The distance AB between the two points is 5.7 units
How to determine the distance AB between the two points?From the question, we have the following parameters that can be used in our computation:
A = (2, 2) and B =(-2, -2)
The distance between the two points can be calculated using the following distance equation
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where
(x, y) = (2, 2) and (-2, -2)
Substitute (x, y) = (2, 2) and (-2, -2) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
distance = √[(2 + 2)² + (2 + 2)²]
Evaluate
distance = 5.7
Hence, the distance is 5.7 units
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How much money would i make a year if i work from6am to 2pm, from Saturday and sundays. And i get paid 13 an hour?
Parts of a Right Triangle
In a right triangle, the sides that meet to form the
right angle are called the legs. The side opposite the
right angle is called the hypotenuse. The hypotenuse is
always the longest of the three sides. It is important
that you can correctly identify the sides of a right tri-
angle, regardless of what position the triangle is in.
leg
leg
60
1. Name the legs.
Practice
AABC is a right triangle.
TRIANGLES AND THE PYTH
hypotenuse
leg
leg
hypotenuse
hypotenuse
2. Name the hypotenuse.
leg
leg
APQR is a right triangle.
3. Name the legs.
4. Name the hypotenuse.
AHLM is a right triangle.
5. Name the legs.
6. Name the hypotenuse.
Review of Squares
and Square Roots
Before you study the Pythagorean theorem, le
first review squares and square roots. Just like add
tion and subtraction are inverses, so are squares
and square roots. In other words, they "undo" e
other. To square a number, you multiply it by itsel
For example, 52 means two factors of 5, or 5 times
5, which is 25. Written algebraically, it looks
this: 52= 5 x 5 = 25. A common mistake is to s
that you multiply by 2, since 2 is the exponent (the
small raised number). But the exponent tells you
how many times to multiply the base (bot
number) by itself.
Twenty-five is a perfect square. It can be writer
as the product of two equal factors. It would be he
1) The legs of △ABC are AB and BC.
2) The name of hypotenuse is AC.
3) The legs of △PQR are PR and RQ.
4) The name of hypotenuse is PQ.
5) The legs of △HLM are LH and ML.
6) The name of hypotenuse is MH.
What is a triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The right angle of △ABC is ∠ABC. Thus AB and BC meet at right angle. Therefore AB and BC are legs of △ABC.
The opposite side of ∠ABC is AC. Therefore the hypotenuse is AC.
The right angle of △PQR is ∠PRQ. Thus PR and RQ meet at right angle. Therefore PR and RQ are legs of △PQR.
The opposite side of ∠PRQ is PQ. Therefore the hypotenuse is PQ.
The right angle of △HLM is ∠HLM. Thus HL and LM meet at right angle. Therefore HL and LM are legs of △HLM.
The opposite side of ∠HLM is MH. Therefore the hypotenuse is MH.
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The formula A=23.1 e^{0.0152t} models the population of a US state, A, in millions, t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ? million.
We want to study the population formula of a given US state according to exponential equation.
a) 23.1 millions.
b) in 2013 - 2014
What is exponential equation?
The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable
Main body:
The population state is:
A = 23.1*e^(0.0153*t)
In millions.
Where t represents the number of years after 2000.
a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).
A(0) = 23.1*e^(0.0153*0) = 23.1
The population at year 2000 was 23.1 millions.
b) Now we want to solve:
A(t) = 28.3 = 23.1*e^(0.0153*t)
28.3/23.1 = e^(0.0153*t)
1.23 = e^(0.0153*t)
Now we can apply the natural logarithm to both sides:
ln(1.23) = ln( e^(0.0153*t) )
ln(1.23) = 0.0153*t
ln(1.23)/0.0153 = t = 13.5
Hence, 13.5 years after 2000 the population will be 28.3 million.
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Graph this line y+4=1/4(x+10)
Answer:
See below
Step-by-step explanation:
I would start off writing the equation in the slope intercept form of a line
y + 4 = 1/4(x + 10) Distribute the 1/4
y + 4 = 1/4x + 10/4 Simplify 10/4
y + 4 = 1/4 x + 5/2 Subtract 4 from both sides
y = 1/4 x + 5/2 -4
y = 1/4 x + 5/2 - 8/2
y = 1/4 x - 3/2
Then I used the free graphing calculator Desmos to graph.
I need helpppp please
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex]\stackrel{\textit{\LARGE line of reflection}}{(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{-2 +4}{1 +1} \implies \cfrac{ 2 }{ 2 } \implies \text{\LARGE 1}[/tex]
now, keeping in mind that perpendicular lines have negative reciprocal slopes, there are three dotted lines, each one of them, hits the line of reflection perpendicularly, so their slope must be
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{1\implies \cfrac{\boxed{1}}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{\boxed{1}}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{\boxed{1}}\implies \text{\LARGE -1}}}[/tex]
What is the slope of the line passing through the points (-3, 4) and (2, - 1)?
Answer:
The slope is -1
Step-by-step explanation:
To find the slope using two points, you must do this:
(y2-y1) divided by (x2-x1) which is -1-4 divided by 2+3 and the answer will be -5/5 or just simply -1
Suppose you can afford to pay $ 325 a month for 9 years towards a new car with no down payment. If the current interest rates are 4.75%, how expensive a car can you afford?
Car sticker price =
Using the interest rates formula, we know that an automobile that costs $24588.44 is within our means.
What are interest rates?The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.
The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
So, let's say the car's affordable price is P:
The entire payback is equal to P r/100 T + P.
In this case, P, r = 4.75, and T = 9 years.
$351,00 = P × (4.75/100 × 9 + 1)
$351,00 = P × ( 0.4275 + 1)
$351,00 = P × 1.4275
P = 351,00 / 1.4275
When you use the division operation, we receive:
P = $24588.44
Therefore, using the interest rates formula, we know that an automobile that costs $24588.44 is within our means.
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A store sells two competitive products, A and B. A model for the revenue from selling qA units of product A and qB units of product B is R = 40qA + 50qB − 6qA2 − 9qB2 − 4qAqB. What values of qA and qB maximize the revenue? (Fractional amounts of the products are permitted)
In differentiation , qA = 13/5 , qB = 11/5 are values of qA and qB maximize the revenue .
What does mathematics differentiation serve?
In mathematics, differentiation is used to compute rates of change. For instance, in mechanics, velocity is the amount at which a displacement changes over time.
The acceleration is the speed at which velocity is changing with respect to time.
R = 40qA + 50qB − 6qA2 − 9qB2 − 4qAqB
Let aA = x , qB = y
so,
R= 40x + 50y - 6x² - 9y² - xy
Partially differentiate above equation with respect to x and y .
Rx = 40 - 12x - 4y
Ry = 50 - 18y - 4y
Set Rx = 0 and Ry = 0 solve x and y .
40 - 12x - 4y = 0
50 - 18y - 4x = 0
Solving above questions
x = 13/5 , y = 11/5
therefore,
qA = 13/5 , qB = 11/5
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Which of the following choices is the area of the rectangle if the length is 8x and the width is 3y-2?
11xy-6x
24xy-16
24xy-16x
None of these choices are correct.
Answer:
Here,
the length=8x
the width =3y-2
We know that,
Area of rectangle=l×b
or, 8x × 3y-2
8x(3y-2)
24xy-16x
Hence, the correct answer is 24xy-16x
3. Write the recursive formula given the following sequence: 20, 15, 10, 5, ...
The recursive formula for the arithmetic succession will be written as aₙ = 25 - 5n.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The sequence is given below.
20, 15, 10, 5, .....
The first term is 20 and the common difference is given as,
d = 15 - 20
d = - 5
Then the recursive formula given the following sequence is given as,
aₙ = a₁ + (n - 1)d
aₙ = 20 + (n - 1) × (-5)
aₙ = 20 - 5n + 5
aₙ = 25 - 5n
The formula for the arithmetic sequence will be written as aₙ = 25 - 5n.
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5(g + 8) - 7 = 117 - g = 14
14 is the answer
The quadrilaterals ABCD and JKLM are similar. Find the length x of JK.
The length of x in the similar quadrilateral is 1.5 units.
How to find the sides of similar quadrilateral?Quadrilaterals are polygons with 4 sides. The sum of the interior angles of a quadrilateral is 360 degrees.
Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same and two adjacent sides have equal ratios.
Therefore, quadrilaterals ABCD and JKLM are similar.
Hence, let's find the side x of the quadrilaterals.
Therefore,
CD / LM = BC / KL
CD = 5
LM = 2.5
BC = 3
KL = x
Hence,
5 / 2.5 = 3 / x
cross multiply
5x = 2.5 × 3
5x = 7.5
x = 7.5 / 5
x = 1.5
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-2x-3y=-9 and-2x-3y=-9 by elimination
The system of equations has infinite solutions, actually, any pair (x, y) is a solution.
How to solve the system by elimination?To solve a system by elimination, we just need to add/subtract the equations in such a way that we can remove one of the variables.
Here the system of equations is:
-2x-3y = -9
-2x-3y = -9
If we subtract the two equations we will get:
(-2x-3y) - (-2x-3y) = -9 - (-9)
0 = 0
This is a trivial equation, that happens because both equations of the system are the same one.
So the system is true for all real values of x and y.
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In the figure below L || M. find X
Answer:
x = 79
Step-by-step explanation:
To find the value of x we first need to find the missing angle of the triangle in the image.
The sum of interior angles in a triangle is equal to 180°.101 + 29 + missing angle = 180
Add like terms130 + missing side = 180
subtract 130 from both sidesmissing side = 50
Now, the sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
So the value of x:
29 + 50 = 79
18.
Which of the following statements is true?
A. Angles are supplementary if and only
if they form a linear pair.
B. It is Valentine's Day if and only if it is
February.
C. A number is even if and only if it is
divisible by 2.
D. Lines are skew if and only if they are
non-coplanar.
Answer: The correct answer is D, Lines are skew if and only if they are non-coplanar.
In geometry, lines are said to be skew if they are non-coplanar, meaning they do not lie in the same plane. They also do not intersect.
Option A is incorrect because angles can be supplementary (add up to 180 degrees) even if they do not form a linear pair (meaning they do not share a common vertex and a common side).
Option B is incorrect because Valentine's Day does not always fall in February. It is February 14th, but it could fall on a different month in a different year.
Option C is correct because a number is even if and only if it is divisible by 2. An even number can be divided evenly by 2, while an odd number cannot.
The diagram shows a frustum which is constructed from a pyramid.
(a) The surface area of the frustum.
(b) Find the volume of the frustum.
(c) Find the surface area of the original pyramid.
The surface area of the frustum is 1744 square units
The volume of the pyramid is 2031.33 cube units.
What is a frustum of a pyramid?
By cutting the top of a typical pyramid, the frustum is created, which is a pyramid. Because of this, it is known as a truncated pyramid. The frustum of the pyramid is that portion of a pyramid that is cut through by a plane parallel to its base and lies between the vertex and the base.
a) First, we calculate the height of the frustum.
Let height be H
The base length be L1=24
Base width be W1=12
Top length is L2=14
To width be W2=13
Side height be C=13
Using the formula, H
[tex]H=\sqrt{ C^{2} - \frac{(L1-L2)^{2}}{2}}\\H=\sqrt{ 13^{2} - \frac{(24-14)^{2}}{2}}\\H=\sqrt{ 169 -50}\\H=\sqrt{119} \\H=11[/tex]
Now, the surface area of the frustum is LSA+area of bases of a frustum
Here, P1= perimeter of the base1 of the frustum
P2 is the perimeter of the base 2 of the frustum
[tex]L.S.A=\frac{1}{2} .(P1+P2).L \\=\frac{1}{2} .(72+42).24 \\=\frac{1}{2} .(114).24 \\=1368[/tex]
Now, S1 =area of base1 of frustum =288
S2= area of base 2 of frustum=98
TSA is given by LSA+area of bases of a frustum
=1368+288+98
=1724.
Therefore the surface area is 1724 square units.
b) Volume is given by
[tex]V=\frac{1}{3}.H.(S1+S2+\sqrt{S1S2} )\\ V=\frac{1}{3} . 11.(386+168)\\V=2031.33[/tex]
Therefore the volume is 2031.33 cube units.
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solve for n n/12=300 n=__
Convert the following equation from standard form to slope-intercept form: -9x +3y = -12
Answer:
y=3x-4
Step-by-step explanation:
-9x+3y=-12
3y=12-9x
y=3x-4
2 1/3 + 5 1/4
Addition of the fraction above
You find yourself in a strange undulating landscape given by the function z = f (x, y) = cos y − cos x, where z is the elevation.
1. Find all maxima, minima, and saddle points. What are the level curves for z = 0?
Graph this function.
You are now at the origin and wish to hike to the point (4π, 0, 0). You contemplate two rather different routes.
2. Your first route always keeps you at the same elevation. Determine such a route of minimal length. What is the length?
3. Your second route always moves along the gradient. Determine such a route of minimal length, assuming you start hiking in the positive x-direction. What is its length? If you cannot find an exact answer, determine an upper bound and a lower bound between which the actual length must lie.
4. Which route is the shorter—that of part (b), or (c)?
Appropriate pictures should be supplied throughout. Justify your answers.
Answer:
24-3-32233'2]/2
Step-by-step explanation:
true or false? in O radius OP intersects chord AC in point B so that AB = 8 units and BC = 8 units. This means that OP is perpendicular to AC
The answer is true, if radius OP intersects chord AC in point B and AB=8 units, BC=8 units.
What is meant by radius?The length of the line segments from a circle's center to its perimeter is referred to as the radius of a circle or sphere in more contemporary use. Radius has two possible plurals: the traditional English plural radiuses or radii. R or r is the most common radius abbreviation and mathematical variable name. Consequently, the diameter D is equal to double the radius.
Given,
In circle radius OP intersects chord AC in point B.
And AB=8 units, BC=8 units
So, OP is perpendicular to AC.
Due to the fact that OA and OC have equal sides and a base length of AC, OAC forms a triangle (the radius of the circle)
When you trace AC, you discover that O, a line perpendicular to AC, intersects the circle's center.
So, the answer is true.
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PLEASE ANSWER CLEARLY WITH EQUATION
Samuel went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 300 mg of sodium and each frozen dinner has 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.
ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.
What is an equation?
There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra.
This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.
Let frozen supper be y and soup cans be x.
X now has 300 mg of sodium in it.
x = 300
Y also has 450 mg of sodium in it.
y = 450
Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.
Let the number of frozen dinners be "b," and the number of soup cans be "a."
ax + by = 6000
⇒ a(300) + b(450) = 6000 ...1
Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation
a + 5 = b ...2
Now, by changing the value of b in equation 1 we obtain,
⇒ a(300) + (a + 5)(450) = 6000
⇒ 300a + 450a = 6000 - 2250
⇒ 750a = 3750
⇒ a = 3750/750
⇒ a = 5
By changing the value of an in equation 2, we obtain
⇒ 5 + 5 = b
⇒ b = 10
So, ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased, respectively, where x and y stand for soup cans and frozen dinners, respectively, and a and b stand for the quantity of soup cans and frozen dinners.
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What is the inequality on this word problem.
Nancy has $240 in the bank. She wants to buy as many $15 video games as possible. How many video games could she buy if she wanted to keep at least $120 in the bank?
Nancy can buy maximum 8 video games.
How to solve inequality?Steps to solve inequality:
Get rid of all fractions by multiplying all terms by the fractions' lowest common denominator. Simplify the inequality by merging like terms on each side.To get the unknown on one side and the numbers on the other, add or subtract the appropriate amounts. multiply each term in the inequality by the unknown coefficient.The inequality will not change if the coefficient is positive.
The inequality will be the other way around if the coefficient is negative.
If Nancy wants to keep at least $120 in her account and at present, she is having $240
So, she can spend = 240-120= $120
And, one video game price= $15
Let us consider she can buy maximum 'X' games
15×X=$120
X = 8 units
Hence, she can buy a maximum of 8 video games.
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Write a related function for - 6x + x - 16= 3x
Answer:
x = -2
Step-by-step explanation:
hope this will help you
jon making a dog house to put in his backyard he uses more than 24 feet of wood for the project
Answer:
thanks.
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Find the equation of the line with slope 0 and passing through (-5,16). Write the equation in standard form.
Lines with a slope of zero can be thought of as y = 0x + b, which simplifies to just "y = b".
In this case, your equation is y = 16.
If you want to force it explicitly into standard form, you could write it at
0x + 1y = 16
Solve for x to the nearest tenth.
Answer:
Answer:
x=9.8
Step-by-step explanation:
Assume the acceleration of the object is a(t) = −32 feet per second per second. (Neglect air resistance.)
A balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 48 feet above the ground.
(a) How many seconds after its release will the bag strike the ground? (Round your answer to two decimal places.)
(b) At what velocity will it strike the ground? (Round your answer to three decimal places.)
(a) 2.79 seconds after its release the bag will strike the ground.
(b) At a velocity of 73.28 ft/second it will hit the ground.
What is velocity?
We are given that a balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the ground.
Assume the acceleration of the object is a(t) = −32 feet per second.
(a) For finding the time it will take the bag to strike the ground after its release, we will use the following formula;
[tex]s=u t+\frac{1}{2} a t^2[/tex]
Here, s= distance of the balloon above the ground =-80 feet
[tex]$\mathrm{u}=$[/tex] intital velocity =16 feet per second
[tex]$\mathrm{a}=$[/tex]acceleration of the object =-32 feet per second
[tex]$\mathrm{t}=$[/tex] required time
So, [tex]$s=u t+\frac{1}{2} a t^2$[/tex]
[tex]$$\begin{aligned}& -80=(16 \times t)+\left(\frac{1}{2} \times-32 \times t^2\right) \\& -80=16 t-16 t^2 \\& 16 t^2-16 t-80=0 \\& t^2-t-5=0\end{aligned}$$[/tex]
Now, we will use the quadratic D formula for finding the value of t, i.e;
[tex]t=\frac{-b \pm \sqrt{D}}{2 a}[/tex]
Here, a=1, b=-1, and c=-5
Also, [tex]$\mathrm{D}=b^2-4 a c=(-1)^2-(4 \times 1 \times-5)=21$[/tex]
So, [tex]$t=\frac{-(-1) \pm \sqrt{21}}{2(1)}$[/tex]
[tex]t=\frac{1 \pm \sqrt{21}}{2}[/tex]
We will neglect the negative value of t as time can't be negative, so;
[tex]t=\frac{1+\sqrt{21}}{2}=2.79 \approx 3 \text { seconds. }[/tex]
Hence, after 3 seconds of its release, the bag will strike the ground.
(b) For finding the velocity at which it hit the ground, we will use the formula;
v=u+a t
Here, v= final velocity
So,[tex]$v=16+(-32 \times 2.79)$[/tex]
v=16-89.28=-73.28 feet per second.
Hence, the bag will hit the ground at a velocity of [tex]$-73.28 \mathrm{ft} / \mathrm{second}$[/tex].
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Which of the following could be an example of a function with a range (-∞, α) and a domain [b, ∞) where a > 0 and b>0?
Explanation:
Choices A and B are ruled out because they are cube root functions, which have a domain and range of "all real numbers".
Choice C is ruled out because the domain is [tex][a, \infty)[/tex]
To determine this domain, we set the radicand (aka stuff under the square root) to be greater than or equal to zero.
[tex]x-a \ge 0 \ \ \text{ solves to } \ \ x \ge a[/tex]
[tex]x \ge a \ \ \text{ turns into the interval notation } \ \ [a, \infty)[/tex]
The square bracket is used to include the value 'a' as part of the interval. This is the interval from x = a to positive infinity.
The domain of choice D is [tex][b, \infty)[/tex] found using similar steps as shown above.
The range is [tex](-\infty, a][/tex] since this square root function is decreasing, due to the negative out front, which means y = a the largest output possible. I recommend graphing it out using a tool like desmos or geogebra. These tools offer a way to use parameters.
Round 54.71 to the nearest tenth
Answer:
the digit 1 is less than 5, so we round 54.71 down to 54.7.
Step-by-step explanation: