Answer:
The coordinate of b = (2, 2)
Step-by-step explanation:
The details of the quadrilateral abcd are;
The quadrilateral is symmetric about the y-axis (the line x = 0)
The coordinates of the vertices are; a(-2, 2), c(2, 1)
The location of the vertex, b = The first quadrant
We have;
The line [tex]\overline {ab}[/tex] is perpendicular to the line [tex]\overline {bc}[/tex]
Let (x, y) represent the coordinate of the vertex b, we have;
(y - 2)/(x - (-2)) = (y - 2)/(x + 2) = -1/(y - 1)/(x - 2) = - (x - 2)/(y - 1)
(y - 2)·(y - 1) = -(x + 2)·(x - 2)
y² + x² - 3·y - 2 = 0...(1)
y² + x² = 3·y + 2
Also we have;
(y - 2)² + (x - 1)² + (y - 2)² + (x - (-2))² = (2 - 1)² + (2 - (-2))² = 17
Therefore;
2·y² + 2·x² - 8·y + 2·x + 13 = 17
2·(3·y + 2) - 8·y + 2·x + 13 = 17
Using an online tool, we have;
x = y
From equation (1), we have;
2·y² - 3·y - 2 = 0
∴ y = 2, or y = -1/2
Where y = 2, we have;
x = y = 2
Therefore, the point b = (2, 2).
x + 3x/2 = 35. Find x.
[tex]\large\sf \: x + \frac{3x}{2} = 35[/tex]
Find x
________________
[tex]\sf \: x + \frac{3x}{2} = 35 \\ \sf \: \frac{x}{1} + \frac{3x}{2} = 35 \: (take \: LCM \: = 2) \\ \sf \: \frac{2x}{2} + \frac{3x}{2} = 35 \\ \sf \: \frac{2x + 3x}{2} = 35 \\ \sf \: 2x + 3x = 35 \times 2 \\ \sf \: 5x = 70 \\ \sf \: x = \frac{70}{5} \\ \sf \: x = \boxed{ \underline{ 14}}[/tex]
_________________
Answer ⟶ [tex]\boxed{\bf{x= 14}}[/tex]
last question. 50 points!
w=-1.5
w=2
Answer:
Solution given:
[tex]\sqrt{2w²-19w+31}+2=7-2w[/tex]
again
keep square root alone
[tex]\sqrt{2w²-19w+31}=7-2w-2[/tex]
solve subtraction of 7-2
[tex]\sqrt{2w²-19w+31}=5-2w[/tex]
Squaring on both side
[tex](\sqrt{2w²-19w+31})²=(5-2w)²[/tex]
2w²-19w+31=5²-2*5*2w+4w²
take terms one side
2w²-19w+31-25+20w-4w²=0
-2w²+w+6=0
2w²-w-6=0
doing middle term factorisation
2w²-(4-3)w-6=0
2w²-4w+3w-6=0
take common from each two term
2w(w-2)+3(w-2)=0
(w-2)(2w+3)=0
either
w=2
or
W=-3/2=-1.5
find the value of 2/5 - 3
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
[tex]\sf{\dfrac{2}{5}-3 }[/tex] [tex]\sf{\dfrac{2-10}{5} }[/tex] [tex]\sf{\dfrac{-8}{5} }[/tex][tex]\sf{ }[/tex]
In the xv-plane, the line determined by the
points (2,k) and (k, 32) passes through the origin.
Which of the following could be the value of k ?
Answer:
8
Step-by-step explanation:
If the diagonal line passes through the origin, that means it is proportional. That means that for every point on the line y/x is constantly the same value. So we have k/2=32/k.
Cross multiply: k^2=64
Square root both sides: k=8
Jeanette wants to raise $3,200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
Total amount she wants to raise = $3200
Amount she'll get for each kilometer = $35
So, number of kilometers she need to run
= Total amount she wants to raise/Amount she'll get for each kilometer
= $3200/$35
= 91.42....
Since her sponser is will donate only for whole kilometers she'll have to run 92 km.
How do I find this? Please help.
Answer:
a.) r = 60ft
b.) ball_distance = 68ft
Step-by-step explanation:
Use Pythagorean theorem:
(r^2) + (32ft)^2 = (r + 8ft)^2
r^2 + 1024sqft = r^2 + (16ft)×r + 64sqft
960sqft = r×(16ft)
(960sqft) / (16ft) = r
r = 60ft
Radius is green. Ball is 8ft further than green. 68ft.
what is the domain of the function is this table?
Answer:
B
Step-by-step explanation:
Domain is the set of x values
Looking at the table we can say that the set of x values ( domain ) is {1,2,3,4}
Find the measure of the missing angle using the triangle angle sum theorm.
Answer:
20 degrees
Step-by-step explanation:
One angle is 70 degrees and the other is 90. Angles of a triangle add up to 180. 180 - 70 - 90 = 20. The final angle is 20 degrees.
write a expression to represent 6 fewer then the quotient of 8 and a number
Answer:
8/x-6
Step-by-step explanation:
When it says a number fewer, that means to put it behind rather than in the front.
Hope this helps!!:)
Answer:
The expression to represent the phrase is 8/x - 6.
Dilate the figure by the scale factor. Then enter
the new coordinates.
A(1,3)
B(4,2)
K=3
A'([?],[ ]
B'([ ],[])
c'[[)
C(1,-3)
Answer:
i think (4,2)
Step-by-step explanation:
Point A is the incenter of △PQR. Find each measure
Answer:
[tex]\angle ARU=40^{\circ}[/tex]
AU=20 units
[tex]m\angle QPA=35^{\circ}[/tex]
Step-by-step explanation:
We are given that
[tex]\angle ARQ=40^{\circ}[/tex]
AT=20 units
Point A is the incenter of triangle PQR.
Incenter is that point where three angle bisector of triangle meets.
AR is the bisector of angle R of triangle PQR.
Therefore, [tex]\angle ARQ=\angle ARU=40^{\circ}[/tex]
All right triangles are similar when two triangles are similar then the ratio of their corresponding sides are equal.
Right angled triangle ATP and Right triangle AUP are similar.
Therefore,
[tex]\frac{AT}{AU}=\frac{AP}{AP}=1[/tex]
[tex]\frac{20}{AU}=1[/tex]
[tex]AU=20[/tex]units
AP is the angle bisector of angle P of triangle PQR
[tex]\angle APQ=\angle APU[/tex]
[tex]3x+2=4x-9[/tex]
[tex]2+9=4x-3x[/tex]
[tex]x=11[/tex]
Using the value of angle x
[tex]\angle APQ=3x+2=3(11)+2[/tex]
[tex]\angle APQ=35^{\circ}[/tex]
Hence, the measure of angle QPA=35 degree
The incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle. This point is equidistant from the sides of a triangle.
Angle ARU = 40 degree
Length of AU = 20
Angle QPA = 35 degree
Here a figure is attached.
Since, AR is angle bisector of angle URK.
So, ∠ARU = ∠ARK = 40 degree
Since, incenter point is equidistant from the sides of a triangle.
So, AT = AU = AK = 20
Since, PA is angle bisector of angle QPU.
So, ∠QPA = ∠UPA
3x + 2 = 4x - 9
4x - 3x = 9 + 2
x = 11
Substituting value of x in angle 3x + 2
We get, ∠QPA = 3(11) + 2 = 35 degree
Learn more:
https://brainly.com/question/1620555
Identify the transformations of the graph of f(x) = x3 that produce the graph of the given function
g(x). Then graph g(x) on the same coordinate plane as the graph of f(x) by applying the
transformations to the reference points (-1,-1),(0,0), and (1,1).
Answer:
Step-by-step explanation:
Find the value of x. Write your answer in simplest form. WILL MAKE BRAINLIEST
============================================
Explanation:
Since we have an isosceles right triangle, the the length of the hypotenuse (let's call it y) is equal to sqrt(2) times the leg length x.
In other words, [tex]y = x*\sqrt{2}[/tex]
If we replaced y with 3*sqrt(2), then we could say,
[tex]y = x*\sqrt{2}\\\\3\sqrt{2} = x*\sqrt{2}[/tex]
in which we can see that x = 3 must be the case. Or you could divide both sides of that last equation by sqrt(2) to find x = 3.
-------------------------
Another method:
We'll use the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\x^2+x^2 = \left(3\sqrt{2}\right)^2\\\\2x^2 = 3^2*\left(\sqrt{2}\right)^2\\\\2x^2 = 9*2\\\\2x^2 = 18\\\\x^2 = 18/2\\\\x^2 = 9\\\\x = \sqrt{9}\\\\x = 3\\\\[/tex]
We get the same answer as before.
At the bulk food store, Jerry bought 200 g of mixed nuts that cost $2.50.
What is the price of 450 g of nuts show ur work pls lol
Given:
Cost of 200 g of mixed nuts = $2.50.
To find:
The price of 450 g of nuts.
Solution:
We have,
Cost of 200 g of mixed nuts = 2.50 dollars
Cost of 1 g of mixed nuts = [tex]\dfrac{2.50}{200}[/tex] dollars
Cost of 450 g of mixed nuts = [tex]\dfrac{2.50}{200}\times 450[/tex] dollars
= [tex]\dfrac{2.50}{4}\times 9[/tex] dollars
= [tex]5.625[/tex] dollars
Therefore, the price of 450 g of nuts is $5.625.
Given the following equation where A = Area of a rectangle and w = width of the rectangle, what value of 'w' would maximize the area?
A = LW
P = 2L+2W
P = 100
w should be 625 units
w should be 25 units
w should be 0 units
w should be 50 units
Answer:
the second option : w should be 25 units
Step-by-step explanation:
the area of the rectangle is length×width = L×W
the perimeter of a rectangle = 2L + 2W
now, we know that the perimeter is 100 units.
and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.
in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?
now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.
W = 0 would render the whole rectangle to a flat line with L = 50 because of
100 = 2L + 2W = 2L + 0 = 2L
L = 50
and A = L×W = 50×0 = 0
an area of 0 is for sure not the largest possible area.
w = 50 would cause L = 0
100 = 2L + 2W = 2L + 2×50 = 2L + 100
0 = 2L
L = 0
and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.
so, the only remaining useful answer is W = 25
100 = 2L + 2W = 2L + 2×25 = 2L + 50
50 = 2L
L = 25
A = L×W = 25×25 = 625 units²
and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.
Which of the following exponential functions represent the graph?
Answer:
dodndbdie9ejrnfudowp2ejdnsmwo2oeidndndoep
The system of equations shown below is graphed on a coordinate grid:
3y + x = 4
2y − x = 6
Which statement is true about the coordinates of the point that is the solution to the system of equations?
A. It is (−2, 2) and lies on both lines.
B. It is (−5, 3) and lies on both lines.
C. It is (−5, 3) and does not lie on either line.
D. It is (−2, 2) and does not lie on either line.
Please help asap!! WILL GIVE BRAINlIEST!! tysssm if u help!!!
Answer:
add 2 equations given
3y+x+2y- x = 10
5y =10
y = 2
find x using the value of y
x = - 2
these values of x and y are can satisfy both equations .so (-2,2) lies on both lines
Can someone help me with this math homework please!
Answer:
The answers are options A and C.
They are (-2,0) and (0,0).
Step-by-step explanation:
x-intercept
(-2,0) and (0,0)
Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level
Answer:
It must be a positive number since it represents a number of hours.
Step-by-step explanation:
Given Pieter's equation :
7h – 5(3h – 8) = –72
Opening up the bracket
7h - 15h + 40 = - 72
7h - 15h = - 72 - 40
-8h = - 112
Divide both sides by -8
-8h / -8 = - 112 / - 8
h = 14
Since, h represents the number of hours, and the value of h equals 14 (h cannot be negative), hence, option 2 is correct.
Answer:
B.It must be a positive number since it represents a numbers of hours.
Step-by-step explanation:
Which of the following is the equation of a line that passes through the point
(1.4) and is parallel to the x-axis?
A.x=1 B.y=4 C.x=4 D.y=1
Given:
A line passes through the point (1,4) and is parallel to the x-axis.
To find:
The equation of the line.
Solution:
If a line is parallel to x-axis, then the line is a horizontal line. We know that the slope of a horizontal line is always 0. So, the slope of the required line is 0.
The point-slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is the slope and [tex](x_1,y_1)[/tex] is the point.
The slope of the required line is 0 and it passes through the point (1,4). So, the equation of the line is:
[tex]y-4=0(x-1)[/tex]
[tex]y-4=0[/tex]
[tex]y-4+4=0+4[/tex]
[tex]y=4[/tex]
The required equation is [tex]y=4[/tex].
Therefore, the correct option is B.
Chris and Josh have a total of 1,800 stamps in their collections, Josh and Jessica have a total of 2,200 stamps, and Jessica and Chris have a total of 2,000. How many stamps in all the three children have?
Answer: 3000 stamps
Step-by-step explanation:
Given
Chris and Josh have 1800 stamps
Josh and Jessica have 2200 stamps
Jessica and Chris have 2000 stamps
Suppose Chris, Josh, and Jessica have [tex]x,y, \text{and}\ z[/tex] stamps
[tex]\therefore x+y=1800\quad \ldots(i)\\\Rightarrow y+z=2200\quad \ldots(ii)\\\Rightarrow z+x=2000\quad \ldots(iii)\\\text{Add (i), (ii), and (iii)}\\\Rightarrow 2(x+y+z)=1800+2200+2000\\\Rightarrow x+y+z=3000[/tex]
Thus, all three have 3000 stamps
Mind helping if you have time on your hands that is
Answer:
C. 2%
Step-by-step explanation:
when you have a decimal and are looking for the percentage, simply move the decimal two places to the right. so .0201= 2%
Answer: C. 2%
Step-by-step explanation:
STEP ONE: Convert the decimal into a percentage
Percentage = Number × 100%
Percentage = 0.0201 × 100%
Percentage = 2.01%
STEP TWO: Round to the nearest ones
2.01% ≈ 2%
Hope this helps!! :)
Please let me know if you have any questions
Show that 4^(x+2)+4^(x+1)+4^x is divisible by 7 for all positive integers of x.
Answer:
Below.
Step-by-step explanation:
4^(x+2)+4^(x+1)+4^x
= 4^x*4^2 + 4^x*4 + 4^4
= 4^x(16 + 4 + 1)
= 21*4^x.
As 21 is divisible by 7, 21*4^x is also divisible by 7 for all positive integers of x.
Thus the original expression must be also divisible by 7 for all positive integers of x.
Find the missing segment in the image below
Answer:
If there are two line which is parallel in a triangle the triangle has a ratio
Step-by-step explanation:
So we can see one side has 6cm and 4cm length. and other side has 20cm in totally. But we know that the small line divided the side with 6/4 ratio and we can say ?=12 and other is 8
Answer:
Step-by-step explanation:
American airlines requires that total outside dimensions (length+width+height) of a checked bag not exceed 62 inches.Suppose you want to check a bag whose height is same as its width.What is the biggest volumn bag of this shape that you can check on an american flight
Answer:
The maximum volume is 35316.4 in^3.
Step-by-step explanation:
Length + width + height is less than equal to 62 inches
Height = width = W
Let the length is L .
[tex]L + W + W = 62 \\\\L= 62 - 2 W\\\\Volume, V = L W H\\\\V = (62 - 2 W)\times W \times W\\\\V = 62 W^2 - 2 W^3\\\\\frac{dV}{dW}=124 W - 6 W^2\\\\So, \frac{dV}{dW} =0\\\\124 = 6 W\\\\W = 20.67 inches[/tex]
So, the maximum volume is
[tex]V =124\times 20.67\times 20.67 - 2 \times 20.67^3\\\\V =52978.86 - 17662.46 = 35316.4 inch^3[/tex]
Help Pleaseeee!!!!!!!
Find the volume of a sphere with radius of 9cm
Answer:
3053.63
Step-by-step explanation:
Not sure how to explain-
but i hope it helps c:
Graph the function f(x) = - squared x + 2
One of the ways to graph this is to use plug in a few x-values and get an idea of the shape. Since the x values keep getting squared, there is an exponential increase on either side of the y-axis. You can see this by plugging in a few values:
When
x=0,f(x)=0
x=1,f(x)=1^2=1
x=2,f(x)=2^2=4
x=3,f(x)=3^2=9
x=4,f(x)=4^2=16
The same holds true for negative x-values to the left of the y-axis since a negative value squared is positive. For example,
x=−1,f(x)=(−1)2=1*−1=1
x=2,f(x)=(−2)2=−2*−2=4
The graph of f(x)=x^2 is called a "Parabola." It looks like this:
The scale of a map is 1:40000. What distance on the map represents a real distance of 5km?
Answer:
0.125
Step-by-step explanation:
1=40000
x-5000
x=5000÷40000=1/8=0.125
Find the interior angle sum for the following polygon
Answer:
140 degrees
Step-by-step explanation:
(n-2) times 180
9-2 times 180
7 times 180
1260
1260/9 = 140
Interior angle sum of the given regular polygon of 9 sides is 1260°.
A regular polygon is a closed figure where all sides are equal. Interior angles of a regular polygon are the angles formed between the edges of the polygon. The formula for calculating the sum of interior angles of a regular polygon = (n-2) * 180
where, n is the number of sides of a regular polygon.
Number of sides in the regular polygon = 9
n = 9
Sum of interior angle of the regular polygon =
(n-2) * 180 = (9-2) * 180 = 7 * 180 = 1260°
Learn more about polygon here
https://brainly.com/question/17756657
#SPJ2
Will give brainiest
∆ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form ∆PQR. The side lengths of ∆ABC are , 5 units; , 4.2 units; and , 4 units. Match each side of ∆PQR to its length.
see file attached
Answer:
QR=5.25 units
PR=5 units
PQ=6.25 units
