Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
[tex]6x+y=-1\\y=-6x-1[/tex]
second equation:
[tex]-6x-4y=4\\-6x=4y+4\\-6x-4=4y\\y=-\frac{3}{2} x-1[/tex]
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation. Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths. What is OB'? 1.5 units 3 units 4.5 units 6 units
If the length of OB was ³/₄, then the length of OB' after dilation is; Option B: 3 units.
Dilation of an object simply means enlarging or shrinking of the object by a scale factor.Now, we are told that Triangle ABC was dilated to Triangle A'B'C' using the rule D₀,₄.What this means is that it was enlarged by a scale factor of 4 with point O as the center of dilation.
Now, if the length of OB is 3/4, it means that the new dilated length is gotten from;Scale factor = new dilated length OB'/(³/₄)
new dilated length OB' = ³/₄ × 4
new dilated length OB' = 3 units
Read more on dilation at; https://brainly.com/question/8532602
Answer:
its 4 units trust just answered it
Step-by-step explanation:
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options. y = –Three-fourthsx + 1 3x − 4y = −4 4x − 3y = −3 y – 2 = –Three-fourths(x – 4) y + 2 = Three-fourths(x + 4)
Answer:
The equation of the parallel line to the given equation is
3 x-4 y = -4 and
The equation of the parallel line to the given equation is
[tex]y = 1 + \frac{3 x}{4}[/tex]
Step-by-step explanation:
Explanation:-
Given equation of the line 3 x -4 y = 7 and given point ( -4 , -2 )
The equation of the parallel line to the given equation is
3 x - 4 y = k
it is passes through the point ( -4 , -2)
3 (-4) - 4 ( -2) = k
-12 +8 = k
k = -4
The equation of the parallel line to the given equation is
3 x- 4 y = -4
Dividing '4' on both sides , we get
[tex]\frac{3 x-4 y}{-4} = 1[/tex]
[tex]\frac{-3 x}{4} +y =1[/tex]
[tex]y = 1 + \frac{3 x}{4}[/tex]
Conclusion:-
∴ The equation of the parallel line to the given equation is
3 x- 4 y = -4
and
The equation of the parallel line to the given equation is
[tex]y = 1 + \frac{3 x}{4}[/tex]
Answer:
the answer is b and d edge 2021
Step-by-step explanation:
I am finished taking the test got a 100%
Elena has a bottle that has a capacity of 34 quarts. What is the maximum amount of liquid that can be stored in this bottle?
What’s the correct answer for this?
Answer:
s = 4.43
Step-by-step explanation:
Using formula for bigger circle
s =r∅
Where s is the Arc length, r is rdius and ∅ is theta(angle)
8.84=5∅
∅= 8.84/5
Angle = 1.77 radians
So both angles equal to 1.77 radians
Now again
Using formula
s = r∅
Where s is the Arc length, r is rdius and ∅ is theta(angle)
s = (2.5)(1.77)
s ≈ 4.43
A door wedge is 5 cm tall. Its has 3.7 cm high triangular bases with 2 congruent 5 cm sides and a 4 cm side. What is its surface area?
Answer:
Surface Area = 84.8 cm²
Step-by-step explanation:
This wedge is simply a triangular prism.
We are given;
Height of door wedge; H = 5 cm
Height of triangular base;h = 3.7 cm
Congruent sides; S2 = S3 = 5cm
base of triangular side;b = S1 = 4 cm
Now, formula for surface area of triangular prism is;
SA = bh + (s1 + s2 + s3)H
Thus, plugging in the relevant values, we have;
SA = (4 x 3.7) + (4 + 5 + 5)5
SA = 14.8 + 70
SA = 84.8 cm²
Simplify (x2y)3. x 5y 3 x 2y 3 x 6y 3
Answer:
[tex]x^{6} y^{3}[/tex]
Step-by-step explanation:
[tex](x^2y)3[/tex]
[tex]x^{2 \times 3} \times y^3[/tex]
[tex]x^{6} \times y^3[/tex]
The system of equations above has solution (x,y).
What is the value of x ?
Answer: [tex]\frac{21}{4}[/tex]
Step-by-step explanation:
Multiply each side by 2 to get rid of the fraction on the right side. That basically gets rid of the 1/2 and the 2.
Youre now stuck with 2x + y = 21. They gave us y which is 2x. 2x + 2x = 4x
You now have 4x = 21
Divide each side by 4 to get x = 21/4
Solve the following equation for x.
|x/4+3|<6
Answer:
x<12
Step-by-step explanation:
subtract both sides by -3 because you need to isolate x. then you have x/4<3. now you need to get rid of the 4. so you do the opposite of division and multiply 4 by both sides so you get x<12
The math SAT is scaled so that the mean score is 500 and the standard deviation is 100. Assuming scores are normally distributed, find the probability that a randomly selected student scores
Answer:
a. P(X>695)=0.026
b. P(X<485)=0.44
Step-by-step explanation:
The question is incomplete:
a. higher than 695 on the test.
b. at most 485 on the test.
We have a normal distribution with mean 500 and standard deviation of 100 for the test scores. We will use the z-scores to calculate the probabilties with the standard normal distribution table.
a. We want to calculate the probability that a randomly selected student scores higher than 695.
We calculate the z-score and then we calculate the probability:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{695-500}{100}=\dfrac{195}{100}=1.95\\\\\\P(X>695)=P(z>1.95)=0.026[/tex]
a. We want to calculate the probability that a randomly selected student scores at most 485.
We calculate the z-score and then we calculate the probability:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{485-500}{100}=\dfrac{-15}{100}=-0.15\\\\\\P(X<485)=P(z<-0.15)=0.44[/tex]
a newborn calf weighs 40 kilograms. Each week its weight increases by 5%. Let W be the weigh in kilograms of the calf after t weeks
A rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height as the connection point between the rope and weight. The distance from the connection point to the ceiling is 30 ft. Suppose the worker stands directly next to the weight (i.e., a total rope length of 60 ft) and begins to walk away at a constant rate of 2 ft/s. How fast is the weight rising when the worker has walked:
Answer: 0.66 ft
Step-by-step explanation:
Let assume that the initial position of the worker is x.
Given that the worker walks away with a constant speed of 2 ft/s. Therefore, dx/dt = 2
As the worker moves away, the rope makes a triangle, with width length x and the height length will be 30.
Using pythagorean theorem, the length of rope on this side of the pulley will be √(x² + 30²)
Also, the length of rope on the other side will be 60 - √(x² + 30²),
and the height h of the weight will be 30 - (60 - √(x² + 30²)) = √(x² + 30²) - 30
dh/dt = dx/dt × x/√(x² + 30²)
= 4x/√(x² + 30²)
dh/dt = 4x/√(x² + 30²)
If the worker moves 5ft away, then
dh/dt = (4×5)/√(5² + 30²)
dh/dt = 20/√(25 + 900)
dh/dt = 0.66 ft
find the value of the expression :1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
A number to the power of a negative exponent, means 1 divided by that same number to the power of the positive exponent.
1/(216^(-2/3)) + 1/(256^(-3/4)) + 1/(243^(-1/5))
Break it apart into three pieces.
1/(216^(-2/3))
216^(2/3) = 36
1/(256^(-3/4))
256^(3/4) = 64
1/(243^(-1/5))
243^(1/5) = 3
So...
1/(216^(-2/3)) = 36
1/(256^(-3/4)) = 64
1/(243^(-1/5)) = 3
Add the numbers gives:
36 + 64 + 3 = 103
What is the average rate of change for this function for the interval from x= 1
to x = 3?
Answer:
The average rate of change is 12x=12.0x.
Description:
Function: x= 1x = 3 convert to short form: x 1x 3
Interval: x= 1 , x 3
Steps:
Input: Find the average rate of change of f(x)=3x2 on the interval [x,3x].
We have that a=x, b=3x, f(x)=3x2
Thus, f(b)−f(a)b−a=3((3x))2−(3(x)2)3x−(x)=12x.
Answer: the average rate of change is 12x=12.0x.
Please mark brainliest
Hope this helps.
Answer:
3
Step-by-step explanation:
A P E X
Estimate and then solve the equation. X - 17 4/5=-13 1/5
Answer: 5 (estimate)
Step-by-step explanation:
x - 17 4/5 = -13 1/5
Estimate: x - 18 = -13
x - 18 + 18 = -13 + 18
x = 5
actual answer without estimating using exact numbers is 4 3/5 (so estimate is reasonable)
An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.
Required:
a. Create a valid probability table.
b. How much should the trader expect to gain or lose?
c. Should the trader buy the stock? Explain.
Answer:
Step-by-step explanation:
An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.
a) Let X represent the price of the option
x P(X=x)
$1000 20/100 = 0.2
$200 50/100 = 0.5
$0 30/100 = 0.3
b) Expected option price
[tex]= \sum x.P(X=x)\\\\ = 1000 * 0.2 + 200 * 0.5 + 0 = \$ 300[/tex]
Therefore expected gain = $300 - $150 = $150
c) The trader should buy the stock. Since there is an positive expected gain($150) in trading that stock option.
A family of five rents a kayak and splits the total time, k, equally. Each family member spent less than 25 minutes kayaking. Which values can be used to complete the math sentence below so that it accurately represents the situation?
Answer:
k ÷ 5 < 25
Step-by-step explanation:
Edg.
Answer:
k ÷ 5 < 25
Step-by-step explanation:
Simplify 6r · s · 4rt. this is the question
Answer=6 . S/R . 4T
This is the answer because u have to simplify so to do this u have to divide all of this by R
A clothing store determines that in order to sell x shirts, the price per shirt should be p(x)=100−x dollars. Getting x shirts from the supplier costs the store C(x)=1,600+20x dollars. If the store’s revenue from selling x shirts is R(x)=x⋅p(x), for what value of x will the store’s cost and revenue be equal?
Answer:
x= -40
Step-by-step explanation:
Cost
C(x)=1,600+20x
P(x)=100-x
Revenue=x*p(x)
=x*(100-x)
=100x-x^2
Cost=Revenue
1600+20x=100x-x^2
1600+20x-100x+x^2=0
1600-80x+x^2=0
Solve using quadratic formula
Formula where
a = 1, b = 80, and c = 1600
x=−b±√b2−4ac/2a
x=−80±√80^2−4(1)(1600) / 2(1)
x=−80±√6400−6400 / 2
x=−80±√0 / 2
The discriminant b^2−4ac=0
so, there is one real root.
x= −80/2
x= -40
Balu and Pumba shared 2/3 of a cake. Balu got to eat three times as much cake as Pumba. What fraction of the whole cake did Balu eat?
Pleas answer help and answer correctly.
Answer:
In fraction, Balu ate 1/2 of the whole cake
Step-by-step explanation:
Balu and Pumba shared 2/3 of a cake.
Balu eats three times as much cake as Pumba.
So let's take the 2/3 they shared as a whole.
Let's Balu share be x
And pumbs share be y
X = 3y
But x + 3y = 2/3
Since x = 3y
Y = x/3
x + x/3 = 2/3
4x/3 = 2/3
X = (2*3)/(4*3)
X = 2/4
X = 1/2
Balu ate half of the whole cake
In fraction, Balu ate 1/2 of the whole cake
A marketing analyst randomly surveyed 150 adults from a certain city and asked which type of tooth paste they were currently using - Extra Whitening or Regular. 96 said they were currently using Extra Whitening while the rest said they were using Regular. The analyst wants to determine if this is evidence that more than half of the adults in this city are using Extra Whitening. Suppose a p-value from the correct hypothesis test was 0.0003. Which of the following is a correct interpretation of this p-value?
A. HA: p_extra White > p_Regular.
B. HA: p > 0.5, where p = the proportion of all adults in this city using Extra Whitening.
C. HA: p = 0.64, where p = the proportion of all adults in this city using Extra Whitening.
D. HA: p=0.5, where p = the proportion of all adults in this city using Extra Whitening.
a cereal box is an example of a
Answer: recantagle
Step-by-step explanation:
PLEASE HELP ME!!! (WILL MARK BRAINLIEST!
Answer:
A) 13/20
Step-by-step explanation:
65% in simplest form,
65/100
= 13/20 (Divided by five)
Answer:
[tex]\frac{13}{20}[/tex].
Step-by-step explanation:
We can begin by converting 65% to a fraction over 100. 65% converts to 0.65, or [tex]\frac{65}{100}[/tex].
We can simplify this down. Both 65 and 100 share a common factor of 5, which allows us to produce a new fraction:
[tex]\frac{65}{100} = \frac{13}{20}[/tex]
Therefore, the simplified version is [tex]\frac{13}{20}[/tex].
Determine whether the stated causal connection is valid. If the causal connection appears to be valid, provide an explanation. Test grades are affected by the amount of time and effort spent studying and preparing for the test. Choose the correct answer below
a. The causal connection is valid. Students who spend more time and effort studying will be able to memorize more information, so their test grades will be higher.
b. The causal connection is valid. Students who spend more time and effort studying tend to be smarter, so their test grades are higher.
c. The causal connection is valid. When students spend more time and effort studying for a test, their test grades tend to be higher.
d. The causal connection is not valid.
Answer:
A. The causal connection is valid. Students who spend more time and effort studying will be able to memorize more information, so their test grades will be higher.
Step-by-step Explanation:
The causal connection between the test grades of students and the amount of time and effort spent the students spend in studying and preparing for the test appears to be valid. This is valid because students who spend more time and effort studying would most likely be able to memorize more information of which they are most likely to come by in the test they take. Invariably, they'd be able to easily recall what they've memorize and give the right answers to the questions they are asked in the test, and this definitely will earn them higher test grades.
I WILLL GIVE BRAINLIEST ANSWER ASAP
Answer: 2ND ONE
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
5x+3=4x
5x-4x=-3
x=-3
Edit: Check by plugging in x = -3
5(-3)+3=4(-3)
-15+3=-12
-12=-12✅
What’s the correct answer for this question?
Answer:
the radius
Step-by-step explanation:
the correct answer is the radius
Which of the following sequences is arithmetic? A 3, 9, 15, 21, 27, . . . B 3, 9, 17, 27, 39, . . . C 3, 9, 27, 81, 243, . . .
Answer:
A) 3, 9, 15, 21, 27, . . .
Step-by-step explanation:
EDGE 2020
Answer:
The second answer is 6.
Step-by-step explanation:
D=6
What are the names for the sides of a triangle?
Answer:
there are none
Step-by-step explanation:
a triangle its is own shape and does not have any name for each side.
Simplify the number into simplest radical form.
Answer:
4 sqrt(6)
Step-by-step explanation:
sqrt(96)
We know sqrt(ab) =sqrt(a) sqrt(b)
sqrt(16*6)
sqrt(16) sqrt(6)
4 sqrt(6)
Find the area of a circle with radius, r = 19cm.
Give your answer rounded to 3 SF.
Answer:
1130
Step-by-step explanation:
since radius of the circle was given and the formula of the area is pie r square
After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.5 6/ (t+4)3 feet per year, where t is the time (in years)
(a) Find the number of feet that the tree will grow in the second year.
(b) Find the number of feet the tree will grow in the third year.
(c) The total number of feet grown during the second year is_____________ ft.
Answer:
a) 0.5367feetb) 0.5223feetc) 0.7292feetStep-by-step explanation:
Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).
The amount of growth can be gotten by integrating the given rate equation as shown;
[tex]\int\limits {0.5 + \frac{6}{(t+4)^{3} } } \, dt \\= \int\limits {0.5} \, dt + \int\limits\frac{6}{(t+4)^{3} } } \, dx } \, \\= 0.5t +\int\limits {6u^{-3} } \, du \ where \ u = t+4 \ and\ du = dt\\= 0.5t + 6*\frac{u^{-2} }{-2} + C\\= 0.5t-3u^{-2} +C\\= 0.5t-3(t+4)^{-2} + C[/tex]
a) The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from t =1 to t = 2
[tex]\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\ = 0.9167 - 0.5 + 0.12\\= 0.5367feet[/tex]
b) The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from t =2 to t = 3
[tex]\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\ = 1.439 - 0.9167\\= 0.5223feet[/tex]
c) The total number of feet grown during the second year can be gotten by substituting the value of limit from t = 0 to t = 2 into the equation as shown
[tex]\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\ = 0.9167 - 0.1875\\= 0.7292feet[/tex]