The vertices of the square are the coordinates of the endpoints
The third vertex of the square could be (0,7) or (-5,1)
How to determine the third vertexTwo vertices of the square are:
(0,-3) and (4,2)
Calculate the distance between these vertices using:
[tex]d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}[/tex]
Square both sides
[tex]d^2 = (x_2 - x_1)^2+(y_2 - y_1)^2[/tex]
The above expression represents the area of the square.
So, we have:
[tex](x_2 - x_1)^2+(y_2 - y_1)^2 = 41[/tex]
Next, we test the options with the given vertices (0,-3) and (4,2)
So, we have:
A. (0,7)
[tex](0 - 0)^2+(7 + 3)^2 = 41[/tex]
[tex]100 \ne 41[/tex]
[tex](0 - 4)^2+(7 - 2)^2 = 41[/tex]
[tex]41 = 41[/tex]
B. (-5,1)
[tex](-5 - 0)^2+(1 + 3)^2 = 41[/tex]
[tex]41 = 41[/tex]
[tex](-5 - 4)^2+(1 -2)^2 = 41[/tex]
[tex]82 \ne 41[/tex]
C.(5,13)
[tex](5 - 0)^2+(13 + 3)^2 = 41[/tex]
[tex]281 \ne 41[/tex]
[tex](5 - 4)^2+(13 -2)^2 = 41[/tex]
[tex]122 \ne 41[/tex]
D.(-2,-2)
[tex](-2 - 0)^2+(-2 + 3)^2 = 41[/tex]
[tex]5 \ne 41[/tex]
[tex](-2 - 4)^2+(-2 -2)^2 = 41[/tex]
[tex]52 \ne 41[/tex]
E.(4,-6)
[tex](4 - 0)^2+(-6 + 3)^2 = 41[/tex]
[tex]25 \ne 41[/tex]
[tex](4 - 4)^2+(-6 -2)^2 = 41[/tex]
[tex]64 \ne 41[/tex]
The vertices where at least one of the equations is true could be a third vertex of the square
Hence, a third vertex of the square could be (0,7) or (-5,1)
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find the length of missing side in the triangle, give answer 1 decimal place
giving brainliest
What polynomial must be added to z2 + 4z – 7 in order for the sum of the two polynomials to be 2z2 + z + 7 ?
Answer: D. (z2-3z+14)
Step-by-step explanation:
took the test
URGENT
Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Volume = 10,000 in.
Answer:
h=39
Step-by-step explanation
V = [tex]\pi[/tex]r^(2) h
V = 10,000[tex]\pi[/tex]
radius = diameter / 2
diameter = 32
radius = 32/2
radius = 16
10,000[tex]\pi[/tex]=[tex]\pi[/tex](16)^(2)(h)
Simplify by dividing [tex]\pi[/tex] from both sides and evaluating 16^2
10,000=256h
Simplify again by dividing 256 from both sides to isolate h.
39.06 = h
Round to the nearest whole number:
39 inches.
A bag contains 5 blue marbles, 4 red marbles, and 3 orange marbles. Mrs. Johnson picks one without looking, replaces it and picks another one.
What is the probability that she picks two that are NOT orange?
Answer:
75%
Step-by-step explanation:
Because there were 12 marbles and only 3 of them are orange so it is a 75% chance she won't pick one and a 25% chance she will.
Hope it helps Have a great afternoon:)
which of these functions is linear?
The only linear function is:
y = x - 5
So the correct option is B.
How to identify a linear function?
A linear function is a polynomial of degree 1, and can be written as:
y = a*x + b
So we have a coefficient multiplying the variable and a constant term, nothing else.
By comparing this with the options, we can see that the only linear function given is the one in option B.
y = x - 5
Where a = 1, and b = 5.
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HELP ASAP
Determine the x-intercepts of the graph with the function
f(x) = x²+6x-7
A (-7,0) & (1,0)
B (0,-7) & (0,1)
D (6,0) & (1,0)
D (7,0) & (-1,0)
Step-by-step explanation:
hope that helps. explanation is on the paper :)
Determine the distance between points A (3, 5) and B (2, 1) rounded to the nearest tenth.
Answer:
4
Step-by-step explanation:
gradient=vertical distance /Horizontal distance
G=V/H
G = -4/-1
G =4
The place kicker for the Cascade Champs, scored 120 points last year. They were all gained on 1-point extra-point kicks and 3-point field goals. He successfully completed sixty-six kicks. How many of each type did he make
Answer:
your equations would be 3x+1y=86 and x+y=42
the answer would be 22 field goals and 20 extra po
Step-by-step explanation:
Can someone help me on these to questions ???
. 1
Sienna had 8 feet of string to make bracelets. If she uses of a foot of string for each bracelet, how many bracelets can she make?
8 bracelets
bracelets
24 bracelets
The number of bracelets she can make is 32
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Length of string=8feet
Now,
This is a word problem on fractions that requires division. To solve it, you need to follow these steps1:
Define a variable. Let x be the number of bracelets Sienna can make.
Write an equation using the variable. Since she uses 1/4 of a foot of string for each bracelet, we can write: x * (1/4) = 8
Solve the equation. To isolate x, we need to multiply both sides by 4: x = 8 * 4
Simplify the expression
x = 32
Therefore, by the unitary method the answer will be 32.
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What is the length of the hypotenuse? If necessary, round to the nearest tenth.
a piece of cloth was 39 feet long. how long is the cloth in yards?
Answer:
13 yards
Step-by-step explanation:
1 yard = 3 feet
39 ÷ 3 = 13 yards
The cloth is 13 yards.
Hope this helps!
Answer:
13 yards
Step-by-step explanation:
What is the area of this shape?
Answer:
144
Step-by-step explanation:
The shape is a trapezoid.
Add 6 and 112, which is eighteen
divide eighteen by 2, which is 9
Finally, multiply 9 and sixteen which is 144
En un edificio de cinco pisos viven las familias grados, sarabia, gutierrez, pardo y castro
Compile a list of words that describe you as a child. Compile a second list that describes you as you are now. How are these lists the same? How are they different?
Answer number 6 pleaseeee
Answer:
look it up :)
Step-by-step explanation:
:)
Answer:
Step-by-step explanation:
For commission on his sales is 7%
He makes a total sales of $ 12500
so 7 / 100 * 12500
it will be $ 875 as his total commission.
Which function has the same slope as the function on the graph?
PLEASE I REALLY NEED HELP WITH THIS
A. y = -2x - 4
B. y = -1/2 x - 2
C. y = 1/2 x - 3
D. y = 2x - 6
Answer:
D -2x-6
Step-by-step explanation:
The surface area of the block is
Answer:
In this rectangular prism, opposite sides are equal.
So if we find the 3 different sides, we would need to multiply those individual sides by 2 (because opposite sides are equal/have the same area) and then add them to get the surface area.
One side (the front and back side);
The width is 8 and the height is 7, so (8 x 7) = 56. Though, it's opposite side is the same as well so we multiply 56 by 2, (56 x 2) = 112
Second side (the left and right side);
The width is 18 and the height is 7, so (18 x 7) = 126. Though, it's opposite side is also the same as well, so we multiply 126 by 2, (126 x 2) = 252
Third side (the top and bottom side);
The width is 8 and the height is 18, so (8 x 18) = 144. Though, it's opposite side is also the same as well, so we multiply 144 by 2, (144 x 2) = 288
Now, we add all the areas we've gathered:-
112 + 252 + 288 = 652 square cm
how many sites are in this data set
Answer:
i think 15
Step-by-step explanation:
You have a puppy named Fido and 60 feet of fencing. You want to make him the largest play area possible. What are the dimensions of the rectangular area that has the greatest area? Show why this is the biggest with diagram or charts
Answer:
15 feet x 15 feet
Step-by-step explanation:
I'm worried about Fido, so I'll use three different approaches to maximizing his play space: Graphing, Chart, and First Derivative. This is perhaps more than Fido wants, but it hopefully offers ideas on how these types of problems can be answered.
=========================
Fido is limited to 60 feet of fence, which will form the perimeter. The area of a rectangle is (length)*(width). Let's set length to L and width to W. I'll use A for area.
Therefore A = L*W
The rectangle's perimeter will be 2L + 2W, and this is equal to 60 feet:
2L + 2W = 60
Let's rearrange this equation to isolate either W or L. I chose L:
L + W = 30
L = 30 - W
Now let's use this definition of L in the Area equation:
A = L*W
A = (30-W)*W
A = 30W - W^2
Graphing
We can graph this function (A = 30W - W^2) to find the maximum area. See the attached image. We find a maximum area of 225 ft^2 when the width is 15 feet. 15 feet would mean that Fido's roaming pen will be in the shape of a square; 15 feet for each side equals 60 feet total fence.
Chart
One can also find a maximum by calculating a variety of conditions set by L = 30 - W. I randomly picked lengths from 2 to 24 feet and calculated the resulting width and then the resultant area for each condition. See attached image. Although I did not pick 15 feet, we can see that the area increases until the length transitions from 14 to 16 feet. It reverses direction at that point. A closer inspection around those values will show that 15 feet is, in fact, the optimum value to produce a pen with the most area.
First Derivative
One could also take the first derivative of the equation A = 30W - W^2 and set it equal to zero. The fist derivative tells us the slope of the line at any point (for a value of W in this example). The slope is zero only when the curve hits a maximum.
A = 30W - W^2
A' = 30 -2W
0 = 30 - 2W
2W = 30
W = 15 feet
The slope is zero when the width is 15 feet. 15 feet is the optimum for creating a pen with the most area possible with 60 feet of fence.
===
All three approaches yield the same result. Graphing is fun when you have access to DESMOS. Charts are fun if you like Excel. Derivatives can also be fun, mostly because I always ponder "Who had the audacity to think this might work?" (Didn't they have something more important to do? Raid a village, etc.?).
====
Arf
Alexa always gives a 15% tip when she eats at a
restaurant. She gives a $2.13 tip. What was the
cost of her meal?
the cost of her meal was "x", which is the 100% of her bill, we also know that $2.13 is 15% of that, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 2.13&15 \end{array}\implies \cfrac{x}{2.13}=\cfrac{100}{15}\implies \cfrac{x}{2.13}=\cfrac{20}{3} \\\\\\ 3x=42.6\implies x=\cfrac{42.6}{3}\implies x=14.2[/tex]
y=(3x+15)(x-2)
in standard form
Answer:
[tex]y=3x^2+9x-30[/tex]
Step-by-step explanation:
To multiply [tex](3x+15)[/tex] with [tex](x-2)[/tex] we can use a method called the FOIL method. FOIL is an acronym standing for First, Outer, Inner, Last. This is the order in which we need to multiply. The first terms of each multiplier are [tex]3x[/tex] and [tex]x[/tex]. Therefore, we multiply these two terms to get [tex]3x^2[/tex]. The outer terms are [tex]3x[/tex] and [tex]-2[/tex]. Once again, we multiply these terms.
[tex](3x)(-2)=-6x[/tex]
Now, our equation looks like this: [tex]y=3x^2-6x[/tex]. We're not finished yet though. Next, we need to multiply the inner terms, [tex]15[/tex] and [tex]x[/tex]. This comes out as simply [tex]15x[/tex]. Now our equation looks like this: [tex]y=3x^2-6x+15x[/tex]. We just need to multiply the last terms, [tex]15[/tex] and [tex]-2[/tex]. This comes out as [tex]-30[/tex].
Our equation at this point has been fully multiplied:
[tex]y=3x^2-6x+15x-30[/tex]
We can see that we still have two like terms, [tex]-6x[/tex] and [tex]15x[/tex]. These can be combined to simply [tex]9x[/tex]. Our final equation, then, is this: [tex]y=3x^2+9x-30[/tex]
What is 1/2 • 1 • 2 please help
Answer:
1
Step-by-step explanation:
1/2x1x2
1
A plumber charged x dollars per hour for a 4-hour job plus $175 for parts. The to- tal charge for the service call was $415.00. Which equation can be used to deter- mine how much the plumber charged per hour?
Answer:
4x + 175 = 415
Step-by-step explanation:
4 is the hours, so it should be multiplied by x to see how much you get every hour (and a total of 4 hours).
175 is the constant and should be added to the equation so that all fees are included.
415 is the total amount so the equation should equal that number.
Hope this helps!
Lana wants to have $100,000 in 20 years. She plans to invest $8,000 to start and make yearly payments of $1,500 to the account. She will be receiving 7.5% interest compounded monthly on her investment. Will she reach her goal?
No
Yes
Answer:
Yes Lana will reach her goal she'll have 10,414.58 by the end of the 6 years,
Step-by-step explanation:
HI PLEASE HELP PLEASE PLEASEE HELP
Answer:
Step-by-step explanation:
[tex]26) tan \ 56 =\dfrac{opposite \ side }{adjacent \ side}\\\\\\ 1.4826 = \dfrac{BC}{12}\\\\\\1.4826*12 = BC[/tex]
BC = 17.8 cm
[tex]27) Cos \ x =\dfrac{adjacent \ side}{hypotenuse}\\\\Cos \ x = \dfrac{15}{18}\\\\\\Cos \ x = 0.83\\\\x = Cos^{-1} \ (0.83)\\\\[/tex]
x = 33.9°
Given p | q and 24 = 130°, find the measure of angle 1:
P
34
5 6
78
9
70°
130°
HELP!!
Answer:
p is equal to 130 reason vertical opposite angles
Which of the following functions, when graphed, is a line with a downward slant?
Answer:
Step-by-step explanation:
A function with a downward slant must have a negative slope.
All these lines are in the format y = mx + b where m is the slope's value.
The only one that fits the requirement is choice (B) which has a slope of -4.
Hope that helps!
What is the surface area of the right cone below?
6
O A. 1307 units2
O B. 1267 units2
O C. 5407 units2
O D. 1807 units
HELPPP PLEASE
The solution is, surface area of the given circular cone is 126π units².
Option B is the correct option.
What is surface area of a cone?The surface area of a cone is equal to the curved surface area plus the area of the base: π r 2 + π L r , \pi r^2 + \pi L r, πr2+πLr,
where r denotes the radius of the base of the cone, and L denotes the slant height of the cone.
here, we have,
Surface area of a cone is given by the expression,
V = πr(r + l)
Here, r = Radius of the circular base
l = Lateral height of the cone
By substituting the given values in the given expression of volume,
here, given that.
r = 6
l = 15
V = π(6)(6 + 15)
= 126π units²
Therefore, surface area of the given circular cone is 126π units².
Option B is the correct option.
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X, Y and Z form the vertices of an isosceles triangle.
XY = 8.7m, YZ = 13.8m.
Find the angle
∠
XYZ rounded to 1 DP.
Answer:
∠XYZ = 37.5
Step-by-step explanation:
IN THE IMAGE ABOVE
