Answer:
The point that lies on the line parallel to line KL would be ( 8, - 10 )
Step-by-step explanation:
Line KL passes through the points ( - 6, 8 ) and ( 6, 0 ) while it's respective parallel line passes through point M, ( - 4, - 2 ).
Our approach here is to first determine the slope of KL such that the slope of it's parallel line will be the same, and hence we can determine a second point on this line.
Slope of KL : ( y₂ - y₁ ) / ( x₂ - x₁ ),
( 0 - 8 ) / ( 6 - ( - 6 ) ) = - 8 / 6 + 6 = - 8 / 12 = - 2 / 3
Slope of respective Parallel line : - 2 / 3,
Another point on Parallel line : ( 8, - 10 )
How can we check if this point really belongs to the parallel line? Let's take the slope given the points ( - 4, - 2 ) and ( 8, - 10 ), and check if it is - 2 / 3.
( y₂ - y₁ ) / ( x₂ - x₁ ),
( - 10 - ( - 2 ) ) / ( 8 - ( - 4 ) ) = ( - 10 + 2 ) / ( 8 + 4 ) = - 8 / 12 = - 2 / 3
And therefore we can confirm that this point belongs to line KL's parallel line, that passes through point M.
Answer:
D
Step-by-step explanation:
Nala can spend no more than $150 per month on gasoline. She has already purchased $60 in gas this month. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30? 30n + 60 > 150 30n + 60 150
Answer:
150<60+30n
Step-by-step explanation:
150 is the maximum amount that she can spend on gas. (which is the total)
she already spend $60
each fill up (n) costs 30
Answer:
the answer is B)
Step-by-step explanation:
Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs.
Answer: 1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar for both recipes.
Step-by-step explanation:
Dante is baking two recipes.
A cookie recipe, that needs 1.5 cups of sugar.
A brownie recipe, that needs 1.25 cups of sugar.
So the total sugar that he needs is:
The sugar for the cookies + the sugar for the brownies:
The equation is:
1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar.
A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special coin and flips it 14 times to evaluate the hypothesis that the coin is weighted, and it shows up heads 12 times. Test this hypothesis (use alpha=.05).
1. What is the appropriate test?
2. State the null hypothesis:
3. State the alternative hypothesis:
4. Find the critical value:
5. Calculate the obtained statistic:
6. Make a decision:
7. What does your decision mean
Answer:
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
Step-by-step explanation:
Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as
H0 :p 0.5 against Ha: p ≠ 0.5
The significance level is approximately 0.05
The test statistic to be used is number of heads x.
Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution
Heads (x) Probability (X=x) Cumulative Decumulative
0 1/16384 (1) 0.000061 0.000061
1 1/16384 (14) 0.00085 0.000911
2 1/16384 (91) 0.00555 0.006461
3 1/16384(364) 0.02222
4 1/16384(1001) 0.0611
5 1/16384(2002) 0.122188
6 1/16384(3003) 0.1833
7 1/16384(3432) 0.2095
8 1/16384(3003) 0.1833
9 1/16384(2002) 0.122188
10 1/16384(1001) 0.0611
11 1/16384(364) 0.02222
12 1/16384(91) 0.00555 0.006461
13 1/16384(14) 0.00085 0.000911
14 1/16384(1) 0.000061 0.000061
We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).
We observe that P (X≤2) = 0.006461 > 0.025
and
P ( X≥12 ) = 0.006461 > 0.025
Therefore true significance level is
∝= P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122
Hence critical region is (X≤0) and ( X≥14)
Computation x= 12
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
Which of the following is NOT true?
A. 5x + 6x = 70 degrees
B. 5x + 6x < 180 degrees
C. 5x + 6x = 110 degrees
D. 5x + 6x + 70 degrees = 180 degrees
Please include ALL work! <3
Answer:
A. 5x + 6x = 70 degrees
Step-by-step explanation:
5x + 6x = 110 degrees because the sum of two interior angles in a triangle is equal to an exterior angle.
3. A ladder is leaning against a wall. The ladder is 5 meters long. The top of the
ladder is 3 meters above the ground. The top of the ladder is sliding down at 8 meters/second.
a) How far is the bottom of the ladder from the wall?
b) How fast is the bottom of the ladder sliding away from the wall?
Answer:
1. The bottom of the ladder is 4 meters away from the wall
2. I'm not sure about this one, someone else answer please :D
Step-by-step explanation:
We can use the Pythagorean Theorem to find how far away the bottom of the ladder is.
The ladder is creating a triangle, with 5 as it's hypotenuse and 3 as one of the left.
[tex]a^2 + 3^2 = 5^2\\a^2 + 9 = 25\\a^2 = 25-9\\a^2 = 16\\a = 4[/tex]
I'm sorry I couldn't answer the second one, but I hope this helped!
Answer:
a. 4m
b. 6m/s
Step-by-step explanation:
wall height = y = 3m
ladder length = L = 5m
distance from bottom of ladder to the wall = x
a. y² + x² = L² -----------eq.(1)
3³ + x² = 5²
x = 4 m
b. How fast is the bottom of the ladder sliding away from the wall? = dx/dt
using eq.1 ---- y² + x² = L²
2y (dy/dt) + 2x (dx/dt) = 0
y (dy/dt) + 2 (dx/dt) = 0
we know that (dy/dt) = -8 m/s
3 (-8) + 4 (dx/dt) = 0
dx/dt = -24 / -4
dx/dt = 6 m/s
what does the inverse of f(x)=2x-3 looks like on a graph
Step-by-step explanation:
To find this inverse of a graph you have to multiply the current equation by -1.
-1(2x-3)
f(x)=-2x+3.
This graph will start at the point (0,3). Then according to the slope the rest of the points will go down two than right one. So the next two point will be (1,1) and (2,-1).
If f(x)=x/2-3and g(x)=4x^2+x-4, find (f+g)(x)
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
= x/2-3 + 4x²+x+4
= ..........
help me besties pls and have a good Bestie
Answer:
6
Step-by-step explanation:
Area = length x width
Input the numbers:
Area = 78
length = 13
78 = 13 x width
width = 78 / 13
width = 6
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
Width=6m
Step-by-step explanation:
Area=78m^2
Length=13m
width=?(let width be x)
[AREA OF RECTANGLE=length× width]
78=13×x
78=13x
×=6
Patios can be made by mixing cubic meters of ash, stone, and wood chips in the ratio 5:7:3. How much stone is needed to make 45 cubic meters of patio?
Answer:
21 m^3
Step-by-step explanation:
5 + 7 + 3 = 15
The ratio of stone to the total is
7:15
If the total needed is 45 m^3, then we multiply both parts of the ratio by 3.
7 * 3 : 15 * 3
21:45
Answer: 21 m^3
Please! David has several chains of length 5 and of length 7. By joining chains one after the other, David can create different lengths. Which of these lengths is impossible to make? A)10 B)12 C)13 D)14 E)15
Answer:
13
Step-by-step explanation:
A)5+5=10
B)5+7=12
C) impossible
D)7+7=14
E)5+5+5=15
please help answer question
Answer:
Mark me brainlist please please please please
Answer:
Step-by-step explanation:
help pls, i have to get this correct
Answer:
Table C
Step-by-step explanation:
r = j+3
In table A
j = 12 so r = 12+3 = 15 not true so it does not fit the equation
In table B
j = 3 so r = 3+3 = 6 not true so it does not fit the equation
In table C
j = 6 so r = 9+3 = 9 this could be the table
In table D
j = 27 so r = 27+3 = 30 not true so it does not fit the equation
Factor this trinomial completely. -6x^2 +26x+20
Answer:
Step-by-step explanation:
-6x²+26x+20
=-2(3x²-13x-10)
=-2(3x²-15x+2x-10)
=-2[3x(x-5)+2(x-5)]
=-2(x-5)(3x+2)
Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.
Answer:
8.66 years
Step-by-step explanation:
Given that:
Interest rate = 8%
Using the exponential growth function:
A = Ao * e^(rt)
Where A = final amount
Ao = Initial amount
r = growth rate
t = time
Here we are to calculate the time it takes an investment earning 8% interest to double;
rate (r) = 8% = 0.08
2A = A * e^(rt)
Divide both sides by A
2 = e^(rt)
2 = e^(0.08 * t)
2 = e^(0.08t)
In(2) = 0.08t
0.6931471 = 0.08t
Divide both sides by 0.08
0.6931471 / 0.08 = 0.08t / 0.08
8.6643397 = t
t = 8.66 years
Answer:
symbolically, the answer would be t= ln(2)/(.08)
Step-by-step explanation:
start by writing out your variables:
rate= .08
*dont forget the investment doubles too, thats where 2P is in the bottom equation
equation should look like:
[tex]2P=Pe^{.08t}[/tex]
then you solve, so divide P on the right and left:
[tex]\frac{2p}{p} = \frac{Pe^{.08t}}{p}[/tex]
now it looks like: [tex]2=e^{.08t}[/tex]
you can take the natural log (ln) of 2 to get the exponent by itself .08t
ln(2)=.08t
then divide .08 to get t by itself
[tex]\frac{ln(2)}{.08} =\frac{.08t}{.08}[/tex]
so symbolically, your equation should be:
[tex]t=\frac{ln(2)}{.08}[/tex]
to get t as your answer you can plug this equation into your calculator to get:
t=8.66 years so approximently 8 years
allowing 20% discount on the marked price of a watch, the value of the watch will be rs 6328, when a VAT of 13% is added find it's marked price
Step-by-step explanation:
let , MP =x
then,
discount amount =D% of MP
= (20/100)× x
= 0.2x
now,Sp without VAT = MP-D
=x - 0.2x
= 0.8x
NoW, SP with VAT = Sp without VAT+ VAT %of SP
or ,6328 = 0.8x + 13% of 0.8x
or, 6328 = 0.8x + (13/100) × 0.8x
or, 6328= 0.8x + 0.104x
or,. 6328= 0.904x
or, X= 6328/0.904
X= 7000 Rs.
Hence ,MP is Rs.7000
Find the work done by the force field F(x,y,z)=6xi+6yj+6k on a particle that moves along the helix r(t)=3 cos(t)i+3sin(t)j+2 tk,0≤t≤2π.
Answer:
the work done by the force field = 24 π
Step-by-step explanation:
From the information given:
r(t) = 3 cos (t)i + 3 sin (t) j + 2 tk
= xi + yj + zk
∴
x = 3 cos (t)
y = 3 sin (t)
z = 2t
dr = (-3 sin (t)i + 3 cos (t) j + 2 k ) dt
Also F(x,y,z) = 6xi + 6yj + 6k
∴ F(t) = 18 cos (t) i + 18 sin (t) j +6 k
Workdone = 0 to 2π ∫ F(t) dr
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (18 cos (t) i + 18 sin (t) j +6k)(-3 sin (t)i+3cos (t) j +2k)\ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (-54 \ cos (t).sin(t) + 54 \ sin (t).cos (t) + 12 ) \ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} 12 \ dt}[/tex]
[tex]\mathbf{= 12 \times 2 \pi}[/tex]
= 24 π
I will rate you brainliest!
Answer:
B
Step-by-step explanation:
X must not be equal to -6, -1, 1 or 3
Need help with the question below.
Answer:
A
Step-by-step explanation:
r=10 and the angle bln 5√3 and -5 is 330 or 11π/6
The price of a technology stock was $ 9.56 yesterday. Today, the price rose to $ 9.69 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer and Step-by-Step explanation:
% increase = 100 x [(new price) - (original price)] / (original price)] = 100 (9.67 - 9.56) / 9.56
% increase ≅ 1.2% (to the nearest tenth)
Karmen returned a bicycle to Earl's Bike Shop. The sales receipt showed a total paid price of $211.86, including the 7% sales tax. What was the cost of the bicycle without the sales tax? Any help would be very appreciated! Thank you very much!
Answer:
$198
Step-by-step explanation:
198x.07=13.86
198+13.86=211.86
Given that log 2 = 0.3010 and log 7 = 0.8451, find the following (a) log 49 (b) log 560
Answer:
ok babababr
Step-by-step explanation:
skwjshehhehdhhshwhhdhwhbeujsbsgehbedheb
Answer:
Log 49= 1.6902
Log 560= 1.7481
Step-by-step explanation:
log49= log7×7
From the rules of logarithms, we have that
log a×b= log a + log b
So log49= log7×7= log7 + log7
= 0.8451 + 0.8451 = 1.6902
Log 560 = log7×8 = log7 + log8
log8= log2^3 = 3log2
log8= 3×0.3010 =0.930
log 560= 0.8451 + 0.930 = 1.7481
A computer is priced at $2,000. If the sales tax rate is 7.5%, find the total cost of the
computer?
9514 1404 393
Answer:
$2150
Step-by-step explanation:
The tax is 7.5% of the price, so is ...
$2000 × 0.075 = $150
The total cost is the price with tax added:
$2000 +150 = $2150
Solve the equation for the given variable x/4=6/8
Answer:
x = 3
Step-by-step explanation:
This process is called cross multiplication.
Multiply 6 · 4 = 24
Divide 24 ÷ 8 = 3
x = 3
Answer:
x = 3
Step-by-step explanation:
x/4 = 6/8
Using cross products
x*8 = 4*6
8x = 24
Divide by 8
8x/8 = 24/8
x = 3
The volume of ice-cream in the cone is half the volume of the cone. The cone has a 3 cm radius and
6 cm height. What is the depth of the ice-cream, correct to two decimal places?
m
3 cm
Ice-cream
6 cm
depth of
ice-cream
5cm
Answer:
h = 5 cm
Step-by-step explanation:
Given that,
The volume of ice-cream in the cone is half the volume of the cone.
Volume of cone is given by :
[tex]V_c=\dfrac{1}{3}\pi r^2h[/tex]
r is radius of cone, r = 3 cm
h is height of cone, h = 6 cm
So,
[tex]V_c=\dfrac{1}{3}\pi (3)^2\times 6\\\\V_c=18\pi\ cm^3[/tex]
Let [tex]V_i[/tex] is the volume of icecream in the cone. So,
[tex]V_i=\dfrac{18\pi}{2}=9\pi\ cm^3[/tex]
Let H be the depth of the icecream.
Two triangles formed by the cone and the icecream will be similiar. SO,
[tex]\dfrac{H}{6}=\dfrac{r}{3}\\\\r=\dfrac{H}{2}[/tex]
So, volume of icecream in the cone is :
[tex]V_c=\dfrac{1}{3}\pi (\dfrac{h}{2})^2(\dfrac{h}{3})\\\\9\pi=\dfrac{h^3}{12}\pi\\\\h^3=108\\\\h=4.76\ cm[/tex]
or
h = 5 cm
So, the depth of the ice-cream is 5 cm.
Find the area bounded by the curves x = 2y2 and x = 1 - y. Your work must include an integral in one variable.
Please help!!
Answer:
Hello,
in order to simplify, i have taken the inverses functions
Step-by-step explanation:
[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]
Solve the following equation for x to find the total number of sale items stocked on the shelves of a toy store for a certain week: x = 0.7x + 24 How many total items were stocked for that week? 14 56 80 10
Answer:
80
Step-by-step explanation:
The total of 80 items were stocked for that week.
What is a system of equations?
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Solve equation for x to find the total number of sale items stocked on the shelves of a toy store for a certain week:
x = 0.7x + 24
We need to find How many total items were stocked for that week
Solving;
x = 0.7x + 24
x - 0.7x = 24
0.3x = 24
x = 80
Therefore, the total of 80 items were stocked for that week.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ2
Lori buys a $586 certificate of deposit (CD) that earns 6.6% interest that compounds monthly. How much will the CD be worth in 13 years? Express your answer rounded correctly to the nearest cent. Do not include units on your answer.
Answer:
$1344.9Step-by-step explanation:
This problem can be solved using the compound interest formula
[tex]A= P(1+r)^t[/tex]
Given data
A, final amount =?
P, principal = $586
rate, r= 6.6% = 0.066
Time, t= 13 years
Substituting our values into the expression we have
[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]
To the nearest cent the in 13 years the CD will be worth $1344.9
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)
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Answer:
b. y = f(x -3)
Step-by-step explanation:
The translation right h and up k units is ...
y -k = f(x -h)
Here, the red graph is translated right 3 and up 0, so the translated function is ...
y = f(x -3)
_____
Additional comment
You can check this if you like by listing a couple of corresponding points:
y = f(x)
1 = f(-3) . . . . left-most point on black graph.
The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...
1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)
Isreal spends the most time on social media with a total of 11.1.peru has a total of 8.3 how much more time does israel spend on social media
Answer:
2.8
Step-by-step explanation:
11.1-8.3=2.8
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
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JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
How to simplify this expression??
Answer :
1
Step-by-step-explanation :
[tex] {x}^{2} + 4x + 5 - {(x + 2)}^{2} \\ {x}^{2} + 4x + 5 - ( {x}^{2} + 4x + 4) \\ [/tex]
[tex]{x}^{2} + 4x + 5 - {x}^{2} - 4x - 4 = {x}^{2} - {x}^{2} + 4x - 4x + 5 - 4 = 5 - 4 = 1[/tex]
Answer:
(x+1) • (x-5)
Step-by-step explanation:
The first term is, x2 its coefficient is 1 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 1 • -5 = -5
Step-2 : Find two factors of -5 whose sum equals the coefficient of the middle term, which is -4 .
-5 + 1 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 1
x2 - 5x + 1x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-5)