Answer: Liz, she is 5 units away from Robbert.
Step-by-step explanation:
Ok, the data that we have is:
Robert is at (4,3 )
Lucy is at (6, 1)
Liz is at (1, 7)
We want to find the units between Robert and the person that is farther away from him.
The distance between Robert and Lucy can be calculated as:
First we calculate the difference in the point or in the position vector:
(4, 3) - (6, 1) = (4 - 6, 3 - 1) = (-2, 2)
To calculate the exact distance, we need to calculate the magnitude of this point, this is:
For a point (x, y), the magnitude is M = √(x^2 + y^2)
Then we have:
D = √( (-2)^2 + 2^2) = √8
Now, the distance between Robert and Liz can be calculated in the same way:
(4, 3) - (1, 7) = (4 - 1, 3 - 7) = (3, -4)
The magnitude is:
D = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5
Now, we know that 5 > √8
Then the person that is farthest away from Robert is Liz, and she is 5 units away.
what is a possible solution to the inequality?
1/4a +1 > 9
Answer:
a > 32 is one possible solution to the inequality 1/4a +1 > 9.
Step-by-step explanation:
Na função y = x² - 2x +1, temos que a = 1, b = -2 e c = 1, calcule as coordenadas do vértice da parábola
Answer:
(1, 0)
Step-by-step explanation:
x = -b / 2a
x = 2 / 2(1)
x = 2 / 2
x = 1
y = x^2 - 2x + 1
y = (1)^2 - 2(1) + 1
y = 1 - 2 + 1
y = -1 + 1
y = 0
vértice: (1, 0)
If tanx+cotx=2 then Cosx =?
Answer:
sqrt(2)/2
Step-by-step explanation:
tan(x) and cot(x) are both 1 when x=pi/4 and since 1+1=2, then we just need to evaluate cos(pi/4) which equals sqrt(2)/2.
What is the distance between the points (5,1) and (-3,-5)?
Answer
[tex] \boxed{10 \: \: units}[/tex]
Step by step explanation
Let the points be A and B
A ( 5 , 1 ) ⇒ ( x₁ , y₁ )
B ( -3 , -5 )⇒ ( x₂ , y₂ )
Now, let's find the distance between theses two points:
Distance = [tex] \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]
Plug the values
[tex] \mathsf{ \sqrt{ {( - 3 - 5)}^{2} + {( - 5 - 1)}^{2} } }[/tex]
Calculate
[tex] \mathsf{ \sqrt{ { ( - 8)}^{2} + {( - 6)}^{2} } }[/tex]
Evaluate the power
[tex] \mathsf{ \sqrt{64 + 36} }[/tex]
Add the numbers
[tex] \mathsf{ \sqrt{100} }[/tex]
Write the number in exponential form with a base of 10
[tex] \mathsf {\sqrt{ {10}^{2} } }[/tex]
Reduce the index of the radical and exponent with 2
[tex] \mathsf{10 \: units}[/tex]
-------------------------------------------------------------------------------
The distance formula is used to determine the distance ( d ) between two points. If the co-ordinates of the two points are ( x₁ , y₁) and ( x₂ , y₂ ) , the distance equals the square root of x₂ - x₁ squared + y₂ - y₁ squared.
Hope I helped!
Best regards!
The value of y varies directly with x, where LaTeX: y=50y = 50 when LaTeX: x=40x = 40. Find the value of x when y is 10.
Group of answer choices
LaTeX: x=8 x = 8 x = 8 x = 8 x = 8 x = 8 x = 8 x = 8
LaTeX: x=12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5
LaTeX: x=1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25
LaTeX: x=0
Answer:
x= 8
Step-by-step explanation:
The equation of direct variation is
y = kx
When y = 50 when x = 40
50 = k* 40
Divide each side by 40
50/40 = k
5/4 = k
The equation is
y = 5/4x
Let y = 10
10 = 5/4x
Multiply each side by 4/5
4/5 * 10 = 5/4 x * 4/5
8 = x
A new scooter is valued at $15 000.
At the end of each year its value is reduced
by 15% of its value at the start of the year.
What will it be worth after 3 years?
here
p= 15000
r=15%
t= 3 yrs
now
depreciation = p(1-r/100)^t
= 15000(1-15/100)^3
=9211.875
=9212 or 9211.88
AABC is reflected across the x-axis and then translated 4 units up to create AA'BC. What are the coordinates of the vertices of AABC?
OA A'(-3, 3), B(-1, 1). C(-2.3)
ОВ.
A'(3.-3), B(1,-1), C(2.-3)
OC. A'(3.-5), B(1, -7), C(3.-5)
OD. A'(-3, 3), B(-1, 1), C(-2,-
Answer:
A
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
A(- 3, 1 ) → (- 3, - 1 )
B(- 1, 3 ) → (- 1, - 3 )
C(- 2, 1 ) → (- 2, - 1 )
A translation of 4 units up means adding 4 to the y- coordinate
( - 3, - 1 ) → A' (- 3, - 1 + 4 ) → A' (- 3, 3 )
(- 1, - 3 ) →B' (- 1, - 3 + 4 ) → B' (- 1, 1 )
(- 2, - 1 ) → C' (- 2, - 1 + 4 ) → C' (- 2, 3 )
PLEASE HELP! Simplify 2x^2+4xy+2y^2
Answer:
(x+y)(2x+2y)
Step-by-step explanation:
=2x^2 + 2xy + 2xy + 2y^2
=2x(x+y) + 2y(x+y)
=(x+y)(2x+2y)
3.1x^3-2.4x² +6x – 3 = 4x² + 3x +2
solving problem
Answer:
The roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2, are;
x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i
Step-by-step explanation:
The given equation is 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2
Which gives;
3.1·x³ - 2.4·x²+ 6·x - 3 - 4·x² - 3·x - 2 = 0
3.1·x³ - 6.4·x²+ 3·x - 5 = 0
Factorizing online, we get;
3.1·x³ - 6.4·x²+ 6·x + 3·x - 5 = 3.1·(x - 1.986)·(x² - 0.0784·x + 0.812) = 0
Therefore, the possible solutions are;
x - 1.986= 0 or x² - 0.0784·x + 0.812 = 0
The roots of the equation are x² - 0.0784·x + 0.812 = 0 are;
x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i
Therefore, the roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2, are;
x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i.
A hiker starts walking due west from Sasquatch Point and gets to the Chupacabra Trailhead before she realizes that she hasn't reset her pedometer. From the Chupacabra Trailhead she hikes for 8 miles along a bearing of N27°W which brings her to the Muffin Ridge Observatory. From there, she knows a bearing of S38°E will take her straight back to Sasquatch Point. How far will she have to walk to get from the Muffin Ridge Observatory to Sasquach Point, to the nearest tenth of a mile?
Answer:
9.05 mile
Step-by-step explanation:
From the information given :
Let represent S for Sasquatch Point
Let C represent Chupacabra Trailhead
Let M represent Muffin Ridge Observatory
The diagram for the bearing of the information given can be seen in the attached file below.
At angel C = 90° -27° = 63°
The Alternate angles are shown in the second diagram below.
In order to determine the distance she will have to walk from the Muffin Ridge Observatory to Sasquatch Point, we use the sine formula:
[tex]\mathtt{\dfrac{sin \ C }{c} = \dfrac{sin \ S}{s}}[/tex]
[tex]\mathtt{\dfrac{sin \ 63 }{c} = \dfrac{sin \ 52}{8}}[/tex]
By cross multiply
8 × sIn 63 = c× sin 52
[tex]\mathtt{c = \dfrac{8 \times Sin 63}{Sin \ 52}}[/tex]
[tex]\mathtt{c = \dfrac{7.1281}{0.7880}}[/tex]
c = 9.0458 mile
c [tex]\simeq[/tex] 9.05 mile to the nearest tenth
1. Find the measure of angle R.
Answer:
the first option 40 degrees
Step-by-step explanation:
the outward angle at the center of the circle between the two tangential points is 220 degrees.
that means that the inward angle between them is
360 - 220 = 140 degrees.
now consider that there is a triangle between the center of the circle, one of the tangential points (it does not matter which one, as the upper and the lower triangles are equal) and the point R.
we know the angle at the tangential point : 90 degrees by definition (otherwise it would not be a tangent).
and we know the angle at center of the circle, which is half of the inward angle
140 / 2 = 70 degrees.
and at point R we have half of the full angle R.
we can calculate that half by using the fact that the sum of all angles in a triangle is always 180 degrees.
180 = 90 + 70 + R/2
180 = 160 + R/2
20 = R/2
R = 40 degrees
If the production rate is 975 brownies per hour at a bakery, how many brownies will be produced in an 8 hour shift?
Answer:
[tex]\large \boxed{\mathrm{7800 \ brownies}}[/tex]
Step-by-step explanation:
975 brownies are produced per 1 hour.
To find how many brownies are produced in 8 hours, multiply the brownies amount by the hours.
975 × 8 = 7800
7800 brownies will be produced in an 8 hour shift.
Answer:
the answer is 7800
Step-by-step explanation:
975 brownies are created per 60 minutes.
To discover what number of brownies are created in 8 hours, duplicate the brownies sum continuously.
975 × 8 = 7800
7800 brownies will be created in a 8 hour move.
The circumference of a circular garden is 106.76 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer.
Answer:
Step-by-step explanation:
The circumference formula is
C = 2πr. If we are solving the for the radius, and we are using 3.14 for π, we can fill in accordingly:
106.76 = 2(3.14)r and
[tex]\frac{106.76}{2(3.14)}=r[/tex] so
r = 17
for the function g(x)=3-8(1/4)^2-x
a) State the y-intercept
b) State the equation of the horizontal asymptote
c) State whether the function is increasing or decreasing.
d) State the domain and range
e) Sketch the graph
Could anyone help?
Using function concepts, it is found that:
a) The y-intercept is y = 2.5.b) The horizontal asymptote is x = 3.c) The function is decreasing.d) The domain is [tex](-\infty,\infty)[/tex] and the range is [tex](-\infty,3)[/tex].e) The graph is given at the end of the answer.------------------------------------
The given function is:
[tex]g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}[/tex]
------------------------------------
Question a:
The y-intercept is g(0), thus:
[tex]g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5[/tex]
The y-intercept is y = 2.5.
------------------------------------
Question b:
The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.
[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3[/tex]
--------------------------------------------------
[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty[/tex]
Thus, the horizontal asymptote is x = 3.
--------------------------------------------------
Question c:
The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.
--------------------------------------------------
Question d:
Exponential function has no restrictions in the domain, so it is all real values, that is [tex](-\infty,\infty)[/tex].From the limits in item c, the range is: [tex](-\infty,3)[/tex]--------------------------------------------------
The sketching of the graph is given appended at the end of this answer.
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State for me GENERAL FORMULA in mathematics
Answer:
"General Formulas" in mathematics is the general equation you can use for certain things, by just adding the numbers given to the equation so that you can solve the problem.
Form example:
The general formula to find the y-intercept: y=mx+b
Hope this helped!
Have a nice day:)
Answer:
"General Formulas" in mathematics is the general equation you can use for certain things, by just adding the numbers given to the equation so that you can solve the problem.
Step-by-step explanation:
3. Which property of similarity can be used to prove triangles STR and VWU are similar?
Answer:
Not enough information
Step-by-step explanation:
Similar triangles must have congruent corresponding angles and proportional corresponding sides.
Answer:
not enough information
Step-by-step explanation:
Julio wants to solve the system shown using the elimination method. Which is the best way to begin?
(x - 12y = 2
-4x + 7y = 12
Add the equations
b. Multiply each term in x - 12y = 2 by 4 and add it to the other original equation.
This system of equations has no solution, so Julio should not do anything.
d. Multiply each term in x - 12y = 2 by 4 and add it to the other original equation.
c.
Answer:
B. Multiply each term in x - 12y = 2 by 4 and add it to the other original equation.
Step-by-step explanation:
The expression are two linear equation and can be solved simultaneously
[tex]x - 12y = 2------------------1[/tex]
[tex]-4x + 7y = 12----------------------2[/tex]
1. we need to multiply each term in eqn 1 by 4 and add it to the other
original equation(2).
[tex]4x - 48y = 8----------------3\\-4x + 7y = 12---------------2\\\\[/tex]
Adding both 3 and 2 we have
[tex]4x - 48y = 8----------------3\\-4x + 7y = 12---------------2\\\\\\[/tex]
2. once we have gotten the value of y
we then substitute it in any of the equations to solve for x
(05.01) A window is 4 feet and 8 feet tall. A manufacturer wants to use a scale factor of 1.5 to enlarged a window. What will the area of the wind will be after it is enlarged?
Answer:
the window would be 72ft²
Step-by-step explanation:
A window is rectangular in shape.
the area of a rectangle is give as length * breadth
but this question say that the manufacturer wants to enlarge the window by 1.5
therefore we are going to multiply the length by 1.5 and the breadth also by 1.5 to get the new area of the bigger window.
length = 8 * 1.5
= 12
width = 4 * 1.5
= 6
The new area would be = l * b
= 12 * 6
= 72ft²
Round 96.1825899389 to 4 decimal places.
Which angle in ABC has the largest measure?
A.
B.
C.
D. Cannot be determined
Answer:
< B has the largest angle measure.
as it is opposite to longest side of triangle.
Under what condition the composite function of any two function is an identity function?
Answer:
under the condition of f(x)=x composite function is an identity one
The perimeter of a rectangle is 18cm . if the length is (x+2), find it's width.
Answer:
W = 7 - x
Step-by-step explanation:
The perimeter is P= 2L + 2×W , where L is the length and W is the width.
If L = (x+2) , replacing L with the expression x+2 we have
P= 2×(X+2) + 2W ⇔ 18 = 2x + 4 + 2W ⇔ 2W =18 - 2x - 4 ⇔ 2W = 14 - 2x
⇔ W = 7 - x
Nate is creating a PSA about building a "green” roof. Which source is most reliable for his research? a blog post written by a community gardener a .com website that advertises fertilizer a .gov or .org website about ecological roofs a book featuring photos of different styles of roof
Answer:
Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of room because
1. It specifically talks about green roof's
2. Unlike the blog post, the .org/.gov is not attempting to sell a product that may change how the article is written.
Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of rooms because It talks explicitly about green roofs.
What is a survey?A survey is research done by any company or an organisation on the group of people or their activity or on any other data like their sells etc to find out the valuable information from that data.
Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of rooms.
1. It specifically talks about green roofs
2. Unlike the blog post, the .org/.gov is not attempting to sell a product that may change how the article is written.
Therefore Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of rooms because It talks explicitly about green roofs.
To know more about surveys follow
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the product of a number and five is eight
Answer:
Assuming x is the number, then [tex]x=1.6[/tex]
Step-by-step explanation:
If the product of a number and 5 is 8, the equation becomes:
[tex]5x=8[/tex] (assuming x is the unknown number).
We can isolate the variable x by dividing both sides by 5.
[tex]5x\div5 = 8\div5\\x = 1.6[/tex]
Hope this helped!
The focus of a parabola is (3,-7) and the directrix is y = -4.
What is an equation of the parabola?
Answer:
(a) (x -3)^2 = -6(y +5.5)
Step-by-step explanation:
The equation of a parabola can be written as ...
(x -h)^2 = 4p(y -k)
where (h, k) is the vertex, and p is the distance from the focus to the vertex.
The vertex is half-way between the focus and directrix, so is ...
(h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)
The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...
-7 -(-5.5) = -1.5
Then the equation for the parabola is ...
(x -3)^2 = 4(-1.5)(y -(-5.5))
(x -3)^2 = -6(y +5.5) . . . . matches the first choice
help w−3/4=8 a) 5 b) 35 c) 29 d) -1
Answer:
w = 35/4
im not exactly sure why the options are whole numbers.
Step-by-step explanation:
8 = w-3/4
-w + 8 = -3/4
-w = -3/4 - 8
-w = -3/4 - 32/4
-w = -35/4
w = 35/4
Simplify 4 to the 2nd power times 4 to the eighth power 
A. 4 to the 16th power
B. 4 to the 10 power
C. 16 to the 16 power
D. 16 to the 10 power
Please help ASAP!!!!!!!!
Answer:
4 to the power of 10.
Step-by-step explanation:
A rule is that x to the power of y + x to the power z of must equal x to the power of z+y.
Answer:
Option B
Step-by-step explanation:
4²×4^8
4^(2+8)
4^10
4 to the 10th power
Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What are all the possible lengths TO? Enter the possible values, separated by commas.
===========================================
Explanation:
Refer to the diagram below.
In order for triangle TOP to be isosceles, the missing side x must be either 5 or 7. This way we have exactly two sides that are the same length.
--------
If TP = 5, then the value of y could be either 5 or 11 to ensure that triangle TIP has exactly two sides the same length.
If TP = 7, then y = 7 or y = 11 for similar reasons.
--------
Therefore, the possible lengths for segment TO are 5, 7, and 11.
Answer:
7, 11
Step-by-step explanation:
its right- trust me-
help with geometry pls
Answer:
option 2 must be the correct answer because the two figure are congruent figure.
Answer:
B
Step-by-step explanation:
Since Δ ABC ~ Δ DEF then the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{DE}[/tex] = [tex]\frac{BC}{EF}[/tex] = [tex]\frac{CA}{FD}[/tex] → B
Identify the segments that are parallel, if any, if ∠KCB≅∠JAC.
The two lines are parallel if they are at same distant, but these lines will never meet at any point.
Parallel lines do not intersect each other. These lines are equidistant from each other.
In the given angles the line CB will be parallel to line AC.
CB ≅ AC
These two lines will be equidistant from each other since they both form an equivalent angle. These lines will not intersect with each other.
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