -3, 9, ...}
Answers
Answer:
the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]
Step-by-step explanation:
We are given the series
1,-3,9,...
the common ratio is:
-3/1 = -3
9/-3 = -3
So, the common ratio in the series is -3
a₁ = 1
The formula used for geometric series is:
[tex]a_{n}= a_{1}(r)^{n-1}[/tex]
Putting values of a₁ and r
[tex]a_{n}= 1(-3)^{n-1}[/tex]
[tex]a_{n}= (-3)^{n-1}[/tex]
So, the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]
Which expression is equivalent to 30(1/2x-2)+40(3/4y-4
Answers
Answer:
= 15x +30y -220
Step-by-step explanation:
We can easily get another expression if we multiply each individual term, and
add together the result
30(1/2x-2)+40(3/4y-4)
= 15x-60 +30y-160
= 15x +30y -220
See attached picture below
Find a1, for the given geometric series. Round to the nearest hundredth if necessary.
Sn= 88,560, r= 2.2, n= 6
a. 8,765.73
b. 2,477.6
c. 945.65
d. 14,754.5
Answers
Answer:
* The value of a1 = 945.65 ⇒ answer c
Step-by-step explanation:
* Lets revise the geometric series
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric Progression:
- U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4
- Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms, n is the position
of the term
- The sum of first n terms of a Geometric series is calculate
from Sn = [a1 (1 - r^n)]/(1 - r) , where a1 is the first term, r is the
common ratio and n is the number of the terms
* Lets solve the problem
∵ Sn = 88,560
∵ r = 2.2
∵ n = 6
∵ Sn = [a1 (1 - r^n)]/(1 - r)
∴ 88,560 = [a1 (1 - 2.2^6)]/(1 - 2.2) ⇒ simplify up and down
∴ 88,560 = [a1 (-112.379904)]/(-1.2) ⇒ simplify the fraction
∴ 88,560 = a1 (93.64992) ⇒ divide both sides by 93.64992
∴ a1 = 945.6494998 ≅ 945.65
* The value of a1 = 945.65
A 12-ounce Pepsi contains 54 mg of caffeine. A can of Red Bull (8.2 oz) has 80 mg of caffeine.
a. What is the average caffeine content per ounce of Pepsi? Round your answer to the nearest tenth, if needed.
Answers
Answer:
4.5 mg per ounce
Step-by-step explanation:
To find the average caffeine content per ounce of Pepsi, take the caffeine and divide by the ounces
54 mg/12 ounces
4.5 mg per ounce
Answer:
The average caffeine content per ounce of Pepsi is 4.5 gm
Step-by-step explanation:
Given :A 12-ounce Pepsi contains 54 mg of caffeine
To Find : What is the average caffeine content per ounce of Pepsi? Round your answer to the nearest tenth, if needed.
Solution :
A 12-ounce Pepsi contains 54 mg of caffeine.
We are supposed to find the average caffeine content per ounce of Pepsi
Amount of caffeine in 12 ounces of Pepsi = 54 mg
Amount of caffeine in 1 ounce of Pepsi = [tex]\frac{54}{12}[/tex]
= [tex]4.5[/tex]
Hence the average caffeine content per ounce of Pepsi is 4.5 gm
In the rectangle to the left, what is the length of each side?
Answers
Answer:
Perimeter = 2 * (x + 15)
Step-by-step explanation:
Rectangle:
l = 2/3x + 10
b = 1/3x + 5
Perimeter = 2 * (l + b)
= 2 * ( 2x/3 + 10 + 1x/3 + 5)
= 2 * (3x/3 + 15)
= 2 * (x + 15)
Solve for x in the equation y^2 + 2x + 1 = 17.
Answers
Answer:
x = −1 ± √17
Hope this helps and have a nice day! :)
Answer:
B
Step-by-step explanation:
So your equation is actually x^2+2x+1=17
Left hand side is already set for rewriting it as a perfect square
So you have actually that (x+1)^2=17
Now you just take square root of both sides
x+1=(pm) sqrt(17) (pm) means plus or minus
x=-1 (pm) sqrt(17) I subtracted 1 on both sides
B
A bag contains 10 green , 10 orange, 10 pink , and 10 purple chips each numbered 1 through 10. a chip is chosen at random.
What is the probability that the chip is purple, given that the card is a 4?
Answers
Answer: [tex]\bold{a.\quad \dfrac{1}{4}}[/tex]
Step-by-step explanation:
Since it is already given that the number is a 4 and each of the four colors only has one 4, then the probability for green is:
[tex]P=\dfrac{\text{number of green 4's}}{\text{total number of 4's}}=\dfrac{1}{4}[/tex]
If you wanted to find the probability that it is a four and it is green then you would calculate the probability as:
[tex]P=\dfrac{\text{number of 4's}}{\text{total number of numbers}}\times \dfrac{\text{number of greens}}{\text{total number of colors}}\\\\\\.\ =\dfrac{4}{40}\times\dfrac{1}{4}\\\\\\.\ =\dfrac{1}{40}[/tex]
Which of the following will give you the incorrect slope? (1 point)
the quantity y subscript two minus y subscript one over the quantity x subscript two minus x subscript one.
the quantity y subscript two minus y subscript one over the quantity x subscript one minus x subscript two.
the quantity y subscript one minus y subscript two over the quantity x subscript one minus x subscript two.
rise over run
Answers
Answer:
2nd one
Step-by-step explanation:
No mixing order so the second one.
You can do either
(y2-y1)/(x2-x1) or (y1-y2)/(x1-x2) which will give you rise/run in either situation
Answer:
2nd one
Step-by-step explanation:
got it right on the test and got 100%
hope this helps :)
justin ran 800 meters in track meet today. How many yards did he run? Round your asnwer to the nearest tenth.
Answers
874.890 i think, sorry if im wrong
A. 8pi
B. pi
C. 2pi
D. 4pi
Answers
Answer: Option C
[tex]AC = 2\pi[/tex]
Step-by-step explanation:
The arc length is calculated as
[tex]L = \theta * R[/tex]
Then
[tex]AC = \theta * R[/tex]
We know that
[tex]BC = 24\ ft[/tex]
If BC is the diameter of the circumference then the radius R is:
[tex]R = \frac{BC}{2}[/tex]
[tex]R = \frac{24}{2}[/tex]
[tex]R = 12\ ft[/tex]
Now we convert the anglo from degrees to radians[tex]\theta= 30\° * \frac{\pi}{180\°}\\\\\theta=\frac{1}{6}\pi[/tex]
Finally
[tex]AC = \frac{1}{6}\pi * 12[/tex]
[tex]AC = 2\pi[/tex]
Answer:
The length of the arc AC is 2π ⇒ answer C
Step-by-step explanation:
* Lets revise some facts in the circle
- The length of the arc is depends on the measure of the arc and the
radius of the circle
- The length of the arc is a part of the length of the circle
- The length of the circle is 2πr
- The rule of the length of the arc = [tex]\frac{\alpha }{360}*2\pi r[/tex],
where α is the measure of the arc
* Now lets solve the problem
- In circle P
∵ BC is a diameter
∵ BC = 24 ft
∵ The length of the radius of the circle is 1/2 the length of the diameter
∴ The length of the radius = 1/2 × 24 = 12 ft
- Ac is an arc in the circle
∵ The measure of the arc = 30°
∵ The length of the arc = [tex]\frac{\alpha }{360}*2\pi r[/tex] ,
where α is the measure of the arc
∴ α = 30°
∵ r = 12 ft
∴ The length of the arc = [tex]\frac{30}{360}*2(12)\pi=\frac{1}{12}*(24)\pi=2\pi[/tex]
∴ The length of the arc AC is 2π