Answer:
a(n)=60-30n
Step-by-step explanation:
Equation to use:
a(n) = a(1) + d(n-1)
where a(1) is the first term, d is the common difference between terms, and n is the nth term you are trying to find.
In this case, a(1) is 30, d is -30, and n is just n.
If you plug that into the equation and use the distributive property, you would get: a(n) = 30 -30n + 30.
Adding the two 30's gets you: a(n) = 60 - 30n, which is the solution.
Which system of equations below has no solution? A. y = 4x + 5 and y = 4x – 5 B. y = 4x + 5 and 2y = 8x + 10 C. y = 4x + 5 and y = One-fourthx + 5 D. y = 4x + 5 and y = 8x + 10
Answer: A y=4x -5 and y=4x+5
Step-by-step explanation:
They have no solutions because they have the same slopes but different y intercepts. That works with any equation.
Answer:
the answer is A
Step-by-step explanation:
HELP NOW PLZ 20-30 POINTS FOR BRAINLIEST LOOK AT MY PROFILE FOR THE SAME QUESTION WITH MORE POINTS Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant! (Recall: Standard Form of a quadratic equation is Ax^2 + Bx + C ). You need to choose a value for A, B, and C that satisfies each of the following conditions. You can use a value of 0 for B for no more than 1 of the 5 questions! Step 2: Solve each of the equations you create. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT FOR THIS STEP! Write your Exact answer in simplest form AND if necessary, round your estimate to the nearest tenth. 1) Equation 1 should represent a parabola that opens up and has a negative y-intercept. Equation 1: ____________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 2) Equation 2 should represent a parabola that opens down and has a negative y- intercept. Equation 2:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 4) Equation 4: You decide what type of parabola you would like to create by answer the following questions: Does your parabola open up or down? _______________ Is there a vertical stretch or vertical compression? _______ What is the y-intercept? __________ Equation 4: ____________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 5) Write a quadratic equation that can only be solved using the quadratic formula. Equation 4: _________________________________________________________________ Show your work for how you use the quadratic formula to solve this equation:
Answer:
This is equation 1.
Step-by-step explanation:
Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant.
Conditons that need to be satisfied: B can be 0 in only one question, parabola should open up and have a negative y intercept.
1. The parabola should open upwards: a> 0
2. [tex]3x^2+7x-6[/tex] (a>0), y-int is negative (0s for x's)
3(0)^2 + 7(0) -6
y= -6
Step 2:
1. Factor the original equation: (3x-2)(x+3)
x=2/3, -3
2. Strategy used (factor by grouping)
what is the area of shape below NEED HELP NOWWW
Answer:
15 units[tex] {}^{2} [/tex]Step-by-step explanation:
Given figure : Trapezium
Upper base of trapezium ( b1 ) = 7
Lower base ( b2 ) = 3
Height ( h ) = 3
Now, finding the area of trapezium:
[tex] \frac{1}{2} (b1 + b2)h[/tex]
Plugging the values
[tex] \frac{1}{2} \times (7 + 3) \times 3[/tex]
Calculate the sum
[tex] \frac{1}{2} \times 10 \times 3[/tex]
Reduce the numbers with G.C.F 2
[tex]5 \times 3[/tex]
Calculate the product
[tex] = 15 \: {units}^{2} [/tex]
Hope this helps..
Best regards!
A 1 km long train is travelling at 30km/h. If the train enters a tunnel that is 1 km long, how much time will it take for the train to clear the tunnel?
Answer: 240 seconds OR 4 minutes
Step-by-step explanation:
Length of the train = 1 km
Length of the tunnel = 1 km
Therefore, length of the train + length of the tunnel = (1 + 1) km = 2 km
= 2000 m
Speed of the train = 30 km/hr = 8.333 metres per second
Therefore, time taken by the train to cross the tunnel = 2000 m/ 8.333 m/sec.
= 240 seconds = 4 minutes
Steve Fossett is approaching the shores of Australia on the first successful solo hot air balloon ride around the world. His balloon, the Bud LightTM Spirit of Freedom, is being escorted by a boat (directly below him) that is 108 meters away. The boat is 144 meters from the shore. How far is Fossett's balloon from the shore?
Answer:
180 meters
Step-by-step explanation:
Distance from the balloon to the boat = 108 meters
Distance from the boat to the shore = 144 meters
Since the boat is directly below the balloon, the problem forms a right triangle in which the distance from the balloon to shore is the hypotenuse.
Let the length of the hypotenuse = l
Using Pythagoras Theorem
[tex]l^2=108^2+144^2\\l^2=11664+20736\\l^2=32400\\l=\sqrt{32400} \\l=180$ meters[/tex]
The distance from Fossett's balloon to the shore is 180 meters.
Fossett's balloon is 180m from the shore
data;
escort boat to the ballon = 108mboat from the shore = 144mdistance between the ballon and the shore = xPythagoras TheoremTo solve this problem we can assume this is situation forms a right angle triangle and we can solve this using pythagoras theorem.
[tex]x^2 = y^2 + z^2\\[/tex]
Let's substitute the values and solve
[tex]x^2 = y^2 + z^2\\x^2 = 108^2 + 144^2\\x^2 = 32400\\x = \sqrt{32400} \\x = 180m[/tex]
Fossett's balloon is 180m from the shore
Learn more on pythagorean theorem here;
https://brainly.com/question/231802
someone please help :( a sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Oregon are: $295, $475, $345, $595, $538, $460. A second sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Washington are: $495, $422, $370, $333, $370, $390. answer the following questions: What is the median price of rent for the University of Oregon? What is the median price of rent for the University of Washington? What is the mean price of rent near the University of Oregon? What is the mean price of rent near the University of Washington? Describe the standard deviation for both Universities.
Answer:
Oregon:
Median: 467.5
Mean: 451.33
Standard Deviation: 113.6
Washington:
median: 380
Mean: 396.6
Standard deviation: 56.3
Step-by-step explanation:
To calculate the median, we need to organize the price and select the value that is in the middle position.
To calculate the mean, we need to sum all the values and divide them by the number of values
To calculate the standard deviation, we need to square the distances between every price and the mean, sum it all and divide them by the number of values less 1 and finally calculate the square root.
So, for Oregon, the organized values are:
$295, $345, $460, $475, $538, $595
The median is a value between $460 and $475. it is calculated as:
[tex]\frac{460+475}{2}=467.5[/tex]
The mean is:
[tex]\frac{295+475+345+595+538+460}{6}=451.33[/tex]
The standard deviation is:
[tex]\sqrt{\frac{(295-451.3)^2+(475-451.3)^2+(345-451.3)^2+(595-451.3)^2+(538-451.3)^2+(460-451.3)^2}{6-1}}=113.6[/tex]
At the same way, we can calculate the median, mean, and standard deviation for Washington and get:
median: 380
Mean: 396.6
Standard deviation: 56.3
What is the speed of a plane that goes 15000 miles per hour in per seconds?
Answer:
There are 60 * 60 = 3600 seconds in one hour so the plane goes 15000 / 3600 = 4 and 1/6 miles per second.
Answer:
[tex]4 \frac{1}{6} \: miles \: per \: seconds[/tex]Step-by-step explanation:
[tex]1500 \: miles \: \: per \: hour[/tex]
[tex] = \frac{15000}{60 \times 60} [/tex]
[tex] = \frac{15000}{3600} [/tex]
[tex] = \frac{25}{6} [/tex]
[tex] = 4 \frac{1}{6} \: miles \: per \: second[/tex]
Hope this helps...
Good luck on your assignment...
Find the interquartile range (IQR) of the data in the dot plot below. chocolate chips 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10. Number of chocolate chips. Chocolate chips in different cookies in a package
*The dot plot is shown in the attachment below
Answer:
2
Step-by-step explanation:
Interquartile range is the difference between the upper median (Q3) and the lower median (Q1).
First, let's write out each value given in the data. Each dot represents a data point.
We have:
2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
=>Find the median:
Our median is the middle value. The middle value is the 6th value = 4
==>Upper median Q3) = the middle value of the set of data we have from the median to our far right.
2, 3, 3, 4, 4, |4,| 4, 5, [5], 6, 7
Our upper median = 5
==>Lower median(Q1) = the middle value of the data set we have from our median to our far left.
2, 3, [3], 4, 4, |4,| 4, 5, 5, 6, 7
Lower median = 3
==>Interquartile range = Q3 - Q1 = 5-3 = 2
Answer:
2
Step-by-step explanation:
Find dy/dx of (3 - 2x)-1/2
Answer:
Step-by-step explanation:
To evaluate the derivative of this function you need the chain rule. The pattern I teach to my calculus students is to find
u =
u' =
f(u) =
f'(u) =
First pick your "u". u will be the inner function, the one inside the parenthesis.
u' will then be the derivative of u.
f(u) is the function in terms of u, and
f'(u) is the derivative of the function in terms of u.
The derivative then, finally, will be u' * f'(u). Let's begin.
Our u, or the part of the function inside the parenthesis is 3 - 2x; hence,
u = 3 - 2x
The derivative, u', then is
u' = -2
f(u) is the function in terms of u, so
f(u) = [tex]u^{-\frac{1}{2}[/tex] and the derivative in terms of u is
f'(u) = [tex]-\frac{1}{2}u^{-\frac{3}{2}[/tex]
u' * f'(u) then is
[tex]-\frac{1}{2}u^{-\frac{3}{2}*(-2)[/tex] Simplify that by subbing back in for u and multiplying -2 by -1/2 to get
[tex]y'=(3-2x)^{-\frac{3}{2}[/tex]
Which answers are equivalent to the fraction below? Check all that apply
12/16
A.1/2 B.6/8 C2/3 D.2/6 E.3/4 F.6/4
Answer: e
Step-by-step explanation: 12/16 6/8 3/4
Answer:
B and E.
Step-by-step Explanation:
B: 6/8
6*2=12
8*2=16
12/16
E: 3/4
3*4=12
4*4=16
12/16
Hope this helps!!!!!
NEED HELP ASAP ‼️‼️I BELIEVE ANSWER IS C
Answer:
I agree with your answer C!!
Step-by-step explanation:
A new hockey stick costs $57.00 at the sporting goods store. If there is a 6%
sales tax, what is the actual cost of the hockey stick?
Answer:
$60.42
Step-by-step explanation:
0.06 x $57 = $3.42
$57 + $3.42 = $60.42
Hope this helped! :)
Which of the following are solutions to the quadratic equation? Check all that
apply.
2x2 + 7x- 14 = x2 + 4
Answer:
[tex]\boxed{\sf \ \ \ x=-9 \ \ or \ \ x=2 \ \ \ }[/tex]
Step-by-step explanation:
hello,
[tex]2x^2+7x-14=x^2+4\\<=> 2x^2+7x-14-x^2-4=0\\<=> x^2+7x-18=0\\<=>x^2-2x+9x-18=0\\<=> x(x-2)+9(x-2)=0\\<=> (x+9)(x-2)=0\\<=> x+9 = 0 \ \text{or} \ x-2=0\\<=> x = -9 \ \text{or} \ x=2[/tex]
hope this helps
Here’s a graph of a linear function. Write the equation that describes that function. Express it in slope
Answer:
y = (1/3)x +4
Step-by-step explanation:
The line intercepts the y-axis at y=4. It has a "rise" of 1 unit for each "run" of 3 units, so its slope is rise/run = 1/3.
The slope-intercept form of the equation of a line is ...
y = mx + b . . . . . where m is the slope and b is the y-intercept.
When we put the proper numbers in the equation, we have ...
y = (1/3)x + 4
(17x10)-(17x4)=(17 x ?)
Answer:
6
Step-by-step explanation:
6 is the answer
? =6
Answer:
6
Step-by-step explanation:
1. 17 * 10 = 170
2. 17 * 4 = 68
3. 170 - 68 = 102
4. 102 / 17 = 6
Malachy, Sushil and Fiona share some sweets in the ratio 1:3:1. Malachy gets 5 sweets. How many did Sushil get?
Answer:
Sushil got 15 sweets
Step-by-step explanation:
we can use law of indices property as shown below
a:b:c = ax:bx:cx
that if we multiply each term of ratio by same number , the ratio does not change
____________________________
given
Malachy, Sushil and Fiona share some sweets in the ratio 1:3:1.
let
Malachy gets 1x sweets
sushil gets 3x sweets
Fiona gets 1x sweets
but given that
Malachy got 5 sweets
thus
1x = 5
x = 5
Sushil got 3x sweets = 3*5 = 15 sweets.
Sushil got 15 sweets.
Wendy is creating a large soup based on a recipe. Her recipe calls for of a pint of milk, but she only has of a pint of milk, so she can only make a portion of her soup. Wendy can only make _____ of her recipe with the amount of milk that she has.
Answer:
She can only make 5/6 of her recipe with the amount of milk that she has.
Step-by-step explanation:
Some data of this problem is missing, the data missing is:
Her recipe calls for 3/4 of a pint of milk and she only has 5/8 of a pint of milk.
Now, to know what's the portion she can do with that amount we need to divide the amount of milk she has by the total amount she needs:
[tex]\frac{5}{8}[/tex] ÷[tex]\frac{3}{4}[/tex]
When we divide we turn the second fraction upside down (the numerator becomes the denominator and viceversa) and multiply, thus:
[tex]\frac{5}{8}[/tex]÷[tex]\frac{3}{4}=\frac{5}{8}[/tex]×[tex]\frac{4}{3} =\frac{20}{24}[/tex]
If we simplify this last expression we have:
[tex]\frac{20}{24}=\frac{10}{12} =\frac{5}{6}[/tex]
Thus, she can only make 5/6 of her recipe with the amount of milk that she has.
Note: In case the data missing is different, you can apply this same procedure with the fractions you have.
Helllppppp
Which rule describes the composition of
transformations that maps AABC to AA'B'C"?
Answer:
reflection and rotation
Step-by-step explanation:
Choose one of the theorems about chords of a circle and state it using your own words. Create a problem about chords that uses the theorem that you explained. Choose a problem that a classmate has posted, and explain how to solve it. Note: If you do not see any other responses, explain how to solve the problem that you posted. Please number your responses to the questions as they are shown (1, 2, and 3).
Answer:
Step-by-step explanation:
1. A given chord on a circle is perpendicular to a radius through its center, and it is at a distance less that the radius of the circle.
2. A circle of center O has a radius of 13 units. If a chord AB of 10 units is drawn at a distance, d, to the center of the circle, determine the value of d.
3. From question 2, the radius = 13 units, length of chord = 10 units and distance of chord to center of the circle is d.
A radius that meet the chord at center C, and divides it into two equal parts.
So that;
AC = CB = 5 units
Applying Pythagoras theorem to ΔOCB,
OC = d, CB = 5 units and OB = 13 units
[tex]13^{2}[/tex] = [tex]5^{2}[/tex] + [tex]d^{2}[/tex]
169 = 25 + [tex]d^{2}[/tex]
169 - 25 = [tex]d^{2}[/tex]
144 = [tex]d^{2}[/tex]
⇒ d = [tex]\sqrt{144}[/tex]
= 12 units
Therefore, the chord is at a distance of 12 units to the center of the circle.
A chord is a straight line joining 2 points on the circumference of a circle.
The line that connects any two points of the circumference of a circle is known as a chord.
Theorem: A radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa.
Converse: The perpendicular bisector of a chord passes through the center of a circle.
Problem: In the given figure the radius of the circle is 5 cms. what is the length of the chord?
Solution:
Given to us,
radius of the circle, r = 5 cms,
RA = 1 cm,
Radius, r = OA = OP = OQ = 5 cms.
Also, OR = OA - OR = 4 cms.
In ΔOPQ,
According to Pythagorus theorum,
OP² = OR² + RP²
5² = 4² + RP²
RP² = 25 -16 = 9
RP = 3,
We know,
A radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa.
A radius (OA) that is perpendicular to a chord divides the chord into two equal parts(RP = RQ).
Therefore, chord = RP + RQ = 3+3 = 6 cms.
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Given: ∆KLM, KL ≅ LM A∈ KM , B ∈ KM AK ≅ BM Prove:△AKL ≅ △BML ΔALB is isosceles
Answer:
ΔAKL is congruent to ΔBML by the Side Angle Side rule of congruency and ΔALB is isosceles as two of its sides [tex]\overline {AL}[/tex] and [tex]\overline {BL}[/tex] are congruent
Step-by-step explanation:
The given parameters are;
The given triangle ΔKLM has sides [tex]\overline {KL}[/tex] ≅ [tex]\overline {LM}[/tex], Given
ΔKLM is isosceles Δ (two equal segments), Definition of isosceles Δ
∠LKM ≅ ∠LMK, Base ∠s of isosceles Δ are ≅
Point A is on segment [tex]\overline {KM}[/tex], Given
Point B is also on segment [tex]\overline {KM}[/tex], Given
Segment [tex]\overline {AK}[/tex] ≅ segment [tex]\overline {BM}[/tex], Given
ΔAKL ≅ ΔBML, SAS rule of congruency
Segment [tex]\overline {AL}[/tex] ≅ segment [tex]\overline {BL}[/tex], CPCTC
ΔALB is isosceles (two equal segments), Definition of isosceles Δ
Where:
SAS = Side Angle Side
CPCTC = Congruent parts of congruent triangles are congruent.
Answer:
m∠AKL=m∠BML | Base Angle Theorem (Base ∠ TH.)
Step-by-step explanation:
KL=LM | Given
A ∈ KM | Given
B ∈ KM | Given
AK=BM | Given
m∠AKL=m∠BML | Base ∠ TH.
1
Select the correct answer.
The edges of a cube are 5 centimeters each and the diagonal of a face is approximately 7 centimeters. What is the approximate area of the cross
section passing through the diagonals of opposite faces of this cube?
OA. 12 square centimeters
OB.
25 square centimeters
O C. 35 square centimeters
OD
49 square centimeters
Answer:35 square
Step-by-step explanation:
help me please :) thanks
Answer: B
Step-by-step explanation: graph b
what is the coefficient of b in the expression b² - 5b +18
Answer:
-5
Step-by-step explanation:
This is a quadratic polynomial that has the form ax²+bx+c :
a = 1b= -5 c= 18here the coefficient of b is -5
Answer:
5
but if you sure just looking for the coefficient to just plain b, it is 5
the coefficient of (b^2) is 1 and the coefficient of b itself -5
the reason i say coefficient to (b^2) is 1 because there is no numder in front
of the variable , it is automatically assumed to be 1
Step-by-step explanation:
a coefficient is a numder that a variable is multiplied by
Find the area of this triangle..
Answer:
39.936 ( not rounded )
Step-by-step explanation:
Use Pythagorean theorem
a^2 + 6.4^2 = 9^2
height = 6.24 (rounded to nearest hundredth)
1/2 * base * height = area
1/2 * 12.8 * 6.24
= 39.936 ( not rounded )
Given that y is directly proportional tox, and when y = 8 when x=
10.
(a) Write down the equation of y in terms of x.
(b) Find the value of y when x = 25.
8
(c) Find the value of x when y==
25
Answer:
see explanation
Step-by-step explanation:
(a)
Given that y is directly proportional to x then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 8 when x = 10. then
8 = 10k ( divide both sides by 10 )
0.8 = k
y = 0.8k ← equation of proportion
(b)
when x = 25, then
y = 0.8 × 25 = 20
(c)
when y = 25, then
25 = 0.8x ( divide both sides by 0.8 )
x = 31.25
Polynomial function in standard form with zeros 5,-4,1
Answer:
[tex]\boxed{\sf \ \ \ x^3-2x^2-19x+20 \ \ \ }[/tex]
Step-by-step explanation:
hello,
by definition we can write
[tex](x-5)(x+4)(x-1)[/tex]
as 5,-4,1 are the zeroes
now we have to write it in the standard form, let's do it
[tex](x-5)(x+4)(x-1)=(x^2+4x-5x-20)(x-1)\\=(x^2-x-20)(x-1)=x^3-x^2-20x-x^2+x+20\\=x^3-2x^2-19x+20[/tex]
hope this helps
Help please........please
Answer:
58, 38 and 76
Step-by-step explanation:
(a)
The median is represented by the vertical line inside the box
median = 58
(b)
The interquartile range is the difference between the upper quartile and the lower quartile.
The upper quartile is the value at the right of the box, that is 72
The lower quartile is the value at the left of the box, that is 34
Interquartile range = 72 - 34 = 38
(c)
The range is the difference between the largest and smallest value
max value is the value at the right of the data, that is 86
min value is the value at the left of the data, that is 10
Range = 86 - 10 = 76
I've attached the question in the picture below.
at a map scale of 1:1500, 12 centimeters on the map is equivalent to 1.8 kilometers on the ground.
step-by-step
since the scale is 1 to 15,000 you simply multiply it by the 12 cm
12cm × 15,000 = 180,000
but you still have to convert it to kilometers (the measurement on the ground).
to go from centimeters to kilometers move the decimal 5 place values to the left.
final answer
1.8 kilometers
PLZ HELP ASAP--------->
On a nearby pond, black and white ducks are swimming in groups of 3. James wants to find the experimental probability of two white ducks and one black duck swimming together. Design a simulation using a coin flip and explain why it is the best choice for James.U Will get BRAINLIEST
Answer:
The answer is below
Step-by-step explanation:
Given that, there are only two available choices, which are a black or white duck, this can be represented using a coin: H→White duck, T→Black Duck
Hence, to represent a set of possible outcomes, the coin has to be tossed three times.
Thus, we assume that, at the minimum we have total number of Ducks = 3 Black + 3 White = 6 Ducks
Total Favorable Outcome = 2 White + 1 Black
Total Possible Outcome = Selecting 3 Ducks (2 White +1 Black) from 6 Ducks
Formula to Calculate Probability
= Total favourable outcome ÷ Total possible outcome
Use ,C(n,r)= n! / (n - r)! r!
Therefore, the Probability of two white ducks one black duck swimming together
= ³C² * ³C¹ ÷ 6C3 = 9/20
To use Simulation Coin Flip, we have the following:
H→White duck, T→Black Duck
HHH→Three White Ducks Swimming together
TTT→Three black ducks Swimming together
HHT→Two white duck and a Black Duck swimming together
HTH→Two white duck and a Black Duck swimming together
THH→Two white duck and a Black Duck swimming together
TTH→Two Black duck and a White Duck swimming together
THT→Two Black duck and a White Duck swimming together
HTT→Two Black duck and a White Duck swimming together
Finally, to find the probability, divide the observed desired outcomes by the total number of trials.
Answer:
There are only two choices, a black or white duck, so a coin is the best choice. To represent a set of possible outcomes, toss the coin three times. Repeat the experiment multiple times. To find the probability, divide the observed desired outcomes by the total number of trials.
Step-by-step explanation:
edg2020