The endpoints of DEF are D(1, 4) and F(16, 14).
Determine and state the coordinates of point E, if
DE: EF = 2:3.
Answers
Answer:
The coordinates of point E are (7,8).
Step-by-step explanation:
Point E:
Is given by (x,y).
DE: EF = 2:3.
This means that, for both coordinates x and y:
[tex]E - D = \frac{2}{2+3}(F-D)[/tex]
[tex]E - D = \frac{2}{5}(F-D)[/tex]
x-coordinate:
x-coordinate of D: 1
x-coordinate of F: 16
[tex]E - D = \frac{2}{5}(F-D)[/tex]
[tex]x - 1 = \frac{2}{5}(16-1)[/tex]
[tex]x - 1 = 2*3[/tex]
[tex]x = 7[/tex]
y-coordiante:
y-coordinate of D: 4
y-coordinate of F: 14
[tex]E - D = \frac{2}{5}(F-D)[/tex]
[tex]y - 4 = \frac{2}{5}(14-4)[/tex]
[tex]y - 4 = 2*2[/tex]
[tex]x = 8[/tex]
The coordinates of point E are (7,8).
Related Questions
f(x)=2x^2-x-6 g(x)=4-x (f+g)(x)
Answers
[tex] \large \boxed{(f + g)(x) = f(x) + g(x)}[/tex]
The property above is distribution property where we distribute x-term in the function.
Substitute both f(x) and g(x) in.
[tex] \large{ \begin{cases} f(x) = 2 {x}^{2} - x - 6 \\ g(x) = 4 - x \end{cases}} \\ \large{f(x) + g(x) = (2 {x}^{2} - x - 6) + (4 - x)} \\ \large{f(x) + g(x) = 2 {x}^{2} - x - 6 + 4 - x}[/tex]
Évaluate/Combine like terms.
[tex] \large{f(x) + g(x) = 2 {x}^{2} - 2x - 2} [/tex]
The function can be factored so there are two answers. (Both of them work as one of them is factored form while the other one is not.)
[tex] \large{(f + g)(x) = 2 {x}^{2} -2x -2}[/tex]
Alternative
[tex] \large{(f + g)(x) = 2({x}^{2} -x - 1)}[/tex]
Answer
(f+g)(x) = 2x²-2x-2(f+g)(x) = 2(x²-x-1)Both answers work. The second answer is in factored form.
Let me know if you have any doubts!
Consider the following equation. -2x + 6 =[-2/3] + 5
Answers
Answer:
that's my answer
hope it helps
What is the MEDIAN or Q2 of the data set: 24, 25, 29, 30, 31, 31, 32, 34, 34?
Answers
Answer:
31
Step-by-step explanation:
Median = middle number in terms of value
Usually the first step is to list the numbers in order from least to greatest however the numbers are already listed in order from least to greatest
24, 25, 29, 30, 31, 31, 32, 34, 34
We the just go to the middle number
The middle number would be 31
So we can conclude that the median is 31
Help meeeeeeeeeeeeeeeeeeeeee
Answers
Step-by-step explanation:
the answer is in the above image
use the app
WOLFRAM ALPHA it helps a lot
Answer:
[tex] \frac{1}{ 2^{1} } + \frac{1}{ {3}^{2} } + \frac{1}{ {4}^{3} } + \frac{1}{ {5}^{4} } + ... \\ \frac{1}{2} + \frac{1}{9} + \frac{1}{64} + \frac{1}{625} + ... \\ = \frac{226201}{360000} \\ = 0.6283..[/tex]
The base of a triangle is 9cm correct to the nearest cm.
The area of this triangle is 40 cm2 correct to the nearest 5 cm?.
Calculate the upper bound for the perpendicular height of this triangle.
Answers
Answer:
can you show the picture plz
Factor the expression completely. 28x2 + 20
Answers
Answer:76
Step-by-step explanation:
which exponential equation is equivalent to the logarithmic equation below? log478=a
A. 478^10 = a
B. a^10 = 478
C. 478^a = 10
D. 10^a = 478
Answers
If the measure of angle 2 Is (4x+10)degrees and the measure of angle 3 is (3x-5)degrees, what is the measure of angle 2 in degrees?
Answers
Answer:
110°
Step-by-step explanation:
4x+10 + (3x-5) = 180
7x + 5 = 180
7x = 175
x = 25
∠2 = 4(25) + 10 = 110
The measure of angle 2 in degrees, when both lines are perpendicular, is approximately 58.56 degrees.
To find the measure of angle 2 when the lines are perpendicular, we can set up an equation. Since the angles are formed by perpendicular lines, we know that the sum of angle 2 and angle 3 will be equal to 90 degrees. Mathematically, we can write this as:
(4x + 10) + (3x - 5) = 90
Now, let's solve the equation to find the value of x. First, combine like terms:
4x + 3x + 10 - 5 = 90
7x + 5 = 90
Next, isolate x by subtracting 5 from both sides:
7x = 85
Finally, divide by 7 to solve for x:
x = 85 / 7 ≈ 12.14
Now that we have the value of x, we can find the measure of angle 2 by substituting x back into its expression:
Angle 2 = 4x + 10
Angle 2 = 4(12.14) + 10
Angle 2 ≈ 48.56 + 10
Angle 2 ≈ 58.56 degrees
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a triangular prism is 37 millimeters long and has a triangular face with a base of 42 millimeters and a height of 28 millimeters.The other two sides of the triangle are each 35 millimeters.What is the surface area of the triangular prism?
No links pls
Answers
Answer: 4145.43
Have a great day! ;)
PLS HELP ASAP!
Shown below is a cylinder. Calculate the volume using 3.14 for π
Answers
Answer:
V = 678.24 cm^3
Step-by-step explanation:
Formula for volume of a cylinder:
the radius is half of the diameter (12/2 = 6)
[tex]V = \pi r^{2} h\\V = \pi 6^{2} 6\\\\V = 678.24[/tex] cm^3
Answer:
678.24 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
We know the diameter
r =d/2 = 12/2 = 6
V = 3.14 * 6^2 * 6
678.24 cm^3
kelly bought two dozen apples she found 1/3 of them were rotten how manu apples were rotten
Answers
the answer is 8 apples were rotten
Answer:
8 apples are rotten.
Step-by-step explanation:
2*12=24 . There are 12 apples in a dozen.
24/3=8
Maria has 24 dollars. If cokes are 3 dollars and
hotdogs are 4 dollars, which inequality represents the
possibilities of how she can spend the 24 dollars:
Answers
Answer:
do 24 divide 3
then 24-4
have maria debate if she wants large quantities of hot dogs or cokes
[tex]\frac{1+siny}{cos y}+\frac{cos y}{1+sin y}[/tex]
[tex]\frac{cot x}{tanx+cot x}=cos^2x[/tex]
csc^2θ·tan^2θ - 1 = tan^2θ
Answers
Step-by-step explanation:
a)
[tex] \frac{1 + \sin y}{ \cos y} + \frac{ \cos y}{1 + \sin y} = \frac{1 + 2 \sin y + \sin^{2} y + \cos ^{2} y}{ \cos y(1 + \sin y)} [/tex]
[tex] = \frac{2 + 2 \sin y}{ \cos y (1+ \sin y)} = \frac{2}{ \cos y} = 2 \sec y[/tex]
b)
[tex] \frac{ \cot x}{ \tan x + \cot x} = \frac{ \cos x}{ \sin x( \frac{ \sin x}{ \cos x} + \frac{ \cos x}{ \sin x} )} [/tex]
[tex] = \frac{ \cos x}{ \frac{ \sin^{2} }{ \cos x} + \cos x } = \frac{ \cos x}{ \frac{ \sin ^{2} x + \cos^{2} x}{ \cos x} } [/tex]
[tex] = \cos ^{2} x[/tex]
c) Note that cscx = 1/sinx so
[tex] \csc^{2} \theta \tan^{2} \theta - 1= \frac{1}{ \cos^{2} \theta } - 1[/tex]
[tex] = \frac{1 - \cos^{2} \theta }{ \cos \theta} = \frac{ \sin^{2} \theta}{ \cos ^{2} \theta } = \tan^{2} \theta[/tex]
A set of eight cards contains one joker. Player A chooses 5 cards at random,
Player B takes the remaining three cards. What is the probability that Player A has the joker?
Player A discards 4 cards and Player B discards two cards. It is known that the joker has not been discarded, what is the probability that Player A has the joker?
Answers
Answer:
56%
Step-by-step explanation:
because of the 56% it had to be true to be in the question at all.
ANSWER ASAP!! Use the substitution method to solve the system of equations. 3x+7y=1 and y=x-7
Answers
Answer:
x=5
y = -2
(5,-2)
Step-by-step explanation:
3x+7y=1 and y=x-7
Substitute the second equation in for y in the first equation
3x+7( x-7)=1
Distribute
3x+ 7x - 49 = 1
Combine like terms
10x - 49 =1
Add 49 to each side
10x-49+49 = 1+49
10x = 50
Divide by 10
10x/10 = 50/10
x = 5
Now find y
y = x-7
y = 5-7
y = -2
Use the listing method to write the following set \ 1,2,3\; [0, 1, 2, 3] O (1, 2)
Answers
Part
The number 3.14 is a rounded value of the mathematical quantity . If you replace 3.14 with 1, what is the exact formula for the circumference in
terms of the diameter, d, and in terms of the radius, r?
B IV x x
Font Sizes
А
E1 E2
Characters used: 0/15000
Submit
I need help
Answers
Answer:
C = 2(3.14)r
C = (3.14)d
Step-by-step explanation:
Circumference in terms of radius:
[tex]c \: = 2\pi \: r[/tex]
So replacing pi with 3.14 you would get 2(3.14)r
Circumference in terms of diameter:
[tex]c = d\pi[/tex]
So replacing pi with 3.14 you would get d(3.14)
Can somone help me solve this
Answers
Answer:
solid shade above
Step-by-step explanation:
graph line same way you would if it was an equal sign
all the y's that are greater are above the line
its solid because is greater than OR equal to. Equal to includes the line itself as a set of solutions
Insurance companies need to maintain a certain amount in reserved funds in order to pay anticipated claims. The average monthly claim amount for the last 60 months for company A was $7,500,000 and the (sample) standard deviation was $1,200,000.
(a) Find a 95% upper confidence bound on the average monthly claim amount.
(b) The regulations on the reserves will be strengthened in the near future. According to the new regulations, insurance companies that do not have sufficient amount in reserve will be subject to a significant penalty. Company A wants to adjust the target reserve amount accordingly, by computing a new upper bound on the average monthly claim amount. Should the company recalculate an upper confidence bound with a higher or a lower level of confidence? Briefly explain why. Then compute a 99.95% upper confidence bound on the average monthly claim amount.
Answers
Answer:
a ) Upper bound of CI is 7803483.87
b) The new upper bound is 8039767.74
Step-by-step explanation:
From sample data:
sample size n = 60
sample mean x = 7500000
Sample standard deviation s = 1200000
a) Confidence Interval 95 % then significance level α = 5 % o α = 0.05
α/2 = 0.025 z(c) from z-table is z(c) = 1.96
CI 95 % = ( x ± z(c) * s/√n
CI 95 % = ( 7500000 ± 1.96 * 1200000/√60
CI 95 % = ( 7500000 ± 303483.87 )
CI 95 % = ( 7196516.13 ; 7803483.87)
Then upper bound of CI is 7803483.87
b) The company has to decrease the significance level equivalent to widen the confidence interval.
If CI now is 99.95 % significance level is α = 0.0005 and
α/2 = 0.00025 z(c) for that α/2 is from z-table z(c) ≈ 3.486
CI 99.95 % = ( x ± z(c)*s/√n
CI 99.95 % = 7500000 ± 3.486*1200000/ √60
CI 99.95 % = (7500000 ±539767.74)
CI 99.95 % = ( 6960232.26 ; 8039767.74)
The new upper bound is 8039767.74
What is the order of rotational symmetry of this shape .for brainlest
Answers
Answer:
4.
Step-by-step explanation:
The orientation of the shape is the same 4 times during 360 degree turn.
Answer:
4
Step-by-step explanation:
Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.
)Which statement best describes the area of the triangle shown below?
A coordinate grid is shown with a triangle.. The base is 4 units, and the height is 4 units.
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is one-half the area of a square of side length 4 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a square of side length 4 units.
Answers
9514 1404 393
Answer:
(b) It is one-half the area of a square of side length 4 units.
Step-by-step explanation:
The triangle described can be formed by drawing the diagonal through a square 4 units on a side. Such a diagonal cuts the square cleanly in half, so the area of the triangle is half the area of the square.
Answer:
B
Step-by-step explanation:
Hope you have a nice day! :o)
Evaluate: (g + ƒ)(2)
Answers
From the graph,
g(2) = 4 ( from the coordinate (2,4))
[ The green line represent the function g(x)]
f(2)= 0
[ The red line represent the function f(x)]
(g + ƒ)(2) = g(2)+f(2) = 4+0 = 4
OPTION A is the correct answer
I need to solve for X Y and Z please and thank you
Answers
9514 1404 393
Answer:
x = 5y = 30z = 8Step-by-step explanation:
The rhombus has several relevant properties.
The sides are all the same lengthDiagonals are perpendicular bisectors of each otherDiagonals divide the rhombus into congruent trianglesThe last of these relations can be used to find x:
7x° = 35°
x = 35°/7° = 5
The second of the relations can be used to find y:
3y° = 90°
y = 90°/3° = 30
The first of the relations can be used to find z:
10z -8 = 5z +32
5z = 40 . . . . . . . . . add 8-5z
z = 40/5 = 8
Answer and I will give you brainiliest
Answers
Answer:
x = 60 degree
Step-by-step explanation:
90 + 90 + 2x - 10 + 2x + 2x + 10 = 540 degree (sum of 5 interior angles)
180 + 6x = 540
6x = 540 - 180
x = 360/6
x = 60 degree
What is the slope of the line described by the equation below?
y=-x+ 8
O A. -8
O B. -1
O C. 8
O D. 1
Answers
Answer:
-1
Step-by-step explanation:
See Image below:)
Answer:
-1
Step-by-step explanation:
Consider the following function:
f(3) = log2(x + 3)
Which interval has the smallest average rate of change in the given function?
O (0,2
O 4,6]
O [2,4
O (6,8)
Answers
In the function f(x) = log2(x + 3)), the smallest average rate of change in the function is in the interval, (6,8)
What is a logarithmic function ?The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.
Formulae for logarithmic function are,
LogAB = LogA + LogB
Logₐaᵇ = b
Given that,
A logarithmic function,
f(x) = = log2(x + 3)
Rate of change = Change in values of function/change in x
= [F(b) - F(a)]/ b-a
For the interval, (0, 2)
f(0) = Log2(0 + 3) = Log(6)
f(2) = Log2(2 + 3) = Log(10)
Rate of change = Log(10) - Log(6) /2
= 0.11
Similarly, for the intervals, (4, 6), (2, 4), (6,8)
Hence, the smallest average rate is for the interval, (6, 8)
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1;3;5;7…(determine the value of the 19th term of the sequence)
Answers
Answer:
37
Step-by-step explanation:
fistly find how much different
3-1=2 5-3=2 7-5=2
so for the next and next value just plus two until the 19th then you will get 37
=============================================================
Explanation:
a = 1 is the first term
d = 2 is the common difference, since we add 2 to each term to get the next term.
The nth term is a+d(n-1) which becomes 1+2(n-1). That simplifies to 2n-1
The last step is to plug in n = 19 and you should get 2(19)-1 = 37
what is the largest six-digit base five number? How do you know?
Answers
Answer:
999999.9>repeating
Step-by-step explanation:
.1 more and it will be 7 digits and not 6 Hope this helps :D
9514 1404 393
Answer:
444444₅ = 15624₁₀
Step-by-step explanation:
It will be 1 less than the smallest 7-digit base-5 number. That number is 5^6 = 15625, so the largest 6-digit base 5 number is 15624 in decimal. In base 5, it is 6 of the largest base-5 digits:
444444₅ = 15624₁₀
__
The digits of the number cannot be any larger than the largest base-5 digit. The base-5 digits are 0 to 4, so the largest is 4.
I need help plzzz
How can you construct the perpendicular bisector of segment RS by folding a piece of paper
Answers
9514 1404 393
Answer:
(c) fold it so R lies on top of S
Step-by-step explanation:
The crease will be the perpendicular bisector of RS when R and S are equidistant from it. That can be accomplished by folding the paper so points R and S lie on top of each other.
Will Mark Brainlest Help pls
Answers
Answer:
13
HOPE THIS HELPS YOU......
