The two possible locations of L are (-2,-1) and (14/3, -5/3).
According to the question,
We have the following information:
JK has endpoints J(-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1.
We know that the following formulas are used to find the coordinates of a point:
x = [tex]\frac{(mx2+nx1)}{(m+n)}[/tex] and x = [tex]\frac{(mx2-nx1)}{(m+n)}[/tex]
y = [tex]\frac{(my2+ny1)}{(m+n)}[/tex] and y = [tex]\frac{(my2-ny1)}{(m+n)}[/tex]
In this case, we have the following values:
x1 = -10 and y1 = 1
x2 = 2 and y2 = -1
m = 2 and n = 1
So, we have:
x = {2*2+1*(-10)}/(2+1)
x = (4-10)/3
x = -6/3
x = -2
For the negative sign:
x = {2*2-1*(-10)}/3
x = (4+10)/3
x = 14/3
x = 4.67
The values of y:
y = {2*(-2)+1*1}/3
y = (-4+1)/3
y = -3/3
y = -1
For the negative sign:
y = {2*(-2)-1*1}/3
y = (-4-1)/3
y = -5/3
y = -1.67
Hence, the two possible locations of L are (-2,-1) and (14/3, -5/3).
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Write the prime factorization for each of the following numbers using exponents if possible.
need help with algebra
The values of x that make the equation true are approximately 5.7 and -0.7 .
The given equation is :
[tex]\frac{x+1}{x} = \frac{2}{x-4}[/tex]
Using cross multiplication this can be written as:
or, ( x + 1 ) ( x - 4 ) = 2 x
or, x² + x - 4x - 4 = 2x
Putting all the like terms together.
or, x² + x - 4x -2x - 4 = 0
or, x² - 5x - 4 = 0
Now we will use the quadratic formula to find the values of x :
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]
or, [tex]{\displaystyle x={\frac {5\pm {\sqrt {(-5)^{2}-4(1)(-4)}}}{2(1)}}\ \ }[/tex]
or, [tex]x = \frac{5+\sqrt{41}}{2} , \frac{5-\sqrt{41}}{2}[/tex]
or, x ≈ 5.7 , -0.7
The roots or zeros of the expression, which are also on the left side of the equation, are used to indicate the values of x that satisfy the equation.
There can only be two possible solutions to a quadratic problem. One argues that if there is only one remedy, there are many different causes of the problem. There are only four possibilities: one real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if each of the coefficients has a real value.
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Friday: Nabil had $80.50 on a gift card before buying four journals at a bookstore. The bookstore charges 50¢ to use the card. He had $44.00 left on the gift card after buying the journals. If each journal cost the same amount, what was the price of each journal?
Answer:
$9.00 a journal.
Step-by-step explanation:
First off, you can start by subtracting $0.50 from $80.50 because it costs $0.50 to use the card.
You’re left with a new value of $80.00. Since Nabil had $44.00 left over on his card, you can subtract $44.00 from $80.00 to figure out how much he spent.
$80.00
-$44.00
————
$36.00
Since Nabil bought four journals, and they are all equal in cost, you can divide $36.00 by 4 (36/4) and get $9.00.
How do I figure the total of a 4:3 ratio?
Step-by-step explanation:
If you take the 4:3 aspect ratio and divide 4 by 3, the result is 1.33. Therefore, you could alternately describe the 4:3 aspect ratio as 1.33:1, meaning that for every 1.33 units in width, there is 1 unit in height. Again, the same applies for the 16:9.
Learn at brainlyPoint E is added to the given figure so that point E lies on segment BD exactly halfway between points B and D. Which statement correctly compares the angle measures?
Answer:
there is no picture but m∠EBD = m∠EBD would be one of the best one as a guess to what the photo might be
Step-by-step explanation:
Point E is added to the given figure so that point E lies on segment BD and it is exactly halfway between points B and D
The sum of $5400 was borrowed from a bank
at the rate of 10% per annum for 3 years. How much would the simple interest payable would be?
(A) $1800
(B) $540
(C) $1620
(D) $486
The simple interest on $5400 at a rate of 10% per annum for 3 years is $ 1620
Simple interest:The interest on a loan at a fixed rate per annum. The formula used for simple interest is given by
Simple interest (I) = ptr
Where p = principal amount
t = time period
r = rate of interest per year.
Here we have
The sum of $5400 was borrowed from a bank at a rate of 10% per annum for 3 years
Find the simple interest that can be payable
From above observations
Principal amount, P = $5400
Rate of interest = 10% = 10/100 = 0.1
Time period, t = 3 years
The simple interest that can be payable = $5400(3)(0.1) = $ 1620
Therefore,
The simple interest on $5400 at a rate of 10% per annum for 3 years is $ 1620
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Express the sample proportion as a percent:
Out of 1150 insurance applicants, 837 have no citations on their driving record.
%
Answer:
837/1150=0.727
Or 73%
Step-by-step explanation:
Rewrite (55•44)•33 using the
Associative Law of Multiplication.
Rewriting the given term (55.44).33 using the Associative Law of Multiplication, we have 55.(44.33). Therefore, 1st option is correct.
The given terms are written as -
(55.44).33
We have to rewrite the given term using the Associative Law of Multiplication.
According to the Associative Law of Multiplication, the terms or factors can be associated in any expected ways, i.e.,
a(bc) = (ab)c
So, our given term in the question (55.44).33 can be rewritten according to the Associative Law of Multiplication as -
(55.44).33 = 55.(44.33)
Thus, rewriting the given term (55.44).33 using the Associative Law of Multiplication gives us 55.(44.33). Therefore, 1st option is correct.
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Aldo is saving money to buy a game. the game cost $18, and so far he has saved one-third of this cost. How much money has Aldo saved
Answer: c=54
Step-by-step explanation:
|||
Solving a word problem on proportions using a unit rate
Ali made $306 for 17 hours of work.
At the same rate, how many hours would he have to work to make $126?
2. Choose the correct answer to 2,412 ÷ 25. 96 96 R12 97 95 R37
Answer: 96 R12
Step-by-step explanation:
Can someone please find the area of the shape below thank you!
Answer:
43 cm^2
Step-by-step explanation:
Area of the triangle:
A = (1/2) x base x height
A = (1/2) x (2 cm + 4 cm) x 7 cm
A = (1/2) x (6 cm) x 7 cm
A = (1/2) x 42 cm^2
A = 21 cm^2
The area of the triangle is 21 cm^2
Area of the rectangle:
A = length x width
A = 11 cm x 2 cm
A = 22 cm^2
The area of the rectangle is 22 cm^2
Area of the figure = Area of the triangle + Area of the rectangle
Area of the figure = 21 cm^2 + 22 cm^2
Area of the figure = 43 cm^2
For f(x)=x+4 and g(x)=3x+2, find the following functions.
Someone please explain how to solve this
The values of the following functions are:
a. (f ºg)(x) = x+2
b. (g º f)(x) = 3x + 14
c. (f º g)(-1) = 3
d. (g º f)(-1) = 11
Given:
f(x) = x+4 and
g(x) = 3x+2
we are asked to determine the following functions:
a. (f º g)(x)
⇒ f(g(x))
⇒ f(3x+2)
⇒ (f º g)(x) = (3x+2)+4
= 3x+6
divide by 3
= x+2
b. (g º f)(x)
⇒ g(f(x))
⇒ g(x+4)
⇒ (g º f)(x) = 3(x+4)+2
= 3x+12+2
= 3x+14
c. (f º g)(-1)
⇒ f(g(-1))
⇒ f(3(-1)+2)
⇒ f(-3+2)
⇒ f(-1)
⇒ (f º g)(-1) = -1+4
= 3
d. (g º f)(-1)
⇒ g(f(-1))
⇒ g(-1+4)
⇒ g(3)
⇒ (g º f)(-1) = 3(3)+2
= 11
Hence we get the required answer.
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Ordered 0.5mg/ kg and supplied 10 mg/ml and weighs 40 kg how many mls do you give
As per the given relation between ordered mg to kg and supplied mg to ml then weighs 40kg is equal to 2ml.
As given in the question,
Relation between mg to kg as per the ordered is given by ,
0.5 mg / kg
⇒ For 1 kg = 0.5 mg
Relation between mg to ml as per the supplied is given by ,
10 mg / ml
⇒ 1 ml = 10 mg
Now for 40 kg weighs the relation is given by,
1 kg = 0.5 mg
⇒ 40 kg = ( 40 × 0.5) mg
⇒ 40 kg = 20 mg ___(1)
And
1 ml = 10 mg
⇒ ( 2 × 1) ml = ( 2 × 10 ) mg
⇒ 2ml = 20mg ____(2)
From (1) and (2) we get ,
For 40 kg weighs we need 2ml.
Therefore, As per the given relation between ordered mg to kg and supplied mg to ml then weighs 40kg is equal to 2ml.
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calculate the sizes of angles marked with letters in the following diagrams, giving reasons for your answers
Can anyone help me with number 2?
what is the equation of the line shown below
A y=-2/3x+1
B y=2/3x-1
C y=2x-1
D y=6x=4
The equation of the line is option (C) y = 2x - 1
First we have to choose two points
The first point = (1, 1)
The second point = (2, 3)
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
Slope of the line = (3-1) / (2-1)
= 2 / 1
= 2
From the graph line is intersecting on y axis at y = -1
The slope intercept form of the line
y = mx + b
where m is the slope of the line
b is the y intercept
Substitute the values
y = 2x - 1
Hence, the equation of the line is option (C) y = 2x - 1
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Write an equation for the trend line shown on the scatter plot.
Answer:
y = 5x + 15
Step-by-step explanation:
You can pick any two points on the graph that intersect the trend line. For instance (5,40) and (3,30)
Formula for Slope:
[tex]y = \frac{y_2 - y_1}{x_2 - x_1} = \frac{40 - 30}{5 - 3} = \frac{10}{2} = 5[/tex]
y intercept:
[tex]y = 15[/tex]
Equation of a line:
[tex]y = mx + b\\m = slope \\b = intercept \\\\y = 5x + 15[/tex]
** also be cautious of the different scaling of the x and y axis.
kims music files takes up 7 gigs of space on her hard drive. about how many bytes is that how many bits is that?
Which is the solution to the system of equations?
y = 1/8x −1
−5x + 4y = −13
A. (0,−1)
B. (8,0)
C. (1,−7/8)
D. (2,−3/4)
The solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.
We are given:
y = 1/8 x − 1 ..............equation i.
− 5x + 4y = − 13 ..............equation ii.
We will use the substitution method to solve the given equation.
substitute the value of y from equation i in equation ii, and we will get;
− 5x + 4(1/8 x − 1) = − 13
− 5x + 1/2 x − 4 = − 13
(-10 + 1) / 2 x = -13 + 4
-9/2 x = -9
x = -9 * 2 / -9
x = 2
Put the value of x in equation i, we will get;
y = 1/8 *2 − 1
y = 1/4 - 1
y = 1 - 4 / 4
y = -3 / 4
So, the value of x = 2 and the value of y = -3 / 4.
Thus, the solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.
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An athlete swings a 7.9 kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.9 m at an angular speed of 0.27 rev/s.
What is the tangential speed of the ball? Answer in units of m/s.
part 2
What is its centripetal acceleration? Answer in units of m/s2.
this is physics
The tangential speed of the ball is 1.5267
The centripetal acceleration is 2.5897 m/s²
How to solve for the tangential speedMass of the ball is m = 7.90 kg
ball moves in a circle having radius r = 0.9 m
angular speed is ω = 0.27 rev /s
given that 1 revolution = 6.283 rad / sec
0.27 rev / sec = ?
ω = 1.696 rad / sec
a. The tangential speed Velocity = rω
w = 1.696
r = 0.9
= 1.696 * 0.9 m
= 1.5267 m / s
b ) centripetal acceleration a = v² / r
= (1.5267 m/s)^2 / 0.9 m
= 2.3308 / 0.9
= 2.5897 m/s²
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Select all symmetries that apply
Two humitos cout $1500. Complete a table to show the con for 3, 7, and 13 borrins at fest rate
Next, find the cost for a single burrito in each case. What do you notice about the values in this
be
Answer:
I would say the answer is 1500/3/7/13
Step-by-step explanation:
con for 3,7,13 find it divife it by 1500 cost of burrito
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
Unless you wrote the wrong expressions, non of your choice answers are correct!
Step-by-step explanation:
Solve for x:
2 (x - 7) = 36
Divide both sides of (x - 7)×2 = 36 by 2:
(2 (x - 7))/2 = 36/2
2/2 = 1:
x - 7 = 36/2
The gcd of 36 and 2 is 2, so 36/2 = (2×18)/(2×1) = 2/2×18 = 18:
x - 7 = 18
Add 7 to both sides:
x + (7 - 7) = 7 + 18
7 - 7 = 0:
x = 18 + 7
18 + 7 = 25:
Answer: x = 25
Which is the best estimate for 2 2/3 × 3 1/4
Identify the change in the parent function that will produce the related function shown as a dashed line. f(x) = x
A standard deck of playing cards contains 52 total cards, 13 of which are "spades".
Suppose you and a friend are playing a game. You can choose any two cards from the deck without looking. If the two cards you choose are both spades, you win!
You pull out one card, and then another, without putting the first one back.
What is the approximate probability that you win? Are your two choices independent or dependent events?
6%, Independent
6%, Dependent
11%, independent
11%, Dependent
The probability that you win is 6%, and the two choices are dependent events option (B) is correct.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
A standard deck of playing cards contains 52 total cards, 13 of which are "spades".
The probability of the first draw:
Probability = favorable outcomes/total outcomes
First draw: 1/4
For the second draw:
Second draw = 12/51
The probability that you win = (1/4)(12/51) = 3/51
In percent:
= (3/51)x100
= 5.88 = 6%
Thus, the probability that you win is 6%, and the two choices are dependent on events option (B) is correct.
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Subtract. (−4x − 1) – (6x – 5)
Answer:
-10x+4
Step-by-step explanation:
distribute the minus
-4x-1-6x+5
-10x+4
hopes this helps please mark brainliest
The radius of a circle is 33 cm. What is the area of the circle? Give your answer to 1 d.p.
The area of the circle with radius 33 cm is 3419.5 square centimeters.
According to the question,
We have the following information:
Radius of the circle = 33 cm
We know that the following formula is used to find the area of the circle:
Area of the circle = π[tex]r^{2}[/tex] where r is the radius of the circle
There are two approximate values of π which are 22/7 and 3.14. In this case, we will use the value of π as 3.14.
So, we have the following expression:
Area of the circle = 3.14*33*33
Area of the circle = 3419.46 square centimeters
Rounding it off to one decimal point:
3419.5 square centimeters
Hence, the area of the circle with radius 33 cm is 3419.5 square centimeters.
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6 to the power of -3 as a simplified fraction or integer
Answer:
Step-by-step explanation:
1. Make Words into Math
6 to the power of -3 =
6^-3=
-6*-6*-6=
0.00462962962
Answer:0.00462962962