What is the equation of the line that passes through (4,-1) and (-2,3)

Answer:

[tex]\left\{x\in \mathbb {Z}\ : \ x \le 0 \right\}[/tex]

Step-by-step explanation:

Set-Builder Notation: A shorthand used to describe sets, often sets with an infinite number of elements.

The set {...,-3, -2, -1, 0} is the set of all negative integers and 0, so you can use such set-builder notation:

[tex]\left\{x\in \mathbb {Z}\ : \ x \le 0 \right\}[/tex]

Note: Here [tex]\mathbb{Z}[/tex] represents the set of all integers.

Final answer:

The set {... -3, -2, -1, 0} can be represented in set builder notation as {x ∈ ℤ | -3 ≤ x < 1 }, which describes all integers x that are greater than or equal to -3 and less than 1.

Explanation:

To express the set that includes the numbers -3, -2, -1, and 0 using set builder notation, we start by recognizing that these numbers can be described by a pattern or rule, which is that they are all the integer numbers greater than or equal to -3 and less than 1. We can then write this using set builder notation as:

{x ∈ ℤ | -3 ≤ x < 1 }

In this notation, the variable 'x' represents the elements of the set and ∈ stands for 'element of.' ℤ is the symbol for integers. The vertical bar or colon (|) stands for 'such that.' Our notation reads as 'the set of all integers x such that -3 is less than or equal to x and x is less than 1.'

1. simply: h+245

2. your answer is right

3. 2+1/3n (i believe)

4. 29+5m

5. I’m pretty sure the answer is 29

Answer:

C

Step-by-step explanation:

Given

[tex]\sqrt{3x+8}[/tex] = [tex]\sqrt{4x+1}[/tex]

[ note that ([tex]\sqrt{x}[/tex])² = x ]

Square both sides

3x + 8 = 4x + 1 ( subtract 4x from both sides )

- x + 8 = 1 ( subtract 8 from both sides )

- x = - 7 ( multiply both sides by - 1 )

x = 7 → C

Answer:

x = 7.

Step-by-step explanation:

Squaring both sides:

3x + 8 = 4x + 1

3x - 4x = 1 - 8

-x = -7

7 = x.

The area of that trapeziod is 28 inches.

Answer:

Step-by-step explanation:

The area is a+b/2

so the answer is 28

Answer:

[tex]y-0=-1(x-8)[/tex]

Step-by-step explanation:

The given line passes through (0,8) and (8,0).

The slope of this line is [tex]m=\frac{8-0}{0-8} =-1[/tex].

The point-slope form is given by:

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the slope and the point (8,0) to get:

[tex]y-8=-1(x-0)[/tex]

We substitute the slope and the point (0,8) to get:

[tex]y-0=-1(x-8)[/tex]

7200. Because 1.2 *30 *200=7200

To estimate the mouse population after 30 days using the given model, M(t)=200(1.2)^t, evaluate the expression with t=30, which results in approximately 47,475 mice.

The student is asking how many mice will be in the building after 30 days according to the exponential growth model M(t) = 200(1.2)^t, where t is the time in days and M(t) is the population of mice at time t. To find the answer, we simply plug the value of 30 days into the model to get M(30) = 200(1.2)^30.

Calculating the expression:

First, calculate 1.2 raised to the power of 30, which gives us approximately 237.3769.

Then, multiply that by the initial population of 200 mice, yielding a result of approximately 47,475.38.

Therefore, after 30 days, assuming no mice die, there will be approximately 47,475 mice in the building.

Answer:

n-2

Step-by-step explanation:

Difference means subtraction

n-2

Answer:

Step-by-step explanation:

This has a very brief answer when you know what it means.

f(x) + g(x) = abs(x) + 9 - 6

f(x) + g(x) = abs(x) + 3

Answer:

f + g)(x) = |x| + 3

Step-by-step explanation:

Add the two functions together:

f(x) = |x| + 9

+g(x) = - 6

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

f(x) + g(x) = |x| + 9 - 6

               = |x| + 3

The label  f(x) + g(x)  can be rewritten as (f + g)(x).  

Thus, f + g)(x) = |x| + 3

Answer:

[tex]\large\boxed{A.\ \dfrac{1}{2}x+\dfrac{11}{2}}[/tex]

Step-by-step explanation:

[tex]-3x-(x-1)+\dfrac{3}{2}(3x+3)\qquad\text{use the distributive property}\\\\=-3x-x-(-1)+\left(\dfrac{3}{2}\right)(3x)+\left(\dfrac{3}{2}\right)(3)\\\\=-3x-x+1+\dfrac{9}{2}x+\dfrac{9}{2}\qquad\text{combine like terms}\\\\=\bigg(-3x-x+\dfrac{9}{2}x\bigg)+\bigg(1+\dfrac{9}{2}\bigg)\\\\=\bigg(\dfrac{-6}{2}x-\dfrac{2}{2}x+\dfrac{9}{2}x\bigg)+\bigg(\dfrac{2}{2}+\dfrac{9}{2}\bigg)\\\\=\dfrac{-6-2+9}{2}x+\dfrac{2+9}{2}=\dfrac{1}{2}x+\dfrac{11}{2}[/tex]

Answer:

1/14

Step-by-step explanation:

The total number of coins in the bag is 10+6+5, or 21.

You reach into the bag and take ONE coin.  The chances of that being a nickel is 6/21, or 2/7, since nickels compose 6 of the 21 coins in the bag.

You don't replace the nickel.

Now you have 20 coins in the bag, including 5 nickels.

The chances of your next draw being a dime is 5/20, or 1/4, since there are 5 dimes in the bag.

The joint probability of drawing a nickel and then a dime is then the product of these two probabilities:

(2/7)(1/4) = 2/28 = 1/14

Answer:

B.30

Step-by-step explanation:

This was picked because if u divide 18 by 3. You get 6 and if u multiply it by 2. You get 12 plus the 18 equals 30.

Answer:

A

Step-by-step explanation:

Note that

x² + 12x + 36 is a perfect square → (x + 6)², hence

[tex]\sqrt{x^2+12x+36}[/tex] = [tex]\sqrt{(x+6)^2}[/tex] = (x + 6)

Hence

f(x) × g(x)

= (x + 6)(x³ - 11)

= [tex]x^{4}[/tex] - 11x + 6x³ - 66

= [tex]x^{4}[/tex] + 6x³ - 11x - 66 → A

(f·g)(x) in mathematics denotes the product of two functions, f(x) and g(x). Its interpretation and output may vary depending on the functions f(x) and g(x), but essentially, it is a multiplication of these two functions.

In mathematics, expressing (f·g)(x) indicates the product of two functions at a given x-coordinate. This is equivalent to f(x) multiplied by g(x). For instance, if f(x) = 2x and g(x) = 3x, then (f · g)(x) would yield (2x)(3x), resulting in 6x².

It's important to note that mathematical functions can vary, and this expression can take on various forms based on the nature of f(x) and g(x).

The provided reference information appears to be a mix of rules from differential calculus and mathematical definitions, which lack a direct relation to the original question about (f·g)(x). The primary concept here is understanding function multiplication.

https://brainly.com/question/13755609

#SPJ3

Answer:

The correct answer is C. g(x) = 1/4x^2

Step-by-step explanation:

In order to determine if the graph fits, take the point that is given on the parabola and see if it fits the equation. To do that we plug it in and see if it gives a true statement.

(2, 1)

g(x) = 1/4x^2

1 = 1/4(2)^2

1 = 1/4(4)

1 = 1 (TRUE)

Answer:

rectangle. trapezoid. triangle. A sphere is sliced so that the cross section does not intersect the center of the sphere

Answer:

sorry im late to this but it is a triangle

Step-by-step explanation:

because when you cut it horizontally and look at the top it is a rectangle so that is wrong trapezoid is when you look at it from the side when cut horizontally so that is wrong there is no square so that instantly becomes wrong because it is a rectangular pyramid  when  perpendicular it will provide you with a triangle  

Answer:

96 deg

Step-by-step explanation:

Polygon ABCDE is a regular hexagon. The sum of the measures of the interior angles is (n - 2)180 = (6 - 2)180 = 4(180) = 720. Since it's a regular hexagon, each interior angle measures 720/6 = 120 deg.

For the interior angle, m<CDE = 120

On the exterior of the polygon, m<CDJ = 136

m<CDE + m<CDJ + m<EDJ = 360

120 + 136 + m<EDJ = 360

m<EDJ + 256 = 360

m<EDJ = 104 deg

Triangle EHG is regular. The sum of the measures of the angles of a triangle is 180. For a regular triangle, each angle measures 60 deg.

m<EGH = 60

For exterior angle m<HGJ = 220

m<HGJ(exterior) + m<EGH + m<EGJ = 360

220 + 60 + m<EGJ = 360

m<EGJ + 280 = 360

m<EGJ = 80

m<EGJ = m<GED, so

m<GED = 80

Polygon DEGJ is a quadrilateral. The sum of the measures of its interior angles is 360 deg.

m<EGJ + m<GED + m<EDJ + m<GJD = 360

80 + 80 + 104 + m<GJD = 360

m<GJD + 264 = 360

m<GJD = 96 deg

Answer:

The measure of angle GJD is 96°.

Step-by-step explanation:

It is given that HGJ=220° on the exterior of the polygon, EGJ is congruent to GED, and CDJ=136° on the exterior of the polygon.

Each side and each interior angle of a regular polygon are same.

It is given that ABCDEF and EHG are regular polygons. It means each interior angle of regular hexagon ABCDEF is 120° and each interior angle of regular triangle EHG is 60°.

[tex]\angle EGH+\angle EGJ+\angle HGJ(exterior)=360^{\circ}[/tex]

[tex]60^{\circ}+\angle EGJ+220^{\circ}=360^{\circ}[/tex]

[tex]\angle EGJ+280^{\circ}=360^{\circ}[/tex]

[tex]\angle EGJ=360^{\circ}-280^{\circ}[/tex]

[tex]\angle EGJ=80^{\circ}[/tex]

[tex]\angle GED=\angle EGJ=80^{\circ}[/tex]

[tex]\angle CDE+\angle EDJ+\angle CDJ(exterior)=360^{\circ}[/tex]

[tex]120^{\circ}+\angle EDJ+136^{\circ}=360^{\circ}[/tex]

[tex]\angle EDJ+256^{\circ}=360^{\circ}[/tex]

[tex]\angle EDJ=360^{\circ}-256^{\circ}[/tex]

[tex]\angle EDJ=104^{\circ}[/tex]

The sum of all interior angles of a quadrilateral is 360°.

[tex]\angle GED=\angle EGJ+\angle EDJ+\angle GJD=360^{\circ}[/tex]

[tex]80^{\circ}+80^{\circ}+104^{\circ}+\angle GJD=360^{\circ}[/tex]

[tex]264^{\circ}+\angle GJD=360^{\circ}[/tex]

[tex]\angle GJD=360^{\circ}-264^{\circ}[/tex]

[tex]\angle GJD=96^{\circ}[/tex]

Therefore the measure of angle GJD is 96°.

Answer:

±6

Step-by-step explanation:

Whenever you are finding the square root of something, it will ALWAYS result in a negative and positive number, or else depending on the situation of a problem.

Ex: Distance Formula → POSITIVE ANSWER ONLY

I am joyous to assist you anytime.

Answer:

(a)

Step-by-step explanation:

To rationalise the fraction multiply the numerator/denominator by the conjugate of the denominator.

The conjugate of [tex]\sqrt{3}[/tex] + [tex]\sqrt{x}[/tex] is [tex]\sqrt{3}[/tex] - [tex]\sqrt{x}[/tex]

Hence

[tex]\frac{\sqrt{9}(\sqrt{3}-\sqrt{x} )  }{(\sqrt{3}+\sqrt{x} )(\sqrt{3}-\sqrt{x} )  }[/tex]

= [tex]\frac{3(\sqrt{3}-\sqrt{x}  }{3-x}[/tex]

= [tex]\frac{3\sqrt{3}-3\sqrt{x}  }{3-x}[/tex] → (a)

Answer:

[tex]\large\boxed{60\pi\ sq.in.}[/tex]

Step-by-step explanation:

The formula of a lateral area of a cone:

[tex]L.A.=\pi rl[/tex]

r - radius

l - lateral height

We have the radius r = 6in and the height H = 8in.

Use the Pythagorean theorem to calculate the lateral height:

[tex]l^2=6^2+8^2\\\\l^2=36+64\\\\l^2=100\to l=\sqrt{100}\\\\l=10\ in[/tex]

Substitute:

[tex]L.A.=\pi(6)(10)=80\pi\ in^2[/tex]

The simulation design that has an appropriate device and a correct trial for this scenario is:

The correct option is C.

The simulation which involves using a table of random digits to select a digit between 0 and 9, letting 0 - 2 represent eating dessert and 3 - 9 represent not eating dessert, and then selecting three digits has an appropriate device and a correct trial.

This simulation design is given below:

To simulate the probability of eating dessert in 3 of the 7 days this week, we would select three digits from the table of random digits and count the number of 0s, 1s, and 2s. The number of 0s, 1s, and 2s would correspond to the number of days the children eat dessert, and the number of 3s, 4s, 5s, 6s, 7s, 8s, and 9s would correspond to the number of days the children do not eat dessert.

We would repeat this process many times (e.g., 1000 times) to obtain an estimate of the probability of eating dessert 3 of the 7 days this week.

Learn more about simulation and probabilities at: https://brainly.com/question/1231005

#SPJ1

Answer:

Commutative Property

Step-by-step explanation:

"Changing the order but not the result"

ANSWER

n=5

EXPLANATION

The area of a square is given by

[tex] {l}^{2} [/tex]

where l is the length of the sides.

If the area is

[tex] {x}^{10} [/tex]

then we can rewrite this as

[tex]( { {x}^{5}) }^{2} [/tex]

This implies that:

[tex] {l}^{2} = ( { {x}^{5}) }^{2} [/tex]

Hence,

[tex]l = {x}^{5}[/tex]

Therefore n=5

Answer:

2b/3 * 2b/3 * 2b/3 * 2b/3

Good luck!!

Answer:

16b^4/81

Step-by-step explanation:

Answer:

Option D. [tex]272[/tex]

Step-by-step explanation:

we know that

To evaluate the sum , use the formula

[tex]S=\frac{1}{2}(a1+an)n[/tex]

where

a1 is the first term

an is the last term

n is the number of terms

In this problem

For n=1 ------> a1=2(1)=2

For n=16 ------> an=2(16)=32

n=16 terms

substitute in the formula

[tex]S=\frac{1}{2}(2+32)16[/tex]

[tex]S=272[/tex]

Answer:

A)

Step-by-step explanation:

We know that the expression (x^2 - a^2) can be written as (x-a)(x+a). So an expression of this type: (x^2 - a^2) wouldn't be completely factored because it could be factorized even more.

So we know that 36 = 6^2, 49= 7^2 and 81 = 9^2. So if we choose any of these options (Option B, C and D) it wouldn't be completely factored.

The correct is the option A, given that if a=12, it wouldn't be a perfect square, so it would be completely factored.

So I just did the problem and im pretty sure the answer is A

Answer:

D. Length = 9 cm; width = 6 cm

Step-by-step explanation:

Find 1/4 of the length and 1/4 of the width.

1/4 * 36 cm = 9 cm

1/4 * 24 cm = 6 cm

Answer: D. Length = 9 cm; width = 6 cm

Answer:

[tex]\large\boxed{\text{If is "or", then}\ x>-2\dfrac{1}{15}}\\\boxed{\text{If is "and", then}\ x>1\dfrac{9}{14}}[/tex]

Step-by-step explanation:

[tex]7x+\dfrac{3}{2}>13\qquad\text{multiply both sides by 2}\\\\14x+3>26\qquad\text{subtract 3 from both sides}\\\\14x>23\qquad\text{divide both sides by 14}\\\\x>\dfrac{23}{14}=1\dfrac{9}{14}\\=====================\\\\\dfrac{5}{2}x-\dfrac{1}{3}>-\dfrac{11}{2}\qquad\text{multiply both sides by 2}\\\\5x-\dfrac{2}{3}>-11\qquad\text{multiply both sides by 3}\\\\15x-2>-33\qquad\text{add 2 to both sides}\\\\15x>-31\qquad\text{divide both sides by 15}\\\\x>-\dfrac{31}{15}=-2\dfrac{1}{15}\\=====================[/tex]

Final answer:

To solve the compound inequality, each inequality is solved individually. The first inequality yields x > 1.64285714, and the second yields x > -2.06666667. As this is an 'or' compound inequality, the solution is the union of both, leading to x > 1.64285714.

Explanation:

To solve the compound inequality 7x + 3/2 > 13 or 5/2x - 1/3 > -11/2, we need to treat each inequality separately and then find the union of their solutions.

For the first inequality:

Subtract 3/2 from both sides to get 7x > 11.5.

Divide both sides by 7 to find x > 11.5/7, which simplifies to x > 1.64285714.

For the second inequality:

Multiply both sides by 6 to clear the fraction, leading to 15x - 2 > -33.

Add 2 to both sides to get 15x > -31.

Divide both sides by 15 to find x > -31/15, which simplifies to x > -2.06666667.

The solution is the set that satisfies at least one of these inequalities. Since x > 1.64285714 or x > -2.06666667, the overall solution is x > 1.64285714.

Answer:

In: 5, 4, 2, 3, 1, and 10.

Out: 40, 32, 16, 24, 8, and 80

Step-by-step explanation:

The first step you should do is to take notice of the pairs that have their "in" and "out" both answered.

The second step is to find out what you must multiply the "in" by to get the "out". In this answer, you must multiply the "in" by 8 to get the "out".

The third step is to do the same thing for all of the values until the chart is completely filled with values.

The fourth step is to check your work!

If you have any questions, please let me know!

The rule is 8

Bc 5 times 8 is 40

32/8 is 4

Either divide or multiply when needed

Answer:

10 necklaces =  50 rocks

15 necklaces = 75 rocks

20 necklaces = 100 rocks

25 necklaces = 125 rocks

Step-by-step explanation:

A table that shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces:

| Number of necklaces | Number of shiny rocks used |

| 10 | 50 |

| 15 | 75 |

| 20 | 100 |

| 25 | 125 |

To calculate the number of shiny rocks used, we simply multiply the number of necklaces by the number of shiny rocks per necklace. For example, to calculate the number of shiny rocks used for 10 necklaces, we multiply 10 by 5:

10 necklaces * 5 shiny rocks/necklace = 50 shiny rocks

We can do the same calculation for 15, 20, and 25 necklaces to get the following results:

15 necklaces * 5 shiny rocks/necklace = 75 shiny rocks

20 necklaces * 5 shiny rocks/necklace = 100 shiny rocks

25 necklaces * 5 shiny rocks/necklace = 125 shiny rocks

Therefore, the table above shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces.

For such more question on number

https://brainly.com/question/30752681

#SPJ12

Answer:

[tex]c=15[/tex]

Step-by-step explanation:

Use the Pythagorean Theorem.

[tex]a^2+b^2=c^2 \\ \\ 9^2+12^2=c^2 \\ \\ 81+144=c^2 \\ \\ c^2=225 \\ \\ c=\sqrt{225} \\ \\ c=15[/tex]

Answer:

[tex]A=452.39\ cm^2[/tex]

Step-by-step explanation:

The formula to calculate the surface area of a sphere is the following:

[tex]A=4\pi r^2[/tex]

Where A is the area of the sphere and r is the radius of the sphere.

In this case we know that the diameter d of the sphere is:

[tex]d = 12\ cm[/tex]

The diameter is:

[tex]d = 2r[/tex].

Thus

[tex]r = \frac{d}{2}\\\\r = \frac{12}{2}\\\\r=6\ cm[/tex]

Then the surface area of the sphere is:

[tex]A=4\pi (6)^2\\\\A = 144\pi\ cm^2\\\\A=452.39\ cm^2[/tex]

Answer is provided in the image attached.