Answer:
1.34 units.
Step-by-step explanation:
The line y = 2x - 5 has a slope of 2 so the line passing through the given point will be perpendicular to y= 2x - 5 and will have a slope of -1/2.
Let this line be y = -1/2x + c.
Its passes through (4, 6) so:
6 = -1/2*4 + c
6 = -2 + c
c = 6 + 2 = 8
So, equation of this line is y = -1/2x + 8.
Now we find the point where the 2 lines intersect:
y = 2x - 5
y = -1/2x + 8
2x - 5 = -1/2x + 8
2x + 1/2 x = 5 + 8
(5/2)x = 13
x = 26/5
= 5.2.
and y = 2(5.2) - 5
= 5.4.
So, the point of intersection is (5.2, 5.4)
and the distance between the point (4,6) and the line y = 2x - 5
= √((6 - 5.4)^2 + (4-5.2)^2)
= √(0.36 + 1.44)
= √1.8
= 1.34
There is a formula you can use directly to solve this.
geometry!!!!! help please!!
Answer:
CD and BG
EF and AH
Step-by-step explanation:
Skew lines are a lines that are on different planes.
BC and CD are on the same plane, and EF and FG are on the same plane.
This leaves CD and BG, and EF and AH, which are on different planes, and thus skew lines.
PLEASE HELP!: I'm so confused about what equations to write for the problem. All I need is the equations and I can solve it alone! I'll give brainly!
You invest $8,000 in 3 investment accounts. The accounts are: paper, metal, and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
Using simple interest, the amounts invested into each account are given as follows:
Paper returns: $3,500.Metal returns: $1,500.Glass returns: $3,000.Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = P(1 + rt)
In which:
P is the initial amount.r is the interest rate, as a decimal.The amount of interest after t years is given by:
I(t) = Prt
You invest $8,000 in 3 investment accounts, hence:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
From the rates of the account, we have that:
[tex]I_1 = 0.02P_1[/tex][tex]I_2 = 0.04P_2[/tex][tex]I_3 = 0.05P_3[/tex]The amount invested in the glass account was double the amount invested in the metal account, hence:
[tex]P_3 = 2P_2[/tex]
The yield was a total of $280 at the end of one year, hence:
[tex]I_1 + I_2 + I_3 = 280[/tex]
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
From the first and the third equations, we have that:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
[tex]P_1 + 3P_2 = 8000[/tex]
[tex]P_1 = 8000 - 3P_2[/tex]
Hence the amount of the metal investment can be found as follows:
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
[tex]0.02(8000 - 3P_2) + 0.04P_2 + 0.05(2P_2) = 280[/tex]
[tex]0.08P_2 = 120[/tex]
[tex]P_2 = \frac{120}{0.08}[/tex]
[tex]P_2 = 1500[/tex]
Hence the other investments are given as follows:
Paper: 8000 - 3 x 1500 = $3,500.Glass: 2 x 1500 = $3,000.More can be learned about simple interest at https://brainly.com/question/20690803
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n(x) = -1-x+4
n(-2) =
n(0)=
n(5)=
Step-by-step:
n(x) = -1 - x + 4
n(-2) = -1 - (-2) + 4
= -1 + 2 + 4
= 5
___________________________
n(0)= -1 - 0 + 4
= 3
___________________________
n(5)= -1 - 5 + 4
= -2
please help meeee!!! :c
Function A
f(x) = x − 9
Function B
graph of line going through ordered pairs negative 1, negative 3 and 2, 3
Which equation best compares the slopes of the two functions?
Slope of Function B = 2 x Slope of Function A
Slope of Function A = Slope of Function B
Slope of Function A = 2 x Slope of Function B
Slope of Function B = − Slope of Function A
The equation best compares the slopes of two functions is,
Slope of function B = 2 × Slope of function A
Given,
The function A, f(x) = x - 9
We have to find slope of Function B
The function is in the form of y = mx + b
Here, m is the slope.
y = x - 9
m is 1 and b is -9
Now, lets consider the graph of line passing through points (-1, -3) and (2, 3)
That is,
(x₁, y₁) = (-1, -3)
(x₂, y₂) = (2, 3)
Now we can find the slope of the line:
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-3)) / (2- (-1))
m = (3 + 3) / (2 + 1)
m = 6/3
m = 2
That is, the slope of function B is 2
Here,
Slope of function A is 1.
That is, slope of function B is twice the slope of function A.
Therefore, the equation best compares the slopes of two functions is,
Slope of function B = 2 × Slope of function A
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help asap please and thank u
Answer:
y = 5, 3
x = 155, 171
(y = 5, x = 155)
(y = 3, x = 171)
Step-by-step explanation:
(8y - 15) = (y²)
-8y + 15 -8y + 15
--------------------------------
y² - 8y + 15 = 0
(y - 5) (y - 3) = 0
--------------
y = 5, 3
----------------------------------------------------------------------------------------------------------
y² + x = 180
(5)² + x = 180
25 + x = 180
-25 -25
--------------------
x = 155
(3)² + x = 180
9 + x = 180
-9 -9
------------------
x = 171
----------------------------------------------------------------------------------------------------------
I really hope this helps!
i need help with this i just need the answer.
We have to find the length of FH.
We know that G is on the line, and we know the length FG and GH, so we can represent this as:
We then, we can apply the rule that states that the length of a segment is equal to the length of the segments that are part of it:
[tex]FH=FG+GH=10+5=15[/tex]Answer: FH = 15
Let f= {(1,2),(2,3),(3,5),(4,7)}
What is f ⁻¹ ∘ f
Test of a horizontal line.Suppose f is a function.F does not have an inverse if any horizontal line crosses the graph of f more than once.F does have an inverse if no horizontal line crosses the graph of f more than once
How do you calculate f's inverse?
Finding a Function's InverseReplace f(x) with y first, then.Every x must be replaced with a y, and vice versa.Solve the y-part of the equation from step two.In place of y, write f1(x) f 1 (x).Check that (ff1)(x)=x (f f f 1) (x) = x and (f1f)(x)=x (f f 1 f) (x) = x are both true to validate your workf= {(1,2),(2,3),(3,5),(4,7)}
Dom(gof)=dom(f)={1,3,4}.
(gof)(1)=g{f(1)}=g(2)=3,
(gof)(3)=g{f(3)}=g(5)=1
(gof)(4)=g{f(4)}=g(1)
∴gof={(1,3),(3,1),(4,3)}.
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Determine the intercepts of the line.
Answer:
x- intercept: ( -10,0)
y- intercept: (0, -45)
Step-by-step explanation:
An x intercept can be determined from the graph above by recognizing where the given line crosses the x-axis. The same is true for the y intercept and the y-axis.
On this graph, we see that the line crosses the x axis at the point ( -10,0), making this our x intercept.
We also see that the line crosses the y axis at the point (0, -45), making this our y intercept.
HOPE THIS HELPS!!
7. If Antonio makes x dollars per regular hours, and his boss tells him that he is
going to get paid over time at double time, write an equation to find his hourly
rate if he makes $1578.5 working 55 hours this week.
The equation for the hourly rate is 55x = 1578.5
For double hourly rate for overtime, it is 55 x 2x= 1578.5
Given
Antonia makes X dollars for regular hours
And 2x dollars for over time
Since he works 55 hours this week he works 8 hours a day
Hence the equation is as follows
55x = 1578.5
x= $28.7
In case of double payment during overtime
He gets double amount as following equation
55 x 2x
55 x 2(28.7) = $3157
Hence the equation to find his hourly rate is 55x = 157.85
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Bob makes some fruit punch that contains apple and mango juice in a 1:5 ratio. If he uses 15 pints of the mango juice how many pints of apple juice will he need
he needs 3 pints of mango
Answer:3
Step-by-step explanation:
If the ratio is 1:5 that means that the number of pints of apple juice is multiplied by 5 to get the nimber of pints of mango juice
Please answer the question in the photo
Answer:
u= 30
Step-by-step explanation:
the sum of all angles on a triangle is 180* so u add the others (120+30)
that brings it to 150 then 180-150=30*
Karen is driving her moterhome. It uses 3 gallons of gas for every 24 milesComplete the table below showing the number of gallons used and the distance traveled.
( The table is 3,24 6, ? 7,? ? , 72 and 10, ?)
Answer: 6, 48 and 7, 56 and 9, 72 and 10,80
Step-by-step explanation:
If f(x) = 4x6 + x² + 4, then what is the remainder when f(x) is divided by x -1?
Answer:
9
Step-by-step explanation:
[tex]p(x)=4x^6+x^2+4 \\ \\ p(1)=4+1+4=9[/tex]
According to a study published in the journal Social Psychological and Personality Science, people with
religious affiliations live longer, on average, than those without religious affiliations. The study analyzed
more than 1,000 obituaries and accounted for other variables like sex and marital status.
What type of study is this, and what is the explanatory variable?
The correct option is Option(c) An observational study where religious affiliation is an independent variable.
How is the study an observational study?According to a study published in the Journal Social Psychological and Personality Science, people with religious affiliations live longer, on average, than those without religious affiliations.Now, as we note, lifespan is said to be higher for people with religious affiliations.So, lifespan is claimed to be dependent on religious affiliation; so religious affiliation is independent and lifespan is dependent.Also, we cannot manipulate anyone's religious affiliation or lifespan; we just observe them by analyzing more than 1000 obituaries.Therefore, it is an observational study where religious affiliation is an independent variable.
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The complete question is: "According to a study published in the journal Social Psychological and Personality Science, people with religious affiliations live longer, on average, than those without religious affiliations. The study analyzed more than 1,000 obituaries and accounted for other variables like sex and marital status.
What type of study is this, and what is the explanatory variable?
A. A manipulative experiment where religious affiliation is an independent variable
B. A manipulative experiment where lifespan is an independent variable
C. An observational study where religious affiliation is an independent variable
D. An observational study where lifespan is an independent variable."
Divide
-36
-8
Enter your answer as a mixed number, in simplified form, in the box.
the answer is this
4 4/8.
Describe the graph of y = -|x + 4| - 5.
please answer correctly this will help me pass my exam
The graph of the absolute value function is an inverted "V" such that the vertex is at (-4, -5) and opens downwards.
How to calculate the modular function?We call a modular function the function f(x) = |x|, in which its domain is given by the real numbers and its range is the positive real numbers. This is because, for every negative value on the y-axis, the modular function will make |-y| = -(-y) = y
Therefore, to plot the graph of a modular function, it is enough to adopt some values for x and apply them to the function f(x) = | x |, in order to obtain their respective values in y.
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You cut a 90-foot rope into 6 pieces of equal length. What is the length of
each piece?
Answer:
Length = 15
Step-by-step explanation:
The problem can be solved by dividing the total length of the rope (90-feet) by the total pieces you want from the rope (6 pieces). This information can be used to make this equation
90 feet / 6 pieces
Which equals
90 feet / 6 pieces = 15 feet/piece (15 feet per peice)
Hope this helps :)
Suppose f(x)=4[[x-1]].
Find: f(1.7),f(-3.4), and f(9.8).
Answer:
I believe it should be
f(1.7) = 2.8
f(-3.4) = -17.6
f(9.8) = 35.
Step-by-step explanation:
Simply plug-in the different numbers for x.
Find the value of x if T is the midpoint of segment XY. Segment XT = 3x-14, Segment XY = 8x-56
The value of x if T is the midpoint segment XY is 14.
How to find the mid point of a segment?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints.
The midpoint is halfway between the two end points.
Therefore, the end point of the segment is XY.
The midpoint is T.
Hence,
XY = XT + YT
XT = 3x - 14 = YT
XY = 8x - 56
Let's find the value x.
Therefore,
8x - 56 = 3x - 14 + 3x - 14
8x - 56 = 6x - 28
8x - 6x = -28 + 56
2x = 28
divide both sides by 2
x = 28 / 2
x = 14
Therefore, the value of x is 14
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1. 5- (-8) =
2. -3 1/2 - 4 1/2 =
3. -7 - 4 =
4. -0.5 - 3.5 =
Answer:
1. 5- (-8) = 13
2. -3 1/2 - 4 1/2 = -7 1/2
3. -7 - 4 = -11
4. -0.5 - 3.5 = -4
Step-by-step explanation:
1. 5- (-8) =
5 + 8
13
2. -3 1/2 - 4 1/2 =
-7 1/2
3. -7 - 4 =
-11
4. -0.5 - 3.5 =
-4
find the number of sides of a regular polygonwhose exterior angle measure 18°
Answer:
20
Step-by-step explanation:
The sum of the exterior angles of a polygon add to 360. 360 divided by 18 is 20.
Someone please help me!!! ( I'll mark brainliest )
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
We can conclude that the probability of the randomly selected person does not use any facility is 0.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.Statistics is the study of events that follow a probability distribution. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability that the selected person does not uses any facility:
According to the given data, we can easily say that all the people use some or the other facility.So, there are 0 people present who do not use the facility.Then, the probability that the selected person does not use any facility will be 0.Therefore, we can conclude that the probability of the randomly selected person does not use any facility is 0.
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Mrs. argueta needed to fill up her gas tank. gas cost $3.66 per gallon and she needed 9 1 2 gallons. how much did it cost mrs. argueta to fill up her tank?
Answer:
$3337.92
Step-by-step explanation:
$3.66 x 912 = $3337.92
18x-51=9(4x+5)-6(3x-10)
[tex]18-51=36x+45-18x-60\\18x-51=36x-18x+45-60\\18x-51=18x-15\\18x-18x=-15+51[/tex]
∴ 18x-18x≠-15+51
THERE IS NO SOLUTION FOR THIS EQUATION
i need help with this, thanks
Answer: 11
Step-by-step explanation:
8x + 7 = 9x - 4
7 = x - 4
11 = x
Find the area of the pool. Write as a polynomial.
Pool
6x
3x-5
How do you do these?
Solve for s.
6/s = 2
Answer:
s=3
Step-by-step explanation:
So you have the equation: [tex]\frac{6}{s}=2[/tex]
If we multiply both sides by this "s" value we should maintain equality, and it conveniently cancels out our division by "s" on the left side giving us the following equation: [tex]6=2s[/tex]
The only "operation" on the value "s" is the coefficient of 2, which is multiplying the value of "s" by 2.
To undo this multiplication of 2, we simply divide by 2, since 2/2 = 1, and now we have a coefficient of 1 for the "s", which is the same as isolating "s"
But we want to divide both sides by 2 to maintain equality, so let's write out our expression
[tex]\frac{6}{2}=\frac{2s}{2}\implies3=\frac{2}{2}*s\implies 3=s[/tex]
We can double check this by plugging in this value for "s" in the original equation: [tex]s=3, \ \frac{6}{s}=2\implies \frac{6}{3}=2\implies 3=3[/tex] which is indeed true, so we have our solution!
round to the underlined digit:
Answer:
c because if the number next to the underlined is above 5 u round up under 4 u round down
Step-by-step explanation:
Answer: c. 76
Step-by-step explanation: 0.758 to the hundredth place is 0.76 because numbers5 and above round up.
a box contains 24 light bulbs of which four are defective. if one person selects 10 bulbs from the box in a random manner, and a second person then takes the remaining 14 bulbs, what is the probability that all four defective bulbs will be obtained by the same person?
The probability that all four defective bulbs will be obtained by the same person is 0.1140 .
In the question ;
it is given that
the total number of light bulbs in the box = 24 bulbs
total number of bulbs available for first person = 24 bulbs
number of defective bulbs = 4
So, the number of ways the first person can select 4 defective bulbs out of 10 selection = C(10,4)
total number of ways that first person can select 4 defective bulbs out of 24 bulbs = C(24,4)
So , the Probability that all four defective bulbs obtained by first person = C(10,4)/C(24,4) . .......(i)
Since 10 bulbs have been selected
So, total number of bulbs available for second person = 14 bulbs
number of defective bulbs = 4
So, the number of ways the first person can select 4 defective bulbs out of 14 remaining bulbs = C(14,4)
total number of ways that first person can select 4 defective bulbs out of 24 bulbs = C(24,4)
So , the Probability that all four defective bulbs obtained by second person = C(14,4)/C(24,4) . .....(ii)
Probability that all four of the defective bulbs will be obtained by the same person
= P(four defective bulbs obtained by first person) + P(four defective bulbs by second person)
Substituting the probabilities from (i) and (ii) , we get
= C(10,4)/C(24,4) + C(14,4)/C(24,4)
= (210/10626 )+(1001/10626) ...as C(10,4)=210 ,C(24,4)=10626, C(14,4)=1001
= 1211/10626
= 0.1139657
≈ 0.1140
Therefore , the probability that all four defective bulbs will be obtained by the same person is 0.1140 .
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