What is the equation of a line that contains the points (2,-2) and (0, -2)?

y=0
x= -2
y=-2
x=0

Step-by-step answer:

If x and y both go by equal steps, not necessarily equal steps between x and y, the relation is linear

Here, x goes by steps of 6 (1,7,13,19) and y goes by steps of 3 (4,7,10,13), therefore the relation is linear.

To find the equation passing through all the points, we find first the slope, which is steps in y divided by steps in x, or

slope, m = 3/6 = 1/2

Next, we take any point from the data, say, P0=(x0,y0)=(1,4), and substitute in the point-slope form of the equation

y-y0 = m(x-x0)...........................(1)

since x0=1, y0=4, and m=1/2, we get the equation

y-4 = (1/2)*(x-1) .........................(2)

Simplify (2) to get the slope-intercept form of the linear relation:

y = (1/2)x + 7/2 ........................(3)

Finally, we check the results of the y-values for given values of x, using the relation given in equation (3):

y(1) = 4

y(2)=7

y(3)=10

y(4)=13

all of which correspond exactly to original data, so the equation of the linear relation is correct.

Answer:

p(z<0.42) = 0.6628

Step-by-step explanation:

A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. That is to say:

μ = 0

σ² = 1

Using a calculator, we find that:

p(z<0.42) = 0.6628 (See picture attached)

Answer:

0.66276.

Step-by-step explanation:

We are asked to find the approximate value of p(z<0.42) for a standard normal distribution.

Our given expression means the probability of getting a z-score less than 0.42.

We need to find the probability of getting the area corresponding to a z-score less than 0.42 under normal distribution curve.

We will normal distribution table to solve our given problem.

[tex]p(z<0.42)=0.66276[/tex]

Therefore, the approximate value of our given expression would be 0.66276.

Final answer:

The value of the discriminant of the quadratic equation -2x² - 8x + 8 is 128. The positive discriminant suggests that the equation has two distinct real roots.

Explanation:

The discriminant of a quadratic equation can be calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0.

In the given quadratic equation -2x² - 8x + 8, a = -2, b = -8, and c = 8. Substituting these values into the discriminant formula:

D = (-8)² - 4(-2)(8) = 64 - (-64) = 128.

The value of the discriminant is 128. The discriminant value can provide information about the nature of the roots of the quadratic equation. If the discriminant is positive (greater than 0), then the equation has two distinct real roots. If the discriminant is 0, then the equation has one real root (a repeated root). If the discriminant is negative, then the equation has no real roots.

Answer:

B and E are the correct answer

Step-by-step explanation:

Because (2,23) and (7,48) are linear

Your question is incomplete and lacks the table. Please check below for the full content.

A group of students is collecting books to add to their library. The table shows the number of books in the library after 1, 3, and 5 days. If the relationship between days and books continues to be linear, which ordered pairs could appear in the table? Check all that apply.

(0, 8)

(2, 23)

(4, 32)

(6, 48)

(7, 48)

The missing table is given below.

The correct options are option 2:(2,23) and 5:(7,48) The ordered pair (2,23),(7,48) will appear in the table.

The equation where highest degree of the variable used in the equation is 1 is called linear equation. Foe example ax+by+c=0

Here given the relationship between days and books is linear.

From the table, it clear that In day 1 the book collected is 18.

in day 3 book collected is 28.

x₁=1,y₁=18

x₂=3,y₂=28

The linear equation will be

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

⇒(y-18)/(x-1)=(28-18)/(3-1)

⇒(y-18)/(x-1)=10/2

⇒(y-18)/(x-1)=5

⇒y-18=5(x-1)

⇒y-18=5x-5

⇒y=5x-5+18

⇒y=5x+13

So the linear equation will be y=5x+13

By ckecking every option,

1. (0, 8)-  y=5*0+13=13≠8  Option 1 is incorrect.

2. (2,23)-  y=5*2+13=23    Option 2 is correct.

3. (4,32)-   y=5*4+13=33≠32   Option 3 is incorrect.

4.(6,48)-   y=5*6+13=43≠48     Option 4 is incorrect.

5. (7,48)    y=5*7+13=48   Option 5 is correct.

Therefore the correct options are option 2 and 5 i.e. The ordered pair (2,23) , (7,48) will appear in the table.

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Answer:

y/2

Step-by-step explanation:

x+3=y+2

------  --------

3          2

Using cross products

2(x+3) = 3(y+2)

Distribute

2x+6 = 3y+6

Subtract 6 from each side

2x+6-6 = 3y+6-6

2x= 3y

Divide each side by 2

2x/2 = 3y/2

x = 3/2 y

We want to find x/3

Divide each side by 3

x/3 = 3/2 y * 1/3

x/3 = 1/2 y

Answer:

|-5| is the answer.

Step-by-step explanation:

The opposite of 5 is -5. The absolute value of a number is always positive (e.g: |-10| = 10 because the negative sign is inside the absolute value bars).

-|5| and -|-5| both equal -5 because there is a negative sign outside of the bars. Since |-5| has a negative sign inside the bars, it equals 5.

I tried hard to explain this, so I hope it makes sense! :)

Hey there Brainly Student! Your answer is   I-5I !! I hope this helped! Have a great day!!

Answer:

[tex]\large\boxed{y=\dfrac{2}{3}x+7}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\y=-\dfrac{3}{2}x+4\to m_1=-\dfrac{3}{2}\\\\m_2=-\dfrac{1}{m_1}\Rightarrow m_2=-\dfrac{1}{-\frac{3}{2}}=\dfrac{2}{3}\\\\\text{Therefore we have the equation:}\ y=\dfrac{2}{3}x+b.\\\\\text{Put the coordinates of the point (3, 9) to the equation:}\\\\9=\dfrac{2}{3}(3)+b\\\\9=2+b\qquad\text{subtract 2 from both sides}\\\\7=b\to b=7[/tex]

Answer:

6 pounds of potatoes = $9

3 pounds of onions = $9

The onions cost $3 per pound

and the potatoes cost $1.50 per pound

Step-by-step explanation:

Answer:

Unit price of  potatoes = $1.50.

Unit price of onions - $3.

Step-by-step explanation:

The system of equations is

6p + 3n = 18

n = 2p

Substitute  n = 2p in the first equation:

6p + 3(2p) = 18

6p + 6p = 18

12p= 18

p = 18/12 = $1.50 .

Now plug p = 1.50 into the second equation:

n = 2*1.50 = $3.

Answer:

1024 cm²

Step-by-step explanation:

There are 16 rods.  A square has 4 equal sides, so each side must consist of 4 rods.  The length of each rod is 8 cm, so the length of each of the square's sides is 32 cm.  Therefore, the area of the square is:

A = s²

A = (32 cm)²

A = 1024 cm²

Answer:

Hi there!

The answer to this question is: x=6

Step-by-step explanation:

All the points are being mirrored across the line x=6.

Answer:

The answer is x=6

Step-by-step explanation:

The two shapes are mirror images of each other around x=6

To find the point where the cost of skiing at both ski slopes is the same, set the equations for the total cost of skiing at each resort equal to each other and solve for 'x'.

To determine at what point the cost of both ski slopes is the same, we need to create an equation based on the given information about the costs of each ski resort. Let's assume 'x' is the number of hours of skiing. The total cost of skiing at Black Diamond Ski Resort is given by the equation: Cost = 50 + 15x. The total cost of skiing at Bunny Hill Ski Resort is given by the equation: Cost = 75 + 10x. To find the point where the costs are the same, we can set the two equations equal to each other: 50 + 15x = 75 + 10x. Now we can solve this equation for 'x': 5x = 25, x = 5.

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Answer:

95

Step-by-step explanation:

(9.5)(-2)(-5)

First multiply the first two terms:

9.5* -2(-5)

9.5* -2 = -19

= -19(-5)

now multiply the product of solved terms by -5

-19(-5)

Negative signs will change into positive because - * - = +

95....

Thus the answer is 95....

Answer:

your answer is 95

Step-by-step explanation:

you multiply (9.5) (-2)(5) and you get 95

Answer:

[tex]4t + 15j > 800[/tex]

Please read explanation below as well.

Step-by-step explanation:

We know the following information:

- The number of T-shirts is represented by the variable [tex]t[/tex]. Each T-shirt costs $4. The total cost depending on the number of T-shirts can be represented by [tex]4t[/tex].

- The number of jeans is represented by the variable [tex]j[/tex]. Each pair of jeans costs $15. The total cost depending on the number of jeans can be represented by [tex]15j[/tex].

- The stores want to sell more than $800. This idea is represented mathematically by writing [tex]>800[/tex].

The total cost of jeans and T-shirts depending on the quantities of each of them is represented as a sum: [tex]4t + 15j[/tex]. This total cost has to be more than $800: [tex]4t + 15j > 800[/tex].

Think for a minute.

Three points are given.

What geometric shape has three points?

Answer: Triangle

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=\dfrac{3}{4}x-12&(1)\\y=-4x-31&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\\dfrac{3}{4}x-12=-4x-31\qquad\text{multiply both sides by 4}\\\\3x-48=-16x-124\qquad\text{add 48 to both sides}\\\\3x=-16x-76\qquad\text{add}\ 16x\ \text{to both sides}\\\\19x=-76\qquad\text{divide both sides by 19}\\\\x=-4\\\\\text{Put it to (2):}\\\\y=-4(-4)-31\\y=16-31\\y=-15[/tex]

Answer:

If there are 5 persons and at a time only 3 can be arranged, the total number of arrangements is 60

Option C is correct

Step-by-step explanation:

There are 5 persons and at a time only 3 can be arranged.

The total number of arrangements = nPr = n!/(n-r)!

Here n = 5 and r = 3

nPr = n!/(n-r)!

nPr = 5!(5-3)!

nPr = 5!/2!

nPr = 5*4*3*2!/2!

nPr = 5*4*3

nPr = 60

So, if there are 5 persons and at a time only 3 can be arranged, the total number of arrangements is 60

Option C is correct.

Answer:

-4x^2-6x+6

(third choice)

Step-by-step explanation:

To do f(x)-g(x) we must insert the expression for f(x) and g(x) into this:

This will give us:

(8x^2-2x+3)

-(12x^2+4x-3)

--------------------

-4x^2-6x+6

Horizontally if you prefer:

(8x^2-2x+3)-(12x^2+4x-3)

Distribute and get rid of paranthesis:

8x^2-2x+3-12x^2-4x+3

Pair up like terms:

8x^2-12x^2-2x-4x+3+3

Combine the like terms:

-4x^2-6x+6

Answer:

h(x) =  -4x^2 - 6x + 6

Step-by-step explanation:

f(x) - g(x)

=  8x^2 - 2x + 3 - (12x^2 + 4x - 3)    (Note the parentheses around g(x))

Distributing the negative over the parentheses:

= 8x^2 - 2x + 3 - 12x^2 - 4x + 3

= -4x^2 - 6x + 6 = h(x).

Answer:

D. 77.6

Step-by-step explanation:

We have been given a triangle ZYA in which B, C, and D are the midpoints. We are asked to find the perimeter of triangle ZYA.

We will triangle mid-segment theorem to solve our given problem.

The triangle mid-segment theorem states that the segment joining midpoints of two sides of a triangle is parallel to 3rd side and half the measure of parallel side.

[tex]\text{Measure of side YA}=2\times BD[/tex]

[tex]\text{Measure of side YA}=2\times 11.1[/tex]

[tex]\text{Measure of side YA}=22.2[/tex]

[tex]\text{Measure of side YZ}=2\times CD[/tex]

[tex]\text{Measure of side YZ}=2\times 13.7[/tex]

[tex]\text{Measure of side YZ}=27.4[/tex]

[tex]\text{Measure of side ZA}=2\times CB[/tex]

[tex]\text{Measure of side ZA}=2\times 14[/tex]

[tex]\text{Measure of side ZA}=28[/tex]

[tex]\text{Perimeter of triangle ZYA}=22.2+27.4+28[/tex]

[tex]\text{Perimeter of triangle ZYA}=77.6[/tex]

Therefore, the perimeter of triangle ZYA is 77.6 units.

Answer:

your answer is "18"

Step-by-step explanation:

Formula is:

A= 1/2 (A+B) X H

A = 1/2 (CD + CF) X H

A = 1/2 (5+6) X 3

A = 16.5 CM SQUARED

Hope this is right!

Since ABCF is a rectangle, angle AFC is a right angle. Angle CFE is also a right angle. Since angle DCF is also a right angle, then trapezium CDEF has parallel sides CD and EF.

BC + CD = BD

4 cm + CD = 9 cm

CD = 5 cm

EF = 3 cm

Sides CD and EF are the parallel bases of the trapezium. Side CF is the height of the trapezium.

area of trapezium = (base1 + base2)h/2

area = (5 cm + 3 cm)(6 cm)/2

area = (8 cm)(6 cm)/2

area = 24 cm^2

The conclusion If AC = AB + BC and AB + BC = 13, then AC = 13 is justified by the transitive property of equality.

The property that justifies the conclusion If AC = AB + BC and AB + BC = 13, then AC = 13 is the transitive property. In mathematics, the transitive property of equality states that if a=b and b=c, then a=c. Here, AB + BC = 13 is equal to AC, hence AC=13 according to the transitive property.

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The transitive property justifies the given conclusion because it dictates that if two values are both equal to a third value, they are equivalent to each other.

The property that justifies the conclusion If AC = AB + BC and AB + BC = 13, then AC = 13 is the transitive property of equality. The transitive property says that if two things are both equal to a third thing, then they are congruent to each other. In this case, because AB + BC equals 13 and AC equals AB + BC, you can conclude that AC must equal 13.

Answer: 5836200

Step-by-step explanation:

[tex]\bf \begin{array}{ll} \stackrel{year}{term}&value\\ \cline{1-2} a_1&3\\ a_2&3r\\ a_3&3rr\\ a_4&3rrr\\ a_5&3rrrr\\ &3r^4 \end{array}\qquad \qquad \stackrel{\textit{5th year}}{108}=3r^4\implies \cfrac{108}{3}=r^4\implies 36=r^4 \\\\\\ \sqrt[4]{36}=r\implies \sqrt[4]{6^2}=r\implies 6^{\frac{2}{4}}=r\implies 6^{\frac{1}{2}}=r\implies \sqrt{6}=r[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} r=\sqrt{6}\\ a_1=3\\ n=11 \end{cases}\implies a_{11}=3(\sqrt{6})^{11-1} \\\\\\ a_{11}=3(\sqrt{6})^{10}\implies a_{11}=3\left(6^{\frac{1}{2}} \right)^{10}\implies a_{11}=3\cdot 6^{\frac{10}{2}} \\\\\\ a_{11}=3\cdot 6^5\implies a_{11}=3\cdot 7776\implies a_{11}=23328[/tex]

Answer:

The investment be worth $23328 after 11 years.

Step-by-step explanation:

It is given that the annual growth reflects a geometric sequence.

An initial investment of $3 is worth $108 after 5 years.

It means the initial value of first term of the gp, a₁ = 3

The 5th term of the gp, a₅ = 108

The nth term of a gp is

[tex]a_n=ar^{n-1}[/tex]              .... (1)

where, a is first term and r is common ratio.

The 5th term of the gp is

[tex]a_5=ar^{5-1}[/tex]

From the given information it is clear that the 5th term of the gp is 108. Substitute a₅ = 108 and a=3.

[tex]108=(3)r^{4}[/tex]

Divide both sides by 3.

[tex]\frac{108}{3}=r^{4}[/tex]

[tex]36=r^{4}[/tex]

Taking fourth root on both the sides.

[tex]\sqrt{6}=r[/tex]

Substitute r=√6, a=3 and n=11 to find the investment worth after 11 years.

[tex]a_{11}=(3)(\sqrt{6})^{11-1}[/tex]

[tex]a_{11}=3(\sqrt{6})^{10}[/tex]

[tex]a_{11}=23328[/tex]

Therefore the investment worth $23328 after 11 years.

I tried solving the problem and it didn't make sense until assuming that 22540.75 was a typo for 2540.75.

Answer:

2540.75 = 6.25x + 5.25y

435 = x + y

x = number of adult tickets

y = number of student and senior tickets

Question is asking to find x

- - - - - - - - - - - - - - - - - -

435 = x + y

2283.75 = 5.25x + 5.25y

Elimination method:

2540.75 = 6.25x + 5.25y

-(2283.75 = 5.25x + 5.25y)

257 = x

257 full priced tickets were sold.

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For any questions, please comment!!

Answer:

Full tickets sold were 257 in count and discounted tickets were 178.

Step-by-step explanation:

Let the full tickets be = f

Let the discounted tickets be = d

Total tickets sold = 435

This can be written as :

[tex]f+d=435[/tex] or[tex]f=435-d[/tex]    .....(1)

The full price of a ticket is $6.25 and discount price is $5.25 and total earning is $2540.75.

In equation form, it can be written as :

[tex]6.25f+5.25d=2540.75[/tex]    ....(2)

Substituting the value of f in (2)

[tex]6.25(435-d)+5.25d=2540.75[/tex]  

[tex]2718.75-6.25d+5.25d=2540.75[/tex]

[tex]-1d=-178[/tex]

so , d = 178

And[tex]f+d=435[/tex]

So,[tex]f=435-178=257[/tex]

Hence, full tickets sold were 257 in count and discounted tickets were 178.

Answer:

Step-by-step explanation:

[tex]3x^2+x-5=0\\\\\text{Use the quadratic formula for}\ ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{For the given equation:}\\\\a=3,\ b=1,\ c=-5\\\\b^2-4ac=1^2-4(3)(-5)=1+60=61\\\\x=\dfrac{-1\pm\sqrt{61}}{(2)(3)}=\dfrac{-1\pm\sqrt{61}}{6}\notin\mathbb{N}[/tex]

Answer:

two real,irrational roots.

GOOD LUCK!

Step-by-step explanation:

Answer:

No solution.

Step-by-step explanation:

If the linear equations in a system are parallel, that means there is no solution.

Answer:

v=26.41 m/s

Step-by-step explanation:

From the Newtons laws of motions, we sew that x= (2v₁²sin∅os∅)/g where x is the horizontal distance v is the initial speed and ∅ is the launch angle.

From trigonometry we see that 2 sin∅cos∅=sin 2∅

Therefore,  x=(v²sin2∅)/g

x=22m

∅=9°

g=9.8m/s²

22m=v²×sin(2×9)/(9.8m/s²)

v²=(22×9.8)/(sin 18)

v²=697.696

v=√697.696

v=26.41 m/s

Answer:

Step-by-step explanation:

SAS - Side Angle Side

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

the opposite sides have the same lengths.

the angles formed by these sides are right angles

Answer:

a. two column proof

Step-by-step explanation:

This is a two column proof, for 2 columns are given to you.

One column is the "Statements" column, which lists everything in mathematical terms.

The other column is the "Reasons" column, which lists everything by definition (either Theorem, Postulate, or Definition).

~

Ex: 96 hours ≈ 4 days

This is one way to convert dates.

I am joyous to assist you anytime.

Converting dates involves understanding time zones and the International Date Line. When crossing the date line from west to east, the date decreases by one day, and when crossing from east to west, the date increases by one day.

Converting dates can be done by understanding the concept of time zones and the International Date Line. Time zones are regions that have the same standard time, while the International Date Line is an imaginary line that marks where the date changes by one day. When crossing the date line from west to east, the date is decreased by one day, and when crossing from east to west, the date is increased by one day.

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Answer:Answer:

the figure is parallelogram

Explanation:

enter image source here

As The mutually edges are parallel each other and equal,

the name of figure is parallelogram .

Step-by-step explanation:

Answer with explanation:

The vertices of Quadrilateral ABCD are ,A(−5,7), B(6,−3), C(10,2), and D(−1,12).

Distance formula between two points (a,b) and (c,d), is given by

          [tex]=\sqrt{(a-c)^2+(b-d)^2[/tex]

[tex]AB=\sqrt{[-5-6]^2+[7-(-3)]^2}\\\\AB=\sqrt{121+100}\\\\AB=\sqrt{221}\\\\BC=\sqrt{[10-6]^2+(2+3)^2}\\\\BC=\sqrt{16+25}\\\\BC=\sqrt{41}\\\\CD=\sqrt{[10+1]^2+[2-12]^2}\\\\CD=\sqrt{121+100}\\\\CD=\sqrt{221}\\\\DA=\sqrt{[-1+5]^2+[12-7]^2}\\\\DA=\sqrt{16+25}\\\\DA=\sqrt{41}\\\\AC=\sqrt{[10+5]^2+[2-7]^2}\\\\AC=\sqrt{225+25}\\\\AC=\sqrt{250}\\\\BD=\sqrt{[6+1]^2+[-3-12]^2]}\\\\BD=\sqrt{49+225}\\\\BD=\sqrt{274}[/tex]

Opposite side of Quadrilateral[AB=CD, AD=BC] is equal, but Diagonals are not equal.

So, it is a Parallelogram.